Financial Reporting 
and Analysis
STUDY SESSIONS
Study Session 6 Financial Reporting and Analysis (1)
Study Session 7 Financial Reporting and Analysis (2)
Study Session 8 Financial Reporting and Analysis (3)
Study Session 9 Financial Reporting and Analysis (4)
TOPIC LEVEL LEARNING OUTCOME 
The candidate should be able to demonstrate a thorough knowledge of financial 
reporting procedures and the standards that govern financial reporting disclosure. 
Emphasis is on basic financial statements and how alternative accounting methods 
affect those statements and the analysis of them.
Financial statement analysis is critical in assessing a company’s overall financial 
position and associated risks over time. Security and business valuation, credit risk 
assessment, and acquisition due diligence all require an understanding of the major 
financial statements including general principles and reporting approaches. Because 
no set of accounting standards has universal acceptance, companies around the world

may differ in reporting treatment based on their jurisdiction.
Financial statement analysis requires the ability to analyze a company’s reported 
results with its economic reality, normalize differences in accounting treatment to make 
valid cross company comparisons, identify quality issues that may exist in reported 
financial statements, and discern evidence of financial statement manipulation by 
management.
© 2018 CFA Institute. All rights reserved.Note:  Changes in accounting 
standards as well as new rulings 
and/or pronouncements issued 
after the publication of the 
readings on financial reporting 
and analysis may cause some 
of the information in these 
readings to become dated. 
Candidates are not responsible 
for anything that occurs after 
the readings were published. 
In addition, candidates are 
expected to be familiar with the 
analytical frameworks contained 
in the readings, as well as the 
implications of alternative 
accounting methods for financial 
analysis and valuation discussed

analysis and valuation discussed 
in the readings. Candidates are 
also responsible for the content 
of accounting standards, but not 
for the actual reference numbers. 
Finally, candidates should be 
aware that certain ratios may 
be defined and calculated 
differently. When alternative 
ratio definitions exist and no 
specific definition is given, 
candidates should use the ratio 
definitions emphasized in the 
readings.

2 Financial Reporting and Analysis
Candidates should be familiar with the material covered in the following prerequi -
site economics reading available in Candidate Resources on the CFA Institute website:
• Financial Reporting Mechanics

and Analysis (1)
This study session introduces the principal information sources used to evaluate a 
company’s financial performance. Primary financial statements (income statement, 
balance sheet, cash flow statement, and statement of changes in equity) in addition 
to notes to these statements and management reporting are examined. A general 
framework for conducting financial statement analysis is provided. The session also 
includes a description of the roles played by financial reporting standard-  setting 
bodies and regulatory authorities.
READING ASSIGNMENTS
Reading 21 Financial Statement Analysis: An Introduction  
by Elaine Henry, PhD, CFA, and Thomas R. Robinson, 
PhD, CFA
Reading 22 Financial Reporting Standards  
by Elaine Henry, PhD, CFA, Jan Hendrik van Greuning, 
DCom, CFA, and Thomas R. Robinson, PhD, CFAFINANCIAL  REPORTIN g AN d A NALYSIS
STU dY SESSION
6
standards as well as new rulings

readings.

Financial Statement Analysis: 
An Introduction
by Elaine Henry, PhD, CFA, and Thomas R. Robinson, PhD, CFA
Elaine Henry, PhD, CFA, is at Stevens Institute of Technology (USA). Thomas R. Robinson, 
PhD, CFA, is at AACSB International (USA).
LEARNING OUTCOMES
Mastery The candidate should be able to:
a. describe the roles of financial reporting and financial statement 
analysis;
b. describe the roles of the statement of financial position, statement 
of comprehensive income, statement of changes in equity, and 
statement of cash flows in evaluating a company’s performance 
and financial position;
c. describe the importance of financial statement notes and 
supplementary information—including disclosures of 
accounting policies, methods, and estimates—and management’s 
commentary;
d. describe the objective of audits of financial statements, the types 
of audit reports, and the importance of effective internal controls;
e. identify and describe information sources that analysts use in

financial statement analysis besides annual financial statements 
and supplementary information;
f. describe the steps in the financial statement analysis framework.REA dINg
21
© 2011 CFA Institute. All rights reserved.Note:  Changes in accounting 
be defined and calculated

readings.

Reading 21 ■ Financial Statement Analysis: An Introduction 6
INTRODUCTION
Financial analysis is the process of examining a company’s performance in the con -
text of its industry and economic environment in order to arrive at a decision or 
recommendation. Often, the decisions and recommendations addressed by financial 
analysts pertain to providing capital to companies—specifically, whether to invest 
in the company’s debt or equity securities and at what price. An investor in debt 
securities is concerned about the company’s ability to pay interest and to repay the 
principal lent. An investor in equity securities is an owner with a residual interest in 
the company and is concerned about the company’s ability to pay dividends and the 
likelihood that its share price will increase. Overall, a central focus of financial analysis 
is evaluating the company’s ability to earn a return on its capital that is at least equal to

the cost of that capital, to profitably grow its operations, and to generate enough cash 
to meet obligations and pursue opportunities. Fundamental financial analysis starts 
with the information found in a company’s financial reports. These financial reports 
include audited financial statements, additional disclosures required by regulatory 
authorities, and any accompanying (unaudited) commentary by management. Basic 
financial statement analysis—as presented in this reading—provides a foundation that 
enables the analyst to better understand information gathered from research beyond 
the financial reports.
This reading is organized as follows: Section 2 discusses the scope of financial 
statement analysis. Section 3 describes the sources of information used in financial 
statement analysis, including the primary financial statements (statement of financial 
position or balance sheet, statement of comprehensive income, statement of changes

in equity, and cash flow statement). Section 4 provides a framework for guiding the 
financial statement analysis process. A summary of the key points and practice prob -
lems in the CFA Institute multiple-  choice format conclude the reading.
SCOPE OF FINANCIAL STATEMENT ANALYSIS
The role of financial reporting by companies is to provide information about a 
company’s performance, financial position, and changes in financial position that is 
useful to a wide range of users in making economic decisions.1 The role of financial 
statement analysis is to use financial reports prepared by companies, combined with 
other information, to evaluate the past, current, and potential performance and finan -
cial position of a company for the purpose of making investment, credit, and other 
economic decisions. (Managers within a company perform financial analysis to make 
operating, investing, and financing decisions but do not necessarily rely on analysis

of related financial statements. They have access to additional financial information 
that can be reported in whatever format is most useful to their decision.)1
2
1 This role of financial reporting is specified in International Accounting Standard (IAS) 1 Presentation of 
Financial Statements , paragraph 9, and paragraph 12 of the Framework for the Preparation and Presentation 
of Financial Statements . In September 2010, the IASB adopted the Conceptual Framework for Financial 
Reporting , which revised the role to focus on users providing resources to the entity. An updated framework 
was a joint project between the International Accounting Standards Board (IASB), which issues International 
Financial Reporting Standards (IFRS), and the Financial Accounting Standards Board (FASB). The FASB 
issues US generally accepted accounting principles (US GAAP) contained in the FASB Accounting Standards

Codification™ (FASB ASC). The set of accounting standards that a company uses to prepare its financial 
reports depends on its jurisdiction. The IASB and FASB will be discussed further in a later reading.

Scope of Financial Statement Analysis 7
In evaluating financial reports, analysts typically have a specific economic decision 
in mind. Examples of these decisions include the following:
■■Evaluating an equity investment for inclusion in a portfolio.
■■Evaluating a merger or acquisition candidate.
■■Evaluating a subsidiary or operating division of a parent company.
■■Deciding whether to make a venture capital or other private equity investment.
■■Determining the creditworthiness of a company in order to decide whether to 
extend a loan to the company and if so, what terms to offer.
■■Extending credit to a customer.
■■Examining compliance with debt covenants or other contractual arrangements.
■■Assigning a debt rating to a company or bond issue.
■■Valuing a security for making an investment recommendation to others.
■■Forecasting future net income and cash flow.
These decisions demonstrate certain themes in financial analysis. In general,

analysts seek to examine the past and current performance and financial position of 
a company in order to form expectations about its future performance and financial 
position. Analysts are also concerned about factors that affect risks to a company’s 
future performance and financial position. An examination of performance can include 
an assessment of a company’s profitability (the ability to earn a profit from delivering 
goods and services) and its ability to generate positive cash flows (cash receipts in 
excess of cash disbursements). Profit and cash flow are not equivalent. Profit (or loss) 
represents the difference between the prices at which goods or services are provided to 
customers and the expenses incurred to provide those goods and services. In addition, 
profit (or loss) includes other income (such as investing income or income from the 
sale of items other than goods and services) minus the expenses incurred to earn that

income. Overall, profit (or loss) equals income minus expenses, and its recognition 
is mostly independent from when cash is received or paid. Example 1 illustrates the 
distinction between profit and cash flow.
EXAMPLE 1   
Profit versus Cash Flow
Sennett Designs (SD) sells furniture on a retail basis. SD began operations during 
December 2009 and sold furniture for €250,000 in cash. The furniture sold by 
SD was purchased on credit for €150,000 and delivered by the supplier during 
December. The credit terms granted by the supplier required SD to pay the 
€150,000 in January for the furniture it received during December. In addition 
to the purchase and sale of furniture, in December, SD paid €20,000 in cash for 
rent and salaries.
1 How much is SD’s profit for December 2009 if no other transactions 
occurred?
2 How much is SD’s cash flow for December 2009?
3 If SD purchases and sells exactly the same amount in January 2010 as it

did in December and under the same terms (receiving cash for the sales 
and making purchases on credit that will be due in February), how much 
will the company’s profit and cash flow be for the month of January?

Reading 21 ■ Financial Statement Analysis: An Introduction 8
Solution to 1:
SD’s profit for December 2009 is the excess of the sales price (€250,000) over 
the cost of the goods that were sold (€150,000) and rent and salaries (€20,000), 
or €80,000.
Solution to 2:
The December 2009 cash flow is €230,000, the amount of cash received from the 
customer (€250,000) less the cash paid for rent and salaries (€20,000).
Solution to 3:
SD’s profit for January 2010 will be identical to its profit in December: €80,000, 
calculated as the sales price (€250,000) minus the cost of the goods that were sold 
(€150,000) and minus rent and salaries (€20,000). SD’s cash flow in January 2010 
will also equal €80,000, calculated as the amount of cash received from the 
customer (€250,000) minus the cash paid for rent and salaries (€20,000) and 
minus the €150,000 that SD owes for the goods it had purchased on credit in 
the prior month.
Although profitability is important, so is a company’s ability to generate positive

cash flow. Cash flow is important because, ultimately, the company needs cash to pay 
employees, suppliers, and others in order to continue as a going concern. A company 
that generates positive cash flow from operations has more flexibility in funding needed 
for investments and taking advantage of attractive business opportunities than an 
otherwise comparable company without positive operating cash flow. Additionally, a 
company needs cash to pay returns (interest and dividends) to providers of debt and 
equity capital. Therefore, the expected magnitude of future cash flows is important 
in valuing corporate securities and in determining the company’s ability to meet its 
obligations. The ability to meet short-  term obligations is generally referred to as liquid -
ity, and the ability to meet long-  term obligations is generally referred to as solvency . 
Cash flow in any given period is not, however, a complete measure of performance

for that period because, as shown in Example 1, a company may be obligated to make 
future cash payments as a result of a transaction that generates positive cash flow in 
the current period.
Profits may provide useful information about cash flows, past and future. If the 
transaction of Example 1 were repeated month after month, the long-  term average 
monthly cash flow of SD would equal €80,000, its monthly profit. Analysts typically 
not only evaluate past profitability but also forecast future profitability.
Exhibit 1 shows how news coverage of corporate earnings announcements places 
corporate results in the context of analysts’ expectations. Panel A shows the earnings 
announcement, and Panel B shows a sample of the news coverage of the announcement. 
Earnings are also frequently used by analysts in valuation. For example, an analyst may 
value shares of a company by comparing its price-  to- earnings ratio (P/E) to the P/

Es of peer companies and/or may use forecasted future earnings as direct or indirect 
inputs into discounted cash flow models of valuation.
Exhibit 1   An Earnings Release and News Media Comparison with Analysts’ 
Expectations
Panel A: Excerpt from Apple Earnings Release
Apple Reports Second Quarter Results
Record March Quarter Revenue and Profit
iPhone Sales More Than Double

Scope of Financial Statement Analysis 9
CUPERTINO, California—April 20, 2010—Apple® today announced 
financial results for its fiscal 2010 second quarter ended March 27, 
2010. The Company posted revenue of $13.50 billion and net quarterly 
profit of $3.07 billion, or $3.33 per diluted share. These results compare 
to revenue of $9.08 billion and net quarterly profit of $1.62 billion, 
or $1.79 per diluted share, in the year-  ago quarter. Gross margin 
was 41.7  percent, up from 39.9  percent in the year-  ago quarter. 
International sales accounted for 58 percent of the quarter’s revenue.
Apple sold 2.94 million Macintosh® computers during the quarter, 
representing a 33  percent unit increase over the year-  ago quarter. 
The Company sold 8.75 million iPhones in the quarter, represent -
ing 131 percent unit growth over the year-  ago quarter. Apple sold 
10.89 million iPods during the quarter, representing a one percent 
unit decline from the year-  ago quarter.

“We’re thrilled to report our best non-  holiday quarter ever, with 
revenues up 49 percent and profits up 90 percent, ” said Steve Jobs, 
Apple’s CEO. “We’ve launched our revolutionary new iPad and users 
are loving it, and we have several more extraordinary products in the 
pipeline for this year. ”
“Looking ahead to the third fiscal quarter of 2010, we expect reve -
nue in the range of about $13.0 billion to $13.4 billion and we expect 
diluted earnings per share in the range of about $2.28 to $2.39, ” said 
Peter Oppenheimer, Apple’s CFO.
Source : www.apple.com/pr/library/2010/04/20results.html
Panel B: Excerpt Downloaded from FOXBusiness.com 
Report: Tuesday, 20 April 2010
“Apple Earnings Surge By 90% in Second Quarter” by Kathryn Glass
In what’s beginning to become its trademark, Apple Inc. (238.7911, 
–9.5489, –3.85%) delivered much better-  than-  expected second-  quarter 
earnings, but gave third-  quarter guidance below expectations.

The personal-  technology behemoth said it expects third-  quarter 
earnings in the range of $2.28 to $2.39 per share on revenue between 
$13 billion and $13.4 billion. Analysts were expecting third-  quarter 
earnings of $2.70 a share on revenue of $12.97 billion, according to 
a poll by Thomson Reuters.
Apple reported second quarter profit of $3.07 billion, or $3.33 
per share, compared with year-  ago profit of $1.62 billion, or $1.79 
per share. Revenue rose to $13.5 billion, compared with revenue of 
$9.08 billion, one year ago. The tech giant said 58% of revenue came 
from international sales.
The results soared above expectations; analysts’ second-  quarter 
profit estimates were for $2.45 per share on revenue of $12.04 billion.
Analysts are also interested in the current financial position of a company. The 
financial position can be measured by comparing the resources controlled by the 
company ( assets ) in relation to the claims against those resources ( liabilities  and

equity ). An example of a resource is cash. In Example  1, if no other transactions Exhibit 1   (Continued)

Reading 21 ■ Financial Statement Analysis: An Introduction 10
occur, the company should have €230,000 more in cash at 31 December 2009 than 
at the start of the period. The cash can be used by the company to pay its obligation 
to the supplier (a claim against the company) and may also be used to make distri -
butions to the owner (who has a residual claim against the company’s assets, net of 
liabilities). Financial position is particularly important in credit analysis, as depicted 
in Exhibit 2. Panel A of the exhibit is an excerpt from an April 2010 announcement 
by a credit rating agency of an upgrade in the credit ratings of Teck Resources Ltd., 
a Canadian mining company. The rating agency explained that it upgraded the credit 
rating of the company (its “corporate credit rating”) and the credit rating of the com -
pany’s debt securities (the “issue-  level rating”) because the company had repaid its 
debt quickly (“accelerated debt repayment”). Panel B of the exhibit is an excerpt from

the company’s second quarter 2010 earnings announcement in which the company’s 
CEO describes the company’s repayment of debt. Panel C of the exhibit is an excerpt 
from the company’s financial report illustrating the change in the company’s financial 
position in June 2010 compared with December 2009. As shown, the amount of the 
company’s debt liabilities relative to the amount of its equity declined substantially 
over the period.
Exhibit 2   
Panel A: Excerpt from Announcement by Standard & 
Poor’s Ratings Services: 16 April 2010
Teck Resources Ltd. Upgraded To ‘BBB’ From ‘BB+’ On Improved 
Financial Risk Profile; Removed From CreditWatch
We are raising our long-  term corporate credit rating on Vancouver-  
based mining company Teck Resources Ltd. to ‘BBB’ from ‘BB+’ .… 
We are also raising the issue-  level rating on the company’s notes 
outstanding to ‘BBB’ from ‘BB+’ …. We base the upgrade on Teck’s 
materially improved financial risk profile following the accelerated

debt repayment in the past year. The stable outlook reflects our opinion 
that Teck will maintain relatively stable credit metrics in the medium 
term, despite inherent volatility in the commodities market.
Source : Market News Publishing.
Panel B: Excerpt from Earnings Announcement by Teck 
Resources Limited: 28 July 2010
Teck Reports Second Quarter Results for 2010
Vancouver, BC—Teck Resources Limited announced quarterly earn -
ings of $260 million, or $0.44 per share, for the second quarter of 
2010. Our operating profit before depreciation was approximately 
$1.0 billion and EBITDA was $844 million in the second quarter.
Don Lindsay, President and CEO said, “During the quarter we 
eliminated the outstanding balance of our term bank loan and have 
now repaid the US$9.8 billion bank debt related to the Fording acqui -
sition in less than 18 months, just over two years ahead of schedule. 
In addition, all of our operations performed well, and we met or

exceeded the guidance given in our previous quarterly report. Our 
second quarter benefitted from a substantial increase in coal sales to 
6.4 million tonnes and the higher benchmark prices negotiated for

Major Financial Statements and Other Information Sources 11
the second quarter. In addition, in the quarter we re-  established our 
investment grade credit ratings from all of the major rating agencies 
and declared a semi-  annual dividend of $0.20 per share. ”
Source : Teck Resources Form 6-  K, filed 11 August 2010.
Panel C: Financial Position of Teck Resources Limited: 28 
July 2010 and 31 December 2009
(in millions of Canadian $) 28 July 2010 31 December 2009
ASSETS $28,570 $29,873
LIABILITIES
Debt 5,678 8,004
All other liabilities 7,273 7,288
Total liabilities 12,951 15,292
EQUITY 15,619 14,581
Debt divided by equity 0.36 0.55
In conducting a financial analysis of a company, the analyst will regularly refer to 
the company’s financial statements, financial notes, and supplementary schedules and 
a variety of other information sources. The next section introduces the major financial 
statements and some commonly used information sources.
MAJOR FINANCIAL STATEMENTS AND OTHER 
INFORMATION SOURCES

In order to perform an equity or credit analysis of a company, an analyst collects a 
great deal of information. The nature of the information collected will vary on the 
basis of the individual decision to be made (or the specific purpose of the analysis) 
but will typically include information about the economy, industry, and company as 
well as information about comparable peer companies. Much of the information will 
likely come from outside the company, such as economic statistics, industry reports, 
trade publications, and databases containing information on competitors. The com -
pany itself provides some of the core information for analysis in its financial reports, 
press releases, investor conference calls, and webcasts.
Companies prepare financial reports at regular intervals (annually, semiannually, 
and/or quarterly depending on the applicable regulatory requirements). Financial 
reports include financial statements along with supplemental disclosures necessary

to assess the company’s financial position and periodic performance. Financial state -
ments are the result of an accounting recordkeeping process that records economic 
activities of a company, following the applicable accounting standards and principles. 
These statements summarize the accounting information, mainly for users outside the 
company (such as investors, creditors, analysts, and others) because users of financial 
information inside a company have direct access to the underlying financial data that 3Exhibit 2   (Continued)

Reading 21 ■ Financial Statement Analysis: An Introduction 12
are summarized in the financial statements and to other information that is collected 
but not included in the financial reporting process. Financial statements are almost 
always audited by independent accountants who provide an opinion on whether the 
financial statements present fairly the company’s performance and financial position 
in accordance with a specified, applicable set of accounting standards and principles.
3.1 Financial Statements and Supplementary Information
A complete set of financial statements include a statement of financial position (i.e., 
a balance sheet), a statement of comprehensive income (i.e., a single statement of 
comprehensive income or an income statement and a statement of comprehensive 
income), a statement of changes in equity, and a statement of cash flows.2 The balance 
sheet portrays the company’s financial position at a given point in time. The statement

of comprehensive income and statement of cash flows present different aspects of a 
company’s performance over a period of time. The statement of changes in equity 
provides additional information regarding the changes in a company’s financial posi -
tion. In addition, the accompanying notes or footnotes to the financial statements are 
required and considered an integral part of a complete set of financial statements.
Along with the required financial statements, a company typically provides addi -
tional information in its financial reports. In many jurisdictions, some or all of this 
additional information is mandated by regulators or accounting standards boards. The 
additional information provided may include a letter from the chairman of the com -
pany, a report from management discussing the results (typically called management 
discussion and analysis [MD&A] or management commentary), an external auditor’s 
report providing assurances, a governance report describing the structure of the

company’s board of directors, and a corporate responsibility report. As part of his or 
her analysis, the financial analyst should read and assess this additional information 
along with the financial statements. The following sections describe and illustrate 
each financial statement and some of the additional information.
3.1.1  Balance Sheet
The balance sheet  (also called the statement of financial position  or statement 
of financial condition ) presents a company’s current financial position by disclosing 
the resources the company controls (assets) and its obligations to lenders and other 
creditors (liabilities) at a specific point in time. Owners’ equity  represents the excess 
of assets over liabilities. This amount is attributable to the company’s owners or share -
holders. Owners’ equity is the owners’ residual interest in (i.e., residual claim on) the 
company’s assets after deducting its liabilities.

The relationship among the three parts of the balance sheet (assets, liabilities, and 
owners’ equity) can be expressed in the following equation form: Assets = Liabilities 
+ Owners’ equity. This equation (sometimes called the accounting equation or the 
balance sheet equation) shows that the total amount of assets must equal or balance  
to the combined total amounts of liabilities and owners’ equity. Alternatively, the 
equation may be rearranged as follows: Assets – Liabilities = Owners’ equity. This 
formulation emphasizes the residual claim aspect of owners’ equity. Depending on 
the form of the organization, owners’ equity may be referred to as “partners’ capital” 
or “shareholders’ equity. ”
Exhibit 3 presents the balance sheet of the Volkswagen Group from its Annual 
Report 2009.
2 The names of the financial statements are those in IAS 1. Commonly used terms for these financial

statements are indicated in parentheses. Later readings will elaborate on each of these financial statements.

Major Financial Statements and Other Information Sources 13
Exhibit 3   Balance Sheet of the Volkswagen Group
€ million Note31 Dec. 
200931 Dec. 
2008
Assets
Noncurrent assets
Intangible assets 12 12,907 12,291
Property, plant and equipment 13 24,444 23,121
Leasing and rental assets 14 10,288 9,889
Investment property 14 216 150
Equity-  accounted investments 15 10,385 6,373
Other equity investments 15 543 583
Financial services receivables 16 33,174 31,855
Other receivables and financial assets 17 3,747 3,387
Noncurrent tax receivables 18 685 763
Deferred tax assets 18 3,013 3,344
99,402 91,756
Current assets
Inventories 19 14,124 17,816
Trade receivables 20 5,692 5,969
Financial services receivables 16 27,403 27,035
Other receivables and financial assets 17 5,927 10,068
Current tax receivables 18 762 1,024
Marketable securities 21 3,330 3,770
Cash and cash equivalents 22 20,539 9,474
Assets held for sale 23 — 1,007
77,776 76,163
Total assets 177,178 167,919
   
Equity and liabilities
Equity 24

Equity 24
Subscribed capital 1,025 1,024
Capital reserves 5,356 5,351
Retained earnings 28,901 28,636
Equity attributable to shareholders of 
Volkswagen AG 35,281 35,011
Minority interests 2,149 2,377
37,430 37,388
Noncurrent liabilities
Noncurrent financial liabilities 25 36,993 33,257
Other noncurrent liabilities 26 3,028 3,235
Deferred tax liabilities 27 2,224 3,654
Provisions for pensions 28 13,936 12,955
Provisions for taxes 27 3,946 3,555
Other noncurrent provisions 29 10,088 9,073
70,215 65,729
(continued)

Reading 21 ■ Financial Statement Analysis: An Introduction 14
2008
Current liabilities
Current financial liabilities 25 40,606 36,123
Trade payables 30 10,225 9,676
Current tax payables 27 73 59
Other current liabilities 26 8,237 8,545
Provisions for taxes 27 973 1,160
Other current provisions 29 9,420 8,473
Liabilities associated with assets held for 
sale 23 — 766
69,534 64,802
Total equity and liabilities 177,178 167,919
Note : Numbers are as shown in the annual report and may not add because of rounding.
In Exhibit 3, the balance sheet is presented with the most recent year in the first 
column and the earlier year in the second column. Although this is a common presen -
tation, analysts should be careful when reading financial statements. In some cases, 
the ordering may be reversed, with years listed from most distant to most recent.
At 31 December 2009, Volkswagen’s total resources or assets were €177 billion.

This number is the sum of non-  current assets of €99 billion and current assets of 
€78 billion.3 Total equity was €37 billion. Although Volkswagen does not give a total 
amount for all the balance sheet liabilities, it can be determined by adding the non-  
current and current liabilities, €70,215 million + €69,534 million = €139,749 million, 
or €140 billion.4
Referring back to the basic accounting equation, Assets = Liabilities + Equity, we 
have €177 billion = €140 billion + €37 billion. In other words, Volkswagen has assets 
of €177 billion, owes €140 billion, and thus has equity of €37 billion. Using the balance 
sheet and applying financial statement analysis, the analyst can answer such questions as
■■Has the company’s liquidity (ability to meet short-  term obligations) improved?
■■Is the company solvent (does it have sufficient resources to cover its 
obligations)?
■■What is the company’s financial position relative to the industry?

Volkswagen, a German-  based automobile manufacturer, prepares its financial 
statements in accordance with International Financial Reporting Standards (IFRS). 
IFRS require companies to present classified balance sheets that show current and 
non-  current assets and current and non-  current liabilities as separate classifications. 
However, IFRS do not prescribe a particular ordering or format, and the order in 
which companies present their balance sheet items is largely a function of tradition. 
As shown, Volkswagen presents non-  current assets before current assets, owners’ Exhibit 3   (Continued)
3 Current assets are defined, in general, as those assets that are cash or cash equivalents; are held for 
trading; or are expected to be converted to cash (realized), sold, or consumed within 12 months or the 
company’s normal operating cycle. All other assets are classified as non-  current.

4 Current liabilities are defined, in general, as those that are expected to be settled within 12 months or 
the company’s normal operating cycle. All other liabilities are classified as non-  current.

Major Financial Statements and Other Information Sources 15
equity before liabilities, and non-  current liabilities before current liabilities. This 
method generally reflects a presentation from least liquid to most liquid. In other 
countries, the typical order of presentation may differ. For example, in the United 
States, Australia, and Canada, companies usually present their assets and liabilities 
from most liquid to least liquid. Cash is typically the first asset shown, and equity is 
presented after liabilities.
As a basis for comparison, Exhibit 4 presents the balance sheet of Wal-  Mart Stores, 
Inc., or Walmart from its 2010 Annual Report.
Exhibit 4   Walmart Consolidated Balance Sheet
31 January
(Amounts in millions except per share data) 2010 2009
ASSETS
Current assets:
Cash and cash equivalents $7,907 $7,275
Receivables, net 4,144 3,905
Inventories 33,160 34,511
Prepaid expenses and other 2,980 3,063
Current assets of discontinued operations 140 195
  Total current assets 48,331 48,949

Total current assets 48,331 48,949
Property and equipment:
Land 22,591 19,852
Buildings and improvements 77,452 73,810
Fixtures and equipment 35,450 29,851
Transportation equipment 2,355 2,307
Property and equipment 137,848 125,820
Less accumulated depreciation (38,304) (32,964)
  Property and equipment, net 99,544 92,856
Property under capital leases:
Property under capital leases 5,669 5,341
Less accumulated amortization (2,906) (2,544)
  Property under capital leases, net 2,763 2,797
Goodwill 16,126 15,260
Other assets and deferred charges 3,942 3,567
  Total assets $170,706 $163,429
LIABILITIES AND EQUITY
Current liabilities:
Short-  term borrowings $523 $1,506
Accounts payable 30,451 28,849
Accrued liabilities 18,734 18,112
Accrued income taxes 1,365 677
Long-  term debt due within one year 4,050 5,848
Obligations under capital leases due within one year 346 315
Current liabilities of discontinued operations 92 83

Reading 21 ■ Financial Statement Analysis: An Introduction 16
31 January
  Total current liabilities 55,561 55,390
Long-  term debt 33,231 31,349
Long-  term obligations under capital leases 3,170 3,200
Deferred income taxes and other 5,508 6,014
Redeemable non-  controlling interest 307 397
Commitments and contingencies
Equity:
Preferred stock ($0.10 par value; 100 shares authorized, none issued) — —
Common stock ($0.10 par value; 11,000 shares authorized, 3,786 and 3,925 issued 
and outstanding at 31 January 2010 and 31 January 2009, respectively) 378 393
Capital in excess of par value 3,803 3,920
Retained earnings 66,638 63,660
Accumulated other comprehensive loss (70) (2,688)
  Total Walmart shareholders’ equity 70,749 65,285
Non-  controlling interest 2,180 1,794
  Total equity 72,929 67,079
  Total liabilities and equity $170,706 $163,429
Walmart has total assets of $170.7 billion. Liabilities and other non-  equity claims

total $97.8 billion, and equity is $72.9 billion. A later reading will cover the analysis 
of the balance sheet in more depth. The next section describes and illustrates the 
statement of comprehensive income.
3.1.2  Statement of Comprehensive Income
The statement of comprehensive income, under IFRS, can be presented as a single 
statement of comprehensive income or as two statements, an income statement and 
a statement of comprehensive income that begins with profit or loss from the income 
statement. The Volkswagen Group chose the latter form of presentation rather than 
a single statement.
3.1.2.1  Income Statement  The income statement presents information on the financial 
results of a company’s business activities over a period of time. The income statement 
communicates how much revenue  and other income the company generated during a 
period and the expenses it incurred to generate that revenue and other income. Revenue

typically refers to amounts charged for the delivery of goods or services in the ordinary 
activities of a business. Other income includes gains, which may or may not arise in 
the ordinary activities of the business. Expenses  reflect outflows, depletions of assets, 
and incurrences of liabilities that decrease equity. Expenses typically include such items 
as cost of sales (cost of goods sold), administrative expenses, and income tax expenses 
and may be defined to include losses. Net income (revenue plus other income minus 
expenses) on the income statement is often referred to as the “bottom line” because of 
its proximity to the bottom of the income statement. Net income may also be referred 
to as “net earnings, ” “net profit, ” and “profit or loss. ” In the event that expenses exceed 
revenues and other income, the result is referred to as “net loss. ”Exhibit 4   (Continued)

Major Financial Statements and Other Information Sources 17
Income statements are reported on a consolidated basis, meaning that they include 
the income and expenses of subsidiary companies under the control of the parent 
(reporting) company. The income statement is sometimes referred to as a statement 
of operations  or profit and loss (P&L) statement . The basic equation underlying 
the income statement is Revenue + Other income – Expenses = Income – Expenses 
= Net income.
In general terms, when one company (the parent) controls another company (the 
subsidiary), the parent presents its own financial statement information consolidated 
with that of the subsidiary. (When a parent company owns more than 50 percent of 
the voting shares of a subsidiary company, it is presumed to control the subsidiary and 
thus presents consolidated financial statements.) Each line item of the consolidated 
income statement includes the entire amount from the relevant line item on the sub -

sidiary’s income statement (after removing any intercompany transactions); however, 
if the parent does not own 100 percent of the subsidiary, it is necessary for the parent 
to present an allocation of net income to the minority interests. Minority interests, 
also called non-  controlling interests, refer to owners of the remaining shares of the 
subsidiary that are not owned by the parent. The share of consolidated net income 
attributable to minority interests is shown at the bottom of the income statement along 
with the net income attributable to shareholders of the parent company. Exhibit 5 
presents the income statement of the Volkswagen Group from its Annual Report 2009.
Exhibit 5   Income Statement of the Volkswagen Group for the Period 1 January to 31 December*
€ million Note 2009 2008
Sales revenue 1 105,187 113,808
Cost of sales 2 –91,608 –96,612
Gross profit 13,579 17,196
Distribution expenses 3 –10,537 –10,552
Administrative expenses 4 –2,739 –2,742

Other operating income 5 7,904 8,770
Other operating expenses 6 –6,352 –6,339
Operating profit 1,855 6,333
Share of profits and losses of equity-  accounted investments 7 701 910
Finance costs 8 –2,268 –1,815
Other financial result 9 972 1,180
Financial result –595 275
Profit before tax 1,261 6,608
Income tax income/expense 10 –349 –1,920
  Current –1,145 –2,338
  Deferred 796 418
Profit after tax 911 4,688
Minority interests –49 –65
Profit attributable to shareholders of Volkswagen AG 960 4,753
Basic earnings per ordinary share in € 11 2.38 11.92
Basic earnings per preferred share in € 11 2.44 11.98

Reading 21 ■ Financial Statement Analysis: An Introduction 18
Diluted earnings per ordinary share in € 11 2.38 11.88
Diluted earnings per preferred share in € 11 2.44 11.94
*The numbers are as shown in the annual report and may not add because of rounding.
Exhibit  5 shows that Volkswagen’s sales revenue for the fiscal year ended 31 
December 2009 was €105,187 million. Subtracting cost of sales from revenue gives 
gross profit of €13,579 million. After subtracting operating costs and expenses and 
adding other operating income, the company’s operating profit totals €1,855 million. 
Operating profit represents the results of the company’s usual business activities 
before deducting interest expense or taxes. Operating profit (also called operating 
income) is thus often referred to as earnings before interest and taxes (EBIT). Next, 
operating profit is increased by Volkswagen’s share of the profits generated by cer -

tain of its investments (€701 million) and by profits from its other financial activities 
(€972 million) and decreased by finance costs (i.e., interest expense) of €2,268 million, 
resulting in profit before tax of €1,261 million. Total income tax expense for 2009 was 
€349 million, resulting in profit after tax (net income) of €911 million.
After allocating the losses attributable to minority interest ownership in Volkswagen 
subsidiary companies, the profit attributable to shareholders of Volkswagen for 2009 
was €960 million. Allocating the losses attributable to minority interest ownership 
resulted in the allocation to shareholders of the parent company, Volkswagen AG, 
exceeding net income (profit after tax). Volkswagen’s disclosures indicate that its 
minority interests relate primarily to Scania AB, a subsidiary in which Volkswagen 
owns about 72 percent of the voting rights (with the minority interests owning the 
remaining 28 percent).

Companies present both basic and diluted earnings per share on the face of the 
income statement. Earnings per share numbers represent net income attributable to 
the class of shareholders divided by the relevant number of shares of stock outstanding 
during the period. Basic earnings per share is calculated using the weighted-  average 
number of common (ordinary) shares that were actually outstanding during the period 
and the profit or loss attributable to the common shareowners. Diluted earnings 
per share uses diluted shares —the number of shares that would hypothetically be 
outstanding if potentially dilutive claims on common shares (e.g., stock options or 
convertible bonds) were exercised or converted by their holders—and an appropriately 
adjusted profit or loss attributable to the common shareowners.
Volkswagen has two types of shareholders, ordinary and preferred, and presents 
earnings per share information for both, although there is no requirement to present

earnings per share information for preferred shareowners. Volkswagen’s basic earnings 
per ordinary share was €2.38. A note to the company’s financial statements explains that 
this number was calculated as follows: €960 million profit attributable to shareholders 
of Volkswagen, of which €703 million is attributable to ordinary shareholders and 
€257 million is attributable to preferred shareholders. The €703 million attributable 
to ordinary shareholders divided by the weighted-  average number of ordinary shares 
of 295 million shares equals basic earnings per share for 2009 of €2.38. Similar detail 
is provided in the notes for each of the earnings per share numbers.
An analyst examining the income statement might note that Volkswagen was 
profitable in both years. The company’s profitability declined substantially in 2009, 
primarily because of lower sales and reduced gross profit. This was not unexpected

given the global financial and economic crisis in that year. A better understanding of Exhibit 5   (Continued)

Major Financial Statements and Other Information Sources 19
Volkswagen’s profitability could likely be gained by examining income statements over 
a longer time period. The analyst might formulate questions related to profitability, 
such as the following:
■■Is the change in revenue related to an increase in units sold, an increase in 
prices, or some combination?
■■If the company has multiple business segments (for example, Volkswagen’s seg -
ments include passenger cars, light commercial vehicles, and financial services, 
among others), how are the segments’ revenue and profits changing?
■■How does the company compare with other companies in the industry?
Answering such questions requires the analyst to gather, analyze, and interpret 
information from a number of sources, including, but not limited to, the income 
statement.
3.1.2.2  Other Comprehensive Income  Comprehensive income includes all items that 
impact owners’ equity but are not the result of transactions with shareowners. Some

of these items are included in the calculation of net income, and some are included in 
other comprehensive income (OCI). When comprehensive income is presented in two 
statements, the statement of comprehensive income begins with the profit or loss from 
the income statement and then presents the components of other comprehensive income. 
Exhibit  6 presents the statement of comprehensive income of the Volkswagen 
Group from its Annual Report 2009.
Exhibit 6   Statement of Comprehensive Income of the Volkswagen Group for the Period 1 January to 31 
December
€ million 2009 2008
Exchange differences on translating foreign operations:
  Fair value changes recognized in other comprehensive income 917 –1,445
  Transferred to profit or loss 57
Actuarial gains/losses –860 190
Cash flow hedges:
  Fair value changes recognized in other comprehensive income 683 1,054
  Transferred to profit or loss –908 –1,427
Available-  for- sale financial assets (marketable securities):

Fair value changes recognized in other comprehensive income 200 –330
  Transferred to profit or loss 71 100
Deferred taxes 216 145
Share of profits and losses of equity-  accounted investments recognized directly in 
equity, after tax 30 –188
Other comprehensive income 406 –1,901
Total comprehensive income 1,317 2,787
Of which attributable to
  Shareholders of Volkswagen AG 1,138 3,310
  Minority interests 179 –523

Reading 21 ■ Financial Statement Analysis: An Introduction 20
Exhibit 6 shows that other comprehensive income, although smaller in absolute 
terms than profit after tax (net income), had a significant effect on total comprehensive 
income. In 2009, other comprehensive income represented approximately 31 percent 
of total comprehensive income and was approximately 45 percent of the size of profit 
after tax (net income). In 2008, other comprehensive income was negative (a loss) and 
was approximately 41 percent of the size of profit after tax (net income) in absolute 
terms. The statement of comprehensive income will be discussed in greater detail in 
a later reading. The next section briefly describes the statement of changes in equity.
3.1.3  Statement of Changes in Equity
The statement of changes in equity, variously called the “statement of changes in 
owners’ equity” or “statement of changes in shareholders’ equity, ” primarily serves to

report changes in the owners’ investment in the business over time. The basic compo -
nents of owners’ equity are paid-  in capital and retained earnings. Retained earnings 
include the cumulative amount of the company’s profits that have been retained in 
the company. In addition, non-  controlling or minority interests and reserves that 
represent accumulated other comprehensive income items are included in equity. The 
latter items may be shown separately or included in retained earnings. Volkswagen 
includes reserves as components of retained earnings.
The statement of changes in equity is organized to present, for each component of 
equity, the beginning balance, any increases during the period, any decreases during 
the period, and the ending balance. For paid-  in capital, an example of an increase is 
a new issuance of equity and an example of a decrease is a repurchase of previously 
issued stock. For retained earnings, income (both net income as reported on the

income statement and other comprehensive income) is the most common increase 
and a dividend payment is the most common decrease.
Volkswagen’s balance sheet in Exhibit  3 shows that equity at the end of 2009 
totaled €37,430 million, compared with €37,388 million at the end of 2008. The com -
pany’s statement of changes in equity presents additional detail on the change in each 
line item. Exhibit 7 presents an excerpt of the statement of changes in equity of the 
Volkswagen Group from its Annual Report 2009.
In Exhibit 7, the sum of the line items total comprehensive income (€1,102 million) 
and deferred taxes (€216 million) equals the amount of total comprehensive income 
reported in the statement of comprehensive income, except for a rounding differ -
ence. Using the balance at 31 December 2009, the sum of the columns accumulated 
profit through equity-  accounted investment equals the amount of retained earnings

on the balance sheet (€28,901 million in Exhibit 3), except for a rounding difference. 
Dividends (€779 million) are reported in this statement and reduce retained earnings. 
Explanatory notes on equity are included in the notes to the consolidated financial 
statements. The next section describes the cash flow statement.
3.1.4  Cash Flow Statement
Although the income statement and balance sheet provide measures of a company’s 
success in terms of performance and financial position, cash flow is also vital to a 
company’s long-  term success. Disclosing the sources and uses of cash helps creditors, 
investors, and other statement users evaluate the company’s liquidity, solvency, and 
financial flexibility. Financial flexibility  is the ability of the company to react and 
adapt to financial adversities and opportunities. The cash flow statement classifies all 
cash flows of the company into three categories: operating, investing, and financing.

Cash flows from operating activities  are those cash flows not classified as investing 
or financing and generally involve the cash effects of transactions that enter into the 
determination of net income and, hence, comprise the day-  to- day operations of the 
company. Cash flows from investing activities  are those cash flows from activities 
associated with the acquisition and disposal of long-  term assets, such as property and

Major Financial Statements and Other Information Sources 21Exhibit 7   Excerpt from Statement of Changes in Equity of the Volkswagen Group for the Period 1 January to 31 December 2009*
Sub-  
scribed 
capitalCapital 
reservesRETAINED EARNINGS
Equity 
attributable 
to 
shareholders 
of VW AGMinority 
interests Total equity € millionsAccumu-  
lated profitCurrency 
translation 
reserveReserve 
for 
actuarial 
gains/
lossesCash flow 
hedge 
reserveFair value 
reserve for 
securitiesEquity- 
accounted 
investments
⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮
Balance at 1 
Jan. 2009 1,024 5,351 31,522 –2,721 –672 1,138 –192 –439 35,011 2,377 37,388
Capital increase 0 4 4 4
Dividend 
payment –779 –779 –95 –874
Capital trans -
actions involv -
ing change in 
ownership –76 –76 –316 –392
Total compre -
hensive income 960 839 –851 –361 271 30 888 214 1,102
Deferred taxes 247 83 –80 250 –34 216
Other changes –21 2 –18 4 –15
Balance at 31 
Dec. 2009 1,025 5,356 31,607 –1,881 –1,274 860 –1 –409 35,281 2,149 37,430
28,902

28,902
*Numbers are as shown in the annual report and may not add and cross-  add because of rounding.

Reading 21 ■ Financial Statement Analysis: An Introduction 22
equipment. Cash flows from financing activities  are those cash flows from activities 
related to obtaining or repaying capital to be used in the business. IFRS permit more 
flexibility than US GAAP in classifying dividend and interest receipts and payments 
within these categories.
Exhibit 8 presents Volkswagen’s statement of cash flows for the fiscal years ended 
31 December 2009 and 2008.
Exhibit 8   Cash Flow Statement of the Volkswagen Group: 1 January to 31 December
Cash and cash equivalents at beginning of period (excluding time deposit 
investments) 9,443 9,914
Income taxes paid –529 –2,075
Depreciation and amortization of property, plant and equipment, intangible assets 
and investment property 5,028 5,198
Amortization of capitalized development costs 1,586 1,392
Impairment losses on equity investments 16 32
Depreciation of leasing and rental assets 2,247 1,816

Gain/loss on disposal of noncurrent assets –547 37
Share of profit or loss of equity-  accounted investments –298 –219
Other noncash expense/income 727 765
Change in inventories 4,155 –3,056
Change in receivables (excluding financial services) 465 –1,333
Change in liabilities (excluding financial liabilities) 260 815
Change in provisions 1,660 509
Change in leasing and rental assets –2,571 –2,734
Change in financial services receivables –719 –5,053
Cash flows from operating activities 12,741 2,702
Investments in property, plant and equipment, intangible assets and investment 
property –5,963 –6,896
Additions to capitalized development costs –1,948 –2,216
Acquisition of equity investments –3,989 –2,597
Disposal of equity investments 1,320 1
Proceeds from disposal of property, plant and equipment, intangible assets and 
investment property 153 95
Change in investments in securities 989 2,041
Change in loans and time deposit investments –236 –1,611
Cash flows from investing activities –9,675 –11,183

Capital contributions 4 218
Dividends paid –874 –722
Capital transactions with minority interests –392 –362
Other changes 23 –3
Proceeds from issue of bonds 15,593 7,671
Repayment of bonds –10,202 –8,470
Change in other financial liabilities 1,405 9,806
Finance lease payments –23 –15

Major Financial Statements and Other Information Sources 23
Cash flows from financing activities 5,536 8,123
Effect of exchange rate changes on cash and cash equivalents 190 –113
Net change in cash and cash equivalents 8,792 –471
Cash and cash equivalents at end of period (excluding time deposit 
investments) 18,235 9,443
Cash and cash equivalents at end of period (excluding time deposit investments) 18,235 9,443
Securities and loans (including time deposit investments) 7,312 7,875
Gross liquidity 25,547 17,318
Total third-  party borrowings –77,599 –69,555
Net liquidity –52,052 –52,237
The operating activities section of Volkswagen’s cash flow statement begins with 
profit before tax,5 €1,261 million, subtracts actual income tax payments, and then 
adjusts this amount for the effects of non-  cash transactions, accruals and deferrals, 
and transactions of an investing and financing nature to arrive at the amount of cash

generated from operating activities of €12,741 million. This approach to reporting 
cash flow from operating activities is termed the indirect method. The direct method 
of reporting cash flows from operating activities discloses major classes of gross cash 
receipts and gross cash payments. Examples of such classes are cash received from 
customers and cash paid to suppliers and employees.
The indirect method emphasizes the different perspectives of the income statement 
and cash flow statement. On the income statement, income is reported when earned, 
not necessarily when cash is received, and expenses are reported when incurred, not 
necessarily when paid. The cash flow statement presents another aspect of performance: 
the ability of a company to generate cash flow from running its business. Ideally, for 
an established company, the analyst would like to see that the primary source of cash 
flow is from operating activities as opposed to investing or financing activities.

The sum of the net cash flows from operating, investing, and financing activities 
and the effect of exchange rates on cash equals the net change in cash during the 
fiscal year. For Volkswagen, the sum of these four items was €8,792 million in 2009, 
which thus increased the company’s cash, excluding amounts held in time deposit 
investments, from €9,443 million at the beginning of the period to €18,235 million 
at the end of the period. As disclosed in a note to the financial statements, the time 
deposit investments are €42 million and €2,304 million for the years 2008 and 2009, 
respectively. The note also disclosed that €11 million of cash and cash equivalents 
held for sale [sic] are included in the cash and cash equivalents as reported in cash 
flow statement but are not included in the cash and cash equivalents as reported in 
the balance sheet in 2008. When these amounts are included with the amounts shown

on the cash flow statement, the total cash and cash equivalents for the years 2008 and 
2009 are €9,474 (= 9443 + 42 – 11) million and €20,539 million. These are the same 
amounts reported as cash and cash equivalents on the balance sheets in Exhibit 3. 
The cash flow statement will be covered in more depth in a later reading.Exhibit 8   (Continued)
5 Other companies may choose to begin with net income.

Reading 21 ■ Financial Statement Analysis: An Introduction 24
3.1.5  Financial Notes and Supplementary Schedules
The notes (also sometimes referred to as footnotes) that accompany the four finan -
cial statements are required and are an integral part of the complete set of financial 
statements. The notes provide information that is essential to understanding the infor -
mation provided in the primary statements. Volkswagen’s 2009 financial statements, 
for example, include 91 pages of notes.
The notes disclose the basis of preparation for the financial statements. For example, 
Volkswagen discloses in its first note that its fiscal year corresponds to the calendar 
year, that its financial statements are prepared in accordance with IFRS as adopted by 
the European Union, that the statements are prepared in compliance with German law, 
that the statements are denominated in millions of euros unless otherwise specified,

and that the figures have been rounded, which might give rise to minor discrepancies 
when figures are added. Volkswagen also discloses that its financial statements are 
on a consolidated basis—that is, including Volkswagen AG and all of the subsidiary 
companies it controls.
The notes also disclose information about the accounting policies, methods, and 
estimates used to prepare the financial statements. As will be discussed in later read -
ings, both IFRS and US GAAP allow some flexibility in choosing among alternative 
policies and methods when accounting for certain items. This flexibility aims to meet 
the divergent needs of many businesses for reporting a variety of economic trans -
actions. In addition to differences in accounting policies and methods, differences 
arise as a result of estimates needed to record and measure transactions, events, and 
financial statement line items.
Overall, flexibility in accounting choices is necessary because, ideally, a company

will select those policies, methods, and estimates that are allowable and most relevant 
and that fairly reflect the unique economic environment of the company’s business 
and industry. Flexibility can, however, create challenges for the analyst because the use 
of different policies, methods, and estimates reduces comparability across different 
companies’ financial statements. Comparability occurs when different companies’ 
information is measured and reported in a similar manner over time. Comparability 
helps the analyst identify and analyze the real economic differences across companies, 
rather than differences that arise solely from different accounting choices. Because 
comparability of financial statements is a critical requirement for objective financial 
analysis, an analyst should be aware of the potential for differences in accounting choices 
even when comparing two companies that use the same set of accounting standards.

For example, if a company acquires a piece of equipment to use in its operations, 
accounting standards require that the cost of the equipment be reported as an expense 
by allocating its cost less any residual value in a systematic manner over the equip -
ment’s useful life. This allocation of the cost is known as depreciation . Accounting 
standards permit flexibility, however, in determining the manner in which each year’s 
expense is determined. Two companies may acquire similar equipment but use dif -
ferent methods and assumptions to record the expense over time. An analyst’s ability 
to compare the companies’ performance is hindered by the difference. Analysts must 
understand reporting choices in order to make appropriate adjustments when com -
paring companies’ financial positions and performance.
A company’s significant accounting choices (policies, methods, and estimates) must 
be discussed in the notes to the financial statements. For example, a note containing a

summary of significant accounting policies includes how the company recognizes its 
revenues and depreciates its non-  current tangible assets. Analysts must understand 
the accounting choices a company makes and determine whether they are similar to 
those of other companies identified and used as benchmarks or comparables. If the 
policies of the companies being compared are different, the analyst who understands 
accounting and financial reporting can often make necessary adjustments so that the 
financial statement data used are more comparable.

Major Financial Statements and Other Information Sources 25
For many companies, the financial notes and supplemental schedules provide 
explanatory information about every line item (or almost every line item) on the bal -
ance sheet and income statement, as illustrated by the note references in Volkswagen’s 
balance sheet and income statement in Exhibits 3 and 5. In addition, note disclosures 
include information about the following (this is not an exhaustive list):
■■financial instruments and risks arising from financial instruments,
■■commitments and contingencies,
■■legal proceedings,
■■related-  party transactions,
■■subsequent events (i.e., events that occur after the balance sheet date),
■■business acquisitions and disposals, and
■■operating segments’ performance.
Exhibit 9   Excerpt from Notes to the Consolidated Financial Statements of the Volkswagen Group for Fiscal 
Y ear Ended 31 December 2009: Selected Data on Operating Segments (€ millions)
2008Passenger Cars and Light

2008Passenger Cars and Light  
Commercial Vehicles ScaniaVolkswagen  
Financial ServicesTotal 
Segments
Sales revenue from external customers 98,710 3,865 10,193 112,768
Segment profit or loss 6,431 417 893 7,741
Segment assets 91,458 10,074 74,690 176,222
2009Passenger Cars and Light  
Segments
Sales revenue from external customers 86,297 6,385 11,095 103,777
Segment profit or loss 2,020 236 606 2,862
Segment assets 87,786 9,512 76,431 173,729
An analyst uses a significant amount of judgment in deciding how to incorporate 
information from note disclosures into the analysis. For example, such information 
as financial instrument risk, contingencies, and legal proceedings can alert an analyst 
to risks that can affect a company’s financial position and performance in the future 
and that require monitoring over time. As another example, information about a 
company’s operating segments can be useful as a means of quickly understanding

what a company does and how and where it earns money. The operating segment data 
shown in Exhibit 9 appear in the notes to the financial statements for Volkswagen. 
(The totals of the segment data do not equal the amounts reported in the company’s 
financial statements because the financial statement data are adjusted for intersegment 
activities and unallocated items. The note provides a complete reconciliation of the 
segment data to the reported data.) From the data in Exhibit 9, an analyst can quickly 
see that most of the company’s revenues and operating profits come from the sale of 
passenger cars and light commercial vehicles. Over 80 percent of the company’s rev -
enues was generated by this segment in both years. In 2008, this segment accounted 
for over 80 percent of the company’s total segment operating profits, although the 
percentage declined to 70 percent in 2009 because of higher sales growth in the other

two segments. Experience using the disclosures of a company and its competitors 
typically enhances an analyst’s judgment about the relative importance of different 
disclosures and the ways in which they can be helpful.

Reading 21 ■ Financial Statement Analysis: An Introduction 26
3.1.6  Management Commentary or Management’s Discussion and Analysis
Publicly held companies typically include a section in their annual reports where 
management discusses a variety of issues of concern, including the nature of the busi -
ness, past results, and future outlook. This section is referred to by a variety of names, 
including management report(ing), management commentary, operating and financial 
review, and management’s discussion and analysis. Inclusion of a management report 
is recommended by the International Organization of Securities Commissions and 
frequently required by regulatory authorities, such as the US Securities and Exchange 
Commission (SEC) or the UK Financial Reporting Council (FRC). In Germany, man -
agement reporting has been required since 1931 and is audited. The discussion by 
management is arguably one of the most useful parts of a company’s annual report

besides the financial statements themselves; however, other than excerpts from the 
financial statements, information included in the management commentary is typically 
unaudited. When using information from the management report, an analyst should 
be aware of whether the information is audited or unaudited.
To help improve the quality of the discussion by management, the International 
Accounting Standards Board (IASB) issued an IFRS Practice Statement, “Management 
Commentary, ” in December 2010 that includes a framework for the preparation and 
presentation of management commentary. The framework provides guidance rather 
than sets forth requirements in a standard. The framework identifies five content 
elements of a “decision-  useful management commentary. ” Those content elements 
include 1) the nature of the business; 2) management’s objectives and strategies; 3) 
the company’s significant resources, risks, and relationships; 4) results of operations;

and 5) critical performance measures.
In the United States, the SEC requires listed companies to provide an MD&A 
and specifies the content.6 Management must highlight any favorable or unfavorable 
trends and identify significant events and uncertainties that affect the company’s 
liquidity, capital resources, and results of operations. The MD&A must also provide 
information about the effects of inflation, changing prices, or other material events 
and uncertainties that may cause the future operating results and financial condition 
to materially depart from the current reported financial information. In addition, the 
MD&A must provide information about off-  balance-  sheet obligations and about con -
tractual commitments such as purchase obligations. Companies should also provide 
disclosure in the MD&A that discusses the critical accounting policies that require 
management to make subjective judgments and that have a significant impact on 
reported financial results.

The management commentary or MD&A is a good starting place for understanding 
information in the financial statements. In particular, the forward-  looking disclosures 
in an MD&A, such as those about planned capital expenditures, new store openings, 
or divestitures, can be useful in projecting a company’s future performance. However, 
the commentary is only one input for the analyst seeking an objective and independent 
perspective on a company’s performance and prospects.
The management report in the Annual Report 2009 of Volkswagen Group includes 
much information of potential interest to an analyst. The 78-  page management report 
contains sections titled Business Development; Shares and Bonds; Net Assets; Financial 
Position; Results of Operations; Volkswagen AG (condensed, according to German 
Commercial Code); Value-  Enhancing Factors; Risk Report; and Report on Expected 
Developments.

6 Relevant sections of SEC requirements are included for reference in the FASB ASC. The FASB ASC does 
not include sections of SEC requirements that deal with matters outside the basic financial statements, 
such as the MD&A.

Major Financial Statements and Other Information Sources 27
3.1.7  Auditor’s Reports
Financial statements presented in companies’ annual reports are generally required to 
be audited (examined) by an independent accounting firm in accordance with specified 
auditing standards. The independent auditor then provides a written opinion on the 
financial statements. This opinion is referred to as the audit report. Audit reports take 
slightly different forms in different jurisdictions, but the basic components, including 
a specific statement of the auditor’s opinion, are similar. Audits of financial statements 
may be required by contractual arrangement, law, or regulation.
International standards for auditing have been developed by the International 
Auditing and Assurance Standards Board of the International Federation of Accountants. 
These standards have been adopted by many countries and are referenced in audit

reports issued in those countries. Other countries, such as the United States, specify 
their own auditing standards. With the enactment of the Sarbanes–Oxley Act of 2002 
in the United States, auditing standards for public companies are promulgated by the 
Public Company Accounting Oversight Board.
Under international standards for auditing (ISAs), the objectives of an auditor in 
conducting an audit of financial statements are
A To obtain reasonable assurance about whether the financial statements as a 
whole are free from material misstatement, whether due to fraud or error, 
thereby enabling the auditor to express an opinion on whether the financial 
statements are prepared, in all material respects, in accordance with an applica -
ble financial reporting framework; and
B To report on the financial statements, and communicate as required by the 
ISAs, in accordance with the auditor’s findings.7
Publicly traded companies may also have requirements set by regulators or stock

exchanges, such as appointing an independent audit committee within its board 
of directors to oversee the audit process. The audit process provides a basis for 
the independent auditor to express an audit opinion on whether the information 
presented in the audited financial statements present fairly the financial position, 
performance, and cash flows of the company in accordance with a specified set of 
accounting standards. Because audits are designed and conducted using audit sam -
pling techniques and financial statement line items may be based on estimates and 
assumptions, independent auditors cannot express an opinion that provides absolute 
assurance about the accuracy or precision of the financial statements. Instead, the 
independent audit report provides reasonable assurance  that the financial statements 
are fairly presented , meaning that there is a high probability that the audited financial

statements are free from material  error, fraud, or illegal acts that have a direct effect 
on the financial statements.
The standard independent audit report for a publicly traded company normally 
has several paragraphs under both the international and US auditing standards. The 
first or “introductory” paragraph describes the financial statements that were audited 
and the responsibilities of both management and the independent auditor. The second 
or “scope” paragraph describes the nature of the audit process and provides the basis 
for the auditor’s expression about reasonable assurance on the fairness of the financial 
statements. The third or “opinion” paragraph expresses the auditor’s opinion on the 
fairness of the audited financial statements.
An unqualified  audit opinion states that the financial statements give a “true and fair 
view” (international) or are “fairly presented” (international and US) in accordance with

applicable accounting standards. This is often referred to as a “clean” opinion and is the 
7 See the International Auditing and Assurance Standards Board (IAASB) Handbook of International 
Quality Control, Auditing, Review, Other Assurance, and Related Services Pronouncements .

Reading 21 ■ Financial Statement Analysis: An Introduction 28
one that analysts would like to see in a financial report. There are several other types 
of opinions. A qualified  audit opinion is one in which there is some scope limitation or 
exception to accounting standards. Exceptions are described in the audit report with 
additional explanatory paragraphs so that the analyst can determine the importance 
of the exception. An adverse  audit opinion is issued when an auditor determines that 
the financial statements materially depart from accounting standards and are not fairly 
presented. An adverse opinion makes analysis of the financial statements easy: Do not 
bother analyzing these statements, because the company’s financial statements cannot 
be relied on. Finally, a disclaimer of opinion  occurs when, for some reason, such as 
a scope limitation, the auditors are unable to issue an opinion. Exhibit 10 presents

the independent auditor’s report for Volkswagen. Note that Volkswagen received an 
unqualified or clean audit opinion from PricewaterhouseCoopers for the company’s 
fiscal year ended 31 December 2009.
Exhibit 10   Volkswagen’s Independent Audit Report
Auditors’ Report
On completion of our audit, we issued the following unqualified auditors’ report 
dated February 17, 2010. This report was originally prepared in German. In case 
of ambiguities the German version takes precedence:
We have audited the consolidated financial statements prepared by VOLKSWAGEN 
AKTIENGESELLSCHAFT, Wolfsburg, comprising the income statement and 
statement of comprehensive income, the balance sheet, the statement of changes 
in equity, the cash flow statement and the notes to the consolidated financial 
statements, together with the group management report, which is combined with 
the management report of the Company for the business year from January 1

to December  31, 2009. The preparation of the consolidated financial state -
ments and the combined management report in accordance with the IFRSs, 
as adopted by the EU, and the additional requirements of German commercial 
law pursuant to § (article) 315a Abs. (paragraph) 1 HGB (“Handelsgesetzbuch”: 
German Commercial Code) are the responsibility of the Company’s Board of 
Management. Our responsibility is to express an opinion on the consolidated 
financial statements and on the combined management report based on our audit.
We conducted our audit of the consolidated financial statements in accor -
dance with § 317 HGB and German generally accepted standards for the audit of 
financial statements promulgated by the Institut der Wirtschaftsprüfer (Institute 
of Public Auditors in Germany) (IDW). Those standards require that we plan and 
perform the audit such that misstatements materially affecting the presentation

of the net assets, financial position and results of operations in the consolidated 
financial statements in accordance with the applicable financial reporting frame -
work and in the combined management report are detected with reasonable 
assurance. Knowledge of the business activities and the economic and legal 
environment of the Group and expectations as to possible misstatements are 
taken into account in the determination of audit procedures. The effectiveness 
of the accounting-  related internal control system and the evidence supporting 
the disclosures in the consolidated financial statements and the combined 
management report are examined primarily on a test basis within the frame -
work of the audit. The audit includes assessing the annual financial statements 
of those entities included in consolidation, the determination of the entities to 
be included in consolidation, the accounting and consolidation principles used

and significant estimates made by the Company’s Board of Management, as well

Major Financial Statements and Other Information Sources 29
as evaluating the overall presentation of the consolidated financial statements 
and the combined management report. We believe that our audit provides a 
reasonable basis for our opinion.
Our audit has not led to any reservations.
In our opinion, based on the findings of our audit, the consolidated finan -
cial statements comply with the IFRSs as adopted by the EU and the additional 
requirements of German commercial law pursuant to Article 315a paragraph 
1 HGB and give a true and fair view of the net assets, financial position and 
results of operations of the Group in accordance with these requirements. The 
combined management report is consistent with the consolidated financial 
statements and as a whole provides a suitable view of the Group’s position and 
suitably presents the opportunities and risks of future development.
Hanover, February 17, 2010
PricewaterhouseCoopers
Aktiengesellschaft
Wirtschaftsprüfungsgesellschaft

Harald Kayser
Wirtschaftsprüfer
ppa. Martin Schröder
Source:  Volkswagen’s Annual Report 2009.
In the United States, under the Sarbanes–Oxley Act, the auditors must also express 
an opinion on the company’s internal control systems. This information may be pro -
vided in a separate opinion or incorporated as a paragraph in the opinion related to 
the financial statements. The internal control system is the company’s internal system 
that is designed, among other things, to ensure that the company’s process for gener -
ating financial reports is sound. Although management has always been responsible 
for maintaining effective internal control, the Sarbanes–Oxley Act greatly increases 
management’s responsibility for demonstrating that the company’s internal controls 
are effective. Management of publicly traded companies in the United States are now

required by securities regulators to explicitly accept responsibility for the effectiveness 
of internal control, evaluate the effectiveness of internal control using suitable control 
criteria, support the evaluation with sufficient competent evidence, and provide a 
report on internal control.
Although these reports and attestations provide some assurances to analysts, they 
are not infallible. The analyst must always use a degree of healthy skepticism when 
analyzing financial statements.
3.2 Other Sources of Information
The information described in Section 3.1 is generally provided to shareholders at least 
annually. In addition, companies also provide information on management and director 
compensation, company stock performance, and any potential conflicts of interest that 
may exist between management, the board, and shareholders. This information may Exhibit 10   (Continued)

Reading 21 ■ Financial Statement Analysis: An Introduction 30
appear in the company’s annual report or other publicly available documents. Public 
companies often provide this information in proxy statements, which are statements 
distributed to shareholders about matters that are to be put to a vote at the company’s 
annual (or special) meeting of shareholders.
Interim reports are also provided by the company either semiannually or quar -
terly, depending on the applicable regulatory requirements. Interim reports generally 
present the four basic financial statements and condensed notes but are not audited. 
These interim reports provide updated information on a company’s performance and 
financial position since the last annual period.
Companies also provide relevant current information on their websites, in press 
releases, and in conference calls with analysts and investors. One type of press release, 
which analysts often consider to be particularly important, is the periodic earnings

announcement. The earnings announcement often happens well before the company 
files its formal financial statements. Such earnings announcements are often followed 
by a conference call in which the company’s senior executives describe the company’s 
performance and answer questions posed by conference call participants. Following 
the earnings conference call, the investor relations portion of the company’s website 
may post a recording of the call accompanied by slides and supplemental information 
discussed during the call.
When performing financial statement analysis, analysts should review all these 
company sources of information as well as information from external sources regard -
ing the economy, the industry, the company, and peer (comparable) companies. 
Information on the economy, industry, and peer companies is useful in putting the 
company’s financial performance and position in perspective and in assessing the

company’s future. In most cases, information from sources apart from the company 
is crucial to an analyst’s effectiveness. For example, an analyst studying a consumer-  
oriented company will typically seek direct experience with the products (taste the 
food or drink, use the shampoo or soap, visit the stores or hotels). An analyst following 
a highly regulated industry will study the existing and expected relevant regulations. 
An analyst following a highly technical industry will gain relevant expertise person -
ally or seek input from a technical specialist. In sum, thorough research goes beyond 
financial reports.
The next section presents a framework for using all this information in financial 
statement analysis.
FINANCIAL STATEMENT ANALYSIS FRAMEWORK
Analysts work in a variety of positions within the investment management industry. 
Some are equity analysts whose main objective is to evaluate potential investments in

a company’s equity securities (i.e., the shares or stock it issues) as a basis for deciding 
whether a prospective investment is attractive and what an appropriate purchase 
price might be. Others are credit analysts who evaluate the credit-  worthiness of a 
company to decide whether (and with what terms) a loan should be made or what 
credit rating should be assigned. Analysts may also be involved in a variety of other 
tasks, such as evaluating the performance of a subsidiary company, evaluating a private 
equity investment, or finding stocks that are overvalued for purposes of taking a short 
position. This section presents a generic framework for financial statement analysis 
that can be used in these various tasks. The framework is summarized in Exhibit 11.84
8 Components of this framework have been adapted from van Greuning and Bratanovic (2003, p. 300) 
and from Benninga and Sarig (1997, pp. 134–156).

Financial Statement Analysis Framework 31
Exhibit 11   Financial Statement Analysis Framework
Phase Sources of Information Output
1 Articulate the purpose and context of 
the analysis.■■The nature of the analyst’s function, 
such as evaluating an equity or 
debt investment or issuing a credit 
rating.
■■Communication with client or 
supervisor on needs and concerns.
■■Institutional guidelines related to 
developing specific work product.■■Statement of the purpose or objec -
tive of analysis.
■■A list (written or unwritten) of 
specific questions to be answered by 
the analysis.
■■Nature and content of report to be 
provided.
■■Timetable and budgeted resources 
for completion.
2 Collect input data.■■Financial statements, other 
financial data, questionnaires, and 
industry/economic data.
■■Discussions with manage -
ment, suppliers, customers, and 
competitors.
■■Company site visits (e.g., to pro -
duction facilities or retail stores).■■Organized financial statements.
■■Financial data tables.

■■Completed questionnaires, if 
applicable.
3 Process data.■■Data from the previous phase. ■■Adjusted financial statements.
■■Common-  size statements.
■■Ratios and graphs.
■■Forecasts.
4 Analyze/interpret the processed data.■■Input data as well as processed 
data.■■Analytical results.
5 Develop and communicate conclu -
sions and recommendations (e.g., 
with an analysis report).■■Analytical results and previous 
reports.
■■Institutional guidelines for pub -
lished reports.■■Analytical report answering ques -
tions posed in Phase 1.
■■Recommendation regarding the 
purpose of the analysis, such as 
whether to make an investment or 
grant credit.
6 Follow-  up.■■Information gathered by period -
ically repeating above steps as 
necessary to determine whether 
changes to holdings or recommen -
dations are necessary.■■Updated reports and 
recommendations.
The following sections discuss the individual phases of financial statement analysis.
4.1 Articulate the Purpose and Context of Analysis

Prior to undertaking any analysis, it is essential to understand the purpose of the 
analysis. An understanding of the purpose is particularly important in financial 
statement analysis because of the numerous available techniques and the substantial 
amount of data.
Some analytical tasks are well defined, in which case articulating the purpose of 
the analysis requires little decision making by the analyst. For example, a periodic 
credit review of an investment-  grade debt portfolio or an equity analyst’s report on

Reading 21 ■ Financial Statement Analysis: An Introduction 32
a particular company may be guided by institutional norms such that the purpose of 
the analysis is given. Furthermore, the format, procedures, and/or sources of infor -
mation may also be given.
For other analytical tasks, articulating the purpose of the analysis requires the 
analyst to make decisions. The purpose of an analysis guides further decisions about 
the approach, the tools, the data sources, the format in which to report the results of 
the analysis, and the relative importance of different aspects of the analysis.
When facing a substantial amount of data, a less experienced analyst may be 
tempted to just start making calculations and generating financial ratios without 
considering what is relevant for the decision at hand. It is generally advisable to 
resist this temptation and thus avoid unnecessary or pointless efforts. Consider the

questions: If you could have all the calculations and ratios completed instantly, what 
conclusion would you be able to draw? What question would you be able to answer? 
What decision would your answer support?
The analyst should also define the context at this stage. Who is the intended audi -
ence? What is the end product—for example, a final report explaining conclusions 
and recommendations? What is the time frame (i.e., when is the report due)? What 
resources and resource constraints are relevant to completion of the analysis? Again, 
the context may be predefined (i.e., standard and guided by institutional norms).
Having clarified the purpose and context of the financial statement analysis, the 
analyst should next compile the specific questions to be answered by the analysis. 
For example, if the purpose of the financial statement analysis (or, more likely, the 
particular stage of a larger analysis) is to compare the historical performance of three

companies operating in a particular industry, specific questions would include the 
following: What has been the relative growth rate of the companies, and what has 
been the relative profitability of the companies?
4.2 Collect Data
Next, the analyst obtains the data required to answer the specific questions. A key 
part of this step is obtaining an understanding of the company’s business, financial 
performance, and financial position (including trends over time and in comparison 
with peer companies). For historical analyses, financial statement data alone are ade -
quate in some cases. For example, to screen a large number of alternative companies 
to find those with a minimum level of profitability, financial statement data alone 
would be adequate. But to address more in-  depth questions, such as why and how 
one company performed better or worse than its competitors, additional information 
would be required. As another example, to compare the historical performance of

two companies in a particular industry, the historical financial statements would be 
sufficient to determine which had faster-  growing sales or earnings and which was 
more profitable; however, a broader comparison with overall industry growth and 
profitability would obviously require industry data.
Furthermore, information on the economy and industry is necessary to understand 
the environment in which the company operates. Analysts often take a top-  down 
approach whereby they 1) gain an understanding of the macroeconomic environment, 
such as prospects for growth in the economy and inflation, 2) analyze the prospects 
of the industry in which the subject company operates based on the expected mac -
roeconomic environment, and 3) determine the prospects for the company in the 
expected industry and macroeconomic environments. For example, an analyst may 
need to forecast future growth in earnings for a company. To project future growth, past

company data provide one basis for statistical forecasting; however, an understanding 
of economic and industry conditions can improve the analyst’s ability to forecast a 
company’s earnings on the basis of forecasts of overall economic and industry activity.

Financial Statement Analysis Framework 33
4.3 Process Data
After obtaining the requisite financial statement and other information, the analyst 
processes these data using appropriate analytical tools. For example, processing the 
data may involve computing ratios or growth rates; preparing common-  size financial 
statements; creating charts; performing statistical analyses, such as regressions or 
Monte Carlo simulations; performing equity valuation; performing sensitivity anal -
yses; or using any other analytical tools or combination of tools that are available 
and appropriate for the task. A comprehensive financial analysis at this stage would 
include the following:
■■Reading and evaluating financial statements for each company being analyzed. 
This includes reading the notes and understanding what accounting standards 
have been used (for example, IFRS or US GAAP), what accounting choices have 
been made (for example, when to report revenue on the income statement), and

what operating decisions have been made that affect reported financial state -
ments (for example, leasing versus purchasing equipment).
■■Making any needed adjustments to the financial statements to facilitate com -
parison when the unadjusted statements of the subject companies reflect differ -
ences in accounting standards, accounting choices, or operating decisions. Note 
that commonly used databases do not make such analyst adjustments.
■■Preparing or collecting common-  size financial statement data (which scale data 
to directly reflect percentages [e.g., of sales] or changes [e.g., from the prior 
year]) and financial ratios (which are measures of various aspects of corporate 
performance based on financial statement elements). On the basis of common-  
size financial statements and financial ratios, analysts can evaluate a company’s 
relative profitability, liquidity, leverage, efficiency, and valuation in relation to 
past results and/or peers’ results.

4.4 Analyze/Interpret the Processed Data
Once the data have been processed, the next step—critical to any analysis—is to 
interpret the output. The answer to a specific financial analysis question is seldom the 
numerical answer alone. Rather, the answer to the analytical question relies on the 
analyst’s interpretation of the output and the use of this interpreted output to support 
a conclusion or recommendation. The answers to the specific analytical questions may 
themselves achieve the underlying purpose of the analysis, but usually, a conclusion 
or recommendation is required. For example, an equity analysis may require a buy, 
hold, or sell decision or a conclusion about the value of a share of stock. In support of 
the decision, the analysis would cite such information as target value, relative perfor -
mance, expected future performance given a company’s strategic position, quality of

management, and whatever other information was important in reaching the decision.
4.5 Develop and Communicate Conclusions/
Recommendations
Communicating the conclusion or recommendation in an appropriate format is the 
next step. The appropriate format will vary by analytical task, by institution, and/
or by audience. For example, an equity analyst’s report would typically include the 
following components:
■■summary and investment conclusion;
■■earnings projections;

Reading 21 ■ Financial Statement Analysis: An Introduction 34
■■valuation;
■■business summary;
■■risk, industry, and competitive analysis;
■■historical performance; and
■■forecasts.
The contents of reports may also be specified by regulatory agencies or profes -
sional standards. For example, the CFA Institute Standards of Practice Handbook  
(Handbook ) dictates standards that must be followed in communicating recommen -
dations. According to the Handbook :
Standard V(B) states that members and candidates should communicate 
in a recommendation the factors that were instrumental in making the 
investment recommendation. A critical part of this requirement is to 
distinguish clearly between opinions and facts. In preparing a research 
report, the member or candidate must present the basic characteristics 
of the security(ies) being analyzed, which will allow the reader to evaluate 
the report and incorporate information the reader deems relevant to his 
or her investment decision making process.9

The Handbook  requires that limitations to the analysis and any risks inherent to the 
investment be disclosed. Furthermore, the Handbook  requires that any report include 
elements important to the analysis and conclusions so that readers can evaluate the 
conclusions themselves.
4.6 Follow-  Up
The process does not end with the report. If an equity investment is made or a credit 
rating is assigned, periodic review is required to determine if the original conclusions 
and recommendations are still valid. In the case of a rejected investment, follow-  up 
may not be necessary but may be useful in determining whether the analysis process 
is adequate or should be refined (for example, if a rejected investment turns out to 
be successful in the market, perhaps the rejection was due to inadequate analysis). 
Follow-  up may involve repeating all the previous steps in the process on a periodic basis.
SUMMARY

SUMMARY
The information presented in financial and other reports, including the financial state -
ments, notes, and management’s commentary, help the financial analyst to assess a 
company’s performance and financial position. An analyst may be called on to perform 
a financial analysis for a variety of reasons, including the valuation of equity securities, 
the assessment of credit risk, the performance of due diligence in an acquisition, and 
the evaluation of a subsidiary’s performance relative to other business units. Major 
considerations in both equity analysis and credit analysis are evaluating a company’s 
financial position, its ability to generate profits and cash flow, and its ability to generate 
future growth in profits and cash flow.
9 Standards of Practice Handbook  (2014, p. 169).

Summary 35
This reading has presented an overview of financial statement analysis. Among 
the major points covered are the following:
■■The primary purpose of financial reports is to provide information and data 
about a company’s financial position and performance, including profitability 
and cash flows. The information presented in financial reports—including the 
financial statements and notes—and other reports—including management’s 
commentary or management’s discussion and analysis—allows the financial 
analyst to assess a company’s financial position and performance and trends in 
that performance.
■■The basic financial statements are the statement of financial position (i.e., the 
balance sheet), the statement of comprehensive income (i.e., a single statement 
of comprehensive income or two statements consisting of an income statement 
and a statement of comprehensive income), the statement of changes in equity, 
and the statement of cash flows.

■■The balance sheet discloses what resources a company controls (assets) and 
what it owes (liabilities) at a specific point in time. Owners’ equity represents 
the net assets of the company; it is the owners’ residual interest in or residual 
claim on the company’s assets after deducting its liabilities. The relationship 
among the three parts of the balance sheet (assets, liabilities, and owners’ 
equity) may be shown in equation form as follows: Assets = Liabilities + 
Owners’ equity.
■■The income statement presents information on the financial results of a com -
pany’s business activities over a period of time. The income statement commu -
nicates how much revenue and other income the company generated during 
a period and what expenses, including losses, it incurred in connection with 
generating that revenue and other income. The basic equation underlying the 
income statement is Revenue + Other income – Expenses = Net income.

■■The statement of comprehensive income includes all items that change own -
ers’ equity except transactions with owners. Some of these items are included 
as part of net income, and some are reported as other comprehensive income 
(OCI).
■■The statement of changes in equity provides information about increases or 
decreases in the various components of owners’ equity.
■■Although the income statement and balance sheet provide measures of a 
company’s success, cash and cash flow are also vital to a company’s long-  term 
success. Disclosing the sources and uses of cash helps creditors, investors, and 
other statement users evaluate the company’s liquidity, solvency, and financial 
flexibility.
■■The notes (also referred to as footnotes) that accompany the financial state -
ments are an integral part of those statements and provide information that 
is essential to understanding the statements. Analysts should evaluate note

disclosures regarding the use of alternative accounting methods, estimates, and 
assumptions.
■■In addition to the financial statements, a company provides other sources of 
information that are useful to the financial analyst. As part of his or her anal -
ysis, the financial analyst should read and assess this additional information, 
particularly that presented in the management commentary (also called man -
agement report[ing], operating and financial review, and management’s discus -
sion and analysis [MD&A]).

Reading 21 ■ Financial Statement Analysis: An Introduction 36
REFERENCES
Benninga, Simon Z., and Oded H. Sarig. 1997. Corporate Finance: 
A Valuation Approach . New York: McGraw-Hill Publishing.
International Auditing and Assurance Standards Board (IAASB).
Handbook of International Quality Control, Auditing, Review, 
Other Assurance, and Related Services Pronouncements , 
Standard 200, available at www.ifac.org/IAASB.van Greuning, Hennie, and Sonja Brajovic Bratanovic. 2003. 
Analyzing and Managing Banking Risk: A Framework 
for Assessing Corporate Governance and Financial Risk . 
Washington, DC: World Bank.■■A publicly traded company must have an independent audit performed on its 
annual financial statements. The auditor’s report expresses an opinion on the 
financial statements and provides some assurance about whether the financial 
statements fairly present a company’s financial position, performance, and cash 
flows. In addition, for US publicly traded companies, auditors must also express

an opinion on the company’s internal control systems.
■■Information on the economy, industry, and peer companies is useful in putting 
the company’s financial performance and position in perspective and in assess -
ing the company’s future. In most cases, information from sources apart from 
the company are crucial to an analyst’s effectiveness.
■■The financial statement analysis framework provides steps that can be followed 
in any financial statement analysis project. These steps are:
■●articulate the purpose and context of the analysis;
■●collect input data;
■●process data;
■●analyze/interpret the processed data;
■●develop and communicate conclusions and recommendations; and
■●follow up.

Practice Problems 37
PRACTICE PROBLEMS
1 Providing information about the performance and financial position of compa -
nies so that users can make economic decisions best describes the role of:
A auditing.
B financial reporting.
C financial statement analysis.
2 Which of the following best describes the role of financial statement analysis?
A To provide information about a company’s performance
B To provide information about a company’s changes in financial position
C To form expectations about a company’s future performance and financial 
position
3 The role of financial statement analysis is  best  described as:
A providing information useful for making investment decisions. 
B evaluating a company for the purpose of making economic decisions. 
C using financial reports prepared by analysts to make economic decisions. 
4 A company’s current financial position would best be evaluated using the:
A balance sheet.
B income statement.
C statement of cash flows.

5 A company’s profitability for a period would best be evaluated using the:
6 The financial statement that presents a shareholder’s residual claim on assets is 
the: 
C cash flow statement.
7 A company’s profitability over a period of time is best evaluated using the:
8 The income statement is best used to evaluate a company’s:
A current financial position.
B sources of cash flow.
C financial results from business activities.
9 Accounting policies, methods, and estimates used in preparing financial state -
ments are most likely  found in the:
A auditor’s report.
B management commentary.
C notes to the financial statements.
© 2017 CFA Institute. All rights reserved.

Reading 21 ■ Financial Statement Analysis: An Introduction 38
10 Information about management and director compensation would least likely  
be found in the:
B proxy statement.
11 Information about a company’s objectives, strategies, and significant risks 
would most likely  be found in the:
12 Which of the following best describes why the notes that accompany the finan -
cial statements are required? The notes:
A permit flexibility in statement preparation.
B standardize financial reporting across companies.
C provide information necessary to understand the financial statements.
13 What type of audit opinion is preferred when analyzing financial statements?
A Qualified.
B Adverse.
C Unqualified.
14 An auditor determines that a company’s financial statements are prepared in 
accordance with applicable accounting standards except with respect to inven -

tory reporting. This exception most likely  results in an audit opinion that is:
A adverse.
B qualified.
C unqualified. 
15 An independent audit report is most likely  to provide:
A absolute assurance about the accuracy of the financial statements. 
B reasonable assurance that the financial statements are fairly presented. 
C a qualified opinion with respect to the transparency of the financial 
statements. 
16 Interim financial reports released by a company are most likely  to be:
A monthly.
B unaudited.
C unqualified.
17 Which of the following sources of information used by analysts is found outside 
a company’s annual report?
A Auditor’s report
B Peer company analysis
C Management’s discussion and analysis
18 Ratios are an input into which step in the financial statement analysis 
framework?
A Process data.
B Collect input data.
C Analyze/interpret the processed data.

Practice Problems 39
19 Which phase in the financial statement analysis framework most likely involves 
producing updated reports and recommendations?
A Follow-  up
B Analyze/interpret the processed data
C Develop and communicate conclusions and recommendations

Reading 21 ■ Financial Statement Analysis: An Introduction 40
SOLUTIONS
1 B is correct. This is the role of financial reporting. The role of financial state -
ment analysis is to evaluate the financial reports.
2 C is correct. In general, analysts seek to examine the past and current perfor -
mance and financial position of a company in order to form expectations about 
its future performance and financial position. 
3 B is correct. The primary role of financial statement analysis is to use financial 
reports prepared by companies to evaluate the past, current, and potential 
performance and financial position of a company for the purpose of making 
investment, credit, and other economic decisions. 
4 A is correct. The balance sheet portrays the current financial position. The 
income statement and statement of cash flows present different aspects of 
performance.
5 B is correct. Profitability is the performance aspect measured by the income

statement. The balance sheet portrays the current financial position. The state -
ment of cash flows presents a different aspect of performance.
6 A is correct. Owners’ equity is the owners’ residual interest in (i.e., residual 
claim on) the company’s assets after deducting its liabilities, which is informa -
tion presented on the balance sheet. 
7 B is correct. A company’s profitability is best evaluated using the income 
statement. The income statement presents information on the financial results 
of a company’s business activities over a period of time by communicating 
how much revenue was generated and the expenses incurred to generate that 
revenue.
8 C is correct. A company’s revenues and expenses are presented on the income 
statement, which is used to evaluate a company’s financial results (or profitabil -
ity) from business activities over a period of time. A company’s current financial 
position is best evaluated by using the balance sheet. A company’s sources of

cash flow are best evaluated using the cash flow statement.
9 C is correct. The notes disclose choices in accounting policies, methods, and 
estimates.
10 A is correct. Information about management and director compensation is 
not found in the auditor’s report. Disclosure of management compensation is 
required in the proxy statement, and some aspects of management compensa -
tion are disclosed in the notes to the financial statements.
11 B is correct. These are components of management commentary.
12 C is correct. The notes provide information that is essential to understanding 
the information provided in the primary statements. 
13 C is correct. An unqualified opinion is a “clean” opinion and indicates that the 
financial statements present the company’s performance and financial position 
fairly in accordance with a specified set of accounting standards.
14 B is correct. A qualified audit opinion is one in which there is some scope

limitation or exception to accounting standards. Exceptions are described in 
the audit report with additional explanatory paragraphs so that the analyst can 
determine the importance of the exception.

Solutions 41
15 B is correct. The independent audit report provides reasonable assurance that 
the financial statements are fairly presented, meaning that there is a high proba -
bility that the audited financial statements are free from material error, fraud, or 
illegal acts that have a direct effect on the financial statements.
16 B is correct. Interim reports are typically provided semiannually or quarterly 
and present the four basic financial statements and condensed notes. They are 
not audited. Unqualified is a type of audit opinion 
17 B is correct. When performing financial statement analysis, analysts should 
review all company sources of information as well as information from external 
sources regarding the economy, the industry, the company, and peer (compara -
ble) companies.
18 C is correct. Ratios are an output of the process data step but are an input into 
the analyze/interpret data step.
19 A is correct. The follow-  up phase involves gathering information and repeating

the analysis to determine whether it is necessary to update reports and recom -
mendations and then updating if necessary.

Financial Reporting Standards
by Elaine Henry, PhD, CFA, Jan Hendrik van Greuning, DCom, CFA, and 
Thomas R. Robinson, PhD, CFA
Elaine Henry, PhD, CFA, is at Stevens Institute of Technology (USA). Jan Hendrik van 
Greuning, DCom, CFA, is at BIBD (Brunei). Thomas R. Robinson, PhD, CFA, is at AACSB 
International (USA).
a. describe the objective of financial statements and the importance 
of financial reporting standards in security analysis and valuation;
b. describe roles and desirable attributes of financial reporting 
standard-  setting bodies and regulatory authorities in establishing 
and enforcing reporting standards, and describe the role of the 
International Organization of Securities Commissions;
c. describe the status of global convergence of accounting standards 
and ongoing barriers to developing one universally accepted set of 
financial reporting standards;
d. describe the International Accounting Standards Board’s

conceptual framework, including the objective and qualitative 
characteristics of financial statements, required reporting 
elements, and constraints and assumptions in preparing financial 
statements;
e. describe general requirements for financial statements under 
International Financial Reporting Standards (IFRS);
f. compare key concepts of financial reporting standards under 
IFRS and US generally accepted accounting principles (US GAAP) 
reporting systems;
g. identify characteristics of a coherent financial reporting 
framework and the barriers to creating such a framework;
h. describe implications for financial analysis of differing 
financial reporting systems and the importance of monitoring 
developments in financial reporting standards;
i. analyze company disclosures of significant accounting policies.REA dINg
22
after the publication of the

readings.

Reading 22 ■ Financial Reporting Standards 44
Financial reporting standards provide principles for preparing financial reports and 
determine the types and amounts of information that must be provided to users of 
financial statements, including investors and creditors, so that they may make informed 
decisions. This reading focuses on the framework within which these standards 
are created. An understanding of the underlying framework of financial reporting 
standards, which is broader than knowledge of specific accounting rules, will allow 
an analyst to assess the valuation implications of financial statement elements and 
transactions—including transactions, such as those that represent new developments, 
which are not specifically addressed by the standards.
Section 2 of this reading discusses the objective of financial statements and the 
importance of financial reporting standards in security analysis and valuation. Section

3 describes the roles of financial reporting standard-  setting bodies and regulatory 
authorities and several of the financial reporting standard-  setting bodies and regula -
tory authorities. Section 4 describes the trend toward and barriers to convergence of 
global financial reporting standards. Section 5 describes the International Financial 
Reporting Standards (IFRS) framework1 and general requirements for financial 
statements. Section 6 discusses the characteristics of an effective financial reporting 
framework along with some of the barriers to a single coherent framework. Section 
7 illustrates some of the specific differences between IFRS and US generally accepted 
accounting practices (US GAAP), and Section 8 discusses the importance of monitor -
ing developments in financial reporting standards. A summary of the key points and 
practice problems in the CFA Institute multiple choice format conclude the reading.
THE OBJECTIVE OF FINANCIAL REPORTING

The financial reports of a company include financial statements and other supplemental 
disclosures necessary to assess a company’s financial position and periodic financial 
performance. Financial reporting is based on a simple premise. The International 
Accounting Standards Board (IASB), which sets financial reporting standards that have 
been adopted in many countries, expressed it as follows in its Conceptual Framework 
for Financial Reporting 2010  (Conceptual Framework 2010 ):2
The objective of general purpose financial reporting is to provide finan -
cial information about the reporting entity that is useful to existing and 
potential investors, lenders, and other creditors in making decisions about 
providing resources to the entity. Those decisions involve buying, selling 
or holding equity and debt instruments, and providing or settling loans 
and other forms of credit.31
2

2
1 The body of standards issued by the International Accounting Standards Board (IASB) is referred to as 
International Financial Reporting Standards.
2 In September 2010, the IASB adopted the Conceptual Framework for Financial Reporting  in place of the 
Framework for the Preparation and Presentation of Financial Statements  (1989 ). The Conceptual Framework  
represents the partial completion of a joint convergence project between the IASB and FASB on an updated 
framework. The Conceptual Framework  (2010 ) contains two updated chapters: The objective of financial 
reporting  and Qualitative characteristics of useful financial information.  The remainder of the material in 
the Conceptual Framework  is from the Framework  (1989 ) and will be updated as the project is completed. 
Also in September  2010, the FASB issued Concepts Statement 8, Conceptual Framework for Financial 
Reporting , to replace Concepts Statements 1 and 2.

3 Conceptual Framework (2010)  Chapter 1, OB2. Under US GAAP , the identical statement appears in 
Concept Statement 8, Chapter 1, OB2.

The Objective of Financial Reporting 45
The objective in the Conceptual Framework  (2010 ) differs from the objective of the 
Framework for the Preparation and Presentation of Financial Statements  (1989 )4 in 
a number of key ways. The scope of the objective now extends to financial reporting, 
which is broader than the previously stated scope that covered financial statements 
only. Another difference is that the objective now specifies the primary users for whom 
the reports are intended (existing and potential investors, etc.) while the previously 
stated objective referred solely to a ‘wide range of users. ’ Also, while the Conceptual 
Framework  (2010 ) identifies information that should be reported—including that 
about financial position (economic resources and claims), changes in economic 
resources and claims, and financial performance reflected by accrual accounting and 
past cash flows—it does not list that information within the objective itself, unlike

the previously stated objective.
Standards are developed in accordance with a framework so it is useful to have an 
agreed upon framework to guide the development of standards. The joint conceptual 
framework project of the IASB and the US Financial Accounting Standards Board 
(FASB) aimed to develop a common foundation for standards. Standards based on 
this foundation were to be principles-  based, internally consistent, and converged. 
Until recently, financial reporting standards were primarily developed independently 
by each country’s standard-  setting body. This independent standard setting created a 
wide range of standards, some of which were quite comprehensive and complex (often 
considered to be rules-  based standards), and others more general (often considered 
to be principles-  based standards). Accounting scandals and the economic crisis of 
2008–2009 increased awareness of the need for high quality, more uniform global

financial reporting standards and provided the impetus for stronger coordination 
among the major standard-  setting bodies. Such coordination is also a natural out -
growth of the increased globalization of capital markets.
Developing financial reporting standards is complicated because the underlying 
economic reality is complicated. The financial transactions and financial position that 
companies aim to represent in their financial reports are also complex. Furthermore, 
uncertainty about various aspects of transactions often results in the need for accru -
als and estimates, both of which necessitate judgment. Judgment varies from one 
preparer to the next. Accordingly, standards are needed to achieve some amount of 
consistency in these judgments. Even with such standards, there usually will be no 
single correct answer to the question of how to reflect economic reality in financial 
reports. Nevertheless, financial reporting standards try to limit the range of acceptable

answers in order to increase consistency in financial reports.
EXAMPLE 1   
Estimates in Financial Reporting
To facilitate comparisons across companies (cross sectional analysis) and over 
time for a single company (time series analysis), it is important that accounting 
methods are comparable and consistently applied. However, accounting standards 
must be flexible enough to recognize that differences exist in the underlying 
economics between businesses.
Suppose two companies buy the same model of machinery to be used in their 
respective businesses. The machine is expected to last for several years. Financial 
reporting standards typically require that both companies account for this 
4 The Framework (1989)  stated that, “The objective of financial statements is to provide information about 
the financial position, performance, and changes in financial position of an entity; this information should 
be useful to a wide range of users for the purpose of making economic decisions. ”

Reading 22 ■ Financial Reporting Standards 46
equipment by initially recording the cost of the machinery as an asset. Without 
such a standard, the companies could report the purchase of the equipment 
differently. For example, one company might record the purchase as an asset 
and the other might record the purchase as an expense. An accounting standard 
ensures that both companies should record the transaction in a similar manner.
Accounting standards typically require the cost of the machine to be appor -
tioned over the estimated useful life of an asset as an expense called depreciation. 
Because the two companies may be operating the machinery differently, financial 
reporting standards must retain some flexibility. One company might operate 
the machinery only a few days per week, whereas the other company operates 
the equipment continuously throughout the week. Given the difference in usage, 
it would not be appropriate to require the two companies to report an identical

amount of depreciation expense each period. Financial reporting standards 
must allow for some discretion such that management can match their financial 
reporting choices to the underlying economics of their business while ensuring 
that similar transactions are recorded in a similar manner between companies.
Financial statements of two companies with identical transactions in the fiscal 
year, prepared in accordance with the same set of financial reporting standards, 
are most likely  to be:
A identical.
B consistent.
C comparable.
Solution:
C is correct. The companies’ financial statements should be comparable (pos -
sible to compare) because they should reflect the underlying economics of the 
transactions for each company. The underlying economics may vary between 
companies, so the financial statements are not likely to be identical. Choices 
made by each company with respect to accounting methods should be consis -

tent but the choice across companies is not necessarily consistent. Information 
about accounting choices will enhance a user’s ability to compare the companies’ 
financial statements.
The IASB and the FASB have developed similar financial reporting frameworks 
which specify the overall objective and qualities of information to be provided. Financial 
reports are intended to provide information to many users, including investors, credi -
tors, employees, customers, and others. As a result of this multipurpose nature, financial 
reports are not designed solely with asset valuation in mind. However, financial reports 
provide important inputs into the process of valuing a company or the securities a 
company issues. Understanding the financial reporting framework—including how and 
when judgments and estimates can affect the numbers reported—enables an analyst 
to evaluate the information reported and to use the information appropriately when

assessing a company’s financial performance. Clearly, such an understanding is also 
important in assessing the financial impact of business decisions by, and in making 
comparisons across, entities.

Standard-  Setting Bodies and Regulatory Authorities 47
STANDARD-  SETTING BODIES AND REGULATORY 
AUTHORITIES
A distinction must be made between standard-  setting bodies and regulatory authori -
ties. Standard-  setting bodies, such as the IASB and FASB, are typically private sector, 
self-  regulated organizations with board members who are experienced accountants, 
auditors, users of financial statements, and academics. The requirement to prepare 
financial reports in accordance with specified accounting standards is the responsibility 
of regulatory authorities. Regulatory authorities, such as the Accounting and Corporate 
Regulatory Authority in Singapore, the Securities and Exchange Commission (SEC) 
in the United States, and the Securities and Exchange Commission in Brazil have the 
legal authority to enforce financial reporting requirements and exert other controls 
over entities that participate in the capital markets within their jurisdiction.

In other words, generally , standard-  setting bodies set the standards and regulatory 
authorities recognise and enforce the standards. Without the recognition of the stan -
dards by the regulatory authorities, the private sector standard-  setting bodies would 
have no authority. Note, however, that regulators often retain the legal authority to 
establish financial reporting standards in their jurisdiction and can overrule the private 
sector standard-  setting bodies.
EXAMPLE 2   
Industry-  Specific Regulation
In certain cases, multiple regulatory bodies affect a company’s financial report -
ing requirements. For example, in almost all jurisdictions around the world, 
banking-  specific regulatory bodies establish requirements related to risk-  based 
capital measurement, minimum capital adequacy, provisions for doubtful loans, 
and minimum monetary reserves. An awareness of such regulations provides 
an analyst with the context to understand a bank’s business, including the

objectives and scope of allowed activities. Insurance is another industry where 
specific regulations typically are in place. An analyst should be aware of such 
regulations to understand constraints on an insurance company.
The following are examples of country-  specific bank regulators. In Canada, 
the Office of the Superintendent of Financial Institutions regulates and super -
vises all banks in Canada as well as some other federally incorporated or regis -
tered financial institutions or intermediaries. In Germany, the German Federal 
Financial Supervisory Authority exercises supervision over financial institutions 
in accordance with the Banking Act. In Japan, the Financial Services Agency 
has regulatory authority over financial institutions. In the United States, the 
Office of the Comptroller of the Currency charters and regulates all national 
banks. In some countries, a single entity serves both as the central bank and as 
the regulatory body for the country’s financial institutions.

In addition, the Basel Accords establish and promote internationally consis -
tent capital requirements and risk management practices for larger international 
banks. The Basel Committee on Banking Supervision, among other functions, 
has evolved into a standard setter for bank supervision. The various regulations 
that affect banks present a challenge for bank analysts.
Which of the following statements is most  accurate?
A As a general rule, it is sufficient for an analyst covering an industry to 
be familiar with financial reporting standards and regulations in his/her 
country of residence.3

Reading 22 ■ Financial Reporting Standards 48
B An analyst should familiarize him/herself with the regulations and 
reporting standards that affect the company and/or industry that he/she is 
analyzing.
C An analyst should be aware that financial reporting standards vary among 
countries and may be industry specific, but standards are so similar that 
the analyst does not have to be concerned about it.
Solution: 
B is correct. An analyst should familiarize him/herself with the regulations and 
reporting standards that affect the company and/or industry being analyzed. 
This can be quite challenging but, given the potential effects, necessary.
This section provides a brief overview of the International Accounting Standards 
Board and the US Financial Accounting Standards Board. The overview is followed 
by descriptions of the International Organization of Securities Commissions, the US 
Securities and Exchange Commission, and capital markets regulation in the European

Union. The topics covered in these overviews were chosen to serve as examples of 
standard-  setting boards, securities commissions, and capital market regulation. After 
reading these descriptions, the reader should be able to describe the functioning and 
roles of standard-  setting bodies and regulatory authorities in more detail than is given 
in the introduction to this section.
3.1 Accounting Standards Boards
Accounting standards boards exist in virtually every national market. These boards 
are typically independent, private, not-  for- profit organizations. Most users of financial 
statements know of the International Accounting Standards Board that issues interna -
tional financial reporting standards and the US Financial Accounting Standards Board 
that is the source of US generally accepted accounting principles. Most countries have 
an accounting standard-  setting body. There are certain attributes that are typically

common to these standard setters. After discussing the IASB and the FASB, some of 
the common and desirable attributes of accounting standards boards will be identified.
3.1.1  International Accounting Standards Board
The IASB is the independent standard-  setting body of the IFRS Foundation,5 an inde -
pendent, not-  for- profit private sector organization. The Trustees of the IFRS Foundation 
reflect a diversity of geographical and professional backgrounds. The Trustees appoint 
the members of the IASB and related entities, ensure the financing of the Foundation, 
establish the budget, and monitor the IASB’s strategy and effectiveness. The Trustees 
of the Foundation are accountable to a monitoring board composed of public author -
ities that include representatives from the European Commission, IOSCO, the Japan 
Financial Services Agency, and the US SEC. The chairman of the Basel Committee on 
Banking Supervision serves as an observer on the Monitoring Board.

The Trustees of the IFRS Foundation make a commitment to act in the public 
interest. The principle objectives of the IFRS Foundation are to develop and promote 
the use and adoption of a single set of high quality financial standards; to ensure the 
standards result in transparent, comparable, and decision-  useful information while 
taking into account the needs of a range of sizes and types of entities in diverse eco -
nomic settings; and to promote the convergence of national accounting standards 
5 The IFRS Foundation was previously named the International Accounting Standards Committee 
Foundation (IASC Foundation).

Standard-  Setting Bodies and Regulatory Authorities 49
and IFRS. The Trustees are responsible for ensuring that the IASB is and is perceived 
as independent. Each member of the IASB is expected to exercise independence of 
judgment in setting standards.
The members of the IASB are appointed by the Trustees on the basis of professional 
competence and practical experience. As is true for the Trustees, the members reflect 
a diversity of geographical and professional backgrounds. The members deliberate, 
develop, and issue international financial reporting standards.6 Two related entities, 
with members appointed by the Trustees, are the IFRS Interpretations Committee 
and the IFRS Advisory Council.7 The Interpretations Committee’s members are 
responsible for reviewing accounting issues that arise in the application of IFRS and 
are not specifically addressed by IFRS, and for issuing appropriate, authoritative, 
IASB-  approved interpretations. Note that the authoritative interpretations must be

approved by the IASB. The IFRS Advisory Council’s members represent a wide range 
of organizations and individuals that are affected by and interested in international 
financial reporting. The Council provides advice to the IASB on, among other items, 
agenda decisions and priorities.
The IASB has a basic process that it goes through when deliberating, developing, 
and issuing international financial reporting standards. A simplified version of the 
typical process is as follows. An issue is identified as a priority for consideration and 
placed on the IASB’s agenda in consultation with the Advisory Council. After con -
sidering an issue, which may include soliciting advice from others including national 
standard-  setters, the IASB may publish an exposure draft for public comment. In 
addition to soliciting public comment, the IASB may hold public hearings to discuss 
proposed standards. After reviewing the input of others, the IASB may issue a new or

revised financial reporting standard. These standards are authoritative to the extent 
that they are recognised and adopted by regulatory authorities.
3.1.2  Financial Accounting Standards Board
The FASB and its predecessor organizations have been issuing financial reporting 
standards in the United States since the 1930s. The FASB operates within a structure 
similar to that of the IASB. The Financial Accounting Foundation oversees, admin -
isters, and finances the organization. The Foundation ensures the independence of 
the standard-  setting process and appoints members to the FASB and related entities 
including the Financial Accounting Standards Advisory Council.
The FASB issues new and revised standards to improve standards of financial 
reporting so that decision-  useful information is provided to users of financial reports. 
This is done through a thorough and independent process that seeks input from

stakeholders and is overseen by the Financial Accounting Foundation. The steps in the 
process are similar to those described for the IASB. The outputs of the standard-  setting 
process are contained in the FASB Accounting Standards Codification™ (Codification).8 
Effective for periods ending after 15 September 2009, the Codification is the source 
of authoritative US generally accepted accounting principles to be applied to non-  
governmental entities. The Codification is organized by topic. Among the specific 
6 Although the name of the IASB incorporates “ Accounting Standards” and early standards were titled 
International Accounting Standards (IAS), the term “International Financial Reporting Standards” (IFRS) 
is being used for new standards. The use of the words “financial reporting” recognizes the importance of 
disclosures outside of the core financial statements, such as management discussion of the business, risks, 
and future plans.

7 The IFRS Interpretations Committee and the IFRS Advisory Council were previously named the 
International Financial Reporting Interpretations Committee and the Standards Advisory Council.
8 The Codification combines literature issued by various standard setters, including the FASB, the Emerging 
Issues Task Force (EITF), the Derivative Implementation Group (DIG), and the American Institute of 
Certified Public Accountants (AICPA).

Reading 22 ■ Financial Reporting Standards 50
motivations for the Codification, the FASB mentions that it will facilitate researching 
accounting issues, improve the usability of the literature, provide accurate updated 
information on an ongoing basis, and help with convergence efforts.
US GAAP , as established by the FASB, is officially recognized as authoritative by the 
SEC (Financial Reporting Release No. 1, Section 101, and reaffirmed in the April 2003 
Policy Statement). However, the SEC retains the authority to establish standards. 
Although it has rarely overruled the FASB, the SEC does issue authoritative financial 
reporting guidance including Staff Accounting Bulletins. These bulletins reflect the 
SEC’s views regarding accounting-  related disclosure practices and can be found on the 
SEC website. Certain portions—but not all portions—of the SEC regulations, releases, 
interpretations, and guidance are included for reference in the FASB Codification.

3.1.3  Desirable Attributes of Accounting Standards Boards
The responsibilities of all parties involved in the standards-  setting process—including 
trustees of a foundation or others that oversee, administer, and finance the organi -
zation and members of the standard setting board—should be clearly defined. All 
parties involved in the standards-  setting process should observe high professional 
standards, including standards of ethics and confidentiality. The organization should 
have adequate authority, resources, and competencies to fulfill its responsibilities. 
The processes that guide the organization and the formation of standards should be 
clear and consistent. The accounting standards board should be guided by a well-  
articulated framework with a clearly stated objective. The accounting standards board 
should operate independently, seeking and considering input from stakeholders but 
making decisions that are consistent with the stated objective of the framework. The

decision-  setting process should not be compromised by pressure from external forces 
and should not be influenced by self- or special interests. The decisions and resulting 
standards should be in the public interest, and culminate in a set of high quality stan -
dards that will be recognised and adopted by regulatory authorities.
3.2 Regulatory Authorities
The requirement to prepare financial reports in accordance with specified accounting 
standards is the responsibility of regulatory authorities. Regulatory authorities are gov -
ernmental entities that have the legal authority to enforce financial reporting require -
ments and exert other controls over entities that participate in the capital markets 
within their jurisdiction. Regulatory authorities may require that financial reports be 
prepared in accordance with one specific set of accounting standards or may specify 
acceptable accounting standards. For example in Switzerland, Swiss-  based companies

listed on the main board of the Swiss Exchange have to prepare their financial state -
ments in accordance with either IFRS or US GAAP if they are multinational.9 Other 
registrants in Switzerland could use IFRS, US GAAP , or Swiss GAAP .
The International Organization of Securities Commissions (IOSCO) is not a regu -
latory authority but its members regulate a significant portion of the world’s financial 
capital markets. This organization has established objectives and principles to guide 
securities and capital market regulation. The US SEC is discussed as an example of a 
regulatory authority. Aspects of capital market regulation in Europe are discussed to 
illustrate a co-  operative approach to regulation.
9 https://www.iasplus.com/en/jurisdictions/europe/switzerland.

Standard-  Setting Bodies and Regulatory Authorities 51
3.2.1  International Organization of Securities Commissions
IOSCO was formed in 1983 as the successor organization to an inter-  American regional 
association (created in 1974). As of 23 September 2010, IOSCO had 114 ordinary 
members, 11 associate members, and 74 affiliate members. Ordinary members are 
the securities commission or similar governmental regulatory authority with primary 
responsibility for securities regulation in the country.10 The members regulate more 
than 90 percent of the world’s financial capital markets.
The IOSCO’s comprehensive set of Objectives and Principles of Securities Regulation  
is updated as required and is recognized as an international benchmark for all mar -
kets. The principles of securities regulation are based upon three core objectives:11
■■protecting investors;
■■ensuring that markets are fair, efficient, and transparent; and
■■reducing systemic risk.

IOSCO’s principles are grouped into nine categories, including principles for 
regulators, for enforcement, for auditing, and for issuers, among others. Within the 
category “Principles for Issuers, ” two principles relate directly to financial reporting:
■■There should be full, accurate, and timely disclosure of financial results, risk, 
and other information which is material to investors’ decisions.
■■Accounting standards used by issuers to prepare financial statements should be 
of a high and internationally acceptable quality.
Historically, regulation and related financial reporting standards were developed 
within individual countries and were often based on the cultural, economic, and 
political norms of each country. As financial markets have become more global, it has 
become desirable to establish comparable financial reporting standards internationally. 
Ultimately, laws and regulations are established by individual jurisdictions, so this

also requires cooperation among regulators. Another IOSCO principle deals with 
the use of self-  regulatory organizations (accounting standards bodies are examples 
of self-  regulating organizations in this context). Principle 9 states:
Where the regulatory system makes use of Self-  Regulatory Organizations 
(SROs) that exercise some direct oversight responsibility for their respec -
tive areas of competence, such SROs should be subject to the oversight of 
the Regulator and should observe standards of fairness and confidentiality 
when exercising powers and delegated responsibilities.12
To ensure consistent application of international financial standards (such as the 
Basel Committee on Banking Supervision’s standards and IFRS), it is important to 
have uniform regulation and enforcement across national boundaries. IOSCO assists 
in attaining this goal of uniform regulation as well as cross-  border co-  operation in 
combating violations of securities and derivatives laws.

3.2.2  The Securities and Exchange Commission (US)
The US SEC has primary responsibility for securities and capital markets regulation 
in the United States and is an ordinary member of IOSCO. Any company issuing 
securities within the United States, or otherwise involved in US capital markets, is 
10 The names of the primary securities regulator vary from country to country. For example: China Securities 
Regulatory Commission, Egyptian Financial Supervisory Authority, Securities and Exchange Board of India, 
Kingdom of Saudi Arabia Capital Market Authority, and Banco Central del Uruguay.
11 Objectives and Principles of Securities Regulation , IOSCO, June 2010.
12 Objectives and Principles of Securities Regulation , IOSCO, June 2010.

Reading 22 ■ Financial Reporting Standards 52
subject to the rules and regulations of the SEC. The SEC, one of the oldest and most 
developed regulatory authorities, originated as a result of reform efforts made after the 
great stock market crash of 1929, sometimes referred to as simply the “Great Crash. ”
A number of laws affect reporting companies, broker/dealers, and other market 
participants. From a financial reporting and analysis perspective, the most significant 
pieces of legislation are the Securities Acts of 1933 and 1934 and the Sarbanes–Oxley 
Act of 2002.
■■Securities Act of 1933  (The 1933 Act): This act specifies the financial and 
other significant information that investors must receive when securities are 
sold, prohibits misrepresentations, and requires initial registration of all public 
issuances of securities.
■■Securities Exchange Act of 1934  (The 1934 Act): This act created the SEC, 
gave the SEC authority over all aspects of the securities industry, and empow -

ered the SEC to require periodic reporting by companies with publicly traded 
securities.
■■Sarbanes–Oxley Act of 2002 : The Sarbanes–Oxley Act of 2002 created the 
Public Company Accounting Oversight Board (PCAOB) to oversee auditors. 
The SEC is responsible for carrying out the requirements of the act and over -
seeing the PCAOB. The act addresses auditor independence; for example, it 
prohibits auditors from providing certain non-  audit services to the companies 
they audit. The act strengthens corporate responsibility for financial reports; for 
example, it requires the chief executive officer and the chief financial officer to 
certify that the company’s financial reports fairly present the company’s con -
dition. Furthermore, Section 404 of the Sarbanes–Oxley Act requires man -
agement to report on the effectiveness of the company’s internal control over 
financial reporting and to obtain a report from its external auditor attesting

to management’s assertion about the effectiveness of the company’s internal 
control.
Companies comply with these acts principally through the completion and sub -
mission (i.e., filing) of standardized forms issued by the SEC. There are more than 
50 different types of SEC forms that are used to satisfy reporting requirements; the 
discussion herein will be limited to those forms most relevant for financial analysts.
In 1993, the SEC began to mandate electronic filings of the required forms through 
its Electronic Data Gathering, Analysis, and Retrieval (EDGAR) system. As of 2005, 
most SEC filings are required to be made electronically. EDGAR has made corporate 
and financial information more readily available to investors and the financial com -
munity. Most of the SEC filings that an analyst would be interested in can be retrieved 
from the internet from one of many websites, including the SEC’s own website. Some

filings are required on the initial offering of securities, whereas others are required on 
a periodic basis thereafter. The following are some of the more common information 
sources used by analysts.
■■Securities Offerings Registration Statement : The 1933 Act requires compa -
nies offering securities to file a registration statement. New issuers as well as 
previously registered companies that are issuing new securities are required to 
file these statements. Required information and the precise form vary depend -
ing upon the size and nature of the offering. Typically, required information 
includes: 1) disclosures about the securities being offered for sale, 2) the rela -
tionship of these new securities to the issuer’s other capital securities, 3) the 
information typically provided in the annual filings, 4) recent audited financial 
statements, and 5) risk factors involved in the business.

Standard-  Setting Bodies and Regulatory Authorities 53
■■Forms 10-  K, 20-  F, and 40-  F: These are forms that companies are required 
to file annually . Form 10-  K is for US registrants, Form 40-  F is for certain 
Canadian registrants, and Form 20-  F is for all other non-  US registrants. These 
forms require a comprehensive overview, including information concerning a 
company’s business, financial disclosures, legal proceedings, and information 
related to management. The financial disclosures include a historical sum -
mary of financial data (usually 10 years), management’s discussion and analysis 
(MD&A) of the company’s financial condition and results of operations, and 
audited financial statements.13
■■Annual Report : In addition to the SEC’s annual filings (e.g., Form 10-  K), most 
companies prepare an annual report to shareholders. This is not a requirement 
of the SEC. The annual report is usually viewed as one of the most significant

opportunities for a company to present itself to shareholders and other exter -
nal parties; accordingly, it is often a highly polished marketing document with 
photographs, an opening letter from the chief executive officer, financial data, 
market segment information, research and development activities, and future 
corporate goals. In contrast, the Form 10-  K is a more legal type of document 
with minimal marketing emphasis. Although the perspectives vary, there is con -
siderable overlap between a company’s annual report and its Form 10-  K. Some 
companies elect to prepare just the Form 10-  K or a document that integrates 
both the 10-  K and annual report.
■■Proxy Statement/Form DEF-  14A : The SEC requires that shareholders of a 
company receive a proxy statement prior to a shareholder meeting. A proxy is 
an authorization from the shareholder giving another party the right to cast its 
vote. Shareholder meetings are held at least once a year, but any special meet -

ings also require a proxy statement. Proxies, especially annual meeting proxies, 
contain information that is often useful to financial analysts. Such information 
typically includes proposals that require a shareholder vote, details of security 
ownership by management and principal owners, biographical information on 
directors, and disclosure of executive compensation. Proxy statement informa -
tion is filed with the SEC as Form DEF-  14A.
■■Forms 10-  Q and 6-  K: These are forms that companies are required to submit 
for interim periods (quarterly for US companies on Form 10-  Q, semiannu -
ally for many non-  US companies on Form 6-  K). The filing requires certain 
financial information, including unaudited financial statements and a MD&A 
for the interim period covered by the report. Additionally, if certain types of 
non-  recurring events—such as the adoption of a significant accounting policy, 
commencement of significant litigation, or a material limitation on the rights of

any holders of any class of registered securities—take place during the period 
covered by the report, these events must be included in the Form 10-  Q report. 
Companies may provide the 10-  Q report to shareholders or may prepare a sepa -
rate, abbreviated, quarterly report to shareholders.
13 Effective as of 2008, the SEC permits foreign private issuers to file financial statements prepared in 
accordance with IFRS (as issued by the IASB) with no reconciliation to US GAAP . Foreign private issuers 
using accounting standards other than US GAAP or IFRS must still provide a reconciliation to US GAAP .

Reading 22 ■ Financial Reporting Standards 54
EXAMPLE 3   
Initial Registration Statement
In 2004, Google filed a Form S-  1 registration statement with the US SEC to 
register its initial public offering of securities (Class A Common Stock). In 
addition to a large amount of financial and business information, the registration 
statement provided a 20-  page discussion of risks related to Google’s business 
and industry. This type of qualitative information is helpful, if not essential, in 
making an assessment of a company’s credit or investment risk.
Which of the following is least likely  to have been included in Google’s 
registration statement?
A Audited financial statements.
B Assessment of risk factors involved in the business.
C Projected cash flows and earnings for the business.
Solution: 
C is correct. Companies provide information useful in developing these projec -
tions but do not typically include these in the registration statement. Information

provided includes audited financial statements, an assessment of risk factors 
involved in the business, names of the underwriters, estimated proceeds from 
the offering, and use of proceeds.
A company or its officers make other SEC filings—either periodically, or, if sig -
nificant events or transactions have occurred, in between the periodic reports noted 
above. By their nature, these forms sometimes contain the most interesting and timely 
information and may have significant valuation implications.
■■Form 8-  K: In addition to filing annual and interim reports, SEC registrants 
must report material corporate events on a more current basis. Form 8-  K (6-  K 
for non-  US registrants) is the “current report” companies must file with the 
SEC to announce such major events as acquisitions or disposals of corporate 
assets, changes in securities and trading markets, matters related to accountants 
and financial statements, corporate governance and management changes, and

Regulation FD disclosures.14
■■Form 144 : This form must be filed with the SEC as notice of the proposed sale 
of restricted securities or securities held by an affiliate of the issuer in reliance 
on Rule 144. Rule 144 permits limited sales of restricted securities without 
registration.
■■Forms 3, 4, and 5 : These forms are required to report beneficial ownership of 
securities. These filings are required for any director or officer of a registered 
company as well as beneficial owners of greater than 10 percent of a class of 
registered equity securities. Form 3 is the initial statement, Form 4 reports 
14 Regulation FD provides that when an issuer discloses material non-  public information to certain 
individuals or entities—generally, securities market professionals such as stock analysts or holders of the 
issuer’s securities who may trade on the basis of the information—the issuer must make public disclosure

of that information. In this way, the rule aims to promote full and fair disclosure.

Standard-  Setting Bodies and Regulatory Authorities 55
changes, and Form 5 is the annual report. These forms, along with Form 144, 
can be used to examine purchases and sales of securities by officers, directors, 
and other affiliates of the company.
■■Form 11-  K: This is the annual report of employee stock purchase, savings, and 
similar plans. It might be of interest to analysts for companies with significant 
employee benefit plans because it contains more information than that dis -
closed in the company’s financial statements.
In jurisdictions other than the United States, similar legislation exists for the pur -
pose of regulating securities and capital markets. Regulatory authorities are responsible 
for enforcing regulation, and securities regulation is intended to be consistent with 
the IOSCO objectives described in the previous section. Within each jurisdiction, 
regulators will either establish or, more typically, recognize and adopt a specified

set or sets of accounting standards. The regulators will also establish reporting and 
filing requirements. IOSCO members have agreed to cooperate in the development, 
implementation, and enforcement of internationally recognised and consistent stan -
dards of regulation.
3.2.3  Capital Markets Regulation in Europe
Each individual member state of the European Union (EU) regulates capital markets 
in its jurisdiction. There are, however, certain regulations that have been adopted at 
the EU level. Importantly, in 2002 the EU agreed that from 1 January 2005, consoli -
dated accounts of EU listed companies would use International Financial Reporting 
Standards. The endorsement process by which newly issued IFRS are adopted by the 
EU reflects the balance between the individual member state’s autonomy and the 
need for cooperation and convergence. When the IASB issues a new standard, the 
European Financial Reporting Advisory Group advises the European Commission on

the standard, and the Standards Advice Review Group provides the Commission an 
opinion about that advice. Based on the input from these two entities, the Commission 
prepares a draft endorsement regulation. The Accounting Regulatory Committee votes 
on the proposal; and if the vote is favorable, the proposal proceeds to the European 
Parliament and the Council of the European Union for approval.15
Two committees related to securities regulation, established in 2001 by the European 
Commission, are the European Securities Committee (ESC) and the Committee of 
European Securities Regulators (CESR). The ESC consists of high-  level representatives 
of member states and advises the European Commission on securities policy issues. 
The CESR, an independent advisory body composed of representatives of regulatory 
authorities of the member states, assists the commission, particularly with technical 
issues. As noted earlier, regulation still rests with the individual member states and,

therefore, requirements for registering shares and filing periodic financial reports 
vary from country to country.
On 1 January 2011, CESR was replaced by the European Securities and Market 
Authority (ESMA) as part of a reform of the EU financial supervisory framework. The 
EU Parliament created ESMA as an EU cross-  border supervisor because the CESR’s 
powers were deemed insufficient to co-  ordinate supervision of the EU market. ESMA 
is one of three European supervisory authorities; the two others supervise the banking 
and insurance industries.
15 Source: European Commission. http://ec.europa.eu/internal_market/accounting/legal_framework/
ias_regulation_en.htm.

Reading 22 ■ Financial Reporting Standards 56
CONVERGENCE OF GLOBAL FINANCIAL REPORTING 
STANDARDS
Activities in the early part of the 21st century have moved the goal of one set of uni -
versally accepted financial reporting standards out of the theoretical sphere and closer 
to reality. IFRS have been or are in the process of being adopted in many countries. 
Other countries maintain their own set of standards but are working with the IASB 
to converge their standards and IFRS.
In some ways, the movement toward one global set of financial reporting stan -
dards has made the challenges related to full convergence or adoption of a single set 
of global standards more apparent. Standard-  setting bodies and regulators can have 
differing views or use a different framework for developing standards. This can be the 
result of differences in institutional, regulatory, business, and cultural environments. 
In addition, there may be resistance to change or advocacy for change from certain

constituents; accounting boards may be influenced by strong industry lobbying groups 
and others that will be subject to these reporting standards. For example, the FASB 
faced strong opposition when it first attempted to adopt standards requiring companies 
to expense employee stock compensation plans.16 The IASB has experienced similar 
political pressures. The issue of political pressure is compounded when international 
standards are involved, simply because there are many more interested parties and 
many more divergent views and objectives. In the financial crisis of 2008 and 2009, 
both the FASB and the IASB faced political pressure to amend the standards related 
to financial instrument accounting. Political pressure and its influence create tension 
as the independence of accounting standards boards are questioned and jeopardized.
The integrity of the financial reporting framework depends on the standard setter’s

ability to invite and balance various points of view and yet to remain independent of 
external pressures. For analysts, it is important to be aware of the pace of change in 
accounting standards and factors potentially influencing those changes.
An additional issue related to convergence involves the application and enforcement 
of accounting standards. Unless the standards are applied consistently and enforcement 
is uniform, a single set of standards may only appear to exist but desirable attributes 
such as comparability may be lacking.
In 2002, the IASB and FASB each acknowledged their commitment to the devel -
opment of high quality, compatible accounting standards that could be used for both 
domestic and cross-  border financial reporting (in an agreement referred to as “the 
Norwalk Agreement”). Both the IASB and FASB pledged to use their best efforts 
to 1) make their existing financial reporting standards fully compatible as soon as

practicable, and 2) to coordinate their future work programs to ensure that, once 
achieved, compatibility is maintained. The Norwalk Agreement was certainly an 
important milestone, and both bodies began working toward convergence. In 2004, 
the IASB and FASB agreed that, in principle, any significant accounting standard 
would be developed cooperatively. In 2006, the IASB and the FASB issued another 
memorandum of understanding (titled “ A Roadmap for Convergence between IFRSs 
and US GAAP”) in which the two Boards identified major projects. They agreed to 
align their conceptual frameworks; in the short term, to remove selected differences; 
and in the medium term, to issue joint standards where significant improvements 
were identified as being required. The joint projects include (but are not limited 
to): the Conceptual Framework, Fair Value Measurement, Consolidations, Financial 
Instruments, Financial Statement Presentation, Insurance Contracts, Leases, Post 4

16 The second attempt was successful and US GAAP requires the expensing of stock options. FASB ASC 
Topic 718 [Compensation–Stock Compensation].

Convergence of Global Financial Reporting Standards 57
Employment Benefits, and Revenue Recognition. In 2009, the IASB and FASB again 
reaffirmed their commitment to achieving convergence and affirmed June 2011 as the 
target completion date for the major projects that had been identified. In mid-  2010, 
however, the Boards acknowledged that all the new standard-  setting activity required 
to achieve that targeted completion would not give stakeholders enough time to pro -
vide high quality input in the process. Therefore, the Boards pushed back the target 
date for some projects to later in 2011.
In April 2012, the IASB and the FASB published a joint report in which they described 
the progress made on financial instruments. This was followed in February 2013, when 
the IASB and FASB published a high-  level update on the status and timetable of the 
remaining convergence projects. The convergence project was completed when the

IASB and FASB issued their standards on lease accounting in 2016. As of year-  end 
2017, no new projects are expected for the IASB/FASB convergence initiative.
When convergence between IFRS and US GAAP was occurring, the SEC began 
certain steps regarding the possible adoption of IFRS in the United States. Effective 
in 2008, the SEC adopted rules to eliminate the reconciliation requirement for foreign 
private issuers’ financial statements prepared in accordance with IFRS as issued by the 
IASB. Previously, any non-  US issuer using accounting standards other than US GAAP 
was required to provide a reconciliation to US GAAP . In November 2008, the SEC 
issued a proposed rule concerning a “Roadmap” for the use of financial statements 
prepared in accordance with IFRS by US issuers; however the rule did not become final. 
In February 2010, the SEC issued a “Statement in Support of Convergence and Global 
Accounting Standards” in which it reiterated its commitment to global accounting

standards and directed its staff to execute a work plan to enable the “Commission in 
2011 to make a determination regarding incorporating IFRS into the financial reporting 
system for US issuers. ”17 By the end of 2014, convergence efforts by the IASB and the 
FASB largely ceased.
Convergence between IFRS and other local GAAP also continued through 2014. 
For example, convergence between IFRS and Japanese GAAP is underway. In 2008, 
the IASB and the Accounting Standards Board of Japan published a memorandum 
of understanding (the “Tokyo Agreement”) outlining work to achieve convergence by 
June 2011. In 2009, the Japanese Business Accounting Council, a key advisory body to 
the Commissioner of the Japanese Financial Services Agency, approved a roadmap for 
the adoption of IFRS in Japan.18 Since 2010, eligible listed companies in Japan have 
been permitted to use IFRS in place of Japanese GAAP in their consolidated financial 
statements as designated by the FSA.

Exhibit 1 provides a summary of the adoption status of IFRS in selected worldwide 
locations. As can be seen, adoption ranges from total adoption of IFRS to requiring 
local GAAP . Between these two extremes, countries demonstrate different levels of 
commitment to IFRS including adoption of a local version of IFRS, requirement for 
certain entities to use IFRS, permission to use IFRS, and use of local GAAP that is 
converging with IFRS.
17 Source: www.sec.gov/rules/other/2010/33-  9109.pdf.
18 Source: www.iasb.org/Use+around+the+world/Global+convergence/IFRS+global+convergence.htm.

Reading 22 ■ Financial Reporting Standards 58
Exhibit 1   International Adoption Status of IFRS in Selected Locations as of June 2010
Europe ■■The EU requires companies listed in EU countries to adopt IFRS beginning with their 2005 finan -
cial statements.
■■As mentioned earlier, Switzerland requires that Swiss multinational companies listed on the main 
board of the Swiss Exchange must choose either IFRS or US GAAP . Non-  multinational listed 
companies are allowed to use either IFRS, US GAAP , or Swiss GAAP .
■■Some countries (for example, Georgia, Macedonia, Moldova, Serbia) use IFRS as adopted locally. 
Georgia, for example, uses the IFRS 2007 edition.
■■Some countries (for example, Czech Republic, Finland, Germany, Ireland, Lithuania, Netherlands, 
Norway, Poland) permit some foreign companies listing on local exchanges to use other specified 
and/or well-  recognised standards.
North America ■■The US SEC accepts IFRS for non-  US registrants and no longer requires a reconciliation to US

GAAP for filers using IFRS.
■■As mentioned earlier, the US FASB had been engaged in numerous projects with the IASB 
to achieve convergence of US GAAP and IFRS. No new projects are currently on the agenda, 
however.
■■The US SEC announced its intention to decide by 2011 whether to incorporate IFRS into finan -
cial reporting by US issuers. However, as of 2017, the SEC has not made a determination about 
whether to do so.
■■In Canada, listed companies are required to use IFRS beginning 1 January 2011. The year ending 
31 December 2010 is the last year of reporting under current Canadian GAAP .
■■In Mexico, IFRS adoption is mandatory for listed companies in 2012, with early adoption permit -
ted as early as 2008. 
■■Most of the island nations off the southeast coast of North America require or permit the use of 
IFRS by listed companies.
Central and South 
America■■Central America, Costa Rica, Honduras, Guatemala, Nicaragua, and Panama require the use of 
IFRS. El Salvador permits the use of IFRS.

■■Brazil requires that listed companies and financial institutions use IFRS, starting with periods 
ending in 2010. Brazilian GAAP continues to converge to IFRS. Ecuador requires listed compa -
nies, other than financial institutions, to use IFRS beginning in 2010, with all companies required 
to use IRFS beginning in 2012.
■■Chile requires major listed companies to use IFRS for 2009 financial statements. Other compa -
nies are permitted to use IFRS.
■■Venezuela permits listed companies to use IFRS. The expectation is that listed companies will be 
required to use IFRS by 2011.
■■Uruguay required all companies to use IFRS in existence at 31 July 2007. In 2011, non-  financial 
services companies were required to adopt IFRS as translated into Spanish from 2012, with finan -
cial services companies adopting IFRS starting in 2014.
■■Peru requires all publicly listed entities in the local stock exchange to prepare financial state -
ments using IFRS from 2012.

■■In Argentina, all companies that publicly offer debt or equity securities must prepare their 
financial statements using IFRS from year end 31 December 2012. Companies are allowed to 
voluntarily use IFRS from January 2011. Financial services companies are not allowed to use 
IFRS. However, in February 2014, the Argentinian authorities announced a plan to converge 
Argentinian GAAP and IFRS for financial institutions.
■■Bolivia is moving towards convergence with IFRS, with listed companied allowed to voluntarily 
use IFRS.
■■In Colombia and Paraguay, the adoption of IFRS is in early stages of consideration, with IFRS 
voluntarily permitted for listed entities in Paraguay.

Convergence of Global Financial Reporting Standards 59
Asia and Middle 
East■■Listed companies in a number of countries—including India and Indonesia—report under local 
GAAP , and plans exist to either converge with or transition to IFRS. Thailand fully adopted IFRS 
for the SET 100 in 2013, and for all listed companies in 2015.
■■Companies in China report under Chinese accounting standards (CAS). CAS are largely con -
verged with IFRS.
■■In Japan, some companies that meet certain criteria may use IFRS, otherwise companies report 
using Japanese GAAP . Japan has launched a joint project with the IASB to reduce differences 
between Japanese GAAP and IFRS.
■■In Malaysia, domestic listed companies report using local GAAP and foreign companies listed on 
Malaysian exchanges are permitted to use IFRS. In 2011, the Malaysian GAAP was updated, mak -
ing it fully IFRS-  compliant and equivalent to IFRS. Malaysian entities may thus be able to assert

that their financial statements are in full compliance with IFRS.
■■Korea requires the use of IFRS beginning 2011. Early adoption was permitted from 2009.
■■Listed companies are required to report under IFRS in a number of other countries, including 
Kyrgyz Republic, Lebanon, and Turkey.
■■A number of countries, including Pakistan, Philippines, and Singapore, require use of IFRS as 
adopted locally. In Singapore, IFRS is permitted for use by companies that list on other exchanges 
that require IFRS or if permission is given by the Accounting and Corporate Regulatory 
Authority.
■■In a number of countries, IFRS is required for some types of entities and permitted for others. 
For example, Armenia requires IFRS for financial organizations and permits its use for oth -
ers, Azerbaijan requires IFRS for banks and state owned public interest entities, Israel requires 
IFRS for domestic listed companies except for banking institutions, Kazakhstan requires IFRS

for domestic listed companies, large business entities and public interest entities, Saudi Arabia 
requires IFRS for all banks regulated by the Saudi Arabian Monetary Agency (central bank), and 
Uzbekistan requires IFRS for all commercial banks and permits IFRS for others. Vietnam requires 
IFRS for state owned banks and permits IFRS for commercial banks; all other listed companies 
report under Vietnamese accounting standards. Some countries, including Afghanistan and 
Qatar, require the use of IFRS.
Oceana ■■Australia requires Australian reporting entities to use IFRS as adopted locally. Foreign compa -
nies listing on local exchanges are permitted to use IFRS or their primary GAAP . The Australian 
regulator may require additional information.
■■New Zealand requires use of IFRS as adopted locally (NZ-  IFRS).
Africa ■■Many African countries, including Botswana, Ghana, Kenya, Malawi, Mauritius, Namibia, South

Africa, Swaziland, Tanzania, Uganda, Zambia, and Zimbabwe, require IFRS for listed companies.
■■Morocco requires the use of IFRS for consolidated financial statements of bank and financial 
institutions and permits its use for others.
■■Mozambique requires the use of IFRS for financial and lending institutions and for certain large 
entities. Use of IFRS is permitted by other entities beginning in 2010.
■■Egypt requires the use of local GAAP which is partially converged with IFRS.
■■The Nigerian Federal Executive Council approved 1 January 2012 as the effective date for conver -
gence of accounting standards in Nigeria with IFRS.
■■In some countries, financial statements are required to be prepared in accordance with the 
Organization for the Harmonization of Business Law in Africa accounting framework. These 
countries include Cameroon, Cote D’Ivoire, and Equatorial Guinea.
Sources:  Based on data from www.iasb.org, www.sec.gov, www.iasplus.com, and www.pwc.com.Exhibit 1   (Continued)

Reading 22 ■ Financial Reporting Standards 60
THE INTERNATIONAL FINANCIAL REPORTING 
STANDARDS FRAMEWORK
The Conceptual Framework for Financial Reporting 2010  sets forth “the concepts that 
underlie the preparation and presentation of financial statements for external users. ” The 
Conceptual Framework  (2010 ) is designed to assist standard setters in developing and 
reviewing standards, to assist preparers of financial statements in applying standards 
and in dealing with issues not specifically covered by standards, to assist auditors in 
forming an opinion on financial statements, and to assist users in interpreting financial 
statement information. It is important to note that an understanding of the Conceptual 
Framework  (2010 ) is expected to assist users of financial statements—including finan -
cial analysts—in interpreting the information contained therein.
The Conceptual Framework  (2010 ) is diagrammed in Exhibit 2. The top part of

the diagram shows the objective of general purpose financial reporting at the center, 
because other aspects of the framework are based upon this core. The qualitative 
characteristics of useful financial information surround the objective (fundamental 
characteristics are listed on the left and enhancing characteristics are listed on the 
right). The reporting elements are shown next with elements of financial statements 
shown at the bottom. Beneath the diagram of the framework are the basic constraint 
(cost) and assumption (going concern) that guide the development of standards and 
the preparation of financial reports.5

The International Financial Reporting Standards Framework 61
Exhibit 2   IFRS Framework for the Preparation and Presentation of Financial 
Reports
Reporting Elements
Qualitat ive Characteristics
Object ive
To Provide Financial Information
Useful in Making Decisions about
Providing Resources to the Entity
   Relevance*
   Faithful Representation   Comparability,
    Verifiability, 
    Timeliness, 
    Understandability
Performance
Income
Expenses
Capital Maintenance Adjustments
Past Cash FlowsFinancial Position
Assets
Liabilities
Equity
Constraint
Cost (cost/benefit considerations)
Underlying Assumption
Accrual Basis
Going Conce rn
*Material is an aspect of relevance.
In the following, we discuss the Conceptual Framework  (2010 ) starting at the core: 
The objective of financial statements.
5.1 Objective of Financial Reports
At the core of the Conceptual Framework  (2010 ) is the objective: The provision of 
financial information that is useful to current and potential providers of resources in

making decisions. All other aspects of the framework flow from that central objective.
The providers of resources are considered to be the primary users of financial 
reports and include investors, lenders, and other creditors. The purpose of providing 
the financial information is to be useful in making decisions about providing resources. 
Other users may find the financial information useful for making economic decisions. 
The types of economic decisions differ by users, so the specific information needed 
differs as well. However, although these users may have unique information needs, 
some information needs are common across all users. Information is needed about the 
company’s financial position: its resources and its financial obligations. Information

Reading 22 ■ Financial Reporting Standards 62
is needed about a company’s financial performance; this information explains how 
and why the company’s financial position changed in the past and can be useful in 
evaluating potential changes in the future. The third common information need 
reflected in the Conceptual Framework  (2010 ) diagram is the need for information 
about a company’s cash. How did the company obtain cash (by selling its products 
and services, borrowing, other)? How did the company use cash (by paying expenses, 
investing in new equipment, paying dividends, other)?
The Conceptual Framework  (2010 ) indicates that to make decisions about pro -
viding resources to the company, users need information that is helpful in assessing 
future net cash inflows to the entity. Such information includes information about the 
economic resources of (assets) and claims against (liabilities and equity) the entity,

and about how well the management and governing board have utilized the resources 
of the entity. It is specifically noted in the Conceptual Framework  (2010 ) that users 
need to consider information from other sources as well in making their decisions. 
Further, it is noted that the financial reports do not show the value of an entity but 
are useful in estimating the value of an entity.
5.2 Qualitative Characteristics of Financial Reports
Flowing from the central objective of providing information that is useful  to providers 
of resources, the Conceptual Framework  (2010 ) elaborates on what constitutes use -
fulness. It identifies two fundamental qualitative characteristics that make financial 
information useful: relevance and faithful representation.19 The concept of materiality 
is discussed within the context of relevance.
1 Relevance : Information is relevant if it would potentially affect or make a dif -
ference in users’ decisions. The information can have predictive value (useful

in making forecasts), confirmatory value (useful to evaluate past decisions or 
forecasts), or both. In other words, relevant information helps users of finan -
cial information to evaluate past, present, and future events, or to confirm 
or correct their past evaluations in a decision-  making context. Materiality:  
Information is considered to be material if omission or misstatement of the 
information could influence users’ decisions. Materiality is a function of the 
nature and/or magnitude of the information.
2 Faithful representation : Information that faithfully represents an economic 
phenomenon that it purports to represent is ideally complete, neutral, and free 
from error. Complete means that all information necessary to understand the 
phenomenon is depicted. Neutral means that information is selected and pre -
sented without bias. In other words, the information is not presented in such a 
manner as to bias the users’ decisions. Free from error means that there are no

errors of commission or omission in the description of the economic phenom -
enon, and that an appropriate process to arrive at the reported information was 
selected and was adhered to without error. Faithful representation maximizes 
the qualities of complete, neutral, and free from error to the extent possible.
Relevance and faithful representation are the fundamental, most critical char -
acteristics of useful financial information. In addition to these two fundamental 
characteristics, the Conceptual Framework  (2010 ) identifies four characteristics that 
19 Conceptual Framework for Financial Reporting (2010) . paragraphs QC 5–18.

The International Financial Reporting Standards Framework 63
enhance the usefulness of relevant and faithfully represented financial information. 
These enhancing qualitative characteristics are comparability, verifiability, timeliness, 
and understandability.20
1 Comparability : Comparability allows users “to identify and understand simi -
larities and differences of items. ” Information presented in a consistent manner 
over time and across entities enables users to make comparisons more easily 
than information with variations in how similar economic phenomena are 
represented.
2 Verifiability : Verifiability means that different knowledgeable and independent 
observers would agree that the information presented faithfully represents the 
economic phenomena it purports to represent.
3 Timelines s: Timely information is available to decision makers prior to their 
making a decision.
4 Understandability : Clear and concise presentation of information enhances

understandability. The Conceptual Framework  (2010 ) specifies that the infor -
mation is prepared for and should be understandable by users who have a 
reasonable knowledge of business and economic activities, and who are willing 
to study the information with diligence. However, some complex economic phe -
nomena cannot be presented in an easily understandable form. Information that 
is useful should not be excluded simply because it is difficult to understand. It 
may be necessary for users to seek assistance to understand information about 
complex economic phenomena.
Financial information exhibiting these qualitative characteristics—fundamental 
and enhancing—should be useful for making economic decisions.
5.3 Constraints on Financial Reports
Although it would be ideal for financial statements to exhibit all of these qualitative 
characteristics and thus achieve maximum usefulness, it may be necessary to make 
tradeoffs across the enhancing characteristics. The application of the enhancing

characteristics follows no set order of priority. Depending on the circumstances, each 
enhancing characteristic may take priority over the others.21 The aim is an appropriate 
balance among the enhancing characteristics.
A pervasive constraint on useful financial reporting is the cost of providing and 
using this information.22 Optimally, benefits derived from information should exceed 
the costs of providing and using it. Again, the aim is a balance between costs and 
benefits.
A limitation of financial reporting not specifically mentioned in the Conceptual 
Framework  (2010 ) involves information not included. Financial statements, by neces -
sity, omit information that is non-  quantifiable. For example, the creativity, innovation, 
and competence of a company’s work force are not directly captured in the financial 
statements. Similarly, customer loyalty, a positive corporate culture, environmental 
responsibility, and many other aspects about a company may not be directly reflected

in the financial statements. Of course, to the extent that these items result in superior 
financial performance, a company’s financial reports will reflect the results.
20 Ibid., paragraphs QC19–34.
21 Ibid., paragraph QC34.
22 Ibid., paragraphs QC35–39.

Reading 22 ■ Financial Reporting Standards 64
EXAMPLE 4   
Balancing Qualitative Characteristics of Useful 
Information
A tradeoff between enhancing qualitative characteristics often occurs. For 
example, when a company records sales revenue, it is required to simultaneously 
estimate and record an expense for potential bad debts (uncollectible accounts). 
Including this estimated expense is considered to represent the economic event 
faithfully and to provide relevant information about the net profits for the 
accounting period. The information is timely and understandable; but because 
bad debts may not be known with certainty until a later period, inclusion of this 
estimated expense involves a sacrifice of verifiability. The bad debt expense is 
simply an estimate. It is apparent that it is not always possible to simultaneously 
fulfill all qualitative characteristics.
Companies are most likely  to make tradeoffs between which of the following 
when preparing financial reports?

A Relevance and materiality.
B Timeliness and verifiability.
C Relevance and faithful representation.
Solution: 
B is correct. Providing timely information implies a shorter time frame between 
the economic event and the information preparation; however, fully verifying 
information may require a longer time frame. Relevance and faithful representa -
tion are fundamental qualitative characteristics that make financial information 
useful. Both characteristics are required; there is no tradeoff between these. 
Materiality is an aspect of relevance.
5.4 The Elements of Financial Statements
Financial statements portray the financial effects of transactions and other events by 
grouping them into broad classes (elements) according to their economic characteris -
tics.23 Three elements of financial statements are directly related to the measurement 
of financial position: assets, liabilities, and equity.24

■■Assets : Resources controlled by the enterprise as a result of past events and 
from which future economic benefits are expected to flow to the enterprise. 
Assets are what a company owns (e.g., inventory and equipment).
■■Liabilities : Present obligations of an enterprise arising from past events, the 
settlement of which is expected to result in an outflow of resources embodying 
economic benefits. Liabilities are what a company owes (e.g., bank borrowings).
■■Equity  (for public companies, also known as “shareholders’ equity” or “stock -
holders’ equity”): Assets less liabilities. Equity is the residual interest in the 
assets after subtracting the liabilities.
23 Chapter 4, the section of The Conceptual Framework (2010)  which deals with the elements of the financial 
statements and their recognition and measurement, has not been amended from The Framework (1989).  
This chapter and the proposed Chapter 2, “The Reporting Entity, ” will be considered further sometime after

2010. The references given will be as they appear in The Conceptual Framework (2010).
24 Conceptual Framework for Financial Reporting (2010) , paragraphs 4.4–4.23.

The International Financial Reporting Standards Framework 65
The elements of financial statements directly related to the measurement of per -
formance (profit and related measures) are income and expenses.25
■■Income : Increases in economic benefits in the form of inflows or enhancements 
of assets, or decreases of liabilities that result in an increase in equity (other 
than increases resulting from contributions by owners). Income includes both 
revenues and gains. Revenues represent income from the ordinary activities of 
the enterprise (e.g., the sale of products). Gains may result from ordinary activi -
ties or other activities (the sale of surplus equipment).
■■Expenses : Decreases in economic benefits in the form of outflows or depletions 
of assets, or increases in liabilities that result in decreases in equity (other than 
decreases because of distributions to owners). Expenses include losses, as well 
as those items normally thought of as expenses, such as the cost of goods sold

or wages.
5.4.1  Underlying Assumptions in Financial Statements
Two important assumptions underlie financial statements: accrual accounting and 
going concern. These assumptions determine how financial statement elements are 
recognized and measured.26
The use of “accrual accounting” assumes that financial statements should reflect 
transactions in the period when they actually occur, not necessarily when cash 
movements occur. For example, accrual accounting specifies that a company reports 
revenues when they are earned (when the performance obligations have been satisfied) , 
regardless of whether the company received cash before delivering the product, after 
delivering the product, or at the time of delivery.
“Going concern” refers to the assumption that the company will continue in 
business for the foreseeable future. To illustrate, consider the value of a company’s 
inventory if it is assumed that the inventory can be sold over a normal period of time

versus the value of that same inventory if it is assumed that the inventory must all be 
sold in a day (or a week). Companies with the intent to liquidate or materially curtail 
operations would require different information for a fair presentation.
In reporting the financial position of a company that is assumed to be a going 
concern, it may be appropriate to list assets at some measure of a current value based 
upon normal market conditions. However, if a company is expected to cease operations 
and be liquidated, it may be more appropriate to list such assets at an appropriate 
liquidation value, namely, a value that would be obtained in a forced sale.
5.4.2  Recognition of Financial Statement Elements
Recognition means that an item is included in the balance sheet or income statement. 
Recognition occurs if the item meets the definition of an element and satisfies the cri -
teria for recognition. A financial statement element (assets, liabilities, equity, income,

and expenses) should be recognized in the financial statements if:27
■■it is probable  that any future economic benefit associated with the item will 
flow to or from the enterprise; and
■■the item has a cost or value that can be measured with reliability .
25 Ibid., paragraphs 4.24–4.36.
26 Ibid., paragraphs OB17 and 4.1.
27 Ibid., paragraphs 4.37–4.38.

Reading 22 ■ Financial Reporting Standards 66
5.4.3  Measurement of Financial Statement Elements
Measurement is the process of determining the monetary amounts at which the 
elements of the financial statements are to be recognized and carried in the balance 
sheet and income statement. The following alternative bases of measurement are used 
to different degrees and in varying combinations to measure assets and liabilities:28
■■Historical cost : Historical cost is simply the amount of cash or cash equivalents 
paid to purchase an asset, including any costs of acquisition and/or preparation. 
If the asset was not bought for cash, historical cost is the fair value of whatever 
was given in order to buy the asset. When referring to liabilities, the historical 
cost basis of measurement means the amount of proceeds received in exchange 
for the obligation.
■■Amortised cost : Historical cost adjusted for amortisation, depreciation, or 
depletion and/or impairment.

■■Current cost : In reference to assets, current cost is the amount of cash or cash 
equivalents that would have to be paid to buy the same or an equivalent asset 
today. In reference to liabilities, the current cost basis of measurement means 
the undiscounted amount of cash or cash equivalents that would be required to 
settle the obligation today.
■■Realizable (settlement) value : In reference to assets, realizable value is the 
amount of cash or cash equivalents that could currently be obtained by sell -
ing the asset in an orderly disposal. For liabilities, the equivalent to realizable 
value is called “settlement value”—that is, settlement value is the undiscounted 
amount of cash or cash equivalents expected to be paid to satisfy the liabilities 
in the normal course of business.
■■Present value (PV) : For assets, present value is the present discounted value of 
the future net cash inflows that the asset is expected to generate in the normal

course of business. For liabilities, present value is the present discounted value 
of the future net cash outflows that are expected to be required to settle the 
liabilities in the normal course of business.
■■Fair value : is a measure of value mentioned but not specifically defined in the 
Conceptual Framework  (2010 ). Fair value is defined in IFRS and US GAAP as an 
exit price, the price that would be received to sell an asset or paid to transfer a 
liability in an orderly transaction between market participants at the measure -
ment date. This may involve either market measures or present value measures 
depending on the availability of information.29
5.5 General Requirements for Financial Statements
The Conceptual Framework  (2010 ) provides a basis for establishing standards and the 
elements of financial statements, but it does not address the contents of the financial 
statements. Having discussed the Conceptual Framework  (2010 ), we now address the

general requirements for financial statements.
International Accounting Standard (IAS) No. 1, Presentation of Financial Statements , 
specifies the required financial statements, general features of financial statements, 
and structure and content of financial statements.30 These general requirements are 
illustrated in Exhibit 3 and described in the subsections below.
28 Ibid., paragraphs 4.54–4.55.
29 IFRS Glossary of Terms . FASB ASC Topic 820 [Fair Value Measurements and Disclosures].
30 For US GAAP , financial statement presentation is covered in Sections 205 through 280 of the Accounting 
Standards Codification.

The International Financial Reporting Standards Framework 67
Exhibit 3   IASB General Requirements for Financial Statements
Required Financial Statements
•S tatement of financial position (Balance sheet)
• Statement of comprehensive income (Single
statement or Income statement + Statement of
comprehensive income)
•S tatement of changes in equity
•S tatement of cash flow s
• In certain cases, Statement of financial position
from earliest comparative period• Notes, summarizing accounting policies and
disclosing other items
Structure and Conten t
•C lassified balance sheet
•M inimum specifie d
information on face
•Comparative information•M inimum specified not e
disclosure sGeneral Features
• Fair presentation 
• Going concern 
• Frequency of reporting
• Comparative information
•Consistency of presentatio n• Accrual basis 
• Materiality and aggregation
•N o offsetting 
In the following sections, we discuss the required financial statements, the general

features underlying the preparation of financial statements, and the specified structure 
and content in greater detail.
5.5.1  Required Financial Statements
Under IAS No. 1, a complete set of financial statements includes:31
■■a statement of financial position (balance sheet);
■■a statement of comprehensive income (a single statement of comprehensive 
income or two statements, an income statement and a statement of comprehen -
sive income that begins with profit or loss from the income statement);
■■a statement of changes in equity, separately showing changes in equity resulting 
from profit or loss, each item of other comprehensive income, and transactions 
with owners in their capacity as owners;32
■■a statement of cash flows; and
■■notes comprising a summary of significant accounting policies and other 
explanatory notes that disclose information required by IFRS and not presented 
elsewhere and that provide information relevant to an understanding of the 

Entities are encouraged to furnish other related financial and non-  financial infor -
mation in addition to that required. Financial statements need to present fairly the 
financial position, financial performance, and cash flows of an entity.
5.5.2  General Features of Financial Statements
A company that applies IFRS is required to state explicitly in the notes to its financial 
statements that it is in compliance with the standards. Such a statement is only made 
when a company is in compliance with all requirements of IFRS. In extremely rare 
31 IAS No. 1, Presentation of Financial Statements , paragraph 10.
32 Examples of transactions with owners acting in their capacity as owners include sale of equity securities 
to investors, distributions of earnings to investors, and repurchases of equity securities from investors.

Reading 22 ■ Financial Reporting Standards 68
circumstances, a company may deviate from a requirement of IFRS if management 
concludes that complying with IFRS would result in misleading financial statements. 
In this case, management must disclose details of the departure from IFRS.
IAS No. 1 specifies a number of general features underlying the preparation of 
financial statements. These features clearly reflect the Conceptual Framework  (2010 ).
■■Fair Presentation : The application of IFRS is presumed to result in financial 
statements that achieve a fair presentation. The IAS describes fair presentation 
as follows:
Fair presentation requires the faithful representation of the effects 
of transactions, other events and conditions in accordance with the 
definitions and recognition criteria for assets, liabilities, income and 
expenses set out in the Framework .33
■■Going Concern : Financial statements are prepared on a going concern basis

unless management either intends to liquidate the entity or to cease trading, 
or has no realistic alternative but to do so. If not presented on a going concern 
basis, the fact and rationale should be disclosed.
■■Accrual Basis : Financial statements (except for cash flow information) are to be 
prepared using the accrual basis of accounting.
■■Materiality and Aggregation : Omissions or misstatements of items are mate -
rial if they could, individually or collectively, influence the economic decisions 
that users make on the basis of the financial statements. Each material class of 
similar items is presented separately. Dissimilar items are presented separately 
unless they are immaterial.
■■No Offsetting : Assets and liabilities, and income and expenses, are not offset 
unless required or permitted by an IFRS.
■■Frequency of Reporting : Financial statements must be prepared at least annually.
■■Comparative Information : Financial statements must include comparative infor -

mation from the previous period. The comparative information of prior periods 
is disclosed for all amounts reported in the financial statements, unless an IFRS 
requires or permits otherwise.
■■Consistency : The presentation and classification of items in the financial state -
ments are usually retained from one period to the next.
5.5.3  Structure and Content Requirements
IAS No. 1 also specifies structure and content of financial statements. These require -
ments include the following:
■■Classified Statement of Financial Position (Balance Sheet) : IAS No. 1 requires 
the balance sheet to distinguish between current and non-  current assets, and 
between current and non-  current liabilities unless a presentation based on 
liquidity provides more relevant and reliable information (e.g., in the case of a 
bank or similar financial institution).
■■Minimum Information on the Face of the Financial Statements : IAS No. 1 
specifies the minimum line item disclosures on the face of, or in the notes to,

the financial statements. For example, companies are specifically required to 
disclose the amount of their plant, property, and equipment as a line item on 
the face of the balance sheet. The specific requirements are listed in Exhibit 4.
33 IAS No. 1, Presentation of Financial Statements , paragraph 15.

The International Financial Reporting Standards Framework 69
■■Minimum Information in the Notes  (or on the face of financial statements): IAS 
No. 1 specifies disclosures about information to be presented in the financial 
statements. This information must be provided in a systematic manner and 
cross-  referenced from the face of the financial statements to the notes. The 
required information is summarized in Exhibit 5.
■■Comparative Information : For all amounts reported in a financial statement, 
comparative information should be provided for the previous period unless 
another standard requires or permits otherwise. Such comparative information 
allows users to better understand reported amounts.
Exhibit 4   IAS No. 1: Minimum Required Line Items in Financial Statements
On the face of the Statement of Financial 
Position■■Plant, property, and equipment
■■Investment property
■■Intangible assets
■■Financial assets (those not included in other specified line items)

■■Investments accounted for using the equity method
■■Biological assets
■■Inventories
■■Trade and other receivables
■■Cash and cash equivalents
■■Total assets in groups held for sale
■■Trade and other payables
■■Provisions
■■Financial liabilities (not listed in other line items)
■■Liabilities and assets for current tax
■■Deferred tax liabilities and deferred tax assets
■■Total liabilities in groups held for sale
■■Non-  controlling interest (i.e., minority interest, presented within equity)
■■Issued capital and reserves attributable to owners of the parent
On the face of the Statement of 
Comprehensive Income, presented either 
in a single statement or in two statements 
(Income statement + Statement of compre -
hensive income)■■Revenue
■■Specified gains and losses for financial assets
■■Finance costs
■■Share of the profit or loss of associates and joint ventures accounted for 
using the equity method
■■Pretax gain or loss recognized on the disposal of assets or settlement of

liabilities attributable to discontinued operations
■■Tax expense
■■Profit or loss
■■Each component of other comprehensive income
■■Amount of profit or loss and amount of comprehensive income attribut -
able to non-  controlling interest (minority interest)
able to the parent

Reading 22 ■ Financial Reporting Standards 70
On the face of the Statement of Changes in 
Equity■■Total comprehensive income for the period, showing separately the total 
amounts attributable to owners of the parent and to non-  controlling 
interest (minority interest)
■■For each component of equity, a reconciliation between beginning 
balances and ending balances, showing separately amounts arising from 
a) profit or loss, b) each item of other comprehensive income, and c) 
transactions with owners in their capacity as owners.
■■For each component of equity, the effects of changes in accounting poli -
cies and corrections of errors recognized in accordance with IAS No. 8
Exhibit 5   Summary of IFRS Required Disclosures in the Notes to the Financial Statements
Disclosure of Accounting Policies ■■Measurement bases used in preparing financial statements
■■Significant accounting policies used
■■Judgments made in applying accounting policies that have the most

significant effect on the amounts recognized in the financial statements
Sources of Estimation Uncertainty ■■Key assumptions about the future and other key sources of estimation 
uncertainty that have a significant risk of causing material adjustment 
to the carrying amount of assets and liabilities within the next year
Other Disclosures ■■Information about capital and about certain financial instruments 
classified as equity
■■Dividends not recognized as a distribution during the period, including 
dividends declared before the financial statements were issued and any 
cumulative preference dividends
■■Description of the entity, including its domicile, legal form, country of 
incorporation, and registered office or business address
■■Nature of operations and principal activities
■■Name of parent and ultimate parent
5.6 Convergence of Conceptual Framework
One of the joint IASB/FASB projects, begun in 2004, aimed to develop an improved,

common conceptual framework. The project was conducted in phases. The Boards’ 
initial, technical work plan included: Objective of and qualitative characteristics of 
financial reporting; Reporting entity; Elements; and Measurement and recognition 
of elements. As of 2010, the objective and qualitative characteristics phase was com -
plete and is incorporated in the reading. In late 2010, convergence as put on hold. In 
December 2012, the IASB reactivated the conceptual framework as an IASB project.
As more countries adopt IFRS, the need to consider other financial reporting sys -
tems will be reduced. Additionally, the IASB and FASB are considering frameworks 
from other jurisdictions in developing their joint framework. Nevertheless, analysts are 
likely to encounter financial statements that are prepared on a basis other than IFRS. 
Although the number and relevance of different local GAAP reporting systems are

likely to decline, industry-  specific financial reports—such as those required for banking 
or insurance companies—will continue to exist. Differences remain between IFRS and 
US GAAP that affect the framework and general financial reporting requirements. Exhibit 4   (Continued)

The International Financial Reporting Standards Framework 71
The readings on individual financial statements and specific topics will review in more 
detail differences in IFRS and US GAAP as they apply to specific financial statements 
and topics.
As mentioned earlier, a joint IASB–FASB project was begun in October  2004 
to develop a common conceptual framework. The initial focus was to achieve the 
convergence of the frameworks and improve particular aspects of the framework 
dealing with objectives, qualitative characteristics, elements and their recognition, 
and measurement. A December 2004 discussion paper presented the broad differ -
ences between the two frameworks. The differences between IFRS and US GAAP 
that affect the framework and general financial reporting requirements have been 
reduced by the agreement by the IASB and FASB on the purpose and scope of the 
Conceptual Framework  (2010 ), the objective of general purpose financial reporting,

and qualitative characteristics of useful financial information. Exhibit 6 summarizes 
the remaining differences as presented in the December 2004 discussion paper. Some 
of the differences identified in December 2004 may no longer apply. The readings 
on individual financial statements and specific topics will discuss relevant and more 
current differences in greater detail.
Exhibit 6   Summary of Differences between IFRS and US GAAP Frameworks 
as of December 2004
US GAAP (FASB) Framework
Financial Statement Elements 
(definition, recognition, and 
measurement) ■■Performance Elements : The FASB framework 
includes three elements relating to financial 
performance in addition to revenue and expenses: 
gains, losses, and comprehensive income. 
Comprehensive income is a more encompassing 
concept than net income, as it includes all changes 
in equity during a period except those resulting 
from investments by and distributions to owners.
■■Financial Position Elements : The FASB framework

defines an asset as “a future economic benefit” 
rather than the “resource” from which future eco -
nomic benefits are expected to flow to the entity 
as in the IASB framework. It also includes the 
term “probable” to define the assets and liabilities 
elements. As discussed below, the term “probable” 
is part of the IASB framework recognition criteria. 
Additionally, the frameworks have different mean -
ings of probable.

Reading 22 ■ Financial Reporting Standards 72
■■Recognition of Elements : The FASB framework 
does not discuss the term “probable” in its 
recognition criteria, whereas the IASB frame -
work requires that it is probable that any future 
economic benefit flow to/from the entity. The 
FASB framework also has a separate recognition 
criterion of relevance.
■■Measurement of Elements : Measurement attri -
butes (historical cost, current cost, settlement 
value, current market value, and present value) are 
broadly consistent, and both frameworks lack fully 
developed measurement concepts. Furthermore, 
the FASB framework prohibits revaluations except 
for certain categories of financial instruments, 
which have to be carried at fair value.
For analysis of financial statements created under different frameworks, recon -
ciliation schedules and disclosures regarding the significant differences between the

reporting bases were formerly available to a greater extent. For example, the SEC 
used to require reconciliation for foreign private issuers that did not prepare financial 
statements in accordance with US GAAP . The SEC no longer requires reconciliation 
for foreign private issuers that prepare their financial reports in compliance with IFRS. 
Such reconciliations can reveal additional information related to the more judgmental 
components of the financial statements. In the absence of a reconciliation, users of 
financial statements must be prepared to consider how the use of different reporting 
standards potentially impact financial reports. This can have important implications 
for comparing the performance of companies and security valuation.
EFFECTIVE FINANCIAL REPORTING
A discussion of the characteristics of an effective framework and the barriers to the 
creation of such a framework offer additional perspective on financial reporting.

6.1 Characteristics of an Effective Financial Reporting 
Framework
Any effective financial reporting system needs to be a coherent one (i.e., a framework 
in which all the pieces fit together according to an underlying logic). Such frameworks 
have several characteristics:
■■Transparency : A framework should enhance the transparency of a company’s 
financial statements. Transparency means that users should be able to see the 
underlying economics of the business reflected clearly in the company’s finan -
cial statements. Full disclosure and fair presentation create transparency.
■■Comprehensiveness : To be comprehensive, a framework should encompass 
the full spectrum of transactions that have financial consequences. This spec -
trum includes not only transactions currently occurring, but also new types of 6Exhibit 6   (Continued)

Effective Financial Reporting 73
transactions as they are developed. So an effective financial reporting frame -
work is based on principles that are universal enough to provide guidance for 
recording both existing and newly developed transactions.
■■Consistency : An effective framework should ensure reasonable consistency 
across companies and time periods. In other words, similar transactions should 
be measured and presented in a similar manner regardless of industry, company 
size, geography, or other characteristics. Balanced against this need for consis -
tency, however, is the need for sufficient flexibility to allow companies sufficient 
discretion to report results in accordance with underlying economic activity.
6.2 Barriers to a Single Coherent Framework
Although effective frameworks all share the characteristics of transparency, compre -
hensiveness, and consistency, there are some conflicts that create inherent limitations

in any financial reporting standards framework. Specifically, it is difficult to completely 
satisfy all these characteristics concurrently, so any framework represents an attempt 
to balance the relative importance of these characteristics. Three areas of conflict 
include valuation, standard-  setting approach, and measurement.
■■Valuation : As discussed, various bases for measuring the value of assets and 
liabilities exist, such as historical cost, current cost, fair value, realizable value, 
and present value. Historical cost valuation, under which an asset’s value is its 
initial cost, requires minimal judgment. In contrast, other valuation approaches, 
such as fair value, require considerable judgment but can provide more relevant 
information.
■■Standard-  Setting Approach : Financial reporting standards can be established 
based on 1) principles, 2) rules, or 3) a combination of principles and rules 
(sometimes referred to as “objectives oriented”). A principles-  based approach

provides a broad financial reporting framework with little specific guidance 
on how to report a particular element or transaction. Such principles-  based 
approaches require the preparers of financial reports and auditors to exer -
cise considerable judgment in financial reporting. In contrast, a rules-  based 
approach establishes specific rules for each element or transaction. Rules-  based 
approaches are characterized by a list of yes-  or- no rules, specific numeri -
cal tests for classifying certain transactions (known as “bright line tests”), 
exceptions, and alternative treatments. Some suggest that rules are created in 
response to preparers’ needs for specific guidance in implementing principles, 
so even standards that begin purely as principles evolve into a combination of 
principles and rules. The third alternative, an objectives-  oriented approach, 
combines the other two approaches by including both a framework of principles

and appropriate levels of implementation guidance. The common conceptual 
framework is likely to be more objectives oriented.
■■Measurement : The balance sheet presents elements at a point in time, whereas 
the income statement reflects changes during a period of time. Because these 
statements are related, standards regarding one of the statements have an effect 
on the other statement. Financial reporting standards can be established taking 
an “asset/liability” approach, which gives preference to proper valuation of 
the balance sheet, or a “revenue/expense” approach that focuses more on the 
income statement. This conflict can result in one statement being reported in 
a theoretically sound manner, but the other statement reflecting less relevant 
information. Standard setters are now predominantly using an asset/liability 
approach.

Reading 22 ■ Financial Reporting Standards 74
EXAMPLE 5   
Conflicts between Measurement Approaches
Prime Retailers (PR), a US-  based distributor of men’s shirts, has a policy of 
marking its merchandise up by $5 per unit. At the beginning of 2009, PR had 
10,000 units of inventory on hand, which cost $15 per unit. During 2009, PR 
purchased 100,000 units of inventory at a cost of $22 per unit. Also during 2009, 
PR sold 100,000 units of inventory at $27 per unit. How shall PR reflect the cost 
of the inventory sold: $15 or $22 or some combination?
In order to match current costs with current revenues, PR (which does not 
operate in an IFRS jurisdiction; last-  in, first-  out is not allowed under IFRS) may 
decide that it is appropriate to use a method of inventory costing that assumes 
that the most recently purchased inventory is sold first. So, the assumption is 
that the 100,000 units of sales had a cost of $22. A partial income statement 
for PR would be:
Sales $2,700,000

Cost of sales $2,200,000
Gross profit $500,000
The gross profit calculated in this manner reflects the current cost of goods 
matched with the current level of revenues.
But PR still has 10,000 units of inventory on hand. The assumption must be 
that the 10,000 remaining units had a cost of $15 per unit. Therefore, the value 
of the inventory reflected on the balance sheet would be $150,000.
Although the income statement reflects current costs, the remaining inven -
tory on the balance sheet does not reflect current information. The inventory 
is reflected at the older cost of $15 per unit. An analyst would likely find this 
older cost less relevant than the current cost of that inventory.
COMPARISON OF IFRS WITH ALTERNATIVE 
REPORTING SYSTEMS
The adoption of IFRS as the required financial reporting standard by the EU and other 
countries has advanced the goal of global convergence. Nevertheless, there are still

significant differences in financial reporting in the global capital markets. Arguably, 
the most critical are the differences that exist between IFRS and US GAAP . After the 
EU adoption of IFRS in 2005, a significant number of the world’s listed companies 
use one of these two reporting standards.
For analyzing financial statements created under different standards, reconciliation 
schedules and disclosures regarding the significant differences between the reporting 
bases—historically available in some jurisdictions—were particularly helpful. For 
example, the SEC historically required reconciliation for foreign private issuers that 
did not prepare financial statements in accordance with US GAAP . In 2007, however, 
the SEC eliminated the reconciliation requirement for companies that prepared their 
financial statements according to IFRS.347
34 The SEC issued Rule 33-  8879 (available at www.sec.gov/rules/final/2007/33-  8879.pdf) on 21

December 2007. The Rule eliminated the reconciliation requirement for companies reporting under IFRS 
as issued by the IASB and applied to financial years ending after 15 November 2007.

Comparison of IFRS with Alternative Reporting Systems 75
Although the disclosures related to any such differences were sometimes dauntingly 
long, the numerical reconciliations of net income and shareholders’ equity appeared 
in charts that were relatively easy to use. As an example, consider the reconciliation 
disclosures made by Syngenta AG, a Swiss agribusiness company in 2006, the last 
year in which reconciliations were required. Syngenta’s 2006 US SEC Form 20-  F 
filing discussed these differences in Note 34, “Significant Differences between IFRS 
and United States Generally Accepted Accounting Principles. ” This note was roughly 
20 pages long! The chart presenting the numerical reconciliation of net income (see 
Exhibit 7) was, however, relatively easy to use and could be reviewed to identify the 
significant items; large amounts could be examined in more detail. The Syngenta 
disclosure indicates that the company’s 2006 net income based on US GAAP was

$504 million, compared with the $634 million of net income reported under IFRS. 
The reconciliation indicates that most significant differences relate to accounting for 
acquisitions (purchase accounting adjustments include a $30 million increase and an 
$86 million decrease), accounting for pension provisions ($48 million), accounting 
for put options ($60 million) and accounting for various tax-  related items. In some 
instances, further analysis would be undertaken to determine the implications of each 
significant difference based on additional disclosures in the notes.
Exhibit 7   Reconciliation of GAAP Income: Syngenta (US$ in Millions)
2006 2005 2004
Net income/(loss) reported under IFRS attributable to 
Syngenta AG shareholders634 622 460
US GAAP adjustments:
  Purchase accounting: Zeneca agrochemicals business 30 (7) 62
  Purchase accounting: other acquisitions (86) (80) (62)
  Restructuring charges (9) (9) 47
  Pension provisions (including post-  retirement 
benefits)(48) (15) 43

  Deferred taxes on share based compensation — 3 (3)
  Deferred taxes on unrealized profit in inventory 26 (33) (61)
  Impairment losses 2 (7) (1)
  Inventory provisions (13) — —
  Revenue recognition (1) — —
  Environmental remediation costs (27) — —
  Other items 9 28 (17)
  Grant of put option to Syngenta AG shareholders (60) — —
  Valuation allowance against deferred tax assets — 26 (34)
  Income tax on undistributed earnings of subsidiaries 1 1 (27)
Deferred tax effect of US GAAP adjustments 46 27 (55)
Net income/(loss) reported under US GAAP 504 556 352
Source:  2005 US SEC Form 20-  F.
Now that reconciliation disclosures are no longer generally available, an analyst 
comparing two companies that use different reporting standards must be aware of 
areas where accounting standards have not converged. For example, data from 2006 
SEC reconciliations (the last year available) indicated that pensions and goodwill

were the dominant IFRS-  to- US GAAP reconciliation items for European companies

Reading 22 ■ Financial Reporting Standards 76
that listed their stock on an exchange in the United States.35 In most cases, a user of 
financial statements prepared under different accounting standards will no longer have 
enough information to make specific adjustments required to achieve comparability. 
Instead, an analyst must maintain general caution in interpreting comparative finan -
cial measures produced under different accounting standards and monitor significant 
developments in financial reporting standards.
Exhibit  836 below discussed the current status of the IASB-  FASB convergence 
project as at 2017. As mentioned earlier, no new projects are expected to be added 
to the project.
Exhibit 8   Current Status of IASB and US GAAP Convergence Project
Short-  Term Convergence Projects
Borrowing costs IASB reissued IAS 23: Borrowing Costs in 2008.
Discontinued operations (IASB only) The IASB issued IFRS 5 Non-  current Assets Held for Sale and Discontinued 
Operations in March 2004.

Fair value option for financial instruments 
(FASB only)Completed.
Government grants Joint work on this project has been discontinued.
Impairment Joint work on this project has been discontinued.
Income taxes Joint work on this project has been discontinued.
Investment properties The FASB is working on this project.
Joint arrangements IASB issued IFRS 11: Joint Arrangements in 2011.
Research and development (FASB only) Completed.
Segment reporting IASB issued IFRS 8 Operating Segments in 2008.
Exhibit 937 below discusses the current status of the major joint IASB-  FASB con -
vergence projects as at 2017.
Exhibit 9   Current Status of Major Joint IASB and US GAAP Convergence Projects
Major Joint Projects
Business Combinations Converged standards issued in 2008.
Conceptual Framework The project has been partially completed. Work on further phases was dis -
continued and the IASB undertook an IASB-  only comprehensive project.
Consolidation Converged standards issued in 2011.

Derecognition The IASB and FASB could not reach a converged solution and instead addi -
tional disclosures were implemented.
Fair value measurement Converged standards issued in 2011.
Financial instruments Comprises a number of projects, some completed and some which are still 
under way. In some areas, divergent outcomes have been developed, and 
timing of the issuance of pronouncements is no longer aligned. The IASB 
has completed work on IFRS 9: Financial Instruments.
35 Henry, Lin, and Yang (2009) “The European-  US ‘GAAP Gap’: IFRS to US GAAP Form 20-  F Reconciliations” 
Accounting Horizons  23(2): 121–150.
36 www.iasplus.com
37 www.iasplus.com

Monitoring Developments in Financial Reporting Standards 77
Financial statement presentation Joint work on this project has been discontinued. Some amendments to 
existing requirements have been made in relation to the presentation of the 
Insurance contracts Joint work on this project has been discontinued, although the IASB and 
FASB continue to liaise on some issues.
Intangible assets The IASB and FASB decided in 2007 to not add this project to the joint 
agenda.
Leases Divergence has occurred regarding some aspects.
Liabilities and equity Joint work on this project has been discontinued.
Post-  employment benefits. Joint work on this project has been discontinued.
Revenue recognition IFRS 15: Revenue from Contracts with Customers was issued in May 2014. 
The standard is fully converged with ASU 2014-  09 Revenue from Contracts 
with Customers.
MONITORING DEVELOPMENTS IN FINANCIAL 
REPORTING STANDARDS

In studying financial reporting and financial statement analysis in general, the analyst 
must be aware that reporting standards are evolving rapidly. Analysts need to monitor 
ongoing developments in financial reporting and assess their implications for security 
analysis and valuation. The need to monitor developments in financial reporting stan -
dards does not mean that analysts should be accountants. An accountant monitors 
these developments from a preparer’s perspective; an analyst needs to monitor from 
a user’s perspective. More specifically, analysts need to know how these developments 
will affect financial reports.
Analysts can remain aware of developments in financial reporting standards by 
monitoring three areas: new products or transactions, actions of standard setters and 
other groups representing users of financial statements (such as CFA Institute), and 
company disclosures regarding critical accounting policies and estimates.

8.1 New Products or Types of Transactions
New products and new types of transactions can have unusual or unique elements to 
them such that no explicit guidance in the financial reporting standards exists. New 
products or transactions typically arise from economic events, such as new businesses 
(e.g., the internet), or from a newly developed financial instrument or financial struc -
ture. Financial instruments, whether exchange traded or not, are typically designed 
to enhance a company’s business or to mitigate inherent risks. However, at times, 
financial instruments or structured transactions have been developed primarily for 
purposes of financial report “window dressing. ”
Although companies might discuss new products and transactions in their finan -
cial reports, the analyst can also monitor business journals and the capital markets to 
identify such items. Additionally, when one company in an industry develops a new

product or transaction, other companies in the industry often do the same. Once new 
products, financial instruments, or structured transactions are identified, it is helpful 
to gain an understanding of the business purpose. If necessary, an analyst can obtain 8Exhibit 9   (Continued)

Reading 22 ■ Financial Reporting Standards 78
further information from a company’s management, which should be able to describe 
the economic purpose, the financial statement reporting, significant estimates, judg -
ments applied in determining the reporting, and future cash flow implications for 
these items. The financial reporting framework described here is useful in evaluating 
the potential effect on financial statements even though a standard may not have been 
issued as to how to report a particular transaction.
8.2 Evolving Standards and the Role of CFA Institute
The actions of standard setters and regulators are unlikely to be helpful in identifying 
new products and transactions, given the lag between new product development and 
regulatory action. Monitoring the actions of these authorities is nonetheless important 
for another reason: Changes in regulations can affect companies’ financial reports and,

thus, valuations. This is particularly true if the financial reporting standards change 
to require more explicit identification of matters affecting asset/liability valuation or 
financial performance. For example, one regulatory change required companies to 
report the value of employee stock options as an expense in the income statement. 
Prior to the required expensing, an analyst could assess the impact of stock options on 
a company’s performance and the dilutive effect to shareholders by reviewing informa -
tion disclosed in the notes to the financial statements. As another example, the new 
standards on leases, IFRS 16, which applies for annual reporting periods beginning 
on 1 January 2019, will result in explicitly recognizing on the balance sheet the assets 
and liabilities associated with “operating leases”; currently, operating leases are not 
recognized on the balance sheet and information concerning the lease is available only

in the notes. To the extent that some market participants do not examine financial 
statement details and thus ignore some items when valuing a company’s securities, more 
explicit identification could affect the value of the company’s securities. Additionally, 
it is plausible to believe that management is more attentive to and rigorous in any 
calculations/estimates of items that appear in the financial statements, compared to 
items that are only disclosed in the notes.
The IASB and FASB have numerous major projects underway that will most likely 
result in new standards. It is important to keep up to date on these evolving standards. 
The IASB (www.iasb.org) and FASB (www.fasb.org) provide a great deal of informa -
tion on their websites regarding new standards and proposals for future changes 
in standards. In addition, the IASB and FASB seek input from the financial analyst 
community—those who regularly use financial statements in making investment and

credit decisions. When a new standard is proposed, an exposure draft is made available 
and users of financial statements can draft comment letters and position papers for 
submission to the IASB and FASB in order to evaluate the proposal.
CFA Institute is active in advocating improvements to financial reporting, through 
its Standards and Financial Market Integrity Division. Volunteer members of CFA 
Institute serve on several liaison committees that meet regularly to make recommen -
dations to the IASB and FASB on proposed standards and to draft comment letters and 
position papers. The comment letters and position papers of these groups on financial 
reporting issues are available at www.cfainstitute.org/ethics/topics/pages/index.aspx.
CFA Institute issued a position paper titled A Comprehensive Business Reporting 
Model: Financial Reporting for Investors , which provides a suggested model for sig -
nificantly improving financial reporting. The position paper, issued in 2007, states:

Corporate financial statements and their related disclosures are fundamental 
to sound investment decision making. The well-  being of the world’s finan -
cial markets, and of the millions of investors who entrust their financial 
present and future to those markets, depends directly on the information 
financial statements and disclosures provide. Consequently, the quality

Monitoring Developments in Financial Reporting Standards 79
of the information drives global financial markets. The quality, in turn, 
depends directly on the principles and standards managers apply when 
recognizing and measuring the economic activities and events affecting 
their companies’ operations….
Investors require timeliness, transparency, comparability, and consis -
tency in financial reporting. Investors have a preference for decision rele -
vance over reliability. As CFA Institute stated in 1993 and as reiterated in 
this paper, “analysts need to know economic reality—what is really going 
on—to the greatest extent it can be depicted by accounting numbers. ” 
Corporate financial statements that fail to reflect this economic reality 
undermine the investment decision-  making process.38
Among other principles, the proposed model stresses the importance of information 
regarding the current fair value of assets and liabilities, of neutrality in financial

reporting, and of providing detailed information on cash flows to investors through 
the choice of the so-  called direct format for the cash flow statement.39
In summary, analysts can improve their investment decision making by keeping 
current on financial reporting standards, and various web-  based sources provide the 
means to do so. In addition, analysts can contribute to improving financial reporting 
by sharing their perspective as users with standard-  setting bodies, which typically 
invite comments concerning proposed changes.
8.3 Company Disclosures
A good source for obtaining information regarding the effect of financial reporting 
standards on a company’s financial statements is typically the company itself. This 
information is provided in the notes to the financial statements and accompanying 
discussion.
8.3.1  Disclosures Relating to Critical and Significant Accounting Policies
As noted earlier, financial reporting standards need to restrict alternatives but retain

flexibility in allowing enterprises to match their accounting methods with underlying 
economics. As a result, companies choose among alternative accounting policies (e.g., 
depreciation methods) and use estimates (e.g., depreciable lives of assets). Under both 
IFRS and US GAAP , companies are required to disclose their accounting policies and 
estimates in the notes to the financial statements. Companies also discuss in the man -
agement commentary (or the management’s discussion and analysis, MD&A) those 
policies that management deems most important. Although many of the policies are 
discussed in both the management commentary and the notes to the financial state -
ment, there is typically a distinction between the two discussions. The management 
commentary generally relates to aspects of the accounting policies deemed important 
by management to understand the financial statements, particularly changes. The 
MD&A disclosure relates to those policies that require significant judgments and

estimates, whereas the note discusses all accounting policies, irrespective of whether 
judgment was required. Each disclosure has value.
In analyzing financial reporting disclosures, the following questions should be 
addressed:
■■What policies have been discussed?
38 A Comprehensive Business Reporting Model: Financial Reporting for Investors , CFA Institute Centre for 
Financial Market Integrity, July 2007, p. 1, 2.
39 See the reading on cash flow statements for further information on the direct format.

Reading 22 ■ Financial Reporting Standards 80
■■Do these policies appear to cover all of the significant balances on the financial 
statements?
■■Which policies are identified as requiring significant estimates?
■■Have there been any changes in these disclosures from one year to the next?
Exhibit 10 summarizes the accounting policies discussed in the management report 
section of Volkswagen’s annual report.
Exhibit 10   Accounting Policy Discussion in Volkswagen’s Management 
Report
Volkswagen’s management report includes the following discussion of account -
ing policies:
The application of IFRS 8 led to a reclassification of the segments 
disclosed in the notes. The following segments are now reported: 
Passenger Cars and Light Commercial Vehicles, Scania, and 
Volkswagen Financial Services. The classification of the Group’s 
activities into the Automotive and Financial Services divisions remains 
unchanged in the management report.
In accordance with the amended IAS 7, as of fiscal year 2009 we

are reporting liquidity movements resulting from changes in leasing 
and rental assets in cash flows from operating activities (previously 
reported in cash flows from investing activities). Accordingly, changes 
in financial services receivables are also allocated to cash flows from 
operating activities. The prior-  year presentation has been adjusted 
accordingly.
The adoption of new or amended accounting standards did not 
otherwise materially affect the 2009 consolidated financial statements.
Source:  Volkswagen’s 2009 Annual Report, page 144.
Exhibit  11 lists the items discussed in the note titled “ Accounting Policies” in 
Volkswagen’s notes to the financial statements. Note that far more items are described 
in the notes to the financial statements as compared to the management’s commentary, 
illustrating the broader disclosure of the notes.
Exhibit 11   Accounting Policies Described in Volkswagen’s Financial 
Statement Notes
■■Property, plant, and equipment

■■Leasing and rental assets
■■Capitalization of borrowing costs
■■Equity-  accounted investments
■■Financial instruments
■■Loans and receivables and financial liabilities
■■Available-  for- sale financial assets
■■Derivatives and hedge accounting

Monitoring Developments in Financial Reporting Standards 81
■■Receivables from finance leases
■■Other receivables and financial assets
■■Impairment losses on financial instruments
■■Deferred taxes
■■Non-  current assets held for sale and discontinued operations
■■Pension provisions
■■Provisions for taxes
■■Other provisions
■■Liabilities
■■Revenue and expense recognition
8.3.2  Disclosures Regarding Changes in Accounting Policies
Companies must disclose information about changes in accounting policies. Such 
changes can occur as a result of initially applying a new accounting standard or as a 
result of the company voluntarily changing which policy it uses (among those allow -
able). In addition, IFRS require discussion about pending implementations of new 
standards and the known or estimable information relevant to assessing the impact 
of the new standards.40 These disclosures can alert an analyst to significant changes

in reported financial statement amounts that could affect security valuation. Although 
each discussion will be different, the conclusions that a company can reach about a 
new standard not yet implemented include:
1 the standard does not apply;
2 the standard will have no material impact;
3 management is still evaluating the impact; or
4 the impact of adoption is discussed.
Clearly, disclosures indicating the expected impact provide the most meaningful 
information. In addition, disclosures indicating that the standard does not apply or 
will not have a material effect are also helpful. However, disclosures indicating that 
management is still evaluating the impact of a new standard create some uncertainty 
about whether the change might materially affect the company.
In addition to the disclosures referred to in Exhibits 10 and 11, Volkswagen also 
provided extensive disclosures about recently issued accounting standards in its 2009

Annual Report. The company confirmed it had adopted all accounting pronouncements 
required to be applied starting in fiscal year 2009, stated the impact of four new or 
revised standards, and listed nine other standards that had no material effect on the 
company’s financial reports. In addition, Volkswagen provided a table summarizing 
standards that had been adopted by the IASB but were not required to be applied for 
fiscal year 2009. The table listed 17 specific standards changes, of which the company 
expected 14 to have no impact and the other three to result in non-  quantified changes 
in disclosures or presentations.Exhibit 11   (Continued)
40 IAS No. 8, Accounting Policies, Changes in Accounting Estimates and Errors .

Reading 22 ■ Financial Reporting Standards 82
In some cases, companies are able to quantify the expected impact of accounting 
standards that have been changed but are not yet effective at the time of the company’s 
report. As an example of quantified disclosures about accounting changes that would 
have a future effect on a company’s financial statements, consider the disclosures in 
Exhibit 12.
Exhibit 12   Impact of New and Amended Accounting Standards: General 
Electric
In its 2009 annual report filed with the SEC in February 2010, General Electric 
(which reports under US GAAP) included disclosures in its MD&A about an 
accounting change that would require consolidation of certain entities that pre -
viously had not been consolidated. The acronym ASU stands for “ Accounting 
Standards Update” and is the means by which the FASB communicates changes 
to US GAAP following the Financial Standards Codification in 2009. The acronym

ASC stands for “ Accounting Standards Codification” and refers to a particular 
section of the Codification.
In 2009, the FASB issued ASU 2009–16 and ASU 2009–17, 
which amended ASC 860, Transfers and Servicing , and ASC 810, 
Consolidation , respectively, and are effective for us on January  1, 
2010…
Upon adoption of the amendments on January 1, 2010, we will 
consolidate the assets and liabilities of these entities at the amount 
they would have been reported in our financial statements had we 
always consolidated them. We will also deconsolidate certain enti -
ties where we do not meet the definition of the primary beneficiary 
under the revised guidance, the effect of which will be insignificant. 
The incremental effect of consolidation on total assets and liabili -
ties, net of our investment in these entities, will be an increase of 
approximately $32 billion and $34 billion, respectively. There also will 
be a net reduction of equity of approximately $2 billion, principally

related to the reversal of previously recognized securitization gains 
as a cumulative effect adjustment to retained earnings, which will be 
earned back over the life of the assets.
Source:  General Electric 2009 Annual Report.
An analyst could use these disclosures to adjust expectations about the company’s 
assets, liabilities, and equity, and confirm the impact (which in this case appear to be 
minimal) on the company’s leverage ratios. Importantly, because these disclosures 
relate to expected changes, the analyst could incorporate these disclosures into fore -
casts of financial statements.
SUMMARY
An awareness of the reporting framework underlying financial reports can assist in 
security valuation and other financial analysis. The framework describes the objectives 
of financial reporting, desirable characteristics for financial reports, the elements 
of financial reports, and the underlying assumptions and constraints of financial

Summary 83
reporting. An understanding of the framework, which is broader than knowledge of a 
particular set of rules, offers an analyst a basis from which to infer the proper financial 
reporting, and thus security valuation implications, of any financial statement element 
or transaction. The reading discusses the conceptual objectives of financial report -
ing standards, the parties involved in standard-  setting processes, and how financial 
reporting standards are converging into one global set of standards.
Some key points of the reading are summarized below:
■■The Objective of Financial Reporting :
■●The objective of general purpose financial reporting is to provide finan -
providing resources to the entity. Those decisions involve buying, selling, 
or holding equity and debt instruments, and providing or settling loans and

other forms of credit.41
■●Financial reporting requires policy choices and estimates. These choices and 
estimates require judgment, which can vary from one preparer to the next. 
Accordingly, standards are needed to ensure increased consistency in these 
judgments.
■■Financial Reporting Standard-  Setting Bodies and Regulatory Authorities : Private 
sector standard setting bodies and regulatory authorities play significant but 
different roles in the standard setting process. In general, standard setting bod -
ies make the rules, and regulatory authorities enforce the rules. However, regu -
lators typically retain legal authority to establish financial reporting standards in 
their jurisdiction.
■■Convergence of Global Financial Reporting Standards : The IASB and FASB, 
along with other standard setters, worked to achieve convergence of financial 
reporting standards. Many countries have adopted or permit the use of IFRS,

have indicated that they will adopt IFRS in the future, or have indicated that 
they are working on convergence with IFRS. Listed companies in many coun -
tries are adopting IFRS. Barriers and challenges to full convergence still exist.
■■The IFRS Framework : The IFRS Framework  sets forth the concepts that under -
lie the preparation and presentation of financial statements for external users, 
provides further guidance on the elements from which financial statements are 
constructed, and discusses concepts of capital and capital maintenance.
■●The objective of fair presentation of useful information is the center 
of the Conceptual Framework  (2010 ). The qualitative characteristics of 
useful information include fundamental and enhancing characteristics. 
Information must exhibit the fundamental characteristics of relevance and 
faithful representation to be useful. The enhancing characteristics identified 
are comparability, verifiability, timeliness, and understandability.

■●The IFRS Framework  identifies the following elements of financial state -
ments: assets, liabilities, equity, income, expenses, and capital maintenance 
adjustments.
■●The Conceptual Framework  (2010 ) is constructed based on the underly -
ing assumptions of accrual basis and going concern and acknowledges the 
inherent constraint of benefit versus cost.
41 Conceptual Framework for Financial Reporting (2010) , International Accounting Standards Board, 
2010, Chapter 1, OB2.

Reading 22 ■ Financial Reporting Standards 84
■■IFRS Financial Statements : IAS No. 1 prescribes that a complete set of financial 
statements includes a statement of financial position (balance sheet), a state -
ment of comprehensive income (either two statements—one for net income 
and one for comprehensive income—or a single statement combining both net 
income and comprehensive income), a statement of changes in equity, a cash 
flow statement, and notes. The notes include a summary of significant account -
ing policies and other explanatory information.
■●Financial statements need to reflect certain basic features: fair presentation, 
going concern, accrual basis, materiality and aggregation, no offsetting, and 
consistency.
■●Financial statements must be prepared at least annually and must include 
comparative information from the previous period.
■●Financial statements must follow certain presentation requirements includ -
ing a classified balance sheet, minimum information on the face of the

financial statements and in the notes.
■■Characteristics of a Coherent Financial Reporting Framework : Effective frame -
works share three characteristics: transparency, comprehensiveness, and 
consistency. Effective standards can, however, differ on appropriate valuation 
bases, the basis for standard setting (principle or rules based), and resolution of 
conflicts between balance sheet and income statement focus.
■■Comparison of IFRS with Alternative Reporting Systems : A significant number of 
the world’s listed companies report under either IFRS or US GAAP .
■●In most cases, a user of financial statements will lack the information 
necessary to make specific adjustments required to achieve comparabil -
ity between companies that use IFRS and companies that use US GAAP . 
Instead, an analyst must maintain general caution in interpreting compara -
tive financial measures produced under different accounting standards and 
monitor significant developments in financial reporting standards.

■■Monitoring Developments : Analysts can remain aware of ongoing developments 
in financial reporting by monitoring three areas: new products or types of 
transactions; actions of standard setters, regulators, and other groups; and com -
pany disclosures regarding critical accounting policies and estimates.

Practice Problems 85
1 Which of the following is most likely  not an objective of financial statements?
A To provide information about the performance of an entity.
B To provide information about the financial position of an entity.
C To provide information about the users of an entity’s financial statements.
2 International financial reporting standards are currently developed by which 
entity?
A The IFRS Foundation.
B The International Accounting Standards Board.
C The International Organization of Securities Commissions.
3 US generally accepted accounting principles are currently developed by which 
entity?
A The Securities and Exchange Commission.
B The Financial Accounting Standards Board.
C The Public Company Accounting Oversight Board.
4 Which of the following statements about desirable attributes of accounting 
standards boards is most  accurate? Accounting standards boards should:
A concede to political pressures.
B be guided by a well articulated framework.

C be adequately funded by companies to which the standards apply.
5 A core objective of the International Organization of Securities Commissions is 
to:
A eliminate systemic risk.
B protect users of financial statements.
C ensure that markets are fair, efficient, and transparent.
6 According to the Conceptual Framework for Financial Reporting (2010) , which 
of the following is not an enhancing qualitative characteristic of information in 
financial statements?
A Accuracy.
B Timeliness.
C Comparability.
7 Which of the following is not a constraint on the financial statements according 
to the Conceptual Framework  (2010 )?
A Understandability.
B Benefit versus cost.
C Balancing of qualitative characteristics.
8 The assumption that an entity will continue to operate for the foreseeable future 
is called:
A accrual basis.
B comparability.
C going concern.
© 2011 CFA Institute. All rights reserved.

Reading 22 ■ Financial Reporting Standards 86
9 The assumption that the effects of transactions and other events are recognized 
when they occur, not when the cash flows occur, is called:
A relevance.
B accrual basis.
10 Neutrality of information in the financial statements most closely contributes to 
which qualitative characteristic?
A Relevance.
B Understandability.
C Faithful representation.
11 Valuing assets at the amount of cash or equivalents paid or the fair value of 
the consideration given to acquire them at the time of acquisition most closely 
describes which measurement of financial statement elements?
A Current cost.
B Historical cost.
C Realizable value.
12 The valuation technique under which assets are recorded at the amount that 
would be received in an orderly disposal is:
A current cost.
B present value.
C realizable value.
13 Which of the following is not a required financial statement according to IAS 
No. 1?
A Statement of financial position.

No. 1?
B Statement of changes in income.
C Statement of comprehensive income.
14 Which of the following elements of financial statements is most  closely related 
to measurement of performance?
A Assets.
B Expenses.
C Liabilities.
15 Which of the following elements of financial statements is most  closely related 
to measurement of financial position?
A Equity.
B Income.
C Expenses.
16 Which of the following is not a characteristic of a coherent financial reporting 
A Timeliness.
B Consistency.
C Transparency.
17 Which of the following is not a recognized approach to standard-  setting?
A A rules-  based approach.
B An asset/liability approach.
C A principles-  based approach.

Practice Problems 87
18 Which of the following disclosures regarding new accounting standards pro -
vides the most  meaningful information to an analyst?
A The impact of adoption is discussed.
B The standard will have no material impact.
C Management is still evaluating the impact.

Reading 22 ■ Financial Reporting Standards 88
SOLUTIONS
1 C is correct. Financial statements provide information, including information 
about the entity’s financial position, performance, and changes in financial posi -
tion, to users. They do not typically provide information about users.
2 B is correct. The IASB is currently charged with developing International 
Financial Reporting Standards.
3 B is correct. The FASB is responsible for the Accounting Standards 
Codification™, the single source of nongovernmental authoritative US generally 
accepted accounting principles.
4 B is correct. Accounting standards boards should be guided by a well articu -
lated framework. They should be independent; and while they consider input 
from stakeholders, the process should not be compromised by pressure from 
external forces, including political pressure. Accounting standards boards 
should have adequate resources.
5 C is correct. A core objective of IOSCO is to ensure that markets are fair, effi -

cient, and transparent. The other core objectives are to reduce, not eliminate, 
systemic risk and to protect investors, not all users of financial statements.
6 A is correct. Accuracy is not an enhancing qualitative characteristic. Faithful 
representation, not accuracy, is a fundamental qualitative characteristic.
7 A is correct. Understandability is an enhancing qualitative characteristic of 
financial information—not a constraint.
8 C is correct. The Conceptual Framework  (2010 ) identifies two important under -
lying assumptions of financial statements: accrual basis and going concern. 
Going concern is the assumption that the entity will continue to operate for the 
foreseeable future. Enterprises with the intent to liquidate or materially curtail 
9 B is correct. Accrual basis reflects the effects of transactions and other events 
being recognized when they occur, not when the cash flows. These effects are

recorded and reported in the financial statements of the periods to which they 
relate.
10 C is correct. The fundamental qualitative characteristic of faithful representa -
tion is contributed to by completeness, neutrality, and freedom from error.
11 B is correct. Historical cost is the consideration paid to acquire an asset.
12 C is correct. The amount that would be received in an orderly disposal is realiz -
able value.
13 B is correct. There is no statement of changes in income. Under IAS No. 1, a 
complete set of financial statements includes a statement of financial position, a 
statement of comprehensive income, a statement of changes in equity, a state -
ment of cash flows, and notes comprising a summary of significant accounting 
policies and other explanatory information.
14 B is correct. The elements of financial statements related to the measure of 
performance are income and expenses.
15 A is correct. The elements of financial statements related to the measurement of

financial position are assets, liabilities, and equity.
16 A is correct. Timeliness is not a characteristic of a coherent financial reporting 
framework. Consistency, transparency, and comprehensiveness are characteris -
tics of a coherent financial reporting framework.

Solutions 89
17 B is correct. Rules-  based, principles-  based, and objectives-  oriented approaches 
are recognized approaches to standard-  setting.
18 A is correct. A discussion of the impact would be the most meaningful, 
although B would also be useful.

and Analysis (2)
This study session addresses the three major financial statements—the income 
statement, the balance sheet, and the cash flow statement—by examining each in 
turn. The purpose, elements of, construction, pertinent ratios, and common-  size 
analysis are presented for each major financial statement. The session concludes with 
a discussion of financial analysis techniques including the use of ratios to evaluate 
corporate financial health. 
Reading 23 Understanding Income Statements  
by Elaine Henry, PhD, CFA, and Thomas R. 
Robinson, PhD, CFA
Reading 24 Understanding Balance Sheets  
Reading 25 Understanding Cash Flow Statements  
by Elaine Henry, PhD, CFA, Thomas R. Robinson, PhD, CFA, 
Jan Hendrik van Greuning, DCom, CFA, and Michael A. 
Broihahn, CPA, CIA, CFA
Reading 26 Financial Analysis Techniques  
by Elaine Henry, PhD, CFA, Thomas R. Robinson, PhD, CFA,

and Jan Hendrik van Greuning, DCom, CFA FINANCIAL  REPORTIN g AN d A NALYSIS
7
specific definition is given,

readings.

Understanding Income Statements
a. describe the components of the income statement and alternative 
presentation formats of that statement;
b. describe general principles of revenue recognition and 
accrual accounting, specific revenue recognition applications 
(including accounting for long-  term contracts, installment 
sales, barter transactions, gross and net reporting of revenue), 
and implications of revenue recognition principles for financial 
analysis;
c. calculate revenue given information that might influence the 
choice of revenue recognition method;
d. describe key aspects of the converged accounting standards 
for revenue recognition issued by the International Accounting 
Standards Board and Financial Accounting Standards Board in 
May 2014;

May 2014;
e. describe general principles of expense recognition, specific 
expense recognition applications, and implications of expense 
recognition choices for financial analysis;
f. describe the financial reporting treatment and analysis of non-  
recurring items (including discontinued operations, unusual or 
infrequent items) and changes in accounting policies;
g. distinguish between the operating and non-  operating components 
of the income statement;
h. describe how earnings per share is calculated and calculate 
and interpret a company’s earnings per share (both basic and 
diluted earnings per share) for both simple and complex capital 
structures;
i. distinguish between dilutive and antidilutive securities and 
describe the implications of each for the earnings per share 
calculation;
(continued)REA dINg
23
© 2015 CFA Institute. All rights reserved.Note:  Changes in accounting 

Reading 23 ■ Understanding Income Statements 94
j. convert income statements to common-  size income statements;
k. evaluate a company’s financial performance using common-  size 
income statements and financial ratios based on the income 
statement;
l. describe, calculate, and interpret comprehensive income;
m. describe other comprehensive income and identify major types of 
items included in it.
The income statement presents information on the financial results of a company’s 
business activities over a period of time. The income statement communicates how 
much revenue the company generated during a period and what costs it incurred in 
connection with generating that revenue. The basic equation underlying the income 
statement, ignoring gains and losses, is Revenue minus Expenses equals Net income. 
The income statement is also sometimes referred to as the “statement of operations, ”

“statement of earnings, ” or “profit and loss (P&L) statement. ” Under International 
Financial Reporting Standards (IFRS), the income statement may be presented as 
a separate statement followed by a statement of comprehensive income that begins 
with the profit or loss from the income statement or as a section of a single statement 
of comprehensive income.1 US generally accepted accounting principles (US GAAP) 
permit the same alternative presentation formats.2 This reading focuses on the income 
statement, but also discusses comprehensive income (profit or loss from the income 
statement plus other comprehensive income).
Investment analysts intensely scrutinize companies’ income statements.3 Equity 
analysts are interested in them because equity markets often reward relatively high- 
or low-  earnings growth companies with above-  average or below-  average valuations, 
respectively, and because inputs into valuation models often include estimates of

earnings. Fixed-  income analysts examine the components of income statements, past 
and projected, for information on companies’ abilities to make promised payments on 
their debt over the course of the business cycle. Corporate financial announcements 
frequently emphasize information reported in income statements, particularly earn -
ings, more than information reported in the other financial statements.
This reading is organized as follows: Section 2 describes the components of the 
income statement and its format. Section 3 describes basic principles and selected 
applications related to the recognition of revenue, and Section 4 describes basic 1
1 The International Accounting Standards Board (IASB) issues International Financial Reporting Standards 
(IFRS), which have been adopted as the accounting standards in many countries in the world. International 
Accounting Standard (IAS) 1, Presentation of Financial Statements , establishes the presentation and mini -

mum content requirements of financial statements and guidelines for the structure of financial statements.
2 The single authoritative source of US GAAP is the Financial Accounting Standards Board (FASB) 
Accounting Standards Codification™ (FASB ASC). FASB ASC Section 220-  10- 45 [Comprehensive Income–
Overall–Other Presentation Matters] discusses acceptable formats in which to present income, other 
comprehensive income, and comprehensive income.
3 In this reading, the term income statement  will be used to describe either the separate statement that 
reports profit or loss used for earnings per share calculations or that section of a statement of comprehensive 
income that reports the same profit or loss.

Components and Format of the Income Statement 95
principles and selected applications related to the recognition of expenses. Section 5 
covers non-  recurring items and non-  operating items. Section 6 explains the calculation 
of earnings per share. Section 7 introduces income statement analysis, and Section 8 
explains comprehensive income and its reporting. A summary of the key points and 
practice problems in the CFA Institute multiple choice format complete the reading.
COMPONENTS AND FORMAT OF THE INCOME 
STATEMENT
On the top line of the income statement, companies typically report revenue. Revenue  
generally refers to amounts charged (and expected to be received) for the delivery 
of goods or services in the ordinary activities  of a business. The term net revenue  
means that the revenue number is reported after adjustments (e.g., for cash or volume 
discounts, or for estimated returns). Revenue may be called sales or turnover.4 Exhibits

1 and 2 show the income statements for Groupe Danone, a French food manufacturer, 
and Kraft Foods, a US food manufacturer.5 For the year ended 31 December 2009, 
Danone reports €14.98 billion of net revenue, whereas Kraft reports $40.39 billion 
of net revenue.
Exhibit 1   Groupe Danone Consolidated Income Statement (in Millions of 
Euros) 
Y ear Ended 31 December
2008 2009
Net revenue 15,220 14,982
Cost of goods sold (7,172) (6,749)
Selling expenses (4,197) (4,212)
General and administrative expenses (1,297) (1,356)
Research and development expenses (198) (206)
Other revenue (expense) (86) (165)
Trading operating income 2,270 2,294
Other operating income (expense) (83) 217
Operating income 2,187 2,511
Interest revenue 58 76
Interest expense (497) (340)
Cost of net debt (439) (264)
Other financial revenue (expense) (145) (225)
Income before tax 1,603 2,022
Income tax (443) (424)
Income from fully consolidated companies 1,160 1,5982

4 Sales  is sometimes understood to refer to the sale of goods, whereas revenue  can include the sale of 
goods or services; however, the terms are often used interchangeably. In some countries, such as South 
Africa, turnover may be used in place of revenue. For an example of this, the reader can look at the Sasol 
Annual Financial Statements 2009.
5 Following net income, the income statement will also present earnings per share , the amount of earn -
ings per common share of the company. Earnings per share will be discussed in detail later in this reading, 
and the per-  share display has been omitted from these exhibits to focus on the core income statement.

Reading 23 ■ Understanding Income Statements 96
2008 2009
Share of profits of associates 62 (77)
Net income from continuing operations 1,222 1,521
Net income from discontinued operations 269 —
NET INCOME 1,491 1,521
  Attributable to the Group 1,313 1,361
  Attributable to minority interests 178 160
Exhibit 2   Kraft Foods and Subsidiaries Consolidated Statements of Earnings (in Millions of Dollars, except 
Per-  Share Data)
2009 2008 2007
Net revenues $40,386 $41,932 $35,858
Cost of sales 25,786 28,088 23,656
  Gross profit 14,600 13,844 12,202
Marketing, administration, and research costs 9,108 8,862 7,587
Asset impairment and exit costs (64) 1,024 440
(Gains)/Losses on divestitures, net 6 92 (14)
Amortisation of intangibles 26 23 13
  Operating income 5,524 3,843 4,176
Interest and other expense, net 1,237 1,240 604
  Earnings from continuing operations before income taxes 4,287 2,603 3,572
Provision for income taxes 1,259 755 1,080

  Earnings from continuing operations 3,028 1,848 2,492
Earnings and gain from discontinued operations, net of income 
taxes (Note 2) — 1,045 232
  Net earnings 3,028 2,893 2,724
Non-  controlling interest 7 9 3
Net earnings attributable to Kraft Foods $3,021 $2,884 $2,721
Note that Danone lists the years in increasing order from left to right with the 
most recent year in the right-  most column, whereas Kraft lists the years in decreasing 
order with the most recent year listed in the left-  most column. Different orderings of 
chronological information are common. Differences in presentations of items, such 
as expenses, are also common. Expenses  reflect outflows, depletions of assets, and 
incurrences of liabilities in the course of the activities of a business. Expenses may 
be grouped and reported in different formats, subject to some specific requirements. Exhibit 1   (Continued)

Components and Format of the Income Statement 97
For example, Danone reports research and development expenses as a separate line 
item whereas Kraft combines research costs with marketing and administration costs 
and reports the total in a single line item.
Another difference is how the companies indicate that an amount on the income 
statement results in a reduction in net income. Danone shows expenses, such as cost 
of goods sold and selling expenses, in parentheses to explicitly indicate that these 
are subtracted from revenue and reduce net income. Kraft, on the other hand, does 
not place cost of sales in parentheses. Rather, Kraft assumes that the user implicitly 
understands that this is an expense and is subtracted in arriving at gross profit, subto -
tals such as operating earnings, and, ultimately, in net income. In general, companies 
may or may not enclose an amount in parentheses (or use a negative sign) to indicate

that it is a reduction in net income. Furthermore, within a list of items that normally 
reduce net income, an item that increases net income may be shown as a negative. In 
this case, the item is actually added rather than subtracted in calculating net income. 
In summary, because there is flexibility in how companies may present the income 
statement, the analyst should always verify the order of years, how expenses are 
grouped and reported, and how to treat items presented as negatives.
At the bottom of the income statement, companies report net income (companies 
may use other terms such as “net earnings” or “profit or loss”). For 2009, Danone 
reports €1,521 million of net income and Kraft reports $3,028 million of net earnings. 
Net income is often referred to as the “bottom line. ” The basis for this expression is 
that net income is the final—or bottom—line item in an income statement. Because 
net income is often viewed as the single most relevant number to describe a compa -

ny’s performance over a period of time, the term “bottom line” sometimes is used in 
business to refer to any final or most relevant result.
Despite this customary terminology, note that the companies both present another 
item below net income: information about how much of that net income is attributable 
to the company itself and how much of that income is attributable to minority inter -
ests, or non-  controlling interests. Danone and Kraft both consolidate subsidiaries over 
which they have control. Consolidation means that they include all of the revenues 
and expenses of the subsidiaries even if they own less than 100 percent. Minority 
interest represents the portion of income that “belongs” to minority shareholders of 
the consolidated subsidiaries, as opposed to the parent company itself. For Danone, 
€1,361 million of the net income amount is attributable to shareholders of Groupe 
Danone and €160 million is attributable to minority interests. For Kraft, $3,021 mil -

lion of the net earnings amount is attributable to the shareholders of Kraft Foods and 
$7 million is attributable to the non-  controlling interest.
Net income also includes gains  and losses , which are increases and decreases in 
economic benefits, respectively, which may or may not arise in the ordinary activi -
ties of the business. For example, when a manufacturing company sells its products, 
these transactions are reported as revenue, and the costs incurred to generate these 
revenues are expenses and are presented separately. However, if a manufacturing 
company sells surplus land that is not needed, the transaction is reported as a gain 
or a loss. The amount of the gain or loss is the difference between the carrying value 
of the land and the price at which the land is sold. For example, in Exhibit 2, Kraft 
reports a loss (proceeds, net of carrying value) of $6 million on divestitures in fiscal 
2009. Kraft discloses in the notes to consolidated financial statements that the assets

sold included a nutritional energy bar operation in the United States, a juice operation 
in Brazil, and a plant in Spain.

Reading 23 ■ Understanding Income Statements 98
The definition of income encompasses both revenue and gains and the definition of 
expenses encompasses both expenses that arise in the ordinary activities of the busi -
ness and losses.6 Thus, net income  (profit or loss) can be defined as: a) income minus 
expenses, or equivalently b) revenue plus other income plus gains minus expenses, or 
equivalently c) revenue plus other income plus gains minus expenses in the ordinary 
activities of the business minus other expenses, and minus losses. The last definition 
can be rearranged as follows: net income equals (i) revenue minus expenses in the 
ordinary activities of the business, plus (ii) other income minus other expenses, plus 
(iii) gains minus losses.
In addition to presenting the net income, income statements also present items, 
including subtotals, which are significant to users of financial statements. Some of the

items are specified by IFRS but other items are not specified.7 Certain items, such as 
revenue, finance costs, and tax expense, are required to be presented separately on 
the face of the income statement. IFRS additionally require that line items, headings, 
and subtotals relevant to understanding the entity’s financial performance should be 
presented even if not specified. Expenses may be grouped together either by their 
nature or function. Grouping together expenses such as depreciation on manufacturing 
equipment and depreciation on administrative facilities into a single line item called 
“depreciation” is an example of a grouping by nature  of the expense. An example of 
grouping by function  would be grouping together expenses into a category such as 
cost of goods sold, which may include labour and material costs, depreciation, some 
salaries (e.g., salespeople’s), and other direct sales related expenses.8 Both Danone

and Kraft present their expenses by function, which is sometimes referred to “cost 
of sales” method.
One subtotal often shown in an income statement is gross profit  or gross margin  
(that is revenue less cost of sales). When an income statement shows a gross profit 
subtotal, it is said to use a multi-  step format  rather than a single-  step format . The 
Kraft Foods income statement is an example of the multi-  step format, whereas the 
Groupe Danone income statement is in a single-  step format. For manufacturing and 
merchandising companies, gross profit is a relevant item and is calculated as reve -
nue minus the cost of the goods that were sold. For service companies, gross profit 
is calculated as revenue minus the cost of services that were provided. In summary, 
gross profit is the amount of revenue available after subtracting the costs of deliver -
ing goods or services. Other expenses related to running the business are subtracted 
after gross profit.

Another important subtotal which may be shown on the income statement is 
operating profit  (or, synonymously, operating income). Operating profit results from 
deducting operating expenses such as selling, general, administrative, and research 
and development expenses from gross profit. Operating profit reflects a company’s 
profits on its usual business activities before deducting taxes, and for non-  financial 
companies, before deducting interest expense. For financial companies, interest expense 
would be included in operating expenses and subtracted in arriving at operating profit 
because it relates to the operating activities for such companies. For some companies 
composed of a number of separate business segments, operating profit can be useful in 
evaluating the performance of the individual business segments, because interest and 
tax expenses may be more relevant at the level of the overall company rather than an

individual segment level. The specific calculations of gross profit and operating profit 
may vary by company, and a reader of financial statements can consult the notes to 
the statements to identify significant variations across companies.
6 IASB Conceptual Framework for Financial Reporting (2010) , paragraphs 4.29 to 4.32.
7 Requirements are presented in IAS 1, Presentation of Financial Statements.
8 Later readings will provide additional information about alternative methods to calculate cost of goods sold.

Revenue Recognition 99
Operating profit is sometimes referred to as EBIT (earnings before interest and 
taxes). However, operating profit and EBIT are not necessarily the same. Note that in 
both Exhibits 1 and 2, interest and taxes do not represent the only differences between 
earnings (net income, net earnings) and operating income. For example, both com -
panies separately report some income from discontinued operations.
Exhibit 3 shows an excerpt from the income statement of CRA International, a 
company providing management consulting services. Accordingly, CRA deducts cost 
of services (rather than cost of goods) from revenues to derive gross profit. CRA’s fiscal 
year ends on the last Saturday in November, and periodically (for example in 2008) 
its fiscal year will contain 53 weeks rather than 52 weeks. Although the extra week 
is likely immaterial in computing year-  to- year growth rates, it may have a material

impact on a quarter containing the extra week. In general, an analyst should be alert 
to the effect of an extra week when making historical comparisons and forecasting 
future performance.
Exhibit 3   CRA International Inc. Consolidated Statements of Income (Excerpt) (in Thousands of Dollars, 
except Per-  Share Data)
Y ear Ended
28 Nov 2009  
(52 weeks)29 Nov 2008  
(53 weeks)24 Nov 2007  
(52 weeks)
Revenues $301,639 $376,751 $394,645
Costs of services 199,861 251,263 248,514
Gross profit 101,778 125,488 146,131
Selling, general, and administrative expenses 76,124 92,797 90,079
Depreciation and amortisation 8,521 12,699 9,782
Income from operations $17,133 $19,992 $46,270
Note : Remaining items omitted
Exhibits 1, 2, and 3 illustrate basic points about the income statement, including 
variations across the statements—some of which depend on the industry and/or 
country, and some of which reflect differences in accounting policies and practices of

a particular company. In addition, some differences within an industry are primarily 
differences in terminology, whereas others are more fundamental accounting differ -
ences. Notes to the financial statements are helpful in identifying such differences.
Having introduced the components and format of an income statement, the next 
objective is to understand the actual reported numbers in it. To accurately interpret 
reported numbers, the analyst needs to be familiar with the principles of revenue and 
expense recognition—that is, how revenue and expenses are measured and attributed 
to a given accounting reporting period.
REVENUE RECOGNITION
Revenue is the top line in an income statement, so we begin the discussion of line 
items in the income statement with revenue recognition. We will first discuss revenue 
recognition under IFRS and US GAAP prior to the application of converged standards 
issued May 2014. In May 2014, the IASB and FASB issued IFRS 15 and ASC Topic 606,

respectively, for revenue recognition. The nearly identical standards resulted from an 3

Reading 23 ■ Understanding Income Statements 100
effort to achieve convergence, consistency, and transparency in revenue recognition 
globally. Key aspects and some implications of the standards are discussed at the end 
of this section. 
A first task is to explain some relevant accounting terminology. The terms revenue, 
sales, gains, losses, and net income (profit, net earnings) have been briefly defined. 
The IASB Conceptual Framework for Financial Reporting  (2010),9 referred to hereafter 
as the Conceptual Framework , further defines and discusses these income statement 
items. The Framework  explains that profit is a frequently used measure of performance 
and is composed of income and expenses.10 It defines income  as follows:
Income is increases in economic benefits during the accounting period in 
the form of inflows or enhancements of assets or decreases of liabilities 
that result in increases in equity, other than those relating to contributions 
from equity participants.11

In IFRS, the term “income” includes revenue and gains. Gains are similar to reve -
nue, but they typically arise from secondary or peripheral activities rather than from a 
company’s primary business activities. For example, for a restaurant, the sale of surplus 
restaurant equipment for more than its carrying value is referred to as a gain rather 
than as revenue. Similarly, a loss typically arises from secondary activities. Gains and 
losses may be considered part of operating activities (e.g., a loss due to a decline in 
the value of inventory) or may be considered part of non-  operating activities (e.g., 
the sale of non-  trading investments).
In the following simple hypothetical scenario, revenue recognition is straightfor -
ward: a company sells goods to a buyer for cash and does not allow returns, so the 
company recognizes revenue when the exchange of goods for cash takes place and

measures revenue at the amount of cash received. In practice, however, determining 
when revenue should be recognized and at what amount is considerably more complex 
for reasons discussed in the following sections.
3.1 General Principles
An important aspect concerning revenue recognition is that it can occur independently 
of cash movements. For example, assume a company sells goods to a buyer on credit, 
so does not actually receive cash until some later time. A fundamental principle of 
accrual accounting is that revenue is recognized (reported on the income statement) 
when it is earned, so the company’s financial records reflect revenue from the sale 
when the risk and reward of ownership is transferred; this is often when the company 
delivers the goods or services. If the delivery was on credit, a related asset, such as 
trade or accounts receivable, is created. Later, when cash changes hands, the compa -

ny’s financial records simply reflect that cash has been received to settle an account 
receivable. Similarly, there are situations when a company receives cash in advance 
and actually delivers the product or service later, perhaps over a period of time. In 
this case, the company would record a liability for unearned revenue  when the cash 
is initially received, and revenue would be recognized as being earned over time as 
products and services are delivered. An example would be a subscription payment 
received for a publication that is to be delivered periodically over time.
9 The IASB is currently in the process of updating its Conceptual Framework for Financial Reporting .
10 Conceptual Framework , paragraph 4.24. The text on the elements of financial statements and their rec -
ognition and measurement is the same in the IASB Conceptual Framework  for Financial Reporting  (2010) 
and the IASB Framework for the Preparation and Presentation of Financial Statements  (1989).

Revenue Recognition 101
When to recognize revenue (report it on the income statement) is a critical issue 
in accounting. Up until 1 January 2018, the original international accounting standard 
(IAS 18), which has been replaced by IFRS 15, specified that revenue from the sale of 
goods should be recognized when the following conditions are satisfied:12
■■the entity has transferred to the buyer the significant risks and rewards of own -
ership of the goods;
■■the entity retains neither continuing managerial involvement to the degree usu -
ally associated with ownership nor effective control over the goods sold;
■■the amount of revenue can be measured reliably;
■■it is probable that the economic benefits associated with the transaction will 
flow to the entity; and
■■the costs incurred or to be incurred in respect of the transaction can be mea -
sured reliably.
In simple words, this basically says revenue is recognized when the seller no longer

bears risks with respect to the goods (for example, if the goods were destroyed by fire, 
it would be a loss to the purchaser), the seller cannot tell the purchaser what to do 
with the goods, the seller knows what it expects to collect and is reasonably certain 
of collection, and the seller knows how much the goods cost.
The transfer of the risks and rewards of ownership normally occurs when goods 
are delivered to the buyer or when legal title to goods transfers. However, as noted by 
the above remaining conditions, physical transfer of goods will not always result in the 
recognition of revenue. For example, if goods are delivered to a retail store to be sold 
on consignment and title is not transferred, the revenue would not yet be recognized.13
IAS 18 specifed similar criteria for recognizing revenue for the rendering of ser -
vices.14 When the outcome could be estimated reliably, revenue associated with the

transaction was recognized by reference to the stage of completion of the transaction 
at the balance sheet date. The conditions for determining whether a transaction could 
be estimated reliably were as follows:
flow to the entity;
■■the stage of completion of the transaction at the balance sheet date can be mea -
sured reliably; and
■■the costs incurred for the transaction and the costs to complete the transaction 
can be measured reliably.
Similar criteria have been applied to recognizing interest, royalties, and dividends: 
it is probable that the economic benefits associated with the transaction will flow to 
the entity and the amount of the revenue can be reliably measured.
US GAAP15 specify that revenue should be recognized when it is “realized or real -
izable and earned. ” The US Securities and Exchange Commission (SEC),16 motivated

in part because of the frequency with which overstating revenue occurs in connection 
12 IAS No. 18, Revenue , paragraph 14.
13 IAS 18 IE describes a “consignment sale” as one in which the recipient undertakes to sell the goods on 
behalf of the shipper (seller). Revenue is recognized by the shipper when the recipient sells the goods to a 
third party. IAS 18 IE, Illustrative Examples , paragraph 2.
14 IAS No. 18, Revenue , paragraph 20.
15 FASB ASC Section 605-  10- 25 [Revenue Recognition-  Overall-  Recognition].
16 The content of SEC Staff Accounting Bulletin 101 is contained in FASB ASC Section 605-  10- S99 
[Revenue Recognition–Overall–SEC Materials].

Reading 23 ■ Understanding Income Statements 102
with fraud and/or misstatements, provides guidance on how to apply the accounting 
principles. This guidance lists four criteria to determine when revenue is realized or 
realizable and earned:
1 There is evidence of an arrangement between buyer and seller. For instance, this 
would disallow the practice of recognizing revenue in a period by delivering the 
product just before the end of an accounting period and then completing a sales 
contract after  the period end.
2 The product has been delivered, or the service has been rendered. For instance, 
this would preclude revenue recognition when the product has been shipped 
but the risks and rewards of ownership  have not actually passed  to the buyer.
3 The price is determined, or determinable. For instance, this would preclude a 
company from recognizing revenue that is based on some contingency .
4 The seller is reasonably sure of collecting money. For instance, this would

preclude a company from recognizing revenue when the customer is unlikely to 
pay.
Companies must disclose their revenue recognition policies in the notes to their 
financial statements (sometimes referred to as footnotes). Analysts should review 
these policies carefully to understand how and when a company recognizes revenue, 
which may differ depending on the types of product sold and services rendered. 
Exhibit 4 presents a portion of the summary of significant accounting policies note 
that discusses revenue recognition for DaimlerChrysler from its 2009 annual report, 
prepared under IFRS.
Exhibit 4   Excerpt from DaimlerChrysler Notes
Revenue from sales of vehicles, service parts and other related prod -
ucts is recognized when the risks and rewards of ownership of the 
goods are transferred to the customer, the amount of revenue can be 
estimated reliably and collectability is reasonably assured. Revenue is 
recognized net of discounts, cash sales incentives, customer bonuses

and rebates granted.
Daimler uses price discounts in response to a number of market 
and product factors, including pricing actions and incentives offered 
by competitors, the amount of excess industry production capacity, 
the intensity of market competition and consumer demand for the 
product. The Group may offer a variety of sales incentive programs 
at any point in time, including cash offers to dealers and consumers, 
lease subsidies which reduce the consumers’ monthly lease payment, 
or reduced financing rate programs offered to consumers.
An analyst comparing Daimler with another company would likely want to ensure 
that revenue recognition policies are similar. For example, Daimler notes that it rec -
ognizes its revenue net of certain items. Does the comparison company deduct the 
same items from revenue? Exhibit 5 presents excerpts from the 2009 annual report’s 
notes to the financial statements of Ford Motor Company prepared under US GAAP .

In Ford’s Note 2, Summary of Accounting Policies, the section titled revenue recogni -
tion mentions the criteria and timing of revenue recognition, but not the recognition 
of revenue net of certain items. In a subsequent section of Note 2, Ford states that

Revenue Recognition 103
its marketing incentives are recognized as revenue reductions. A comparison of the 
disclosed revenue recognition policies suggests that the companies do have similar 
revenue recognition policies despite minor differences in presentation.
Exhibit 5   Excerpt from Ford Motor Company Notes
Revenue Recognition — Automotive Sector
Automotive sales consist primarily of revenue generated from the 
sale of vehicles. Sales are recorded when the risks and rewards of 
ownership are transferred to our customers (generally dealers and 
distributors). For the majority of our sales, this occurs when prod -
ucts are shipped from our manufacturing facilities or delivered to 
our customers. When vehicles are shipped to customers or vehicle 
modifiers on consignment, revenue is recognized when the vehicle 
is sold to the ultimate customer.
[portions omitted ]
Marketing Incentives and Interest Supplements
Marketing incentives generally are recognized by the Automotive

sector as revenue reductions in Automotive sales. These include cus -
tomer and dealer cash payments and costs for special financing and 
leasing programs paid to the Financial Services sector. The revenue 
reductions are accrued at the later of the date the related vehicle sales 
to the dealers are recorded or the date the incentive program is both 
approved and communicated. We generally estimate these accruals 
using marketing programs that are approved as of the balance sheet 
date and are expected to be effective at the beginning of the subse -
quent period. The Financial Services sector identifies payments for 
special financing and leasing programs as interest supplements or 
other support costs and recognizes them consistent with the earnings 
process of the underlying receivable or operating lease.
The topic of revenue recognition remains important and new challenges have 
evolved, particularly in areas of e-  commerce and services such as software development.

Standard setters continue to evaluate current revenue recognition standards and issue 
new guidance periodically to deal with new types of transactions. Additionally, there 
are occasional special cases for revenue recognition, as discussed in the next section.
3.2 Revenue Recognition in Special Cases
The general principles discussed above are helpful for dealing with most revenue rec -
ognition issues. There are some instances where revenue recognition is more difficult 
to determine. For example, in limited circumstances, revenue may be recognized before 
or after goods are delivered or services are rendered, as summarized in Exhibit 6.

Reading 23 ■ Understanding Income Statements 104
Exhibit 6   Revenue Recognition in Special Cases
Before  Goods Are Fully 
Delivered or Services 
Completely RenderedAt the Time Goods Are 
RenderedAfter  Goods Are Delivered 
or Services Rendered
For example, with long-  
term contracts where the 
outcome can be reliably 
measured, the percentage-  
of- completion method is 
used.Recognize revenues using 
normal revenue recogni -
tion criteria.For example, with real 
estate sales where there 
is doubt about the buy -
er’s ability to complete 
payments, the installment 
method and cost recovery 
method are appropriate.
The following sections discuss revenue recognition in the case of long-  term con -
tracts, installment sales, and barter.
3.2.1  Long-  Term Contracts
A long-  term contract  is one that spans a number of accounting periods. Such 
contracts raise issues in determining when the transaction has been completed and

revenue recognition should occur. How should a company apportion the revenue 
earned under a long-  term contract to each accounting period? If, for example, the 
contract is a service contract or a licensing arrangement, the company may recognize 
the revenue on a prorated basis over the period of the contract rather than at the end 
of the contract term. Under the original IAS standards (IAS 18 and IAS 11), this was 
done using the percentage-  of- completion method.17 Under this method, revenue 
is recognized based on the stage of completion of a transaction or contract and is, 
thus, recognized when the services are rendered. Construction contracts are notable 
examples of such contracts.18 When the outcome of a construction contract could be 
measured reliably, revenue and expenses were recognized in reference to the stage of 
completion. US GAAP have similar requirements for long-  term contracts including 
construction contracts.

Under the percentage-  of- completion  method, in each accounting period, the 
company estimates what percentage of the contract is complete and then reports 
that percentage of the total contract revenue in its income statement. Contract costs 
for the period are expensed against the revenue. Therefore, net income or profit is 
reported each year as work is performed.
Under IFRS, if the outcome of the contract cannot be measured reliably, then 
revenue may be recognized to the extent of contract costs incurred (but only if it is 
probable the costs will be recovered). Costs are expensed in the period incurred. Under 
this method, no profit is recognized until all the costs had been recovered. Under US 
GAAP , but not under IFRS, a revenue recognition method used when the outcome 
cannot be measured reliably is the completed contract method. Under the completed 
contract  method, the company does not report any income until the contract is

substantially finished (the remaining costs and potential risks are insignificant in 
amount), although provision should be made for expected losses. Billings and costs are 
accumulated on the balance sheet rather than flowing through the income statement. 
Under US GAAP , the completed contract method is also acceptable when the entity 
17 IAS No. 18, Revenue , paragraph 21.
18 IAS No. 11, Construction Contracts .

Revenue Recognition 105
has primarily short-  term contracts. Note that if a contract is started and completed 
in the same period, there is no difference between the percentage-  of- completion and 
completed contract methods.
Examples 1, 2, and 3 provide illustrations of these revenue recognition methods. As 
shown, the percentage-  of- completion method results in revenue recognition sooner 
than the completed contract method and thus may be considered a less conservative 
approach. In addition, the percentage-  of- completion method relies on management 
estimates and is thus not as objective as the completed contract method. However, an 
advantage of the percentage-  of- completion method is that it results in better matching 
of revenue recognition with the accounting period in which it was earned. Because 
of better matching with the periods in which work is performed, the percentage-  of- 
completion method is the preferred method of revenue recognition for long-  term

contracts and is required when the outcome can be measured reliably under both IFRS 
and US GAAP . Under both IFRS and US GAAP , if a loss is expected on the contract, 
the loss is reported immediately, not upon completion of the contract, regardless of 
the method used (e.g., percentage-  of- completion or completed contract).
EXAMPLE 1   
Revenue Recognition for Long-  Term Contracts: 
Recognizing Revenue on a Prorated Basis
New Era Network Associates has a five-  year license to provide networking sup -
port services to a customer. The total amount of the license fee to be received by 
New Era is $1 million. New Era recognizes license revenue on a prorated basis 
regardless of the time at which cash is received. How much revenue will New 
Era recognize for this license in each year?
Solution:
For this license, New Era Network Associates will recognize $200,000 each year 
for five years (calculated as $1 million divided by 5).
EXAMPLE 2   
Revenue Recognition for Long-  Term Contracts:

Percentage-  of- Completion Method
Stelle Technology has a contract to build a network for a customer for a total 
sales price of €10 million. The network will take an estimated three years to 
build, and total building costs are estimated to be €6 million. Stelle recognizes 
long-  term contract revenue using the percentage-  of- completion method and 
estimates percentage complete based on expenditure incurred as a percentage 
of total estimated expenditures.
1 At the end of Year 1, the company had spent €3 million. Total costs to 
complete are estimated to be another €3 million. How much revenue will 
Stelle recognize in Year 1?

Reading 23 ■ Understanding Income Statements 106
2 At the end of Year 2, the company had spent an additional €2.4 million for 
an accumulated total of €5.4 million. Total costs to complete are estimated 
to be another €0.6 million. How much revenue will Stelle recognize in 
Year 2?
3 At the end of Year 3, the contract is complete. The company spent an 
accumulated total of €6 million. How much revenue will Stelle recognize 
in Year 3?
Stelle has spent 50  percent of the total project costs (€3  million divided by 
€6 million), so in Year 1, the company will recognize 50 percent of the total 
contract revenue (i.e., €5 million).
Because Stelle has spent 90 percent of the total project costs (€5.4 million divided 
by €6 million), by the end of Year 2, it will need to have recognized 90 percent of 
the total contract revenue (i.e., €9 million). Stelle has already recognized €5 mil -
lion of revenue in Year 1, so in Year 2, the company will recognize €4 million

revenue (€9 million minus €5 million).
Because Stelle has spent 100 percent of the total project costs, by the end of Year 
3, it will need to have recognized 100 percent of the total contract revenue (i.e., 
€10 million). Stelle had already recognized €9 million of revenue by the end of 
Year 2, so in Year 3, the company will recognize €1 million revenue (€10 million 
minus €9 million).
Y ear 1 Y ear 2 Y ear 3 Total
Revenue €5 million €4 million €1 million €10 million
EXAMPLE 3   
Revenue Recognition for Long-  Term Contracts: Outcome 
Cannot Be Reliably Measured
Kolenda Technology Group has a contract to build a network for a customer for 
a total sales price of $10 million. This network will take an estimated three years 
to build, but considerable uncertainty surrounds total building costs because 
new technologies are involved. In other words, the outcome cannot be reliably 
measured, but it is probable that the costs up to the agreed upon price will be 
recovered.

Assuming the following expenditures, how much revenue, expense (cost 
of construction), and income would the company recognize each year under 
IFRS and using the completed contract method under US GAAP? The amounts 
periodically billed to the customer and received from the customer are not 
necessarily equivalent to the amount of revenue being recognized in the period. 
For simplicity, assume Kolenda pays cash for all expenditures.
1 At the end of Year 1, Kolenda has spent $3 million.

Revenue Recognition 107
2 At the end of Year 2, Kolenda has spent a total of $5.4 million.
3 At the end of Year 3, the contract is complete. Kolenda spent a total of 
$6 million.
Solution:
Under IFRS, revenue may be recognized to the extent of contract costs incurred 
if the outcome of the contract cannot be measured reliably and it is probable 
that costs will be recovered. In this example, the outcome is uncertain but it is 
probable that Kolenda will recover the costs up to $10 million. Under US GAAP , 
the company would use the completed contract method. No revenue will be 
recognized until the contract is complete.
Year 1 . Under IFRS, Kolenda would recognize $3 million cost of construction, 
$3 million revenue, and thus $0 income. Under US GAAP , Kolenda would rec -
ognize $0 cost of construction, $0 revenue, and thus $0 income. The $3 million 
expenditure would be reported as an increase in the inventory account “con -
struction in progress” and a decrease in cash.

Year 2 . Under IFRS, Kolenda would recognize $2.4 million cost of construction, 
$2.4  million revenue, and thus $0 income. Under US GAAP , Kolenda would 
recognize $0 cost of construction, $0 revenue, and thus $0 income. The $2.4 mil -
lion expenditures would be reported as an increase in the inventory account 
“construction in progress” and a decrease in cash.
Year 3 . Under IFRS, Kolenda would recognize the $0.6  million cost of con -
struction incurred in the period. Because the contract has been completed and 
the outcome is now measurable, the company would recognize the remaining 
$4.6 million revenue on the contract, and thus $4 million income. Under US 
GAAP , because the contract has been completed, Kolenda would recognize the 
total contract revenue (i.e., $10 million). Kolenda would recognize $6 million 
cost of construction and thus $4 million income. The inventory account “con -
struction in progress” would be eliminated.
Summary

Summary
Revenue recognition to the extent of contract costs incurred: IFRS
Revenue $3 million $2.4 million $4.6 million $10 million
Cost of 
construction $3 million $2.4 million $0.6 million $6 million
Profit $0 million $0 million $4 million $4 million
Completed Contract Method: US GAAP
Revenue $0 million $0 million $10 million $10 million
Cost of 
construction $0 million $0 million $6 million $6 million

Reading 23 ■ Understanding Income Statements 108
3.2.2  Installment Sales
As noted above, revenue is normally reported when goods are delivered or services 
are rendered, independent of the period in which cash payments for those goods or 
services are received. This principle applies even to installment sales —sales in which 
proceeds are to be paid in installments over an extended period. For installment sales, 
IFRS separate the installments into the sale price, which is the discounted present 
value of the installment payments, and an interest component. Revenue attributable to 
the sale price is recognized at the date of sale, and revenue attributable to the interest 
component is recognized over time.19 International standards note, however, that the 
guidance for revenue recognition must be considered in light of local laws regarding 
the sale of goods in a particular country. Under limited circumstances, recognition

of revenue or profit may be required to be deferred for some installment sales. An 
example of such deferral arises for certain sales of real estate on an installment basis. 
Revenue recognition for sales of real estate varies depending on specific aspects of 
the sale transaction.20
Under US GAAP , when the seller has completed the significant activities in the 
earnings process and is either assured of collecting the selling price or able to estimate 
amounts that will not be collected, a sale of real estate is reported at the time of sale 
using the normal revenue recognition conditions.21 When those two conditions are 
not fully met, under US GAAP some of the profit is deferred. Two of the methods may 
be appropriate in these limited circumstances and relate to the amount of profit to 
be recognized each year from the transaction: the installment method  and the cost 
recovery method . Under the installment method, the portion of the total profit of

the sale that is recognized in each period is determined by the percentage of the total 
sales price for which the seller has received cash. Under the cost recovery method, the 
seller does not report any profit until the cash amounts paid by the buyer—including 
principal and interest on any financing from the seller—are greater than all the seller’s 
costs of the property. Note that the cost recovery method is similar to the revenue 
recognition method under international standards, described above, when the outcome 
of a contract cannot be measured reliably (although the term cost recovery method 
is not used in the international standard).
Example 4 illustrates the differences between the installment method and the cost 
recovery method. Installment sales and cost recovery treatment of revenue recognition 
are rare for financial reporting purposes, especially for assets other than real estate.
EXAMPLE 4   
The Installment and Cost Recovery Methods of Revenue 
Recognition

Assume the total sales price and cost of a property are $2,000,000 and $1,100,000, 
respectively, so that the total profit to be recognized is $900,000. The amount of 
cash received by the seller as a down payment is $300,000, with the remainder 
of the sales price to be received over a 10-  year period. It has been determined 
19 IAS No. 18 IE, Illustrative Examples , paragraph 8.
20 IFRIC Interpretation 15, Agreements for the Construction of Real Estate , distinguishes three types of 
agreements for real estate construction (construction contract, rendering services, sale of goods) to deter -
mine whether the revenue recognition methods described under long-  term contracts apply.
21 FASB ASC Section 360-  20- 55 [Property, Plant, and Equipment–Real Estate Sales–Implementation 
Guidance and Illustrations].

Revenue Recognition 109
that there is significant doubt about the ability and commitment of the buyer 
to complete all payments. How much profit will be recognized attributable to 
the down payment if:
1 The installment method is used?
2 The cost recovery method is used?
The installment method apportions the cash receipt between cost recov -
ered and profit using the ratio of profit to sales value; here, this ratio equals 
$900,000/$2,000,000 = 0.45 or 45 percent. Therefore, the seller will recognize 
the following profit attributable to the down payment: 45 percent of $300,000 = 
$135,000.
Under the cost recovery method of revenue recognition, the company would not 
recognize any profit attributable to the down payment because the cash amounts 
paid by the buyer still do not exceed the cost of $1,100,000.
3.2.3  Barter
Revenue recognition issues related to barter transactions (non-  monetary exchanges)

became particularly important as e-  commerce developed. As an example, if Company 
A exchanges advertising space for computer equipment from Company B but no 
cash changes hands, can Company A and B both report revenue? Such an exchange 
is referred to as a “barter transaction. ”
An even more challenging revenue recognition issue evolved from a specific type 
of barter transaction, a round-  trip transaction. As an example, if Company A sells 
advertising services (or energy contracts, or commodities) to Company B and almost 
simultaneously buys an almost identical product from Company B, can Company A 
report revenue at the fair value of the product sold? Because the company’s revenue 
would be approximately equal to its expense, the net effect of the transaction would 
have no impact on net income or cash flow. However, the amount of revenue reported 
would be higher, and the amount of revenue can be important to a company’s valuation.

In the earlier stages of e-  commerce, for example, some equity valuations were based 
on sales (because many early internet companies reported no net income).
Under IFRS, revenue from barter transactions must be measured based on the fair 
value of revenue from similar non-  barter transactions with unrelated parties (parties 
other than the barter partner).22 US GAAP state that revenue can be recognized at 
fair value only if a company has historically received cash payments for such services 
and can thus use this historical experience as a basis for determining fair value; oth -
erwise, the revenue from the barter transaction is recorded at the carrying amount 
of the asset surrendered.23
3.2.4  Gross versus Net Reporting
Another revenue recognition issue that became particularly important with the 
emergence of e-  commerce is the issue of gross versus net reporting. Merchandising 
companies typically sell products that they purchased from a supplier. In accounting for

their sales, the company records the amount of the sale proceeds as sales revenue and 
their cost of the products as the cost of goods sold. As internet-  based merchandising 
22 IASB, SIC Interpretation 31, Revenue—Barter Transactions Involving Advertising Services , paragraph 5.
23 FASB ASC paragraph 605-  20- 25- 14 [Revenue Recognition–Services–Recognition–Advertising Barter 
Services].

Reading 23 ■ Understanding Income Statements 110
companies developed, many sold products that they had never held in inventory; 
they simply arranged for the supplier to ship the products directly to the end cus -
tomer. In effect, many such companies were agents of the supplier company, and the 
net difference between their sales proceeds and their costs was equivalent to a sales 
commission. What amount should these companies record as their revenues—the 
gross amount of sales proceeds received from their customers, or the net difference 
between sales proceeds and their cost?
US GAAP indicate that the approach should be based on the specific situation 
and provides guidance for determining when revenue should be reported gross ver -
sus net.24 To report gross revenues, the following criteria are relevant: the company 
is the primary obligor under the contract, bears inventory risk and credit risk, can 
choose its supplier, and has reasonable latitude to establish price. If these criteria are

not met, the company should report revenues net. Example 5 provides an illustration.
EXAMPLE 5   
Gross versus Net Reporting of Revenues
Flyalot has agreements with several major airlines to obtain airline tickets at 
reduced rates. The company pays only for tickets it sells to customers. In the 
most recent period, Flyalot sold airline tickets to customers over the internet 
for a total of $1.1 million. The cost of these tickets to Flyalot was $1 million. 
The company’s direct selling costs were $2,000. Once the customers receive 
their ticket, the airline is responsible for providing all services associated with 
the customers’ flights.
1 Demonstrate the reporting of revenues under:
A gross reporting.
B net reporting.
2 Determine and justify the appropriate method for reporting revenues.
The table below shows how reporting would appear on a gross and a net basis:
A. Gross Reporting B. Net Reporting
Revenues $1,100,000 $100,000
Cost of sales 1,002,000 2,000
Gross margin $ 98,000 $ 98,000

Flyalot should report revenue on a net basis. Flyalot pays only for tickets it sells 
to customers and thus does not bear inventory risk. In addition, the airline—not 
Flyalot—is the primary obligor under the contract. Revenues should be reported 
as $100,000.
24 FASB ASC Section 605-  45- 45 [Revenue Recognition–Principal Agent Considerations–Other Presentation 
Matters].

Revenue Recognition 111
3.3 Implications for Financial Analysis
As we have seen, companies use a variety of revenue recognition methods. Furthermore, 
a single company may use different revenue recognition policies for different businesses. 
Companies disclose their revenue recognition policies in the notes to their financial 
statement, often in the first note.
The following aspects of a company’s revenue recognition policy are particularly 
relevant to financial analysis: whether a policy results in recognition of revenue sooner 
rather than later (sooner is less conservative), and to what extent a policy requires 
the company to make estimates. In order to analyze a company’s financial statements, 
and particularly to compare one company’s financial statements with those of another 
company, it is helpful to understand any differences in their revenue recognition 
policies. Although it may not be possible to calculate the monetary effect of differ -

ences between particular companies’ revenue recognition policies and estimates, it 
is generally possible to characterize the relative conservatism of a company’s policies 
and to qualitatively assess how differences in policies might affect financial ratios.
EXAMPLE 6   
Revenue Recognition Policy for Apple
As disclosed in the excerpt from notes to the consolidated financial statements 
shown below (emphasis added), Apple Inc. uses different revenue recognition 
policies depending on the type of revenue producing activity, including product 
sales, service and support contracts, and products obtained from other compa -
nies. Note that these are only the first three paragraphs of Apple’s disclosure on 
revenue recognition; the entire revenue recognition portion has nine paragraphs.
Revenue Recognition
Net sales consist primarily of revenue from the sale of hardware, 
software, digital content and applications, peripherals, and service

and support contracts. The Company recognizes revenue when per -
suasive evidence of an arrangement exists, delivery has occurred, 
the sales price is fixed or determinable, and collection is probable. 
Product is considered delivered to the customer once it has been 
shipped and title and risk of loss have been transferred. For most of 
the Company’s product sales , these criteria are met at the time the 
product is shipped. For online sales to individuals, for some sales to 
education customers in the United States, and for certain other sales, 
the Company defers revenue until the customer receives the product 
because the Company legally retains a portion of the risk of loss on 
these sales during transit [portions omitted].
Revenue from service and support contracts  is deferred and 
recognized ratably over the service coverage periods. These contracts 
typically include extended phone support, repair services, web-  based 
support resources, diagnostic tools, and extend the service coverage

offered under the Company’s standard limited warranty.
The Company sells software and peripheral products obtained 
from other companies . The Company generally establishes its own 
pricing and retains related inventory risk, is the primary obligor in 
sales transactions with its customers, and assumes the credit risk for 
amounts billed to its customers. Accordingly, the Company gener -
ally recognizes revenue for the sale of products obtained from other 
companies based on the gross amount billed.

Reading 23 ■ Understanding Income Statements 112
Source : Apple Inc. 10-  K/A for the year ended 26 September 2009, as filed 
with the SEC on 25 January 2010. Emphasis added.
1 What criteria does Apple apply to determine when to recognize revenue 
from product sales?
2 What principle underpins the company’s deferral of revenue from service 
and support contracts?
Apple recognizes revenue when persuasive evidence of an arrangement exists, 
delivery has occurred, the sales price is fixed or determinable, and collection 
is probable. Note that these are just the four US GAAP revenue recognition 
criteria described in Section 3.1. Note also that Apple recognizes revenue on 
some product sales at the time of shipment and others at the time of delivery, 
depending on when its risk of loss ends.
The basic principle underpinning the company’s deferral of revenue for service 
and sales contracts is that revenue should be recognized in the period it is earned.

Because service under these contracts will be performed in future periods, the 
company defers the revenue and then recognizes it over the time it is earned.
3.4 Revenue Recognition Accounting Standards Issued 
May 2014
It is clear from the preceding sections that revenue recognition varies globally, which 
makes comparisons of revenue challenging. The converged accounting standards issued 
by the IASB and FASB in May 2014 introduce some changes to the basic principles 
of revenue recognition and should enhance comparability.25 The standards became 
effective for reporting periods beginning after 1 January 2018 under IFRS (IFRS 15) 
and 15 December 2017 under US GAAP . The following section describes key aspects 
of the standards: the core principle, the five steps in recognizing revenue, treatment 
of some related costs, and disclosure requirements.
The content of the two standards is nearly identical, and this discussion pertains

to both, unless specified otherwise. Issuance of this converged standard is significant 
because of the differences between IFRS and US GAAP on revenue recognition prior 
to the converged standard. The converged standard aims to provide a principles-  based 
approach to revenue recognition that can be applied to many types of revenue-  
generating activities.
The core principle of the converged standard is that revenue should be recognized 
to “depict the transfer of promised goods or services to customers in an amount that 
reflects the consideration to which the entity expects to be entitled in an exchange 
for those goods or services. ” To achieve the core principle, the standard describes the 
application of five steps in recognizing revenue:
1 Identify the contract(s) with a customer
2 Identify the separate or distinct performance obligations in the contract
3 Determine the transaction price
25 IFRS 15 Revenue from Contracts with Customers  and FASB ASC Topic 606 (Revenue from Contracts

Revenue Recognition 113
4 Allocate the transaction price to the performance obligations in the contract
5 Recognize revenue when (or as) the entity satisfies a performance obligation 
According to the standard, a contract is an agreement and commitment, with 
commercial substance, between the contacting parties. It establishes each party’s 
obligations  and rights, including payment terms. In addition, a contract exists only if 
collectability is probable. Each standard uses the same wording, but the threshold for 
probable collectability differs. Under IFRS, probable means more likely than not, and 
under US GAAP it means likely to occur. As a result, economically similar contracts 
may be treated differently under IFRs and US GAAP . 
The performance obligations within a contract represent promises to transfer 
distinct good(s) or service(s). A good or service is distinct if the customer can benefit 
from it on its own or in combination with readily available resources and if the promise

to transfer it can be separated from other promises in the contract. Each identified 
performance obligation is accounted for separately.
The transaction price is what the seller estimates will be received in exchange for 
transferring the good(s) or service(s) identified in the contract. The transaction price 
is then allocated to each identified performance obligation. Revenue is recognized 
when a performance obligation is fulfilled. Steps three and four address amount, and 
step five addresses timing of recognition. The amount recognized reflects expectations 
about collectability and (if applicable) an allocation to multiple obligations within the 
same contract. Revenue is recognized when the obligation-  satisfying transfer is made.
Revenue should only be recognized when it is highly probable that it will not be 
subsequently reversed. This may result in the recording of a minimal amount of rev -
enue upon sale when an estimate of total revenue is not reliable. The balance sheet

will be required to reflect the entire refund obligation as a liability and will include 
an asset for the “right to returned goods” based on the carrying amount of inventory 
less costs of recovery.
When revenue is recognized, a contract asset is presented on the balance sheet. It is 
only at the point when all performance obligations have been met except for payment 
that a receivable appears on the seller’s balance sheet. If consideration is received in 
advance of transferring good(s) or service(s), the seller presents a contract liability.
The entity will recognize revenue when it is able to satisfy the performance obli -
gation by transferring control to the customer. Factors to consider when assessing 
whether the customer has obtained control of an asset at a point in time:
■■Entity has a present right to payment,
■■Customer has legal title,
■■Customer has physical possession,
■■Customer has the significant risks and rewards of ownership, and
■■Custer has accepted the asset.

For a simple contract with only one deliverable at a single point in time, complet -
ing the five steps is straight-  forward. For more complex contracts—such as when the 
performance obligations are satisfied over time, when the terms of the multi-  period 
contracts change, when the performance obligation includes various components of 
goods and services, or when the compensation is “variable”—accounting choices can 
be less obvious. The steps in the standards are intended to provide guidance that can 
be generalized to most situations. 
In addition, the standard provides many specific examples. These examples are 
intended to provide guidance as to how to approach more complex contracts. Some 
of these examples are summarized in Exhibit 7. Note that the end result for many

Reading 23 ■ Understanding Income Statements 114
examples may not differ substantially from that under revenue recognition standards 
that were in effect prior to the adoption of the converged standard; instead it is the 
conceptual approach and, in some cases, the terminology that will differ. 
Exhibit 7   Applying the Converged Revenue Recognition Standard
The references in this exhibit are to Examples in IFRS 15 Revenue from Contracts 
with Customers  (and ASU 2014-  09 (FASB ASC Topic 606)), on which these 
summaries are based.
Part 1 ( ref. Example 10 ).
Builder Co. enters into a contract with Customer Co. to construct a commer -
cial building. Builder Co. identifies various goods and services to be provided, 
such as pre-  construction engineering, construction of the building’s individual 
components, plumbing, electrical wiring, and interior finishes. With respect to 
“Identifying the Performance Obligation, ” should Builder Co. treat each specific

item as a separate performance obligation to which revenue should be allocated?
The standard provides two criteria, which must be met, to determine if a 
good or service is distinct for purposes of identifying performance obligations. 
First, the customer can benefit from the good or service either on its own or 
together with other readily available resources. Second, the seller’s “promise 
to transfer the good or service to the customer is separately identifiable from 
other promises in the contract. ” In this example, the second criterion is not 
met because it is the building for which the customer has contracted, not the 
separate goods and services. The seller will integrate all the goods and services 
into a combined output and each specific item should not be treated as a distinct 
good or service but accounted for together as a single performance obligation.
Part 2 ( ref. Example 8 ). 
Builder Co. ’s contract with Customer Co. to construct the commercial build -

ing specifies consideration of $1 million. Builder Co. ’s expected total costs are 
$700,000. The Builder incurs $420,000 in costs in the first year. Assuming that 
costs incurred provide an appropriate measure of progress toward completing 
the contract, how much revenue should Builder Co. recognize for the first year?
The standard states that for performance obligations satisfied over time, 
revenue is recognized over time by measuring progress toward satisfying the 
obligation. In this case, the Builder has incurred 60% of the total expected costs 
($420,000/$700,000) and will thus recognize $600,000 (60% × $1  million) in 
revenue for the first year. 
This is the same amount of revenue that would be recognized using 
“percentage-  of- completion, ” but that term is not used in the converged standard. 
Instead, the requirement is to measure progress toward complete satisfaction 
of the performance obligation. 
Part 3 ( ref. Example 8 ).

Part 3 ( ref. Example 8 ). 
Assume that Builder Co. ’s contract with Customer Co. to construct the com -
mercial building specifies consideration of $1 million plus a bonus of $200,000 
if the building is completed within 2 years. Builder Co. has only limited expe -
rience with similar types of contracts and knows that many factors outside its 
control (e.g., weather, regulatory requirements) could cause delay. Builder Co. ’s 
expected total costs are $700,000. The Builder incurs $420,000 in costs in the 
first year. Assuming that costs incurred provide an appropriate measure of 
progress toward completing the contract, how much revenue should Builder 
Co. recognize for the first year?

Revenue Recognition 115
The standard addresses so-  called “variable consideration” as part of deter -
mining the transaction price. A company is only allowed to recognize variable 
consideration if it can conclude that it will not have to reverse the cumulative 
revenue in the future. In this case, Builder Co. does not recognize any of the 
bonus in year one because it cannot reach the non-  reversible conclusion given 
its limited experience with similar contracts and potential delays from factors 
outside its control.
Part 4 ( ref. Example 8 ). 
Assume all facts from Part 3. In the beginning of year two, Builder Co. and 
Customer Co. agree to change the building floor plan and modify the contract. 
As a result the consideration will increase by $150,000, and the allowable time 
for achieving the bonus is extended by 6 months. Builder expects its costs will 
increase by $120,000. Also, given the additional 6 months to earn the completion

bonus, Builder concludes that it now meets the criteria for including the $200,000 
bonus in revenue. How should Builder account for this change in the contract?
Note that previous standards did not provide a general framework for contract 
modifications. The converged standard provides guidance on whether a change 
in a contract is a new contract or a modification of an existing contract. To be 
considered a new contract, the change would need to involve goods and services 
that are distinct from the goods and services already transferred.
In this case, the change does not meet the criteria of a new contract and is 
therefore considered a modification of the existing contract, which requires the 
company to reflect the impact on a cumulative catch-  up basis. Therefore, the com -
pany must update its transaction price and measure of progress. Builder’s total 
revenue on the transaction (transaction price) is now $1.35 million ($1 million

original plus the $150,000 new consideration plus $200,000 for the completion 
bonus). Builder Co. ’s progress toward completion is now 51.2% ($420,000 costs 
incurred divided by total expected costs of $820,000). Based on the changes 
in the contract, the amount of additional revenue to be recognized is $91,200, 
calculated as (51.2% × $1.35 million) minus the $600,000 already recognized. The 
additional $91,200 of revenue would be recognized as a “cumulative catch-  up 
adjustment” on the date of the contract modification.
Some related costs require specific accounting treatment under the new standards. 
In particular, incremental costs of obtaining a contract and certain costs incurred 
to fulfill a contract must be capitalized under the new standards (i.e., reported as 
an asset on the balance sheet rather than as an expense on the income statement). 
If a company had previously expensed these incremental costs in the years prior to

adopting the converged standard, all else equal, its profitability will initially appear 
higher under the converged standards.
The disclosure requirements are quite extensive. Companies are required at year 
end26 to disclose information about contracts with customers disaggregated into differ -
ent categories of contracts. The categories might be based on the type of product, the 
geographic region, the type of customer or sales channel, the type of contract pricing 
terms, the contract duration, or the timing of transfers. Companies are also required to 
disclose balances of any contract-  related assets and liabilities and significant changes 
in those balances, remaining performance obligations and transaction price allocated Exhibit 7   (Continued)
26 Interim period disclosures are required under IFRS and US GAAP but differ between them.

Reading 23 ■ Understanding Income Statements 116
to those obligations, and any significant judgments and changes in judgments related 
to revenue recognition. Significant judgments are those used in determining timing 
and amounts of revenue to be recognized. 
The converged standard is expected to affect some industries more than others. 
For example, industries where bundled sales are common, such as the telecommu -
nications and software industries, are expected to be significantly affected by the 
converged standard. For the periods prior to mandated adoption, analysts will give 
careful attention to early adopters under both IFRS and US GAAP and to all compa -
nies’ disclosures about the impact of the converged standard. 
EXPENSE RECOGNITION
Expenses are deducted against revenue to arrive at a company’s net profit or loss. 
Under the IASB Conceptual Framework , expenses  are “decreases in economic ben -
efits during the accounting period in the form of outflows or depletions of assets or

incurrences of liabilities that result in decreases in equity, other than those relating 
to distributions to equity participants. ”27
The IASB Conceptual Framework  also states:
The definition of expenses encompasses losses as well as those expenses 
that arise in the course of the ordinary activities of the enterprise. Expenses 
that arise in the course of the ordinary activities of the enterprise include, 
for example, cost of sales, wages and depreciation. They usually take the 
form of an outflow or depletion of assets such as cash and cash equivalents, 
inventory, property, plant and equipment.
Losses represent other items that meet the definition of expenses and 
may, or may not, arise in the course of the ordinary activities of the enter -
prise. Losses represent decreases in economic benefits and as such they are 
no different in nature from other expenses. Hence, they are not regarded 
as a separate element in this Conceptual Framework .

Losses include, for example, those resulting from disasters such as fire 
and flood, as well as those arising on the disposal of non-  current assets.28
Similar to the issues with revenue recognition, in a simple hypothetical scenario, 
expense recognition would not be an issue. For instance, assume a company purchased 
inventory for cash and sold the entire inventory in the same period. When the company 
paid for the inventory, absent indications to the contrary, it is clear that the inventory 
cost has been incurred and when that inventory is sold, it should be recognized as an 
expense (cost of goods sold) in the financial records. Assume also that the company 
paid all operating and administrative expenses in cash within each accounting period. 
In such a simple hypothetical scenario, no issues of expense recognition would arise. 
In practice, however, as with revenue recognition, determining when expenses should 
be recognized can be somewhat more complex.4

27 IASB Conceptual Framework , paragraph 4.25(b).
28 Ibid., paragraphs 4.33–4.35.

Expense Recognition 117
4.1 General Principles
In general, a company recognizes expenses in the period that it consumes (i.e., uses 
up) the economic benefits associated with the expenditure, or loses some previously 
recognized economic benefit.29
A general principle of expense recognition is the matching principle . Strictly 
speaking, IFRS do not refer to a “matching principle” but rather to a “matching con -
cept” or to a process resulting in “matching of costs with revenues. ”30 The distinction 
is relevant in certain standard setting deliberations. Under matching, a company 
recognizes some expenses (e.g., cost of goods sold) when associated revenues are 
recognized and thus, expenses and revenues are matched. Associated revenues and 
expenses are those that result directly and jointly from the same transactions or events. 
Unlike the simple scenario in which a company purchases inventory and sells all of 
the inventory within the same accounting period, in practice, it is more likely that

some of the current period’s sales are made from inventory purchased in a previous 
period or previous periods. It is also likely that some of the inventory purchased in 
the current period will remain unsold at the end of the current period and so will be 
sold in a following period. Matching requires that a company recognizes cost of goods 
sold in the same period as revenues from the sale of the goods.
Period costs , expenditures that less directly match revenues, are reflected in 
the period when a company makes the expenditure or incurs the liability to pay. 
Administrative expenses are an example of period costs. Other expenditures that 
also less directly match revenues relate more directly to future expected benefits; in 
this case, the expenditures are allocated systematically with the passage of time. An 
example is depreciation expense.
Examples 7 and 8 demonstrate matching applied to inventory and cost of goods sold.
EXAMPLE 7   
The Matching of Inventory Costs with Revenues

Kahn Distribution Limited (KDL) purchases inventory items for resale. At the 
beginning of 2009, Kahn had no inventory on hand. During 2009, Kahn had the 
following transactions:
Inventory Purchases
First quarter 2,000 units at $40 per unit
Second quarter 1,500 units at $41 per unit
Third quarter 2,200 units at $43 per unit
Fourth quarter 1,900 units at $45 per unit
Total 7,600 units at a total cost of $321,600
KDL sold 5,600 units of inventory during the year at $50 per unit, and received 
cash. KDL determines that there were 2,000 remaining units of inventory and 
specifically identifies that 1,900 were those purchased in the fourth quarter and 
100 were purchased in the third quarter. What are the revenue and expense 
associated with these transactions during 2009 based on specific identification 
of inventory items as sold or remaining in inventory?
29 Ibid., paragraph 4.49.
30 Ibid., paragraph 4.50.

Reading 23 ■ Understanding Income Statements 118
Solution:
The revenue for 2009 would be $280,000 (5,600 units × $50 per unit). Initially, 
the total cost of the goods purchased would be recorded as inventory (an asset) 
in the amount of $321,600. During 2009, the cost of the 5,600 units sold would 
be expensed (matched against the revenue) while the cost of the 2,000 remaining 
unsold units would remain in inventory as follows:
Cost of Goods Sold
From the first quarter 2,000 units at $40 per unit = $ 80,000
From the second quarter 1,500 units at $41 per unit = $ 61,500
From the third quarter 2,100 units at $43 per unit = $ 90,300
Total cost of goods sold $231,800
Cost of Goods Remaining in Inventory
From the third quarter 100 units at $43 per unit = $ 4,300
From the fourth quarter 1,900 units at $45 per unit = $85,500
Total remaining (or ending) inventory cost $89,800
To confirm that total costs are accounted for: $231,800 + $89,800 = $321,600.

The cost of the goods sold would be expensed against the revenue of $280,000 
Revenue $280,000
Cost of goods sold 231,800
Gross profit $ 48,200
An alternative way to think about this is that the company created an asset 
(inventory) of $321,600 as it made its purchases. At the end of the period, the 
value of the company’s inventory on hand is $89,800. Therefore, the amount of 
the Cost of goods sold expense recognized for the period should be the differ -
ence: $231,800.
The remaining inventory amount of $89,800 will be matched against revenue 
in a future year when the inventory items are sold.
EXAMPLE 8   
Alternative Inventory Costing Methods
In Example 7, KDL was able to specifically identify which inventory items were 
sold and which remained in inventory to be carried over to later periods. This is 
called the specific identification method  and inventory and cost of goods sold 
are based on their physical flow. It is generally not feasible to specifically iden -

tify which items were sold and which remain on hand, so accounting standards 
permit the assignment of inventory costs to costs of goods sold and to ending 
inventory using cost formulas (IFRS terminology) or cost flow assumptions (US 
GAAP). The cost formula or cost flow assumption determines which goods are 
assumed to be sold and which goods are assumed to remain in inventory. Both 
IFRS and US GAAP permit the use of the first in, first out (FIFO) method, and 
the weighted average cost method to assign costs.
Under the FIFO method , the oldest goods purchased (or manufactured) are 
assumed to be sold first and the newest goods purchased (or manufactured) are 
assumed to remain in inventory. Cost of goods in beginning inventory and costs

Expense Recognition 119
of the first items purchased (or manufactured) flow into cost of goods sold first, 
as if the earliest items purchased sold first. Ending inventory would, therefore, 
include the most recent purchases. It turns out that those items specifically iden -
tified as sold in Example 7 were also the first items purchased, so in this example, 
under FIFO, the cost of goods sold would also be $231,800, calculated as above.
The weighted average cost method  assigns the average cost of goods 
available for sale to the units sold and remaining in inventory. The assignment 
is based on the average cost per unit (total cost of goods available for sale/total 
units available for sale) and the number of units sold and the number remaining 
in inventory.
For KDL, the weighted average cost per unit would be
$321,600/7,600 units = $42.3158 per unit
Cost of goods sold using the weighted average cost method would be
5,600 units at $42.3158 = $236,968

Ending inventory using the weighted average cost method would be
2,000 units at $42.3158 = $84,632
Another method is permitted under US GAAP but is not permitted under 
IFRS. This is the last in, first out (LIFO) method. Under the LIFO method , the 
newest goods purchased (or manufactured) are assumed to be sold first and the 
oldest goods purchased (or manufactured) are assumed to remain in inventory. 
Costs of the latest items purchased flow into cost of goods sold first, as if the 
most recent items purchased were sold first. Although this may seem contrary 
to common sense, it is logical in certain circumstances. For example, lumber in a 
lumberyard may be stacked up with the oldest lumber on the bottom. As lumber 
is sold, it is sold from the top of the stack, so the last lumber purchased and put 
in inventory is the first lumber out. Theoretically, a company should choose a 
method linked to the physical inventory flows.31 Under the LIFO method, in

the KDL example, it would be assumed that the 2,000 units remaining in ending 
inventory would have come from the first quarter’s purchases:32
Ending inventory 2,000 units at $40 per unit = $80,000
The remaining costs would be allocated to cost of goods sold under LIFO:
Total costs of $321,600 less $80,000 remaining in ending inventory = 
$241,600
Alternatively, the cost of the last 5,600 units purchased is allocated to cost of 
goods sold under LIFO:
1,900 units at $45 per unit + 2,200 units at $43 per unit + 1,500 units at $41 
per unit = $241,600
31 Practically, the reason some companies choose to use LIFO in the United States is to reduce taxes. 
When prices and inventory quantities are rising, LIFO will normally result in higher cost of goods sold 
and lower income and hence lower taxes. US tax regulations require that if LIFO is used on a company’s 
tax return, it must also be used on the company’s GAAP financial statements.

32 If data on the precise timing of quarterly sales were available, the answer would differ because the cost 
of goods sold would be determined during the quarter rather than at the end of the quarter.

Reading 23 ■ Understanding Income Statements 120
An alternative way to think about expense recognition is that the company 
created an asset (inventory) of $321,600 as it made its purchases. At the end 
of the period, the value of the company’s inventory is $80,000. Therefore, the 
amount of the Cost of goods sold expense recognized for the period should be 
the difference: $241,600.
Exhibit 8 summarizes and compares inventory costing methods.
Exhibit 8   Summary Table on Inventory Costing Methods
Method DescriptionCost of Goods Sold When 
Prices Are Rising, Relative 
to Other Two MethodsEnding Inventory When 
to Other Two Methods
FIFO (first in, first out) Costs of the earliest items 
purchased flow to cost of goods 
sold firstLowest Highest
LIFO (last in, first out) Costs of the most recent items 
sold firstHighest* Lowest*
Weighted average cost Averages total costs over total 
units availableMiddle Middle

*Assumes no LIFO layer liquidation. LIFO layer liquidation  occurs when the volume of sales exceeds the volume of purchases in the period 
so that some sales are assumed to be made from existing, relatively low-  priced inventory rather than from more recent purchases. 
4.2 Issues in Expense Recognition
The following sections cover applications of the principles of expense recognition to 
certain common situations.
4.2.1  Doubtful Accounts
When a company sells its products or services on credit, it is likely that some cus -
tomers will ultimately default on their obligations (i.e., fail to pay). At the time of the 
sale, it is not known which customer will default. (If it were known that a particular 
customer would ultimately default, presumably a company would not sell on credit 
to that customer.) One possible approach to recognizing credit losses on customer 
receivables would be for the company to wait until such time as a customer defaulted

and only then recognize the loss ( direct write-  off method ). Such an approach would 
usually not be consistent with generally accepted accounting principles.
Under the matching principle, at the time revenue is recognized on a sale, a com -
pany is required to record an estimate of how much of the revenue will ultimately be 
uncollectible. Companies make such estimates based on previous experience with 
uncollectible accounts. Such estimates may be expressed as a proportion of the overall 
amount of sales, the overall amount of receivables, or the amount of receivables over -
due by a specific amount of time. The company records its estimate of uncollectible 
amounts as an expense on the income statement, not as a direct reduction of revenues.
4.2.2  Warranties
At times, companies offer warranties on the products they sell. If the product proves 
deficient in some respect that is covered under the terms of the warranty, the company

will incur an expense to repair or replace the product. At the time of sale, the com -
pany does not know the amount of future expenses it will incur in connection with its

Expense Recognition 121
warranties. One possible approach would be for a company to wait until actual expenses 
are incurred under the warranty and to reflect the expense at that time. However, this 
would not result in a matching of the expense with the associated revenue.
Under the matching principle, a company is required to estimate the amount of 
future expenses resulting from its warranties, to recognize an estimated warranty 
expense in the period of the sale, and to update the expense as indicated by experience 
over the life of the warranty.
4.2.3  Depreciation and Amortisation
Companies commonly incur costs to obtain long-  lived assets. Long-  lived assets  are 
assets expected to provide economic benefits over a future period of time greater than 
one year. Examples are land (property), plant, equipment, and intangible assets  (assets 
lacking physical substance) such as trademarks. The costs of most long-  lived assets

are allocated over the period of time during which they provide economic benefits. 
The two main types of long-  lived assets whose costs are not allocated over time are 
land and those intangible assets with indefinite useful lives.
Depreciation  is the process of systematically allocating costs of long-  lived assets 
over the period during which the assets are expected to provide economic benefits. 
“Depreciation” is the term commonly applied to this process for physical long-  lived 
assets such as plant and equipment (land is not depreciated), and amortisation  is 
the term commonly applied to this process for intangible long-  lived assets with a 
finite useful life.33 Examples of intangible long-  lived assets with a finite useful life 
include an acquired mailing list, an acquired patent with a set expiration date, and 
an acquired copyright with a set legal life. The term “amortisation” is also commonly

applied to the systematic allocation of a premium or discount relative to the face value 
of a fixed-  income security over the life of the security.
IFRS allow two alternative models for valuing property, plant, and equipment: 
the cost model and the revaluation model.34 Under the cost model, the depreciable 
amount of that asset (cost less residual value) is allocated on a systematic basis over 
the remaining useful life of the asset. Under the cost model, the asset is reported at 
its cost less any accumulated depreciation. Under the revaluation model, the asset is 
reported at its fair value. The revaluation model is not permitted under US GAAP . 
Here, we will focus only on the cost model. There are two other differences between 
IFRS and US GAAP to note: IFRS require each component of an asset to be depreciated 
separately and US GAAP do not require component depreciation; and IFRS require 
an annual review of residual value and useful life, and US GAAP do not explicitly

require such a review.
The method used to compute depreciation should reflect the pattern over which 
the economic benefits of the asset are expected to be consumed. IFRS do not pre -
scribe a particular method for computing depreciation but note that several methods 
are commonly used, such as the straight-  line method, diminishing balance method 
(accelerated depreciation), and the units of production method (depreciation varies 
depending upon production or usage).
The straight-  line method  allocates evenly the cost of long-  lived assets less esti -
mated residual value over the estimated useful life of an asset. (The term “straight line” 
derives from the fact that the annual depreciation expense, if represented as a line 
graph over time, would be a straight line. In addition, a plot of the cost of the asset 
33 Intangible assets with indefinite life are not amortised. Instead, they are reviewed each period as to

the reasonableness of continuing to assume an indefinite useful life and are tested at least annually for 
impairment (i.e., if the recoverable or fair value of an intangible asset is materially lower than its value in 
the company’s books, the value of the asset is considered to be impaired and its value must be decreased). 
IAS 38, Intangible Assets  and FASB ASC Topic 350 [Intangibles–Goodwill and Other].
34 IAS No. 16, Property, Plant, and Equipment.

Reading 23 ■ Understanding Income Statements 122
minus the cumulative amount of annual depreciation expense, if represented as a line 
graph over time, would be a straight line with a negative downward slope.) Calculating 
depreciation and amortisation requires two significant estimates: the estimated useful 
life of an asset and the estimated residual value (also known as “salvage value”) of 
an asset. Under IFRS, the residual value is the amount that the company expects to 
receive upon sale of the asset at the end of its useful life. Example 9 assumes that an 
item of equipment is depreciated using the straight-  line method and illustrates how 
the annual depreciation expense varies under different estimates of the useful life and 
estimated residual value of an asset. As shown, annual depreciation expense is sensitive 
to both the estimated useful life and to the estimated residual value.
EXAMPLE 9   
Sensitivity of Annual Depreciation Expense to Varying

Estimates of Useful Life and Residual Value
Using the straight-  line method of depreciation, annual depreciation expense is 
calculated as:
Cost Residua l value
Estimated useful lif e  −
Assume the cost of an asset is $10,000. If, for example, the residual value of 
the asset is estimated to be $0 and its useful life is estimated to be 5 years, the 
annual depreciation expense under the straight-  line method would be ($10,000 
– $0)/5 years = $2,000. In contrast, holding the estimated useful life of the asset 
constant at 5 years but increasing the estimated residual value of the asset to 
$4,000 would result in annual depreciation expense of only $1,200 [calculated as 
($10,000 – $4,000)/5 years]. Alternatively, holding the estimated residual value 
at $0 but increasing the estimated useful life of the asset to 10 years would result 
in annual depreciation expense of only $1,000 [calculated as ($10,000 – $0)/10 
years]. Exhibit 9 shows annual depreciation expense for various combinations

of estimated useful life and residual value.
Exhibit 9   Annual Depreciation Expense (in Dollars) 
Estimated 
Useful Life 
(Y ears) Estimated Residual Value
0 1,000 2,000 3,000 4,000 5,000
2 5,000 4,500 4,000 3,500 3,000 2,500
4 2,500 2,250 2,000 1,750 1,500 1,250
5 2,000 1,800 1,600 1,400 1,200 1,000
8 1,250 1,125 1,000 875 750 625
10 1,000 900 800 700 600 500
Generally, alternatives to the straight-  line method of depreciation are called accel -
erated methods  of depreciation because they accelerate (i.e., speed up) the timing of 
depreciation. Accelerated depreciation methods allocate a greater proportion of the 
cost to the early years of an asset’s useful life. These methods are appropriate if the

Expense Recognition 123
plant or equipment is expected to be used up faster in the early years (e.g., an auto -
mobile). A commonly used accelerated method is the diminishing balance method , 
(also known as the declining balance method). The diminishing balance method is 
demonstrated in Example 10.
EXAMPLE 10   
An Illustration of Diminishing Balance Depreciation
Assume the cost of computer equipment was $11,000, the estimated residual 
value is $1,000, and the estimated useful life is five years. Under the diminishing 
or declining balance method, the first step is to determine the straight-  line rate, 
the rate at which the asset would be depreciated under the straight-  line method. 
This rate is measured as 100 percent divided by the useful life or 20 percent for 
a five-  year useful life. Under the straight-  line method, 1/5 or 20 percent of the 
depreciable cost of the asset (here, $11,000 – $1,000 = $10,000) would be expensed

each year for five years: The depreciation expense would be $2,000 per year.
The next step is to determine an acceleration factor that approximates the 
pattern of the asset’s wear. Common acceleration factors are 150 percent and 
200 percent. The latter is known as double declining balance depreciation  
because it depreciates the asset at double the straight-  line rate. Using the 
200 percent acceleration factor, the diminishing balance rate would be 40 per -
cent (20 percent × 2.0). This rate is then applied to the remaining undepreciated 
balance of the asset each period (known as the net book value ).
At the beginning of the first year, the net book value is $11,000. Depreciation 
expense for the first full year of use of the asset would be 40 percent of $11,000, 
or $4,400. Under this method, the residual value, if any, is generally not used in 
the computation of the depreciation each period (the 40 percent is applied to

$11,000 rather than to $11,000 minus residual value). However, the company 
will stop taking depreciation when the salvage value is reached.
At the beginning of Year 2, the net book value is measured as
Asset cost $11,000
Less: Accumulated depreciation (4,400)
Net book value $6,600
For the second full year, depreciation expense would be $6,600 × 40 percent, or 
$2,640. At the end of the second year (i.e., beginning of the third year), a total 
of $7,040 ($4,400 + $2,640) of depreciation would have been recorded. So, the 
remaining net book value at the beginning of the third year would be
Less: Accumulated depreciation (7,040)
Net book value $3,960
For the third full year, depreciation would be $3,960 × 40 percent, or $1,584. 
At the end of the third year, a total of $8,624 ($4,400  + $2,640  + $1,584) of 
depreciation would have been recorded. So, the remaining net book value at 
the beginning of the fourth year would be
Less: Accumulated depreciation (8,624)

Reading 23 ■ Understanding Income Statements 124
For the fourth full year, depreciation would be $2,376 × 40 percent, or $950. At 
the end of the fourth year, a total of $9,574 ($4,400 + $2,640 + $1,584 + $950) 
of depreciation would have been recorded. So, the remaining net book value at 
the beginning of the fifth year would be
Less: Accumulated depreciation (9,574)
Net book value $1,426
For the fifth year, if deprecation were determined as in previous years, it would 
amount to $570 ($1,426 × 40 percent). However, this would result in a remain -
ing net book value of the asset below its estimated residual value of $1,000. So, 
instead, only $426 would be depreciated, leaving a $1,000 net book value at the 
end of the fifth year.
Less: Accumulated depreciation (10,000)
Net book value $1,000
Companies often use a zero or small residual value, which creates problems for 
diminishing balance depreciation because the asset never fully depreciates. In

order to fully depreciate the asset over the initially estimated useful life when a 
zero or small residual value is assumed, companies often adopt a depreciation 
policy that combines the diminishing balance and straight-  line methods. An 
example would be a deprecation policy of using double-  declining balance depre -
ciation and switching to the straight-  line method halfway through the useful life.
Under accelerated depreciation methods, there is a higher depreciation expense 
in early years relative to the straight-  line method. This results in higher expenses and 
lower net income in the early depreciation years. In later years, there is a reversal with 
accelerated depreciation expense lower than straight-  line depreciation. Accelerated 
depreciation is sometimes referred to as a conservative accounting choice because it 
results in lower net income in the early years of asset use.
For those intangible assets that must be amortised (those with an identifiable

useful life), the process is the same as for depreciation; only the name of the expense 
is different. IFRS state that if a pattern cannot be determined over the useful life, then 
the straight-  line method should be used.35 In most cases under IFRS and US GAAP , 
amortisable intangible assets are amortised using the straight-  line method with no 
residual value. Goodwill36 and intangible assets with indefinite life are not amortised. 
Instead, they are tested at least annually for impairment (i.e., if the current value of an 
intangible asset or goodwill is materially lower than its value in the company’s books, 
the value of the asset is considered to be impaired and its value in the company’s 
books must be decreased).
In summary, to calculate depreciation and amortisation, a company must choose a 
method, estimate the asset’s useful life, and estimate residual value. Clearly, different 
choices have a differing effect on depreciation or amortisation expense and, therefore,

on reported net income.
35 IAS 38, Intangible Assets.
36 Goodwill is recorded in acquisitions and is the amount by which the price to purchase an entity 
exceeds the amount of net identifiable assets acquired (the total amount of identifiable assets acquired 
less liabilities assumed).

Non-  Recurring Items and Non-  Operating Items 125
4.3 Implications for Financial Analysis
A company’s estimates for doubtful accounts and/or for warranty expenses can affect 
its reported net income. Similarly, a company’s choice of depreciation or amortisation 
method, estimates of assets’ useful lives, and estimates of assets’ residual values can 
affect reported net income. These are only a few of the choices and estimates that 
affect a company’s reported net income.
As with revenue recognition policies, a company’s choice of expense recognition 
can be characterized by its relative conservatism. A policy that results in recognition 
of expenses later rather than sooner is considered less conservative. In addition, many 
items of expense require the company to make estimates that can significantly affect net 
income. Analysis of a company’s financial statements, and particularly comparison of 
one company’s financial statements with those of another, requires an understanding

of differences in these estimates and their potential impact.
If, for example, a company shows a significant year-  to- year change in its estimates 
of uncollectible accounts as a percentage of sales, warranty expenses as a percentage 
of sales, or estimated useful lives of assets, the analyst should seek to understand the 
underlying reasons. Do the changes reflect a change in business operations (e.g., lower 
estimated warranty expenses reflecting recent experience of fewer warranty claims 
because of improved product quality)? Or are the changes seemingly unrelated to 
changes in business operations and thus possibly a signal that a company is manip -
ulating estimates in order to achieve a particular effect on its reported net income?
As another example, if two companies in the same industry have dramatically 
different estimates for uncollectible accounts as a percentage of their sales, warranty 
expenses as a percentage of sales, or estimated useful lives as a percentage of assets,

it is important to understand the underlying reasons. Are the differences consistent 
with differences in the two companies’ business operations (e.g., lower uncollectible 
accounts for one company reflecting a different, more creditworthy customer base 
or possibly stricter credit policies)? Another difference consistent with differences in 
business operations would be a difference in estimated useful lives of assets if one 
of the companies employs newer equipment. Or, alternatively, are the differences 
seemingly inconsistent with differences in the two companies’ business operations, 
possibly signaling that a company is manipulating estimates?
Information about a company’s accounting policies and significant estimates are 
described in the notes to the financial statements and in the management discussion 
and analysis section of a company’s annual report.
When possible, the monetary effect of differences in expense recognition policies

and estimates can facilitate more meaningful comparisons with a single company’s 
historical performance or across a number of companies. An analyst can use the mon -
etary effect to adjust the reported expenses so that they are on a comparable basis.
Even when the monetary effects of differences in policies and estimates cannot 
be calculated, it is generally possible to characterize the relative conservatism of the 
policies and estimates and, therefore, to qualitatively assess how such differences 
might affect reported expenses and thus financial ratios.
NON-  RECURRING ITEMS AND NON-  OPERATING 
ITEMS
From a company’s income statements, we can see its earnings from last year and in 
the previous year. Looking forward, the question is: What will the company earn next 
year and in the years after?5

Reading 23 ■ Understanding Income Statements 126
To assess a company’s future earnings, it is helpful to separate those prior years’ 
items of income and expense that are likely to continue in the future from those items 
that are less likely to continue.37 Some items from prior years are clearly not expected 
to continue in the future periods and are separately disclosed on a company’s income 
statement. This is consistent with “ An entity shall present additional line items, head -
ings, and subtotals … when such presentation is relevant to an understanding of the 
entity’s financial performance. ”38 IFRS describe considerations that enter into the 
decision to present information other than that explicitly specified by a standard. US 
GAAP specify some of the items that should be reported separately. Two such items 
are 1) discontinued operations, and 2) extraordinary items (the latter category is not 
permitted under IFRS). These two items, if applicable, must be reported separately

from continuing operations under US GAAP .39 US GAAP for fiscal periods beginning 
after December 15, 2015, will no longer include the concept of extraordinary items. 
Other items that may be reported separately on a company’s income statement, such 
as unusual items, items that occur infrequently, effects due to accounting changes, 
and non-  operating income, require the analyst to make some judgments.
5.1 Discontinued Operations
When a company disposes of or establishes a plan to dispose of one of its component 
operations and will have no further involvement in the operation, the income state -
ment reports separately the effect of this disposal as a “discontinued” operation under 
both IFRS and US GAAP . Financial standards provide various criteria for reporting 
the effect separately, which are generally that the discontinued component must be 
separable both physically and operationally.40
Because the discontinued operation will no longer provide earnings (or cash flow)

to the company, an analyst can eliminate discontinued operations in formulating 
expectations about a company’s future financial performance.
In Exhibit 2, Kraft reported earnings and gains from discontinued operations of 
$1,045 million in 2008 and $232 million in 2007. In Note 2 of its financial statements, 
Kraft explains that it split off its Post Cereals business. The earnings and gains from 
discontinued operations of $1,045 million in 2008 and $232 million in 2007 refer to 
the amount of earnings of the cereal business in each of those years, up to the date 
it was split off.
5.2 Extraordinary Items
IFRS prohibit classification of any income or expense items as being “extraordinary. ”41 
For reporting periods beginning after December 15, 2015, US GAAP will no longer 
include the concept of extraordinary items. Under US GAAP , extraordinary items, 
which were both unusual in nature and occur infrequently, were presented separately

on the income statement and allow a reader of the statements to see that these items 
are not part of a company’s operating activities and are not expected to occur on an 
ongoing basis. Extraordinary items were shown net of tax and appear on the income 
statement below discontinued operations. An example of an extraordinary item is 
provided in Exhibit 10.
37 In business writing, items expected to continue in the future are often described as “persistent” or 
“permanent, ” whereas those not expected to continue are described as “transitory. ”
38 IAS No. 1, Presentation of Financial Statements , paragraph 85.
39 These requirements apply to material amounts.
40 IFRS No. 5, Non-  Current Assets Held for Sale and Discontinued Operations , paragraphs 31–33.
41 IAS No. 1, Presentation of Financial Statements , paragraph 87.

Non-  Recurring Items and Non-  Operating Items 127
Exhibit 10   Extraordinary Gain on Debt Forgiveness
In its annual report, ForgeHouse, Inc. made the following disclosure describing 
an extraordinary gain on debt forgiveness:
On September 30, 2009, the Company entered into a Debt Forgiveness 
Agreement with Insurance Medical Group Limited (f/k/a After All 
Limited), Bryan Irving, and Ian Morl, pursuant to which $785,000 
(plus accrued and unpaid interest and any penalties of $80,141) of 
the Company’s outstanding obligations in favor of Arngrove Group 
Holdings were forgiven and all $200,000 (plus accrued and unpaid 
interest and any penalties of $23,418) of the Company’s outstanding 
obligations in favor of After All Group, Limited, was forgiven. Gain 
on these two debt restructurings was a gross of $1,088,559 for the 
year ended December 31, 2009.
In December 2009, the Company entered into agreements with 
two of its vendors to reduce the amounts owed to the vendors in

exchange for upfront payments. Gain on the restructure of amounts 
owed to the two vendors was $244,041.
These amounts are presented in the statement of operations net 
of income taxes of $453,084 for a net extraordinary gain on debt 
restructuring of $879,516.
Source:  ForgeHouse, Inc. 10-  K for fiscal year ended 31 December 2009, filed 14 May 2010: Note 
6.
Companies had to apply judgment, which was time consuming, to determine 
whether an item was extraordinary based on guidance from accounting standards.42 
Given the requirements for classification of an item as extraordinary—unusual 
and infrequent—the classification was rarely used. Under the new guidance, items 
will simply be classified as unusual, infrequent, or unusual and infrequent. 
5.3 Unusual or Infrequent Items
IFRS require that items of income or expense that are material and/or relevant to the 
understanding of the entity’s financial performance should be disclosed separately.

Unusual or infrequent items are likely to meet these criteria. Under US GAAP , mate -
rial items that are unusual or infrequent, and that are both as of reporting periods 
beginning after December  15, 2015, are shown as part of a company’s continuing 
operations but are presented separately. For example, restructuring charges, such 
as costs to close plants and employee termination costs, are considered part of a 
company’s ordinary activities. As another example, gains and losses arising when a 
company sells an asset or part of a business, for more or less than its carrying value, 
are also disclosed separately on the income statement. These sales are considered 
ordinary business activities.
Highlighting the unusual or infrequent nature of these items assists an analyst in 
judging the likelihood that such items will reoccur. This meets the IFRS criteria of 
disclosing items that are relevant to the understanding of an entity’s financial perfor -
mance. Exhibit 11 shows such disclosure.

42 FASB ASC Section 225–20–45 [Income Statement-  Extraordinary and Unusual Items–Other Presentation 
Matters].

Reading 23 ■ Understanding Income Statements 128
Exhibit 11   Highlighting Infrequent Nature of Items Excerpt from Roche 
Group Consolidated Income Statement (in millions of CHF, Y ear 
ended 31 December 2009) 
[portions omitted]
Operating profit before exceptional items 15,012
  Major legal cases (320)
  Changes in Group organisation (2,415)
Operating profit 12,277
      [portions omitted]
In Exhibit 11, Roche Group, a Swiss healthcare company, shows operating profit 
before and after exceptional items. The exceptional items relate to major legal cases 
and changes in the organization. The company’s notes explain both items further. 
The costs for changes in the organization relate to Roche’s acquisition of Genentech 
and major changes to certain manufacturing and commercial centers. Generally, in 
forecasting future operations, an analyst would assess whether the items reported are 
likely to reoccur and also possible implications for future earnings. It is generally not

advisable simply to ignore all unusual items.
5.4 Changes in Accounting Policies
At times, standard setters issue new standards that require companies to change 
accounting policies. Companies may be permitted to adopt the standards prospectively 
(in the future) or retrospectively (restate financial statements as though the standard 
existed in the past). In other cases, changes in accounting policies (e.g., from one 
acceptable inventory costing method to another) are made for other reasons, such as 
providing a better reflection of the company’s performance. Changes in accounting 
policies are reported through retrospective application43 unless it is impractical to do so.
Retrospective application  means that the financial statements for all fiscal years 
shown in a company’s financial report are presented as if the newly adopted account -
ing principle had been used throughout the entire period. Notes to the financial

statements describe the change and explain the justification for the change. Because 
changes in accounting principles are retrospectively applied, the financial statements 
that appear within a financial report are comparable. So, if a company’s annual report 
for 2009 includes its financial statements for fiscal years 2007, 2008, and 2009, all of 
these statements will be comparable.
Example 11 presents an excerpt from the 25 January 2010 10-  K/A of Apple Inc. 
Apple amended its previously filed 10-  K to reflect the company’s retrospective adoption 
of an FASB accounting standard related to revenue recognition for multi-  deliverables. 
43 IAS No. 8, Accounting Policies , Changes in Accounting Estimates and Errors,  and FASB ASC Topic 250 
[Accounting Changes and Error Corrections].

Non-  Recurring Items and Non-  Operating Items 129
EXAMPLE 11   
Revenue Recognition: A Change in Accounting Principle
Apple’s amended 10-  K for the year ended 26 September 2009 explains how a 
change in accounting standards (the company refers to these as accounting prin -
ciples) affects its financial statements. The following excerpt (emphasis added) 
is from the explanatory note included in the amendment.
Under the historical accounting principles, the Company was required 
to account for sales of both iPhone and Apple TV using subscription 
accounting because the Company indicated it might from time-  to- time 
provide future unspecified software upgrades and features for those 
products free of charge. Under subscription accounting , revenue 
and associated product cost of sales for iPhone and Apple TV were 
deferred at the time of sale and recognized on a straight-  line basis 
over each product’s estimated economic life. This resulted in the

deferral of significant amounts of revenue and cost of sales related to 
iPhone and Apple TV. Costs incurred by the Company for engineer -
ing, sales, marketing and warranty were expensed as incurred. As of 
September 26, 2009, based on the historical accounting principles, 
total accumulated deferred revenue and deferred costs associated with 
past iPhone and Apple TV sales were $12.1 billion and $5.2 billion, 
respectively.
The new accounting principles generally require the Company 
to account for the sale of both iPhone and Apple TV as two deliv -
erables . The first deliverable is the hardware and software delivered 
at the time of sale, and the second deliverable is the right included 
with the purchase of iPhone and Apple TV to receive on a when-  and-  
if- available basis future unspecified software upgrades and features 
relating to the product’s software. The new accounting principles 
result in the recognition of substantially all of the revenue and

product costs from sales of iPhone and Apple TV at the time of 
sale. Additionally, the Company is required to estimate a standalone 
selling price for the unspecified software upgrade right included with 
the sale of iPhone and Apple TV and recognizes that amount ratably 
over the 24-  month estimated life of the related hardware device. For 
all periods presented, the Company’s estimated selling price for the 
software upgrade right included with each iPhone and Apple TV 
sold is $25 and $10, respectively. The adoption of the new accounting 
principles increased the Company’s net sales by $6.4 billion, $5.0 bil -
lion and $572 million for 2009, 2008 and 2007, respectively. As of 
September 26, 2009, the revised total accumulated deferred revenue 
associated with iPhone and Apple TV sales to date was $483 million; 
revised accumulated deferred costs for such sales were zero.
Source : Apple Inc. 10-  K/A for the year ended 26 September 2009, as filed

1 Under the historical accounting principle, how would the revenue from a 
sale of an iPhone be reflected in Apple’s financial statements?
2 How and why did adoption of the new accounting principles affect Apple’s 
revenues in 2009?

Reading 23 ■ Understanding Income Statements 130
Under the historical accounting principle (standard), a sale of an iPhone was 
treated as a subscription sale and revenue was not recognized at the time of 
sale. Rather, the sale would result in a liability entitled “deferred revenue. ” In 
subsequent periods, the company would recognize as revenue a portion of the 
revenue from that sale and reduce the amount of deferred revenue by the same 
amount. Disclosures about deferred revenue can be helpful to an analyst in 
developing expectations about future revenues.
Adoption of the new accounting principles (standards) increased the company’s 
2009 net sales (revenue) by $6.4 billion. The reason for the increase is that the 
new standard allowed the company to separate the revenue from the iPhone 
into two separate components and to report revenue from them separately.
In years prior to 2005, under both IFRS and US GAAP , the cumulative effect of

changes in accounting policies was typically shown at the bottom of the income state -
ment in the year of change instead of using retrospective application. It is possible 
that future accounting standards may occasionally require a company to report the 
change differently than retrospective application. Note disclosures are required to 
explain how the transition from the old standard to the new one is handled. During 
the period when companies make the transition from the old standard to the new, an 
analyst can examine disclosures to ensure comparability across companies.
In contrast to changes in accounting policies (such as whether to expense the cost 
of employee stock options), companies sometimes make changes in accounting esti -
mates  (such as the useful life of a depreciable asset). Changes in accounting estimates 
are handled prospectively, with the change affecting the financial statements for the 
period of change and future periods. No adjustments are made to prior statements,

and the adjustment is not shown on the face of the income statement. Significant 
changes should be disclosed in the notes.
Another possible adjustment is a correction of an error for a prior period  (e.g., 
in financial statements issued for an earlier year). This cannot be handled by simply 
adjusting the current period income statement. Correction of an error for a prior 
period is handled by restating the financial statements (including the balance sheet, 
statement of owners’ equity, and cash flow statement) for the prior periods presented 
in the current financial statements.44 Note disclosures are required regarding the error. 
These disclosures should be examined carefully because they may reveal weaknesses 
in the company’s accounting systems and financial controls.
5.5 Non-  Operating Items
Non-  operating items are typically reported separately from operating income because 
they are material and/or relevant to the understanding of the entity’s financial per -

formance. Under IFRS, there is no definition of operating activities, and companies 
that choose to report operating income or the results of operating activities should 
ensure that these represent activities that are normally regarded as operating. Under 
US GAAP , operating activities generally involve producing and delivering goods and 
providing services and include all transactions and other events that are not defined 
as investing or financing activities.45 For example, if a non-  financial service company 
44 Ibid.
45 FASB ASC Master Glossary.

Earnings per Share 131
invests in equity or debt securities issued by another company, any interest, dividends, 
or profits from sales of these securities will be shown as non-  operating income. In 
general, for non-  financial services companies,46 non-  operating income that is dis -
closed separately on the income statement (or in the notes) includes amounts earned 
through investing activities.
Among non-  operating items on the income statement (or accompanying notes), 
non-  financial service companies also disclose the interest expense on their debt 
securities, including amortisation of any discount or premium. The amount of inter -
est expense is related to the amount of a company’s borrowings and is generally 
described in the notes to the financial statements. For financial service companies, 
interest income and expense are likely components of operating activities. (Note that 
the characterization of interest and dividends as non-  operating items on the income

statement is not necessarily consistent with the classification on the statement of cash 
flows. Specifically, under IFRS, interest and dividends received can be shown either as 
operating or as investing on the statement of cash flows, while under US GAAP interest 
and dividends received are shown as operating cash flows. Under IFRS, interest and 
dividends paid can be shown either as operating or as financing on the statement of 
cash flows, while under US GAAP , interest paid is shown as operating and dividends 
paid are shown as financing.)
In practice, investing and financing activities may be disclosed on a net basis, with 
the components disclosed separately in the notes. In its income statement for 2009 
(Exhibit 1), Groupe Danone, for example, disclosed net interest expense (cost of net 
debt) of €264 million. The net amount is the €340 million of interest expense minus 
€76 million interest revenue. The financial statement notes (not shown) provide further 
disclosure about the expense.

For purposes of assessing a company’s future performance, the amount of financing 
expense will depend on the company’s financing policy (target capital structure) and 
borrowing costs. The amount of investing income will depend on the purpose and 
success of investing activities. For a non-  financial company, a significant amount of 
financial income would typically warrant further exploration. What are the reasons 
underlying the company’s investments in the securities of other companies? Is the 
company simply investing excess cash in short-  term securities to generate income 
higher than cash deposits, or is the company purchasing securities issued by other 
companies for strategic reasons, such as access to raw material supply or research?
EARNINGS PER SHARE
One metric of particular importance to an equity investor is earnings per share (EPS). 
EPS is an input into ratios such as the price/earnings ratio. Additionally, each share -

holder in a company owns a different number of shares. IFRS require the presentation 
of EPS on the face of the income statement for net profit or loss (net income) and 
profit or loss (income) from continuing operations.47 Similar presentation is required 
under US GAAP .48 This section outlines the calculations for EPS and explains how 
the calculation differs for a simple versus complex capital structure.6
46 Examples of financial services companies are insurance companies, banks, brokers, dealers, and 
investment companies.
47 IAS No. 33, Earnings Per Share.
48 FASB ASC Topic 260 [Earnings Per Share].

Reading 23 ■ Understanding Income Statements 132
6.1 Simple versus Complex Capital Structure
A company’s capital is composed of its equity and debt. Some types of equity have 
preference over others, and some debt (and other instruments) may be converted 
into equity. Under IFRS, the type of equity for which EPS is presented is referred to 
as ordinary. Ordinary shares  are those equity shares that are subordinate to all other 
types of equity. The ordinary shareholders are basically the owners of the company—the 
equity holders who are paid last in a liquidation of the company and who benefit the 
most when the company does well. Under US GAAP , this ordinary equity is referred 
to as common stock  or common shares , reflecting US language usage. The terms 
“ordinary shares, ” “common stock, ” and “common shares” are used interchangeably 
in the following discussion.
When a company has issued any financial instruments that are potentially con -

vertible into common stock, it is said to have a complex capital structure. Examples 
of financial instruments that are potentially convertible into common stock include 
convertible bonds, convertible preferred stock, employee stock options, and warrants.49 
If a company’s capital structure does not include such potentially convertible financial 
instruments, it is said to have a simple capital structure.
The distinction between simple versus complex capital structure is relevant to 
the calculation of EPS because financial instruments that are potentially convertible 
into common stock could, as a result of conversion or exercise, potentially dilute (i.e., 
decrease) EPS. Information about such a potential dilution is valuable to a company’s 
current and potential shareholders; therefore, accounting standards require companies 
to disclose what their EPS would be if all dilutive financial instruments were converted

into common stock. The EPS that would result if all dilutive financial instruments 
were converted is called diluted EPS . In contrast, basic EPS  is calculated using the 
reported earnings available to common shareholders of the parent company and the 
weighted average number of shares outstanding.
Companies are required to report both basic and diluted EPS. For example, Danone 
reported basic EPS (“before dilution”) and diluted EPS (“after dilution”) of €2.57 for 
2009, somewhat lower than 2008. Kraft reported basic EPS of $2.04 and diluted EPS 
of $2.03 for 2009, much higher than basic and diluted EPS (from continuing oper -
ations) of $1.22 and $1.21 for 2008. (The EPS information appears at the bottom of 
Danone’s and Kraft’s income statements.) An analyst would try to determine the causes 
underlying the changes in EPS, a topic we will address following an explanation of the 
calculations of both basic and diluted EPS.
6.2 Basic EPS

Basic EPS is the amount of income available to common shareholders divided by the 
weighted average number of common shares outstanding over a period. The amount 
of income available to common shareholders is the amount of net income remaining 
after preferred dividends (if any) have been paid. Thus, the formula to calculate basic 
EPS is:
Basic EP SNet income Preferred dividends
Weighted average=−  
  number of shares outstanding(1)
49 A warrant is a call option typically attached to securities issued by a company, such as bonds. A warrant 
gives the holder the right to acquire the company’s stock from the company at a specified price within a 
specified time period. IFRS and US GAAP standards regarding earnings per share apply equally to call 
options, warrants, and equivalent instruments.

Earnings per Share 133
The weighted average number of shares outstanding is a time weighting of common 
shares outstanding. For example, assume a company began the year with 2,000,000 
common shares outstanding and repurchased 100,000 common shares on 1 July. 
The weighted average number of common shares outstanding would be the sum of 
2,000,000 shares × 1/2 year + 1,900,000 shares × 1/2 year, or 1,950,000 shares. So the 
company would use 1,950,000 shares as the weighted average number of shares in 
calculating its basic EPS.
If the number of shares of common stock increases as a result of a stock dividend 
or a stock split, the EPS calculation reflects the change retroactively to the beginning 
of the period.
Examples 12, 13, and 14 illustrate the computation of basic EPS.
EXAMPLE 12   
A Basic EPS Calculation (1)
For the year ended 31 December 2009, Shopalot Company had net income of 
$1,950,000. The company had 1,500,000 shares of common stock outstanding,

no preferred stock, and no convertible financial instruments. What is Shopalot’s 
basic EPS?
Solution:
Shopalot’s basic EPS is $1.30 ($1,950,000 divided by 1,500,000 shares).
EXAMPLE 13   
A Basic EPS Calculation (2)
For the year ended 31 December  2009, Angler Products had net income of 
$2,500,000. The company declared and paid $200,000 of dividends on preferred 
stock. The company also had the following common stock share information:
Shares outstanding on 1 January 2009 1,000,000
Shares issued on 1 April 2009 200,000
Shares repurchased (treasury shares) on 1 October 2009 (100,000)
Shares outstanding on 31 December 2009 1,100,000
1 What is the company’s weighted average number of shares outstanding?
2 What is the company’s basic EPS?
The weighted average number of shares outstanding is determined by the length 
of time each quantity of shares was outstanding:
1,000,000 × (3 months/12 months) = 250,000
1,200,000 × (6 months/12 months) = 600,000
1,100,000 × (3 months/12 months) = 275,000

Weighted average number of shares outstanding 1,125,000

Reading 23 ■ Understanding Income Statements 134
Basic EPS = (Net income – Preferred dividends)/Weighted average number of 
shares = ($2,500,000 – $200,000)/1,125,000 = $2.04
EXAMPLE 14   
A Basic EPS Calculation (3)
Assume the same facts as in Example 13 except that on 1 December 2009, a 
previously declared 2 for 1 stock split took effect. Each shareholder of record 
receives two shares in exchange for each current share that he or she owns. 
What is the company’s basic EPS?
Solution:
For EPS calculation purposes, a stock split is treated as if it occurred at the begin -
ning of the period. The weighted average number of shares would, therefore, be 
2,250,000, and the basic EPS would be $1.02 [= ($2,500,000 – $200,000)/2,250,000].
6.3 Diluted EPS
If a company has a simple capital structure (in other words, one that includes no 
potentially dilutive financial instruments), then its basic EPS is equal to its diluted

EPS. However, if a company has potentially dilutive financial instruments, its diluted 
EPS may differ from its basic EPS. Diluted EPS, by definition, is always equal to or less 
than basic EPS. The sections below describe the effects of three types of potentially 
dilutive financial instruments on diluted EPS: convertible preferred, convertible debt, 
and employee stock options. The final section explains why not all potentially dilutive 
financial instruments actually result in a difference between basic and diluted EPS.
6.3.1  Diluted EPS When a Company Has Convertible Preferred Stock Outstanding
When a company has convertible preferred stock outstanding, diluted EPS is cal -
culated using the if- converted method . The if-  converted method is based on what 
EPS would have been if the convertible preferred securities had been converted at 
the beginning of the period. In other words, the method calculates what the effect

would have been if the convertible preferred shares converted at the beginning of 
the period. If the convertible shares had been converted, there would be two effects. 
First, the convertible preferred securities would no longer be outstanding; instead, 
additional common stock would be outstanding. Thus, under the if-  converted method, 
the weighted average number of shares outstanding would be higher than in the basic 
EPS calculation. Second, if such a conversion had taken place, the company would not 
have paid preferred dividends. Thus, under the if-  converted method, the net income 
available to common shareholders would be higher than in the basic EPS calculation.

Earnings per Share 135
Diluted EPS using the if-  converted method for convertible preferred stock is equal 
to net income divided by the weighted average number of shares outstanding from 
the basic EPS calculation plus the additional shares of common stock that would be 
issued upon conversion of the preferred. Thus, the formula to calculate diluted EPS 
using the if-  converted method for preferred stock is:
Diluted EPSNet income
Weighted average number of share s=()
(
o outstanding New common shares that
would ha ve been issu e  +
dd at conv ersion )
A diluted EPS calculation using the if-  converted method for preferred stock is 
provided in Example 15.
EXAMPLE 15   
A Diluted EPS Calculation Using the If-  Converted Method 
for Preferred Stock
For the year ended 31 December 2009, Bright-  Warm Utility Company had net 
income of $1,750,000. The company had an average of 500,000 shares of com -
mon stock outstanding, 20,000 shares of convertible preferred, and no other

potentially dilutive securities. Each share of preferred pays a dividend of $10 per 
share, and each is convertible into five shares of the company’s common stock. 
Calculate the company’s basic and diluted EPS.
Solution:
If the 20,000 shares of convertible preferred had each converted into 5 shares 
of the company’s common stock, the company would have had an additional 
100,000 shares of common stock (5 shares of common for each of the 20,000 
shares of preferred). If the conversion had taken place, the company would not 
have paid preferred dividends of $200,000 ($10 per share for each of the 20,000 
shares of preferred). As shown in Exhibit 12, the company’s basic EPS was $3.10 
and its diluted EPS was $2.92.
Exhibit 12   Calculation of Diluted EPS for Bright-  Warm Utility 
Company Using the If-  Converted Method: Case of 
Preferred Stock
Basic EPSDiluted EPS Using If-  
Converted Method
Net income $1,750,000 $1,750,000
Preferred dividend –200,000 0
Numerator $1,550,000 $1,750,000

Weighted average number of shares 
outstanding500,000 500,000
Additional shares issued if preferred 
converted0 100,000
Denominator 500,000 600,000(2)

Reading 23 ■ Understanding Income Statements 136
EPS $3.10 $2.92
6.3.2  Diluted EPS When a Company Has Convertible Debt Outstanding
When a company has convertible debt outstanding, the diluted EPS calculation also 
uses the if-  converted method. Diluted EPS is calculated as if the convertible debt 
had been converted at the beginning of the period. If the convertible debt had been 
converted, the debt securities would no longer be outstanding; instead, additional 
shares of common stock would be outstanding. Also, if such a conversion had taken 
place, the company would not have paid interest on the convertible debt, so the net 
income available to common shareholders would increase by the after-  tax amount of 
interest expense on the debt converted.
Thus, the formula to calculate diluted EPS using the if-  converted method for 
convertible debt is:
Diluted EPSNet income After-tax interest on
conv ertible=+ (   
  debt Preferred dividends

Weighted average number of s h − )
aares
outstanding A dditiona l commo n
shares that woul d hav(
+  
ee been
issued at conv ersion )
A diluted EPS calculation using the if-  converted method for convertible debt is 
provided in Example 16.
EXAMPLE 16   
for Convertible Debt
Oppnox Company reported net income of $750,000 for the year ended 31 
December  2009. The company had a weighted average of 690,000 shares of 
common stock outstanding. In addition, the company has only one potentially 
dilutive security: $50,000 of 6 percent convertible bonds, convertible into a total 
of 10,000 shares. Assuming a tax rate of 30 percent, calculate Oppnox’s basic 
and diluted EPS.
Solution:
If the debt securities had been converted, the debt securities would no longer be 
outstanding and instead, an additional 10,000 shares of common stock would be

outstanding. Also, if the debt securities had been converted, the company would 
not have paid interest of $3,000 on the convertible debt, so net income available 
to common shareholders would have increased by $2,100 [= $3,000(1 – 0.30)] 
on an after-  tax basis. Exhibit 13 illustrates the calculation of diluted EPS using 
the if-  converted method for convertible debt.(3)Exhibit 12   (Continued)

Earnings per Share 137
Exhibit 13   Calculation of Diluted EPS for Oppnox Company Using the 
If- Converted Method: Case of a Convertible Bond
Net income $750,000 $750,000
After-  tax cost of interest 2,100
Numerator $750,000 $752,100
outstanding690,000 690,000
If converted 0 10,000
Denominator 690,000 700,000
EPS $1.09 $1.07
6.3.3  Diluted EPS When a Company Has Stock Options, Warrants, or Their Equivalents 
Outstanding
When a company has stock options, warrants, or their equivalents50 outstanding, 
diluted EPS is calculated as if the financial instruments had been exercised and the 
company had used the proceeds from exercise to repurchase as many shares of common 
stock as possible at the average market price of common stock during the period. The 
weighted average number of shares outstanding for diluted EPS is thus increased by 
the number of shares that would be issued upon exercise minus the number of shares

that would have been purchased with the proceeds. This method is called the treasury 
stock method  under US GAAP because companies typically hold repurchased shares 
as treasury stock. The same method is used under IFRS but is not named.
For the calculation of diluted EPS using this method, the assumed exercise of these 
financial instruments would have the following effects:
■■The company is assumed to receive cash upon exercise and, in exchange, to 
issue shares.
■■The company is assumed to use the cash proceeds to repurchase shares at the 
weighted average market price during the period.
As a result of these two effects, the number of shares outstanding would increase 
by the incremental number of shares issued (the difference between the number of 
shares issued to the holders and the number of shares assumed to be repurchased 
by the company). For calculating diluted EPS, the incremental number of shares is 
weighted based upon the length of time the financial instrument was outstanding

in the year. If the financial instrument was issued prior to the beginning of the year, 
the weighted average number of shares outstanding increases by the incremental 
number of shares. If the financial instruments were issued during the year, then the 
incremental shares are weighted by the amount of time the financial instruments were 
outstanding during the year.
50 Hereafter, options, warrants, and their equivalents will be referred to simply as “options” because the 
accounting treatment for EPS calculations is interchangeable for these instruments under IFRS and US GAAP .

Reading 23 ■ Understanding Income Statements 138
The assumed exercise of these financial instruments would not affect net income. 
For calculating EPS, therefore, no change is made to the numerator. The formula to 
calculate diluted EPS using the treasury stock method (same method as used under 
IFRS but not named) for options is:
Diluted EPSNet income Preferred dividends
Weighted ave=− ()   
rrage number of share s
outstanding New shares that woul d[
+  ( (
− have been issued at option exercise
Shares that could h 
aave been purchased
with cash recei ved upon exercise
Prop)×  
o ortion of y ear during which the
financial instruments we r(
e e outstanding )
A diluted EPS calculation using the treasury stock method for options is provided 
in Example 17.
EXAMPLE 17   
A Diluted EPS Calculation Using the Treasury Stock 
Method for Options
Hihotech Company reported net income of $2.3 million for the year ended 30 
June 2009 and had a weighted average of 800,000 common shares outstanding.

At the beginning of the fiscal year, the company has outstanding 30,000 options 
with an exercise price of $35. No other potentially dilutive financial instruments 
are outstanding. Over the fiscal year, the company’s market price has averaged 
$55 per share. Calculate the company’s basic and diluted EPS.
Solution:
Using the treasury stock method, we first calculate that the company would 
have received $1,050,000 ($35 for each of the 30,000 options exercised) if all 
the options had been exercised. The options would no longer be outstanding; 
instead, 30,000 shares of common stock would be outstanding. Under the trea -
sury stock method, we assume that shares would be repurchased with the cash 
received upon exercise of the options. At an average market price of $55 per 
share, the $1,050,000 proceeds from option exercise, the company could have 
repurchased 19,091 shares. Therefore, the incremental number of shares issued

is 10,909 (calculated as 30,000 minus 19,091). For the diluted EPS calculation, 
no change is made to the numerator. As shown in Exhibit 14, the company’s 
basic EPS was $2.88 and the diluted EPS was $2.84.
Exhibit 14   Calculation of Diluted EPS for Hihotech Company Using the 
Treasury Stock Method: Case of Stock Options
Basic EPSDiluted EPS Using 
Treasury Stock 
Method
Net income $2,300,000 $2,300,000
Numerator $2,300,000 $2,300,000(4)

Earnings per Share 139
Method
outstanding800,000 800,000
If converted 0 10,909
Denominator 800,000 810,909
EPS $2.88 $2.84
As noted, IFRS require a similar computation but does not refer to it as the “treasury 
stock method. ” The company is required to consider that any assumed proceeds are 
received from the issuance of new shares at the average market price for the period. 
These new “inferred” shares would be disregarded in the computation of diluted 
EPS, but the excess of the new shares that would be issued under options contracts 
minus the new inferred shares would be added to the weighted average number of 
shares outstanding. The results are the same as the treasury stock method, as shown 
in Example 18.
EXAMPLE 18   
Diluted EPS for Options under IFRS
Assuming the same facts as in Example  17, calculate the weighted average 
number of shares outstanding for diluted EPS under IFRS.
Solution:

Solution:
If the options had been exercised, the company would have received $1,050,000. 
If this amount had been received from the issuance of new shares at the average 
market price of $55 per share, the company would have issued 19,091 shares. 
IFRS refer to the 19,091 shares the company would have issued at market prices 
as the inferred shares. The number of shares issued under options (30,000) minus 
the number of inferred shares (19,091) equals 10,909. This amount is added to 
the weighted average number of shares outstanding of 800,000 to get diluted 
shares of 810,909. Note that this is the same result as that obtained under US 
GAAP; it is just derived in a different manner.
6.3.4  Other Issues with Diluted EPS
It is possible that some potentially convertible securities could be antidilutive  (i.e., 
their inclusion in the computation would result in an EPS higher than the company’s 
basic EPS). Under IFRS and US GAAP , antidilutive securities are not included in the

calculation of diluted EPS. Diluted EPS should reflect the maximum potential dilution 
from conversion or exercise of potentially dilutive financial instruments. Diluted EPS 
will always be less than or equal to basic EPS. Example 19 provides an illustration of 
an antidilutive security.Exhibit 14   (Continued)

Reading 23 ■ Understanding Income Statements 140
EXAMPLE 19   
An Antidilutive Security
For the year ended 31 December  2009, Dim-  Cool Utility Company had net 
mon stock outstanding, 20,000 shares of convertible preferred, and no other 
potentially dilutive securities. Each share of preferred pays a dividend of $10 
per share, and each is convertible into three shares of the company’s common 
stock. What was the company’s basic and diluted EPS?
Solution:
If the 20,000 shares of convertible preferred had each converted into 3 shares of 
the company’s common stock, the company would have had an additional 60,000 
shares of common stock (3 shares of common for each of the 20,000 shares of 
preferred). If the conversion had taken place, the company would not have paid 
preferred dividends of $200,000 ($10 per share for each of the 20,000 shares of

preferred). The effect of using the if-  converted method would be EPS of $3.13, 
as shown in Exhibit 15. Because this is greater than the company’s basic EPS of 
$3.10, the securities are said to be antidilutive and the effect of their conversion 
would not be included in diluted EPS. Diluted EPS would be the same as basic 
EPS (i.e., $3.10).
Exhibit 15   Calculation for an Antidilutive Security
Weighted average number of 
shares outstanding500,000 500,000
If converted 0 60,000
Denominator 500,000 560,000
EPS $3.10 $3.13 ←Exceeds basic EPS; 
security is antidilutive and, 
therefore, not included. 
Reported diluted EPS  = 
$3.10 .
6.4 Changes in EPS
Having explained the calculations of both basic and diluted EPS, we return to an 
examination of changes in EPS. As noted above, Kraft’s fully diluted EPS from con -

tinuing operations increased from $1.21 in 2008 to $2.03 in 2009. One cause of the 
increase in EPS is found in the notes to the financial statements (not shown). The 
note describing the calculation of EPS indicates that the number of weighted-  average 
shares decreased, and another note indicates that one reason for the decrease was the 
company’s repurchase of some of its own shares during the year. A more important

Analysis of the Income Statement 141
cause of the increase in EPS—shown on the income statement itself—was the sig -
nificant increase in earnings from continuing operations, from $1,848  million to 
$3,028 million. Changes in the numerator and denominator explain the changes in 
EPS arithmetically. To understand the business drivers of those changes requires 
further research. The next section presents analytical tools that an analyst can use to 
highlight areas for further examination.
ANALYSIS OF THE INCOME STATEMENT
In this section, we apply two analytical tools to analyze the income statement: 
common-  size analysis and income statement ratios. The objective of this analysis is 
to assess a company’s performance over a period of time—compared with its own 
past performance or the performance of another company.
7.1 Common-  Size Analysis of the Income Statement
Common-  size analysis of the income statement can be performed by stating each line

item on the income statement as a percentage of revenue.51 Common-  size statements 
facilitate comparison across time periods (time series analysis) and across companies 
(cross-  sectional analysis) because the standardization of each line item removes the 
effect of size.
To illustrate, Panel A of Exhibit 16 presents an income statement for three hypo -
thetical companies in the same industry. Company A and Company B, each with 
$10 million in sales, are larger (as measured by sales) than Company C, which has 
only $2 million in sales. In addition, Companies A and B both have higher operating 
profit: $2 million and $1.5 million, respectively, compared with Company C’s operating 
profit of only $400,000.
How can an analyst meaningfully compare the performance of these companies? 
By preparing a common-  size income statement, as illustrated in Panel B, an analyst 
can readily see that the percentages of Company C’s expenses and profit relative to

its sales are exactly the same as for Company A. Furthermore, although Company C’s 
operating profit is lower than Company B’s in absolute dollars, it is higher in percentage 
terms (20 percent for Company C compared with only 15 percent for Company B). 
For each $100 of sales, Company C generates $5 more operating profit than Company 
B. In other words, Company C is relatively more profitable than Company B based 
on this measure.
The common-  size income statement also highlights differences in companies’ 
strategies. Comparing the two larger companies, Company A reports significantly 
higher gross profit as a percentage of sales than does Company B (70 percent com -
pared with 25 percent). Given that both companies operate in the same industry, why 
can Company A generate so much higher gross profit? One possible explanation is 
found by comparing the operating expenses of the two companies. Company A spends 
significantly more on research and development and on advertising than Company

B. Expenditures on research and development likely result in products with superior 
technology. Expenditures on advertising likely result in greater brand awareness. So, 
based on these differences, it is likely that Company A is selling technologically superior 7
51 This format can be distinguished as “vertical common-  size analysis. ” As the reading on financial state -
ment analysis discusses, there is another type of common-  size analysis, known as “horizontal common-  
size analysis, ” that states items in relation to a selected base year value. Unless otherwise indicated, text 
references to “common-  size analysis” refer to vertical analysis.

Reading 23 ■ Understanding Income Statements 142
products with a better brand image. Company B may be selling its products more 
cheaply (with a lower gross profit as a percentage of sales) but saving money by not 
investing in research and development or advertising. In practice, differences across 
companies are more subtle, but the concept is similar. An analyst, noting significant 
differences, would do more research and seek to understand the underlying reasons 
for the differences and their implications for the future performance of the companies.
Exhibit 16   
Panel A: Income Statements for Companies A, B, and C ($)
A B C
Sales $10,000,000 $10,000,000 $2,000,000
Cost of sales 3,000,000 7,500,000 600,000
Gross profit 7,000,000 2,500,000 1,400,000
Selling, general, and administrative expenses 1,000,000 1,000,000 200,000
Research and development 2,000,000 — 400,000
Advertising 2,000,000 — 400,000
Operating profit 2,000,000 1,500,000 400,000

Panel B: Common-  Size Income Statements for Companies A, B, and C (%)
A B C
Sales 100% 100% 100%
Cost of sales 30 75 30
Gross profit 70 25 70
Selling, general, and administrative expenses 10 10 10
Research and development 20 0 20
Advertising 20 0 20
Operating profit 20 15 20
Note : Each line item is expressed as a percentage of the company’s sales.
For most expenses, comparison to the amount of sales is appropriate. However, 
in the case of taxes, it is more meaningful to compare the amount of taxes with the 
amount of pretax income. Using note disclosure, an analyst can then examine the causes 
for differences in effective tax rates. To project the companies’ future net income, an 
analyst would project the companies’ pretax income and apply an estimated effective 
tax rate determined in part by the historical tax rates.
Vertical common-  size analysis of the income statement is particularly useful in

cross-  sectional analysis—comparing companies with each other for a particular time 
period or comparing a company with industry or sector data. The analyst could select 
individual peer companies for comparison, use industry data from published sources, 
or compile data from databases based on a selection of peer companies or broader 
industry data. For example, Exhibit 17 presents median common-  size income state -
ment data compiled for the components of the S&P 500 classified into the 10 S&P/
MSCI Global Industrial Classification System (GICS) sectors using 2008 data. Note 
that when compiling aggregate data such as this, some level of aggregation is neces -
sary and less detail may be available than from peer company financial statements. 
The performance of an individual company can be compared with industry or peer 
company data to evaluate its relative performance.

Analysis of the Income Statement 143
Exhibit 17   Median Common-  Size Income Statement Statistics for the S&P 500 Classified by S&P/MSCI GICS 
Sector Data for 2008
Energy Materials IndustrialsConsumer 
DiscretionaryConsumer 
Staples
No. observations 40 29 59 86 40
Operating margin 20.81 10.59 12.47 8.65 13.19
Pretax margin 17.73 7.11 10.92 5.37 9.49
Profit margin 10.76 5.01 7.22 3.35 6.03
Cost of goods sold/sales 63.03 73.93 69.56 62.82 59.18
Selling, general, and administrative 
expenses/sales5.21 8.91 14.70 23.78 21.79
Taxes/Pretax income 33.30 30.72 32.30 32.56 33.51
Health 
Care FinancialsInformation 
TechnologyTelecom. 
Services Utilities
No. observations 55 87 77 9 33
Operating margin 19.77 16.69 16.91 27.76 17.22
Pretax margin 14.13 4.43 13.19 16.35 12.80
Profit margin 9.42 4.62 9.63 10.37 8.09
Cost of goods sold/sales 40.19 71.53 42.74 36.71 72.72
expenses/sales33.13 26.36 35.76 24.04 4.42
Taxes/Pretax income 24.27 25.63 25.81 36.43 32.71

Source:  Based on data from Compustat.
7.2 Income Statement Ratios
One aspect of financial performance is profitability. One indicator of profitability is net 
profit margin , also known as profit margin  and return on sales , which is calculated 
as net income divided by revenue (or sales).52
Net profit margi nNet income
Revenue=
Net profit margin measures the amount of income that a company was able to gen -
erate for each dollar of revenue. A higher level of net profit margin indicates higher 
profitability and is thus more desirable. Net profit margin can also be found directly 
on the common-  size income statements.
For Kraft Foods, net profit margin for 2009 was 7.5 percent (calculated as earn -
ings from continuing operations, net of non-  controlling interests, of $3,021 million, 
divided by net revenues of $40,386 million). To judge this ratio, some comparison is

needed. Kraft’s profitability can be compared with that of another company or with 
its own previous performance. Compared with previous years, Kraft’s profitability is 
higher than in 2008 and roughly equivalent to 2007. In 2008, net profit margin was 
6.9 percent, and in 2007, it was 7.6 percent.
52 In the definition of margin ratios of this type, “sales” is often used interchangeably with “revenue. ” “Return 
on sales” has also been used to refer to a class of profitability ratios having revenue in the denominator.

Reading 23 ■ Understanding Income Statements 144
Another measure of profitability is the gross profit margin. Gross profit (gross 
margin) is calculated as revenue minus cost of goods sold, and the gross profit margin  
is calculated as the gross profit divided by revenue.
Gross profit marginGross profit
Revenue=
The gross profit margin measures the amount of gross profit that a company gen -
erated for each dollar of revenue. A higher level of gross profit margin indicates higher 
profitability and thus is generally more desirable, although differences in gross profit 
margins across companies reflect differences in companies’ strategies. For example, 
consider a company pursuing a strategy of selling a differentiated product (e.g., a 
product differentiated based on brand name, quality, superior technology, or patent 
protection). The company would likely be able to sell the differentiated product at a 
higher price than a similar, but undifferentiated, product and, therefore, would likely

show a higher gross profit margin than a company selling an undifferentiated product. 
Although a company selling a differentiated product would likely show a higher gross 
profit margin, this may take time. In the initial stage of the strategy, the company would 
likely incur costs to create a differentiated product, such as advertising or research 
and development, which would not be reflected in the gross margin calculation.
Kraft’s gross profit (shown in Exhibit 2) was $14,600 million in 2009, $13,844 million 
in 2008, and $12,202 million in 2007. Expressing gross profit as a percentage of net 
revenues, we see that the gross profit margin was 36.2 percent in 2009, 33.0 percent 
in 2008, and 34.0 percent in 2007. In absolute terms, Kraft’s gross profit was higher 
in 2008 than in 2007. However Kraft’s gross profit margin  was lower in 2008.
Exhibit 18 presents a common-  size income statement for Kraft, and highlights

certain profitability ratios. The net profit margin and gross profit margin described 
above are just two of the many subtotals that can be generated from common-  size 
income statements. Other “margins” used by analysts include the operating profit 
margin  (operating income divided by revenue) and the pretax margin  (earnings 
before taxes divided by revenue).
Exhibit 18   Kraft’s Margins Abbreviated Common-  Size Income Statement
$ millions Percent $ millions Percent $ millions Percent
Net revenues 40,386 100.0 41,932 100.0 35,858 100.0
Cost of sales 25,786 63.8 28,088 67.0 23,656 66.0
Gross profit 14,600 36.2 a13,844 33.0 a12,202 34.0 a
Marketing, administration and 
research costs 9,108 22.6 8,862 21.1 7,587 21.2
Asset impairment and exit costs –64 –0.2 1,024 2.4 440 1.2
(Gains) / losses on divestitures, 
net 6 0.0 92 0.2 –14 0.0
Amortisation of intangibles 26 0.1 23 0.1 13 0.0
Operating income 5,524 13.7 b3,843 9.2 b4,176 11.6 b

Interest and other expense, net 1,237 3.1 1,240 3.0 604 1.7
Earnings from continuing oper -
ations before income taxes 4,287 10.6 c2,603 6.2 c3,572 10.0 c

Comprehensive Income 145
   [Portions omitted]
Net earnings attributable to 
Kraft Foods 3,021 7.5 d2,884 6.9 d2,721 7.6 d
Notes:
a Gross profit margin
b Operating profit margin
c Pretax margin
d Net profit margin
The profitability ratios and the common-  size income statement yield quick insights 
about changes in a company’s performance. For example, Kraft’s increase in profit -
ability in 2009 was not driven by an increase in revenues. (In fact, net revenues were 
lower than in 2008.) Instead the company’s improved profitability in 2009 was driven 
primarily by its higher gross profit margins. Given the economic climate in 2008, the 
company likely had to lower prices and/or incur higher promotional costs in order 
to stimulate demand for its products (downward pressure on net revenues). Another 
driver of the company’s improved profitability in 2009 was a lower amount of asset

impairment and exit costs. The profitability ratios and the common-  size income 
statement thus serve to highlight areas about which an analyst might wish to gain 
further understanding.
COMPREHENSIVE INCOME
The general expression for net income is revenue minus expenses. There are, however, 
certain items of revenue and expense that, by accounting convention, are excluded 
from the net income calculation. To understand how reported shareholders’ equity 
of one period links with reported shareholders’ equity of the next period, we must 
understand these excluded items, known as other comprehensive income .
Under IFRS, total comprehensive income  is “the change in equity during a 
period resulting from transaction and other events, other than those changes result -
ing from transactions with owners in their capacity as owners. ”53 Under US GAAP , 
comprehensive income  is defined as “the change in equity [net assets] of a business

enterprise during a period from transactions and other events and circumstances 
from non-  owner sources. It includes all changes in equity during a period except 
those resulting from investments by owners and distributions to owners. ”54 While 
the wording differs, comprehensive income includes the same items under IFRS and 
US GAAP . So, comprehensive income includes both  net income and other revenue 
and expense items that are excluded from the net income calculation (other compre -
hensive income). Assume, for example, a company’s beginning shareholders’ equity 
is €110 million, its net income for the year is €10 million, its cash dividends for the 
year are €2 million, and there was no issuance or repurchase of common stock. If the 8Exhibit 18   (Continued)
53 IAS 1, Presentation of Financial Statements,  paragraph 7.
54 FASB ASC Section 220-  10- 05 [Comprehensive Income–Overall–Overview and Background].

Reading 23 ■ Understanding Income Statements 146
company’s actual ending shareholders’ equity is €123 million, then €5 million [€123 
– (€110 + €10 – €2)] has bypassed the net income calculation by being classified as 
other comprehensive income. If the company had no other comprehensive income, 
its ending shareholders’ equity would have been €118 million [€110 + €10 – €2].
Four types of items are treated as other comprehensive income under both IFRS 
and US GAAP .55 (The specific treatment of some of these items differs between the 
two sets of standards, but these types of items are common to both.)
■■Foreign currency translation adjustments. In consolidating the financial state -
ments of foreign subsidiaries, the effects of translating the subsidiaries’ balance 
sheet assets and liabilities at current exchange rates are included as other com -
prehensive income.
■■Unrealized gains or losses on derivatives contracts accounted for as hedges.

Changes in the fair value of derivatives are recorded each period, but these 
changes in value for certain derivatives (those considered hedges) are treated as 
other comprehensive income and thus bypass the income statement.
■■Unrealized holding gains and losses on a certain category of investment securi -
ties, namely, available-  for- sale securities.
■■Certain costs of a company’s defined benefit post-  retirement plans that are not 
recognized in the current period.
In addition, under IFRS, other comprehensive income includes certain changes in 
the value of long-  lived assets that are measured using the revaluation model rather 
than the cost model.
The third type of item is perhaps the simplest to illustrate. Holding gains on 
securities arise when a company owns securities over an accounting period, during 
which time the securities’ value increases. Similarly, holding losses on securities arise 
when a company owns securities over a period during which time the securities’ value

decreases. If the company has not sold the securities (i.e., realized the gain or loss), 
its holding gain or loss is said to be unrealized. The question is: Should the company 
reflect these unrealized holding gains and losses in its income statement?
According to accounting standards, the answer depends on how the company has 
categorized the securities. Categorization depends on what the company intends to do 
with the securities. If the company intends to actively trade the securities, the answer 
is yes; the company should categorize the securities as trading securities  and reflect 
unrealized holding gains and losses in its income statement. However, if the company 
does not intend to actively trade the securities, the securities may be categorized as 
available-  for-  sale  securities. For available-  for- sale securities, the company does not 
reflect unrealized holding gains and losses in its profit and loss statement. Instead,

unrealized holding gains and losses on available-  for- sale securities bypass the income 
statement and go directly to shareholders’ equity through other comprehensive income.
Even though unrealized holding gains and losses on available-  for- sale securities 
are excluded from a company’s net income, they are included  in a company’s com -
The “available-  for- sale” classification no longer appears in IFRS with the issuance 
of IFRS 9 ( Financial Instruments ) as of 1 January 2018. Although the available-  for- sale 
category will not exist, IFRS still permit certain equity investments to be measured at 
fair value with any unrealized holding gains or losses recognized in other comprehen -
sive income. Specifically, at the time a company buys an equity investment that is not 
55 IAS 1, Presentation of Financial Statements,  paragraph 7, and FASB ASC Section 220-  10- 55- 02 
[Comprehensive Income–Overall–Implementation Guidance and Illustrations].

Comprehensive Income 147
held for trading, the company is permitted to make an irrevocable election to measure 
the asset in this manner. These assets are referred to as financial assets measured at 
fair value through other comprehensive income.
EXAMPLE 20   
Other Comprehensive Income
Assume a company’s beginning shareholders’ equity is €200  million, its net 
income for the year is €20 million, its cash dividends for the year are €3 million, 
and there was no issuance or repurchase of common stock. The company’s actual 
ending shareholders’ equity is €227 million.
1 What amount has bypassed the net income calculation by being classified 
as other comprehensive income?
A €0.
B €7 million.
C €10 million.
2 Which of the following statements best describes other comprehensive 
income?
A Income earned from diverse geographic and segment activities.
B Income that increases stockholders’ equity but is not reflected as part 
of net income.

C Income earned from activities that are not part of the company’s ordi -
nary business activities.
C is correct. If the company’s actual ending shareholders’ equity is €227 mil -
lion, then €10 million [€227– (€200 + €20 – €3)] has bypassed the net income 
calculation by being classified as other comprehensive income.
B is correct. Answers A and C are not correct because they do not specify whether 
such income is reported as part of net income and shown in the income statement.
EXAMPLE 21   
Other Comprehensive Income in Analysis
An analyst is looking at two comparable companies. Company A has a lower 
price/earnings (P/E) ratio than Company B, and the conclusion that has been 
suggested is that Company A is undervalued. As part of examining this con -
clusion, the analyst decides to explore the question: What would the company’s 
P/E look like if total comprehensive income per share—rather than net income 
per share—were used as the relevant metric?

Company A Company B
Price $35 $30
EPS $1.60 $0.90
P/E ratio 21.9× 33.3×

Reading 23 ■ Understanding Income Statements 148
Other comprehensive income (loss) $ million ($16.272) $(1.757)
Shares (millions) 22.6 25.1
Solution:
As shown in the following table, part of the explanation for Company A’s lower 
P/E ratio may be that its significant losses—accounted for as other comprehensive 
income (OCI)—are not included in the P/E ratio.
OCI (loss) $ million ($16.272) $(1.757)
OCI (loss) per share $(0.72) $(0.07)
Comprehensive EPS = EPS + OCI per share $ 0.88 $0.83
Price/Comprehensive EPS ratio 39.8× 36.1×
Both IFRS and US GAAP currently provide companies with some flexibility in 
reporting comprehensive income. IFRS currently allow companies two alternative 
presentations: either two statements—a separate income statement and a second 
statement additionally including other comprehensive income—or a single statement

of other comprehensive income.56 US GAAP give companies both of those alternatives 
plus another. Under US GAAP , a company can report comprehensive income at the 
bottom of the income statement, on a separate statement of comprehensive income, 
or as a column in the statement of shareholders’ equity.57 Particularly in comparing 
financial statements of two companies, it is relevant to examine significant differences 
in comprehensive income.
SUMMARY
This reading has presented the elements of income statement analysis. The income 
statement presents information on the financial results of a company’s business 
activities over a period of time; it communicates how much revenue the company 
generated during a period and what costs it incurred in connection with generating 
that revenue. A company’s net income and its components (e.g., gross margin, oper -
ating earnings, and pretax earnings) are critical inputs into both the equity and credit

analysis processes. Equity analysts are interested in earnings because equity markets 
often reward relatively high- or low-  earnings growth companies with above-  average 
or below-  average valuations, respectively. Fixed-  income analysts examine the com -
ponents of income statements, past and projected, for information on companies’ 
56 IAS 1, Presentation of Financial Statements , paragraph 81.
57 FASB ASC 220-  10- 45 [Comprehensive Income–Overall–Other Presentation Matters] and FASB ASC 
220-  10- 55 [Comprehensive Income–Overall–Implementation Guidance and Illustrations].

Summary 149
abilities to make promised payments on their debt over the course of the business 
cycle. Corporate financial announcements frequently emphasize income statements 
more than the other financial statements.
Key points to this reading include the following:
■■The income statement presents revenue, expenses, and net income.
■■The components of the income statement include: revenue; cost of sales; sales, 
general, and administrative expenses; other operating expenses; non-  operating 
income and expenses; gains and losses; non-  recurring items; net income; and 
EPS.
■■An income statement that presents a subtotal for gross profit (revenue minus 
cost of goods sold) is said to be presented in a multi-  step format. One that does 
not present this subtotal is said to be presented in a single-  step format.
■■Revenue is recognized in the period it is earned, which may or may not be in 
the same period as the related cash collection. Recognition of revenue when

earned is a fundamental principal of accrual accounting.
■■In limited circumstances, specific revenue recognition methods may be applica -
ble, including percentage of completion, completed contract, installment sales, 
and cost recovery.
■■An analyst should identify differences in companies’ revenue recognition 
methods and adjust reported revenue where possible to facilitate comparabil -
ity. Where the available information does not permit adjustment, an analyst 
can characterize the revenue recognition as more or less conservative and thus 
qualitatively assess how differences in policies might affect financial ratios and 
judgments about profitability.
■■In May 2014, the IASB and FASB each issued a converged standard for revenue 
recognition. The standards became effective for reporting periods beginning 
after 1 January 2018 under IFRS and 15 December 2017 under US GAAP . The 
core principle of the converged standards is that revenue should be recognized

to “depict the transfer of promised goods or services to customers in an amount 
that reflects the consideration to which the entity expects to be entitled in an 
exchange for those goods or services. ”
■■To achieve the core principle, the standard describes the application of five 
steps in recognizing revenue. The standard also specifies the treatment of some 
related contract costs and disclosure requirements.
■■The general principles of expense recognition include a process to match 
expenses either to revenue (such as, cost of goods sold) or to the time period 
in which the expenditure occurs (period costs such as, administrative sala -
ries) or to the time period of expected benefits of the expenditures (such as, 
depreciation).
■■In expense recognition, choice of method (i.e., depreciation method and 
inventory cost method), as well as estimates (i.e., uncollectible accounts, 
warranty expenses, assets’ useful life, and salvage value) affect a company’s

reported income. An analyst should identify differences in companies’ expense 
recognition methods and adjust reported financial statements where possible 
to facilitate comparability. Where the available information does not permit 
adjustment, an analyst can characterize the policies and estimates as more or 
less conservative and thus qualitatively assess how differences in policies might 
affect financial ratios and judgments about companies’ performance.
■■To assess a company’s future earnings, it is helpful to separate those prior years’ 
items of income and expense that are likely to continue in the future from those 
items that are less likely to continue.

Reading 23 ■ Understanding Income Statements 150
■■Under IFRS, a company should present additional line items, headings, and 
subtotals beyond those specified when such presentation is relevant to an 
understanding of the entity’s financial performance. Some items from prior 
years clearly are not expected to continue in future periods and are separately 
disclosed on a company’s income statement. Under US GAAP , unusual and/
or infrequently occurring items, which are material, are presented separately 
within income from continuing operations.
■■Non-  operating items are reported separately from operating items on the 
income statement. Under both IFRS and US GAAP , the income statement 
reports separately the effect of the disposal of a component operation as a “dis -
continued” operation.
■■Basic EPS is the amount of income available to common shareholders divided 
by the weighted average number of common shares outstanding over a period.

The amount of income available to common shareholders is the amount of net 
income remaining after preferred dividends (if any) have been paid.
■■If a company has a simple capital structure (i.e., one with no potentially dilutive 
securities), then its basic EPS is equal to its diluted EPS. If, however, a company 
has dilutive securities, its diluted EPS is lower than its basic EPS.
■■Diluted EPS is calculated using the if-  converted method for convertible securi -
ties and the treasury stock method for options.
■■Common-  size analysis of the income statement involves stating each line item 
on the income statement as a percentage of sales. Common-  size statements 
facilitate comparison across time periods and across companies of different 
sizes.
■■Two income-  statement-  based indicators of profitability are net profit margin 
and gross profit margin.
■■Comprehensive income includes both  net income and other revenue and 
expense items that are excluded from the net income calculation.

Practice Problems 151
1 Expenses on the income statement may be grouped by:
A nature, but not by function.
B function, but not by nature.
C either function or nature.
2 An example of an expense classification by function is:
A tax expense.
B interest expense.
C cost of goods sold.
3 Denali Limited, a manufacturing company, had the following income statement 
information:
Revenue $4,000,000
Cost of goods sold $3,000,000
Other operating expenses $500,000
Interest expense $100,000
Tax expense $120,000
 Denali’s gross profit is equal to:
A $280,000.
B $500,000.
C $1,000,000.
4 Under IFRS, income includes increases in economic benefits from:
A increases in liabilities not related to owners’ contributions.
B enhancements of assets not related to owners’ contributions.
C increases in owners’ equity related to owners’ contributions.
5 Fairplay had the following information related to the sale of its products during 
2009, which was its first year of business:
Revenue $1,000,000

Returns of goods sold $100,000
Cash collected $800,000
Cost of goods sold $700,000
 Under the accrual basis of accounting, how much net revenue would be 
reported on Fairplay’s 2009 income statement?
A $200,000.
B $900,000.
6 If the outcome of a long-  term contract can be measured reliably, the preferred 
accounting method under both IFRS and US GAAP is:
A the cost recovery method.
B the completed contract method.
C the percentage-  of- completion method.

Reading 23 ■ Understanding Income Statements 152
7 At the beginning of 2009, Florida Road Construction entered into a contract to 
build a road for the government. Construction will take four years. The follow -
ing information as of 31 December 2009 is available for the contract:
Total revenue according to contract $10,000,000
Total expected cost $8,000,000
Cost incurred during 2009 $1,200,000
 Assume that the company estimates percentage complete based on costs 
incurred as a percentage of total estimated costs. Under the completed contract 
method, how much revenue will be reported in 2009?
A None.
B $300,000.
C $1,500,000.
8 During 2009, Argo Company sold 10 acres of prime commercial zoned land to 
a builder for $5,000,000. The builder gave Argo a $1,000,000 down payment and 
will pay the remaining balance of $4,000,000 to Argo in 2010. Argo purchased 
the land in 2002 for $2,000,000. Using the installment method, how much profit 
will Argo report for 2009?
A $600,000.
B $1,000,000.
C $3,000,000.

9 Using the same information as in Question 8, how much profit will Argo report 
for 2009 using the cost recovery method?
A None.
B $600,000.
10 Under IFRS, revenue from barter transactions should be measured based on the 
fair value of revenue from:
A similar barter transactions with unrelated parties.
B similar non-  barter transactions with related parties.
C similar non-  barter transactions with unrelated parties.
11 Apex Consignment sells items over the internet for individuals on a consign -
ment basis. Apex receives the items from the owner, lists them for sale on the 
internet, and receives a 25 percent commission for any items sold. Apex collects 
the full amount from the buyer and pays the net amount after commission to 
the owner. Unsold items are returned to the owner after 90 days. During 2009, 
Apex had the following information:
■●Total sales price of items sold during 2009 on consignment was €2,000,000.

■●Total commissions retained by Apex during 2009 for these items was 
€500,000.
 How much revenue should Apex report on its 2009 income statement?
A €500,000.
B €2,000,000.
C €1,500,000.
12 A company previously expensed the incremental costs of obtaining a contract. 
All else being equal, adopting the May 2014 IASB and FASB converged account -
ing standards on revenue recognition makes the company’s profitability initially 
appear:

Practice Problems 153
A lower.
B unchanged.
C higher.
13 During 2009, Accent Toys Plc., which began business in October of that year, 
purchased 10,000 units of a toy at a cost of ₤10 per unit in October. The toy 
sold well in October. In anticipation of heavy December sales, Accent pur -
chased 5,000 additional units in November at a cost of ₤11 per unit. During 
2009, Accent sold 12,000 units at a price of ₤15 per unit. Under the first in, first 
out (FIFO) method, what is Accent’s cost of goods sold for 2009?
A ₤120,000.
B ₤122,000.
C ₤124,000.
14 Using the same information as in Question 13, what would Accent’s cost of 
goods sold be under the weighted average cost method?
15 Which inventory method is least likely to be used under IFRS?
A First in, first out (FIFO).
B Last in, first out (LIFO).
C Weighted average.
16 At the beginning of 2009, Glass Manufacturing purchased a new machine for 
its assembly line at a cost of $600,000. The machine has an estimated useful

life of 10 years and estimated residual value of $50,000. Under the straight-  line 
method, how much depreciation would Glass take in 2010 for financial report -
ing purposes?
A $55,000.
B $60,000.
C $65,000.
17 Using the same information as in Question 16, how much depreciation would 
Glass take in 2009 for financial reporting purposes under the double-  declining 
balance method?
A $60,000.
B $110,000.
C $120,000.
18 Which combination of depreciation methods and useful lives is most conserva -
tive in the year a depreciable asset is acquired?
A Straight-  line depreciation with a short useful life.
B Declining balance depreciation with a long useful life.
C Declining balance depreciation with a short useful life.
19 Under IFRS, a loss from the destruction of property in a fire would most likely 
be classified as:
A continuing operations.
B discontinued operations.
C other comprehensive income.

Reading 23 ■ Understanding Income Statements 154
20 A company chooses to change an accounting policy. This change requires that, 
if practical, the company restate its financial statements for:
A all prior periods. 
B current and future periods.
C prior periods shown in a report.
21 For 2009, Flamingo Products had net income of $1,000,000. At 1 January 2009, 
there were 1,000,000 shares outstanding. On 1 July 2009, the company issued 
100,000 new shares for $20 per share. The company paid $200,000 in dividends 
to common shareholders. What is Flamingo’s basic earnings per share for 2009?
A $0.80.
B $0.91.
C $0.95.
22 For its fiscal year-  end, Calvan Water Corporation (CWC) reported net income 
of $12 million and a weighted average of 2,000,000 common shares outstanding. 
The company paid $800,000 in preferred dividends and had 100,000 options 
outstanding with an average exercise price of $20. CWC’s market price over the 
year averaged $25 per share. CWC’s diluted EPS is closest  to:
A $5.33.
B $5.54.

A $5.33.
B $5.54.
C $5.94.
23 A company with no debt or convertible securities issued publicly traded com -
mon stock three times during the current fiscal year. Under both IFRS and US 
GAAP , the company’s: 
A basic EPS equals its diluted EPS.
B capital structure is considered complex at year-  end.
C basic EPS is calculated by using a simple average number of shares 
outstanding.
24 Laurelli Builders (LB) reported the following financial data for year-  end 31 
December:
Common shares outstanding, 1 January 2,020,000
Common shares issued as stock dividend, 1 June 380,000
Warrants outstanding, 1 January 500,000
Net income $3,350,000
Preferred stock dividends paid $430,000
Common stock dividends paid $240,000
 Which statement about the calculation of LB’s EPS is most accurate? 
A LB’s basic EPS is $1.12. 
B LB’s diluted EPS is equal to or less than its basic EPS.
C The weighted average number of shares outstanding is 2,210,000.

25 Cell Services Inc. (CSI) had 1,000,000 average shares outstanding during all 
of 2009. During 2009, CSI also had 10,000 options outstanding with exercise 
prices of $10 each. The average stock price of CSI during 2009 was $15. For pur -
poses of computing diluted earnings per share, how many shares would be used 
in the denominator?
A 1,003,333.
B 1,006,667.

Practice Problems 155
C 1,010,000.
26 For its fiscal year-  end, Sublyme Corporation reported net income of $200 mil -
lion and a weighted average of 50,000,000 common shares outstanding. There 
are 2,000,000 convertible preferred shares outstanding that paid an annual div -
idend of $5. Each preferred share is convertible into two shares of the common 
stock. The diluted EPS is closest to :
A $3.52.
B $3.65.
C $3.70.
27 When calculating diluted EPS, which of the following securities in the capital 
structure increases the weighted average number of common shares outstand -
ing without affecting net income available to common shareholders? 
A Stock options
B Convertible debt that is dilutive
C Convertible preferred stock that is dilutive
28 Which statement is most  accurate? A common size income statement:
A restates each line item of the income statement as a percentage of net 
income. 
B allows an analyst to conduct cross-  sectional analysis by removing the effect 
of company size.

C standardizes each line item of the income statement but fails to help an 
analyst identify differences in companies’ strategies.
29 Selected year-  end financial statement data for Workhard are shown below. 
$ millions
Beginning shareholders’ equity 475
Ending shareholders’ equity 493
Unrealized gain on available-  for- sale securities 5
Unrealized loss on derivatives accounted for as 
hedges–3
Foreign currency translation gain on consolidation 2
Dividends paid 1
Net income 15
 Workhard’s comprehensive income for the year: 
A is $18 million.
B is increased by the derivatives accounted for as hedges.
C includes $4 million in other comprehensive income.
30 When preparing an income statement, which of the following items would most 
likely be classified as other comprehensive income?
A A foreign currency translation adjustment 
B An unrealized gain on a security held for trading purposes 
C A realized gain on a derivative contract not accounted for as a hedge

Reading 23 ■ Understanding Income Statements 156
SOLUTIONS
1 C is correct. IAS No. 1 states that expenses may be categorized by either nature 
or function.
2 C is correct. Cost of goods sold is a classification by function. The other two 
expenses represent classifications by nature.
3 C is correct. Gross margin is revenue minus cost of goods sold. Answer A rep -
resents net income and B represents operating income.
4 B is correct. Under IFRS, income includes increases in economic benefits from 
increases in assets, enhancement of assets, and decreases in liabilities.
5 B is correct. Net revenue is revenue for goods sold during the period less any 
returns and allowances, or $1,000,000 minus $100,000 = $900,000.
6 C is correct. The preferred method is the percentage-  of- completion method. 
The completed contract method should be used under US GAAP only when the 
outcome cannot be measured reliably. A method similar to, but not referred to

as, the cost recovery method is used under IFRS when the outcome cannot be 
measured reliably.
7 A is correct. Under the completed contract method, no revenue would be 
reported until the project is completed.
8 A is correct. The installment method apportions the cash receipt between cost 
recovered and profit using the ratio of profit to sales value (i.e., $3,000,000 ÷ 
$5,000,000 = 60 percent). Argo will, therefore, recognize $600,000 in profit for 
2009 ($1,000,000 cash received × 60 percent).
9 A is correct. Under the cost recovery method, the company would not recog -
nize any profit until the cash amounts paid by the buyer exceeded Argo’s cost of 
$2,000,000.
10 C is correct. Revenue for barter transactions should be measured based on 
the fair value of revenue from similar non-  barter transactions with unrelated 
parties.
11 A is correct. Apex is not the owner of the goods and should only report its net 
commission as revenue.

12 C is correct. Under the converged accounting standards, the incremental costs 
of obtaining a contract and certain costs incurred to fulfill a contract must be 
capitalized. If a company expensed these incremental costs in the years prior 
to adopting the converged standards, all else being equal, its profitability will 
appear higher under the converged standards. 
13 B is correct. Under the first in, first out (FIFO) method, the first 10,000 units 
sold came from the October purchases at £10, and the next 2,000 units sold 
came from the November purchases at £11.
14 C is correct. Under the weighted average cost method:
October purchases 10,000 units $100,000
November purchases 5,000 units $55,000
  Total 15,000 units $155,000
 $155,000/15,000 units = $10.3333 × 12,000 units = $124,000.
15 B is correct. The last in, first out (LIFO) method is not permitted under IFRS. 
The other two methods are permitted.

Solutions 157
16 A is correct. Straight-  line depreciation would be ($600,000 – $50,000)/10, or 
$55,000.
17 C is correct. Double-  declining balance depreciation would be $600,000 × 
20 percent (twice the straight-  line rate). The residual value is not subtracted 
from the initial book value to calculate depreciation. However, the book value 
(carrying amount) of the asset will not be reduced below the estimated residual 
value.
18 C is correct. This would result in the highest amount of depreciation in the first 
year and hence the lowest amount of net income relative to the other choices.
19 A is correct. A fire may be infrequent, but it would still be part of continuing 
operations and reported in the profit and loss statement. Discontinued opera -
tions relate to a decision to dispose of an operating division.
20 C is correct. If a company changes an accounting policy, the financial state -
ments for all fiscal years shown in a company’s financial report are presented,

if practical, as if the newly adopted accounting policy had been used through -
out the entire period; this retrospective application of the change makes the 
financial results of any prior years included in the report comparable. Notes to 
the financial statements describe the change and explain the justification for the 
change. 
21 C is correct. The weighted average number of shares outstanding for 2009 is 
1,050,000. Basic earnings per share would be $1,000,000 divided by 1,050,000, 
or $0.95.
22 B is correct. The formula to calculate diluted EPS is as follows: 
Diluted EPS = (Net income – Preferred dividends)/[Weighted average 
number of shares outstanding + (New shares that would have been issued at 
option exercise – Shares that could have been purchased with cash received 
upon exercise) × (Proportion of year during which the financial instruments 
were outstanding)]. 
 The underlying assumption is that outstanding options are exercised, and then

the proceeds from the issuance of new shares are used to repurchase shares 
already outstanding: 
Proceeds from option exercise = 100,000 × $20 = $2,000,000
Shares repurchased = $2,000,000/$25 = 80,000
 The net increase in shares outstanding is thus 100,000 – 80,000 = 20,000. 
Therefore, the diluted EPS for CWC = ($12,000,000 – $800,000)/2,020,000 = 
$5.54. 
23 A is correct. Basic and diluted EPS are equal for a company with a simple 
capital structure. A company that issues only common stock, with no financial 
instruments that are potentially convertible into common stock has a simple 
capital structure. Basic EPS is calculated using the weighted average number of 
shares outstanding. 
24 B is correct. LB has warrants in its capital structure; if the exercise price is 
less than the weighted average market price during the year, the effect of their 
conversion is to increase the weighted average number of common shares out -

standing, causing diluted EPS to be lower than basic EPS. If the exercise price is 
equal to the weighted average market price, the number of shares issued equals 
the number of shares repurchased. Therefore, the weighted average number of 
common shares outstanding is not affected and diluted EPS equals basic EPS. If 
the exercise price is greater than the weighted average market price, the effect

Reading 23 ■ Understanding Income Statements 158
of their conversion is anti-  dilutive. As such, they are not included in the calcula -
tion of basic EPS. LB’s basic EPS is $1.22 [= ($3,350,000 – $430,000)/2,400,000]. 
Stock dividends are treated as having been issued retroactively to the beginning 
of the period. 
25 A is correct. With stock options, the treasury stock method must be used. 
Under that method, the company would receive $100,000 (10,000 × $10) and 
would repurchase 6,667 shares ($100,000/$15). The shares for the denominator 
would be:
Shares outstanding 1,000,000
Options exercises 10,000
Treasury shares purchased (6,667)
Denominator 1,003,333
26 C is correct. 
 Diluted EPS =  (Net income)/(Weighted average number of shares out -
standing + New common shares that would have been issued 
at conversion)
  = $200,000,000/[50,000,000 + (2,000,000 × 2)]
  = $3.70
 The diluted EPS assumes that the preferred dividend is not paid and that the 
shares are converted at the beginning of the period.

27 A is correct. When a company has stock options outstanding, diluted EPS is 
calculated as if the financial instruments had been exercised and the company 
had used the proceeds from the exercise to repurchase as many shares possible 
at the weighted average market price of common stock during the period. As a 
result, the conversion of stock options increases the number of common shares 
outstanding but has no effect on net income available to common sharehold -
ers. The conversion of convertible debt increases the net income available to 
common shareholders by the after-  tax amount of interest expense saved. The 
conversion of convertible preferred shares increases the net income available to 
common shareholders by the amount of preferred dividends paid; the numera -
tor becomes the net income.
28 B is correct. Common size income statements facilitate comparison across time 
periods (time-  series analysis) and across companies (cross-  sectional analysis)

by stating each line item of the income statement as a percentage of revenue. 
The relative performance of different companies can be more easily assessed 
because scaling the numbers removes the effect of size. A common size income 
statement states each line item on the income statement as a percentage of 
revenue. The standardization of each line item makes a common size income 
statement useful for identifying differences in companies’ strategies. 
29 C is correct. Comprehensive income includes both net income and other com -
prehensive income. 
 Other comprehensive income =  Unrealized gain on available-  for- sale 
securities – Unrealized loss on derivatives 
accounted for as hedges + Foreign currency 
translation gain on consolidation
  = $5 million – $3 million + $2 million
  = $4 million

Solutions 159
 Alternatively, 
Comprehensive income – Net income = Other comprehensive income
 Comprehensive income =  (Ending shareholders equity – Beginning share -
holders equity) + Dividends
  = ($493 million – $475 million) + $1 million
  = $18 million + $1 million = $19 million
 Net income is $15 million so other comprehensive income is $4 million. 
30 A is correct. Other comprehensive income includes items that affect sharehold -
ers’ equity but are not reflected in the company’s income statement. In consoli -
dating the financial statements of foreign subsidiaries, the effects of translating 
the subsidiaries’ balance sheet assets and liabilities at current exchange rates are 
included as other comprehensive income.

Understanding Balance Sheets
a. describe the elements of the balance sheet: assets, liabilities, and 
equity;
b. describe uses and limitations of the balance sheet in financial 
analysis;
c. describe alternative formats of balance sheet presentation;
d. distinguish between current and non-  current assets and current 
and non-  current liabilities;
e. describe different types of assets and liabilities and the 
measurement bases of each;
f. describe the components of shareholders’ equity;
g. convert balance sheets to common-  size balance sheets and 
interpret common-  size balance sheets;
h. calculate and interpret liquidity and solvency ratios.REA dINg
24
© 2011 CFA Institute. All rights reserved.Note:  Changes in accounting

Reading 24 ■ Understanding Balance Sheets 162
The balance sheet provides information on a company’s resources (assets) and its 
sources of capital (equity and liabilities/debt). This information helps an analyst assess 
a company’s ability to pay for its near-  term operating needs, meet future debt obliga -
tions, and make distributions to owners. The basic equation underlying the balance 
sheet is Assets = Liabilities + Equity.
Analysts should be aware that different items of assets and liabilities may be 
measured differently. For example, some items are measured at historical cost or a 
variation thereof and others at fair value.1 An understanding of the measurement 
issues will facilitate analysis. The balance sheet measurement issues are, of course, 
closely linked to the revenue and expense recognition issues affecting the income 
statement. Throughout this reading, we describe and illustrate some of the linkages

between the measurement issues affecting the balance sheet and the revenue and 
expense recognition issues affecting the income statement.
This reading is organized as follows: In Section 2, we describe and give examples 
of the elements and formats of balance sheets. Section 3 discusses current assets and 
current liabilities. Section 4 focuses on assets, and Section 5 focuses on liabilities. 
Section 6 describes the components of equity and illustrates the statement of changes 
in shareholders’ equity. Section 7 introduces balance sheet analysis. A summary of 
the key points and practice problems in the CFA Institute multiple-  choice format 
conclude the reading.
COMPONENTS AND FORMAT OF THE BALANCE 
SHEET
The balance sheet  (also called the statement of financial position  or statement of 
financial condition ) discloses what an entity owns (or controls), what it owes, and 
what the owners’ claims are at a specific point in time.2

The financial position of a company is described in terms of its basic elements 
(assets, liabilities, and equity):
■■Assets  (A) are what the company owns (or controls). More formally, assets are 
resources controlled by the company as a result of past events and from which 
future economic benefits are expected to flow to the entity.
■■Liabilities  (L) are what the company owes. More formally, liabilities represent 
obligations of a company arising from past events, the settlement of which is 
expected to result in an outflow of economic benefits from  the entity.
■■Equity  (E) represents the owners’ residual interest in the company’s assets after 
deducting its liabilities. Commonly known as shareholders’ equity  or owners’ 
equity , equity is determined by subtracting the liabilities from the assets of a 
company, giving rise to the accounting equation: A – L = E  or A = L + E .1
2
1 IFRS and US GAAP define “fair value” as an exit price, i.e., the price that would be received to sell an

asset or paid to transfer a liability in an orderly transaction between market participants at the measurement 
date (IFRS 13, FASB ASC Topic 820).
2 IFRS uses the term “statement of financial position” (IAS 1 Presentation of Financial Statements ), although 
US GAAP uses the two terms interchangeably (ASC 210-  10- 05 [Balance Sheet–Overall–Overview and 
Background).

Components and Format of the Balance Sheet 163
The equation A = L + E is sometimes summarized as follows: The left side of the 
equation reflects the resources controlled by the company and the right side reflects 
how those resources were financed. For all financial statement items, an item should 
only be recognized in the financial statements if it is probable that any future economic 
benefit associated with the item will flow to or from the entity and if the item has a 
cost or value that can be measured with reliability.3
The balance sheet provides important information about a company’s financial 
condition, but the balance sheet amounts of equity (assets, net of liabilities) should not 
be viewed as a measure of either the market or intrinsic value of a company’s equity 
for several reasons. First, the balance sheet under current accounting standards is a 
mixed model with respect to measurement. Some assets and liabilities are measured

based on historical cost, sometimes with adjustments, whereas other assets and lia -
bilities are measured based on a current value. The measurement bases may have a 
significant effect on the amount reported. Second, even the items measured at current 
value reflect the value that was current at the end of the reporting period. The values 
of those items obviously can change after the balance sheet is prepared. Third, the 
value of a company is a function of many factors, including future cash flows expected 
to be generated by the company and current market conditions. Important aspects 
of a company’s ability to generate future cash flows—for example, its reputation and 
management skills—are not included in its balance sheet.
2.1 Balance Sheet Components
To illustrate the components and formats of balance sheets, we show the major sub -
totals from two companies’ balance sheets. Exhibit 1 and Exhibit 2 are based on the

balance sheets of SAP Group and Apple Inc. SAP Group is a leading business software 
company based in Germany and prepares its financial statements in accordance with 
IFRS. Apple is a technology manufacturer based in the United States and prepares 
its financial statements in accordance with US GAAP . For purposes of discussion, 
Exhibits 1 and 2 show only the main subtotals and totals of these companies’ balance 
sheets. Additional exhibits throughout this reading will expand on these subtotals.
Exhibit 1   SAP Group Consolidated Statements of Financial Position  
(Excerpt) (in millions of €)
31 December
Assets 2009 2008
Total current assets 5,255 5,571
Total non-  current assets 8,119 8,329
Total assets 13,374 13,900
Total current liabilities 3,416 5,824
Total non-  current liabilities 1,467 905
Total liabilities 4,883 6,729
3 Framework for the Preparation and Presentation of Financial Statements , International Accounting

Standards Committee, 1989, adopted by IASB 2001, paragraph 83. Conceptual Framework for Financial 
Reporting (2010 ), paragraph 4.38.

Reading 24 ■ Understanding Balance Sheets 164
Total equity 8,491 7,171
Equity and liabilities 13,374 13,900
Source:  SAP Group 2009 annual report.
Exhibit 2   Apple Inc. Consolidated Balance Sheet  
(Excerpt)* (in millions of $)
Assets 26 September 2009 27 September 2008
Total current assets 31,555 30,006
[All other assets] 15,946 6,165
Total assets 47,501 36,171
Liabilities and shareholders’ 
equity
Total current liabilities 11,506 11,361
[Total non-  current liabilities] 4,355 2,513
Total liabilities 15,861 13,874
Total shareholders’ equity 31,640 22,297
Total liabilities and shareholders’ 
equity47,501 36,171
*Note : The italicized subtotals presented in this excerpt are not explicitly shown on the face of the 
financial statement as prepared by the company.
Source:  Apple Inc. 2009 annual report (Form 10K/A).
SAP Group uses the title Statement of Financial Position, consistent with IFRS, 
and Apple uses the title Balance Sheet. Despite their different titles, both statements

report the three basic elements: assets, liabilities, and equity. Both companies are 
reporting on a consolidated basis, i.e., including all their controlled subsidiaries. The 
numbers in SAP Group’s balance sheet are in millions of euro, and the numbers in 
Apple’s balance sheet are in millions of dollars.
Balance sheet information is as of a specific point in time. These exhibits are from 
the companies’ annual financial statements, so the balance sheet information is as of 
the last day of their respective fiscal years. SAP Group’s fiscal year is the same as the 
calendar year and the balance sheet information is as of 31 December. Apple’s fiscal 
year ends on the last Saturday of September so the actual date changes from year to 
year. About every six years, Apple’s fiscal year will include 53 weeks rather than 52 
weeks. This feature of Apple’s fiscal year should be noted, but in general, the extra 
week is more relevant to evaluating statements spanning a period of time (the income

and cash flow statements) rather than the balance sheet which captures information 
as of a specific point in time.
A company’s ability to pay for its short term operating needs relates to the concept 
of liquidity . With respect to a company overall, liquidity refers to the availability of 
cash to meet those short-  term needs. With respect to a particular asset or liability, 
liquidity refers to its “nearness to cash. ” A liquid asset is one that can be easily converted Exhibit 1   (Continued)

Components and Format of the Balance Sheet 165
into cash in a short period of time at a price close to fair market value. For example, 
a small holding of an actively traded stock is much more liquid than an asset such as 
a commercial real estate property in a weak property market.
The separate presentation of current and non-  current assets and liabilities enables 
an analyst to examine a company’s liquidity position (at least as of the end of the fiscal 
period). Both IFRS and US GAAP require that the balance sheet distinguish between 
current and non-  current assets and between current and non-  current liabilities and 
present these as separate classifications. An exception to this requirement, under IFRS, 
is that the current and non-  current classifications are not required if a liquidity-  based 
presentation provides reliable and more relevant information. Presentations distin -
guishing between current and non-  current elements are shown in Exhibits 1 and 2.

Exhibit 3 in Section 2.3 shows a liquidity-  based presentation.
2.2 Current and Non-  Current Classification
Assets held primarily for the purpose of trading or expected to be sold, used up, or 
otherwise realized in cash within one year or one operating cycle of the business, 
whichever is greater, after the reporting period are classified as current assets . A 
company’s operating cycle is the average amount of time that elapses between acquiring 
inventory and collecting the cash from sales to customers. For a manufacturer, this 
is the average amount of time between acquiring raw materials and converting these 
into cash from a sale. Examples of companies that might be expected to have operat -
ing cycles longer than one year include those operating in the tobacco, distillery, and 
lumber industries. Even though these types of companies often hold inventories longer 
than one year, the inventory is classified as a current asset because it is expected to

be sold within an operating cycle. Assets not expected to be sold or used up within 
one year or one operating cycle of the business, whichever is greater, are classified as 
non-  current assets  (long-  term, long-  lived assets).
Current assets are generally maintained for operating purposes, and these assets 
include—in addition to cash—items expected to be converted into cash (e.g., trade 
receivables), used up (e.g., office supplies, prepaid expenses), or sold (e.g., inventories) 
in the current period. Current assets provide information about the operating activities 
and the operating capability of the entity. For example, the item “trade receivables” or 
“accounts receivable” would indicate that a company provides credit to its customers. 
Non-  current assets represent the infrastructure from which the entity operates and 
are not consumed or sold in the current period. Investments in such assets are made 
from a strategic and longer term perspective.

Similarly, liabilities expected to be settled within one year or within one operating 
cycle of the business, whichever is greater, after the reporting period are classified 
as current liabilities . The specific criteria for classification of a liability as current 
■■It is expected to be settled in the entity’s normal operating cycle;
■■It is held primarily for the purpose of being traded;4
■■It is due to be settled within one year after the balance sheet date; or
■■The entity does not have an unconditional right to defer settlement of the liabil -
ity for at least one year after the balance sheet date.5
4 Examples of these are financial liabilities classified as held for trading in accordance with IAS 39, which 
is replaced by IFRS 9 effective 2018.
5 IAS 1, Presentation of Financial Statements , paragraph 69.

Reading 24 ■ Understanding Balance Sheets 166
IFRS specify that some current liabilities, such as trade payables and some accruals 
for employee and other operating costs, are part of the working capital used in the 
entity’s normal operating cycle. Such operating items are classified as current liabilities 
even if they will be settled more than one year after the balance sheet date. When the 
entity’s normal operating cycle is not clearly identifiable, its duration is assumed to 
be one year. All other liabilities are classified as non-  current liabilities . Non-  current 
liabilities include financial liabilities that provide financing on a long-  term basis.
The excess of current assets over current liabilities is called working capital . The 
level of working capital tells analysts something about the ability of an entity to meet 
liabilities as they fall due. Although adequate working capital is essential, working

capital should not be too large because funds may be tied up that could be used more 
productively elsewhere.
A balance sheet with separately classified current and non-  current assets and lia -
bilities is referred to as a classified balance sheet . Classification also refers generally 
to the grouping of accounts into subcategories. Both companies’ balance sheets that 
are summarized in Exhibits 1 and 2 are classified balance sheets. Although both com -
panies’ balance sheets present current assets before non-  current assets and current 
liabilities before non-  current liabilities, this is not required. IFRS does not specify 
the order or format in which a company presents items on a current/non-  current 
classified balance sheet.
2.3 Liquidity-  Based Presentation
A liquidity-  based presentation, rather than a current/non-  current presentation, is 
used when such a presentation provides information that is reliable and more relevant.

With a liquidity-  based presentation, all assets and liabilities are presented broadly in 
order of liquidity.
Entities such as banks are candidates to use a liquidity-  based presentation. Exhibit 3 
presents the assets portion of the balance sheet of China Construction Bank, a 
commercial bank based in Beijing that reports using IFRS. [The Bank's H-  shares are 
listed on the Hong Kong Stock Exchange (Stock Code: 939), and the Bank's A-  shares 
are listed on the Shanghai Stock Exchange (Stock Code: 601939).] Its balance sheet 
is ordered using a liquidity-  based presentation. As shown, the asset section begins 
with Cash and deposits with central banks. Less liquid items such as fixed assets and 
land use rights appear near the bottom of the asset listing.
Exhibit 3   China Construction Bank Corporation Consolidated Statement 
of Financial Position (Excerpt: Assets Only) as of 31 December (in 
millions of RMB) 
Cash and deposits with central banks 1,458,648 1,247,450

Deposits with banks and non-  bank financial 
institutions101,163 33,096
Precious metals 9,229 5,160
Placements with banks and non-  bank financial 
institutions22,217 16,836
Financial assets at fair value through profit or loss 18,871 50,309
Positive fair value of derivatives 9,456 21,299
Financial assets held under resale agreements 589,606 208,548
Interest receivable 40,345 38,317

Current Assets and Current Liabilities 167
Loans and advances to customers 4,692,947 3,683,575
Available-  for- sale financial assets 651,480 550,838
Held-  to- maturity investments 1,408,873 1,041,783
Debt securities classified as receivables 499,575 551,818
Interests in associates and jointly controlled entities 1,791 1,728
Fixed assets 74,693 63,957
Land use rights 17,122 17,295
Intangible assets 1,270 1,253
Goodwill 1,590 1,527
Deferred tax assets 10,790 7,855
Other assets 13,689 12,808
Total assets 9,623,355 7,555,452
Source:  China Construction Bank 2009 Annual Report.
CURRENT ASSETS AND CURRENT LIABILITIES
This section examines current assets and current liabilities in greater detail.
3.1 Current Assets
Accounting standards require that certain specific line items, if they are material, must 
be shown on a balance sheet. Among the current assets’ required line items are cash 
and cash equivalents, trade and other receivables, inventories, and financial assets

(with short maturities). Companies present other line items as needed, consistent 
with the requirements to separately present each material class of similar items. As 
examples, Exhibit 4 and Exhibit 5 present balance sheet excerpts for SAP Group and 
Apple Inc. showing the line items for the companies’ current assets.
Exhibit 4   SAP Group Consolidated Statements of Financial Position 
(Excerpt: Current Assets Detail) (in millions of €)
as of 31 December
Cash and cash equivalents 1,884 1,280
Other financial assets 486 588
Trade and other receivables 2,546 3,178
Other non-  financial assets 147 126
Tax assets 192 399
Equity and liabilities3
(continued)Exhibit 3   (Continued)

Reading 24 ■ Understanding Balance Sheets 168
Exhibit 5   Apple Inc. Consolidated Balance Sheet (Excerpt: Current Assets 
Detail) * (in millions of $)
Cash and cash equivalents 5,263 11,875
Short-  term marketable securities 18,201 10,236
Accounts receivable, less allow -
ances of $52 and $47, respectively3,361 2,422
Inventories 455 509
Deferred tax assets 1,135 1,044
Other current assets 3,140 3,920
equity
Total liabilities and

Total liabilities and 
shareholders’ equity47,501 36,171
3.1.1  Cash and Cash Equivalents
Cash equivalents are highly liquid, short-  term investments that are so close to maturity,6 
the risk is minimal that their value will change significantly with changes in interest 
rates. Cash and cash equivalents are financial assets. Financial assets, in general, are 
measured and reported at either amortised cost  or fair value . Amortised cost is the 
historical cost (initially recognised cost) of the asset adjusted for amortisation and Exhibit 4   (Continued)
6 Generally, three months or less.

Current Assets and Current Liabilities 169
impairment. Under IFRS and US GAAP , fair value is based on an exit price, the price 
received to sell an asset or paid to transfer a liability in an orderly transaction between 
two market participants at the measurement date.
For cash and cash equivalents, amortised cost and fair value are likely to be 
immaterially different. Examples of cash equivalents are demand deposits with banks 
and highly liquid investments (such as US Treasury bills, commercial paper, and 
money market funds) with original maturities of three months or less. Cash and cash 
equivalents excludes amounts that are restricted in use for at least 12 months. For all 
companies, the Statement of Cash Flows presents information about the changes in 
cash over a period. For the fiscal year 2009, SAP Group’s cash and cash equivalents 
increased from €1,280 million to €1,844 million, and Apple’s cash and cash equivalents 
decreased from $11,875 million to $5,263 million.

3.1.2  Marketable Securities
Marketable securities are also financial assets and include investments in debt or 
equity securities that are traded in a public market, and whose value can be deter -
mined from price information in a public market. Examples of marketable securities 
include treasury bills, notes, bonds, and equity securities, such as common stocks 
and mutual fund shares. Companies disclose further detail in the notes to their 
financial statements about their holdings. For example, SAP Group discloses that 
its other financial assets consist mainly of time deposits, investment in insurance 
policies, and loans to employees. Apple’s short-  term marketable securities, totaling 
$18.2 billion and $10.2 billion at the end of fiscal 2009 and 2008, respectively, consist 
of fixed-  income securities with a maturity of less than one year. Financial assets such

as investments in debt and equity securities involve a variety of measurement issues 
and will be addressed in Section 4.5.
3.1.3  Trade Receivables
Trade receivables, also referred to as accounts receivable, are another type of financial 
asset. These are amounts owed to a company by its customers for products and services 
already delivered. They are typically reported at net realisable value, an approximation 
of fair value, based on estimates of collectability. Several aspects of accounts receivable 
are usually relevant to an analyst. First, the overall level of accounts receivable relative 
to sales (a topic to be addressed further in ratio analysis) is important because a sig -
nificant increase in accounts receivable relative to sales could signal that the company 
is having problems collecting cash from its customers.
A second relevant aspect of accounts receivable is the allowance for doubtful 
accounts. The allowance for doubtful accounts reflects the company’s estimate of

amounts that will ultimately be uncollectible. Additions to the allowance in a par -
ticular period are reflected as bad debt expenses, and the balance of the allowance 
for doubtful accounts reduces the gross receivables amount to a net amount that is 
an estimate of fair value. When specific receivables are deemed to be uncollectible, 
they are written off by reducing accounts receivable and the allowance for doubtful 
accounts. The allowance for doubtful accounts is called a contra account  because it 
is netted against (i.e., reduces) the balance of accounts receivable, which is an asset 
account. SAP Group’s balance sheet, for example, reports current net trade and other 
receivables of €2,546 million as of 31 December 2009. The amount of the allowance for 
doubtful accounts (€48 million) is disclosed in the notes to the financial statements. 
Apple discloses the allowance for doubtful accounts on the balance sheet; as of 26

September 2009, the allowance was $52 million. The $3,361 million of accounts receiv -
able on that date is net of the allowance. Apple’s disclosures state that the allowance 
is based on “historical experience, the age of the accounts receivable balances, credit 
quality of the Company’s customers, current economic conditions, and other factors

Reading 24 ■ Understanding Balance Sheets 170
that may affect customers’ ability to pay. ” The age of an accounts receivable balance 
refers to the length of time the receivable has been outstanding, including how many 
days past the due date.
Another relevant aspect of accounts receivable is the concentration of credit risk. 
For example, SAP Group’s note on trade and other receivables discloses that concen -
tration of credit risk is limited because they have a large customer base diversified 
across various industries and countries, and because no single customer accounted 
for 10 percent or more of either revenue or receivables.
EXAMPLE 1   
Analysis of Accounts Receivable
1 Based on the balance sheet excerpt for Apple Inc. in Exhibit 5, what 
percentage of its total accounts receivable in 2009 and 2008 does Apple 
estimate will be uncollectible?
2 In general, how does the amount of allowance for doubtful accounts relate 
to bad debt expense?

3 In general, what are some factors that could cause a company’s allowance 
for doubtful accounts to decrease?
($ millions) The percentage of 2009 accounts receivable estimated to be uncollect -
ible is 1.5 percent, calculated as $52/($3,361 + $52). Note that the $3,361 is net 
of the $52 allowance, so the gross amount of accounts receivable is determined 
by adding the allowance to the net amount. The percentage of 2008 accounts 
receivable estimated to be uncollectible is 1.9 percent [$47/($2,422 + $47)].
Bad debt expense is an expense of the period, based on a company’s estimate 
of the percentage of credit sales in the period, for which cash will ultimately 
not be collected. The allowance for bad debts is a contra asset account, which 
is netted against the asset accounts receivable.
To record the estimated bad debts, a company recognizes a bad debt expense 
(which affects net income) and increases the balance in the allowance for doubtful

accounts by the same amount. To record the write off of a particular account 
receivable, a company reduces the balance in the allowance for doubtful accounts 
and reduces the balance in accounts receivable by the same amount.
In general, a decrease in a company’s allowance for doubtful accounts in absolute 
terms could be caused by a decrease in the amount of credit sales.
Some factors that could cause a company’s allowance for doubtful accounts 
to decrease as a percentage of accounts receivable include the following:
■■Improvements in the credit quality of the company’s existing customers 
(whether driven by a customer-  specific improvement or by an improve -
ment in the overall economy);

Current Assets and Current Liabilities 171
■■Stricter credit policies (for example, refusing to allow less creditworthy 
customers to make credit purchases and instead requiring them to pay 
cash, to provide collateral, or to provide some additional form of financial 
backing); and/or
■■Stricter risk management policies (for example, buying more insurance 
against potential defaults).
In addition to the business factors noted above, because the allowance is based 
on management’s estimates of collectability, management can potentially bias 
these estimates to manipulate reported earnings. For example, a management 
team aiming to increase reported income could intentionally over-  estimate 
collectability and under-  estimate the bad debt expense for a period. Conversely, 
in a period of good earnings, management could under-  estimate collectability 
and over-  estimate the bad debt expense with the intent of reversing the bias in 
a period of poorer earnings.
3.1.4  Inventories

Inventories are physical products that will eventually be sold to the company’s custom -
ers, either in their current form (finished goods) or as inputs into a process to man -
ufacture a final product (raw materials and work-  in- process). Like any manufacturer, 
Apple holds inventories. The 2009 balance sheet of Apple Inc. shows $455 million of 
inventories. SAP Group’s balance sheet does not include a line item for inventory, but 
its note disclosures indicate that inventory is included as a part of other non-  financial 
assets on its balance sheet. SAP Group is primarily a software and services provider 
and the amount of its inventory is not material enough to require disclosure as a 
separate line item on the balance sheet.
Inventories are measured at the lower of cost and net realisable value under IFRS 
and, depending upon inventory method, under US GAAP . The cost of inventories com -

prises all costs of purchase, costs of conversion, and other costs incurred in bringing 
the inventories to their present location and condition. The following amounts are 
excluded from the determination of inventory costs:
■■abnormal amounts of wasted materials, labor, and overheads;
■■storage costs, unless they are necessary prior to a further production process;
■■administrative overheads; and
■■selling costs.
The following techniques can be used to measure the cost of inventories if the 
resulting valuation amount approximates cost:
■■Standard cost , which should take into account the normal levels of materials, 
labor, and actual capacity. The standard cost should be reviewed regularly to 
ensure that it approximates actual costs.
■■The retail method  in which the sales value is reduced by the gross margin to 
calculate cost. An average gross margin percentage should be used for each 
homogeneous group of items. In addition, the impact of marked-  down prices

should be taken into consideration.
Net realisable value (NRV), the measure used by IFRS, is the estimated selling price 
less the estimated costs of completion and costs necessary to make the sale. Under 
US GAAP , inventories were measured at the lower of cost or market value. Market 
value is current replacement cost but with upper and lower limits: It cannot exceed

Reading 24 ■ Understanding Balance Sheets 172
NRV and cannot be lower than NRV less a normal profit margin. Under US GAAP , 
inventories measured using other than last-  in, first-  out and retail inventory methods 
are measured at the lower of cost and NRV.
If the net realisable value (under IFRS) or market value (under US GAAP) of a 
company’s inventory falls below its carrying amount, the company must write down 
the value of the inventory. The loss in value is reflected in the income statement. For 
example, within its Management’s Discussion and Analysis and notes, Apple indicates 
that the company reviews its inventory each quarter and records write-  downs of 
inventory that has become obsolete, exceeds anticipated demand, or is carried at a 
value higher than its market value. Under IFRS, if inventory that was written down in 
a previous period subsequently increases in value, the amount of the original write-

down is reversed. Subsequent reversal of an inventory write-  down is not permitted 
under US GAAP .
When inventory is sold, the cost of that inventory is reported as an expense, “cost 
of goods sold. ” Accounting standards allow different valuation methods for determining 
the amounts that are included in cost of goods sold on the income statement and thus 
the amounts that are reported in inventory on the balance sheet. (Inventory valua -
tion methods are referred to as cost formulas and cost flow assumptions under IFRS 
and US GAAP , respectively.) IFRS allows only the first-  in, first-  out (FIFO), weighted 
average cost, and specific identification methods. Some accounting standards (such 
as US GAAP) also allow last-  in, first-  out (LIFO) as an additional inventory valuation 
method. The LIFO method is not allowed under IFRS.
EXAMPLE 2   
Analysis of Inventory
Cisco Systems is a global provider of networking equipment. In its third quarter

2001 Form 10-  Q filed with the US Securities and Exchange Commission (US 
SEC) on 1 June 2001, the company made the following disclosure:
We recorded a provision for inventory, including purchase commit -
ments, totaling $2.36  billion in the third quarter of fiscal 2001, of 
which $2.25 billion related to an additional excess inventory charge. 
Inventory purchases and commitments are based upon future sales 
forecasts. To mitigate the component supply constraints that have 
existed in the past, we built inventory levels for certain components 
with long lead times and entered into certain longer-  term commit -
ments for certain components. Due to the sudden and significant 
decrease in demand for our products, inventory levels exceeded our 
requirements based on current 12-  month sales forecasts. This addi -
tional excess inventory charge was calculated based on the inventory 
levels in excess of 12-  month demand for each specific product. We

do not currently anticipate that the excess inventory subject to this 
provision will be used at a later date based on our current 12-  month 
demand forecast.
After the inventory charge, Cisco reported approximately $2 billion of inventory 
on the balance sheet, suggesting that the write-  off amounted to approximately 
half of its inventory. In addition to the obvious concerns raised as to manage -
ment’s poor performance in anticipating how much inventory was required, 
many analysts were concerned about how the write-  off would affect Cisco’s 
future reported earnings. If this inventory is sold in a future period, a “gain”

Current Assets and Current Liabilities 173
could be reported based on a lower cost basis for the inventory. In this case, 
management indicated that the intent was to scrap the inventory. When the 
company subsequently released its annual earnings, the press release stated:7
Net sales for fiscal 2001 were $22.29 billion, compared with $18.93 bil -
lion for fiscal 2000, an increase of 18%. Pro forma net income, which 
excludes the effects of acquisition charges, payroll tax on stock option 
exercises, restructuring costs and other special charges, excess inven -
tory charge (benefit), and net gains realized on minority investments, 
was $3.09 billion or $0.41 per share for fiscal 2001, compared with 
pro forma net income of $3.91 billion or $0.53 per share for fiscal 
2000, decreases of 21% and 23%, respectively.
Actual net loss for fiscal 2001 was $1.01 billion or $0.14 per share, 
compared with actual net income of $2.67 billion or $0.36 per share 
for fiscal 2000.

1 What concerns would an analyst likely have about the company’s $2.3 bil -
lion write-  off of inventory? What is the significance of the company indi -
cating its intent to scrap the written off inventory?
2 What concerns might an analyst have about the company’s earnings press 
release when the company subsequently released its annual earnings?
Solution to 1: 
First, an analyst would likely have concerns about management’s abilities to 
anticipate how much and what type of inventory was required. While errors 
in forecasting demand are understandable, the amount of inventory written off 
represented about half of the company’s inventory. A second concern would relate 
to how the write-  off would affect the company’s future reported earnings. If the 
inventory that had been written off were sold in a future period, a “gain” could 
be reported based on a lower cost basis for the inventory. The company’s intent

to scrap the written off inventory would alleviate but not eliminate concerns 
about distortions to future reported earnings.
Solution to 2: 
An analyst might be concerned that the company’s press release focused mainly 
on “pro forma earnings, ” which excluded the impact of many items, including 
the inventory write-  off. The company only gave a brief mention of actual (US 
GAAP) results.
Note : A 2003 SEC regulation now requires companies to give at least equal emphasis to GAAP 
measures (for example, reported net income) when using a non-  GAAP measure (for example, pro 
forma net income) and to provide a reconciliation of the two measures.8
3.1.5  Other Current Assets
The amounts shown in “other current assets” reflect items that are individually not 
material enough to require a separate line item on the balance sheet and so are aggre -
gated into a single amount. Companies usually disclose the components in a note to

the financial statements. A typical item included in other current assets is prepaid 
expenses. Prepaid expenses  are normal operating expenses that have been paid in 
7 Cisco press release dated 7 August 2001 from www.cisco.com.
8 US Securities and Exchange Commission. (January 2003). Final rule: Conditions for use of non-  GAAP 
financial measures  (Releases 33-  8176 and 34-  47226, File S7-  43- 02).

Reading 24 ■ Understanding Balance Sheets 174
advance. Because expenses are recognized in the period in which they are incurred—and 
not necessarily the period in which the payment is made—the advance payment of a 
future expense creates an asset. The asset (prepaid expenses) will be recognized as an 
expense in future periods as it is used up. For example, consider prepaid insurance. 
Assume a company pays its insurance premium for coverage over the next calendar 
year on 31 December of the current year. At the time of the payment, the company 
recognizes an asset (prepaid insurance expense). The expense is not incurred at that 
date; the expense is incurred as time passes (in this example, one-  twelfth, 1/12, in 
each following month). Therefore, the expense is recognized and the value of the asset 
is reduced in the financial statements over the course of the year.
Portions of the amounts shown as tax assets on SAP’s balance sheet and deferred

tax assets  on Apple’s balance sheet represent income taxes incurred prior to the time 
that the income tax expense will be recognized on the income statement. Deferred 
tax assets may result when the actual income tax payable  based on income for tax 
purposes in a period exceeds the amount of income tax expense based on the reported 
financial statement income due to temporary timing differences. For example, a 
company may be required to report certain income for tax purposes in the current 
period but to defer recognition of that income for financial statement purposes to 
subsequent periods. In this case, the company will pay income tax as required by 
tax laws, and the difference between the taxes payable and the tax expense related 
to the income for which recognition was deferred on the financial statements will 
be reported as a deferred tax asset. When the income is subsequently recognized on 
the income statement, the related tax expense is also recognised which will reduce

the deferred tax asset.
Also, a company may claim certain expenses for financial statement purposes that 
it is only allowed to claim in subsequent periods for tax purposes. In this case, as in 
the previous example, the financial statement income before taxes is less than taxable 
income. Thus, income taxes payable based on taxable income exceeds income tax 
expense based on accounting net income before taxes. The difference is expected to 
reverse in the future when the income reported on the financial statements exceeds 
the taxable income as a deduction for the expense becomes allowed for tax purposes. 
Deferred tax assets may also result from carrying forward unused tax losses and 
credits (these are not temporary timing differences). Deferred tax assets are only to 
be recognised if there is an expectation that there will be taxable income in the future, 
against which the temporary difference or carried forward tax losses or credits can 
be applied to reduce taxes payable.

3.2 Current Liabilities
Current liabilities  are those liabilities that are expected to be settled in the entity’s 
normal operating cycle, held primarily for trading, or due to be settled within 12 months 
after the balance sheet date. Exhibit 6 and Exhibit 7 present balance sheet excerpts for 
SAP Group and Apple Inc. showing the line items for the companies’ current liabilities. 
Some of the common types of current liabilities, including trade payables, financial 
liabilities, accrued expenses, and deferred income, are discussed below.

Current Assets and Current Liabilities 175
Exhibit 6   SAP Group Consolidated Statements of Financial Position 
(Excerpt: Current Liabilities Detail) (in millions of €)
As of 31 December
Trade and other payables 638 599
Tax liabilities 125 363
Bank loans and other financial liabilities 146 2,563
Other non-  financial liabilities 1,577 1,428
Provisions 332 248
Deferred income 598 623
Exhibit 7   Apple Inc. Consolidated Balance Sheet (Excerpt: Current 
Liabilities Detail)* (in millions of $)
equity

equity
Accounts payable 5,601 5,520
Accrued expenses 3,852 4,224
Deferred revenue 2,053 1,617

Reading 24 ■ Understanding Balance Sheets 176
Trade payables , also called accounts payable , are amounts that a company owes 
its vendors for purchases of goods and services. In other words, these represent the 
unpaid amount as of the balance sheet date of the company’s purchases on credit. 
An issue relevant to analysts is the trend in overall levels of trade payables relative to 
purchases (a topic to be addressed further in ratio analysis). Significant changes in 
accounts payable relative to purchases could signal potential changes in the company’s 
credit relationships with its suppliers. The general term “trade credit” refers to credit 
provided to a company by its vendors. Trade credit is a source of financing that allows 
the company to make purchases and then pay for those purchases at a later date.
Notes payable  are financial liabilities owed by a company to creditors, including 
trade creditors and banks, through a formal loan agreement. Any notes payable, loans

payable, or other financial liabilities that are due within one year (or the operating 
cycle, whichever is longer) appear in the current liability section of the balance sheet. 
In addition, any portions of long-  term liabilities that are due within one year (i.e., the 
current portion of long-  term liabilities) are also shown in the current liability section 
of the balance sheet. On SAP Group’s balance sheet, current liabilities include bank 
loans and other financial liabilities. Apple Inc. does not have any current notes payable 
or loans payable.
Income taxes payable reflect taxes, based on taxable income, that have not yet been 
paid. SAP Group’s balance sheet shows €125 million of tax liabilities in its current 
liabilities. Apple Inc. ’s balance sheet does not show a separate line item for current 
taxes payable; instead a note discloses that income taxes payable of $430 million are 
included within the $3,852 million of “ Accrued expenses. ” Accrued expenses  (also

called accrued expenses payable, accrued liabilities, and other non-  financial liabili -
ties) are expenses that have been recognized on a company’s income statement but 
which have not yet been paid as of the balance sheet date. In addition to income taxes 
payable, other common examples of accrued expenses are accrued interest payable, 
accrued warranty costs, and accrued employee compensation (i.e., wages payable). 
SAP Group’s notes disclose that the €1,577 million line item of other non-  financial 
liabilities, for example, includes €1,343 million of employee-  related liabilities.
Deferred income  (also called deferred revenue  and unearned revenue ) arises 
when a company receives payment in advance of delivery of the goods and services 
associated with the payment. The company has an obligation either to provide the 
goods or services or to return the cash received. Examples include lease payments

received at the beginning of a lease, fees for servicing office equipment received at the 
beginning of the service period, and payments for magazine subscriptions received at 
the beginning of the subscription period. SAP Group’s balance sheet shows deferred 
income of €598 million at the end of 2009, down slightly from €623 million at the 
end of 2008. Apple Inc. ’s balance sheet shows deferred revenue of $2,053 million at 
the end of fiscal 2009, up 27 percent from $1,617 million at the end of fiscal 2008. 
Example 3 presents each company’s disclosures about deferred revenue and discusses 
some of the implications.
EXAMPLE 3   
Analysis of Deferred Revenue
In the notes to its 2009 financial statements, SAP Group describes its deferred 
income as follows:

Current Assets and Current Liabilities 177
Deferred income consists mainly of prepayments made by our cus -
tomers for support services and professional services, fees for multiple 
element arrangements allocated to undelivered elements, and amounts 
… for obligations to perform under acquired support contracts in 
connection with acquisitions.
Apple’s deferred revenue arises from sales involving components, some delivered 
at the time of sale and others to be delivered in the future. In its 2009 financial 
statements, Apple Inc. explains that accounting for sale of some of its products 
is treated as two deliverables:
…The first deliverable is the hardware and software delivered at the 
time of sale, and the second deliverable is the right included with 
the purchase of iPhone and Apple TV to receive on a when-  and-  
relating to the product’s software… the Company is required to esti -

mate a standalone selling price for the unspecified software upgrade 
right included with the sale of iPhone and Apple TV and recognizes 
that amount ratably over the 24-  month estimated life of the related 
hardware device...
1 In general, in the period a transaction occurs, how would a company’s 
balance sheet reflect $100 of deferred revenue resulting from a sale? 
(Assume, for simplicity, that the company receives cash for all sales, the 
company’s income tax payable is 30 percent based on cash receipts, and 
the company pays cash for all relevant income tax obligations as they 
arise. Ignore any associated deferred costs.)
2 In general, how does deferred revenue impact a company’s financial state -
ments in the periods following its initial recognition?
3 Interpret the amounts shown by SAP Group as deferred income and by 
Apple Inc. as deferred revenue.
4 Both accounts payable and deferred revenue are classified as current lia -
bilities. Discuss the following statements:

A When assessing a company’s liquidity, the implication of amounts in 
accounts payable differs from the implication of amounts in deferred 
revenue.
B Some investors monitor amounts in deferred revenue as an indicator 
of future revenue growth.
In the period that deferred revenue arises, the company would record a $100 
increase in the asset Cash and a $100 increase in the liability Deferred Revenues. 
In addition, because the company’s income tax payable is based on cash receipts 
and is paid in the current period, the company would record a $30 decrease in 
the asset Cash and a $30 increase in the asset Deferred Tax Assets. Deferred tax 
assets increase because the company has paid taxes on revenue it has not yet 
recognised for accounting purposes. In effect, the company has prepaid taxes 
from an accounting perspective.

Reading 24 ■ Understanding Balance Sheets 178
In subsequent periods, the company will recognize the deferred revenue as it 
is earned. When the revenue is recognized, the liability Deferred Revenue will 
decrease. In addition, the tax expense is recognized on the income statement 
as the revenue is recognised and thus the associated amounts of Deferred Tax 
Assets will decrease.
Solution to 3: 
The deferred income on SAP Group’s balance sheet and deferred revenue on 
Apple Inc. ’s balance sheet at the end of their respective 2009 fiscal years will be 
recognized as revenue, sales, or a similar item in income statements subsequent 
to the 2009 fiscal year, as the goods or services are provided or the obligation is 
reduced. The costs of delivering the goods or services will also be recognised.
Solution to 4A: 
The amount of accounts payable represents a future obligation to pay cash to 
suppliers. In contrast, the amount of deferred revenue represents payments that

the company has already received from its customers, and the future obligation is 
to deliver the related services. With respect to liquidity, settling accounts payable 
will require cash outflows whereas settling deferred revenue obligations will not.
Solution to 4B: 
Some investors monitor amounts in deferred revenue as an indicator of future 
growth because the amounts in deferred revenue will be recognized as revenue 
in the future. Thus, growth in the amount of deferred revenue implies future 
growth of that component of a company’s revenue.
NON-  CURRENT ASSETS
This section provides an overview of assets other than current assets, sometimes 
collectively referred to as non-  current, long-  term, or long-  lived assets. The catego -
ries discussed are property, plant, and equipment; investment property; intangible 
assets; goodwill; and financial assets. Exhibit 8 and Exhibit 9 present balance sheet 
excerpts for SAP Group and Apple Inc. showing the line items for the companies’

non-  current assets.
Exhibit 8   SAP Group Consolidated Statements of Financial Position 
(Excerpt: Non-  Current Assets Detail) (in millions of €)
Goodwill 4,994 4,975
Intangible assets 894 1,140
Property, plant, and equipment 1,371 1,405
Other financial assets 284 262
Trade and other receivables 52 41
Other non-  financial assets 35 32
Tax assets 91 334

Non-  Current Assets 179
Deferred tax assets 398 441
Exhibit 9   Apple Inc. Consolidated Balance Sheet (Excerpt: Non-  Current 
Assets Detail)* (in millions of $)
Long-  term marketable securities 10,528 2,379
Property, plant and equipment, 
net2,954 2,455
Goodwill 206 207
Acquired intangible assets, net 247 285
Other assets 2,011 839
equity

shareholders’ equity 47,501 36,171
4.1 Property, Plant, and Equipment
Property, plant, and equipment  (PPE) are tangible assets that are used in company 
operations and expected to be used (provide economic benefits) over more than one 
fiscal period. Examples of tangible assets treated as property, plant, and equipment, 
include land, buildings, equipment, machinery, furniture, and natural resources such Exhibit 8   (Continued)

Reading 24 ■ Understanding Balance Sheets 180
as mineral and petroleum resources. IFRS permits companies to report PPE using 
either a cost model or a revaluation model.9 While IFRS permits companies to use 
the cost model for some classes of assets and the revaluation model for others, the 
company must apply the same model to all assets within a particular class of assets. 
US GAAP permits only the cost model for reporting PPE.
Under the cost model, PPE is carried at amortised cost (historical cost less any 
accumulated depreciation or accumulated depletion, and less any impairment losses). 
Historical cost generally consists of an asset’s purchase price, its delivery cost, and 
any other additional costs incurred to make the asset operable (such as costs to install 
a machine). Depreciation and depletion is the process of allocating (recognizing as 
an expense) the cost of a long-  lived asset over its useful life. Land is not depreciated.

Because PPE is presented on the balance sheet net of depreciation and depreciation 
expense is recognised in the income statement, the choice of depreciation method 
and the related estimates of useful life and salvage value impact both a company’s 
balance sheet and income statement.
Whereas depreciation is the systematic allocation of cost over an asset’s useful life, 
impairment losses reflect an unanticipated decline in value. Impairment occurs when 
the asset’s recoverable amount is less than its carrying amount, with terms defined 
as follows under IFRS:10
■■Recoverable amount: The higher of an asset’s fair value less cost to sell, and its 
value in use.
■■Fair value less cost to sell: The amount obtainable in a sale of the asset in an 
arms-  length transaction between knowledgeable willing parties, less the costs of 
the sale.
■■Value in use: The present value of the future cash flows expected to be derived 
from the asset.

When an asset is considered impaired, the company recognizes the impairment loss 
in the income statement. Reversals of impairment losses are permitted under IFRS 
but not under US GAAP .
Under the revaluation model, the reported and carrying value for PPE is the fair 
value at the date of revaluation less any subsequent accumulated depreciation. Changes 
in the value of PPE under the revaluation model affect equity directly or profit and 
loss depending upon the circumstances.
In Exhibits 8 and 9, SAP Group reports €1,371 million of PPE and Apple Inc. reports 
$2,954 million of PPE at the end of fiscal year 2009. For SAP Group, PPE represents 
approximately 10 percent of total assets and for Apple, PPE represents approximately 
6 percent of total assets. SAP Group discloses in its notes that land is not depreciated, 
that they use a cost model for PPE, and that PPE are generally depreciated over their

expected useful lives using the straight line method. Apple Inc. discloses similar pol -
icies but does not specifically disclose that land is not depreciated.
4.2 Investment Property
Some property is not used in the production of goods or services or for administrative 
purposes. Instead, it is used to earn rental income or capital appreciation (or both). 
Under IFRS, such property is considered to be investment property .11 US GAAP 
does not include a specific definition for investment property. IFRS provides compa -
nies with the choice to report investment property using either a cost model or a fair 
9 IAS 16, Property, Plant and Equipment , paragraphs 29-  31.
10 IAS 36, Impairment of Assets , paragraph 6. US GAAP uses a different approach to impairment.
11 IAS 40, Investment Property .

Non-  Current Assets 181
value model. In general, a company must apply its chosen model (cost or fair value) 
to all of its investment property. The cost model for investment property is identical 
to the cost model for PPE: In other words, investment property is carried at cost less 
any accumulated depreciation and any accumulated impairment losses. Under the 
fair value model, investment property is carried at its fair value. When a company 
uses the fair value model to measure the value of its investment property, any gain or 
loss arising from a change in the fair value of the investment property is recognized 
in profit and loss, i.e., on the income statement, in the period in which it arises.12
Neither SAP Group nor Apple disclose ownership of investment property. The 
types of companies that typically hold investment property are real estate investment 
companies or property management companies. Entities such as life insurance com -

panies and endowment funds may also hold investment properties as part of their 
investment portfolio.
4.3 Intangible Assets
Intangible assets  are identifiable non-  monetary assets without physical substance.13 
An identifiable asset can be acquired singly (can be separated from the entity) or is the 
result of specific contractual or legal rights or privileges. Examples include patents, 
licenses, and trademarks. The most common asset that is not a separately identifiable 
asset is accounting goodwill, which arises in business combinations and is discussed 
further in Section 4.4.
IFRS allows companies to report intangible assets using either a cost model or a 
revaluation model. The revaluation model can only be selected when there is an active 
market for an intangible asset. These measurement models are essentially the same 
as described for PPE. US GAAP permits only the cost model.
For each intangible asset, a company assesses whether the useful life of the asset

is finite or indefinite. Amortisation and impairment principles apply as follows:
■■An intangible asset with a finite useful life is amortised on a systematic basis 
over the best estimate of its useful life, with the amortisation method and useful 
life estimate reviewed at least annually.
■■Impairment principles for an intangible asset with a finite useful life are the 
same as for PPE.
■■An intangible asset with an indefinite useful life is not amortised. Instead, at 
least annually, the reasonableness of assuming an indefinite useful life for the 
asset is reviewed and the asset is tested for impairment.
Financial analysts have traditionally viewed the values assigned to intangible assets, 
particularly goodwill, with caution. Consequently, in assessing financial statements, 
analysts often exclude the book value assigned to intangibles, reducing net equity 
by an equal amount and increasing pretax income by any amortisation expense or

impairment associated with the intangibles. An arbitrary assignment of zero value to 
intangibles is not advisable; instead, an analyst should examine each listed intangible 
and assess whether an adjustment should be made. Note disclosures about intangible 
assets may provide useful information to the analyst. These disclosures include infor -
mation about useful lives, amortisation rates and methods, and impairment losses 
recognised or reversed.
Further, a company may have developed intangible assets internally that can only 
be recognised in certain circumstances. Companies may also have assets that are 
never recorded on a balance sheet because they have no physical substance and are 
12 IAS 40, Investment Property , paragraph 35.
13 IAS 38, Intangible Assets , paragraph 8.

Reading 24 ■ Understanding Balance Sheets 182
non-  identifiable. These assets might include management skill, name recognition, a 
good reputation, and so forth. Such assets are valuable and are, in theory, reflected 
in the price at which the company’s equity securities trade in the market (and the 
price at which the entirety of the company’s equity would be sold in an acquisition 
transaction). Such assets may be recognised as goodwill if a company is acquired, but 
are not recognised until an acquisition occurs.
4.3.1  Identifiable Intangibles
Under IFRS, identifiable intangible assets are recognised on the balance sheet if it is 
probable that future economic benefits will flow to the company and the cost of the asset 
can be measured reliably. Examples of identifiable intangible assets include patents, 
trademarks, copyrights, franchises, licenses, and other rights. Identifiable intangible 
assets may have been created internally or purchased by a company. Determining the

cost of internally created intangible assets can be difficult and subjective. For these 
reasons, under IFRS and US GAAP , the general requirement is that internally created 
identifiable intangibles are expensed rather than reported on the balance sheet.
IFRS provides that for internally created intangible assets, the company must 
separately identify the research phase and the development phase.14 The research 
phase includes activities that seek new knowledge or products. The development 
phase occurs after the research phase and includes design or testing of prototypes 
and models. IFRS require that costs to internally generate intangible assets during 
the research phase must be expensed on the income statement. Costs incurred in the 
development stage can be capitalized as intangible assets if certain criteria are met, 
including technological feasibility, the ability to use or sell the resulting asset, and the 
ability to complete the project.

US GAAP prohibits the capitalization as an asset of most costs of internally 
developed intangibles and research and development. All such costs usually must be 
expensed. Costs related to the following categories are typically expensed under IFRS 
and US GAAP . They include:
■■internally generated brands, mastheads, publishing titles, customer lists, etc.;
■■start-  up costs;
■■training costs;
■■administrative and other general overhead costs;
■■advertising and promotion;
■■relocation and reorganization expenses; and
■■redundancy and other termination costs.
Generally, acquired intangible assets are reported as separately identifiable intangi -
bles (as opposed to goodwill) if they arise from contractual rights (such as a licensing 
agreement), other legal rights (such as patents), or have the ability to be separated 
and sold (such as a customer list).
EXAMPLE 4   
Measuring Intangible Assets

EXAMPLE 4   
Alpha Inc., a motor vehicle manufacturer, has a research division that worked 
on the following projects during the year:
14 IAS 38, Intangible Assets , paragraphs 51–67.

Non-  Current Assets 183
Project 1  Research aimed at finding a steering mechanism that does not 
operate like a conventional steering wheel but reacts to the 
impulses from a driver’s fingers.
Project 2  The design of a prototype welding apparatus that is controlled 
electronically rather than mechanically. The apparatus has 
been determined to be technologically feasible, salable, and 
feasible to produce.
The following is a summary of the expenses of the research division (in thou -
sands of €):
General Project 1 Project 2
Material and services 128 935 620
Labor
• Direct labor — 630 320
• Administrative personnel 720 — —
Overhead
• Direct — 340 410
• Indirect 270 110 60
Five percent of administrative personnel costs can be attributed to each of 
Projects 1 and 2. Explain the accounting treatment of Alpha’s costs for Projects 
1 and 2 under IFRS and US GAAP .
Solution: 
Under IFRS, the capitalization of development costs for Projects 1 and 2 would 
be as follows:
Amount Capitalized as 
an Asset (€’000)

Project 1: Classified as in the research stage, 
so all costs are recognized as 
expensesNIL
Project 2: Classified as in the development 
stage, so costs may be capitalized. 
Note that administrative costs are 
not capitalized.(620 + 320 + 410 + 60)  
= 1,410
Under US GAAP , the costs of Projects 1 and 2 are expensed.
As presented in Exhibits 8 and 9, SAP Group’s 2009 balance sheet shows €894 mil -
lion of intangible assets, and Apple’s 2009 balance sheet shows acquired intangible 
assets, net of $247 million.
4.4 Goodwill
When one company acquires another, the purchase price is allocated to all the iden -
tifiable assets (tangible and intangible) and liabilities acquired, based on fair value. 
If the purchase price is greater than the acquirer’s interest in the fair value of the 
identifiable assets and liabilities acquired, the excess is described as goodwill  and is 
recognized as an asset. To understand why an acquirer would pay more to purchase a

Reading 24 ■ Understanding Balance Sheets 184
company than the fair value of the target company’s identifiable assets and liabilities, 
consider the following three observations. First, as noted, certain items not recognized 
in a company’s own financial statements (e.g., its reputation, established distribution 
system, trained employees) have value. Second, a target company’s expenditures in 
research and development may not have resulted in a separately identifiable asset 
that meets the criteria for recognition but nonetheless may have created some value. 
Third, part of the value of an acquisition may arise from strategic positioning versus a 
competitor or from perceived synergies. The purchase price might not pertain solely 
to the separately identifiable assets and liabilities acquired and thus may exceed the 
value of those net assets due to the acquisition’s role in protecting the value of all of the

acquirer’s existing assets or to cost savings and benefits from combining the companies.
The subject of recognizing goodwill in financial statements has found both propo -
nents and opponents among professionals. The proponents of goodwill recognition 
assert that goodwill is the present value of excess returns that a company is able to 
earn. This group claims that determining the present value of these excess returns is 
analogous to determining the present value of future cash flows associated with other 
assets and projects. Opponents of goodwill recognition claim that the prices paid for 
acquisitions often turn out to be based on unrealistic expectations, thereby leading 
to future write-  offs of goodwill.
Analysts should distinguish between accounting goodwill and economic goodwill. 
Economic goodwill is based on the economic performance of the entity, whereas 
accounting goodwill is based on accounting standards and is reported only in the case

of acquisitions. Economic goodwill is important to analysts and investors, and it is not 
necessarily reflected on the balance sheet. Instead, economic goodwill is reflected in 
the stock price (at least in theory). Some financial statement users believe that good -
will should not be listed on the balance sheet, because it cannot be sold separately 
from the entity. These financial statement users believe that only assets that can be 
separately identified and sold should be reflected on the balance sheet. Other financial 
statement users analyze goodwill and any subsequent impairment charges to assess 
management’s performance on prior acquisitions.
Under both IFRS and US GAAP , accounting goodwill arising from acquisitions 
is capitalized. Goodwill is not amortised but is tested for impairment annually. If 
goodwill is deemed to be impaired, an impairment loss is charged against income in 
the current period. An impairment loss reduces current earnings. An impairment loss

also reduces total assets, so some performance measures, such as return on assets 
(net income divided by average total assets), may actually increase in future periods. 
An impairment loss is a non-  cash item.
Accounting standards’ requirements for recognizing goodwill can be summarized 
by the following steps:
A The total cost to purchase the target company (the acquiree) is determined.
B The acquiree’s identifiable assets are measured at fair value. The acquiree’s 
liabilities and contingent liabilities are measured at fair value. The difference 
between the fair value of identifiable assets and the fair value of the liabilities 
and contingent liabilities equals the net identifiable assets acquired.
C Goodwill arising from the purchase is the excess of a) the cost to purchase 
the target company and b) the net identifiable assets acquired. Occasionally, 
a transaction will involve the purchase of net identifiable assets with a value

greater than the cost to purchase. Such a transaction is called a “bargain pur -
chase. ” Any gain from a bargain purchase is recognized in profit and loss in the 
period in which it arises.15
15 IFRS 3 Business Combinations  and FASB ASC 805 [Business Combinations].

Non-  Current Assets 185
Companies are also required to disclose information that enables users to evaluate 
the nature and financial effect of business combinations. The required disclosures 
include, for example, the acquisition date fair value of the total cost to purchase the 
target company, the acquisition date amount recognized for each major class of assets 
and liabilities, and a qualitative description of the factors that make up the goodwill 
recognized.
Despite the guidance incorporated in accounting standards, analysts should be 
aware that the estimations of fair value involve considerable management judgment. 
Values for intangible assets, such as computer software, might not be easily validated 
when analyzing acquisitions. Management judgment about valuation in turn impacts 
current and future financial statements because identifiable intangible assets with 
definite lives are amortised over time. In contrast, neither goodwill nor identifiable

intangible assets with indefinite lives are amortised; instead both are tested annually 
for impairment.
The recognition and impairment of goodwill can significantly affect the compa -
rability of financial statements between companies. Therefore, analysts often adjust 
the companies’ financial statements by removing the impact of goodwill. Such adjust -
ments include:
■■excluding goodwill from balance sheet data used to compute financial ratios, 
and
■■excluding goodwill impairment losses from income data used to examine oper -
ating trends.
In addition, analysts can develop expectations about a company’s performance fol -
lowing an acquisition by taking into account the purchase price paid relative to the 
net assets and earnings prospects of the acquired company.
EXAMPLE 5   
Goodwill Impairment
Safeway, Inc., is a North American food and drug retailer. On 25 February 2010, 
Safeway issued a press release that included the following information:

Safeway Inc. today reported a net loss of $1,609.1 million ($4.06 per 
diluted share) for the 16-  week fourth quarter of 2009. Excluding a 
non-  cash goodwill impairment charge of $1,818.2 million, net of tax 
($4.59 per diluted share), net income would have been $209.1 million 
($0.53 per diluted share). Net income was $338.0 million ($0.79 per 
diluted share) for the 17-  week fourth quarter of 2008.
In the fourth quarter of 2009, Safeway recorded a non-  cash good -
will impairment charge of $1,974.2 million ($1,818.2 million, net of 
tax). The impairment was due primarily to Safeway’s reduced market 
capitalization and a weak economy….The goodwill originated from 
previous acquisitions.
Safeway’s balance sheet as of 2 January 2010 showed goodwill of 
$426.6 million and total assets of $14,963.6 million. The company’s 
balance sheet as of 3 January 2009 showed goodwill of $2,390.2 million 
and total assets of $17,484.7 million.
1 How significant is this goodwill impairment charge?

2 With reference to acquisition prices, what might this goodwill impairment 
indicate?

Reading 24 ■ Understanding Balance Sheets 186
The goodwill impairment was more than 80 percent of the total value of good -
will and 11 percent of total assets, so it was clearly significant. (The charge of 
$1,974.2 million equals 82.6 percent of the $2,390.2 million of goodwill at the 
beginning of the year and 11.3 percent of the $17,484.7 million total assets at 
the beginning of the year.)
The goodwill had originated from previous acquisitions. The impairment charge 
implies that the acquired operations are now worth less than the price that was 
paid for their acquisition.
As presented in Exhibits 8 and 9, SAP Group’s 2009 balance sheet shows €4,994 mil -
lion of goodwill, and Apple’s 2009 balance sheet shows goodwill of $206  million. 
Goodwill represents 37.3 percent of SAP Group’s total assets and only 0.4 percent 
of Apple’s total assets. An analyst may be concerned that goodwill represents such a 
high proportion of SAP Group’s total assets.

4.5 Financial Assets
IFRS define a financial instrument as a contract that gives rise to a financial asset 
of one entity, and a financial liability or equity instrument of another entity.16 This 
section will focus on financial assets such as a company’s investments in stocks issued 
by another company or its investments in the notes, bonds, or other fixed-  income 
instruments issued by another company (or issued by a governmental entity). Financial 
liabilities such as notes payable and bonds payable issued by the company itself will 
be discussed in the liability portion of this reading. Some financial instruments may 
be classified as either an asset or a liability depending on the contractual terms and 
current market conditions. One example of such a financial instrument is a derivative. 
Derivatives  are financial instruments for which the value is derived based on some

underlying factor (interest rate, exchange rate, commodity price, security price, or 
credit rating) and for which little or no initial investment is required.
All financial instruments are recognized when the entity becomes a party to the 
contractual provisions of the instrument. In general, there are two basic alternative 
ways that financial instruments are measured: fair value or amortised cost. Recall that 
fair value is the arm’s length transaction price at which an asset could be exchanged 
or a liability settled between knowledgeable and willing parties under IFRS, and the 
price that would be received to sell an asset or paid to transfer a liability under US 
GAAP . The amortised cost of a financial asset (or liability) is the amount at which it was 
initially recognized, minus any principal repayments, plus or minus any amortisation 
of discount or premium, and minus any reduction for impairment.
Financial assets are measured at amortised cost if the asset’s cash flows occur on

specified dates and consist solely of principal and interest, and if the business model is 
to hold the asset to maturity. This category of asset is referred to as held-  to- maturity . 
An example is an investment in a long-  term bond issued by another company; the 
value of the bond will fluctuate, for example with interest rate movements, but if the 
bond is classified as held-  to- maturity, it will be measured at amortised cost. Other 
types of financial assets measured at historical cost are loans (to other companies).
16 IAS 32, Financial Instruments: Presentation , paragraph 11.

Non-  Current Assets 187
Financial assets not measured at amortised cost are measured at fair value. For 
financial instruments measured at fair value, there are two basic alternatives in how 
net changes in fair value are recognized: as profit or loss on the income statement, or 
as other comprehensive income (loss) which bypasses the income statement. Note that 
these alternatives refer to unrealized changes in fair value, i.e., changes in the value 
of a financial asset that has not been sold and is still owned at the end of the period. 
Unrealized gains and losses are also referred to as holding period gains and losses. 
If a financial asset is sold within the period, a gain is realized if the selling price is 
greater than the carrying value and a loss is realized if the selling price is less than the 
carrying value. When a financial asset is sold, any realized gain or loss is reported on 
the income statement. The category held for trading  (or “trading securities” under

US GAAP) refers to a category of financial assets that is acquired primarily for the 
purpose of selling in the near term. These assets are likely to be held only for a short 
period of time. These trading assets are measured at fair value, and any unrealized 
holding gains or losses are recognized as profit or loss on the income statement. Mark 
to market  refers to the process whereby the value of a financial instrument is adjusted 
to reflect current fair value based on market prices.
Some financial assets are not classified as held for trading, even though they are 
available to be sold. Such available-  for-  sale  assets are measured at fair value, with 
any unrealized holding gains or losses recognized in other comprehensive income. 
The “available-  for- sale” classification is no longer in effect under IFRS with the release 
of IFRS 9 ( Financial Instruments) . IFRS 9 is based on the concept that financial assets

should be classified and measured at either amortised cost or at fair value, and sub -
sequently recognised in either the income statement or other comprehensive income 
when they arise. Although the available-  for- sale category no longer exists, IFRS still 
permit certain equity investments to be measured at fair value with any unrealized 
holding gains or losses recognized in other comprehensive income. Specifically, at the 
time a company buys an equity investment that is not held for trading, the company 
is permitted to make an irrevocable election to measure the asset in this manner. 
These assets are referred to as “financial assets measured at fair value through other 
comprehensive income. ”17
IFRS 9 adopts a new approach for the impairment of financial assets that are 
measured at amortised cost (e.g., loans and receivables, including trade receivables). 
IFRS requires an “expected loss” impairment method, in which the recognition of

losses is based on the risk that a loan will default rather than on whether a loss has 
been incurred (as was the case under IFRS 39).
Exhibit 10 summarizes how various financial assets are classified and measured.
17 IFRS 7 Financial Instruments: Disclosures , paragraph 8(h) and IFRS 9 Financial Instruments , paragraph 
5.7.5.

Reading 24 ■ Understanding Balance Sheets 188
Exhibit 10   Measurement of Financial Assets
Measured at Fair Value Measured at Cost or Amortised Cost
■■Financial assets held for trading (e.g., 
stocks and bonds issued by another 
company)
■■Available-  for- sale financial assets (e.g., 
company)*
■■Derivatives whether stand-  alone or 
embedded in non-  derivative instruments
■■Non-  derivative instruments (including 
financial assets) with fair value exposures 
hedged by derivatives■■Unquoted equity instruments (in 
limited circumstances where the fair 
value is not reliably measurable, cost 
may serve as a proxy (estimate) for 
fair value)
■■Held-  to- maturity investments (invest -
ments in bonds issued by another 
company, intended to be held to 
maturity)
■■Loans to and receivables from 
another company
*As described above, the available-  for- sale category is no longer be a choice under IFRS upon the 
1 January 2018 effective date of IFRS 9.

To illustrate the different accounting treatments of the gains and losses on financial 
assets, consider an entity that invests €100,000,000 on 1 January 200X in a fixed-  income 
security investment, with a 5 percent coupon paid semi-  annually. After six months, 
the company receives the first coupon payment of €2,500,000. Additionally, market 
interest rates have declined such that the value of the fixed-  income investment has 
increased by €2,000,000 as of 30 June 200X. Exhibit 11 illustrates how this situation will 
be portrayed in the balance sheet assets and equity, as well as the income statement 
(ignoring taxes) of the entity concerned, under each of the following three accounting 
policies for financial assets: assets held for trading purposes, assets available for sale, 
and held-  to- maturity assets.
Exhibit 11   Accounting for Gains and Losses on Marketable Securities
Balance Sheet As of 30 June 200X Trading PortfolioAvailable-  for-  Sale

Portfolio Held to Maturity
Assets
Cash and cash equivalents 2,500,000 2,500,000 2,500,000
Cost of securities 100,000,000 100,000,000 100,000,000
Unrealized gains on securities 2,000,000 2,000,000 —
104,500,000 104,500,000 102,500,000
Equity
Paid-  in capital 100,000,000 100,000,000 100,000,000
Retained earnings 4,500,000 2,500,000 2,500,000
Accumulated other comprehensive income — 2,000,000 —

Non-  Current Assets 189
Income Statement For period 1 January–30 
June 200X
Interest income 2,500,000 2,500,000 2,500,000
Unrealized gains 2,000,000 — —
Impact on profit and loss 4,500,000 2,500,000 2,500,000
In the case of marketable securities classified as either trading or available-  for- sale, 
the investments are listed under assets and measured at fair market value. To highlight 
the impact of the change in value, Exhibit 11 shows the unrealized gain on a separate 
line. Practically, the investments would be listed at their fair value of €102,000,000 on 
one line within assets. In the case of trading securities, the unrealized gain is included 
on the income statement and thus reflected in retained earnings within owners’ equity. 
In the case of available-  for- sale securities, the unrealized gain is not included on the 
income statement as profit and loss; rather, it is treated as part of other comprehen -
sive income and thus reflected in accumulated other comprehensive income within

owners’ equity. Other comprehensive income includes gains and losses that have not 
been reported on the income statement due to particular accounting standards. As 
noted previously, under IFRS 9 the “available for sale” method no longer applies and 
the unrealised gain is recognised in the income statement. In the case of held-  to- 
maturity securities, the securities are measured at cost rather than fair value; therefore, 
no unrealized gain is reflected on either the balance sheet or income statement or 
through comprehensive income.
In Exhibits 4 and 8, SAP Group’s 2009 balance sheet shows other financial assets of 
€486 million (current) and €284 million (non-  current). The company’s notes disclose 
that most of these financial assets are loans and receivables, €422 million (current) 
and €168 million (non-  current). Also, €87 million of the non-  current other financial 
assets are classified as available-  for- sale equity investments, of which €62 million are

venture capital investments without quoted market prices. The notes disclose that fair 
values could not be estimated by reference to quoted market prices or by discount -
ing estimated future cash flows and that “such investments are accounted for at cost 
approximating fair value with impairment being assessed … ”
In Exhibits 5 and 9, Apple’s 2009 balance sheet shows $18,201 million of short-  
term marketable securities and $10,528 million of long-  term marketable securities. 
In total, marketable securities represent around 60 percent of Apple’s $47.5 billion in 
total assets. Marketable securities plus cash and cash equivalents represent around 
72 percent of the company’s total assets. Apple’s notes disclose that most of the com -
pany’s marketable securities are fixed-  income securities issued by the US government 
($3,327 million) or its agencies ($10,835 million), and by other companies including 
commercial paper ($12,602 million). In accordance with its investment policy, Apple

invests in highly rated securities (which the company defines as investment grade, 
primarily rated single A or better). The company classifies its marketable securities 
as available for sale and reports them on the balance sheet at fair value. Unrealized 
gains and losses are reported in other comprehensive income.Exhibit 11   (Continued)

Reading 24 ■ Understanding Balance Sheets 190
NON-  CURRENT LIABILITIES
All liabilities that are not classified as current are considered to be non-  current or 
long-  term. Exhibits 12 and 13 present balance sheet excerpts for SAP Group and Apple 
Inc. showing the line items for the companies’ non-  current liabilities.
Both companies’ balance sheets show non-  current unearned revenue (deferred 
income for SAP Group and deferred revenue for Apple). These amounts represent the 
amounts of unearned revenue relating to goods and services expected to be delivered 
in periods beyond twelve months following the reporting period. The sections that 
follow focus on two common types of non-  current (long-  term) liabilities: long-  term 
financial liabilities and deferred tax liabilities.
Exhibit 12   SAP Group Consolidated Statements of Financial Position 
(Excerpt: Non-  Current Liabilities Detail) (in millions of €)

Trade and other payables 35 42
Tax liabilities 239 278
  Bank loans 699 2
  Other financial liabilities 30 38
Financial liabilities 729 40
Other non-  financial liabilities 12 13
Provisions 198 232
Deferred tax liabilities 190 239
Deferred income 64 61
Exhibit 13   Apple Inc. Consolidated Balance Sheet (Excerpt: Non-  Current 
Total assets 47,501 36,1715

Non-  Current Liabilities 191
equity
Deferred revenue non-  current 853 768
Other non-  current liabilities 3,502 1,745
Total liabilities and share -
holders’ equity47,501 36,171
5.1 Long-  term Financial Liabilities
Typical long-  term financial liabilities include loans (i.e., borrowings from banks) and 
notes or bonds payable (i.e., fixed-  income securities issued to investors). Liabilities 
such as loans payable and bonds payable are usually reported at amortised cost on 
the balance sheet. At maturity, the amortised cost of the bond (carrying amount) will

be equal to the face value of the bond. For example, if a company issues $10,000,000 
of bonds at par, the bonds are reported as a long-  term liability of $10 million. The 
carrying amount (amortised cost) from issue to maturity remains at $10 million. As 
another example, if a company issues $10,000,000 of bonds at a price of 97.50 (a dis -
count to par), the bonds are reported as a liability of $9,750,000. Over the bond’s life, 
the discount of $250,000 is amortised so that the bond will be listed as a liability of 
$10,000,000 at maturity. Similarly, any bond premium would be amortised for bonds 
issued at a price in excess of face or par value.
In certain cases, liabilities such as bonds issued by a company are reported at fair 
value. Those cases include financial liabilities held for trading, derivatives that are a 
liability to the company, and some non-  derivative instruments such as those which 
are hedged by derivatives.

SAP Group’s balance sheet in Exhibit 12 shows €699 million of bank loans and 
€30  million of other financial liabilities. Apple’s balance sheet does not show any 
non-  current financial liabilities.
5.2 Deferred Tax Liabilities
Deferred tax liabilities  result from temporary timing differences between a company’s 
income as reported for tax purposes (taxable income) and income as reported for 
financial statement purposes (reported income). Deferred tax liabilities result when 
taxable income and the actual income tax payable in a period based on it is less than 
the reported financial statement income before taxes and the income tax expense 
based on it. Deferred tax liabilities are defined as the amounts of income taxes pay -
able in future periods in respect of taxable temporary differences.18 In the previous 
discussion of unearned revenue, inclusion of revenue in taxable income in an earlier

period created a deferred tax asset (essentially prepaid tax).Exhibit 13   (Continued)
18 IAS 12, Income Taxes , paragraph 5.

Reading 24 ■ Understanding Balance Sheets 192
Deferred tax liabilities typically arise when items of expense are included in tax -
able income in earlier periods than for financial statement net income. This results 
in taxable income being less than income before taxes in the earlier periods. As 
a result, taxes payable based on taxable income are less than income tax expense 
based on accounting income before taxes. The difference between taxes payable and 
income tax expense results in a deferred tax liability—for example, when companies 
use accelerated depreciation methods for tax purposes and straight-  line depreciation 
methods for financial statement purposes. Deferred tax liabilities also arise when 
items of income are included in taxable income in later periods—for example, when 
a company’s subsidiary has profits that have not yet been distributed and thus have 
not yet been taxed.
SAP Group’s balance sheet in Exhibit 12 shows €190 million of deferred tax lia -

bilities. Apple’s balance sheet in Exhibit 13 does not show a separate line item for 
deferred tax liabilities, however, note disclosures indicate that the $3,502 million of 
non-  current liabilities reported on Apple’s balance sheet includes deferred tax liabil -
ities of $2,216 million.
EQUITY
Equity  is the owners’ residual claim on a company’s assets after subtracting its lia -
bilities.19 It represents the claim of the owner against the company. Equity includes 
funds directly invested in the company by the owners, as well as earnings that have 
been reinvested over time. Equity can also include items of gain or loss that are not 
yet recognized on the company’s income statement.
6.1 Components of Equity
Six potential components comprise total owners’ equity. The first five components 
listed below comprise equity attributable to owners of parent. The sixth component 
is the equity attributable to non-  controlling interests.

1 Capital contributed by owners  (or common stock, or issued capital). The 
amount contributed to the company by owners. Ownership of a corporation is 
evidenced through the issuance of common shares. Common shares may have a 
par value (or stated value) or may be issued as no par shares (depending on reg -
ulations governing the incorporation). Where par or stated value requirements 
exist, it must be disclosed in the equity section of the balance sheet. In addition, 
the number of shares authorized, issued, and outstanding must be disclosed for 
each class of share issued by the company. The number of authorized shares 
is the number of shares that may be sold by the company under its articles of 
incorporation. The number of issued shares refers to those shares that have 
been sold to investors. The number of outstanding shares consists of the issued 
shares less treasury shares.
2 Preferred shares . Classified as equity or financial liabilities based upon their

characteristics rather than legal form. For example, perpetual, non-  redeemable 
preferred shares are classified as equity. In contrast, preferred shares with man -
datory redemption at a fixed amount at a future date are classified as financial 6
19 IASB Conceptual Framework (2010) , paragraph 4.4 (c) and FASB ASC 505-  10- 05- 3 [Equity–Overview 
and Background].

Equity 193
liabilities. Preferred shares have rights that take precedence over the rights of 
common shareholders—rights that generally pertain to receipt of dividends and 
receipt of assets if the company is liquidated.
3 Treasury shares  (or treasury stock or own shares repurchased). Shares in the 
company that have been repurchased by the company and are held as treasury 
shares, rather than being cancelled. The company is able to sell (reissue) these 
shares. A company may repurchase its shares when management considers the 
shares undervalued, needs shares to fulfill employees’ stock options, or wants to 
limit the effects of dilution from various employee stock compensation plans. A 
purchase of treasury shares reduces shareholders’ equity by the amount of the 
acquisition cost and reduces the number of total shares outstanding. If treasury 
shares are subsequently reissued, a company does not recognize any gain or loss

from the reissuance on the income statement. Treasury shares are non-  voting 
and do not receive any dividends declared by the company.
4 Retained earnings.  The cumulative amount of earnings recognized in the 
company’s income statements which have not been paid to the owners of the 
company as dividends.
5 Accumulated other comprehensive income  (or other reserves). The cumula -
tive amount of other  comprehensive income or loss. Comprehensive income 
includes both a) net income, which is recognized on the income statement and 
is reflected in retained earnings, and b) other comprehensive income which 
is not recognized as part of net income and is reflected in accumulated other 
comprehensive income.20
6 Noncontrolling interest  (or minority interest). The equity interests of minority 
shareholders in the subsidiary companies that have been consolidated by the 
parent (controlling) company but that are not wholly owned by the parent 
company.

company.
Exhibits 14 and 15 present excerpts of the balance sheets of SAP Group and 
Apple Inc., respectively, with detailed line items for each company’s equity section. 
SAP’s balance sheet indicates that the company has 1,226 million shares of no-  par 
common stock outstanding with a corresponding amount shown in issued capital 
of €1,226 million. Presentation of the amount of treasury shares, –€1,320 million, is 
explained in the company’s notes:
Treasury shares are recorded at acquisition cost and are presented as a 
deduction from total equity. Gains and losses on the subsequent reissu -
ance of treasury shares are credited or charged to share premium on an 
after-  tax basis.
Source : SAP Group 2009 annual report
Thus, the line item share premium of €317 million includes amounts from treasury 
share transactions (and certain other transactions). The amount of retained earnings, 
€8,571 million, represents the cumulative amount of earnings that the company has

recognized in its income statements, net of dividends. SAP Group’s –€317 million of 
20 Comprehensive income is defined as “the change in equity [net assets] of a business enterprise during 
a period from transactions and other events and circumstances from non-  owner sources. It includes all 
changes in equity during a period except those resulting from investments by owners and distributions 
to owners. ” FASB ASC Section 220-  10- 05 [Comprehensive Income–Overall–Overview and Background]. 
There is no explicit definition of comprehensive income in IFRS; the implicit definition is similar to that 
above. IFRS defines income in the glossary as “increases in economic benefits during the accounting period 
in the form of inflows or enhancements of assets or decreases of liabilities that result in increases in equity, 
other than those relating to contributions from equity participants. ”

Reading 24 ■ Understanding Balance Sheets 194
“Other components of equity” includes the company’s accumulated other compre -
hensive income. The consolidated statement of changes in equity shows that this is 
composed of €319 million of losses on exchange differences in translation, €13 million 
gains on remeasuring available-  for- sale financial assets, and €11 million losses on cash 
flow hedges. The balance sheet presents a subtotal for the amount of equity attributable 
to the parent company €8,477 million followed by the amount of equity attributable to 
non-  controlling interests. Total equity includes both equity attributable to the parent 
company and equity attributable to non-  controlling interests.
The equity section of Apple’s balance sheet consists of only three line items: com -
mon stock, retained earnings, and accumulated other comprehensive income/(loss). 
The company holds no treasury stock and has no minority interests.

Exhibit 14   SAP Group Consolidated Statements of Financial Position 
(Excerpt: Equity Detail) (in millions of €)
  Issued capital1)1,226 1,226
  Treasury shares –1,320 –1,362
  Share premium 317 320
  Retained earnings 8,571 7,422
  Other components of equity –317 –437
Equity attributable to owners of parent 8,477 7,169
Non-  controlling interests 14 2
1)Authorized–not issued or outstanding: 480 million no-  par shares at 31 December 2009 and 2008.
Authorized–issued and outstanding: 1,226 million no-  par shares at 31 December 2009 and 2008.
Exhibit 15   Apple Inc. Consolidated Balance Sheet (Excerpt: Equity Detail) 
(in millions of $)
equity

equity
Common stock, no par value; 
1,800,000,000 shares authorized; 
899,805,500 and 888,325,973 
shares issued and outstanding, 
respectively8,210 7,177
Retained earnings 23,353 15,129

Equity 195
Accumulated other comprehen -
sive income/(loss)77 (9)
Source:  Apple Inc. 2009 annual report (10K/A).
6.2 Statement of Changes in Equity
The statement of changes in equity  (or statement of shareholders’ equity) presents 
information about the increases or decreases in a company’s equity over a period. IFRS 
requires the following information in the statement of changes in equity:
■■total comprehensive income for the period;
■■the effects of any accounting changes that have been retrospectively applied to 
previous periods;
■■capital transactions with owners and distributions to owners; and
■■reconciliation of the carrying amounts of each component of equity at the 
beginning and end of the year.21
Under US GAAP , the requirement as specified by the SEC is for companies to provide

an analysis of changes in each component of stockholders’ equity that is shown in 
the balance sheet.22
Exhibit 16 presents an excerpt from Apple’s Consolidated Statements of Changes 
in Shareholders’ Equity. The excerpt shows only one of the years presented on the 
actual statement. It begins with the balance as of 27 September 2008 (i.e., the begin -
ning of fiscal 2009) and presents the analysis of changes to 26 September 2009 in 
each component of equity that is shown on Apple’s balance sheet. As shown, the 
company issued 11.48 million new shares in connection with its employee stock plans, 
increasing the number of shares outstanding from 888.326 million to 899.806 million. 
The dollar balance in common stock also increased in connection with stock-  based 
compensation. Retained earnings increased by $8,235 million net income, net of an 
$11 million adjustment in connection with stock plans. For companies that pay div -

idends, the amount of dividends are shown separately as a deduction from retained 
earnings. Apple did not pay dividends. The statement also provides details on the 
$86 million change in Apple’s Accumulated other comprehensive income. Note that 
the statement provides a subtotal for total comprehensive income that includes net 
income and each of the components of other comprehensive income.Exhibit 15   (Continued)
21 IAS 1, Presentation of Financial Statements , paragraph 106.
22 FASB ASC 505-  10- S99 [Equity–Overall–SEC materials] indicates that a company can present the 
analysis of changes in stockholders’ equity either in the notes or in a separate statement.

Reading 24 ■ Understanding Balance Sheets 196
Exhibit 16   Excerpt from Apple Inc. ’s Consolidated Statements of Changes in Shareholders’ Equity (in 
millions, except share amounts which are reflected in thousands)
Common StockRetained 
EarningsAccumulated Other 
Comprehensive IncomeTotal Share-  
holders’ Equity Shares Amount
Balances as of 27 
September 2008888,326 $ 7,177 $ 15,129 $ (9) $ 22,297
  Components of com -
prehensive income:
   Net income — — 8,235 — 8,235
   Change in for -
eign currency 
translation— — — (14) (14)
   Change in unre -
alized loss on 
available-  for- sale 
securities, net of 
tax— — — 118 118
   Change in unreal -
ized gain on deriv -
ative instruments, 
net of tax— — — (18) (18)
   Total comprehen -
sive income8,321
Stock-  based 
compensation— 707 — — 707
Common stock issued 
under stock plans, net 
of shares withheld for 
employee taxes11,480 404 (11) — 393
Tax benefit from 
employee stock 
plan awards, includ -
ing transfer pricing 
adjustments— (78) — — (78)
Balances as of 26

Balances as of 26 
September 2009899,806 $ 8,210 $ 23,353 $ 77 $ 31,640
ANALYSIS OF THE BALANCE SHEET
This section describes two tools for analyzing the balance sheet: common-  size analysis 
and balance sheet ratios. Analysis of a company’s balance sheet can provide insight 
into the company’s liquidity and solvency—as of the balance sheet date—as well as 
the economic resources the company controls. Liquidity  refers to a company’s abil -
ity to meet its short-  term financial commitments. Assessments of liquidity focus a 
company’s ability to convert assets to cash and to pay for operating needs. Solvency  
refers to a company’s ability to meet its financial obligations over the longer term. 
Assessments of solvency focus on the company’s financial structure and its ability to 
pay long-  term financing obligations.7

Analysis of the Balance Sheet 197
7.1 Common-  Size Analysis of the Balance Sheet
The first technique, vertical common-  size analysis, involves stating each balance sheet 
item as a percentage of total assets.23 Common-  size statements are useful in comparing 
a company’s balance sheet composition over time (time-  series analysis) and across 
companies in the same industry. To illustrate, Panel A of Exhibit 17 presents a balance 
sheet for three hypothetical companies. Company C, with assets of $9.75 million is 
much larger than Company A and Company B, each with only $3.25 million in assets. 
The common-  size balance sheet presented in Panel B facilitates a comparison of these 
different sized companies.
Exhibit 17   
Panel A: Balance Sheets for Companies A, B, and C
($ Thousands) A B C
ASSETS
  Cash and cash equivalents 1,000 200 3,000
  Short-  term marketable securities 900 — 300
  Accounts receivable 500 1,050 1,500
  Inventory 100 950 300
Total current assets 2,500 2,200 5,100

Property, plant, and equipment, net 750 750 4,650
Intangible assets — 200 —
Goodwill — 100 —
Total assets 3,250 3,250 9,750
LIABILITIES AND SHAREHOLDERS’ EQUITY
  Accounts payable — 2,500 600
Total current liabilities — 2,500 600
Long term bonds payable 10 10 9,000
Total liabilities 10 2,510 9,600
Total shareholders’ equity 3,240 740 150
Total liabilities and shareholders’ equity 3,250 3,250 9,750
Panel B: Common-  Size Balance Sheets for Companies A, B, and C
(Percent) A B C
ASSETS
  Cash and cash equivalents 30.8 6.2 30.8
  Short-  term marketable securities 27.7 0.0 3.1
23 As discussed in the curriculum reading on financial statement analysis, another type of common-  size 
analysis, known as “horizontal common-  size analysis, ” states quantities in terms of a selected base-  year 
value. Unless otherwise indicated, text references to “common-  size analysis” refer to vertical analysis.

Reading 24 ■ Understanding Balance Sheets 198
  Accounts receivable 15.4 32.3 15.4
  Inventory 3.1 29.2 3.1
Total current assets 76.9 67.7 52.3
Property, plant and equipment, net 23.1 23.1 47.7
Intangible assets 0.0 6.2 0.0
Goodwill 0.0 3.1 0.0
Total assets 100.0 100.0 100.0
  Accounts payable 0.0 76.9 6.2
Total current liabilities 0.0 76.9 6.2
Long term bonds payable 0.3 0.3 92.3
Total liabilities 0.3 77.2 98.5
Total shareholders’ equity 99.7 22.8 1.5
Total liabilities and shareholders’ equity 100.0 100.0 100.0
Most of the assets of Company A and B are current assets; however, Company A 
has nearly 60 percent of its total assets in cash and short-  term marketable securities 
while Company B has only 6 percent of its assets in cash. Company A is more liquid 
than Company B. Company A shows no current liabilities (its current liabilities round

to less than $10 thousand), and it has cash on hand of $1.0 million to meet any near-  
term financial obligations it might have. In contrast, Company B has $2.5 million of 
current liabilities which exceed its available cash of only $200 thousand. To pay those 
near-  term obligations, Company B will need to collect some of its accounts receiv -
ables, sell more inventory, borrow from a bank, and/or raise more long-  term capital 
(e.g., by issuing more bonds or more equity). Company C also appears more liquid 
than Company B. It holds over 30 percent of its total assets in cash and short-  term 
marketable securities, and its current liabilities are only 6.2 percent of the amount 
of total assets.
Company C’s $3.3 million in cash and short-  term marketable securities is sub -
stantially more than its current liabilities of $600 thousand. Turning to the question 
of solvency, however, note that 98.5 percent of Company C’s assets are financed with

liabilities. If Company C experiences significant fluctuations in cash flows, it may be 
unable to pay the interest and principal on its long-  term bonds. Company A is far 
more solvent than Company C, with less than one percent of its assets financed with 
liabilities.
Note that these examples are hypothetical only. Other than general comparisons, 
little more can be said without further detail. In practice, a wide range of factors 
affect a company’s liquidity management and capital structure. The study of optimal 
capital structure  is a fundamental issue addressed in corporate finance. Capital refers 
to a company’s long-  term debt and equity financing; capital structure refers to the 
proportion of debt versus equity financing.Exhibit 17   (Continued)

Analysis of the Balance Sheet 199
Common-  size balance sheets can also highlight differences in companies’ strat -
egies. Comparing the asset composition of the companies, Company C has made a 
greater proportional investment in property, plant, and equipment—possibly because 
it manufactures more of its products in-  house. The presence of goodwill on Company 
B’s balance sheet signifies that it has made one or more acquisitions in the past. In 
contrast, the lack of goodwill on the balance sheets of Company A and Company C 
suggests that these two companies may have pursued a strategy of internal growth 
rather than growth by acquisition. Company A may be in either a start-  up or liquida -
tion stage of operations as evidenced by the composition of its balance sheet. It has 
relatively little inventory and no accounts payable. It either has not yet established trade 
credit or it is in the process of paying off its obligations in the process of liquidating.
EXAMPLE 6   
Common-  Size Analysis

EXAMPLE 6   
Applying common-  size analysis to the excerpts of SAP Group’s balance sheets 
presented in Exhibits 4, 6, 8, and 12, answer the following: In 2009 relative to 
2008, which two of the following line items increased as a percentage of assets?
A Cash and cash equivalents.
B Other financial assets.
C Trade and other receivables.
D Tax assets.
E Bank loans classified as current (i.e., due within one year).
F Bank loans classified as non-  current (i.e., due after one year).
Solution: 
(€ amounts shown are in millions.) A and F are correct. Both cash and longer-  
term bank loans increased as a percentage of total assets. Cash and cash equiv -
alents increased from 9.2 percent of total assets in 2008 (€1,280 ÷ €13,900) to 
14.1 percent in 2009 (€1,884 ÷ €13,374). Bank loans due after one year increased 
from 0.01 percent in 2008 (€2 ÷ €13,900) to 5.2 percent in 2009 (€699 ÷ €13,374). 
The company may have borrowed funds for a strategic purpose that it has not

yet acted upon.
The other items (other financial assets, trade and other receivables, tax assets, 
and bank loans classified as current) all decreased both in absolute Euro amounts 
and as a percentage of total assets when compared with the previous year. Note 
that some amounts of the company’s other financial assets, trade and other 
receivables, and tax assets are classified as current assets (shown in Exhibit 4) 
and some amounts are classified as non-  current assets (shown in Exhibit 8). 
The total amounts—current and non-  current—of other financial assets, trade 
and other receivables, and tax assets, therefore, are obtained by summing the 
amounts in Exhibits 4 and 8.
Overall, the company strengthened its liquidity position in 2009. Total 
current assets were approximately the same percentage of total assets, whereas 
cash was a much higher percentage of total assets; total current liabilities were 
a much smaller percentage of the amount of total assets.

Common-  size analysis of the balance sheet is particularly useful in cross-  sectional 
analysis—comparing companies to each other for a particular time period or compar -
ing a company with industry or sector data. The analyst could select individual peer

Reading 24 ■ Understanding Balance Sheets 200
companies for comparison, use industry data from published sources, or compile data 
from databases. When analyzing a company, many analysts prefer to select the peer 
companies for comparison or to compile their own industry statistics.
Exhibit 18 presents common-  size balance sheet data compiled for the 10 sectors 
of the S&P 500 using 2008 data. The sector classification follows the S&P/MSCI 
Global Industrial Classification System (GICS). The exhibit presents mean and median 
common-  size balance sheet data for those companies in the S&P 500 for which 2008 
data was available in the Compustat database.24
Some interesting general observations can be made from these data:
■■Energy and utility companies have the largest amounts of property, plant, and 
equipment (PPE). Telecommunication services, followed by utilities, have the 
highest level of long-  term debt. Utilities also use some preferred stock.

■■Financial companies have the greatest percentage of total liabilities. Financial 
companies typically have relatively high financial leverage.
■■Telecommunications services and utility companies have the lowest level of 
receivables.
■■Inventory levels are highest for consumer discretionary. Materials and con -
sumer staples have the next highest inventories.
■■Information technology companies use the least amount of leverage as evi -
denced by the lowest percentages for long-  term debt and total liabilities and 
highest percentages for common and total equity.
Example 7 discusses an analyst using cross-  sectional common-  size balance sheet 
data.
EXAMPLE 7   
Cross-  Sectional Common-  Size Analysis
Jason Lu is examining three companies in the computer industry to evaluate their 
relative financial position as reflected on their balance sheets. He has compiled 
the following vertical common-  size data for Apple, Dell, and Hewlett-  Packard.

Cross-  Sectional Analysis Consolidated Balance Sheets (in Percent of Total Assets)
APPLE  
30 Sept 2009DELL  
29 Jan 2010HPQ  
31 Oct 2009
ASSETS:
  Cash and cash equivalents 11.1 31.6 11.6
  Short-  term marketable securities 38.3 1.1 0.0
  Accounts receivable and financing receivables 7.1 25.4 16.7
  Inventories 1.0 3.1 5.3
  Deferred tax assets 2.4 0.0 0.0
  Other current assets 6.6 10.8 12.1
Total current assets 66.4 72.0 45.8
Long-  term marketable securities 22.2 2.3 0.0
24 An entry of zero for an item (e.g., current assets) was excluded from the data, except in the case of 
preferred stock. Note that most financial institutions did not provide current asset or current liability data, 
so these are reported as not available in the database.

Analysis of the Balance Sheet 201Exhibit 18   Common-  Size Balance Sheet Statistics for the S&P 500 Grouped by S&P/MSCI GICS Sector  
(in percent except No. of Observations; data for 2008) 
Panel A. Median Data
10 15 20 25 30 35 40 45 50 55
StaplesHealth 
TechnologyTelecommunication 
Number of 
observations 40 29 59 86 40 55 87 77 9 33
Cash 4.31 4.50 5.90 5.92 4.09 11.62 7.36 26.12 2.85 1.66
Receivables 8.34 12.22 16.41 9.43 8.82 11.45 18.25 9.44 5.77 5.29
Inventories 3.33 12.06 8.71 15.20 12.81 6.07 0.00 3.17 0.32 2.27
Other current 2.59 2.29 2.79 3.78 2.70 4.30 0.00 4.88 1.26 3.10
Total current 
assets 19.88 35.07 35.65 41.24 30.05 39.43 31.07 49.53 8.85 13.77
PPE 69.25 32.46 15.85 21.84 22.69 11.04 1.09 9.79 42.77 61.67
Intangibles 3.39 13.53 27.99 18.45 30.58 33.22 2.34 18.46 40.43 3.95
Accounts 
payable 6.05 6.28 6.43 7.84 7.88 3.61 9.37 3.17 2.06 3.46
Current

Current 
liabilities 15.81 17.63 24.55 26.38 26.27 17.94 24.00 22.59 10.70 13.52
LT debt 17.86 22.94 19.15 22.50 26.75 18.66 11.86 9.64 52.75 30.86
Total liabilities 50.74 66.89 63.44 64.08 68.46 53.34 88.16 49.00 66.34 74.53
Preferred stock 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.18
Common 
equity 47.68 30.88 36.55 35.56 31.48 46.43 9.45 49.88 20.61 25.43
Total equity 47.68 31.03 36.55 35.56 31.48 46.43 11.81 49.88 20.61 25.47

Reading 24 ■ Understanding Balance Sheets 202
Exhibit 18   (Continued) 
Panel B. Mean Data
Number of 
Cash 5.66 6.72 7.82 10.06 6.81 15.00 10.18 27.63 3.08 2.43
Receivables 9.43 11.80 18.76 11.40 9.62 13.24 29.68 12.16 4.63 5.92
Inventories 5.98 13.64 10.49 17.93 13.44 8.04 2.39 4.70 0.43 2.82
Other current 3.17 2.87 3.44 4.09 3.62 4.75 3.18 7.56 1.77 4.64
assets 23.94 34.98 38.35 39.88 33.31 41.07 34.25 51.97 9.91 15.73
PPE 62.93 37.88 24.15 26.83 27.09 13.52 2.75 13.41 48.81 61.62
Intangibles 7.43 16.52 28.04 21.40 32.75 33.80 9.30 23.08 35.95 5.16
Accounts 
payable 7.02 6.64 7.69 10.51 8.65 8.50 26.87 5.03 2.46 3.90
Current 
liabilities 16.33 20.33 25.82 27.48 27.65 22.73 32.76 25.89 10.27 16.02
LT debt 20.08 22.83 20.48 24.94 28.01 19.76 21.04 14.84 49.17 30.99

Total liabilities 52.29 64.02 64.23 66.31 69.32 53.36 79.79 51.21 80.00 73.73
Preferred stock 0.12 0.58 0.00 0.15 0.00 0.16 1.47 0.00 0.00 0.44
Common 
equity 46.77 35.55 35.41 33.00 30.04 46.08 18.02 48.69 17.95 25.44
Total equity 46.89 36.14 35.41 33.15 30.04 46.25 19.49 48.69 17.95 25.88
PPE = Property, plant, and equipment, LT = Long term.

Analysis of the Balance Sheet 203
APPLE  
31 Oct 2009
Long-  term financing receivables 0.0 0.0 9.8
Property, plant and equipment, net 6.2 6.5 9.8
Goodwill 0.4 12.1 28.8
Acquired intangible assets, net 0.5 5.0 5.7
Other assets 4.2 2.0 0.0
LIABILITIES AND SHAREHOLDERS’ 
EQUITY:
  Accounts payable 11.8 33.8 12.9
  Short-  term debt 0.0 2.0 1.6
  Accrued expenses 8.1 11.5 17.6
  Deferred revenue 4.3 9.0 5.4
Total current liabilities 24.2 56.3 37.5
Long-  term debt 0.0 10.2 12.2
Deferred revenue non-  current 1.8 9.0 0.0
Other non-  current liabilities 7.4 7.7 15.1
Total liabilities 33.4 83.2 64.7
Total shareholders’ equity 66.6 16.8 35.3
APPLE = Apple Inc.; DELL = Dell Inc.; HPQ = Hewlett-  Packard Co.
Source:  Based on data from companies’ annual reports.

From this data, Lu learns the following:
■■Apple and Dell have a high level of cash and short-  term marketable 
securities, consistent with the information technology sector as reported 
in Exhibit 18. Hewlett-  Packard’s percentage of cash and marketable 
securities is lower, perhaps reflecting its broader range of information 
technology products and services. Apple has a higher balance in cash and 
investments combined than Dell, Hewlett-  Packard, or the industry sector 
as reported in Exhibit 18. This may reflect the success of the company’s 
business model, which has generated large operating cash flows in recent 
years.
■■Apple has the lowest level of accounts receivable. Further research is 
necessary to learn the extent to which this is related to Apple’s cash sales 
through its own retail stores. An alternative explanation would be that the 
company has been selling/factoring receivables to a greater degree than 
the other companies; however, that explanation is unlikely given Apple’s

cash position.
■■Apple and Dell both have low levels of inventory compared to the indus -
try sector as reported in Exhibit 18. Both utilize a just-  in- time inventory 
system and rely on suppliers to hold inventory until needed. Additional 
scrutiny of the notes accompanying their annual reports reveals Apple

Reading 24 ■ Understanding Balance Sheets 204
regularly makes purchase commitments that are not currently recorded 
as inventory and uses contract manufacturers to assemble and test some 
finished products. All of the companies have some purchase commit -
ments and make some use of contract manufacturers, which implies that 
inventory may be “understated. ”
■■Apple and Dell have a level of property, plant, and equipment below that 
of the sector, whereas Hewlett-  Packard is very close to the sector median 
as reported in Exhibit 18.
■■Hewlett-  Packard has a large amount of goodwill from its steady stream of 
acquisitions over the last decade.
■■Dell has a large amount of accounts payable. Because of Dell’s high level of 
cash and investments, this is likely not a problem for Dell.
■■Consistent with the industry, Dell and Hewlett-  Packard have very low 
levels of long-  term debt. Apple has no long term debt.
7.2 Balance Sheet Ratios

Ratios facilitate time-  series and cross-  sectional analysis of a company’s financial 
position. Balance sheet ratios  are those involving balance sheet items only. Each of 
the line items on a vertical common-  size balance sheet is a ratio in that it expresses a 
balance sheet amount in relation to total assets. Other balance sheet ratios compare 
one balance sheet item to another. For example, the current ratio expresses current 
assets in relation to current liabilities as an indicator of a company’s liquidity. Balance 
sheet ratios include liquidity ratios  (measuring the company’s ability to meet its 
short-  term obligations) and solvency ratios  (measuring the company’s ability to 
meet long-  term and other obligations). These ratios and others are discussed in a 
later reading. Exhibit 19 summarizes the calculation and interpretation of selected 
balance sheet ratios.
Exhibit 19   Balance Sheet Ratios
Liquidity Ratios Calculation Indicates

Current Current assets ÷ Current 
liabilitiesAbility to meet current 
liabilities
Quick (acid test) (Cash + Marketable 
securities + Receivables) ÷ 
Current liabilitiesAbility to meet current 
Cash (Cash + Marketable securi -
ties) ÷ Current liabilitiesAbility to meet current 
Solvency Ratios
Long-  term 
debt-  to- equityTotal long-  term debt ÷ Total 
equityFinancial risk and financial 
leverage
Debt-  to- equity Total debt ÷ Total equity Financial risk and financial 
leverage
Total debt Total debt ÷ Total assets Financial risk and financial 
leverage
Financial leverage Total assets ÷ Total equity Financial risk and financial 
leverage

Analysis of the Balance Sheet 205
EXAMPLE 8   
Ratio Analysis
For the following ratio questions, refer to the balance sheet information for the 
SAP Group presented in Exhibits 1, 4, 6, 8, and 12.
1 The current ratio for SAP Group at 31 December 2009 is closest  to:
A 1.54.
B 1.86.
C 2.33.
2 Which two of the following ratios decreased in 2009 relative to 2008?
A Cash.
B Quick.
C Current.
D Debt-  to- equity.
E Financial leverage.
F Long-  term debt-  to- equity.
3 For the ratios listed in Question 2, how are the changes interpreted?
A is correct. SAP Group’s current ratio (Current assets ÷ Current liabilities) at 
31 December 2009 is 1.54 (€5,255 million ÷ €3,416 million).
D and E are correct. The ratios are shown in the table below. The debt-  to- equity 
and financial leverage ratios are lower in 2009 than in 2008. Bank loans (short-  
term debt) were reduced and equity increased. All other ratios are higher.
Liquidity Ratios Calculation 2009 € in millions 2008 € in millions

Current Current assets ÷ Current liabilities €5,255 ÷ €3,416 = 1.54 €5, 571 ÷ €5,824 = 0.96
Quick (acid test) (Cash + Marketable securities + 
Receivables) ÷ Current liabilities(€1,884 + €486 + €2,546) 
÷ €3,416 = 1.44(€1,280 + €588 + €3,178) ÷ 
€5,824 = 0.87
Cash (Cash + Marketable securities) ÷ 
Current liabilities(€1,884 + €486) ÷ 
€3,416 = 0.69(€1,280 + €588) ÷ €5,824 = 
0.32
Long-  term 
debt-  to- equityTotal long-  term debt ÷ Total equity €729 ÷ €8,491 = 8.6% €40 ÷ €7,171 = 0.6%
Debt-  to- equity Total debt ÷ Total equity (€146 + €729 ) ÷ €8,491 = 
10.3%(€ 2,563 + €40) ÷ €7,171 = 
36.3%
Financial Leverage Total assets ÷ Total equity €13,374 ÷ €8,491 = 1.58 €13,900 ÷ €7,171 = 1.94
■■The increase in each of the liquidity ratios (current, quick, and cash) 
in 2009 indicates that the company’s liquidity position strengthened. 
Compared with the end of 2008, the company reported a greater amount 
of current assets relative to current liabilities.

Reading 24 ■ Understanding Balance Sheets 206
■■The long-  term debt-  to- equity ratio indicates the amount of long-  term 
debt capital relative to the amount of equity capital. In general, an 
increase in the long-  term debt-  to- equity ratio implies that a company’s 
solvency has weakened. In this case, however, several points should be 
noted. First, despite the increase, this company’s ratio remains very low, 
indicating its solvency position is strong. Second, securing long-  term 
financing in 2009—when credit market disruptions had caused difficulty 
for some companies seeking to borrow—could be considered a very pru -
dent action. Third, the company’s overall financial leverage decreased, i.e., 
improved.
■■The debt-  to- equity ratio indicates the amount of total debt capital relative 
to the amount of equity capital. Financial leverage indicates the amount of 
total asset relative to equity. A decrease in the debt-  to- equity and finan -

cial leverage ratios implies that a company’s total leverage decreased and 
thus its solvency has improved. In this case, the company’s total leverage 
decreased largely because the company repaid most of its short-  term bank 
loans and increased its equity in 2009.
Cross-  sectional financial ratio analysis can be limited by differences in accounting 
methods. In addition, lack of homogeneity of a company’s operating activities can 
limit comparability. For diversified companies operating in different industries, using 
industry-  specific ratios for different lines of business can provide better comparisons. 
Companies disclose information on operating segments. The financial position and 
performance of the operating segments can be compared to the relevant industry.
Ratio analysis requires a significant amount of judgment. One key area requiring 
judgment is understanding the limitations of any ratio. The current ratio, for example,

is only a rough measure of liquidity at a specific point in time. The ratio captures only 
the amount of current assets, but the components of current assets differ significantly 
in their nearness to cash (e.g., marketable securities versus inventory). Another lim -
itation of the current ratio is its sensitivity to end-  of- period financing and operating 
decisions that can potentially impact current asset and current liability amounts. 
Another overall area requiring judgment is determining whether a ratio for a company 
is within a reasonable range for an industry. Yet another area requiring judgment is 
evaluating whether a ratio signifies a persistent condition or reflects only a temporary 
condition. Overall, evaluating specific ratios requires an examination of the entire 
operations of a company, its competitors, and the external economic and industry 
setting in which it is operating.
SUMMARY
The balance sheet (also referred to as the statement of financial position) discloses

what an entity owns (assets) and what it owes (liabilities) at a specific point in time. 
Equity is the owners’ residual interest in the assets of a company, net of its liabilities. 
The amount of equity is increased by income earned during the year, or by the issuance 
of new equity. The amount of equity is decreased by losses, by dividend payments, 
or by share repurchases.

Summary 207
An understanding of the balance sheet enables an analyst to evaluate the liquidity, 
solvency, and overall financial position of a company.
■■The balance sheet distinguishes between current and non-  current assets and 
liquidity provides more relevant and reliable information.
■■The concept of liquidity relates to a company’s ability to pay for its near-  term 
operating needs. With respect to a company overall, liquidity refers to the avail -
ability of cash to pay those near-  term needs. With respect to a particular asset 
or liability, liquidity refers to its “nearness to cash. ”
■■Some assets and liabilities are measured on the basis of fair value and some 
are measured at historical cost. Notes to financial statements provide informa -
tion that is helpful in assessing the comparability of measurement bases across 
companies.
■■Assets expected to be liquidated or used up within one year or one operat -

ing cycle of the business, whichever is greater, are classified as current assets. 
Assets not expected to be liquidated or used up within one year or one oper -
ating cycle of the business, whichever is greater, are classified as non-  current 
assets.
■■Liabilities expected to be settled or paid within one year or one operating 
cycle of the business, whichever is greater, are classified as current liabilities. 
Liabilities not expected to be settled or paid within one year or one operat -
ing cycle of the business, whichever is greater, are classified as non-  current 
■■Trade receivables, also referred to as accounts receivable, are amounts owed 
to a company by its customers for products and services already delivered. 
Receivables are reported net of the allowance for doubtful accounts.
■■Inventories are physical products that will eventually be sold to the company’s 
customers, either in their current form (finished goods) or as inputs into a

process to manufacture a final product (raw materials and work-  in- process). 
Inventories are reported at the lower of cost or net realizable value. If the net 
realizable value of a company’s inventory falls below its carrying amount, the 
company must write down the value of the inventory and record an expense.
■■Inventory cost is based on specific identification or estimated using the first-  in, 
first-  out or weighted average cost methods. Some accounting standards (includ -
ing US GAAP but not IFRS) also allow last-  in, first-  out as an additional inven -
tory valuation method.
■■Accounts payable, also called trade payables, are amounts that a business owes 
its vendors for purchases of goods and services.
■■Deferred revenue (also known as unearned revenue) arises when a company 
receives payment in advance of delivery of the goods and services associated 
with the payment received.
■■Property, plant, and equipment (PPE) are tangible assets that are used in

company operations and expected to be used over more than one fiscal period. 
Examples of tangible assets include land, buildings, equipment, machinery, fur -
niture, and natural resources such as mineral and petroleum resources.
■■IFRS provide companies with the choice to report PPE using either a historical 
cost model or a revaluation model. US GAAP permit only the historical cost 
model for reporting PPE.
■■Depreciation is the process of recognizing the cost of a long-  lived asset over its 
useful life. (Land is not depreciated.)

Reading 24 ■ Understanding Balance Sheets 208
■■Under IFRS, property used to earn rental income or capital appreciation is 
considered to be investment property. IFRS provide companies with the choice 
to report investment property using either a historical cost model or a fair value 
model.
■■Intangible assets refer to identifiable non-  monetary assets without physical sub -
stance. Examples include patents, licenses, and trademarks. For each intangible 
asset, a company assesses whether the useful life is finite or indefinite.
over the best estimate of its useful life, with the amortisation method and 
useful-  life estimate reviewed at least annually. Impairment principles for an 
intangible asset with a finite useful life are the same as for PPE.
■■An intangible asset with an indefinite useful life is not amortised. Instead, it is 
tested for impairment at least annually.

■■For internally generated intangible assets, IFRS require that costs incurred 
during the research phase must be expensed. Costs incurred in the develop -
ment stage can be capitalized as intangible assets if certain criteria are met, 
including technological feasibility, the ability to use or sell the resulting asset, 
and the ability to complete the project.
■■The most common asset that is not a separately identifiable asset is goodwill, 
which arises in business combinations. Goodwill is not amortised; instead it is 
■■Financial instruments are contracts that give rise to both a financial asset of one 
entity and a financial liability or equity instrument of another entity. In general, 
there are two basic alternative ways that financial instruments are measured: 
fair value or amortised cost. For financial instruments measured at fair value,

there are two basic alternatives in how net changes in fair value are recognized: 
as profit or loss on the income statement, or as other comprehensive income 
(loss) which bypasses the income statement.
■■Typical long-  term financial liabilities include loans (i.e., borrowings from banks) 
and notes or bonds payable (i.e., fixed-  income securities issued to investors). 
Liabilities such as bonds issued by a company are usually reported at amortised 
cost on the balance sheet.
■■Deferred tax liabilities arise from temporary timing differences between a com -
pany’s income as reported for tax purposes and income as reported for financial 
statement purposes.
■■Six potential components that comprise the owners’ equity section of the 
balance sheet include: contributed capital, preferred shares, treasury shares, 
retained earnings, accumulated other comprehensive income, and non-  
controlling interest.
■■The statement of changes in equity reflects information about the increases or

decreases in each component of a company’s equity over a period.
■■Vertical common-  size analysis of the balance sheet involves stating each balance 
sheet item as a percentage of total assets.
■■Balance sheet ratios include liquidity ratios (measuring the company’s ability to 
meet its short-  term obligations) and solvency ratios (measuring the company’s 
ability to meet long-  term and other obligations).

Practice Problems 209
1 Resources controlled by a company as a result of past events are:
A equity.
B assets.
C liabilities.
2 Equity equals:
A Assets – Liabilities.
B Liabilities – Assets.
C Assets + Liabilities.
3 Distinguishing between current and non-  current items on the balance sheet 
and presenting a subtotal for current assets and liabilities is referred to as:
A a classified balance sheet.
B an unclassified balance sheet.
C a liquidity-  based balance sheet.
4 Shareholders’ equity reported on the balance sheet is most likely  to differ from 
the market value of shareholders’ equity because:
A historical cost basis is used for all assets and liabilities.
B some factors that affect the generation of future cash flows are excluded.
C shareholders’ equity reported on the balance sheet is updated continuously.
5 The information provided by a balance sheet item is limited because of uncer -
tainty regarding:
A measurement of its cost or value with reliability.

B the change in current value following the end of the reporting period.
C the probability that any future economic benefit will flow to or from the 
entity.
6 Which of the following is most likely  classified as a current liability?
A Payment received for a product due to be delivered at least one year after 
the balance sheet date
B Payments for merchandise due at least one year after the balance sheet date 
but still within a normal operating cycle
C Payment on debt due in six months for which the company has the uncon -
ditional right to defer  settlement for at least one year after the balance sheet 
date
7 The most likely company to use a liquidity-  based balance sheet presentation is a:
A bank.
B computer manufacturer holding inventories.
C software company with trade receivables and payables. 
8 All of the following are current assets except :
A cash.
B goodwill.
C inventories.

Reading 24 ■ Understanding Balance Sheets 210
9 The most likely costs included in both the cost of inventory and property, plant, 
and equipment are:
A selling costs.
B storage costs.
C delivery costs.
10 Debt due within one year is considered:
A current.
B preferred.
C convertible.
11 Money received from customers for products to be delivered in the future is 
recorded as:
A revenue and an asset.
B an asset and a liability.
C revenue and a liability.
12 An example of a contra asset account is:
A depreciation expense.
B sales returns and allowances.
C allowance for doubtful accounts.
13 The carrying value of inventories reflects:
A their historical cost.
B their current value.
C the lower of historical cost or net realizable value.
14 When a company pays its rent in advance, its balance sheet will reflect a reduc -
tion in:
A assets and liabilities.
B assets and shareholders’ equity.
C one category of assets and an increase in another.
15 Accrued expenses (accrued liabilities) are:
A expenses that have been paid.

B created when another liability is reduced.
C expenses that have been reported on the income statement but not yet paid.
16 The initial measurement of goodwill is most likely  affected by:
A an acquisition’s purchase price.
B the acquired company’s book value.
C the fair value of the acquirer’s assets and liabilities.
17 Defining total asset turnover as revenue divided by average total assets, all else 
equal, impairment write-  downs of long-  lived assets owned by a company will 
most likely  result in an increase for that company in:
A the debt-  to- equity ratio but not the total asset turnover.
B the total asset turnover but not the debt-  to- equity ratio.
C both the debt-  to- equity ratio and the total asset turnover.
18 A company has total liabilities of £35 million and total stockholders’ equity of 
£55 million. Total liabilities are represented on a vertical common-  size balance 
sheet by a percentage closest  to:
A 35%.

Practice Problems 211
B 39%.
C 64%.
19 For financial assets classified as trading securities, how are unrealized gains and 
losses reflected in shareholders’ equity?
A They are not recognized.
B They flow through income into retained earnings.
C They are a component of accumulated other comprehensive income.
20 For financial assets classified as available for sale, how are unrealized gains and 
B They flow through retained earnings.
21 For financial assets classified as held to maturity, how are unrealized gains and 
22 The non-  controlling (minority) interest in consolidated subsidiaries is presented 
on the balance sheet:
A as a long-  term liability.

B separately, but as a part of shareholders’ equity.
C as a mezzanine item between liabilities and shareholders’ equity.
23 The item “retained earnings” is a component of:
A assets.
B liabilities.
C shareholders’ equity.
24 When a company buys shares of its own stock to be held in treasury, it records 
a reduction in:
A both assets and liabilities.
B both assets and shareholders’ equity.
C assets and an increase in shareholders’ equity.
25 Which of the following would an analyst most likely  be able to determine from a 
common-  size analysis of a company’s balance sheet over several periods?
A An increase or decrease in sales.
B An increase or decrease in financial leverage.
C A more efficient or less efficient use of assets.
26 An investor concerned whether a company can meet its near-  term obligations 
is most likely  to calculate the:
A current ratio.
B return on total capital.
C financial leverage ratio.

27 The most stringent test of a company’s liquidity is its:
A cash ratio.
B quick ratio.
C current ratio.

Reading 24 ■ Understanding Balance Sheets 212
28 An investor worried about a company’s long-  term solvency would most likely  
examine its:
B return on equity.
C debt-  to- equity ratio.
29 Using the information presented in Exhibit 4, the quick ratio for SAP Group at 
31 December 2009 is closest  to:
A 1.01.
B 1.44.
C 1.54.
30 Using the information presented in Exhibit 12, the financial leverage ratio for 
SAP Group at 31 December 2009 is closest  to:
A 0.08.
B 0.58.
C 1.58.
Questions 31 through 34 refer to Exhibit 1.
Exhibit 1   Common-  Size Balance Sheets for Company A, Company B, and 
Sector Average
Company 
ACompany 
BSector 
Average
ASSETS
Cash and cash equivalents 5 5 7
Marketable securities 5 0 2
Accounts receivable, net 5 15 12
Inventories 15 20 16
Prepaid expenses 5 15 11
Total current assets 35 55 48
Property, plant, and equipment, net 40 35 37
Goodwill 25 0 8
Other assets 0 10 7
Total assets 100 100 100
     
Accounts payable 10 10 10
Short-  term debt 25 10 15
Accrued expenses 0 5 3
Total current liabilities 35 25 28

Practice Problems 213
Long-  term debt 45 20 28
Other non-  current liabilities 0 10 7
Total liabilities 80 55 63
Total shareholders’ equity 20 45 37
Total liabilities and shareholders’ equity 100 100 100
     
31 Based on Exhibit 1, which statement is most likely correct?
A Company A has below-  average liquidity risk. 
B Company B has above-  average solvency risk.
C Company A has made one or more acquisitions.
32 The quick ratio for Company A is closest to:
A 0.43.
B 0.57.
C 1.00.
33 Based on Exhibit 1, the financial leverage ratio for Company B is closest to:
A 0.55.
B 1.22.
C 2.22.
34 Based on Exhibit 1, which ratio indicates lower liquidity risk for Company A 
compared with Company B?
A Cash ratio
B Quick ratio
C Current ratioExhibit 1   (Continued)

Reading 24 ■ Understanding Balance Sheets 214
SOLUTIONS
1 B is correct. Assets are resources controlled by a company as a result of past 
events.
2 A is correct. Assets = Liabilities + Equity and, therefore, Assets – Liabilities = 
Equity.
3 A is correct. A classified balance sheet is one that classifies assets and liabilities 
as current or non-  current and provides a subtotal for current assets and current 
liabilities. A liquidity-  based balance sheet broadly presents assets and liabilities 
in order of liquidity.
4 B is correct. The balance sheet omits important aspects of a company’s ability 
to generate future cash flows, such as its reputation and management skills. The 
balance sheet measures some assets and liabilities based on historical cost and 
measures others based on current value. Market value of shareholders’ equity 
is updated continuously. Shareholders’ equity reported on the balance sheet is 
updated for reporting purposes and represents the value that was current at the

end of the reporting period.
5 B is correct. Balance sheet information is as of a specific point in time, and 
items measured at current value reflect the value that was current at the end of 
the reporting period. For all financial statement items, an item should be recog -
nized in the financial statements only if it is probable that any future economic 
benefit associated with the item will flow to or from the entity and if the item 
has a cost or value that can be measured with reliability.
6 B is correct. Payments due within one operating cycle of the business, even if 
they will be settled more than one year after the balance sheet date, are classi -
fied as current liabilities. Payment received in advance of the delivery of a good 
or service creates an obligation or liability. If the obligation is to be fulfilled at 
least one year after the balance sheet date, it is recorded as a non-  current liabil -
ity, such as deferred revenue or deferred income. Payments that the company

has the unconditional right to defer for at least one year after the balance sheet 
may be classified as non-  current liabilities. 
7 A is correct. A liquidity-  based presentation, rather than a current/non-  current 
presentation, may be used by such entities as banks if broadly presenting assets 
and liabilities in order of liquidity is reliable and more relevant.
8 B is correct. Goodwill is a long-  term asset, and the others are all current assets.
9 C is correct. Both the cost of inventory and property, plant, and equipment 
include delivery costs, or costs incurred in bringing them to the location for use 
or resale.
10 A is correct. Current liabilities are those liabilities, including debt, due within 
one year. Preferred refers to a class of stock. Convertible refers to a feature of 
bonds (or preferred stock) allowing the holder to convert the instrument into 
common stock.
11 B is correct. The cash received from customers represents an asset. The obliga -

tion to provide a product in the future is a liability called “unearned income” or 
“unearned revenue. ” As the product is delivered, revenue will be recognized and 
the liability will be reduced.

Solutions 215
12 C is correct. A contra asset account is netted against (i.e., reduces) the balance 
of an asset account. The allowance for doubtful accounts reduces the balance of 
accounts receivable. Accumulated depreciation, not depreciation expense, is a 
contra asset account. Sales returns and allowances create a contra account that 
reduce sales, not an asset.
13 C is correct. Under IFRS, inventories are carried at historical cost, unless net 
realizable value of the inventory is less. Under US GAAP , inventories are carried 
at the lower of cost or market.
14 C is correct. Paying rent in advance will reduce cash and increase prepaid 
expenses, both of which are assets.
15 C is correct. Accrued liabilities are expenses that have been reported on a com -
pany’s income statement but have not yet been paid.
16 A is correct. Initially, goodwill is measured as the difference between the 
purchase price paid for an acquisition and the fair value of the acquired, not

acquiring, company’s net assets (identifiable assets less liabilities).
17 C is correct. Impairment write-  downs reduce equity in the denominator of 
the debt-  to- equity ratio but do not affect debt, so the debt-  to- equity ratio is 
expected to increase. Impairment write-  downs reduce total assets but do not 
affect revenue. Thus, total asset turnover is expected to increase.
18 B is correct. Vertical common-  size analysis involves stating each balance sheet 
item as a percentage of total assets. Total assets are the sum of total liabilities 
(£35 million) and total stockholders’ equity (£55 million), or £90 million. Total 
liabilities are shown on a vertical common-  size balance sheet as (£35 mil -
lion/£90 million) ≈ 39%.
19 B is correct. For financial assets classified as trading securities, unrealized gains 
and losses are reported on the income statement and flow to shareholders’ 
equity as part of retained earnings.

20 C is correct. For financial assets classified as available for sale, unrealized gains 
and losses are not recorded on the income statement and instead are part of 
other  comprehensive income. Accumulated other comprehensive income is a 
component of Shareholders’ equity
21 A is correct. Financial assets classified as held to maturity are measured at 
amortised cost. Gains and losses are recognized only when realized.
22 B is correct. The non-  controlling interest in consolidated subsidiaries is shown 
separately as part of shareholders’ equity.
23 C is correct. The item “retained earnings” is a component of shareholders’ 
equity.
24 B is correct. Share repurchases reduce the company’s cash (an asset). 
Shareholders’ equity is reduced because there are fewer shares outstanding and 
treasury stock is an offset to owners’ equity.
25 B is correct. Common-  size analysis (as presented in the reading) provides infor -

mation about composition of the balance sheet and changes over time. As a 
result, it can provide information about an increase or decrease in a company’s 
financial leverage.
26 A is correct. The current ratio provides a comparison of assets that can be 
turned into cash relatively quickly and liabilities that must be paid within one 
year. The other ratios are more suited to longer-  term concerns.
27 A is correct. The cash ratio determines how much of a company’s near-  term 
obligations can be settled with existing amounts of cash and marketable 

Reading 24 ■ Understanding Balance Sheets 216
28 C is correct. The debt-  to- equity ratio, a solvency ratio, is an indicator of finan -
cial risk.
29 B is correct. The quick ratio ([Cash + Marketable securities + Receivables] ÷ 
Current liabilities) is 1.44 ([= 1,884 + 486 + 2,546] ÷ 3,416). Given the place -
ment of other financial assets between cash and receivables, it is reasonable to 
assume these are highly liquid and are probably marketable securities.
30 C is correct. The financial leverage ratio (Total assets ÷ Total equity) is 1.58 (= 
13,374 ÷ 8,491).
31 C is correct. The presence of goodwill on Company A’s balance sheet signi -
fies that it has made one or more acquisitions in the past. The current, cash, 
and quick ratios are lower for Company A than for the sector average. These 
lower liquidity ratios imply above-  average liquidity risk. The total debt, long-  
term debt-  to- equity, debt-  to- equity, and financial leverage ratios are lower

for Company B than for the sector average. These lower solvency ratios imply 
below-  average solvency risk.
 Current ratio is (35/35) = 1.00 for Company A, versus (48/28) = 1.71 for the 
sector average.
 Cash ratio is (5 + 5)/35 = 0.29 for Company A, versus (7 + 2)/28 = 0.32 for the 
sector average. 
 Quick ratio is (5 + 5 + 5)/35 = 0.43 for Company A, versus (7 + 2 + 12)/28 = 
0.75 for the sector average.
 Total debt ratio is (55/100) = 0.55 for Company B, versus (63/100) = 0.63 for the 
 Long-  term debt-  to- equity ratio is (20/45) = 0.44 for Company B, versus (28/37) 
= 0.76 for the sector average. 
 Debt-  to- equity ratio is (55/45) = 1.22 for Company B, versus (63/37) = 1.70 for 
the sector average.
 Financial leverage ratio is (100/45) = 2.22 for Company B, versus (100/37) = 
2.70 for the sector average.
32 A is correct. The quick ratio is defined as (Cash and cash equivalents + 
Marketable securities + receivables) ÷ Current liabilities. For Company A, this

calculation is (5 + 5 + 5)/35 = 0.43. 
33 C is correct. The financial leverage ratio is defined as Total assets ÷ Total equity. 
For Company B, total assets are 100 and total equity is 45; hence, the financial 
leverage ratio is 100/45 = 2.22. 
34 A is correct. The cash ratio is defined as (Cash + Marketable securities)/Current 
liabilities. Company A’s cash ratio, (5 + 5)/35 = 0.29, is higher than (5 + 0)/25 = 
0.20 for Company B.

Understanding Cash Flow Statements
by Elaine Henry, PhD, CFA, Thomas R. Robinson, PhD, CFA, 
Jan Hendrik van Greuning, DCom, CFA, and 
Michael A. Broihahn, CPA, CIA, CFA
PhD, CFA, is at AACSB International (USA). Jan Hendrik van Greuning, DCom, CFA, is at 
BIBD (Brunei). Michael A. Broihahn, CPA, CIA, CFA, is at Barry University (USA).
a. compare cash flows from operating, investing, and financing 
activities and classify cash flow items as relating to one of those 
three categories given a description of the items;
b. describe how non-  cash investing and financing activities are 
reported;
c. contrast cash flow statements prepared under International 
Financial Reporting Standards (IFRS) and US generally accepted 
accounting principles (US GAAP);
d. distinguish between the direct and indirect methods of presenting

cash from operating activities and describe arguments in favor of 
each method;
e. describe how the cash flow statement is linked to the income 
statement and the balance sheet;
f. describe the steps in the preparation of direct and indirect cash 
flow statements, including how cash flows can be computed using 
income statement and balance sheet data;
g. convert cash flows from the indirect to direct method;
h. analyze and interpret both reported and common-  size cash flow 
i. calculate and interpret free cash flow to the firm, free cash flow to 
equity, and performance and coverage cash flow ratios.REA dINg
25
the readings were published.

readings.

Reading 25 ■ Understanding Cash Flow Statements 218
The cash flow statement provides information about a company’s cash receipts  and 
cash payments  during an accounting period. The cash-  based information provided by 
the cash flow statement contrasts with the accrual-  based information from the income 
statement. For example, the income statement reflects revenues when earned rather 
than when cash is collected; in contrast, the cash flow statement reflects cash receipts 
when collected as opposed to when the revenue was earned. A reconciliation between 
reported income and cash flows from operating activities provides useful information 
about when, whether, and how a company is able to generate cash from its operating 
activities. Although income is an important measure of the results of a company’s 
activities, cash flow is also essential. As an extreme illustration, a hypothetical com -
pany that makes all sales on account, without regard to whether it will ever collect its

accounts receivable, would report healthy sales on its income statement and might 
well report significant income; however, with zero cash inflow, the company would 
not survive. The cash flow statement also provides a reconciliation of the beginning 
and ending cash on the balance sheet.
In addition to information about cash generated (or, alternatively, cash used) in 
operating activities, the cash flow statement provides information about cash provided 
(or used) in a company’s investing and financing activities. This information allows 
the analyst to answer such questions as:
■■Does the company generate enough cash from its operations to pay for its new 
investments, or is the company relying on new debt issuance to finance them?
■■Does the company pay its dividends to common stockholders using cash gener -
ated from operations, from selling assets, or from issuing debt?
Answers to these questions are important because, in theory, generating cash

from operations can continue indefinitely, but generating cash from selling assets, 
for example, is possible only as long as there are assets to sell. Similarly, generating 
cash from debt financing is possible only as long as lenders are willing to lend, and 
the lending decision depends on expectations that the company will ultimately have 
adequate cash to repay its obligations. In summary, information about the sources 
and uses of cash helps creditors, investors, and other statement users evaluate the 
company’s liquidity, solvency, and financial flexibility.
This reading explains how cash flow activities are reflected in a company’s cash 
flow statement. The reading is organized as follows. Section 2 describes the compo -
nents and format of the cash flow statement, including the classification of cash flows 
under International Financial Reporting Standards (IFRS) and US generally accepted 
accounting principles (GAAP) and the direct and indirect formats for presenting the

cash flow statement. Section 3 discusses the linkages of the cash flow statement with 
the income statement and balance sheet and the steps in the preparation of the cash 
flow statement. Section 4 demonstrates the analysis of cash flow statements, including 
the conversion of an indirect cash flow statement to the direct method and how to 
use common-  size cash flow analysis, free cash flow measures, and cash flow ratios 
used in security analysis. A summary of the key points and practice problems in the 
CFA Institute multiple-  choice format conclude the reading.1

Components and Format of the Cash Flow Statement 219
COMPONENTS AND FORMAT OF THE CASH FLOW 
STATEMENT
The analyst needs to be able to extract and interpret information on cash flows from 
financial statements. The basic components and allowable formats of the cash flow 
statement are well established.
■■The cash flow statement has subsections relating specific items to the operating, 
investing, and financing activities of the company.
■■Two presentation formats for the operating section are allowable: direct and 
indirect.
The following discussion presents these topics in greater detail.
2.1 Classification of Cash Flows and Non-  Cash Activities
All companies engage in operating, investing, and financing activities. These activities 
are the classifications used in the cash flow statement under both IFRS and US GAAP 
and are described as follows:1
■■Operating activities  include the company’s day-  to- day activities that create

revenues, such as selling inventory and providing services, and other activities 
not classified as investing or financing. Cash inflows result from cash sales and 
from collection of accounts receivable. Examples include cash receipts from the 
provision of services and royalties, commissions, and other revenue. To gener -
ate revenue, companies undertake such activities as manufacturing inventory, 
purchasing inventory from suppliers, and paying employees. Cash outflows 
result from cash payments for inventory, salaries, taxes, and other operating-  
related expenses and from paying accounts payable. Additionally, operating 
activities include cash receipts and payments related to dealing securities  or 
trading securities  (as opposed to buying or selling securities as investments, as 
discussed below).
■■Investing activities  include purchasing and selling long-  term assets and other 
investments. These long-  term assets and other investments include property,

plant, and equipment; intangible assets; other long-  term assets; and both long-  
term and short-  term investments in the equity and debt (bonds and loans) 
issued by other companies. For this purpose, investments in equity and debt 
securities exclude a) any securities considered cash equivalents (very short-  
term, highly liquid securities) and b) securities held for dealing or trading pur -
poses, the purchase and sale of which are considered operating activities even 
for companies where this is not a primary business activity. Cash inflows in the 
investing category include cash receipts from the sale of non-  trading securities; 
property, plant, and equipment; intangibles; and other long-  term assets. Cash 
outflows include cash payments for the purchase of these assets.
■■Financing activities  include obtaining or repaying capital, such as equity 
and long-  term debt. The two primary sources of capital are shareholders and

creditors. Cash inflows in this category include cash receipts from issuing 
stock (common or preferred) or bonds and cash receipts from borrowing. Cash 
outflows include cash payments to repurchase stock (e.g., treasury stock) and to 
repay bonds and other borrowings. Note that indirect borrowing using accounts 
payable is not considered a financing activity—such borrowing is classified as 2
1 IAS 7 Statement of Cash Flows .

Reading 25 ■ Understanding Cash Flow Statements 220
an operating activity. The new IFRS standard relating to lease accounting (IFRS 
16) affects how operating leases are represented in the cash flow statement.2 
Under IFRS 16, operating leases are treated similarly to finance leases—that is, 
the interest component of lease payments will be reflected in either the oper -
ating or financing section, and the principal component of lease payments is 
included in the financing section.
EXAMPLE 1   
Net Cash Flow from Investing Activities
A company recorded the following in Year 1:
Proceeds from issuance of long-  term debt €300,000
Purchase of equipment €200,000
Loss on sale of equipment €70,000
Proceeds from sale of equipment €120,000
Equity in earnings of affiliate €10,000
On the Year 1 statement of cash flows, the company would report net cash 
flow from investing activities closest  to:
A (€150,000).
B (€80,000).
C €200,000.
Solution

Solution
B is correct. The only two items that would affect the investing section are the 
purchase of equipment and the proceeds from sale of equipment: (€200,000) + 
€120,000 = (€80,000). The loss on sale of equipment and the equity in earnings 
of affiliate affect net income but are not cash flows. The issuance of debt is a 
financing cash flow.
IFRS provide companies with choices in reporting some items of cash flow, par -
ticularly interest and dividends. IFRS explain that although for a financial institution 
interest paid and received would normally be classified as operating activities, for other 
entities, alternative classifications may be appropriate. For this reason, under IFRS, 
interest received may be classified either as an operating activity or as an investing 
activity. Under IFRS, interest paid may be classified as either an operating activity or 
a financing activity. Furthermore, under IFRS, dividends received may be classified as

either an operating activity or an investing activity and dividends paid may be classified 
as either an operating activity or a financing activity. Companies must use a consistent 
classification from year to year and disclose separately the amounts of interest and 
dividends received and paid and where the amounts are reported.
Under US GAAP , discretion is not permitted in classifying interest and dividends. 
Interest received and interest paid are reported as operating activities for all compa -
nies.3 Under US GAAP , dividends received are always reported as operating activities 
and dividends paid are always reported as financing activities.
2 IFRS 16 is effective for fiscal years beginning 1 January 2019, with earlier voluntary adoption allowed.
3 FASB ASC Topic 230 [Statement of Cash Flows].

Components and Format of the Cash Flow Statement 221
EXAMPLE 2   
Operating versus Financing Cash Flows
On 31 December 2009, a company issued a £30,000 180-  day note at 8 percent 
and used the cash received to pay for inventory and issued £110,000 long-  term 
debt at 11 percent annually and used the cash received to pay for new equipment. 
Which of the following most  accurately reflects the combined effect of both 
transactions on the company’s cash flows for the year ended 31 December 2009 
under IFRS? Cash flows from:
A operations are unchanged.
B financing increase £110,000.
C operations decrease £30,000.
Solution: 
C is correct. The payment for inventory would decrease cash flows from oper -
ations. The issuance of debt (both short-  term and long-  term debt) is part of 
financing activities and would increase cash flows from financing activities by 
£140,000. The purchase of equipment is an investing activity. Note that the 
treatment under US GAAP would be the same for these transactions.

Companies may also engage in non-  cash investing and financing transactions. A 
non-  cash transaction is any transaction that does not involve an inflow or outflow 
of cash. For example, if a company exchanges one non-  monetary asset for another 
non-  monetary asset, no cash is involved. Similarly, no cash is involved when a com -
pany issues common stock either for dividends or in connection with conversion of a 
convertible bond or convertible preferred stock. Because no cash is involved in non-  
cash transactions (by definition), these transactions are not incorporated in the cash 
flow statement. However, because such transactions may affect a company’s capital 
or asset structures, any significant non-  cash transaction is required to be disclosed, 
either in a separate note or a supplementary schedule to the cash flow statement.
2.2 A Summary of Differences between IFRS and US GAAP
As highlighted in the previous section, there are some differences in cash flow state -

ments prepared under IFRS and US GAAP that the analyst should be aware of when 
comparing the cash flow statements of companies prepared in accordance with different 
sets of standards. The key differences are summarized in Exhibit 1. Most significantly, 
IFRS allow more flexibility in the reporting of such items as interest paid or received 
and dividends paid or received and in how income tax expense is classified.
US GAAP classify interest and dividends received from investments as operating 
activities, whereas IFRS allow companies to classify those items as either operating 
or investing cash flows. Likewise, US GAAP classify interest expense as an operating 
activity, even though the principal amount of the debt issued is classified as a financ -
ing activity. IFRS allow companies to classify interest expense as either an operating 
activity or a financing activity. US GAAP classify dividends paid to stockholders as a

financing activity, whereas IFRS allow companies to classify dividends paid as either 
an operating activity or a financing activity.
US GAAP classify all income tax expenses as an operating activity. IFRS also classify 
income tax expense as an operating activity, unless the tax expense can be specifically 
identified with an investing or financing activity (e.g., the tax effect of the sale of a 
discontinued operation could be classified under investing activities).

Reading 25 ■ Understanding Cash Flow Statements 222
Exhibit 1   Cash Flow Statements: Differences between IFRS and US GAAP
Topic IFRS US GAAP
Classification of cash flows:
■■Interest received Operating or investing Operating
■■Interest paid Operating or financing Operating
■■Dividends received Operating or investing Operating
■■Dividends paid Operating or financing Financing
■■Bank overdrafts Considered part of cash equivalents Not considered part of cash and 
cash equivalents and classified as 
financing
■■Taxes paid Generally operating, but a portion can 
be allocated to investing or financing if it 
can be specifically identified with these 
categoriesOperating
Format of statement Direct or indirect; direct is encouraged Direct or indirect; direct is encour -
aged. A reconciliation of net income 
to cash flow from operating activi -
ties must be provided regardless of 
method used

Sources:  IAS 7; FASB ASC Topic 230; and “IFRS and US GAAP: Similarities and Differences, ” PricewaterhouseCoopers (September 2009), 
available at www.pwc.com.
Under either set of standards, companies currently have a choice of formats for 
presenting cash flow statements, as discussed in the next section.
2.3 Direct and Indirect Methods for Reporting Cash Flow from 
Operating Activities
There are two acceptable formats for reporting cash flow from operating activities  
(also known as cash flow from operations  or operating cash flow ), defined as the 
net amount of cash provided from operating activities: the direct and the indirect 
methods. The amount  of operating cash flow is identical under both methods; only 
the presentation format  of the operating cash flow section differs. The presentation 
format of the cash flows from investing and financing is exactly the same, regardless 
of which method is used to present operating cash flows.

The direct method  shows the specific cash inflows and outflows that result in 
reported cash flow from operating activities. It shows each cash inflow and outflow 
related to a company’s cash receipts and disbursements. In other words, the direct 
method eliminates any impact of accruals and shows only cash receipts and cash 
payments. The primary argument in favor of the direct method is that it provides 
information on the specific sources of operating cash receipts and payments. This is 
in contrast to the indirect method, which shows only the net result of these receipts 
and payments. Just as information on the specific sources of revenues and expenses is 
more useful than knowing only the net result—net income—the analyst gets additional 
information from a direct-  format cash flow statement. The additional information is 
useful in understanding historical performance and in predicting future operating 
cash flows.

The indirect method  shows how cash flow from operations can be obtained from 
reported net income as the result of a series of adjustments. The indirect format  begins 
with net income. To reconcile net income with operating cash flow, adjustments are

Components and Format of the Cash Flow Statement 223
made for non-  cash items, for non-  operating items, and for the net changes in operating 
accruals. The main argument for the indirect approach is that it shows the reasons for 
differences between net income and operating cash flows. (However, the differences 
between net income and operating cash flows are equally visible on an indirect-  format 
cash flow statement and in the supplementary reconciliation required under US GAAP 
if the company uses the direct method.) Another argument for the indirect method 
is that it mirrors a forecasting approach that begins by forecasting future income and 
then derives cash flows by adjusting for changes in balance sheet accounts that occur 
because of the timing differences between accrual and cash accounting.
IFRS and US GAAP both encourage the use of the direct method but permit either 
method. US GAAP encourage the use of the direct method but also require companies

to present a reconciliation between net income and cash flow (which is equivalent to 
the indirect method).4 If the indirect method is chosen, no direct-  format disclosures 
are required. The majority of companies, reporting under IFRS or US GAAP , present 
using the indirect method for operating cash flows.
Many users of financial statements prefer the direct format , particularly analysts 
and commercial lenders, because of the importance of information about operating 
receipts and payments in assessing a company’s financing needs and capacity to repay 
existing obligations. Preparers argue that adjusting net income to operating cash flow, 
as in the indirect format, is easier and less costly than reporting gross operating cash 
receipts and payments, as in the direct format. With advances in accounting systems 
and technology, it is not clear that gathering the information required to use the direct 
method is difficult or costly. CFA Institute has advocated that standard setters require

the use of the direct format for the main presentation of the cash flow statement, with 
indirect cash flows as supplementary disclosure.5
2.3.1  An Indirect-  Format Cash Flow Statement Prepared under IFRS
Exhibit 2 presents the consolidated cash flow statement prepared under IFRS from 
Unilever Group’s 2009 annual report.6 The statement, covering the fiscal years ended 
31 December 2009, 2008, and 2007, shows the use of the indirect method. Unilever 
is an Anglo-  Dutch consumer products company with headquarters in the United 
Kingdom and the Netherlands.7
Exhibit 2   Unilever Group Consolidated Cash Flow Statement (€ millions)
For the year ended 31 December
Cash flow from operating activities
Net profit 3,659 5,285 4,136
  Taxation 1,257 1,844 1,137
  Share of net profit of joint ventures/associates and other income from 
non-  current investments (489) (219) (191)
  Net finance costs: 593 257 252

Net finance costs: 593 257 252
4 FASB ASC Section 230-  10- 45 [Statement of Cash Flows–Overall–Other Presentation Matters].
5 A Comprehensive Business Reporting Model: Financial Reporting for Investors , CFA Institute Centre for 
Financial Market Integrity (July 2007), p. 13.
6 The cash flow statement presented here includes a reconciliation of net income to cash generated 
from operations, which Unilever Group reports in Note 28 to the financial statement rather than on the 
statement itself.
7 Unilever NV and Unilever PLC have independent legal structures, but a series of agreements enable the 
companies to operate as a single economic entity.

Reading 25 ■ Understanding Cash Flow Statements 224
   Finance income (75) (106) (147)
   Finance cost 504 506 550
   Preference shares provision — — 7
   Pensions and similar obligations 164 (143) (158)
Operating profit (continuing and discontinued operations) 5,020 7,167 5,334
  Depreciation, amortisation and impairment 1,032 1,003 943
  Changes in working capital: 1,701 (161) 27
   Inventories 473 (345) (333)
   Trade and other current receivables 640 (248) (43)
   Trade payables and other current liabilities 588 432 403
  Pensions and similar provisions less payments (1,028) (502) (910)
  Provisions less payments (258) (62) 145
  Elimination of (profits)/losses on disposals 13 (2,259) (459)
  Non-  cash charge for share-  based compensation 195 125 118
  Other adjustments 58 15 (10)
Cash flow from operating activities 6,733 5,326 5,188
Income tax paid (959) (1,455) (1,312)
Net cash flow from operating activities 5,774 3,871 3,876

Interest received 73 105 146
  Purchase of intangible assets (121) (147) (136)
  Purchase of property, plant and equipment (1,248) (1,142) (1,046)
  Disposal of property, plant and equipment 111 190 163
  Sale and leaseback transactions resulting in operating leases — — 36
  Acquisition of group companies, joint ventures and associates (409) (211) (214)
  Disposal of group companies, joint ventures and associates 270 2,476 164
  Acquisition of other non-  current investments (95) (126) (50)
  Disposal of other non-  current investments 224 47 33
  Dividends from joint ventures, associates and other non-  current 
investments 201 132 188
  (Purchase)/sale of financial assets (269) 91 93
Net cash flow (used in)/from investing activities (1,263) 1,415 (623)
  Dividends paid on ordinary share capital (2,106) (2,086) (2,182)
  Interest and preference dividends paid (517) (487) (552)
  Additional financial liabilities 2,913 4,544 4,283
  Repayment of financial liabilities (4,456) (3,427) (2,896)

Sale and leaseback transactions resulting in finance leases — (1) 25
  Capital element of finance lease rental payments (24) (66) (74)
  Share buy-  back programme — (1,503) (1,500)
  Other movements on treasury stock 103 103 442
  Other financing activities (214) (207) (555)
Net cash flow (used in)/from financing activities (4,301) (3,130) (3,009)
Net increase/(decrease) in cash and cash equivalents 210 2,156 244Exhibit 2   (Continued)

Components and Format of the Cash Flow Statement 225
Cash and cash equivalents at the beginning of the year 2,360 901 710
Effect of foreign exchange rate changes (173) (697) (53)
Cash and cash equivalents at the end of the year 2,397 2,360 901
Beginning first at the bottom of the statement, we note that cash increased from 
€710 million at the beginning of 2007 to €2,397 million at the end of 2009, with the 
largest increase occurring in 2008. To understand the changes, we next examine the 
sections of the statement. In each year, the primary cash inflow derived from operating 
activities, as would be expected for a mature company in a relatively stable industry. 
In each year, the operating cash flow was more than the reported net profit, again, 
as would be expected from a mature company, with the largest differences primarily 
arising from the add-  back of depreciation. Also, in each year, the operating cash flow

was more than enough to cover the company’s capital expenditures. For example, 
in 2009, the company generated €5,774 million in net cash from operating activities 
and—as shown in the investing section—spent €1,137 million on property, plant, and 
equipment (€1,248  million, net of €111  million proceeds from disposals). Also, as 
shown in the investing section, the main reason for the large increase in cash in 2008 
was the €2,476 million inflow from the disposal of group companies, joint ventures, 
and associates.
The financing section of the statement shows that each year the company returned 
about €2.1 billion to its common shareholders and around €500 million to its debt 
holders and preferred shareholders via interest and dividends. The company also 
repurchased about €1.5 billion in common stock in both 2007 and 2008. In 2009, the 
company repaid debt (repayments of €4,456 million exceeded additional financing 
liabilities of €2,913 million).

Having examined each section of the statement, we return to the operating activ -
ities section of Unilever’s cash flow statement, which presents a reconciliation of net 
profit to net cash flow from operating activities (i.e., uses the indirect method). The 
following discussion of certain adjustments to reconcile net profit to operating cash 
flows explains some of the main reconciliation adjustments and refers to the amounts 
in 2009. The first adjustment adds back the €1,257 million income tax expense (labeled 
“Taxation”) that had been recognized as an expense in the computation of net profit. 
A €959 million deduction for the (cash) income taxes paid is then shown separately, as 
the last item in the operating activities section, consistent with the IFRS requirement 
that cash flows arising from income taxes be separately disclosed. The classification of 
taxes on income paid should be indicated. The classification is in operating activities

unless the taxes can be specifically identified with financing or investing activities.
The next adjustment “removes” from the operating cash flow section the €489 mil -
lion representing Unilever’s share of joint ventures’ income that had been included 
in the computation of net profit. A €201 million inflow of (cash) dividends received 
from those joint ventures is then shown in the investing activities section. Similarly, 
a €593 million adjustment removes the net finance costs from the operating activities 
section. Unilever then reports its €73 million (cash) interest received in the investing 
activities section and its €517 million (cash) interest paid (and preference dividends 
paid) in the financing activities section. The next adjustment in the operating section 
of this indirect-  method statement adds back €1,032  million depreciation, amorti -
sation, and impairment, all of which are expenses that had been deducted in the Exhibit 2   (Continued)

Reading 25 ■ Understanding Cash Flow Statements 226
computation of net income but which did not involve any outflow of cash in the period. 
The €1,701 million adjustment for changes in working capital is necessary because 
these changes result from applying accrual accounting and thus do not necessarily 
correspond to the actual cash movement. These adjustments are described in greater 
detail in a later section.
In summary, some observations from an analysis of Unilever’s cash flow statement 
include:
■■Total cash increased from €710 million at the beginning of 2007 to €2,397 mil -
lion at the end of 2009, with the largest increase occurring in 2008.
■■In each year, the operating cash flow was more than the reported net profit, as 
would generally be expected from a mature company.
■■In each year, the operating cash flow was more than enough to cover the com -
pany’s capital expenditures.
■■The company returned cash to its equity investors through dividends in each

year and through share buybacks in 2007 and 2008.
2.3.2  A Direct-  Format Cash Flow Statement Prepared under IFRS
In the direct format of the cash flow statement, the cash received from customers, as 
well as other operating items, is clearly shown.
Exhibit 3 presents a direct-  method format cash flow statement prepared under IFRS 
for Telefónica Group, a diversified telecommunications company based in Madrid.8
Exhibit 3   Telefónica Group Consolidated Statement of Cash Flows (€ millions)
for the years ended 31 December 2009 2008 2007
Cash flows from operating activities
  Cash received from customers 67,358 69,060 67,129
  Cash paid to suppliers and employees (46,198) (48,500) (47,024)
  Dividends received 100 113 124
  Net interest and other financial expenses paid (2,170) (2,894) (3,221)
  Taxes paid (2,942) (1,413) (1,457)
  Net cash from operating activities 16,148 16,366 15,551
Cash flows from investing activities
  Proceeds on disposals of property, plant and equipment and

intangible assets 242 276 198
  Payments on investments in property, plant and equipment 
and intangible assets (7,593) (7,889) (7,274)
  Proceeds on disposals of companies, net of cash and cash 
equivalents disposed 34 686 5,346
  Payments on investments in companies, net of cash and cash 
equivalents acquired (48) (2,178) (2,798)
  Proceeds on financial investments not included under cash 
equivalents 6 31 14
  Payments made on financial investments not included under 
cash equivalents (1,411) (114) (179)
8 This statement excludes the supplemental cash flow reconciliation provided at the bottom of the original 
cash flow statement by the company.

Components and Format of the Cash Flow Statement 227
  Interest (paid) received on cash surpluses not included under 
cash equivalents (548) 76 74
  Government grants received 18 11 27
  Net cash used in investing activities (9,300) (9,101) (4,592)
Cash flows from financing activities
  Dividends paid (4,838) (4,440) (3,345)
  Transactions with equity holders (947) (2,241) (2,152)
  Proceeds on issue of debentures and bonds 8,617 1,317 4,209
  Proceeds on loans, borrowings and promissory notes 2,330 3,693 6,658
  Cancellation of debentures and bonds (1,949) (1,167) (1,756)
  Repayments of loans, borrowings and promissory notes (5,494) (4,927) (13,039)
  Net cash flow used in financing activities (2,281) (7,765) (9,425)
  Effect of foreign exchange rate changes on collections and 
payments 269 (302) (261)
  Effect of changes in consolidation methods and other non-  
monetary effects — 14 —
Net increase (decrease) in cash and cash equivalents during 
the period 4,836 (788) 1,273

Cash and cash equivalents at 1 January 4,277 5,065 3,792
Cash and cash equivalents at 31 December 9,113 4,277 5,065
As shown at the bottom of the statement, cash and cash equivalents increased 
from €3,792 million at the beginning of 2007 to €9,113 million at the end of 2009. The 
largest increase in cash occurred in 2009, with 2008 showing a decrease. Cash from 
operations was the primary source of cash, consistent with the profile of a mature 
company in a relatively stable industry. Each year, the company generated significantly 
more cash from operations than it required for its capital expenditures. For example, 
in 2009, the company generated €16.1  billion cash from operations and spent—as 
shown in the investing section—only €7.4 billion on property, plant, and equipment 
(€7,593 million, net of €242 million from disposals). Another notable item from the 
investing section is the company’s limited acquisition activity in 2009 compared with

2008 and 2007. In both 2007 and 2008, the company made over €2 billion of acquisi -
tions, and in 2007, the company also received €5.5 billion from disposals. Instead of 
using cash for acquisition activity in 2009 when net acquisitions used only €14 million 
(€48 million acquisitions, net of €34 million from disposals), the company invested 
€1,411 million in financial investments excluded from cash and cash equivalents (i.e., 
long-  term financial investments).
As shown in the financing section, in 2009, the net cash inflow from debt issu -
ance was €3,504 million (€8,617 million proceeds from debentures and bonds plus 
€2,330 million proceeds from loans, borrowings, and promissory notes, net of repay -
ments and cancellations totaling €7,443 million).
In summary, some observations from an analysis of Telefónica’s cash flow state -
ment include
■■Total cash and cash equivalents increased over the three-  year period, with 2009 
showing the biggest increase.

■■Cash from operating activities was large enough in each year to cover the com -
pany’s capital expenditures.Exhibit 3   (Continued)

Reading 25 ■ Understanding Cash Flow Statements 228
■■The amount paid for property, plant, and equipment and intangible assets was 
the largest investing expenditure each year and did not significantly vary from 
year to year.
■■The company had a significant amount of acquisition and divestiture activity in 
2007 and 2008 but not in 2009.
■■The company paid an increasing amount of dividends over the three-  year 
period.
An analyst can also make some comparisons between the income statement (not 
shown here) and the statement of cash flows. For example, contrast the change in 
revenues from the income statement to the change in cash received from customers. 
An increase in revenues coupled with a decrease in cash received from customers, for 
example, could signal collection problems. As shown in Exhibit 3, cash received from 
customers in 2009 decreased 2.46 percent compared with 2008, from €69,060 mil -
lion to €67,358 million. The company reported revenues on the income statement of

€56,731 million and €57,946 million for 2009 and 2008, respectively. Thus, the decrease 
in cash received from customers was slightly greater than the 2.10 percent decrease 
in total revenue and would not in itself indicate any collection issue.
2.3.3  Illustrations of Cash Flow Statements Prepared under US GAAP
Previously, we presented cash flow statements prepared under IFRS. In this section, 
we illustrate cash flow statements prepared under US GAAP . This section presents 
the cash flow statements of two companies, Tech Data Corporation and Walmart. 
Tech Data reports its operating activities using the direct method, whereas Walmart 
reports its operating activities using the more common indirect method.
Tech Data Corporation is a leading distributor of information technology prod -
ucts. Exhibit 4 presents comparative cash flow statements from the company’s annual 
report for the fiscal years ended 31 January 2008 through 2010.

Exhibit 4   Tech Data Corporation and Subsidiaries Consolidated Cash Flow Statements (in Thousands)
Y ears Ended 31 January 2010 2009 2008
Cash flows from operating activities:
  Cash received from customers $21,927,372 $23,989,567 $23,473,295
  Cash paid to vendors and employees (21,320,637) (23,636,388) (23,053,048)
  Interest paid, net (14,015) (20,382) (14,273)
  Income taxes paid (48,790) (52,987) (48,552)
Net cash provided by operating activities 543,930 279,810 357,422
Cash flows from investing activities:
  Acquisition of business, net of cash 
acquired (8,153) (78,266) (21,503)
  Proceeds from sale of business 0 0 7,161
  Proceeds from sale of property and 
equipment 5,491 0 0
  Expenditures for property and equipment (14,486) (17,272) (21,474)
  Software and software development costs (14,379) (15,275) (16,885)
Net cash used in investing activities (31,527) (110,813) (52,701)
Cash flows from financing activities:
  Proceeds from the issuance of common

Proceeds from the issuance of common 
stock and reissuance of treasury stock 37,959 1,530 12,542

Components and Format of the Cash Flow Statement 229
  Cash paid for purchase of treasury stock 0 (100,000) (100,019)
  Capital contributions and net borrowings 
from joint venture partner 23,208 10,810 9,000
  Net (repayments) borrowings on revolving 
credit loans (19,116) 42,834 (56,297)
  Principal payments on long-  term debt (5,654) (1,786) (2,371)
  Excess tax benefit from stock-  based 
compensation 963 0 212
Net cash provided by (used in) financing 
activities 37,360 (46,612) (136,933)
Effect of exchange rate changes on cash and 
cash equivalents 38,793 (41,702) 14,546
Net increase in cash and cash equivalents 588,556 80,683 182,334
Cash and cash equivalents at beginning of 
year 528,023 447,340 265,006
Cash and cash equivalents at end of year $1,116,579 $528,023 $447,340
Reconciliation of net income to net cash provided by operating activities:
Net income attributable to shareholders of 
Tech Data Corporation $180,155 $117,278 $102,129

Net income (loss) attributable to non-  
controlling interest 1,045 (1,822) (3,559)
Consolidated net income 181,200 115,456 98,570
Adjustments to reconcile net income to net 
cash provided by (used in) operating activities:
  Loss on disposal of subsidiaries 0 0 14,471
  Depreciation and amortization 45,954 51,234 53,881
  Provision for losses on accounts receivable 10,953 15,000 11,200
  Stock-  based compensation expense 11,225 11,990 10,287
  Accretion of debt discount on convertible 
senior debentures 10,278 10,278 10,278
  Deferred income taxes (2,541) 18,221 2,629
compensation (963) 0 (212)
  Changes in operating assets and liabilities:
  Accounts receivable (168,152) (86,423) 57,419
  Inventories 116,543 (261,974) 57,904
  Prepaid expenses and other assets 21,290 (18,761) (40,951)
  Accounts payable 336,587 374,696 83,845
  Accrued expenses and other liabilities (18,444) 50,093 (1,899)

Total adjustments 362,730 164,354 258,852
Net cash provided by operating activities $543,930 $279,810 $357,422Exhibit 4   (Continued)

Reading 25 ■ Understanding Cash Flow Statements 230
Tech Data Corporation prepares its cash flow statements under the direct method. 
The company’s cash increased from $265 million at the beginning of 2008 to $1.1 billion 
at the end of January 2010, with the biggest increase occurring in the most recent year. 
The 2010 increase was driven by changes across all three sections of the statement. In 
the cash flows from operating activities section of Tech Data’s cash flow statements, 
the company identifies the amount of cash it received from customers, $21.9 billion 
for 2010, and the amount of cash that it paid to suppliers and employees, $21.3 billion 
for 2010. Cash receipts decreased from $24.0 billion in the prior year, but cash paid 
decreased by even more such that cash provided by operating activities increased in 
2010 compared with 2009. Net cash provided by operating activities of $543.9 mil -
lion was adequate to cover the company’s investing activities, primarily purchases of

property and equipment ($14.5 million) and software development ($14.4 million). 
Overall, investing activities in 2010 used far less cash than in 2009, primarily because 
of reduced amounts of cash used for acquisition of businesses. In 2010, the company 
issued $38 million of common stock and received $23.2 million in contributions and 
borrowings from its joint venture partner, providing net cash from financing activities 
of $37.4 million after its debt repayments.
Whenever the direct method is used, US GAAP require a disclosure note and a 
schedule that reconciles net income with the net cash flow from operating activities. 
Tech Data shows this reconciliation at the bottom of its consolidated statements of 
cash flows. The disclosure note and reconciliation schedule are exactly the information 
that would have been presented in the body of the cash flow statement if the company 
had elected to use the indirect method rather than the direct method. For 2009, the

reconciliation highlights an increase in the company’s accounts receivable, a decrease 
in inventory, and a significant increase in payables.
In summary, some observations from an analysis of Tech Data’s cash flow state -
ment include:
■■The company’s cash increased by $852 (= 1,117 – 265 or = 589 + 81 + 182) 
million over the three years ending in January 2010, with the biggest increase 
occurring in the most recent year.
■■The company’s operating cash was adequate to cover the company’s investments 
in all three years.
■■In 2009, the company issued stock and received financing from its joint venture 
partner, which provided the company with a stronger cash cushion.
Walmart is a global retailer that conducts business under the names of Walmart 
and Sam’s Club. Exhibit 5 presents the comparative cash flow statements from the 
company’s annual report for the fiscal years ended 31 January 2010, 2009, and 2008.
Exhibit 5   Walmart Cash Flow Statements Fiscal Y ears Ended 31 January ($ millions)

Fiscal Y ear Ended 31 January 2010 2009 2008
Consolidated net income 14,848 13,899 13,137
Loss (income) from discontinued operations, net of tax 79 (146) 132
Income from continuing operations 14,927 13,753 13,269
Adjustments to reconcile income from continuing operations to net 
cash provided by operating activities:
  Depreciation and amortization 7,157 6,739 6,317
  Deferred income taxes (504) 581 (8)
  Other operating activities 301 769 504

Components and Format of the Cash Flow Statement 231
  Changes in certain assets and liabilities, net of effects of 
acquisitions:
  Increase in accounts receivable (297) (101) (564)
  Decrease (increase) in inventories 2,265 (220) (775)
  Increase (decrease) in accounts payable 1,052 (410) 865
  Increase in accrued liabilities 1,348 2,036 1,034
Net cash provided by operating activities 26,249 23,147 20,642
  Payments for property and equipment (12,184) (11,499) (14,937)
  Proceeds from disposal of property and equipment 1,002 714 957
  Proceeds from (payments for) disposal of certain international 
operations, net — 838 (257)
  Investment in international operations, net of cash acquired — (1,576) (1,338)
  Other investing activities (438) 781 (95)
Net cash used in investing activities (11,620) (10,742) (15,670)

  Increase (decrease) in short-  term borrowings, net (1,033) (3,745) 2,376
  Proceeds from issuance of long-  term debt 5,546 6,566 11,167
  Payment of long-  term debt (6,033) (5,387) (8,723)
  Dividends paid (4,217) (3,746) (3,586)
  Purchase of Company stock (7,276) (3,521) (7,691)
  Purchase of redeemable non-  controlling interest (436) — —
  Payment of capital lease obligations (346) (352) (343)
  Other financing activities (396) 267 (622)
Net cash used in financing activities (14,191) (9,918) (7,422)
Effect of exchange rates on cash and cash equivalents 194 (781) 252
Net increase (decrease) in cash and cash equivalents 632 1,706 (2,198)
Cash and cash equivalents at beginning of year17,275 5,569 7,767
Cash and cash equivalents at end of year27,907 7,275 5,569
Supplemental disclosure of cash flow information
Income tax paid 7,389 6,596 6,299
Interest paid 2,141 1,787 1,622
Capital lease obligations incurred 61 284 447

1 Includes cash and cash equivalents of discontinued operations of $51 million at 1 February 2007.
2 Includes cash and cash equivalents of discontinued operations of $77 million at 31 January 2008.
Walmart’s cash flow statement indicates the following:
■■Cash and cash equivalents changed only slightly over the three years, from 
$7.8 billion at the beginning of fiscal 2008 to $7.9 billion at the end of fiscal 
2010, but year-  to- year cash flows varied significantly.Exhibit 5   (Continued)

Reading 25 ■ Understanding Cash Flow Statements 232
■■Operating cash flow increased steadily from $20.6 billion in fiscal 2008 to 
$26.2 billion in 2010 and was significantly greater than the company’s expendi -
tures on property and equipment in every year.
■■In 2009 and 2010, the company used cash to repay borrowing, to pay dividends, 
and to repurchase its common stock.
Walmart prepares its cash flow statements under the indirect method. In the 
cash flows from operating activities section of Walmart’s cash flow statement, the 
company reconciles its net income of $14.8 billion to net cash provided by operating 
activities of $26.2 billion. Whenever the indirect method is used, US GAAP mandate 
disclosure of how much cash was paid for interest and income taxes. Note that these 
are line items in cash flow statements using the direct method, so disclosure does 
not have to be mandated. Walmart discloses the amount of cash paid for income tax

($7.4 billion), interest ($2.1 billion), and capital lease obligations ($61 million) at the 
bottom of its cash flow statements.
THE CASH FLOW STATEMENT: LINKAGES AND 
PREPARATION
The indirect format of the cash flow statement demonstrates that changes in balance 
sheet accounts are an important factor in determining cash flows. The next section 
addresses the linkages between the cash flow statement and other financial statements.
3.1 Linkages of the Cash Flow Statement with the Income 
Statement and Balance Sheet
Recall the accounting equation that summarizes the balance sheet:
Assets = Liabilities + Equity
Cash is an asset. The statement of cash flows ultimately shows the change in cash 
during an accounting period. The beginning and ending balances of cash are shown 
on the company’s balance sheets for the previous and current years, and the bottom of 
the cash flow statement reconciles beginning cash with ending cash. The relationship, 
stated in general terms, is as shown below.

Beginning Balance Sheet  
at 31 December 20X8Statement of Cash Flows  
for Y ear Ended 31 December 20X9Ending Balance Sheet  
at 31 December 20X9
Beginning cash Plus: Cash receipts (from 
operating, investing, and 
financing activities)Less: Cash payments (for 
financing activities)Ending cash
In the case of cash held in foreign currencies, there would also be an impact from 
changes in exchange rates. For example, Walmart’s cash flow statement for 2010, pre -
sented in Exhibit 5, shows cash flows from operating, investing, and financing activities 
that total $438 million during the year ($26,249 – $11,620 – $14,191). Combined with 
the $194 million net effect of exchange rates on cash and cash equivalents, the net 
increase in cash and cash equivalents was $632 million, the amount by which end-  
of- year cash and cash equivalents ($7,907) exceeds beginning-  of- year cash and cash 
equivalents ($7,275).3

The Cash Flow Statement: Linkages and Preparation 233
The body of Walmart’s cash flow statement shows why the change in cash occurred; 
in other words, it shows the company’s operating, investing, and financing activities (as 
well as the impact of foreign currency translation). The beginning and ending balance 
sheet values of cash and cash equivalents are linked through the cash flow statement.
The current assets and current liabilities sections of the balance sheet typically 
reflect a company’s operating decisions and activities. Because a company’s operating 
activities are reported on an accrual basis in the income statement, any differences 
between the accrual basis and the cash basis of accounting for an operating transaction 
result in an increase or decrease in some (usually) short-  term asset or liability on the 
balance sheet. For example, if revenue reported using accrual accounting is higher 
than the cash actually collected, the result will typically be an increase in accounts

receivable. If expenses reported using accrual accounting are lower than cash actually 
paid, the result will typically be a decrease in accounts payable or another accrued 
liability account9. As an example of how items on the balance sheet are related to the 
income statement and/or cash flow statement through the change in the beginning 
and ending balances, consider accounts receivable:
at 31 December 20X8Income Statement for Y ear 
Ended 31 December 20X9Statement of Cash 
Flows for Y ear Ended 31 
December 20X9Ending Balance Sheet  
Beginning accounts receivable Plus: Revenues Minus: Cash collected from 
customersEquals: Ending accounts 
receivable
Knowing any three of these four items makes it easy to compute the fourth. For 
example, if you know beginning accounts receivable, revenues, and cash collected 
from customers, you can easily compute ending accounts receivable. Understanding

the interrelationships between the balance sheet, income statement, and cash flow 
statement is useful in not only understanding the company’s financial health but also 
in detecting accounting irregularities. Recall the extreme illustration of a hypothetical 
company that makes sales on account without regard to future collections and thus 
reports healthy sales and significant income on its income statement yet lacks cash 
inflow. Such a pattern would occur if a company improperly recognized revenue.
A company’s investing activities typically relate to the long-  term asset section of 
the balance sheet, and its financing activities typically relate to the equity and long-  
term debt sections of the balance sheet. The next section demonstrates the preparation 
of cash flow information based on income statement and balance sheet information.
3.2 Steps in Preparing the Cash Flow Statement
The preparation of the cash flow statement uses data from both the income statement

and the comparative balance sheets.
As noted earlier, companies often only disclose indirect operating cash flow 
information, whereas analysts prefer direct-  format information. Understanding how 
cash flow information is put together will enable you to take an indirect statement 
apart and reconfigure it in a more useful manner. The result is an approximation of 
a direct cash flow statement, which—while not perfectly accurate—can be helpful to 
an analyst. The following demonstration of how an approximation of a direct cash 
flow statement is prepared uses the income statement and the comparative balance 
sheets for Acme Corporation (a fictitious retail company) shown in Exhibits 6 and 7.
9 There are other less typical explanations of the differences. For example, if revenue reported using accrual 
accounting is higher than the cash actually collected, it is possible that it is the result of a decrease in an

unearned revenue liability account. If expenses reported using accrual accounting are lower than cash actually 
paid, it is possible that it is the result of an increase in prepaid expenses, inventory, or another asset account.

Reading 25 ■ Understanding Cash Flow Statements 234
Exhibit 6   Acme Corporation Income Statement Y ear Ended 31 
December 2009
Revenue $23,598
Cost of goods sold 11,456
Gross profit 12,142
Salary and wage expense $4,123
Depreciation expense 1,052
Other operating expenses 3,577
  Total operating expenses 8,752
Operating profit 3,390
Other revenues (expenses):
  Gain on sale of equipment 205
  Interest expense (246) (41)
Income before tax 3,349
Income tax expense 1,139
Net income $2,210
Exhibit 7   Acme Corporation Comparative Balance Sheets 31 
December 2009 and 2008
2009 2008 Net Change
Cash $1,011 $1,163 $(152)
Accounts receivable 1,012 957 55
Inventory 3,984 3,277 707
Prepaid expenses 155 178 (23)
  Total current assets 6,162 5,575 587
Land 510 510 —
Buildings 3,680 3,680 —
Equipment* 8,798 8,555 243
Less: accumulated depreciation (3,443) (2,891) (552)
  Total long-  term assets 9,545 9,854 (309)
Total assets $15,707 $15,429 $278
Accounts payable $3,588 $3,325 $263
Salary and wage payable 85 75 10

Interest payable 62 74 (12)
Income tax payable 55 50 5
Other accrued liabilities 1,126 1,104 22
  Total current liabilities 4,916 4,628 288
Long-  term debt 3,075 3,575 (500)
Common stock 3,750 4,350 (600)

The Cash Flow Statement: Linkages and Preparation 235
Retained earnings 3,966 2,876 1,090
Total liabilities and equity $15,707 $15,429 $278
*During 2009, Acme purchased new equipment for a total cost of $1,300. No items impacted retained 
earnings other than net income and dividends.
The first step in preparing the cash flow statement is to determine the total cash 
flows from operating activities. The direct method of presenting cash from operating 
activities is illustrated in sections 3.2.1 through 3.2.4. Section 3.2.5 illustrates the 
indirect method of presenting cash flows from operating activities. Cash flows from 
investing activities and from financing activities are identical under either method.
3.2.1  Operating Activities: Direct Method
We first determine how much cash Acme received from its customers, followed by 
how much cash was paid to suppliers and to employees as well as how much cash was 
paid for other operating expenses, interest, and income taxes.

3.2.1.1  Cash Received from Customers  The income statement for Acme reported 
revenue of $23,598 for the year ended 31 December 2009. To determine the approximate 
cash receipts from its customers, it is necessary to adjust this revenue amount by the 
net change in accounts receivable for the year. If accounts receivable increase during 
the year, revenue on an accrual basis is higher than cash receipts from customers, 
and vice versa. For Acme Corporation, accounts receivable increased by $55, so cash 
received from customers was $23,543, as follows:
Less: Increase in accounts receivable (55)
Cash received from customers $23,543
Cash received from customers affects the accounts receivable account as follows:
Beginning accounts receivable 957
Plus revenue 23,598
Minus cash collected from customers (23,543)
Ending accounts receivable $1,012
The accounts receivable account information can also be presented as follows:
Beginning accounts receivable $957

Minus ending accounts receivable (1,012)
Cash collected from customers $23,543Exhibit 7   (Continued)

Reading 25 ■ Understanding Cash Flow Statements 236
EXAMPLE 3   
Computing Cash Received from Customers
Blue Bayou, a fictitious advertising company, reported revenues of $50 million, 
total expenses of $35 million, and net income of $15 million in the most recent 
year. If accounts receivable decreased by $12 million, how much cash did the 
company receive from customers?
A $38 million.
B $50 million.
C $62 million.
Solution: 
C is correct. Revenues of $50 million plus the decrease in accounts receivable 
of $12 million equals $62 million cash received from customers. The decrease 
in accounts receivable means that the company received more in cash than the 
amount of revenue it reported.
“Cash received from customers” is sometimes referred to as “cash collections from 
customers” or “cash collections. ”
3.2.1.2  Cash Paid to Suppliers  For Acme, the cash paid to suppliers was $11,900, 
determined as follows:
Cost of goods sold $11,456
Plus: Increase in inventory 707

Equals purchases from suppliers $12,163
Less: Increase in accounts payable (263)
Cash paid to suppliers $11,900
There are two pieces to this calculation: the amount of inventory purchased and 
the amount paid for it. To determine purchases from suppliers, cost of goods sold is 
adjusted for the change in inventory. If inventory increased during the year, then pur -
chases during the year exceeded cost of goods sold, and vice versa. Acme reported cost 
of goods sold of $11,456 for the year ended 31 December 2009. For Acme Corporation, 
inventory increased by $707, so purchases from suppliers was $12,163. Purchases from 
suppliers affect the inventory account, as shown below:
Beginning inventory $3,277
Plus purchases 12,163
Minus cost of goods sold (11,456)
Ending inventory $3,984
Acme purchased $12,163 of inventory from suppliers in 2009, but is this the amount 
of cash that Acme paid to its suppliers during the year? Not necessarily. Acme may

not have yet paid for all of these purchases and may yet owe for some of the purchases 
made this year. In other words, Acme may have paid less cash to its suppliers than 
the amount of this year’s purchases, in which case Acme’s liability (accounts payable) 
will have increased by the difference. Alternatively, Acme may have paid even more to 
its suppliers than the amount of this year’s purchases, in which case Acme’s accounts 
payable will have decreased.

The Cash Flow Statement: Linkages and Preparation 237
Therefore, once purchases have been determined, cash paid to suppliers can be 
calculated by adjusting purchases for the change in accounts payable. If the company 
made all purchases with cash, then accounts payable would not change and cash 
outflows would equal purchases. If accounts payable increased during the year, then 
purchases on an accrual basis would be higher than they would be on a cash basis, 
and vice versa. In this example, Acme made more purchases than it paid in cash, so 
the balance in accounts payable increased. For Acme, the cash paid to suppliers was 
$11,900, determined as follows:
Purchases from suppliers $12,163
The amount of cash paid to suppliers is reflected in the accounts payable account, 
as shown below:
Beginning accounts payable $3,325
Minus cash paid to suppliers (11,900)
Ending accounts payable $3,588
EXAMPLE 4

EXAMPLE 4   
Computing Cash Paid to Suppliers
Orange Beverages Plc., a fictitious manufacturer of tropical drinks, reported cost 
of goods sold for the year of $100 million. Total assets increased by $55 million, 
but inventory declined by $6 million. Total liabilities increased by $45 million, 
but accounts payable decreased by $2 million. How much cash did the company 
pay to its suppliers during the year?
A $96 million.
B $104 million.
C $108 million.
Solution: 
A is correct. Cost of goods sold of $100 million less the decrease in inventory 
of $6 million equals purchases from suppliers of $94 million. The decrease in 
accounts payable of $2 million means that the company paid $96 million in cash 
($94 million plus $2 million).
3.2.1.3  Cash Paid to Employees  To determine the cash paid to employees, it is 
necessary to adjust salary and wages expense by the net change in salary and wages

payable for the year. If salary and wages payable increased during the year, then salary 
and wages expense on an accrual basis would be higher than the amount of cash paid 
for this expense, and vice versa. For Acme, salary and wages payable increased by $10, 
so cash paid for salary and wages was $4,113, as follows:
Salary and wages expense $4,123
Less: Increase in salary and wages payable (10)
Cash paid to employees $4,113

Reading 25 ■ Understanding Cash Flow Statements 238
The amount of cash paid to employees is reflected in the salary and wages payable 
account, as shown below:
Beginning salary and wages payable $75
Plus salary and wages expense 4,123
Minus cash paid to employees (4,113)
Ending salary and wages payable $85
3.2.1.4  Cash Paid for Other Operating Expenses  To determine the cash paid for other 
operating expenses, it is necessary to adjust the other operating expenses amount on the 
income statement by the net changes in prepaid expenses and accrued expense liabilities 
for the year. If prepaid expenses increased during the year, other operating expenses 
on a cash basis would be higher than on an accrual basis, and vice versa. Likewise, if 
accrued expense liabilities increased during the year, other operating expenses on a cash 
basis would be lower than on an accrual basis, and vice versa. For Acme Corporation, 
the amount of cash paid for operating expenses in 2009 was $3,532, as follows:

Other operating expenses $3,577
Less: Decrease in prepaid expenses (23)
Less: Increase in other accrued liabilities (22)
Cash paid for other operating expenses $3,532
EXAMPLE 5   
Computing Cash Paid for Other Operating Expenses
Black Ice, a fictitious sportswear manufacturer, reported other operating expenses 
of $30 million. Prepaid insurance expense increased by $4 million, and accrued 
utilities payable decreased by $7 million. Insurance and utilities are the only two 
components of other operating expenses. How much cash did the company pay 
in other operating expenses?
A $19 million.
B $33 million.
C $41 million.
Solution: 
C is correct. Other operating expenses of $30 million plus the increase in prepaid 
insurance expense of $4 million plus the decrease in accrued utilities payable of 
$7 million equals $41 million.
3.2.1.5  Cash Paid for Interest  The cash paid for interest is included in operating cash 
flows under US GAAP and may be included in operating or financing cash flows under

IFRS. To determine the cash paid for interest, it is necessary to adjust interest expense 
by the net change in interest payable for the year. If interest payable increases during 
the year, then interest expense on an accrual basis will be higher than the amount of 
cash paid for interest, and vice versa. For Acme Corporation, interest payable decreased 
by $12, and cash paid for interest was $258, as follows:
Interest expense $246
Plus: Decrease in interest payable 12
Cash paid for interest $258

The Cash Flow Statement: Linkages and Preparation 239
Alternatively, cash paid for interest may also be determined by an analysis of the 
interest payable account, as shown below:
Beginning interest payable $74
Plus interest expense 246
Minus cash paid for interest (258)
Ending interest payable $62
3.2.1.6  Cash Paid for Income Taxes  To determine the cash paid for income taxes, it 
is necessary to adjust the income tax expense amount on the income statement by the 
net changes in taxes receivable, taxes payable, and deferred income taxes for the year. 
If taxes receivable or deferred tax assets increase during the year, income taxes on a 
cash basis will be higher than on an accrual basis, and vice versa. Likewise, if taxes 
payable or deferred tax liabilities increase during the year, income tax expense on a cash 
basis will be lower than on an accrual basis, and vice versa. For Acme Corporation, the 
amount of cash paid for income taxes in 2009 was $1,134, as follows:
Income tax expense $1,139

Less: Increase in income tax payable (5)
Cash paid for income taxes $1,134
3.2.2  Investing Activities
The second and third steps in preparing the cash flow statement are to determine the 
total cash flows from investing activities and from financing activities. The presentation 
of this information is identical, regardless of whether the direct or indirect method 
is used for operating cash flows.
Purchases and sales of equipment were the only investing activities undertaken 
by Acme in 2009, as evidenced by the fact that the amounts reported for land and 
buildings were unchanged during the year. An informational note in Exhibit 7 tells us 
that Acme purchased  new equipment in 2009 for a total cost of $1,300. However, the 
amount of equipment shown on Acme’s balance sheet increased by only $243 (ending 
balance of $8,798 minus beginning balance of $8,555); therefore, Acme must have 
also sold or otherwise disposed of  some equipment during the year. To determine the

cash inflow from the sale of equipment, we analyze the equipment and accumulated 
depreciation accounts as well as the gain on the sale of equipment from Exhibits 6 
and 7. Assuming that the entire accumulated depreciation is related to equipment, 
the cash received from sale of equipment is determined as follows.
The historical cost of the equipment sold was $1,057. This amount is determined 
Beginning balance equipment (from balance sheet) $8,555
Plus equipment purchased (from informational note) 1,300
Minus ending balance equipment (from balance sheet) (8,798)
Equals historical cost of equipment sold $1,057
The accumulated depreciation on the equipment sold was $500, determined as follows:
Beginning balance accumulated depreciation (from balance sheet) $2,891
Plus depreciation expense (from income statement) 1,052
Minus ending balance accumulated depreciation (from balance sheet) (3,443)
Equals accumulated depreciation on equipment sold $500

The historical cost information, accumulated depreciation information, and infor -
mation from the income statement about the gain on the sale of equipment can be 
used to determine the cash received from the sale.

Reading 25 ■ Understanding Cash Flow Statements 240
Historical cost of equipment sold (calculated above) $1,057
Less accumulated depreciation on equipment sold (calculated above) (500)
Equals book value of equipment sold $557
Plus gain on sale of equipment (from the income statement) 205
Equals cash received from sale of equipment $762
EXAMPLE 6   
Computing Cash Received from the Sale of Equipment
Copper, Inc., a fictitious brewery and restaurant chain, reported a gain on the sale 
of equipment of $12 million. In addition, the company’s income statement shows 
depreciation expense of $8 million and the cash flow statement shows capital 
expenditure of $15 million, all of which was for the purchase of new equipment.
Balance sheet item 12/31/2009 12/31/2010 Change
Equipment $100 million $109 million $9 million
Accumulated 
depreciation—equipment$30 million $36 million $6 million
Using the above information from the comparative balance sheets, how much

cash did the company receive from the equipment sale?
A $12 million.
B $16 million.
C $18 million.
Solution: 
B is correct. Selling price (cash inflow) minus book value equals gain or loss on 
sale; therefore, gain or loss on sale plus book value equals selling price (cash 
inflow). The amount of gain is given, $12 million. To calculate the book value 
of the equipment sold, find the historical cost of the equipment and the accu -
mulated depreciation on the equipment.
■■Beginning balance of equipment of $100 million plus equipment pur -
chased of $15 million minus ending balance of equipment of $109 million 
equals historical cost of equipment sold, or $6 million.
■■Beginning accumulated depreciation on equipment of $30 million plus 
depreciation expense for the year of $8 million minus ending balance of 
accumulated depreciation of $36 million equals accumulated depreciation 
on the equipment sold, or $2 million.
■■Therefore, the book value of the equipment sold was $6 million minus

$2 million, or $4 million.
■■Because the gain on the sale of equipment was $12 million, the amount of 
cash received must have been $16 million.
3.2.3  Financing Activities
As with investing activities, the presentation of financing activities is identical, 
regardless of whether the direct or indirect method is used for operating cash flows.

The Cash Flow Statement: Linkages and Preparation 241
3.2.3.1  Long-  Term Debt and Common Stock  The change in long-  term debt, based 
on the beginning 2009 (ending 2008) and ending 2009 balances in Exhibit 7, was a 
decrease of $500. Absent other information, this indicates that Acme retired $500 of 
long-  term debt. Retiring long-  term debt is a cash outflow relating to financing activities.
Similarly, the change in common stock during 2009 was a decrease of $600. Absent 
other information, this indicates that Acme repurchased $600 of its common stock. 
Repurchase of common stock is also a cash outflow related to financing activity.
3.2.3.2  Dividends  Recall the following relationship:
Beginning retained earnings + Net income – Dividends = Ending retained 
earnings
Based on this relationship, the amount of cash dividends paid in 2009 can be deter -
mined from an analysis of retained earnings, as follows:
Beginning balance of retained earnings (from the balance sheet) $2,876

Plus net income (from the income statement) 2,210
Minus ending balance of retained earnings (from the balance sheet) (3,966)
Equals dividends paid $1,120
Note that dividends paid are presented in the statement of changes in equity.
3.2.4  Overall Statement of Cash Flows: Direct Method
Exhibit 8 summarizes the information about Acme’s operating, investing, and financing 
cash flows in the statement of cash flows. At the bottom of the statement, the total 
net change in cash is shown to be a decrease of $152 (from $1,163 to $1,011). This 
decrease can also be seen on the comparative balance sheet in Exhibit 7. The cash 
provided by operating activities of $2,606 was adequate to cover the net cash used in 
investing activities of $538; however, the company’s debt repayments, cash payments 
for dividends, and repurchase of common stock (i.e., its financing activities) of $2,220 
resulted in an overall decrease in cash of $152.
Exhibit 8   Acme Corporation Cash Flow Statement (Direct Method) for Y ear

Ended 31 December 2009
Cash flow from operating activities:
  Cash received from customers $23,543
  Cash paid to suppliers (11,900)
  Cash paid to employees (4,113)
  Cash paid for other operating expenses (3,532)
  Cash paid for interest (258)
  Cash paid for income tax (1,134)
Net cash provided by operating activities 2,606
Cash flow from investing activities:
  Cash received from sale of equipment 762
  Cash paid for purchase of equipment (1,300)
Net cash used for investing activities (538)
Cash flow from financing activities:
  Cash paid to retire long-  term debt (500)

Reading 25 ■ Understanding Cash Flow Statements 242
  Cash paid to retire common stock (600)
  Cash paid for dividends (1,120)
Net cash used for financing activities (2,220)
Net increase (decrease) in cash (152)
Cash balance, 31 December 2008 1,163
Cash balance, 31 December 2009 $1,011
3.2.5  Overall Statement of Cash Flows: Indirect Method
Using the alternative approach to reporting cash from operating activities, the indirect 
method, we will present the same amount of cash provided by operating activities. 
Under this approach, we reconcile Acme’s net income of $2,210 to its operating cash 
flow of $2,606.
To perform this reconciliation, net income is adjusted for the following: a) any 
non-  operating activities, b) any non-  cash expenses, and c) changes in operating 
working capital items.
The only non-  operating activity in Acme’s income statement, the sale of equip -
ment, resulted in a gain of $205. This amount is removed from the operating cash flow

section; the cash effects of the sale are shown in the investing section.
Acme’s only non-  cash expense was depreciation expense of $1,052. Under the 
indirect method, depreciation expense must be added back to net income because it 
was a non-  cash deduction in the calculation of net income.
Changes in working capital accounts include increases and decreases in the cur -
rent operating asset and liability accounts. The changes in these accounts arise from 
applying accrual accounting; that is, recognizing revenues when they are earned and 
expenses when they are incurred instead of when the cash is received or paid. To 
make the working capital adjustments under the indirect method, any increase in 
a current operating asset account is subtracted from net income and a net decrease 
is added to net income. As described above, the increase in accounts receivable, for 
example, resulted from Acme recording income statement revenue higher than the

amount of cash received from customers; therefore, to reconcile back to operating 
cash flow, that increase in accounts receivable must be deducted from net income. For 
current operating liabilities, a net increase is added to net income and a net decrease 
is subtracted from net income. As described above, the increase in wages payable, 
for example, resulted from Acme recording income statement expenses higher than 
the amount of cash paid to employees.
Exhibit 9 presents a tabulation of the most common types of adjustments that 
are made to net income when using the indirect method to determine net cash flow 
from operating activities.Exhibit 8   (Continued)

The Cash Flow Statement: Linkages and Preparation 243
Exhibit 9   Adjustments to Net Income Using the Indirect Method
Additions ■■Non-  cash items
■●Depreciation expense of tangible assets
■●Amortisation expense of intangible assets
■●Depletion expense of natural resources
■●Amortisation of bond discount
■■Non-  operating losses
■●Loss on sale or write-  down of assets
■●Loss on retirement of debt
■●Loss on investments accounted for under the equity method
■■Increase in deferred income tax liability
■■Changes in working capital resulting from accruing higher 
amounts for expenses than the amounts of cash payments or lower 
amounts for revenues than the amounts of cash receipts 
■●Decrease in current operating assets (e.g., accounts receivable, 
inventory, and prepaid expenses)
■●Increase in current operating liabilities (e.g., accounts payable 
and accrued expense liabilities)
Subtractions ■■Non-  cash items (e.g., amortisation of bond premium)
■■Non-  operating items 
■●Gain on sale of assets

■●Gain on retirement of debt
■●Income on investments accounted for under the equity method
■■Decrease in deferred income tax liability
■■Changes in working capital resulting from accruing lower amounts 
for expenses than for cash payments or higher amounts for reve -
nues than for cash receipts 
■●Increase in current operating assets (e.g., accounts receivable, 
■●Decrease in current operating liabilities (e.g., accounts payable 
Accordingly, for Acme Corporation, the $55 increase in accounts receivable and 
the $707 increase in inventory are subtracted from net income and the $23 decrease in 
prepaid expenses is added to net income. For Acme’s current liabilities, the increases 
in accounts payable, salary and wage payable, income tax payable, and other accrued 
liabilities ($263, $10, $5, and $22, respectively) are added to net income and the $12

decrease in interest payable is subtracted from net income. Exhibit 10 presents the 
cash flow statement for Acme Corporation under the indirect method by using the 
information that we have determined from our analysis of the income statement and 
the comparative balance sheets. Note that the investing and financing sections are 
identical to the statement of cash flows prepared using the direct method.
Exhibit 10   Acme Corporation Cash Flow Statement (Indirect Method) Y ear 
  Net income $2,210

Reading 25 ■ Understanding Cash Flow Statements 244
  Depreciation expense 1,052
  Gain on sale of equipment (205)
  Increase in accounts receivable (55)
  Increase in inventory (707)
  Decrease in prepaid expenses 23
  Increase in accounts payable 263
  Increase in salary and wage payable 10
  Decrease in interest payable (12)
  Increase in income tax payable 5
  Increase in other accrued liabilities 22
Net decrease in cash (152)
EXAMPLE 7   
Adjusting Net Income to Compute Operating Cash Flow

Based on the following information for Pinkerly Inc., a fictitious company, what 
are the total adjustments that the company would make to net income in order 
to derive operating cash flow?
Year Ended
Income statement item 12/31/2009
Net income $30 million
Depreciation $7 million
Balance sheet item 12/31/2008 12/31/2009 Change
Accounts receivable $15 million $30 million $15 million
Inventory $16 million $13 million ($3 million)
Accounts payable $10 million $20 million $10 million
A Add $5 million.Exhibit 10   (Continued)

The Cash Flow Statement: Linkages and Preparation 245
B Add $21 million.
C Subtract $9 million.
Solution: 
A is correct. To derive operating cash flow, the company would make the following 
adjustments to net income: add depreciation (a non-  cash expense) of $7 million; 
add the decrease in inventory of $3 million; add the increase in accounts payable 
of $10 million; and subtract the increase in accounts receivable of $15 million. 
Total additions of $20 million and total subtractions of $15 million result in net 
total additions of $5 million.
3.3 Conversion of Cash Flows from the Indirect to the Direct 
Method
An analyst may desire to review direct-  format operating cash flow to review trends 
in cash receipts and payments (such as cash received from customers or cash paid 
to suppliers). If a direct-  format statement is not available, cash flows from operating 
activities reported under the indirect method can be converted to the direct method.

Accuracy of conversion depends on adjustments using data available in published 
financial reports. The method described here is sufficiently accurate for most ana -
lytical purposes.
The three-  step conversion process is demonstrated for Acme Corporation in 
Exhibit 11. Referring again to Exhibits 6 and 7 for Acme Corporation’s income state -
ment and balance sheet information, begin by disaggregating net income of $2,210 
into total revenues and total expenses (Step 1). Next, remove any non-  operating and 
non-  cash items (Step 2). For Acme, we therefore remove the non-  operating gain on 
the sale of equipment of $205 and the non-  cash depreciation expense of $1,052. Then, 
convert accrual amounts of revenues and expenses to cash flow amounts of receipts 
and payments by adjusting for changes in working capital accounts (Step 3). The results 
of these adjustments are the items of information for the direct format of operating

cash flows. These line items are shown as the results of Step 3.
Exhibit 11   Conversion from the Indirect to the Direct Method
Step 1 Total revenues $23,803
Aggregate all revenue and all expenses Total expenses 21,593
Step 2 Total revenue less noncash item revenues:
Remove all noncash items from aggre -
gated revenues and expenses and break 
out remaining items into relevant cash 
flow items($23,803 – $205) = $23,598
Total expenses less noncash item expenses:
($21,593 – $1,052) = $20,541
Salary and wage expenses 4,123
Interest expense 246
Total $20,541

Reading 25 ■ Understanding Cash Flow Statements 246
Step 3 Cash received from customersa$23,543
Convert accrual amounts to cash flow 
amounts by adjusting for working 
capital changesCash paid to suppliersb(11,900)
Cash paid to employeesc(4,113)
Cash paid for other operating expensesd(3,532)
Cash paid for intereste(258)
Cash paid for income taxf(1,134)
Net cash provided by operating activities $2,606
Calculations for Step 3:
a Revenue of $23,598 less increase in accounts receivable of $55.
b Cost of goods sold of $11,456 plus increase in inventory of $707 less increase in accounts payable of $263.
c Salary and wage expense of $4,123 less increase in salary and wage payable of $10.
d Other operating expenses of $3,577 less decrease in prepaid expenses of $23 less increase in other accrued liabilities of $22.
e Interest expense of $246 plus decrease in interest payable of $12.
f Income tax expense of $1,139 less increase in income tax payable of $5.
CASH FLOW STATEMENT ANALYSIS

The analysis of a company’s cash flows can provide useful information for under -
standing a company’s business and earnings and for predicting its future cash flows. 
This section describes tools and techniques for analyzing the statement of cash flows, 
including the analysis of sources and uses of cash and cash flow, common-  size analysis, 
and calculation of free cash flow measures and cash flow ratios.
4.1 Evaluation of the Sources and Uses of Cash
Evaluation of the cash flow statement should involve an overall assessment of the 
sources and uses of cash between the three main categories as well as an assessment 
of the main drivers of cash flow within each category, as follows:
1 Evaluate where the major sources and uses of cash flow are between operating, 
investing, and financing activities.
2 Evaluate the primary determinants of operating cash flow.
3 Evaluate the primary determinants of investing cash flow.

4 Evaluate the primary determinants of financing cash flow.
Step 1  The major sources of cash for a company can vary with its stage of growth. 
For a mature company, it is expected and desirable that operating activities are the 
primary source of cash flows. Over the long term, a company must generate cash from 
its operating activities. If operating cash flow were consistently negative, a company 
would need to borrow money or issue stock (financing activities) to fund the shortfall. 
Eventually, these providers of capital need to be repaid from operations or they will no 
longer be willing to provide capital. Cash generated from operating activities can be 
used in either investing or financing activities. If the company has good opportunities 
to grow the business or other investment opportunities, it is desirable to use the cash 
in investing activities. If the company does not have profitable investment opportuni -

ties, the cash should be returned to capital providers, a financing activity. For a new or 4Exhibit 11   (Continued)

Cash Flow Statement Analysis 247
growth stage company, operating cash flow may be negative for some period of time as 
it invests in such assets as inventory and receivables (extending credit to new custom -
ers) in order to grow the business. This situation is not sustainable over the long term, 
so eventually the cash must start to come primarily from operating activities so that 
capital can be returned to the providers of capital. Lastly, it is desirable that operating 
cash flows are sufficient to cover capital expenditures (in other words, the company 
has free cash flow as discussed further in Section 4.3). In summary, major points to 
consider at this step are:
■■What are the major sources and uses of cash flow?
■■Is operating cash flow positive and sufficient to cover capital expenditures?
Step 2  Turning to the operating section, the analysts should examine the most signif -
icant determinants of operating cash flow. Companies need cash for use in operations

(for example, to hold receivables and inventory and to pay employees and suppliers) and 
receive cash from operating activities (for example, payments from customers). Under 
the indirect method, the increases and decreases in receivables, inventory, payables, 
and so on can be examined to determine whether the company is using or generat -
ing cash in operations and why. It is also useful to compare operating cash flow with 
net income. For a mature company, because net income includes non-  cash expenses 
(depreciation and amortisation), it is expected and desirable that operating cash flow 
exceeds net income. The relationship between net income and operating cash flow is 
also an indicator of earnings quality. If a company has large net income but poor oper -
ating cash flow, it may be a sign of poor earnings quality. The company may be making 
aggressive accounting choices to increase net income but not be generating cash for

its business. You should also examine the variability of both earnings and cash flow 
and consider the impact of this variability on the company’s risk as well as the ability 
to forecast future cash flows for valuation purposes. In summary:
■■What are the major determinants of operating cash flow?
■■Is operating cash flow higher or lower than net income? Why?
■■How consistent are operating cash flows?
Step 3  Within the investing section, you should evaluate each line item. Each line 
item represents either a source or use of cash. This enables you to understand where 
the cash is being spent (or received). This section will tell you how much cash is being 
invested for the future in property, plant, and equipment; how much is used to acquire 
entire companies; and how much is put aside in liquid investments, such as stocks and 
bonds. It will also tell you how much cash is being raised by selling these types of assets.

If the company is making major capital investments, you should consider where the 
cash is coming from to cover these investments (e.g., is the cash coming from excess 
operating cash flow or from the financing activities described in Step 4). If assets are 
being sold, it is important to determine why and to assess the effects on the company.
Step 4  Within the financing section, you should examine each line item to under -
stand whether the company is raising capital or repaying capital and what the nature 
of its capital sources are. If the company is borrowing each year, you should consider 
when repayment may be required. This section will also present dividend payments 
and repurchases of stock that are alternative means of returning capital to owners. It 
is important to assess why capital is being raised or repaid.
We now provide an example of a cash flow statement evaluation.

Reading 25 ■ Understanding Cash Flow Statements 248
EXAMPLE 8   
Analysis of the Cash Flow Statement
Derek Yee, CFA, is preparing to forecast cash flow for Groupe Danone as an 
input into his valuation model. He has asked you to evaluate the historical cash 
flow statement of Groupe Danone, which is presented in Exhibit 12. Groupe 
Danone prepares its financial statements in conformity with IFRS. Note that 
Groupe Danone presents the most recent period on the right.
Exhibit 12   Groupe Danone Consolidated Financial Statements Consolidated Statements of Cash 
Flows (in € Millions)
Y ears Ended 31 December 2008 2009
Net income attributable to the Group 1,313 1,361
  Net income attributable to minority interests 178 160
  Net income from discontinued operations (269) —
  Share of profits of associates (62) 77
  Depreciation and amortization 525 549
  Dividends received from associates 29 174
  Other flows with impact on cash (113) (157)
  Other flows with no impact on cash 98 (72)

Other flows with no impact on cash 98 (72)
Cash flows provided by operating activities, excluding changes in net working 
capital 1,699 2,092
  (Increase) decrease in inventories 3 37
  (Increase) decrease in trade accounts receivable (74) (112)
  Increase (decrease) in trade accounts payable 36 (127)
  Changes in other accounts receivable and payable 90 110
  Change in other working capital requirements 55 (92)
Cash flows provided by (used in) operating activities 1,754 2,000
  Capital expenditure (706) (699)
  Purchase of businesses and other investments, net of cash and cash equivalents 
acquired (259) (147)
  Proceeds from the sale of businesses and other investments, including indebtedness 
of companies sold 329 1,024
  (Increase) decrease in long-  term loans and other long-  term assets 67 36
Cash flows provided by (used in) investing activities (569) 214
  Increase in capital and additional paid-  in capital 48 2,977
  Purchases of treasury stock (net of disposals) 46 100

Dividends paid to Danone shareholders and to minority interests (705) (451)
  Settlement of debt hedge financial instruments (mainly equalization payments) (154)
  Increase (decrease) in non-  current financial liabilities 1,338 (4,154)
  Increase (decrease) in current financial liabilities (1,901) (427)
  Increase (decrease) in marketable securities 63 (60)
Cash flows provided by (used in) financing activities (1,111) (2,169)
Effect of exchange rate changes (31) 8
Increase (decrease) in cash and cash equivalents 43 53
Cash and cash equivalents at beginning of period 548 591

Cash Flow Statement Analysis 249
Cash and cash equivalents at end of period 591 644
Supplemental disclosures
Payments during the year of:
• net interest 433 272
• income tax 430 413
Yee would like answers to the following questions:
■■What are the major sources of cash for Groupe Danone?
■■What are the major uses of cash for Groupe Danone?
■■What is the relationship between net income and cash flow from operat -
ing activities?
■■Is cash flow from operating activities sufficient to cover capital 
expenditures?
■■Other than capital expenditures, is cash being used or generated in invest -
■■What types of financing cash flows does Groupe Danone have?
Solution: 
The major categories of cash flows can be summarized as follows (in € millions):
2008 2009
Cash flows provided by operating activities 1,754 2,000
Cash flows provided by (used in) investing 
activities(569) 214
Cash flows provided by (used in) financing 
activities(1,111) (2,169)

Exchange rate effects on cash (31) 8
Increase in cash 43 53
The primary source of cash for Groupe Danone is operating activities. In 2009, 
investing activities provided cash as the result of the sale of businesses and other 
investments. Cash flow is being used in financing activities, primarily to repay 
financial liabilities and to pay dividends. The fact that the primary source of cash 
is from operations is positive and desirable for a mature company. Additionally, 
the fact that operating cash flow exceeds net income in both years is a positive 
sign. Finally, operating cash flows exceed capital expenditures, indicating that 
the company can fund capital expenditures from operations.
4.2 Common-  Size Analysis of the Statement of Cash Flows
In common-  size analysis of a company’s income statement, each income and expense 
line item is expressed as a percentage of net revenues (net sales). For the common-  size

balance sheet, each asset, liability, and equity line item is expressed as a percentage 
of total assets. For the common-  size cash flow statement, there are two alternative Exhibit 12   (Continued)

Reading 25 ■ Understanding Cash Flow Statements 250
approaches. The first approach is to express each line item of cash inflow (outflow) as 
a percentage of total inflows (outflows) of cash, and the second approach is to express 
each line item as a percentage of net revenue.
Exhibit  13 demonstrates the total cash inflows/total cash outflows method for 
Acme Corporation. Under this approach, each of the cash inflows is expressed as a 
percentage of the total cash inflows, whereas each of the cash outflows is expressed as 
a percentage of the total cash outflows. In Panel A, Acme’s common-  size statement is 
based on a cash flow statement using the direct method of presenting operating cash 
flows. Operating cash inflows and outflows are separately presented on the cash flow 
statement, and therefore, the common-  size cash flow statement shows each of these 
operating inflows (outflows) as a percentage of total inflows (outflows). In Panel B,

Acme’s common-  size statement is based on a cash flow statement using the indirect 
method of presenting operating cash flows. When a cash flow statement has been 
presented using the indirect method, operating cash inflows and outflows are not 
separately presented; therefore, the common-  size cash flow statement shows only 
the net operating cash flow (net cash provided by or used in operating activities) as a 
percentage of total inflows or outflows, depending on whether the net amount was a 
cash inflow or outflow. Because Acme’s net operating cash flow is positive, it is shown 
as a percentage of total inflows.
Exhibit 13   Acme Corporation Common-  Size Cash Flow Statement Y ear 
Panel A. Direct Format for Cash Flow
InflowsPercentage of 
Total Inflows
Receipts from customers $23,543 96.86%
Sale of equipment 762 3.14
   Total $24,305 100.00%
OutflowsPercentage of 
Total Outflows
Payments to suppliers $11,900 48.66%
Payments to employees 4,113 16.82

Payments for other operating expenses 3,532 14.44
Payments for interest 258 1.05
Payments for income tax 1,134 4.64
Purchase of equipment 1,300 5.32
Retirement of long-  term debt 500 2.04
Retirement of common stock 600 2.45
Dividend payments 1,120 4.58
  Total $24,457 100.00%
  Net increase (decrease) in cash ($152)

Cash Flow Statement Analysis 251
Panel B. Indirect Format for Cash Flow
Net cash provided by operating activities $2,606 77.38%
Sale of equipment 762 22.62
  Total $3,368 100.00%
Purchase of equipment $1,300 36.93%
Retirement of long-  term debt 500 14.20
Retirement of common stock 600 17.05
Dividend payments 1,120 31.82
  Total $3,520 100.00%
Exhibit 14 demonstrates the net revenue common-  size cash flow statement for 
Acme Corporation. Under the net revenue approach, each line item in the cash flow 
statement is shown as a percentage of net revenue. The common-  size statement in 
this exhibit has been developed based on Acme’s cash flow statement using the indi -
rect method for operating cash flows and using net revenue of $23,598 as shown in 
Exhibit 6. Each line item of the reconciliation between net income and net operating

cash flows is expressed as a percentage of net revenue. The common-  size format makes 
it easier to see trends in cash flow rather than just looking at the total amount. This 
method is also useful to the analyst in forecasting future cash flows because individual 
items in the common-  size statement (e.g., depreciation, fixed capital expenditures, 
debt borrowing, and repayment) are expressed as a percentage of net revenue. Thus, 
once the analyst has forecast revenue, the common-  size statement provides a basis 
for forecasting cash flows for those items with an expected relation to net revenue.
Exhibit 14   Acme Corporation Common-  Size Cash Flow Statement: Indirect 
Format Y ear Ended 31 December 2009
Percentage of 
Net Revenue
  Net income $2,210 9.37%
  Depreciation expense 1,052 4.46
  Gain on sale of equipment (205) (0.87)
  Increase in accounts receivable (55) (0.23)
  Increase in inventory (707) (3.00)
  Decrease in prepaid expenses 23 0.10

Decrease in prepaid expenses 23 0.10
  Increase in accounts payable 263 1.11
(continued)Exhibit 13   (Continued)

Reading 25 ■ Understanding Cash Flow Statements 252
  Increase in salary and wage payable 10 0.04
  Decrease in interest payable (12) (0.05)
  Increase in income tax payable 5 0.02
  Increase in other accrued liabilities 22 0.09
Net cash provided by operating activities $2,606 11.04%
  Cash received from sale of equipment $762 3.23%
  Cash paid for purchase of equipment (1,300) (5.51)
Net cash used for investing activities $(538) (2.28)%
  Cash paid to retire long-  term debt $(500) (2.12)%
  Cash paid to retire common stock (600) (2.54)
  Cash paid for dividends (1,120) (4.75)
Net cash used for financing activities $(2,220) (9.41)%
Net decrease in cash $(152) (0.64)%
EXAMPLE 9   
Analysis of a Common-  Size Cash Flow Statement
Andrew Potter is examining an abbreviated common-  size cash flow statement 
for Dell Inc., a provider of technological products and services. The common-

size cash flow statement was prepared by dividing each line item by total net 
revenue for the same year. The terminology is that used by Dell. “Change in cash 
from” is used instead of “cash provided by (used in). ”
29 Jan 10 30 Jan 09 1 Feb 08
Net income 2.71% 4.06% 4.82%
Adjustments to reconcile net income to net cash pro -
vided by operating activities:
  Depreciation and amortization 1.61 1.26 0.99
  Stock-  based compensation 0.59 0.68 0.54
  In- process research and development charges 0.00 0.00 0.14
  Effects of exchange rate changes on monetary assets 
and liabilities denominated in foreign currencies 0.11 (0.19) 0.05
  Deferred income taxes (0.10) 0.14 (0.50)Exhibit 14   (Continued)

Cash Flow Statement Analysis 253
  Provision for doubtful accounts—including financ -
ing receivables 0.81 0.51 0.31
  Other 0.19 0.05 0.05
  Changes in operating assets and liabilities, net of 
effects from acquisitions:
  Accounts receivable (1.25) 0.79 (1.78)
  Financing receivables (2.05) (0.49) (0.64)
  Inventories (0.35) 0.51 (0.81)
  Other assets (0.43) (0.17) (0.20)
  Accounts payable 5.36 (5.10) 1.37
  Deferred services revenue 0.26 1.09 1.69
  Accrued and other liabilities (0.08) (0.02) 0.45
Change in cash from operating activities 7.38 3.10 6.46
  Investments: Purchases (2.61) (2.59) (3.92)
  Investments: Maturities and sales 2.91 3.82 6.02
  Capital expenditures (0.69) (0.72) (1.36)
  Proceeds from sale of facility and land 0.03 0.07 0.00
  Acquisition of business, net of cash received (6.83) (0.29) (3.63)
Change in cash from investing activities (7.20) 0.29 (2.88)

  Repurchase of common stock 0.00 (4.69) (6.55)
  Issuance of common stock under employee plans 0.00 0.13 0.22
  Issuance of commercial paper (maturity 90 days or 
less), net 0.14 0.16 (0.16)
  Proceeds from debt 3.89 2.49 0.11
  Repayments of debt (0.23) (0.39) (0.27)
  Other 0.00 0.00 (0.09)
Change in cash from financing activities 3.80 (2.30) (6.74)
  Effect of exchange rate changes on cash and cash 
equivalents 0.33 –0.13 0.25
Change in cash and cash equivalents 4.32% 0.96% –2.91%
Based on the information in the above exhibit:
1 Discuss the significance of
A depreciation and amortization.
B capital expenditures.
2 Compare Dell’s operating cash flow as a percentage of revenue with Dell’s 
net profit margin.
3 Discuss Dell’s use of its positive operating cash flow.
A Dell’s depreciation and amortization expense is less than 2 percent of total 
net revenue in the year ended 29 January 2010. However, as a percentage

of total revenue, it has been increasing each year. In the year ended 29 
January 2010, adding this expense back to determine operating cash flow

Reading 25 ■ Understanding Cash Flow Statements 254
has a significant impact on cash flow from operations as a percentage of 
total revenue because its size was approximately 60 percent of net profit 
margin (net income/total net revenue).
B Dell’s level of capital expenditures is relatively small, less than 1 percent of 
revenues in the most recent years. Cash flow from operations as a per -
centage of total revenue indicates that operating cash flows are more than 
sufficient to cover these expenditures.
Dell’s operating cash flow as a percentage of revenue is usually much higher 
than net profit margin, with the exception of the year ended 30 January 2009. 
In that year, the net profit margin was 4.06 percent and operating cash flow as 
a percentage of total revenue was 3.10 percent. The primary difference between 
that year and the other years appears to have been a significant reduction in 
accounts payable; in each of the other years, accounts payable increased. For

the year ended 29 January 2010, operating cash flow as a percentage of total 
revenue was 7.38 percent and net profit margin was 2.71 percent.
In the year ended 29 January 2010, the largest cash outflow was for an acquisition 
of business (investing activities). In prior years, much of Dell’s operating cash 
flow was used to repurchase its own stock (financing activities). In each of the 
three years, Dell’s purchases of investments (investing activities) were less than 
the amounts of maturities and sales; thus, on a net basis, investments provided 
a net source of cash.
4.3 Free Cash Flow to the Firm and Free Cash Flow to Equity
It was mentioned earlier that it is desirable that operating cash flows are sufficient to 
cover capital expenditures. The excess of operating cash flow over capital expenditures 
is known generically as free cash flow . For purposes of valuing a company or its equity 
securities, an analyst may want to determine and use other cash flow measures, such

as free cash flow to the firm (FCFF) or free cash flow to equity (FCFE).
FCFF is the cash flow available to the company’s suppliers of debt and equity capital 
after all operating expenses (including income taxes) have been paid and necessary 
investments in working capital and fixed capital have been made. FCFF can be com -
puted starting with net income as
FCFF = NI + NCC + Int(1 – Tax rate) – FCInv – WCInv
where
 NI = Net income
 NCC = Non-  cash charges (such as depreciation and amortisation)
 Int = Interest expense
 FCInv = Capital expenditures (fixed capital, such as equipment)
 WCInv = Working capital expenditures
The reason for adding back interest is that FCFF is the cash flow available to the 
suppliers of debt capital as well as equity capital. Conveniently, FCFF can also be 
computed from cash flow from operating activities as
FCFF = CFO + Int(1 – Tax rate) – FCInv

Cash Flow Statement Analysis 255
CFO represents cash flow from operating activities under US GAAP or under 
IFRS where the company has included interest paid in operating activities. If interest 
paid was included in financing activities, then CFO does not have to be adjusted 
for Int(1 – Tax rate). Under IFRS, if the company has placed interest and dividends 
received in investing activities, these should be added back to CFO to determine FCFF. 
Additionally, if dividends paid were subtracted in the operating section, these should 
be added back in to compute FCFF.
The computation of FCFF for Acme Corporation (based on the data from Exhibits 
6, 7, and 8) is as follows:
CFO $2,606
Plus: Interest paid times (1 – income tax rate)
  {$258 [1 – 0.34a]} 170
Less: Net investments in fixed capital
  ($1,300 – $762) (538)
FCFF $2,238
a Income tax rate of 0.34 = (Tax expense ÷ Pretax income) = ($1,139 ÷ $3,349).
FCFE is the cash flow available to the company’s common stockholders after all

operating expenses and borrowing costs (principal and interest) have been paid and 
necessary investments in working capital and fixed capital have been made. FCFE 
can be computed as
FCFE = CFO – FCInv + Net borrowing
When net borrowing is negative, debt repayments exceed receipts of borrowed 
funds. In this case, FCFE can be expressed as
FCFE = CFO – FCInv – Net debt repayment
The computation of FCFE for Acme Corporation (based on the data from Exhibits 
CFO $2,606
Less: Net investments in fixed capital ($1,300 – $762) (538)
Less: Debt repayment (500)
FCFE $1,568
Positive FCFE means that the company has an excess of operating cash flow over 
amounts needed for capital expenditures and repayment of debt. This cash would be 
available for distribution to owners.
4.4 Cash Flow Ratios
The statement of cash flows provides information that can be analyzed over time to 
obtain a better understanding of the past performance of a company and its future

prospects. This information can also be effectively used to compare the performance 
and prospects of different companies in an industry and of different industries. There 
are several ratios based on cash flow from operating activities that are useful in this 
analysis. These ratios generally fall into cash flow performance (profitability) ratios 
and cash flow coverage (solvency) ratios. Exhibit 15 summarizes the calculation and 
interpretation of some of these ratios.

Reading 25 ■ Understanding Cash Flow Statements 256
Exhibit 15   Cash Flow Ratios
Performance Ratios Calculation What It Measures
Cash flow to revenue CFO ÷ Net revenue Operating cash generated per dollar of 
revenue
Cash return on assets CFO ÷ Average total assets Operating cash generated per dollar of 
asset investment
Cash return on equity CFO ÷ Average shareholders’ equity Operating cash generated per dollar of 
owner investment
Cash to income CFO ÷ Operating income Cash generating ability of operations
Cash flow per sharea(CFO – Preferred dividends) ÷ Number of 
common shares outstandingOperating cash flow on a per-  share basis
Coverage Ratios Calculation What It Measures
Debt coverage CFO ÷ Total debt Financial risk and financial leverage
Interest coverageb(CFO + Interest paid + Taxes paid) ÷ 
Interest paidAbility to meet interest obligations
Reinvestment CFO ÷ Cash paid for long-  term assets Ability to acquire assets with operating 
cash flows
Debt payment CFO ÷ Cash paid for long-  term debt

Debt payment CFO ÷ Cash paid for long-  term debt 
repaymentAbility to pay debts with operating cash 
flows
Dividend payment CFO ÷ Dividends paid Ability to pay dividends with operating 
cash flows
Investing and financing CFO ÷ Cash outflows for investing and 
financing activitiesAbility to acquire assets, pay debts, and 
make distributions to owners
Notes:
a If the company reports under IFRS and includes total dividends paid as a use of cash in the operating section, total dividends should be 
added back to CFO as reported and then preferred dividends should be subtracted. Recall that CFO reported under US GAAP and IFRS 
may differ depending on the treatment of interest and dividends, received and paid.
b If the company reports under IFRS and included interest paid as a use of cash in the financing section, then interest paid should not be 
added back to the numerator.
EXAMPLE 10   
A Cash Flow Analysis of Comparables

EXAMPLE 10   
Andrew Potter is comparing the cash-  flow-  generating ability of Dell Inc. with that 
of other computer manufacturers: Hewlett Packard and Apple Inc. He collects 
information from the companies’ annual reports and prepares the following table.
Cash Flow from Operating Activities as a Percentage of Total Net 
Revenue
2009 (%) 2008 (%) 2007 (%)
DELL 7.38 3.10 6.46
HPQ 11.68 12.33 9.22
APPLE 23.68 29.55 22.79

Summary 257
As a Percentage of Ending Total Assets
DELL 11.61 7.15 14.33
HPQ 11.65 12.87 10.84
APPLE 21.39 24.25 21.58
DELL = Dell Inc.; AAPLE = Apple Inc.; HPQ = Hewlett Packard.
What is Potter likely to conclude about the relative cash-  flow-  generating ability 
of these companies?
Solution: 
On both measures—operating cash flow divided by revenue and operating cash 
flow divided by assets—Apple’s performance was much stronger than the two 
comparable companies. Dell’s operating cash flow divided by revenue is lower 
than HP’s for all three years. Dell’s operating cash flow relative to assets is similar 
to HP’s in 2009, lower than HP’s in 2008, and higher than HP’s in 2007. Apple’s 
measures are significantly higher than the others, indicating that it has the best 
cash generating ability. Note that Apple’s cash generating ability presumably 
reflects the company’s successful introduction and sales of new products (includ -

ing the iPhone), tightly managed inventory, and ability to generate revenues 
(and operating cash flow) from businesses not requiring significant investment 
in such assets as service contracts and sales of third-  party compatible products. 
Overall, Potter should undertake additional research to understand the under -
lying business reasons for the differences in the companies’ cash flow profiles.
SUMMARY
The cash flow statement provides important information about a company’s cash 
receipts and cash payments during an accounting period as well as information about 
a company’s operating, investing, and financing activities. Although the income 
statement provides a measure of a company’s success, cash and cash flow are also 
vital to a company’s long-  term success. Information on the sources and uses of cash 
helps creditors, investors, and other statement users evaluate the company’s liquidity, 
solvency, and financial flexibility. Key concepts are as follows:

■■Cash flow activities are classified into three categories: operating activities, 
investing activities, and financing activities. Significant non-  cash transaction 
activities (if present) are reported by using a supplemental disclosure note to 
the cash flow statement.
■■Cash flow statements under IFRS and US GAAP are similar; however, IFRS 
provide companies with more choices in classifying some cash flow items as 
operating, investing, or financing activities.
■■Companies can use either the direct or the indirect method for reporting their 
operating cash flow:

Reading 25 ■ Understanding Cash Flow Statements 258
■●The direct method discloses operating cash inflows by source (e.g., cash 
received from customers, cash received from investment income) and oper -
ating cash outflows by use (e.g., cash paid to suppliers, cash paid for inter -
est) in the operating activities section of the cash flow statement.
■●The indirect method reconciles net income to operating cash flow by adjust -
ing net income for all non-  cash items and the net changes in the operating 
working capital accounts.
■■The cash flow statement is linked to a company’s income statement and com -
parative balance sheets and to data on those statements.
■■Although the indirect method is most commonly used by companies, an analyst 
can generally convert it to an approximation of the direct format by following a 
simple three-  step process.
■■An evaluation of a cash flow statement should involve an assessment of the

sources and uses of cash and the main drivers of cash flow within each category 
of activities.
■■The analyst can use common-  size statement analysis for the cash flow state -
ment. Two approaches to developing the common-  size statements are the total 
cash inflows/total cash outflows method and the percentage of net revenues 
method.
■■The cash flow statement can be used to determine free cash flow to the firm 
(FCFF) and free cash flow to equity (FCFE).
■■The cash flow statement may also be used in financial ratios that measure a 
company’s profitability, performance, and financial strength.

Practice Problems 259
1 The three major classifications of activities in a cash flow statement are:
A inflows, outflows, and net flows.
B operating, investing, and financing.
C revenues, expenses, and net income.
2 The sale of a building for cash would be classified as what type of activity on the 
cash flow statement?
A Operating.
B Investing.
C Financing.
3 Under which section of a manufacturing company’s cash flow statement are the 
following activities reported?
Item 1: Purchases of securities held for trading
Item 2: Sales of securities considered cash equivalents
A Both items are investing activities.
B Both items are operating activities.
C Only Item 1 is an investing activity.
4 Which of the following is an example of a financing activity on the cash flow 
statement under US GAAP?
A Payment of interest.
B Receipt of dividends.
C Payment of dividends.
5 A conversion of a face value $1 million convertible bond for $1 million of com -
mon stock would most likely be:

A reported as a $1 million investing cash inflow and outflow.
B reported as a $1 million financing cash outflow and inflow.
C reported as supplementary information to the cash flow statement.
6 A company recently engaged in a non-  cash transaction that significantly 
affected its property, plant, and equipment. The transaction is: 
A reported under the investing section of the cash flow statement.
B reported differently in cash flow from operations under the direct and indi -
rect methods.
C disclosed as a separate note or in a supplementary schedule to the cash flow 
7 Interest paid is classified as an operating cash flow under:
A US GAAP but may be classified as either operating or investing cash flows 
under IFRS.
B IFRS but may be classified as either operating or investing cash flows under 
US GAAP .
C US GAAP but may be classified as either operating or financing cash flows 

8 Cash flows from taxes on income must be separately disclosed under:

Reading 25 ■ Understanding Cash Flow Statements 260
A IFRS only.
B US GAAP only.
C both IFRS and US GAAP .
9 Which of the following components of the cash flow statement may be prepared 
under the indirect method under both IFRS and US GAAP?
10 Which of the following is most likely  to appear in the operating section of a 
cash flow statement under the indirect method?
A Net income.
B Cash paid to suppliers.
C Cash received from customers.
11 A benefit of using the direct method rather than the indirect method when 
reporting operating cash flows is that the direct method:
A mirrors a forecasting approach.
B is easier and less costly.
C provides specific information on the sources of operating cash flows.
12 Mabel Corporation (MC) reported accounts receivable of $66 million at the end 
of its second fiscal quarter. MC had revenues of $72 million for its third fiscal 
quarter and reported accounts receivable of $55 million at the end of its third

fiscal quarter. Based on this information, the amount of cash MC collected from 
customers during the third fiscal quarter is:
A $61 million.
B $72 million.
C $83 million.
13 When computing net cash flow from operating activities using the indirect 
method, an addition to net income is most likely  to occur when there is a:
A gain on the sale of an asset.
B loss on the retirement of debt.
C decrease in a deferred tax liability.
14 Red Road Company, a consulting company, reported total revenues of $100 mil -
lion, total expenses of $80 million, and net income of $20 million in the most 
recent year. If accounts receivable increased by $10 million, how much cash did 
the company receive from customers?
A $90 million.
B $100 million.
C $110 million.
15 In 2014, a company using US GAAP made cash payments of $6 million for sala -
ries, $2 million for interest expense, and $4 million for income taxes. Additional 
information for the company is provided in the table:
($ millions) 2013 2014
Revenue 42 37

Cost of goods sold 18 16
Inventory 36 40

Practice Problems 261
Accounts receivable 22 19
Accounts payable 14 12
 Based only on the information given, the company’s operating cash flow for 
2014 is closest to :
A $6 million.
B $10 million.
C $14 million.
16 Green Glory Corp., a garden supply wholesaler, reported cost of goods sold 
for the year of $80 million. Total assets increased by $55 million, including an 
increase of $5 million in inventory. Total liabilities increased by $45 million, 
including an increase of $2 million in accounts payable. The cash paid by the 
company to its suppliers is most likely closest  to:
A $73 million.
B $77 million.
17 Purple Fleur S.A., a retailer of floral products, reported cost of goods sold for 
the year of $75 million. Total assets increased by $55 million, but inventory 
declined by $6 million. Total liabilities increased by $45 million, and accounts 
payable increased by $2 million. The cash paid by the company to its suppliers 
is most likely closest  to:

A $67 million.
B $79 million.
18 White Flag, a women’s clothing manufacturer, reported salaries expense of 
$20 million. The beginning balance of salaries payable was $3 million, and the 
ending balance of salaries payable was $1 million. How much cash did the com -
pany pay in salaries?
A $18 million.
B $21 million.
C $22 million.
19 An analyst gathered the following information from a company’s 2010 financial 
statements (in $ millions):
Y ear ended 31 December 2009 2010
Net sales 245.8 254.6
Cost of goods sold 168.3 175.9
Accounts receivable 73.2 68.3
Inventory 39.0 47.8
Accounts payable 20.3 22.9
 Based only on the information above, the company’s 2010 statement of cash 
flows in the direct format would include amounts (in $ millions) for cash 
received from customers and cash paid to suppliers, respectively, that are closest  
to:

Reading 25 ■ Understanding Cash Flow Statements 262
cash received from customers cash paid to suppliers
A 249.7 169.7
B 259.5 174.5
C 259.5 182.1
20 Golden Cumulus Corp., a commodities trading company, reported interest 
expense of $19 million and taxes of $6 million. Interest payable increased by 
$3 million, and taxes payable decreased by $4 million over the period. How 
much cash did the company pay for interest and taxes?
A $22 million for interest and $10 million for taxes.
B $16 million for interest and $2 million for taxes.
C $16 million for interest and $10 million for taxes.
21 An analyst gathered the following information from a company’s 2010 financial 
Balances as of Y ear Ended 31 December 2009 2010
Retained earnings 120 145
Accounts receivable 38 43
Inventory 45 48
Accounts payable 36 29
 In 2010, the company declared and paid cash dividends of $10 million and 
recorded depreciation expense in the amount of $25 million. The company con -

siders dividends paid a financing activity. The company’s 2010 cash flow from 
operations (in $ millions) was closest  to
A 25.
B 45.
C 75.
22 Silverago Incorporated, an international metals company, reported a loss on 
the sale of equipment of $2 million in 2010. In addition, the company’s income 
statement shows depreciation expense of $8 million and the cash flow statement 
shows capital expenditure of $10 million, all of which was for the purchase of 
new equipment. Using the following information from the comparative balance 
sheets, how much cash did the company receive from the equipment sale?
Balance Sheet Item 12/31/2009 12/31/2010 Change
Equipment $100 million $105 million $5 million
depreciation—equipment$40 million $46 million $6 million
A $1 million.
B $2 million.
C $3 million.
23 Jaderong Plinkett Stores reported net income of $25 million. The company has 
no outstanding debt. Using the following information from the comparative

balance sheets (in millions), what should the company report in the financing 
section of the statement of cash flows in 2010?

Practice Problems 263
Common stock $100 $102 $2
Additional paid-  in capital common 
stock$100 $140 $40
Retained earnings $100 $115 $15
Total stockholders’ equity $300 $357 $57
A Issuance of common stock of $42 million; dividends paid of $10 million.
B Issuance of common stock of $38 million; dividends paid of $10 million.
C Issuance of common stock of $42 million; dividends paid of $40 million.
24 Based on the following information for Star Inc., what are the total net adjust -
ments that the company would make to net income in order to derive operating 
cash flow?
Y ear Ended
Income Statement Item 12/31/2010
Net income $20 million
Depreciation $2 million
Accounts receivable $25 million $22 million ($3 million)
Inventory $10 million $14 million $4 million
Accounts payable $8 million $13 million $5 million
A Add $2 million.
B Add $6 million.
C Subtract $6 million.

25 The first step in cash flow statement analysis should be to:
A evaluate consistency of cash flows.
B determine operating cash flow drivers.
C identify the major sources and uses of cash.
26 Which of the following would be valid conclusions from an analysis of the cash 
flow statement for Telefónica Group presented in Exhibit 3?
A The primary use of cash is financing activities.
B The primary source of cash is operating activities.
C Telefónica classifies interest received as an operating activity.
27 The following information is extracted from Sweetfall Incorporated’s financial 
Income Statement Balance Sheet Changes
Revenue $56,800 Decrease in accounts receivable $1,324
Cost of goods sold 27,264 Decrease in inventory 501
Other operating 
expense 562 Increase in prepaid expense 6
Depreciation expense 2,500 Increase in accounts payable 1,063
 The amount of cash Sweetfall Inc. paid to suppliers is:

Reading 25 ■ Understanding Cash Flow Statements 264
A $25,700.
B $26,702.
C $27,826.
28 Which is an appropriate method of preparing a common-  size cash flow 
statement?
A Show each item of revenue and expense as a percentage of net revenue.
B Show each line item on the cash flow statement as a percentage of net 
revenue.
C Show each line item on the cash flow statement as a percentage of total cash 
outflows.
29 Which of the following is an appropriate method of computing free cash flow to 
the firm?
A Add operating cash flows to capital expenditures and deduct after-  tax inter -
est payments.
B Add operating cash flows to after-  tax interest payments and deduct capital 
expenditures.
C Deduct both after-  tax interest payments and capital expenditures from 
operating cash flows.
30 An analyst has calculated a ratio using as the numerator the sum of operating 
cash flow, interest, and taxes and as the denominator the amount of interest.

What is this ratio, what does it measure, and what does it indicate?
A This ratio is an interest coverage ratio, measuring a company’s ability to 
meet its interest obligations and indicating a company’s solvency.
B This ratio is an effective tax ratio, measuring the amount of a company’s 
operating cash flow used for taxes and indicating a company’s efficiency in 
tax management.
C This ratio is an operating profitability ratio, measuring the operating cash 
flow generated accounting for taxes and interest and indicating a company’s 
liquidity.

Solutions 265
SOLUTIONS
1 B is correct. Operating, investing, and financing are the three major classifica -
tions of activities in a cash flow statement. Revenues, expenses, and net income 
are elements of the income statement. Inflows, outflows, and net flows are items 
of information in the statement of cash flows.
2 B is correct. Purchases and sales of long-  term assets are considered investing 
activities. Note that if the transaction had involved the exchange of a build -
ing for other than cash (for example, for another building, common stock of 
another company, or a long-  term note receivable), it would have been consid -
ered a significant non-  cash activity.
3 B is correct. The purchase and sale of securities considered cash equivalents 
and securities held for trading are considered operating activities even for com -
panies in which this activity is not a primary business activity. 
4 C is correct. Payment of dividends is a financing activity under US GAAP .

Payment of interest and receipt of dividends are included in operating cash 
flows under US GAAP . Note that IFRS allow companies to include receipt of 
interest and dividends as either operating or investing cash flows and to include 
payment of interest and dividends as either operating or financing cash flows.
5 C is correct. Non-  cash transactions, if significant, are reported as supplemen -
tary information, not in the investing or financing sections of the cash flow 
6 C is correct. Because no cash is involved in non-  cash transactions, these trans -
actions are not incorporated in the cash flow statement. However, non-  cash 
transactions that significantly affect capital or asset structures are required to 
be disclosed either in a separate note or a supplementary schedule to the cash 
flow statement. 
7 C is correct. Interest expense is always classified as an operating cash flow 
under US GAAP but may be classified as either an operating or financing cash 
flow under IFRS.

8 C is correct. Taxes on income are required to be separately disclosed under 
IFRS and US GAAP . The disclosure may be in the cash flow statement or 
elsewhere.
9 A is correct. The operating section may be prepared under the indirect method. 
The other sections are always prepared under the direct method.
10 A is correct. Under the indirect method, the operating section would begin with 
net income and adjust it to arrive at operating cash flow. The other two items 
would appear in the operating section under the direct method.
11 C is correct. The primary argument in favor of the direct method is that it pro -
vides information on the specific sources of operating cash receipts and pay -
ments. Arguments for the indirect method include that it mirrors a forecasting 
approach and it is easier and less costly 
12 C is correct. The amount of cash collected from customers during the quarter 
is equal to beginning accounts receivable plus revenues minus ending accounts

receivable: $66 million + $72 million – $55 million = $83 million. A reduction 
in accounts receivable indicates that cash collected during the quarter was 
greater than revenue on an accrual basis.

Reading 25 ■ Understanding Cash Flow Statements 266
13 B is correct. An addition to net income is made when there is a loss on the 
retirement of debt, which is a non-  operating loss. A gain on the sale of an asset 
and a decrease in deferred tax liability are both subtracted from net-  income. 
14 A is correct. Revenues of $100 million minus the increase in accounts receivable 
of $10 million equal $90 million cash received from customers. The increase 
in accounts receivable means that the company received less in cash than it 
reported as revenue.
15 A is correct. 
 Operating cash flows =  Cash received from customers – (Cash 
paid to suppliers + Cash paid to employees 
+ Cash paid for other operating expenses 
+ Cash paid for interest + Cash paid for 
income taxes)
 Cash received from customers =  Revenue – Decrease in accounts 
  = $37 – ($19 – $22) = $40 million
 Cash paid to suppliers =  Cost of goods sold + Decrease in inven -
tory – Increase in accounts payable

  = $16 + ($40 – $36) – ($12 – $14) = 
$22 million
 Therefore, the company’s operating cash flow = $40 – $22 – Cash paid for sala -
ries – Cash paid for interest – Cash paid for taxes = $40 – $22 – $6 – $2 – $4 = 
$6 million. 
16 C is correct. Cost of goods sold of $80 million plus the increase in inventory 
of $5 million equals purchases from suppliers of $85 million. The increase in 
accounts payable of $2 million means that the company paid $83 million in cash 
($85 million minus $2 million) to its suppliers.
17 A is correct. Cost of goods sold of $75 million less the decrease in inventory 
of $6 million equals purchases from suppliers of $69 million. The increase in 
accounts payable of $2 million means that the company paid $67 million in cash 
($69 million minus $2 million).
18 C is correct. Beginning salaries payable of $3 million plus salaries expense of 
$20 million minus ending salaries payable of $1 million equals $22 million.

Alternatively, the expense of $20 million plus the $2 million decrease in salaries 
payable equals $22 million.
19 C is correct. Cash received from customers = Sales + Decrease in accounts 
receivable = 254.6 + 4.9 = 259.5. Cash paid to suppliers = Cost of goods sold + 
Increase in inventory – Increase in accounts payable = 175.9 + 8.8 – 2.6 = 182.1.
20 C is correct. Interest expense of $19 million less the increase in interest payable 
of $3 million equals interest paid of $16 million. Tax expense of $6 million plus 
the decrease in taxes payable of $4 million equals taxes paid of $10 million.
21 B is correct. All dollar amounts are in millions. Net income (NI) for 2010 is 
$35. This amount is the increase in retained earnings, $25, plus the dividends 
paid, $10. Depreciation of $25 is added back to net income, and the increases 
in accounts receivable, $5, and in inventory, $3, are subtracted from net income 
because they are uses of cash. The decrease in accounts payable is also a use of

cash and, therefore, a subtraction from net income. Thus, cash flow from opera -
tions is $25 + $10 + $25 – $5 – $3 – $7 = $45.

Solutions 267
22 A is correct. Selling price (cash inflow) minus book value equals gain or loss 
on sale; therefore, gain or loss on sale plus book value equals selling price (cash 
inflow). The amount of loss is given—$2 million. To calculate the book value of 
the equipment sold, find the historical cost of the equipment and the accumu -
lated depreciation on the equipment.
■●Beginning balance of equipment of $100 million plus equipment purchased 
of $10 million minus ending balance of equipment of $105 million equals 
the historical cost of equipment sold, or $5 million.
■●Beginning accumulated depreciation of $40 million plus depreciation 
expense for the year of $8 million minus ending balance of accumulated 
depreciation of $46 million equals accumulated depreciation on the equip -
ment sold, or $2 million.
■●Therefore, the book value of the equipment sold was $5 million minus 
$2 million, or $3 million.
■●Because the loss on the sale of equipment was $2 million, the amount of

cash received must have been $1 million.
23 A is correct. The increase of $42 million in common stock and additional 
paid-  in capital indicates that the company issued stock during the year. The 
increase in retained earnings of $15 million indicates that the company paid 
$10 million in cash dividends during the year, determined as beginning retained 
earnings of $100 million plus net income of $25 million minus ending retained 
earnings of $115 million, which equals $10 million in cash dividends.
24 B is correct. To derive operating cash flow, the company would make the 
following adjustments to net income: Add depreciation (a non-  cash expense) 
of $2 million; add the decrease in accounts receivable of $3 million; add the 
increase in accounts payable of $5 million; and subtract the increase in inven -
tory of $4 million. Total additions would be $10 million, and total subtractions 
would be $4 million, which gives net additions of $6 million.

25 C is correct. An overall assessment of the major sources and uses of cash should 
be the first step in evaluating a cash flow statement.
26 B is correct. The primary source of cash is operating activities. The primary use 
of cash is investing activities. Interest received for Telefónica is classified as an 
investing activity.
27 A is correct. The amount of cash paid to suppliers is calculated as follows: 
  = Cost of goods sold – Decrease in inventory – Increase in accounts 
payable 
  = $27,264 – $501 – $1,063
  = $25,700.
28 B is correct. An appropriate method to prepare a common-  size cash flow state -
ment is to show each line item on the cash flow statement as a percentage of 
net revenue. An alternative way to prepare a statement of cash flows is to show 
each item of cash inflow as a percentage of total inflows and each item of cash 
outflows as a percentage of total outflows.
29 B is correct. Free cash flow to the firm can be computed as operating cash flows

plus after-  tax interest expense less capital expenditures.
30 A is correct. This ratio is an interest coverage ratio, measuring a company’s 
ability to meet its interest obligations and indicating a company’s solvency. This 
coverage ratio is based on cash flow information; another common coverage 
ratio uses a measure based on the income statement (earnings before interest, 
taxes, depreciation, and amortisation).

Financial Analysis Techniques
by Elaine Henry, PhD, CFA, Thomas R. Robinson, PhD, CFA, and 
Jan Hendrik van Greuning, DCom, CFA
BIBD (Brunei).
a. describe tools and techniques used in financial analysis, including 
their uses and limitations;
b. classify, calculate, and interpret activity, liquidity, solvency, 
profitability, and valuation ratios;
c. describe relationships among ratios and evaluate a company using 
ratio analysis;
d. demonstrate the application of DuPont analysis of return on 
equity and calculate and interpret effects of changes in its 
components;
e. calculate and interpret ratios used in equity analysis and credit 
analysis;
f. explain the requirements for segment reporting and calculate and 
interpret segment ratios;

g. describe how ratio analysis and other techniques can be used to 
model and forecast earnings.REA dINg
26
ratio definitions exist and no

readings.

Reading 26 ■ Financial Analysis Techniques 270
Financial analysis tools can be useful in assessing a company’s performance and trends 
in that performance. In essence, an analyst converts data into financial metrics that 
assist in decision making. Analysts seek to answer such questions as: How successfully 
has the company performed, relative to its own past performance and relative to its 
competitors? How is the company likely to perform in the future? Based on expectations 
about future performance, what is the value of this company or the securities it issues?
A primary source of data is a company’s annual report, including the financial 
statements and notes, and management commentary (operating and financial review 
or management’s discussion and analysis). This reading focuses on data presented in 
financial reports prepared under International Financial Reporting Standards (IFRS) 
and United States generally accepted accounting principles (US GAAP). However,

financial reports do not contain all the information needed to perform effective financial 
analysis. Although financial statements do contain data about the past  performance 
of a company (its income and cash flows) as well as its current  financial condition 
(assets, liabilities, and owners’ equity), such statements do not necessarily provide 
all the information useful for analysis nor do they forecast future  results. The finan -
cial analyst must be capable of using financial statements in conjunction with other 
information to make projections and reach valid conclusions. Accordingly, an analyst 
typically needs to supplement the information found in a company’s financial reports 
with other information, including information on the economy, industry, comparable 
companies, and the company itself.
This reading describes various techniques used to analyze a company’s financial 
statements. Financial analysis of a company may be performed for a variety of reasons,

such as valuing equity securities, assessing credit risk, conducting due diligence related 
to an acquisition, or assessing a subsidiary’s performance. This reading will describe 
techniques common to any financial analysis and then discuss more specific aspects 
for the two most common categories: equity analysis and credit analysis.
Equity analysis incorporates an owner’s perspective, either for valuation or perfor -
mance evaluation. Credit analysis incorporates a creditor’s (such as a banker or bond -
holder) perspective. In either case, there is a need to gather and analyze information 
to make a decision (ownership or credit); the focus of analysis varies because of the 
differing interest of owners and creditors. Both equity and credit analyses assess the 
entity’s ability to generate and grow earnings, and cash flow, as well as any associated 
risks. Equity analysis usually places a greater emphasis on growth, whereas credit

analysis usually places a greater emphasis on risks. The difference in emphasis reflects 
the different fundamentals of these types of investments: The value of a company’s 
equity generally increases as the company’s earnings and cash flow increase, whereas 
the value of a company’s debt has an upper limit.
The balance of this reading is organized as follows: Section 2 recaps the frame -
work for financial statements and the place of financial analysis techniques within 
the framework. Section 3 provides a description of analytical tools and techniques. 
Section 4 explains how to compute, analyze, and interpret common financial ratios. 
Sections 5 through 8 explain the use of ratios and other analytical data in equity 
analysis, credit analysis, segment analysis, and forecasting, respectively. A summary 
of the key points and practice problems in the CFA Institute multiple-  choice format 
conclude the reading.1

The Financial Analysis Process 271
THE FINANCIAL ANALYSIS PROCESS
In financial analysis, it is essential to clearly identify and understand the final objective 
and the steps required to reach that objective. In addition, the analyst needs to know 
where to find relevant data, how to process and analyze the data (in other words, know 
the typical questions to address when interpreting data), and how to communicate 
the analysis and conclusions.
2.1 The Objectives of the Financial Analysis Process
Because of the variety of reasons for performing financial analysis, the numerous 
available techniques, and the often substantial amount of data, it is important that 
the analytical approach be tailored to the specific situation. Prior to beginning any 
financial analysis, the analyst should clarify the purpose and context, and clearly 
understand the following:
■■What is the purpose of the analysis? What questions will this analysis answer?

■■What level of detail will be needed to accomplish this purpose?
■■What data are available for the analysis?
■■What are the factors or relationships that will influence the analysis?
■■What are the analytical limitations, and will these limitations potentially impair 
the analysis?
Having clarified the purpose and context of the analysis, the analyst can select 
the set of techniques (e.g., ratios) that will best assist in making a decision. Although 
there is no single approach to structuring the analysis process, a general framework 
is set forth in Exhibit 1. The steps in this process were discussed in more detail in 
an earlier reading; the primary focus of this reading is on Phases 3 and 4, processing 
and analyzing data.
Exhibit 1   A Financial Statement Analysis Framework
1 Articulate the purpose and context of the 
analysis.■■The nature of the analyst’s 
function, such as evaluating an 
equity or debt investment or 
issuing a credit rating.

■■Communication with client 
or supervisor on needs and 
concerns.
■■Institutional guidelines related 
to developing specific work 
product.■■Statement of the purpose or 
objective of analysis.
■■A list (written or unwritten) 
of specific questions to be 
answered by the analysis.
■■Nature and content of report to 
be provided.
■■Timetable and budgeted 
resources for completion.
financial data, questionnaires, 
and industry/economic data.
■■Discussions with management, 
suppliers, customers, and 
■■Company site visits (e.g., to 
production facilities or retail 
stores).■■Organized financial statements.
applicable.2

Reading 26 ■ Financial Analysis Techniques 272
5 Develop and communicate conclusions and 
recommendations (e.g., with an analysis 
report).■■Analytical results and previous 
reports.
■■Institutional guidelines for 
published reports.■■Analytical report answering 
questions posed in Phase 1.
whether to make an investment 
or grant credit.
6 Follow-  up.■■Information gathered by peri -
odically repeating above steps 
as necessary to determine 
whether changes to holdings 
or recommendations are 
necessary.■■Updated reports and 
2.2 Distinguishing between Computations and Analysis

An effective analysis encompasses both computations and interpretations. A well-  
reasoned analysis differs from a mere compilation of various pieces of information, 
computations, tables, and graphs by integrating the data collected into a cohesive whole. 
Analysis of past performance, for example, should address not only what happened 
but also why it happened and whether it advanced the company’s strategy. Some of 
the key questions to address include:
■■What aspects of performance are critical for this company to successfully com -
pete in this industry?
■■How well did the company’s performance meet these critical aspects? 
(Established through computation and comparison with appropriate bench -
marks, such as the company’s own historical performance or competitors’ 
performance.)
■■What were the key causes of this performance, and how does this performance 
reflect the company’s strategy? (Established through analysis.)
If the analysis is forward looking, additional questions include:

■■What is the likely impact of an event or trend? (Established through interpreta -
tion of analysis.)
■■What is the likely response of management to this trend? (Established through 
evaluation of quality of management and corporate governance.)
■■What is the likely impact of trends in the company, industry, and economy on 
future cash flows? (Established through assessment of corporate strategy and 
through forecasts.)Exhibit 1   (Continued)

The Financial Analysis Process 273
■■What are the recommendations of the analyst? (Established through interpreta -
tion and forecasting of results of analysis.)
■■What risks should be highlighted? (Established by an evaluation of major 
uncertainties in the forecast and in the environment within which the company 
operates.)
Example 1 demonstrates how a company’s financial data can be analyzed in the 
context of its business strategy and changes in that strategy. An analyst must be able 
to understand the “why” behind the numbers and ratios, not just what the numbers 
and ratios are.
EXAMPLE 1   
Strategy Reflected in Financial Performance
Apple Inc. and Dell Inc. engage in the design, manufacture, and sale of com -
puter hardware and related products and services. Selected financial data for 
2007 through 2009 for these two competitors are given below. Apple’s fiscal 
year (FY) ends on the final Saturday in September (for example, FY2009 ended

on 26 September 2009). Dell’s fiscal year ends on the Friday nearest 31 January 
(for example, FY2009 ended on 29 January  2010 and FY2007 ended on 1 
February 2008).
Selected Financial Data for Apple (Dollars in Millions)
Fiscal year 2009 2008 2007
Net sales 42,905 37,491 24,578
Gross margin 17,222 13,197 8,152
Operating income 11,740 8,327 4,407
Selected Financial Data for Dell (Dollars in Millions)
Net sales 52,902 61,101 61,133
Gross margin 9,261 10,957 11,671
Operating income 2,172 3,190 3,440
Source:  Apple’s Forms 10-  K and 10-  K/A and Dell’s Form 10-  K.
Apple reported a 53 percent increase in net sales from FY2007 to FY2008 
and a further increase in FY2009 of approximately 14 percent. Gross margin 
increased 62 percent from FY2007 to FY2008 and increased 30 percent from 
FY2008 to FY2009. From FY2007 to FY2009, the gross margin more than dou -
bled. Also, the company’s operating income almost tripled over the three-  year

period. From FY2007 to 2009, Dell reported a decrease in sales, gross margin, 
and operating income
What caused Apple’s dramatic growth in sales and operating income and 
Dell’s comparatively sluggish performance? One of the most important factors 
was the introduction of innovative and stylish products, the linkages with

Reading 26 ■ Financial Analysis Techniques 274
iTunes, and expansion of the distinctive Apple stores. Among the company’s 
most important and most successful new products was the iPhone. Apple’s 2009 
10- K indicates that iPhone unit sales grew 78 percent from 11.6 million units 
in 2008 to 20.7 million units in 2009. By 2009, the company’s revenues from 
iPhones and related services had grown to $13.0 billion and were nearly as large 
as the company’s $13.8 billion revenues from sales of Mac computers. The new 
products and linkages among the products not only increased demand but also 
increased the potential for higher pricing. As a result, gross profit margins and 
operating profit margins increased over the period because costs did not increase 
at the same pace as sales. Moreover, the company’s products revolutionized the 
delivery channel for music and video. The financial results reflect a successful 
execution of the company’s strategy to deliver integrated, innovative products

by controlling the design and development of both hardware and software.
Dell continued to concentrate in the personal computer market, which 
arguably is in the market maturity stage of the product life cycle. Dell’s results 
are consistent with a market maturity stage where industry sales level off and 
competition increases so that industry profits decline. With increased compe -
tition, some companies cannot compete and drop out of the market.
Analysts often need to communicate the findings of their analysis in a written 
report. Their reports should communicate how conclusions were reached and why 
recommendations were made. For example, a report might present the following:
■■the purpose of the report, unless it is readily apparent;
■■relevant aspects of the business context:
■●economic environment (country/region, macro economy, sector);
■●financial and other infrastructure (accounting, auditing, rating agencies);

■●legal and regulatory environment (and any other material limitations on the 
company being analyzed);
■■evaluation of corporate governance and assessment of management strategy, 
including the company’s competitive advantage(s);
■■assessment of financial and operational data, including key assumptions in the 
analysis; and
■■conclusions and recommendations, including limitations of the analysis and 
risks.
An effective narrative and well supported conclusions and recommendations are nor -
mally enhanced by using 3–10 years of data, as well as analytic techniques appropriate 
to the purpose of the report.
ANALYTICAL TOOLS AND TECHNIQUES
The tools and techniques presented in this section facilitate evaluations of company 
data. Evaluations require comparisons. It is difficult to say that a company’s financial 
performance was “good” without clarifying the basis for comparison. In assessing a 
company’s ability to generate and grow earnings and cash flow, and the risks related

to those earnings and cash flows, the analyst draws comparisons to other companies 
(cross-  sectional analysis) and over time (trend or time-  series analysis).3

Analytical Tools and Techniques 275
For example, an analyst may wish to compare the profitability of companies com -
peting in a global industry. If the companies differ significantly in size and/or report 
their financial data in different currencies, comparing net income as reported is not 
useful. Ratios (which express one number in relation to another) and common-  size 
financial statements can remove size as a factor and enable a more relevant compari -
son. To achieve comparability across companies reporting in different currencies, one 
approach is to translate all reported numbers into a common currency using exchange 
rates at the end of a period. Others may prefer to translate reported numbers using 
the average exchange rates during the period. Alternatively, if the focus is primarily 
on ratios, comparability can be achieved without translating the currencies.
The analyst may also want to examine comparable performance over time. Again,

the nominal currency amounts of sales or net income may not highlight significant 
changes. However, using ratios (see Example 2), horizontal financial statements where 
quantities are stated in terms of a selected base year value, and graphs can make such 
changes more apparent. Another obstacle to comparison is differences in fiscal year 
end. To achieve comparability, one approach is to develop trailing twelve months data, 
which will be described in a section below. Finally, it should be noted that differences 
in accounting standards can limit comparability.
EXAMPLE 2   
An analyst is examining the profitability of three Asian companies with large 
shares of the global personal computer market: Acer Inc., Lenovo Group Limited, 
and Toshiba Corporation. Acer has pursued a strategy of selling its products at 
affordable prices. In contrast, Lenovo aims to achieve higher selling prices by 
stressing the high engineering quality of its personal computers for business use.

Toshiba is a conglomerate with varied product lines in addition to computers. 
For its personal computer business, one aspect of Toshiba’s strategy has been 
to focus on laptops only, in contrast with other manufacturers that also make 
desktops. Acer reports in New Taiwan dollars (TW$), Lenovo reports in US 
dollars (US$), and Toshiba reports in Japanese yen (JP¥). For Acer, fiscal year 
end is 31 December. For both Lenovo and Toshiba, fiscal year end is 31 March; 
thus, for these companies, FY2009 ended 31 March 2010.
The analyst collects the data shown in Exhibit 2 below. Use this information 
to answer the following questions:
1 Which of the three companies is largest based on the amount of revenue, 
in US$, reported in fiscal year 2009? For FY2009, assume the relevant, 
average exchange rates were 32.2 TW$/US$ and 92.5 JP¥/US$.
2 Which company had the highest revenue growth from FY2005 to FY2009?
3 How do the companies compare, based on profitability?
Exhibit 2   
ACER

Exhibit 2   
ACER
TW$ Millions FY2005 FY2006 FY2007 FY2008 FY2009
Revenue 318,088 350,816 462,066 546,274 573,983
Gross profit 34,121 38,171 47,418 57,286 58,328
Net income 8,478 10,218 12,959 11,742 11,353

Reading 26 ■ Financial Analysis Techniques 276
LENOVO
US$ Millions FY2005 FY2006 FY2007 FY2008 FY2009
Revenue 13,276 14,590 16,352 14,901 16,605
Gross profit 1,858 2,037 2,450 1,834 1,790
Net income (Loss) 22 161 484 (226) 129
TOSHIBA
JP¥ Millions FY2005 FY2006 FY2007 FY2008 FY2009
Revenue 6,343,506 7,116,350 7,665,332 6,654,518 6,381,599
Gross profit 1,683,711 1,804,171 1,908,729 1,288,431 1,459,362
Net income (Loss) 78,186 137,429 127,413 (343,559) (19,743)
Toshiba is far larger than the other two companies based on FY2009 revenues 
in US$. Toshiba’s FY2009 revenues of US$69.0 billion are far higher than either 
Acer’s US$17.8 billion or Lenovo’s US$16.6 billion.
Acer : At the assumed average exchange rate of 32.2 TW$/US$, Acer’s FY2009 
revenues are equivalent to US$17.8 billion (= TW$573.983 billion ÷ 32.2 TW$/
US$).
Lenovo : Lenovo’s FY2009 revenues totaled US$16.6 billion.
Toshiba : At the assumed average exchange rate of 92.5 JP¥/US$, Toshiba’s

revenues for FY2009 are equivalent to US$69.0 billion (= JP¥ 6,381.599 billion 
÷ 92.5 JP¥/US$).
Note : Comparing the size of companies reporting in different currencies 
requires translating reported numbers into a common currency using exchange 
rates at some point in time. This solution converts the revenues of Acer and 
Toshiba to billions of US dollars using the average exchange rate of the fiscal 
period. It would be equally informative (and would yield the same conclusion) 
to convert the revenues of Acer and Lenovo to Japanese yen, or to convert the 
revenues of Toshiba and Lenovo to New Taiwan dollars.
The growth in Acer’s revenue was much higher than either of the other two 
Change in Revenue FY2009  
versus FY2005 (%)Compound Annual Growth Rate  
from FY2005 to FY2009 (%)
Acer 80.4 15.9
Lenovo 25.1 5.8
Toshiba 0.6 0.1
The table shows two growth metrics. Calculations are illustrated using the 
revenue data for Acer:

The change in Acer’s revenue for FY2009 versus FY2005 is 80.4 percent cal -
culated as (573,983 – 318,088) ÷ 318,088 or equivalently (573,983 ÷ 318,088) – 1.Exhibit 2   (Continued)

Analytical Tools and Techniques 277
The compound annual growth rate in Acer’s revenue from FY2005 to FY2009 
is 15.9 percent, calculated using a financial calculator with the following inputs: 
Present Value = – 318,088; Future value = 573,983; N = 4; Payment = 0; and then 
Interest = ? to solve for growth.
Calculation of the compound annual growth rate can also be expressed as 
follows: [(Ending value ÷ Beginning value)(1/number of periods)] – 1 = [(573,983 ÷ 
318,088)(1/4) – 1 = 0.159 or 15.9 percent.
Profitability can be assessed by comparing the amount of gross profit to revenue 
and the amount of net income to revenue. The following table presents these 
two profitability ratios— gross profit margin  (gross profit divided by revenue) 
and net profit margin  (net income divided by revenue)—for each year.
ACER FY2005 (%) FY2006 (%) FY2007 (%) FY2008 (%) FY2009 (%)
Gross profit margin 10.7 10.9 10.3 10.5 10.2
Net profit margin 2.7 2.9 2.8 2.1 2.0

LENOVO FY2005 (%) FY2006 (%) FY2007 (%) FY2008 (%) FY2009 (%)
Gross profit margin 14.0 14.0 15.0 12.3 10.8
Net profit margin 0.2 1.1 3.0 –1.5 0.8
TOSHIBA FY2005 (%) FY2006 (%) FY2007 (%) FY2008 (%) FY2009 (%)
Gross profit margin 26.5 25.4 24.9 19.4 22.9
Net profit margin 1.2 1.9 1.7 –5.2 –0.3
The net profit margins indicate that Acer has been the most profitable of the 
three companies. The company’s net profit margin was somewhat lower in the 
most recent two years (only 2.1 percent and 2.0 percent in FY2008 and FY2009, 
respectively, compared to 2.7 percent, 2.9 percent and 2.8 percent in FYs 2005, 
2006, and 2007, respectively), but has nonetheless remained positive and has 
remained higher than the competing companies.
Acer’s gross profit margin has remained consistently above 10 percent in all 
5 fiscal years. In contrast, Lenovo’s gross profit margin has declined markedly 
over the 5-  year period, but remains higher than Acer’s, which is consistent with

the company’s strategic objective to achieve higher selling prices by stressing 
the high engineering quality of its personal computers. However, Lenovo’s net 
profit margin has typically been lower than Acer’s. Further analysis is needed 
to determine the cause of Lenovo’s gross profitability decline over the period 
FY2005 to 2009 (lower selling prices and/or higher costs), to assess whether this 
decline is likely to persist in future years, and to determine the reason Lenovo’s 
net profit margins are generally lower than Acer’s despite Lenovo’s higher gross 
profit margins.
Because Toshiba is a conglomerate, profit ratios based on data for the entire 
company give limited information about the company’s personal computer 
business. Ratios based on segment data would likely be more useful than profit 
ratios for the entire company. Based on the aggregate information, Toshiba’s 
gross profit margins are higher than either Acer’s or Lenovo’s gross profit mar -

gins, whereas Toshiba’s net profit margins are generally lower than the net profit 
margins of either of the other two companies.

Reading 26 ■ Financial Analysis Techniques 278
Section 3.1 describes the tools and techniques of ratio analysis in more detail. 
Sections 3.2 to 3.4 describe other tools and techniques.
3.1 Ratios
There are many relationships between financial accounts and between expected rela -
tionships from one point in time to another. Ratios are a useful way of expressing these 
relationships. Ratios express one quantity in relation to another (usually as a quotient).
Extensive academic research has examined the importance of ratios in predicting 
stock returns (Ou and Penman, 1989; Abarbanell and Bushee, 1998) or credit failure 
(Altman, 1968; Ohlson, 1980; Hopwood et al., 1994). This research has found that 
financial statement ratios are effective in selecting investments and in predicting 
financial distress. Practitioners routinely use ratios to derive and communicate the 
value of companies and securities.
Several aspects of ratio analysis are important to understand. First, the computed

ratio is not “the answer. ” The ratio is an indicator  of some aspect of a company’s per -
formance, telling what happened but not why it happened. For example, an analyst 
might want to answer the question: Which of two companies was more profitable? 
As demonstrated in the previous example, the net profit margin, which expresses 
profit relative to revenue, can provide insight into this question. Net profit margin is 
calculated by dividing net income by revenue:
Net income
Revenue
Assume Company A has €100,000 of net income and Company B has €200,000 
of net income. Company B generated twice as much income as Company A, but was 
it more profitable? Assume further that Company A has €2,000,000 of revenue, and 
thus a net profit margin of 5 percent, and Company B has €6,000,000 of revenue, and 
thus a net profit margin of 3.33 percent. Expressing net income as a percentage of 
revenue clarifies the relationship: For each €100 of revenue, Company A earns €5 in

net income, whereas Company B earns only €3.33 for each €100 of revenue. So, we 
can now answer the question of which company was more profitable in percentage 
terms: Company A was more profitable, as indicated by its higher net profit margin of 
5 percent. Note that Company A was more profitable  despite the fact that Company 
B reported higher absolute amounts of net income and revenue. However, this ratio 
by itself does not tell us why Company A has a higher profit margin. Further analysis 
is required to determine the reason (perhaps higher relative sales prices or better cost 
control or lower effective tax rates).
Company size sometimes confers economies of scale, so the absolute amounts of 
net income and revenue are useful in financial analysis. However, ratios reduce the 
effect of size, which enhances comparisons between companies and over time.
A second important aspect of ratio analysis is that differences in accounting policies

(across companies and across time) can distort ratios, and a meaningful comparison 
may, therefore, involve adjustments to the financial data. Third, not all ratios are nec -
essarily relevant to a particular analysis. The ability to select a relevant ratio or ratios 
to answer the research question is an analytical skill. Finally, as with financial analysis 
in general, ratio analysis does not stop with computation; interpretation of the result 
is essential. In practice, differences in ratios across time and across companies can be 
subtle, and interpretation is situation specific.
3.1.1  The Universe of Ratios
There are no authoritative bodies specifying exact formulas for computing ratios or 
providing a standard, comprehensive list of ratios. Formulas and even names of ratios 
often differ from analyst to analyst or from database to database. The number of

Analytical Tools and Techniques 279
different ratios that can be created is practically limitless. There are, however, widely 
accepted ratios that have been found to be useful. Section 4 of this reading will focus 
primarily on these broad classes and commonly accepted definitions of key ratios. 
However, the analyst should be aware that different ratios may be used in practice 
and that certain industries have unique ratios tailored to the characteristics of that 
industry. When faced with an unfamiliar ratio, the analyst can examine the underlying 
formula to gain insight into what the ratio is measuring. For example, consider the 
following ratio formula:
Operating incom e
Average total assets
Never having seen this ratio, an analyst might question whether a result of 12 per -
cent is better than 8 percent. The answer can be found in the ratio itself. The numer -
ator is operating income and the denominator is average total assets, so the ratio can

be interpreted as the amount of operating income generated per unit of assets. For 
every €100 of average total assets, generating €12 of operating income is better than 
generating €8 of operating income. Furthermore, it is apparent that this particular 
ratio is an indicator of profitability (and, to a lesser extent, efficiency in use of assets 
in generating operating profits). When facing a ratio for the first time, the analyst 
should evaluate the numerator and denominator to assess what the ratio is attempt -
ing to measure and how it should be interpreted. This is demonstrated in Example 3.
EXAMPLE 3   
Interpreting a Financial Ratio
A US insurance company reports that its “combined ratio” is determined by 
dividing losses and expenses incurred by net premiums earned. It reports the 
following combined ratios:
Fiscal Y ear 5 4 3 2 1
Combined ratio 90.1% 104.0% 98.5% 104.1% 101.1%
Explain what this ratio is measuring and compare the results reported for each

of the years shown in the chart. What other information might an analyst want 
to review before making any conclusions on this information?
Solution:
The combined ratio is a profitability measure. The ratio is explaining how much 
costs (losses and expenses) were incurred for every dollar of revenue (net pre -
miums earned). The underlying formula indicates that a lower ratio is better. 
The Year 5 ratio of 90.1 percent means that for every dollar of net premiums 
earned, the costs were $0.901, yielding a gross profit of $0.099. Ratios greater 
than 100 percent indicate an overall loss. A review of the data indicates that 
there does not seem to be a consistent trend in this ratio. Profits were achieved 
in Years 5 and 3. The results for Years 4 and 2 show the most significant costs 
at approximately 104 percent.
The analyst would want to discuss this data further with management and 
understand the characteristics of the underlying business. He or she would want

to understand why the results are so volatile. The analyst would also want to 
determine what should be used as a benchmark for this ratio.

Reading 26 ■ Financial Analysis Techniques 280
The Operating income/Average total assets ratio shown above is one of many 
versions of the return on assets (ROA)  ratio. Note that there are other ways of spec -
ifying this formula based on how assets are defined. Some financial ratio databases 
compute ROA using the ending value of assets rather than average assets. In limited 
cases, one may also see beginning assets in the denominator. Which one is right? It 
depends on what you are trying to measure and the underlying company trends. If 
the company has a stable level of assets, the answer will not differ greatly under the 
three measures of assets (beginning, average, and ending). However, if the assets are 
growing (or shrinking), the results will differ among the three measures. When assets 
are growing, operating income divided by ending assets may not make sense because 
some of the income would have been generated before some assets were purchased,

and this would understate the company’s performance. Similarly, if beginning assets 
are used, some of the operating income later in the year may have been generated only 
because of the addition of assets; therefore, the ratio would overstate the company’s 
performance. Because operating income occurs throughout the period, it generally 
makes sense to use some average measure of assets. A good general rule is that when 
an income statement or cash flow statement number is in the numerator of a ratio 
and a balance sheet number is in the denominator, then an average should be used 
for the denominator. It is generally not necessary to use averages when only balance 
sheet numbers are used in both the numerator and denominator because both are 
determined as of the same date. However, in some instances, even ratios that only use 
balance sheet data may use averages. For example, return on equity (ROE) , which is 
defined as net income divided by average shareholders’ equity, can be decomposed

into other ratios, some of which only use balance sheet data. In decomposing ROE 
into component ratios, if an average is used in one of the component ratios then it 
should be used in the other component ratios. The decomposition of ROE is discussed 
further in Section 4.6.2.
If an average is used, judgment is also required about what average should be used. 
For simplicity, most ratio databases use a simple average of the beginning and end-  
of- year balance sheet amounts. If the company’s business is seasonal so that levels of 
assets vary by interim period (semiannual or quarterly), then it may be beneficial to 
take an average over all interim periods, if available. (If the analyst is working within 
a company and has access to monthly data, this can also be used.)
3.1.2  Value, Purposes, and Limitations of Ratio Analysis
The value of ratio analysis is that it enables a financial analyst to evaluate past perfor -

mance, assess the current financial position of the company, and gain insights useful 
for projecting future results. As noted previously, the ratio itself is not “the answer” 
but is an indicator of some aspect of a company’s performance. Financial ratios pro -
vide insights into:
■■microeconomic relationships within a company that help analysts project earn -
ings and free cash flow;
■■a company’s financial flexibility, or ability to obtain the cash required to grow 
and meet its obligations, even if unexpected circumstances develop;
■■management’s ability;
■■changes in the company and/or industry over time; and
■■comparability with peer companies or the relevant industry(ies).
There are also limitations to ratio analysis. Factors to consider include:
■■The heterogeneity or homogeneity of a company’s operating activities.  Companies 
may have divisions operating in many different industries. This can make it 
difficult to find comparable industry ratios to use for comparison purposes.

Analytical Tools and Techniques 281
■■The need to determine whether the results of the ratio analysis are consistent.  
One set of ratios may indicate a problem, whereas another set may indicate that 
the potential problem is only short term in nature.
■■The need to use judgment.  A key issue is whether a ratio for a company is within 
a reasonable range. Although financial ratios are used to help assess the growth 
potential and risk of a company, they cannot be used alone to directly value 
a company or its securities, or to determine its creditworthiness. The entire 
operation of the company must be examined, and the external economic and 
industry setting in which it is operating must be considered when interpreting 
financial ratios.
■■The use of alternative accounting methods.  Companies frequently have latitude 
when choosing certain accounting methods. Ratios taken from financial state -
ments that employ different accounting choices may not be comparable unless

adjustments are made. Some important accounting considerations include the 
following:
■●FIFO (first in, first out), LIFO (last in, first out), or average cost inventory 
valuation methods (IFRS does not allow LIFO);
■●Cost or equity methods of accounting for unconsolidated affiliates;
■●Straight line or accelerated methods of depreciation; and
■●Capital or operating lease treatment.
The expanding use of IFRS and the convergence efforts between IFRS and US GAAP 
has sought to make the financial statements of different companies more comparable 
and may overcome some of these difficulties. Nonetheless, there will remain accounting 
choices that the analyst must consider.
3.1.3  Sources of Ratios
Ratios may be computed using data obtained directly from companies’ financial state -
ments or from a database such as Bloomberg, Compustat, FactSet, or Thomson Reuters. 
The information provided by the database may include information as reported in

companies’ financial statements and ratios calculated based on the information. These 
databases are popular because they provide easy access to many years of historical data 
so that trends over time can be examined. They also allow for ratio calculations based 
on periods other than the company’s fiscal year, such as for the trailing 12 months 
(TTM) or most recent quarter (MRQ).
EXAMPLE 4   
Trailing Twelve Months
On 15 July, an analyst is examining a company with a fiscal year ending on 31 
December. Use the following data to calculate the company’s trailing 12 month 
earnings (for the period ended 30 June 2010):
■■Earnings for the year ended 31 December, 2009: $1,200;
■■Earnings for the six months ended 30 June 2009: $550; and
■■Earnings for the six months ended 30 June 2010: $750.
Solution:
The company’s trailing 12 months earnings is $1,400, calculated as $1,200 – 
$550 + $750.

Reading 26 ■ Financial Analysis Techniques 282
Analysts should be aware that the underlying formulas for ratios may differ by 
vendor. The formula used should be obtained from the vendor, and the analyst should 
determine whether any adjustments are necessary. Furthermore, database providers 
often exercise judgment when classifying items. For example, operating income may 
not appear directly on a company’s income statement, and the vendor may use judg -
ment to classify income statement items as “operating” or “non-  operating. ” Variation 
in such judgments would affect any computation involving operating income. It is 
therefore a good practice to use the same source for data when comparing different 
companies or when evaluating the historical record of a single company. Analysts 
should verify the consistency of formulas and data classifications by the data source. 
Analysts should also be mindful of the judgments made by a vendor in data classifi -

cations and refer back to the source financial statements until they are comfortable 
that the classifications are appropriate.
Systems are under development that collect financial data from regulatory filings 
and can automatically compute ratios. The eXtensible Business Reporting Language 
(XBRL) is a mechanism that attaches “smart tags” to financial information (e.g., 
total assets), so that software can automatically collect the data and perform desired 
computations. The organization developing XBRL (www.xbrl.org) is an international 
nonprofit consortium of over 600 members from companies, associations, and agencies, 
including the International Accounting Standards Board. Many stock exchanges and 
regulatory agencies around the world now use XBRL for receiving and distributing 
public financial reports from listed companies.
Analysts can compare a subject company to similar (peer) companies in these 
databases or use aggregate industry data. For non-  public companies, aggregate indus -

try data can be obtained from such sources as Annual Statement Studies by the Risk 
Management Association or Dun & Bradstreet. These publications typically provide 
industry data with companies sorted into quartiles. By definition, twenty-  five percent 
of companies’ ratios fall within the lowest quartile, 25 percent have ratios between the 
lower quartile and median value, and so on. Analysts can then determine a company’s 
relative standing in the industry.
3.2 Common-  Size Analysis
Common-  size analysis  involves expressing financial data, including entire financial 
statements, in relation to a single financial statement item, or base. Items used most 
frequently as the bases are total assets or revenue. In essence, common-  size analysis 
creates a ratio between every financial statement item and the base item.
Common-  size analysis was demonstrated in readings for the income statement, 
balance sheet, and cash flow statement. In this section, we present common-  size

analysis of financial statements in greater detail and include further discussion of 
their interpretation.
3.2.1  Common-  Size Analysis of the Balance Sheet
A vertical common-  size balance sheet, prepared by dividing each item on the balance 
sheet by the same period’s total assets and expressing the results as percentages, high -
lights the composition of the balance sheet. What is the mix of assets being used? How 
is the company financing itself? How does one company’s balance sheet composition 
compare with that of peer companies, and what are the reasons for any differences?
A horizontal common-  size balance sheet, prepared by computing the increase 
or decrease in percentage terms of each balance sheet item from the prior year or 
prepared by dividing the quantity of each item by a base year quantity of the item, 
highlights changes in items. These changes can be compared to expectations. The 
section on trend analysis below will illustrate a horizontal common-  size balance sheet.

Analytical Tools and Techniques 283
Exhibit 3 presents a vertical common-  size (partial) balance sheet for a hypothet -
ical company in two time periods. In this example, receivables have increased from 
35 percent to 57 percent of total assets and the ratio has increased by 63 percent from 
Period 1 to Period 2. What are possible reasons for such an increase? The increase might 
indicate that the company is making more of its sales on a credit basis rather than a 
cash basis, perhaps in response to some action taken by a competitor. Alternatively, 
the increase in receivables as a percentage of assets may have occurred because of a 
change in another current asset category, for example, a decrease in the level of inven -
tory; the analyst would then need to investigate why that asset category has changed. 
Another possible reason for the increase in receivables as a percentage of assets is that 
the company has lowered its credit standards, relaxed its collection procedures, or

adopted more aggressive revenue recognition policies. The analyst can turn to other 
comparisons and ratios (e.g., comparing the rate of growth in accounts receivable 
with the rate of growth in sales) to help determine which explanation is most likely.
Exhibit 3   Vertical Common-  Size (Partial) Balance Sheet for a Hypothetical 
Company
Period 1  
Percent of Total AssetsPeriod 2  
Percent of Total Assets
Cash 25 15
Receivables 35 57
Inventory 35 20
Fixed assets, net of 
depreciation 5 8
Total assets 100 100
3.2.2  Common-  Size Analysis of the Income Statement
A vertical common-  size income statement divides each income statement item by 
revenue, or sometimes by total assets (especially in the case of financial institutions). 
If there are multiple revenue sources, a decomposition of revenue in percentage terms 
is useful. Exhibit 4 presents a hypothetical company’s vertical common-  size income 
statement in two time periods. Revenue is separated into the company’s four services,

each shown as a percentage of total revenue.
In this example, revenues from Service A have become a far greater percentage 
of the company’s total revenue (30 percent in Period 1 and 45 percent in Period 2). 
What are possible reasons for and implications of this change in business mix? Did 
the company make a strategic decision to sell more of Service A, perhaps because it 
is more profitable? Apparently not, because the company’s earnings before interest, 
taxes, depreciation, and amortisation (EBITDA) declined from 53 percent of sales to 
45 percent, so other possible explanations should be examined. In addition, we note 
from the composition of operating expenses that the main reason for this decline in 
profitability is that salaries and employee benefits have increased from 15 percent to 
25 percent of total revenue. Are more highly compensated employees required for 
Service A? Were higher training costs incurred in order to increase revenues from

Service A? If the analyst wants to predict future performance, the causes of these 
changes must be understood.
In addition, Exhibit 4 shows that the company’s income tax as a percentage of 
sales has declined dramatically (from 15 percent to 8 percent). Furthermore, taxes as 
a percentage of earnings before tax (EBT) (the effective tax rate, which is usually the 
more relevant comparison), have decreased from 36 percent (= 15/42) to 24 percent

Reading 26 ■ Financial Analysis Techniques 284
(= 8/34). Is Service A, which in Period 2 is a greater percentage of total revenue, 
provided in a jurisdiction with lower tax rates? If not, what is the explanation for the 
change in effective tax rate?
The observations based on Exhibit  4 summarize the issues that can be raised 
through analysis of the vertical common-  size income statement.
Exhibit 4   Vertical Common-  Size Income Statement for Hypothetical 
Company
Period 1  
Percent of 
Total RevenuePeriod 2  
Percent of Total 
Revenue
Revenue source: Service A 30 45
Revenue source: Service B 23 20
Revenue source: Service C 30 30
Revenue source: Service D 17 5
Total revenue 100 100
Operating expenses (excluding depreciation)
  Salaries and employee benefits 15 25
  Administrative expenses 22 20
  Rent expense 10 10
EBITDA 53 45
  Depreciation and amortisation 4 4
EBIT 49 41
  Interest paid 7 7
EBT 42 34
  Income tax provision 15 8
Net income 27 26
EBIT = earnings before interest and tax.

3.2.3  Cross-  Sectional Analysis
As noted previously, ratios and common-  size statements derive part of their meaning 
through comparison to some benchmark. Cross-  sectional analysis  (sometimes called 
“relative analysis”) compares a specific metric for one company with the same metric 
for another company or group of companies, allowing comparisons even though the 
companies might be of significantly different sizes and/or operate in different curren -
cies. This is illustrated in Exhibit 5.
Exhibit 5   Vertical Common-  Size (Partial) Balance Sheet for Two 
Hypothetical Companies
AssetsCompany 1  
Percent of Total AssetsCompany 2  
Cash 38 12
Receivables 33 55
Inventory 27 24

Analytical Tools and Techniques 285
Fixed assets net of 
depreciation1 2
Investments 1 7
Total Assets 100 100
Exhibit 5 presents a vertical common-  size (partial) balance sheet for two hypothet -
ical companies at the same point in time. Company 1 is clearly more liquid (liquidity 
is a function of how quickly assets can be converted into cash) than Company 2, 
which has only 12  percent of assets available as cash, compared with the highly 
liquid Company 1, which has 38 percent of assets available as cash. Given that cash 
is generally a relatively low-  yielding asset and thus not a particularly efficient use of 
excess funds, why does Company 1 hold such a large percentage of total assets in 
cash? Perhaps the company is preparing for an acquisition, or maintains a large cash 
position as insulation from a particularly volatile operating environment. Another

issue highlighted by the comparison in this example is the relatively high percentage 
of receivables in Company 2’s assets, which may indicate a greater proportion of credit 
sales, overall changes in asset composition, lower credit or collection standards, or 
aggressive accounting policies.
3.2.4  Trend Analysis
When looking at financial statements and ratios, trends in the data, whether they are 
improving or deteriorating, are as important as the current absolute or relative levels. 
Trend analysis provides important information regarding historical performance and 
growth and, given a sufficiently long history of accurate seasonal information, can be 
of great assistance as a planning and forecasting tool for management and analysts.
Exhibit 6A presents a partial balance sheet for a hypothetical company over five 
periods. The last two columns of the table show the changes for Period 5 compared 
with Period 4, expressed both in absolute currency (in this case, dollars) and in per -

centages. A small percentage change could hide a significant currency change and vice 
versa, prompting the analyst to investigate the reasons despite one of the changes being 
relatively small. In this example, the largest percentage change was in investments, 
which decreased by 33.3 percent. However, an examination of the absolute currency 
amount of changes shows that investments changed by only $2 million, and the more 
significant change was the $12 million increase in receivables.
Another way to present data covering a period of time is to show each item in 
relation to the same item in a base year (i.e., a horizontal common-  size balance sheet). 
Exhibits 6B and 6C illustrate alternative presentations of horizontal common-  size 
balance sheets. Exhibit 6B presents the information from the same partial balance 
sheet as in Exhibit 6A, but indexes each item relative to the same item in Period 1. 
For example, in Period 2, the company had $29 million cash, which is 74 percent or

0.74 of the amount of cash it had in Period 1. Expressed as an index relative to Period 
1, where each item in Period 1 is given a value of 1.00, the value in Period 2 would 
be 0.74 ($29/$39 = 0.74). In Period 3, the company had $27 million cash, which is 
69 percent of the amount of cash it had in Period 1 ($27/$39 = 0.69).
Exhibit 6C presents the percentage change in each item, relative to the previous 
year. For example, the change in cash from Period 1 to Period 2 was –25.6 percent 
($29/$39 – 1  = –0.256), and the change in cash from Period 2 to Period 3 was Exhibit 5   (Continued)

Reading 26 ■ Financial Analysis Techniques 286
–6.9 percent ($27/$29 – 1 = –0.069). An analyst will select the horizontal common-  size 
balance that addresses the particular period of interest. Exhibit 6B clearly highlights 
that in Period 5 compared to Period 1, the company has less than half the amount of 
cash, four times the amount of investments, and eight times the amount of property, 
plant, and equipment. Exhibit 6C highlights year-  to- year changes: For example, cash 
has declined in each period. Presenting data this way highlights significant changes. 
Again, note that a mathematically big change is not necessarily an important change. 
For example, fixed assets increased 100 percent, i.e., doubled between Period 1 and 2; 
however, as a proportion of total assets, fixed assets increased from 1 percent of total 
assets to 2 percent of total assets. The company’s working capital assets (receivables 
and inventory) are a far higher proportion of total assets and would likely warrant

more attention from an analyst.
An analysis of horizontal common-  size balance sheets highlights structural changes 
that have occurred in a business. Past trends are obviously not necessarily an accurate 
predictor of the future, especially when the economic or competitive environment 
changes. An examination of past trends is more valuable when the macroeconomic 
and competitive environments are relatively stable and when the analyst is reviewing 
a stable or mature business. However, even in less stable contexts, historical analysis 
can serve as a basis for developing expectations. Understanding of past trends is 
helpful in assessing whether these trends are likely to continue or if the trend is likely 
to change direction.
Exhibit 6A   Partial Balance Sheet for a Hypothetical Company over Five 
Periods
PeriodChange  
4 to 5  
($ Million)Change  
4 to 5  
(Percent)Assets 
($ Millions) 1 2 3 4 5
Cash 39 29 27 19 16 –3 –15.8
Investments 1 7 7 6 4 –2 –33.3
Receivables 44 41 37 67 79 12 17.9

Inventory 15 25 36 25 27 2 8.0
Fixed assets net 
of depreciation 1 2 6 9 8 –1 –11.1
Total assets 100 104 113 126 134 8 6.3
Exhibit 6B   Horizontal Common-  Size (Partial) Balance Sheet for a 
Hypothetical Company over Five Periods, with Each Item 
Expressed Relative to the Same Item in Period One
Period
Assets 1 2 3 4 5
Cash 1.00 0.74 0.69 0.49 0.41
Investments 1.00 7.00 7.00 6.00 4.00
Receivables 1.00 0.93 0.84 1.52 1.80
Inventory 1.00 1.67 2.40 1.67 1.80

Analytical Tools and Techniques 287
Period
Fixed assets net of depreciation 1.00 2.00 6.00 9.00 8.00
Total assets 1.00 1.04 1.13 1.26 1.34
Exhibit 6C   Horizontal Common-  Size (Partial) Balance Sheet for a 
Hypothetical Company over Five Periods, with Percent Change 
in Each Item Relative to the Prior Period
Period
Assets 2 (%) 3 (%) 4 (%) 5 (%)
Cash –25.6 –6.9 –29.6 –15.8
Investments 600.0 0.0 –14.3 –33.3
Receivables –6.8 –9.8 81.1 17.9
Inventory 66.7 44.0 –30.6 8.0
Fixed assets net of depreciation 100.0 200.0 50.0 –11.1
Total assets 4.0 8.7 11.5 6.3
One measure of success is for a company to grow at a rate greater than the rate of 
the overall market in which it operates. Companies that grow slowly may find them -
selves unable to attract equity capital. Conversely, companies that grow too quickly 
may find that their administrative and management information systems cannot keep 
up with the rate of expansion.
3.2.5  Relationships among Financial Statements

Trend data generated by a horizontal common-  size analysis can be compared across 
financial statements. For example, the growth rate of assets for the hypothetical 
company in Exhibit 6 can be compared with the company’s growth in revenue over 
the same period of time. If revenue is growing more quickly than assets, the com -
pany may be increasing its efficiency (i.e., generating more revenue for every dollar 
invested in assets).
As another example, consider the following year-  over-  year percentage changes 
for a hypothetical company:
Revenue +20%
Net income +25%
Operating cash flow –10%
Total assets +30%
Net income is growing faster than revenue, which indicates increasing profitabil -
ity. However, the analyst would need to determine whether the faster growth in net 
income resulted from continuing operations or from non-  operating, non-  recurring 
items. In addition, the 10 percent decline in operating cash flow despite increasing

revenue and net income clearly warrants further investigation because it could indicate 
a problem with earnings quality (perhaps aggressive reporting of revenue). Lastly, the Exhibit 6B   (Continued)

Reading 26 ■ Financial Analysis Techniques 288
fact that assets have grown faster than revenue indicates the company’s efficiency may 
be declining. The analyst should examine the composition of the increase in assets 
and the reasons for the changes. Example 5 illustrates a company where comparisons 
of trend data from different financial statements were actually indicative of aggressive 
accounting policies.
EXAMPLE 5   
Use of Comparative Growth Information
In July 1996, Sunbeam, a US company, brought in new management to turn 
the company around. In the following year, 1997, using 1996 as the base, the 
following was observed based on reported numbers:
Revenue +19%
Inventory +58%
Receivables +38%
It is generally more desirable to observe inventory and receivables growing at a 
slower (or similar) rate compared to revenue growth. Receivables growing faster 
than revenue can indicate operational issues, such as lower credit standards

or aggressive accounting policies for revenue recognition. Similarly, inventory 
growing faster than revenue can indicate an operational problem with obsoles -
cence or aggressive accounting policies, such as an improper overstatement of 
inventory to increase profits.
In this case, the explanation lay in aggressive accounting policies. Sunbeam 
was later charged by the US Securities and Exchange Commission with improperly 
accelerating the recognition of revenue and engaging in other practices, such as 
billing customers for inventory prior to shipment.
3.3 The Use of Graphs as an Analytical Tool
Graphs facilitate comparison of performance and financial structure over time, high -
lighting changes in significant aspects of business operations. In addition, graphs 
provide the analyst (and management) with a visual overview of risk trends in a busi -
ness. Graphs may also be used effectively to communicate the analyst’s conclusions 
regarding financial condition and risk management aspects.

Exhibit 7 presents the information from Exhibit 6A in a stacked column format. 
The graph makes the significant decline in cash and growth in receivables (both in 
absolute terms and as a percentage of assets) readily apparent. In Exhibit 7, the vertical 
axis shows US$ millions and the horizontal axis denotes the period.
Choosing the appropriate graph to communicate the most significant conclusions 
of a financial analysis is a skill. In general, pie graphs are most useful to communicate 
the composition of a total value (e.g., assets over a limited amount of time, say one or 
two periods). Line graphs are useful when the focus is on the change in amount for a 
limited number of items over a relatively longer time period. When the composition 
and amounts, as well as their change over time, are all important, a stacked column 
graph can be useful.

Analytical Tools and Techniques 289
Exhibit 7   Stacked Column Graph of Asset Composition of Hypothetical Company over Five Periods
020406080100120140160
5 4 3 2 1
Fixed assets InventoryReceivables Investments Cash
When comparing Period 5 with Period 4, the growth in receivables appears to be 
within normal bounds; but when comparing Period 5 with earlier periods, the dramatic 
growth becomes apparent. In the same manner, a simple line graph will also illustrate 
the growth trends in key financial variables. Exhibit 8 presents the information from 
Exhibit 6A as a line graph, illustrating the growth of assets of a hypothetical company 
over five periods. The steady decline in cash, volatile movements of inventory, and 
dramatic growth of receivables is clearly illustrated. Again, the vertical axis is shown 
in US$ millions and the horizontal axis denotes periods.

Reading 26 ■ Financial Analysis Techniques 290
Exhibit 8   Line Graph of Growth of Assets of Hypothetical Company over Five Periods
0102030405060708090
Fixed assets InventoryReceivables Investments Cash5 4 3 2 1
3.4 Regression Analysis
When analyzing the trend in a specific line item or ratio, frequently it is possible simply 
to visually evaluate the changes. For more complex situations, regression analysis can 
help identify relationships (or correlation) between variables. For example, a regres -
sion analysis could relate a company’s sales to GDP over time, providing insight into 
whether the company is cyclical. In addition, the statistical relationship between sales 
and GDP could be used as a basis for forecasting sales.
Other examples include the relationship between a company’s sales and inventory 
over time, or the relationship between hotel occupancy and a company’s hotel rev -
enues. In addition to providing a basis for forecasting, regression analysis facilitates

identification of items or ratios that are not behaving as expected, given historical 
statistical relationships.
COMMON RATIOS USED IN FINANCIAL ANALYSIS
In the previous section, we focused on ratios resulting from common-  size analysis. 
In this section, we expand the discussion to include other commonly used financial 
ratios and the broad classes into which they are categorized. There is some overlap 
with common-  size financial statement ratios. For example, a common indicator of 
profitability is the net profit margin, which is calculated as net income divided by 
sales. This ratio appears on a vertical common-  size income statement. Other ratios 
involve information from multiple financial statements or even data from outside the 
financial statements.4

Common Ratios Used in Financial Analysis 291
Because of the large number of ratios, it is helpful to think about ratios in terms of 
broad categories based on what aspects of performance a ratio is intended to detect. 
Financial analysts and data vendors use a variety of categories to classify ratios. The 
category names and the ratios included in each category can differ. Common ratio 
categories include activity, liquidity, solvency, profitability, and valuation. These cat -
egories are summarized in Exhibit 9. Each category measures a different aspect of 
the company’s business, but all are useful in evaluating a company’s overall ability to 
generate cash flows from operating its business and the associated risks.
Exhibit 9   Categories of Financial Ratios
Category Description
Activity Activity ratios  measure how efficiently a company performs day-  
to- day tasks, such as the collection of receivables and management 
of inventory.

Liquidity Liquidity ratios  measure the company’s ability to meet its short-  
term obligations.
Solvency Solvency ratios  measure a company’s ability to meet long-  term 
obligations. Subsets of these ratios are also known as “leverage” 
and “long-  term debt” ratios.
Profitability Profitability ratios  measure the company’s ability to generate 
profits from its resources (assets).
Valuation Valuation ratios  measure the quantity of an asset or flow (e.g., 
earnings) associated with ownership of a specified claim (e.g., a 
share or ownership of the enterprise).
These categories are not mutually exclusive; some ratios are useful in measuring 
multiple aspects of the business. For example, an activity ratio measuring how quickly a 
company collects accounts receivable is also useful in assessing the company’s liquidity 
because collection of revenues increases cash. Some profitability ratios also reflect the

operating efficiency of the business. In summary, analysts appropriately use certain 
ratios to evaluate multiple aspects of the business. Analysts also need to be aware of 
variations in industry practice in the calculation of financial ratios. In the text that 
follows, alternative views on ratio calculations are often provided.
4.1 Interpretation and Context
Financial ratios can only be interpreted in the context of other information, including 
benchmarks. In general, the financial ratios of a company are compared with those 
of its major competitors (cross-  sectional and trend analysis) and to the company’s 
prior periods (trend analysis). The goal is to understand the underlying causes of 
divergence between a company’s ratios and those of the industry. Even ratios that 
remain consistent require understanding because consistency can sometimes indicate 
accounting policies selected to smooth earnings. An analyst should evaluate financial 
ratios based on the following:

1 Company goals and strategy . Actual ratios can be compared with company 
objectives to determine whether objectives are being attained and whether the 
results are consistent with the company’s strategy.

Reading 26 ■ Financial Analysis Techniques 292
2 Industry norms  (cross-  sectional analysis ). A company can be compared with 
others in its industry by relating its financial ratios to industry norms or to a 
subset of the companies in an industry. When industry norms are used to make 
judgments, care must be taken because:
■●Many ratios are industry specific, and not all ratios are important to all 
industries.
■●Companies may have several different lines of business. This will cause 
aggregate financial ratios to be distorted. It is better to examine industry-  
specific ratios by lines of business.
■●Differences in accounting methods used by companies can distort financial 
ratios.
■●Differences in corporate strategies can affect certain financial ratios.
3 Economic conditions . For cyclical companies, financial ratios tend to improve 
when the economy is strong and weaken during recessions. Therefore, financial 
ratios should be examined in light of the current phase of the business cycle.

The following sections discuss activity, liquidity, solvency, and profitability ratios 
in turn. Selected valuation ratios are presented later in the section on equity analysis.
4.2 Activity Ratios
Activity ratios are also known as asset utilization ratios  or operating efficiency 
ratios . This category is intended to measure how well a company manages various 
activities, particularly how efficiently it manages its various assets. Activity ratios are 
analyzed as indicators of ongoing operational performance—how effectively assets 
are used by a company. These ratios reflect the efficient management of both working 
capital and longer term assets. As noted, efficiency has a direct impact on liquidity 
(the ability of a company to meet its short-  term obligations), so some activity ratios 
are also useful in assessing liquidity.
4.2.1  Calculation of Activity Ratios
Exhibit 10 presents the most commonly used activity ratios. The exhibit shows the 
numerator and denominator of each ratio.

Exhibit 10   Definitions of Commonly Used Activity Ratios
Activity Ratios Numerator Denominator
Inventory turnover Cost of sales or cost of 
goods soldAverage inventory
Days of inventory on hand 
(DOH)Number of days in 
periodInventory turnover
Receivables turnover Revenue Average receivables
Days of sales outstanding 
(DSO)Number of days in 
periodReceivables turnover
Payables turnover Purchases Average trade payables
Number of days of payables Number of days in 
periodPayables turnover
Working capital turnover Revenue Average working capital

Common Ratios Used in Financial Analysis 293
Fixed asset turnover Revenue Average net fixed assets
Total asset turnover Revenue Average total assets
Activity ratios measure how efficiently the company utilizes assets. They generally 
combine information from the income statement in the numerator with balance sheet 
items in the denominator. Because the income statement measures what happened 
during  a period whereas the balance sheet shows the condition only at the end of the 
period, average balance sheet data are normally used for consistency. For example, to 
measure inventory management efficiency, cost of sales or cost of goods sold (from 
the income statement) is divided by average inventory (from the balance sheet). Most 
databases, such as Bloomberg and Baseline, use this averaging convention when income 
statement and balance sheet data are combined. These databases typically average

only two points: the beginning of the year and the end of the year. The examples that 
follow based on annual financial statements illustrate that practice. However, some 
analysts prefer to average more observations if they are available, especially if the 
business is seasonal. If a semiannual report is prepared, an average can be taken over 
three data points (beginning, middle, and end of year). If quarterly data are available, 
a five-  point average can be computed (beginning of year and end of each quarterly 
period) or a four-  point average using the end of each quarterly period. Note that if 
the company’s year ends at a low or high point for inventory for the year, there can 
still be bias in using three or five data points, because the beginning and end of year 
occur at the same time of the year and are effectively double counted.
Because cost of goods sold measures the cost of inventory that has been sold, this

ratio measures how many times per year the entire inventory was theoretically turned 
over, or sold. (We say that the entire inventory was “theoretically” sold because in 
practice companies do not generally sell out their entire inventory.) If, for example, a 
company’s cost of goods sold for a recent year was €120,000 and its average inventory 
was €10,000, the inventory turnover ratio would be 12. The company theoretically 
turns over (i.e., sells) its entire inventory 12 times per year (i.e., once a month). (Again, 
we say “theoretically” because in practice the company likely carries some inventory 
from one month into another.) Turnover can then be converted to days of inventory on 
hand (DOH) by dividing inventory turnover into the number of days in the account -
ing period. In this example, the result is a DOH of 30.42 (365/12), meaning that, on 
average, the company’s inventory was on hand for about 30 days, or, equivalently, the

company kept on hand about 30 days’ worth of inventory, on average, during the period.
Activity ratios can be computed for any annual or interim period, but care must be 
taken in the interpretation and comparison across periods. For example, if the same 
company had cost of goods sold for the first quarter (90 days) of the following year 
of €35,000 and average inventory of €11,000, the inventory turnover would be 3.18 
times. However, this turnover rate is 3.18 times per quarter, which is not directly com -
parable to the 12 times per year in the preceding year. In this case, we can annualize 
the quarterly inventory turnover rate by multiplying the quarterly turnover by 4 (12 
months/3 months; or by 4.06, using 365 days/90 days) for comparison to the annual 
turnover rate. So, the quarterly inventory turnover is equivalent to a 12.72 annual 
inventory turnover (or 12.91 if we annualize the ratio using a 90-  day quarter and a

365-  day year). To compute the DOH using quarterly data, we can use the quarterly 
turnover rate and the number of days in the quarter for the numerator—or, we can use 
the annualized turnover rate and 365 days; either results in DOH of around 28.3, with Exhibit 10   (Continued)

Reading 26 ■ Financial Analysis Techniques 294
slight differences due to rounding (90/3.18 = 28.30 and 365/12.91 = 28.27). Another 
time-  related computational detail is that for companies using a 52/53-  week annual 
period and for leap years, the actual days in the year should be used rather than 365.
In some cases, an analyst may want to know how many days of inventory are on 
hand at the end of the year rather than the average for the year. In this case, it would 
be appropriate to use the year-  end inventory balance in the computation rather 
than the average. If the company is growing rapidly or if costs are increasing rapidly, 
analysts should consider using cost of goods sold just for the fourth quarter in this 
computation because the cost of goods sold of earlier quarters may not be relevant. 
Example  6 further demonstrates computation of activity ratios using Hong Kong 
Exchange-  listed Lenovo Group Limited.
EXAMPLE 6   
Computation of Activity Ratios

EXAMPLE 6   
An analyst would like to evaluate Lenovo Group’s efficiency in collecting its 
trade accounts receivable during the fiscal year ended 31 March 2010 (FY2009). 
The analyst gathers the following information from Lenovo’s annual and interim 
reports:
US$ in Thousands
Trade receivables as of 31 March 2009 482,086
Trade receivables as of 31 March 2010 1,021,062
Revenue for year ended 31 March 2010 16,604,815
Calculate Lenovo’s receivables turnover and number of days of sales out -
standing (DSO) for the fiscal year ended 31 March 2010.
Solution:
Receivables turnover = Revenue/Average receivables
= 16,604,815/ [(1,021,062 + 482,086)/2]
= 16,604,815/751,574
= 22.0934 times, or 22.1 rounded
DSO = Number of days in period/Receivables 
turnover
= 365/22.1
= 16.5 days
On average, it took Lenovo 16.5 days to collect receivables during the fiscal year 
ended 31 March 2010.
4.2.2  Interpretation of Activity Ratios

In the following section, we further discuss the activity ratios that were defined in 
Exhibit 10.
Inventory Turnover and DOH  Inventory turnover lies at the heart of operations for 
many entities. It indicates the resources tied up in inventory (i.e., the carrying costs) 
and can, therefore, be used to indicate inventory management effectiveness. A higher 
inventory turnover ratio implies a shorter period that inventory is held, and thus a 
lower DOH. In general, inventory turnover and DOH should be benchmarked against 
industry norms.

Common Ratios Used in Financial Analysis 295
A high inventory turnover ratio relative to industry norms might indicate highly 
effective inventory management. Alternatively, a high inventory turnover ratio (and 
commensurately low DOH) could possibly indicate the company does not carry 
adequate inventory, so shortages could potentially hurt revenue. To assess which 
explanation is more likely, the analyst can compare the company’s revenue growth 
with that of the industry. Slower growth combined with higher inventory turnover 
could indicate inadequate inventory levels. Revenue growth at or above the industry’s 
growth supports the interpretation that the higher turnover reflects greater inventory 
management efficiency.
A low inventory turnover ratio (and commensurately high DOH) relative to the 
rest of the industry could be an indicator of slow-  moving inventory, perhaps due to 
technological obsolescence or a change in fashion. Again, comparing the company’s

sales growth with the industry can offer insight.
Receivables Turnover and DSO.  The number of DSO represents the elapsed time 
between a sale and cash collection, reflecting how fast the company collects cash from 
customers to whom it offers credit. Although limiting the numerator to sales made on 
credit in the receivables turnover would be more appropriate, credit sales information is 
not always available to analysts; therefore, revenue as reported in the income statement 
is generally used as an approximation.
A relatively high receivables turnover ratio (and commensurately low DSO) might 
indicate highly efficient credit and collection. Alternatively, a high receivables turnover 
ratio could indicate that the company’s credit or collection policies are too stringent, 
suggesting the possibility of sales being lost to competitors offering more lenient 
terms. A relatively low receivables turnover ratio would typically raise questions about

the efficiency of the company’s credit and collections procedures. As with inventory 
management, comparison of the company’s sales growth relative to the industry can 
help the analyst assess whether sales are being lost due to stringent credit policies. 
In addition, comparing the company’s estimates of uncollectible accounts receivable 
and actual credit losses with past experience and with peer companies can help assess 
whether low turnover reflects credit management issues. Companies often provide 
details of receivables aging (how much receivables have been outstanding by age). 
This can be used along with DSO to understand trends in collection, as demonstrated 
in Example 7.
EXAMPLE 7   
Evaluation of an Activity Ratio
An analyst has computed the average DSO for Lenovo for fiscal years ended 31 
March 2010 and 2009:
2010 2009
Days of sales outstanding 16.5 15.2
Revenue increased from US$14.901 billion for fiscal year ended 31 March 2009

(FY2008) to US$16.605 billion for fiscal year ended 31 March 2010 (FY2009). The 
analyst would like to better understand the change in the company’s DSO from 
FY2008 to FY2009 and whether the increase is indicative of any issues with the 
customers’ credit quality. The analyst collects accounts receivable aging infor -
mation from Lenovo’s annual reports and computes the percentage of accounts 
receivable by days outstanding. This information is presented in Exhibit 11:

Reading 26 ■ Financial Analysis Techniques 296
Exhibit 11   
FY2009 FY2008 FY2007
US$000 Percent US$000 Percent US$000 Percent
Accounts receivable
0–30 days 907,412 87.39 391,098 76.41 691,428 89.32
31–60 days 65,335 6.29 9,014 1.76 0 0.00
61–90 days 32,730 3.15 21,515 4.20 32,528 4.20
Over 90 days 32,904 3.17 90,214 17.63 50,168 6.48
Total 1,038,381 100.00 511,841 100.00 774,124 100.00
Less: Provision for 
impairment–17,319 –1.67 –29,755 –5.81 –13,885 –1.79
Trade receivables, net 1,021,062 98.33 482,086 94.19 760,239 98.21
Total sales 16,604,815 14,900,931 16,351,503
Note : Lenovo’s footnotes disclose that general trade customers are provided with 30-  day credit terms.
These data indicate that total accounts receivable more than doubled in 
FY2009 versus FY2008, while total sales increased by only 11.4 percent. This 
suggests that, overall, the company has been increasing customer financing to 
drive its sales growth. The significant increase in accounts receivable in total was

the primary reason for the increase in DSO. The percentage of receivables older 
than 61 days has declined significantly which is generally positive. However, the 
large increase in 0–30 day receivables may be indicative of aggressive account -
ing policies or sales practices. Perhaps Lenovo offered incentives to generate a 
large amount of year-  end sales. While the data may suggest that the quality of 
receivables improved in FY2009 versus FY2008, with a much lower percentage 
of receivables (and a much lower absolute amount) that are more than 90 days 
outstanding and, similarly, a lower percentage of estimated uncollectible receiv -
ables, this should be investigated further by the analyst.
Payables Turnover and the Number of Days of Payables  The number of days of 
payables reflects the average number of days the company takes to pay its suppliers, 
and the payables turnover ratio measures how many times per year the company the -

oretically pays off all its creditors. For purposes of calculating these ratios, an implicit 
assumption is that the company makes all its purchases using credit. If the amount of 
purchases is not directly available, it can be computed as cost of goods sold plus ending 
inventory less beginning inventory. Alternatively, cost of goods sold is sometimes used 
as an approximation of purchases.
A payables turnover ratio that is high (low days payable) relative to the industry 
could indicate that the company is not making full use of available credit facilities; 
alternatively, it could result from a company taking advantage of early payment dis -
counts. An excessively low turnover ratio (high days payable) could indicate trouble 
making payments on time, or alternatively, exploitation of lenient supplier terms. This 
is another example where it is useful to look simultaneously at other ratios. If liquidity 
ratios indicate that the company has sufficient cash and other short-  term assets to pay

obligations and yet the days payable ratio is relatively high, the analyst would favor 
the lenient supplier credit and collection policies as an explanation.

Common Ratios Used in Financial Analysis 297
Working Capital Turnover  Working capital  is defined as current assets minus current 
liabilities. Working capital turnover indicates how efficiently the company generates 
revenue with its working capital. For example, a working capital turnover ratio of 4.0 
indicates that the company generates €4 of revenue for every €1 of working capital. 
A high working capital turnover ratio indicates greater efficiency (i.e., the company is 
generating a high level of revenues relative to working capital). For some companies, 
working capital can be near zero or negative, rendering this ratio incapable of being 
interpreted. The following two ratios are more useful in those circumstances.
Fixed Asset Turnover  This ratio measures how efficiently the company generates 
revenues from its investments in fixed assets. Generally, a higher fixed asset turnover 
ratio indicates more efficient use of fixed assets in generating revenue. A low ratio can

indicate inefficiency, a capital-  intensive business environment, or a new business not 
yet operating at full capacity—in which case the analyst will not be able to link the ratio 
directly to efficiency. In addition, asset turnover can be affected by factors other than 
a company’s efficiency. The fixed asset turnover ratio would be lower for a company 
whose assets are newer (and, therefore, less depreciated and so reflected in the financial 
statements at a higher carrying value) than the ratio for a company with older assets 
(that are thus more depreciated and so reflected at a lower carrying value). The fixed 
asset ratio can be erratic because, although revenue may have a steady growth rate, 
increases in fixed assets may not follow a smooth pattern; so, every year-  to- year change 
in the ratio does not necessarily indicate important changes in the company’s efficiency.
Total Asset Turnover  The total asset turnover ratio measures the company’s overall

ability to generate revenues with a given level of assets. A ratio of 1.20 would indicate 
that the company is generating €1.20 of revenues for every €1 of average assets. A higher 
ratio indicates greater efficiency. Because this ratio includes both fixed and current 
assets, inefficient working capital management can distort overall interpretations. It is 
therefore helpful to analyze working capital and fixed asset turnover ratios separately.
A low asset turnover ratio can be an indicator of inefficiency or of relative capital 
intensity of the business. The ratio also reflects strategic decisions by management—for 
example, the decision whether to use a more labor-  intensive (and less capital-  intensive) 
approach to its business or a more capital-  intensive (and less labor-  intensive) approach.
When interpreting activity ratios, the analysts should examine not only the 
individual ratios but also the collection of relevant ratios to determine the overall

efficiency of a company. Example  8 demonstrates the evaluation of activity ratios, 
both narrow (e.g., days of inventory on hand) and broad (e.g., total asset turnover) 
for a hypothetical manufacturer.
EXAMPLE 8   
Evaluation of Activity Ratios
ZZZ Company is a hypothetical manufacturing company. As part of an analysis 
of management’s operating efficiency, an analyst collects the following activity 
ratios from a data provider:
Ratio 2009 2008 2007 2006
DOH 35.68 40.70 40.47 48.51
DSO 45.07 58.28 51.27 76.98
Total asset turnover 0.36 0.28 0.23 0.22

Reading 26 ■ Financial Analysis Techniques 298
These ratios indicate that the company has improved on all three measures 
of activity over the four-  year period. The company appears to be managing its 
inventory more efficiently, is collecting receivables faster, and is generating a 
higher level of revenues relative to total assets. The overall trend appears good, 
but thus far, the analyst has only determined what  happened. A more important 
question is why the ratios improved, because understanding good changes as well 
as bad ones facilitates judgments about the company’s future performance. To 
answer this question, the analyst examines company financial reports as well as 
external information about the industry and economy. In examining the annual 
report, the analyst notes that in the fourth quarter of 2009, the company experi -
enced an “inventory correction” and that the company recorded an allowance for 
the decline in market value and obsolescence of inventory of about 15 percent

of year-  end inventory value (compared with about a 6 percent allowance in the 
prior year). This reduction in the value of inventory accounts for a large portion 
of the decline in DOH from 40.70 in 2008 to 35.68 in 2009. Management claims 
that this inventory obsolescence is a short-  term issue; analysts can watch DOH 
in future interim periods to confirm this assertion. In any event, all else being 
equal, the analyst would likely expect DOH to return to a level closer to 40 days 
going forward.
More positive interpretations can be drawn from the total asset turnover. The 
analyst finds that the company’s revenues increased more than 35 percent while 
total assets only increased by about 6 percent. Based on external information 
about the industry and economy, the analyst attributes the increased revenues 
both to overall growth in the industry and to the company’s increased market 
share. Management was able to achieve growth in revenues with a comparatively

modest increase in assets, leading to an improvement in total asset turnover. 
Note further that part of the reason for the increase in asset turnover is lower 
DOH and DSO.
4.3 Liquidity Ratios
Liquidity analysis, which focuses on cash flows, measures a company’s ability to meet 
its short-  term obligations. Liquidity measures how quickly assets are converted into 
cash. Liquidity ratios also measure the ability to pay off short-  term obligations. In day-  
to- day operations, liquidity management is typically achieved through efficient use of 
assets. In the medium term, liquidity in the non-  financial sector is also addressed by 
managing the structure of liabilities. (See the discussion on financial sector below.)
The level of liquidity needed differs from one industry to another. A particular 
company’s liquidity position may vary according to the anticipated need for funds at 
any given time. Judging whether a company has adequate liquidity requires analysis

of its historical funding requirements, current liquidity position, anticipated future 
funding needs, and options for reducing funding needs or attracting additional funds 
(including actual and potential sources of such funding).
Larger companies are usually better able to control the level and composition 
of their liabilities than smaller companies. Therefore, they may have more potential 
funding sources, including public capital and money markets. Greater discretionary 
access to capital markets also reduces the size of the liquidity buffer needed relative 
to companies without such access.
Contingent liabilities, such as letters of credit or financial guarantees, can also be 
relevant when assessing liquidity. The importance of contingent liabilities varies for 
the non-  banking and banking sector. In the non-  banking sector, contingent liabilities 
(usually disclosed in the footnotes to the company’s financial statements) represent

potential cash outflows, and when appropriate, should be included in an assessment of

Common Ratios Used in Financial Analysis 299
a company’s liquidity. In the banking sector, contingent liabilities represent potentially 
significant cash outflows that are not dependent on the bank’s financial condition. 
Although outflows in normal market circumstances typically may be low, a general 
macroeconomic or market crisis can trigger a substantial increase in cash outflows 
related to contingent liabilities because of the increase in defaults and business 
bankruptcies that often accompany such events. In addition, such crises are usually 
characterized by diminished levels of overall liquidity, which can further exacerbate 
funding shortfalls. Therefore, for the banking sector, the effect of contingent liabilities 
on liquidity warrants particular attention.
4.3.1  Calculation of Liquidity Ratios
Common liquidity ratios are presented in Exhibit 12. These liquidity ratios reflect a 
company’s position at a point in time and, therefore, typically use data from the ending

balance sheet rather than averages. The current, quick, and cash ratios reflect three 
measures of a company’s ability to pay current liabilities. Each uses a progressively 
stricter definition of liquid assets.
The defensive interval ratio  measures how long a company can pay its daily 
cash expenditures using only its existing liquid assets, without additional cash flow 
coming in. This ratio is similar to the “burn rate” often computed for start-  up internet 
companies in the late 1990s or for biotechnology companies. The numerator of this 
ratio includes the same liquid assets used in the quick ratio, and the denominator is 
an estimate of daily cash expenditures. To obtain daily cash expenditures, the total of 
cash expenditures for the period is divided by the number of days in the period. Total 
cash expenditures for a period can be approximated by summing all expenses on the 
income statement—such as cost of goods sold; selling, general, and administrative

expenses; and research and development expenses—and then subtracting any non-  cash 
expenses, such as depreciation and amortisation. (Typically, taxes are not included.)
The cash conversion cycle , a financial metric not in ratio form, measures the 
length of time required for a company to go from cash paid (used in its operations) 
to cash received (as a result of its operations). The cash conversion cycle is sometimes 
expressed as the length of time funds are tied up in working capital. During this period 
of time, the company needs to finance its investment in operations through other 
sources (i.e., through debt or equity).
Exhibit 12   Definitions of Commonly Used Liquidity Ratios
Liquidity Ratios Numerator Denominator
Current ratio Current assets Current liabilities
Quick ratio Cash + Short-  term mar -
ketable investments + 
ReceivablesCurrent liabilities
Cash ratio Cash + Short-  term market -
able investmentsCurrent liabilities
Defensive interval ratio Cash + Short-  term mar -

ReceivablesDaily cash expenditures
Additional Liquidity Measure
Cash conversion cycle  
(net operating cycle)DOH + DSO – Number of days of payables

Reading 26 ■ Financial Analysis Techniques 300
4.3.2  Interpretation of Liquidity Ratios
In the following, we discuss the interpretation of the five basic liquidity measures 
presented in Exhibit 12.
Current Ratio  This ratio expresses current assets in relation to current liabilities. A 
higher ratio indicates a higher level of liquidity (i.e., a greater ability to meet short-  term 
obligations). A current ratio of 1.0 would indicate that the book value of its current 
assets exactly equals the book value of its current liabilities.
A lower ratio indicates less liquidity, implying a greater reliance on operating cash 
flow and outside financing to meet short-  term obligations. Liquidity affects the com -
pany’s capacity to take on debt. The current ratio implicitly assumes that inventories 
and accounts receivable are indeed liquid (which is presumably not the case when 
related turnover ratios are low).
Quick Ratio  The quick ratio is more conservative than the current ratio because it

includes only the more liquid current assets (sometimes referred to as “quick assets”) 
in relation to current liabilities. Like the current ratio, a higher quick ratio indicates 
greater liquidity.
The quick ratio reflects the fact that certain current assets—such as prepaid 
expenses, some taxes, and employee-  related prepayments—represent costs of the 
current period that have been paid in advance and cannot usually be converted back 
into cash. This ratio also reflects the fact that inventory might not be easily and quickly 
converted into cash, and furthermore, that a company would probably not be able to 
sell all of its inventory for an amount equal to its carrying value, especially if it were 
required to sell the inventory quickly. In situations where inventories are illiquid (as 
indicated, for example, by low inventory turnover ratios), the quick ratio may be a 
better indicator of liquidity than is the current ratio.

Cash Ratio  The cash ratio normally represents a reliable measure of an entity’s 
liquidity in a crisis situation. Only highly marketable short-  term investments and cash 
are included. In a general market crisis, the fair value of marketable securities could 
decrease significantly as a result of market factors, in which case even this ratio might 
not provide reliable information.
Defensive Interval Ratio  This ratio measures how long the company can continue to 
pay its expenses from its existing liquid assets without receiving any additional cash 
inflow. A defensive interval ratio of 50 would indicate that the company can continue 
to pay its operating expenses for 50 days before running out of quick assets, assuming 
no additional cash inflows. A higher defensive interval ratio indicates greater liquidity. 
If a company’s defensive interval ratio is very low relative to peer companies or to the 
company’s own history, the analyst would want to ascertain whether there is sufficient

cash inflow expected to mitigate the low defensive interval ratio.
Cash Conversion Cycle (Net Operating Cycle)  This metric indicates the amount of 
time that elapses from the point when a company invests in working capital until the 
point at which the company collects cash. In the typical course of events, a merchan -
dising company acquires inventory on credit, incurring accounts payable. The company 
then sells that inventory on credit, increasing accounts receivable. Afterwards, it pays 
out cash to settle its accounts payable, and it collects cash in settlement of its accounts 
receivable. The time between the outlay of cash and the collection of cash is called 
the “cash conversion cycle. ” A shorter cash conversion cycle indicates greater liquid -
ity. A short cash conversion cycle implies that the company only needs to finance its 
inventory and accounts receivable for a short period of time. A longer cash conversion

cycle indicates lower liquidity; it implies that the company must finance its inventory 
and accounts receivable for a longer period of time, possibly indicating a need for a

Common Ratios Used in Financial Analysis 301
higher level of capital to fund current assets. Example 9 demonstrates the advantages 
of a short cash conversion cycle as well as how a company’s business strategies are 
reflected in financial ratios.
EXAMPLE 9   
Evaluation of Liquidity Measures
An analyst is evaluating the liquidity of Dell and finds that Dell’s 10-  K provides 
a computation of the number of days of receivables, inventory, and accounts 
payable, as well as the overall cash conversion cycle, as follows:
Fiscal Y ear Ended 29 Jan 2010 30 Jan 2009 1 Feb 2008
DSO 38 35 36
DOH 8 7 8
Less: Number of days 
of payables 82 67 80
Equals: Cash conver -
sion cycle (36) (25) (36)
The minimal DOH indicates that Dell maintains lean inventories, which is 
attributable to key aspects of the company’s business model. The company does 
not build a computer until it is ordered and maintains a just-  in- time approach 
to inventory management. In isolation, the increase in number of days payable

(from 67 days in 2009 to 82 days in 2010) might suggest an inability to pay 
suppliers; however, in Dell’s case, the balance sheet indicates that the company 
has more than $10 billion of cash and short-  term investments, which would be 
more than enough to pay suppliers sooner if Dell chose to do so. Instead, Dell 
takes advantage of the favorable credit terms granted by its suppliers. The overall 
effect is a negative cash cycle, a somewhat unusual result. Instead of requiring 
additional capital to fund working capital as is the case for most companies, 
Dell has excess cash to invest for about 37 days (reflected on the balance sheet 
as short-  term investments) on which it is earning, rather than paying, interest.
For comparison, the analyst finds the cash conversion cycle reported in the 
annual reports of two of Dell’s competitors, Lenovo and Hewlett-  Packard:
Fiscal Y ear 2009 2008 2007
Lenovo (30) (23) (28)
Hewlett-  Packard 14 20 24

The analyst notes that of the three, only Hewlett-  Packard has to raise capital 
for working capital purposes. While both Dell and Lenovo have consistently 
negative cash conversion cycles, Lenovo has been slightly less liquid than Dell, 
evidenced by its slightly less negative cash conversion cycle.

Reading 26 ■ Financial Analysis Techniques 302
EXAMPLE 10   
Bounds and Context of Financial Measures
The previous example focused on the cash conversion cycle, which many com -
panies identify as a key performance metric. The less positive the number of 
days in the cash conversion cycle, typically, the better it is considered to be. 
However, is this always true?
This example considers the following question: If a larger negative number 
of days in a cash conversion cycle is considered to be a desirable performance 
metric, does identifying a company with a large negative cash conversion cycle 
necessarily imply good performance?
Using the Compustat database, the company identified as the US computer 
technology company with the most negative number of days in its cash conver -
sion cycle during the 2005 to 2009 period is National Datacomputer Inc., which 
had a negative cash conversion cycle of 275.5 days in 2008.
Exhibit 13   National Datacomputer Inc. ($ millions)

Fiscal year 2004 2005 2006 2007 2008 2009
Sales 3.248 2.672 2.045 1.761 1.820 1.723
Cost of goods sold 1.919 1.491 0.898 1.201 1.316 1.228
Receivables, Total 0.281 0.139 0.099 0.076 0.115 0.045
Inventories, Total 0.194 0.176 0.010 0.002 0.000 0.000
Accounts payable 0.223 0.317 0.366 1.423 0.704 0.674
DSO 28.69 21.24 18.14 19.15 16.95
DOH 45.29 37.80 1.82 0.28 0.00
Less: Number of days of payables* 66.10 138.81 271.85 294.97 204.79
Equals: Cash conversion cycle 7.88 –79.77 –251.89 –275.54 –187.84
*Notes : Calculated using Cost of goods sold as an approximation of purchases. Ending inventories 2008 and 2009 are reported as 
$0 million; therefore, inventory turnover for 2009 cannot be measured. However, given inventory and average sales per day, DOH 
in 2009 is 0.00.
Source:  Raw data from Compustat. Ratios calculated.
The reason for the negative cash conversion cycle is that the company’s 
accounts payable increased substantially over the period. An increase from

approximately 66 days in 2005 to 295 days in 2008 to pay trade creditors is clearly 
a negative signal. In addition, the company’s inventories disappeared, most likely 
because the company did not have enough cash to purchase new inventory and 
was unable to get additional credit from its suppliers.
Of course, an analyst would have immediately noted the negative trends in 
these data, as well as additional data throughout the company’s financial state -
ments. In its MD&A, the company clearly reports the risks as follows:
Because we have historically had losses and only a limited amount 
of cash has been generated from operations, we have funded our 
operating activities to date primarily from the sale of securities and 
from the sale of a product line in 2009. In order to continue to fund 
our operations, we may need to raise additional capital, through the 
sale of securities. We cannot be certain that any such financing will

Common Ratios Used in Financial Analysis 303
be available on acceptable terms, or at all. Moreover, additional equity 
financing, if available, would likely be dilutive to the holders of our 
common stock, and debt financing, if available, would likely involve 
restrictive covenants and a security interest in all or substantially all 
of our assets. If we fail to obtain acceptable financing when needed, 
we may not have sufficient resources to fund our normal operations 
which would have a material adverse effect on our business.
IF WE ARE UNABLE TO GENERATE ADEQUATE WORKING 
CAPITAL FROM OPERATIONS OR RAISE ADDITIONAL CAPITAL 
THERE IS SUBSTANTIAL DOUBT ABOUT THE COMPANY’S 
ABILITY TO CONTINUE AS A GOING CONCERN. (emphasis 
added by company)
Source : National Datacomputer Inc., 2009 Form 10-  K, page 7.
In summary, it is always necessary to consider ratios within bounds of reason -
ability and to understand the reasons underlying changes in ratios. Ratios must

not only be calculated but must also be interpreted by an analyst.
4.4 Solvency Ratios
Solvency  refers to a company’s ability to fulfill its long-  term debt obligations. 
Assessment of a company’s ability to pay its long-  term obligations (i.e., to make interest 
and principal payments) generally includes an in-  depth analysis of the components 
of its financial structure. Solvency ratios provide information regarding the relative 
amount of debt in the company’s capital structure and the adequacy of earnings and 
cash flow to cover interest expenses and other fixed charges (such as lease or rental 
payments) as they come due.
Analysts seek to understand a company’s use of debt for several main reasons. 
One reason is that the amount of debt in a company’s capital structure is important 
for assessing the company’s risk and return characteristics, specifically its financial 
leverage. Leverage is a magnifying effect that results from the use of fixed costs —costs

that stay the same within some range of activity—and can take two forms: operating 
leverage and financial leverage.
Operating leverage  results from the use of fixed costs in conducting the compa -
ny’s business. Operating leverage magnifies the effect of changes in sales on operating 
income. Profitable companies may use operating leverage because when revenues 
increase, with operating leverage, their operating income increases at a faster rate. 
The explanation is that, although variable costs  will rise proportionally with revenue, 
fixed costs will not.
When financing a company (i.e., raising capital for it), the use of debt constitutes 
financial leverage  because interest payments are essentially fixed financing costs. As 
a result of interest payments, a given percent change in EBIT results in a larger per -
cent change in earnings before taxes (EBT). Thus, financial leverage tends to magnify 
the effect of changes in EBIT on returns flowing to equity holders. Assuming that a

company can earn more on funds than it pays in interest, the inclusion of some level 
of debt in a company’s capital structure may lower a company’s overall cost of capital 
and increase returns to equity holders. However, a higher level of debt in a company’s 
capital structure increases the risk of default and results in higher borrowing costs 
for the company to compensate lenders for assuming greater credit risk. Starting with 
Modigliani and Miller (1958, 1963), a substantial amount of research has focused 
on determining a company’s optimal capital structure and the subject remains an 
important one in corporate finance.

Reading 26 ■ Financial Analysis Techniques 304
In analyzing financial statements, an analyst aims to understand levels and trends 
in a company’s use of financial leverage in relation to past practices and the prac -
tices of peer companies. Analysts also need to be aware of the relationship between 
operating leverage (results from the use of non-  current assets with fixed costs) and 
financial leverage (results from the use of long-  term debt with fixed costs). The greater 
a company’s operating leverage, the greater the risk of the operating income stream 
available to cover debt payments; operating leverage can thus limit a company’s 
capacity to use financial leverage.
A company’s relative solvency is fundamental to valuation of its debt securities 
and its creditworthiness. Finally, understanding a company’s use of debt can provide 
analysts with insight into the company’s future business prospects because manage -

ment’s decisions about financing may signal their beliefs about a company’s future. For 
example, the issuance of long-  term debt to repurchase common shares may indicate 
that management believes the market is underestimating the company’s prospects 
and that the shares are undervalued.
4.4.1  Calculation of Solvency Ratios
Solvency ratios are primarily of two types. Debt ratios, the first type, focus on the 
balance sheet and measure the amount of debt capital relative to equity capital. 
Coverage ratios, the second type, focus on the income statement and measure the 
ability of a company to cover its debt payments. These ratios are useful in assessing 
a company’s solvency and, therefore, in evaluating the quality of a company’s bonds 
and other debt obligations.
Exhibit 14 describes commonly used solvency ratios. The first three of the debt 
ratios presented use total debt in the numerator. The definition of total debt used in

these ratios varies among informed analysts and financial data vendors, with some 
using the total of interest-  bearing short-  term and long-  term debt, excluding liabilities 
such as accrued expenses and accounts payable. (For calculations in this reading, we 
use this definition.) Other analysts use definitions that are more inclusive (e.g., all 
liabilities) or restrictive (e.g., long-  term debt only, in which case the ratio is sometimes 
qualified as “long-  term, ” as in “long-  term debt-  to- equity ratio”). If using different 
definitions of total debt materially changes conclusions about a company’s solvency, 
the reasons for the discrepancies warrant further investigation.
Exhibit 14   Definitions of Commonly Used Solvency Ratios
Solvency Ratios Numerator Denominator
Debt Ratios
Debt-  to- assets ratioaTotal debtbTotal assets
Debt-  to- capital ratio Total debtbTotal debtb + Total shareholders’ 
equity
Debt-  to- equity ratio Total debtbTotal shareholders’ equity
Financial leverage

Financial leverage 
ratioAverage total assets Average total equity

Common Ratios Used in Financial Analysis 305
Coverage Ratios
Interest coverage EBIT Interest payments
Fixed charge coverage EBIT + Lease 
paymentsInterest payments + Lease payments
a “Total debt ratio” is another name sometimes used for this ratio.
b In this reading, we take total debt in this context to be the sum of interest-  bearing short-  term 
and long-  term debt.
4.4.2  Interpretation of Solvency Ratios
In the following, we discuss the interpretation of the basic solvency ratios presented 
in Exhibit 14.
Debt-  to- Assets Ratio  This ratio measures the percentage of total assets financed with 
debt. For example, a debt-  to- assets ratio  of 0.40 or 40 percent indicates that 40 percent 
of the company’s assets are financed with debt. Generally, higher debt means higher 
financial risk and thus weaker solvency.
Debt-  to- Capital Ratio  The debt-  to- capital ratio  measures the percentage of a 
company’s capital (debt plus equity) represented by debt. As with the previous ratio, a

higher ratio generally means higher financial risk and thus indicates weaker solvency.
Debt-  to- Equity Ratio  The debt-  to- equity ratio  measures the amount of debt capital 
relative to equity capital. Interpretation is similar to the preceding two ratios (i.e., a 
higher ratio indicates weaker solvency). A ratio of 1.0 would indicate equal amounts of 
debt and equity, which is equivalent to a debt-  to- capital ratio of 50 percent. Alternative 
definitions of this ratio use the market value of stockholders’ equity rather than its book 
value (or use the market values of both stockholders’ equity and debt).
Financial Leverage Ratio  This ratio (often called simply the “leverage ratio”) measures 
the amount of total assets supported for each one money unit of equity. For example, 
a value of 3 for this ratio means that each €1 of equity supports €3 of total assets. The 
higher the financial leverage ratio , the more leveraged the company is in the sense of

using debt and other liabilities to finance assets. This ratio is often defined in terms of 
average total assets and average total equity and plays an important role in the DuPont 
decomposition of return on equity that will be presented in Section 4.6.2.
Interest Coverage  This ratio measures the number of times a company’s EBIT 
could cover its interest payments. Thus, it is sometimes referred to as “times interest 
earned. ” A higher interest coverage  ratio indicates stronger solvency, offering greater 
assurance that the company can service its debt (i.e., bank debt, bonds, notes) from 
operating earnings.
Fixed Charge Coverage  This ratio relates fixed charges, or obligations, to the cash 
flow generated by the company. It measures the number of times a company’s earnings 
(before interest, taxes, and lease payments) can cover the company’s interest and lease 
payments. Similar to the interest coverage ratio, a higher fixed charge coverage  ratio

implies stronger solvency, offering greater assurance that the company can service 
its debt (i.e., bank debt, bonds, notes, and leases) from normal earnings. The ratio is 
sometimes used as an indication of the quality of the preferred dividend, with a higher 
ratio indicating a more secure preferred dividend.Exhibit 14   (Continued)

Reading 26 ■ Financial Analysis Techniques 306
Example 11 demonstrates the use of solvency ratios in evaluating the creditwor -
thiness of a company.
EXAMPLE 11   
Evaluation of Solvency Ratios
A credit analyst is evaluating the solvency of Alcatel-  Lucent as of the beginning 
of 2010. The following data are gathered from the company’s 2009 annual report 
(in € millions):
2009 2008
Total equity 4,309 5,224
Accrued pension 5,043 4,807
Long-  term debt 4,179 3,998
Other long term liabilities* 1,267 1,595
Current liabilities* 9,050 11,687
Total equity + Liabilities (equals Total assets) 23,848 27,311
* For purposes of this example, assume that these items are non-  interest bearing, and that 
long-  term debt equals total debt. In practice, an analyst could refer to Alcatel’s footnotes to 
confirm details, rather than making an assumption.
1 A Calculate the company’s financial leverage ratio for 2009.
B Interpret the financial leverage ratio calculated in Part A.

2 A What are the company’s debt-  to- assets, debt-  to- capital, and debt-  to- 
equity ratios for the two years?
B Is there any discernable trend over the two years?
Solutions to 1:
(Amounts are millions of euro.)
A Average total assets was (27,311 + 23,848)/2 = 25,580 and average 
total equity was (5,224 + 4,309)/2 = 4,767. Thus, financial leverage was 
25,580/4,767 = 5.37.
B For 2009, every €1 in total equity supported €5.37 in total assets, on 
average.
Solutions to 2:
A Debt-  to- assets for 2008 = 3,998/27,311 = 14.64%
 Debt-  to- assets for 2009 = 4,179/23,848 = 17.52%
 Debt-  to- capital for 2008 = 3,998/(3,998 + 5,224) = 43.35%
 Debt-  to- capital for 2009 = 4,179/(4,179 + 4,309) = 49.23%
 Debt-  to- equity for 2008 = 3,998/5,224 = 0.77

Common Ratios Used in Financial Analysis 307
 Debt-  to- equity for 2009 = 4,179/4,309 = 0.97
B On all three metrics, the company’s leverage has increased. The increase 
in debt as part of the company’s capital structure indicates that the 
company’s solvency has weakened. From a creditor’s perspective, lower 
solvency (higher debt) indicates higher risk of default on obligations.
As with all ratio analysis, it is important to consider leverage ratios in a broader 
context. In general, companies with lower business risk and operations that generate 
steady cash flows are better positioned to take on more leverage without a commen -
surate increase in the risk of insolvency. In other words, a higher proportion of debt 
financing poses less risk of non-  payment of interest and debt principal to a company 
with steady cash flows than to a company with volatile cash flows.
4.5 Profitability Ratios
The ability to generate profit on capital invested is a key determinant of a company’s

overall value and the value of the securities it issues. Consequently, many equity ana -
lysts would consider profitability to be a key focus of their analytical efforts.
Profitability reflects a company’s competitive position in the market, and by 
extension, the quality of its management. The income statement reveals the sources 
of earnings and the components of revenue and expenses. Earnings can be distributed 
to shareholders or reinvested in the company. Reinvested earnings enhance solvency 
and provide a cushion against short-  term problems.
4.5.1  Calculation of Profitability Ratios
Profitability ratios measure the return earned by the company during a period. 
Exhibit 15 provides the definitions of a selection of commonly used profitability ratios. 
Return-  on- sales profitability ratios express various subtotals on the income statement 
(e.g., gross profit, operating profit, net profit) as a percentage of revenue. Essentially,

these ratios constitute part of a common-  size income statement discussed earlier. 
Return on investment profitability ratios measure income relative to assets, equity, 
or total capital employed by the company. For operating ROA, returns are measured 
as operating income, i.e., prior to deducting interest on debt capital. For ROA and 
ROE, returns are measured as net income, i.e., after deducting interest paid on debt 
capital. For return on common equity, returns are measured as net income minus 
preferred dividends (because preferred dividends are a return to preferred equity).
Exhibit 15   Definitions of Commonly Used Profitability Ratios
Profitability Ratios Numerator Denominator
Return on Salesa
Gross profit margin Gross profit Revenue
Operating profit margin Operating incomebRevenue
Pretax margin EBT (earnings before tax but 
after interest)Revenue
Net profit margin Net income Revenue

Reading 26 ■ Financial Analysis Techniques 308
Return on Investment
Operating ROA Operating income Average total assets
ROA Net income Average total assets
Return on total capital EBIT Short- and long-  term 
debt and equity
ROE Net income Average total equity
Return on common equity Net income – Preferred 
dividendsAverage common 
equity
a “Sales” is being used as a synonym for “revenue. ”
b Some analysts use EBIT as a shortcut representation of operating income. Note that EBIT, strictly 
speaking, includes non-  operating items such as dividends received and gains and losses on investment 
securities. Of utmost importance is that the analyst compute ratios consistently whether comparing 
different companies or analyzing one company over time.
4.5.2  Interpretation of Profitability Ratios
In the following, we discuss the interpretation of the profitability ratios presented 
in Exhibit  15. For each of the profitability ratios, a higher ratio indicates greater 
profitability.

Gross Profit Margin  Gross profit margin  indicates the percentage of revenue avail -
able to cover operating and other expenses and to generate profit. Higher gross profit 
margin indicates some combination of higher product pricing and lower product costs. 
The ability to charge a higher price is constrained by competition, so gross profits are 
affected by (and usually inversely related to) competition. If a product has a competitive 
advantage (e.g., superior branding, better quality, or exclusive technology), the company 
is better able to charge more for it. On the cost side, higher gross profit margin can also 
indicate that a company has a competitive advantage in product costs.
Operating Profit Margin  Operating profit is calculated as gross profit minus operating 
costs. So, an operating profit margin  increasing faster than the gross profit margin can 
indicate improvements in controlling operating costs, such as administrative overheads.

In contrast, a declining operating profit margin could be an indicator of deteriorating 
control over operating costs.
Pretax Margin  Pretax income (also called “earnings before tax” or “EBT”) is calculated 
as operating profit minus interest, and the pretax margin  is the ratio of pretax income 
to revenue. The pretax margin reflects the effects on profitability of leverage and other 
(non-  operating) income and expenses. If a company’s pretax margin is increasing pri -
marily as a result of increasing amounts of non-  operating income, the analyst should 
evaluate whether this increase reflects a deliberate change in a company’s business 
focus and, therefore, the likelihood that the increase will continue.
Net Profit Margin  Net profit, or net income, is calculated as revenue minus all expenses. 
Net income includes both recurring and non-  recurring components. Generally, the net 
income used in calculating the net profit margin is adjusted for non-  recurring items

to offer a better view of a company’s potential future profitability.Exhibit 15   (Continued)

Common Ratios Used in Financial Analysis 309
ROA  ROA measures the return earned by a company on its assets. The higher the 
ratio, the more income is generated by a given level of assets. Most databases compute 
this ratio as:
Net income
An issue with this computation is that net income is the return to equity holders, 
whereas assets are financed by both equity holders and creditors. Interest expense 
(the return to creditors) has already been subtracted in the numerator. Some analysts, 
therefore, prefer to add back interest expense in the numerator. In such cases, interest 
must be adjusted for income taxes because net income is determined after taxes. With 
this adjustment, the ratio would be computed as:
Net income Interest expens eT ax rat e
Average total as s  +− ()1
eets
Alternatively, some analysts elect to compute ROA on a pre-  interest and pre-  tax basis 
(operating ROA in Exhibit 15) as:
Operating income or EBI T

In this ROA calculation, returns are measured prior to deducting interest on debt 
capital (i.e., as operating income or EBIT). This measure reflects the return on all assets 
invested in the company, whether financed with liabilities, debt, or equity. Whichever 
form of ROA is chosen, the analyst must use it consistently in comparisons to other 
companies or time periods.
Return on Total Capital  Return on total capital  measures the profits a company earns 
on all of the capital that it employs (short-  term debt, long-  term debt, and equity). As 
with operating ROA, returns are measured prior to deducting interest on debt capital 
(i.e., as operating income or EBIT).
ROE  ROE measures the return earned by a company on its equity capital, including 
minority equity, preferred equity, and common equity. As noted, return is measured as 
net income (i.e., interest on debt capital is not included in the return on equity capital).

A variation of ROE is return on common equity, which measures the return earned by 
a company only on its common equity.
Both ROA and ROE are important measures of profitability and will be explored in 
more detail in section 4.6.2. As with other ratios, profitability ratios should be evaluated 
individually and as a group to gain an understanding of what is driving profitability 
(operating versus non-  operating activities). Example 12 demonstrates the evaluation 
of profitability ratios and the use of the management report (sometimes called man -
agement’s discussion and analysis or management commentary) that accompanies 
financial statements to explain the trend in ratios.
EXAMPLE 12   
Evaluation of Profitability Ratios
An analyst is evaluating the profitability of Daimler AG over a five-  year period. 
He gathers the following revenue data and calculates the following profitability 
ratios from information in Daimler’s annual reports:

Reading 26 ■ Financial Analysis Techniques 310
2009 2008 2007 2006 2005
Revenues (€ millions) 78,924 98,469 101,569 99,222 95,209
Gross profit margin 16.92% 21.89% 23.62% 20.60% 19.48%
Operating profit (EBIT) 
margina–1.92% 2.77% 8.58% 5.03% 3.02%
Pretax margin –2.91% 2.84% 9.04% 4.94% 2.55%
Net profit margin –3.35% 1.73% 4.78% 3.19% 2.37%
a EBIT (Earnings before interest and taxes) is the operating profit metric used by Daimler.
Daimler’s revenue declined from 2007 to 2008 and from 2008 to 2009. 
Further, Daimler’s 2009 revenues were the lowest of the five years. Management’s 
discussion of the decline in revenue and EBIT in the 2009 Annual Report notes 
the following:
The main reason for the decline [in EBIT] was a significant drop in 
revenue due to markedly lower unit sales in all vehicle segments as 
a result of the global economic downturn. Cost savings achieved 
through permanent and temporary cost reductions and efficiency 
improvements realized through ongoing optimization programs could

only partially compensate for the drop in revenue.
1 Compare gross profit margins and operating profit margins over the 2005 
to 2009 period.
2 Explain the decline in operating profit margin in 2009.
3 Explain why the pretax margin might have decreased to a greater extent 
than the operating profit margin in 2009.
4 Compare net profit margins and pretax margins over 2007 to 2009
Gross profit margin improved from 2005 to 2007 as a result of some combination 
of price increases and/or cost control. However, gross profit margin declined 
from 2007 to 2009. Operating profit margin showed a similar trend. In 2009, 
the operating profit margin was negative.
The decline in operating profit from 2.77 percent in 2008 to –1.92 percent in 2009 
appears to be the result of Daimler’s operating leverage. Management indicated 
that revenue declined in 2009 and reductions in expenses were not enough to 
offset the revenue decline. Management tried to increase efficiency and reduce

costs, including personnel expenses, but this did not sufficiently counteract 
the decrease in revenues. Expenses thus increased as a proportion of revenue, 
lowering the gross and operating profit margins. This is an example of the effects 
of operating leverage (fixed costs that could not be reduced) on profitability. In 
general, as revenue increases, to the extent that costs remain fixed, operating 
profit margins should increase. As revenue declines, the opposite occurs.
Pretax margin was down substantially in 2009, indicating that the company 
may have had some non-  operating losses or high interest expense in that year. 
A review of the company’s annual report confirms that the cause was higher 
net interest expense. Specifically, the company increased financing liabilities,

Common Ratios Used in Financial Analysis 311
faced higher financing costs because of higher risk premiums on borrowing, and 
had lower interest income on investments. This is an example of the effects of 
financial leverage on profitability.
Solution to 4:
Net profit margin followed the same pattern as pretax margin, increasing from 
2005 to 2007 and then decreasing from 2007 to 2009. In the absence of major 
variation in the applicable tax rates, this would be expected as net profit margin 
is based on net income while pretax margin is based on EBT, and net income 
is EBT(1 – Tax rate).
4.6 Integrated Financial Ratio Analysis
In prior sections, the text presented separately activity, liquidity, solvency, and profit -
ability ratios. Prior to discussing valuation ratios, the following sections demonstrate 
the importance of examining a variety of financial ratios—not a single ratio or category 
of ratios in isolation—to ascertain the overall position and performance of a com -

pany. Experience shows that the information from one ratio category can be helpful 
in answering questions raised by another category and that the most accurate overall 
picture comes from integrating information from all sources. Section 4.6.1 provides 
some introductory examples of such analysis and Section 4.6.2 shows how return on 
equity can be analyzed into components related to profit margin, asset utilization 
(activity), and financial leverage.
4.6.1  The Overall Ratio Picture: Examples
This section presents two simple illustrations to introduce the use of a variety of ratios 
to address an analytical task. Example 13 shows how the analysis of a pair of activity 
ratios resolves an issue concerning a company’s liquidity. Example  14 shows that 
examining the overall ratios of multiple companies can assist an analyst in drawing 
conclusions about their relative performances.
EXAMPLE 13   
A Variety of Ratios
An analyst is evaluating the liquidity of a Canadian manufacturing company

and obtains the following liquidity ratios:
Fiscal Y ear 10 9 8
Current ratio 2.1 1.9 1.6
Quick ratio 0.8 0.9 1.0
The ratios present a contradictory picture of the company’s liquidity. Based 
on the increase in its current ratio from 1.6 to 2.1, the company appears to have 
strong and improving liquidity; however, based on the decline of the quick ratio 
from 1.0 to 0.8, its liquidity appears to be deteriorating. Because both ratios have 
exactly the same denominator, current liabilities, the difference must be the 
result of changes in some asset that is included in the current ratio but not in the 
quick ratio (e.g., inventories). The analyst collects the following activity ratios:
DOH 55 45 30
DSO 24 28 30

Reading 26 ■ Financial Analysis Techniques 312
The company’s DOH has deteriorated from 30 days to 55 days, meaning that the 
company is holding increasingly larger amounts of inventory relative to sales. 
The decrease in DSO implies that the company is collecting receivables faster. If 
the proceeds from these collections were held as cash, there would be no effect 
on either the current ratio or the quick ratio. However, if the proceeds from 
the collections were used to purchase inventory, there would be no effect on 
the current ratio and a decline in the quick ratio (i.e., the pattern shown in this 
example). Collectively, the ratios suggest that liquidity is declining and that the 
company may have an inventory problem that needs to be addressed.
EXAMPLE 14   
A Comparison of Two Companies (1)
An analyst collects the information shown in Exhibit 16 for two companies:
Exhibit 16   
Fiscal Y ear
Anson Industries 5 4 3 2
Inventory turnover 76.69 89.09 147.82 187.64
DOH 4.76 4.10 2.47 1.95

Receivables turnover 10.75 9.33 11.14 7.56
DSO 33.95 39.13 32.77 48.29
Accounts payable turnover 4.62 4.36 4.84 4.22
Days payable 78.97 83.77 75.49 86.56
Cash from operations/Total liabilities 31.41% 11.15% 4.04% 8.81%
ROE 5.92% 1.66% 1.62% –0.62%
ROA 3.70% 1.05% 1.05% –0.39%
Net profit margin (Net income/
Revenue)3.33% 1.11% 1.13% –0.47%
Total asset turnover (Revenue/Average 
assets)1.11 0.95 0.93 0.84
Leverage (Average assets/Average 
equity)1.60 1.58 1.54 1.60
Clarence Corporation 5 4 3 2
Inventory turnover 9.19 9.08 7.52 14.84
DOH 39.73 40.20 48.51 24.59
Receivables turnover 8.35 7.01 6.09 5.16
DSO 43.73 52.03 59.92 70.79
Accounts payable turnover 6.47 6.61 7.66 6.52
Days payable 56.44 55.22 47.64 56.00
Cash from operations/Total liabilities 13.19% 16.39% 15.80% 11.79%
ROE 9.28% 6.82% –3.63% –6.75%

Common Ratios Used in Financial Analysis 313
ROA 4.64% 3.48% –1.76% –3.23%
Revenue)4.38% 3.48% –1.60% –2.34%
assets)1.06 1.00 1.10 1.38
equity)2.00 1.96 2.06 2.09
Which of the following choices best describes reasonable conclusions an analyst 
might make about the companies’ efficiency?
A Over the past four years, Anson has shown greater improvement in effi -
ciency than Clarence, as indicated by its total asset turnover ratio increas -
ing from 0.84 to 1.11.
B In FY5, Anson’s DOH of only 4.76 indicated that it was less efficient at 
inventory management than Clarence, which had DOH of 39.73.
C In FY5, Clarence’s receivables turnover of 8.35 times indicated that it was 
more efficient at receivables management than Anson, which had receiv -
ables turnover of 10.75.
Solution:
A is correct. Over the past four years, Anson has shown greater improvement in

efficiency than Clarence, as indicated by its total asset turnover ratio increasing 
from 0.84 to 1.11. Over the same period of time, Clarence’s total asset turnover 
ratio has declined from 1.38 to 1.06. Choices B and C are incorrect because 
DOH and receivables turnover are misinterpreted.
4.6.2  DuPont Analysis: The Decomposition of ROE
As noted earlier, ROE measures the return a company generates on its equity capital. 
To understand what drives a company’s ROE, a useful technique is to decompose ROE 
into its component parts. (Decomposition of ROE is sometimes referred to as DuPont 
analysis  because it was developed originally at that company.) Decomposing ROE 
involves expressing the basic ratio (i.e., net income divided by average shareholders’ 
equity) as the product of component ratios. Because each of these component ratios 
is an indicator of a distinct aspect of a company’s performance that affects ROE,

the decomposition allows us to evaluate how these different aspects of performance 
affected the company’s profitability as measured by ROE.
Decomposing ROE is useful in determining the reasons for changes in ROE over 
time for a given company and for differences in ROE for different companies in a given 
time period. The information gained can also be used by management to determine 
which areas they should focus on to improve ROE. This decomposition will also show 
why a company’s overall profitability, measured by ROE, is a function of its efficiency, 
operating profitability, taxes, and use of financial leverage. DuPont analysis shows the 
relationship between the various categories of ratios discussed in this reading and 
how they all influence the return to the investment of the owners.Exhibit 16   (Continued)

Reading 26 ■ Financial Analysis Techniques 314
Analysts have developed several different methods of decomposing ROE. The 
decomposition presented here is one of the most commonly used and the one found 
in popular research databases, such as Bloomberg. Return on equity is calculated as:
ROE = Net income/Average shareholders’ equity
The decomposition of ROE makes use of simple algebra and illustrates the relationship 
between ROE and ROA. Expressing ROE as a product of only two of its components, 
we can write:
ROENet income
Average shareholders ' equity
Net income
Avera=
=gge total  assetsAverage total assets
Average shareholders '×  equity
which can be interpreted as:
ROE = ROA × Leverage
In other words, ROE is a function of a company’s ROA and its use of financial leverage 
(“leverage” for short, in this discussion). A company can improve its ROE by improving 
ROA or making more effective use of leverage. Consistent with the definition given

earlier, leverage is measured as average total assets divided by average shareholders’ 
equity. If a company had no leverage (no liabilities), its leverage ratio would equal 
1.0 and ROE would exactly equal ROA. As a company takes on liabilities, its leverage 
increases. As long as a company is able to borrow at a rate lower than the marginal 
rate it can earn investing the borrowed money in its business, the company is mak -
ing an effective use of leverage and ROE would increase as leverage increases. If a 
company’s borrowing cost exceeds the marginal rate it can earn on investing in the 
business, ROE would decline as leverage increased because the effect of borrowing 
would be to depress ROA.
Using the data from Example 14 for Anson Industries, an analyst can examine the 
trend in ROE and determine whether the increase from an ROE of –0.625 percent in 
FY2 to 5.925 percent in FY5 is a function of ROA or the use of leverage:
FY5 5.92% 3.70% 1.60
FY4 1.66% 1.05% 1.58

FY3 1.62% 1.05% 1.54
FY2 –0.62% –0.39% 1.60
Over the four-  year period, the company’s leverage factor was relatively stable. The pri -
mary reason for the increase in ROE is the increase in profitability measured by ROA.
Just as ROE can be decomposed, the individual components such as ROA can be 
decomposed. Further decomposing ROA, we can express ROE as a product of three 
component ratios:
Net income
Average shareholders ' equityNet income
RevenueR=×eevenue
Average sh×aareholders ' equity
ROE = Net profit margin × Total asset turnover × Leverage
The first term on the right-  hand side of this equation is the net profit margin, an 
indicator of profitability: how much income a company derives per one monetary unit 
(e.g., euro or dollar) of sales. The second term on the right is the asset turnover ratio, (1a)
(1b)

Common Ratios Used in Financial Analysis 315
an indicator of efficiency: how much revenue a company generates per one money 
unit of assets. Note that ROA is decomposed into these two components: net profit 
margin and total asset turnover. A company’s ROA is a function of profitability (net 
profit margin) and efficiency (total asset turnover). The third term on the right-  hand 
side of Equation 1b is a measure of financial leverage, an indicator of solvency: the 
total amount of a company’s assets relative to its equity capital. This decomposition 
illustrates that a company’s ROE is a function of its net profit margin, its efficiency, 
and its leverage. Again, using the data from Example 14 for Anson Industries, the 
analyst can evaluate in more detail the reasons behind the trend in ROE:
FY5 5.92% 3.33% 1.11 1.60
FY4 1.66% 1.11% 0.95 1.58
FY3 1.62% 1.13% 0.93 1.54
FY2 –0.62% –0.47% 0.84 1.60

This further decomposition confirms that increases in profitability (measured here 
as net profit margin) are indeed an important contributor to the increase in ROE over 
the four-  year period. However, Anson’s asset turnover has also increased steadily. The 
increase in ROE is, therefore, a function of improving profitability and improving 
efficiency. As noted above, ROE decomposition can also be used to compare the ROEs 
of peer companies, as demonstrated in Example 15.
EXAMPLE 15   
A Comparison of Two Companies (2)
Referring to the data for Anson Industries and Clarence Corporation in 
Example 14, which of the following choices best describes reasonable conclu -
sions an analyst might make about the companies’ ROE?
A Anson’s inventory turnover of 76.69 indicates it is more profitable than 
Clarence.
B The main driver of Clarence’s superior ROE in FY5 is its more efficient 
use of assets.
C The main drivers of Clarence’s superior ROE in FY5 are its greater use of

debt financing and higher net profit margin.
Solution:
C is correct. The main driver of Clarence’s superior ROE (9.28 percent compared 
with only 5.92 percent for Anson) in FY5 is its greater use of debt financing 
(leverage of 2.00 compared with Anson’s leverage of 1.60) and higher net profit 
margin (4.38 percent compared with only 3.33 percent for Anson). A is incorrect 
because inventory turnover is not a direct indicator of profitability. An increase 
in inventory turnover may indicate more efficient use of inventory which in 
turn could affect profitability; however, an increase in inventory turnover would 
also be observed if a company was selling more goods even if it was not selling 
those goods at a profit. B is incorrect because Clarence has less efficient use of 
assets than Anson, indicated by turnover of 1.06 for Clarence compared with 
Anson’s turnover of 1.11.

Reading 26 ■ Financial Analysis Techniques 316
To separate the effects of taxes and interest, we can further decompose the net 
profit margin and write:
Net income
EBTEBT
EB=×IITEBIT
Revenue
Revenue
Average total assetsAverage total ×
××aassets
 ROE = Tax burden × Interest burden × EBIT margin × Total asset turnover × 
Leverage
This five-  way decomposition is the one found in financial databases such as Bloomberg. 
The first term on the right-  hand side of this equation measures the effect of taxes on 
ROE. Essentially, it reflects one minus the average tax rate, or how much of a com -
pany’s pretax profits it gets to keep. This can be expressed in decimal or percentage 
form. So, a 30 percent tax rate would yield a factor of 0.70 or 70 percent. A higher 
value for the tax burden implies that the company can keep a higher percentage of its

pretax profits, indicating a lower tax rate. A decrease in the tax burden ratio implies 
the opposite (i.e., a higher tax rate leaving the company with less of its pretax profits).
The second term on the right-  hand side captures the effect of interest on ROE. 
Higher borrowing costs reduce ROE. Some analysts prefer to use operating income 
instead of EBIT for this term and the following term. Either operating income or 
EBIT is acceptable as long as it is applied consistently. In such a case, the second term 
would measure both the effect of interest expense and non-  operating income on ROE.
The third term on the right-  hand side captures the effect of operating margin (if 
operating income is used in the numerator) or EBIT margin (if EBIT is used) on ROE. 
In either case, this term primarily measures the effect of operating profitability on ROE.
The fourth term on the right-  hand side is again the total asset turnover ratio, an

indicator of the overall efficiency of the company (i.e., how much revenue it generates 
per unit of total assets). The fifth term on the right-  hand side is the financial leverage 
ratio described above—the total amount of a company’s assets relative to its equity 
capital.
This decomposition expresses a company’s ROE as a function of its tax rate, interest 
burden, operating profitability, efficiency, and leverage. An analyst can use this frame -
work to determine what factors are driving a company’s ROE. The decomposition of 
ROE can also be useful in forecasting ROE based upon expected efficiency, profitability, 
financing activities, and tax rates. The relationship of the individual factors, such as 
ROA to the overall ROE, can also be expressed in the form of an ROE tree to study the 
contribution of each of the five factors, as shown in Exhibit 17 for Anson Industries.
Exhibit 17 shows that Anson’s ROE of 5.92 percent in FY5 can be decomposed

into ROA of 3.70 percent and leverage of 1.60. ROA can further be decomposed into 
a net profit margin of 3.33 percent and total asset turnover of 1.11. Net profit margin 
can be decomposed into a tax burden of 0.70 (an average tax rate of 30 percent), an 
interest burden of 0.90, and an EBIT margin of 5.29 percent. Overall ROE is decom -
posed into five components.(1c)

Common Ratios Used in Financial Analysis 317
Exhibit 17   DuPont Analysis of Anson Industries’ ROE: Fiscal Y ear 5
Return on Equity:
Net income
Average shareholders ’ equity
= 5.92%
Return on Assets:
Net income
= 3.7%Leverage:
= 1.60
Net Profit Margin:
Net income
Revenues
= 3.33%Total Asset Turnover:
Revenues
= 1.11
Interest Burden:
EBT
EBIT
= 0.90EBIT Margin:
EBIT
Revenues
= 5.29%Tax Burden:
Net income
EBT
= 0.70
Example 16 demonstrates how the five-  component decomposition can be used to 
determine reasons behind the trend in a company’s ROE.
EXAMPLE 16   
Five-  Way Decomposition of ROE
An analyst examining Royal Dutch Shell PLC wishes to understand the factors 
driving the trend in ROE over a four-  year period. The analyst obtains and cal -
culates the following data from Shell’s annual reports:
2009 2008 2007 2006
ROE 9.53% 20.78% 26.50% 24.72%
Tax burden 60.50% 52.10% 63.12% 58.96%
Interest burden 97.49% 97.73% 97.86% 97.49%

EBIT margina7.56% 11.04% 13.98% 13.98%
Asset turnover 0.99 1.71 1.47 1.44
Leverage 2.15 2.17 2.10 2.14
a Shell’s income statement does not present a separate subtotal for operating income. EBIT 
was calculated as Earnings before taxes plus interest.
What might the analyst conclude?

Reading 26 ■ Financial Analysis Techniques 318
Solution:
The tax burden measure has varied, with no obvious trend. In the most recent 
year, 2009, taxes declined as a percentage of pretax profit. (Because the tax bur -
den reflects the relation of after-  tax profits to pretax profits, the increase from 
52.10 percent in 2008 to 60.50 percent in 2009 indicates that taxes declined as a 
percentage of pretax profits.) This decline in average tax rates could be a result 
of lower tax rates from new legislation or revenue in a lower tax jurisdiction. The 
interest burden has remained fairly constant over the four-  year period indicating 
that the company maintains a fairly constant capital structure. Operating margin 
(EBIT margin) declined over the period, indicating the company’s operations 
were less profitable. This decline is generally consistent with declines in oil prices 
in 2009 and declines in refining industry gross margins in 2008 and 2009. The

company’s efficiency (asset turnover) decreased in 2009. The company’s lever -
age remained constant, consistent with the constant interest burden. Overall, 
the trend in ROE (declining substantially over the recent years) resulted from 
decreases in operating profits and a lower asset turnover. Additional research on 
the causes of these changes is required in order to develop expectations about 
the company’s future performance.
The most detailed decomposition of ROE that we have presented is a five-  way 
decomposition. Nevertheless, an analyst could further decompose individual com -
ponents of a five-  way analysis. For example, EBIT margin (EBIT/Revenue) could be 
further decomposed into a non-  operating component (EBIT/Operating income) and 
an operating component (Operating income/Revenue). The analyst can also examine 
which other factors contributed to these five components. For example, an improve -
ment in efficiency (total asset turnover) may have resulted from better management

of inventory (DOH) or better collection of receivables (DSO).
EQUITY ANALYSIS
One application of financial analysis is to select securities as part of the equity port -
folio management process. Analysts are interested in valuing a security to assess its 
merits for inclusion or retention in a portfolio. The valuation process has several 
steps, including:
1 understanding the business and the existing financial profile
2 forecasting company performance
3 selecting the appropriate valuation model
4 converting forecasts to a valuation
5 making the investment decision
Financial analysis assists in providing the core information to complete the first two 
steps of this valuation process: understanding the business and forecasting performance.
Fundamental equity analysis involves evaluating a company’s performance and 
valuing its equity in order to assess its relative attractiveness as an investment. Analysts 
use a variety of methods to value a company’s equity, including valuation ratios (e.g.,

the price-  to- earnings or P/E ratio), discounted cash flow approaches, and residual 
income approaches (ROE compared with the cost of capital), among others. The 
following section addresses the first of these approaches—the use of valuation ratios.5

Equity Analysis 319
5.1 Valuation Ratios
Valuation ratios have long been used in investment decision making. A well known 
example is the price to earnings ratio  (P/E ratio)—probably the most widely cited 
indicator in discussing the value of equity securities—which relates share price to the 
earnings per share (EPS). Additionally, some analysts use other market multiples, such 
as price to book value (P/B) and price to cash flow (P/CF). The following sections 
explore valuation ratios and other quantities related to valuing equities.
5.1.1  Calculation of Valuation Ratios and Related Quantities
Exhibit 18 describes the calculation of some common valuation ratios and related 
quantities.
Exhibit 18   Definitions of Selected Valuation Ratios and Related Quantities
Valuation Ratios Numerator Denominator
P/E Price per share Earnings per share
P/CF Price per share Cash flow per share
P/S Price per share Sales per share
P/BV Price per share Book value per share

Per-  Share Quantities Numerator Denominator
Basic EPS Net income minus pre -
ferred dividendsWeighted average number of 
ordinary shares outstanding
Diluted EPS Adjusted income avail -
able for ordinary shares, 
reflecting conversion of 
dilutive securitiesWeighted average number of 
ordinary and potential ordi -
nary shares outstanding
Cash flow per share Cash flow from 
operationsWeighted average number of 
shares outstanding
EBITDA per share EBITDA Weighted average number of 
Dividends per share Common dividends 
declaredWeighted average number of 
Dividend-  Related 
Quantities Numerator Denominator
Dividend payout ratio Common share 
dividendsNet income attributable to 
common shares
Retention rate ( b) Net income attributable 
to common shares –Net income attributable to 
Common share 
dividends
Sustainable growth rate b × ROE

dividends
The P/E ratio expresses the relationship between the price per share and the amount 
of earnings attributable to a single share. In other words, the P/E ratio tells us how 
much an investor in common stock pays per dollar of earnings.

Reading 26 ■ Financial Analysis Techniques 320
Because P/E ratios are calculated using net income, the ratios can be sensitive to 
non-  recurring earnings or one-  time earnings events. In addition, because net income 
is generally considered to be more susceptible to manipulation than are cash flows, 
analysts may use price to cash flow  as an alternative measure—particularly in situations 
where earnings quality may be an issue. EBITDA per share, because it is calculated 
using income before interest, taxes, and depreciation, can be used to eliminate the 
effect of different levels of fixed asset investment across companies. It facilitates com -
parison between companies in the same sector but at different stages of infrastructure 
maturity. Price to sales  is calculated in a similar manner and is sometimes used as a 
comparative price metric when a company does not have positive net income.
Another price-  based ratio that facilitates useful comparisons of companies’ stock

prices is price to book value , or P/B, which is the ratio of price to book value per 
share. This ratio is often interpreted as an indicator of market judgment about the 
relationship between a company’s required rate of return and its actual rate of return. 
Assuming that book values reflect the fair values of the assets, a price to book ratio of 
one can be interpreted as an indicator that the company’s future returns are expected 
to be exactly equal to the returns required by the market. A ratio greater than one 
would indicate that the future profitability of the company is expected to exceed the 
required rate of return, and values of this ratio less than one indicate that the company 
is not expected to earn excess returns.
5.1.2  Interpretation of Earnings per Share
Exhibit 18 presented a number of per-  share quantities that can be used in valuation 
ratios. In this section, we discuss the interpretation of one such critical quantity, 
earnings per share or EPS.

EPS is simply the amount of earnings attributable to each share of common stock. 
In isolation, EPS does not provide adequate information for comparison of one com -
pany with another. For example, assume that two companies have only common stock 
outstanding and no dilutive securities outstanding. In addition, assume the two com -
panies have identical net income of $10 million, identical book equity of $100 million 
and, therefore, identical profitability (10 percent, using ending equity in this case for 
simplicity). Furthermore, assume that Company A has 100 million weighted average 
common shares outstanding, whereas Company B has 10 million weighted average 
common shares outstanding. So, Company A will report EPS of $0.10 per share, and 
Company B will report EPS of $1 per share. The difference in EPS does not reflect a 
difference in profitability—the companies have identical profits and profitability. The

difference reflects only a different number of common shares outstanding. Analysts 
should understand in detail the types of EPS information that companies report:
Basic EPS  provides information regarding the earnings attributable to each share 
of common stock. To calculate basic EPS, the weighted average number of shares 
outstanding during the period is first calculated. The weighted average number of 
shares consists of the number of ordinary shares outstanding at the beginning of the 
period, adjusted by those bought back or issued during the period, multiplied by a 
time-  weighting factor.
Accounting standards generally require the disclosure of basic as well as diluted 
EPS (diluted EPS includes the effect of all the company’s securities whose conversion 
or exercise would result in a reduction of basic EPS; dilutive securities include con -
vertible debt, convertible preferred, warrants, and options). Basic EPS and diluted

EPS must be shown with equal prominence on the face of the income statement for 
each class of ordinary share. Disclosure includes the amounts used as the numera -
tors in calculating basic and diluted EPS, and a reconciliation of those amounts to 
the company’s profit or loss for the period. Because both basic and diluted EPS are

Equity Analysis 321
presented in a company’s financial statements, an analyst does not need to calculate 
these measures for reported financial statements. Understanding the calculations is, 
however, helpful for situations requiring an analyst to calculate expected future EPS.
To calculate diluted EPS, earnings are adjusted for the after-  tax effects assuming 
conversion, and the following adjustments are made to the weighted number of shares:
■■The weighted average number of shares for basic EPS, plus those that would be 
issued on conversion of all dilutive potential ordinary shares. Potential ordinary 
shares are treated as dilutive when their conversion would decrease net profit 
per share from continuing ordinary operations.
■■These shares are deemed to have been converted into ordinary shares at the 
beginning of the period or, if later, at the date of the issue of the shares.
■■Options, warrants (and their equivalents), convertible instruments, contingently

issuable shares, contracts that can be settled in ordinary shares or cash, pur -
chased options, and written put options should be considered.
5.1.3  Dividend-  Related Quantities
In this section, we discuss the interpretation of the dividend-  related quantities pre -
sented in Exhibit 18. These quantities play a role in some present value models for 
valuing equities.
Dividend Payout Ratio  The dividend payout ratio  measures the percentage of earn -
ings that the company pays out as dividends to shareholders. The amount of dividends 
per share tends to be relatively fixed because any reduction in dividends has been 
shown to result in a disproportionately large reduction in share price. Because dividend 
amounts are relatively fixed, the dividend payout ratio tends to fluctuate with earnings. 
Therefore, conclusions about a company’s dividend payout policies should be based 
on examination of payout over a number of periods. Optimal dividend policy, similar

to optimal capital structure, has been examined in academic research and continues 
to be a topic of significant interest in corporate finance.
Retention Rate  The retention rate, or earnings retention rate, is the complement of 
the payout ratio or dividend payout ratio (i.e., 1 – payout ratio). Whereas the payout 
ratio measures the percentage of earnings that a company pays out as dividends, the 
retention rate is the percentage of earnings that a company retains. (Note that both 
the payout ratio and retention rate are both percentages of earnings. The difference in 
terminology—“ratio” versus “rate” versus “percentage”—reflects common usage rather 
than any substantive differences.)
Sustainable Growth Rate  A company’s sustainable growth rate  is viewed as a func -
tion of its profitability (measured as ROE) and its ability to finance itself from internally 
generated funds (measured as the retention rate). The sustainable growth rate is ROE

times the retention rate. A higher ROE and a higher retention rate result in a higher 
sustainable growth rate. This calculation can be used to estimate a company’s growth 
rate, a factor commonly used in equity valuation.
5.2 Industry-  Specific Ratios
As stated earlier in this reading, a universally accepted definition and classification of 
ratios does not exist. The purpose of ratios is to serve as indicators of important aspects 
of a company’s performance and value. Aspects of performance that are considered 
important in one industry may be irrelevant in another, and industry-  specific ratios 
reflect these differences. For example, companies in the retail industry may report 
same-  store sales changes because, in the retail industry, it is important to distinguish

Reading 26 ■ Financial Analysis Techniques 322
between growth that results from opening new stores and growth that results from 
generating more sales at existing stores. Industry-  specific metrics can be especially 
important to the value of equity in early stage industries, where companies are not 
yet profitable.
In addition, regulated industries—especially in the financial sector—often are 
required to comply with specific regulatory ratios. For example, the banking sector’s 
liquidity and cash reserve ratios provide an indication of banking liquidity and reflect 
monetary and regulatory requirements. Banking capital adequacy requirements attempt 
to relate banks’ solvency requirements directly to their specific levels of risk exposure.
Exhibit  19 presents, for illustrative purposes only, some industry-  specific and 
task-  specific ratios.
Exhibit 19   Definitions of Some Common Industry- and Task-  Specific Ratios
Ratio Numerator Denominator
Business Risk
Coefficient of variation of

Coefficient of variation of 
operating incomeStandard deviation of 
operating incomeAverage operating income
net incomeStandard deviation of net 
incomeAverage net income
revenuesStandard deviation of 
revenueAverage revenue
Financial Sector Ratios Numerator Denominator
Capital adequacy—banks Various components of 
capitalVarious measures such 
as risk-  weighted assets, 
market risk exposure, or 
level of operational risk 
assumed
Monetary reserve require -
ment (Cash reserve ratio)Reserves held at central 
bankSpecified deposit liabilities
Liquid asset requirement Approved “readily market -
able” securitiesSpecified deposit liabilities
Net interest margin Net interest income Total interest-  earning 
assets
Retail Ratios Numerator Denominator
Same (or comparable) store 
salesAverage revenue growth 
year over year for stores 
open in both periodsNot applicable
Sales per square meter (or 
square foot)Revenue Total retail space in

square foot)Revenue Total retail space in 
square meters (or square 
feet)
Service Companies Numerator Denominator
Revenue per employee Revenue Total number of 
employees
Net income per employee Net income Total number of 
employees

Equity Analysis 323
Hotel Numerator Denominator
Average daily rate Room revenue Number of rooms sold
Occupancy rate Number of rooms sold Number of rooms 
available
5.3 Research on Ratios in Equity Analysis
Some ratios may be particularly useful in equity analysis. The end product of equity 
analysis is often a valuation and investment recommendation. Theoretical valuation 
models are useful in selecting ratios that would be useful in this process. For exam -
ple, a company’s P/B is theoretically linked to ROE, growth, and the required return. 
ROE is also a primary determinant of residual income in a residual income valuation 
model. In both cases, higher ROE relative to the required return denotes a higher 
valuation. Similarly, profit margin is related to justified price-  to- sales (P/S) ratios. 
Another common valuation method involves forecasts of future cash flows that are 
discounted back to the present. Trends in ratios can be useful in forecasting future

earnings and cash flows (e.g., trends in operating profit margin and collection of cus -
tomer receivables). Future growth expectations are a key component of all of these 
valuation models. Trends may be useful in assessing growth prospects (when used 
in conjunction with overall economic and industry trends). The variability in ratios 
and common-  size data can be useful in assessing risk, an important component of 
the required rate of return in valuation models. A great deal of academic research 
has focused on the use of these fundamental ratios in evaluating equity investments.
A classic study, Ou and Penman (1989a and 1989b), found that ratios and common-  
size metrics generated from accounting data were useful in forecasting earnings and 
stock returns. Ou and Penman examined 68 such metrics and found that these could 
be reduced to a more parsimonious list of relevant variables, including percentage

changes in a variety of measures such as current ratio, inventory, and sales; gross and 
pretax margins; and returns on assets and equity. These variables were found to be 
useful in forecasting earnings and stock returns.
Subsequent studies have also demonstrated the usefulness of ratios in evaluation of 
equity investments and valuation. Lev and Thiagarajan (1993) examined fundamental 
financial variables used by analysts to assess whether they are useful in security valu -
ation. They found that fundamental variables add about 70 percent to the explanatory 
power of earnings alone in predicting excess returns (stock returns in excess of those 
expected). The fundamental variables they found useful included percentage changes 
in inventory and receivables relative to sales, gross margin, sales per employee, and 
the change in bad debts relative to the change in accounts receivable, among others. 
Abarbanell and Bushee (1997) found some of the same variables useful in predicting

future accounting earnings. Abarbanell and Bushee (1998) devised an investment 
strategy using these same variables and found that they can generate excess returns 
under this strategy.
Piotroski (2000) used financial ratios to supplement a value investing strategy 
and found that he can generate significant excess returns. Variables used by Piotroski 
include ROA, cash flow ROA, change in ROA, change in leverage, change in liquidity, 
change in gross margin, and change in inventory turnover.
This research shows that in addition to being useful in evaluating the past per -
formance of a company, ratios can be useful in predicting future earnings and equity 
returns.Exhibit 19   (Continued)

Reading 26 ■ Financial Analysis Techniques 324
CREDIT ANALYSIS
Credit risk  is the risk of loss caused by a counterparty’s or debtor’s failure to make a 
promised payment. For example, credit risk with respect to a bond is the risk that the 
obligor (the issuer of the bond) is not able to pay interest and principal according to the 
terms of the bond indenture (contract). Credit analysis  is the evaluation of credit risk.
Approaches to credit analysis vary and, as with all financial analysis, depend on 
the purpose of the analysis and the context in which it is done. Credit analysis for 
specific types of debt (e.g., acquisition financing and other highly leveraged financing) 
often involves projections of period-  by- period cash flows similar to projections made 
by equity analysts. Whereas the equity analyst may discount projected cash flows to 
determine the value of the company’s equity, a credit analyst would use the projected

cash flows to assess the likelihood of a company complying with its financial cove -
nants in each period and paying interest and principal as due. The analysis would also 
include expectations about asset sales and refinancing options open to the company.
Credit analysis may relate to the borrower’s credit risk in a particular transaction 
or to its overall creditworthiness. In assessing overall creditworthiness, one general 
approach is credit scoring, a statistical analysis of the determinants of credit default.
Another general approach to credit analysis is the credit rating process that is 
used, for example, by credit rating agencies to assess and communicate the probabil -
ity of default by an issuer on its debt obligations (e.g., commercial paper, notes, and 
bonds). A credit rating can be either long term or short term and is an indication of 
the rating agency’s opinion of the creditworthiness of a debt issuer with respect to a

specific debt security or other obligation. Where a company has no debt outstanding, 
a rating agency can also provide an issuer credit rating that expresses an opinion of 
the issuer’s overall capacity and willingness to meet its financial obligations. The fol -
lowing sections review research on the use of ratios in credit analysis and the ratios 
commonly used in credit analysis.
6.1 The Credit Rating Process
The rating process involves both the analysis of a company’s financial reports as well 
as a broad assessment of a company’s operations. The credit evaluation process by 
any analyst includes many of the following procedures performed by analysts at credit 
rating agencies:
■■Meeting with management, typically including the chief financial officer, to 
discuss, for example, industry outlook, overview of major business segments, 
financial policies and goals, distinctive accounting practices, capital spending 
plans, and financial contingency plans.

■■Tours of major facilities, time permitting.
■■Meeting of a ratings committee where the analyst’s recommendations are voted 
on, after considering factors that include:
■●Business risk, including the evaluation of:
 ■operating environment;
 ■industry characteristics (e.g., cyclicality and capital intensity);
 ■success factors and areas of vulnerability; and
 ■company’s competitive position, including size and diversification.
■●Financial risk, including:
 ■the evaluation of capital structure, interest coverage, and profitability 
using ratio analysis, and6

Credit Analysis 325
 ■the examination of debt covenants.
■●Evaluation of management.
■■Monitoring of publicly distributed ratings—including reconsideration of ratings 
due to changing conditions.
In assigning credit ratings, rating agencies emphasize the importance of the relation -
ship between a company’s business risk profile and its financial risk. “The company’s 
business risk profile determines the level of financial risk appropriate for any rating 
category. ”19
When analyzing financial ratios, rating agencies normally investigate deviations of 
ratios from the median ratios of the universe of companies for which such ratios have 
been calculated and also use the median ratings as an indicator for the ratings grade 
given to a specific debt issuer. This so-  called universe of rated companies changes 
constantly, and any calculations are obviously affected by economic factors as well as 
by mergers and acquisitions. International ratings include the influence of country

and economic risk factors. Exhibit 20 presents key financial ratios used by Standard 
& Poor’s in evaluating industrial companies. Note that before calculating ratios, rating 
agencies make certain adjustments to reported financials such as adjusting debt to 
include off-  balance sheet debt in a company’s total debt.
Exhibit 20   Selected Credit Ratios Used by Standard & Poor’s
Credit Ratio NumeratorbDenominatorc
EBIT interest coverage EBIT Gross interest (prior to deductions 
for capitalized interest or interest 
income)
EBITDA interest coverage EBITDA Gross interest (prior to deductions 
income)
FFOa (Funds from operations) 
interest coverageFFO plus interest 
paid, minus 
operating lease 
adjustmentsGross interest (prior to deductions 
income)
Return on capital EBIT Average capital, where capital = 
equity, plus non-  current deferred 
taxes, plus debt
FFO (Funds from operations) 
to debtFFO Total debt

Free operating cash flow to 
debtCFO (adjusted) 
minus capital 
expendituresTotal debt
Discretionary cash flow to 
debtCFO minus cap -
ital expenditures 
minus dividends 
paidTotal debt
Net cash flow to capital 
expendituresFFO minus 
dividendsCapital expenditures

Reading 26 ■ Financial Analysis Techniques 326
Debt to EBITDA Total debt EBITDA
Total debt to total debt plus 
equityTotal debt Total debt plus equity
a FFO = funds from operations, defined as net income adjusted for non-  cash items; CFO = cash 
flow from operations.
b Emphasis is on earnings from continuing  operations.
c Note that both the numerator and denominator definitions are adjusted from ratio to ratio and 
may not correspond to the definitions used elsewhere in this reading.
Source:  Based on data from Standard & Poor’s Corporate Ratings Criteria  (2008), p. 52.
6.2 Research on Ratios in Credit Analysis
A great deal of academic and practitioner research has focused on determining 
which ratios are useful in assessing the credit risk of a company, including the risk 
of bankruptcy.
One of the earliest studies examined individual ratios to assess their ability to 
predict failure of a company up to five years in advance. Beaver (1967) found that six

ratios could correctly predict company failure one year in advance 90 percent of the 
time and five years in advance at least 65 percent of the time. The ratios found effective 
by Beaver were cash flow to total debt, ROA, total debt to total assets, working capital 
to total assets, the current ratio, and the no-  credit interval ratio (the length of time a 
company could go without borrowing). Altman (1968) and Altman, Haldeman, and 
Narayanan (1977) found that financial ratios could be combined in an effective model 
for predicting bankruptcy. Altman’s initial work involved creation of a Z-score that 
was able to correctly predict financial distress. The Z-score was computed as
Z= 1.2 × (Current assets – Current liabilities)/Total assets
  + 1.4 × (Retained earnings/Total assets)
  + 3.3 × (EBIT/Total assets)
  + 0.6 × (Market value of stock/Book value of liabilities)
  + 1.0 × (Sales/Total assets)
In his initial study, a Z-score of lower than 1.81 predicted failure and the model was

able to accurately classify 95 percent of companies studied into a failure group and 
a non-  failure group. The original model was designed for manufacturing companies. 
Subsequent refinements to the models allow for other company types and time peri -
ods. Generally, the variables found to be useful in prediction include profitability 
ratios, coverage ratios, liquidity ratios, capitalization ratios, and earnings variability 
(Altman 2000).
Similar research has been performed on the ability of ratios to predict bond ratings 
and bond yields. For example, Ederington, Yawtiz, and Roberts (1987) found that a 
small number of variables (total assets, interest coverage, leverage, variability of cov -
erage, and subordination status) were effective in explaining bond yields. Similarly, 
Ederington (1986) found that nine variables in combination could correctly classify 
more than 70  percent of bond ratings. These variables included ROA, long-  term

debt to assets, interest coverage, cash flow to debt, variability of coverage and cash 
flow, total assets, and subordination status. These studies have shown that ratios are 
effective in evaluating credit risk, bond yields, and bond ratings.Exhibit 20   (Continued)

Business and Geographic Segments 327
BUSINESS AND GEOGRAPHIC SEGMENTS
Analysts often need to evaluate the performance underlying business segments 
(subsidiary companies, operating units, or simply operations in different geographic 
areas) to understand in detail the company as a whole. Although companies are not 
required to provide full financial statements for segments, they are required to provide 
segment information under both IFRS and US GAAP .
7.1 Segment Reporting Requirements
An operating segment is defined as a component of a company: a) that engages in 
activities that may generate revenue and create expenses, including a start-  up segment 
that has yet to earn revenues, b) whose results are regularly reviewed by the compa -
ny’s senior management, and c) for which discrete financial information is available. 
A company must disclose separate information about any operating segment which 
meets certain quantitative criteria—namely, the segment constitutes 10 percent or

more of the combined operating segments’ revenue, assets, or profit. (For purposes 
of determining whether a segment constitutes 10 percent or more of combined prof -
its or losses, the criteria is expressed in terms of the absolute value of the segment’s 
profit or loss as a percentage of the greater of (i) the combined profits of all profitable 
segments and (ii) the absolute amount of the combined losses of all loss-  making 
segments.) If, after applying these quantitative criteria, the combined revenue from 
external customers for all reportable segments combined is less than 75 percent of 
the total company revenue, the company must identify additional reportable segments 
until the 75 percent level is reached. Small segments might be combined as one if they 
share a substantial number of factors that define a business or geographical segment, 
or they might be combined with a similar significant reportable segment. Information

about operating segments and businesses that are not reportable is combined in an 
“all other segments” category.
Companies may internally report business results in a variety of ways (e.g., product 
segments and geographical segments). Companies identify the segments for external 
reporting purposes considering the definition of an operating segment and using 
factors such as what information is reported to the board of directors and whether a 
manager is responsible for each segment. Companies must disclose the factors used 
to identify reportable segments and the types of products and services sold by each 
reportable segment.
For each reportable segment, the following should also be disclosed:
■■a measure of profit or loss;
■■a measure of total assets and liabilities (if these amounts are regularly reviewed 
by the company’s chief decision-  making officer);
■■segment revenue, distinguishing between revenue to external customers and 
revenue from other segments;

■■interest revenue and interest expense;
■■cost of property, plant, and equipment, and intangible assets acquired;
■■depreciation and amortisation expense;
■■other non-  cash expenses;
■■income tax expense or income; and
■■share of the net profit or loss of an investment accounted for under the equity 
method.7

Reading 26 ■ Financial Analysis Techniques 328
Companies also must provide a reconciliation between the information of reportable 
segments and the consolidated financial statements in terms of segment revenue, 
profit or loss, assets, and liabilities.
Another disclosure required is the company’s reliance on any single customer. If 
any single customer represents 10 percent or more of the company’s total revenues, the 
company must disclose that fact. From an analysts’ perspective, information about a 
concentrated customer base can be useful in assessing the risks faced by the company.
7.2 Segment Ratios
Based on the segment information that companies are required to present, a variety 
of useful ratios can be computed, as shown in Exhibit 21.
Exhibit 21   Definitions of Segment Ratios
Segment Ratios Numerator Denominator
Segment margin Segment profit (loss) Segment revenue
Segment turnover Segment revenue Segment assets
Segment ROA Segment profit (loss) Segment assets

Segment debt ratio Segment liabilities Segment assets
The segment margin measures the operating profitability of the segment relative to 
revenues, whereas the segment ROA measures the operating profitability relative to 
assets. Segment turnover measures the overall efficiency of the segment: how much 
revenue is generated per unit of assets. The segment debt ratio examines the level of 
liabilities (hence solvency) of the segment. Example 17 demonstrates the evaluation 
of segment ratios.
EXAMPLE 17   
The Evaluation of Segment Ratios
The information contained in Exhibit  22 relates to the business segments of 
Groupe Danone for 2008 and 2009 in millions of euro. According to the com -
pany’s 2009 annual report:
Over the course of the past 10 years, the Group has refocused its 
activities on the health food industry. On October 31, 2007, the acqui -
sition of Royal Numico N.V. and its subsidiaries (“Numico”), a group

specialized in baby nutrition and medical nutrition, marked a new 
phase in the Group’s development by adding these lines of business 
to Danone’s portfolio. The Group has since operated in four markets 
corresponding to its four business lines: (i) Fresh Dairy Products, (ii) 
Waters, (iii) Baby Nutrition, and (iv) Medical Nutrition.
Evaluate the performance of the segments using the segment margin, segment 
ROA, and segment turnover.

Business and Geographic Segments 329
Exhibit 22   
2009 2008
(In € millions) Revenue  
(3rd party)Operating  
income AssetsRevenue  
income Assets
Fresh Dairy Products 8,555 1,240 7,843 8,697 1,187 7,145
Waters 2,578 646 2,773 2,874 323 3,426
Baby Nutrition 2,924 547 10,203 2,795 462 9,999
Medical Nutrition 925 190 4,781 854 217 4,450
Business Line Total 14,982 2,623 25,600 15,220 2,189 25,020
Segment Ratios
2009 2008
Segment  
Revenue  
as percent  
of totalSegment  
MarginSegment  
ROAaSegment  
TurnoverSegment  
Revenue  
as 
percent  
Turnover
Fresh Dairy 
Products57.1% 14.5% 15.8% 1.1 57.1% 13.6% 16.6% 1.2
Waters 17.2% 25.1% 23.3% 0.9 18.9% 11.2% 9.4% 0.8
Baby 
Nutrition19.5% 18.7% 5.4% 0.3 18.4% 16.5% 4.6% 0.3
Medical 
Nutrition6.2% 20.5% 4.0% 0.2 5.6% 25.4% 4.9% 0.2
a As used in this table, ROA refers to operating income divided by ending assets.
Solution:
The waters segment (Evian and Volvic) was the most profitable in 2009 as mea -

sured by margin and ROA; however, in 2009 the segment did not grow as fast as 
the company’s other segments. In 2008, the segment represented 18.9 percent 
of total segment revenues, but in 2009 the percentage was only 17.2 percent.
The company’s largest segment by revenue, fresh dairy products had the 
lowest margin in 2009 but a much higher segment ROA than the baby and 
medical nutrition segments. Medical nutrition is the second highest segment in 
terms of segment margin but lowest in turnover (an indicator of efficiency, i.e., 
the ability to generate revenue from assets). As a result, medical nutrition had 
the lowest segment ROA (Segment ROA = Segment operating income/Segment 
assets = (Segment operating income/Segment revenue) × (Segment revenue/
Segment Assets) = Segment margin × Segment turnover. Reported percentages 
may differ due to rounding). Part of the explanation for segment differences in 
ROA may be that the medical and baby nutrition businesses were acquired in

2007. In an acquisition, the acquiring company reports the acquired assets at 
fair value at the time of the acquisition. Most of a company’s other assets are 
reported at historical costs, and over time, most long-  term assets are depreciated. 
Thus, compared to assets in other segments, it is likely that the assets of the 
nutrition segments are reported at amounts more reflective of current prices.

Reading 26 ■ Financial Analysis Techniques 330
MODEL BUILDING AND FORECASTING
Analysts often need to forecast future financial performance. For example, EPS 
forecasts of analysts are widely followed by Wall Street. Analysts use data about the 
economy, industry, and company in arriving at a company’s forecast. The results of 
an analyst’s financial analysis, including common-  size and ratio analyses, are integral 
to this process, along with the judgment of the analysts.
Based upon forecasts of growth and expected relationships among the financial 
statement data, the analyst can build a model (sometimes referred to as an “earnings 
model”) to forecast future performance. In addition to budgets, pro forma financial 
statements are widely used in financial forecasting within companies, especially for 
use by senior executives and boards of directors. Last but not least, these budgets 
and forecasts are also used in presentations to credit analysts and others in obtaining 
external financing.

For example, based on a revenue forecast, an analyst may budget expenses based 
on expected common-  size data. Forecasts of balance sheet and cash flow statements 
can be derived from expected ratio data, such as DSO. Forecasts are not limited to 
a single point estimate but should involve a range of possibilities. This can involve 
several techniques:
■■Sensitivity analysis : Also known as “what if” analysis, sensitivity analysis 
shows the range of possible outcomes as specific assumptions are changed; this 
could, in turn, influence financing needs or investment in fixed assets.
■■Scenario analysis : This type of analysis shows the changes in key financial 
quantities that result from given (economic) events, such as the loss of cus -
tomers, the loss of a supply source, or a catastrophic event. If the list of events 
is mutually exclusive and exhaustive and the events can be assigned probabili -

ties, the analyst can evaluate not only the range of outcomes but also standard 
statistical measures such as the mean and median value for various quantities of 
interest.
■■Simulation : This is computer-  generated sensitivity or scenario analysis based 
on probability models for the factors that drive outcomes. Each event or possi -
ble outcome is assigned a probability. Multiple scenarios are then run using the 
probability factors assigned to the possible values of a variable.
SUMMARY
Financial analysis techniques, including common-  size and ratio analysis, are useful in 
summarizing financial reporting data and evaluating the performance and financial 
position of a company. The results of financial analysis techniques provide important 
inputs into security valuation. Key facets of financial analysis include the following:
■■Common-  size financial statements and financial ratios remove the effect of 
size, allowing comparisons of a company with peer companies (cross-  sectional

analysis) and comparison of a company’s results over time (trend or time-  series 
analysis).8

References 331
Abarbanell, J.S., and B. J. Bushee. 1997. “Fundamental Analysis, 
Future Earnings, and Stock Prices. ” Journal of Accounting 
Research , vol. 35, no. 1:1–24. 
Abarbanell, J.S., and B.J. Bushee. 1998. “ Abnormal Returns to a 
Fundamental Analysis Strategy. ” Accounting Review , vol. 73, 
no. 1:19–46.
Altman, E. 1968. “Financial Ratios, Discriminant Analysis and 
the Prediction of Corporate Bankruptcy. ” Journal of Finance , 
vol. 23, no. 4:589–609. 
Altman, E.I. 2013, “Predicting Financial Distress of Companies: 
Revisiting the Z-Score and Zeta Models, ” in Prokopczuk, 
Marcel; Brooks, Chris; Bell, Adrian R., Handbook of Research 
Methods and Applications in Empirical Finance : 428-456.
Altman, E., R. Haldeman, and P . Narayanan. 1977. “Zeta Analysis: 
A New Model to Identify Bankruptcy Risk of Corporations. ” 
Journal of Banking & Finance , vol. 1, no. 1. Beaver, W. 1967. “Financial Ratios as Predictors of Failures. ”

Empirical Research in Accounting , selected studies supple -
ment to Journal of Accounting Research , 4 (1).
Ederington, L.H. 1986. “Why Split Ratings Occur. ” Financial 
Management , vol. 15, no. 1:37–47. 
Ederington, L.H., J.B. Yawitz, and B.E. Robert. 1987. “The 
Information Content of Bond Ratings. ” Journal of Financial 
Research , vol. 10, no. 3:211–226.
Lev, B., and S.R. Thiagarajan. 1993. “Fundamental Information 
Analysis. ” Journal of Accounting Research , vol. 31, no. 
2:190–215. 
Modigliani, F., and M. Miller. 1958. “The Cost of Capital, 
Corporation Finance and the Theory of Investment. ” American 
Economic Review , vol. 48:261–298.■■Activity ratios measure the efficiency of a company’s operations, such as col -
lection of receivables or management of inventory. Major activity ratios include

inventory turnover, days of inventory on hand, receivables turnover, days of 
sales outstanding, payables turnover, number of days of payables, working capi -
tal turnover, fixed asset turnover, and total asset turnover.
■■Liquidity ratios measure the ability of a company to meet short-  term obliga -
tions. Major liquidity ratios include the current ratio, quick ratio, cash ratio, 
and defensive interval ratio.
■■Solvency ratios measure the ability of a company to meet long-  term obligations. 
Major solvency ratios include debt ratios (including the debt-  to- assets ratio, 
debt-  to- capital ratio, debt-  to- equity ratio, and financial leverage ratio) and cov -
erage ratios (including interest coverage and fixed charge coverage).
■■Profitability ratios measure the ability of a company to generate profits from 
revenue and assets. Major profitability ratios include return on sales ratios 
(including gross profit margin, operating profit margin, pretax margin, and net

profit margin) and return on investment ratios (including operating ROA, ROA, 
return on total capital, ROE, and return on common equity).
■■Ratios can also be combined and evaluated as a group to better understand how 
they fit together and how efficiency and leverage are tied to profitability.
■■ROE can be analyzed as the product of the net profit margin, asset turnover, 
and financial leverage. This decomposition is sometimes referred to as DuPont 
analysis.
■■Valuation ratios express the relation between the market value of a company or 
its equity (for example, price per share) and some fundamental financial metric 
(for example, earnings per share).
■■Ratio analysis is useful in the selection and valuation of debt and equity securi -
ties and is a part of the credit rating process.
■■Ratios can also be computed for business segments to evaluate how units within 
a business are performing.
■■The results of financial analysis provide valuable inputs into forecasts of future

Reading 26 ■ Financial Analysis Techniques 332
Modigliani, F., and M. Miller. 1963. “Corporate Income Taxes 
and the Cost of Capital: A Correction. ” American Economic 
Review , vol. 53:433–444.
Ou, J.A., and S.H. Penman. 1989a. “Financial Statement Analysis 
and the Prediction of Stock Returns. ” Journal of Accounting 
and Economics , vol. 11, no. 4:295–329. 
Ou, J.A., and S.H. Penman. 1989b. “ Accounting Measurement, 
Price-  Earnings Ratio, and the Information Content of 
Security Prices. ” Journal of Accounting Research , vol. 27, no. 
Supplement:111–144. Piotroski, J.D. 2000. “Value Investing: The Use of Historical 
Financial Statement Information to Separate Winners 
from Losers. ” Journal of Accounting Research , vol. 38, no. 
Supplement:1–41. 
Robinson, T., and P . Munter. 2004. “Financial Reporting Quality: 
Red Flags and Accounting Warning Signs. ” Commercial 
Lending Review , vol. 19, no. 1:2–15.
van Greuning, H., and S. Brajovic Bratanovic. 2003. Analyzing

and Managing Banking Risk: A Framework for Assessing 
Corporate Governance and Financial Risk . Washington, DC: 
World Bank.

Practice Problems 333
1 Comparison of a company’s financial results to other peer companies for the 
same time period is called:
A technical analysis.
B time-  series analysis.
C cross-  sectional analysis.
2 In order to assess a company’s ability to fulfill its long-  term obligations, an ana -
lyst would most likely  examine:
A activity ratios.
B liquidity ratios.
C solvency ratios.
3 Which ratio would a company most likely  use to measure its ability to meet 
short-  term obligations?
A Current ratio.
B Payables turnover.
C Gross profit margin.
4 Which of the following ratios would be most  useful in determining a company’s 
ability to cover its lease and interest payments?
A ROA.
B Total asset turnover.
C Fixed charge coverage.
5 An analyst is interested in assessing both the efficiency and liquidity of 
Spherion PLC. The analyst has collected the following data for Spherion:
FY3 FY2 FY1
Days of inventory on hand 32 34 40
Days sales outstanding 28 25 23
Number of days of payables 40 35 35

 Based on this data, what is the analyst least likely  to conclude?
A Inventory management has contributed to improved liquidity.
B Management of payables has contributed to improved liquidity.
C Management of receivables has contributed to improved liquidity.
6 An analyst is evaluating the solvency and liquidity of Apex Manufacturing and 
has collected the following data (in millions of euro):
FY5 (€) FY4 (€) FY3 (€)
Total debt 2,000 1,900 1,750
Total equity 4,000 4,500 5,000
 Which of the following would be the analyst’s most likely  conclusion?
A The company is becoming increasingly less solvent, as evidenced by the 
increase in its debt-  to- equity ratio from 0.35 to 0.50 from FY3 to FY5.

Reading 26 ■ Financial Analysis Techniques 334
B The company is becoming less liquid, as evidenced by the increase in its 
debt-  to- equity ratio from 0.35 to 0.50 from FY3 to FY5.
C The company is becoming increasingly more liquid, as evidenced by the 
7 With regard to the data in Problem 6, what would be the most  reasonable expla -
nation of the financial data?
A The decline in the company’s equity results from a decline in the market 
value of this company’s common shares.
B The €250 increase in the company’s debt from FY3 to FY5 indicates that 
lenders are viewing the company as increasingly creditworthy.
C The decline in the company’s equity indicates that the company may be 
incurring losses, paying dividends greater than income, and/or repurchasing 
shares.
8 An analyst observes a decrease in a company’s inventory turnover. Which of the 
following would most likely  explain this trend?

A The company installed a new inventory management system, allowing more 
efficient inventory management.
B Due to problems with obsolescent inventory last year, the company wrote 
off a large amount of its inventory at the beginning of the period.
C The company installed a new inventory management system but expe -
rienced some operational difficulties resulting in duplicate orders being 
placed with suppliers.
9 Which of the following would best explain an increase in receivables turnover?
A The company adopted new credit policies last year and began offering credit 
to customers with weak credit histories.
B Due to problems with an error in its old credit scoring system, the company 
had accumulated a substantial amount of uncollectible accounts and wrote 
off a large amount of its receivables.
C To match the terms offered by its closest competitor, the company adopted 
new payment terms now requiring net payment within 30 days rather than

15 days, which had been its previous requirement.
10 Brown Corporation had average days of sales outstanding of 19 days in the 
most recent fiscal year. Brown wants to improve its credit policies and collec -
tion practices and decrease its collection period in the next fiscal year to match 
the industry average of 15 days. Credit sales in the most recent fiscal year were 
$300 million, and Brown expects credit sales to increase to $390 million in the 
next fiscal year. To achieve Brown’s goal of decreasing the collection period, the 
change in the average accounts receivable balance that must occur is closest  to:
A +$0.41 million.
B –$0.41 million.
C –$1.22 million.
11 An analyst observes the following data for two companies:
Company A ($) Company B ($) 
Revenue 4,500 6,000
Net income 50 1,000
Current assets 40,000 60,000
Total assets 100,000 700,000

Practice Problems 335
Current liabilities 10,000 50,000
Total debt 60,000 150,000
Shareholders’ equity 30,000 500,000
 Which of the following choices best describes reasonable conclusions that the 
analyst might make about the two companies’ ability to pay their current and 
long-  term obligations?
A Company A’s current ratio of 4.0 indicates it is more liquid than Company B, 
whose current ratio is only 1.2, but Company B is more solvent, as indicated 
by its lower debt-  to- equity ratio.
B Company A’s current ratio of 0.25 indicates it is less liquid than Company B, 
whose current ratio is 0.83, and Company A is also less solvent, as indicated 
by a debt-  to- equity ratio of 200 percent compared with Company B’s debt-  
to- equity ratio of only 30 percent.
C Company A’s current ratio of 4.0 indicates it is more liquid than Company 
B, whose current ratio is only 1.2, and Company A is also more solvent, as

indicated by a debt-  to- equity ratio of 200 percent compared with Company 
B’s debt-  to- equity ratio of only 30 percent.
The following information relates to Questions 
12–15
The data in Exhibit 1 appear in the five-  year summary of a major international com -
pany. A business combination with another major manufacturer took place in FY13.
Exhibit 1   
FY10 FY11 FY12 FY13 FY14
Financial statements GBP m GBP m GBP m GBP m GBP m
Income statements
Revenue 4,390 3,624 3,717 8,167 11,366
Profit before interest and taxation 
(EBIT)844 700 704 933 1,579
Net interest payable –80 –54 –98 –163 –188
Taxation –186 –195 –208 –349 –579
Minorities –94 –99 –105 –125 –167
Profit for the year 484 352 293 296 645
Balance sheets
Fixed assets 3,510 3,667 4,758 10,431 11,483
Current asset investments, cash at 
bank and in hand316 218 290 561 682
Other current assets 558 514 643 1,258 1,634
Total assets 4,384 4,399 5,691 12,250 13,799
Interest bearing debt (long term) –602 –1,053 –1,535 –3,523 –3,707

Reading 26 ■ Financial Analysis Techniques 336
Other creditors and provisions 
(current)–1,223 –1,054 –1,102 –2,377 –3,108
Total liabilities –1,825 –2,107 –2,637 –5,900 –6,815
Net assets 2,559 2,292 3,054 6,350 6,984
Shareholders’ funds 2,161 2,006 2,309 5,572 6,165
Equity minority interests 398 286 745 778 819
Capital employed 2,559 2,292 3,054 6,350 6,984
Cash flow
Working capital movements –53 5 71 85 107
Net cash inflow from operating 
activities864 859 975 1,568 2,292
12 The company’s total assets at year-  end FY9 were GBP 3,500 million. Which of 
the following choices best describes reasonable conclusions an analyst might 
make about the company’s efficiency?
A Comparing FY14 with FY10, the company’s efficiency improved, as indi -
cated by a total asset turnover ratio of 0.86 compared with 0.64.
B Comparing FY14 with FY10, the company’s efficiency deteriorated, as indi -
cated by its current ratio.
C Comparing FY14 with FY10, the company’s efficiency deteriorated due to

asset growth faster than turnover revenue growth.
13 Which of the following choices best describes reasonable conclusions an analyst 
might make about the company’s solvency?
A Comparing FY14 with FY10, the company’s solvency improved, as indicated 
by an increase in its debt-  to- assets ratio from 0.14 to 0.27.
B Comparing FY14 with FY10, the company’s solvency deteriorated, as indi -
cated by a decrease in interest coverage from 10.6 to 8.4.
C Comparing FY14 with FY10, the company’s solvency improved, as indicated 
by the growth in its profits to GBP 645 million.
14 Which of the following choices best describes reasonable conclusions an analyst 
might make about the company’s liquidity?
A Comparing FY14 with FY10, the company’s liquidity improved, as indicated 
B Comparing FY14 with FY10, the company’s liquidity deteriorated, as indi -

C Comparing FY14 with FY10, the company’s liquidity improved, as indicated 
by an increase in its current ratio from 0.71 to 0.75.
15 Which of the following choices best describes reasonable conclusions an analyst 
might make about the company’s profitability?
A Comparing FY14 with FY10, the company’s profitability improved, as indi -
cated by an increase in its debt-  to- assets ratio from 0.14 to 0.27.Exhibit 1   (Continued)

Practice Problems 337
B Comparing FY14 with FY10, the company’s profitability deteriorated, 
as indicated by a decrease in its net profit margin from 11.0 percent to 
5.7 percent.
C Comparing FY14 with FY10, the company’s profitability improved, as indi -
cated by the growth in its shareholders’ equity to GBP 6,165 million.
16 Assuming no changes in other variables, which of the following would decrease 
ROA?
A A decrease in the effective tax rate.
B A decrease in interest expense.
C An increase in average assets.
17 An analyst compiles the following data for a company:
FY13 FY14 FY15
ROE 19.8% 20.0% 22.0%
Return on total assets 8.1% 8.0% 7.9%
Total asset turnover 2.0 2.0 2.1
 Based only on the information above, the most  appropriate conclusion is that, 
over the period FY13 to FY15, the company’s:
A net profit margin and financial leverage have decreased.
B net profit margin and financial leverage have increased.
C net profit margin has decreased but its financial leverage has increased.

18 A decomposition of ROE for Integra SA is as follows:
FY12 FY11
ROE 18.90% 18.90%
Tax burden 0.70 0.75
Interest burden 0.90 0.90
EBIT margin 10.00% 10.00%
Asset turnover 1.50 1.40
Leverage 2.00 2.00
 Which of the following choices best describes reasonable conclusions an analyst 
might make based on this ROE decomposition?
A Profitability and the liquidity position both improved in FY12.
B The higher average tax rate in FY12 offset the improvement in profitability, 
leaving ROE unchanged.
C The higher average tax rate in FY12 offset the improvement in efficiency, 
19 A decomposition of ROE for Company A and Company B is as follows:
FY15 FY14 FY15 FY14
ROE 26.46% 18.90% 26.33% 18.90%
Tax burden 0.7 0.75 0.75 0.75
Interest burden 0.9 0.9 0.9 0.9

Reading 26 ■ Financial Analysis Techniques 338
EBIT margin 7.00% 10.00% 13.00% 10.00%
Asset turnover 1.5 1.4 1.5 1.4
Leverage 4 2 2 2
 An analyst is most likely  to conclude that:
A Company A’s ROE is higher than Company B’s in FY15, and one explanation 
consistent with the data is that Company A may have purchased new, more 
efficient equipment.
B Company A’s ROE is higher than Company B’s in FY15, and one explanation 
consistent with the data is that Company A has made a strategic shift to a 
product mix with higher profit margins.
C The difference between the two companies’ ROE in FY15 is very small and 
Company A’s ROE remains similar to Company B’s ROE mainly due to 
Company A increasing its financial leverage.
20 What does the P/E ratio measure?
A The “multiple” that the stock market places on a company’s EPS.
B The relationship between dividends and market prices.
C The earnings for one common share of stock.

21 A creditor most likely  would consider a decrease in which of the following ratios 
to be positive news?
A Interest coverage (times interest earned).
B Debt-  to- total assets.
C Return on assets.
22 When developing forecasts, analysts should most likely :
A develop possibilities relying exclusively on the results of financial analysis.
B use the results of financial analysis, analysis of other information, and 
judgment.
C aim to develop extremely precise forecasts using the results of financial 
analysis.

Solutions 339
SOLUTIONS
1 C is correct. Cross-  sectional analysis involves the comparison of companies 
with each other for the same time period. Technical analysis uses price and 
volume data as the basis for investment decisions. Time-  series or trend analysis 
is the comparison of financial data across different time periods.
2 C is correct. Solvency ratios are used to evaluate the ability of a company to 
meet its long-  term obligations. An analyst is more likely to use activity ratios to 
evaluate how efficiently a company uses its assets. An analyst is more likely to 
use liquidity ratios to evaluate the ability of a company to meet its short-  term 
obligations.
3 A is correct. The current ratio is a liquidity ratio. It compares the net amount of 
current assets expected to be converted into cash within the year with liabilities 
falling due in the same period. A current ratio of 1.0 would indicate that the 
company would have just enough current assets to pay current liabilities.

4 C is correct. The fixed charge coverage ratio is a coverage ratio that relates 
known fixed charges or obligations to a measure of operating profit or cash flow 
generated by the company. Coverage ratios, a category of solvency ratios, mea -
sure the ability of a company to cover its payments related to debt and leases.
5 C is correct. The analyst is unlikely  to reach the conclusion given in Statement 
C because days of sales outstanding increased from 23 days in FY1 to 25 days 
in FY2 to 28 days in FY3, indicating that the time required to collect receivables 
has increased over the period. This is a negative factor for Spherion’s liquidity. 
By contrast, days of inventory on hand dropped over the period FY1 to FY3, a 
positive for liquidity. The company’s increase in days payable, from 35 days to 
40 days, shortened its cash conversion cycle, thus also contributing to improved 
6 A is correct. The company is becoming increasingly less solvent, as evidenced

by its debt-  to- equity ratio increasing from 0.35 to 0.50 from FY3 to FY5. The 
amount of a company’s debt and equity do not provide direct information about 
the company’s liquidity position.
 Debt to equity:
 FY5: 2,000/4,000 = 0.5000
 FY4: 1,900/4,500 = 0.4222
 FY3: 1,750/5,000 = 0.3500
7 C is correct. The decline in the company’s equity indicates that the company 
may be incurring losses, paying dividends greater than income, or repurchasing 
shares. Recall that Beginning equity + New shares issuance – Shares repur -
chased + Comprehensive income – Dividends = Ending equity. The book value 
of a company’s equity is not affected by changes in the market value of its 
common stock. An increased amount of lending does not necessarily indicate 
that lenders view a company as increasingly creditworthy. Creditworthiness is 
not evaluated based on how much a company has increased its debt but rather 
on its willingness and ability to pay its obligations. (Its financial strength is

indicated by its solvency, liquidity, profitability, efficiency, and other aspects of 
credit analysis.)
8 C is correct. The company’s problems with its inventory management system 
causing duplicate orders would likely result in a higher amount of inventory and 
would, therefore, result in a decrease in inventory turnover. A more efficient 
inventory management system and a write off of inventory at the beginning of

Reading 26 ■ Financial Analysis Techniques 340
the period would both likely decrease the average inventory for the period (the 
denominator of the inventory turnover ratio), thus increasing the ratio rather 
than decreasing it.
9 B is correct. A write off of receivables would decrease the average amount of 
accounts receivable (the denominator of the receivables turnover ratio), thus 
increasing this ratio. Customers with weaker credit are more likely to make 
payments more slowly or to pose collection difficulties, which would likely 
increase the average amount of accounts receivable and thus decrease receiv -
ables turnover. Longer payment terms would likely increase the average amount 
of accounts receivable and thus decrease receivables turnover.
10 A is correct. The average accounts receivable balances (actual and desired) must 
be calculated to determine the desired change. The average accounts receivable 
balance can be calculated as an average day’s credit sales times the DSO. For the

most recent fiscal year, the average accounts receivable balance is $15.62 million 
[= ($300,000,000/365) × 19]. The desired average accounts receivable balance 
for the next fiscal year is $16.03 million (= ($390,000,000/365) × 15). This is 
an increase of $0.41 million (= 16.03 million – 15.62 million). An alternative 
approach is to calculate the turnover and divide sales by turnover to determine 
the average accounts receivable balance. Turnover equals 365 divided by DSO. 
Turnover is 19.21 (= 365/19) for the most recent fiscal year and is targeted to 
be 24.33 (= 365/15) for the next fiscal year. The average accounts receivable 
balances are $15.62 million (= $300,000,000/19.21), and $16.03 million (= 
$390,000,000/24.33). The change is an increase in receivables of $0.41 million
11 A is correct. Company A’s current ratio of 4.0 (= $40,000/$10,000) indi -
cates it is more liquid than Company B, whose current ratio is only 1.2 (=

$60,000/$50,000). Company B is more solvent, as indicated by its lower debt-  to- 
equity ratio of 30 percent (= $150,000/$500,000) compared with Company A’s 
debt-  to- equity ratio of 200 percent (= $60,000/$30,000).
12 C is correct. The company’s efficiency deteriorated, as indicated by the decline 
in its total asset turnover ratio from 1.11 {= 4,390/[(4,384 + 3,500)/2]} for 
FY10 to 0.87 {= 11,366/[(12,250 + 13,799)/2]} for FY14. The decline in the 
total asset turnover ratio resulted from an increase in average total assets from 
GBP3,942 [= (4,384 + 3,500)/2] for FY10 to GBP13,024.5 for FY14, an increase 
of 230 percent, compared with an increase in revenue from GBP4,390 in FY10 
to GBP11,366 in FY14, an increase of only 159 percent. The current ratio is not 
an indicator of efficiency.
13 B is correct. Comparing FY14 with FY10, the company’s solvency deteriorated, 
as indicated by a decrease in interest coverage from 10.6 (= 844/80) in FY10

to 8.4 (= 1,579/188) in FY14. The debt-  to- asset ratio increased from 0.14 (= 
602/4,384) in FY10 to 0.27 (= 3,707/13,799) in FY14. This is also indicative of 
deteriorating solvency. In isolation, the amount of profits does not provide 
enough information to assess solvency.
14 C is correct. Comparing FY14 with FY10, the company’s liquidity improved, 
as indicated by an increase in its current ratio from 0.71 [= (316 + 558)/1,223] 
in FY10 to 0.75 [= (682 + 1,634)/3,108] in FY14. Note, however, comparing 
only current investments with the level of current liabilities shows a decline in 
liquidity from 0.26 (= 316/1,223) in FY10 to 0.22 (= 682/3,108) in FY14. Debt-  
to- assets ratio and interest coverage are measures of solvency not liquidity.

Solutions 341
15 B is correct. Comparing FY14 with FY10, the company’s profitability deterio -
rated, as indicated by a decrease in its net profit margin from 11.0 percent (= 
484/4,390) to 5.7 percent (= 645/11,366). Debt-  to- assets ratio is a measure of 
solvency not an indicator of profitability. Growth in shareholders’ equity, in 
isolation, does not provide enough information to assess profitability.
16 C is correct. Assuming no changes in other variables, an increase in average 
assets (an increase in the denominator) would decrease ROA. A decrease in 
either the effective tax rate or interest expense, assuming no changes in other 
variables, would increase ROA.
17 C is correct. The company’s net profit margin has decreased and its financial 
leverage has increased. ROA = Net profit margin × Total asset turnover. ROA 
decreased over the period despite the increase in total asset turnover; therefore, 
the net profit margin must have decreased.

 ROE = Return on assets × Financial leverage. ROE increased over the period 
despite the drop in ROA; therefore, financial leverage must have increased.
18 C is correct. The increase in the average tax rate in FY12, as indicated by the 
decrease in the value of the tax burden (the tax burden equals one minus the 
average tax rate), offset the improvement in efficiency indicated by higher asset 
turnover) leaving ROE unchanged. The EBIT margin, measuring profitability, 
was unchanged in FY12 and no information is given on liquidity.
19 C is correct. The difference between the two companies’ ROE in 2010 is very 
small and is mainly the result of Company A’s increase in its financial leverage, 
indicated by the increase in its Assets/Equity ratio from 2 to 4. The impact of 
efficiency on ROE is identical for the two companies, as indicated by both com -
panies’ asset turnover ratios of 1.5. Furthermore, if Company A had purchased

newer equipment to replace older, depreciated equipment, then the company’s 
asset turnover ratio (computed as sales/assets) would have declined, assuming 
constant sales. Company A has experienced a significant decline in its operating 
margin, from 10 percent to 7 percent which, all else equal, would not suggest 
that it is selling more products with higher profit margins.
20 A is correct. The P/E ratio measures the “multiple” that the stock market places 
on a company’s EPS.
21 B is correct. In general, a creditor would consider a decrease in debt to total 
assets as positive news. A higher level of debt in a company’s capital structure 
increases the risk of default and will, in general, result in higher borrowing 
costs for the company to compensate lenders for assuming greater credit risk. A 
decrease in either interest coverage or return on assets is likely to be considered 
negative news.
22 B is correct. The results of an analyst’s financial analysis are integral to the pro -

cess of developing forecasts, along with the analysis of other information and 
judgment of the analysts. Forecasts are not limited to a single point estimate but 
should involve a range of possibilities.

and Analysis (3)
This study session examines financial reporting for specific categories of assets and 
liabilities. Inventories, long-  lived assets, income taxes, and non-  current liabilities are 
examined in greater detail because of their effect on financial statements and reported 
measures of profitability, liquidity, and solvency. For these items in particular, the 
analyst should be attentive to chosen accounting treatment, corresponding effect on 
reported performance, and the potential for financial statement manipulation.
Reading 27 Inventories  
by Michael Broihahn, CPA, CIA, CFA
Reading 28 Long-  lived Assets  
by Elaine Henry, PhD, CFA, and Elizabeth A. Gordon, PhD, 
MBA, CPA
Reading 29 Income Taxes  
By Elbie Louw, PhD, CFA, CIPM, and Michael A. Broihahn, 
CPA, CIA, CFA
Reading 30 Non-  current (Long-  term) Liabilities  
by Elizabeth A. Gordon, PhD, MBA, CPA, and Elaine 
Henry, PhD, CFAFINANCIAL  REPORTIN g AN d A NALYSIS
8

8
readings.

Inventories
by Michael A. Broihahn, CPA, CIA, CFA
Michael A. Broihahn, CPA, CIA, CFA, is at Barry University (USA).
a. distinguish between costs included in inventories and costs 
recognised as expenses in the period in which they are incurred;
b. describe different inventory valuation methods (cost formulas);
c. calculate and compare cost of sales, gross profit, and ending 
inventory using different inventory valuation methods and using 
perpetual and periodic inventory systems;
d. calculate and explain how inflation and deflation of inventory 
costs affect the financial statements and ratios of companies that 
use different inventory valuation methods;
e. explain LIFO reserve and LIFO liquidation and their effects on 
financial statements and ratios;
f. convert a company’s reported financial statements from LIFO to 
FIFO for purposes of comparison;
g. describe the measurement of inventory at the lower of cost and 
net realisable value;

h. describe implications of valuing inventory at net realisable value 
for financial statements and ratios;
i. describe the financial statement presentation of and disclosures 
relating to inventories;
j. explain issues that analysts should consider when examining 
a company’s inventory disclosures and other sources of 
information;
k. calculate and compare ratios of companies, including companies 
that use different inventory methods;
l. analyze and compare the financial statements of companies, 
including companies that use different inventory methods.REA dINg
27
In addition, candidates are

readings.

Reading 27 ■ Inventories 346
Merchandising and manufacturing companies generate revenues and profits through 
the sale of inventory. Further, inventory may represent a significant asset on these 
companies’ balance sheets. Merchandisers (wholesalers and retailers) purchase inven -
tory, ready for sale, from manufacturers and thus account for only one type of inven -
tory—finished goods inventory. Manufacturers, however, purchase raw materials 
from suppliers and then add value by transforming the raw materials into finished 
goods. They typically classify inventory into three different categories:1 raw materials, 
work in progress,2 and finished goods. Work-  in- progress inventories have started the 
conversion process from raw materials but are not yet finished goods ready for sale. 
Manufacturers may report either the separate carrying amounts of their raw materi -
als, work-  in- progress, and finished goods inventories on the balance sheet or simply

the total inventory amount. If the latter approach is used, the company must then 
disclose the carrying amounts of its raw materials, work-  in- progress, and finished 
goods inventories in a footnote to the financial statements.
Inventories and cost of sales (cost of goods sold)3 are significant items in the finan -
cial statements of many companies. Comparing the performance of these companies 
is challenging because of the allowable choices for valuing inventories: Differences in 
the choice of inventory valuation method can result in significantly different amounts 
being assigned to inventory and cost of sales. Financial statement analysis would be 
much easier if all companies used the same inventory valuation method or if inventory 
price levels remained constant over time. If there was no inflation or deflation with 
respect to inventory costs and thus unit costs were unchanged, the choice of inventory 
valuation method would be irrelevant. However, inventory price levels typically do

change over time.
International Financial Reporting Standards (IFRS) permit the assignment of inven -
tory costs (costs of goods available for sale) to inventories and cost of sales by three 
cost formulas: specific identification, first-  in, first-  out (FIFO), and weighted average 
cost.4 US generally accepted accounting principles (US GAAP) allow the same three 
inventory valuation methods, referred to as cost flow assumptions in US GAAP , but 
also include a fourth method called last-  in, first-  out (LIFO).5 The choice of inventory 
valuation method affects the allocation of the cost of goods available for sale to ending 
inventory and cost of sales. Analysts must understand the various inventory valuation 
methods and the related impact on financial statements and financial ratios in order 
to evaluate a company’s performance over time and relative to industry peers. The 
company’s financial statements and related notes provide important information that

the analyst can use in assessing the impact of the choice of inventory valuation method 
on financial statements and financial ratios.
This reading is organized as follows: Section 2 discusses the costs that are included 
in inventory and the costs that are recognised as expenses in the period in which they 
are incurred. Section 3 describes inventory valuation methods and compares the 
measurement of ending inventory, cost of sales and gross profit under each method, 
and when using periodic versus perpetual inventory systems. Section 4 describes the 
LIFO method, LIFO reserve, and effects of LIFO liquidations, and demonstrates the 
adjustments required to compare a company that uses LIFO with one that uses FIFO. 1
1 Other classifications are possible. Inventory classifications should be appropriate to the entity.
2 This category is commonly referred to as work in process  under US GAAP .
3 Typically, cost of sales  is IFRS terminology and cost of goods sold  is US GAAP terminology.

4 International Accounting Standard (IAS) 2 [Inventories].
5 Financial Accounting Standards Board Accounting Standards Codification  (FASB ASC) Topic 330 
[Inventory].

Cost of Inventories 347
Section 5 describes the financial statement effects of a change in inventory valuation 
method. Section 6 discusses the measurement and reporting of inventory when its 
value changes. Section 7 describes the presentation of inventories on the financial 
statements and related disclosures, discusses inventory ratios and their interpretation, 
and shows examples of financial analysis with respect to inventories. A summary and 
practice problems conclude the reading.
COST OF INVENTORIES
Under IFRS, the costs to include in inventories are “all costs of purchase, costs of 
conversion, and other costs incurred in bringing the inventories to their present loca -
tion and condition. ”6 The costs of purchase include the purchase price, import and 
tax- related duties, transport, insurance during transport, handling, and other costs 
directly attributable to the acquisition of finished goods, materials, and services. Trade

discounts, rebates, and similar items reduce the price paid and the costs of purchase. 
The costs of conversion include costs directly related to the units produced, such as 
direct labour, and fixed and variable overhead costs.7 Including these product-  related 
costs in inventory (i.e., as an asset) means that they will not be recognised as an expense 
(i.e., as cost of sales) on the income statement until the inventory is sold. US GAAP 
provide a similar description of the costs to be included in inventory.8
Both IFRS and US GAAP exclude the following costs from inventory: abnormal 
costs incurred as a result of waste of materials, labour or other production conver -
sion inputs, any storage costs (unless required as part of the production process), 
and all administrative overhead and selling costs. These excluded costs are treated 
as expenses and recognised on the income statement in the period in which they are

incurred. Including costs in inventory defers their recognition as an expense on the 
income statement until the inventory is sold. Therefore, including costs in inventory 
that should be expensed will overstate profitability on the income statement (because 
of the inappropriate deferral of cost recognition) and create an overstated inventory 
value on the balance sheet.
EXAMPLE 1   
Treatment of Inventory-  Related Costs
Acme Enterprises, a hypothetical company that prepares its financial statements 
in accordance with IFRS, manufactures tables. In 2009, the factory produced 
900,000 finished tables and scrapped 1,000 tables. For the finished tables, raw 
material costs were €9 million, direct labour conversion costs were €18 million, 
and production overhead costs were €1.8  million. The 1,000 scrapped tables 
(attributable to abnormal waste) had a total production cost of €30,000 (€10,000 
raw material costs and €20,000 conversion costs; these costs are not included in

the €9 million raw material and €19.8 million total conversion costs of the finished 2
6 International Accounting Standard (IAS) 2 [Inventories].
7 Fixed production overhead costs (depreciation, factory maintenance, and factory management and 
administration) represent indirect costs of production that remain relatively constant regardless of the 
volume of production. Variable production overhead costs are indirect production costs (indirect labour 
and materials) that vary with the volume of production.
8 FASB Accounting Standards Codification™ (ASC) Topic 330 [Inventory].

Reading 27 ■ Inventories 348
tables). During the year, Acme spent €1 million for freight delivery charges on 
raw materials and €500,000 for storing finished goods inventory. Acme does not 
have any work-  in- progress inventory at the end of the year.
1 What costs should be included in inventory in 2009?
2 What costs should be expensed in 2009?
Total inventory costs for 2009 are as follows:
Raw materials €9,000,000
Direct labour 18,000,000
Production overhead 1,800,000
Transportation for raw materials 1,000,000
Total inventory costs €29,800,000
Total costs that should be expensed (not included in inventory) are as follows:
Abnormal waste €30,000
Storage of finished goods inventory 500,000
Total €530,000
INVENTORY VALUATION METHODS
Generally, inventory purchase costs and manufacturing conversion costs change over 
time. As a result, the allocation of total inventory costs (i.e., cost of goods available

for sale) between cost of sales on the income statement and inventory on the balance 
sheet will vary depending on the inventory valuation method used by the company. 
As mentioned in the introduction, inventory valuation methods are referred to as 
cost formulas and cost flow assumptions under IFRS and US GAAP , respectively. If 
the choice of method results in more cost being allocated to cost of sales and less 
cost being allocated to inventory than would be the case with other methods, the 
chosen method will cause, in the current year, reported gross profit, net income, and 
inventory carrying amount to be lower than if alternative methods had been used. 
Accounting for inventory, and consequently the allocation of costs, thus has a direct 
impact on financial statements and their comparability.
Both IFRS and US GAAP allow companies to use the following inventory valuation 
methods: specific identification; first-  in, first-  out (FIFO); and weighted average cost.

US GAAP allow companies to use an additional method: last-  in, first-  out (LIFO). A 
company must use the same inventory valuation method for all items that have a 
similar nature and use. For items with a different nature or use, a different inventory 
valuation method can be used.9 When items are sold, the carrying amount of the 
inventory is recognised as an expense (cost of sales) according to the cost formula 
(cost flow assumption) in use.3
9 For example, if a clothing manufacturer produces both a retail line and one-  of- a-kind designer garments, 
the retail line might be valued using FIFO and the designer garments using specific identification.

Inventory Valuation Methods 349
Specific identification is used for inventory items that are not ordinarily inter -
changeable, whereas FIFO, weighted average cost, and LIFO are typically used when 
there are large numbers of interchangeable items in inventory. Specific identification 
matches the actual historical costs of the specific inventory items to their physical 
flow; the costs remain in inventory until the actual identifiable inventory is sold. FIFO, 
weighted average cost, and LIFO are based on cost flow assumptions. Under these 
methods, companies must make certain assumptions about which goods are sold 
and which goods remain in ending inventory. As a result, the allocation of costs to 
the units sold and to the units in ending inventory can be different from the physical 
movement of the items.
The choice of inventory valuation method would be largely irrelevant if inventory 
costs remained constant or relatively constant over time. Given relatively constant

prices, the allocation of costs between cost of goods sold and ending inventory 
would be very similar under each of the four methods. Given changing price levels, 
however, the choice of inventory valuation method can have a significant impact on 
the amount of reported cost of sales and inventory. And the reported cost of sales 
and inventory balances affect other items, such as gross profit, net income, current 
assets, and total assets.
3.1 Specific Identification
The specific identification method is used for inventory items that are not ordinarily 
interchangeable and for goods that have been produced and segregated for specific 
projects. This method is also commonly used for expensive goods that are uniquely 
identifiable, such as precious gemstones. Under this method, the cost of sales and 
the cost of ending inventory reflect the actual costs incurred to purchase (or manu -
facture) the items specifically identified as sold and the items specifically identified

as remaining in inventory. Therefore, this method matches the physical flow of the 
specific items sold and remaining in inventory to their actual cost.
3.2 First-  In, First-  Out (FIFO)
FIFO assumes that the oldest goods purchased (or manufactured) are sold first and 
the newest goods purchased (or manufactured) remain in ending inventory. In other 
words, the first units included in inventory are assumed to be the first units sold from 
inventory. Therefore, cost of sales reflects the cost of goods in beginning inventory plus 
the cost of items purchased (or manufactured) earliest in the accounting period, and 
the value of ending inventory reflects the costs of goods purchased (or manufactured) 
more recently. In periods of rising prices, the costs assigned to the units in ending 
inventory are higher than the costs assigned to the units sold. Conversely, in periods 
of declining prices, the costs assigned to the units in ending inventory are lower than 
the costs assigned to the units sold.

3.3 Weighted Average Cost
Weighted average cost assigns the average cost of the goods available for sale (beginning 
inventory plus purchase, conversion, and other costs) during the accounting period 
to the units that are sold as well as to the units in ending inventory. In an accounting 
period, the weighted average cost per unit is calculated as the total cost of the units 
available for sale divided by the total number of units available for sale in the period 
(Total cost of goods available for sale/Total units available for sale).

Reading 27 ■ Inventories 350
3.4 Last-  In, First-  Out (LIFO)
LIFO is permitted only under US GAAP . This method assumes that the newest goods 
purchased (or manufactured) are sold first and the oldest goods purchased (or manu -
factured), including beginning inventory, remain in ending inventory. In other words, 
the last units included in inventory are assumed to be the first units sold from inven -
tory. Therefore, cost of sales reflects the cost of goods purchased (or manufactured) 
more recently, and the value of ending inventory reflects the cost of older goods. In 
periods of rising prices, the costs assigned to the units in ending inventory are lower 
than the costs assigned to the units sold. Conversely, in periods of declining prices, 
the costs assigned to the units in ending inventory are higher than the costs assigned 
to the units sold.
3.5 Calculation of Cost of Sales, Gross Profit, and Ending 
Inventory

Inventory
In periods of changing prices, the allocation of total inventory costs (i.e., cost of goods 
available for sale) between cost of sales on the income statement and inventory on 
the balance sheet will vary depending on the inventory valuation method used by the 
company. The following example illustrates how cost of sales, gross profit, and ending 
inventory differ based on the choice of inventory valuation method.
EXAMPLE 2   
Inventory Cost Flow Illustration for the Specific 
Identification, Weighted Average Cost, FIFO, and LIFO 
Methods
Global Sales, Inc. (GSI) is a hypothetical distributor of consumer products, 
including bars of violet essence soap. The soap is sold by the kilogram. GSI began 
operations in 2009, during which it purchased and received initially 100,000 
kg of soap at 110 yuan/kg, then 200,000 kg of soap at 100 yuan/kg, and finally 
300,000 kg of soap at 90 yuan/kg. GSI sold 520,000 kg of soap at 240 yuan/kg.

GSI stores its soap in its warehouse so that soap from each shipment received is 
readily identifiable. During 2009, the entire 100,000 kg from the first shipment 
received, 180,000 kg of the second shipment received, and 240,000 kg of the final 
shipment received was sent to customers. Answers to the following questions 
should be rounded to the nearest 1,000 yuan.
1 What are the reported cost of sales, gross profit, and ending inventory 
balances for 2009 under the specific identification method?
2 What are the reported cost of sales, gross profit, and ending inventory 
balances for 2009 under the weighted average cost method?
3 What are the reported cost of sales, gross profit, and ending inventory 
balances for 2009 under the FIFO method?
4 What are the reported cost of sales, gross profit, and ending inventory 
balances for 2009 under the LIFO method?
Under the specific identification method, the physical flow of the specific inven -

tory items sold is matched to their actual cost.
Sales = 520,000 × 240 = 124,800,000 yuan

Inventory Valuation Methods 351
Cost of sales = (100,000 × 110) + (180,000 × 100) + (240,000 × 90) = 
50,600,000 yuan
Gross profit = 124,800,000 – 50,600,000 = 74,200,000 yuan
Ending inventory = (20,000 × 100) + (60,000 × 90) = 7,400,000 yuan
Note that in spite of the segregation of inventory within the warehouse, it would 
be inappropriate to use specific identification for this inventory of interchange -
able items. The use of specific identification could potentially result in earnings 
manipulation through the shipment decision.
Under the weighted average cost method, costs are allocated to cost of sales and 
ending inventory by using a weighted average mix of the actual costs incurred for 
all inventory items. The weighted average cost per unit is determined by dividing 
the total cost of goods available for sale by the number of units available for sale.
Weighted average cost = [(100,000 × 110) + (200,000 × 100) + (300,000 × 
90)]/600,000 = 96.667 yuan/kg

Cost of sales = 520,000 × 96.667 = 50,267,000 yuan
Gross profit = 124,800,000 – 50,267,000 = 74,533,000 yuan
Ending inventory = 80,000 × 96.667 = 7,733,000 yuan
Under the FIFO method, the oldest inventory units acquired are assumed to be 
the first units sold. Ending inventory, therefore, is assumed to consist of those 
inventory units most recently acquired.
Cost of sales = (100,000 × 110) + (200,000 × 100) + (220,000 × 90) = 
50,800,000 yuan
Gross profit = 124,800,000 – 50,800,000 = 74,000,000 yuan
Ending inventory = 80,000 × 90 = 7,200,000 yuan
Under the LIFO method, the newest inventory units acquired are assumed to 
be the first units sold. Ending inventory, therefore, is assumed to consist of the 
oldest inventory units.
Cost of sales = (20,000 × 110) + (200,000 × 100) + (300,000 × 90) = 
49,200,000 yuan

Gross profit = 124,800,000 – 49,200,000 = 75,600,000 yuan
Ending inventory = 80,000 × 110 = 8,800,000 yuan
The following table (in thousands of yuan) summarizes the cost of sales, the 
ending inventory, and the cost of goods available for sale that were calculated 
for each of the four inventory valuation methods. Note that in the first year of 
operation, the total cost of goods available for sale is the same under all four 
methods. Subsequently, the cost of goods available for sale will typically differ 
because beginning inventories will differ. Also shown is the gross profit figure 
for each of the four methods. Because the cost of a kg of soap declined over the

Reading 27 ■ Inventories 352
period, LIFO had the highest ending inventory amount, the lowest cost of sales, 
and the highest gross profit. FIFO had the lowest ending inventory amount, the 
highest cost of sales, and the lowest gross profit.
Inventory Valuation 
MethodSpecific 
IDWeighted 
Average 
Cost FIFO LIFO
Cost of sales 50,600 50,267 50,800 49,200
Ending inventory 7,400 7,733 7,200 8,800
Total cost of goods available 
for sale58,000 58,000 58,000 58,000
Gross profit 74,200 74,533 74,000 75,600
3.6 Periodic versus Perpetual Inventory Systems
Companies typically record changes to inventory using either a periodic inventory 
system or a perpetual inventory system. Under a periodic inventory system, inventory 
values and costs of sales are determined at the end of an accounting period. Purchases 
are recorded in a purchases account. The total of purchases and beginning inventory 
is the amount of goods available for sale during the period. The ending inventory

amount is subtracted from the goods available for sale to arrive at the cost of sales. 
The quantity of goods in ending inventory is usually obtained or verified through a 
physical count of the units in inventory. Under a perpetual inventory system, inven -
tory values and cost of sales are continuously updated to reflect purchases and sales.
Under either system, the allocation of goods available for sale to cost of sales and 
ending inventory is the same if the inventory valuation method used is either specific 
identification or FIFO. This is not generally true for the weighted average cost method. 
Under a periodic inventory system, the amount of cost of goods available for sale 
allocated to cost of sales and ending inventory may be quite different using the FIFO 
method compared to the weighted average cost method. Under a perpetual inventory 
system, inventory values and cost of sales are continuously updated to reflect purchases

and sales. As a result, the amount of cost of goods available for sale allocated to cost 
of sales and ending inventory is similar under the FIFO and weighted average cost 
methods. Because of lack of disclosure and the dominance of perpetual inventory 
systems, analysts typically do not make adjustments when comparing a company 
using the weighted average cost method with a company using the FIFO method.
Using the LIFO method, the periodic and perpetual inventory systems will generally 
result in different allocations to cost of sales and ending inventory. Under either a per -
petual or periodic inventory system, the use of the LIFO method will generally result 
in significantly different allocations to cost of sales and ending inventory compared to 
other inventory valuation methods. When inventory costs are increasing and inventory 
unit levels are stable or increasing, using the LIFO method will result in higher cost of

sales and lower inventory carrying amounts than using the FIFO method. The higher 
cost of sales under LIFO will result in lower gross profit, operating income, income 
before taxes, and net income. Income tax expense will be lower under LIFO, causing 
the company’s net operating cash flow to be higher. On the balance sheet, the lower 
inventory carrying amount will result in lower reported current assets, working capital, 
and total assets. Analysts must carefully assess the financial statement implications 
of the choice of inventory valuation method when comparing companies that use the 
LIFO method with companies that use the FIFO method.
Example 3 illustrates the impact of the choice of system under LIFO.

Inventory Valuation Methods 353
EXAMPLE 3   
Perpetual versus Periodic Inventory Systems
If GSI (the company in Example 2) had used a perpetual inventory system, the 
timing of purchases and sales would affect the amounts of cost of sales and 
inventory. Below is a record of the purchases, sales, and quantity of inventory 
on hand after the transaction in 2009.
Date Purchased Sold Inventory on Hand
5 January 100,000 kg at 110 yuan/kg 100,000 kg
1 February 80,000 kg at 240 yuan/kg 20,000 kg
8 March 200,000 kg at 100 yuan/kg 220,000 kg
6 April 100,000 kg at 240 yuan/kg 120,000 kg
23 May 60,000 kg at 240 yuan/kg 60,000 kg
7 July 40,000 kg at 240 yuan/kg 20,000 kg
2 August 300,000 kg at 90 yuan/kg 320,000 kg
5 September 70,000 kg at 240 yuan/kg 250,000 kg
17 November 90,000 kg at 240 yuan/kg 160,000 kg
8 December 80,000 kg at 240 yuan/kg 80,000 kg
Total goods available for sale = 
58,000,000 yuanTotal sales = 124,800,000 yuan
The amounts for total goods available for sale and sales are the same under

either the perpetual or periodic system in this first year of operation. The carry -
ing amount of the ending inventory, however, may differ because the perpetual 
system will apply LIFO continuously throughout the year. Under the periodic 
system, it was assumed that the ending inventory was composed of 80,000 units 
of the oldest inventory, which cost 110 yuan/kg.
What are the ending inventory, cost of sales, and gross profit amounts using 
the perpetual system and the LIFO method? How do these compare with the 
amounts using the periodic system and the LIFO method, as in Example 2?
Solution:
The carrying amounts of the inventory at the different time points using the 
perpetual inventory system are as follows:
Date Quantity on Hand Quantities and Cost Carrying Amount
5 January 100,000 kg 100,000 kg at 110 yuan/kg 11,000,000 yuan
1 February 20,000 kg 20,000 kg at 110 yuan/kg 2,200,000 yuan
8 March 220,000 kg 20,000 kg at 110 yuan/kg + 
200,000 kg at 100 yuan/kg22,200,000 yuan

6 April 120,000 kg 20,000 kg at 110 yuan/kg + 
100,000 kg at 100 yuan/kg12,200,000 yuan
23 May 60,000 kg 20,000 kg at 110 yuan/kg + 
40,000 kg at 100 yuan/kg6,200,000 yuan
7 July 20,000 kg 20,000 kg at 110 yuan/kg 2,200,000 yuan
2 August 320,000 kg 20,000 kg at 110 yuan/kg + 
300,000 kg at 90 yuan/kg29,200,000 yuan
5 September 250,000 kg 20,000 kg at 110 yuan/kg + 
230,000 kg at 90 yuan/kg22,900,000 yuan

Reading 27 ■ Inventories 354
17 November 160,000 kg 20,000 kg at 110 yuan/kg + 
140,000 kg at 90 yuan/kg14,800,000 yuan
8 December 80,000 kg 20,000 kg at 110 yuan/kg + 
60,000 kg at 90 yuan/kg7,600,000 yuan
Perpetual system
Cost of sales = 58,000,000 – 7,600,000 = 50,400,000 yuan
Gross profit = 124,800,000 – 50,400,000 = 74,400,000 yuan
Ending inventory = 7,600,000 yuan
Periodic system from Example 2
In this example, the ending inventory amount is lower under the perpetual 
system because only 20,000 kg of the oldest inventory with the highest cost is 
assumed to remain in inventory. The cost of sales is higher and the gross profit

is lower under the perpetual system compared to the periodic system.
3.7 Comparison of Inventory Valuation Methods
As shown in Example 2, the allocation of the total cost of goods available for sale 
to cost of sales on the income statement and to ending inventory on the balance 
sheet varies under the different inventory valuation methods. In an environment of 
declining inventory unit costs and constant or increasing inventory quantities, FIFO 
(in comparison with weighted average cost or LIFO) will allocate a higher amount of 
the total cost of goods available for sale to cost of sales on the income statement and 
a lower amount to ending inventory on the balance sheet. Accordingly, because cost 
of sales will be higher under FIFO, a company’s gross profit, operating profit, and 
income before taxes will be lower.
Conversely, in an environment of rising inventory unit costs and constant or 
increasing inventory quantities, FIFO (in comparison with weighted average cost or

LIFO) will allocate a lower amount of the total cost of goods available for sale to cost 
of sales on the income statement and a higher amount to ending inventory on the 
balance sheet. Accordingly, because cost of sales will be lower under FIFO, a company’s 
gross profit, operating profit, and income before taxes will be higher.
The carrying amount of inventories under FIFO will more closely reflect current 
replacement values because inventories are assumed to consist of the most recently 
purchased items. The cost of sales under LIFO will more closely reflect current replace -
ment value. LIFO ending inventory amounts are typically not reflective of current 
replacement value because the ending inventory is assumed to be the oldest inventory 
and costs are allocated accordingly. Example 4 illustrates the different results obtained 
by using either the FIFO or LIFO methods to account for inventory

Inventory Valuation Methods 355
EXAMPLE 4   
Impact of Inflation Using LIFO Compared to FIFO
Company L and Company F are identical in all respects except that Company L 
uses the LIFO method and Company F uses the FIFO method. Each company has 
been in business for five years and maintains a base inventory of 2,000 units each 
year. Each year, except the first year, the number of units purchased equaled the 
number of units sold. Over the five year period, unit sales increased 10 percent 
each year and the unit purchase and selling prices increased at the beginning of 
each year to reflect inflation of 4 percent per year. In the first year, 20,000 units 
were sold at a price of $15.00 per unit and the unit purchase price was $8.00.
1 What was the end of year inventory, sales, cost of sales, and gross profit 
for each company for each of the five years?
2 Compare the inventory turnover ratios (based on ending inventory 
carrying amounts) and gross profit margins over the five year period and

between companies.
Company L using 
LIFO Y ear 1 Y ear 2 Y ear 3 Y ear 4 Y ear 5
Ending inventorya$16,000 $16,000 $16,000 $16,000 $16,000
Salesb$300,000 $343,200 $392,621 $449,158 $513,837
Cost of salesc160,000 183,040 209,398 239,551 274,046
Gross profit $140,000 $160,160 $183,223 $209,607 $239,791
a Inventory is unchanged at $16,000 each year (2,000 units × $8). 2,000 of the 
units acquired in the first year are assumed to remain in inventory.
b Sales Year X = (20,000 × $15)(1.10)X–1(1.04)X–1. The quantity sold increases 
by 10 percent each year and the selling price increases by 4 percent each year.
c Cost of sales Year X = (20,000 × $8)(1.10)X–1(1.04)X–1. In Year 1, 20,000 
units are sold with a cost of $8. In subsequent years, the number of units pur -
chased equals the number of units sold and the units sold are assumed to be 
those purchased in the year. The quantity purchased increases by 10 percent 
each year and the purchase price increases by 4 percent each year.

Note that if the company sold more units than it purchased in a year, inventory 
would decrease. This is referred to as LIFO liquidation. The cost of sales of the 
units sold in excess of those purchased would reflect the inventory carrying 
amount. In this example, each unit sold in excess of those purchased would 
have a cost of sales of $8 and a higher gross profit.

Reading 27 ■ Inventories 356
Company F using 
FIFO Y ear 1 Y ear 2 Y ear 3 Y ear 4 Y ear 5
Ending inventorya$16,000 $16,640 $17,306 $17,998 $18,718
Cost of salesc160,000 182,400 208,732 238,859 273,326
Gross profit $140,000 $160,800 $183,889 $210,299 $240,511
a Ending Inventory Year X = 2,000 units × Cost in Year X = 2,000 units [$8 × 
(1.04)X–1]. 2,000 units of the units acquired in Year X are assumed to remain 
b Sales Year X = (20,000 × $15)(1.10)X–1(1.04)X–1
c Cost of sales Year 1 = $160,000 (= 20,000 units × $8). There was no begin -
ning inventory.
Cost of sales Year X (where X ≠ 1) = Beginning inventory plus purchases 
less ending inventory
= (Inventory at Year X–1) + [(20,000 × $8)(1.10)X–1(1.04)X–1] − (Inventory 
at Year X)
= 2,000($8)(1.04)X–2 + [(20,000 × $8)(1.10)X–1(1.04)X–1] – [2,000 ($8)(1.04)
X–1]
For example, cost of sales Year 2 = 2,000($8) + [(20,000 × $8)(1.10)(1.04)] –

[2,000 ($8)(1.04)] = $16,000 + 183,040 – 16,640 = $182,400
Company L Company F
Y ear 1 2 3 4 5 1 2 3 4 5
Inventory 
turnover10.0 11.4 13.1 15.0 17.1 10.0 11.0 12.1 13.3 14.6
Gross profit 
margin (%)46.7 46.7 46.7 46.7 46.7 46.7 46.9 46.8 46.8 46.8
Inventory turnover ratio  = Cost of sales ÷ Ending inventory. The inventory 
turnover ratio increased each year for both companies because the units sold 
increased, whereas the units in ending inventory remained unchanged. The 
increase in the inventory turnover ratio is higher for Company L because 
Company L’s cost of sales is increasing for inflation but the inventory carrying 
amount is unaffected by inflation. It might appear that a company using the 
LIFO method manages its inventory more effectively, but this is deceptive. Both 
companies have identical quantities and prices of purchases and sales and only 
differ in the inventory valuation method used.
Gross profit margin  = Gross profit ÷ Sales. The gross profit margin is stable

under LIFO because both sales and cost of sales increase at the same rate of 
inflation. The gross profit margin is slightly higher under the FIFO method 
after the first year because a proportion of the cost of sales reflects an older 
purchase price.

The LIFO Method 357
THE LIFO METHOD
In the United States, the LIFO method is widely used (approximately 36 percent of 
US companies use the LIFO method). The potential income tax savings are a benefit 
of using the LIFO method when inventory costs are increasing. The higher cash flows 
due to lower income taxes may make the company more valuable because the value 
of a company is based on the present value of its future cash flows. Under the “LIFO 
conformity rule, ” the US tax code requires that companies using the LIFO method 
for tax purposes must also use the LIFO method for financial reporting. Under the 
LIFO method, ending inventory is assumed to consist of those units that have been 
held the longest. This generally results in ending inventories with carrying amounts 
lower than current replacement costs because inventory costs typically increase over 
time. Cost of sales will more closely reflect current replacement costs.

If the purchase prices (purchase costs) or production costs of inventory are increas -
ing, the income statement consequences of using the LIFO method compared to other 
methods will include higher cost of sales, and lower gross profit, operating profit, 
income tax expense, and net income. The balance sheet consequences include lower 
ending inventory, working capital, total assets, retained earnings, and shareholders’ 
equity. The lower income tax paid will result in higher net cash flow from operating 
activities. Some of the financial ratio effects are a lower current ratio, higher debt-  to- 
equity ratios, and lower profitability ratios.
If the purchase prices or production costs of inventory are decreasing, it is unlikely 
that a company will use the LIFO method for tax purposes (and therefore for financial 
reporting purposes due to the LIFO conformity rule) because this will result in lower 
cost of sales, and higher taxable income and income taxes. However, if the company

had elected to use the LIFO method and cannot justify changing the inventory valu -
ation method for tax and financial reporting purposes when inventory costs begin to 
decrease, the income statement, balance sheet, and ratio effects will be opposite to 
the effects during a period of increasing costs.
The US Securities Exchange Commission (SEC) has proposed the full adoption of 
IFRS by all US reporting companies beginning in 2014. An important consequence 
of this proposal would be the complete elimination of the LIFO inventory method 
for financial reporting and, due to the LIFO conformity rule, tax reporting by US 
companies. As a consequence of the restatement of financial statements to the FIFO 
or weighted average cost method, significant immediate income tax liabilities may 
arise in the year of transition from the LIFO method to either the FIFO or weighted 
average cost method.
4.1 LIFO Reserve
For companies using the LIFO method, US GAAP requires disclosure, in the notes to

the financial statements or on the balance sheet, of the amount of the LIFO reserve. The 
LIFO reserve  is the difference between the reported LIFO inventory carrying amount 
and the inventory amount that would have been reported if the FIFO method had 
been used (in other words, the FIFO inventory value less the LIFO inventory value). 
The disclosure provides the information that analysts need to adjust a company’s cost 
of sales (cost of goods sold) and ending inventory balance based on the LIFO method, 
to the FIFO method.
To compare companies using LIFO with companies not using LIFO, inventory 
is adjusted by adding the disclosed LIFO reserve to the inventory balance that is 
reported on the balance sheet. The reported inventory balance, using LIFO, plus the 
LIFO reserve equals the inventory that would have been reported under FIFO. Cost 
of sales is adjusted by subtracting the increase in the LIFO reserve during the period 4

Reading 27 ■ Inventories 358
from the cost of sales amount that is reported on the income statement. If the LIFO 
reserve has declined during the period,10 the decrease in the reserve is added to the 
cost of sales amount that is reported on the income statement. The LIFO reserve dis -
closure can be used to adjust the financial statements of a US company using the LIFO 
method to make them comparable with a similar company using the FIFO method.
EXAMPLE 5   
Inventory Conversion from LIFO to FIFO
Caterpillar Inc. (CAT), based in Peoria, Illinois, USA, is the largest maker of 
construction and mining equipment, diesel and natural gas engines, and indus -
trial gas turbines in the world. Excerpts from CAT’s consolidated financial state -
ments are shown in Exhibits 1 and 2; notes pertaining to CAT’s inventories are 
presented in Exhibit 3. Assume tax rates of 20 percent for 2008 and 30 percent 
for earlier years. The assumed tax rates are based on the provision for taxes as

a percentage of consolidated profits before taxes rather than the US corporate 
statutory tax rate of 35 percent.
1 What inventory values would CAT report for 2008, 2007, and 2006 if it 
had used the FIFO method instead of the LIFO method?
2 What amount would CAT’s cost of goods sold for 2008 and 2007 be if it 
3 What net income (profit) would CAT report for 2008 and 2007 if it had 
used the FIFO method instead of the LIFO method?
4 By what amount would CAT’s 2008 and 2007 net cash flow from operat -
ing activities decline if CAT used the FIFO method instead of the LIFO 
method?
5 What is the cumulative amount of income tax savings that CAT has 
generated through 2008 by using the LIFO method instead of the FIFO 
method?
6 What amount would be added to CAT’s retained earnings (profit 
employed in the business) at 31 December 2008 if CAT had used the FIFO 
method instead of the LIFO method?

7 What would be the change in Cat’s cash balance if CAT had used the 
FIFO method instead of the LIFO method?
8 Calculate and compare the following for 2008 under the LIFO method and 
the FIFO method: inventory turnover ratio, days of inventory on hand, 
gross profit margin, net profit margin, return on assets, current ratio, and 
total liabilities-  to- equity ratio.
Exhibit 1   Caterpillar Inc. Consolidated Results of Operation (US$ 
millions)
For the years ended 31 December 2008 2007 2006
Sales and revenues:
  Sales of Machinery and Engines 48,044 41,962 38,869
10 This typically results from a reduction in inventory units and is referred to as LIFO liquidation. LIFO 
liquidation is discussed in Section 4.2.

The LIFO Method 359
  Revenue of Financial Products 3,280 2,996 2,648
   Total sales and revenues 51,324 44,958 41,517
Operating costs:
  Cost of goods sold 38,415 32,626 29,549
  ⋮ ⋮ ⋮ ⋮
  Interest expense of Financial Products 1,153 1,132 1,023
  ⋮ ⋮ ⋮ ⋮
   Total operating costs 46,876 40,037 36,596
Operating profit 4,448 4,921 4,921
  Interest expense excluding Financial Products 274 288 274
  Other income (expense) 299 320 214
Consolidated profit before taxes 4,473 4,953 4,861
  Provision for income taxes 953 1,485 1,405
  Profit of consolidated companies 3,520 3,468 3,456
  Equity in profit of unconsolidated affiliated 
companies37 73 81
Profit 3,557 3,541 3,537
Exhibit 2   Caterpillar Inc. Consolidated Financial Position (US$ 
millions) 
31 December 2008 2007 2006
Assets
  Current assets:
   Cash and short-  term investments 2,736 1,122 530
   ⋮ ⋮ ⋮ ⋮
   Inventories 8,781 7,204 6,351
  Total current assets 31,633 25,477 23,663
   ⋮ ⋮ ⋮ ⋮

⋮ ⋮ ⋮ ⋮
Total assets 67,782 56,132 51,449
Total current liabilities 26,069 22,245 19,822
⋮ ⋮ ⋮ ⋮
Total liabilities 61,171 47,249 44,590
Redeemable noncontrolling interest (Note 25) 524
Stockholders’ equity
  Common stock of $1.00 par value:
  Authorized shares: 900,000,000
(continued)Exhibit 1   (Continued)

Reading 27 ■ Inventories 360
  Issued shares (2008, 2007 and 2006 – 
814,894,624) at paid-  in amount3,057 2,744 2,465
  Treasury stock (2008 – 213,367,983 shares; 
2007 – 190,908,490 shares and 2006 – 
169,086,448 shares) at cost(11,217) (9,451) (7,352)
  Profit employed in the business 19,826 17,398 14,593
  Accumulated other comprehensive income (5,579) (1,808) (2,847)
Total stockholders’ equity 6,087 8,883 6,859
Total liabilities and stockholders’ equity 67,782 56,132 51,449
Exhibit 3   Caterpillar Inc. Selected Notes to Consolidated Financial 
Statements
Note 1. Operations and Summary of Significant Accounting Policies
D. Inventories
Inventories are stated at the lower of cost or market. Cost is principally 
determined using the last-  in, first-  out (LIFO) method. The value of inven -
tories on the LIFO basis represented about 70% of total inventories at 
December 31, 2008 and about 75% of total inventories at December 31, 
2007 and 2006.

If the FIFO (first-  in, first-  out) method had been in use, inventories 
would have been $3,183 million, $2,617 million and $2,403 million higher 
than reported at December 31, 2008, 2007 and 2006, respectively.
Note 9. Inventories
31 December (millions of dollars) 2008 2007 2006
Raw Materials 3,356 2,990 2,698
Work-  in- process 1,107 863 591
Finished goods 4,022 3,066 2,785
Supplies 296 285 277
Total inventories 8,781 7,204 6,351
We had long-  term material purchase obligations of approximately $363 mil -
lion at December 31, 2008.
Total inventories (LIFO method) 8,781 7,204 6,351
From Note 1.D (LIFO reserve) 3,183 2,617 2,403
Total inventories (FIFO method) 11,964 9,821 8,754Exhibit 2   (Continued)

The LIFO Method 361
31 December (millions of dollars) 2008 2007
Cost of goods sold (LIFO method) 38,415 32,626
Less: Increase in LIFO reserve* −566 −214
Cost of goods sold (FIFO method) 37,849 32,412
* From Note 1.D, the increase in LIFO reserve for 2008 is 566 (3,183 – 2,617) and for 2007 
is 214 (2,617 – 2,403).
Net income (LIFO method) 3,557 3,541
Reduction in cost of goods sold (increase in 
operating profit)566 214
Taxes on increased operating profit* −113 −64
Net income (FIFO method) 4,010 3,691
* The taxes on the increased operating profit are assumed to be 113 (566 × 20%) for 2008 
and 64 (214 × 30%) for 2007.
The effect on a company’s net cash flow from operating activities is limited to the 
impact of the change on income taxes paid; changes in allocating inventory costs 
to ending inventory and cost of goods sold does not change any cash flows except

income taxes. Consequently, the effect of using FIFO on CAT’s net operating 
cash flow from operating activities would be a decline of $113 million in 2008 
and a decline of $64 million in 2007. These are the approximate incremental 
increases in income taxes that CAT would have incurred if the FIFO method 
were used instead of the LIFO method (see solution to 3 above).
Solution to 5:
Assuming tax rates of 20 percent for 2008 and 30 percent for earlier years, the 
cumulative amount of income tax savings that CAT has generated by using 
the LIFO method instead of FIFO is approximately $898 million (566 × 20% + 
2,617 × 30%). Note 1.D indicates a LIFO reserve of $2,617 million at the end of 
2007 and an increase in the LIFO reserve of $566 million in 2008. Therefore, 
under the FIFO method, cumulative gross profits would have been $2,617 million 
higher as of the end of 2007 and an additional $566 million higher as of the end

of 2008. The estimated tax savings would be higher (lower) if income tax rates 
were assumed to be higher (lower).
Solution to 6:
The amount that would be added to CAT’s retained earnings is $2,285 million 
(3,183 – 898) or (566 × 80% + 2,617 × 70%). This represents the cumulative 
increase in operating profit due to the decrease in cost of goods sold (LIFO 
reserve of $3,183 million) less the assumed taxes on that profit ($898 million, see 
solution to 5 above). Some analysts advocate ignoring the tax consequences and 
suggest simply adjusting inventory and equity by the same amount. They argue

Reading 27 ■ Inventories 362
that the reported equity of the firm is understated by the difference between 
the current value of its inventory (approximated by the value under FIFO) and 
its carrying value (value under LIFO).
Solution to 7:
Under the FIFO method, an additional $898 million is assumed to have been 
incurred for tax expenses. If CAT switched to FIFO, it would have an additional 
tax liability of $898 million as a consequence of the restatement of financial state -
ments to the FIFO method. This illustrates the significant immediate income tax 
liabilities that may arise in the year of transition from the LIFO method to the 
FIFO method. If CAT switched to FIFO for tax purposes, there would be a cash 
outflow for the additional taxes. However, because the company is not actually 
converting at this point for either tax or reporting purposes, it is appropriate 
to reflect a deferred tax liability rather than a reduction in cash. In this case

for analysis purposes, under FIFO, inventory would increase by $3,183 million, 
equity by $2,285 million, and non-  current liabilities by $898 million.
Solution to 8:
CAT’s ratios for 2008 under the LIFO and FIFO methods are as follows:
LIFO FIFO
Inventory turnover 4.81 3.47
Days of inventory on hand 76.1 days 105.5 days
Gross profit margin 20.04% 21.22%
Net profit margin 6.93% 7.81%
Return on assets 5.74% 6.18%
Current ratio 1.21 1.34
Total liabilities-  to- equity ratio 10.05 7.41
Inventory turnover ratio  = Cost of goods sold ÷ Average inventory
LIFO = 4.81 = 38,415 ÷ [(8,781 + 7,204) ÷ 2]
FIFO = 3.47 = 37,849 ÷ [(11,964 + 9,821) ÷ 2]
The ratio is higher under LIFO because, given rising inventory costs, cost of 
goods sold will be higher and inventory carrying amounts will be lower under 
LIFO. If an analyst made no adjustment for the difference in inventory methods, 
it might appear that a company using the LIFO method manages its inventory 
more effectively.

Days of inventory on hand  = Number of days in period ÷ Inventory turnover ratio
LIFO = 76.1 days = (366 days* ÷ 4.81)
FIFO = 105.5 days = (366 days ÷ 3.47)
*2008 was a leap year.
Without adjustment, a company using the LIFO method might appear to manage 
its inventory more effectively. This is primarily the result of the lower inventory 
carrying amounts under LIFO.
Gross profit margin  = Gross profit ÷ Total revenue
LIFO = 20.04 percent = [(48,044 – 38,415) ÷ 48,044]
FIFO = 21.22 percent = [(48,044 – 37,849) ÷ 48,044]

The LIFO Method 363
Revenue of financial products is excluded from the calculation of gross profit. 
Gross profit is sales of machinery and engines less cost of goods sold. The gross 
profit margin is lower under LIFO because the cost of goods sold is higher given 
rising inventory costs.
Net profit margin  = Net income ÷ Total revenue
LIFO = 6.93 percent = (3,557 ÷ 51,324)
FIFO = 7.81 percent = (4,010 ÷ 51,324]
The net profit margin is lower under LIFO because the cost of goods sold is 
higher. The absolute percentage difference is less than that of the gross profit 
margin because of income taxes on the increased income reported under FIFO 
and because net income is divided by total revenue including sales of machinery 
and engines and revenue of financial products. The company appears to be less 
profitable under LIFO.
Return on assets  = Net income ÷ Average total assets
LIFO = 5.74 percent = 3,557 ÷ [(67,782 + 56,132) ÷ 2]
FIFO = 6.18 percent = 4,010 ÷ [(67,782 + 3,183) + (56,132 + 2,617) ÷ 2]

The total assets under FIFO are the LIFO total assets increased by the LIFO 
reserve. The return on assets is lower under LIFO because the lower net income 
due to the higher cost of goods sold has a greater impact on the ratio than the 
lower total assets, which are the result of lower inventory carrying amounts. 
The company appears to be less profitable under LIFO.
Current ratio  = Current assets ÷ Current liabilities
LIFO = 1.21 = (31,633 ÷ 26,069)
FIFO = 1.34 = [(31,633 + 3,183) ÷ 26,069]
The current ratio is lower under LIFO primarily because of lower inventory 
carrying amount. The company appears to be less liquid under LIFO.
Total liabilities-  to- equity ratio  = Total liabilities ÷ Total shareholders’ equity
LIFO = 10.05 = (61,171 ÷ 6,087)
FIFO = 7.41 = [(61,171 + 898) ÷ (6,087 + 2,285)]
The ratio is higher under LIFO because the addition to retained earnings under 
FIFO reduces the ratio. The company appears to be more highly leveraged under 
LIFO.

LIFO.
In summary, the company appears to be less profitable, less liquid, and more 
highly leveraged under LIFO. Yet, because a company’s value is based on the 
present value of future cash flows, LIFO will increase the company’s value because 
the cash flows are higher in earlier years due to lower taxes. LIFO is primarily 
used for the tax benefits it provides.
4.2 LIFO Liquidations
In periods of rising inventory unit costs, the carrying amount of inventory under FIFO 
will always exceed the carrying amount of inventory under LIFO. The LIFO reserve 
may increase over time as the result of the increasing difference between the older 
costs used to value inventory under LIFO and the more recent costs used to value

Reading 27 ■ Inventories 364
inventory under FIFO. Also, when the number of inventory units manufactured or 
purchased exceeds the number of units sold, the LIFO reserve may increase as the 
result of the addition of new LIFO layers (the quantity of inventory units is increasing 
and each increase in quantity creates a new LIFO layer).
When the number of units sold exceeds the number of units purchased or manu -
factured, the number of units in ending inventory is lower than the number of units 
in beginning inventory and a company using LIFO will experience a LIFO liquidation 
(some of the older units held in inventory are assumed to have been sold). If inven -
tory unit costs have been rising from period to period and LIFO liquidation occurs, 
this will produce an inventory-  related increase in gross profits. The increase in gross 
profits occurs because of the lower inventory carrying amounts of the liquidated units.

The lower inventory carrying amounts are used for cost of sales and the sales are at 
the current prices. The gross profit on these units is higher than the gross profit that 
would be recognised using more current costs. These inventory profits caused by a 
LIFO liquidation, however, are one-  time events and are not sustainable.
LIFO liquidations can occur for a variety of reasons. The reduction in inventory 
levels may be outside of management’s control; for example, labour strikes at a sup -
plier may force a company to reduce inventory levels to meet customer demands. In 
periods of economic recession or when customer demand is declining, a company 
may choose to reduce existing inventory levels rather than invest in new inventory. 
Analysts should be aware that management can potentially manipulate and inflate 
their company’s reported gross profits and net income at critical times by intentionally 
reducing inventory quantities and liquidating older layers of LIFO inventory (selling

some units of beginning inventory). During economic downturns, LIFO liquidation 
may result in higher gross profit than would otherwise be realised. If LIFO layers of 
inventory are temporarily depleted and not replaced by fiscal year-  end, LIFO liquidation 
will occur resulting in unsustainable higher gross profits. Therefore, it is imperative 
to review the LIFO reserve footnote disclosures to determine if LIFO liquidation has 
occurred. A decline in the LIFO reserve from the prior period may be indicative of 
LIFO liquidation.
EXAMPLE 6   
LIFO Liquidation: Financial Statement Impact and 
Disclosure
The following excerpts are from the 2007 10-  K of Sturm Ruger & Co., Inc.:
Item 7 — Management’s Discussion and Analysis of Financial 
Condition and Results of Operations
“Reduction in inventory generated positive cash flow for the 
Company, partially offset by the tax impact of the consequent LIFO 
liquidation, which generated negative cash flow as it created taxable

income, resulting in higher tax payments. ”
Balance Sheets  
(In thousands, except per share data)   
December 31, 2007 2006
Assets
Current Assets
  ⋮ ⋮ ⋮
Gross inventories: 64,330 87,477

The LIFO Method 365
Less LIFO reserve (46,890) (57,555)
Less excess and obsolescence reserve (4,143) (5,516)
Net inventories 13,297 24,406
  ⋮ ⋮ ⋮
Total Current Assets 73,512 81,785
  ⋮ ⋮ ⋮
Total Assets $101,882 $117,066
Statements of Income  
Y ear ended December 31, 2007 2006
  ⋮ ⋮ ⋮
Total net sales 156,485 167,620
Cost of products sold 117,186 139,610
Gross profit 39,299 28,010
Expenses:
  ⋮ ⋮ ⋮
Total expenses 30,184 27,088
Operating income 9,115 922
  ⋮ ⋮ ⋮
Total other income, net 7,544 921
Income before income taxes 16,659 1,843
Income taxes 6,330 739
Net income $10,329 $1,104
Basic and Diluted Earnings Per Share $0.46 $0.04
Cash Dividends Per Share $0.00 $0.00
Notes to Financial Statements
1. Significant Accounting Policies
   ⋮
Inventories are stated at the lower of cost, principally determined by the last-  in,

first-  out (LIFO) method, or market. If inventories had been valued using the 
first-  in, first-  out method, inventory values would have been higher by approxi -
mately $46.9 million and $57.6 million at December 31, 2007 and 2006, respec -
tively. During 2007 and 2006, inventory quantities were reduced. This reduction 
resulted in a liquidation of LIFO inventory quantities carried at lower costs 
prevailing in prior years as compared with the current cost of purchases, the 
effect of which decreased costs of products sold by approximately $12.1 million 
and $7.1 million in 2007 and 2006, respectively. There was no LIFO liquidation 
in 2005.
1 What is the decrease in the LIFO reserve on the balance sheet? How 
much less was the cost of products sold in 2007, because of LIFO liquida -
tion, according to the note disclosure?

Reading 27 ■ Inventories 366
2 How did the decreased cost of products sold compare to operating 
income in 2007?
3 How did the LIFO liquidation affect cash flows?
The LIFO reserve decreased by $10,665 thousands (57,555 – 46,890) in 2007. The 
LIFO liquidation decreased costs of products sold by approximately $12.1 million 
in 2007. The decrease in the LIFO reserve is indicative of a LIFO liquidation but 
is not sufficient to determine the exact amount of the LIFO liquidation.
The decreased cost of products sold of approximately $12.1 million exceeds the 
operating income of approximately $9 million.
The LIFO liquidation (reduction in inventory) generated positive cash flow. The 
positive cash flow effect of the LIFO liquidation was reduced by its tax impact. 
The LIFO liquidation resulted in higher taxable income and higher tax payments.
EXAMPLE 7   
LIFO Liquidation Illustration

EXAMPLE 7   
Reliable Fans, Inc. (RF), a hypothetical company, sells high quality fans and has 
been in business since 2006. Exhibit 4 provides relevant data and financial state -
ment information about RF’s inventory purchases and sales of fan inventory for 
the years 2006 through 2009. RF uses the LIFO method and a periodic inventory 
system. What amount of RF’s 2009 gross profit is due to LIFO liquidation?
Exhibit 4   RF Financial Statement Information under LIFO
2006 2007 2008 2009
Fans units purchased 12,000 12,000 12,000 12,000
Purchase cost per fan $100 $105 $110 $115
Fans units sold 10,000 12,000 12,000 13,000
Sales price per fan $200 $205 $210 $215
LIFO Method
Beginning inventory $0 $200,000 $200,000 $200,000
Purchases 1,200,000 1,260,000 1,320,000 1,380,000
Goods available for sale 1,200,000 1,460,000 1,520,000 1,580,000
Ending inventory* (200,000) (200,000) (200,000) (100,000)
Cost of goods sold $1,000,000 1,260,000 $1,320,000 $1,480,000
Income Statement

Sales $2,000,000 $2,460,000 $2,520,000 $2,795,000
Cost of goods sold 1,000,000 1,260,000 1,320,000 1,480,000
Gross profit $1,000,000 $1,200,000 $1,200,000 $1,315,000

Inventory Method Changes 367
Balance Sheet
Inventory $200,000 $200,000 $200,000 $100,000
* Ending inventory 2006, 2007, and 2008 = (2,000 × $100); Ending inventory 2009 = (1,000 × 
$100).
Solution:
RF’s reported gross profit for 2009 is $1,315,000. RF’s 2009 gross profit due to 
LIFO liquidation is $15,000. If RF had purchased 13,000 fans in 2009 rather than 
12,000 fans, the cost of goods sold under the LIFO method would have been 
$1,495,000 (13,000 fans sold at $115.00 purchase cost per fan), and the reported 
gross profit would have been $1,300,000 ($2,795,000 less $1,495,000). The gross 
profit due to LIFO liquidation is $15,000 ($1,315,000 reported gross profit less 
the $1,300,000 gross profit that would have been reported without the LIFO 
liquidation). The gross profit due to LIFO liquidation may also be determined 
by multiplying the number of units liquidated times the difference between the

replacement cost of the units liquidated and their historical purchase cost. For 
RF, 1,000 units times $15 ($115 replacement cost per fan less the $100 historical 
cost per fan) equals the $15,000 gross profit due to LIFO liquidation.
INVENTORY METHOD CHANGES
Companies on rare occasion change inventory valuation methods. Under IFRS, a 
change in method is acceptable only if the change “results in the financial statements 
providing reliable and more relevant information about the effects of transactions, 
other events, or conditions on the business entity’s financial position, financial perfor -
mance, or cash flows. ”11 If the change is justifiable, then it is applied retrospectively.
This means that the change is applied to comparative information for prior peri -
ods as far back as is practicable. The cumulative amount of the adjustments relating 
to periods prior to those presented in the current financial statements is made to

the opening balance of each affected component of equity (i.e., retained earnings or 
comprehensive income) of the earliest period presented. For example, if a company 
changes its inventory method in 2009 and it presents three years of comparative 
financial statements (2007, 2008, and 2009) in its annual report, it would retrospec -
tively reflect this change as far back as possible. The change would be reflected in the 
three years of financial statements presented; the financial statements for 2007 and 
2008 would be restated as if the new method had been used in these periods, and 
the cumulative effect of the change on periods prior to 2007 would be reflected in 
the 2007 opening balance of each affected component of equity. An exemption to the 
restatement applies when it is impracticable to determine either the period-  specific 
effects or the cumulative effect of the change.5Exhibit 4   (Continued)
11 IAS 8 [Accounting Policies, Changes in Accounting Estimates and Errors].

Reading 27 ■ Inventories 368
Under US GAAP , the conditions to make a change in accounting policy and the 
accounting for a change in inventory policy are similar to IFRS.12 US GAAP , however, 
requires companies to thoroughly explain why the newly adopted inventory account -
ing method is superior and preferable to the old method. If a company decides to 
change from LIFO to another inventory method, US GAAP requires a retrospective 
restatement as described above. However, if a company decides to change to the LIFO 
method, it must do so on a prospective basis and retrospective adjustments are not 
made to the financial statements. The carrying amount of inventory under the old 
method becomes the initial LIFO layer in the year of LIFO adoption.
Analysts should carefully evaluate changes in inventory valuation methods. 
Although the stated reason for the inventory change may be to better match inven -
tory costs with sales revenue (or some other plausible business explanation), the real

underlying (and unstated) purpose may be to reduce income tax expense (if changing 
to LIFO from FIFO or average cost), or to increase reported profits (if changing from 
LIFO to FIFO or average cost). As always, the choice of inventory valuation method 
can have a significant impact on financial statements and the financial ratios that are 
derived from them. As a consequence, analysts must carefully consider the impact of 
the change in inventory valuation methods and the differences in inventory valuation 
methods when comparing a company’s performance with that of its industry or its 
INVENTORY ADJUSTMENTS
Significant financial risk can result from the holding of inventory. The cost of inventory 
may not be recoverable due to spoilage, obsolescence, or declines in selling prices. 
IFRS state that inventories shall be measured (and carried on the balance sheet) at the 
lower of cost and net realisable value.13 Net realisable value  is the estimated selling

price in the ordinary course of business less the estimated costs necessary to make 
the sale and estimated costs to get the inventory in condition for sale. The assessment 
of net realisable value is typically done item by item or by groups of similar or related 
items. In the event that the value of inventory declines below the carrying amount 
on the balance sheet, the inventory carrying amount must be written down to its net 
realisable value14 and the loss (reduction in value) recognised as an expense on the 
income statement. This expense may be included as part of cost of sales or reported 
separately.
In each subsequent period, a new assessment of net realisable value is made. 
Reversal (limited to the amount of the original write-  down) is required for a sub -
sequent increase in value of inventory previously written down. The reversal of any 
write-  down of inventories is recognised as a reduction in cost of sales (reduction in 
the amount of inventories recognised as an expense).

US GAAP used to specify the lower of cost or market to value inventories.15 For 
fiscal years beginning after December  15, 2016, inventories measured using other 
than LIFO and retail inventory methods are measured at the lower of cost or net 
realisable value. This is broadly consistent with IFRS with one major difference: US 
GAAP prohibit the reversal of write-  downs. For inventories measured using LIFO and 6
12 FASB ASC Topic 250 [Accounting Changes and Error Corrections].
13 IAS 2 paragraphs 28–33 [Inventories – Net realisable value].
14 Frequently, rather than writing inventory down directly, an inventory valuation allowance account is 
used. The allowance account is netted with the inventory accounts to arrive at the carrying amount that 
appears on the balance sheet.
15 FASB ASC Section 330-  10- 35 [Inventory – Overall – Subsequent Measurement].

Inventory Adjustments 369
retail inventory methods, market value is defined as current replacement cost subject 
to upper and lower limits. Market value cannot exceed net realisable value (selling 
price less reasonably estimated costs of completion and disposal). The lower limit of 
market value is net realisable value less a normal profit margin. Any write-  down to 
market value or net realisable value reduces the value of the inventory, and the loss in 
value (expense) is generally reflected in the income statement in cost of goods sold.
An inventory write-  down reduces both profit and the carrying amount of inven -
tory on the balance sheet and thus has a negative effect on profitability, liquidity, 
and solvency ratios. However, activity ratios (for example, inventory turnover and 
total asset turnover) will be positively affected by a write-  down because the asset 
base (denominator) is reduced. The negative impact on some key ratios, due to the

decrease in profit, may result in the reluctance by some companies to record inventory 
write-  downs unless there is strong evidence that the decline in the value of inventory 
is permanent. This is especially true under US GAAP where reversal of a write-  down 
is prohibited.
IAS 2 [Inventories] does not apply to the inventories of producers of agricultural 
and forest products and minerals and mineral products, nor to commodity broker–
traders. These inventories may be measured at net realisable value (fair value less 
costs to sell and complete) according to well-  established industry practices. If an 
active market exists for these products, the quoted market price in that market is the 
appropriate basis for determining the fair value of that asset. If an active market does 
not exist, a company may use market determined prices or values (such as the most 
recent market transaction price) when available for determining fair value. Changes

in the value of inventory (increase or decrease) are recognised in profit or loss in the 
period of the change. US GAAP is similar to IFRS in its treatment of inventories of 
agricultural and forest products and mineral ores. Mark-  to- market inventory account -
ing is allowed for bullion.
EXAMPLE 8   
Accounting for Declines and Recoveries of Inventory 
Value
Acme Enterprises, a hypothetical company, manufactures computers and prepares 
its financial statements in accordance with IFRS. In 2008, the cost of ending 
inventory was €5.2  million but its net realisable value was €4.9  million. The 
current replacement cost of the inventory is €4.7 million. This figure exceeds 
the net realisable value less a normal profit margin. In 2009, the net realisable 
value of Acme’s inventory was €0.5 million greater than the carrying amount.
1 What was the effect of the write-  down on Acme’s 2008 financial state -
ments? What was the effect of the recovery on Acme’s 2009 financial 

2 Under US GAAP , if Acme used the LIFO method, what would be the 
effects of the write-  down on Acme’s 2008 financial statements and of the 
recovery on Acme’s 2009 financial statements?
3 What would be the effect of the recovery on Acme’s 2009 financial 
statements if Acme’s inventory were agricultural products instead of 
computers?

Reading 27 ■ Inventories 370
For 2008, Acme would write its inventory down to €4.9 million and record the 
change in value of €0.3  million as an expense on the income statement. For 
2009, Acme would increase the carrying amount of its inventory and reduce 
the cost of sales by €0.3 million (the recovery is limited to the amount of the 
original write-  down).
Under US GAAP , for 2008, Acme would write its inventory down to €4.7 million 
and typically include the change in value of €0.5 million in cost of goods sold 
on the income statement. For 2009, Acme would not reverse the write-  down.
If Acme’s inventory were agricultural products instead of computers, inventory 
would be measured at net realisable value and Acme would, therefore, increase 
inventory by and record a gain of €0.5 million for 2009.
Analysts should consider the possibility of an inventory write-  down because the

impact on a company’s financial ratios may be substantial. The potential for inventory 
write-  downs can be high for companies in industries where technological obsolescence 
of inventories is a significant risk. Analysts should carefully evaluate prospective inven -
tory impairments (as well as other potential asset impairments) and their potential 
effects on the financial ratios when debt covenants include financial ratio requirements. 
The breaching of debt covenants can have a significant impact on a company.
Companies that use specific identification, weighted average cost, or FIFO methods 
are more likely to incur inventory write-  downs than companies that use the LIFO 
method. Under the LIFO method, the oldest  costs are reflected in the inventory car -
rying amount on the balance sheet. Given increasing inventory costs, the inventory 
carrying amounts under the LIFO method are already conservatively presented at the

oldest and lowest costs. Thus, it is far less likely that inventory write-  downs will occur 
under LIFO—and if a write-  down does occur, it is likely to be of a lesser magnitude.
EXAMPLE 9   
Effect of Inventory Write-  downs on Financial Ratios
The Volvo Group, based in Göteborg, Sweden, is a leading supplier of commercial 
transport products such as construction equipment, trucks, busses, and drive 
systems for marine and industrial applications as well as aircraft engine com -
ponents.16 Excerpts from Volvo’s consolidated financial statements are shown 
in Exhibits 5 and 6. Notes pertaining to Volvo’s inventories are presented in 
Exhibit 7.
1 What inventory values would Volvo have reported for 2008, 2007, and 
2006 if it had no allowance for inventory obsolescence?
2 Assuming that any changes to the allowance for inventory obsolescence 
are reflected in the cost of sales, what amount would Volvo’s cost of sales 
be for 2008 and 2007 if it had not recorded inventory write-  downs in 2008

and 2007?
16 As of this writing, the Volvo line of automobiles is not under the control and management of the 
Volvo Group.

Inventory Adjustments 371
3 What amount would Volvo’s profit (net income) be for 2008 and 2007 if it 
had not recorded inventory write-  downs in 2008 and 2007? Assume tax 
rates of 28.5 percent for 2008 and 30 percent for 2007.
4 What would Volvo’s 2008 profit (net income) have been if it had reversed 
all past inventory write-  downs in 2008? This question is independent of 1, 
2, and 3. Assume a tax rate of 28.5 percent for 2008.
5 Compare the following for 2008 based on the numbers as reported and 
those assuming no allowance for inventory obsolescence as in questions 1, 
2, and 3: inventory turnover ratio, days of inventory on hand, gross profit 
margin, and net profit margin.
6 CAT (Example 5) has no disclosures indicative of either inventory write-  
downs or a cumulative allowance for inventory obsolescence in its 2008 
financial statements. Provide a conceptual explanation as to why Volvo 
incurred inventory write-  downs for 2008 but CAT did not.

Exhibit 5   Volvo Group Consolidated Income Statements (Swedish 
Krona in millions, except per share data)
Net sales 303,667 285,405 258,835
Cost of sales (237,578) (219,600) (199,054)
Gross income 66,089 65,805 59,781
  ⋮ ⋮ ⋮ ⋮
Operating income 15,851 22,231 20,399
Interest income and similar credits 1,171 952 666
Income expenses and similar charges (1,935) (1,122) (585)
Other financial income and expenses (1,077) (504) (181)
Income after financial items 14,010 21,557 20,299
Income taxes (3,994) (6,529) (3,981)
Income for the period 10,016 15,028 16,318
Attributable to:
Equity holders of the parent company 9,942 14,932 16,268
Minority interests 74 96 50
Profit 10,016 15,028 16,318
Exhibit 6   Volvo Group Consolidated Balance Sheets (Swedish Krona in 
millions)
Assets    
Total non-  current assets 196,381 162,487 124,039
Current assets:      
Inventories 55,045 43,645 34,211
  ⋮ ⋮ ⋮ ⋮
Cash and cash equivalents 17,712 14,544 10,757

Reading 27 ■ Inventories 372
Total current assets 176,038 159,160 134,388
Total assets 372,419 321,647 258,427
     
Shareholders’ equity and liabilities      
Shareholders’ equity:      
  Share capital 2,554 2,554 2,554
  Reserves 5,078 2,146 1,664
  Retained earnings 66,436 62,570 66,418
  Income for the period 9,942 14,932 16,268
Equity attributable to equity holders of 
the parent company84,010 82,202 86,904
Minority interests 630 579 284
Total shareholders’ equity 84,640 82,781 87,188
Total non-  current provisions 29,031 26,202 19,864
Total non-  current liabilities 92,608 71,729 45,457
Total current provisions 11,750 10,656 9,799
Total current liabilities 154,390 130,279 96,119
Total shareholders’ equity and 
liabilities372,419 321,647 258,427
Exhibit 7   Volvo Group Selected Notes to Consolidated Financial 
Note 1. Accounting Principles
Inventories are reported at the lower of cost, in accordance with the

first-  in, first-  out method (FIFO), or net realisable value. The acquisition 
value is based on the standard cost method, including costs for all direct 
manufacturing expenses and the apportionable share of the capacity and 
other related manufacturing costs. The standard costs are tested regularly 
and adjustments are made based on current conditions. Costs for research 
and development, selling, administration and financial expenses are not 
included. Net realisable value is calculated as the selling price less costs 
attributable to the sale.
Note 2. Key Sources of Estimation Uncertainty
Inventory obsolescence
Inventories are reported at the lower of cost, in accordance with the 
first-  in, first-  out method (FIFO), or net realisable value. The estimated 
net realisable value includes management consideration of out-  dated 
articles, over-  stocking, physical damages, inventory-  lead-  time, handling 
and other selling costs. If the estimated net realisable value is lower than

cost, a valuation allowance is established for inventory obsolescence. The 
total inventory value, net of inventory obsolescence allowance, is per 31 
December 2008, SEK (in millions) 55,045.Exhibit 6   (Continued)

Inventory Adjustments 373
Note 18. Inventories
31 December (millions of Krona) 2008 2007 2006
Finished products 39,137 28,077 20,396
Production materials, etc. 15,908 15,568 13,815
Total 55,045 43,645 34,211
Increase (decrease) in allowance for inventory obsolescence
Balance sheet, 31 December, preced -
ing year2,837 2,015 2,401
Increase in allowance for inventory 
obsolescence charged to income1,229 757 186
Scrapping (325) (239) (169)
Translation differences 305 2 (130)
Reclassifications, etc. (524) 302 (273)
Balance sheet, 31 December 3,522 2,837 2,015
31 December (Swedish krona in 
millions) 2008 2007 2006
Total inventories, net 55,045 43,645 34,211
From Note 18. (Allowance for 
obsolescence)3,522 2,837 2,015
Total inventories (without allowance) 58,567 46,482 36,226
31 December (Swedish krona in millions) 2008 2007
Cost of sales 237,578 219,600
Less: Increase in allowance for obsolescence* −685 −822

Cost of sales (without allowance) 236,893 218,778
* From Note 18, the increase in allowance for obsolescence for 2008 is 685 (3,522 – 2,837) 
and for 2007 is 822 (2,837 – 2,015).Exhibit 7   (Continued)

Reading 27 ■ Inventories 374
Profit (Net income) 10,016 15,028
Reduction in cost of sales (increase in operat -
ing profit)685 822
Taxes on increased operating profit* −195 −247
Profit (without allowance) 10,506 15,603
* Taxes on the increased operating profit are assumed to be 195 (685 × 28.5%) for 2008 and 
247 (822 × 30%) for 2007.
31 December (Swedish krona in millions) 2008
Profit (Net income) 10,016
Reduction in cost of sales (increase in operating profit) 3,522
Taxes on increased operating profit* −1,004
Profit (after recovery of previous write-  downs) 12,534
* Taxes on the increased operating profit are assumed to be 1,004 (3,522 × 28.5%) for 2008.
The Volvo Group’s financial ratios for 2008 with the allowance for inventory 
obsolescence and without the allowance for inventory obsolescence are as follows:
With Allowance  
(As Reported)Without Allowance  
(Adjusted)
Inventory turnover ratio 4.81 4.51

Days of inventory on hand 76.1 81.2
Gross profit margin 21.76% 21.99%
Net profit margin 3.30% 3.46%
Inventory turnover ratio  = Cost of sales ÷ Average inventory
With allowance (as reported) = 4.81 = 237,578 ÷ [(55,045 + 43,645) ÷ 2]
Without allowance (adjusted) = 4.51 = 236,893 ÷ [(58,567 + 46,482) ÷ 2]
Inventory turnover is higher based on the numbers as reported because cost 
of sales will be higher (assuming inventory write-  downs are reported as part of 
cost of sales) and inventory carrying amounts will be lower with an allowance 
for inventory obsolescence. The company appears to manage its inventory more 
efficiently when it has inventory write-  downs.
With allowance (as reported) = 76.1 days = (366 days* ÷ 4.81)
Without allowance (adjusted) = 81.2 days = (366 days ÷ 4.51)

Evaluation of Inventory Management 375
Days of inventory on hand are lower based on the numbers as reported because 
the inventory turnover is higher. A company with inventory write-  downs might 
appear to manage its inventory more effectively. This is primarily the result of 
the lower inventory carrying amounts.
Gross profit margin  = Gross income ÷ Net sales
With allowance (as reported) = 21.76 percent = (66,089 ÷ 303,667)
Without allowance (adjusted) = 21.99 percent = [(66,089 + 685) ÷ 303,667]
The gross profit margin is lower with inventory write-  downs because the cost 
of sales is higher. This assumes that inventory write-  downs are reported as part 
of cost of sales.
Net profit margin  = Profit ÷ Net sales
With allowance (as reported) = 3.30 percent = (10,016 ÷ 303,667)
Without allowance (adjusted) = 3.46 percent = (10,506 ÷ 303,667)
The net profit margin is lower with inventory write-  downs because the cost of

sales is higher (assuming the inventory write-  downs are reported as part of cost 
of sales). The absolute percentage difference is less than that of the gross profit 
margin because of income taxes on the increased income without write-  downs.
The profitability ratios (gross profit margin and net profit margin) for Volvo 
Group would have been slightly better (higher) for 2008 if the company had not 
recorded inventory write-  downs. The activity ratio (inventory turnover ratio) 
would appear less attractive without the write-  downs. The inventory turnover 
ratio is slightly better (higher) with inventory write-  downs because inventory 
write-  downs increase cost of sales (numerator) and decrease the average inven -
tory (denominator), making inventory management appear more efficient with 
write-  downs.
CAT uses the LIFO method whereas Volvo uses the FIFO method. Given increas -
ing inventory costs, companies that use the FIFO inventory method are far more

likely to incur inventory write-  downs than those companies that use the LIFO 
method. This is because under the LIFO method, the inventory carrying amounts 
reflect the oldest  costs and therefore the lowest  costs given increasing inventory 
costs. Because inventory carrying amounts under the LIFO method are already 
conservatively presented, it is less likely that inventory write-  downs will occur.
EVALUATION OF INVENTORY MANAGEMENT
The choice of inventory valuation method impacts the financial statements. The 
financial statement items impacted include cost of sales, gross profit, net income, 
inventories, current assets, and total assets. Therefore, the choice of inventory valuation 
method also affects financial ratios that contain these items. Ratios such as current 
ratio, return on assets, gross profit margin, and inventory turnover are impacted. As a 
consequence, analysts must carefully consider inventory valuation method differences

when evaluating a company’s performance over time or when comparing its perfor -
mance with the performance of the industry or industry competitors. Additionally, 
the financial statement items and ratios may be impacted by adjustments of inventory 
carrying amounts to net realisable value or current replacement cost.7

Reading 27 ■ Inventories 376
7.1 Presentation and Disclosure
Disclosures are useful when analyzing a company. IFRS require the following financial 
statement disclosures concerning inventory:
a the accounting policies adopted in measuring inventories, including the cost 
formula (inventory valuation method) used;
b the total carrying amount of inventories and the carrying amount in classifica -
tions (for example, merchandise, raw materials, production supplies, work in 
progress, and finished goods) appropriate to the entity;
c the carrying amount of inventories carried at fair value less costs to sell;
d the amount of inventories recognised as an expense during the period (cost of 
sales);
e the amount of any write-  down of inventories recognised as an expense in the 
period;
f the amount of any reversal of any write-  down that is recognised as a reduction 
in cost of sales in the period;
g the circumstances or events that led to the reversal of a write-  down of invento -
ries; and

ries; and
h the carrying amount of inventories pledged as security for liabilities.
Inventory-  related disclosures under US GAAP are very similar to the disclosures 
above, except that requirements (f) and (g) are not relevant because US GAAP do 
not permit the reversal of prior-  year inventory write-  downs. US GAAP also require 
disclosure of significant estimates applicable to inventories and of any material amount 
of income resulting from the liquidation of LIFO inventory.
7.2 Inventory Ratios
Three ratios often used to evaluate the efficiency and effectiveness of inventory man -
agement are inventory turnover , days of inventory on hand , and gross profit mar -
gin.17 These ratios are directly impacted by a company’s choice of inventory valuation 
method. Analysts should be aware, however, that many other ratios are also affected 
by the choice of inventory valuation method, although less directly. These include

the current ratio, because inventory is a component of current assets; the return-  
on- assets ratio, because cost of sales is a key component in deriving net income and 
inventory is a component of total assets; and even the debt-  to- equity ratio, because 
the cumulative measured net income from the inception of a business is an aggregate 
component of retained earnings.
The inventory turnover ratio measures the number of times during the year a 
company sells (i.e., turns over) its inventory. The higher the turnover ratio, the more 
times that inventory is sold during the year and the lower the relative investment of 
resources in inventory. Days of inventory on hand can be calculated as days in the 
period divided by inventory turnover. Thus, inventory turnover and days of inventory 
on hand are inversely related. It may be that inventory turnover, however, is calculated 
using average inventory in the year whereas days of inventory on hand is based on

the ending inventory amount. In general, inventory turnover and the number of days 
of inventory on hand should be benchmarked against industry norms and compared 
across years.
17 Days of inventory on hand  is also referred to as days in inventory  and average inventory days outstanding .

Evaluation of Inventory Management 377
A high inventory turnover ratio and a low number of days of inventory on hand 
might indicate highly effective inventory management. Alternatively, a high inventory 
ratio and a low number of days of inventory on hand could indicate that the company 
does not carry an adequate amount of inventory or that the company has written 
down inventory values. Inventory shortages could potentially result in lost sales or 
production problems in the case of the raw materials inventory of a manufacturer. To 
assess which explanation is more likely, analysts can compare the company’s inventory 
turnover and sales growth rate with those of the industry and review financial statement 
disclosures. Slower growth combined with higher inventory turnover could indicate 
inadequate inventory levels. Write-  downs of inventory could reflect poor inventory 
management. Minimal write-  downs and sales growth rates at or above the industry’s

growth rates would support the interpretation that the higher turnover reflects greater 
efficiency in managing inventory.
A low inventory turnover ratio and a high number of days of inventory on hand 
relative to industry norms could be an indicator of slow-  moving or obsolete inventory. 
Again, comparing the company’s sales growth across years and with the industry and 
reviewing financial statement disclosures can provide additional insight.
The gross profit margin, the ratio of gross profit to sales, indicates the percentage 
of sales being contributed to net income as opposed to covering the cost of sales. 
Firms in highly competitive industries generally have lower gross profit margins than 
firms in industries with fewer competitors. A company’s gross profit margin may be a 
function of its type of product. A company selling luxury products will generally have 
higher gross profit margins than a company selling staple products. The inventory

turnover of the company selling luxury products, however, is likely to be much lower 
than the inventory turnover of the company selling staple products.
7.3 Financial Analysis Illustrations
IFRS and US GAAP require companies to disclose, either on the balance sheet or in the 
notes to the financial statements, the carrying amounts of inventories in classifications 
suitable to the company. For manufacturing companies, these classifications might 
include production supplies, raw materials, work in progress, and finished goods. For 
a retailer, these classifications might include significant categories of merchandise or 
the grouping of inventories with similar attributes. These disclosures may provide 
signals about a company’s future sales and profits.
For example, a significant increase (attributable to increases in unit volume rather 
than increases in unit cost) in raw materials and/or work-  in- progress inventories may

signal that the company expects an increase in demand for its products. This suggests 
an anticipated increase in sales and profit. However, a substantial increase in finished 
goods inventories while raw materials and work-  in- progress inventories are declining 
may signal a decrease in demand for the company’s products and hence lower future 
sales and profit. This may also signal a potential future write down of finished goods 
inventory. Irrespective of the signal, an analyst should thoroughly investigate the 
underlying reasons for any significant changes in a company’s raw materials, work-  
in- progress, and finished goods inventories.
Analysts also should compare the growth rate of a company’s sales to the growth 
rate of its finished goods inventories, because this could also provide a signal about 
future sales and profits. For example, if the growth of inventories is greater than the 
growth of sales, this could indicate a decline in demand and a decrease in future earn -

ings. The company may have to lower (mark down) the selling price of its products to 
reduce its inventory balances, or it may have to write down the value of its inventory 
because of obsolescence, both of which would negatively affect profits. Besides the 
potential for mark-  downs or write-  downs, having too much inventory on hand or the 
wrong type of inventory can have a negative financial effect on a company because

Reading 27 ■ Inventories 378
it increases inventory related expenses such as insurance, storage costs, and taxes. 
In addition, it means that the company has less cash and working capital available to 
use for other purposes.
Inventory write-  downs may have a substantial impact on a company’s activity, 
profitability, liquidity, and solvency ratios. It is critical for the analyst to be aware 
of industry trends toward product obsolescence and to analyze the financial ratios 
for their sensitivity to potential inventory impairment. Companies can minimise the 
impact of inventory write-  downs by better matching their inventory composition 
and growth with prospective customer demand. To obtain additional information 
about a company’s inventory and its future sales, a variety of sources of information 
are available. Analysts should consider the Management Discussion and Analysis 
(MD&A) or similar sections of the company’s financial reports, industry related news

and publications, and industry economic data.
When conducting comparisons, differences in the choice of inventory valuation 
method can significantly affect the comparability of financial ratios between compa -
nies. A restatement from the LIFO method to the FIFO method is critical to make a 
valid comparison with companies using a method other than the LIFO method such 
as those companies reporting under IFRS. Analysts should seek out as much infor -
mation as feasible when analyzing the performance of companies.
EXAMPLE 10   
Comparative Illustration
1 Using CAT’s LIFO numbers as reported and FIFO adjusted numbers 
(Example 5) and Volvo’s numbers as reported (Example 9), compare the 
following for 2008: inventory turnover ratio, days of inventory on hand, 
gross profit margin, net profit margin, return on assets, current ratio, 
total liabilities-  to- equity ratio, and return on equity. For the current 
ratio, include current provisions as part of current liabilities. For the total

liabilities-  to- equity ratio, include provisions in total liabilities.
2 How much do inventories represent as a component of total assets for 
CAT using LIFO numbers as reported and FIFO adjusted numbers, and 
for Volvo using reported numbers in 2007 and 2008? Discuss any changes 
that would concern an analyst.
3 Using the reported numbers, compare the 2007 and 2008 growth rates of 
CAT and Volvo for sales, finished goods inventory, and inventories other 
than finished goods.
The comparisons between Caterpillar and Volvo for 2008 are as follows:
CAT (LIFO) CAT (FIFO) Volvo
Inventory turnover ratio 4.81 3.47 4.81
Days of inventory on hand 76.1 days 105.5 days 76.1 days
Gross profit margin 20.04% 21.22% 21.76%
Net profit margin 6.93% 7.81% 3.30%
Return on assetsa5.74% 6.18% 2.89%
Current ratiob1.21 1.34 1.06

Evaluation of Inventory Management 379
Total liabilities-  to- equity ratioc10.05 7.41 3.40
Return on equityd47.5% 42.0% 12.0%
Calculations for ratios previously calculated (see Examples 5 and 9) are not shown again.
a Return on assets = Net income ÷ Average total assets
Volvo = 2.89 percent = 10,016 ÷ [(372,419 + 321,647) ÷ 2]
b Current ratio = Current assets ÷ Current liabilities
Volvo = 1.06 = [176,038 ÷ (11,750 + 154,390)]
The question indicates to include current provisions in current liabilities.
c Total liabilities-  to- equity ratio = Total liabilities ÷ Total shareholders’ equity
Volvo = 3.40 = [(29,031 + 92,608 + 11,750 + 154,390) ÷ 84,640]
The question indicates to include provisions in total liabilities.
d Return on equity = Net income ÷ Average shareholders’ equity
CAT (LIFO) = 47.5 percent = 3,557 ÷ [(6,087 + 8,883) ÷ 2]
CAT (FIFO) = 42.0 percent = 4,010 ÷ {[(6,087 + 3,183 – 898) + (8,883 + 2,617 
– 785)] ÷ 2}

– 785)] ÷ 2}
Volvo = 12.0 percent = 10,016 ÷ [(84,640 + 82,781) ÷ 2]
Comparing CAT (FIFO) and Volvo, it appears that Volvo manages its inven -
tory more effectively. It has higher inventory turnover and less days of inventory 
on hand. CAT appears to have superior profitability based on net profit margins. 
CAT did report some losses as other comprehensive income in the balance sheet 
(see Exhibit 2) as indicated by the absolute increase in the negative accumulated 
other comprehensive income. The absolute increase in the negative accumulated 
other comprehensive income results in a reduction of shareholders’ equity which 
makes CAT’s return on equity higher. The higher leverage of CAT also increases 
the return on equity. The sources of CAT’s higher return on equity (reporting 
losses through other comprehensive income and higher leverage) should be of 
concern to an analyst. An analyst should investigate further, rather than reaching

a conclusion based on ratios alone (in other words, try to identify the underlying 
causes of changes or differences in ratios).
The 2008 and 2007 inventory to total assets ratios for CAT using LIFO and 
adjusted to FIFO and for Volvo as reported, are as follows:
2008 12.95% 17.08% 14.78%
2007 12.83% 16.94% 13.57%
Inventory to total assets
CAT (LIFO) 2008 =12.95 percent = 8,781 ÷ 67,782
CAT (LIFO) 2007 = 12.83 percent = 7,204 ÷ 56,132
CAT (FIFO) 2008 = 17.08 percent = 11,964 ÷ (67,782 + 3,183 
– 898)
CAT (FIFO) 2007 = 16.94 percent = 9,821 ÷ (56,132 + 2,617 
– 785)
Volvo 2008 = 14.78 percent = 55,045 ÷ 372,419
Volvo 2007 = 13.57 percent = 43,645 ÷ 321,647

Reading 27 ■ Inventories 380
Based on the numbers as reported, CAT appears to have a lower percentage 
of assets tied up in inventory than Volvo. However, when CAT’s inventory is 
adjusted to FIFO, it has a higher percentage of its assets tied up in inventory 
than Volvo.
The increase in Volvo’s inventory as a percentage of total assets is cause for 
some concern. Higher inventory typically results in higher maintenance costs 
(for example, storage and financing costs). In addition, Volvo may be building up 
slow moving or obsolete inventories that may result in future inventory write-  
downs for 2009. In Volvo’s Note 18, the breakdown by inventory classification 
shows a small increase in the inventory of production materials. It appears that 
Volvo is planning on reducing production until it reduces its finished goods 
inventory. Looking at CAT’s Note 9, all classifications of inventory seem to be 
increasing and because these are valued using the LIFO method, there is some

cause for concern. The company must be increasing inventory quantities and 
adding LIFO layers.
CAT’s and Volvo’s 2008 and 2007 growth rates for sales (for CAT use Sales of 
machinery and engines and for Volvo use Net sales), finished goods, and inven -
tories other than finished goods are as follows:
2008 CAT Volvo
Sales 14.5% 6.4%
Finished goods 31.2% 39.4%
Inventories other than finished goods 15.0% 2.2%
2007 CAT Volvo
Sales 8.0% 10.3%
Finished goods 10.1% 37.7%
Inventories other than finished goods 16.0% 12.7%
Growth rate = (Value for year – Value for previous year)/Value for previous year
2008 CAT
Sales = 14.5 percent = (48,044 – 41,962) ÷ 41,962
Finished goods = 31.2 percent = (4,022 – 3,066) ÷ 3,066
Inventories other than finished goods = 15.0 percent = [(3,356 + 1,107 + 
296) – (2,990 + 863 + 285)] ÷ (2,990 + 863 + 285)
2008 Volvo
Sales = 6.4 percent = (303,667 – 285,405) ÷ 285,405
Finished products = 39.4 percent = (39,137 – 28,077) ÷ 28,077

Inventories other than finished products =2.2 percent = (15,908 – 15,568) 
÷ 15,568
2007 CAT
Sales = 8.0 percent = (41,962 – 38,869) ÷ 38,869
Finished goods = 10.1 percent = (3,066 – 2,785) ÷ 2,785
Inventories other than finished goods = 16.0 percent = [(2,990 + 863 + 285) 
– (2,698 + 591 + 277)] ÷ (2,698 + 591 + 277)
2007 Volvo
Sales = 10.3 percent = (285,405 – 258,835) ÷ 258,835

Evaluation of Inventory Management 381
Finished products = 37.7 percent = (28,077 – 20,396) ÷ 20,396
Inventories other than finished products = 12.7 percent = (15,568 – 13,815) 
÷ 13,815
For both companies, the growth rates in finished goods inventory exceeds the 
growth rate in sales; this could be indicative of accumulating excess inventory. 
Volvo’s growth rate in finished goods compared to its growth rate in sales is 
significantly higher but the lower growth rates in finished goods inventory for 
CAT is potentially a result of using the LIFO method versus the FIFO method. 
It appears Volvo is aware that an issue exists and is planning on cutting back 
production given the relatively small increase in inventories other than finished 
products. Regardless, an analyst should do further investigation before reaching 
any conclusion about a company’s future prospects for sales and profit.
EXAMPLE 11   
Management Discussion and Analysis

EXAMPLE 11   
The following excerpts commenting on inventory management are from the 
Volvo Group Annual Report, 2008:
From the CEO Comment : “In a declining economy, it is extremely 
important to act quickly to reduce the Group’s cost level and ensure 
we do not build inventories, since large inventories generally lead 
to pressure on prices. ” … “During the second half of the year, we 
implemented sharp production cutbacks to lower inventories of new 
trucks and construction equipment as part of efforts to maintain our 
product prices, which represent one of the most important factors in 
securing favorable profitability in the future. We have been successful 
in these efforts. During the fourth quarter, inventories of new trucks 
declined 13% and of new construction equipment by 19%. During the 
beginning of 2009, we have continued to work diligently and focused 
to reduce inventories to the new, lower levels of demand that prevail

in most of our markets, and for most of our products. ”
From the Board of Directors’ Report 2008 : “Inventory reduction 
contributed to positive operating cash flow of SEK 1.8  billion in 
Industrial Operations. ” … “The value of inventories increased during 
2008 by SEK 11.4 billion. Adjusted for currency changes, the increase 
amounted to SEK 5.8 billion. The increase is mainly related to the 
truck operations and to construction equipment and is an effect of 
the rapidly weakening demand during the second half of the year. ” 
… “In order to reduce the capital tied-  up in inventory, a number of 
shutdown days in production were carried out during the end of 
year. Measures aimed at selling primarily trucks and construction 
equipment in inventory were prioritized. These measures have con -
tinued during the beginning of 2009. ” and “Overcapacity within the 
industry can occur if there is a lack of demand, potentially leading 
to increased price pressure. ”

Reading 27 ■ Inventories 382
From Business Areas 2008 (Ambitions 2009) : “Execute on cost 
reduction and adjust production to ensure inventory levels in line 
with demand. ”
Assume inventory write-  downs are reported as part of cost of sales. Based on 
the excerpts above, discuss the anticipated direction of the following for 2009 
compared to 2008:
1 Inventory carrying amounts
2 Inventory turnover ratio
3 Sales
4 Gross profit margin
5 Return on assets
6 Current ratio
Inventory carrying amounts are expected to decrease as the company cuts back 
on inventory levels and pressures are exerted on costs and prices.
Inventory turnover ratio is expected to increase. Any potential change in cost 
of sales will be more than offset by the decline in inventory carrying amounts.
Unit sales and sales revenues are expected to decline due to decrease in demand 
and pressure on prices.

Gross profit margin is difficult to predict. Sales revenues are expected to decline 
but cost of sales as a percentage of sales revenue may decline if cost controls are 
effective, stay the same if cost controls are offset by increased inventory write-  
downs, or increase if inventory write-  downs more than offset cost controls. In 
this case, an analyst might use 2008’s gross profit margin of 21.8 percent as a 
reasonable prediction. It is less than the 2006 and 2007 gross profit margin of 
23.1 percent and may already reflect cost controls, price pressures, and inven -
tory write-  downs.
Return on assets is expected to decline. The positive effects of cost controls 
and reduction in assets is likely to be offset by decreased net income due to the 
declining sales revenues.
The direction of change in the current ratio is difficult to predict. Current

assets are expected to be reduced but current liabilities are also expected to be 
reduced as costs are controlled and purchases are reduced resulting in lower 
accounts payable.

Evaluation of Inventory Management 383
EXAMPLE 12   
Single Company Illustration
Selected excerpts from the consolidated financial statements and notes to consol -
idated financial statements for Alcatel-  Lucent (ALU) are presented in Exhibits 8, 
9, and 10. Exhibit 8 contains excerpts from the consolidated income statements, 
and Exhibit 9 contains excerpts from the consolidated balance sheets. Exhibit 10 
contains excerpts from three of the notes to consolidated financial statements.
Note 1 (i) discloses that ALU’s finished goods inventories and work in progress 
are valued at the lower of cost or net realisable value. Note 2 (a) discloses that the 
impact of inventory and work in progress write-  downs on ALU’s income before 
tax was a net reduction of €285 million in 2008, a net reduction of €186 million 
in 2007, and a net reduction of €77 million in 2006.18 The inventory impairment 
loss amounts steadily increased from 2006 to 2008 and are included as a compo -

nent, (additions)/reversals, of ALU’s change in valuation allowance as disclosed 
in Note 19 (b) from Exhibit 10. Observe also that ALU discloses its valuation 
allowance at 31 December 2008, 2007, and 2006 in Note 19 (b) and details on 
the allocation of the allowance are included in Note 19 (a). The €654 million 
valuation allowance is the total of a €629 million allowance for inventories and 
a €25 million allowance for work in progress on construction contracts. Finally, 
observe that the €2,196 million net value for inventories (excluding construc -
tion contracts) at 31 December 2008 in Note 19 (a) reconciles with the balance 
sheet amount for inventories and work in progress, net, on 31 December 2008, 
as presented in Exhibit 9.
The inventory valuation allowance represents the total amount of inventory 
write-  downs taken for the inventory reported on the balance sheet (which is 
measured at the lower of cost or net realisable value). Therefore, an analyst can

determine the historical cost of the company’s inventory by adding the inventory 
valuation allowance to the reported inventory carrying amount on the balance 
sheet. The valuation allowance increased in magnitude and as a percentage of 
gross inventory values from 2006 to 2008.
Exhibit 8   Alcatel-  Lucent Consolidated Income Statements (€ millions)
For years ended 31 December 2008 2007 2006
Revenues 16,984 17,792 12,282
Cost of sales (11,190) (12,083) (8,214)
Gross profit 5,794 5,709 4,068
Administrative and selling expenses (3,093) (3,462) (1,911)
Research and development costs (2,757) (2,954) (1,470)
Income from operating activities before restructuring costs, impair -
ment of assets, gain/(loss) on disposal of consolidated entities, and 
post-  retirement benefit plan amendments(56) (707) 687
Restructuring costs (562) (856) (707)
Impairment of assets (4,725) (2,944) (141)
Gain/(loss) on disposal of consolidated entities (7) — 15
Post-  retirement benefit plan amendments 47 258 —

18 This reduction is often referred to as a charge.  An accounting charge is the recognition of a loss or 
expense. In this case, the charge is attributable to the impairment of assets.

Reading 27 ■ Inventories 384
Income (loss) from operating activities (5,303) (4,249) (146)
⋮ ⋮ ⋮ ⋮
Income (loss) from continuing operations (5,206) (4,087) (219)
Income (loss) from discontinued operations 33 610 158
Net income (loss) (5,173) (3,477) (61)
Exhibit 9   Alcatel-  Lucent Consolidated Balance Sheets (€ millions)
⋮ ⋮ ⋮ ⋮
Total non-  current assets 12,742 20,135 25,665
Inventories and work in progress, net 2,196 2,235 2,259
Amounts due from customers on construction contracts 495 704 615
Trade receivables and related accounts, net 4,330 4,163 3,877
Advances and progress payments 99 110 87
⋮ ⋮ ⋮ ⋮
Total current assets 14,569 13,695 16,225
Total assets 27,311 33,830 41,890
⋮ ⋮ ⋮ ⋮
Retained earnings, fair value, and other reserves (8,820) (3,821) (3,441)
⋮ ⋮ ⋮ ⋮
Total shareholders’ equity 5,224 11,702 16,323
Pensions, retirement indemnities, and other post-  retirement benefits 4,807 4,447 5,449

Bonds and notes issued, long-  term 3,931 4,517 4,901
Other long-  term debt 67 48 147
Deferred tax liabilities 1,152 1,897 2,583
Other non-  current liabilities 443 366 276
Total non-  current liabilities 10,400 11,275 13,356
Provisions 2,424 2,566 2,366
Current portion of long-  term debt 1,097 483 1,161
Customers’ deposits and advances 929 847 778
Amounts due to customers on construction contracts 188 407 273
Trade payables and related accounts 4,571 4,514 4,027
Liabilities related to disposal groups held for sale — — 1,606
Current income tax liabilities 185 70 66
Other current liabilities 2,293 1,966 1,934
Total current liabilities 11,687 10,853 12,211
Total liabilities and shareholders’ equity 27,311 33,830 41,890Exhibit 8   (Continued)

Evaluation of Inventory Management 385
Exhibit 10   Alcatel-  Lucent Selected Notes to Consolidated Financial 
Note 1. Summary of Significant Accounting Policies
(i) Inventories and work in progress
Inventories and work in progress are valued at the lower of cost (includ -
ing indirect production costs where applicable) or net realizable value.19 
Net realizable value is the estimated sales revenue for a normal period of 
activity less expected completion and selling costs.
Note 2. Principal uncertainties regarding the use of estimates
(a) Valuation allowance for inventories and work in progress
Inventories and work in progress are measured at the lower of cost or 
net realizable value. Valuation allowances for inventories and work in 
progress are calculated based on an analysis of foreseeable changes in 
demand, technology, or the market, in order to determine obsolete or 
excess inventories and work in progress.
The valuation allowances are accounted for in cost of sales or in

restructuring costs, depending on the nature of the amounts concerned.
(€ millions) 2008 2007 2006
Valuation allowance for inventories 
and work in progress on construction 
contracts(654) (514) (378)
Impact of inventory and work in progress 
write-  downs on income (loss) before 
income tax related reduction of goodwill 
and discounted operations(285) (186) (77)
Note 19. Inventories and work in progress
(a) Analysis of net value
Raw materials and goods 649 564 542
Work in progress excluding con -
struction contracts972 958 752
Finished goods 1,204 1,185 1,320
Gross value (excluding construc -
tion contracts)2,825 2,707 2,614
Valuation allowance (629) (472) (355)
Net value (excluding construction 
contracts)2,196 2,235 2,259
Work in progress on construction 
contracts, gross*219 272 347
Valuation allowance (25) (42) (23)
contracts, net194 230 324
Total, net 2,390 2,465 2,583
* Included in the amounts due from/to construction contracts.

Reading 27 ■ Inventories 386
(b) Change in valuation allowance
At 1 January (514) (378) (423)
(Additions)/reversals (285) (186) (77)
Utilization 69 38 54
Changes in consolidation group — — 54
Net effect of exchange rate changes 
and other changes75 12 14
At 31 December (654) (514) (378)
Rounding differences may result in totals that are different from the sum.
1 Calculate ALU’s inventory turnover, number of days of inventory on hand, 
gross profit margin, current ratio, debt-  to- equity ratio, and return on total 
assets for 2008 and 2007 based on the numbers reported. Use an average 
for inventory and total asset amounts and year-  end numbers for other 
ratio items. For debt, include only bonds and notes issued, long-  term; 
other long-  term debt; and current portion of long-  term debt.
2 Based on the answer to Question 1, comment on the changes from 2007 
to 2008.
3 If ALU had used the weighted average cost method instead of the FIFO

method during 2008, 2007, and 2006, what would be the effect on ALU’s 
reported cost of sales and inventory carrying amounts? What would be 
the directional impact on the financial ratios that were calculated for ALU 
in Question 1, above? 
The financial ratios are as follows: 
2008 2007
Inventory turnover ratio 5.05 5.38
Number of days of inventory 72.3 days 67.8 days
Gross profit margin 34.1% 32.1%
Current ratio 1.25 1.26
Debt-  to- equity ratio 0.98 0.43
Return on total assets –16.9% –9.2%
Inventory turnover ratio = Cost of sales ÷ Average inventory 
2008 inventory turnover ratio = 5.05 = 11,190 ÷ [(2,196 + 2,235) ÷ 2]
2007 inventory turnover ratio = 5.38 = 12,083 ÷ [(2,235 + 2,259) ÷ 2]
Number of days of inventory = 365 days ÷ Inventory turnover ratio
2008 number of days of inventory = 72.3 days = 365 days ÷ 5.05
2007 number of days of inventory = 67.8 days = 365 days ÷ 5.38

Evaluation of Inventory Management 387
Gross profit margin = Gross profit ÷ Total revenue
2008 gross profit margin = 34.1% = 5,794 ÷ 16,984
2007 gross profit margin = 32.1% = 5,709 ÷ 17,792
Current ratio = Current assets ÷ Current liabilities
2008 current ratio = 1.25 = 14,569 ÷ 11,687
2007 current ratio = 1.26 = 13,695 ÷ 10,853
Debt-  to- equity ratio = Total debt ÷ Total shareholders’ equity
2008 debt-  to- equity ratio = 0.98 = (3,931 + 67 + 1,097) ÷ 5,224
2007 debt-  to- equity ratio = 0.43 = (4,517 + 48 + 483) ÷ 11,702
Return on assets = Net income ÷ Average total assets
2008 return on assets = –16.9% = –5,173 ÷ [(27,311 + 33,830) ÷ 2]
2007 return on assets = –9.2% = –3,477 ÷ [(33,830 + 41,890) ÷ 2]
From 2007 to 2008, the inventory turnover ratio declined and the number of days 
of inventory increased by 4.5 days. ALU appears to be managing inventory less 
efficiently. The gross profit margin improved by 2.0 percent, from 32.1 percent

in 2007 to 34.1 percent in 2008. The current ratio is relatively unchanged from 
2007 to 2008. The debt-  to- equity ratio has risen significantly in 2008 compared 
to 2007. Although ALU’s total debt has been relatively stable during this time 
period, the company’s equity has been declining rapidly because of the cumu -
lative effect of its net losses on retained earnings.
The return on assets is negative and got worse in 2008 compared to 2007. A 
larger net loss and lower total assets in 2008 resulted in a higher negative return 
on assets. The analyst should investigate the underlying reasons for the sharp 
decline in ALU’s return on assets. From Exhibit 8, it is apparent that ALU’s gross 
profit margins were insufficient to cover the administrative and selling expenses 
and research and development costs in 2007 and 2008. Large restructuring costs 
and asset impairment losses contributed to the loss from operating activities in 
both 2007 and 2008.

If inventory replacement costs were increasing during 2006, 2007, and 2008 (and 
inventory quantity levels were stable or increasing), ALU’s cost of sales would 
have been higher and its gross profit margin would have been lower under the 
weighted average cost inventory method than what was reported under the FIFO 
method (assuming no inventory write-  downs that would otherwise neutralize 
the differences between the inventory valuation methods). FIFO allocates the 
oldest inventory costs to cost of sales; the reported cost of sales would be lower 
under FIFO given increasing inventory costs. Inventory carrying amounts would 
be higher under the FIFO method than under the weighted average cost method 
because the more recently purchased inventory items would be included in 
inventory at their higher costs (again assuming no inventory write-  downs that 
would otherwise neutralize the differences between the inventory valuation

methods). Consequently, ALU’s reported gross profit, net income, and retained 
earnings would also be higher for those years under the FIFO method.

Reading 27 ■ Inventories 388
The effects on ratios are as follows:
■■The inventory turnover ratios would all be higher under the weighted 
average cost method because the numerator (cost of sales) would be 
higher and the denominator (inventory) would be lower than what was 
reported by ALU under the FIFO method.
■■The number of days of inventory would be lower under the weighted aver -
age cost method because the inventory turnover ratios would be higher.
■■The gross profit margin ratios would all be lower under the weighted aver -
age cost method because cost of sales would be higher under the weighted 
average cost method than under the FIFO method.
■■The current ratios would all be lower under the weighted average cost 
method because inventory carrying values would be lower than under the 
FIFO method (current liabilities would be the same under both methods).
■■The return-  on- assets ratios would all be lower under the weighted average

cost method because the incremental profit added to the numerator 
(net income) has a greater impact than the incremental increase to the 
denominator (total assets). By way of example, assume that a company 
has €3 million in net income and €100 million in total assets using the 
weighted average cost method. If the company reports another €1 million 
in net income by using FIFO instead of weighted average cost, it would 
then also report an additional €1 million in total assets (after tax). Based 
on this example, the return on assets is 3.00 percent (€3/€100) under the 
weighted average cost method and 3.96 percent (€4/€101) under the FIFO 
method.
■■The debt-  to- equity ratios would all be higher under the weighted aver -
age cost method because retained earnings would be lower than under 
the FIFO method (again assuming no inventory write-  downs that would 
otherwise neutralize the differences between the inventory valuation 
methods).

methods).
Conversely, if inventory replacement costs were decreasing during 2006, 
2007, and 2008 (and inventory quantity levels were stable or increasing), ALU’s 
cost of sales would have been lower and its gross profit and inventory would 
have been higher under the weighted average cost method than were reported 
under the FIFO method (assuming no inventory write-  downs that would oth -
erwise neutralize the differences between the inventory valuation methods). As 
a result, the ratio assessment that was performed above would result in directly 
opposite conclusions.
SUMMARY
The choice of inventory valuation method (cost formula or cost flow assumption) 
can have a potentially significant impact on inventory carrying amounts and cost of 
sales. These in turn impact other financial statement items, such as current assets, 
total assets, gross profit, and net income. The financial statements and accompanying

Summary 389
notes provide important information about a company’s inventory accounting policies 
that the analyst needs to correctly assess financial performance and compare it with 
that of other companies. Key concepts in this reading are as follows:
■■Inventories are a major factor in the analysis of merchandising and manufactur -
ing companies. Such companies generate their sales and profits through inven -
tory transactions on a regular basis. An important consideration in determining 
profits for these companies is measuring the cost of sales when inventories are 
sold.
■■The total cost of inventories comprises all costs of purchase, costs of conver -
sion, and other costs incurred in bringing the inventories to their present loca -
tion and condition. Storage costs of finished inventory and abnormal costs due 
to waste are typically treated as expenses in the period in which they occurred.
■■The allowable inventory valuation methods implicitly involve different assump -

tions about cost flows. The choice of inventory valuation method determines 
how the cost of goods available for sale during the period is allocated between 
inventory and cost of sales.
■■IFRS allow three inventory valuation methods (cost formulas): first-  in, first-  out 
(FIFO); weighted average cost; and specific identification. The specific identi -
fication method is used for inventories of items that are not ordinarily inter -
changeable and for goods or services produced and segregated for specific proj -
ects. US GAAP allow the three methods above plus the last-  in, first-  out (LIFO) 
method. The LIFO method is widely used in the United States for both tax and 
financial reporting purposes because of potential income tax savings.
■■The choice of inventory method affects the financial statements and any 
financial ratios that are based on them. As a consequence, the analyst must 
carefully consider inventory valuation method differences when evaluating a

company’s performance over time or in comparison to industry data or industry 
■■A company must use the same cost formula for all inventories having a similar 
nature and use to the entity.
■■The inventory accounting system (perpetual or periodic) may result in different 
values for cost of sales and ending inventory when the weighted average cost or 
LIFO inventory valuation method is used.
■■Under US GAAP , companies that use the LIFO method must disclose in their 
financial notes the amount of the LIFO reserve or the amount that would have 
been reported in inventory if the FIFO method had been used. This information 
can be used to adjust reported LIFO inventory and cost of goods sold balances 
to the FIFO method for comparison purposes.
■■LIFO liquidation occurs when the number of units in ending inventory declines 
from the number of units that were present at the beginning of the year. If 
inventory unit costs have generally risen from year to year, this will produce an

inventory-  related increase in gross profits.
■■Consistency of inventory costing is required under both IFRS and US GAAP . 
If a company changes an accounting policy, the change must be justifiable and 
applied retrospectively to the financial statements. An exception to the retro -
spective restatement is when a company reporting under US GAAP changes to 
the LIFO method.
■■Under IFRS, inventories are measured at the lower of cost and net realis -
able value. Net realisable value is the estimated selling price in the ordinary 
course of business less the estimated costs necessary to make the sale. Under 
US GAAP , inventories are measured at the lower of cost, market value, or net

Reading 27 ■ Inventories 390
realisable value depending upon the inventory method used. Market value is 
defined as current replacement cost subject to an upper limit of net realizable 
value and a lower limit of net realizable value less a normal profit margin. 
Reversals of previous write-  downs are permissible under IFRS but not under US 
G A A P.
■■Reversals of inventory write-  downs may occur under IFRS but are not allowed 
■■Changes in the carrying amounts within inventory classifications (such as raw 
materials, work-  in- process, and finished goods) may provide signals about a 
company’s future sales and profits. Relevant information with respect to inven -
tory management and future sales may be found in the Management Discussion 
and Analysis or similar items within the annual or quarterly reports, industry 
news and publications, and industry economic data.
■■The inventory turnover ratio, number of days of inventory ratio, and gross profit

margin ratio are useful in evaluating the management of a company’s inventory.
■■Inventory management may have a substantial impact on a company’s activ -
ity, profitability, liquidity, and solvency ratios. It is critical for the analyst to be 
aware of industry trends and management’s intentions.
■■Financial statement disclosures provide information regarding the accounting 
policies adopted in measuring inventories, the principal uncertainties regarding 
the use of estimates related to inventories, and details of the inventory carrying 
amounts and costs. This information can greatly assist analysts in their evalua -
tion of a company’s inventory management.

Practice Problems 391
1 Inventory cost is least likely  to include:
A production-  related storage costs.
B costs incurred as a result of normal waste of materials.
C transportation costs of shipping inventory to customers.
2 Mustard Seed PLC adheres to IFRS. It recently purchased inventory for 
€100 million and spent €5 million for storage prior to selling the goods. The 
amount it charged to inventory expense (€ millions) was closest  to:
A €95.
B €100.
C €105.
3 Carrying inventory at a value above its historical cost would most likely  be per -
mitted if:
A the inventory was held by a producer of agricultural products.
B financial statements were prepared using US GAAP .
C the change resulted from a reversal of a previous write-  down.
The following information relates to Questions 4 
and 5. 
A retail company is comparing different approaches to valuing inventory. The company 
has one product that it sells for $50. 
Table 1   Units Purchased and Sold (first quarter)

Date Units Purchased Purchase Price Units Sold Selling Price Inventory Units on Hand
2 Jan 1,000 $20.00 1,000
17 Jan 500 $50.00 500
16 Feb 1,000 $18.00 1,500
3 Mar 1,200 $50.00 300
13 Mar 1,000 $17.00 1,300
23 Mar 500 $50.00 800
End of quarter 
totals:3,000 $55,000 2,200 $110,000

Reading 27 ■ Inventories 392
Table 2   Comparison of Inventory Methods and Models
End of Quarter Valuations  
31 March Perpetual LIFO Periodic LIFO Perpetual FIFO
Sales $110,000 $110,000 $110,000
Ending inventory $16,000 $13,600
Cost of goods sold $39,000 $41,400
Gross profit $71,000 $68,600
Inventory turnover ratio 279%
Note : LIFO is last in, first out and FIFO is first in, first out.
4 What is the value of ending inventory for the first quarter if the company uses a 
perpetual LIFO inventory valuation method?
A $14,500
B $15,000
C $16,000
5 Which inventory accounting method results in the lowest inventory turnover 
ratio for the first quarter?
A Periodic LIFO
B Perpetual LIFO
C Perpetual FIFO
6 During periods of rising inventory unit costs, a company using the FIFO 
method rather than the LIFO method will report a lower:
A current ratio. 
B inventory turnover. 
C gross profit margin. 
7 LIFO reserve is most likely  to increase when inventory unit:
A costs are increasing. 
B costs are decreasing.

B costs are decreasing. 
C levels are decreasing.
8 If inventory unit costs are increasing from period-  to- period, a LIFO liquidation 
is most likely  to result in an increase in:
A gross profit.
B LIFO reserve.
C inventory carrying amounts.
9 A company using the LIFO method reports the following in £:
2015 2014
Cost of goods sold (COGS) 50,800 48,500
Ending inventories 10,550 10,000
LIFO reserve 4,320 2,600
 Cost of goods sold for 2015 under the FIFO method is closest  to:

Practice Problems 393
A £48,530.
B £49,080.
C £52,520.
10 Eric’s Used Book Store prepares its financial statements in accordance with 
IFRS. Inventory was purchased for £1 million and later marked down to 
£550,000. One of the books, however, was later discovered to be a rare collect -
ible item, and the inventory is now worth an estimated £3 million. The inven -
tory is most likely  reported on the balance sheet at:
A £550,000.
B £1,000,000.
C £3,000,000.
11 Fernando’s Pasta purchased inventory and later wrote it down. The current net 
realisable value is higher than the value when written down. Fernando’s inven -
tory balance will most likely  be:
A higher if it complies with IFRS.
B higher if it complies with US GAAP .
C the same under US GAAP and IFRS.
12 A write down of the value of inventory to its net realizable value will have a 
positive effect on the:
C inventory turnover ratio.
For questions 13–24, assume the companies use a 
periodic inventory system.

13 Cinnamon Corp. started business in 2007 and uses the weighted average cost 
method. During 2007, it purchased 45,000 units of inventory at €10 each and 
sold 40,000 units for €20 each. In 2008, it purchased another 50,000 units at €11 
each and sold 45,000 units for €22 each. Its 2008 cost of sales (€ thousands) was 
closest  to: 
A €490.
B €491.
C €495.
14 Zimt AG started business in 2007 and uses the FIFO method. During 2007, it 
purchased 45,000 units of inventory at €10 each and sold 40,000 units for €20 
each. In 2008, it purchased another 50,000 units at €11 each and sold 45,000 
units for €22 each. Its 2008 ending inventory balance (€ thousands) was closest  
to:
A €105.
B €109.
C €110.
15 Zimt AG uses the FIFO method, and Nutmeg Inc. uses the LIFO method. 
Compared to the cost of replacing the inventory, during periods of rising prices, 
the cost of sales reported by:

Reading 27 ■ Inventories 394
A Zimt is too low.
B Nutmeg is too low.
C Nutmeg is too high.
16 Zimt AG uses the FIFO method, and Nutmeg Inc. uses the LIFO method. 
Compared to the cost of replacing the inventory, during periods of rising prices 
the ending inventory balance reported by:
A Zimt is too high.
17 Like many technology companies, TechnoTools operates in an environment 
of declining prices. Its reported profits will tend to be highest  if it accounts for 
inventory using the:
A FIFO method.
B LIFO method.
C weighted average cost method.
18 Compared to using the weighted average cost method to account for inventory, 
during a period in which prices are generally rising, the current ratio of a com -
pany using the FIFO method would most likely  be:
A lower.
B higher.
C dependent upon the interaction with accounts payable.
19 Zimt AG wrote down the value of its inventory in 2007 and reversed the write-

down in 2008. Compared to the ratios that would have been calculated if the 
write-  down had never occurred, Zimt’s reported 2007:
A current ratio was too high.
B gross margin was too high.
C inventory turnover was too high.
20 Zimt AG wrote down the value of its inventory in 2007 and reversed the write-  
down in 2008. Compared to the results the company would have reported if the 
write-  down had never occurred, Zimt’s reported 2008:
A profit was overstated.
B cash flow from operations was overstated.
C year-  end inventory balance was overstated.
21 Compared to a company that uses the FIFO method, during periods of rising 
prices a company that uses the LIFO method will most likely  appear more:
A liquid.
B efficient.
C profitable.
22 Nutmeg, Inc. uses the LIFO method to account for inventory. During years 
in which inventory unit costs are generally rising and in which the company 
purchases more inventory than it sells to customers, its reported gross profit 
margin will most likely  be:

A lower than it would be if the company used the FIFO method.
B higher than it would be if the company used the FIFO method.
C about the same as it would be if the company used the FIFO method.

Practice Problems 395
23 Compared to using the FIFO method to account for inventory, during peri -
ods of rising prices, a company using the LIFO method is most likely  to report 
higher:
A net income.
B cost of sales.
C income taxes.
24 Carey Company adheres to US GAAP , whereas Jonathan Company adheres to 
IFRS. It is least likely  that:
A Carey has reversed an inventory write-  down.
B Jonathan has reversed an inventory write-  down.
C Jonathan and Carey both use the FIFO inventory accounting method.
25 Company A adheres to US GAAP and Company B adheres to IFRS. Which of 
the following is most likely  to be disclosed on the financial statements of both 
companies?
A Any material income resulting from the liquidation of LIFO inventory
B The amount of inventories recognized as an expense during the period 
C The circumstances that led to the reversal of a write down of inventories
26 Which of the following most likely  signals that a manufacturing company 
expects demand for its product to increase?

A Finished goods inventory growth rate higher than the sales growth rate
B Higher unit volumes of work in progress and raw material inventories
C Substantially higher finished goods, with lower raw materials and 
work-  in- process 
27 Compared with a company that uses the FIFO method, during a period of rising 
unit inventory costs, a company using the LIFO method will most likely  appear 
more:
A liquid. 
B efficient. 
C profitable. 
28 In a period of declining inventory unit costs and constant or increasing inven -
tory quantities, which inventory method is most likely  to result in a higher debt-  
to- equity ratio?
A LIFO
B FIFO
C Weighted average cost
29–36
Hans Annan, CFA, a food and beverage analyst, is reviewing Century Chocolate’s 
inventory policies as part of his evaluation of the company. Century Chocolate, based 
in Switzerland, manufactures chocolate products and purchases and resells other

confectionery products to complement its chocolate line. Annan visited Century 
Chocolate’s manufacturing facility last year. He learned that cacao beans, imported

Reading 27 ■ Inventories 396
from Brazil, represent the most significant raw material and that the work-  in- progress 
inventory consists primarily of three items: roasted cacao beans, a thick paste pro -
duced from the beans (called chocolate liquor), and a sweetened mixture that needs 
to be “conched” to produce chocolate. On the tour, Annan learned that the conch -
ing process ranges from a few hours for lower-  quality products to six days for the 
highest-  quality chocolates. While there, Annan saw the facility’s climate-  controlled 
area where manufactured finished products (cocoa and chocolate) and purchased 
finished goods are stored prior to shipment to customers. After touring the facility, 
Annan had a discussion with Century Chocolate’s CFO regarding the types of costs 
that were included in each inventory category.
Annan has asked his assistant, Joanna Kern, to gather some preliminary information 
regarding Century Chocolate’s financial statements and inventories. He also asked

Kern to calculate the inventory turnover ratios for Century Chocolate and another 
chocolate manufacturer for the most recent five years. Annan does not know Century 
Chocolate’s most direct competitor, so he asks Kern to do some research and select 
the most appropriate company for the ratio comparison.
Kern reports back that Century Chocolate prepares its financial statements in 
accordance with IFRS. She tells Annan that the policy footnote states that raw materials 
and purchased finished goods are valued at purchase cost whereas work in progress 
and manufactured finished goods are valued at production cost. Raw material inven -
tories and purchased finished goods are accounted for using the FIFO (first-  in, first-  
out) method, and the weighted average cost method is used for other inventories. An 
allowance is established when the net realisable value of any inventory item is lower 
than the value calculated above.

Kern provides Annan with the selected financial statements and inventory data 
for Century Chocolate shown in Exhibits 1 through 5. The ratio exhibit Kern pre -
pared compares Century Chocolate’s inventory turnover ratios to those of Gordon’s 
Goodies, a US-  based company. Annan returns the exhibit and tells Kern to select a 
different competitor that reports using IFRS rather than US GAAP . During this initial 
review, Annan asks Kern why she has not indicated whether Century Chocolate uses 
a perpetual or a periodic inventory system. Kern replies that she learned that Century 
Chocolate uses a perpetual system but did not include this information in her report 
because inventory values would be the same under either a perpetual or periodic 
inventory system. Annan tells Kern she is wrong and directs her to research the matter.
While Kern is revising her analysis, Annan reviews the most recent month’s Cocoa

Market Review from the International Cocoa Organization. He is drawn to the state -
ment that “the ICCO daily price, averaging prices in both futures markets, reached a 
29- year high in US$ terms and a 23-  year high in SDRs terms (the SDR unit comprises 
a basket of major currencies used in international trade: US$, euro, pound sterling 
and yen). ” Annan makes a note that he will need to factor the potential continuation 
of this trend into his analysis.
Exhibit 1   Century Chocolate Income Statements (CHF Millions)
For Y ears Ended 31 December 2009 2008
Sales 95,290 93,248
Cost of sales –41,043 –39,047
Marketing, administration, and other expenses –35,318 –42,481
Profit before taxes 18,929 11,720
Taxes –3,283 –2,962
Profit for the period 15,646 8,758

Practice Problems 397
Exhibit 2   Century Chocolate Balance Sheets (CHF Millions)
31 December 2009 2008
Cash, cash equivalents, and short-  term investments 6,190 8,252
Trade receivables and related accounts, net 11,654 12,910
Inventories, net 8,100 7,039
Other current assets 2,709 2,812
Total current assets 28,653 31,013
Property, plant, and equipment, net 18,291 19,130
Other non-  current assets 45,144 49,875
Total assets 92,088 100,018
Trade and other payables 10,931 12,299
Other current liabilities 17,873 25,265
Total current liabilities 28,804 37,564
Non-  current liabilities 15,672 14,963
Total liabilities 44,476 52,527
Equity
Share capital 332 341
Retained earnings and other reserves 47,280 47,150
Total equity 47,612 47,491
Total liabilities and shareholders’ equity 92,088 100,018
Exhibit 3   Century Chocolate Supplementary Footnote Disclosures: 
Inventories (CHF Millions)
Raw Materials 2,154 1,585
Work in Progress 1,061 1,027
Finished Goods 5,116 4,665

  Total inventories before allowance 8,331 7,277
Allowance for write-  downs to net realisable value –231 –238
  Total inventories net of allowance 8,100 7,039
Exhibit 4   Century Chocolate Inventory Record for Purchased Lemon Drops
Date CartonsPer Unit Amount  
(CHF)
Beginning inventory 100 22
4 Feb 09 Purchase 40 25

Reading 27 ■ Inventories 398
(CHF)
3 Apr 09 Sale 50 32
23 Jul 09 Purchase 70 30
16 Aug 09 Sale 100 32
9 Sep 09 Sale 35 32
15 Nov 09 Purchase 100 28
Exhibit 5   Century Chocolate Net Realisable Value Information for Black 
Licorice Jelly Beans
2009 2008
FIFO cost of inventory at 31 December (CHF) 314,890 374,870
Ending inventory at 31 December (Kilograms) 77,750 92,560
Cost per unit (CHF) 4.05 4.05
Net Realisable Value (CHF per Kilograms) 4.20 3.95
29 The costs least likely  to be included by the CFO as inventory are: 
A storage costs for the chocolate liquor.
B excise taxes paid to the government of Brazil for the cacao beans.
C storage costs for chocolate and purchased finished goods awaiting shipment 
to customers.
30 What is the most likely  justification for Century Chocolate’s choice of inventory 
valuation method for its purchased finished goods?
A It is the preferred method under IFRS.
B It allocates the same per unit cost to both cost of sales and inventory.

C Ending inventory reflects the cost of goods purchased most recently.
31 In Kern’s comparative ratio analysis, the 2009 inventory turnover ratio for 
Century Chocolate is closest  to:
A 5.07.
B 5.42.
C 5.55.
32 The most accurate  statement regarding Annan’s reasoning for requiring Kern 
to select a competitor that reports under IFRS for comparative purposes is that 
under US GAAP:
A fair values are used to value inventory.
B the LIFO method is permitted to value inventory.
C the specific identification method is permitted to value inventory.
33 Annan’s statement regarding the perpetual and periodic inventory systems is 
most significant when which of the following costing systems is used?
A LIFO.Exhibit 4   (Continued)

Practice Problems 399
B FIFO.
C Specific identification.
34 Using the inventory record for purchased lemon drops shown in Exhibit 4, the 
cost of sales for 2009 will be closest  to:
A CHF 3,550.
B CHF 4,550.
C CHF 4,850.
35 Ignoring any tax effect, the 2009 net realisable value reassessment for the black 
licorice jelly beans will most likely  result in:
A an increase in gross profit of CHF 7,775.
B an increase in gross profit of CHF 11,670.
C no impact on cost of sales because under IFRS, write-  downs cannot be 
reversed.
36 If the trend noted in the ICCO report continues and Century Chocolate plans 
to maintain constant or increasing inventory quantities, the most likely  impact 
on Century Chocolate’s financial statements related to its raw materials inven -
tory will be:
A a cost of sales that more closely reflects current replacement values.
B a higher allocation of the total cost of goods available for sale to cost of 
sales.

sales.
C a higher allocation of the total cost of goods available for sale to ending 
inventory.
37–42
John Martinson, CFA, is an equity analyst with a large pension fund. His supervisor, 
Linda Packard, asks him to write a report on Karp Inc. Karp prepares its financial 
statements in accordance with US GAAP . Packard is particularly interested in the 
effects of the company’s use of the LIFO method to account for its inventory. For this 
purpose, Martinson collects the financial data presented in Exhibits 1 and 2.
Exhibit 1   Balance Sheet Information (US$ Millions)
As of 31 December 2009 2008
Cash and cash equivalents 172 157
Accounts receivable 626 458
Inventories 620 539
Other current assets 125 65
  Total current assets 1,543 1,219
Property and equipment, net 3,035 2,972
  Total assets 4,578 4,191
Total current liabilities 1,495 1,395
Long-  term debt 644 604

Reading 27 ■ Inventories 400
  Total liabilities 2,139 1,999
Common stock and paid in capital 1,652 1,652
Retained earnings 787 540
  Total shareholders’ equity 2,439 2,192
  Total liabilities and shareholders’ equity 4,578 4,191
Exhibit 2   Income Statement Information (US$ Millions)
For the Y ear Ended 31 December 2009 2008
Sales 4,346 4,161
Cost of goods sold 2,211 2,147
Depreciation and amortisation expense 139 119
Selling, general, and administrative expense 1,656 1,637
Interest expense 31 18
Income tax expense 62 48
Net income 247 192
Martinson finds the following information in the notes to the financial statements:
■■The LIFO reserves as of 31 December 2009 and 2008 are $155 million and 
$117 million respectively, and
■■The effective income tax rate applicable to Karp for 2009 and earlier periods is 
20 percent.
37 If Karp had used FIFO instead of LIFO, the amount of inventory reported as of 
31 December 2009 would have been closest  to:
A $465 million.
B $658 million.

C $775 million.
38 If Karp had used FIFO instead of LIFO, the amount of cost of goods sold 
reported by Karp for the year ended 31 December 2009 would have been closest  
to:
A $2,056 million.
B $2,173 million.
C $2,249 million.
39 If Karp had used FIFO instead of LIFO, its reported net income for the year 
ended 31 December 2009 would have been higher by an amount closest to :
A $30 million.
B $38 million.
C $155 million.Exhibit 1   (Continued)

Practice Problems 401
40 If Karp had used FIFO instead of LIFO, Karp’s retained earnings as of 31 
December 2009 would have been higher by an amount closest to :
A $117 million.
B $124 million.
C $155 million.
41 If Karp had used FIFO instead of LIFO, which of the following ratios computed 
as of 31 December 2009 would most likely  have been lower?
A Cash ratio.
B Current ratio.
42 If Karp had used FIFO instead of LIFO, its debt to equity ratio computed as of 
31 December 2009 would have:
A increased.
B decreased.
C remained unchanged.
43–48
Robert Groff, an equity analyst, is preparing a report on Crux Corp. As part of his 
report, Groff makes a comparative financial analysis between Crux and its two main 
competitors, Rolby Corp. and Mikko Inc. Crux and Mikko report under US GAAP 
and Rolby reports under IFRS.
Groff gathers information on Crux, Rolby, and Mikko. The relevant financial infor -

mation he compiles is in Exhibit 1. Some information on the industry is in Exhibit 2.
Exhibit 1   Selected Financial Information (US$ Millions)
Crux Rolby Mikko
Inventory valuation method LIFO FIFO LIFO
From the Balance Sheets
As of 31 December 2009
Inventory, gross 480 620 510
Valuation allowance 20 25 14
Inventory, net 460 595 496
Total debt 1,122 850 732
Total shareholders’ equity 2,543 2,403 2,091
As of 31 December 2008
Inventory, gross 465 602 401
Valuation allowance 23 15 12
Inventory, net 442 587 389
From the Income Statements
Year Ended 31 December 2009

Reading 27 ■ Inventories 402
Revenues 4,609 5,442 3,503
Cost of goods solda3,120 3,782 2,550
Net income 229 327 205
aCharges included in cost of goods sold for 
inventory write-  downs*13 15 15
* This does not match the change in the inventory valuation allowance because the valuation 
allowance is reduced to reflect the valuation allowance attached to items sold and increased for 
additional necessary write-  downs.
LIFO Reserve
As of 31 December 2009 55 0 77
As of 31 December 2008 72 0 50
As of 31 December 2007 96 0 43
Tax Rate
Effective tax rate 30% 30% 30%
Exhibit 2   Industry Information
Raw materials price index 112 105 100
Finished goods price index 114 106 100
To compare the financial performance of the three companies, Groff decides to 
convert LIFO figures into FIFO figures, and adjust figures to assume no valuation 
allowance is recognized by any company.
After reading Groff’s draft report, his supervisor, Rachel Borghi, asks him the 
following questions:

Question 1  Which company’s gross profit margin would best reflect current 
costs of the industry?
Question 2  Would Rolby’s valuation method show a higher gross profit mar -
gin than Crux’s under an inflationary, a deflationary, or a stable 
price scenario?
Question 3  Which group of ratios usually appears more favorable with an 
inventory write-  down?
43 Crux’s inventory turnover ratio computed as of 31 December 2009, after the 
adjustments suggested by Groff, is closest  to:
A 5.67.
B 5.83.
C 6.13.Exhibit 1   (Continued)

Practice Problems 403
44 Rolby’s net profit margin for the year ended 31 December 2009, after the adjust -
ments suggested by Groff, is closest  to:
A 6.01%.
B 6.20%.
C 6.28%.
45 Compared with its unadjusted debt-  to- equity ratio, Mikko’s debt-  to- equity ratio 
as of 31 December 2009, after the adjustments suggested by Groff, is:
A lower.
B higher.
C the same.
46 The best answer to Borghi’s Question 1 is:
A Crux’s.
B Rolby’s.
C Mikko’s.
47 The best answer to Borghi’s Question 2 is:
A Stable.
B Inflationary.
C Deflationary.
48 The best answer to Borghi’s Question 3 is:
A Activity ratios.
B Solvency ratios.
C Profitability ratios.
49–56
ZP Corporation is a (hypothetical) multinational corporation headquartered in Japan 
that trades on numerous stock exchanges. ZP prepares its consolidated financial 
statements in accordance with US GAAP . Excerpts from ZP’s 2009 annual report are 
shown in Exhibits 1–3.
Exhibit 1   Consolidated Balance Sheets (¥ Millions)

31 December 2008 2009
Cash and cash equivalents ¥542,849 ¥814,760
  ⋮ ⋮ ⋮
Inventories 608,572 486,465
  ⋮ ⋮ ⋮
Total current assets 4,028,742 3,766,309
  ⋮ ⋮ ⋮
Total assets ¥10,819,440 ¥9,687,346

Reading 27 ■ Inventories 404
  ⋮ ⋮ ⋮
Total current liabilities ¥3,980,247 ¥3,529,765
  ⋮ ⋮ ⋮
Total long-  term liabilities 2,663,795 2,624,002
Minority interest in consolidated subsidiaries 218,889 179,843
Total shareholders’ equity 3,956,509 3,353,736
Total liabilities and shareholders’ equity ¥10,819,440 ¥9,687,346
Exhibit 2   Consolidated Statements of Income (¥ Millions)
For the years ended 31 
December 2007 2008 2009
Net revenues
Sales of products ¥7,556,699 ¥8,273,503 ¥6,391,240
Financing operations 425,998 489,577 451,950
7,982,697 8,763,080 6,843,190
Cost and expenses
Cost of products sold 6,118,742 6,817,446 5,822,805
Cost of financing operations 290,713 356,005 329,128
Selling, general and 
administrative827,005 832,837 844,927
   ⋮ ⋮ ⋮ ⋮
Operating income (loss) 746,237 756,792 –153,670
   ⋮ ⋮ ⋮ ⋮
Net income ¥548,011 ¥572,626 –¥145,646
Exhibit 3   Selected Disclosures in the 2009 Annual Report
Management’s Discussion and Analysis of Financial Condition 
and Results of Operations

Cost reduction efforts were offset by increased prices of raw mate -
rials, other production materials and parts … Inventories decreased 
during fiscal 2009 by ¥122.1 billion, or 20.1%, to ¥486.5 billion. This 
reflects the impacts of decreased sales volumes and fluctuations in 
foreign currency translation rates. 
Management & Corporate Information
Risk Factors
Industry and Business RisksExhibit 1   (Continued)

Practice Problems 405
The worldwide market for our products is highly competitive. ZP 
faces intense competition from other manufacturers in the respective 
markets in which it operates. Competition has intensified due to the 
worldwide deterioration in economic conditions. In addition, com -
petition is likely to further intensify because of continuing globaliza -
tion, possibly resulting in industry reorganization. Factors affecting 
competition include product quality and features, the amount of time 
required for innovation and development, pricing, reliability, safety, 
economy in use, customer service and financing terms. Increased 
competition may lead to lower unit sales and excess production 
capacity and excess inventory. This may result in a further downward 
price pressure. 
ZP’s ability to adequately respond to the recent rapid changes in 
the industry and to maintain its competitiveness will be fundamental 
to its future success in maintaining and expanding its market share

in existing and new markets. 
Notes to Consolidated Financial Statements
2. Summary of significant accounting policies:  
Inventories.  Inventories are valued at cost, not in excess of market. 
Cost is determined on the “average-  cost” basis, except for the cost 
of finished products carried by certain subsidiary companies which 
is determined “last-  in, first-  out” (“LIFO”) basis. Inventories valued 
on the LIFO basis totaled ¥94,578  million and ¥50,037  million at 
December 31, 2008 and 2009, respectively. Had the “first-  in, first-  out” 
basis been used for those companies using the LIFO basis, inventories 
would have been ¥10,120 million and ¥19,660 million higher than 
reported at December 31, 2008 and 2009, respectively. 
9. Inventories:  
Inventories consist of the following: 
31 December (¥ Millions) 2008 2009
Finished goods ¥ 403,856 ¥ 291,977
Raw materials 99,869 85,966
Work in process 79,979 83,890
Supplies and other 24,868 24,632
¥ 608,572 ¥ 486,465

49 The MD&A indicated that the prices of raw material, other production materi -
als, and parts increased. Based on the inventory valuation methods described 
in Note 2, which inventory classification would least accurately  reflect current 
prices?
A Raw materials.
B Finished goods.
C Work in process.Exhibit 3   (Continued)

Reading 27 ■ Inventories 406
50 The 2008 inventory value as reported on the 2009 Annual Report if the com -
pany had used the FIFO inventory valuation method instead of the LIFO inven -
tory valuation method for a portion of its inventory would be closest  to:
A ¥104,698 million.
B ¥506,125 million.
C ¥618,692 million.
51 What is the least likely  reason why ZP may need to change its accounting poli -
cies regarding inventory at some point after 2009?
A The US SEC is likely to require companies to use the same inventory valua -
tion method for all inventories.
B The US SEC is likely to prohibit the use of one of the methods ZP currently 
uses for inventory valuation.
C One of the inventory valuation methods used for US tax purposes may be 
repealed as an acceptable method.
52 If ZP had prepared its financial statement in accordance with IFRS, the inven -
tory turnover ratio (using average inventory) for 2009 would be:
A lower.
B higher.
C the same.

A lower.
B higher.
C the same.
53 Inventory levels decreased from 2008 to 2009 for all of the following reasons 
except :
A LIFO liquidation.
B decreased sales volume.
C fluctuations in foreign currency translation rates.
54 Which observation is most likely  a result of looking only at the information 
reported in Note 9?
A Increased competition has led to lower unit sales.
B There have been significant price increases in supplies.
C Management expects a further downturn in sales during 2010.
55 Note 2 indicates that, “Inventories valued on the LIFO basis totaled 
¥94,578 million and ¥50,037 million at December 31, 2008 and 2009, respec -
tively. ” Based on this, the LIFO reserve should most likely :
A increase.
B decrease.
C remain the same.
56 The Industry and Business Risk excerpt states that, “Increased competition may 
lead to lower unit sales and excess production capacity and excess inventory. 
This may result in a further downward price pressure. ” The downward price

pressure could lead to inventory that is valued above current market prices 
or net realisable value. Any write-  downs of inventory are least likely  to have a 
significant effect on the inventory valued using:
A weighted average cost.
B first-  in, first-  out (FIFO).
C last-  in, first-  out (LIFO).

Solutions 407
SOLUTIONS
1 C is correct. Transportation costs incurred to ship inventory to customers 
are an expense and may not be capitalized in inventory. (Transportation costs 
incurred to bring inventory to the business location can be capitalized in inven -
tory.) Storage costs required as part of production, as well as costs incurred as 
a result of normal waste of materials, can be capitalized in inventory. (Costs 
incurred as a result of abnormal waste must be expensed.)
2 B is correct. Inventory expense includes costs of purchase, costs of conversion, 
and other costs incurred in bringing the inventories to their present loca -
tion and condition. It does not include storage costs not required as part of 
production.
3 A is correct. IFRS allow the inventories of producers and dealers of agricultural 
and forest products, agricultural produce after harvest, and minerals and min -
eral products to be carried at net realisable value even if above historical cost.

(US GAAP treatment is similar.)
4 A is correct. A perpetual inventory system updates inventory values and quan -
tities and cost of goods sold continuously to reflect purchases and sales. The 
ending inventory of 800 units consists of 300 units at $20 and 500 units at $17. 
(300 × $20) + (500 × $17) = $14,500 
5 A is correct. In an environment with falling inventory costs and declining 
inventory levels, periodic LIFO will result in a higher ending inventory value 
and lower cost of goods sold versus perpetual LIFO and perpetual FIFO meth -
ods. This results in a lower inventory turnover ratio, which is calculated as 
follows:
Inventory turnover ratio = Cost of goods sold/Ending inventory 
 The inventory turnover ratio using periodic LIFO is $39,000/$16,000 = 244% or 
2.44 times.
 The inventory turnover ratio using perpetual LIFO is 279% or 2.79 times, which 
is provided in Table 2 (= 40,500/14,500 from previous question).
 The inventory turnover for perpetual FIFO is $41,400/$13,600 = 304% or 3.04

times.
6 B is correct. During a period of rising inventory costs, a company using the 
FIFO method will allocate a lower amount to cost of goods sold and a higher 
amount to ending inventory as compared with the LIFO method. The inventory 
turnover ratio is the ratio of cost of sales to ending inventory. A company using 
the FIFO method will produce a lower inventory turnover ratio as compared 
with the LIFO method. The current ratio (current assets/current liabilities) and 
the gross profit margin [gross profit/sales = (sales less cost of goods sold)/sales] 
will be higher under the FIFO method than under the LIFO method in periods 
of rising inventory unit costs. 
7 A is correct. LIFO reserve is the FIFO inventory value less the LIFO inventory 
value. In periods of rising inventory unit costs, the carrying amount of inven -
tory under FIFO will always exceed the carrying amount of inventory under 
LIFO. The LIFO reserve may increase over time as a result of the increasing

difference between the older costs used to value inventory under LIFO and the

Reading 27 ■ Inventories 408
more recent costs used to value inventory under FIFO. When inventory unit 
levels are decreasing, the company will experience a LIFO liquidation, reducing 
the LIFO reserve.
8 A is correct. When the number of units sold exceeds the number of units 
purchased, a company using LIFO will experience a LIFO liquidation. If inven -
tory unit costs have been rising from period-  to- period and a LIFO liquida -
tion occurs, it will produce an increase in gross profit as a result of the lower 
inventory carrying amounts of the liquidated units (lower cost per unit of the 
liquidated units).
9 B is correct. The adjusted COGS under the FIFO method is equal to COGS 
under the LIFO method less the increase in LIFO reserve:
 COGS (FIFO) =  COGS (LIFO) – Increase in LIFO reserve
 COGS (FIFO) =  £50,800 – (£4,320 – £2,600)
 COGS (FIFO) =  £49,080
10 B is correct. Under IFRS, the reversal of write-  downs is required if net real -

isable value increases. The inventory will be reported on the balance sheet at 
£1,000,000. The inventory is reported at the lower of cost or net realisable value. 
Under US GAAP , inventory is carried at the lower of cost or market value. After 
a write-  down, a new cost basis is determined and additional revisions may only 
reduce the value further. The reversal of write-  downs is not permitted.
11 A is correct. IFRS require the reversal of inventory write-  downs if net realisable 
values increase; US GAAP do not permit the reversal of write-  downs.
12 C is correct. Activity ratios (for example, inventory turnover and total asset 
turnover) will be positively affected by a write down to net realizable value 
because the asset base (denominator) is reduced. On the balance sheet, the 
inventory carrying amount is written down to its net realizable value and the 
loss in value (expense) is generally reflected on the income statement in cost of

goods sold, thus reducing gross profit, operating profit, and net income. 
13 B is correct. Cinnamon uses the weighted average cost method, so in 2008, 
5,000 units of inventory were 2007 units at €10 each and 50,000 were 2008 
purchases at €11. The weighted average cost of inventory during 2008 was thus 
(5,000 × 10) + (50,000 × 11) = 50,000 + 550,000 = €600,000, and the weighted 
average cost was approximately €10.91 = €600,000/55,000. Cost of sales was 
€10.91 × 45,000, which is approximately €490,950.
14 C is correct. Zimt uses the FIFO method, and thus the first 5,000 units sold in 
2008 depleted the 2007 inventory. Of the inventory purchased in 2008, 40,000 
units were sold and 10,000 remain, valued at €11 each, for a total of €110,000.
15 A is correct. Zimt uses the FIFO method, so its cost of sales represents units 
purchased at a (no longer available) lower price. Nutmeg uses the LIFO method, 
so its cost of sales is approximately equal to the current replacement cost of 

16 B is correct. Nutmeg uses the LIFO method, and thus some of the inventory 
on the balance sheet was purchased at a (no longer available) lower price. Zimt 
uses the FIFO method, so the carrying value on the balance sheet represents the 
most recently purchased units and thus approximates the current replacement 
cost.
17 B is correct. In a declining price environment, the newest inventory is the 
lowest-  cost inventory. In such circumstances, using the LIFO method (selling 
the newer, cheaper inventory first) will result in lower cost of sales and higher 
profit.

Solutions 409
18 B is correct. In a rising price environment, inventory balances will be higher for 
the company using the FIFO method. Accounts payable are based on amounts 
due to suppliers, not the amounts accrued based on inventory accounting.
19 C is correct. The write-  down reduced the value of inventory and increased cost 
of sales in 2007. The higher numerator and lower denominator mean that the 
inventory turnover ratio as reported was too high. Gross margin and the cur -
rent ratio were both too low.
20 A is correct. The reversal of the write-  down shifted cost of sales from 2008 to 
2007. The 2007 cost of sales was higher because of the write-  down, and the 
2008 cost of sales was lower because of the reversal of the write-  down. As a 
result, the reported 2008 profits were overstated. Inventory balance in 2008 is 
the same because the write-  down and reversal cancel each other out. Cash flow 
from operations is not affected by the non-  cash write-  down, but the higher

profits in 2008 likely resulted in higher taxes and thus lower cash flow from 
operations.
21 B is correct. LIFO will result in lower inventory and higher cost of sales. Gross 
margin (a profitability ratio) will be lower, the current ratio (a liquidity ratio) 
will be lower, and inventory turnover (an efficiency ratio) will be higher.
22 A is correct. LIFO will result in lower inventory and higher cost of sales in 
periods of rising costs compared to FIFO. Consequently, LIFO results in a lower 
gross profit margin than FIFO.
23 B is correct. The LIFO method increases cost of sales, thus reducing profits and 
the taxes thereon.
24 A is correct. US GAAP do not permit inventory write-  downs to be reversed.
25 B is correct. Both US GAAP and IFRS require disclosure of the amount of 
inventories recognized as an expense during the period. Only US GAAP allows 
the LIFO method and requires disclosure of any material amount of income

resulting from the liquidation of LIFO inventory. US GAAP does not permit the 
reversal of prior-  year inventory write downs. 
26 B is correct. A significant increase (attributable to increases in unit volume 
rather than increases in unit cost) in raw materials and/or work-  in- progress 
inventories may signal that the company expects an increase in demand for its 
products. If the growth of finished goods inventories is greater than the growth 
of sales, it could indicate a decrease in demand and a decrease in future earn -
ings. A substantial increase in finished goods inventories while raw materials 
and work-  in- progress inventories are declining may signal a decrease in demand 
for the company’s products. 
27 B is correct. During a period of rising inventory prices, a company using the 
LIFO method will have higher cost of cost of goods sold and lower inventory 
compared with a company using the FIFO method. The inventory turnover

ratio will be higher for the company using the LIFO method, thus making it 
appear more efficient. Current assets and gross profit margin will be lower for 
the company using the LIFO method, thus making it appear less liquid and less 
profitable. 
28 B is correct. In an environment of declining inventory unit costs and constant 
or increasing inventory quantities, FIFO (in comparison with weighted average 
cost or LIFO) will have higher cost of goods sold (and net income) and lower 
inventory. Because both inventory and net income are lower, total equity is 
lower, resulting in a higher debt-  to- equity ratio.

Reading 27 ■ Inventories 410
29 C is correct. The storage costs for inventory awaiting shipment to customers are 
not costs of purchase, costs of conversion, or other costs incurred in bringing 
the inventories to their present location and condition and are not included in 
inventory. The storage costs for the chocolate liquor occur during the produc -
tion process and are thus part of the conversion costs. Excise taxes are part of 
the purchase cost.
30 C is correct. The carrying amount of inventories under FIFO will more closely 
reflect current replacement values because inventories are assumed to consist 
of the most recently purchased items. FIFO is an acceptable, but not preferred, 
method under IFRS. Weighted average cost, not FIFO, is the cost formula that 
allocates the same per unit cost to both cost of sales and inventory.
31 B is correct. Inventory turnover = Cost of sales/Average inventory = 
41,043/7,569.5 = 5.42. Average inventory is (8,100 + 7,039)/2 = 7,569.5.

32 B is correct. For comparative purposes, the choice of a competitor that reports 
under IFRS is requested because LIFO is permitted under US GAAP .
33 A is correct. The carrying amount of the ending inventory may differ because 
the perpetual system will apply LIFO continuously throughout the year, liqui -
dating layers as sales are made. Under the periodic system, the sales will start 
from the last layer in the year. Under FIFO, the sales will occur from the same 
layers regardless of whether a perpetual or periodic system is used. Specific 
identification identifies the actual products sold and remaining in inventory, 
and there will be no difference under a perpetual or periodic system.
34 B is correct. The cost of sales is closest to CHF 4,550. Under FIFO, the inven -
tory acquired first is sold first. Using Exhibit 4, a total of 310 cartons were 
available for sale (100 + 40 + 70 + 100) and 185 cartons were sold (50 + 100 +

35), leaving 125 in ending inventory. The FIFO cost would be as follows:
100 (beginning inventory) × 22 = 2,200
40 (4 February 2009) × 25 = 1,000
45 (23 July 2009) × 30 = 1,350
Cost of sales = 2,200 + 1,000 + 1,350 = CHF 4,550
35 A is correct. Gross profit will most likely increase by CHF 7,775. The net realis -
able value has increased and now exceeds the cost. The write-  down from 2008 
can be reversed. The write-  down in 2008 was 9,256 [92,560 × (4.05 – 3.95)]. 
IFRS require the reversal of any write-  downs for a subsequent increase in value 
of inventory previously written down. The reversal is limited to the lower of 
the subsequent increase or the original write-  down. Only 77,750 kilograms 
remain in inventory; the reversal is 77,750 × (4.05 – 3.95) = 7,775. The amount 
of any reversal of a write-  down is recognised as a reduction in cost of sales. This 
reduction results in an increase in gross profit.
36 C is correct. Using the FIFO method to value inventories when prices are rising

will allocate more of the cost of goods available for sale to ending inventories 
(the most recent purchases, which are at higher costs, are assumed to remain 
in inventory) and less to cost of sales (the oldest purchases, which are at lower 
costs, are assumed to be sold first).

Solutions 411
37 C is correct. Karp’s inventory under FIFO equals Karp’s inventory under LIFO 
plus the LIFO reserve. Therefore, as of 31 December 2009, Karp’s inventory 
under FIFO equals:
 Inventory (FIFO method) =  Inventory (LIFO method) + LIFO 
reserve
  = $620 million + 155 million 
  = $775 million
38 B is correct. Karp’s cost of goods sold (COGS) under FIFO equals Karp’s cost of 
goods sold under LIFO minus the increase in the LIFO reserve. Therefore, for 
the year ended 31 December 2009, Karp’s cost of goods sold under FIFO equals:
 COGS (FIFO method) =  COGS (LIFO method) – Increase in LIFO 
reserve
  = $2,211 million – (155 million – 117 million)
  = $2,173 million
39 A is correct. Karp’s net income (NI) under FIFO equals Karp’s net income under 
LIFO plus the after-  tax increase in the LIFO reserve. For the year ended 31 
December 2009, Karp’s net income under FIFO equals:
 NI (FIFO method) =  NI (LIFO method) + Increase in LIFO reserve × 
(1 – Tax rate)

  = $247 million + 38 million × (1 – 20%)
  = $277.4 million
 Therefore, the increase in net income is: 
 Increase in NI =  NI (FIFO method) – NI (LIFO method)
  = $277 million – 247 million 
  = $30.4 million
40 B is correct. Karp’s retained earnings (RE) under FIFO equals Karp’s retained 
earnings under LIFO plus the after-  tax LIFO reserve. Therefore, for the year 
ended 31 December 2009, Karp’s retained earnings under FIFO equals:
 RE (FIFO method) =  RE (LIFO method) + LIFO reserve × (1 – Tax 
rate)
  = $787 million + 155 million × (1 – 20%)
  = $911 million
 Therefore, the increase in retained earnings is: 
 Increase in RE =  RE (FIFO method) – RE (LIFO method)
  = $911 million – 787 million
  = $124 million
41 A is correct. The cash ratio (cash and cash equivalents ÷ current liabilities) 
would be lower because cash would have been less under FIFO. Karp’s income 
before taxes would have been higher under FIFO, and consequently taxes paid

by Karp would have also been higher and cash would have been lower. There 
is no impact on current liabilities. Both Karp’s current ratio and gross profit 
margin would have been higher if FIFO had been used. The current ratio would 
have been higher because inventory under FIFO increases by a larger amount 
than the cash decreases for taxes paid. Because the cost of goods sold under 
FIFO is lower than under LIFO, the gross profit margin would have been higher.

Reading 27 ■ Inventories 412
42 B is correct. If Karp had used FIFO instead of LIFO, the debt-  to- equity ratio 
would have decreased. No change in debt would have occurred, but sharehold -
ers’ equity would have increased as a result of higher retained earnings.
43 B is correct. Crux’s adjusted inventory turnover ratio must be computed using 
cost of goods sold (COGS) under FIFO and excluding charges for increases in 
valuation allowances.
 COGS (adjusted) =  COGS (LIFO method) – Charges included in 
cost of goods sold for inventory write-  downs – Change 
in LIFO reserve
  = $3,120 million – 13 million – (55 million – 72 million)
  = $3,124 million
 Note : Minus the change in LIFO reserve is equivalent to plus the decrease in 
LIFO reserve. The adjusted inventory turnover ratio is computed using average 
inventory under FIFO. 
Ending inventory (FIFO) = Ending inventory (LIFO) + LIFO reserve
Ending inventory 2009 (FIFO) = $480 + 55 = $535
Ending inventory 2008 (FIFO) = $465 + 72 = $537

Average inventory = ($535 + 537)/2 = $536
 Therefore, adjusted inventory turnover ratio equals: 
Inventory turnover ratio = COGS/Average inventory = $3,124/$536 = 5.83
44 B is correct. Rolby’s adjusted net profit margin must be computed using net 
income (NI) under FIFO and excluding charges for increases in valuation 
allowances.
 NI (adjusted) =  NI (FIFO method) + Charges, included in cost of goods 
sold for inventory write-  downs, after tax
  = $327 million + 15 million × (1 – 30%)
  = $337.5 million
 Therefore, adjusted net profit margin equals: 
Net profit margin = NI/Revenues = $337.5/$5,442 = 6.20%
45 A is correct. Mikko’s adjusted debt-  to- equity ratio is lower because the debt 
(numerator) is unchanged and the adjusted shareholders’ equity (denominator) 
is higher. The adjusted shareholders’ equity corresponds to shareholders’ equity 
under FIFO, excluding charges for increases in valuation allowances. Therefore,

adjusted shareholders’ equity is higher than reported (unadjusted) shareholders’ 
equity.
46 C is correct. Mikko’s and Crux’s gross margin ratios would better reflect the 
current gross margin of the industry than Rolby because both use LIFO. LIFO 
recognizes as cost of goods sold the cost of the most recently purchased units, 
therefore, it better reflects replacement cost. However, Mikko’s gross margin 
ratio best reflects the current gross margin of the industry because Crux’s LIFO 
reserve is decreasing. This could reflect a LIFO liquidation by Crux which 
would distort gross profit margin.
47 B is correct. The FIFO method shows a higher gross profit margin than the 
LIFO method in an inflationary scenario, because FIFO allocates to cost of 
goods sold the cost of the oldest units available for sale. In an inflationary envi -
ronment, these units are the ones with the lowest cost.

Solutions 413
48 A is correct. An inventory write-  down increases cost of sales and reduces 
profit and reduces the carrying value of inventory and assets. This has a nega -
tive effect on profitability and solvency ratios. However, activity ratios appear 
positively affected by a write-  down because the asset base, whether total assets 
or inventory (denominator), is reduced. The numerator, sales, in total asset 
turnover is unchanged, and the numerator, cost of sales, in inventory turnover 
is increased. Thus, turnover ratios are higher and appear more favorable as the 
result of the write-  down.
49 B is correct. Finished goods least accurately reflect current prices because some 
of the finished goods are valued under the “last-  in, first-  out” (“LIFO”) basis. The 
costs of the newest units available for sale are allocated to cost of goods sold, 
leaving the oldest units (at lower costs) in inventory. ZP values raw materials

and work in process using the weighted average cost method. While not fully 
reflecting current prices, some inflationary effect will be included in the inven -
tory values.
50 C is correct. FIFO inventory = Reported inventory + LIFO reserve = ¥608,572 + 
10,120 = ¥618,692. The LIFO reserve is disclosed in Note 2 of the notes to con -
solidated financial statements.
51 A is correct. The SEC does not require companies to use the same inventory 
valuation method for all inventories, so this is the least likely  reason to change 
accounting policies regarding inventory. The SEC is currently evaluating 
whether all US companies should be required to adopt IFRS. If the SEC requires 
companies to adopt IFRS, the LIFO method of inventory valuation would no 
longer be allowed.
52 A is correct. The inventory turnover ratio would be lower. The average inven -
tory would be higher under FIFO and cost of products sold would be lower by 
the increase in LIFO reserve. LIFO is not permitted under IFRS.

Inventory turnover ratio = Cost of products sold ÷ Average inventory
2009 inventory turnover ratio as reported = 10.63 = ¥5,822,805/[(608,572 + 
486,465)/2].
2009 inventory turnover ratio adjusted to FIFO as necessary = 10.34 = 
[¥5,822,805 – (19,660 – 10,120)]/[(608,572 + 10,120 + 486,465 + 19,660)/2].
53 A is correct. No LIFO liquidation occurred during 2009; the LIFO reserve 
increased from ¥10,120 million in 2008 to ¥19,660 million in 2009. Management 
stated in the MD&A that the decrease in inventories reflected the impacts of 
decreased sales volumes and fluctuations in foreign currency translation rates.
54 C is correct. Finished goods and raw materials inventories are lower in 2009 
when compared to 2008. Reduced levels of inventory typically indicate an antic -
ipated business contraction.
55 B is correct. The decrease in LIFO inventory in 2009 would typically indicate 
that more inventory units were sold than produced or purchased. Accordingly,

one would expect a liquidation of some of the older LIFO layers and the LIFO 
reserve to decrease. In actuality, the LIFO reserve increased  from ¥10,120 mil -
lion in 2008 to ¥19,660 million in 2009. This is not to be expected and is likely 
caused by the increase in prices of raw materials, other production materials, 
and parts of foreign currencies as noted in the MD&A. An analyst should seek 
to confirm this explanation.
56 B is correct. If prices have been decreasing, write-  downs under FIFO are least 
likely to have a significant effect because the inventory is valued at closer to 
the new, lower prices. Typically, inventories valued using LIFO are less likely to

Reading 27 ■ Inventories 414
incur inventory write-  downs than inventories valued using weighted average 
cost or FIFO. Under LIFO, the oldest  costs are reflected in the inventory carry -
ing value on the balance sheet. Given increasing inventory costs, the inventory 
carrying values under the LIFO method are already conservatively presented at 
the oldest and lowest costs. Thus, it is far less likely that inventory write-  downs 
will occur under LIFO; and if a write-  down does occur, it is likely to be of a 
lesser magnitude.

Long-  Lived Assets
by Elaine Henry, PhD, CFA, and Elizabeth A. Gordon, PhD, MBA, CPA
Elaine Henry, PhD, CFA, is at Stevens Institute of Technology (USA). Elizabeth A. Gordon, 
PhD, MBA, CPA, is at Temple University (USA).
a. distinguish between costs that are capitalised and costs that are 
expensed in the period in which they are incurred;
b. compare the financial reporting of the following types of 
intangible assets: purchased, internally developed, acquired in a 
business combination;
c. explain and evaluate how capitalising versus expensing costs in 
the period in which they are incurred affects financial statements 
and ratios;
d. describe the different depreciation methods for property, plant, 
and equipment and calculate depreciation expense;
e. describe how the choice of depreciation method and assumptions 
concerning useful life and residual value affect depreciation 
expense, financial statements, and ratios;

f. describe the different amortisation methods for intangible assets 
with finite lives and calculate amortisation expense;
g. describe how the choice of amortisation method and assumptions 
concerning useful life and residual value affect amortisation 
h. describe the revaluation model;
i. explain the impairment of property, plant, and equipment and 
intangible assets;
j. explain the derecognition of property, plant, and equipment and 
k. explain and evaluate how impairment, revaluation, and 
derecognition of property, plant, and equipment and intangible 
assets affect financial statements and ratios;
l. describe the financial statement presentation of and disclosures 
relating to property, plant, and equipment and intangible assets;
28
and/or pronouncements issued

readings.

Reading 28 ■ Long-  Lived Assets 416
m. analyze and interpret financial statement disclosures regarding 
property, plant, and equipment and intangible assets;
n. compare the financial reporting of investment property with that 
of property, plant, and equipment;
o. explain and evaluate how leasing rather than purchasing assets 
affects financial statements and ratios;
p. explain and evaluate how finance leases and operating leases 
affect financial statements and ratios from the perspective of both 
the lessor and the lessee.
Long-  lived assets , also referred to as non-  current assets or long-  term assets, are assets 
that are expected to provide economic benefits over a future period of time, typically 
greater than one year.1 Long-  lived assets may be tangible, intangible, or financial 
assets. Examples of long-  lived tangible assets, typically referred to as property, plant,

and equipment  and sometimes as fixed assets, include land, buildings, furniture and 
fixtures, machinery and equipment, and vehicles; examples of long-  lived intangible 
assets  (assets lacking physical substance) include patents and trademarks; and examples 
of long-  lived financial assets include investments in equity or debt securities issued 
by other companies. The scope of this reading is limited to long-  lived tangible and 
intangible assets (hereafter, referred to for simplicity as long-  lived assets).
The first issue in accounting for a long-  lived asset is determining its cost at acqui -
sition. The second issue is how to allocate the cost to expense over time. The costs of 
most long-  lived assets are capitalised and then allocated as expenses in the profit or 
loss (income) statement over the period of time during which they are expected to 
provide economic benefits. The two main types of long-  lived assets with costs that are

typically not allocated over time are land, which is not depreciated, and those intan -
gible assets with indefinite useful lives. Additional issues that arise are the treatment 
of subsequent costs incurred related to the asset, the use of the cost model versus 
the revaluation model, unexpected declines in the value of the asset, classification of 
the asset with respect to intent (for example, held for use or held for sale), and the 
derecognition of the asset.
This reading is organised as follows. Section 2 describes and illustrates account -
ing for the acquisition of long-  lived assets, with particular attention to the impact 
of capitalizing versus expensing expenditures. Section 3 describes the allocation of 
the costs of long-  lived assets over their useful lives. Section 4 discusses the revalu -
ation model that is based on changes in the fair value of an asset. Section 5 covers 
the concepts of impairment (unexpected decline in the value of an asset). Section 6

describes accounting for the derecognition of long-  lived assets. Section 7 describes 
financial statement presentation, disclosures, and analysis of long-  lived assets. Section 1
1 In some instances, industry practice is to include as current assets (inventory) some assets that will be 
held longer than one year (e.g., leaf tobacco, which is cured and aged over a period longer than one year, 
and whiskey, which is barrel aged for a period longer than one year).

Acquisition of Long-  Lived Assets 417
8 discusses differences in financial reporting of investment property compared with 
property, plant, and equipment. Section 9 describes accounting for leases. A summary 
is followed by practice problems.
ACQUISITION OF LONG-  LIVED ASSETS
Upon acquisition, property, plant, and equipment (tangible assets with an economic 
life of longer than one year and intended to be held for the company’s own use) are 
recorded on the balance sheet at cost, which is typically the same as their fair value.2 
Accounting for an intangible asset depends on how the asset is acquired. If several 
assets are acquired as part of a group, the purchase price is allocated to each asset on 
the basis of its fair value. An asset’s cost potentially includes expenditures additional 
to the purchase price.
A key concept in accounting for expenditures related to long-  lived assets is whether 
and when such expenditures are capitalised (i.e., included in the asset shown on the

balance sheet) versus expensed (i.e., treated as an expense of the period on the income 
statement). After examining the specific treatment of certain expenditures, we will 
consider the general financial statement impact of capitalising versus expensing and 
two analytical issues related to the decision—namely, the effects on an individual 
company’s trend analysis and on comparability across companies.
2.1 Property, Plant, and Equipment
This section primarily discusses the accounting treatment for the acquisition of 
long-  lived tangible assets (property, plant, and equipment) through purchase. Assets 
can be acquired by methods other than purchase.3 When an asset is exchanged for 
another asset, the asset acquired is recorded at fair value if reliable measures of fair 
value exist. Fair value is the fair value of the asset given up unless the fair value of 
the asset acquired is more clearly evident. If there is no reliable measure of fair value,

the acquired asset is measured at the carrying amount of the asset given up. In this 
case, the carrying amount of the assets is unchanged, and no gain or loss is reported.
Typically, accounting for the exchange involves removing the carrying amount 
of the asset given up, adding a fair value for the asset acquired, and reporting any 
difference between the carrying amount and the fair value as a gain or loss. A gain 
would be reported when the fair value used for the newly acquired asset exceeds the 
carrying amount of the asset given up. A loss would be reported when the fair value 
used for the newly acquired asset is less than the carrying amount of the asset given up.
When property, plant, or equipment is purchased, the buyer records the asset at 
cost. In addition to the purchase price, the buyer also includes, as part of the cost of 
an asset, all the expenditures necessary to get the asset ready for its intended use.

For example, freight costs borne by the purchaser to get the asset to the purchaser’s 
place of business and special installation and testing costs required to make the asset 
usable are included in the total cost of the asset.2
2 Fair value is defined in International Financial Reporting Standards (IFRS) and under US generally 
accepted accounting principles (US GAAP) in the Financial Accounting Standards Board (FASB) Accounting 
Standards Codification (ASC) as “the price that would be received to sell an asset or paid to transfer a 
liability in an orderly transaction between market participants at the measurement date. ” [IFRS 13 and 
FASB ASC Topic 820]
3 IAS 16 Property, Plant and Equipment , paragraphs 24–26 [Measurement of Cost]; IAS 38 Intangible Assets , 
paragraphs 45–47 [Exchange of Assets]; and FASB ASC Section 845-  10- 30 [Nonmonetary Transactions 
– Overall – Initial Measurement].

Reading 28 ■ Long-  Lived Assets 418
Subsequent expenditures related to long-  lived assets are included as part of the 
recorded value of the assets on the balance sheet (i.e., capitalised) if they are expected 
to provide benefits beyond one year in the future and are expensed if they are not 
expected to provide benefits in future periods. Expenditures that extend the original 
life of the asset are typically capitalised. Example 1 illustrates the difference between 
costs that are capitalised and costs that are expensed in a period.
EXAMPLE 1   
Acquisition of PPE
Assume a (hypothetical) company, Trofferini S.A., incurred the following expen -
ditures to purchase a towel and tissue roll machine: €10,900 purchase price 
including taxes, €200 for delivery of the machine, €300 for installation and 
testing of the machine, and €100 to train staff on maintaining the machine. In 
addition, the company paid a construction team €350 to reinforce the factory

floor and ceiling joists to accommodate the machine’s weight. The company also 
paid €1,500 to repair the factory roof (a repair expected to extend the useful 
life of the factory by five years) and €1,000 to have the exterior of the factory 
and adjoining offices repainted for maintenance reasons. The repainting neither 
extends the life of factory and offices nor improves their usability.
1 Which of these expenditures will be capitalised and which will be 
expensed?
2 How will the treatment of these expenditures affect the company’s finan -
cial statements?
The company will capitalise as part of the cost of the machine all costs that are 
necessary to get the new machine ready for its intended use: €10,900 purchase 
price, €200 for delivery, €300 for installation and testing, and €350 to reinforce 
the factory floor and ceiling joists to accommodate the machine’s weight (which 
was necessary to use the machine and does not increase the value of the factory).

The €100 to train staff is not necessary to get the asset ready for its intended 
use and will be expensed.
The company will capitalise the expenditure of €1,500 to repair the factory 
roof because the repair is expected to extend the useful life of the factory. The 
company will expense the €1,000 to have the exterior of the factory and adjoin -
ing offices repainted because the painting does not extend the life or alter the 
productive capacity of the buildings.
The costs related to the machine that are capitalised—€10,900 purchase price, 
€200 for delivery, €300 for installation and testing, and €350 to prepare the 
factory—will increase the carrying amount of the machine asset as shown on 
the balance sheet and will be included as investing cash outflows. The item 
related to the factory that is capitalised—the €1,500 roof repair—will increase 
the carrying amount of the factory asset as shown on the balance sheet and is

an investing cash outflow. The expenditures of €100 to train staff and €1,000 to 
paint are expensed in the period and will reduce the amount of income reported 
on the company’s income statement (and thus reduce retained earnings on the 
balance sheet) and the operating cash flow.

Acquisition of Long-  Lived Assets 419
Example 1 describes capitalising versus expensing in the context of purchasing 
property, plant, and equipment. When a company constructs an asset (or acquires 
an asset that requires a long period of time to get ready for its intended use), bor -
rowing costs incurred directly related to the construction are generally capitalised. 
Constructing a building, whether for sale (in which case, the building is classified 
as inventory) or for the company’s own use (in which case, the building is classified 
as a long-  lived asset), typically requires a substantial amount of time. To finance 
construction, any borrowing costs incurred prior to the asset being ready for its 
intended use are capitalised as part of the cost of the asset. The company determines 
the interest rate to use on the basis of its existing borrowings or, if applicable, on a 
borrowing specifically incurred for constructing the asset. If a company takes out a

loan specifically to construct a building, the interest cost on that loan during the time 
of construction would be capitalised as part of the building’s cost. Under IFRS, but 
not under US GAAP , income earned on temporarily investing the borrowed monies 
decreases the amount of borrowing costs eligible for capitalisation.
Thus, a company’s interest costs for a period are included either on the balance 
sheet (to the extent they are capitalised as part of an asset) or on the income statement 
(to the extent they are expensed). If the interest expenditure is incurred in connec -
tion with constructing an asset for the company’s own use, the capitalised interest 
appears on the balance sheet as a part of the relevant long-  lived asset (i.e., property, 
plant, and equipment). The capitalised interest is expensed over time as the prop -
erty is depreciated and is thus part of subsequent years’ depreciation expense rather

than interest expense of the current period. If the interest expenditure is incurred in 
connection with constructing an asset to sell (for example, by a home builder), the 
capitalised interest appears on the company’s balance sheet as part of inventory. The 
capitalised interest is expensed as part of the cost of goods sold when the asset is 
sold. Interest payments made prior to completion of construction that are capitalised 
are classified as an investing cash outflow. Expensed interest may be classified as an 
operating or financing cash outflow under IFRS and is classified as an operating cash 
outflow under US GAAP .
EXAMPLE 2   
Capitalised Borrowing Costs
BILDA S.A., a hypothetical company, borrows €1,000,000 at an interest rate of 
10 percent per year on 1 January 2010 to finance the construction of a factory 
that will have a useful life of 40 years. Construction is completed after two 
years, during which time the company earns €20,000 by temporarily investing 
the loan proceeds.

1 What is the amount of interest that will be capitalised under IFRS, and 
how would that amount differ from the amount that would be capitalised 
under US GAAP?
2 Where will the capitalised borrowing cost appear on the company’s finan -
The total amount of interest paid on the loan during construction is €200,000 (= 
€1,000,000 × 10% × 2 years). Under IFRS, the amount of borrowing cost eligible 
for capitalisation is reduced by the €20,000 interest income from temporarily 
investing the loan proceeds, so the amount to be capitalised is €180,000. Under 
US GAAP , the amount to be capitalised is €200,000.

Reading 28 ■ Long-  Lived Assets 420
The capitalised borrowing costs will appear on the company’s balance sheet as a 
component of property, plant, and equipment. In the years prior to completion 
of construction, the interest paid will appear on the statement of cash flows as 
an investment activity. Over time, as the property is depreciated, the capitalised 
interest component is part of subsequent years’ depreciation expense on the 
company’s income statement.
2.2 Intangible Assets
Intangible assets are assets lacking physical substance. Intangible assets include items 
that involve exclusive rights, such as patents, copyrights, trademarks, and franchises. 
Under IFRS, identifiable intangible assets must meet three definitional criteria. They 
must be (1) identifiable (either capable of being separated from the entity or arising 
from contractual or legal rights), (2) under the control of the company, and (3) expected

to generate future economic benefits. In addition, two recognition criteria must be 
met: (1) It is probable that the expected future economic benefits of the asset will 
flow to the company, and (2) the cost of the asset can be reliably measured. Goodwill, 
which is not considered an identifiable intangible asset,4 arises when one company 
purchases another and the acquisition price exceeds the fair value of the identifiable 
assets (both the tangible assets and the identifiable intangible assets) acquired.
Accounting for an intangible asset depends on how it is acquired. The following 
sections describe accounting for intangible assets obtained in three ways: purchased 
in situations other than business combinations, developed internally, and acquired 
in business combinations.
2.2.1  Intangible Assets Purchased in Situations Other Than Business Combinations
Intangible assets purchased in situations other than business combinations, such as

buying a patent, are treated at acquisition the same as long-  lived tangible assets; they 
are recorded at their fair value when acquired, which is assumed to be equivalent to 
the purchase price. If several intangible assets are acquired as part of a group, the 
purchase price is allocated to each asset on the basis of its fair value.
In deciding how to treat individual intangible assets for analytical purposes, analysts 
are particularly aware that companies must use a substantial amount of judgment and 
numerous assumptions to determine the fair value of individual intangible assets. For 
analysis, therefore, understanding the types of intangible assets acquired can often 
be more useful than focusing on the values assigned to the individual assets. In other 
words, an analyst would typically be more interested in understanding what assets a 
company acquired (for example, franchise rights and a mailing list) than in the precise

portion of the purchase price a company allocated to each asset. Understanding the 
types of assets a company acquires can offer insights into the company’s strategic 
direction and future operating potential.
2.2.2  Intangible Assets Developed Internally
In contrast with the treatment of construction costs of tangible assets, the costs to 
internally develop intangible assets are generally expensed when incurred. There 
are some situations, however, in which the costs incurred to internally develop an 
4 The IFRS definition of an intangible asset as an “identifiable non-  monetary asset without physical sub -
stance” applies to intangible assets not specifically dealt with in standards other than IAS 38. The definition 
of intangible assets under US GAAP—“assets (other than financial assets) that lack physical substance”—
includes goodwill in the definition of an intangible asset.

Acquisition of Long-  Lived Assets 421
intangible asset are capitalised. The general analytical issues related to the capitalising-  
versus-  expensing decision apply here—namely, comparability across companies and 
the effect on an individual company’s trend analysis.
The general requirement that costs to internally develop intangible assets be 
expensed should be compared with capitalising the cost of acquiring intangible assets 
in situations other than business combinations. Because costs associated with internally 
developing intangible assets are usually expensed, a company that has internally devel -
oped such intangible assets as patents, copyrights, or brands through expenditures on 
R&D or advertising will recognise a lower amount of assets than a company that has 
obtained intangible assets through external purchase. In addition, on the statement of 
cash flows, costs of internally developing intangible assets are classified as operating

cash outflows whereas costs of acquiring intangible assets are classified as investing 
cash outflows. Differences in strategy (developing versus acquiring intangible assets) 
can thus impact financial ratios.
IFRS require that expenditures on research (or during the research phase of an 
internal project) be expensed rather than capitalised as an intangible asset.5 Research 
is defined as “original and planned investigation undertaken with the prospect of 
gaining new scientific or technical knowledge and understanding. ”6 The “research 
phase of an internal project” refers to the period during which a company cannot 
demonstrate that an intangible asset is being created—for example, the search for 
alternative materials or systems to use in a production process. IFRS allow companies 
to recognise an intangible asset arising from development (or the development phase 
of an internal project) if certain criteria are met, including a demonstration of the

technical feasibility of completing the intangible asset and the intent to use or sell 
the asset. Development is defined as “the application of research findings or other 
knowledge to a plan or design for the production of new or substantially improved 
materials, devices, products, processes, systems or services before the start of com -
mercial production or use. ”7
Generally, US GAAP require that both research and development costs be expensed 
as incurred but require capitalisation of certain costs related to software development.8 
Costs incurred to develop a software product for sale are expensed until the prod -
uct’s technological feasibility is established and are capitalised thereafter. Similarly, 
companies expense costs related to the development of software for internal use until 
it is probable that the project will be completed and that the software will be used 
as intended. Thereafter, development costs are capitalised. The probability that the

project will be completed is easier to demonstrate than is technological feasibility. 
The capitalised costs, related directly to developing software for sale or internal use, 
include the costs of employees who help build and test the software. The treatment 
of software development costs under US GAAP is similar to the treatment of all costs 
of internally developed intangible assets under IFRS.
5 IAS 38 Intangible Assets .
6 IAS 38 Intangible Assets , paragraph 8 [Definitions].
7 IAS 38 Intangible Assets , paragraph 8 [Definitions].
8 FASB ASC Section 350-  40- 25 [Intangibles—Goodwill and Other – Internal-  Use Software – Recognition] 
and FASB ASC Section 985-  20- 25 [Software – Costs of Software to be Sold, Leased, or Marketed – 
Recognition] specify US GAAP accounting for software development costs for software for internal use 
and for software to be sold, respectively.

Reading 28 ■ Long-  Lived Assets 422
EXAMPLE 3   
Software Development Costs
Assume REH AG, a hypothetical company, incurs expenditures of €1,000 per 
month during the fiscal year ended 31 December 2009 to develop software for 
internal use. Under IFRS, the company must treat the expenditures as an expense 
until the software meets the criteria for recognition as an intangible asset, after 
which time the expenditures can be capitalised as an intangible asset.
1 What is the accounting impact of the company being able to demonstrate 
that the software met the criteria for recognition as an intangible asset on 
1 February versus 1 December?
2 How would the treatment of expenditures differ if the company reported 
under US GAAP and it had established in 2008 that the project was likely 
to be completed?
If the company is able to demonstrate that the software met the criteria for 
recognition as an intangible asset on 1 February, the company would recognise

€1,000 of expense (on the income statement) during the fiscal year ended 31 
December 2009. The other €11,000 of expenditures would be recognised as an 
intangible asset (on the balance sheet). Alternatively, if the company is not able 
to demonstrate that the software met the criteria for recognition as an intangible 
asset until 1 December, the company would recognise €11,000 of expense during 
the fiscal year ended 31 December 2009, with the other €1,000 of expenditures 
recognised as an intangible asset.
Under US GAAP , the company would capitalise the entire €12,000 spent to 
develop software for internal use.
2.2.3  Intangible Assets Acquired in a Business Combination
When one company acquires another company, the transaction is accounted for using 
the acquisition method  of accounting.9 Under the acquisition method, the company 
identified as the acquirer allocates the purchase price to each asset acquired (and each

liability assumed) on the basis of its fair value. If the purchase price exceeds the sum 
of the amounts that can be allocated to individual identifiable assets and liabilities, 
the excess is recorded as goodwill. Goodwill cannot be identified separately from the 
business as a whole.
Under IFRS, the acquired individual assets include identifiable intangible assets that 
meet the definitional and recognition criteria.10 Otherwise, if the item is acquired in a 
business combination and cannot be recognised as a tangible or identifiable intangible 
asset, it is recognised as goodwill. Under US GAAP , there are two criteria to judge 
whether an intangible asset acquired in a business combination should be recognised 
separately from goodwill: The asset must be either an item arising from contractual 
or legal rights or an item that can be separated from the acquired company. Examples 
of intangible assets treated separately from goodwill include the intangible assets

9 Both IFRS and US GAAP require the use of the acquisition method in accounting for business combi -
nations (IFRS 3 and FASB ASC Section 805).
10 As previously described, the definitional criteria are identifiability, control by the company, and 
expected future benefits. The recognition criteria are probable flows of the expected economic benefits to 
the company and measurability.

Acquisition of Long-  Lived Assets 423
previously mentioned that involve exclusive rights (patents, copyrights, franchises, 
licenses), as well as such items as internet domain names and video and audiovisual 
materials.
Exhibit 1 describes how InBev allocated the €40.3 billion purchase price for its 
acquisition of Anheuser-  Busch. The majority of the identifiable intangible asset val -
uation (€16.473 billion) relates to brands with indefinite life. Another €256 million or 
€0.256 billion was for the identifiable intangible assets with definite useful lives—distri -
bution agreements and favorable contracts. These assets are being amortised over the 
life of the associated contracts. In addition, €24.7 billion of goodwill was recognised.
Exhibit 1   Acquisition of Intangible Assets through a Business Combination
Excerpt from the 2008 annual report of AB InBev:
On 18 November, InBev has completed the acquisition of Anheuser-  
Busch, following approval from shareholders of both companies. . . .

Effective the date of the closing, InBev has changed its name to AB 
InBev to reflect the heritage and traditions of Anheuser-  Busch. Under 
the terms of the merger agreement, all shares of Anheuser-  Busch were 
acquired for 70 US dollar per share in cash for an aggregate amount 
of approximately 52.5b US dollar or 40.3b euro.
The transaction resulted in 24.7b euro goodwill provisionally allo -
cated primarily to the US business on the basis of expected synergies. 
. . . The valuation of the property, plant and equipment, intangible 
assets, investment in associates, interest bearing loans and borrow -
ings and employee benefits is based on the valuation performed by 
independent valuation specialist. The other assets and liabilities are 
based on the current best estimates of AB InBev’s management.
The majority of the intangible asset valuation relates to brands 
with indefinite life. The valuation of the brands with indefinite life is

based on a series of factors, including the brand history, the operating 
plan and the countries in which the brands are sold. The brands with 
indefinite life include the Budweiser family (including Bud and Bud 
Light), the Michelob brand family, the Busch brand family and the 
Natural brand family and have been fair valued for a total amount 
of 16,473m euro. Distribution agreements and favorable contracts 
have been fair valued for a total amount of 256m euro. These are 
being amortised over the term of the associated contracts ranging 
from 3 to 18 years.
Source : AB InBev 2008 Annual Report, pp. 74–75.
2.3 Capitalising versus Expensing: Impact on Financial 
Statements and Ratios
This section discusses the implications for financial statements and ratios of capitalising 
versus expensing costs in the period in which they are incurred. We first summarize 
the general financial statement impact of capitalising versus expensing and two ana -

lytical issues related to the decision—namely the effect on an individual company’s 
trend analysis and on comparability across companies.
In the period of the expenditure, an expenditure that is capitalised increases the 
amount of assets on the balance sheet and appears as an investing cash outflow on the 
statement of cash flows. After initial recognition, a company allocates the capitalised

Reading 28 ■ Long-  Lived Assets 424
amount over the asset’s useful life as depreciation or amortisation expense (except assets 
that are not depreciated, i.e., land, or amortised, e.g., intangible assets with indefinite 
lives). This expense reduces net income on the income statement and reduces the 
value of the asset on the balance sheet. Depreciation and amortisation are non-  cash 
expenses and therefore, apart from their effect on taxable income and taxes payable, 
have no impact on the cash flow statement. In the section of the statement of cash 
flows that reconciles net income to operating cash flow, depreciation and amortisation 
expenses are added back to net income.
Alternatively, an expenditure that is expensed reduces net income by the after-  
tax amount of the expenditure in the period it is made. No asset is recorded on the 
balance sheet and thus no depreciation or amortisation occurs in subsequent periods.

The lower amount of net income is reflected in lower retained earnings on the balance 
sheet. An expenditure that is expensed appears as an operating cash outflow in the 
period it is made. There is no effect on the financial statements of subsequent periods.
Example 4 illustrates the impact on the financial statements of capitalising versus 
expensing an expenditure.
EXAMPLE 4   
General Financial Statement Impact of Capitalising Versus 
Expensing
Assume two identical (hypothetical) companies, CAP Inc. (CAP) and NOW 
Inc. (NOW), start with €1,000 cash and €1,000 common stock. Each year the 
companies recognise total revenues of €1,500 cash and make cash expenditures, 
excluding an equipment purchase, of €500. At the beginning of operations, each 
company pays €900 to purchase equipment. CAP estimates the equipment will 
have a useful life of three years and an estimated salvage value of €0 at the end 
of the three years. NOW estimates a much shorter useful life and expenses

the equipment immediately. The companies have no other assets and make no 
other asset purchases during the three-  year period. Assume the companies pay 
no dividends, earn zero interest on cash balances, have a tax rate of 30 percent, 
and use the same accounting method for financial and tax purposes.
The left side of Exhibit 2 shows CAP’s financial statements; i.e., with the 
expenditure capitalised and depreciated at €300 per year based on the straight-  
line method of depreciation (€900 cost minus €0 salvage value equals €900, 
divided by a three-  year life equals €300 per year). The right side of the exhibit 
shows NOW’s financial statements, with the entire €900 expenditure treated as 
an expense in the first year. All amounts are in euro.
Exhibit 2   Capitalising versus Expensing
CAP Inc. NOW Inc.
Capitalise €900 as asset and depreciate Expense €900 immediately
For Y ear 1 2 3 For Y ear 1 2 3
Revenue 1,500 1,500 1,500 Revenue 1,500 1,500 1,500

Cash expenses 500 500 500 Cash expenses 1,400 500 500
Depreciation 300 300 300 Depreciation 0 0 0
Income before tax
700 700 700Income before 
tax 100 1,000 1,000
Tax at 30% 210 210 210 Tax at 30% 30 300 300

Acquisition of Long-  Lived Assets 425
Net income 490 490 490 Net income 70 700 700
           
Cash from 
operations 790 790 790Cash from 
operations 70 700 700
Cash used in 
investing (900) 0 0Cash used in 
investing 0 0 0
Total change in 
cash (110) 790 790Total change in 
cash 70 700 700
As ofTime 
0End of 
Y ear 1End of 
Y ear2End of 
Y ear 3 TimeTime 
0End of 
Y ear 2End of 
Y ear 3
Cash 1,000 890 1,680 2,470 Cash 1,000 1,070 1,770 2,470
PP & E (net) — 600 300 —PP & E 
(net) — — — —
Total Assets 1,000 1,490 1,980 2,470Total 
Assets 1,000 1,070 1,770 2,470
Retained 
earnings 0 490 980 1,470Retained 
earnings 0 70 770 1,470
Common 
stock 1,000 1,000 1,000 1,000Common 
stock 1,000 1,000 1,000 1,000
Total share -
holders’ 
equity 1,000 1,490 1,980 2,470Total 
sharehold -
ers’ equity 1,000 1,070 1,770 2,470
1 Which company reports higher net income over the three years? Total

cash flow? Cash from operations?
2 Based on ROE and net profit margin, how does the profitability of the two 
companies compare?
3 Why does NOW report change in cash of €70 in Year 1, while CAP 
reports total change in cash of (€110)?
Neither company reports higher total net income or cash flow over the three 
years. The sum of net income over the three years is identical (€1,470 total) 
whether the €900 is capitalised or expensed. Also, the sum of the change in cash 
(€1,470 total) is identical under either scenario. CAP reports higher cash from 
operations by an amount of €900 because, under the capitalisation scenario, the 
€900 purchase is treated as an investing cash flow.
Note : Because the companies use the same accounting method for both 
financial and taxable income, absent the assumption of zero interest on cash 
balances, expensing the €900 would have resulted in higher income and cash 
flow for NOW because the lower taxes paid in the first year (€30 versus €210)

would have allowed NOW to earn interest income on the tax savings.Exhibit 2   (Continued)

Reading 28 ■ Long-  Lived Assets 426
In general, Ending shareholders’ equity = Beginning shareholders’ equity + Net 
income + Other comprehensive income – Dividends + Net capital contribu -
tions from shareholders. Because the companies in this example do not have 
other comprehensive income, did not pay dividends, and reported no capital 
contributions from shareholders, Ending retained earnings = Beginning retained 
earnings + Net income, and Ending shareholders’ equity = Beginning sharehold -
ers’ equity + Net income.
ROE is calculated as Net income divided by Average shareholders’ equity, 
and Net profit margin is calculated as Net income divided by Total revenue. For 
example, CAP had Year 1 ROE of 39 percent (€490/[(€1,000 + €1,490)/2]), and 
Year 1 net profit margin of 33 percent (€490/€1,500).
Capitalise €900 as asset and 
depreciate Expense €900 immediately
For year 1 2 3 For year 1 2 3
ROE 39% 28% 22% ROE 7% 49% 33%
Net profit 
margin33% 33% 33% Net profit

Net profit 
margin33% 33% 33% Net profit 
margin5% 47% 47%
As shown, capitalising results in higher profitability ratios (ROE and net profit 
margin) in the first year, and lower profitability ratios in subsequent years. For 
example, CAP’s Year 1 ROE of 39 percent was higher than NOW’s Year 1 ROE 
of 7 percent, but in Years 2 and 3, NOW reports superior profitability.
Note also that NOW’s superior growth in net income between Year 1 and 
Year 2 is not attributable to superior performance compared to CAP but rather 
to the accounting decision to recognise the expense sooner than CAP . In general, 
all else equal, accounting decisions that result in recognising expenses sooner will 
give the appearance of greater subsequent growth. Comparison of the growth 
of the two companies’ net incomes without an awareness of the difference in 
accounting methods would be misleading. As a corollary, NOW’s income and 
profitability exhibit greater volatility across the three years, not because of more

volatile performance but rather because of the different accounting decision.
NOW reports an increase in cash of €70 in Year 1, while CAP reports a decrease 
in cash of €110 because NOW’s taxes were €180 lower than CAP’s taxes (€30 
versus €210).
Note  that this problem assumes the accounting method used by each com -
pany for its tax purposes is identical to the accounting method used by the 
company for its financial reporting. In many countries, companies are allowed 
to use different depreciation methods for financial reporting and taxes, which 
may give rise to deferred taxes.
As shown, discretion regarding whether to expense or capitalise expenditures can 
impede comparability across companies. Example 4 assumes the companies purchase 
a single asset in one year. Because the sum of net income over the three-  year period 
is identical whether the asset is capitalised or expensed, it illustrates that although

capitalising results in higher profitability compared to expensing in the first year, it 
results in lower profitability ratios in the subsequent years. Conversely, expensing 
results in lower profitability in the first year but higher profitability in later years, 
indicating a favorable trend.

Acquisition of Long-  Lived Assets 427
Similarly, shareholders’ equity for a company that capitalises the expenditure will 
be higher in the early years because the initially higher profits result in initially higher 
retained earnings. Example 4 assumes the companies purchase a single asset in one 
year and report identical amounts of total net income over the three-  year period, so 
shareholders’ equity (and retained earnings) for the firm that expenses will be identical 
to shareholders’ equity (and retained earnings) for the capitalising firm at the end of 
the three-  year period.
Although Example 4 shows companies purchasing an asset only in the first year, 
if a company continues to purchase similar or increasing amounts of assets each year, 
the profitability-  enhancing effect of capitalising continues if the amount of the expen -
ditures in a period continues to be more than the depreciation expense. Example 5 
illustrates this point.
EXAMPLE 5

EXAMPLE 5   
Impact of Capitalising Versus Expensing for Ongoing 
Purchases
A company buys a £300 computer in Year 1 and capitalises the expenditure. 
The computer has a useful life of three years and an expected salvage value of 
£0, so the annual depreciation expense using the straight-  line method is £100 
per year. Compared to expensing the entire £300 immediately, the company’s 
pre-  tax profit in Year 1 is £200 greater.
1 Assume that the company continues to buy an identical computer each 
year at the same price. If the company uses the same accounting treat -
ment for each of the computers, when does the profit-  enhancing effect of 
capitalising versus expensing end?
2 If the company buys another identical computer in Year 4, using the same 
accounting treatment as the prior years, what is the effect on Year 4 prof -
its of capitalising versus expensing these expenditures?
The profit-  enhancing effect of capitalising versus expensing would end in Year

3. In Year 3, the depreciation expense on each of the three computers bought 
in Years 1, 2, and 3 would total £300 (£100 + £100 + £100). Therefore, the total 
depreciation expense for Year 3 will be exactly equal to the capital expenditure in 
Year 3. The expense in Year 3 would be £300, regardless of whether the company 
capitalised or expensed the annual computer purchases.
There is no impact on Year 4 profits. As in the previous year, the depreciation 
expense on each of the three computers bought in Years 2, 3, and 4 would total 
£300 (£100 + £100 + £100). Therefore, the total depreciation expense for Year 4 
will be exactly equal to the capital expenditure in Year 4. Pre-  tax profits would 
be reduced by £300, regardless of whether the company capitalised or expensed 
the annual computer purchases.
Compared to expensing an expenditure, capitalising the expenditure typically 
results in greater amounts reported as cash from operations. Capitalised expenditures

are typically treated as an investment cash outflow whereas expenses reduce operating 
cash flows. Because cash flow from operating activities is an important consideration 
in some valuation models, companies may try to maximise reported cash flow from

Reading 28 ■ Long-  Lived Assets 428
operations by capitalising expenditures that should be expensed. Valuation models 
that use free cash flow will consider not only operating cash flows but also investing 
cash flows. Analysts should be alert to evidence of companies manipulating reported 
cash flow from operations by capitalising expenditures that should be expensed.
In summary, holding all else constant, capitalising an expenditure enhances cur -
rent profitability and increases reported cash flow from operations. The profitability-  
enhancing effect of capitalising continues so long as capital expenditures exceed the 
depreciation expense. Profitability-  enhancing motivations for decisions to capitalise 
should be considered when analyzing performance. For example, a company may 
choose to capitalise more expenditures (within the allowable bounds of accounting 
standards) to achieve earnings targets for a given period. Expensing a cost in the period

reduces current period profits but enhances future profitability and thus enhances 
the profit trend. Profit trend-  enhancing motivations should also be considered when 
analyzing performance. If the company is in a reporting environment which requires 
identical accounting methods for financial reporting and taxes (unlike the United 
States, which permits companies to use depreciation methods for reporting purposes 
that differ from the depreciation method required by tax purposes), then expensing 
will have a more favorable cash flow impact because paying lower taxes in an earlier 
period creates an opportunity to earn interest income on the cash saved.
In contrast with the relatively simple examples above, it is generally neither pos -
sible nor desirable to identify individual instances involving discretion about whether 
to capitalise or expense expenditures. An analyst can, however, typically identify 
significant items of expenditure treated differently across companies. The items of

expenditure giving rise to the most relevant differences across companies will vary 
by industry. This cross-  industry variation is apparent in the following discussion of 
the capitalisation of expenditures.
2.4 Capitalisation of Interest Costs
As noted above, companies generally must capitalise interest costs associated with 
acquiring or constructing an asset that requires a long period of time to get ready for 
its intended use.11
As a consequence of this accounting treatment, a company’s interest costs for a 
period can appear either on the balance sheet (to the extent they are capitalised) or 
on the income statement (to the extent they are expensed).
If the interest expenditure is incurred in connection with constructing an asset for 
the company’s own use, the capitalised interest appears on the balance sheet as a part 
of the relevant long-  lived asset. The capitalised interest is expensed over time as the

property is depreciated—and is thus part of depreciation expense rather than interest 
expense. If the interest expenditure is incurred in connection with constructing an 
asset to sell, for example by a real estate construction company, the capitalised interest 
appears on the company’s balance sheet as part of inventory. The capitalised interest 
is then expensed as part of the cost of sales when the asset is sold.
The treatment of capitalised interest poses certain issues that analysts should 
consider. First, capitalised interest appears as part of investing cash outflows, whereas 
expensed interest reduces operating cash flow. Although the treatment is consistent 
with accounting standards, an analyst may want to examine the impact on reported 
cash flows. Second, interest coverage ratios are solvency indicators measuring the 
extent to which a company’s earnings (or cash flow) in a period covered its interest

11 IAS 23 [Borrowing Costs] and FASB ASC Subtopic 835-  20 [Interest – Capitalization of Interest] specify 
respectively IFRS and US GAAP for capitalisation of interest costs. Although the standards are not com -
pletely converged, the standards are in general agreement.

Acquisition of Long-  Lived Assets 429
costs. To provide a true picture of a company’s interest coverage, the entire amount of 
interest expenditure, both the capitalised portion and the expensed portion, should be 
used in calculating interest coverage ratios. Additionally, if a company is depreciating 
interest that it capitalised in a previous period, income should be adjusted to eliminate 
the effect of that depreciation. Example 6 illustrates the calculation.
EXAMPLE 6   
Effect of Capitalised Interest Costs on Coverage Ratios 
and Cash Flow
MTR Gaming Group, Inc. disclosed the following information in one of the 
footnotes to its financial statements: “Interest is allocated and capitalized to 
construction in progress by applying our cost of borrowing rate to qualifying 
assets. Interest capitalized in 2007 and 2006 was $2.2 million and $6.0 million, 
respectively. There was no interest capitalized during 2008. ” (Form 10-  K filed 
13 March 2009).

Exhibit 3   MTR Gaming Group Selected Data, as Reported (Dollars in 
thousands)
2008 2007 2006
EBIT (from income statement) 432,686 389,268 268,800
Interest expense (from income statement) 40,764 34,774 17,047
Interest capitalised (from footnote) 0 2,200 6,000
Net cash provided by operating activities 14,693 14,980 42,206
Net cash from (used) in investing activities 41,620 (144,824) (162,415)
1 Calculate and interpret MTR’s interest coverage ratio with and without 
capitalised interest. Assume that capitalised interest increases deprecia -
tion expense by $475 thousand in 2008 and 2007, and by $365 thousand in 
2006.
2 Calculate MTR’s percentage change in operating cash flow from 2006 to 
2007 and from 2007 to 2008. Assuming the financial reporting does not 
affect reporting for income taxes, what were the effects of capitalised 
interest on operating and investing cash flows?
MTR did not capitalise any interest during 2008, so the interest coverage ratio for

this year is affected only by depreciation expense related to previously capitalised 
interest. The interest coverage ratio, measured as earnings before interest and 
taxes (EBIT) divided by interest expense, was as follows for 2008:
10.61 ($432,686 ÷ $40,764) for 2008 without adjusting for capitalised interest
10.63 [($432,686 + $475) ÷ $40,764] including an adjustment to EBIT for 
depreciation of previously capitalised interest
For the years 2007 and 2006, interest coverage ratios with and without capitalised 
interest were as follows:

Reading 28 ■ Long-  Lived Assets 430
For 2007
11.19 ($389,268 ÷ $34,774) without adjusting for capitalised interest; and
10.54 [($389,268 + $475) ÷ ($34,774 + $2,200)] including an adjustment to 
EBIT for depreciation of previously capitalised interest and an adjustment to 
interest expense for the amount of interest capitalised in 2007.  
For 2006
15.77 ($268,800 ÷ $17,047) without adjusting for capitalised interest; and
11.68 [($268,800 + $365) ÷ ($17,047 + $6,000)] including an adjustment to 
interest expense for the amount of interest capitalised in 2006.  
Because MTR capitalises interest in previous years, EBIT is adjusted by adding 
in depreciation expense due to capitalised interest costs.
The above calculations indicate that MTR’s interest coverage deteriorated 
over the three-  year period from 2006 to 2008, even with no adjustments for

capitalised interest. In both 2006 and 2007, the coverage ratio is lower when 
adjusted for capitalised interest. For 2006, the interest coverage ratio of 11.68 
that includes capitalised interest is substantially lower than the ratio without 
capitalised interest.
If the interest had been expensed rather than capitalised, operating cash flows 
would have been substantially lower in 2006, slightly lower in 2007, but unchanged 
in 2008. If the interest had been expensed rather than capitalised, the trend—at 
least in the last two years—would have been more favorable; operating cash flows 
would have increased rather than decreased over the 2007 to 2008 period. On 
an unadjusted basis, for 2008 compared with 2007, MTR’s operating cash flow 
declined by 1.9 percent [($14,693 ÷ $14,980) – 1]. If the $2,200 of interest had 
been expensed rather than capitalised in 2007, the change in operating cash flow 
would have been positive, 15.0 percent {[$14,693 ÷ ($14,980 – $2,200)] – 1}.

If interest had been expensed rather than capitalised, the amount of cash 
outflow for investing activities would have been lower in 2006 and 2007 but 
unaffected in 2008. The percentage decline in cash outflows for investing activ -
ities from 2006 to 2007 would have been slightly smaller excluding capitalised 
interest from investing activities, 8.8 percent {[($144,824 – $2,200) ÷ ($162,415 
– $6,000)] – 1}.
The treatment of capitalised interest raises issues for consideration by an analyst. 
First, capitalised interest appears as part of investing cash outflows, whereas expensed 
interest reduces operating or financing cash flow under IFRS and operating cash flow 
under US GAAP . An analyst may want to examine the impact on reported cash flows 
of interest expenditures when comparing companies. Second, interest coverage ratios 
are solvency indicators measuring the extent to which a company’s earnings (or cash

flow) in a period covered its interest costs. To provide a true picture of a company’s 
interest coverage, the entire amount of interest, both the capitalised portion and the 
expensed portion, should be used in calculating interest coverage ratios.
Generally, including capitalised interest in the calculation of interest coverage 
ratios provides a better assessment of a company’s solvency. In assigning credit ratings, 
rating agencies include capitalised interest in coverage ratios. For example, Standard 
& Poor’s calculates the EBIT interest coverage ratio as EBIT divided by gross interest 
(defined as interest prior to deductions for capitalised interest or interest income).

Acquisition of Long-  Lived Assets 431
Maintaining a minimum interest coverage ratio is a financial covenant often 
included in lending agreements, e.g., bank loans and bond indentures. The definition 
of the coverage ratio can be found in the company’s credit agreement. The definition is 
relevant because treatment of capitalised interest in calculating coverage ratios would 
affect an assessment of how close a company’s actual ratios are to the levels specified 
by its financial covenants and thus the probability of breaching those covenants.
2.5 Capitalisation of Internal Development Costs
As noted above, accounting standards require companies to capitalise software devel -
opment costs after a product’s feasibility is established. Despite this requirement, 
judgment in determining feasibility means that companies’ capitalisation practices 
may differ. For example, as illustrated in Exhibit 4, Microsoft judges product feasibility

to be established very shortly before manufacturing begins and, therefore, effectively 
expenses—rather than capitalises—research and development costs.
Exhibit 4   Disclosure on Software Development Costs
Excerpt from Management’s Discussion and Analysis (MD&A) of Microsoft 
Corporation, Application of Critical Accounting Policies, Research and 
Development Costs:
SFAS No. 86 specifies that costs incurred internally in researching 
and developing a computer software product should be charged to 
expense until technological feasibility has been established for the 
product. Once technological feasibility is established, all software costs 
should be capitalized until the product is available for general release 
to customers. Judgment is required in determining when technolog -
ical feasibility of a product is established. We have determined that 
technological feasibility for our software products is reached after all 
high-  risk development issues have been resolved through coding and

testing. Generally, this occurs shortly before the products are released 
to manufacturing. The amortization of these costs is included in cost 
of revenue over the estimated life of the products.
Source : Microsoft Corporation Annual Report 2009, p. 36.
Expensing rather than capitalising development costs results in lower net income 
in the current period. Expensing rather than capitalising will continue to result in 
lower net income so long as the amount of the current-  period development expenses 
is higher than the amortisation expense that would have resulted from amortising 
prior periods’ capitalised development costs—the typical situation when a company’s 
development costs are increasing. On the statement of cash flows, expensing rather 
than capitalising development costs results in lower net operating cash flows and 
higher net investing cash flows. This is because the development costs are reflected 
as operating cash outflows rather than investing cash outflows.

In comparing the financial performance of a company that expenses most or all 
software development costs, such as Microsoft, with another company that capitalises 
software development costs, adjustments can be made to make the two comparable. 
For the company that capitalises software development costs, an analyst can adjust 
(a) the income statement to include software development costs as an expense and to 
exclude amortisation of prior years’ software development costs; (b) the balance sheet 
to exclude capitalised software (decrease assets and equity); and (c) the statement of

Reading 28 ■ Long-  Lived Assets 432
cash flows to decrease operating cash flows and decrease cash used in investing by 
the amount of the current period development costs. Any ratios that include income, 
long-  lived assets, or cash flow from operations—such as return on equity—will also 
be affected.
EXAMPLE 7   
You are working on a project involving the analysis of JHH Software, a (hypo -
thetical) software development company that established technical feasibility 
for its first product in 2007. Part of your analysis involves computing certain 
market-  based ratios, which you will use to compare JHH to another company 
that expenses all of its software development expenditures. Relevant data and 
excerpts from the company’s annual report are included in Exhibit 5.
Exhibit 5   JHH SOFTWARE (Dollars in Thousands, Except Per-  Share 
Amounts)
CONSOLIDATED STATEMENT OF EARNINGS—abbreviated
For year ended 31 December: 2009 2008 2007
Total revenue $91,424 $91,134 $96,293

Total operating expenses 78,107 78,908 85,624
Operating income 13,317 12,226 10,669
Provision for income taxes 3,825 4,232 3,172
Net income $9,492 $7,994 $7,479
Earnings per share (EPS) $1.40 $0.82 $0.68
STATEMENT OF CASH FLOWS—abbreviated
Net cash provided by operating 
activities$15,007 $14,874 $15,266
Net cash used in investing 
activities*(11,549) (4,423) (5,346)
Net cash used in financing 
activities(8,003) (7,936) (7,157)
Net change in cash and cash 
equivalents($4,545) $2,515 $2,763
*Includes software development 
expenses of and includes capital 
expenditures of($6,000) ($4,000) ($2,000)
($2,000) ($1,600) ($1,200)
Additional information:
Market value of outstanding debt 0 0 0
Amortisation of capitalised soft -
ware development expenses($2,000) ($667) 0
Depreciation expense ($2,200) ($1,440) ($1,320)

Acquisition of Long-  Lived Assets 433
Market price per share of com -
mon stock$42 $26 $17
Shares of common stock out -
standing (thousands)6,780 9,765 10,999
Footnote disclosure of accounting policy for software development:
Expenses that are related to the conceptual formulation and design of software products are 
expensed to research and development as incurred. The company capitalises expenses that are 
incurred to produce the finished product after technological feasibility has been established.
1 Compute the following ratios for JHH based on the reported financial 
statements for fiscal year ended 31 December 2009, with no adjustments. 
Next, determine the approximate impact on these ratios if the company 
had expensed rather than capitalised its investments in software. (Assume 
the financial reporting does not affect reporting for income taxes. There 
would be no change in the effective tax rate.)

A P/E: Price/Earnings per share
B P/CFO: Price/Operating cash flow per share
C EV/EBITDA: Enterprise value/EBITDA, where enterprise value is 
defined as the total market value of all sources of a company’s financ -
ing, including equity and debt, and EBITDA is earnings before inter -
est, taxes, depreciation, and amortisation.
2 Interpret the changes in the ratios.
(Dollars are in thousands, except per-  share amounts.) JHH’s 2009 ratios are 
presented in the following table:
Ratios As reported As adjusted
A. P/E ratio 30.0   42.9
B. P/CFO 19.0   31.6
C. EV/EBITDA 16.3   24.7
A Based on the information as reported, the P/E ratio was 30.0 ($42 ÷ 
$1.40). Based on EPS adjusted to expense software development costs, the 
P/E ratio was 42.9 ($42 ÷ $0.98).
■●Price: Assuming that the market value of the company’s equity is 
based on its fundamentals, the price per share is $42, regardless of a 
difference in accounting.

■●EPS: As reported, EPS was $1.40. Adjusted EPS was $0.98. Expensing 
software development costs would have reduced JHH’s 2009 operating 
income by $6,000, but the company would have reported no amortisa -
tion of prior years’ software costs, which would have increased oper -
ating income by $2,000. The net change of $4,000 would have reduced 
operating income from the reported $13,317 to $9,317. The effective 
tax rate for 2009 ($3,825 ÷ $13,317) is 28.72%, and using this effec -
tive tax rate would give an adjusted net income of $6,641 [$9,317 × (1 Exhibit 5   (Continued)

Reading 28 ■ Long-  Lived Assets 434
– 0.2872)], compared to $9,492 before the adjustment. The EPS would 
therefore be reduced from the reported $1.40 to $0.98 (adjusted net 
income of $6,641 divided by 6,780 shares).
B Based on information as reported, the P/CFO was 19.0 ($42 ÷ $2.21). 
Based on CFO adjusted to expense software development costs, the P/
CFO was 31.6 ($42 ÷ $1.33).
■●CFO per share, as reported, was $2.21 (total operating cash flows 
$15,007 ÷ 6,780 shares).
■●CFO per share, as adjusted, was $1.33. The company’s $6,000 expen -
diture on software development costs was reported as a cash outflow 
from investing activities, so expensing those costs would reduce cash 
from operating activities by $6,000, from the reported $15,007 to 
$9,007. Dividing adjusted total operating cash flow of $9,007 by 6,780

shares results in cash flow per share of $1.33.
C Based on information as reported, the EV/EBITDA was 16.3 ($284,760 ÷ 
$17,517). Based on EBITDA adjusted to expense software development 
costs, the EV/EBITDA was 24.7 ($284,760 ÷ $11,517).
■●Enterprise Value: Enterprise value is the sum of the market value of 
the company’s equity and debt. JHH has no debt, and therefore the 
enterprise value is equal to the market value of its equity. The market 
value of its equity is $284,760 ($42 per share × 6,780 shares).
■●EBITDA, as reported, was $17,517 (earnings before interest and taxes 
of $13,317 plus $2,200 depreciation plus $2,000 amortisation).
■●EBITDA, adjusted for expensing software development costs by 
the inclusion of $6,000 development expense and the exclusion of 
$2,000 amortisation of prior expense, would be $11,517 (earnings 
before interest and taxes of $9,317 plus $2,200 depreciation plus $0 
amortisation).

Expensing software development costs would decrease historical profits, oper -
ating cash flow, and EBITDA, and would thus increase all market multiples. So 
JHH’s stock would appear more expensive if it expensed rather than capitalised 
the software development costs.
If the unadjusted market-  based ratios were used in the comparison of JHH 
to its competitor that expenses all software development expenditures, then 
JHH might appear to be under-  priced when the difference is solely related to 
accounting factors. JHH’s adjusted market-  based ratios provide a better basis 
for comparison.
For the company in Example 7, current period software development expenditures 
exceed the amortisation of prior periods’ capitalised software development expendi -
tures. As a result, expensing rather than capitalising software development costs would 
have the effect of lowering income. If, however, software development expenditures

slowed such that current expenditures were lower than the amortisation of prior 
periods’ capitalised software development expenditures, then expensing software 
development costs would have the effect of increasing income relative to capitalising it.

Depreciation and Amortisation of Long-  Lived Assets 435
This section illustrated how decisions about capitalising versus expensing impact 
financial statements and ratios. Earlier expensing lowers current profits but enhances 
trends, whereas capitalising now and expensing later enhances current profits. Having 
described the accounting for acquisition of long-  lived assets, we now turn to the topic 
of measuring long-  lived assets in subsequent periods.
DEPRECIATION AND AMORTISATION OF LONG-  LIVED 
ASSETS
Under the cost model of reporting long-  lived assets, which is permitted under IFRS and 
required under US GAAP , the capitalised costs of long-  lived tangible assets (other than 
land, which is not depreciated) and intangible assets with finite useful lives are allocated 
to subsequent periods as depreciation and amortisation expenses. Depreciation and 
amortisation are effectively the same concept, with the term depreciation referring to

the process of allocating tangible assets’ costs and the term amortisation referring to 
the process of allocating intangible assets’ costs.12 The alternative model of reporting 
long-  lived assets is the revaluation model , which is permitted under IFRS but not 
under US GAAP . Under the revaluation model, a company reports the long-  lived 
asset at fair value rather than at acquisition cost (historical cost) less accumulated 
depreciation or amortisation, as in the cost model.
An asset’s carrying amount is the amount at which the asset is reported on the 
balance sheet. Under the cost model, at any point in time, the carrying amount (also 
called carrying value or net book value) of a long-  lived asset is equal to its historical 
cost minus the amount of depreciation or amortisation that has been accumulated 
since the asset’s purchase (assuming that the asset has not been impaired, a topic 
which will be addressed in Section 5). Companies may present on the balance sheet

the total net amount of property, plant, and equipment and the total net amount of 
intangible assets. However, more detail is disclosed in the notes to financial state -
ments. The details disclosed typically include the acquisition costs, the depreciation 
and amortisation expenses, the accumulated depreciation and amortisation amounts, 
the depreciation and amortisation methods used, and information on the assumptions 
used to depreciate and amortise long-  lived assets.
3.1 Depreciation Methods and Calculation of Depreciation 
Expense
Depreciation methods include the straight-  line method , in which the cost of an 
asset is allocated to expense evenly over its useful life; accelerated methods , in 
which the allocation of cost is greater in earlier years; and the units-  of- production 
method , in which the allocation of cost corresponds to the actual use of an asset in 
a particular period. The choice of depreciation method affects the amounts reported

on the financial statements, including the amounts for reported assets and operating 
and net income. This, in turn, affects a variety of financial ratios, including fixed asset 
turnover, total asset turnover, operating profit margin, operating return on assets, 
and return on assets.3
12 Depletion is the term applied to a similar concept for natural resources; costs associated with those 
resources are allocated to a period on the basis of the usage or extraction of those resources.

Reading 28 ■ Long-  Lived Assets 436
Using the straight-  line method, depreciation expense is calculated as depreciable 
cost divided by estimated useful life and is the same for each period. Depreciable 
cost is the historical cost of the tangible asset minus the estimated residual (salvage) 
value.13 A commonly used accelerated method is the declining balance method, in 
which the amount of depreciation expense for a period is calculated as some per -
centage of the carrying amount (i.e., cost net of accumulated depreciation at the 
beginning of the period). When an accelerated method is used, depreciable cost is 
not used to calculate the depreciation expense but the carrying amount should not be 
reduced below the estimated residual value. In the units-  of- production method, the 
amount of depreciation expense for a period is based on the proportion of the asset’s 
production during the period compared with the total estimated productive capacity

of the asset over its useful life. The depreciation expense is calculated as depreciable 
cost times production in the period divided by estimated productive capacity over 
the life of the asset. Equivalently, the company may estimate a depreciation cost 
per unit (depreciable cost divided by estimated productive capacity) and calculate 
depreciation expense as depreciation cost per unit times production in the period. 
Regardless of the depreciation method used, the carrying amount of the asset is not 
reduced below the estimated residual value. Example 8 provides an example of these 
depreciation methods.
EXAMPLE 8   
Alternative Depreciation Methods
You are analyzing three hypothetical companies: EVEN-  LI Co., SOONER Inc., 
and AZUSED Co. At the beginning of Year 1, each company buys an identical 
piece of box manufacturing equipment for $2,300 and has the same assumptions 
about useful life, estimated residual value, and productive capacity. The annual

production of each company is the same, but each company uses a different 
method of depreciation. As disclosed in each company’s notes to the financial 
statements, each company’s depreciation method, assumptions, and production 
are as follows:
Depreciation method
■■EVEN-  LI Co.: straight-  line method
■■SOONER Inc.: double-  declining balance method (the rate applied to 
the carrying amount is double the depreciation rate for the straight-  line 
method)
■■AZUSED Co.: units-  of- production method
Assumptions and production
■■Estimated residual value: $100
■■Estimated useful life: 4 years
13 The residual value is the estimated amount that an entity will obtain from disposal of the asset at the 
end of its useful life.

Depreciation and Amortisation of Long-  Lived Assets 437
■■Total estimated productive capacity: 800 boxes
■■Production in each of the four years: 200 boxes in the first year, 300 in the 
second year, 200 in the third year, and 100 in the fourth year
1 Using the following template for each company, record its beginning 
and ending net book value (carrying amount), end-  of- year accumulated 
depreciation, and annual depreciation expense for the box manufacturing 
equipment.
 Template:
Beginning Net 
Book ValueDepreciation 
ExpenseAccumulated 
DepreciationEnding Net 
Book Value
Year 1
Year 2
Year 3
Year 4
2 Explain the significant differences in the timing of the recognition of the 
depreciation expense.
3 For each company, assume that sales, earnings before interest, taxes, and 
depreciation, and assets other than the box manufacturing equipment are 
as shown in the following table. Calculate the total asset turnover ratio, 
the operating profit margin, and the operating return on assets for each

company for each of the four years. Discuss the ratios, comparing results 
within and across companies.
SalesEarnings 
before Interest, 
Taxes, and 
DepreciationCarrying Amount of Total 
Assets, Excluding the Box 
Manufacturing Equipment, 
at Y ear End*
Year 1 $300,000 $36,000 $30,000
Year 2 320,000 38,400 32,000
Year 3 340,000 40,800 34,000
Year 4 360,000 43,200 36,000
* Assume that total assets at the beginning of Year 1, including  the box manufacturing 
equipment, had a value of $30,300. Assume that depreciation expense on assets other than 
the box manufacturing equipment totaled $1,000 per year.
For each  company, the following information applies: Beginning net book value 
in Year 1 equals the purchase price of $2,300; accumulated year-  end depreciation 
equals the balance from the previous year plus the current year’s depreciation 
expense; ending net book value (carrying amount) equals original cost minus

accumulated year-  end depreciation (which is the same as beginning net book 
value minus depreciation expense); and beginning net book value in Years 2, 
3, and 4 equals the ending net book value of the prior year. The following text 
and filled-  in templates describe how depreciation expense  is calculated for each 
company.

Reading 28 ■ Long-  Lived Assets 438
EVEN-  LI Co. uses the straight-  line method, so depreciation expense in each 
year equals $550, which is calculated as ($2,300 original cost – $100 residual 
value)/4 years. The net book value at the end of Year 4 is the estimated residual 
value of $100.
EVEN-  LI Co.Beginning 
Net Book 
ValueDepreciation 
Y ear-  End 
Book Value
Year 1 $2,300 $550 $550 $1,750
Year 2 1,750 550 1,100 1,200
Year 3 1,200 550 1,650 650
Year 4 650 550 2,200 100
SOONER Inc. uses the double-  declining balance method. The depreciation 
rate for the double-  declining balance method is double the depreciation rate for 
the straight-  line method. The depreciation rate under the straight-  line method 
is 25 percent (100 percent divided by 4 years). Thus, the depreciation rate for 
the double-  declining balance method is 50 percent (2 times 25 percent). The 
depreciation expense for the first year is $1,150 (50 percent of $2,300). Note that

under this method, the depreciation rate of 50 percent is applied to the carrying 
amount (net book value) of the asset, without adjustment for expected residual 
value. Because the carrying amount of the asset is not depreciated below its 
estimated residual value, however, the depreciation expense in the final year 
of depreciation decreases the ending net book value (carrying amount) to the 
estimated residual value.
SOONER Inc.Beginning 
Net Book 
Y ear-  End 
Book Value
Year 1 $2,300 $1,150 $1,150 $1,150
Year 2 1,150 575 1,725 575
Year 3 575 288 2,013 287
Year 4 287 187 2,200 100
Another common approach (not required in this question) is to use an 
accelerated method, such as the double-  declining method, for some period (a 
year or more) and then to change to the straight-  line method for the remaining 
life of the asset. If SOONER had used the double-  declining method for the

first year and then switched to the straight-  line method for Years 2, 3, and 4, 
the depreciation expense would be $350 [($1,150 – $100 estimated residual 
value)/3 years] a year for Years 2, 3, and 4. The results for SOONER under this 
alternative approach are shown below.
Net Book 
Y ear-  End 
Book Value
Year 2 1,150 350 1,500 800
Year 3 800 350 1,850 450
Year 4 450 350 2,200 100
AZUSED Co. uses the units-  of- production method. Dividing the equipment’s 
total depreciable cost by its total productive capacity gives a cost per unit of $2.75, 
calculated as ($2,300 original cost – $100 residual value)/800. The depreciation

Depreciation and Amortisation of Long-  Lived Assets 439
expense recognised each year is the number of units produced times $2.75. For 
Year 1, the amount of depreciation expense is $550 (200 units times $2.75). For 
Year 2, the amount is $825 (300 units times $2.75). For Year 3, the amount is 
$550. For Year 4, the amount is $275.
AZUSED Co.Beginning 
Net Book 
Y ear-  End 
Book Value
Year 2 1,750 825 1,375 925
Year 3 925 550 1,925 375
Year 4 375 275 2,200 100
All three methods result in the same total amount of accumulated depreciation 
over the life of the equipment. The significant differences are simply in the 
timing of the recognition of the depreciation expense. The straight-  line method 
recognises the expense evenly, the accelerated method recognises most of the 
expense in the first year, and the units-  of- production method recognises the

expense on the basis of production (or use of the asset). Under all three methods, 
the ending net book value is $100.
Total asset turnover ratio = Total revenue ÷ Average total assets
Operating profit margin = Earnings before interest and taxes ÷ Total revenue
Operating return on assets = Earnings before interest and taxes ÷ Average 
total assets
Ratios are shown in the table below, and details of the calculations for Years 1 
and 2 are described after discussion of the ratios.
EVEN-  LI Co. SOONER Inc. AZUSED Co.
Ratio* AT PM (%) ROA (%) AT PM (%) ROA (%) AT PM (%) ROA (%)
Year 1 9.67 11.48 111.04 9.76 11.28 110.17 9.67 11.48 111.04
Year 2 9.85 11.52 113.47 10.04 11.51 115.57 9.90 11.43 113.10
Year 3 10.02 11.54 115.70 10.17 11.62 118.21 10.10 11.54 116.64
Year 4 10.18 11.57 117.74 10.23 11.67 119.42 10.22 11.65 118.98
* AT = Total asset turnover ratio. PM = Operating profit margin. ROA = Operating return on assets.

For all companies, the asset turnover ratio increased over time because sales 
grew at a faster rate than that of the assets. SOONER had consistently higher 
asset turnover ratios than the other two companies, however, because higher 
depreciation expense in the earlier periods decreased its average total assets. In 
addition, the higher depreciation in earlier periods resulted in SOONER having 
lower operating profit margin and operating ROA in the first year and higher 
operating profit margin and operating ROA in the later periods. SOONER appears 
to be more efficiently run, on the basis of its higher asset turnover and greater 
increases in profit margin and ROA over time; however, these comparisons 
reflect differences in the companies’ choice of depreciation method. In addition,

Reading 28 ■ Long-  Lived Assets 440
an analyst might question the sustainability of the extremely high ROAs for all 
three companies because such high profitability levels would probably attract 
new competitors, which would likely put downward pressure on the ratios.
EVEN-  LI Co.
Year 1:
 Total asset turnover ratio = 300,000/[(30,300 + 30,000 + 1,750)/2]
  = 300,000/31,025 = 9.67
 Operating profit margin = (36,000 – 1,000 – 550)/300,000
  = 34,450/300,000 = 11.48%
 Operating ROA = 34,450/31,025 = 111.04%
Year 2:
 Total asset turnover ratio = 320,000/[(30,000 + 1,750 + 32,000 + 1,200)/2]
  = 320,000/32,475 = 9.85
 Operating profit margin = (38,400 – 1,000 – 550)/320,000
  = 36,850/320,000 = 11.52%
 Operating ROA = 36,850/32,475 = 113.47%
SOONER Inc.
Year 1:
 Total asset turnover ratio = 300,000/[(30,300 + 30,000 + 1,150)/2]
  = 300,000/30,725 = 9.76
 Operating profit margin = (36,000 – 1,000 – 1,150)/300,000
  = 33,850/300,000 = 11.28%
 Operating ROA = 33,850/30,725 = 110.17%
Year 2:

Operating ROA = 33,850/30,725 = 110.17%
Year 2:
 Total asset turnover ratio = 320,000/[(30,000 + 1,150 + 32,000 + 575)/2]
  = 320,000/31,862.50 = 10.04
 Operating profit margin = (38,400 – 1,000 – 575)/320,000
  = 36,825/320,000 = 11.51%
 Operating ROA = 36,825/31,862.50 = 115.57%
AZUSED Co.
Year 1:
Year 2:
 Total asset turnover ratio = 320,000/[(30,000 + 1,750 + 32,000 + 925)/2]
  = 320,000/32,337.50 = 9.90
 Operating profit margin = (38,400 – 1,000 – 825)/320,000
  = 36,575/320,000 = 11.43%
 Operating ROA = 36,575/32,337.50 = 113.10%

Depreciation and Amortisation of Long-  Lived Assets 441
In many countries, a company must use the same depreciation methods for both 
financial and tax reporting. In other countries, including the United States, a company 
need not use the same depreciation method for financial reporting and taxes. As a 
result of using different depreciation methods for financial and tax reporting, pre-  tax 
income on the income statement and taxable income on the tax return may differ. 
Thus, the amount of tax expense computed on the basis of pre-  tax income and the 
amount of taxes actually owed on the basis of taxable income may differ. Although 
these differences eventually reverse because the total depreciation is the same regardless 
of the timing of its recognition in financial statements versus on tax returns, during 
the period of the difference, the balance sheet will show what is known as deferred 
taxes. For instance, if a company uses straight-  line depreciation for financial reporting

and an accelerated depreciation method for tax purposes, the company’s financial 
statements will report lower depreciation expense and higher pre-  tax income in the 
first year, compared with the amount of depreciation expense and taxable income in 
its tax reporting. (Compare the depreciation expense in Year 1 for EVEN-  LI Co. and 
SOONER Inc. in the previous example.) Tax expense calculated on the basis of the 
financial statements’ pre-  tax income will be higher than taxes payable on the basis 
of taxable income; the difference between the two amounts represents a deferred tax 
liability. The deferred tax liability will be reduced as the difference reverses (i.e., when 
depreciation for financial reporting is higher than the depreciation for tax purposes) 
and the income tax is paid.
Significant estimates required for calculating depreciation include the useful life 
of the asset (or its total lifetime productive capacity) and its expected residual value

at the end of that useful life. A longer useful life and higher expected residual value 
decrease the amount of annual depreciation expense relative to a shorter useful life and 
lower expected residual value. Companies should review their estimates periodically to 
ensure they remain reasonable. IFRS require companies to review estimates annually.
Although no significant differences exist between IFRS and US GAAP with respect 
to the definition of depreciation and the acceptable depreciation methods, IFRS require 
companies to use a component method of depreciation.14 Companies are required to 
separately depreciate the significant components of an asset (parts of an item with a 
cost that is significant in relation to the total cost and/or with different useful lives) 
and thus require additional estimates for the various components. For instance, it may 
be appropriate to depreciate separately the engine, frame, and interior furnishings of

an aircraft. Under US GAAP , the component method of depreciation is allowed but 
is seldom used in practice.15 The following example illustrates depreciating compo -
nents of an asset.
EXAMPLE 9   
Illustration of Depreciating Components of an Asset
CUTITUP Co., a hypothetical company, purchases a milling machine, a type 
of machine used for shaping metal, at a total cost of $10,000. $2,000 was esti -
mated to represent the cost of the rotating cutter, a significant component of 
the machine. The company expects the machine to have a useful life of eight 
years and a residual value of $3,000 and that the rotating cutter will need to be 
14 IAS 16 Property, Plant and Equipment , paragraphs 43–47 [Depreciation].
15 According to the Ernst & Young Academic Resource Center.

Reading 28 ■ Long-  Lived Assets 442
replaced every two years. Assume the entire residual value is attributable to the 
milling machine itself, and assume the company uses straight-  line depreciation 
for all assets.
1 How much depreciation expense would the company report in Year 1 if it 
uses the component method of depreciation, and how much depreciation 
expense would the company report in Year 1 if it does not use the compo -
nent method?
2 Assuming a new cutter with an estimated two-  year useful life is purchased 
at the end of Year 2 for $2,000, what depreciation expenses would the 
company report in Year 3 if it uses the component method and if it does 
not use the component method?
3 Assuming replacement of the cutter every two years at a price of $2,000, 
what is the total depreciation expense over the eight years if the com -
pany uses the component method compared with the total depreciation 
expense if the company does not use the component method?

4 How many different items must the company estimate in the first year to 
compute depreciation expense for the milling machine if it uses the com -
ponent method, and how does this compare with what would be required 
if it does not use the component method?
Depreciation expense in Year 1 under the component method would be $1,625. 
For the portion of the machine excluding the cutter, the depreciable base is total 
cost minus the cost attributable to the cutter minus the estimated residual value 
= $10,000 – $2,000 – $3,000 = $5,000. Depreciation expense for the machine 
excluding the cutter in the first year equals $625 (depreciable cost divided by 
the useful life of the machine = $5,000/8 years). For the cutter, the depreciation 
expense equals $1,000 (depreciable cost divided by the useful life of the cutter 
= $2,000/2 years). Thus, the total depreciation expense for Year 1 under the 
component method is $1,625 (the sum of the depreciation expenses of the two

components = $625 + $1,000). Depreciation expense in Year 2 would also be 
$1,625.
If the company does not use the component method, depreciation expense 
in Year 1 is $875 (the depreciable cost of the total milling machine divided by 
its useful life = [$10,000 – $3,000]/8 years). Depreciation expense in Year 2 
would also be $875.
Assuming that at the end of Year 2, the company purchases a new cutter for 
$2,000 with an estimated two-  year life, under the component method, the 
depreciation expense in Year 3 will remain at $1,625. If the company does not 
use the component method and purchases a new cutter with an estimated two-  
year life for $2,000 at the end of Year 2, the depreciation expense in Year 3 will 
be $1,875 [$875 + ($2,000/2) = $875 + $1,000].
Over the eight years, assuming replacement of the cutters every two years at a 
price of $2,000, the total depreciation expense will be $13,000 [$1,625 × 8 years]

when the component method is used. When the component method is not used, 
the total depreciation expense will also be $13,000 [$875 × 2 years + $1,875 × 6 
years]. This amount equals the total expenditures of $16,000 [$10,000 + 3 cutters 
× $2,000] less the residual value of $3,000.

Depreciation and Amortisation of Long-  Lived Assets 443
The following table summarizes the estimates required in the first year to compute 
depreciation expense if the company does or does not use the component method:
EstimateRequired using 
component 
method?Required if not 
using component 
method?
Useful life of milling machine Yes Yes
Residual value of milling machine Yes Yes
Portion of machine cost attributable to 
cutterYes No
Portion of residual value attributable 
to cutterYes No
Useful life of cutter Yes No
Total depreciation expense may be allocated between the cost of sales and other 
expenses. Within the income statement, depreciation expense of assets used in 
production is usually allocated to the cost of sales, and the depreciation expense of 
assets not used in production may be allocated to some other expense category. For 
instance, depreciation expense may be allocated to selling, general, and administrative

expenses if depreciable assets are used in those functional areas. Notes to the financial 
statements sometimes disclose information regarding which income statement line 
items include depreciation expense, although the exact amount of detail disclosed by 
individual companies varies.
3.2 Amortisation Methods and Calculation of Amortisation 
Expense
Amortisation is similar in concept to depreciation. The term amortisation applies to 
intangible assets, and the term depreciation applies to tangible assets. Both terms refer 
to the process of allocating the cost of an asset over the asset’s useful life. Only those 
intangible assets assumed to have finite useful lives are amortised over their useful 
lives, following the pattern in which the benefits are used up. Acceptable amortisation 
methods are the same as the methods acceptable for depreciation. Assets assumed 
to have an indefinite useful life (in other words, without a finite useful life) are not

amortised. An intangible asset is considered to have an indefinite useful life when there 
is “no foreseeable limit to the period over which the asset is expected to generate net 
cash inflows” for the company.16
Intangible assets with finite useful lives include an acquired customer list expected 
to provide benefits to a direct-  mail marketing company for two to three years, an 
acquired patent or copyright with a specific expiration date, an acquired license with 
a specific expiration date and no right to renew the license, and an acquired trade -
mark for a product that a company plans to phase out over a specific number of years. 
Examples of intangible assets with indefinite useful lives include an acquired license 
that, although it has a specific expiration date, can be renewed at little or no cost and 
an acquired trademark that, although it has a specific expiration, can be renewed at 
a minimal cost and relates to a product that a company plans to continue selling for

the foreseeable future.
16 IAS 38 Intangible Assets , paragraph 88.

Reading 28 ■ Long-  Lived Assets 444
As with depreciation for a tangible asset, the calculation of amortisation for an 
intangible asset requires the original amount at which the intangible asset is recognised 
and estimates of the length of its useful life and its residual value at the end of its 
useful life. Useful lives are estimated on the basis of the expected use of the asset, 
considering any factors that may limit the life of the asset, such as legal, regulatory, 
contractual, competitive, or economic factors.
EXAMPLE 10   
Amortisation Expense
IAS 38 Intangible Assets  provides illustrative examples regarding the accounting 
for intangible assets, including the following:
A direct-  mail marketing company acquires a customer list and expects 
that it will be able to derive benefit from the information on the list 
for at least one year, but no more than three years. The customer list 
would be amortised over management’s best estimate of its useful

life, say 18 months. Although the direct-  mail marketing company 
may intend to add customer names and other information to the 
list in the future, the expected benefits of the acquired customer list 
relate only to the customers on that list at the date it was acquired.
In this example, in what ways would management’s decisions and estimates 
affect the company’s financial statements?
Solution:
Because the acquired customer list is expected to generate future economic 
benefits for a period greater than one year, the cost of the list should be capital -
ised and not expensed. The acquired customer list is determined to not have an 
indefinite life and must be amortised. Management must estimate the useful life 
of the customer list and must select an amortisation method. In this example, 
the list appears to have no residual value. Both the amortisation method and 
the estimated useful life affect the amount of the amortisation expense in each

period. A shorter estimated useful life, compared with a longer estimated useful 
life, results in a higher amortisation expense each year over a shorter period, but 
the total  accumulated amortisation expense over the life of the intangible asset 
is unaffected by the estimate of the useful life. Similarly, the total accumulated 
amortisation expense over the life of the intangible asset is unaffected by the 
choice of amortisation method. The amortisation expense per period depends 
on the amortisation method. If the straight-  line method is used, the amortisation 
expense is the same for each year of useful life. If an accelerated method is used, 
the amortisation expense will be higher in earlier years.
THE REVALUATION MODEL
The revaluation model is an alternative to the cost model for the periodic valuation 
and reporting of long-  lived assets. IFRS permit the use of either the revaluation 
model or the cost model, but the revaluation model is not allowed under US GAAP .

Revaluation changes the carrying amounts of classes of long-  lived assets to fair value 
(the fair value must be measured reliably). Under the cost model, carrying amounts 4

The Revaluation Model 445
are historical costs less accumulated depreciation or amortisation. Under the reval -
uation model, carrying amounts are the fair values at the date of revaluation less any 
subsequent accumulated depreciation or amortisation.
IFRS allow companies to value long-  lived assets either under a cost model at his -
torical cost minus accumulated depreciation or amortisation or under a revaluation 
model at fair value. In contrast, US accounting standards require that the cost model 
be used. A key difference between the two models is that the cost model allows only 
decreases in the values of long-  lived assets compared with historical costs but the 
revaluation model may result in increases in the values of long-  lived assets to amounts 
greater than historical costs.
IFRS allow a company to use the cost model for some classes of assets and the 
revaluation model for others, but the company must apply the same model to all assets

within a particular class of assets and must revalue all items within a class to avoid 
selective revaluation. Examples of different classes of assets include land, land and 
buildings, machinery, motor vehicles, furniture and fixtures, and office equipment. 
The revaluation model may be used for classes of intangible assets but only if an 
active market for the assets exists, because the revaluation model may only be used 
if the fair values of the assets can be measured reliably. For practical purposes, the 
revaluation model is rarely used for either tangible or intangible assets, but its use is 
especially rare for intangible assets.
Under the revaluation model, whether an asset revaluation affects earnings depends 
on whether the revaluation initially increases or decreases an asset class’ carrying 
amount. If a revaluation initially decreases the carrying amount of the asset class, the 
decrease is recognised in profit or loss. Later, if the carrying amount of the asset class

increases, the increase is recognised in profit or loss to the extent that it reverses a 
revaluation decrease of the same asset class previously recognised in profit or loss. 
Any increase in excess of the reversal amount will not be recognised in the income 
statement but will be recorded directly to equity in a revaluation surplus account. 
An upward revaluation is treated the same as the amount in excess of the reversal 
amount. In other words, if a revaluation initially increases the carrying amount of the 
asset class, the increase in the carrying amount of the asset class bypasses the income 
statement and goes directly to equity under the heading of revaluation surplus. Any 
subsequent decrease in the asset’s value first decreases the revaluation surplus and 
then goes to income. When an asset is retired or disposed of, any related amount of 
revaluation surplus included in equity is transferred directly to retained earnings.

Asset revaluations offer several considerations for financial statement analyses. 
First, an increase in the carrying amount of depreciable long-  lived assets increases 
total assets and shareholders’ equity, so asset revaluations that increase the carrying 
amount of an asset can be used to reduce reported leverage. Defining leverage as aver -
age total assets divided by average shareholders’ equity, increasing both the numerator 
(assets) and denominator (equity) by the same amount leads to a decline in the ratio. 
(Mathematically, when a ratio is greater than one, as in this case, an increase in both 
the numerator and the denominator by the same amount leads to a decline in the 
ratio.) Therefore, the leverage motivation for the revaluation should be considered in 
analysis. For example, a company may revalue assets up if it is seeking new capital or 
approaching leverage limitations set by financial covenants.

Second, assets revaluations that decrease the carrying amount of the assets reduce 
net income. In the year of the revaluation, profitability measures such as return on assets 
and return on equity decline. However, because total assets and shareholders’ equity 
are also lower, the company may appear more profitable in future years. Additionally, 
reversals of downward revaluations also go through income, thus increasing earnings. 
Managers can then opportunistically time the reversals to manage earnings and increase 
income. Third, asset revaluations that increase the carrying amount of an asset ini -
tially increase depreciation expense, total assets, and shareholders’ equity. Therefore,

Reading 28 ■ Long-  Lived Assets 446
profitability measures, such as return on assets and return on equity, would decline. 
Although upward asset revaluations also generally decrease income (through higher 
depreciation expense), the increase in the value of the long-  lived asset is presumably 
based on increases in the operating capacity of the asset, which will likely be evidenced 
in increased future revenues.
Finally, an analyst should consider who did the appraisal—i.e. an independent 
external appraiser or management—and how often revaluations are made. Appraisals 
of the fair value of long-  lived assets involve considerable judgment and discretion. 
Presumably, appraisals of assets from independent external sources are more reliable. 
How often assets are revalued can provide an indicator of whether their reported 
value continues to be representative of their fair values.
The next two examples illustrate revaluation of long-  lived assets under IFRS.
EXAMPLE 11

EXAMPLE 11   
Revaluation Resulting in an Increase in Carrying Amount 
Followed by Subsequent Revaluation Resulting in a 
Decrease in Carrying Amount
UPFIRST, a hypothetical manufacturing company, has elected to use the reval -
uation model for its machinery. Assume for simplicity that the company owns 
a single machine, which it purchased for €10,000 on the first day of its fiscal 
period, and that the measurement date occurs simultaneously with the compa -
ny’s fiscal period end.
1 At the end of the first fiscal period after acquisition, assume the fair value 
of the machine is determined to be €11,000. How will the company’s 
financial statements reflect the asset?
2 At the end of the second fiscal period after acquisition, assume the fair 
value of the machine is determined to be €7,500. How will the company’s 
At the end of the first fiscal period, the company’s balance sheet will show the

asset at a value of €11,000. The €1,000 increase in the value of the asset will 
appear in other comprehensive income and be accumulated in equity under the 
heading of revaluation surplus.
At the end of the second fiscal period, the company’s balance sheet will show the 
asset at a value of €7,500. The total decrease in the carrying amount of the asset 
is €3,500 (€11,000 – €7,500). Of the €3,500 decrease, the first €1,000 will reduce 
the amount previously accumulated in equity under the heading of revaluation 
surplus. The other €2,500 will be shown as a loss on the income statement.

The Revaluation Model 447
EXAMPLE 12   
Revaluation Resulting in a Decrease in Asset’s Carrying 
Amount Followed by Subsequent Revaluation Resulting 
in an Increase in Asset’s Carrying Amount
DOWNFIRST, a hypothetical manufacturing company, has elected to use the 
revaluation model for its machinery. Assume for simplicity that the company 
owns a single machine, which it purchased for €10,000 on the first day of its 
fiscal period, and that the measurement date occurs simultaneously with the 
company’s fiscal period end.
of the machine is determined to be €7,500. How will the company’s finan -
cial statements reflect the asset?
value of the machine is determined to be €11,000. How will the company’s 

asset at a value of €7,500. The €2,500 decrease in the value of the asset will 
appear as a loss on the company’s income statement.
At the end of the second fiscal period, the company’s balance sheet will show 
the asset at a value of €11,000. The total increase in the carrying amount of the 
asset is an increase of €3,500 (€11,000 – €7,500). Of the €3,500 increase, the first 
€2,500 reverses a previously reported loss and will be reported as a gain on the 
income statement. The other €1,000 will bypass profit or loss and be reported as 
other comprehensive income and be accumulated in equity under the heading 
of revaluation surplus.
Exhibit 6 provides an example of a company’s disclosures concerning revaluation. 
The exhibit shows an excerpt from the 2006 annual report of KPN, a Dutch telecom -
munications and multimedia company. The excerpt is from the section of the annual 
report in which the company explains differences between its reporting under IFRS

and its reporting under US GAAP .17 One of these differences, as previously noted, 
is that US GAAP do not allow revaluation of fixed assets held for use. KPN elected 
to report a class of fixed assets (cables) at fair value and explained that under US 
GAAP , using the cost model, the value of the class at the end of 2006 would have 
been €350 million lower.
Exhibit 6   Impact of Revaluation
Excerpt from the annual report of Koninklijke KPN N.V. explaining certain 
differences between IFRS and US GAAP regarding “Deemed cost fixed assets”:
17 On 15 November 2007, the SEC approved rule amendments under which financial statements from 
foreign private issuers in the United States will be accepted without reconciliation to US GAAP if the finan -
cial statements are prepared in accordance with IFRS as issued by the International Accounting Standards 
Board. The rule took effect for the 2007 fiscal year. As a result, companies such as KPN no longer need to

Reading 28 ■ Long-  Lived Assets 448
KPN elected the exemption to revalue certain of its fixed assets upon 
the transition to IFRS to fair value and to use this fair value as their 
deemed cost. KPN applied the depreciated replacement cost method to 
determine this fair value. The revalued assets pertain to certain cables, 
which form part of property, plant & equipment. Under US GAAP , 
this revaluation is not allowed and therefore results in a reconciling 
item. As a result, the value of these assets as of December 31, 2006 
under US GAAP is EUR 350 million lower (2005: EUR 415 million; 
2004: EUR 487 million) than under IFRS.
Source : KPN’s Form 20-  F, p. 168, filed 1 March 2007.
Clearly, the use of the revaluation model as opposed to the cost model can have a 
significant impact on the financial statements of companies. This has potential con -
sequences for comparing financial performance using financial ratios of companies 
that use different models.
IMPAIRMENT OF ASSETS

In contrast with depreciation and amortisation charges, which serve to allocate the 
depreciable cost of a long-  lived asset over its useful life, impairment charges reflect 
an unanticipated decline in the value of an asset. Both IFRS and US GAAP require 
companies to write down the carrying amount of impaired assets. Impairment rever -
sals for identifiable, long-  lived assed are permitted under IFRS but typically not under 
US GAAP .
An asset is considered to be impaired when its carrying amount exceeds its recov -
erable amount (“the higher of fair value less cost to sell or value in use” according to 
IAS 36 Impairment of Assets ) or under US GAAP when its carrying amount exceeds 
its fair value. Under US GAAP , however, impairment losses are only recognisable 
when the carrying amount of the impaired asset is determined to be not recoverable. 
Therefore, in general, impairment losses are recognised when the asset’s carrying

amount is not recoverable. However, IFRS and US GAAP define recoverability dif -
ferently. The following paragraphs describe accounting for impairment for different 
categories of assets.
5.1 Impairment of Property, Plant, and Equipment
Accounting standards do not require that property, plant, and equipment be tested 
annually for impairment. Rather, at the end of each reporting period (generally, a 
fiscal year), a company assesses whether there are indications of asset impairment. 
If there is no indication of impairment, the asset is not tested for impairment. If 
there is an indication of impairment, such as evidence of obsolescence, decline in 
demand for products, or technological advancements, the recoverable amount of the 
asset should be measured in order to test for impairment. For property, plant, and 
equipment, impairment losses are recognised when the asset’s carrying amount is not

recoverable; the carrying amount is more than the recoverable amount. The amount 5Exhibit 6   (Continued)

Impairment of Assets 449
of the impairment loss will reduce the carrying amount of the asset on the balance 
sheet and will reduce net income on the income statement. The impairment loss is a 
non-  cash item and will not affect cash from operations.
IFRS and US GAAP differ somewhat both in the guidelines for determining that 
impairment has occurred and in the measurement of an impairment loss. Under IAS 36, 
an impairment loss is measured as the excess of carrying amount over the recoverable 
amount of the asset. The recoverable amount of an asset is defined as “the higher of its 
fair value less costs to sell and its value in use. ” Value in use is a discounted measure 
of expected future cash flows. Under US GAAP , assessing recoverability is separate 
from measuring the impairment loss. An asset’s carrying amount is considered not 
recoverable when it exceeds the undiscounted expected future cash flows. If the asset’s

carrying amount is considered not recoverable, the impairment loss is measured as 
the difference between the asset’s fair value and carrying amount.
EXAMPLE 13   
Impairment of Property, Plant, and Equipment
Sussex, a hypothetical manufacturing company in the United Kingdom, has 
a machine it uses to produce a single product. The demand for the product 
has declined substantially since the introduction of a competing product. The 
company has assembled the following information with respect to the machine:
Carrying amount £18,000
Undiscounted expected future cash flows £19,000
Present value of expected future cash flows £16,000
Fair value if sold £17,000
Costs to sell £2,000
1 Under IFRS, what would the company report for the machine?
2 Under US GAAP , what would the company report for the machine?
Under IFRS, the company would compare the carrying amount (£18,000) with the 
higher of its fair value less costs to sell (£15,000) and its value in use (£16,000).

The carrying amount exceeds the value in use, the higher of the two amounts, 
by £2,000. The machine would be written down to the recoverable amount of 
£16,000, and a loss of £2,000 would be reported in the income statement. The 
carrying amount of the machine is now £16,000. A new depreciation schedule 
based on the carrying amount of £16,000 would be developed.
Under US GAAP , the carrying amount (£18,000) is compared with the undis -
counted expected future cash flows (£19,000). The carrying amount is less 
than the undiscounted expected future cash flows, so the carrying amount is 
considered recoverable. The machine would continue to be carried at £18,000, 
and no loss would be reported.
In Example 13, a write down in the value of a piece of property, plant, and equip -
ment occurred under IFRS but not under US GAAP . In Example 14, a write down 
occurs under both IFRS and US GAAP .

Reading 28 ■ Long-  Lived Assets 450
EXAMPLE 14   
Essex, a hypothetical manufacturing company, has a machine it uses to produce 
a single product. The demand for the product has declined substantially since the 
introduction of a competing product. The company has assembled the following 
information with respect to the machine:
Undiscounted expected future cash flows £16,000
Present value of expected future cash flows £14,000
Fair value if sold £10,000
Under IFRS, the company would compare the carrying amount (£18,000) with 
the higher of its fair value less costs to sell (£8,000) and its value in use (£14,000). 
by £4,000. The machine would be written down to the recoverable amount of

£14,000, and a loss of £4,000 would be reported in the income statement. The 
carrying amount of the machine is now £14,000. A new depreciation schedule 
based on the carrying amount of £14,000 would be developed.
counted expected future cash flows (£16,000). The carrying amount exceeds the 
undiscounted expected future cash flows, so the carrying amount is considered 
not recoverable. The machine would be written down to fair value of £10,000, 
and a loss of £8,000 would be reported in the income statement. The carrying 
amount of the machine is now £10,000. A new depreciation schedule based on 
the carrying amount of £10,000 would be developed.
Example 14 shows that the write down to value in use under IFRS can be less 
than the write down to fair value under US GAAP . The difference in recognition of 
impairment losses is ultimately reflected in difference in book value of equity.

5.2 Impairment of Intangible Assets with a Finite Life
Intangible assets with a finite life are amortised (carrying amount decreases over 
time) and may become impaired. As is the case with property, plant, and equipment, 
the assets are not tested annually for impairment. Instead, they are tested only when 
significant events suggest the need to test. The company assesses at the end of each 
reporting period whether a significant event suggesting the need to test for impairment 
has occurred. Examples of such events include a significant decrease in the market price 
or a significant adverse change in legal or economic factors. Impairment accounting 
for intangible assets with a finite life is essentially the same as for tangible assets; the 
amount of the impairment loss will reduce the carrying amount of the asset on the 
balance sheet and will reduce net income on the income statement.

Derecognition 451
5.3 Impairment of Intangibles with Indefinite Lives
Intangible assets with indefinite lives are not amortised. Instead, they are carried on 
the balance sheet at historical cost but are tested at least annually for impairment. 
Impairment exists when the carrying amount exceeds its fair value.
5.4 Impairment of Long-  Lived Assets Held for Sale
A long-  lived (non-  current) asset is reclassified as held for sale rather than held for 
use when it ceases to be used and management’s intent is to sell it. For instance, if a 
building ceases to be used and management’s intent is to sell it, the building is reclas -
sified from property, plant, and equipment to non-  current assets held for sale. At the 
time of reclassification, assets previously held for use are tested for impairment. If 
the carrying amount at the time of reclassification exceeds the fair value less costs 
to sell, an impairment loss is recognised and the asset is written down to fair value

less costs to sell. Long-  lived assets held for sale cease to be depreciated or amortised.
5.5 Reversals of Impairments of Long-  Lived Assets
After an asset has been deemed impaired and an impairment loss has been reported, 
the asset’s recoverable amount could potentially increase. For instance, a lawsuit 
appeal may successfully challenge a patent infringement by another company, with 
the result that a patent previously written down has a higher recoverable amount. 
IFRS permit impairment losses to be reversed if the recoverable amount of an asset 
increases regardless of whether the asset is classified as held for use or held for sale. 
Note that IFRS permit the reversal of impairment losses only. IFRS do not permit the 
revaluation to the recoverable amount if the recoverable amount exceeds the previ -
ous carrying amount. Under US GAAP , the accounting for reversals of impairments 
depends on whether the asset is classified as held for use or held for sale.18 Under US

GAAP , once an impairment loss has been recognised for assets held for use, it cannot 
be reversed. In other words, once the value of an asset held for use has been decreased 
by an impairment charge, it cannot be increased. For assets held for sale, if the fair 
value increases after an impairment loss, the loss can be reversed.
DERECOGNITION
A company derecognises an asset (i.e., removes it from the financial statements) 
when the asset is disposed of or is expected to provide no future benefits from either 
use or disposal. A company may dispose of a long-  lived operating asset by selling it, 
exchanging it, or abandoning it. As previously described, non-  current assets that are 
no longer in use and are to be sold are reclassified as non-  current assets held for sale.
6.1 Sale of Long-  Lived Assets
The gain or loss on the sale of long-  lived assets is computed as the sales proceeds minus 
the carrying amount of the asset at the time of sale. An asset’s carrying amount is

typically the net book value (i.e., the historical cost minus accumulated depreciation), 
unless the asset’s carrying amount has been changed to reflect impairment and/or 
revaluation, as previously discussed.6
18 FASB ASC Section 360-  10- 35 [Property, Plant, and Equipment – Overall – Subsequent Measurement].

Reading 28 ■ Long-  Lived Assets 452
EXAMPLE 15   
Calculation of Gain or Loss on the Sale of Long-  Lived 
Assets
Moussilauke Diners Inc., a hypothetical company, as a result of revamping its 
menus to focus on healthier food items, sells 450 used pizza ovens and reports a 
gain on the sale of $1.2 million. The ovens had a carrying amount of $1.9 million 
(original cost of $5.1 million less $3.2 million of accumulated depreciation). At 
what price did Moussilauke sell the ovens?
A $0.7 million
B $3.1 million
C $6.3 million
Solution:
B is correct. The ovens had a carrying amount of $1.9 million, and Moussilauke 
recognised a gain of $1.2 million. Therefore, Moussilauke sold the ovens at a 
price of $3.1 million. The gain on the sale of $1.2 million is the selling price of 
$3.1  million minus the carrying amount of $1.9  million. Ignoring taxes, the 
cash flow from the sale is $3.1 million, which would appear as a cash inflow 
from investing.

A gain or loss on the sale of an asset is disclosed on the income statement, either 
as a component of other gains and losses or in a separate line item when the amount 
is material. A company typically discloses further detail about the sale in the man -
agement discussion and analysis and/or financial statement footnotes. In addition, 
a statement of cash flows prepared using the indirect method adjusts net income 
to remove any gain or loss on the sale from operating cash flow and to include the 
amount of proceeds from the sale in cash from investing activities. Recall that the 
indirect method of the statement of cash flows begins with net income and makes all 
adjustments to arrive at cash from operations, including removal of gains or losses 
from non-  operating activities.
6.2 Long-  Lived Assets Disposed of Other Than by a Sale
Long-  lived assets to be disposed of other than by a sale (e.g., abandoned, exchanged

for another asset, or distributed to owners in a spin-  off) are classified as held for use 
until disposal.19 Thus, the long-  lived assets continue to be depreciated and tested for 
impairment, unless their carrying amount is zero, as required for other long-  lived 
assets owned by the company.
When an asset is retired or abandoned, the accounting is similar to a sale, except 
that the company does not record cash proceeds. Assets are reduced by the carrying 
amount of the asset at the time of retirement or abandonment, and a loss equal to 
the asset’s carrying amount is recorded.
When an asset is exchanged, accounting for the exchange typically involves 
removing the carrying amount of the asset given up, adding a fair value for the asset 
acquired, and reporting any difference between the carrying amount and the fair value 
as a gain or loss. The fair value used is the fair value of the asset given up unless the

19 In a spin-  off, shareholders of the parent company receive a proportional number of shares in a new, 
separate entity.

Presentation and Disclosures 453
fair value of the asset acquired is more clearly evident. If no reliable measure of fair 
value exists, the acquired asset is measured at the carrying amount of the asset given 
up. A gain is reported when the fair value used for the newly acquired asset exceeds 
the carrying amount of the asset given up. A loss is reported when the fair value used 
for the newly acquired asset is less than the carrying amount of the asset given up. If 
the acquired asset is valued at the carrying amount of the asset given up because no 
reliable measure of fair value exists, no gain or loss is reported.
When a spin-  off occurs, typically, an entire cash generating unit of a company with 
all its assets is spun off. As an illustration of a spin-  off, Altria Group, Inc. effected a 
spin-  off of Kraft Foods on 30 March 2007 by distributing about 89 percent of Kraft’s 
shares to Altria’s shareholders. The company prepared unaudited pro forma income

statements and balance sheets (for illustrative purposes only) as if the spin-  off had 
occurred at the beginning of the year. Exhibit 7 summarizes information from the 
asset portion of the company’s pro forma balance sheets. The items in the column 
labeled “Spin-  off of Kraft” reflect Kraft’s assets being removed from Altria’s balance 
sheet at the time of the spin-  off. For example, Kraft’s property, plant, and equipment 
(net of depreciation) totaled $9.7 billion.
Exhibit 7   Altria Group, Inc. and Subsidiaries Pro Forma Condensed Consolidated Balance Sheet [Partial]  
As of 31 December 2006 (Unaudited)
Assets ($ millions)Historical 
AltriaaSpin-  off of 
KraftbAdjustmentscPro forma 
Altria
Cash and cash equivalents $5,020 ($239) $369 $5,150
Receivables, net 6,070 (3,869) 2,201
Inventories 12,186 (3,506) 8,680
Other current assets 2,876 (640) 2,236
Total current assets $26,152 ($8,254) $369 $18,267
Property, plant, and equipment, net 17,274 (9,693) 7,581
Goodwill 33,235 (25,553) (1,485) 6,197

Other intangible assets, net 12,085 (10,177) 1,908
Other assets 8,734 (1,897) 305 7,142
Total consumer products assets $97,480 ($55,574) ($811) $41,095
Financial services assets 6,790 0 6,790
Total assets $104,270 ($55,574) ($811) $47,885
a Historical consolidated balance sheet of Altria.
b Reflects the removal of Kraft’s consolidated balance sheet from the Altria historical consolidated balance sheet.
c Represents adjustments, such as for pro forma cash payments by Kraft to Altria, arising from modifications to existing stock awards and 
tax contingencies, adjustments to goodwill, etc.
Source:  Altria’s Form 8-  K filed with the SEC on 5 April 2007.
PRESENTATION AND DISCLOSURES
Under IFRS, for each class of property, plant, and equipment, a company must disclose 
the measurement bases, the depreciation method, the useful lives (or, equivalently, the 
depreciation rate) used, the gross carrying amount and the accumulated depreciation

at the beginning and end of the period, and a reconciliation of the carrying amount at 7

Reading 28 ■ Long-  Lived Assets 454
the beginning and end of the period.20 In addition, disclosures of restrictions on title 
and pledges as security of property, plant, and equipment and contractual agreements 
to acquire property, plant, and equipment are required. If the revaluation model is 
used, the date of revaluation, details of how the fair value was obtained, the carrying 
amount under the cost model, and the revaluation surplus must be disclosed.
The disclosure requirements under US GAAP are less exhaustive.21 A company 
must disclose the depreciation expense for the period, the balances of major classes 
of depreciable assets, accumulated depreciation by major classes or in total, and a 
general description of the depreciation method(s) used in computing depreciation 
expense with respect to the major classes of depreciable assets.
Under IFRS, for each class of intangible assets, a company must disclose whether

the useful lives are indefinite or finite. If finite, for each class of intangible asset, a 
company must disclose the useful lives (or, equivalently, the amortisation rate) used, 
the amortisation methods used, the gross carrying amount and the accumulated amor -
tisation at the beginning and end of the period, where amortisation is included on the 
income statement, and a reconciliation of the carrying amount at the beginning and 
end of the period.22 If an asset has an indefinite life, the company must disclose the 
carrying amount of the asset and why it is considered to have an indefinite life. Similar 
to property, plant, and equipment, disclosures of restrictions on title and pledges as 
security of intangible assets and contractual agreements to acquire intangible assets 
are required. If the revaluation model is used, the date of revaluation, details of how 
the fair value was obtained, the carrying amount under the cost model, and the reval -
uation surplus must be disclosed.

Under US GAAP , companies are required to disclose the gross carrying amounts 
and accumulated amortisation in total and by major class of intangible assets, the 
aggregate amortisation expense for the period, and the estimated amortisation expense 
for the next five fiscal years.23
The disclosures related to impairment losses also differ under IFRS and US GAAP . 
Under IFRS, a company must disclose for each class of assets the amounts of impair -
ment losses and reversals of impairment losses recognised in the period and where 
those are recognised on the financial statements.24 The company must also disclose 
in aggregate the main classes of assets affected by impairment losses and reversals of 
impairment losses and the main events and circumstances leading to recognition of 
these impairment losses and reversals of impairment losses. Under US GAAP , there 
is no reversal of impairment losses. The company must disclose a description of the

impaired asset, what led to the impairment, the method of determining fair value, 
the amount of the impairment loss, and where the loss is recognised on the financial 
statements.25
Disclosures about long-  lived assets appear throughout the financial statements: in 
the balance sheet, the income statement, the statement of cash flows, and the notes. 
The balance sheet reports the carrying value of the asset. For the income statement, 
depreciation expense may or may not appear as a separate line item. Under IFRS, 
whether the income statement discloses depreciation expense separately depends on 
whether the company is using a ‘nature of expense’ method or a ‘function of expense’ 
method. Under the nature of expense method, a company aggregates expenses “accord -
ing to their nature (for example, depreciation, purchases of materials, transport costs, 
20 IAS 16 Property, Plant and Equipment , paragraphs 73–78 [Disclosure].

21 FASB ASC Section 360-  10- 50 [Property, Plant, and Equipment – Overall – Disclosure].
22 IAS 38 Intangible Assets , paragraphs 118–128 [Disclosure].
23 FASB ASC Section 350-  30- 50 [Intangibles – General – Disclosure].
24 IAS 36 Impairment of Assets , paragraphs 126–131 [Disclosure].
25 FASB ASC Section 360-  10- 50 [Property, Plant, and Equipment – Overall – Disclosure] and FASB ASC 
Section 350-  30- 50 [Intangibles – General – Disclosure].

Presentation and Disclosures 455
employee benefits and advertising costs), and does not reallocate them among func -
tions within the entity. ”26 Under the function of expense method, a company classifies 
expenses according to the function, for example as part of cost of sales or of SG&A 
(selling, general, and administrative expenses). At a minimum, a company using the 
function of expense method must disclose cost of sales, but the other line items vary.
The statement of cash flows reflects acquisitions and disposals of fixed assets in the 
investing section. In addition, when prepared using the indirect method, the statement 
of cash flows typically shows depreciation expense (or depreciation plus amortisation) 
as a line item in the adjustments of net income to cash flow from operations. The notes 
to the financial statements describe the company’s accounting method(s), the range 
of estimated useful lives, historical cost by main category of fixed asset, accumulated

depreciation, and annual depreciation expense.
To illustrate financial statement presentation and disclosures, the following exam -
ple provides excerpts relating to intangible assets and property, plant, and equipment 
from the annual report of Vodafone Group Plc for the year ended 31 March 2009.
EXAMPLE 16   
Financial Statement Presentation and Disclosures for 
The following exhibits include excerpts from the annual report for the year ended 
31 March 2009 of Vodafone Group Plc, a global mobile telecommunications 
company headquartered in the United Kingdom.
Exhibit 8   Vodafone Group Plc  
Excerpts from the Consolidated Financial Statements 
Excerpt from the Consolidated Income Statement for the Y ears 
Ended 31 March (Currency in £ Millions)
Note 2009 2008
Revenue 3 41,017 35,478
   ⋮ ⋮ ⋮ ⋮
Impairment losses 10* (5,900) —
   ⋮ ⋮ ⋮ ⋮
Operating profit/(loss) 4 5,857 10,047
   ⋮ ⋮ ⋮ ⋮
Profit/(loss) before taxation 4,189 9,001
Income tax expense 6 (1,109) (2,245)

Profit/(loss) for the financial year from 
continuing operations3,080 6,756
Loss for the year from discontinued 
operations30 — —
Profit/(loss) for the financial year 3,080 6,756
− Equity shareholders 23 3,078 6,660
26 IAS 1 paragraph 102.

Reading 28 ■ Long-  Lived Assets 456
− Minority interests 2 96
3,080 6,756
* Notes relating to property, plant, and equipment and intangible assets are underlined.
Excerpt from the Consolidated Statement of Recognised Income and 
Expense for the Y ears Ended 31 March (Currency in £ Millions)
(Losses)/gains on revaluation of available-  
for- sale investments, net of tax22 (2,383) 1,949
   ⋮ ⋮ ⋮ ⋮
Revaluation gain 22 68 —
   ⋮ ⋮ ⋮ ⋮
Net gain/(loss) recognised directly in 
equity9,854 6,909
Total recognised income and expense 
relating to the year12,934 13,665
− Equity shareholders 13,037 13,912
− Minority interests (103) (247)
12,934 13,665
Excerpt from the Consolidated Balance Sheet at 31 March (Currency 
in £ Millions)
Non-  current assets
Goodwill 9 53,958 51,336

Other intangible assets 9 20,980 18,995
Property, plant and equipment 11 19,250 16,735
   ⋮ ⋮ ⋮ ⋮
139,670 118,546
Current assets 13,029 8,724
Total assets 152,699 127,270
Equity
   ⋮ ⋮ ⋮ ⋮
Accumulated other recognised 
income and expense22 20,517 10,588Exhibit 8   (Continued)

Presentation and Disclosures 457
   ⋮ ⋮ ⋮ ⋮
Total equity 84,777 76,471
Non-  current liabilities 39,975 28,826
Current liabilities 27,947 21,973
Total equity and liabilities 152,699 127,270
Exhibit 9   Vodafone Group Plc  
Excerpts from the Notes to the Consolidated Financial Statements
Excerpt from Note 9, Intangible Assets (Currency in £ Millions)
Intangible assets GoodwillLicences and 
SpectrumComputer 
Software Other Total
Cost:
31 March 2008 91,762 22,040 5,800 1,188 120,790
Exchange movements 14,298 2,778 749 153 17,978
Arising on acquisition 613 199 69 130 1,011
Additions — 1,138 1,144 — 2,282
Disposals — (1) (403) — (404)
Transfer to investments in asso -
ciated undertakings(9) (16) — — (25)
31 March 2009 106,664 26,138 7,359 1,471 141,632
Accumulated impairment losses 
and amortisation:
31 March 2008 40,426 5,132 4,160 741 50,459
Exchange movements 6,630 659 569 126 7,984

Amortisation charge for the year — 1,522 885 346 2,753
Impairment losses 5,650 250 — — 5,900
Disposals — — (391) — (391)
Transfers to investments in 
associated undertakings— (11) — — (11)
31 March 2009 52,706 7,552 5,223 1,213 66,694
Net book value:
31 March 2008 51,336 16,908 1,640 447 70,331
31 March 2009 53,958 18,586 2,136 258 74,938
For licences and spectrum and other intangible assets, amortisation is 
included within the cost of sales line within the consolidated income 
statement. Licences and spectrum with a net book value of £2,765m (2008: 
£nil) have been pledged as security against borrowings.

Reading 28 ■ Long-  Lived Assets 458
Excerpt from Note 10, Impairment Losses
Impairment losses recognised in the consolidated income statement as 
a separate line item within operating profit, in respect of goodwill and 
licences and spectrum fees are as follows (£m):
Cash 
generating 
unit Reportable segment 2009 2008 2007
⋮ ⋮ ⋮ — —
Turke y Other Africa and Central 
Europe2,250 — —
⋮ ⋮ ⋮ — —
Total 5,900 — 11,600
The impairment losses were based on value in use calculations.…
Turke y
At 30 September 2008, the goodwill was impaired by £1,700 million.… 
During the second half of the 2009 financial year, impairment losses of 
£300 million in relation to goodwill and £250 million in relation to licences 
and spectrum resulted from adverse changes in both the discount rate 
and a fall in the long term GDP growth rate. The cash flow projections … 
were substantially unchanged from those used at 30 September 2008.…
Sensitivity to changes in assumptions

The estimated recoverable amount of the Group’s operations in Spain, 
Turkey and Ghana equaled their respective carrying value and, conse -
quently, any adverse change in key assumption would, in isolation, cause 
a further impairment loss to be recognised.…
The changes in the following table to assumptions used in the impairment 
review would, in isolation, lead to an (increase)/decrease to the aggregate 
impairment loss recognised in the year ended 31 March 2009:
Spain Turkey GhanaAll 
other
⋮ ⋮ Increase 
by 2%  
£bnDecrease 
by 2%  
£bn⋮ ⋮ ⋮ ⋮
Pre-  tax adjusted 
discount rate⋮ ⋮ (0.4) 0.6 ⋮ ⋮ ⋮ ⋮
Long term growth 
rate⋮ ⋮ 0.3 (0.2) ⋮ ⋮ ⋮ ⋮
Budgeted EBITDA ⋮ ⋮ 0.1 (0.1) ⋮ ⋮ ⋮ ⋮
Budgeted capital 
expenditure⋮ ⋮ (0.1) 0.1 ⋮ ⋮ ⋮ ⋮Exhibit 9   (Continued)

Presentation and Disclosures 459
Excerpt from Note 11, Property, Plant, and Equipment
The net book value of land and buildings and equipment, fixtures 
and fittings includes £106 million and £82 million, respectively (2008: 
£110 million and £51 million) in relation to assets held under finance 
leases. Included in the net book value of land and buildings and equip -
ment, fixtures and fittings are assets in the course of construction, 
which are not depreciated, with a cost of £44 million and £1,186 million, 
respectively (2008: £28 million and £1,013 million). Property, plant and 
equipment with a net book value of £148 million (2008: £1,503 million) 
has been pledged as security against borrowings.
Excerpt from Note 22, Movements in Accumulated Other Recognised Income and Expense (Currency in 
£ Millions)
Translation 
ReservePensions 
ReserveAvailable-  
for- Sale 
Investments 
ReserveAsset 
Revaluation 
Surplus Other Total
⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮
31 March 2008 5,974 (96) 4.531 112 37 10,558

Gains/(losses) arising in 
the year⋮ ⋮ ⋮ 68 ⋮ 10,023
Transfer to the income 
statement on disposal⋮ ⋮ ⋮ — ⋮ (3)
Tax effect ⋮ ⋮ ⋮ — ⋮ (61)
31 March 2009 18,451 (259) 2,148 180 (3) 20,517
1 As of 31 March 2009, what percentage of other intangible assets and 
property, plant, and equipment is pledged as security against borrowings?
2 What caused the £250 million impairment losses in relation to licences 
and spectrum during the year ended 31 March 2009?
3 By what amount would impairment losses related to Turkey change if the 
pre-  tax adjusted discount rate decreased by 2 percent?
4 Where are impairment losses reported on the financial statements? Where 
is amortisation included within the consolidated income statement?
5 What percentage of property, plant, and equipment, based on net 
book value, is held under finance leases rather than owned as of 31 
March 2009?
6 The gains and losses arising in the year on asset revaluation most likely  
are:

are:
A reflected on the consolidated income statement.
B reported in the notes to the financial statements only.
C recognised directly in equity and shown on the consolidated statement 
of recognised income and expense.Exhibit 9   (Continued)

Reading 28 ■ Long-  Lived Assets 460
Assets that have been pledged as security against borrowings are licences and 
spectrum, with a net book value of £2,765 million (Note 9), and property, plant, 
and equipment, with a net book value of £148 million (Note 11). These assets 
represent 7.24 percent [(2,765 + 148)/(20,980 + 19,250)] of the other intangible 
assets and property, plant, and equipment.
The £250 million impairment losses in relation to licences and spectrum resulted 
from an increase in the pre-  tax adjusted discount rate and a decrease in the 
long-  term growth rate in Turkey (Note 10).
A 2 percent decrease in the pre-  tax adjusted discount rate related to Turkey 
would reduce impairment losses by £0.6 billion or £600 million (Note 10).
Impairment losses are reported on the consolidated income statement (Exhibit 8). 
Impairment losses reduce the value of the assets impaired (Note 9) and are thus

recognised within the consolidated balance sheet. Amortisation is included 
within the cost of sales line within the consolidated income statement (Note 9).
The net book value of land and buildings and equipment, fixtures, and fittings 
includes £106 million and £82 million, respectively, in relation to assets held 
under finance leases (Note 22). The sum of these values represents 0.98 percent 
of the property, plant, and equipment [(106 + 82)/19,250].
C is correct. The gains and losses arising in the year on asset revaluation are 
recognised directly in equity and shown on the consolidated statement of rec -
ognised income and expense. They are also reported in the notes to the financial 
statements (Note 22).
Note that the exhibits in the previous example contain relatively brief excerpts 
from the company’s disclosures. The complete text of the disclosures concerning the 
company’s non-  current assets spans seven different footnotes, most of which are several

pages long. In addition to information about the discount rate and other assumptions 
used to calculate impairment charges, the disclosures provide information about the 
sensitivity of impairment charges to changes in the assumptions.
Overall, an analyst can use the disclosures to understand a company’s investments 
in tangible and intangible assets, how those investments changed during a reporting 
period, how those changes affected current performance, and what those changes 
might indicate about future performance.
Ratios used in analyzing fixed assets include the fixed asset turnover ratio and 
several asset age ratios. The fixed asset turnover ratio (total revenue divided by aver -
age net fixed assets) reflects the relationship between total revenues and investment 
in PPE. The higher this ratio, the higher the amount of sales a company is able to 
generate with a given amount of investment in fixed assets. A higher asset turnover

ratio is often interpreted as an indicator of greater efficiency.
Asset age ratios generally rely on the relationship between historical cost and 
depreciation. Under the revaluation model (permitted under IFRS but not US GAAP), 
the relationship between carrying amount, accumulated depreciation, and depreciation

Presentation and Disclosures 461
expense will differ when the carrying amount differs significantly from the depreciated 
historical cost. Therefore, the following discussion of asset age ratios applies primarily 
to PPE reported under the cost model.
Asset age and remaining useful life, two asset age ratios, are important indicators 
of a company’s need to reinvest in productive capacity. The older the assets and the 
shorter the remaining life, the more a company may need to reinvest to maintain 
productive capacity. The average age of a company’s asset base can be estimated as 
accumulated depreciation divided by depreciation expense. The average remaining life 
of a company’s asset base can be estimated as net PPE divided by depreciation expense. 
These estimates simply reflect the following relationships for assets accounted for on 
a historical cost basis: total historical cost minus accumulated depreciation equals

net PPE; and, under straight-  line depreciation, total historical cost less salvage value 
divided by estimated useful life equals annual depreciation expense. Equivalently, 
total historical cost less salvage value divided by annual depreciation expense equals 
estimated useful life. Assuming straight-  line depreciation and no salvage value (for 
simplicity), we have the following:
Estimated total useful 
life= Time elapsed since 
purchase (Age)+ Estimated remaining life
Historical cost ÷ annual 
depreciation expense= Estimated total useful 
life
Historical cost = Accumulated 
depreciation+ Net PPE
Equivalently,
life= Estimated age of 
equipment+ Estimated remaining life
Historical cost ÷  
annual depreciation 
expense= Accumulated depreci -
ation ÷ annual depre -
ciation expense+ Net PPE ÷  
expense
The application of these estimates can be illustrated by a hypothetical example of

a company with a single depreciable asset. Assume the asset initially cost $100, had 
an estimated useful life of 10 years, and an estimated salvage value of $0. Each year, 
the company records a depreciation expense of $10, so accumulated depreciation will 
equal $10 times the number of years since the asset was acquired (when the asset is 
7 years old, accumulated depreciation will be $70). Equivalently, the age of the asset 
will equal accumulated depreciation divided by the annual depreciation expense.
In practice, such estimates are difficult to make with great precision. Companies 
use depreciation methods other than the straight-  line method and have numerous 
assets with varying useful lives and salvage values, including some assets that are 
fully depreciated, so this approach produces an estimate only. Moreover, fixed asset 
disclosures are often quite general. Consequently, these estimates may be primarily 
useful to identify areas for further investigation.

One further measure compares a company’s current reinvestment in productive 
capacity. Comparing annual capital expenditures to annual depreciation expense 
provides an indication of whether productive capacity is being maintained. It is a very 
general indicator of the rate at which a company is replacing its PPE relative to the 
rate at which PPE is being depreciated.

Reading 28 ■ Long-  Lived Assets 462
EXAMPLE 17   
Using Fixed Asset Disclosure to Compare Companies’ 
Fixed Asset Turnover and Average Age of Depreciable 
Assets
You are analyzing the property, plant, and equipment of three international 
paper and paper products companies:
■■AbitibiBowater Inc. (ABY) is a Canadian company that manufactures 
newsprint, commercial printing papers, and other wood products.
■■International Paper Company (IP) is a US paper and packaging company.
■■UPM-  Kymmene Corporation (UPM) is a Finnish company that manufac -
tures fine and specialty papers, newsprint, magazine papers, and other 
related products. The company’s common stock is listed on the Helsinki 
and New York stock exchanges.
Exhibit  10 presents selected information from the companies’ financial 
statements.
Exhibit 10   
ABY IP UPM
Currency, Millions of: Canadian $ US $ Euro €
Historical cost total PPE, end of year $9,013 $29,815 €16,382
Accumulated depreciation, end of year 4,553 15,613 10,694

Net PPE, end of year 4,460 14,202 5,688
Land included in PPE 161 Not separated 347
Average Net PPE 5,067 12,172 5,934
Net Sales 6,771 24,829 9,461
Annual depreciation expense (annual 
impairment)726 1,347 745
(182)
Capital expenditure 186 1,002 558
Accounting standards Canadian GAAP US GAAP IFRS
PPE measurement Historical cost Historical cost Historical cost
Depreciation method Straight-  line Units-  of- production 
for pulp and paper 
mills;* straight-  line 
for otherStraight-  line
Useful life of assets, in years, except as 
noted20–40 (buildings); 
5–20 (machinery 
and equipment); 40 
(power plants)Straight-  line depre -
ciation rates are 
2.5% to 8.5% (build -
ings), and 5% to 
33% (machinery and 
equipment)25–40 (buildings); 
15–20 (heavy equip.); 
5–15 (light equip.)
* Pulp and paper mills historical cost as disclosed in a footnote total $21,819 million. Depreciation expense and accumulated depre -
ciation is not separately reported for mills.
Sources:

Sources:
For ABY, Form 10-  K for the year ended 31 December 2008, filed 31 March 2009.

Presentation and Disclosures 463
For IP, Form 10-  K for the year ended 31 December 2008, filed 20 February 2009.
For UPM, annual report for the year ended 31 December 2008.
1 Based on the above data for each company, estimate the total useful life, 
age, and remaining useful life of PPE.
2 Interpret the estimates. What items might affect comparisons across these 
3 How does each company’s 2008 depreciation expense compare to its capi -
tal expenditures for the year?
4 Calculate and compare fixed asset turnover for each company.
The following table presents the estimated total useful life, estimated age, and 
estimated remaining useful life of PPE for each of the companies.
Estimates ABY IP UPM
Estimated total useful life (years) 12.4 22.1 22.0
Estimated age (years) 6.3 11.6 14.4
Estimated remaining life (years) 6.1 10.5 7.6
The computations are explained using UPM’s data. The estimated total 
useful life of PPE is total historical cost of PPE of €16,382 divided by annual

depreciation expense of €745, giving 22.0 years. Estimated age and estimated 
remaining life are obtained by dividing accumulated depreciation of €10,694 
and net PPE of €5,688 by the annual depreciation expense of €745, giving 14.4 
years and 7.6 years, respectively.
Ideally, the estimates of asset lives illustrated in this example should exclude 
land, which is not depreciable, when the information is available; however, IP does 
not separately disclose land. We will use UPM, for which land appeared to be 
disclosed separately in the above table, to illustrate the estimates with adjusting 
for land. As an illustration of the calculations to exclude land, excluding UPM’s 
land would give an estimated total useful life for the non-  land PPE of 21.5 years 
[(total cost €16,382 minus land cost of €347) divided by annual depreciation 
expense of €745 million].
The estimated total useful life suggests that IP and UPM depreciate PPE over a

much longer period than ABY: 22.1 and 22.0 years for IP and UPM, respectively, 
versus 12.4 years for ABY. This result can be compared, to an extent, to the useful 
life of assets noted by the companies, and the composition of fixed assets. For 
instance, ABY and UPM depreciate their buildings over similar periods and their 
equipment over the same period (5 to 20 years). That the estimated useful life 
of PPE overall differs so much between the companies suggests that equipment 
reflects a higher proportion of ABY’s assets. An inspection of the companies’ 
footnoted information (not shown above) on asset composition confirms that 
equipment accounts for a larger portion of ABY gross fixed assets (86%) com -
pared to UPM (76%).
The estimated age of the equipment suggests that ABY has the newest PPE 
with an estimated age of 6.3 years. Additionally, the estimates suggest that around 
50 percent of ABY’s assets’ useful lives have passed (6.3 years ÷ 12.4 years, or Exhibit 10   (Continued)

Reading 28 ■ Long-  Lived Assets 464
equivalently, C$4,553 million ÷ C$9,013 million). In comparison, around 67 per -
cent of the useful lives of the PPE of UPM have passed. Items that can affect 
comparisons across the companies include business differences, such as differ -
ences in composition of the companies’ operations and differences in acquisition 
and divestiture activity. In addition, the companies all report under different 
accounting standards, and IP discloses that it uses the units-  of- production 
method for the largest component of its PPE. Differences in disclosures, e.g. in 
the categories of assets disclosed, also can affect comparisons.
Capital expenditure as a percentage of depreciation is 26 percent for ABY, 74 per -
cent for IP , and 75 percent for UPM. Based on this measure, IP and UPM are 
replacing their PPE at rates closer to the rate PPE are being depreciated. ABY’s 
measure suggests the company is replacing its PPE at a slower rate than the PPE

is being depreciated, consistent with the company’s apparently newer asset base.
Fixed asset turnover for each company is presented below, calculated as total 
revenues divided by average net PPE. Net sales is used as an approximation for 
total revenues, because differences like sales returns are not consistently disclosed 
by companies. We can see that IP’s fixed asset turnover is highest, implying it is 
able to generate more sales from each unit of investment in fixed assets.
ABY IP UPM
Fixed Asset Turnover 1.3 2.0 1.6
Currency, millions of: Canadian $ US $ Euro €
INVESTMENT PROPERTY
Investment property is defined under IFRS as property that is owned (or, in some cases, 
leased under a finance lease) for the purpose of earning rentals or capital appreciation 
or both.27 An example of investment property is a building owned by a company

and leased out to tenants. In contrast, other long-  lived tangible assets (i.e., property 
considered to be property, plant, and equipment) are owner-  occupied properties 
used for producing the company’s goods and services or for housing the company’s 
administrative activities. Investment properties do not include long-  lived tangible 
assets held for sale in the ordinary course of business. For example, the houses and 
property owned by a housing construction company are considered to be its inventory.
Under IFRS, companies are allowed to value investment properties using either a 
cost model or a fair value model. The cost model is identical to the cost model used for 
property, plant, and equipment. If the cost model is used, the fair value of investment 
property must be disclosed.28 The fair value model, however, differs from the reval -
uation model used for property, plant, and equipment. Under the revaluation model,

whether an asset revaluation affects net income depends on whether the revaluation 
initially increases or decreases the carrying amount of the asset. In contrast, under 8
27 IAS 40 Investment Property  prescribes the accounting treatment for investment property.
28 Ibid., paragraph 32.

Investment Property 465
the fair value model, all changes in the fair value of the asset affect net income. To 
use the fair value model, a company must be able to reliably determine the property’s 
fair value on a continuing basis. 
Example 18 presents an excerpt from the annual report of a property company 
reporting under IFRS.
EXAMPLE 18   
The following exhibit presents an excerpt from the annual report for the year 
ended 31 March 2009 of Daejan Holdings PLC, a property company headquar -
tered in the United Kingdom.
Exhibit 11   Excerpt from the Consolidated Income Statements at 31 
March (Currency in £ thousands)
2009 2008
Gross rental income 83,918 73,590
Service charge income 12,055 13,362
Total Rental and Related Income from 
Investment Properties95,973 86,952
Property operating expenses (53,470) (46,464)
Net Rental and Related Income from Investment 
Properties42,503 40,488

Profit on Disposal of Investment Properties 6,758 6,578
Valuation gains on investment properties 6,646 46,646
Valuation losses on investment properties (268,249) (25,982)
Net Valuation (Losses)/Gains on Investment 
Properties(261,603) 20,664
Administrative expenses (12,039) (8,629)
Net Operating (Loss)/Profit before Net Financing 
Costs(224,381) 59,101
1 What was the primary cause of the company’s £224,381 thousand 
net operating loss before net financing costs for the year ended 31 
2 What was the primary cause of the company’s £59,101 thousand net oper -
ating profit before financing costs for the year ended 31 March 2008?
3 What was the primary cause of the change from a £59,101 thousand net 
operating profit in 2008 to a £224,381 thousand net operating loss in 
2009?
4 Do the valuation gains and losses on investment properties indicate that 
the properties have been sold?

Reading 28 ■ Long-  Lived Assets 466
The primary cause of the company’s net operating loss for the year ended 31 
March 2009 was the net valuation loss on investment properties. The net valua -
tion loss of £262 million (valuation gain of £6,646 thousand minus the valuation 
loss of £268,249 thousand) exceeded the company’s net rental income plus its 
profit on disposal of investment properties.
The primary cause of the company’s net operating profit for the year ended 31 
March 2008 was the £40 million net rental income. Additionally, the company 
reported net valuation gains on investment properties of £21 million (valuation 
gain of £46,646 thousand minus the valuation loss of £25,982 thousand) and 
profit on disposal of investment properties of £7 million.
The change from a net operating profit to a net operating loss was primarily due 
to valuation gains exceeding valuation losses (net valuation gains) in 2008 and

valuation losses significantly exceeding valuation gains (net valuation losses) 
in 2009.
No. The valuation gains and losses on investment properties arise from changes in 
the fair value of properties that are owned by the company. The gains and losses 
on properties that have been sold are reported as Profit (Loss) on Disposal of 
Investment Properties. In neither 2008 nor 2009 did the company experience a 
loss on disposal of investment properties so the line item was reported as Profit 
on Disposal of Investment Properties.
In general, a company must apply its chosen model (cost or fair value) to all of 
its investment property. If a company chooses the fair value model for its investment 
property, it must continue to use the fair value model until it disposes of the property 
or changes its use such that it is no longer considered investment property (e.g., it 
becomes owner-  occupied property or part of inventory). The company must continue

to use the fair value model for that property even if transactions on comparable prop -
erties, used to estimate fair value, become less frequent.
Certain valuation issues arise when a company changes the use of property such 
that it moves from being an investment property to owner-  occupied property or part 
of inventory. If a company’s chosen model for investment property is the cost model, 
such transfers do not change the carrying amount of the property transferred. If a 
company’s chosen model is the fair value model, transfers from investment property 
to owner-  occupied property or to inventory are made at fair value. In other words, 
the property’s fair value at the time of transfer is considered to be its cost for ongoing 
accounting for the property. If a company’s chosen model for investment property is 
the fair value model and it transfers a property from owner-  occupied to investment 
property, the change in measurement of the property from depreciated cost to fair

value is treated like a revaluation. If a company’s chosen model is the fair value model 
and it transfers a property from inventory to investment property, any difference 
between the inventory carrying amount and the property’s fair value at the time of 
transfer is recognised as profit or loss.
Investment property appears as a separate line item on the balance sheet. Companies 
are required to disclose whether they use the fair value model or the cost model for 
their investment property. If the company uses the fair value model, it must make addi -
tional disclosures about how it determines fair value and must provide reconciliation

Leasing 467
between the beginning and ending carrying amounts of investment property. If the 
company uses the cost model, it must make additional disclosures similar to those 
for property, plant, and equipment—for example, the depreciation method and useful 
lives must be disclosed. In addition, if the company uses the cost model, it must also 
disclose the fair value of investment property.
Under US GAAP , there is no specific definition of investment property. Most oper -
ating companies and real estate companies in the United States that hold investment-  
type property use the historical cost model.
LEASING
A lease is a contract between the owner of an asset—the lessor —and another party 
seeking use of the assets—the lessee . Through the lease, the lessor grants the right to 
use the asset to the lessee. The right to use the asset can be a long period, such as 20 
years, or a much shorter period such as a month. In exchange for the right to use the

asset, the lessee makes periodic lease payments to the lessor. A lease, then, is a form 
of financing to the lessee provided by the lessor that enables the lessee to purchase 
the use of the leased asset.
9.1 The Lease versus Buy Decision
There are several advantages to leasing an asset compared to purchasing it. Leases 
can provide less costly financing, usually require little, if any, down payment, and are 
often at fixed interest rates. The negotiated lease contract may contain less restrictive 
provisions than other forms of borrowing. A lease can also reduce the risks of obso -
lescence, residual value, and disposition to the lessee because the lessee does not own 
the asset. The lessor may be better positioned to manage servicing the asset and to 
take advantage of tax benefits of ownership. As a result, leasing the asset may be less 
costly than owning the asset for the lessee.
Leases also have perceived financial and tax reporting advantages. While providing

a form of financing, certain types of leases are not reported as debt on the balance 
sheet. The items leased under these types of leases also do not appear as assets on 
the balance sheet. Therefore, no interest expense or depreciation expense is included 
in the income statement. Additionally, in some countries such as the United States, 
financial reporting standards may differ from reporting under tax regulations; thus, 
in some cases, a company may own an asset for tax purposes (and thus obtain deduc -
tions for depreciation expense for tax purposes) while not reflecting the ownership in 
its financial statements. A lease that is structured to provide a company with the tax 
benefits of ownership while not requiring the asset to be reflected on the company’s 
financial statements is known as a synthetic lease .
9.2 Finance versus Operating Leases
Differences in economic substance and accounting have traditionally existed for two

main types of leases—finance and operating. The economic substance of a finance 
(or capital)29 lease has been regarded as different from an operating lease, as are the 9
29 Finance lease is IFRS terminology and capital lease is US GAAP terminology. IAS 17 [Leases] and 
FASB ASC Topic 840 [Leases]. New standards were issued in early 2016, IFRS 16 [Leases] and FASB ASC 
Topic 842 [Leases], which are effective 1 January 2019 and for fiscal years beginning after December 15, 
2019, respectively.

Reading 28 ■ Long-  Lived Assets 468
implications of each for the financial statements of the lessee and lessor. In substance, 
a finance lease  is equivalent to the purchase of an asset (lease to own) by the buyer 
(lessee) that is directly financed by the seller (lessor). An operating lease  is an 
agreement allowing the lessee to use the asset for a period of time, similar to a rental.
Under previous international accounting standards, if substantially all the risks and 
rewards incidental to ownership are transferred to the lessee, the lease was classified 
as a finance lease. Otherwise, the lease was reported as an operating lease. Under the 
new international accounting standard (IFRS 16), the lessee is required to recognize 
leases of more than 12 months duration (other than small asset leases) on the balance 
sheet, and the lessee can no longer classify a lease as an operating lease. The lessor 
continues to classify its leases as operating or finance leases under IFRS 16.

While a similar principle of the transfer of benefits and risks guides US GAAP , 
US accounting standards have been more prescriptive in their criteria for classifying 
finance and operating leases. Under US GAAP , a lease that meets any one of four 
specific requirements is classified as a finance lease;30 however, the new accounting 
standard (ASC Topic 842) requires the lessee to recognize a liability for its lease obli -
gation (initially measured at the present value of the future lease payments not yet paid 
over the lease term), and an asset for its right to use the underlying asset equal to the 
lease liability, adjusted for lease payments made at or before lease commencement, 
lease incentives, and any initial direct costs.
The example below illustrates and compares the accounting and financial state -
ment effects of buying an asset using debt, leasing an asset under an operating lease, 
and leasing an asset under a finance lease. Under IFRS 16, the treatment of operating

leases is similar to finance leases.
EXAMPLE 19   
Comparison of Accounting and Financial Statement 
Effects of the Buy versus Lease Decision
Bi- ly Company is considering the following alternatives in obtaining the use of 
a new piece of equipment at the beginning of Year 1:
Alternative 1  Buy the equipment and finance the purchase with new 
debt.
Alternative 2  Lease the equipment under an operating lease (the equip -
ment is not reported as an asset, the lease payments each 
period are treated as an operating expense on the income 
statement).
Alternative 3  Lease the equipment under a finance lease (the equipment 
is reported as an asset and an obligation is recorded equal 
to the present value of future lease payments).
30 The four criteria are: (1) ownership of the leased asset transfers to lessee at end of lease, (2) the lease 
contains an option for the lessee to purchase the leased asset cheaply (bargain purchase option), (3) the

lease term is 75 percent or more of the useful life of the leased asset, and (4) the present value of lease 
payments is 90 percent or more of the fair value of the leased asset (ASC 840-  10- 25- 1). These criteria have 
been superseded by the requirements under ASC 842.

Leasing 469
The fair value of the equipment, having a five-  year useful life and no salvage 
value, is $1,000. If Bi-  ly leases the equipment, annual lease payments would be 
$264 due at the end of each year. Bi-  ly’s discount rate is 10%. The company uses 
straight-  line depreciation. (For illustration, assume the company can record the 
lease as either operating or financing.)
1 For each alternative under consideration, determine the effect on assets 
and liabilities at the beginning of Year 1.
2 For each alternative, determine the effect on the income statement in Year 
1.
3 For each alternative, calculate Bi-  ly’s return on assets and debt-  to- asset 
ratio at the end of Year 1. For simplicity, assume that—excluding any 
effects of Bi-  ly’s choice among the three alternatives for obtaining the 
assets—total assets at the beginning and end of the year are $4,500, total 
liabilities at the beginning and end of the year are $3,000, and net income 
for the year is $800.

At the beginning of Year 1, Bi-  ly would show the following assets and debt:
Alternative 1 2 3
Buy/Lease Buy Lease Lease
Finance/Accounting Issue new debt Operating Finance*
Long-  lived asset $1,000 $1,000
Debt/lease obligation 1,000 1,000
* Under a finance lease, the present value of five future lease payments of $264 discounted at 
10% is reported on the balance sheet as a lease obligation and an asset of $1,000 (rounded).
For Year 1, Bi-  ly would show the following expenses related to the equipment:
Rent expense   $264  
Depreciation expense $200   $200
Interest expense 100   100
Total expenses $300 $264 $300
For Alternatives 1 and 3, depreciation expense is the acquisition cost of 
$1,000 divided by the 5-  year useful life. Salvage value is 0.
For Alternatives 1 and 3, interest expense is the beginning balance of debt, 
$1,000 times the discount rate of 10%. Each year the interest expense will decline.

For Alternative 2, rent expense is the lease payment of $264.
To calculate the return on assets:
Net income, excluding new asset $800 $800 $800
Add additional expenses (solution to 2 
above)$300 $264 $300

Reading 28 ■ Long-  Lived Assets 470
Net income, adjusted $500 $536 $500
Total assets, beginning, excluding new 
asset$4,500 $4,500 $4,500
Add additional asset (solution to 1 
above)1,000 1,000
Total assets, beginning, adjusted $5,500 $4,500 $5,500
Total assets, end, excluding new asset $4,500 $4,500 $4,500
Add additional asset* 800 800
Total assets, end, adjusted $5,300 $4,500 $5,300
Average total assets $5,400 $4,500 $5,400
Return on assets, adjusted 9.3% 11.9% 9.3%
* The book value of the new asset at the end of the year is its beginning balance of $1,000 
less $200 accumulated depreciation.
In this example, the highest return on assets is found when the equipment is 
leased under an operating lease which is expected because net income is highest 
and the asset base is lowest. Buying an asset and seeking to finance it with new 
debt and leasing it under a finance lease result in the same return on assets.
To calculate the debt-  to- asset ratio at the end of the year:

Total assets, end, excluding new 
Add additional asset 800   800
     
Total liabilities, end, excluding new 
asset $3,000 $3,000 $3,000
Add additional debt* 837   837
Total liabilities, end, adjusted $3,837 $3,000 $3,837
     
Debt-  to- asset ratio 0.724 0.667 0.724
* Additional debt at the end of the first year is the present value of the four remaining debt/
lease payments of $264 discounted at 10% (and rounded).
In this example, the lowest debt-  to- asset ratio is found when the equipment 
is financed through an operating lease. Buying an asset and seeking to finance 
it with new debt and leasing it under a finance lease result in the same return 
on assets.

Leasing 471
9.2.1  Accounting and Reporting by the Lessee
A finance lease has traditionally been viewed as economically similar to borrowing 
money and buying an asset; therefore, a company that enters into a finance lease as the 
lessee reports an asset (leased asset) and related debt (lease payable) on the balance 
sheet. The initial value of both the leased asset and the lease payable is the lower of 
the fair value of the leased asset or the present value of future lease payments. On the 
income statement, the company reports interest expense on the debt; and if the asset 
acquired is depreciable, the company reports depreciation expense. (The lessor, as we 
illustrate in Section 9.2.2, reports the sale of an asset and the lease as a receivable.)
An operating lease has been viewed as economically similar to renting an asset, 
so the lessee has recorded a lease expense on its income statement during the period

of use with no asset or liability recorded on its balance sheet. The main accounting 
differences between a finance lease and an operating lease are that under a finance 
lease, reported debt and assets are higher and expenses are generally higher in the 
early years. Because of the higher reported assets, debt and expenses—and therefore 
the lower ROA, all else equal—lessees have often preferred operating leases to finance 
leases. As we illustrate in the next section, lessors’ preferences generally differ. Lessors 
would prefer a finance lease because, under an operating lease, lessors continue to 
show the asset and its associated financing on their balance sheets.
On the lessee’s statement of cash flows, for an operating lease, the full lease 
payment is shown as an operating cash outflow. For a finance lease, only the portion 
of the lease payment relating to interest expense potentially reduces operating cash

flows,31 the portion of the lease payment that reduces the lease liability appears as a 
cash outflow in the financing section.
A company reporting a lease as an operating lease will typically show higher profits 
in early years, higher return measures in early years, and a stronger solvency position 
than an identical company reporting an identical lease as a finance lease. However, the 
company reporting the lease as a finance lease will show higher operating cash flows 
because a portion of the lease payment will be reflected as a financing cash outflow 
rather than an operating cash outflow.
The following example illustrates the effect on a lessee’s income, debt, and cash 
flows when reporting a lease as a finance lease versus an operating lease. Example 20 
uses current US GAAP and the recognition of operating leases.
EXAMPLE 20   
Financial Statement Impact of a Finance versus Operating 
Lease for the Lessee
Assume two similar (hypothetical) companies, CAPBS Inc. and OPIS Inc., enter

into similar lease agreements for a piece of machinery on 1 January Year 1. The 
leases require four annual payments of €28,679 starting on 1 January Year 1. 
The useful life of the machine is four years and its salvage value is zero. CAPBS 
accounts for the lease as a finance lease and uses straight-  line depreciation, 
while OPIS has determined the lease is an operating lease. For simplicity, this 
example assumes that the accounting rules governing these hypothetical com -
panies do not mandate either type of lease. The present value of lease payments 
and fair value of the equipment is €100,000. (A reminder relevant for present 
value calculations: Lease payments are made at the beginning of each period.)
31 Interest expense may be classified as a financing cash flow or an operating cash flow under IFRS 
(IAS 7 paragraph 33) but is classified as an operating cash flow under US GAAP (FASB ASC paragraph 
230-  10- 45- 17).

Reading 28 ■ Long-  Lived Assets 472
At the beginning of Year 1, before entering into the lease agreements, both 
companies reported liabilities of €100,000 and equity of €200,000. Each year the 
companies receive total revenues of €50,000, and all revenues are cash. Assume 
the companies have a tax rate of 30 percent, and use the same accounting for 
financial and tax purposes. Both companies’ discount rate is 10 percent. In order 
to focus only on the differences in the type of lease, assume neither company 
incurs expenses other than those associated with the lease, and neither invests 
excess cash.
1 Which company reports higher expenses/net income in Year 1? Over the 
four years?
2 Which company reports higher total cash flow over the four years? Cash 
flow from operations?
3 Based on return on equity (ROE), how do the two companies’ profitability 
measures compare?
4 Based on the ratio of debt-  to- equity, how do the two companies’ solvency 
positions compare?

In Year 1 and Year 2, CAPBS reports higher expenses because the depreciation 
expense and interest expense of its finance lease exceeds the lease expense of 
OPIS’s operating lease. Therefore, OPIS reports higher net income in Year 1 and 
Year 2. The companies’ total expense over the entire four-  year period, however, 
is equal as is the companies’ total net income.
Each year, OPIS reports lease expense of €28,679 associated with its operating 
lease. For CAPBS, its finance lease is treated as being economically similar to 
borrowing money and purchasing an asset. So, on its income statement, CAPBS 
reports depreciation expense on the leased asset acquired and interest expense 
on the lease liability.
The table below shows by year CAPBS’s depreciation expense and book 
values on the leased asset.
Y earAcquisition 
Cost  
(a)Depreciation 
Expense  
(b)Accumulated 
Depreciation  
(c)Carrying 
Amount (Y ear 
End)  
(d)
1 €100,000 €25,000 €25,000 €75,000

End)  
(d)
2 100,000 25,000 50,000 50,000
3 100,000 25,000 75,000 25,000
4 100,000 25,000 100,000 0
€100,000
■■Column (a) is acquisition cost of €100,000 of the leased equipment.
■■Column (b) is depreciation expense of €25,000 per year, calculated using 
the straight line convention, as the acquisition costs less salvage value 
divided by useful life [(€100,000 – €0)/4 years].

Leasing 473
■■Column (c) is the accumulated depreciation on the leased asset calculated 
as the prior year’s accumulated depreciation plus the current year’s depre -
ciation expense.
■■Column (d) is the carrying amount at year end of the leased equipment, 
which is the difference between the acquisition cost and accumulated 
depreciation.
The table below shows CAPBS’s lease payment, interest expense, and carrying 
amount for its lease liability by year.32
Y earLease 
Liability,  
1 January  
(a)Annual Lease  
Payment,  
1 January  
(b)Interest  
(at 10%; 
Accrued in 
Previous Y ear)  
(c)Reduction  
of Lease Liability,  
1 January  
(d)Lease Liability on  
31 December after  
Lease Payment on  
1 January Same Y ear  
(e)
1 €100,000 €28,679 €0 €28,679 €71,321
2 71,321 28,679 7,132 21,547 49,774
3 49,774 28,679 4,977 23,702 26,072
4 26,072 28,679 2,607 26,072 0
€114,717 €14,717 €100,000
■■Column (a) is the lease liability at the beginning of the year.
Year 1: €100,000

Years thereafter: lease liability at end of previous year
■■Column (b) is the annual lease payment made at the beginning of the 
year. Part of the lease payment pays any interest accrued in the previous 
year, and the remainder of the lease payment reduces the lease liability. 
For example, in Year 2, the €28,679 paid on 1 January reduces the interest 
payable of €7,132 that accrued in Year 1 (0.10 × 71,321) and then reduces 
the lease liability by €21,547.
■■Column (c) is the interest portion of the 1 January lease payment made on 
that date. This amount of interest was accrued as interest payable during 
the prior  year and is reported as the interest expense of the prior  year.
■■Column (d) is the reduction of the lease liability, which is the difference 
between the annual lease payment and the interest portion.
■■Column (e) is the lease liability on 31 December of a given year just before 
the lease payment is made on the first day of the next year. It is equal to

the lease liability on 1 January of the same year (column a) less the reduc -
tion of the lease liability (column d).
The table below summarizes and compares the income statement effects 
of the lease for CAPBS and OPIS. Notice that over the four-  year lease, both 
companies report the same total amount of expense but CAPBS shows higher 
expenses earlier in the life of the lease.
32 The computations included throughout the example were made using an Excel worksheet; small dis -
crepancies in the calculations are due to rounding.

Reading 28 ■ Long-  Lived Assets 474
CAPBS OPIS
Y earDepreciation 
ExpenseInterest 
Expense TotalLease 
Expense Difference
1 €25,000 €7,132 €32,132 €28,679 €3,453
2 25,000 4,977 29,977 28,679 1,298
3 25,000 2,607 27,607 28,679 (1,072)
4 25,000 — 25,000 28,679 (3,679)
Total €100,000 €14,717 €114,717 €114,717 €(0)
The complete income statements for CAPBS and OPIS are presented below. 
Notice under the assumption that the same accounting is used for financial and 
tax purposes, CAPBS’s taxes are lower in Year 1 and Year 2. The lower taxes in 
the earlier years reflect the higher expenses in those years.
CAPBS OPIS
Income 
Statements 1 2 3 4 Total 1 2 3 4 Total
Sales €50,000 €50,000 €50,000 €50,000 €200,000 €50,000 €50,000 €50,000 €50,000 €200,000
Depreciation 
expense 25,000 25,000 25,000 25,000 €100,000
Interest 
expense 7,132 4,977 2,607 14,717
Lease expense 28,679 28,679 28,679 28,679 114,717
Income 
before taxes 17,868 20,023 22,393 25,000 85,283 21,321 21,321 21,321 21,321 85,283

Tax expense 5,360 6,007 6,718 7,500 25,585 6,396 6,396 6,396 6,396 25,585
Net income €12,508 €14,016 €15,675 €17,500 €59,698 €14,925 €14,925 €14,925 €14,925 €59,698
On the statement of cash flows, observe that over the four years, both CAPBS 
and OPIS report the same total change in cash of €59,698. Operating cash flows 
reported by CAPBS are higher because a portion of the lease payment each 
year is categorised as a financing cash flow rather than an operating cash flow. 
In the first two years, CAPBS’s change in cash is higher due to its lower taxes 
in those years.
Statements 
of Cash 
FlowsCAPBS OPIS
1 2 3 4 Total 1 2 3 4 Total
Interest paid — 7,132 4,977 2,607 €14,717
Taxes paid 5,360 6,007 6,718 7,500 25,585 6,396 6,396 6,396 6,396 €25,585
Lease 
expense — — — — — 28,679 28,679 28,679 28,679 114,717
Operating 
cash flows 44,640 36,861 38,305 39,893 159,698 14,925 14,925 14,925 14,925 59,698

Leasing 475
of Cash 
Payment to 
reduce lease 
liability (28,679) (21,547) (23,702) (26,072) (100,000)
Financing 
cash flows (28,679) (21,547) (23,702) (26,072) (100,000) — — — —
Total change 
in cash €15,960 €15,314 €14,603 €13,821 €59,698 €14,925 €14,925 €14,925 €14,925 €59,698
Based on ROE, CAPBS looks less profitable than OPIS in the earlier years. 
Computing ROE requires forecasting shareholders’ equity. In general, ending 
Shareholders’ equity = Beginning shareholders’ equity + Net income + Other 
comprehensive income – Dividends + Net capital contributions by sharehold -
ers. Because the companies in this example do not have other comprehensive 
income, did not pay dividends, and experienced no capital contributions from 
shareholders, Ending shareholders’ equity = Beginning shareholders’ equity + 
Net income. The forecasts are presented below.
CAPBS 0 1 2 3 4
Retained earnings €0 €12,508 €26,523 €42,198 €59,698

Common stock 200,000 200,000 200,000 200,000 200,000
Total shareholders’ 
equity €200,000 €212,508 €226,523 €242,198 €259,698
         
OPIS 0 1 2 3 4
Retained earnings €0 €14,925 €29,849 €44,774 €59,698
equity €200,000 €214,925 €229,849 €244,774 €259,698
ROE is calculated as Net income divided by Average shareholders’ equity. 
For example, CAPBS Inc. had Year 1 ROE of 6.1 percent: €12,508/ [(€200,000 + 
€212,508)/2].
CAPBS OPIS
1 2 3 4 1 2 3 4
ROE 6.1% 6.4% 6.7% 7.0% 7.2% 6.7% 6.3% 5.9%
Based on the ratio of debt-  to- equity, the solvency position of CAPBS appears 
weaker than that of OPIS.
For the debt-  to- equity ratio, take the total shareholders’ equity from Part 3 
above. Initially, both companies had reported liabilities of €100,000. For OPIS, 
the amount of total liabilities remains constant at €100,000. For CAPBS, add

Reading 28 ■ Long-  Lived Assets 476
the lease liability at the end of the year and the amount of accrued interest 
payable at the end of each year from Part 1 above. So at the end of Year 1, 
CAPBS’s total liabilities are €178,453 (€100,000 + €71,321 lease liability + €7,132 
accrued interest payable at the end of the year), and its debt-  to- equity ratio is 
0.84 (€178,453/€212,508). At the end of Year 2, CAPBS total liabilities equal 
€154,751 (€100,000 + €49,774 lease liability + €4,977 accrued interest payable 
at the end of the year). The remaining years are computed in the same manner. 
The table below presents the ratios for each year.
CAPBS OPIS
1 2 3 4 1 2 3 4
Total debt 178,453 154,751 128,679 100,000 100,000 100,000 100,000 100,000
Shareholders’ 
equity212,508 226,523 242,198 259,698 214,925 229,849 244,774 259,698
Debt-  to- equity 
ratio0.84 0.68 0.53 0.39 0.47 0.44 0.41 0.39
In summary, a company reporting a lease as an operating lease will typically show

higher profits in early years, higher return measures in early years, and a stronger 
solvency position than an identical company reporting an identical lease as a finance 
lease.33 However, the company reporting the lease as a finance lease will show higher 
operating cash flows because a portion of the lease payment will be reflected as a 
financing cash outflow rather than an operating cash outflow.
The precisely defined accounting standards in the United States that determine 
when a company should report a capital (finance) versus an operating lease enable a 
company to structure a lease so as to avoid meeting any of the four capital lease criteria 
and thereby record an operating lease. Similar to debt disclosures, lease disclosures 
show payments under both capital and operating leases for the next five years and 
afterwards. Future payments under US GAAP are disclosed year by year for the first 
five years and then aggregated for all subsequent years. Under IFRS, future payments

are disclosed for the first year, in aggregate for years two through five, and then in 
aggregate for all subsequent years. These disclosures can help to estimate the extent 
of a company’s off-  balance-  sheet lease financing through operating leases. Example 21 
illustrates the disclosures under current US GAAP and how these disclosures can be 
used to determine the effect on the financial statements if all operating leases were 
capitalised, as under IFRS 16.
EXAMPLE 21   
Financial Statement Impact of Treating Operating Leases 
as Finance Leases for the Lessee
CEC Entertainment, Inc. (CEC) has significant commitments under capital 
(finance) and operating leases. Presented below is selected financial statement 
information and note disclosure to the financial statements for the company.
Commitments and Contingencies Footnote from CEC’s Financial 
Statements:
33 Example 11 assumes the company uses the straight-  line depreciation method, which is common under

IFRS and US GAAP . If the company estimated depreciation expense based on the “economic” depreciation of 
the leased asset, there would be no difference in reported income under a finance lease and operating lease.

Leasing 477
8. Commitments and contingencies:
The company leases certain restaurants and related property and 
equipment under operating and capital leases. All leases require the 
company to pay property taxes, insurance, and maintenance of the 
leased assets. The leases generally have initial terms of 10 to 20 years 
with various renewal options.
Scheduled annual maturities of the obligations for capital and operating leases 
as of 28 December 2008 are as follows (US$ thousands):
Y ears Capital Operating
2009 $1,683 $66,849
2010 1,683 66,396
2011 1,683 66,558
2012 1,600 65,478
2013 1,586 63,872
Thereafter 9,970 474,754
Minimum future lease payments 18,205 $803,907
Less amounts representing interest (5,997)
Present value of future minimum lease 
payments12,208
Less current portion (806)
Long-  term finance lease obligation $11,402
Selected Financial Statement Information for CEC:
28 December 2008 30 December 2007
Total liabilities $608,854 $519,900
Shareholders’ equity $128,586 $217,993

1 A Calculate the implicit interest rate used to discount the “scheduled 
annual maturities” under capital leases to obtain the “present value 
of future minimum lease payments” of $12,208 disclosed in the 
Commitments and Contingencies footnote. To simplify the calcula -
tion, assume that future minimum lease payments on the company’s 
capital leases for the “thereafter” lump sum are as follows: $1,586 
on 31 December of each year from 2014 to 2019, and $454 in 2020. 
Assume annual lease payments are made at the end of each year.
B Why is the implicit interest rate estimate in Part A important in 
assessing a company’s leases?
2 If the operating lease agreements had been treated as capital leases, what 
additional amount would be reported as a lease obligation on the balance 
sheet at 28 December 2008? To simplify the calculation, assume that 
future minimum lease payments on the company’s operating leases for the

“thereafter” lump sum are as follows: $63,872 on 31 December each year 
from 2014 to 2020, and $27,650 in 2021. Based on the implicit interest 
rate obtained in Part 1A, use 7.245% to discount future cash flows on the 
operating leases.
3 What would be the effect on the debt-  to- equity ratio of treating all operat -
ing leases as finance leases (i.e., the ratio of total liabilities to equity) at 28 
December 2008?

Reading 28 ■ Long-  Lived Assets 478
Solution to 1A:
The implicit interest rate on finance leases is 7.245 percent. The implicit interest 
rate used to discount the finance lease payments is the internal rate of return on 
the stream of cash flows; i.e., the interest rate that will make the present value 
of the lease payments equal to $12,208. You can use an Excel spreadsheet or a 
financial calculator for the computations. Set the cash flow at time zero equal 
to $12,208 (note on Excel and on most financial calculators, you will input this 
amount as a negative number), input each of the annual payments on the finance 
leases, and solve for the internal rate of return.
To demonstrate how the internal rate of return corresponds to the individual 
present values, refer to the following schedule of the undiscounted minimum 
lease payments based on information from footnote 8 and the assumptions 
given. Exhibit 12 presents the present value computations.

Exhibit 12   Present Value Computations Implicit Interest Rate (Internal Rate of Return) based on 
Capital Leases (7.245%)
Fiscal Y earY ears to 
DiscountMinimum Capital Lease 
Payment Times Present Value Factor Equals Present Value
2009 1 1,683 1/(1+interest rate)11,569
2010 2 1,683 1/(1+interest rate)21,463
2011 3 1,683 1/(1+interest rate)31,364
2012 4 1,600 1/(1+interest rate)41,210
2013 5 1,586 1/(1+interest rate)51,118
2014 6 1,586 1/(1+interest rate)61,042
2015 7 1,586 1/(1+interest rate)7972
2016 8 1,586 1/(1+interest rate)8906
2017 9 1,586 1/(1+interest rate)9845
2018 10 1,586 1/(1+interest rate)10788
2019 11 1,586 1/(1+interest rate)11735
2020 12 454 1/(1+interest rate)12196
Undiscounted sum of minimum 
future lease payments$18,205
Present value of future mini -
mum lease payments$12,208 $12,208
The interest rate of 7.245 percent approximately equates the future minimum 
lease payments with the present value of future minimum lease payments of 
$12,208 that CEC reports.
Solution to 1B:

The implicit interest rate is important because it will be used to estimate the 
present value of the lease obligations reported as a liability, the value of the leased 
assets on the balance sheet, the interest expense, and the lease amortisation on 
the income statement. For instance, by selecting a higher rate a company could, 
if desired, opportunistically reduce the present value of its finance leases and 
thus its reported debt. The reasonableness of the implicit interest rate can be 
gauged by comparing it to the interest rates of the company’s other debt instru -
ments outstanding, which are disclosed in financial statement footnotes, and

Leasing 479
by considering recent market conditions. Note, however, that the interest rate 
implicit in capitalisation of the finance lease obligations reflects the interest rate 
at the time the lease occurred and thus may differ from current rates.
If the operating leases had been treated as finance leases, the additional 
amount that would be reported as a lease obligation on the balance sheet at 
28 December 2008, using a discount rate of 7.245 percent determined in Part 1 
above, is $520,256. Exhibit 13 presents the present value computations. An alter -
native short cut approach is to divide the discounted finance lease cash flows of 
$12,208 by the undiscounted finance lease cash flows of $18,205 and then apply 
the resulting percentage of 67.06 percent to the undiscounted operating lease 
cash flows of $803,907. The shortcut approach estimates the present value of the 
operating lease payments as $539,100, which is close to the estimate obtained

using the longer method. It is likely to be most accurate when the timing and 
relative quantities of the two sets of cash flows are similar.
Exhibit 13   Present Value Computations (Implicit Interest Rate: 7.245%)
DiscountOperating Lease 
Payments Times Present Value Factor Equals Present Value
2009 1 66,849 1/(1+0.07245)1$62,333
2010 2 66,396 1/(1+0.07245)257,728
2011 3 66,558 1/(1+0.07245)353,960
2012 4 65,478 1/(1+0.07245)449,498
2013 5 63,872 1/(1+0.07245)545,022
2014 6 63,872 1/(1+0.07245)641,981
2015 7 63,872 1/(1+0.07245)739,145
2016 8 63,872 1/(1+0.07245)836,500
2017 9 63,872 1/(1+0.07245)934,034
2018 10 63,872 1/(1+0.07245)1031,735
2019 11 63,872 1/(1+0.07245)1129,591
2020 12 63,872 1/(1+0.07245)1227,592
2021 13 27,650 1/(1+0.07245)1311,138
Undiscounted sum of future 
operating lease payment$803,907
Present value of future operat -
ing lease payments$520,256
The debt-  to- equity ratio almost doubles, increasing to 8.78x from 4.74x when

capitalising the operating leases. The adjusted debt-  to- equity ratio is computed 

Reading 28 ■ Long-  Lived Assets 480
Unadjusted 
for Operating 
LeasesAdjustment 
to Capitalise 
Operating 
LeasesAdjusted to 
Capitalise 
Operating 
Leases
Total liabilities $608,854 $520,256 $1,129,110
Common shareholders’ 
equity128,586 128,586
Debt-  to- equity ratio 4.74x 8.78x
9.2.2  Accounting and Reporting by the Lessor
Lessors that report under US GAAP determine whether a lease is a finance (also 
called “capital lease”) or operating lease using the same four criteria as a lessee, plus 
additional revenue recognition criteria. If a lessor enters into an operating lease, the 
lessor records any lease revenue when earned. The lessor also continues to report the 
leased asset on the balance sheet and the asset’s associated depreciation expense on 
the income statement.
Under a finance lease, the lessor reports a lease receivable based on the present 
value of future lease payments, and the lessor also reduces its assets by the carrying

amount of the asset leased. Under both US GAAP and IFRS, the carrying amount of 
the asset leased relative to the present value of lease payments distinguishes a direct 
financing lease from a sales-  type lease. The income statement will show interest 
revenue on the lease.
EXAMPLE 22   
Financial Statement Impact of a Direct Financing Lease 
versus Operating Lease for the Lessor
Assume two similar (hypothetical) companies, DIRFIN Inc. and LOPER Inc., 
own a similar piece of machinery and make similar agreements to lease the 
machinery on 1 January Year 1. In the lease contract, each company requires 
four annual payments of €28,679 starting on 1 January Year 1. The useful life of 
the machine is four years and its salvage value is zero. DIRFIN Inc. accounts for 
the lease as a direct financing lease while LOPER has determined the lease is an 
operating lease. (For simplicity, this example assumes that the accounting rules

governing these hypothetical companies do not mandate either type of lease.) 
The present value of lease payments and fair value of the equipment is €100,000.
At the beginning of Year 1, before entering into the lease agreement, both 
companies reported liabilities of €100,000 and equity of €200,000. Assets on 
hand include the asset about to be leased. Each year the companies receive total 
revenues of €50,000 cash, apart from any revenue earned on the lease. Assume 
financial and tax purposes. Both companies’ discount rate is 10  percent. In 
order to focus only on the differences in the type of lease, assume that neither 
company incurs revenues or expenses other than those associated with the lease 
and that neither invests excess cash.

Leasing 481
3 Based on ROE, how do the two companies’ profitability measures 
compare?
LOPER reports higher expenses in Year 1 because, under an operating lease, 
the lessor retains ownership of the asset and continues to report associated 
depreciation expense. DIRFIN, treating the lease as a finance lease, does not 
reflect ownership of the asset or the associated depreciation expense. DIRFIN 
has higher net income in Year 1 because the interest revenue component of 
the lease payment in that year exceeds the lease revenue net of depreciation 
reported by LOPER.
On its income statement, LOPER reports depreciation expense for the asset it 
has leased and lease revenue based on the lease payment received. The table below 
shows LOPER’s depreciation and book values on leased equipment by year.34
Y earCost  
Expense  
(c)Book Value  
(Y ear End)  
(d)

(Y ear End)  
(d)
€100,000
■■Column (a) is the cost of €100,000 of the leased equipment.
the straight-  line method as the cost less the salvage value divided by the 
useful life [(€100,000 – €0)/4 years].
■■Column (d) is the ending book value of the leased equipment, which is the 
difference between the cost and accumulated depreciation.
DIRFIN, however, records the lease as a direct financing lease. It removes 
the leased asset from its assets and records a lease receivable. On its income 
statement, DIRFIN reports interest revenues earned from financing the lease.

The table below shows DIRFIN’s interest revenues and carrying amounts on 
the lease receivable.
34 The computations included throughout the example were made using an Excel worksheet; small apparent 
discrepancies in the calculations are due to the rounding.

Reading 28 ■ Long-  Lived Assets 482
Y earLease 
Receivable,  
1 January  
(a)Annual Lease 
Payment 
Received, 1 
January  
(at 10%; 
Accrued in 
Previous 
Y ear)  
(c)Reduction 
of Lease 
1 January  
(d)Lease Receivable on 31 
December after Lease 
Payment on 1 January of 
Same Y ear  
(e)
■■Column (a) is the lease receivable at the beginning of the year.
■■Column (b) is annual lease payment received at the beginning of the year, 
which is allocated to interest and reduction of the lease receivable.
■■Column (c) is interest accrued in the previous year calculated as the lease 
receivable outstanding for the year times the interest rate.
■■Column (d) is the reduction of the lease receivable which is the difference 
between the annual lease payments received and interest. Because the

lease payment is due on 1 January, this amount of interest is a receivable 
at the end of the prior  year and is reported as interest revenue in the prior  
year.
■■Column (e) is the lease receivable after the lease payment is received and 
at the end of the year. It is the lease receivable at 1 January (Column a) 
less the reduction of the lease receivable (Column d).
The table below summarises and compares the income statement effects 
of the lease for DIRFIN and LOPER. Notice that over the four-  year lease, both 
companies report the same total amount of revenue, but DIRFIN’s revenues 
in the earlier years of the lease are higher than the net of lease revenues less 
depreciation reported by LOPER in those years.
DIRFIN LOPER
Y earLease 
Revenue Lease RevenueDepreciation 
Expense Total Difference
1 €7,132 €28,679 €25,000 €3,679 €3,453
2 4,977 28,679 25,000 3,679 1,298
3 2,607 28,679 25,000 3,679 (1,072)
4 — 28,679 25,000 3,679 (–3,679)
Total €14,717 €114,717 €100,000 €14,717 €0

The complete income statements for DIRFIN and LOPER are presented 
below. Notice that, under the assumption that the same accounting is used for 
financial and tax purposes, DIRFIN’s taxes are higher than those of LOPER in 
Years 1 and 2.

Leasing 483
Income 
expense (25,000) (25,000) (25,000) (25,000) (100,000)
Interest 
revenue 7,132 4,977 2,607 14,717
Lease revenue — — — — — 28,679 28,679 28,679 28,679 114,717
Income before 
taxes €57,132 €54,977 €52,607 €50,000 €214,717 €53,679 €53,679 €53,679 €53,679 €214,717
Tax expense 17,140 16,493 15,782 15,000 64,415 16,104 16,104 16,104 16,104 64,415
Net income €39,992 €38,484 €36,825 €35,000 €150,302 €37,575 €37,575 €37,575 €37,575 €150,302
Looking at the statement of cash flows, observe that operating cash flows reported 
by DIRFIN are lower, but investing cash flows are higher than LOPER. Over 
the four years, both DIRFIN and LOPER report the same total change in cash.
of Cash 
Flows 1 2 3 4 Total 1 2 3 4 Total

Increase 
(decrease) 
in interest 
receivable 7,132 (2,155) (2,370) (2,607) 0
Add back 
depreciation 
expense — — — — — 25,000 25,000 25,000 25,000 100,000
Operating 
cash flows €32,860 €40,639 €39,195 €37,607 €150,302 €62,575 €62,575 €62,575 €62,575 €250,302
Payments 
received 
on finance 
leases 28,679 21,547 23,702 26,072 100,000
Investing 
cash flows 28,679 21,547 23,702 26,072 100,000 — — — — —
Change in 
cash €61,540 €62,186 €62,897 €63,679 €250,302 €62,575 €62,575 €62,575 €62,575 €250,302
Based on ROE, DIRFIN appears more profitable than LOPER in the early years 
of the lease.
Computing ROE requires forecasting shareholders’ equity. In general, Ending 
shareholders’ equity = Beginning shareholders’ equity + Net income + Other 
ers. Because the companies in this example do not have other comprehensive

Reading 28 ■ Long-  Lived Assets 484
income, do not pay dividends, and have no capital contributions, Ending share -
holders’ equity = Beginning shareholders’ equity + Net income. The forecasts 
are presented below.
DIRFIN 0 1 2 3 4
Retained 
earnings €0 €39,992 €78,477 €115,302 €150,302
holders’ equity €200,000 €239,992 €278,477 €315,302 €350,302
LOPER 0 1 2 3 4
Retained 
earnings €0 €37,575 €75,151 €112,726 €150,302
holders’ equity €200,000 €237,575 €275,151 €312,726 €350,302
ROE is calculated as net income divided by average shareholders’ equity. For 
example, DIRFIN Inc. had Year 1 ROE of 18.2 percent: €39,992/[(€200,000 + 
€239,992)/2].
1 2 3 4 1 2 3 4
ROE 18.2% 14.8% 12.4% 10.5% 17.2% 14.7% 12.8% 11.3%
From the comparisons above, DIRFIN looks more profitable in the early 
years of the lease, but less profitable in the later years.

US GAAP make a further distinction in defining two types of non-  operating leases: 
(1) direct financing leases , and (2) sales-  type leases  from the lessor’s perspective.35 
A direct financing lease results when the present value of lease payments (and thus 
the amount recorded as a lease receivable) equals the carrying amount of the leased 
asset. Because there is no “profit” on the asset itself, the lessor is essentially providing 
financing to the lessee, and the revenues earned by the lessor are financing in nature 
(i.e., interest revenue). If, however, the present value of lease payments (and thus the 
amount recorded as a lease receivable) exceeds the carrying value of the leased asset, 
the lease is treated as a sale.
When a company enters into a sales-  type lease, a lease agreement where the pres -
ent value of lease payment is greater than the value of the leased asset to the lessor, 
it will show a profit on the transaction in the year of inception and interest revenue

over the life of the lease.
35 IFRS does not make the distinction between a sales-  type lease and a direct financing lease. However, a 
similar treatment to ‘sales-  type’ is allowed for finance leases originated by ‘manufacturer or dealer lessors, ’ 
within the general provisions for finance leases.

Leasing 485
EXAMPLE 23   
Financial Statement Impact of a Sales-  type Lease for the 
Lessor
Assume a (hypothetical) company, Selnow Inc., owns a piece of machinery and 
enters into an agreement to lease the machinery on 1 January Year 1. In the 
lease contract, the company requires four annual payments of €28,679 starting 
on 1 January Year 1. The present value of the lease payments (using a 10 percent 
discount rate) is €100,000, and the fair value of the equipment is €90,000. The 
useful life of the machinery is four years and its salvage value is zero.
1 Is the lease a direct financing or sales-  type lease?
2 What is Selnow’s income related to the lease in Year 1? In Year 2? Ignore 
taxes.
This is a sales-  type lease: The present value of lease payments is more than the 
lessor’s carrying amount of the leased asset. The difference between the pres -
ent value of the lease payments and the carrying amount of the leased asset is

the lessor’s profit from selling the machinery. The lessor will record a profit of 
€10,000 on the sale of the leased equipment in Year 1 (€100,000 present value 
of lease payments receivable less €90,000 value of leased equipment).
In Year 1, Selnow shows income of €17,132 related to the lease. One part of 
this is the €10,000 gain on the sale of the lease equipment (sales revenues of 
€100,000 less costs of goods sold of €90,000). Selnow also shows interest revenue 
of €7,132 on its financing of the lease (lease receivable of €71,321 after the initial 
lease payment is received times the 10 percent discount rate). In Year 2, Selnow 
reports only the interest revenue of €4,977 (lease receivable of €49,774 after the 
1 January lease payment is received times the 10 percent discount rate). The 
table below shows lease payments received, interest revenue, and reduction of 
the lease receivable for Selnow’s sales-  type lease. Note that this table is the same

as DIRFIN’s table in the previous example with the direct financing lease. They 
are the same because the present value of the lease payments in both cases is the 
same. It is the fair value of the equipment that differs between the two examples.
Y earLease 
1 January  
Payment 
Received,  
1 January  
(at 10%; Accrued 
in Previous Y ear)  
of Lease 
1 January  
(d)Lease Receivable on 
31 December after 
Lease Payment on 1 
January Same Y ear  
(e)

Reading 28 ■ Long-  Lived Assets 486
SUMMARY
Understanding the reporting of long-  lived assets at inception requires distinguishing 
between expenditures that are capitalised (i.e., reported as long-  lived assets) and those 
that are expensed. Once a long-  lived asset is recognised, it is reported under the cost 
model at its historical cost less accumulated depreciation (amortisation) and less any 
impairment or under the revaluation model at its fair value. IFRS permit the use of 
either the cost model or the revaluation model, whereas US GAAP require the use of 
the cost model. Most companies reporting under IFRS use the cost model. The choice 
of different methods to depreciate (amortise) long-  lived assets can create challenges 
for analysts comparing companies.
Key points include the following:
■■Expenditures related to long-  lived assets are capitalised as part of the cost of 
assets if they are expected to provide future benefits, typically beyond one year.

Otherwise, expenditures related to long-  lived assets are expensed as incurred.
■■Although capitalising expenditures, rather than expensing them, results in 
higher reported profitability in the initial year, it results in lower profitability 
in subsequent years; however, if a company continues to purchase similar or 
increasing amounts of assets each year, the profitability-  enhancing effect of 
capitalisation continues.
■■Capitalising an expenditure rather than expensing it results in a greater amount 
reported as cash from operations because capitalised expenditures are classified 
as an investing cash outflow rather than an operating cash outflow.
■■Companies must capitalise interest costs associated with acquiring or con -
structing an asset that requires a long period of time to prepare for its intended 
use.
■■Including capitalised interest in the calculation of interest coverage ratios pro -
vides a better assessment of a company’s solvency.

■■IFRS require research costs be expensed but allow all development costs (not 
only software development costs) to be capitalised under certain conditions. 
Generally, US accounting standards require that research and development 
costs be expensed; however, certain costs related to software development are 
required to be capitalised.
■■When one company acquires another company, the transaction is accounted 
for using the acquisition method of accounting in which the company identified 
as the acquirer allocates the purchase price to each asset acquired (and each 
liability assumed) on the basis of its fair value. Under acquisition accounting, if 
the purchase price of an acquisition exceeds the sum of the amounts that can be 
allocated to individual identifiable assets and liabilities, the excess is recorded as 
goodwill.
■■The capitalised costs of long-  lived tangible assets and of intangible assets with

finite useful lives are allocated to expense in subsequent periods over their use -
ful lives. For tangible assets, this process is referred to as depreciation, and for 
intangible assets, it is referred to as amortisation.
■■Long-  lived tangible assets and intangible assets with finite useful lives are 
reviewed for impairment whenever changes in events or circumstances indicate 
that the carrying amount of an asset may not be recoverable.
■■Intangible assets with an indefinite useful life are not amortised but are 
reviewed for impairment annually.

Summary 487
■■Impairment disclosures can provide useful information about a company’s 
expected cash flows.
■■Methods of calculating depreciation or amortisation expense include the 
straight-  line method, in which the cost of an asset is allocated to expense in 
equal amounts each year over its useful life; accelerated methods, in which 
the allocation of cost is greater in earlier years; and the units-  of- production 
method, in which the allocation of cost corresponds to the actual use of an asset 
in a particular period.
■■Estimates required for depreciation and amortisation calculations include the 
useful life of the equipment (or its total lifetime productive capacity) and its 
expected residual value at the end of that useful life. A longer useful life and 
higher expected residual value result in a smaller amount of annual deprecia -
tion relative to a shorter useful life and lower expected residual value.
■■IFRS permit the use of either the cost model or the revaluation model for the

valuation and reporting of long-  lived assets, but the revaluation model is not 
allowed under US GAAP .
■■Under the revaluation model, carrying amounts are the fair values at the date of 
revaluation less any subsequent accumulated depreciation or amortisation.
■■In contrast with depreciation and amortisation charges, which serve to allocate 
the cost of a long-  lived asset over its useful life, impairment charges reflect an 
unexpected decline in the fair value of an asset to an amount lower than its 
carrying amount.
■■IFRS permit impairment losses to be reversed, with the reversal reported in 
profit. US GAAP do not permit the reversal of impairment losses.
■■The gain or loss on the sale of long-  lived assets is computed as the sales pro -
ceeds minus the carrying amount of the asset at the time of sale.
■■Estimates of average age and remaining useful life of a company’s assets reflect 
the relationship between assets accounted for on a historical cost basis and 
depreciation amounts.

■■The average remaining useful life of a company’s assets can be estimated as net 
PPE divided by depreciation expense, although the accounting useful life may 
not necessarily correspond to the economic useful life.
■■Long-  lived assets reclassified as held for sale cease to be depreciated or amor -
tised. Long-  lived assets to be disposed of other than by a sale (e.g., by abandon -
ment, exchange for another asset, or distribution to owners in a spin-  off) are 
classified as held for use until disposal. Thus, they continue to be depreciated 
and tested for impairment.
■■Investment property is defined as property that is owned (or, in some cases, 
leased under a finance lease) for the purpose of earning rentals, capital appreci -
ation, or both.
■■Under IFRS, companies are allowed to value investment properties using either 
a cost model or a fair value model. The cost model is identical to the cost model

used for property, plant, and equipment, but the fair value model differs from 
the revaluation model used for property, plant, and equipment. Under the fair 
value model, all changes in the fair value of investment property affect net 
income.
■■Under US GAAP , investment properties are generally measured using the cost 
model.
■■Accounting standards have traditionally defined two types of leases: operating 
leases and finance (or capital) leases. US GAAP specify four criteria to deter -
mine when a lease is classified as a capital lease, although proposed standards

Reading 28 ■ Long-  Lived Assets 488
would eliminate those specific criteria. IFRS have been less prescriptive in 
determining the classification of a lease as a finance lease. The new IFRS 16 
requires that both operating leases and financing leases are recognized and 
accounted for as finance leases by the lessee.
■■When a lessee reports a lease as an operating lease rather than a finance lease, 
it usually appears more profitable in early years of the lease and less so later, 
and it appears less leveraged over the entire lease period.
■■When a lessor reports a lease as a finance lease rather than an operating lease, 
it usually appears more profitable in early years of the lease.

Practice Problems 489
1 JOOVI Inc. has recently purchased and installed a new machine for its manu -
facturing plant. The company incurred the following costs:
Purchase price $12,980
Freight and insurance $1,200
Installation $700
Testing $100
Maintenance staff training costs $500
 The total cost of the machine to be shown on JOOVI’s balance sheet is closest  
to:
A $14,180.
B $14,980.
C $15,480.
2 Which costs incurred with the purchase of property and equipment are 
expensed?
A Delivery charges
B Installation and testing
C Training required to use the property and equipment
3 When constructing an asset for sale, directly related borrowing costs are most 
likely : 
A expensed as incurred.
B capitalized as part of inventory.
C capitalized as part of property, plant, and equipment.
4 BAURU, S.A., a Brazilian corporation, borrows capital from a local bank to 
finance the construction of its manufacturing plant. The loan has the following 
conditions:
Borrowing date 1 January 2009

Amount borrowed 500 million Brazilian real (BRL)
Annual interest rate 14 percent
Term of the loan 3 years
Payment method Annual payment of interest only. Principal amortization 
is due at the end of the loan term.
 The construction of the plant takes two years, during which time BAURU 
earned BRL 10 million by temporarily investing the loan proceeds. Which of 
the following is the amount of interest related to the plant construction (in BRL 
million) that can be capitalized in BAURU’s balance sheet?
A 130.
B 140.
C 210.
5 After reading the financial statements and footnotes of a company that follows 
IFRS, an analyst identified the following intangible assets:
■●product patent expiring in 40 years;

Reading 28 ■ Long-  Lived Assets 490
■●copyright with no expiration date; and
■●goodwill acquired 2 years ago in a business combination.
 Which of these assets is an intangible asset with a finite useful life?
Product Patent Copyright Goodwill
A Yes Yes No
B Yes No No
C No Yes Yes
6 Intangible assets with finite useful lives mostly  differ from intangible assets with 
infinite useful lives with respect to accounting treatment of:
A revaluation.
B impairment.
C amortization.
7 Costs incurred for intangible assets are generally expensed when they are:
A internally developed.
B individually acquired.
C acquired in a business combination.
8 Under US GAAP , when assets are acquired in a business combination, goodwill 
most likely  arises from: 
A contractual or legal rights.
B assets that can be separated from the acquired company.
C assets that are neither tangible nor identifiable intangible assets.
9 All else equal, in the fiscal year when long-  lived equipment is purchased:

A depreciation expense increases. 
B cash from operations decreases.
C net income is reduced by the amount of the purchase.
10 Companies X and Z have the same beginning-  of- the- year book value of equity 
and the same tax rate. The companies have identical transactions throughout 
the year and report all transactions similarly except for one. Both companies 
acquire a £300,000 printer with a three-  year useful life and a salvage value of £0 
on 1 January of the new year. Company X capitalizes the printer and depreciates 
it on a straight-  line basis, and Company Z expenses the printer. The following 
year-  end information is gathered for Company X. 
Company X  
Ending shareholders’ equity £10,000,000
Tax rate 25%
Dividends £0.00
Net income £750,000
 Based on the information given, Company Z’s return on equity using year-  end 
equity will be closest  to:
A 5.4%.
B 6.1%.
C 7.5%.

Practice Problems 491
11 A financial analyst is studying the income statement effect of two alternative 
depreciation methods for a recently acquired piece of equipment. She gathers 
the following information about the equipment’s expected production life and 
use:
Y ear 1 Y ear 2 Y ear 3 Y ear 4 Y ear 5 Total
Units of production 2,000 2,000 2,000 2,000 2,500 10,500
 Compared with the units-  of- production method of depreciation, if the com -
pany uses the straight-  line method to depreciate the equipment, its net income 
in Year 1 will most likely  be:
A lower.
B higher.
C the same.
12 A company purchases a piece of equipment for €1,500. The equipment is 
expected to have a useful life of five years and no residual value. In the first 
year of use, the units of production are expected to be 15% of the equipment’s 
lifetime production capacity and the equipment is expected to generate €1,500 
of revenue and incur €500 of cash expenses.

of revenue and incur €500 of cash expenses. 
 The depreciation method yielding the lowest operating profit on the equipment 
in the first year of use is:
A straight line.
B units of production.
C double-  declining balance.
13 Juan Martinez, CFO of VIRMIN, S.A., is selecting the depreciation method to 
use for a new machine. The machine has an expected useful life of six years. 
Production is expected to be relatively low initially but to increase over time. 
The method chosen for tax reporting must be the same as the method used for 
financial reporting. If Martinez wants to minimize tax payments in the first year 
of the machine’s life, which of the following depreciation methods is Martinez 
most likely  to use?
A Straight-  line method.
B Units-  of- production method.
C Double-  declining balance method.
14–15
Miguel Rodriguez of MARIO S.A., an Uruguayan corporation, is computing the depre -

ciation expense of a piece of manufacturing equipment for the fiscal year ended 31 
December 2009. The equipment was acquired on 1 January 2009. Rodriguez gathers 
the following information (currency in Uruguayan pesos, UYP):
Cost of the equipment UYP 1,200,000
Estimated residual value UYP 200,000
Expected useful life 8 years
Total productive capacity 800,000 units

Reading 28 ■ Long-  Lived Assets 492
Production in FY 2009 135,000 units
Expected production for the next 7 years 95,000 units each year
14 If MARIO uses the straight-  line method, the amount of depreciation expense 
on MARIO’s income statement related to the manufacturing equipment is clos-
est to:
A 125,000.
B 150,000.
C 168,750.
15 If MARIO uses the units-  of- production method, the amount of depreciation 
expense (in UYP) on MARIO’s income statement related to the manufacturing 
equipment is closest  to:
A 118,750.
B 168,750.
C 202,500.
16 Which of the following amortization methods is most likely  to evenly distribute 
the cost of an intangible asset over its useful life?
17 Which of the following will cause a company to show a lower amount of amor -
tization of intangible assets in the first year after acquisition?
A A higher residual value.
B A higher amortization rate.
C A shorter useful life.

18 A company purchases equipment for $200,000 with a five-  year useful life and 
salvage value of zero. It uses the double-  declining balance method of depreci -
ation for two years, then shifts to straight-  line depreciation at the beginning of 
Year 3. Compared with annual depreciation expense under the double-  declining 
balance method, the resulting annual depreciation expense in Year 4 is:
A smaller.
B the same.
C greater. 
19 An analyst in the finance department of BOOLDO S.A., a French corporation, 
is computing the amortization of a customer list, an intangible asset, for the fis -
cal year ended 31 December 2009. She gathers the following information about 
the asset:
Acquisition cost €2,300,000
Acquisition date 1 January 2008
Expected residual value at time of acquisition €500,000
The customer list is expected to result in extra sales for three years after acquisition. 
The present value of these expected extra sales exceeds the cost of the list.

If the analyst uses the straight-  line method, the amount of accumulated amorti -
zation related to the customer list as of 31 December 2009 is closest  to:

Practice Problems 493
A €600,000.
B €1,200,000.
C €1,533,333.
20 A financial analyst is analyzing the amortization of a product patent acquired by 
MAKETTI S.p.A., an Italian corporation. He gathers the following information 
about the patent:
Acquisition cost €5,800,000
Acquisition date 1 January 2009
Patent expiration date 31 December 2015
Total plant capacity of patented product 40,000 units per year
Production of patented product in fiscal year ended 31 
December 200920,000 units
Expected production of patented product during life of 
the patent175,000 units
 If the analyst uses the units-  of- production method, the amortization expense 
on the patent for fiscal year 2009 is closest  to:
A €414,286.
B €662,857.
C €828,571.
21 A company acquires a patent with an expiration date in six years for ¥100 mil -
lion. The company assumes that the patent will generate economic benefits that 
will decline over time and decides to amortize the patent using the double-

declining balance method. The annual amortization expense in Year 4 is closest 
to:
A ¥6.6 million.
B ¥9.9 million.
C ¥19.8 million.
22 A company is comparing straight-  line and double-  declining balance amortiza -
tion methods for a non-  renewable six-  year license, acquired for €600,000. The 
difference between the Year 4 ending net book values using the two methods is 
closest to :
A €81,400.
B €118,600.
23 MARU S.A. de C.V., a Mexican corporation that follows IFRS, has elected to use 
the revaluation model for its property, plant, and equipment. One of MARU’s 
machines was purchased for 2,500,000 Mexican pesos (MXN) at the beginning 
of the fiscal year ended 31 March 2010. As of 31 March 2010, the machine has a 
fair value of MXN 3,000,000. Should MARU show a profit for the revaluation of 
the machine?
A Yes .
B No, because this revaluation is recorded directly in equity.
C No, because value increases resulting from revaluation can never be recog -
nized as a profit.

24 An analyst is studying the impairment of the manufacturing equipment of WLP 
Corp., a UK-  based corporation that follows IFRS. He gathers the following 
information about the equipment:

Reading 28 ■ Long-  Lived Assets 494
Fair value £16,800,000
Costs to sell £800,000
Value in use £14,500,000
Net carrying amount £19,100,000
 The amount of the impairment loss on WLP Corp. ’s income statement related to 
its manufacturing equipment is closest  to:
A £2,300,000.
B £3,100,000.
C £4,600,000.
25 Under IFRS, an impairment loss on a property, plant, and equipment asset is 
measured as the excess of the carrying amount over the asset’s:
A fair value.
B recoverable amount.
C undiscounted expected future cash flows.
26 A financial analyst at BETTO S.A. is analyzing the result of the sale of a vehicle 
for 85,000 Argentine pesos (ARP) on 31 December 2009. The analyst compiles 
the following information about the vehicle:
Acquisition cost of the vehicle ARP 100,000
Acquisition date 1 January 2007
Estimated residual value at acquisition date ARP 10,000
Expected useful life 9 years
Depreciation method Straight-  line
 The result of the sale of the vehicle is most likely :
A a loss of ARP 15,000.

B a gain of ARP 15,000.
C a gain of ARP 18,333.
27 CROCO S.p.A sells an intangible asset with a historical acquisition cost of 
€12 million and an accumulated depreciation of €2 million and reports a loss on 
the sale of €3.2 million. Which of the following amounts is most likely  the sale 
price of the asset?
A €6.8 million
B €8.8 million
C €13.2 million
28 The impairment of intangible assets with finite lives affects:
A the balance sheet but not the income statement.
B the income statement but not the balance sheet. 
C both the balance sheet and the income statement. 
29 The gain or loss on a sale of a long-  lived asset to which the revaluation model 
has been applied is most likely calculated using sales proceeds less:
A carrying amount.
B carrying amount adjusted for impairment.
C historical cost net of accumulated depreciation.

Practice Problems 495
30 According to IFRS, all of the following pieces of information about property, 
plant, and equipment must be disclosed in a company’s financial statements and 
footnotes except for :
A useful lives.
B acquisition dates.
C amount of disposals.
31 According to IFRS, all of the following pieces of information about intangible 
assets must be disclosed in a company’s financial statements and footnotes 
except for :
B impairment loss.
C amortization rate.
32 Which of the following is a required financial statement disclosure for long-  
lived intangible assets under US GAAP?
A The useful lives of assets
B The reversal of impairment losses
C Estimated amortization expense for the next five fiscal years
33 Which of the following characteristics is most likely  to differentiate investment 
property from property, plant, and equipment?
A It is tangible.
B It earns rent.
C It is long-  lived.
34 If a company uses the fair value model to value investment property, changes in

the fair value of the asset are least likely  to affect:
B net operating income.
35 Investment property is most likely  to:
A earn rent.
B be held for resale.
C be used in the production of goods and services.
36 A company is most likely  to:
A use a fair value model for some investment property and a cost model for 
other investment property.
B change from the fair value model when transactions on comparable proper -
ties become less frequent.
C change from the fair value model when the company transfers investment 
property to property, plant, and equipment.
37 Under the revaluation model for property, plant, and equipment and the fair 
model for investment property:
A fair value of the asset must be able to be measured reliably.
B net income is affected by all changes in the fair value of the asset.
C net income is never affected if the asset increases in value from its carrying 
amount.

amount.
38 Under IFRS, what must be disclosed under the cost model of valuation for 
investment properties?

Reading 28 ■ Long-  Lived Assets 496
A Useful lives
B The method for determining fair value
C Reconciliation between beginning and ending carrying amounts of invest -
ment property
39 A potential advantage of leasing through a finance lease, compared with pur -
chasing an asset, is most likely :
A no effect on the balance sheet.
B no reporting of interest expense.
C reduced risk related to asset obsolescence.
40–45
Melanie Hart, CFA, is a transportation analyst. Hart has been asked to write a research 
report on Altai Mountain Rail Company (AMRC). Like other companies in the railroad 
industry, AMRC’s operations are capital intensive, with significant investments in such 
long-  lived tangible assets as property, plant, and equipment. In November of 2008, 
AMRC’s board of directors hired a new team to manage the company. In reviewing 
the company’s 2009 annual report, Hart is concerned about some of the accounting

choices that the new management has made. These choices differ from those of the 
previous management and from common industry practice. Hart has highlighted the 
following statements from the company’s annual report:
Statement 1  “In 2009, AMRC spent significant amounts on track replacement 
and similar improvements. AMRC expensed rather than capital -
ised a significant proportion of these expenditures. ”
Statement 2  “ AMRC uses the straight-  line method of depreciation for both 
financial and tax reporting purposes to account for plant and 
equipment. ”
Statement 3  “In 2009, AMRC recognized an impairment loss of €50 million 
on a fleet of locomotives. The impairment loss was reported as 
‘other income’ in the income statement and reduced the carrying 
amount of the assets on the balance sheet. ”
Statement 4  “ AMRC acquires the use of many of its assets, including a large 
portion of its fleet of rail cars, under long-  term lease contracts.

In 2009, AMRC acquired the use of equipment with a fair value 
of €200 million under 20-  year lease contracts. These leases were 
classified as operating leases. Prior to 2009, most of these lease 
contracts were classified as finance leases. ”
Exhibits 1 and 2 contain AMRC’s 2009 consolidated income statement and bal -
ance sheet. AMRC prepares its financial statements in accordance with International 

Practice Problems 497
Exhibit 1   Consolidated Statement of Income
2009 2008
For the Y ears Ended 31 December € Millions % Revenues € Millions % Revenues
Operating revenues 2,600 100.0 2,300 100.0
Operating expenses
  Depreciation (200) (7.7) (190) (8.3)
  Lease payments (210) (8.1) (195) (8.5)
  Other operating expense (1,590) (61.1) (1,515) (65.9)
Total operating expenses (2,000) (76.9) (1,900) (82.6)
Operating income 600 23.1 400 17.4
Other income (50) (1.9) — 0.0
Interest expense (73) (2.8) (69) (3.0)
Income before taxes 477 18.4 331 14.4
Income taxes (189) (7.3) (125) (5.4)
Net income 288 11.1 206 9.0
Exhibit 2   Consolidated Balance Sheet
Assets € Millions % Assets € Millions % Assets
Current assets 500 9.4 450 8.5
Property & equipment:
  Land 700 13.1 700 13.2
  Plant & equipment 6,000 112.1 5,800 109.4
Total property & equipment 6,700 125.2 6,500 122.6
Accumulated depreciation (1,850) (34.6) (1,650) (31.1)
Net property & equipment 4,850 90.6 4,850 91.5

Total assets 5,350 100.0 5,300 100.0
Liabilities and Shareholders’ Equity    
Current liabilities 480 9.0 430 8.1
Long-  term debt 1,030 19.3 1,080 20.4
Other long-  term provisions and liabilities 1,240 23.1 1,440 27.2
Total liabilities 2,750 51.4 2,950 55.7
Shareholders’ equity  
  Common stock and paid-  in- surplus 760 14.2 760 14.3
  Retained earnings 1,888 35.5 1,600 30.2
  Other comprehensive losses (48) (0.9) (10) (0.2)

Reading 28 ■ Long-  Lived Assets 498
Total shareholders’ equity 2,600 48.6 2,350 44.3
Total liabilities & shareholders’ equity 5,350 100.0 5,300 100.0
40 With respect to Statement 1, which of the following is the most likely  effect of 
management’s decision to expense rather than capitalise these expenditures?
A 2009 net profit margin is higher than if the expenditures had been 
capitalised.
B 2009 total asset turnover is lower than if the expenditures had been 
C Future profit growth will be higher than if the expenditures had been 
41 With respect to Statement 2, what would be the most likely  effect in 2010 if 
AMRC were to switch to an accelerated depreciation method for both financial 
and tax reporting?
A Net profit margin would increase.
B Total asset turnover would decrease.
C Cash flow from operating activities would increase.

42 With respect to Statement 3, what is the most likely  effect of the impairment 
loss?
A Net income in years prior to 2009 was likely understated.
B Net profit margins in years after 2009 will likely exceed the 2009 net profit 
margin.
C Cash flow from operating activities in 2009 was likely lower due to the 
impairment loss.
43 Based on Exhibits 1 and 2, the best estimate  of the average remaining useful life 
of the company’s plant and equipment at the end of 2009 is:
A 20.75 years.
B 24.25 years.
C 30.00 years.
44 With respect to Statement 4, if AMRC had used its old classification method for 
its leases instead of its new classification method, its 2009 total asset turnover 
ratio would most likely  be:
A lower.
B higher.
C the same.
45 With respect to Statement 4 and Exhibit 1, if AMRC had used its old classifi -
cation method for its leases instead of its new classification method, the most 
likely  effect on its 2009 ratios would be a:
A higher net profit margin.Exhibit 2   (Continued)

Practice Problems 499
B higher fixed asset turnover.
C higher total liabilities-  to- total assets ratio.
46–52
Brian Jordan is interviewing for a junior equity analyst position at Orion Investment 
Advisors. As part of the interview process, Mary Benn, Orion’s Director of Research, 
provides Jordan with information about two hypothetical companies, Alpha and Beta, 
and asks him to comment on the information on their financial statements and ratios. 
Both companies prepare their financial statements in accordance with International 
Financial Reporting Standards (IFRS) and are identical in all respects except for their 
accounting choices.
Jordan is told that at the beginning of the current fiscal year, both companies 
purchased a major new computer system and began building new manufacturing 
plants for their own use. Alpha capitalised and Beta expensed the cost of the com -

puter system; Alpha capitalised and Beta expensed the interest costs associated with 
the construction of the manufacturing plants. In mid-  year, both companies leased 
new office headquarters. Alpha classified the lease as an operating lease, and Beta 
classified it as a finance lease.
Benn asks Jordan, “What was the impact of these decisions on each company’s 
current fiscal year financial statements and ratios?”
Jordan responds, “ Alpha’s decision to capitalise the cost of its new computer system 
instead of expensing it results in lower net income, lower total assets, and higher cash 
flow from operating activities in the current fiscal year. Alpha’s decision to capitalise 
its interest costs instead of expensing them results in a lower fixed asset turnover 
ratio and a higher interest coverage ratio. Alpha’s decision to classify its lease as an 
operating lease instead of a finance lease results in higher net income, higher cash flow

from operating activities, and stronger solvency and activity ratios compared to Beta. ”
Jordan is told that Alpha uses the straight-  line depreciation method and Beta uses 
an accelerated depreciation method; both companies estimate the same useful lives 
for long-  lived assets. Many companies in their industry use the units-  of- production 
method.
Benn asks Jordan, “What are the financial statement implications of each depre -
ciation method, and how do you determine a company’s need to reinvest in its pro -
ductive capacity?”
Jordan replies, “ All other things being equal, the straight-  line depreciation method 
results in the least variability of net profit margin over time, while an accelerated 
depreciation method results in a declining trend in net profit margin over time. The 
units-  of- production can result in a net profit margin trend that is quite variable. I use 
a three-  step approach to estimate a company’s need to reinvest in its productive capac -

ity. First, I estimate the average age of the assets by dividing net property, plant, and 
equipment by annual depreciation expense. Second, I estimate the average remaining 
useful life of the assets by dividing accumulated depreciation by depreciation expense. 
Third, I add the estimates of the average remaining useful life and the average age of 
the assets in order to determine the total useful life. ”
Jordan is told that at the end of the current fiscal year, Alpha revalued a manufac -
turing plant; this increased its reported carrying amount by 15 percent. There was no 
previous downward revaluation of the plant. Beta recorded an impairment loss on a 
manufacturing plant; this reduced its carrying by 10 percent.

Reading 28 ■ Long-  Lived Assets 500
Benn asks Jordan “What was the impact of these decisions on each company’s 
current fiscal year financial ratios?”
Jordan responds, “Beta’s impairment loss increases its debt to total assets and 
fixed asset turnover ratios, and lowers its cash flow from operating activities. Alpha’s 
revaluation increases its debt to capital and return on assets ratios, and reduces its 
return on equity. ”
At the end of the interview, Benn thanks Jordan for his time and states that a hiring 
decision will be made shortly.
46 Jordan’s response about the financial statement impact of Alpha’s decision to 
capitalise the cost of its new computer system is most likely correct  with respect 
to: 
A lower net income.
B lower total assets.
C higher cash flow from operating activities.
47 Jordan’s response about the ratio impact of Alpha’s decision to capitalise inter -
est costs is most likely correct  with respect to the:
A interest coverage ratio.
B fixed asset turnover ratio.

C interest coverage and fixed asset turnover ratios.
48 Jordan’s response about the impact of Alpha’s decision to classify its lease as an 
operating lease instead of finance lease is most likely incorrect  with respect to:
B solvency and activity ratios.
C cash flow from operating activities.
49 Jordan’s response about the impact of the different depreciation methods on net 
profit margin is most likely incorrect  with respect to:
A accelerated depreciation.
B straight-  line depreciation.
C units-  of- production depreciation.
50 Jordan’s response about his approach to estimating a company’s need to reinvest 
in its productive capacity is most likely correct  regarding:
A estimating the average age of the asset base.
B estimating the total useful life of the asset base.
C estimating the average remaining useful life of the asset base.
51 Jordan’s response about the effect of Beta’s impairment loss is most likely incor -

rect with respect to the impact on its:
A debt to total assets.
B fixed asset turnover.
52 Jordan’s response about the effect of Alpha’s revaluation is most likely correct  
with respect to the impact on its:
A return on equity.
B return on assets.
C debt to capital ratio.

Solutions 501
SOLUTIONS
1 B is correct. Only costs necessary for the machine to be ready to use can be 
capitalized. Therefore, Total capitalized costs = 12,980 + 1,200 + 700 + 100 = 
$14,980.
2 C is correct. When property and equipment are purchased, the assets are 
recorded on the balance sheet at cost. Costs for the assets include all expen -
ditures required to prepare the assets for their intended use. Any other costs 
are expensed. Costs to train staff for using the machine are not required to 
prepare the property and equipment for their intended use, and these costs are 
expensed.
3 B is correct. When a company constructs an asset, borrowing costs incurred 
directly related to the construction are generally capitalized. If the asset is con -
structed for sale, the borrowing costs are classified as inventory.
4 A is correct. Borrowing costs can be capitalized under IFRS until the tangible 
asset is ready for use. Also, under IFRS, income earned on temporarily investing

the borrowed monies decreases the amount of borrowing costs eligible for cap -
italization. Therefore, Total capitalized interest = (500 million × 14% × 2 years) 
– 10 million = 130 million.
5 B is correct. A product patent with a defined expiration date is an intangible 
asset with a finite useful life. A copyright with no expiration date is an intan -
gible asset with an indefinite useful life. Goodwill is no longer considered an 
intangible asset under IFRS and is considered to have an indefinite useful life.
6 C is correct. An intangible asset with a finite useful life is amortized, whereas 
an intangible asset with an indefinite useful life is not.
7 A is correct. The costs to internally develop intangible assets are generally 
expensed when incurred. 
8 C is correct. Under both International Financial Reporting Standards (IFRS) 
and US GAAP , if an item is acquired in a business combination and cannot be 
recognized as a tangible asset or identifiable intangible asset, it is recognized as

goodwill. Under US GAAP , assets arising from contractual or legal rights and 
assets that can be separated from the acquired company are recognized sepa -
rately from goodwill.
9 A is correct. In the fiscal year when long-  lived equipment is purchased, the 
assets on the balance sheet increase and depreciation expense on the income 
statement increases because of the new long-  lived asset.
10 B is correct. Company Z’s return on equity based on year-  end equity value will 
be 6.1%. Company Z will have an additional £200,000 of expenses compared 
with Company X. Company Z expensed the printer for £300,000 rather than 
capitalizing the printer and having a depreciation expense of £100,000 like 
Company X. Company Z’s net income and shareholders’ equity will be £150,000 
lower (= £200,000 × 0.75) than that of Company X.
Shareholders ' Equity=


=££600 000 9 850 00,, ,0 0
0616 1 ==.. %

Reading 28 ■ Long-  Lived Assets 502
11 A is correct. If the company uses the straight-  line method, the depreciation 
expense will be one-  fifth (20 percent) of the depreciable cost in Year 1. If it uses 
the units-  of- production method, the depreciation expense will be 19 percent 
(2,000/10,500) of the depreciable cost in Year 1. Therefore, if the company uses 
the straight-  line method, its depreciation expense will be higher and its net 
income will be lower.
12 C is correct. The operating income or earnings before interest and taxes will 
be lowest for the method that results in the highest depreciation expense. The 
double-  declining balance method results in the highest depreciation expense in 
the first year of use.
 Depreciation expense: 
Straight line = €1,500/5 = €300.
Double-  declining balance = €1,500 × 0.40 = €600.
Units of production = €1,500 × 0.15 = €225.
13 C is correct. If Martinez wants to minimize tax payments in the first year of

the machine’s life, he should use an accelerated method, such as the double-  
declining balance method.
14 A is correct. Using the straight-  line method, depreciation expense amounts to
Depreciation expense = (1,200,000 – 200,000)/8 years = 125,000.
15 B is correct. Using the units-  of- production method, depreciation expense 
amounts to
Depreciation expense = (1,200,000 – 200,000) × (135,000/800,000) = 
168,750.
16 A is correct. The straight-  line method is the method that evenly distributes the 
cost of an asset over its useful life because amortization is the same amount 
every year.
17 A is correct. A higher residual value results in a lower total depreciable cost 
and, therefore, a lower amount of amortization in the first year after acquisition 
(and every year after that).
18 C is correct. Shifting at the end of Year 2 from double-  declining balance to 
straight-  line depreciation methodology results in depreciation expense being

the same in each of Years 3, 4, and 5. Shifting to the straight-  line methodology 
at the beginning of Year 3 results in a greater depreciation expense in Year 4 
than would have been calculated using the double-  declining balance method. 
 Depreciation expense Year 4 (Using double-  declining balance method all five 
years)
  = 2 × Annual depreciation % using straight-  line method × Carrying amount 
at end of Year 3
  = 40% × $43,200
 Depreciation expense Year 4 with switch to straight-  line method in Year 3
  = 1/3 × Remaining depreciable cost at start of Year 3
  = 1/3 × $72,000
  = $24,000

Solutions 503
19 B is correct. Using the straight-  line method, accumulated amortization amounts 
to
 Accumulated amortization =  [(2,300,000 – 500,000)/3 years] × 2 years
  = 1,200,000
20 B is correct. Using the units-  of- production method, depreciation expense 
amounts to
Depreciation expense = 5,800,000 × (20,000/175,000) = 662,857
21 B is correct. As shown in the following calculations, under the double-  declining 
balance method, the annual amortization expense in Year 4 is closest to 
¥9.9 million.
 Annual amortization expense = 2 × Straight-  line amortization rate × Net book 
value.
 Amortization expense Year 4 = 33.3% × ¥29.6 million = ¥9.9 million.
22 A is correct. As shown in the following calculations, at the end of Year 4, the 
difference between the net book values calculated using straight-  line versus 
double-  declining balance is closest to €81,400.
 Net book value end of Year 4 using straight-  line method = €600,000 – [4 × 
(€600,000/6)] = €200,000.

 Net book value end of Year 4 using double-  declining balance method = 
€600,000 (1 – 33.33%)4 ≈ €118,600.
23 B is correct. In this case, the value increase brought about by the revaluation 
should be recorded directly in equity. The reason is that under IFRS, an increase 
in value brought about by a revaluation can only be recognized as a profit to 
the extent that it reverses a revaluation decrease of the same asset previously 
recognized in the income statement.
24 B is correct. The impairment loss equals £3,100,000.
 Impairment =  max(Fair value less costs to sell; Value in use) – Net car -
rying amount
  = max(16,800,000 – 800,000; 14,500,000) – 19,100,000 
  = –3,100,000.
25 B is correct. Under IFRS, an impairment loss is measured as the excess of the 
carrying amount over the asset’s recoverable amount. The recoverable amount 
is the higher of the asset’s fair value less costs to sell and its value in use. Value

in use is a discounted measure of expected future cash flows. Under US GAAP , 
assessing recoverability is separate from measuring the impairment loss. If the 
asset’s carrying amount exceeds its undiscounted expected future cash flows, 
the asset’s carrying amount is considered unrecoverable and the impairment 
loss is measured as the excess of the carrying amount over the asset’s fair value.
26 B is correct. The result on the sale of the vehicle equals
 Gain or loss on the sale =  Sale proceeds – Carrying amount
  = Sale proceeds – (Acquisition cost – Accumulated 
depreciation)
  = 85,000 – {100,000 – [((100,000 – 10,000)/9 years) 
× 3 years]}
  = 15,000.

Reading 28 ■ Long-  Lived Assets 504
27 A is correct. Gain or loss on the sale = Sale proceeds – Carrying amount. 
Rearranging this equation, Sale proceeds = Carrying amount + Gain or loss on 
sale. Thus, Sale price = (12 million – 2 million) + (–3.2 million) = 6.8 million.
28 C is correct. The carrying amount of the asset on the balance sheet is reduced 
by the amount of the impairment loss, and the impairment loss is reported on 
the income statement. 
29 A is correct. The gain or loss on the sale of long-  lived assets is computed as the 
sales proceeds minus the carrying amount of the asset at the time of sale. This is 
true under the cost and revaluation models of reporting long-  lived assets. In the 
absence of impairment losses, under the cost model, the carrying amount will 
equal historical cost net of accumulated depreciation.
30 B is correct. IFRS do not require acquisition dates to be disclosed.
31 A is correct. IFRS do not require fair value of intangible assets to be disclosed.

32 C is correct. Under US GAAP , companies are required to disclose the estimated 
amortization expense for the next five fiscal years. Under US GAAP , there is no 
reversal of impairment losses. Disclosure of the useful lives—finite or indefinite 
and additional related details—is required under IFRS.
33 B is correct. Investment property earns rent. Investment property and property, 
plant, and equipment are tangible and long-  lived.
34 C is correct. When a company uses the fair value model to value investment 
property, changes in the fair value of the property are reported in the income 
statement—not in other comprehensive income.
35 A is correct. Investment property earns rent. Inventory is held for resale, 
and property, plant, and equipment are used in the production of goods and 
services.
36 C is correct. A company will change from the fair value model to either the cost 
model or revaluation model when the company transfers investment property 
to property, plant, and equipment.

37 A is correct. Under both the revaluation model for property, plant, and equip -
ment and the fair model for investment property, the asset’s fair value must 
be able to be measured reliably. Under the fair value model, net income is 
affected  by all changes in the asset’s fair value. Under the revaluation model, any 
increase in an asset’s value to the extent that it reverses a previous revaluation 
decrease will be recognized on the income statement and increase net income.
38 A is correct. Under IFRS, when using the cost model for its investment prop -
erties, a company must disclose useful lives. The method for determining fair 
value, as well as reconciliation between beginning and ending carrying amounts 
of investment property, is a required disclosure when the fair value model is 
used.
39 C is correct. A lease can reduce the risks of obsolescence to the lessee because 
the lessee does not own the asset. Under a finance lease, a leased asset and a

lease obligation are reported on the balance sheet, and depreciation expense 
and interest expense are reported on the income statement.
40 C is correct. Expensing rather than capitalising an investment in long-  term 
assets will result in higher expenses and lower net income and net profit margin 
in the current year. Future years’ incomes will not include depreciation expense 
related to these expenditures. Consequently, year-  to- year growth in profitability 
will be higher. If the expenses had been capitalised, the carrying amount of the 
assets would have been higher and the 2009 total asset turnover would have 
been lower.

Solutions 505
41 C is correct. In 2010, switching to an accelerated depreciation method would 
increase depreciation expense and decrease income before taxes, taxes payable, 
and net income. Cash flow from operating activities would increase because of 
the resulting tax savings.
42 B is correct. 2009 net income and net profit margin are lower because of the 
impairment loss. Consequently, net profit margins in subsequent years are likely 
to be higher. An impairment loss suggests that insufficient depreciation expense 
was recognized in prior years, and net income was overstated in prior years. 
The impairment loss is a non-  cash item and will not affect operating cash flows.
43 A is correct. The estimated average remaining useful life is 20.75 years.
 Estimate of remaining useful life =  Net plant and equipment ÷ Annual 
depreciation expense
 Net plant and equipment =  Gross P & E – Accumulated depreciation
  = €6000 – €1850 = €4150

= €6000 – €1850 = €4150
 Estimate of remaining useful life =  Net P & E ÷ Depreciation expense
  = €4150 ÷ €200 = 20.75
44 A is correct. When leases are classified as finance leases, the lessee initially 
reports an asset and liability at a carrying amount equal to the lower of the 
fair value of the leased asset or the present value of the future lease payments. 
Under an operating lease, the lessee does not report an asset or liability. 
Therefore, total asset turnover (total revenue ÷ average total assets) would be 
lower if the leases were classified as finance leases.
45 C is correct. Total liabilities-  to- assets would be higher. When leases are classi -
fied as finance leases, the lessee initially reports an asset and liability at a carry -
ing amount equal to the lower of the fair value of the leased asset or the present 
value of the future lease payments. Both the numerator and denominator would 
increase by an equal amount, but the proportional increase in the numerator is

higher and the ratio would be higher. The following exhibit shows what would 
happen to 2009 total liabilities, assets, and total liabilities-  to- assets if €200 mil -
lion, the fair value of the leased equipment, is added to AMRC’s total liabilities 
and assets. This simple example ignores the impact of accounting for the 2009 
lease payment.
2009 Actual Under 
Operating Lease2009 Hypothetical Under 
Finance Lease
Total liabilities €2,750 €2,950
Total assets €5,350 €5,550
Total liabilities-  to- assets 51.4% 53.2%
 The depreciation and interest expense under a finance lease tends to be higher 
than the operating lease payment in the early years of the lease. The finance 
lease would result in lower net income and net profit margin. Long-  lived (fixed) 
assets are higher under a finance lease and fixed asset turnover is lower.
46 C is correct. The decision to capitalise the costs of the new computer system 
results in higher cash flow from operating activities; the expenditure is reported

as an outflow of investing activities. The company allocates the capitalised 
amount over the asset’s useful life as depreciation or amortisation expense 
rather than expensing it in the year of expenditure. Net income and total assets 
are higher in the current fiscal year.

Reading 28 ■ Long-  Lived Assets 506
47 B is correct. Alpha’s fixed asset turnover will be lower because the capitalised 
interest will appear on the balance sheet as part of the asset being constructed. 
Therefore, fixed assets will be higher and the fixed asset turnover ratio (total 
revenue/average net fixed assets) will be lower than if it had expensed these 
costs. Capitalised interest appears on the balance sheet as part of the asset 
being constructed instead of being reported as interest expense in the period 
incurred. However, the interest coverage ratio should be based on interest 
payments, not interest expense (earnings before interest and taxes/interest 
payments), and should be unchanged. To provide a true picture of a company’s 
interest coverage, the entire amount of interest expenditure, both the capital -
ised portion and the expensed portion, should be used in calculating interest 
coverage ratios.

48 C is correct. The cash flow from operating activities will be lower, not higher, 
because the full lease payment is treated as an operating cash outflow. With a 
finance lease, only the portion of the lease payment relating to interest expense 
potentially reduces operating cash outflows. A company reporting a lease as 
an operating lease will typically show higher profits in early years, because the 
lease expense is less than the sum of the interest and depreciation expense. The 
company reporting the lease as an operating lease will typically report stronger 
solvency and activity ratios.
49 A is correct. Accelerated depreciation will result in an improving, not declin -
ing, net profit margin over time, because the amount of depreciation expense 
declines each year. Under straight-  line depreciation, the amount of depreciation 
expense will remain the same each year. Under the units-  of- production method,

the amount of depreciation expense reported each year varies with the number 
of units produced.
50 B is correct. The estimated average total useful life of a company’s assets is 
calculated by adding the estimates of the average remaining useful life and the 
average age of the assets. The average age of the assets is estimated by divid -
ing accumulated depreciation by depreciation expense. The average remaining 
useful life of the asset base is estimated by dividing net property, plant, and 
equipment by annual depreciation expense.
51 C is correct. The impairment loss is a non-  cash charge and will not affect cash 
flow from operating activities. The debt to total assets and fixed asset turn -
over ratios will increase, because the impairment loss will reduce the carrying 
amount of fixed assets and therefore total assets.
52 A is correct. In an asset revaluation, the carrying amount of the assets 
increases. The increase in the asset’s carrying amount bypasses the income

statement and is reported as other comprehensive income and appears in equity 
under the heading of revaluation surplus. Therefore, shareholders’ equity will 
increase but net income will not be affected, so return on equity will decline. 
Return on assets and debt to capital ratios will also decrease.

Income Taxes
by Elbie Louw, PhD, CFA, CIPM, and Michael A. Broihahn, CPA, CIA, CFA
Elbie Louw, PhD, CFA, CIPM (South Africa). Michael A. Broihahn, CPA, CIA, CFA, is at 
Barry University (USA).
Mastery The candidate should be able to: 
a. describe the differences between accounting profit and taxable 
income and define key terms, including deferred tax assets, 
deferred tax liabilities, valuation allowance, taxes payable, and 
income tax expense; 
b. explain how deferred tax liabilities and assets are created and the 
factors that determine how a company’s deferred tax liabilities 
and assets should be treated for the purposes of financial analysis;
c. calculate the tax base of a company’s assets and liabilities;
d. calculate income tax expense, income taxes payable, deferred tax 
assets, and deferred tax liabilities, and calculate and interpret the 
adjustment to the financial statements related to a change in the 
income tax rate;

e. evaluate the effect of tax rate changes on a company’s financial 
statements and ratios;
f. distinguish between temporary and permanent differences in pre-  
tax accounting income and taxable income;
g. describe the valuation allowance for deferred tax assets—when it 
is required and what effect it has on financial statements;
h. explain recognition and measurement of current and deferred tax 
items;
i. analyze disclosures relating to deferred tax items and the effective 
tax rate reconciliation and explain how information included in 
these disclosures affects a company’s financial statements and 
financial ratios;
j. identify the key provisions of and differences between income tax 
accounting under International Financial Reporting Standards 
(IFRS) and US generally accepted accounting principles (GAAP).REA dINg
29
International Financial Statement Analysis , by Thomas R. Robinson, CFA, Jan Hendrik van Greuning, CFA,

Elaine Henry, CFA, and Michael A. Broihahn, CFA. © 2008 CFA Institute. All rights reserved.Note:  Changes in accounting 
candidates should use the ratio

readings.

Reading 29 ■ Income Taxes 508
For those companies reporting under International Financial Reporting Standards 
(IFRS), IAS 12 [Income Taxes] covers accounting for a company's income taxes and 
the reporting of deferred taxes. For those companies reporting under United States 
generally accepted accounting principles (US GAAP), FASB ASC Topic 740 [Income 
Taxes] is the primary source for information on accounting for income taxes. Although 
IFRS and US GAAP follow similar conventions on many income tax issues, there are 
some key differences that will be discussed in the reading.
Differences between how and when transactions are recognized for financial 
reporting purposes relative to tax reporting can give rise to differences in tax expense 
and related tax assets and liabilities. To reconcile these differences, companies that 
report under either IFRS or US GAAP create a provision on the balance sheet called

deferred tax assets or deferred tax liabilities, depending on the nature of the situation.
Deferred tax assets or liabilities usually arise when accounting standards and 
tax authorities recognize the timing of revenues and expenses at different times. 
Because timing differences such as these will eventually reverse over time, they are 
called “temporary differences. ” Deferred tax assets represent taxes that have been 
recognized for tax reporting purposes (or often the carrying forward of losses from 
previous periods) but have not yet been recognized on the income statement prepared 
for financial reporting purposes. Deferred tax liabilities represent tax expense that 
has appeared on the income statement for financial reporting purposes, but has not 
yet become payable under tax regulations.
This reading provides a primer on the basics of income tax accounting and report -
ing. The reading is organized as follows. Section 2 describes the differences between

taxable income and accounting profit. Section 3 explains the determination of tax 
base, which relates to the valuation of assets and liabilities for tax purposes. Section 
4 discusses several types of timing differences between the recognition of taxable 
and accounting profit. Section 5 examines unused tax losses and tax credits. Section 
6 describes the recognition and measurement of current and deferred tax. Section 7 
discusses the disclosure and presentation of income tax information on companies' 
financial statements and illustrates its practical implications for financial analysis. 
Section 8 provides an overview of the similarities and differences for income-  tax 
reporting between IFRS and US GAAP . A summary of the key points and practice 
problems in the CFA Institute multiple-  choice format conclude the reading.
DIFFERENCES BETWEEN ACCOUNTING PROFIT AND 
TAXABLE INCOME
A company’s accounting profit  is reported on its income statement in accordance

with prevailing accounting standards. Accounting profit (also referred to as income 
before taxes or pretax income) does not include a provision for income tax expense.1 
A company’s taxable income  is the portion of its income that is subject to income 
taxes under the tax laws of its jurisdiction. Because of different guidelines for how 
income is reported on a company’s financial statements and how it is measured for 
income tax purposes, accounting profit and taxable income may differ.1
2
1 As defined under IAS 12, paragraph 5.

Differences between Accounting Profit and Taxable Income 509
A company’s taxable income is the basis for its income tax payable  (a liability) 
or recoverable (an asset), which is calculated on the basis of the company’s tax rate 
and appears on its balance sheet. A company’s tax expense , or tax benefit in the case 
of a recovery, appears on its income statement and is an aggregate of its income tax 
payable (or recoverable in the case of a tax benefit) and any changes in deferred tax 
assets and liabilities.
When a company’s taxable income is greater than its accounting profit, then its 
income taxes payable will be higher than what would have otherwise been the case 
had the income taxes been determined based on accounting profit. Deferred tax 
assets , which appear on the balance sheet, arise when an excess amount is paid for 
income taxes (taxable income higher than accounting profit) and the company expects

to recover the difference during the course of future operations. Actual income taxes 
payable will thus exceed the financial accounting income tax expense (which is reported 
on the income statement and is determined based on accounting profit). Related 
to deferred tax assets is a valuation allowance , which is a reserve created against 
deferred tax assets. The valuation allowance is based on the likelihood of realizing 
the deferred tax assets in future accounting periods. Deferred tax liabilities , which 
also appear on the balance sheet, arise when a deficit amount is paid for income taxes 
and the company expects to eliminate the deficit over the course of future operations. 
In this case, financial accounting income tax expense exceeds income taxes payable.
Income tax paid  in a period is the actual amount paid for income taxes (not a 
provision, but the actual cash outflow). The income tax paid may be less than the

income tax expense because of payments in prior periods or refunds received in the 
current period. Income tax paid reduces the income tax payable, which is carried on 
the balance sheet as a liability.
The tax base  of an asset or liability is the amount at which the asset or liability 
is valued for tax purposes, whereas the carrying amount  is the amount at which the 
asset or liability is valued according to accounting principles.2 Differences between 
the tax base and the carrying amount also result in differences between accounting 
profit and taxable income. These differences can carry through to future periods. For 
example, a tax loss carry forward  occurs when a company experiences a loss in the 
current period that may be used to reduce future taxable income. The company’s tax 
expense on its income statement must not only reflect the taxes payable based on 
taxable income, but also the effect of these differences.
2.1 Current Tax Assets and Liabilities

A company’s current tax liability is the amount payable in taxes and is based on current 
taxable income. If the company expects to receive a refund for some portion previ -
ously paid in taxes, the amount recoverable is referred to as a current tax asset. The 
current tax liability or asset may, however, differ from what the liability would have 
been if it was based on accounting profit rather than taxable income for the period. 
Differences in accounting profit and taxable income are the result of the application 
of different rules. Such differences between accounting profit and taxable income can 
occur in several ways, including:
■■Revenues and expenses may be recognized in one period for accounting pur -
poses and a different period for tax purposes;
2 The terms “tax base” and “tax basis” are interchangeable. “Tax basis” is more commonly used in the 
United States. Similarly, “carrying amount” and “book value” refer to the same concept.

Reading 29 ■ Income Taxes 510
■■Specific revenues and expenses may be either recognized for accounting pur -
poses and not for tax purposes; or not recognized for accounting purposes but 
recognized for tax purposes;
■■The carrying amount and tax base of assets and/or liabilities may differ;
■■The deductibility of gains and losses of assets and liabilities may vary for 
accounting and income tax purposes;
■■Subject to tax rules, tax losses of prior years might be used to reduce taxable 
income in later years, resulting in differences in accounting and taxable income 
(tax loss carryforward); and
■■Adjustments of reported financial data from prior years might not be rec -
ognized equally for accounting and tax purposes or might be recognized in 
different periods.
2.2 Deferred Tax Assets and Liabilities
Deferred tax assets represent taxes that have been paid (or often the carrying forward 
of losses from previous periods) but have not yet been recognized on the income state -

ment. Deferred tax liabilities occur when financial accounting income tax expense is 
greater than regulatory income tax expense. Deferred tax assets and liabilities usually 
arise when accounting standards and tax authorities recognize the timing of taxes due 
at different times; for example, when a company uses accelerated depreciation when 
reporting to the tax authority (to increase expense and lower tax payments in the 
early years) but uses the straight-  line method on the financial statements. Although 
not similar in treatment on a year-  to- year basis (e.g., depreciation of 5 percent on a 
straight-  line basis may be permitted for accounting purposes whereas 10 percent is 
allowed for tax purposes) over the life of the asset, both approaches allow for the total 
cost of the asset to be depreciated (or amortized). Because these timing differences 
will eventually reverse or self-  correct over the course of the asset’s depreciable life, 
they are called “temporary differences. ”

Under IFRS, deferred tax assets and liabilities are always classified as noncurrent. 
Under US GAAP , however, deferred tax assets and liabilities are classified on the 
balance sheet as current and noncurrent based on the classification of the underlying 
asset or liability.
Any deferred tax asset or liability is based on temporary differences that result in 
an excess or a deficit amount paid for taxes, which the company expects to recover 
from future operations. Because taxes will be recoverable or payable at a future date, it 
is only a temporary difference and a deferred tax asset or liability is created. Changes 
in the deferred tax asset or liability on the balance sheet reflect the difference between 
the amounts recognized in the previous period and the current period. The changes 
in deferred tax assets and liabilities are added to income tax payable to determine the

company’s income tax expense (or credit) as it is reported on the income statement.
At the end of each fiscal year, deferred tax assets and liabilities are recalculated by 
comparing the tax bases and carrying amounts of the balance sheet items. Identified 
temporary differences should be assessed on whether the difference will result in 
future economic benefits. For example, Pinto Construction (a hypothetical com -
pany) depreciates equipment on a straight-  line basis of 10 percent per year. The tax 
authorities allow depreciation of 15 percent per year. At the end of the fiscal year, the 
carrying amount of the equipment for accounting purposes would be greater than the 
tax base of the equipment thus resulting in a temporary difference. A deferred tax 
item may only be created if it is not doubtful that the company will realize economic 
benefits in the future. In our example, the equipment is used in the core business of

Differences between Accounting Profit and Taxable Income 511
Pinto Construction. If the company is a going concern and stable, there should be no 
doubt that future economic benefits will result from the equipment and it would be 
appropriate to create the deferred tax item.
Should it be doubtful that future economic benefits will be realized from a tempo -
rary difference (such as Pinto Construction being under liquidation), the temporary 
difference will not lead to the creation of a deferred tax asset or liability. If a deferred 
tax asset or liability resulted in the past, but the criteria of economic benefits is not 
met on the current balance sheet date, then, under IFRS, an existing deferred tax 
asset or liability related to the item will be reversed. Under US GAAP , a valuation 
allowance is established. In assessing future economic benefits, much is left to the 
discretion of the auditor in assessing the temporary differences and the issue of future 
economic benefits.
EXAMPLE 1

EXAMPLE 1   
The following information pertains to a fictitious company, Reston Partners: 
Reston Partners Consolidated Income Statement
Period Ending 31 March (£ Millions) 2017 2016 2015
Revenue £40,000 £30,000 £25,000
Other net gains 2,000 0 0
Changes in inventories of finished goods 
and work in progress400 180 200
Raw materials and consumables used (5,700) (4,000) (8,000)
Depreciation expense (2,000) (2,000) (2,000)
Other expenses (6,000) (5,900) (4,500)
Interest expense (2,000) (3,000) (6,000)
Profit before tax £26,700 £15,280 £4,700
The financial performance and accounting profit of Reston Partners on 
this income statement is based on accounting principles appropriate for the 
jurisdiction in which Reston Partners operates. The principles used to calcu -
late accounting profit (profit before tax in the example above) may differ from 
the principles applied for tax purposes (the calculation of taxable income).

For illustrative purposes, however, assume that all income and expenses on 
the income statement are treated identically for tax and accounting purposes 
except  depreciation.
The depreciation is related to equipment owned by Reston Partners. For 
simplicity, assume that the equipment was purchased at the beginning of the 
2015 fiscal year. Depreciation should thus be calculated and expensed for the 
full year. Assume that accounting standards permit equipment to be depreciated 
on a straight-  line basis over a 10-  year period, whereas the tax standards in the 
jurisdiction specify that equipment should be depreciated on a straight-  line basis 
over a 7-  year period. For simplicity, assume a salvage value of £0 at the end of 
the equipment’s useful life. Both methods will result in the full depreciation of 
the asset over the respective tax or accounting life.
The equipment was originally purchased for £20,000. In accordance with

accounting standards, over the next 10 years the company will recognize annual 
depreciation of £2,000 (£20,000 ÷ 10) as an expense on its income statement 
and for the determination of accounting profit. For tax purposes, however, the 
company will recognize £2,857 (£20,000 ÷ 7) in depreciation each year. Each

Reading 29 ■ Income Taxes 512
fiscal year the depreciation expense related to the use of the equipment will, 
therefore, differ for tax and accounting purposes (tax base vs. carrying amount), 
resulting in a difference between accounting profit and taxable income.
The previous income statement reflects accounting profit (depreciation at 
£2,000 per year). The following table shows the taxable income for each fiscal year.
Taxable Income (£ Millions) 2017 2016 2015
Depreciation expense (2,857) (2,857) (2,857)
Taxable income £25,843 £14,423 £3,843
The carrying amount and tax base for the equipment is as follows:
(£ Millions) 2017 2016 2015
Equipment value for accounting purposes 
(carrying amount ) (depreciation of £2,000/

year)£14,000 £16,000 £18,000
Equipment value for tax purposes ( tax 
base ) (depreciation of £2,857/year)£11,429 £14,286 £17,143
Difference £2,571 £1,714 £857
At each balance sheet date, the tax base and carrying amount of all assets 
and liabilities must be determined. The income tax payable by Reston Partners 
will be based on the taxable income of each fiscal year. If a tax rate of 30 percent 
is assumed, then the income taxes payable for 2015, 2016, and 2017 are £1,153 
(30% × 3,843), £4,327 (30% × 14,423), and £7,753 (30% × 25,843).
Remember, though, that if the tax obligation is calculated based on account -
ing profits, it will differ because of the differences between the tax base and the 
carrying amount of equipment. The difference in each fiscal year is reflected 
in the table above. In each fiscal year the carrying amount of the equipment 
exceeds its tax base. For tax purposes, therefore, the asset tax base is less than

its carrying value under financial accounting principles. The difference results 
in a deferred tax liability.
Deferred tax liability £771 £514 £257
  (Difference between tax base and carrying amount) × tax rate
  2004: £(18,000 − 17,143) × 30% = 257
  2005: £(16,000 − 14,286) × 30% = 514
  2006: £(14,000 − 11,429) × 30% = 771
The comparison of the tax base and carrying amount of equipment shows 
what the deferred tax liability should be on a particular balance sheet date. In 
each fiscal year, only the change in the deferred tax liability should be included 
in the calculation of the income tax expense reported on the income statement 
prepared for accounting purposes.

Determining the Tax Base of Assets and Liabilities 513
On the income statement, the company’s income tax expense will be the sum 
of change in the deferred tax liability and the income tax payable.
Income tax payable (based on tax 
accounting)£7,753 £4,327 £1,153
Change in deferred tax liability 257 257 257
Income tax (based on financial accounting) £8,010 £4,584 £1,410
Note that because the different treatment of depreciation is a temporary 
difference, the income tax on the income statement is 30 percent of the account -
ing profit, although only a part is income tax payable and the rest is a deferred 
tax liability.
The consolidated income statement of Reston Partners including income 
tax is presented as follows:

Income tax (8,010) (4,584) (1,410)
Profit after tax £18,690 £10,696 £3,290
Any amount paid to the tax authorities will reduce the liability for income 
tax payable and be reflected on the statement of cash flows of the company.
DETERMINING THE TAX BASE OF ASSETS AND 
As mentioned in Section 2, temporary differences arise from a difference in the tax 
base and carrying amount of assets and liabilities. The tax base of an asset or liability 
is the amount attributed to the asset or liability for tax purposes, whereas the carrying 
amount is based on accounting principles. Such a difference is considered temporary 
if it is expected that the taxes will be recovered or payable at a future date.
3.1 Determining the Tax Base of an Asset

The tax base of an asset is the amount that will be deductible for tax purposes in 
future periods as the economic benefits become realized and the company recovers 
the carrying amount of the asset.3

Reading 29 ■ Income Taxes 514
For example, our previously mentioned Reston Partners (from Example 1) depre -
ciates equipment on a straight-  line basis at a rate of 10  percent per year. The tax 
authorities allow depreciation of approximately 15 percent per year. At the end of 
the fiscal year, the carrying amount of equipment for accounting purposes is greater 
than the asset tax base thus resulting in a temporary difference.
EXAMPLE 2   
Determining the Tax Base of an Asset
The following information pertains to Entiguan Sports, a hypothetical developer 
of products used to treat sports-  related injuries. (The treatment of items for 
accounting and tax purposes is based on fictitious accounting and tax standards 
and is not specific to a particular jurisdiction.) Calculate the tax base and car -
rying amount for each item.
1 Dividends receivable : On its balance sheet, Entiguan Sports reports divi -
dends of €1 million receivable from a subsidiary. Assume that dividends 
are not taxable.

2 Development costs : Entiguan Sports capitalized development costs of 
€3 million during the year. Entiguan amortized €500,000 of this amount 
during the year. For tax purposes amortization of 25 percent per year is 
allowed.
3 Research costs : Entiguan incurred €500,000 in research costs, which were 
all expensed in the current fiscal year for financial reporting purposes. 
Assume that applicable tax legislation requires research costs to be 
expensed over a four-  year period rather than all in one year.
4 Accounts receivable : Included on the income statement of Entiguan Sports 
is a provision for doubtful debt of €125,000. The accounts receivable 
amount reflected on the balance sheet, after taking the provision into 
account, amounts to €1,500,000. The tax authorities allow a deduction of 
25 percent of the gross amount for doubtful debt.
Solutions:
Carrying  
Amount (€) Tax Base (€)Temporary  
Difference (€)
1. Dividends receivable 1,000,000 1,000,000 0

2. Development costs 2,500,000 2,250,000 250,000
3. Research costs 0 375,000 (375,000)
4. Accounts receivable 1,500,000 1,218,750 281,250
Comments:
1 Dividends receivable : Although the dividends received are economic 
benefits from the subsidiary, we are assuming that dividends are not 
taxable. Therefore, the carrying amount equals the tax base for dividends 
receivable.
2 Development costs : First, we assume that development costs will generate 
economic benefits for Entiguan Sports. Therefore, it may be included as 
an asset on the balance sheet for the purposes of this example. Second, 
the amortization allowed by the tax authorities exceeds the amortization 
accounted for based on accounting rules. Therefore, the carrying amount

Determining the Tax Base of Assets and Liabilities 515
of the asset exceeds its tax base. The carrying amount is (€3,000,000 − 
€500,000) = €2,500,000 whereas the tax base is [€3,000,000 − (25% × 
€3,000,000)] = €2,250,000.
3 Research costs : We assume that research costs will result in future eco -
nomic benefits for the company. If this were not the case, creation of 
a deferred tax asset or liability would not be allowed. The tax base of 
research costs exceeds their carrying amount. The carrying amount is 
€0 because the full amount has been expensed for financial reporting 
purposes in the year in which it was incurred. Therefore, there would not 
have been a balance sheet item “Research costs” for tax purposes, and 
only a proportion may be deducted in the current fiscal year. The tax base 
of the asset is (€500,000 − €500,000/4) = €375,000.
4 Accounts receivable : The economic benefits that should have been received 
from accounts receivable have already been included in revenues included

in the calculation of the taxable income when the sales occurred. Because 
the receipt of a portion of the accounts receivable is doubtful, the provi -
sion is allowed. The provision, based on tax legislation, results in a greater 
amount allowed in the current fiscal year than would be the case under 
accounting principles. This results in the tax base of accounts receivable 
being lower than its carrying amount. Note that the example specifically 
states that the balance sheet amount for accounts receivable after the 
provision for accounting purposes amounts to €1,500,000. Therefore, 
accounts receivable before any provision was €1,500,000 + €125,000 = 
€1,625,000. The tax base is calculated as (€1,500,000 + €125,000) − [25% × 
(€1,500,000 + €125,000)] = €1,218,750.
3.2 Determining the Tax Base of a Liability
The tax base of a liability is the carrying amount of the liability less any amounts that 
will be deductible for tax purposes in the future. With respect to payments from

customers received in advance of providing the goods and services, the tax base of 
such a liability is the carrying amount less any amount of the revenue that will not 
be taxable in future. Keep in mind the following fundamental principle: In general, a 
company will recognize a deferred tax asset or liability when recovery/settlement of 
the carrying amount will affect future tax payments by either increasing or reducing 
the taxable profit. Remember, an analyst is not only evaluating the difference between 
the carrying amount and the tax base, but the relevance of that difference on future 
profits and losses and thus by implication future taxes.
IFRS offers specific guidelines with regard to revenue received in advance: IAS 12 
states that the tax base is the carrying amount less any amount of the revenue that 
will not be taxed at a future date. Under US GAAP , an analysis of the tax base would 
result in a similar outcome. The tax legislation within the jurisdiction will determine

the amount recognized on the income statement and whether the liability (revenue 
received in advance) will have a tax base greater than zero. This will depend on how 
tax legislation recognizes revenue received in advance.

Reading 29 ■ Income Taxes 516
EXAMPLE 3   
Determining the Tax Base of a Liability
The following information pertains to Entiguan Sports for the 2017 year-  end. 
The treatment of items for accounting and tax purposes is based on fictitious 
accounting and tax standards and is not specific to a particular jurisdiction. 
Calculate the tax base and carrying amount for each item.
1 Donations : Entiguan Sports made donations of €100,000 in the current 
fiscal year. The donations were expensed for financial reporting purposes, 
but are not tax deductible based on applicable tax legislation.
2 Interest received in advance : Entiguan Sports received in advance interest 
of €300,000. The interest is taxed because tax authorities recognize the 
interest to accrue to the company (part of taxable income) on the date of 
receipt.
3 Rent received in advance : Entiguan recognized €10 million for rent 
received in advance from a lessee for an unused warehouse building. Rent

received in advance is deferred for accounting purposes but taxed on a 
cash basis.
4 Loan : Entiguan Sports secured a long-  term loan for €550,000 in the 
current fiscal year. Interest is charged at 13.5 percent per annum and is 
payable at the end of each fiscal year.
Carrying  
Amount (€)Tax Base  
(€)Temporary  
1. Donations 0 0 0
2. Interest received in advance 300,000 0 (300,000)
3. Rent received in advance 10,000,000 0 (10,000,000)
4. Loan (capital) 550,000 550,000 0
Interest paid 0 0 0
Comments:
1 Donations : The amount of €100,000 was immediately expensed on 
Entiguan’s income statement; therefore, the carrying amount is €0. Tax 
legislation does not allow donations to be deducted for tax purposes, 
so the tax base of the donations equals the carrying amount. Note that 
while the carrying amount and tax base are the same, the difference in 
the treatment of donations for accounting and tax purposes (expensed

for accounting purposes, but not deductible for tax purposes) represents 
a permanent difference (a difference that will not be reversed in future). 
Permanent and temporary differences are elaborated on in Section 4 and 
it will refer to this particular case with an expanded explanation.
2 Interest received in advance : Based on the information provided, for tax 
purposes, interest is deemed to accrue to the company on the date of 
receipt. For tax purposes, it is thus irrelevant whether it is for the current 
or a future accounting period; it must be included in taxable income in 
the financial year received. Interest received in advance is, for accounting 
purposes though, included in the financial period in which it is deemed to 
have been earned. For this reason, the interest income received in advance

Determining the Tax Base of Assets and Liabilities 517
is a balance sheet liability. It was not included on the income statement 
because the income relates to a future financial year. Because the full 
€300,000 is included in taxable income in the current fiscal year, the tax 
base is €300,000 − 300,000 = €0. Note that although interest received in 
advance and rent received in advance are both taxed, the timing depends 
on how the particular item is treated in tax legislation.
3 Rent received in advance : The result is similar to interest received in 
advance. The carrying amount of rent received in advance would be 
€10,000,000 while the tax base is €0.
4 Loan : Repayment of the loan has no tax implications. The repayment of 
the capital amount does not constitute an income or expense. The inter -
est paid is included as an expense in the calculation of taxable income as 
well as accounting income. Therefore, the tax base and carrying amount

is €0. For clarity, the interest paid that would be included on the income 
statement for the year amounts to 13.5% × €550,000 = €74,250 if the loan 
was acquired at the beginning of the current fiscal year.
3.3 Changes in Income Tax Rates
The measurement of deferred tax assets and liabilities is based on current tax law. 
But if there are subsequent changes in tax laws or new income tax rates, existing 
deferred tax assets and liabilities must be adjusted for the effects of these changes. 
The resulting effects of the changes are also included in determining accounting profit 
in the period of change.
When income tax rates change, the deferred tax assets and liabilities are adjusted 
to the new tax rate. If income tax rates increase, deferred taxes (that is, the deferred 
tax assets and liabilities) will also increase. Likewise, if income tax rates decrease, 
deferred taxes will decrease. A decrease in tax rates decreases deferred tax liabilities,

which reduces future tax payments to the taxing authorities. A decrease in tax rates 
will also decrease deferred tax assets, which reduces their value toward the offset of 
future tax payments to the taxing authorities.
To illustrate the effect of a change in tax rate, consider Example 1 again. In that 
illustration, the timing difference that led to the recognition of a deferred tax liability 
for Reston Partners was attributable to differences in the method of depreciation and 
the related effects on the accounting carrying value and the asset tax base. The relevant 
information is restated below.
The carrying amount and tax base for the equipment is:
Equipment value for accounting purposes ( car-
rying amount ) (depreciation of £2,000/year)£14,000 £16,000 £18,000
Equipment value for tax purposes ( tax base ) 
(depreciation of £2,857/year)£11,429 £14,286 £17,143

At a 30 percent income tax rate, the deferred tax liability was then determined as 
follows:
  (Difference between tax base and carrying amount)
  2015: £(18,000 − 17,143) × 30% = £257

Reading 29 ■ Income Taxes 518
  2016: £(16,000 − 14,286) × 30% = £514
  2017: £(14,000 − 11,429) × 30% = £771
For this illustration, assume that the taxing authority has changed the income tax rate 
to 25 percent for 2017. Although the difference between the carrying amount and 
the tax base of the depreciable asset are the same, the deferred tax liability for 2017 
will be £643 (instead of £771 or a reduction of £128 in the liability). 2017: £(14,000 
− 11,429) × 25% = £643.
Reston Partners’ provision for income tax expense is also affected by the change 
in tax rates. Taxable income for 2017 will now be taxed at a rate of 25 percent. The 
benefit of the 2017 accelerated depreciation tax shield is now only £214 (£857 × 25%) 
instead of the previous £257 (a reduction of £43). In addition, the reduction in the 
beginning carrying value of the deferred tax liability for 2017 (the year of change)

further reduces the income tax expense for 2017. The reduction in income tax expense 
attributable to the change in tax rate is £85. 2017: (30% − 25%) × £1,714 = £85. Note 
that these two components together account for the reduction in the deferred tax 
liability (£43 + £85 = £128).
As may be seen from this discussion, changes in the income tax rate have an effect 
on a company’s deferred tax asset and liability carrying values as well as an effect on 
the measurement of income tax expense in the year of change. The analyst must thus 
note that proposed changes in tax law can have a quantifiable effect on these accounts 
(and any related financial ratios that are derived from them) if the proposed changes 
are subsequently enacted into law.
TEMPORARY AND PERMANENT DIFFERENCES 
BETWEEN TAXABLE AND ACCOUNTING PROFIT
Temporary differences arise from a difference between the tax base and the carrying 
amount of assets and liabilities. The creation of a deferred tax asset or liability from

a temporary difference is only possible if the difference reverses itself at some future 
date and to such an extent that the balance sheet item is expected to create future 
economic benefits for the company. IFRS and US GAAP both prescribe the balance 
sheet liability method for recognition of deferred tax. This balance sheet method 
focuses on the recognition of a deferred tax asset or liability should there be a tem -
porary difference between the carrying amount and tax base of balance sheet items.3
Permanent differences  are differences between tax and financial reporting of 
revenue (expenses) that will not  be reversed at some future date. Because they will 
not be reversed at a future date, these differences do not give rise to deferred tax. 
These items typically include
■■Income or expense items not allowed by tax legislation, and
■■Tax credits for some expenditures that directly reduce taxes.4

3 Previously, IAS 12 required recognition of deferred tax based on the deferred method (also known as the 
income statement method), which focused on timing differences. Timing differences are differences in the 
recognition of income and expenses for accounting and tax purposes that originate in one period and will 
reverse in a future period. Given the definition of timing differences, all timing differences are temporary 
differences, such as the different treatment of depreciation for tax and accounting purposes (although the 
timing is different with regard to the allowed depreciation for tax and accounting purposes, the asset will 
eventually be fully depreciated).

Temporary and Permanent Differences Between Taxable and Accounting Profit 519
Because no deferred tax item is created for permanent differences, all permanent dif -
ferences result in a difference between the company’s effective tax rate and statutory 
tax rate. The effective tax rate is also influenced by different statutory taxes should 
an entity conduct business in more than one tax jurisdiction. The formula for the 
reported effective tax rate is thus equal to:
 Reported effective tax rate = Income tax expense ÷ 
Pretax income (accounting profit) 
The net change in deferred tax during a reporting period is the difference between 
the balance of the deferred tax asset or liability for the current period and the balance 
of the previous period.
4.1 Taxable Temporary Differences
Temporary differences are further divided into two categories, namely taxable tempo -
rary differences and deductible temporary differences. Taxable temporary differences

are temporary differences that result in a taxable amount in a future period when 
determining the taxable profit as the balance sheet item is recovered or settled. Taxable 
temporary differences result in a deferred tax liability when the carrying amount of 
an asset exceeds its tax base and, in the case of a liability, when the tax base of the 
liability exceeds its carrying amount.
Under US GAAP , a deferred tax asset or liability is not recognized for unamortizable 
goodwill. Under IFRS, a deferred tax account is not recognized for goodwill arising 
in a business combination. Since goodwill is a residual, the recognition of a deferred 
tax liability would increase the carrying amount of goodwill. Discounting deferred 
tax assets or liabilities is generally not allowed for temporary differences related to 
business combinations as it is for other temporary differences.
IFRS provides an exemption (that is, deferred tax is not provided on the tempo -

rary difference) for the initial recognition of an asset or liability in a transaction that: 
a) is not a business combination (e.g., joint ventures, branches and unconsolidated 
investments); and b) affects neither accounting profit nor taxable profit at the time of 
the transaction. US GAAP does not provide an exemption for these circumstances.
As a simple example of a temporary difference with no recognition of deferred tax 
liability, assume that a fictitious company, Corporate International, a holding company 
of various leisure related businesses and holiday resorts, buys an interest in a hotel in 
the current financial year. The goodwill related to the transaction will be recognized 
on the financial statements, but the related tax liability will not, as it relates to the 
initial recognition of goodwill.
4.2 Deductible Temporary Differences
Deductible temporary differences  are temporary differences that result in a reduc -

tion or deduction of taxable income in a future period when the balance sheet item is 
recovered or settled. Deductible temporary differences result in a deferred tax asset 
when the tax base of an asset exceeds its carrying amount and, in the case of a lia -
bility, when the carrying amount of the liability exceeds its tax base. The recognition 
of a deferred tax asset is only allowed to the extent there is a reasonable expectation 
of future profits against which the asset or liability (that gave rise to the deferred tax 
asset) can be recovered or settled.

Reading 29 ■ Income Taxes 520
To determine the probability of sufficient future profits for utilization, one must 
consider the following: 1) Sufficient taxable temporary differences must exist that 
are related to the same tax authority and the same taxable entity; and 2) The taxable 
temporary differences that are expected to reverse in the same periods as expected 
for the reversal of the deductible temporary differences.
As with deferred tax liabilities, IFRS states that deferred tax assets should not be 
recognized in cases that would arise from the initial recognition of an asset or liabil -
ity in transactions that are not a business combination and when, at the time of the 
transaction, there is no impact on either accounting or taxable profit. Subsequent to 
initial recognition under IFRS and US GAAP , any deferred tax assets that arise from 
investments in subsidiaries, branches, associates, and interests in joint ventures are 
recognized as a deferred tax asset.

IFRS and US GAAP allow the creation of a deferred tax asset in the case of tax 
losses and tax credits. These two unique situations will be further elaborated on in 
Section 6. IAS 12 does not  allow the creation of a deferred tax asset arising from 
negative goodwill. Negative goodwill arises when the amount that an entity pays for 
an interest in a business is less than the net fair market value of the portion of assets 
and liabilities of the acquired company, based on the interest of the entity.
4.3 Examples of Taxable and Deductible Temporary 
Differences
Exhibit 1 summarizes how differences between the tax bases and carrying amounts 
of assets and liabilities give rise to deferred tax assets or deferred tax liabilities.
Exhibit 1   Treatment of Temporary Differences
Balance Sheet Item Carrying Amount vs. Tax Base Results in Deferred Tax Asset/Liability
Asset Carrying amount > tax base Deferred tax liability

Asset Carrying amount < tax base Deferred tax asset
Liability Carrying amount > tax base Deferred tax asset
Liability Carrying amount < tax base Deferred tax liability
EXAMPLE 4   
Taxable and Deductible Temporary Differences
Examples 2 and 3 illustrated how to calculate the tax base of assets and liabilities, 
respectively. Based on the information provided in Examples 2 and 3, indicate 
whether the difference in the tax base and carrying amount of the assets and 
liabilities are temporary or permanent differences and whether a deferred tax 
asset or liability will be recognized based on the difference identified.

Temporary and Permanent Differences Between Taxable and Accounting Profit 521
Solution to Example 2:
Carrying  
Difference (€)Will Result in Deferred  
Tax Asset/Liability
1. Dividends receivable 1,000,000 1,000,000 0 N/A
2. Development costs 2,500,000 2,250,000 250,000 Deferred tax liability
3. Research costs 0 375,000 (375,000) Deferred tax asset
4. Accounts receivable 1,500,000 1,218,750 281,250 Deferred tax liability
Example 2 included comments on the calculation of the carrying amount and 
tax base of the assets.
1 Dividends receivable : As a result of non-  taxability, the carrying amount 
equals the tax base of dividends receivable. This constitutes a permanent 
difference and will not result in the recognition of any deferred tax asset 
or liability. A temporary difference constitutes a difference that will, at 
some future date, be reversed. Although the timing of recognition is 
different for tax and accounting purposes, in the end the full carrying

amount will be expensed/recognized as income. A permanent difference 
will never be reversed. Based on tax legislation, dividends from a subsid -
iary are not recognized as income. Therefore, no amount will be reflected 
as dividend income when calculating the taxable income, and the tax 
base of dividends receivable must be the total amount received, namely 
€1,000,000. The taxable income and accounting profit will permanently 
differ with the amount of dividends receivable, even on future financial 
statements as an effect on the retained earnings reflected on the balance 
sheet.
2 Development costs : The difference between the carrying amount and tax 
base is a temporary difference that, in the future, will reverse. In this fiscal 
year, it will result in a deferred tax liability.
3 Research costs : The difference between the carrying amount and tax base 
is a temporary difference that results in a deferred tax asset. Remember

the explanation in Section 2 for deferred tax assets—a deferred tax asset 
arises because of an excess amount paid for taxes (when taxable income 
is greater than accounting profit), which is expected to be recovered from 
future operations. Based on accounting principles, the full amount was 
deducted resulting in a lower accounting profit, while the taxable income 
by implication, should be greater because of the lower amount expensed.
4 Accounts receivable : The difference between the carrying amount and tax 
base of the asset is a temporary difference that will result in a deferred tax 
liability.
Solution to Example 3:
Carrying  
1. Donations 0 0 0 N/A
2. Interest received in advance 300,000 0 (300,000) Deferred tax asset
3. Rent received in advance 10,000,000 0 (10,000,000) Deferred tax asset
4. Loan (capital) 550,000 550,000 0 N/A
 Interest paid 0 0 0 N/A

Reading 29 ■ Income Taxes 522
Example  3 included extensive comments on the calculation of the carrying 
amount and tax base of the liabilities.
1 Donations : It was assumed that tax legislation does not allow donations 
to be deducted for tax purposes. No temporary difference results from 
donations, and thus a deferred tax asset or liability will not be recognized. 
This constitutes a permanent difference.
2 Interest received in advance : Interest received in advance results in a 
temporary difference that gives rise to a deferred tax asset. A deferred 
tax asset arises because of an excess amount paid for taxes (when taxable 
income is greater than accounting profit), which is expected to be recov -
ered from future operations.
3 Rent received in advance : The difference between the carrying amount 
and tax base is a temporary difference that leads to the recognition of a 
deferred tax asset.
4 Loan : There are no temporary differences as a result of the loan or interest

paid, and thus no deferred tax item is recognized.
4.4 Temporary Differences at Initial Recognition of Assets and 
In some situations the carrying amount and tax base of a balance sheet item may vary 
at initial recognition. For example, a company may deduct a government grant from 
the initial carrying amount of an asset or liability that appears on the balance sheet. 
For tax purposes, such grants may not be deducted when determining the tax base 
of the balance sheet item. In such circumstances, the carrying amount of the asset 
or liability will be lower than its tax base. Differences in the tax base of an asset or 
liability as a result of the circumstances described above may not be recognized as 
deferred tax assets or liabilities.
For example, a government may offer grants to Small, Medium, and Micro 
Enterprises (SMME) in an attempt to assist these entrepreneurs in their endeavors 
that contribute to the country’s GDP and job creation. Assume that a particular grant

is offered for infrastructure needs (office furniture, property, plant, and equipment, 
etc.). In these circumstances, although the carrying amount will be lower than the 
tax base of the asset, the related deferred tax may not be recognized. As mentioned 
earlier, deferred tax assets and liabilities should not be recognized in cases that would 
arise from the initial recognition of an asset or liability in transactions that are not a 
business combination and when, at the time of the transaction, there is no impact on 
either accounting or taxable profit.
A deferred tax liability will also not be recognized at the initial recognition of 
goodwill. Although goodwill may be treated differently across tax jurisdictions, which 
may lead to differences in the carrying amount and tax base of goodwill, IAS 12 does 
not allow the recognition of such a deferred tax liability. Any impairment that an entity 
should, for accounting purposes, impose on goodwill will again result in a temporary

difference between its carrying amount and tax base. Any impairment that an entity 
should, for accounting purposes, impose on goodwill and if part of the goodwill is 
related to the initial recognition, that part of the difference in tax base and carrying 
amount should not result in any deferred taxation because the initial deferred tax 
liability was not recognized. Any future differences between the carrying amount 
and tax base as a result of amortization and the deductibility of a portion of goodwill 
constitute a temporary difference for which provision should be made.

Unused Tax Losses and Tax Credits 523
4.5 Business Combinations and Deferred Taxes
The fair value of assets and liabilities acquired in a business combination is determined 
on the acquisition date and may differ from the previous carrying amount. It is highly 
probable that the values of acquired intangible assets, including goodwill, would differ 
from their carrying amounts. This temporary difference will affect deferred taxes as 
well as the amount of goodwill recognized as a result of the acquisition.
4.6 Investments in Subsidiaries, Branches, Associates and 
Interests in Joint Ventures
Investments in subsidiaries, branches, associates and interests in joint ventures may 
lead to temporary differences on the consolidated versus the parent’s financial state -
ments. The related deferred tax liabilities as a result of temporary differences will be 
recognized unless both of the following criterion are satisfied:
■■The parent is in a position to control the timing of the future reversal of the

temporary difference, and
■■It is probable that the temporary difference will not reverse in the future.
With respect to deferred tax assets related to subsidiaries, branches, and associates 
and interests, deferred tax assets will only be recognized if the following criteria are 
satisfied:
■■The temporary difference will reverse in the future, and
■■Sufficient taxable profits exist against which the temporary difference can be 
used.
UNUSED TAX LOSSES AND TAX CREDITS
IAS 12 allows the recognition of unused tax losses and tax credits only to the extent 
that it is probable that in the future there will be taxable income against which the 
unused tax losses and credits can be applied. Under US GAAP , a deferred tax asset 
is recognized in full but is then reduced by a valuation allowance if it is more likely 
than not that some or all of the deferred tax asset will not be realized. The same 
requirements for creation of a deferred tax asset as a result of deductible temporary

differences also apply to unused tax losses and tax credits. The existence of tax losses 
may indicate that the entity cannot reasonably be expected to generate sufficient future 
taxable income. All other things held constant, the greater the history of tax losses, the 
greater the concern regarding the company’s ability to generate future taxable profits.
Should there be concerns about the company’s future profitability, then the deferred 
tax asset may not be recognized until it is realized. When assessing the probability 
that sufficient taxable profit will be generated in the future, the following criteria can 
serve as a guide:
■■If there is uncertainty as to the probability of future taxable profits, a deferred 
tax asset as a result of unused tax losses or tax credits is only recognized to the 
extent of the available taxable temporary differences;
■■Assess the probability that the entity will in fact generate future taxable profits

before the unused tax losses and/or credits expire pursuant to tax rules regard -
ing the carry forward of the unused tax losses;5

Reading 29 ■ Income Taxes 524
■■Verify that the above is with the same tax authority and based on the same 
taxable entity;
■■Determine whether the past tax losses were a result of specific circumstances 
that are unlikely to be repeated; and
■■Discover if tax planning opportunities are available to the entity that will result 
in future profits. These may include changes in tax legislation that is phased in 
over more than one financial period to the benefit of the entity.
It is imperative that the timing of taxable and deductible temporary differences also 
be considered before creating a deferred tax asset based on unused tax credits.
RECOGNITION AND MEASUREMENT OF CURRENT 
AND DEFERRED TAX
Current taxes payable or recoverable from tax authorities are based on the applicable 
tax rates at the balance sheet date. Deferred taxes should be measured at the tax rate 
that is expected to apply when the asset is realized or the liability settled. With respect

to the income tax for a current or prior period not yet paid, it is recognized as a tax 
liability until paid. Any amount paid in excess of any tax obligation is recognized as 
an asset. The income tax paid in excess or owed to tax authorities is separate from 
deferred taxes on the company’s balance sheet.
When measuring deferred taxes in a jurisdiction, there are different forms of tax -
ation such as income tax, capital gains tax (any capital gains made), or secondary tax 
on companies (tax payable on the dividends that a company declares) and possibly 
different tax bases for a balance sheet item (as in the case of government grants influ -
encing the tax base of an asset such as property). In assessing which tax laws should 
apply, it is dependent on how the related asset or liability will be settled. It would be 
prudent to use the tax rate and tax base that is consistent with how it is expected the 
tax base will be recovered or settled.

Although deferred tax assets and liabilities are related to temporary differences 
expected to be recovered or settled at some future date, neither are discounted to 
present value in determining the amounts to be booked. Both must be adjusted for 
changes in tax rates.
Deferred taxes as well as income taxes should always be recognized on the income 
statement of an entity unless it pertains to:
■■Taxes or deferred taxes charged directly to equity, or
■■A possible provision for deferred taxes relates to a business combination.
The carrying amount of the deferred tax assets and liabilities should also be 
assessed. The carrying amounts may change even though there may have been no 
change in temporary differences during the period evaluated. This can result from:
■■Changes in tax rates;
■■Reassessments of the recoverability of deferred tax assets; or
■■Changes in the expectations for how an asset will be recovered and what influ -

ences the deferred tax asset or liability.
All unrecognized deferred tax assets and liabilities must be reassessed at the balance 
sheet date and measured against the criteria of probable future economic benefits. If 
such a deferred asset is likely to be recovered, it may be appropriate to recognize the 
related deferred tax asset.6

Recognition and Measurement of Current and Deferred Tax 525
Different jurisdictions have different requirements for determining tax obligations 
that can range from different forms of taxation to different tax rates based on taxable 
income. When comparing financial statements of entities that conduct business in 
different jurisdictions subject to different tax legislation, the analyst should be cautious 
in reaching conclusions because of the potentially complex tax rules that may apply.
6.1 Recognition of a Valuation Allowance
Deferred tax assets must be assessed at each balance sheet date. If there is any doubt 
whether the deferral will be recovered, then the carrying amount should be reduced 
to the expected recoverable amount. Should circumstances subsequently change and 
suggest the future will lead to recovery of the deferral, the reduction may be reversed.
Under US GAAP , deferred tax assets are reduced by creating a valuation allowance.

Establishing a valuation allowance reduces the deferred tax asset and income in the 
period in which the allowance is established. Should circumstances change to such 
an extent that a deferred tax asset valuation allowance may be reduced, the reversal 
will increase the deferred tax asset and operating income. Because of the subjective 
judgment involved, an analyst should carefully scrutinize any such changes.
6.2 Recognition of Current and Deferred Tax Charged Directly 
to Equity
In general, IFRS and US GAAP require that the recognition of deferred tax liabilities 
and current income tax should be treated similarly to the asset or liability that gave 
rise to the deferred tax liability or income tax based on accounting treatment. Should 
an item that gives rise to a deferred tax liability be taken directly to equity, the same 
should hold true for the resulting deferred tax.
The following are examples of such items:

■■Revaluation of property, plant, and equipment (revaluations are not permissible 
under US GAAP);
■■Long-  term investments at fair value;
■■Changes in accounting policies;
■■Errors corrected against the opening balance of retained earnings;
■■Initial recognition of an equity component related to complex financial instru -
ments; and
■■Exchange rate differences arising from the currency translation procedures for 
foreign operations.
Whenever it is determined that a deferred tax liability will not be reversed, an 
adjustment should be made to the liability. The deferred tax liability will be reduced 
and the amount by which it is reduced should be taken directly to equity. Any deferred 
taxes related to a business combination must also be recognized in equity.
Depending on the items that gave rise to the deferred tax liabilities, an analyst should 
exercise judgment regarding whether the taxes should be included with deferred tax

liabilities or whether it should be taken directly to equity. It may be more appropriate 
simply to ignore deferred taxes.

Reading 29 ■ Income Taxes 526
EXAMPLE 5   
Taxes Charged Directly to Equity
The following information pertains to Anderson Company (a hypothetical com -
pany). A building owned by Anderson Company was originally purchased for 
€1,000,000 on 1 January 2015. For accounting purposes, buildings are depreciated 
at 5 percent a year on a straight-  line basis, and depreciation for tax purposes is 
10 percent a year on a straight-  line basis. On the first day of 2017, the building 
is revalued at €1,200,000. It is estimated that the remaining useful life of the 
building from the date of revaluation is 20 years. Important : For tax purposes 
the revaluation of the building is not recognized.
Based on the information provided, the following illustrates the difference 
in treatment of the building for accounting and tax purposes.
Carrying Amount  
of BuildingTax Base  
of Building
Balance on 1 January 2015 €1,000,000 €1,000,000
Depreciation 2015 50,000 100,000
  Balance on 31 December 2015 €950,000 €900,000

Balance on 31 December 2015 €950,000 €900,000
Depreciation 2016 50,000 100,000
  Balance on 31 December 2016 €900,000 €800,000
Revaluation on 1 January 2017 300,000 n/a
Balance on 1 January 2017 €1,200,000 €800,000
Depreciation 2017 60,000 100,000
  Balance on 31 December 2017 €1,140,000 €700,000
Accumulated depreciation
Balance on 1 January 2015 €0 €0
  Balance on 31 December 2015 €50,000 €100,000
  Balance on 31 December 2016 €100,000 €200,000
Revaluation at 1 January 2017 (100,000) n/a
Balance on 1 January 2017 €0 €200,000
  Balance on 30 November 2017 €60,000 €300,000
Carrying Amount Tax Base
On 31 December 2015 €950,000 €900,000
On 31 December 2016 €900,000 €800,000
On 31 December 2017 €1,140,000 €700,000
31 December 2015 : On 31 December 2015, different treatments for depre -
ciation expense result in a temporary difference that gives rise to a deferred

tax liability. The difference in the tax base and carrying amount of the building 
was a result of different depreciation amounts for tax and accounting purposes. 
Depreciation appears on the income statement. For this reason the deferred 
tax liability will also be reflected on the income statement. If we assume that 
the applicable tax rate in 2015 was 40 percent, then the resulting deferred tax 
liability will be 40% × (€950,000 − €900,000) = €20,000.

Recognition and Measurement of Current and Deferred Tax 527
31 December 2016 : As of 31 December 2016, the carrying amount of the 
building remains greater than the tax base. The temporary difference again 
gives rise to a deferred tax liability. Again, assuming the applicable tax rate to 
be 40 percent, the deferred tax liability from the building is 40% × (€900,000 − 
€800,000) = €40,000.
31 December 2017 : On 31 December 2017, the carrying amount of the build -
ing again exceeds the tax base. This is not the result of disposals or additions, 
but is a result of the revaluation at the beginning of the 2017 fiscal year and the 
different rates of depreciation. The deferred tax liability would seem to be 40% 
× (€1,140,000 − €700,000) = €176,000, but the treatment is different than it was 
for the 2015 and 2016. In 2017, revaluation of the building gave rise to a balance 
sheet equity account, namely “Revaluation Surplus” in the amount of €300,000, 
which is not recognized for tax purposes.

The deferred tax liability would usually have been calculated as follows:
2017 2016 2015
Deferred tax liability (closing balance at 
end of fiscal year)€176,000 €40,000 €20,000
(Difference between tax base and carrying 
amount)
2015: €(950,000 − 900,000) × 40% = 20,000
2016: €(900,000 − 800,000) × 40% = 40,000
2017: €(1,140,000 − 700,000) × 40% = 
176,000
The change in the deferred tax liability in 2015 is €20,000, in 2016: €20,000 
(€40,000 − €20,000) and, it would seem, in 2017: €136,000 (€176,000 − €40,000). 
In 2017, although it would seem that the balance for deferred tax liability should 
be €176,000, the revaluation is not recognized for tax purposes. Only the portion 
of the difference between the tax base and carrying amount that is not a result 
of the revaluation is recognized as giving rise to a deferred tax liability.
The effect of the revaluation surplus and the associated tax effects are

accounted for in a direct adjustment to equity. The revaluation surplus is reduced 
by the tax provision associated with the excess of the fair value over the carry 
value and it affects retained earnings (€300,000 × 40% = €120,000).
The deferred tax liability that should be reflected on the balance sheet is 
thus not €176,000 but only €56,000 (€176,000 − €120,000). Given the balance 
of deferred tax liability at the beginning of the 2017 fiscal year in the amount 
of €40,000, the change in the deferred tax liability is only €56,000 − €40,000 = 
€16,000.
In the future, at the end of each year, an amount equal to the depreciation 
as a result of the revaluation minus the deferred tax effect will be transferred 
from the revaluation reserve to retained earnings. In 2017 this will amount to a 
portion of depreciation resulting from the revaluation, €15,000 (€300,000 ÷ 20), 
minus the deferred tax effect of €6,000 (€15,000 × 40%), thus €9,000.

Reading 29 ■ Income Taxes 528
PRESENTATION AND DISCLOSURE
We will discuss the presentation and disclosure of income tax related information by 
way of example. The Consolidated Statements of Operations (Income Statements) and 
Consolidated Balance Sheets for Micron Technology (MU) are provided in Exhibits 
2 and 3, respectively. Exhibit 4 provides the income tax note disclosures for MU for 
the 2014, 2015, and 2016 fiscal years.
MU’s income tax provision (i.e., income tax expense) for fiscal year 2016 is $19 mil -
lion (see Exhibit 2). The income tax note disclosure in Exhibit 4 reconciles how the 
income tax provision was determined beginning with MU’s reported loss before taxes 
(shown in Exhibit 4 as $281 million for fiscal year 2016). The note disclosure then 
denotes the income tax provision for 2016 that is current ($28 million), which is then 
offset by the deferred tax benefit for foreign taxes ($9 million), for a net income tax

provision of $19 million. Exhibit 4 further shows a reconciliation of how the income 
tax provision was derived from the US federal statutory rate. Many public companies 
comply with this required disclosure by displaying the information in percentage terms, 
but MU has elected to provide the disclosure in absolute dollar amounts. From this 
knowledge, for 2016 we can see that the dollar amount shown for US federal income 
tax benefit at the statutory rate ($98 million) was determined by multiplying MU’s 
loss before taxes by the 35 percent US federal statutory rate ($281 × 0.35 = $98). 
In addition, the note disclosure in Exhibit 4 provides detailed information about 
the derivation of the deferred tax assets ($657 million for 2016) and deferred tax lia -
bilities ($2 million for 2016). These deferred tax assets are shown separately on MU’s 
consolidated balance sheet for fiscal year 2016 with noncurrent assets (see Exhibit 3),

while the deferred tax liabilities are included in other noncurrent liabilities (also see 
Exhibit 3).
Exhibit 2   Micron Technology, Inc. Consolidated Statements of Operations 
(Amounts in Millions except Per Share) 
For the Y ear Ended1 Sept. 
20163 Sept. 
201528 Aug. 
2014
Net sales $12,399 $16,192 $16,358
Cost of goods sold 9,894 10,977 10,921
  Gross margin 2,505 5,215 5,437
Selling, general and administrative 659 719 707
Research and development 1,617 1,540 1,371
Restructure and asset impairments 67 3 40
Other operating (income) expense, net (6) (45) 232
  Operating income 168 2,998 3,087
Interest income (expense), net (395) (336) (329)
Other non-  operating income (expense), 
net(54) (53) (25)
Income tax (provision) benefit (19) (157) (128)
Equity in net income (loss) of equity 
method investees25 447 474
Net income (loss) attributable to non -
controlling interests (1) — (34)
Net income (loss) attributable to Micron $(276) $2,899 $3,045
Earnings (loss) per share:7

Presentation and Disclosure 529
2014
  Basic $(0.27) $2.71 $2.87
  Diluted $(0.27) $2.47 $2.54
Number of shares used in per share 
calculations:
  Basic 1,036 1,070 1,060
  Diluted 1,036 1,170 1,198
Exhibit 3   Micron Technology, Inc. Consolidated Balance Sheets (Dollars in 
Millions) 
As of 1 Sept. 2016 3 Sept. 2015
Assets
Cash and equivalents $4,140 $2,287
Short-  term investments 258 1,234
Receivables 2,068 2,507
Inventories 2,889 2,340
Other current assets 140 228
  Total current assets 9,495 8,596
Long-  term marketable investments 414 2,113
Property, plant and equipment, net 14,686 10,554
Equity method investments 1,364 1,379
Intangible assets, net 464 449
Deferred tax assets 657 597
Other noncurrent assets 460 455
  Total assets $27,540 $24,143
Liabilities and shareholders’ equity
Accounts payable and accrued expenses $3,879 $2,611
Deferred income 200 205
Current debt 756 1,089
  Total current liabilities 4,835 3,905
Long-  term debt 9,154 6,252

Other noncurrent liabilities 623 698
  Total liabilities 14,612 10,855
Commitments and contingencies — —
Redeemable convertible notes — 49
Micron shareholder’s equity
Common stock of $0.10 par value, 3,000 
shares authorized, 1,094 shares issued 
and outstanding (1,084 as of September 3, 
2015)109 108
Additional capital 7,736 7,474
(continued)Exhibit 2   (Continued)

Reading 29 ■ Income Taxes 530
Retained earnings 5,299 5,588
Treasury stock, 54 shares held (45 as of 
September 3, 2015)(1,029) (881)
  Accumulated other comprehensive 
income (loss)(35) 13
  Total Micron shareholders’ equity 12,080 12,302
Noncontrolling interests in subsidiaries 848 937
Total equity 12,928 13,239
  Total liabilities and shareholders’ equity $27,540 $24,143
Exhibit 4   Micron Technology, Inc. Income Taxes Note to the Consolidated 
Financial Statements
Income (loss) before taxes and the income tax (provision) benefit consisted of 
(Millions) 2016 2015 2014
Income (loss) before income taxes, net 
income (loss) attributable to noncontrolling 
interests, and equity in net income (loss) of 
equity method investees
  Foreign $(353) $2,431 $2,619
  US 72 178 114
$(281) $2,609 $2,733
Income tax (provision) benefit:
  Current:
   Foreign $(27) $(93) $(46)
   State (1) (1) (2)
   US federal — 6 (3)
(28) (88) (51)
  Deferred:
   US federal 39 15 4
   State 2 1 —

Deferred:
   State 2 1 —
   Foreign (32) (85) (81)
9 (69) (77)
Income tax (provision) $(19) $(157) $(128)
The company’s income tax (provision) computed using the US federal statutory 
rate and the company’s income tax (provision) benefit is reconciled as follows:Exhibit 3   (Continued)

Presentation and Disclosure 531
US federal income tax (provision) ben -
efit at statutory rate$98 $(913) $(956)
Foreign tax rate differential (300) 515 474
Change in valuation allowance 63 260 544
Change in unrecognized tax benefits 52 (118) (152)
Tax credits 48 53 11
State taxes, net of federal benefit 3 19 (39)
Noncontrolling investment transactions — 57 —
Other 17 (30) (10)
Income tax (provision) benefit $(19) $(157) $(128)
State taxes reflect investment tax credits of $211 million as at 1 September 2016. 
Deferred income taxes reflect the net tax effects of temporary differences between 
the bases of assets and liabilities for financial reporting and income tax purposes. 
The company’s deferred tax assets and liabilities consist of the following as of 
the end of the periods shown below:
($ Millions) 2016 2015
Deferred tax assets:
  Net operating loss and tax credit carryforwards $3,014 $2,869
  Accrued salaries, wages, and benefits 142 143
  Other accrued liabilities 76 97

Other accrued liabilities 76 97
  Other 65 86
   Gross deferred assets 3,297 3,195
  Less valuation allowance (2,107) (2,051)
   Deferred tax assets, net of valuation allowance 1,190 1,144
Deferred tax liabilities:
  Debt discount (170) (207)
  Property, plant, and equipment (135) (2)
  Unremitted earnings on certain subsidiaries (121) (162)
  Product and process technology (81) (43)
  Other (28) (55)
   Deferred tax liabilities (535) (469)
Net deferred tax assets $655 $675
Reported as:
  Current deferred tax assets (included in other 
current assets)$— $104
  Deferred tax assets 657 597
Current deferred tax liabilities (included in accounts 
payable and accrued expenses)— (4)
  Deferred tax liabilities (included in other noncur -
rent liabilities)(2) (22)
   Net deferred tax assets $655 $675Exhibit 4   (Continued)

Reading 29 ■ Income Taxes 532
The company has a valuation allowance against substantially all of its US net 
deferred tax assets. As of 1 September 2016, the company had aggregate US tax net 
operating loss carryforwards of $3.9 billion and unused US tax credit carryforwards of 
$351 million. The company also has unused state tax net operating loss carryforwards 
of $1.9 billion and unused state tax credits of $211 million. The majority of the net 
operating loss carryforwards and the tax credit carryforwards expire between 2021 
to 2036 and 2022 to 2036, respectively.
The changes in valuation allowance of $63 million and $260 million in 2016 and 
2015, respectively, are primarily a result of uncertainties of realizing certain US and 
foreign net operating losses and certain tax credit carryforwards. 
Provision has been made for deferred taxes on undistributed earnings of non-  US 
subsidiaries to the extent that dividend payments from such companies are expected

to result in additional tax liability. Remaining undistributed earnings of $6.74 billion as 
of 1 September 2016 have been indefinitely reinvested. Determination of the amount 
of unrecognized deferred tax liability on these unremitted earnings is not practicable.
EXAMPLE 6   
Financial Analysis Example
Use the financial statement information and disclosures provided by MU in 
Exhibits 2, 3, and 4 to answer the following questions:
1 MU discloses a valuation allowance of $2,107 million (see Exhibit 4) 
against gross deferred assets of $3,297 million in 2016. Does the existence 
of this valuation allowance have any implications concerning MU’s future 
earning prospects?
2 How would MU’s deferred tax assets and deferred tax liabilities be 
affected if the federal statutory tax rate was changed to 32 percent? Would 
a change in the rate to 32 percent be beneficial to MU?
3 How would reported earnings have been affected if MU were not using a 
valuation allowance?

4 How would MU’s $3,014 million in net operating loss carryforwards in 
2016 (see Exhibit 4) affect the valuation that an acquiring company would 
be willing to offer?
5 Under what circumstances should the analyst consider MU’s deferred tax 
liability as debt or as equity? Under what circumstances should the analyst 
exclude MU’s deferred tax liability from both debt and equity when calcu -
lating the debt-  to- equity ratio?
According to Exhibit 4, MU’s deferred tax assets expire gradually until 2036 
(2027 to 2036 for the net operating loss carryforwards and 2022 to 2036 for the 
tax credit carryforwards).
Because the company is still relatively young, it is likely that most of these 
expirations occur toward the end of that period. Because cumulative US tax net 
operating loss carryforwards total $3.9 billion, the valuation allowance could 
imply that MU is not reasonably expected to earn $3.9 billion over the next 20

years. However, as we can see in Exhibit 2, MU earned a profit for 2015 and 
2014, thereby showing that the allowance could be adjusted downward if the 
company continues to generate profits in the future, and making it more likely 
than not that the deferred tax asset would be recognized.

Comparison of IFRS and US GAAP 533
MU’s total deferred tax assets exceed total deferred tax liabilities by $655 million. 
A change in the federal statutory tax rate to 32 percent from the current rate 
of 35 percent would make these net deferred assets less valuable. Also, because 
it is possible that the deferred tax asset valuation allowance could be adjusted 
downward in the future (see discussion to solution 1), the impact could be far 
greater in magnitude.
The disclosure in Exhibit 4 shows that the increase in the valuation allowance 
increased the income tax provision as reported on the income statement by 
$63 million in 2016. Additional potential reductions in the valuation allowance 
could similarly reduce reported income taxes (actual income taxes would not be 
affected by a valuation allowance established for financial reporting) in future 
years (see discussion to solution 1).

If an acquiring company is profitable, it may be able to use MU’s tax loss carry -
forwards to offset its own tax liabilities. The value to an acquirer would be the 
present value of the carryforwards, based on the acquirer’s tax rate and expected 
timing of realization. The higher the acquiring company’s tax rate, and the more 
profitable the acquirer, the sooner it would be able to benefit. Therefore, an 
acquirer with a high current tax rate would theoretically be willing to pay more 
than an acquirer with a lower tax rate.
The analyst should classify the deferred tax liability as debt if the liability is 
expected to reverse with subsequent tax payment. If the liability is not expected 
to reverse, there is no expectation of a cash outflow and the liability should be 
treated as equity. By way of example, future company losses may preclude the 
payment of any income taxes, or changes in tax laws could result in taxes that

are never paid. The deferred tax liability should be excluded from both debt and 
equity when both the amounts and timing of tax payments resulting from the 
reversals of temporary differences are uncertain.
COMPARISON OF IFRS AND US GAAP
As mentioned earlier, though IFRS and US GAAP follow similar conventions on 
many tax issues, there are some notable differences (such as revaluation). Exhibit 5 
summarizes many of the key similarities and differences between IFRS and US GAAP . 
Though both frameworks require a provision for deferred taxes, there are differences 
in the methodologies.
Exhibit 5   Deferred Income Tax Issues IFRS and US GAAP Methodology Similarities and Differences
Issue IFRS US GAAP
General considerations:
General approach Full provision. Similar to IFRS.8

Reading 29 ■ Income Taxes 534
Basis for deferred tax assets 
and liabilitiesTemporary differences—i.e., the difference 
between carrying amount and tax base of 
assets and liabilities (see exceptions below).Similar to IFRS.
Exceptions (i.e., deferred tax is 
not provided on the temporary 
difference)Nondeductible goodwill (that which is not 
deductible for tax purposes) does not give 
rise to taxable temporary differences.Similar to IFRS, except no initial recogni -
tion exemption and special requirements 
apply in computing deferred tax on lever -
aged leases.
Initial recognition of an asset or liability in 
a transaction that: a) is not a business com -
bination; and b) affects neither accounting 
profit nor taxable profit at the time of 
the transaction. Other amounts that do 
not have a tax consequence (commonly 
referred to as permanent differences) exist 
and depend on the tax rules and jurisdic -
tion of the entity.
Specific applications:

Revaluation of plant, property, 
and equipment and intangible 
assetsDeferred tax recognized in equity. Not applicable, as revaluation is prohibited.
Foreign nonmonetary assets/
liabilities when the tax report -
ing currency is not the func -
tional currencyDeferred tax is recognized on the dif -
ference between the carrying amount, 
determined using the historical rate of 
exchange, and the tax base, determined 
using the balance sheet date exchange rate.No deferred tax is recognized for differ -
ences related to assets and liabilities that 
are remeasured from local currency into 
the functional currency resulting from 
changes in exchange rates or indexing for 
tax purposes.
Investments in subsidiaries—
treatment of undistributed 
profitDeferred tax is recognized except when the 
parent is able to control the distribution of 
profit and it is probable that the temporary 
difference will not reverse in the foresee -

able future.Deferred tax is required on temporary 
differences arising after 1992 that relate 
to investments in domestic subsidiaries, 
unless such amounts can be recovered 
tax- free and the entity expects to use that 
method. No deferred taxes are recog -
nized on undistributed profits of foreign 
subsidiaries that meet the indefinite 
reversal criterion. Deferred tax assets may 
be recorded only to the extent they will 
reverse in the foreseeable future.
Investments in joint ventures—
venturer can control the sharing of profits 
and if it is probable that the temporary 
to investment in domestic corporate joint 
ventures. No deferred taxes are recognized 
on undistributed profits of foreign corpo -
rate joint ventures that meet the indefinite

rate joint ventures that meet the indefinite 
Investment in associates—
investor can control the sharing of profits 
and it is probable that the temporary dif -
ference will not reverse in the foreseeable 
future.Deferred tax is recognized on temporary 
differences relating to investments in 
investees.Exhibit 5   (Continued)

Comparison of IFRS and US GAAP 535
Uncertain tax positions Reflects the tax consequences that follow 
from the manner in which the entity 
expects, at the balance sheet date, to be 
paid to (recovered from) the taxation 
authorities.A tax benefit from an uncertain tax posi -
tion may be recognized only if it is “more 
likely than not” that the tax position is 
sustainable based on its technical merits. 
The tax position is measured as the largest 
amount of tax benefit that is greater than 
50 percent likely of being realized upon 
ultimate settlement.
Measurement of deferred tax:
Tax rates Tax rates and tax laws that have been 
enacted or substantively enacted.Use of substantively enacted rates is not 
permitted. Tax rate and tax laws used must 
have been enacted.
Recognition of deferred tax 
assetsA deferred tax asset is recognized if it 
is probable (more likely than not) that 
sufficient taxable profit will be available 
against which the temporary difference can

against which the temporary difference can 
be utilized.A deferred tax asset is recognized in full 
but is then reduced by a valuation allow -
ance if it is more likely than not that some 
or all of the deferred tax asset will not be 
realized.
Business combinations—Acquisitions:
Step-  up of acquired assets/lia -
bilities to fair valueDeferred tax is recorded unless the tax 
base of the asset is also stepped up.Similar to IFRS.
Previously unrecognized tax 
losses of the acquirerA deferred tax asset is recognized if the 
recognition criteria for the deferred tax 
asset are met as a result of the acquisition. 
Offsetting credit is recorded in income.Similar to IFRS, except the offsetting credit 
is recorded against goodwill.
Tax losses of the acquiree (ini -
tial recognition)Similar requirements as for the acquirer 
except the offsetting credit is recorded 
against goodwill.Similar to IFRS.
Subsequent resolution of 
income tax uncertainties in a 
business combinationIf the resolution is more than one year

after the year in which the business com -
bination occurred, the result is recognized 
on the income statement.The subsequent resolution of any tax 
uncertainty relating to a business combina -
tion is recorded against goodwill.
Subsequent recognition of 
deferred tax assets that were 
not “probable” at the time of 
the business combinationA deferred tax asset that was not consid -
ered probable at the time of the business 
combination but later becomes probable is 
recognized. The adjustment is to income 
tax expense with a corresponding adjust -
ment to goodwill. The income statement 
shows a debit to goodwill expense and a 
credit to income tax expense. There is no 
time limit for recognition of this deferred 
tax asset.The subsequent resolution of any tax 
tion is recorded first against goodwill, then 
noncurrent intangibles, and then income 
tax expense. There is no time limit for 
recognition of this deferred tax asset.
Presentation of deferred tax:

Offset of deferred tax assets 
and liabilitiesPermitted only when the entity has a 
legally enforceable right to offset and the 
balance relates to tax levied by the same 
authority.Similar to IFRS.
(continued)Exhibit 5   (Continued)

Reading 29 ■ Income Taxes 536
Current/noncurrent Deferred tax assets and liabilities are 
classified net as noncurrent on the balance 
sheet, with supplemental note disclosure 
for 1) the components of the temporary 
differences, and 2) amounts expected to be 
recovered within 12 months and more than 
12 months from the balance sheet date.Deferred tax assets and liabilities are either 
classified as current or noncurrent, based 
on the classification of the related non-  tax 
asset or liability for financial reporting. Tax 
assets or liabilities not associated with an 
underlying asset or liability are classified 
based on the expected reversal period.
Reconciliation of actual and 
expected tax expenseRequired. Computed by applying the 
applicable tax rates to accounting profit, 
disclosing also the basis on which the 
applicable tax rates are calculated.Required for public companies only. 
Calculated by applying the domestic fed -
eral statutory tax rates to pre-  tax income

eral statutory tax rates to pre-  tax income 
from continuing operations.
Sources:  IFRS: IAS 1, IAS 12, and IFRS 3.
US GAAP: FAS 109 and FIN 48.
“Similarities and Differences—A Comparison of IFRS and US GAAP , ” PricewaterhouseCoopers, October 2006.
SUMMARY
Income taxes are a significant category of expense for profitable companies. Analyzing 
income tax expenses is often difficult for the analyst because there are many permanent 
and temporary timing differences between the accounting that is used for income 
tax reporting and the accounting that is used for financial reporting on company 
financial statements. The financial statements and notes to the financial statements 
of a company provide important information that the analyst needs to assess financial 
performance and to compare a company’s financial performance with other companies. 
Key concepts in this reading are as follows:
■■Differences between the recognition of revenue and expenses for tax and

accounting purposes may result in taxable income differing from accounting 
profit. The discrepancy is a result of different treatments of certain income and 
expenditure items.
■■The tax base of an asset is the amount that will be deductible for tax purposes 
as an expense in the calculation of taxable income as the company expenses the 
tax basis of the asset. If the economic benefit will not be taxable, the tax base of 
the asset will be equal to the carrying amount of the asset.
■■The tax base of a liability is the carrying amount of the liability less any amounts 
that will be deductible for tax purposes in the future. With respect to revenue 
received in advance, the tax base of such a liability is the carrying amount less 
any amount of the revenue that will not be taxable in the future.
■■Temporary differences arise from recognition of differences in the tax base and 
carrying amount of assets and liabilities. The creation of a deferred tax asset or

liability as a result of a temporary difference will only be allowed if the differ -
ence reverses itself at some future date and to the extent that it is expected that 
the balance sheet item will create future economic benefits for the company.Exhibit 5   (Continued)

Summary 537
■■Permanent differences result in a difference in tax and financial reporting of 
revenue (expenses) that will not be reversed at some future date. Because it will 
not be reversed at a future date, these differences do not constitute temporary 
differences and do not give rise to a deferred tax asset or liability.
■■Current taxes payable or recoverable are based on the applicable tax rates on 
the balance sheet date of an entity; in contrast, deferred taxes should be mea -
sured at the tax rate that is expected to apply when the asset is realized or the 
liability settled.
■■All unrecognized deferred tax assets and liabilities must be reassessed on the 
appropriate balance sheet date and measured against their probable future 
economic benefit.
■■Deferred tax assets must be assessed for their prospective recoverability. If it 
is probable that they will not be recovered at all or partly, the carrying amount

should be reduced. Under US GAAP , this is done through the use of a valuation 
allowance.

Reading 29 ■ Income Taxes 538
1 Using the straight-  line method of depreciation for reporting purposes and 
accelerated depreciation for tax purposes would most likely  result in a:
A valuation allowance.
B deferred tax asset.
C temporary difference.
2 In early 2017 Sanborn Company must pay the tax authority €37,000 on the 
income it earned in 2016. This amount was recorded on the company’s 31 
December 2016 financial statements as:
A taxes payable.
B income tax expense.
C a deferred tax liability.
3 Income tax expense reported on a company’s income statement equals taxes 
payable, plus the net increase in:
A deferred tax assets and deferred tax liabilities.
B deferred tax assets, less the net increase in deferred tax liabilities.
C deferred tax liabilities, less the net increase in deferred tax assets.
4 Analysts should treat deferred tax liabilities that are expected to reverse as:
A equity.
C neither liabilities nor equity.

5 Deferred tax liabilities should be treated as equity when:
A they are not expected to reverse.
B the timing of tax payments is uncertain.
C the amount of tax payments is uncertain.
6 When both the timing and amount of tax payments are uncertain, analysts 
should treat deferred tax liabilities as:
A equity.
7 When accounting standards require recognition of an expense that is not per -
mitted under tax laws, the result is a:
A deferred tax liability.
B temporary difference.
C permanent difference.
8 When certain expenditures result in tax credits that directly reduce taxes, the 
company will most likely  record:
A a deferred tax asset.
B a deferred tax liability.
C no deferred tax asset or liability.
Practice Problems and Solutions adapted from: International Financial Statement Analysis , by Thomas R. 
Robinson, CFA, Jan Hendrik van Greuning, CFA, Elaine Henry, CFA, and Michael A. Broihahn, CFA. ©

Practice Problems 539
9 When accounting standards require an asset to be expensed immediately but 
tax rules require the item to be capitalized and amortized, the company will 
most likely  record:
10 A company incurs a capital expenditure that may be amortized over five years 
for accounting purposes, but over four years for tax purposes. The company will 
11 A company receives advance payments from customers that are immediately 
taxable but will not be recognized for accounting purposes until the company 
fulfills its obligation. The company will most likely  record:
12–14
Note I  
The components of earnings before income taxes are as follows ($ thousands):

Earnings before income taxes:
United States $ 88,157 $ 75,658 $ 59,973
Foreign 116,704 113,509 94,760
Total $204,861 $189,167 $154,733
The components of the provision for income taxes are as follows ($ thousands):
Income taxes
Current:
Federal $30,632 $22,031 $18,959
Foreign 28,140 27,961 22,263
$58,772 $49,992 $41,222
Deferred:
Federal ($4,752) $5,138 $2,336
Foreign 124 1,730 621

Reading 29 ■ Income Taxes 540
(4,628) 6,868 2,957
Total $54,144 $56,860 $44,179
12 In 2017, the company’s US GAAP income statement recorded a provision for 
income taxes closest  to:
A $30,632.
B $54,144.
C $58,772.
13 The company’s effective tax rate was highest  in:
A 2015.
B 2016.
C 2017.
14 Compared to the company’s effective tax rate on US income, its effective tax 
rate on foreign income was:
A lower in each year presented.
B higher in each year presented.
C higher in some periods and lower in others.
15 Zimt AG presents its financial statements in accordance with US GAAP . In 
2017, Zimt discloses a valuation allowance of $1,101 against total deferred 
tax assets of $19,201. In 2016, Zimt disclosed a valuation allowance of $1,325 
against total deferred tax assets of $17,325. The change in the valuation allow -
ance most likely  indicates that Zimt’s:
A deferred tax liabilities were reduced in 2017.
B expectations of future earning power has increased.

C expectations of future earning power has decreased.
16 Cinnamon, Inc. recorded a total deferred tax asset in 2017 of $12,301, offset by 
a $12,301 valuation allowance. Cinnamon most likely :
A fully utilized the deferred tax asset in 2017.
B has an equal amount of deferred tax assets and deferred tax liabilities.
C expects not to earn any taxable income before the deferred tax asset expires.
17–19
The tax effects of temporary differences that give rise to deferred tax assets and lia -
bilities are as follows ($ thousands):
2017 2016
Accrued expenses $8,613 $7,927
Tax credit and net operating loss carryforwards 2,288 2,554

Practice Problems 541
2017 2016
LIFO and inventory reserves 5,286 4,327
Other 2,664 2,109
Deferred tax assets 18,851 16,917
Valuation allowance (1,245) (1,360)
Net deferred tax assets $17,606 $15,557
Depreciation and amortization $(27,338) $(29,313)
Compensation and retirement plans (3,831) (8,963)
Other (1,470) (764)
Deferred tax liabilities (32,639) (39,040)
Net deferred tax liability ($15,033) ($23,483)
17 A reduction in the statutory tax rate would most likely  benefit the company’s:
A income statement and balance sheet.
B income statement but not the balance sheet.
C balance sheet but not the income statement.
18 If the valuation allowance had been the same in 2017 as it was in 2016, the 
company would have reported $115 higher :
B deferred tax assets.
C income tax expense.
19 Compared to the provision for income taxes in 2017, the company’s cash tax 
payments were:
A lower.
B higher.
C the same.
20–22

20–22
A company’s provision for income taxes resulted in effective tax rates attributable 
to loss from continuing operations before cumulative effect of change in accounting 
principles that varied from the statutory federal income tax rate of 34 percent, as 
summarized in the table below.
Y ear Ended 30 June 2017 2016 2015
Expected federal income tax expense 
(benefit) from continuing operations at 
34 percent($112,000) $768,000 $685,000
Expenses not deductible for income tax 
purposes357,000 32,000 51,000
State income taxes, net of federal benefit 132,000 22,000 100,000

Reading 29 ■ Income Taxes 542
Change in valuation allowance for 
deferred tax assets(150,000) (766,000) (754,000)
Income tax expense $227,000 $56,000 $82,000
20 In 2017, the company’s net income (loss) was closest  to:
A ($217,000).
B ($329,000).
C ($556,000).
21 The $357,000 adjustment in 2017 most likely  resulted in:
A an increase in deferred tax assets.
B an increase in deferred tax liabilities.
C no change to deferred tax assets and liabilities.
22 Over the three years presented, changes in the valuation allowance for deferred 
tax assets were most likely  indicative of:
A decreased prospect for future profitability.
B increased prospects for future profitability.
C assets being carried at a higher value than their tax base.

Solutions 543
SOLUTIONS
1 C is correct. Because the differences between tax and financial accounting will 
correct over time, the resulting deferred tax liability, for which the expense was 
charged to the income statement but the tax authority has not yet been paid, 
will be a temporary difference. A valuation allowance would only arise if there 
was doubt over the company’s ability to earn sufficient income in the future to 
require paying the tax.
2 A is correct. The taxes a company must pay in the immediate future are taxes 
payable.
3 C is correct. Higher reported tax expense relative to taxes paid will increase the 
deferred tax liability, whereas lower reported tax expense relative to taxes paid 
increases the deferred tax asset.
4 B is correct. If the liability is expected to reverse (and thus require a cash tax 
payment) the deferred tax represents a future liability.
5 A is correct. If the liability will not reverse, there will be no required tax pay -

ment in the future and the “liability” should be treated as equity.
6 C is correct. The deferred tax liability should be excluded from both debt and 
7 C is correct. Accounting items that are not deductible for tax purposes will not 
be reversed and thus result in permanent differences.
8 C is correct. Tax credits that directly reduce taxes are a permanent difference, 
and permanent differences do not give rise to deferred tax.
9 A is correct. The capitalization will result in an asset with a positive tax base 
and zero carrying value. The amortization means the difference is temporary. 
Because there is a temporary difference on an asset resulting in a higher tax 
base than carrying value, a deferred tax asset is created.
10 B is correct. The difference is temporary, and the tax base will be lower

(because of more rapid amortization) than the carrying value of the asset. The 
result will be a deferred tax liability.
11 A is correct. The advances represent a liability for the company. The carrying 
value of the liability exceeds the tax base (which is now zero). A deferred tax 
asset arises when the carrying value of a liability exceeds its tax base.
12 B is correct. The income tax provision in 2017 was $54,144, consisting of 
$58,772 in current income taxes, of which $4,628 were deferred.
13 B is correct. The effective tax rate of 30.1 percent ($56,860/$189,167) was higher 
than the effective rates in 2015 and 2017.
14 A is correct. In 2017 the effective tax rate on foreign operations was 24.2 per -
cent [($28,140 + $124)/$116,704] and the effective US tax rate was [($30,632 − 
$4,752)/$88,157] = 29.4 percent. In 2016 the effective tax rate on foreign oper -
ations was 26.2 percent and the US rate was 35.9 percent. In 2015 the foreign 
rate was 24.1 percent and the US rate was 35.5 percent.

15 B is correct. The valuation allowance is taken against deferred tax assets to 
represent uncertainty that future taxable income will be sufficient to fully utilize 
the assets. By decreasing the allowance, Zimt is signaling greater likelihood that 
future earnings will be offset by the deferred tax asset.

Reading 29 ■ Income Taxes 544
16 C is correct. The valuation allowance is taken when the company will “more 
likely than not” fail to earn sufficient income to offset the deferred tax asset. 
Because the valuation allowance equals the asset, by extension the company 
expects no taxable income prior to the expiration of the deferred tax assets.
17 A is correct. A lower tax rate would increase net income on the income state -
ment, and because the company has a net deferred tax liability, the net liability 
position on the balance sheet would also improve (be smaller).
18 C is correct. The reduction in the valuation allowance resulted in a correspond -
ing reduction in the income tax provision.
19 B is correct. The net deferred tax liability was smaller in 2017 than it was in 
2016, indicating that in addition to meeting the tax payments provided for in 
2017 the company also paid taxes that had been deferred in prior periods.

20 C is correct. The income tax provision at the statutory rate of 34 percent 
is a benefit of $112,000, suggesting that the pre-  tax income was a loss of 
$112,000/0.34 = ($329,412). The income tax provision was $227,000. ($329,412) 
− $227,000 = ($556,412).
21 C is correct. Accounting expenses that are not deductible for tax purposes 
result in a permanent difference, and thus do not give rise to deferred taxes.
22 B is correct. Over the three-  year period, changes in the valuation allowance 
reduced cumulative income taxes by $1,670,000. The reductions to the valuation 
allowance were a result of the company being “more likely than not” to earn suf -
ficient taxable income to offset the deferred tax assets.

Non-  Current (Long-  Term) Liabilities
by Elizabeth A. Gordon, PhD, MBA, CPA, and Elaine Henry, PhD, CFA
Elizabeth A. Gordon, PhD, MBA, CPA, is at Temple University (USA). Elaine Henry, PhD, 
CFA, is at Stevens Institute of Technology (USA).
Mastery The candidate should be able to
a. determine the initial recognition, initial measurement and 
subsequent measurement of bonds;
b. describe the effective interest method and calculate interest 
expense, amortisation of bond discounts/premiums, and interest 
payments;
c. explain the derecognition of debt;
d. describe the role of debt covenants in protecting creditors;
e. describe the financial statement presentation of and disclosures 
relating to debt;
f. explain motivations for leasing assets instead of purchasing them;
g. distinguish between a finance lease and an operating lease from 
the perspectives of the lessor and the lessee;
h. determine the initial recognition, initial measurement, and 
subsequent measurement of finance leases;

i. compare the disclosures relating to finance and operating leases;
j. compare the presentation and disclosure of defined contribution 
and defined benefit pension plans;
k. calculate and interpret leverage and coverage ratios.REA dINg
30
for the actual reference numbers.

readings.

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 546
A non-  current liability (long-  term liability) broadly represents a probable sacrifice of 
economic benefits in periods generally greater than one year in the future. Common 
types of non-  current liabilities  reported in a company’s financial statements include 
long-  term debt (e.g., bonds payable, long-  term notes payable), finance leases, pension 
liabilities, and deferred tax liabilities. This reading focuses on bonds payable and leases. 
Pension liabilities are also introduced.
This reading is organised as follows. Section 2 describes and illustrates the account -
ing for long-  term bonds, including the issuance of bonds, the recording of interest 
expense and interest payments, the amortisation of any discount or premium, the 
derecognition of debt, and the disclosure of information about debt financings. In 
discussing the financial statement effects and analyses of these issues, we focus on

solvency and coverage ratios. Section 3 discusses leases, including benefits of leasing 
and accounting for leases by both lessees and lessors. Section 4 provides an intro -
duction to pension accounting and the resulting non-  current liabilities. Section 5 
discusses the use of leverage and coverage ratios in evaluating solvency. Section 6 
concludes and summarises the reading. Practice problems in the CFA Institute format 
are included after the reading.
BONDS PAYABLE
This section discusses accounting for bonds payable—a common form of long-  term 
debt. In some contexts (e.g., some government debt obligations), the word “bond” is 
used only for a debt security with a maturity of 10 years or longer; “note” refers to a 
debt security with a maturity between 2 and 10 years; and “bill” refers to a debt security 
with a maturity of less than 2 years. In this reading, we use the terms bond and note 
interchangeably because the accounting treatments of bonds payable and long-  term

notes payable are similar. In the following sections, we discuss bond issuance (initial 
recognition and measurement); bond amortisation, interest expense, and interest pay -
ments; market rates and fair value (subsequent measurement); repayment of bonds, 
including retirements and redemptions (derecognition); and other issues concerning 
disclosures related to debt. We also discuss debt covenants.
2.1 Accounting for Bond Issuance
Bonds are contractual promises made by a company (or other borrowing entity) to 
pay cash in the future to its lenders (i.e., bondholders) in exchange for receiving cash 
in the present. The terms of a bond contract are contained in a document called an 
indenture. The cash or sales proceeds received by a company when it issues bonds is 
based on the value (price) of the bonds at the time of issue; the price at the time of 
issue is determined as the present value of the future cash payments promised by the 
company in the bond agreement.

Ordinarily, bonds contain promises of two types of future cash payments: 1) the 
face value of the bonds, and 2) periodic interest payments. The face value  of the bonds 
is the amount of cash payable by the company to the bondholders when the bonds 
mature. The face value is also referred to as the principal, par value, stated value, or 
maturity value. The date of maturity of the bonds (the date on which the face value 
is paid to bondholders) is stated in the bond contract and typically is a number of 
years in the future. Periodic interest payments are made based on the interest rate 
promised in the bond contract applied to the bonds’ face value. The interest rate 1
2

Bonds Payable 547
promised in the contract, which is the rate used to calculate the periodic interest 
payments, is referred to as the coupon rate , nominal rate, or stated rate. Similarly, 
the periodic interest payment is referred to as the coupon payment or simply the 
coupon. For fixed rate bonds (the primary focus of our discussion here), the coupon 
rate remains unchanged throughout the life of the bonds. The frequency with which 
interest payments are made is also stated in the bond contract. For example, bonds 
paying interest semi-  annually will make two interest payments per year.1
The future cash payments are discounted to the present to arrive at the market 
value of the bonds. The market rate of interest  is the rate demanded by purchasers 
of the bonds given the risks associated with future cash payment obligations of the 
particular bond issue. The market rate of interest at the time of issue often differs

from the coupon rate because of interest rate fluctuations that occur between the time 
the issuer establishes the coupon rate and the day the bonds are actually available to 
investors. If the market rate of interest when the bonds are issued equals the coupon 
rate, the market value (price) of the bonds will equal the face value of the bonds. Thus, 
ignoring issuance costs, the issuing company will receive sales proceeds (cash) equal 
to the face value of the bonds. When a bond is issued at a price equal to its face value, 
the bond is said to have been issued at par.
If the coupon rate when the bonds are issued is higher than the market rate, the 
market value of the bonds—and thus the amount of cash the company receives—will 
be higher than the face value of the bonds. In other words, the bonds will sell at a 
premium to face value because they are offering an attractive coupon rate compared 
to current market rates. If the coupon rate is lower than the market rate, the market

value and thus the sale proceeds from the bonds will be less than the face value of 
the bonds; the bond will sell at a discount to face value. The market rate at the time 
of issuance is the effective interest rate  or borrowing rate that the company incurs 
on the debt. The effective interest rate is the discount rate that equates the present 
value of the two types of promised future cash payments to their selling price. For the 
issuing company, interest expense reported for the bonds in the financial statements 
is based on the effective interest rate.
On the issuing company’s statement of cash flows, the cash received (sales proceeds) 
from issuing bonds is reported as a financing cash inflow. On the issuing company’s 
balance sheet at the time of issue, bonds payable normally are measured and reported 
at the sales proceeds. In other words, the bonds payable are initially reported at the 
face value of the bonds minus any discount, or plus any premium.

Using a three-  step approach, the following two examples illustrate accounting for 
bonds issued at face value and then accounting for bonds issued at a discount to face 
value. Accounting for bonds issued at a premium involves steps similar to the steps 
followed in the examples below. For simplicity, these examples assume a flat interest 
rate yield curve (i.e., that the market rate of interest is the same for each period). 
More-  precise bond valuations use the interest rate applicable to each time period in 
which a payment of interest or principal occurs.
1 Interest rates are stated on an annual basis regardless of the frequency of payment.

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 548
EXAMPLE 1   
Bonds Issued at Face Value
Debond Corp. (a hypothetical company) issues £1,000,000 worth of five-  year 
bonds, dated 1 January 2010, when the market interest rate on bonds of compa -
rable risk and terms is 5 percent per annum. The bonds pay 5 percent interest 
annually on 31 December. What are the sales proceeds of the bonds when issued, 
and how is the issuance reflected in the financial statements?
Solution:
Calculating the value of the bonds at issuance and thus the sales proceeds 
involves three steps: 1) identifying key features of the bonds and the market 
interest rate, 2) determining future cash outflows, and 3) discounting the future 
cash flows to the present.
First, identify key features of the bonds and the market interest rate necessary 
to determine sales proceeds:
Face value (principal): £1,000,000
Time to maturity: 5 years
Coupon rate: 5%
Market rate at issuance: 5%
Frequency of interest 
payments:annual

Interest payment: £50,000 Each annual interest payment is the face value times the coupon 
rate (£1,000,000 × 5%). If interest is paid other than annually, 
adjust the interest rate to match the interest payment period (e.g., 
divide the annual coupon rate by two for semi-  annual interest 
payments).
Second, determine future cash outflows. Debond will pay bondholders 
£1,000,000 when the bonds mature in five years. On 31 December of each year 
until the bonds mature, Debond will make an interest payment of £50,000.
Third, sum the present value2 of the future payments of interest and principal 
to obtain the value of the bonds and thus the sales proceeds from issuing the 
bonds. In this example, the sum is £1,000,000 = (£216,474 + £783,526).
DateInterest 
PaymentPresent Value 
at Market Rate  
(5%)Face Value 
(5%)Total  
Present Value
31 December 2010 £50,000 £47,619
31 December 2011 50,000 45,352
31 December 2012 50,000 43,192

31 December 2013 50,000 41,135
31 December 2014 50,000 39,176 £1,000,000 £783,526
Total £216,474 £783,526 £1,000,000
Sales Proceeds
2 Alternative ways to calculate the present value include 1) to treat the five annual interest payments as 
an annuity and use the formula for finding the present value of an annuity and then add the present value 
of the principal payment, or 2) to use a financial calculator to calculate the total present value.

Bonds Payable 549
The sales proceeds of the bonds when issued are £1,000,000. There is no 
discount or premium because these bonds are issued at face value. The issu -
ance is reflected on the balance sheet as an increase of cash and an increase in 
a long-  term liability, bonds payable, of £1,000,000. The issuance is reflected in 
the statement of cash flows as a financing cash inflow of £1,000,000.
The price of bonds is often expressed as a percentage of face value. For example, 
the price of bonds issued at par, as in Example  1, is 100 (i.e., 100  percent of face 
value). In Example 2, in which bonds are issued at a discount, the price is 95.79 (i.e., 
95.79 percent of face value).
EXAMPLE 2   
Bonds Issued at a Discount
Debond Corp. issues £1,000,000 worth of five-  year bonds, dated 1 January 2010, 
when the market interest rate on bonds of comparable risk and terms is 6 per -
cent. The bonds pay 5 percent interest annually on 31 December. What are the

sales proceeds of the bonds when issued, and how is the issuance reflected in 
the financial statements?
Solution:
The key features of the bonds and the market interest rate are:
Market rate at issuance: 6%
Frequency of interest payments: annual
Interest payment: £50,000 Each annual interest payment is the face value 
times the coupon rate (£1,000,000 × 5%).
The future cash outflows (interest payments and face value payment), the 
present value of the future cash outflows, and the total present value are:
(6%)Face Value 
(6%)Total  
31 December 2010 £50,000 £47,170
31 December 2011 50,000 44,500
31 December 2012 50,000 41,981
31 December 2013 50,000 39,605
31 December 2014 50,000 37,363 £1,000,000 £747,258
Total £210,618 £747,258 £957,876
   Sales Proceeds
The sales proceeds of the bonds when issued are £957,876. The bonds sell

at a discount of £42,124  = (£1,000,000 – £957,876) because the market rate 
when the bonds are issued (6 percent) is greater than the bonds’ coupon rate 
(5  percent). The issuance is reflected on the balance sheet as an increase of 
cash and an increase in a long-  term liability, bonds payable, of £957,876. The

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 550
bonds payable is composed of the face value of £1,000,000 minus a discount of 
£42,124. The issuance is reflected in the statement of cash flows as a financing 
cash inflow of £957,876.
In Example 2, the bonds were issued at a discount to face value because the bonds’ 
coupon rate of 5 percent was less than the market rate. Bonds are issued at a premium 
to face value when the bonds’ coupon rate exceeds the market rate.
Bonds issued with a coupon rate of zero (zero-  coupon bonds) are always issued 
at a discount to face value. The value of zero-  coupon bonds is based on the present 
value of the principal payment only because there are no periodic interest payments.
Such issuance costs as printing, legal fees, commissions, and other types of charges 
are costs incurred when bonds are issued. Under International Financial Reporting 
Standards (IFRS), all debt issuance costs are included in the measurement of the lia -

bility, bonds payable. Under US generally accepted accounting principles (US GAAP), 
companies generally used to show these debt issuance costs as an asset (a deferred 
charge), which was amortised on a straight-  line basis to the relevant expense (e.g., legal 
fees) over the life of the bonds. Under US GAAP , debt issuance costs are deducted 
from the related debt liability. Companies reporting under US GAAP may still report 
debt issuance costs for lines of credit as an asset because the SEC indicated that it 
would not object to this treatment. Under IFRS and US GAAP , cash outflows related 
to bond issuance costs are included in the financing section of the statement of cash 
flows, usually netted against bond proceeds.
2.2 Accounting for Bond Amortisation, Interest Expense, and 
Interest Payments
In this section, we discuss accounting and reporting for bonds after they are issued. 
Most companies maintain the historical cost (sales proceeds) of the bonds after

issuance, and they amortise any discount or premium over the life of the bond. The 
amount reported on the balance sheet for bonds is thus the historical cost plus or 
minus the cumulative amortisation, which is referred to as amortised cost. Companies 
also have the option to report the bonds at their current fair values.
The rationale for reporting the bonds at amortised historical cost is the company’s 
intention to retain the debt until it matures. Therefore, changes in the underlying 
economic value of the debt are not relevant from the issuing company’s perspective. 
From an investor’s perspective, however, analysis of a company’s underlying economic 
liabilities and solvency is more difficult when debt is reported at amortised historical 
cost. The rest of this section illustrates accounting and reporting of bonds at amortised 
historical cost. Section 2.3 discusses the alternative of reporting bonds at fair value.

Companies initially report bonds as a liability on their balance sheet at the amount 
of the sales proceeds net of issuance costs under both IFRS and US GAAP , ignoring 
any bond issuance costs. The amount at which bonds are reported on the company’s 
balance sheet is referred to as the carrying amount, carrying value, book value, or net 
book value. If the bonds are issued at par, the initial carrying amount will be identical 
to the face value, and usually the carrying amount will not change over the life of the 
bonds.3 For bonds issued at face value, the amount of periodic interest expense  will 
be the same as the amount of periodic interest payment  to bondholders.
If, however, the market rate differs from the bonds’ coupon rate at issuance such 
that the bonds are issued at a premium or discount, the premium or discount is amor -
tised systematically over the life of the bonds as a component of interest expense. For

3 If a company reports debt at fair value, rather than amortised cost, the carrying value may change.

Bonds Payable 551
bonds issued at a premium to face value, the carrying amount of the bonds is initially 
greater than the face value. As the premium is amortised, the carrying amount (amor -
tised cost) of the bonds will decrease to the face value. The reported interest expense 
will be less than the coupon payment. For bonds issued at a discount to face value, 
the carrying amount of the bonds is initially less than the face value. As the discount 
is amortised, the carrying amount (amortised cost) of the bonds will increase to the 
face value. The reported interest expense will be higher than the coupon payment.
The accounting treatment for bonds issued at a discount reflects the fact that the 
company essentially paid some of its borrowing costs at issuance by selling its bonds 
at a discount. Rather than there being an actual cash transfer in the future, this “pay -
ment” was made in the form of accepting less than the face value for the bonds at the

date of issuance. The remaining borrowing cost occurs as a cash interest payment 
to investors each period. The total interest expense reflects both components of the 
borrowing cost: the periodic interest payments plus the amortisation of the discount. 
The accounting treatment for bonds issued at a premium reflects the fact that the 
company essentially received a reduction on its borrowing costs at issuance by selling 
its bonds at a premium. Rather than there being an actual reduced cash transfer in the 
future, this “reduction” was made in the form of receiving more than face value for the 
bonds at the date of issuance. The total interest expense reflects both components of 
the borrowing cost: the periodic interest payments less the amortisation of the pre -
mium. When the bonds mature, the carrying amount will be equal to the face value 
regardless of whether the bonds were issued at face value, a discount, or a premium.

Two methods for amortising the premium or discount of bonds that were issued 
at a price other than par are the effective interest rate method and the straight-  line 
method. The effective interest rate method is required under IFRS and preferred 
under US GAAP because it better reflects the economic substance of the transaction. 
The effective interest rate method applies the market rate in effect when the bonds 
were issued (historical market rate or effective interest rate) to the current amortised 
cost (carrying amount) of the bonds to obtain interest expense for the period. The 
difference between the interest expense (based on the effective interest rate and 
amortised cost) and the interest payment (based on the coupon rate and face value) 
is the amortisation  of the discount or premium. The straight-  line method of amor -
tisation evenly amortises the premium or discount over the life of the bond, similar

to straight-  line depreciation on long-  lived assets. Under either method, as the bond 
approaches maturity, the amortised cost approaches face value.
Example 3 illustrates both methods of amortisation for bonds issued at a discount. 
Example 4 shows amortisation for bonds issued at a premium.
EXAMPLE 3   
Amortising a Bond Discount
Debond Corp. issues £1,000,000 face value of five-  year bonds, dated 1 January 2010, 
when the market interest rate is 6 percent. The sales proceeds are £957,876. The 
bonds pay 5 percent interest annually on 31 December.
1 What is the interest payment  on the bonds each year?
2 What amount of interest expense  on the bonds would be reported in 2010 
and 2011 using the effective interest rate method?
3 Determine the reported value of the bonds (i.e., the carrying amount) at 
31 December 2010 and 2011, assuming the effective interest rate method 
is used to amortise the discount.
4 What amount of interest expense on the bonds would be reported under

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 552
The interest payment equals £50,000 annually (£1,000,000 × 5%).
The sales proceeds of £957,876 are less than the face value of £1,000,000; the 
bonds were issued at a discount of £42,124. The bonds are initially reported 
as a long-  term liability, bonds payable, of £957,876, which comprises the face 
value of £1,000,000 minus a discount of £42,124. The discount is amortised over 
time, ultimately, increasing the carrying amount (amortised cost) to face value.
Under the effective interest rate method, interest expense on the bonds is 
calculated as the bonds’ carrying amount times the market rate in effect when the 
bonds are issued (effective interest rate). For 2010, interest expense is £57,473 = 
(£957,876 × 6%). The amount of the discount amortised in 2010 is the difference 
between the interest expense of £57,473 and the interest payment of £50,000 (i.e.,

£7,473). The bonds’ carrying amount increases by the discount amortisation; 
at 31 December 2010, the bonds’ carrying amount is £965,349 (beginning bal -
ance of £957,876 plus £7,473 discount amortisation). At this point, the carrying 
amount reflects a remaining unamortised discount of £34,651 (£42,124 discount 
at issuance minus £7,473 amortised).
For 2011, interest expense is £57,921 = (£965,349 × 6%), the carrying amount 
of the bonds on 1 January 2011 times the effective interest rate. The amount of 
the discount amortised in 2011 is the difference between the interest expense of 
£57,921 and the interest payment of £50,000 (i.e., £7,921). At 31 December 2011, 
the bonds’ carrying amount is £973,270 (beginning balance of £965,349 plus 
£7,921 discount amortisation).
The following table illustrates interest expense, discount amortisation, and 
carrying amount (amortised cost) over the life of the bonds.
Y earCarrying Amount 
(beginning of 
year)Interest Expense (at 
effective interest rate

effective interest rate 
of 6%)Interest 
Payment (at 
coupon rate of 
5%)Amortisation 
of DiscountCarrying 
Amount (end 
of year)
(a) (b) (c) (d) (e)
2010 £957,876 £57,473 £50,000 £7,473 £965,349
2011 965,349 57,921 50,000 7,921 973,270
2012 973,270 58,396 50,000 8,396 981,666
2013 981,666 58,900 50,000 8,900 990,566
2014 990,566 59,434 50,000 9,434 1,000,000
Total £292,124 £250,000 £42,124
The carrying amounts of the bonds at 31 December 2010 and 2011 are £965,349 
and £973,270, respectively. Observe that the carrying amount of the bonds issued 
at a discount increases over the life of the bonds. At maturity, 31 December 2014, 
the carrying amount of the bonds equals the face value of the bonds. The carrying 
amount of the bonds will be reduced to zero when the principal payment is made.

Bonds Payable 553
Under the straight-  line method, the discount (or premium) is evenly amortised 
over the life of the bonds. In this example, the £42,124 discount would be amor -
tised by £8,424.80 (£42,124 divided by 5 years) each year under the straight-  line 
method. So, the annual interest expense under the straight-  line method would 
be £58,424.80 (£50,000 plus £8,424.80).
The accounting and reporting for zero-  coupon bonds is similar to the example 
above except that no interest payments are made; thus, the amount of interest expense 
each year is the same as the amount of the discount amortisation for the year.
EXAMPLE 4   
Amortising a Bond Premium
Prembond Corp. issues £1,000,000 face value of five-  year bonds, dated 1 
January 2010, when the market interest rate is 4 percent. The sales proceeds 
are £1,044,518. The bonds pay 5 percent interest annually on 31 December.

is used to amortise the premium.
4 What amount of interest expense on the bonds would be reported under 
the straight-  line method of amortising the premium?
The sales proceeds of £1,044,518 are more than the face value of £1,000,000; the 
bonds were issued at a premium of £44,518. The bonds are initially reported 
as a long-  term liability, bonds payable, of £1,044,518, which comprises the face 
value of £1,000,000 plus a premium of £44,518. The premium is amortised over 
time, ultimately decreasing the carrying amount (amortised cost) to face value.
Under the effective interest rate method, interest expense on the bonds is

calculated as the bonds’ carrying amount times the market rate in effect when 
the bonds are issued (effective interest rate). For 2010, interest expense is 
£41,781 = (£1,044,518 × 4%). The amount of the premium amortised in 2010 is 
the difference between the interest expense of £41,781 and the interest payment 
of £50,000 (i.e., £8,219). The bonds’ carrying amount decreases by the premium 
amortisation; at 31 December 2010, the bonds’ carrying amount is £1,036,299 
(beginning balance of £1,044,518 less £8,219 premium amortisation). At this 
point, the carrying amount reflects a remaining unamortised premium of £36,299 
(£44,518 premium at issuance minus £8,219 amortised).
For 2011, interest expense is £41,452 = (£1,036,299 × 4%). The amount of the 
premium amortised in 2011 is the difference between the interest expense of 
£41,452 and the interest payment of £50,000 (i.e., £8,548). At 31 December 2011, 
the bonds’ carrying amount is £1,027,751 (beginning balance of £1,036,299 less

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 554
The following table illustrates interest expense, premium amortisation, and 
Y ear Carrying Amount 
effective interest 
rate of 4%)Interest Payment 
(at coupon rate 
of 5%)Amortisation of 
PremiumCarrying 
Amount (end of 
year)
2010 £1,044,518 £41,781 £50,000 £8,219 £1,036,299
2011 1,036,299 41,452 50,000 8,548 1,027,751
2012 1,027,751 41,110 50,000 8,890 1,018,861
2013 1,018,861 40,754 50,000 9,246 1,009,615
2014 1,009,615 40,385 50,000 9,615 1,000,000
Total £44,518
The carrying amounts of the bonds at 31 December 2010 and 2011 are £1,036,299 
and £1,027,751, respectively. Observe that the carrying amount of the bonds 
issued at a premium decreases over the life of the bonds. At maturity, 31 
December 2014, the carrying amount of the bonds equals the face value of the

bonds. The carrying amount of the bonds will be reduced to zero when the 
principal payment is made.
Under the straight-  line method, the premium is evenly amortised over the life of 
the bonds. In this example, the £44,518 premium would be amortised by £8,903.64 
(£44,518 divided by 5 years) each year under the straight-  line method. So, the 
annual interest expense under the straight-  line method would be £41,096.36 
(£50,000 less £8,903.64).
The reporting of interest payments on the statement of cash flows can differ under 
IFRS and US GAAP . Under IFRS, interest payments on bonds can be included as 
an outflow in either the operating section or the financing section of the statement 
of cash flows. US GAAP requires interest payments on bonds to be included as an 
operating cash outflow. (Some financial statement users consider the placement of 
interest payments in the operating section to be inconsistent with the placement of

bond issue proceeds in the financing section of the statement of cash flows.) Typically, 
cash interest paid is not shown directly on the statement of cash flows, but companies 
are required to disclose interest paid separately.
Amortisation of a discount (premium) is a non-  cash item and thus, apart from its 
effect on taxable income, has no effect on cash flow. In the section of the statement 
of cash flows that reconciles net income to operating cash flow, amortisation of a 
discount (premium) is added back to (subtracted from) net income.
2.3 Current Market Rates and Fair Value Reporting Option
Reporting bonds at amortised historical costs (historical cost plus or minus the cumu -
lative amortisation) reflects the market rate at the time the bonds were issued  (i.e., 
historical market rate or effective interest rate). As market interest rates change, the 
bonds’ carrying amount diverges from the bonds’ fair market value. When market

interest rates decline, the fair value of a bond with a fixed coupon rate increases. As 
a result, a company’s economic liabilities may be higher than its reported debt based 
on amortised historical cost. Conversely, when market interest rates increase, the

Bonds Payable 555
fair value of a bond with a fixed coupon rate decreases and the company’s economic 
liability may be lower than its reported debt. Using financial statement amounts based 
on amortised cost may underestimate (or overestimate) a company’s debt-  to- total-  
capital ratio and similar leverage ratios.
Companies recently have been given the option to report financial liabilities at fair 
values. Financial liabilities reported at fair value are designated as financial liabilities 
at fair value through profit or loss. Even if a company does not opt to report finan -
cial liabilities at fair value, the availability of fair value information in the financial 
statements has increased. IFRS and US GAAP require fair value disclosures in the 
financial statements unless the carrying amount approximates fair value or the fair 
value cannot be reliably measured.4
A company selecting the fair value option for a liability with a fixed coupon rate

will report gains (losses) when market interest rates increase (decrease). When market 
interest rates increase or other factors cause the fair value of a company’s bonds to 
decline, the company reports a decrease in the fair value of its liability and a corre -
sponding gain. When interest rates decrease or other factors cause the fair value of a 
company’s bonds to increase, the company reports an increase in the fair value of its 
liability and a corresponding loss. The gains or losses resulting from changes in fair 
values are recognised in profit or loss.
Few companies have selected the option to report financial liabilities at fair value. 
Those that have are primarily companies in the financial sector. Reporting standards 
for financial investments and derivatives already required these companies to report a 
significant portion of their assets at fair values. Measuring financial liabilities at other 
than fair value, when financial assets are measured at fair value, results in earnings

volatility. This volatility is the result of using different bases of measurement for 
financial assets and financial liabilities. Goldman Sachs elected to account for some 
financial liabilities at fair value under the fair value option. In its fiscal year 2008 10-  K 
filing (page 74), Goldman explains this choice:
The primary reasons for electing the fair value option are to reflect economic 
events in earnings on a timely basis, to mitigate volatility in earnings from 
using different measurement attributes and to address simplification and 
cost-  benefit considerations.
Most companies, as required under IFRS and US GAAP , disclose the fair values 
of financial liabilities. The primary exception to the disclosure occurs when fair value 
cannot be reliably measured. Example  5 illustrates Sony’s fair value disclosures, 
including the fair values of long-  term debt.
EXAMPLE 5   
Fair Value Disclosures of Debt and Financial Instruments

The following are excerpts from Notes 2 and 13 of Sony Corporation’s 20-  F filing 
for the fiscal year ended 31 March 2009. These discuss the option for reporting 
fair values in the balance sheet and illustrate financial statement disclosures of 
fair values.
Excerpt from  Note 2: Summary of significant accounting policies
… “The Fair Value Option for Financial Assets and Financial 
Liabilities. ” …permits companies to choose to measure, on an 
instrument-  by- instrument basis, various financial instruments and 
4 IFRS (IAS 32, IAS 39, and IFRS 7) and US GAAP (FASB ASC 820 and 825).

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 556
certain other items at fair value that are not currently required to 
be measured at fair value. The fair value measurement election is 
irrevocable and subsequent changes in fair value must be recorded 
in earnings. … Sony did not elect the fair value option for any assets 
or liabilities that were not previously carried at fair value.
Excerpt from  Note 13: Fair value measurements
The estimated fair values of Sony’s financial instruments are sum -
marised as follows. The following summary excludes cash and cash 
equivalents, call loans, time deposits, notes and accounts receivable, 
trade, call money, short-  term borrowings, notes and accounts payable, 
trade and deposits from customers in the banking business because 
the carrying values of these financial instruments approximated their 
fair values due to their short-  term nature.
Y en in millions
March 31, 2008 March 31, 2009
Carrying 
amountEstimated fair 
valueCarrying

Carrying 
valueCarrying 
value
Long-  term debt including the current 
portion 1,020,938 1,024,879 807,687 809,377
Investment contracts included in poli -
cyholders’ account in the life insurance 
business274,779 275,967 286,104 289,905
The fair values of long-  term debt including the current portion and 
investment contracts included in policyholders’ account in the life 
insurance business were estimated based on either the market value 
or the discounted future cash flows using Sony’s current incremental 
borrowing rates for similar liabilities.
Use the excerpts from the notes to Sony’s financial statements to address the 
1 Does Sony report the fair values of its long-  term debt on the balance 
sheet?
2 How does Sony measure the long-  term debt reported on the balance 
sheet?
3 As of 31 March 2008 and 31 March 2009, what is the percent difference in 
the carrying amount and fair value of Sony’s long-  term debt?

Sony does not report the fair values of its long-  term debt on the balance sheet; 
Sony discloses that it did not elect the fair value option for any assets or liabili -
ties that were not previously carried at fair value in Note 2. In Note 13, we also 
observe that Sony discloses the estimated fair value of long-  term debt separately 
from its carrying amount.
Notes 2 and 13 indicate that Sony did not elect the fair value option. Therefore, 
the carrying amount of its debt must be its amortised historical cost.

Bonds Payable 557
In each year, the fair value of Sony’s long-  term debt is less than 0.5% greater than 
its carrying amount: 0.4% [= (1,024,879/1,020,938) – 1] on 31 March 2008 and 
0.2% [= (809,377/807,687) – 1] on 31 March 2009. Although the estimated fair 
values are higher, the difference is small and would most likely not materially 
affect an analysis of the company.
2.4 Derecognition of Debt
Once bonds are issued, a company may leave the bonds outstanding until maturity 
or redeem the bonds before maturity either by calling the bonds (if the bond issue 
includes a call provision) or by purchasing the bonds in the open market. If the bonds 
remain outstanding until the maturity date, the company pays bondholders the face 
value of the bonds at maturity. The discount or premium on the bonds would be fully 
amortised at maturity; the carrying amount would equal face value. Upon repayment, 
bonds payable is reduced by the carrying amount at maturity (face value) of the bonds

and cash is reduced by an equal amount. Repayment of the bonds appears in the 
statement of cash flows as a financing cash outflow.
If a company decides to redeem bonds before maturity and thus extinguish the 
liability early, bonds payable is reduced by the carrying amount of the redeemed 
bonds. The difference between the cash required to redeem the bonds and the carrying 
amount of the bonds is a gain or loss on the extinguishment of debt. Under IFRS, debt 
issuance costs are included in the measurement of the liability and are thus part of its 
carrying amount. Under US GAAP , debt issuance costs are accounted for separately 
from bonds payable and are amortised over the life of the bonds. Any unamortised 
debt issuance costs must be written off at the time of redemption and included in the 
gain or loss on debt extinguishment.
For example, a company reporting under IFRS has a £10 million bond issuance 
with a carrying amount equal to its face value and five years remaining until matu -

rity. The company redeems the bonds at a call price of 103. The redemption cost is 
£10.3 million (= £10 million × 103%). The company’s loss on redemption would be 
£300 thousand (£10 million carrying amount minus £10.3 million cash paid to redeem 
the callable bonds).
A gain or loss on the extinguishment of debt is disclosed on the income statement, 
in a separate line item, when the amount is material. A company typically discloses 
further detail about the extinguishment in the management discussion and analysis 
(MD&A) and/or notes to the financial statements.5 In addition, in a statement of cash 
flows prepared using the indirect method, net income is adjusted to remove any gain 
or loss on the extinguishment of debt from operating cash flows and the cash paid to 
redeem the bonds is classified as cash used for financing activities. (Recall that the 
indirect method of the statement of cash flows begins with net income and makes

necessary adjustments to arrive at cash from operations, including removal of gains 
or losses from non-  operating activities.)
To illustrate the financial statement impact of the extinguishment of debt, consider 
the notes payable repurchase by B+H Ocean Carriers in Example 6 below.
5 We use the term MD&A generally to refer to any management commentary provided on a company’s 
financial condition, changes in financial condition, and results of operations. In the United States, the 
Securities and Exchange Commission (SEC) requires a management discussion and analysis for companies 
listed on US public markets. Reporting requirements for such a commentary as the SEC-  required MD&A 
vary across exchanges, but some are similar to the SEC requirements. The IASB issued an IFRS Practice 
Statement, “Management Commentary, ” in December 2010 to guide all companies reporting under IFRS.

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 558
EXAMPLE 6   
Debt Extinguishment Disclosure
The following excerpts are from the 2008 20-  F filing of B+H Ocean Carriers. In 
its statement of cash flows, the company uses the indirect method to reconcile 
net income with net cash (used in) provided by operations.
Excerpt from  Consolidated Statements of Income  
For the years ended 31 December 2008, 2007, and 2006
Revenues:
⋮ ⋮ ⋮ ⋮
Total revenues 104,908,915 112,416,831 96,879,051
⋮ ⋮ ⋮ ⋮
Total operating expenses 100,279,906 96,140,562 71,018,929
Income from vessel operations 4,629,009 16,276,269 25,860,122
Other income (expense):
⋮ ⋮ ⋮ ⋮
Gain on debt extinguishment 2,345,000 — —
⋮ ⋮ ⋮ ⋮
Total other income (expense), net 11,236,107 (14,257,092) (7,085,809)
Net income $15,865,116 $2,019,177 $18,774,313
Excerpt from  Consolidated Statements of Cash Flows  
CASH FLOWS FROM OPERATING 
ACTIVITIES:

ACTIVITIES: 
Net Income $15,865,116 $2,019,177 $18,774,313
Adjustments to reconcile net income to net cash 
(used in) provided by operating activities:
⋮ ⋮ ⋮ ⋮
Gain on debt extinguishment (2,345,000) — —
⋮ ⋮ ⋮ ⋮
Total adjustments (16,635,993) 38,842,386 19,815,773
Net cash (used in) provided by operating 
activities(770,877) 40,861,563 38,590,086
⋮ ⋮ ⋮ ⋮
CASH FLOWS FROM FINANCING 
Payments for debt financing costs (294,999) (1,526,501) (1,481,505)
⋮ ⋮ ⋮ ⋮

Bonds Payable 559
Purchase of debt securities (2,155,000) — (5,000,000)
⋮ ⋮ ⋮ ⋮
Payments of unsecured debt — (31,402,960) (1,356,092)
Excerpt from  NOTE 2: SUMMARY OF SIGNIFICANT 
ACCOUNTING POLICIES
… The carrying amount of the Company’s variable rate long-  term 
debt approximates fair value.
Excerpt from  NOTE 8: BONDS PAYABLE
On December 12, 2006, the Company issued $25 million of unse -
cured bonds… Interest on the bonds is equal to Libor plus 4%, payable 
quarterly in arrears. … During the 4th quarter of 2008, the Company 
repurchased the unsecured bonds with a face value of $4.5 million 
and realized a $2.3 million gain. 
1 The balance in bonds payable was reduced at redemption by:
A $2,155,000.
B $2,345,000.
C $4,500,000.
C is correct. The bonds payable is reduced at redemption by the carrying amount 
of the bonds redeemed. The cash paid to extinguish the bonds plus the gain on 
redemption equals the carrying amount of the bonds. The carrying amount of

the bonds was $4,500,000. In this case, the carrying amount equals the face 
value. The company recognised a gain of $2,345,000 when it extinguished the 
debt of $4,500,000 by paying only $2,155,000.
2.5 Debt Covenants
Borrowing agreements (the bond indenture) often include restrictions called covenants 
that protect creditors by restricting activities of the borrower. Debt covenants benefit 
borrowers to the extent that they lower the risk to the creditors and thus reduce the 
cost of borrowing. Affirmative covenants restrict the borrower’s activities by requiring 
certain actions. For instance, covenants may require that the borrower maintain certain 
ratios above a specified amount or perform regular maintenance on real assets used 
as collateral. Negative covenants require that the borrower not take certain actions. 
Covenants may restrict the borrower’s ability to invest, pay dividends, or make other 
operating and strategic decisions that might adversely affect the company’s ability to

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 560
Common covenants include limitations on how borrowed monies can be used, 
maintenance of collateral pledged as security (if any), restrictions on future borrowings, 
requirements that limit dividends, and requirements to meet specific working capital 
requirements. Covenants may also specify minimum acceptable levels of financial 
ratios, such as debt-  to- equity, current, or interest coverage.
When a company violates a debt covenant, it is a breach of contract. Depending on 
the severity of the breach and the terms of the contract, lenders may choose to waive 
the covenant, be entitled to a penalty payment or higher interest rate, renegotiate, 
or call for payment of the debt. Bond contracts typically require that the decision to 
call for immediate repayment be made, on behalf of all the bondholders, by holders 
of some minimum percentage of the principal amount of the bond issue.

Example 7 illustrates common disclosures related to debt covenants included in 
financial statement disclosures (notes to the financial statements).
EXAMPLE 7   
Illustration of Debt Covenant Disclosures
The following excerpt is from TORM A/S from the Risk Factors section of Item 
3, Key Information, in its fiscal year 2008 20-  F filing. The excerpt illustrates debt 
covenants and their disclosure:
Certain of our loan agreements contain restrictive covenants, which 
may limit our liquidity and corporate activities and prevent proper 
service of debt, which could result in the loss of our vessels.
Some loan agreements impose operating and financial restrictions 
upon us. These restrictions may limit our ability to:
■■change the management of our vessels without the lenders’ 
consent (which they are not entitled to unreasonably with -
hold); and
■■enter into mergers or corporate restructurings, or effect 
material divestments, if such would be materially adverse to 
the company.

Our lenders’ interests may be different from ours and we cannot 
guarantee that we will be able to obtain our lenders’ permission 
when needed. This may prevent us from taking actions that are in 
our best interest. 
The following excerpt is an additional excerpt from “Note 8: Bonds Payable” of 
B+H Ocean Carriers that was referenced in Example 6.
The bond facility contains certain restrictive covenants which restrict 
the payment of dividends. The facility requires a minimum value 
adjusted equity ratio (as defined) of 25%. At December 31, 2008, the 
Company was in compliance with these covenants and is likely to 
remain in compliance throughout 2009. However, the bond agreement 
contains a cross default provision that essentially enables the lender to 
call the bonds if the Company defaults on a separate loan facility. The 
Company reclassified its long term debt because of a determination

Bonds Payable 561
prospectively that certain covenants in certain long term agreements 
may be breached during 2009. As such, the Company has recorded 
the entire balance of the bonds as current as of December 31, 2008.
1 Which of the covenants described in the above excerpts is an affirmative 
covenant?
2 Based on the excerpt from B+H Ocean Carriers, what is the implied con -
sequence of breaching certain covenants?
The requirement that “a minimum value adjusted equity ratio (as defined) of 
25 percent” be maintained by B+H Ocean Carriers is an example of an affirma -
tive covenant. It requires the issuer to do something. The covenants on TORM 
A/S require that TORM not take certain actions (e.g., not change management 
of vessels without lenders’ consent and not enter into mergers that would be 
materially adverse) and are negative covenants.
If B+H Ocean Carriers breaches certain covenants, it seems that the entire bal -

ance of bonds payable becomes due. The bonds payable have been prospectively 
moved from non-  current to current liabilities.
2.6 Presentation and Disclosure of Long-  Term Debt
The non-  current (long-  term) liabilities section of the balance sheet usually includes a 
single line item of the total amount of a company’s long-  term debt due after one year, 
with the portion of long-  term debt due in the next twelve months shown as a current 
liability. Notes to the financial statements provide more information on the types 
and nature of a company’s debt. These note disclosures can be used to determine the 
amount and timing of future cash outflows. The notes generally include stated and 
effective interest rates, maturity dates, restrictions imposed by creditors (covenants), 
and collateral pledged (if any). The amount of scheduled debt repayments for the next 
five years also is shown in the notes.
Example 8 contains an excerpt from Johnson & Johnson’s 2008 10-  K filing that

illustrates common long-  term debt disclosures.
EXAMPLE 8   
Illustration of Long-  Term Debt Disclosures
Exhibit 1 is an excerpt from Note 6 of Johnson & Johnson’s 2008 financial state -
ments that illustrates financial statement disclosure for long-  term debt, including 
type and nature of long-  term debt, effective interest rates, and required payments 
over the next five years. Johnson & Johnson reports its debt at amortised cost.
Exhibit 1   Johnson & Johnson
Excerpt from 6. Borrowings
The components of long-  term debt are as follows:

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 562
(Dollars in Millions) 2008Effective  
Rate % 2007Effective  
Rate %
3% Zero Coupon Convertible Subordinated 
Debentures due 2020$183 3 178 3
4.95% Debentures due 2033 500 4.95 500 4.95
3.80% Debentures due 2013 500 3.82 500 3.82
6.95% Notes due 2029 294 7.14 294 7.14
6.73% Debentures due 2023 250 6.73 250 6.73
6.625% Notes due 2009 199 6.8 199 6.8
5.55% Debentures due 2017 1,000 5.55 1,000 5.55
5.95% Notes due 2037 995 5.99 995 5.99
5.50% Notes due 2024  
(500 GBP1.4759)b(500 GBP 1.9944)c731 5.71 989 5.71
4.75% Notes due 2019  
(1B Euro 1.4000)b( 1B Euro 1.4573)c1,390 5.35 1,447 5.35
5.15% Debentures due 2012 599 5.18 599 5.18
5.86% Debentures due 2038 700 5.86
5.15% Debentures due 2018 898 5.15
Other (Includes Industrial Revenue Bonds) 102 132
8,341d5.46a7,083d5.47a
Less current portion 221 9 —
$8,120 7,074
a Weighted average effective rate.  
b Translation rate at December 28, 2008.  
c Translation rate at December 30, 2007.

c Translation rate at December 30, 2007.  
d The excess of the fair value over the carrying value of debt was $1.4 billion in 2008 and $0.3 billion in 2007.
The Company has access to substantial sources of funds at numerous 
banks worldwide. In September 2008, the Company secured a new 364-  day 
and 5-  year Credit Facility. Total credit available to the Company approx -
imates $7.7 billion of which $6.3 billion expires September 24, 2009, and 
$1.4 billion expires September 25, 2013. Interest charged on borrowings 
under the credit line agreements is based on either bids provided by banks, 
the prime rate or London Interbank Offered Rates (Libor), plus applicable 
margins. Commitment fees under the agreements are not material.
…
Aggregate maturities of long-  term obligations commencing in 2007 
are (dollars in millions):
2009 2010 2011 2012 2013 After 2014 
$221 22 18 620 507 6,953
Use the information in Exhibit 1 to answer the following questions:

1 Why are the effective interest rates unchanged from 2007 and 2008 for the 
first 11 borrowings listed?Exhibit 1   (Continued)

Bonds Payable 563
2 Why does the carrying amount of the “4.95% Debentures due 2033” 
remain the same in 2007 and 2008?
3 Why does the carrying amount of the “4.75% Notes due 2019” decrease 
from 2007 to 2008?
The effective interest rate is the market rate at which the bonds are issued and 
does not change from year to year.
The carrying amount of the “4.95% Debentures due 2033” remains the same 
because the effective interest rate at which the debentures were issued is the 
same as the coupon rate. The debentures were issued at par, and the carrying 
amount does not change.
The notes are denominated in euros, with a face value of €1 billion. The dollar/
euro translation exchange rate at the end of 2008 was lower than the exchange 
rate at the end of 2007 (1.4000 versus 1.4573). That decline explains the decrease 
in carrying value. Note that the face amount of the debt at the translation rate (at

the end of 2008, €1 billion times 1.4000 = $1.4 billion) is higher than the carrying 
amount (at the end of 2008, $1.39 billion). The reason for this difference is that 
the notes were issued at a discount; the effective interest rate of 5.35 percent 
is higher than the 4.75 percent coupon rate. The carrying amount of the notes 
thus reflects the amortisation of the discount at issuance; the amortisation of 
the discount will increase the carrying amount.
In this reading, we focus on accounting for simple debt contracts. Debt contracts 
can take on additional features, which lead to more complexity. For instance, convert -
ible debt and debt with warrants are more complex instruments that have both debt 
and equity features. Convertible debt gives the debt holder the option to exchange the 
debt for equity. Bonds issued with warrants give holders the right to purchase shares 
of the issuer’s common stock at a specific price, similar to stock options. Issuance of

bonds with warrants is more common by non-  US companies. Example 9 provides 
an example of a financial statement disclosure of bonds with warrants issued by a 
Chinese company.
EXAMPLE 9   
Financial Statement Disclosure of Bonds with Warrants
The following excerpt is from the fiscal year 2008 Annual Report of the China 
Petroleum & Chemical Corporation.
Excerpt from NOTE 29: DEBENTURES PAYABLE
On 26 February  2008, the Company issued convertible bonds 
with stock warrants due 2014 with an aggregate principal amount of 
RMB 30 billion in the PRC (the “Bonds with Warrants”). The Bonds 
with Warrants with fixed interest rate of 0.8% per annum and interest 
payable annually, were issued at par value of RMB 100. The Bonds 
with Warrants were guaranteed by Sinopec Group Company. Each 
lot of the Bonds with Warrants, comprising ten Bonds with Warrants 
are entitled to warrants (the “Warrants”) to subscribe 50.5 A shares of

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 564
the Company during the 5 trading days prior to 3 March 2010 at an 
initial exercise price of RMB 19.68 per share, subject to adjustment 
for, amongst other things, cash dividends, subdivision or consolidation 
of shares, bonus issues, rights issues, capital distribution, change of 
control and other events which have a dilutive effect on the issued 
share capital of the Company.
If all warrants were exercised, how many shares would be subscribed for?
Solution:
1,515,000,000 shares would be subscribed for [aggregate principal amount divided 
by par value of a lot times shares subscribed per lot = (RMB 30,000,000,000/
RMB 1,000) × 50.5 shares].
In addition to disclosures in the notes to the financial statements, an MD&A 
commonly provides other information about a company’s capital resources, including 
debt financing and off-  balance-  sheet financing. In the MD&A, management often

provides a qualitative discussion on any material trends, favorable or unfavorable, in 
capital resources and indicates any expected material changes in their mix and relative 
cost. Additional quantitative information is typically provided, including schedules 
summarising a company’s contractual obligations (e.g., bond payables) and other 
commitments (e.g., lines of credit and guarantees) in total and over the next five years.
LEASES
A company wishing to obtain the use of an asset can either purchase the asset or lease 
the asset. Section 3.1 describes some advantages to leasing from the viewpoint of the 
lessee  (the party obtaining the use of an asset through a lease). Section 3.2 describes 
the classification of leases. Section 3.2.1 describes the accounting treatments of dif -
ferent types of leases from the perspective of the lessee, and section 3.2.2 discusses 
leases from the perspective of the lessor  (the owner of the asset).
3.1 Advantages of Leasing

A lease is a contract between the owner of an asset—the lessor—and another party 
seeking use of the asset—the lessee. Through the lease, the lessor grants the right to 
use the asset to the lessee. The right to use the asset can be for a long period, such 
as 20 years, or a much shorter period, such as a month. In exchange for the right to 
use the asset, the lessee makes periodic lease payments to the lessor. A lease, then, 
is a form of financing to the lessee provided by the lessor that enables the lessee to 
obtain the use of the leased asset.
can provide less costly financing; they usually require little, if any, down payment and 
often are at lower fixed interest rates than those incurred if the asset was purchased. 
This financing advantage is the result of the lessor having advantages over the lessee

and/or another lender. The lessor may be in a better position to take advantage of tax 
benefits of ownership, such as depreciation and interest. The lessor may be better able 
to value and bear the risks associated with ownership, such as obsolescence, residual 
value, and disposition of asset. The lessor may enjoy economies of scale for servicing 
assets. As a result of these advantages, the lessor may offer attractive lease terms and 3

Leases 565
leasing the asset may be less costly for the lessee than owning the asset. Further, the 
negotiated lease contract may contain less-  restrictive provisions than other forms of 
borrowing.
Companies have also used certain types of leases because of perceived financial 
reporting and tax advantages. Although they provide a form of financing, certain 
types of leases are not shown as debt on the balance sheet. The items leased under 
these operating leases have not appeared as assets on the balance sheet. Therefore, 
no interest expense or depreciation expense is included in the income statement. In 
addition, in some countries—including the United States—because financial reporting 
rules differ from tax regulations, a company may own an asset for tax purposes (and 
thus obtain deductions for depreciation expense for tax purposes) while not reflecting 
the ownership in its financial statements. A lease that is structured to provide a com -

pany with the tax benefits of ownership while not requiring the asset to be reflected 
on the company’s financial statements is known as a synthetic lease.
3.2 Finance (or Capital) Leases versus Operating Leases
There are two main classifications of leases: finance leases  (or capital leases ) and 
operating leases .6 The economic substance of a finance (or capital) lease is very 
different from an operating lease, as are the implications of each for the financial 
statements for the lessee and lessor. In substance, a finance (capital) lease is equiva -
lent to the purchase of some asset (lease to own) by the buyer (lessee) that is directly 
financed by the seller (lessor). An operating lease is an agreement allowing the lessee 
to use some asset for a period of time, as if it were a rental.
Under the existing IFRS standard (IAS 17), the classification of a lease as a finance 
lease or an operating lease depends on the transfer of the risks and rewards incidental

to ownership of the leased asset. If substantially all the risks and rewards are transferred 
to the lessee, the lease is classified as a finance lease and the lessee reports a leased 
asset and lease obligation on its balance sheet. Otherwise, the lease is reported as an 
operating lease, in which case the lessee reports neither an asset nor a liability—only 
the lease expense. Similarly, if the lessor transfers substantially all the risks and rewards 
incidental to legal ownership, the lease is reported as a finance lease and the lessor 
reports a lease receivable on its balance sheet and removes the leased asset from its 
balance sheet. Otherwise, the lease is reported as an operating lease, and the lessor 
keeps the leased asset on its balance sheet. Examples of situations that would normally 
lead to a lease being classified as a finance lease include the following:7
■■The lease transfers ownership of the asset to the lessee by the end of the lease 
term.

term.
■■The lessee has the option to purchase the asset at a price that is expected to be 
sufficiently lower than the fair value at the date the option becomes exercisable 
for it to be reasonably certain, at the inception of the lease, that the option will 
be exercised.
■■The lease term is for the major part of the economic life of the asset, even if the 
title is not transferred.
6 “Finance lease” is IFRS terminology and “capital lease” is US GAAP terminology. New standards IFRS 
16 (Leases) and FASB ASC Topic 842 (Leases) are effective 1 January 2019 and for fiscal years beginning 
after December 15, 2019, respectively. A consequence of these standards is that both operating and finance 
leases will appear on a lessee’s balance sheets.
7 Examples are from IAS 17, paragraph 10, and do not include all indicators that would lead to a lease 
being classified as a finance lease.

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 566
■■At the inception of the lease, the present value of the minimum lease payments 
amounts to at least substantially all of the fair value of the leased asset.
■■The leased assets are of such a specialized nature that only the lessee can use 
them without major modifications.
As mentioned previously, a new IFRS standard for accounting for leases (IFRS 16) 
is applicable for financial years beginning 1 January 2019. IFRS 16 defines a lease as a 
contract, or part of a contract, that conveys the right to use an asset (the underlying 
asset) for a period of time in exchange for consideration.8
Under IFRS 16, if a contract meets the above criteria, the lessee is required to rec -
ognize all of its leases on the balance sheet.9 This involves recognizing both a “right to 
use” asset and a lease liability in the lessee’s balance sheet. In essence, IFRS 16 requires 
lessees to record both finance and operating leases in an identical manner—that is,

as assets and associated liabilities in the lessee’s balance sheet.
Although accounting for leases under US GAAP is guided by a similar principle 
of the transfer of benefits and risks, US GAAP is more prescriptive in its criteria for 
classifying capital and operating leases. Under US GAAP ,10 leases can be recognized 
as either a capital (finance) or an operating lease. Four criteria are specified to identify 
when a lease is a capital lease:11
1 Ownership of the leased asset transfers to the lessee at the end of the lease.
2 The lease contains an option for the lessee to purchase the leased asset cheaply 
(bargain purchase option).
3 The lease term is 75 percent or more of the useful life of the leased asset.
4 The present value of lease payments is 90 percent or more of the fair value of 
the leased asset.
Only one of these criteria has to be met for the lease to be considered a capital 
lease by the lessee. On the lessor side, satisfying at least one of these four criteria plus

meeting revenue recognition requirements (that is, being reasonably assured of cash 
collection and having performed substantially under the lease) determine a capital 
lease. If none of the four criteria are met or if the revenue recognition requirement 
is not met, the lessor reports the lease as an operating lease.
3.2.1  Accounting and Reporting by the Lessee
Because a finance lease is economically similar to borrowing money and buying an 
asset, a company that enters into a finance lease as the lessee reports an asset (leased 
asset) and related debt (lease payable) on its balance sheet. The initial value of both 
the leased asset and lease payable is the lower of the present value of future lease 
payments and the fair value of the leased asset; in many cases, these will be equal. 
On the income statement, the company reports interest expense on the debt, and if 
the asset acquired is depreciable, the company reports depreciation expense. (The

lessor, as we illustrate in the next section, reports the sale of an asset and a lease as 
receivable.) Note that following the introduction of IFRS 16, all contracts meeting the 
criteria of a lease are classified as finance leases by the lessee, and the lessor continues 
to classify leases as either financial or operating.
8 http://www.ifrs.org/-/media/project/leases/ifrs/published-  documents/ifrs16-  project-  summary.pdf
9 IFRS 16 allows the lessee to elect to account for lease payments as an expense on a straight line basis 
over the lease term or another systematic basis for two types of leases: (1) leases with a lease term of 12 
months or less and containing no purchase options, and (2) leases where the underlying asset has a low 
value when new.
10 FASB ASC Topic 842 [Leases].
11 FASB ASC Topic 840 [Leases].

Leases 567
Because an operating lease is economically similar to renting an asset, a company 
that enters into an operating lease as the lessee records a lease expense on its income 
statement during the period it uses the asset. No asset or liability is recorded on its 
balance sheet. This has led lessees to often prefer operating leases to finance leases. 
(Although classifying a lease as an operating lease can make reported profitability 
ratios and debt-  to- equity ratios appear better, financial analysts are aware of this 
impact and typically adjust the reported numbers accordingly.)
On the lessee’s statement of cash flows, for an operating lease, the lease payment 
is shown as an operating cash outflow. For a finance lease, only the portion of the 
lease payment relating to interest expense potentially reduces operating cash flow; the 
portion of the lease payment that reduces the lease liability appears as a cash outflow 
in the financing section.

Example 10 illustrates the accounting of a finance lease by a lessee.
EXAMPLE 10   
Determining the Initial Recognition and Measurement 
and Subsequent Measurement of a Finance Lease for a 
Lessee
CAPBS Inc. enters into a lease agreement to acquire the use of a piece of machin -
ery for four years beginning on 1 January 2010. The lease requires four annual 
payments of €28,679 starting on 1 January 2010. The useful life of the machine 
is four years, and its salvage value is zero. CAPBS accounts for the lease as a 
finance lease. The fair value of the machine is €100,000. The present value of the 
lease payments using the company’s discount rate of 10 percent is €100,000. (A 
reminder is relevant for present value calculations: Lease payments are made 
at the beginning of each period.) The company uses straight-  line depreciation.
1 Comment on the appropriateness of CAPBS treating the lease agreement 
as a finance lease under IFRS and a capital lease under US GAAP .

2 What is the amount reported as a leased asset on the balance sheet on 1 
January 2010? What depreciation expense is reported in fiscal year 2010?
3 What is the amount of the machinery reported as a leased asset on the 
balance sheet on 31 December 2010?
4 What is the amount of the lease liability reported on the balance sheet on 
1 January 2010? What interest expense is reported in fiscal year 2010?
5 What is the amount of the lease liability reported on the balance sheet on 
31 December 2010? What interest expense is reported in fiscal year 2011?
6 If CAPBS had determined that the above lease was an operating lease, 
what amount of expenses would be reported on the income statements 
in fiscal 2010 and 2011? How does this expense compare to the expenses 
reported under a capital lease?
CAPBS should treat this lease as a finance lease under IFRS. The machine is 
leased for the major part of its useful life (the useful life of the machine and

the lease are each four years). Also, the present value of lease payments equals 
substantially the fair value of the machine (both are €100,000). CAPBS should 
treat this lease as a capital lease under US GAAP . The machine is leased for more 
than 75 percent of its useful life, and the present value of the lease payments 
exceeds 90 percent of the fair value of the leased asset.

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 568
The amount initially reported as a leased asset on 1 January 2010 is €100,000. 
Depreciation expense each year is €25,000 [(€100,000 – €0)/4 years].
The table below shows CAPBS’s depreciation expense and carrying amount 
for the leased asset by year.
Y earInitial 
Recognition 
AmountDepreciation 
DepreciationCarrying 
Amount  
(year-  end)
(a) (b) (c ) (d)
2010 €100,000 €25,000 €25,000 €75,000
2011 100,000 25,000 50,000 50,000
2012 100,000 25,000 75,000 25,000
2013 100,000 25,000 100,000 0
€100,000
■■Column (a) is the lower of the fair value of the machinery and the present 
value (PV) of lease payments at lease inception. In this example, they are 
the same.
■■Column (b) is the depreciation expense of €25,000 per year [straight-  line 
depreciation = acquisition cost less salvage value divided by useful life = 
(€100,000 – €0)/4 years].
■■Column (c) is the accumulated depreciation on the leased asset calculated

■■Column (d) is the carrying amount of the machine (the leased asset), 
which is the difference between the initial recognition amount and accu -
mulated depreciation.
From the table presented in Solution to 2 , the carrying amount on 31 
December 2010 is €75,000.
The amount of the lease liability initially recognised on 1 January 2010 is €100,000, 
which is both the fair value of the leased asset and the present value of lease 
payments. However, the first lease payment of €28,679, due on 1 January 2010, 
immediately reduces the lease liability balance to €71,321. Interest expense in 
2010 is based on the €71,321 carrying amount. Interest expense reported in 
fiscal year 2010 is €7,132 (€71,321 × 10%).
values for its lease liability by year.12

12 The computations included throughout the example were made using an Excel worksheet; small apparent 
discrepancies in the calculations are because of rounding.

Leases 569
Y earLease 
Liability, 1 
JanuaryAnnual Lease 
Payment, 1 
JanuaryInterest (at 
10%; accrued in 
previous year)Reduction of 
Lease Liability, 
1 JanuaryLease Liability on 
January Same Y ear
2010 €100,000 €28,679 €0 €28,679 €71,321
2011 71,321 28,679 7,132 21,547 49,774
2012 49,774 28,679 4,977 23,702 26,072
2013 26,072 28,679 2,607 26,072 0
■●2010: €100,000
■●Years thereafter: It is the lease liability at the end of the previous year
■■Column (b) is the annual lease payment made at the beginning of the year. 
A portion of the lease payment reduces interest accrued in the previous 
year, and the remainder of the lease payment reduces the carrying amount 
of the lease liability.
■●For example, in 2011, the €28,679 paid on 1 January reduces the inter -
est payable of €7,132 that accrued in 2010 (€71,321 × 10%) and then

reduces the lease liability by €21,547.
the prior  year and is reported as the interest expense of the prior  year. For 
example, at 31 December 2010, interest expense and interest payable in 
the amount of €7,132 was recognised.
the lease payment is made on the first day of the next year. It is equal to 
From the table presented in Solution to 4 , the interest expense in fiscal year 2011 
is €4,977 (€49,744 × 10%).
As an operating lease, a rent expense of €28,679 would be reported on the

income statement each year. Under a capital lease, the expenses related to the 
lease are depreciation and interest expense. In 2010, the depreciation expense 
is €25,000 and the interest expense is €7,132. In 2011, the depreciation expense 
is €25,000 and the interest expense is €4,977.
than an identical company reporting an identical lease as a finance lease. However, 
the company reporting the lease as a finance lease will show higher operating cash 
flows because the portion of the lease payment that reduces the carrying amount of

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 570
the lease liability will be reflected as a financing cash outflow rather than an operating 
cash outflow. The interest expense portion of the lease payment on the statement of 
cash flows can be treated as operating or financing cash outflow under IFRS and is 
treated as an operating cash outflow under US GAAP . However, the effect of reporting 
under either an operating lease or finance lease over the life of the lease is neutral 
with respect to pretax profits.
The explicit standards in the United States that determine when a company 
should report a capital lease versus an operating lease make it easier for a company to 
structure a lease so that it is reported as an operating lease. The company structures 
the lease so that none of the four capital lease identifying criteria is met. Similar to 
debt disclosures, however, lease disclosures show payments under both capital and

operating leases for the next five years and afterward. These disclosures can help to 
estimate the extent of a company’s off-  balance-  sheet lease financing through operating 
leases. Example 11 illustrates the disclosures of operating and finance leases. Although 
these disclosures can be used to determine the effect on the financial statements if 
all operating leases were capitalized, this reading focuses solely on the information 
that is disclosed.
EXAMPLE 11   
Financial Statement Disclosure of Leases by the Lessee
BASF Group has significant commitments under finance and operating leases. 
Presented below is selected note disclosure from its fiscal year 2008 financial 
27. LEASING
Leased assets
Property, plant and equipment include those assets which are 
considered to be economically owned through a finance lease. They 
primarily concern the following items: 
Leased assets (million €) 2008 2007
Acquisition  
costNet book  
valueAcquisition  
value

value
Land, land rights and buildings 20 13 26 18
Machinery and technical equipment 223 96 226 118
Miscellaneous equipment and fixtures 73 18 71 20
Advance payments and construction in progress — — — —
316 127 323 156
Liabilities from finance leases 
(million €)2008 2007
Minimum 
lease 
paymentsInterest 
portionLeasing 
liabilityMinimum 
lease 
liability
Following year 1 20 5 15 29 6 23
Following year 2 20 5 14 19 5 13
Following year 3 22 5 18 18 5 13
Following year 4 11 2 9 21 5 16

Leases 571
Minimum 
lease 
lease 
liability
Following year 5 7 2 4 10 3 8
Over 5 years 29 10 20 35 12 23
108 29 80 132 36 96
In the current business year and in 2007, no additional lease payments arising 
from contractual obligations were recognized in income above the minimum 
lease payments. 
In 2008, leasing liabilities were not offset by any expected minimum lease 
payments from sub-  leases.
In addition, BASF is a lessee under operating lease contracts. The resulting 
lease obligations totaling €1,449 million in 2008 and €1,272 in 2007 are due in 
the following years:
Commitments due to operating lease contracts (million €)
Nominal value of the future minimum payments
Dec. 31, 2008 Dec. 31, 2007
Less than 1 year 280 292
1–5 years 613 505
Over 5 years 556 475
1,449 1,272
1 At the end of fiscal year 2008, what is the total amount of finance lease

liabilities BASF reports on its balance sheet?
2 Based on finance lease agreements in place at the end of fiscal year 2008, 
how much will BASF pay out on finance lease commitments in fiscal year 
2009?
3 Based on finance lease agreements in place at the end of fiscal year 2008, 
what is the amount of interest expense that BASF will report in fiscal year 
2009?
4 At the end of fiscal 2008, what are BASF’s total commitments under oper -
ating leases?
5 Based on operating lease agreements in place at the end of fiscal year 
2008, what is the minimum amount of rent expense that BASF will report 
in fiscal year 2009?
6 At the end of fiscal year 2008, what is the amount of leased assets (carry -
ing amount) BASF reports on its balance sheet?
€80 million—the total of the 2008 column “Leasing liability” in the “Liabilities 
from finance leases” table.
€20  million—reported in the 2008 column “Minimum lease payments, ” row

“Following year 1, ” in the “Liabilities from finance leases” table.

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 572
€5 million—reported in the 2008 column “Interest portion, ” row “Following year 
1, ” in the “Liabilities from finance leases” table.
€1,449 million—the total of the 2008 column “Nominal value of the future min -
imum payments” in the “Commitments due to operating lease contracts” table.
€280 million—reported in the 2008 column “Nominal value of the future mini -
mum payments, ” row “Less than 1 year, ” in the “Commitments due to operating 
lease contracts” table.
€127 million—the total of the 2008 column “Net book value” in the “Leased 
assets” table.
Example 12 contains information from Royal Dutch Shell’s 2008 financial state -
ments. As required by IFRS, the balance sheet presents finance lease obligations in the 
line items labeled “Debt. ” Additionally, IFRS require certain disclosures to be made in

the notes; the layout of disclosure notes on debt varies across companies. For Royal 
Dutch, the disclosure note on debt, Note 18[A], first shows a breakdown of total debt 
reported on the balance sheet into two components: the amount of debt excluding 
finance lease obligations and the amount of finance lease obligations. Note 18[B] 
provides disclosures on the component of on-  balance-  sheet debt, excluding finance 
lease obligations. Next, Note 18[C] presents information about all the companies’ 
lease obligations—both finance leases (which are a component of the on-  balance-  
sheet total debt) and operating leases (for which no obligation appears on the balance 
sheet). This disclosure clearly illustrates that although finance leases and operating 
leases are both contractual obligations, only the finance leases are reported on the 
balance sheet. As mentioned above, a subsequent reading demonstrates how analysts

adjust the total amount of debt as reported on the balance sheet to also include the 
off- balance-  sheet obligations for operating leases. As mentioned previously, analysts 
also should be aware that IFRS 16 requires lessees to account for leases of more than 
one year in a similar way to finance leases.
EXAMPLE 12   
Long-  Term Debt and Lease Disclosures
Use the following excerpts taken from Royal Dutch Shell 2008 consolidated 
financial statements and notes to the consolidated financial statements to answer 
the questions below.
Excerpt from CONSOLIDATED BALANCE SHEET
$ million NOTES Dec 31, 2008 Dec 31, 2007
Non-  current liabilities
Debt 18 13,772 12,363
⋮ ⋮ ⋮

Leases 573
Debt 18 9,497 5,736
⋮ ⋮ ⋮
Total liabilities 153,535 143,502
EQUITY
⋮ ⋮ ⋮
Total equity 128,866 125,968
Total liabilities and equity 282,401 269,470
Excerpt from CONSOLIDATED STATEMENT OF CASH FLOWS
Dec 31, 2008 Dec 31, 2007
Net increase/(decrease) in debt with matu -
rity period within three months4,161 (455)
Other debt:  
New borrowings3,555 4,565
Repayments (2,890) (2,796)
Excerpt from  Note 1: Basis of Preparation
The Consolidated Financial Statements of Royal Dutch Shell plc 
(the Company) and its subsidiaries (collectively known as “Shell” or the 
“Shell group”) have been prepared in accordance with the provisions 
of the Companies Act 1985, Article 4 of the International Accounting 
Standards (IAS) Regulation and with International Financial Reporting 
Standards (IFRS) as adopted by the European Union. As applied to 
Shell, there are no material differences with IFRS as issued by the

International Accounting Standards Board (IASB), therefore the 
Consolidated Financial Statements have been prepared in accordance 
with IFRS as issued by the IASB.
Excerpt from  Note 2: Accounting Policies
Financial liabilities
Debt and accounts payable are recognised initially at fair value 
based on amounts exchanged and subsequently at amortised cost, 
except for fixed rate debt subject to fair value hedging, which is re-  
measured for the hedged risk (see “Derivative contracts”). 
Interest on debt is accounted for using the effective interest method 
and, other than interest capitalised, is recognised in income. 
Where fair value is not applied subsequent to initial recognition 
but is required for disclosure purposes, it is based on market prices 
where available, otherwise it is calculated as the net present value of 
expected future cash flows. (Continued)

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 574
Excerpt from  Note 18: Debt and Lease Arrangements  
[A] DEBT ($ million)
Debt 
(excluding 
finance 
lease 
obligations)Finance 
lease 
obligations TotalDebt 
finance 
lease 
obligations)Finance lease 
obligations Total
Short-  term debt 7,879 — 7,879 3,292 — 3,292
Long-  term debt 
due within one 
year1,314 304 1,618 2,290 154 2,444
Current debt 9,193 304 9,497 5,582 154 5,736
Non-  current debt 10,061 3,711 13,772 8,533 3,830 12,363
Total 19,254 4,015 23,269 14,115 3,984 18,099
The fair value of debt approximates the carrying amount.
[B] DEBT (EXCLUDING FINANCE LEASE OBLIGATIONS)
The following tables compare contractual cash flows for debt 
(excluding finance lease obligations) owed by subsidiaries at 
December 31, by year of maturity, with the carrying amount in the 
Consolidated Balance Sheet. The carrying amount reflects the effects 
of discounting, premiums and fair value adjustments where hedging 
is applied.

2008 $ million, except where otherwise indicated
Contractual repayments (excluding interest)
2009 2010 2011 2012 20132014 
and 
after TotalDifference 
from 
carrying 
amountCarrying 
Amount
Fixed rate 
dollar6,821 506 1,001 503 1 3,539 12,371 290 12,661
  Average 
interest 
rate2.6% 5.2% 5.6% 5.0% 7.3% 5.4%
Variable rate 
dollar debt521 156 5 — — 122 804 — 804
  Average 
interest 
rate1.8% 3.8% 6.3% — — 0.0%
Fixed rate 
European 
debt568 1,146 285 — — 2,117 4,116 197 4,313
  Average 
interest 
rate2.9% 4.8% 2.0% — — 4.6%
European 
debt237 — — — — — 237 — 237

Leases 575
and 
from 
carrying 
Amount
  Average 
interest 
rate3.1% — — — — —
Other fixed 
rate debt426 — 2 — 1 — 429 — 429
  Average 
interest 
rate18.4% — 11.7% — 12.4% —
Other 
variable rate 
debt620 33 143 14 — — 810 — 810
  Average 
interest 
rate9.4% 11.5% 7.8% 4.8% — —
Total 9,193 1,841 1,436 517 2 5,778 18,767 487 19,254
The table above excludes interest estimated to be $827 million in 
2009, $480 million in 2010, $389 million in 2011, $316 million in 2012, 
$290 million in 2013 and $290 million in 2014 and after (assuming 
interest rates with respect to variable rate debt remain constant and 
there is no change in aggregate principal amount of debt other than 
repayment at scheduled maturity as reflected in the table).
The weighted average interest rate on short-  term debt excluding

the short-  term portion of long-  term debt at December 31, 2008, was 
4% (2007: 7%).
[C] LEASE ARRANGEMENTS
The future minimum lease payments for finance and operating 
leases and the present value of minimum finance lease payments at 
December 31, by maturity date are as follows:
2008 $ million 
Total future 
minimum finance 
lease payments InterestPresent value of 
lease paymentsTotal future minimum 
payments
2009 608 304 304 4,648
2010–2013 2,008 1,094 914 9,905
2014 and after 4,076 1,279 2,797 4,712
Total 6,692 2,677 4,015 19,265
Operating lease expenses were as follows ($ million):
Minimum lease payments 3,339 3,091 2,571
Contingent rentals 68 63 59
Sub-  lease income (161) (138) (132)
Total 3,246 3,016 2,498

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 576
Use the above information to answer the following questions:
1 How does Royal Dutch Shell initially value its debt on the balance sheet? 
How is debt subsequently measured on the balance sheet?
2 What method does Shell use to calculate interest expense on its debt?
3 What is the total amount of debt appearing within current liabilities on 
the balance sheet at 31 December 2008, and what does it include?
4 What is the total amount of debt due after one year appearing on the 
balance sheet at 31 December 2008, and what does it include?
5 How does the interest rate in 2008 on short-  term debt (excluding finance 
lease obligations and the short-  term portion of long-  term debt) compare 
to that in 2007?
6 What is the fair value of Royal Dutch Shell’s debt at 31 December 2008?
7 What was Royal Dutch Shell’s rent expense in fiscal year 2008 related to 
operating leases?
8 Comment on the relative magnitude of operating leases compared to

finance leases?
9 What are Shell’s debt-  to- equity ratios for 2008 and 2007? Comment on 
year-  to- year changes.
From Note 2, debt is initially reported at fair value based on amounts exchanged. 
After issuance, debt is reported at amortised cost except for certain fixed rate 
debt that is subject to fair value hedging. That debt is remeasured to fair value.
Note 2 indicates that Shell uses the effective interest rate method to calculate 
interest expense.
The total amount of debt included in current liabilities on the balance sheet is 
$9,497. Note 18[A] shows that this amount comprises $7,879 short-  term debt 
(excluding finance lease obligations), $1,314 long-  term debt due within one year 
(excluding finance lease obligations), and $304 finance lease obligations. The 
finance lease obligations are those due within one year.
The total amount of debt due after next year (non-  current debt) is $13,722. Note

18[A] shows that this amount comprises $10,061 debt (excluding finance lease 
obligations) and $3,711 finance lease obligations.
In Note 18 [B], Shell indicates that the interest rate on short-  term debt has 
declined significantly. The weighted average interest rate at 31 December on 
short-  term debt was 4 percent in 2008 and 7 percent in 2007.
From Note 18 [A], Shell reports that the fair value of debt approximates its 
carrying amount. The carrying amount is $23,269.
From Note 18 [C], rent expense on operating leases was $3,246 in 2008.

Leases 577
Although operating and finance leases are accounted for differently, we can 
compare the undiscounted future minimum lease payments under operating 
leases and finance leases reported in Note 18 [C] to gain an initial understanding 
of their relative magnitude. The total future minimum lease payments under 
operating leases of $19,265 are more than two and one-  half times the $6,692 
under finance leases.
Solution to 9:
Debt-  to- equity ratios are calculated as follows ($ million):
2008 2007
Debt (included in non-  current liabilities) 13,772 12,363
Debt (included in current liabilities) 9,497 5,736
Total current and non-  current debt 23,269 18,099
Total equity 128,866 125,966
Debt-  to- equity 18.06% 14.37%
The debt-  to- equity ratio increased to 18.06 percent in 2008 from 14.37 percent 
in 2007. This increase is primarily attributable to an increase in short-  term debt. 
From Note 18 [A] disclosures, short-  term debt increased by $4,587 million (from

$3,292 million in 2007 to $7,879 million in 2008), while the current portion of 
long-  term debt decreased by $826 million (from $2,444 million to $1,618 million) 
and the non-  current portion of debt increased by only $1,409  million (from 
$12,363 million to $13,772 million). The financing section of the statement of 
cash flows discloses that Shell issued $4,161 million in short-  term debt in 2008, 
compared with repaying short-  term debt in 2007.
3.2.2  Accounting and Reporting by the Lessor
Similar to accounting and reporting on the lessee side, the lessor also must determine 
whether a lease is classified as operating or finance. Under IFRS, the determination 
of a finance lease on the lessor’s side mirrors that of the lessee’s. That is, in a finance 
lease the lessor transfers substantially all the risks and rewards incidental to legal 
ownership.13 Under US GAAP , the lessor determines whether a lease is a capital or

operating lease using the same four identifying criteria as a lessee, plus the addi -
tional revenue recognition criteria. That is, the lessor must be reasonably assured of 
cash collection and has performed substantially under the lease. From the lessor’s 
perspective, US GAAP distinguishes between types of capital leases. There are two 
main types of capital leases from a lessor’s perspective: 1) direct financing leases , 
and 2) sales-  type leases .14
Under IFRS and US GAAP , if a lessor enters into an operating lease, the lessor 
records any lease revenue when earned. The lessor also continues to report the leased 
asset on the balance sheet and the asset’s associated depreciation expense on the 
income statement.
Under IFRS, if a lessor enters into a finance lease, the lessor reports a receivable at 
an amount equal to the net investment in the lease (the present value of the minimum 
lease payments receivable and any estimated unguaranteed residual value accruing 
13 IAS 17, paragraph 36.

14 A leveraged lease is a third type of capital lease from the lessor’s perspective under US GAAP . FASB 
ASC paragraph 840-  3-05-  4.

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 578
to the lessor).15 The leased asset is derecognised; assets are reduced by the carrying 
amount of the leased asset. Initial direct costs incurred by a lessor, other than a 
manufacturer or dealer lessor, are added to the receivable and reduce the amount of 
income recognised over the lease term. The lease payment is treated as repayment of 
principal (reduces lease receivable) and finance income. The recognition of finance 
income should reflect a constant periodic rate of return on the lessor’s net investment 
in the lease. Under the new IFRS on lease accounting (IFRS 16), lessors continue to 
recognize leases as either finance or operating leases in a similar manner to IAS 17.
For lessors that are manufacturers or dealers, the initial direct costs are treated as 
an expense when the selling profit is recognised; typically, selling profit is recognised

at the beginning of the lease term. Sales revenue equals the lower of the fair value of 
the asset or the present value of the minimum lease payments. The cost of sale is the 
carrying amount of the leased asset less the present value of the estimated unguar -
anteed residual value.
Under US GAAP , a direct financing lease results when the present value of lease 
payments (and thus the amount recorded as a lease receivable) equals the carrying 
value of the leased asset. Because there is no “profit” on the asset itself, the lessor is 
essentially providing financing to the lessee and the revenues earned by the lessor 
are financing in nature (i.e., interest revenue). If, however, the present value of lease 
payments (and thus the amount recorded as a lease receivable) exceeds the carrying 
amount of the leased asset, the lease is treated as a sales-  type lease.
Both types of capital leases have similar effects on the balance sheet: The lessor

reports a lease receivable based on the present value of future lease payments and 
derecognises the leased asset. The carrying value of the leased asset relative to the 
present value of lease payments distinguishes a direct financing lease from a sales-  type 
lease. A direct financing lease is reported when the present value of lease payment is 
equal to the value of the leased asset to the lessor. When the present value of lease 
payments is greater than the value of the leased asset, the lease is a sales-  type lease. 
The income statement effect will thus differ based on the type of lease.
In a direct financing lease, the lessor exchanges a lease receivable for the leased 
asset, no longer reporting the leased asset on its books. The lessor’s revenue is derived 
from interest on the lease receivable. In a sales-  type lease, the lessor “sells” the asset 
to the lessee and also provides financing on the sale. Therefore, in a sales-  type lease,

a lessor reports revenue from the sale, cost of goods sold (i.e., the carrying amount 
of the asset leased), profit on the sale, and interest revenue earned from financing 
the sale. The lessor will show a profit on the transaction in the year of inception and 
interest revenue over the life of the lease.
EXAMPLE 13   
Determining Initial Recognition and Measurement and 
Subsequent Measurement of a Finance Lease when the 
Present Value of Lease Payments Equals the Value of the 
Leased Asset
DIRFIN Inc. owns a piece of machinery and plans to lease the machine on 1 
January 2010. In the lease contract, DIRFIN requires four annual payments of 
€28,679 starting on 1 January 2010. DIRFIN is confident that the payments will 
be received. The useful life of the machine is four years, and its salvage value is 
15 Some lease contracts specify minimum lease payments with the potential for additional payments 
based upon some criteria.

Leases 579
zero. The present value of the lease payments and the fair value of the machine 
are each €100,000. The carrying amount for the machine also is €100,000. 
DIRFIN’s discount rate is 10 percent.
1 Comment on the appropriateness of DIRFIN’s treating the lease as a 
finance lease under IFRS and a capital lease under US GAAP .
2 What is the amount of the lease receivable reported on the balance sheet 
on 1 January 2010? What is interest revenue reported in fiscal year 2010?
3 What is the carrying amount of the machine reported on the balance 
sheet on 1 January 2010?
4 What is the amount of the lease receivable reported on the balance sheet 
on 31 December 2010? What is interest income reported in fiscal year 
2011?
5 If DIRFIN had determined the above lease was an operating lease, what 
amount of income would be reported on the income statement in fiscal 
year 2010?
Treating this lease as a finance lease under IFRS and a capital lease under US

GAAP is appropriate. Under the old international standard, the lease needed 
to meet at least two of the suggested criteria for a finance lease: 1) The lease 
term is for the major part of the economic life of the asset, and 2) at inception 
of the lease, the present value of the minimum lease payments amounts to at 
least substantially all of the fair value of the leased asset. Under IFRS 16, most 
long-  term leases are accounted for as finance leases. Under US GAAP , the lease 
meets more than one of the required criteria for a capital lease: 1) The lease 
term is 75 percent or more of the useful life of the leased asset (the lease term 
and useful life are both four years), and 2) the present value is 90 percent or 
more of the fair value of the leased asset (the present value of lease payments 
approximately equals the fair value of the machine). The revenue recognition 
requirement also is met. Under US GAAP , this capital lease is classified as a

direct financing lease because the present value of lease payment is equal to 
the value of the leased asset.
DIRFIN removes the leased asset from its records and records a lease receivable. 
On its income statement, DIRFIN reports interest revenues earned from financ -
ing the lease. The table below shows DIRFIN’s interest revenue and carrying 
amounts for the lease receivable.
On 1 January  2010, the lease receivable is initially recorded at €100,000. 
Immediately after the first lease payment is received on 1 January  2010, the 
carrying amount of the lease receivable decreases to €71,321 and remains at this 
amount through 31 December 2010. Interest revenue for 2010 is €7,132 (10 per -
cent interest rate times the loan receivable balance of €71,321 throughout 2010).
Y earLease 
Receivable, 1 
Payment 
Received,  
1 JanuaryInterest (at 
10%; accrued 
in previous 
year)Reduction 
of Lease 
1 JanuaryLease Receivable on 
Lease Payment on 1

January of Same Y ear

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 580
Y earLease 
Payment 
Received,  
of Lease 
■■Column (b) is the annual lease payment received at the beginning of the 
year, which is allocated to interest and reduction of the lease receivable.
■■Column (c) is interest for the year calculated as the lease receivable out -
standing for the year multiplied by the interest rate.
■■Column (d) is the reduction of the lease receivable, which is the difference 
between the annual lease payments received and interest. Because the 
at the end of the prior  year and interest revenue of the prior  year.

at the end of the year. It is the lease receivable at 1 January (column a) less 
the reduction of the lease receivable (column d).
DIRFIN effectively sells the machine through the finance lease and so reports 
no carrying amount for the machine.
The lease receivable is €71,321 at 31 December 2010. At 1 January 2011, the 
lease receivable decreases to €49,774 after the second lease payment is received 
on 1 January 2011. Interest revenue for 2011 is €4,977 (10 percent interest rate 
times the loan receivable balance of €49,774 throughout 2011).
As an operating lease, rent income of €28,679 would be reported on the income 
statement. Note that IFRS 16 does not allow the lease to be recognised as an 
operating lease.
When a lessor enters into a sales-  type lease (a lease agreement where the present

value of the future lease payments is greater than the value of the leased asset to 
the lessor), it will show a profit on the transaction in the year of lease inception and 
EXAMPLE 14   
Determining the Financial Statement Impact of a Finance 
Lease by the Lessor when the Present Value of Lease 
Payments Is Greater than the Value of the Leased Asset
Assume a (hypothetical) company, Selnow, manufactures machinery and enters 
into an agreement to lease a machine on 1 January 2010. Under the lease, the 
company is to receive four annual payments of €28,679 starting on 1 January 2010. 
Selnow is confident that the payments will be received. The fair value of the

Leases 581
machine and present value of the lease payments (using a 10 percent discount 
rate) are each €100,000, and the carrying amount of the machine is €90,000. The 
useful life of the machine is four years, and its salvage value is zero.
1 Comment on the appropriateness of Selnow’s treatment of the lease 
agreement as a finance lease under IFRS and a capital lease under US 
G A A P.
2 Ignoring taxes, what is Selnow’s income related to the lease in 2010? In 
2011?
Treating this lease as a finance lease under IFRS and a capital lease under US 
GAAP is appropriate.
Under IFRS, the lease meets at least two of the suggested criteria for a finance 
lease: 1) The lease term is for the major part of the economic life of the asset 
(the lease term and useful life of the machine are both four years), and 2) at 
inception of the lease the present value of the minimum lease payments amounts 
to at least substantially all of the fair value of the leased asset (the present value

of lease payments equals the fair value of the machine). Note that under IFRS 
16, the lessor needs to account for the lease as a finance lease even if the above 
criteria are not met.
Under US GAAP , the lease meets more than one of the required capital lease 
criteria, including the following: 1) The lease term is 75 percent or more of the 
useful life of the leased asset (the lease term and useful life of the machine are 
both four years), and 2) the present value is 90 percent or more of the fair value 
of the leased asset. The revenue recognition requirement also is met (Selnow 
is confident that the payments will be received). Further, under US GAAP this 
lease is classified as a sales-  type lease because the present value of the lease 
payments is greater than the carrying amount of the leased asset.
There is no difference, however, in accounting between IFRS and US GAAP 
as a result of this additional classification under US GAAP . The present value

of the future lease payments is more than the lessor’s carrying amount for the 
machine, and the difference is the lessor’s profit from selling the machine. The 
lessor will record a profit of €10,000 on the sale of the machine in 2010 (€100,000 
present value of lease payments receivable less €90,000 value of the machine).
In 2010, Selnow shows income of €17,132 related to the lease. One part of this 
income is the €10,000 gain on the sale of the machine (sales revenues of €100,000 
less costs of goods sold of €90,000). Selnow also shows interest revenue of 
€7,132 on its financing of the lease (lease receivable of €71,321 after the initial 
lease payment is received times the 10 percent discount rate). In 2011, Selnow 
table below shows lease payments received, interest revenue, and reduction of

the lease receivable for Selnow’s sales-  type lease. Note that this table is the same 
as DIRFIN’s table in Example 13 with the direct financing lease. They are the 
same because the present value of the lease payments in both cases is the same. 
It is the carrying amount of the machine that differs between the two examples.

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 582
Y earLease 
Payment 
of Lease 
1 JanuaryLease Receivable on 31 
Payment on 1 January 
of Same Y ear
Exhibit 2 summarises the financial statement impact of operating and financing 
leases on the lessee and lessor.
Exhibit 2   Summary of Financial Statement Impact of Operating and Financing Leases on the Lessee and 
Lessor
Balance Sheet Income Statement Statement of Cash Flows
Lessee
Operating Lease No effect Reports rent expense Rent payment is an operating cash 
outflow
Finance Lease under IFRS 
(capital lease under US 
GAAP)Recognises leased asset 
and lease liabilityReports depreciation 
expense on leased asset

expense on leased asset  
Reports interest expense 
on lease liabilityReduction of lease liability is a 
financing cash outflow  
Interest portion of lease payment is 
either an operating or financing cash 
outflow under IFRS and an operat -
ing cash outflow under US GAAP
Lessor
Operating Lease Retains asset on balance 
sheetReports rent income  
Reports depreciation 
expense on leased assetRent payments received are an oper -
ating cash inflow
Finance Leasea

Introduction to Pensions and Other Post-  Employment Benefits 583
When present value of lease 
payments equals the car -
rying amount of the leased 
asset (called a direct financ -
ing lease in US GAAP)Removes asset from bal -
ance sheet  
Recognises lease 
receivableReports interest revenue 
on lease receivableInterest portion of lease payment 
received is either an operating or 
investing cash inflow under IFRS 
and an operating cash inflow under 
US GAAP  
Receipt of lease principal is an 
investing cash inflowb
payments exceeds the car -
asset (called a sales-  type 
lease in US GAAP)Removes asset  
receivableReports profit on sale  
Reports interest revenue 
US GAAP  

a US GAAP distinguishes between a direct financing lease and a sales-  type lease, but IFRS does not. The accounting is the same for IFRS 
and US GAAP despite this additional classification under US GAAP .
b If providing leases is part of a company’s normal business activity, the cash flows related to the leases are classified as operating cash.
INTRODUCTION TO PENSIONS AND OTHER POST-  
EMPLOYMENT BENEFITS
Pensions and other post-  employment benefits give rise to non-  current liabilities 
reported by many companies. Companies may offer various types of benefits to their 
employees following retirement, such as pension plans, health care plans, medical 
insurance, and life insurance. Pension plans often are the most significant post-  
employment benefits provided to retired employees.
The accounting and reporting for pension plans depends on the type of pension 
plan offered. Two common types of pension plans are defined contribution pension

plans  and defined benefit pension plans . Under a defined-  contribution plan, a com -
pany contributes an agreed-  upon (defined) amount into the plan. The agreed-  upon 
amount is the pension expense. The amount the company contributes to the plan is 
treated as an operating cash outflow. The only impact on assets and liabilities is a 
decrease in cash, although if some portion of the agreed-  upon amount has not been 
paid by fiscal year-  end, a liability would be recognised on the balance sheet. Because 
the amount of the contribution is defined and the company has no further obligation 
once the contribution has been made, accounting for a defined-  contribution plan is 
fairly straightforward.
Accounting for a defined-  benefit plan is more complicated. Under a defined-  benefit 
plan, a company makes promises of future benefits to be paid to the employee during 
retirement. For example, a company could promise an employee annual pension pay -

ments equal to 70 percent of his final salary at retirement until death. Estimating the 
eventual amount of the obligation arising from that promise requires the company to 
make many assumptions, such as the employee’s expected salary at retirement and the 
number of years the employee is expected to live beyond retirement. The company 
estimates the future amounts to be paid and discounts the future estimated amounts 
to a present value (using a rate reflective of a high-  quality corporate bond yield) to 4Exhibit 2   (Continued)

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 584
determine the pension obligation. The discount rate used to determine the pension 
obligation significantly affects the amount of the pension obligation. The pension 
obligation is allocated over the employee’s employment as part of pension expense.
Most defined-  benefit pension plans are funded through a separate legal entity, 
typically a pension trust fund. A company makes payments into the pension fund, and 
retirees are paid from the fund. The payments that a company makes into the fund are 
invested until they are needed to pay the retirees. If the fair value of the fund’s assets 
is higher than the present value of the estimated pension obligation, the plan has a 
surplus and the company’s balance sheet will reflect a net pension asset.16 Conversely, 
if the present value of the estimated pension obligation exceeds the fund’s assets, the 
plan has a deficit and the company’s balance sheet will reflect a net pension liability.17

Thus, a company reports either a net pension asset or a net pension liability. Each 
period, the change in the net pension asset or liability is recognised either in profit 
or loss or in other comprehensive income.
Under IFRS, the change in the net pension asset or liability each period is viewed 
as having three general components. Two of the components of this change are rec -
ognised as pension expense in profit and loss: (1) employees’ service costs and (2) 
the net interest expense or income accrued on the beginning net pension asset or 
liability. The service cost during the period for an employee is the present value of 
the increase in the pension benefit earned by the employee as a result of providing 
one more year of service. The service cost also includes past service costs, which are 
changes in the present value of the estimated pension obligation related to employees’ 
service in prior periods, such as might arise from changes in the plan. The net interest

expense or income is calculated as the net pension asset or liability multiplied by the 
discount rate used in estimating the present value of the pension obligation. The third 
component of the change in the net pension asset or liability during a period—“remea -
surements”—is recognised in other comprehensive income. Remeasurements are not 
amortised into profit or loss over time.
Remeasurements include (a) actuarial gains and losses and (b) the actual return on 
plan assets less any return included in the net interest expense or income. Actuarial 
gains and losses can occur when changes are made to the assumptions on which a 
company bases its estimated pension obligation (e.g., employee turnover, mortality 
rates, retirement ages, compensation increases). The actual return on plan assets would 
likely differ from the amount included in the net interest expense or income, which 
is calculated using a rate reflective of a high-  quality corporate bond yield; plan assets

are typically allocated across various asset classes, including equity as well as bonds.
Under US GAAP , the change in net pension asset or liability each period is viewed 
as having five components, some of which are recognised in profit and loss in the 
period incurred and some of which are recognised in other comprehensive income 
and amortised into profit and loss over time. The three components recognised in 
profit and loss in the period incurred are (1) employees’ service costs for the period, 
(2) interest expense accrued on the beginning pension obligation, and (3) expected 
return on plan assets, which reduces the amount of expense recognised. The other two 
components are past service costs and actuarial gains and losses. Past service costs 
are recognised in other comprehensive income in the period in which they arise and 
then subsequently amortised into pension expense over the future service period of

the employees covered by the plan. Actuarial gains and losses are also recognised in 
16 The amount of any reported net pension asset is capped at the amount of any expected future economic 
benefits to the company from the plan; this cap is referred to as the asset ceiling.
17 The description of accounting for pensions presented in this reading corresponds to the June 2011 
version of IAS 19 Employee Benefits , which took effect on 1 January 2013. Both IFRS and US GAAP require 
companies to present the amount of net pension liability or asset on the balance sheet.

Introduction to Pensions and Other Post-  Employment Benefits 585
other comprehensive income in the period in which they occur and then amortised 
into pension expense over time. In effect, US GAAP allows companies to “smooth” 
the effects on pension expense over time for these latter two components.
Similar to other forms of employee compensation for a manufacturing company, 
the pension expense related to production employees is added to inventory and 
expensed through cost of sales (cost of goods sold). For employees not involved 
directly in the production process, the pension expense is included with salaries and 
other administrative expenses. Therefore, pension expense is not directly reported 
on the income statement. Rather, extensive disclosures are included in the notes to 
the financial statements.
Example 15 presents excerpts of pension-  related disclosures from Novo Nordisk’s 
2010 Annual Report.
EXAMPLE 15   
Pension-  Related Disclosures

EXAMPLE 15   
The following are excerpts of pension-  related disclosures from Novo Nordisk’s 
2010 Annual Report. Novo Nordisk reports under IFRS. These financial state -
ments were issued prior to the updated IFRS for pension accounting, which 
(effective January  2013) requires companies to show the entire amount of net 
liability or asset on the balance sheet and to recognise the entire change in that 
amount each period.
1 Summary of significant accounting policies
Pensions
The Group operates a number of defined contribution plans 
throughout the world. In a few countries the group still operates 
defined benefit plans. The costs for the year for defined benefit 
plans are determined using the projected unit credit method. This 
reflects services rendered by employees to the dates of valuation and 
is based on actuarial assumptions primarily regarding discount rates 
used in determining the present value of benefits, projected rates of

remuneration growth and long-  term expected rates of return for plan 
assets. Discount rates are based on the market yields of high-  rated 
corporate bonds in the country concerned. 
21 Retirement Benefit Obligations
DKK million 2010 2009 2008 2007 2006
Retirement obligations 1,452 1,063 1,103 885 938
Plan assets (766) (620) (649) (566) (495)
Use information in the excerpts to answer the following questions:
1 What type(s) of pension plans does Novo Nordisk have?
2 Under the updated standards, what would have been reported on Novo 
Nordisk’s 2009 and 2010 balance sheets with respect to pensions?
3 Under the updated standards, what amount of pension costs would Novo 
Nordisk have recognised in 2010? Describe how these costs would have 
been reported.

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 586
Note 1 “Summary of significant accounting policies” indicates that the company 
has both defined contribution and defined benefit pension plans. The note 
indicates that the company continues to operate defined benefit plans in only 
a few countries.
Under the updated standards, Novo Nordisk would have reported a net pension 
obligation of DKK686 million in 2010 and DKK 443 million in 2009:
(DKK million) 2010 2009
Retirement obligations 1,452 1,063
Plan assets (766) (620)
Deficit/(surplus) 686 443
Under the updated standards, Novo Nordisk would have reported total pension 
cost of DKK 243 million in 2010, which is the change in the pension deficit from 
DKK 443 million in 2009 to DKK 686 million in 2010.
Of the total pension cost, two components would be recognised in profit and 
loss (service costs and net interest expense on the pension deficit) and one com -

ponent would be recognised in other comprehensive income (remeasurements).
EVALUATING SOLVENCY: LEVERAGE AND COVERAGE 
RATIOS
Solvency refers to a company’s ability to meet its long-  term debt obligations, including 
both principal and interest payments. In evaluating a company’s solvency, ratio analyses 
can provide information about the relative amount of debt in the company’s capital 
structure and the adequacy of earnings and cash flow to cover interest expense and 
other fixed charges (such as lease or rental payments) as they come due. Ratios are 
useful to evaluate a company’s performance over time compared to the performance 
of other companies and industry norms. Ratio analysis has the advantage of allowing 
the comparison of companies regardless of their size and reporting currency.
The two primary types of solvency ratios are leverage ratios and coverage ratios. 
Leverage ratios focus on the balance sheet and measure the extent to which a com -

pany uses liabilities rather than equity to finance its assets. Coverage ratios focus on 
the income statement and cash flows and measure the ability of a company to cover 
its debt-  related payments.
Exhibit 3 describes the two types of commonly used solvency ratios. The first three 
leverage ratios use total debt in the numerator.18 The debt-  to- assets ratio  expresses 
the percentage of total assets financed with debt. Generally, the higher the ratio, the 
higher the financial risk and thus the weaker the solvency. The debt-  to- capital  ratio  
measures the percentage of a company’s total capital (debt plus equity) financed 5
18 For calculations in this reading, total debt is the sum of interest-  bearing short-  term and long-  term debt, 
excluding non-  interest-  bearing liabilities, such as accrued expenses, accounts payable, and deferred income 
taxes. This definition of total debt differs from other definitions that are more inclusive (e.g., all liabilities) or

more restrictive (e.g., long-  term debt only). If the use of different definitions of total debt materially changes 
conclusions about a company’s solvency, the reasons for the discrepancies should be further investigated.

Evaluating Solvency: Leverage and Coverage Ratios 587
through debt. The debt-  to- equity rati o measures the amount of debt financing relative 
to equity financing. A debt-  to- equity ratio  of 1.0 indicates equal amounts of debt and 
equity, which is the same as a debt-  to- capital ratio of 50 percent. Interpretations of 
these ratios are similar. Higher debt-  to- capital or debt-  to- equity ratios imply weaker 
solvency. A caveat must be made when comparing debt ratios of companies in differ -
ent countries. Within certain countries, companies historically have obtained more 
capital from debt than equity financing, so debt ratios tend to be higher for companies 
in these countries.
Exhibit 3   Definitions of Commonly Used Solvency Ratios
Leverage ratios
Debt-  to- assets ratio Total debtaTotal assets
Debt-  to- capital ratio Total debtaTotal debta + Total shareholders’ 
equity
Debt-  to- equity ratio Total debtaTotal shareholders’ equity

Financial leverage ratio Average total assets Average shareholders’ equity
Coverage ratios
Interest coverage ratio EBITbInterest payments
Fixed charge coverage ratio EBITb + lease 
paymentsInterest payments + lease 
payments
a In this reading, debt is defined as the sum of interest-  bearing short-  term and long-  term debt.
b EBIT is earnings before interest and taxes.
The financial leverage ratio  (also called the ‘leverage ratio’ or ‘equity multiplier’) 
measures the amount of total assets supported by one money unit of equity. For 
example, a value of 4 for this ratio means that each €1 of equity supports €4 of total 
assets. The higher the financial leverage ratio, the more leveraged the company in the 
sense of using debt and other liabilities to finance assets. This ratio often is defined 
in terms of average total assets and average total equity and plays an important role 
in the DuPont decomposition of return on equity.19

The interest coverage ratio  measures the number of times a company’s EBIT 
could cover its interest payments. A higher interest coverage ratio indicates stron -
ger solvency, offering greater assurance that the company can service its debt from 
operating earnings. The fixed charge coverage ratio  relates fixed financing charges, or 
obligations, to the cash flow generated by the company. It measures the number of 
times a company’s earnings (before interest, taxes, and lease payments) can cover the 
company’s interest and lease payments.
Example 16 demonstrates the use of solvency ratios in evaluating the creditwor -
19 The basic DuPont decomposition is: Return on Equity = Net income/Average shareholders’ equity = 
(Sales/Average total assets) × (Net income/Sales) × (Average total assets/Average shareholders’ equity).

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 588
EXAMPLE 16   
Evaluating Solvency Ratios
A credit analyst is evaluating and comparing the solvency of two companies—
Nokia Corporation and LM Ericsson Telephone Company—at the beginning of 
2009. The following data are gathered from the companies’ 2008 annual reports 
and 20-  F filings:
Nokia  
(€ millions)Ericsson  
(SEK millions)
2008 2007 2008 2007
Short-  term borrowings 3,578 714 1,639 2,831
Current portion of long-  term 
interest bearing debt13 173 3,903 3,068
Long-  term interest bearing debt 861 203 24,939 21,320
Total shareholders' equity 14,208 14,773 140,823 134,112
Total assets 39,582 37,599 285,684 245,117
EBIT 4,966 7,985 16,252 30,646
Interest payments 155 59 1,689 1,513
1 A What are each company’s debt-  to- assets, debt-  to- capital, and debt-  to- 
equity ratios for 2008 and 2007?
B Comment on any changes in the calculated leverage ratios from year-

to- year for both companies.
C Comment on the calculated leverage ratios of Nokia compared to 
Ericsson.
2 A What is each company’s interest coverage ratio for 2008 and 2007?
B Comment on any changes in the interest coverage ratio from year to 
year for both companies.
C Comment on the interest coverage ratio of Nokia compared to 
Ericsson.
A For Nokia
Debt-  to- assets for 2008: 11.2% = (3,578 + 13 + 861)/39,582
Debt-  to- assets for 2007: 2.9% = (714 + 173 + 203)/37,599
Debt-  to- capital for 2008: 23.9% = (3,578 + 13 + 861)/(3,578 + 13 + 
861 + 14,208)
Debt-  to- capital for 2007: 6.9% = (714 + 173 + 203)/(714 + 173 + 203 + 
14,773)
Debt-  to- equity for 2008: 31.3% = (3,578 + 13+861)/(14,208)
Debt-  to- equity for 2007: 7.4% = (714 + 173 + 203)/(14,773)

Evaluating Solvency: Leverage and Coverage Ratios 589
 For Ericsson
Debt-  to- assets for 2008: 10.7% = (1,639 + 3,903 + 24,939)/(285,684)
Debt-  to- assets for 2007: 11.1% = (2,831 + 3,068 + 21,320)/(245,117)
Debt-  to- capital for 2008: 17.8% = (1,639 + 3,903 + 24,939)/(1,639 + 
3,903 + 24,939 + 140,823)
Debt-  to- capital for 2007: 16.9% = (2,831 + 3,068 + 21,320)/(2,831 + 
3,068 + 21,320 + 134,112)
Debt-  to- equity for 2008: 21.6% = (1,639 + 3,903 + 24,939)/(140,823)
Debt-  to- equity for 2007: 20.3% = (2,831 + 3,068 + 21,320)/(134,112)
B Nokia’s leverage ratios all increased from 2007 to 2008, suggesting weak -
ening solvency. Comparing debt year to year, we observe that leverage 
ratios increased because of a significant increase in short-  term borrow -
ings and an increase in long-  term interest bearing debt without a similar 
increase in shareholders’ equity. In fact, shareholders’ equity declined.
 On the other hand, Ericsson’s leverage ratios appear fairly similar for 2007

and 2008. During 2008, it appears as though Ericsson shifted away from 
short borrowings to long-  term debt.
C In 2007, all three of Nokia’s leverage ratios were lower than Ericsson’s. 
In 2008, the opposite was true. Ericsson’s capital structure seems fairly 
constant over the two years, whereas Nokia’s capital structure has shifted 
toward more debt.
A For Nokia
Interest coverage ratio for 2008: 32.0 = (4,966/155)
Interest coverage ratio for 2007: 135.3 = (7,985/59)
Interest coverage ratio for 2008: 9.6 = (16,252/1,689)
Interest coverage ratio for 2007: 20.3 = (30,646/1,513) 
B Nokia’s interest coverage ratio decreased from 2007 to 2008 because of 
a decrease in EBIT and an increase in interest payments. Even with the 
decrease, Nokia appears to have sufficient operating earnings to cover 
interest payments. Similarly, Ericsson’s interest coverage ratio decreased 
from 2007 to 2008, primarily because of a decrease in EBIT. Ericsson also

appears to have sufficient operating earnings to cover interest payments.
C Nokia’s ability to cover interest payments is greater than Ericsson’s, 
although both companies appear to have sufficient operating earnings to 
cover interest payments.

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 590
SUMMARY
Non-  current liabilities arise from different sources of financing and different types 
of creditors. Bonds are a common source of financing from debt markets. Bonds 
are initially valued at fair value when issued, and then companies have the choice of 
whether to subsequently measure bonds at fair value or amortised cost.
Leases are related to the use of specific assets. In a finance lease, the lessee assumes 
substantially all the risks and benefits of ownership of the leased asset so the lessee 
reports an asset and related obligation. Typically, the lessor will report a lease receiv -
able and derecognise the asset. In an operating lease, the lessee secures the right to 
use the leased asset but substantially all the risk and rewards of ownership are not 
transferred. The lessor does not derecognise the asset and reports lease (rent) income.

Under IFRS 16, leases of more than one year are treated in a manner similar to finance 
leases—that is, as assets and associated liabilities in the lessee’s balance sheet.
Pensions and other post-  employment benefits are additional forms of compensa -
tion. Employees work currently to earn current salaries and wages and also to earn 
benefits for retirement or post-  employment. Companies with defined contribution 
plans report the agreed upon contribution paid into a plan as an expense. Defined 
benefit plans provide for agreed upon future benefits. Understanding the reporting 
of non-  current liabilities when they arise and how they are subsequently valued is 
important in assessing a company’s solvency and potential changes in its solvency.
Key points in accounting and reporting of non-  current liabilities include the 
■■The sales proceeds of a bond issue are determined by discounting future cash 
payments using the market rate of interest at the time of issuance (effective

interest rate). The reported interest expense on bonds is based on the effective 
interest rate.
■■Future cash payments on bonds usually include periodic interest payments 
(made at the stated interest rate or coupon rate) and the principal amount at 
maturity.
■■When the market rate of interest equals the coupon rate for the bonds, the 
bonds will sell at par (i.e., at a price equal to the face value). When the market 
rate of interest is higher than the bonds’ coupon rate, the bonds will sell at a 
discount. When the market rate of interest is lower than the bonds’ coupon 
rate, the bonds will sell at a premium.
■■An issuer amortises any issuance discount or premium on bonds over the life of 
the bonds.
■■If a company redeems bonds before maturity, it reports a gain or loss on debt 
extinguishment computed as the net carrying amount of the bonds (including 
bond issuance costs under IFRS) less the amount required to redeem the bonds.

■■Debt covenants impose restrictions on borrowers, such as limitations on future 
borrowing or requirements to maintain a minimum debt-  to- equity ratio.
■■The carrying amount of bonds is typically amortised historical cost, which can 
differ from their fair value.
■■Companies are required to disclose the fair value of financial liabilities, includ -
ing debt. Although permitted to do so, few companies opt to report debt at fair 
values on the balance sheet.

Summary 591
■■Accounting standards have traditionally required leases to be classified as either 
operating leases or finance (capital) leases. Leases are classified as finance leases 
when substantially all the risks and rewards of legal ownership are transferred 
to the lessee.
the lessee usually reports higher profits before tax in the early years of the lease 
and lower profits in later years; however, the impact on pretax profits will be 
neutral between the choice of leases.
the lessor usually appears more profitable in the early years of the lease.
■■In a finance lease where the present value of lease payments equals the carrying 
amount of the leased asset, a lessor earns only interest revenue. In a finance 
lease where the present value of lease payments exceeds the carrying amount of

the leased asset, a lessor earns both interest revenue and a profit (or loss) on the 
sale of the leased asset.
■■Two types of pension plans are defined contribution plans and defined benefits 
plans. In a defined contribution plan, the amount of contribution into the plan 
is specified (i.e., defined) and the amount of pension that is ultimately paid 
by the plan (received by the retiree) depends on the performance of the plan’s 
assets. In a defined benefit plan, the amount of pension that is ultimately paid 
by the plan (received by the retiree) is defined, usually according to a benefit 
formula.
■■Under a defined contribution plan, the cash payment made into the plan is 
recognised as pension expense.
■■Under both IFRS and US GAAP , companies must report the difference between 
the defined benefit pension obligation and the pension assets as an asset or 
liability on the balance sheet.
■■Under IFRS, the change in the defined benefit plan net asset or liability is

recognised as a cost of the period, with two components of the change (service 
cost and net interest expense or income) recognised in profit and loss and one 
component (remeasurements) of the change recognised in other comprehensive 
income.
■■Under US GAAP , the change in the defined benefit plan net asset or liability is 
also recognised as a cost of the period with three components of the change 
(current service costs, interest expense on the beginning pension obligation, 
and expected return on plan assets) recognised in profit and loss and two com -
ponents (past service costs and actuarial gains and losses) recognised in other 
comprehensive income.
■■Solvency refers to a company’s ability to meet its long-  term debt obligations.
■■In evaluating solvency, leverage ratios focus on the balance sheet and measure 
the amount of debt financing relative to equity financing.
■■In evaluating solvency, coverage ratios focus on the income statement and cash

flows and measure the ability of a company to cover its interest payments.

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 592
1 A company issues €1 million of bonds at face value. When the bonds are issued, 
the company will record a:
A cash inflow from investing activities.
B cash inflow from financing activities.
C cash inflow from operating activities.
2 At the time of issue of 4.50% coupon bonds, the effective interest rate was 
5.00%. The bonds were most likely  issued at:
A par.
B a discount.
C a premium.
3 Oil Exploration LLC paid $45,000 in printing, legal fees, commissions, and 
other costs associated with its recent bond issue. It is most likely  to record these 
costs on its financial statements as:
A an asset under US GAAP and reduction of the carrying value of the debt 
B a liability under US GAAP and reduction of the carrying value of the debt 
C a cash outflow from investing activities under both US GAAP and IFRS.
4 A company issues $1,000,000 face value of 10-  year bonds on 1 January 2015

when the market interest rate on bonds of comparable risk and terms is 5%. The 
bonds pay 6% interest annually on 31 December. At the time of issue, the bonds 
payable reflected on the balance sheet is closest  to:
A $926,399.
C $1,077,217.
5 Midland Brands issues three-  year bonds dated 1 January 2015 with a face value 
of $5,000,000. The market interest rate on bonds of comparable risk and term is 
3%. If the bonds pay 2.5% annually on 31 December, bonds payable when issued 
are most likely reported as closest to:
A $4,929,285.
B $5,000,000.
C $5,071,401.
6 A firm issues a bond with a coupon rate of 5.00% when the market interest rate 
is 5.50% on bonds of comparable risk and terms. One year later, the market 
interest rate increases to 6.00%. Based on this information, the effective interest 
rate is:
A 5.00%.
B 5.50%.
C 6.00%.
7 On 1 January 2010, Elegant Fragrances Company issues £1,000,000 face value, 
five-  year bonds with annual interest payments of £55,000 to be paid each 31

December. The market interest rate is 6.0 percent. Using the effective interest 
rate method of amortisation, Elegant Fragrances is most likely  to record:

Practice Problems 593
A an interest expense of £55,000 on its 2010 income statement.
B a liability of £982,674 on the 31 December 2010 balance sheet.
C a £58,736 cash outflow from operating activity on the 2010 statement of 
8 Consolidated Enterprises issues €10 million face value, five-  year bonds with a 
coupon rate of 6.5 percent. At the time of issuance, the market interest rate is 
6.0 percent. Using the effective interest rate method of amortisation, the carry -
ing value after one year will be closest  to:
A €10.17 million.
B €10.21 million.
C €10.28 million.
9 A company issues €10,000,000 face value of 10-  year bonds dated 1 January 2015 
when the market interest rate on bonds of comparable risk and terms is 6%. The 
bonds pay 7% interest annually on 31 December. Based on the effective interest 
rate method, the interest expense on 31 December 2015 is closest  to:
A €644,161.
B €700,000.
C €751,521.
10 A company issues $30,000,000 face value of five-  year bonds dated 1

January 2015 when the market interest rate on bonds of comparable risk and 
terms is 5%. The bonds pay 4% interest annually on 31 December. Based on 
the effective interest rate method, the carrying amount of the bonds on 31 
December 2015 is closest  to:
A $28,466,099.
B $28,800,000.
C $28,936,215.
11 Lesp Industries issues five-  year bonds dated 1 January 2015 with a face value 
of $2,000, 000 and 3% coupon rate paid annually on 31 December. The market 
interest rate on bonds of comparable risk and term is 4%. The sales proceeds of 
the bonds are $1,910,964. Under the effective interest rate method, the interest 
expense in 2017 is closest to:
A $77,096.
B $77,780.
C $77,807.
12 For a bond issued at a premium, using the effective interest rate method, the:
A carrying amount increases each year.
B amortization of the premium increases each year.
C premium is evenly amortized over the life of the bond.
13 Comte Industries issues $3,000,000 worth of three-  year bonds dated 1

January 2015. The bonds pay interest of 5.5% annually on 31 December. The 
market interest rate on bonds of comparable risk and term is 5%. The sales pro -
ceeds of the bonds are $3,040,849. Under the straight-  line method, the interest 
expense in the first year is closest to:
A $150,000.
B $151,384.
C $152,042.

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 594
14 The management of Bank EZ repurchases its own bonds in the open market. 
They pay €6.5 million for bonds with a face value of €10.0 million and a carry -
ing value of €9.8 million. The bank will most likely  report:
A other comprehensive income of €3.3 million.
B other comprehensive income of €3.5 million.
C a gain of €3.3 million on the income statement.
15 A company redeems $1,000,000 face value bonds with a carrying value of 
$990,000. If the call price is 104 the company will:
A reduce bonds payable by $1,000,000.
B recognize a loss on the extinguishment of debt of $50,000.
C recognize a gain on the extinguishment of debt of $10,000.
16 Innovative Inventions, Inc. needs to raise €10 million. If the company chooses 
to issue zero-  coupon bonds, its debt-  to- equity ratio will most likely :
A rise as the maturity date approaches.
B decline as the maturity date approaches.
C remain constant throughout the life of the bond.

17 Fairmont Golf issued fixed rate debt when interest rates were 6 percent. Rates 
have since risen to 7 percent. Using only the carrying amount (based on his -
torical cost) reported on the balance sheet to analyze the company’s financial 
position would most likely  cause an analyst to:
A overestimate Fairmont’s economic liabilities.
B underestimate Fairmont’s economic liabilities.
C underestimate Fairmont’s interest coverage ratio.
18 Which of the following is an example of an affirmative debt covenant? The bor -
rower is: 
A prohibited from entering into mergers.
B prevented from issuing excessive additional debt.
C required to perform regular maintenance on equipment pledged as 
collateral.
19 Debt covenants are least likely  to place restrictions on the issuer’s ability to:
A pay dividends.
B issue additional debt.
C issue additional equity.
20 Regarding a company’s debt obligations, which of the following is most likely

presented on the balance sheet?
A Effective interest rate
B Maturity dates for debt obligations
C The portion of long-  term debt due in the next 12 months
21 Compared to using a finance lease, a lessee that makes use of an operating lease 
will most likely  report higher:
A debt.
B rent expense.
C cash flow from operating activity.
22 Which of the following is most likely  a lessee’s disclosure about operating 
leases?
A Lease liabilities.

Practice Problems 595
B Future obligations by maturity.
C Net carrying amounts of leased assets.
23 For a lessor, the leased asset appears on the balance sheet and continues to be 
depreciated when the lease is classified as:
A a sales-  type lease.
B an operating lease.
C a financing lease.
24 Under US GAAP , a lessor’s reported revenues at lease inception will be highest  
if the lease is classified as:
C a direct financing lease.
25 A lessor will record interest income if a lease is classified as:
A a capital lease.
C either a capital or an operating lease.
26 Compared with a finance lease, an operating lease:
A is similar to renting an asset.
B is equivalent to the purchase of an asset.
C term is for the majority of the economic life of the asset.
27 Under US GAAP , which of the following would require the lessee to classify a 
lease as a capital lease?
A The term is 60% of the useful life of the asset.

B The lease contains an option to purchase the asset at fair value.
C The present value of the lease payments is 95% of the fair value.
28 A lessee that enters into a finance lease will report the:
A lease payable on its balance sheet.
B full lease payment on its income statement. 
C full lease payment as an operating cash flow.
29 A company enters into a finance lease agreement to acquire the use of an asset 
for three years with lease payments of €19,000,000 starting next year. The leased 
asset has a fair market value of €49,000,000 and the present value of the lease 
payments is €47,250,188. Based on this information, the value of the lease pay -
able reported on the company’s balance sheet is closest  to:
A €47,250,188.
B €49,000,000.
C €57,000,000.
30 Which of the following best describes reporting and disclosure requirements for 
a company that enters into an operating lease as the lessee? The operating lease 
obligation is:

A reported as a receivable on the balance sheet.
B disclosed in notes to the financial statements.
C reported as a component of debt on the balance sheet.

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 596
31 Cavalier Copper Mines has $840 million in total liabilities and $520 million in 
shareholders’ equity. It discloses operating lease commitments over the next five 
years with a present value of $100 million. If the lease commitments are treated 
as debt, the debt-  to- total-  capital ratio is closest  to:
A 0.58.
B 0.62.
C 0.64.
32 The following presents selected financial information for a company:
$ Millions
Short-  term borrowing 4,231
Current portion of long-  term interest-  bearing debt 29
Long-  term interest-  bearing debt 925
Average shareholders’ equity 18,752
Average total assets 45,981
 The financial leverage ratio is closest  to:
A 0.113
B 0.277
C 2.452
33 An analyst evaluating three industrial companies calculates the following ratios:
Company A Company B Company C
Debt-  to- Equity 23.5% 22.5% 52.5%
Interest Coverage 15.6 49.5 45.5
 The company with both the lowest financial leverage and the greatest ability to

meet interest payments is:
A Company A.
B Company B.
C Company C.
34 An analyst evaluating a company’s solvency gathers the following information:
$ Millions
Short-  term interest-  bearing debt 1,258
Long-  term interest-  bearing debt 321
Total shareholder’s equity 4,285
Total assets 8,750
EBIT 2,504
Interest payments 52
 The company’s debt-  to- assets ratio is closest to:
A 0.18.
B 0.27.
C 0.37.

Practice Problems 597
35 Penben Corporation has a defined benefit pension plan. At 31 December, its 
pension obligation is €10 million and pension assets are €9 million. Under 
either IFRS or US GAAP , the reporting on the balance sheet would be closest  to 
which of the following?
A €10 million is shown as a liability, and €9 million appears as an asset.
B €1 million is shown as a net pension obligation.
C Pension assets and obligations are not required to be shown on the balance 
sheet but only disclosed in footnotes.
36 The following information is associated with a company that offers its employ -
ees a defined benefit plan:
Fair value of fund’s assets $1,500,000,000
Estimated pension obligations $2,600,000,000
Present value of estimated pension obligations $1,200,000,000
 Based on this information, the company’s balance sheet will present a net 
pension:
A asset of $300,000,000.
B asset of $1,400,000,000. 
C liability of $1,100,000,000.

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 598
SOLUTIONS
1 B is correct. The company receives €1 million in cash from investors at the time 
the bonds are issued, which is recorded as a financing activity.
2 B is correct. The effective interest rate is greater than the coupon rate and the 
bonds will be issued at a discount.
3 A is correct. Under US GAAP , expenses incurred when issuing bonds are gener -
ally recorded as an asset and amortised to the related expense (legal, etc.) over 
the life of the bonds. Under IFRS, they are included in the measurement of the 
liability. The related cash flows are financing activities.
4 C is correct. The bonds will be issued at a premium because the coupon rate is 
higher than the market interest rate. The future cash outflows, the present value 
of the cash outflows, and the total present value are as follows:
Payment ($)Present Value at 
Market Rate 5% 
($)Present Value at 
($)Total Present 
Value ($)

Value ($)
31 December 2015 60,000.00 57,142.86
31 December 2016 60,000.00 54,421.77
31 December 2017 60,000.00 51,830.26
31 December 2018 60,000.00 49,362.15
31 December 2019 60,000.00 47,011.57
31 December 2020 60,000.00 44,772.92
31 December 2021 60,000.00 42,640.88
31 December 2022 60,000.00 40,610.36
31 December 2023 60,000.00 38,676.53
31 December 2024 60,000.00 36,834.80 1,000,000.00 613,913.25
463,304.10 613,913.25 1,077,217.35
 The following illustrates the keystrokes for many financial calculators to calcu -
late sales proceeds of $1,077,217.35:
Calculator NotationNumerical Value for This 
Problem
N 10
% i or I/Y 5
FV $1,000,000.00
PMT $60,000.00
PV compute X
 Thus, the sales proceeds are reported on the balance sheet as an increase in 
long-  term liability, bonds payable of $1,077,217. 
5 A is correct. The bonds payable reported at issue is equal to the sales proceeds. 
The interest payments and future value of the bond must be discounted at the

Solutions 599
PaymentPresent 
Value at 
Market Rate 
(3%)Face Value 
at Market Rate 
(3%)Total Present 
Value
31 December 2015 $125,000.00 $121,359.22
31 December 2016 $125,000.00 $117,824.49
31 December 2017 $125,000.00 $114,392.71 $5,000,000.00 $4,575,708.30
Total $353,576.42 $4,575,708.30 $4,929,284.72
Problem
N 3
% i or I/Y 3.0
FV $5,000,000.00
PMT $125,000.00
6 B is correct. The market interest rate at the time of issuance is the effective 
interest rate that the company incurs on the debt. The effective interest rate 
is the discount rate that equates the present value of the coupon payments 
and face value to their selling price. Consequently, the effective interest rate is 
5.50%. 
7 B is correct. The bonds will be issued at a discount because the market inter -

est rate is higher than the stated rate. Discounting the future payments to 
their present value indicates that at the time of issue, the company will record 
£978,938 as both a liability and a cash inflow from financing activities. Interest 
expense in 2010 is £58,736 (£978,938 times 6.0 percent). During the year, the 
company will pay cash of £55,000 related to the interest payment, but interest 
expense on the income statement will also reflect £3,736 related to amortisation 
of the initial discount (£58,736 interest expense less the £55,000 interest pay -
ment). Thus, the value of the liability at 31 December 2010 will reflect the initial 
value (£978,938) plus the amortised discount (£3,736), for a total of £982,674. 
The cash outflow of £55,000 may be presented as either an operating or financ -
ing activity under IFRS.
8 A is correct. The coupon rate on the bonds is higher than the market rate, 
which indicates that the bonds will be issued at a premium. Taking the present

value of each payment indicates an issue date value of €10,210,618. The interest 
expense is determined by multiplying the carrying amount at the beginning of 
the period (€10,210,618) by the market interest rate at the time of issue (6.0 per -
cent) for an interest expense of €612,637. The value after one year will equal 
the beginning value less the amount of the premium amortised to date, which 
is the difference between the amount paid (€650,000) and the expense accrued 
(€612,637) or €37,363. €10,210,618 – €37,363 = €10,173,255 or €10.17 million.
9 A is correct. The future cash outflows, the present value of the cash outflows, 
and the total present value are as follows:

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 600
Payment (€)Present Value at 
Market Rate 6% 
(€)Present Value 
6% (€)Total Present 
Value (€)
31 December 2015 700,000.00 660,377.36
31 December 2016 700,000.00 622,997.51
31 December 2017 700,000.00 587,733.50
31 December 2018 700,000.00 554,465.56
31 December 2019 700,000.00 523,080.72
31 December 2020 700,000.00 493,472.38
31 December 2021 700,000.00 465,539.98
31 December 2022 700,000.00 439,188.66
31 December 2023 700,000.00 414,328.92
31 December 2024 700,000.00 390,876.34 10,000,000.00 5,583,947.77
5,152,060.94 5,583,947.77 10,736,008.71
late sales proceeds of €10,736,008.71:
Problem
N 10
% i or I/Y 6
FV $10,000,000.00
PMT $700,000.00
 The interest expense is calculated by multiplying the carrying amount at the

beginning of the year by the effective interest rate at issuance. As a result, the 
interest expense at 31 December 2015 is €644,161 (€10,736,008.71 × 6%).
10 C is correct. The future cash outflows, the present value of the cash outflows, 
Payment ($)Present Value 
5% ($)Present Value at 
Value ($)
31 December 2015 1,200,000 1,142,857.14
31 December 2016 1,200,000 1,088,435.37
31 December 2017 1,200,000 1,036,605.12
31 December 2018 1,200,000 987,242.97
31 December 2019 1,200,000 940,231.40 30,000,000 23,505,785.00
5,195,372.00 23,505,785.00 28,701,157.00
late sales proceeds of $28,701,157.00:

Solutions 601
Problem
N 5
% i or I/Y 5
FV $30,000,000.00
PMT $1,200,000.00
 The following table illustrates interest expense, premium amortization, and 
carrying amount (amortized cost) for 2015.
(beginning of year)Interest Expense (at 
rate of 5%)Interest Payment 
(at coupon rate of 
4%)Amortization of 
DiscountCarrying Amount 
(end of year)
2015 $28,701,157.00 $1,435,057.85 $1,200,000.00 $235,057.85 $28,936,214.85
 The carrying amount at the end of the year is found by adding the amortization 
of the discount to the carrying amount at the beginning of the year. As a result, 
the carrying amount on 31 December 2015 is $28,936,215. 
 Alternatively, the following illustrates the keystrokes for many financial calcula -
tors to calculate the carrying value at the end of first year of $28,936, 215:
Problem
N 4
% i or I/Y 5

11 B is correct. The interest expense for a given year is equal to the carrying 
amount at the beginning of the year times the effective interest of 4%. Under the 
effective interest rate method, the difference between the interest expense and 
the interest payment (based on the coupon rate and face value) is the discount 
amortized in the period, which increases the carrying amount annually. For 
2017, the interest expense is the beginning carrying amount ($1,944,499) times 
the effective interest of 4%. 
(beginning)Interest Expense 
(at effective 
interest of 4%)Interest Payment 
3%)Amortization of 
Discount Carrying Amount 
2015 $1,910,964 $76,439 $60,000.00 $16,439 $1,927,403
2016 $1,927,403 $77,096 $60,000.00 $17,096 $1,944,499
2017 $1,944,499 $77,780 $60,000.00 $17,780 $1,962,279
12 B is correct. The amortization of the premium equals the interest payment

minus the interest expense. The interest payment is constant and the interest 
expense decreases as the carrying amount decreases. As a result, the amortiza -
tion of the premium increases each year.

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 602
13 B is correct. Under the straight-  line method, the bond premium is amortized 
equally over the life of the bond. The annual interest payment is $165,000 
($3,000,000 × 5.5%) and annual amortization of the premium under the 
straight-  line method is $13,616 [($3,040,849 – $3,000,000)/3)]. The interest 
expense is the interest payment less the amortization of the premium ($165,000 
– $13,616 = $151,384).
14 C is correct. A gain of €3.3 million (carrying amount less amount paid) will be 
reported on the income statement.
15 B is correct. If a company decides to redeem a bond before maturity, bonds 
payable is reduced by the carrying amount of the debt. The difference between 
the cash required to redeem the bonds and the carrying amount of the bonds 
is a gain or loss on the extinguishment of debt. Because the call price is 104 
and the face value is $1,000,000, the redemption cost is 104% of $1,000,000 or

$1,040,000. The company’s loss on redemption would be $50,000 ($990,000 car -
rying amount of debt minus $1,040,000 cash paid to redeem the callable bonds).
16 A is correct. The value of the liability for zero-  coupon bonds increases as the 
discount is amortised over time. Furthermore, the amortised interest will 
reduce earnings at an increasing rate over time as the value of the liability 
increases. Higher relative debt and lower relative equity (through retained earn -
ings) will cause the debt-  to- equity ratio to increase as the zero-  coupon bonds 
approach maturity.
17 A is correct. When interest rates rise, bonds decline in value. Thus, the carrying 
amount of the bonds being carried on the balance sheet is higher than the mar -
ket value. The company could repurchase the bonds for less than the carrying 
amount, so the economic liabilities are overestimated. Because the bonds are 
issued at a fixed rate, there is no effect on interest coverage.

18 C is correct. Affirmative covenants require certain actions of the borrower. 
Requiring the company to perform regular maintenance on equipment pledged 
as collateral is an example of an affirmative covenant because it requires the 
company to do something. Negative covenants require that the borrower not 
take certain actions. Prohibiting the borrower from entering into mergers and 
preventing the borrower from issuing excessive additional debt are examples of 
negative covenants. 
19 C is correct. Covenants protect debtholders from excessive risk taking, typically 
by limiting the issuer’s ability to use cash or by limiting the overall levels of 
debt relative to income and equity. Issuing additional equity would increase the 
company’s ability to meet its obligations, so debtholders would not restrict that 
ability.
20 C is correct. The non-  current liabilities section of the balance sheet usually 
includes a single line item of the total amount of a company’s long-  term debt

due after 1 year, and the current liabilities section shows the portion of a 
company’s long-  term debt due in the next 12 months. Notes to the financial 
statements generally present the stated and effective interest rates and maturity 
dates for a company’s debt obligations 
21 B is correct. An operating lease is not recorded on the balance sheet (debt is 
lower), and lease payments are entirely categorised as rent (interest expense is 
lower.) Because the rent expense is an operating outflow but principal repay -
ments are financing cash flows, the operating lease will result in lower cash flow 
from operating activity.
22 B is correct. The lessee will disclose the future obligation by maturity of its 
operating leases. The future obligations by maturity, leased assets, and lease 
liabilities will all be shown for finance leases.

Solutions 603
23 B is correct. When a lease is classified as an operating lease, the underlying 
asset remains on the lessor’s balance sheet. The lessor will record a depreciation 
expense that reduces the asset’s value over time.
24 A is correct. A sales-  type lease treats the lease as a sale of the asset, and rev -
enue is recorded at the time of sale equal to the present value of future lease 
payments. Under a direct financing lease, only interest income is reported as 
earned. Under an operating lease, revenue from rent is reported when collected.
25 A is correct. A portion of the payments for capital leases, either direct financing 
or sales-  type, is reported as interest income. With an operating lease, all reve -
nue is recorded as rental revenue.
26 A is correct. An operating lease is an agreement that allows the lessee to use an 
asset for a period of time. Thus, an operating lease is similar to renting an asset,

whereas a finance lease is equivalent to the purchase of an asset by the lessee 
that is directly financed by the lessor.
27 C is correct. If the present value of the lease payments is greater than 90% of 
the fair value of the asset, the lease is considered a capital lease. A lease with a 
term that is 75% or more of the useful life of the asset is deemed to be a capital 
lease. The option to purchase the asset must be deemed to be cheap (bargain 
purchase option), not just include the option to purchase the asset.
28 A is correct. A finance lease is similar to borrowing money and buying an asset; 
a company that enters into a finance lease as the lessee reports an asset (leased 
asset) and related debt (lease payable) on its balance sheet. A company that 
enters into a finance lease as the lessee will report interest expense and depreci -
ation expense on its income statement. A company that enters into an operating

lease will report the lease payment on its income statement. For a finance lease, 
only the portion of the lease payment relating to interest expense reduces oper -
ating cash flow; the portion of the lease payment that reduces the lease liability 
appears as a cash outflow in the financing section. A company that enters into 
an operating lease as the lessee will report the full lease payment as an operat -
ing cash outflow. 
29 A is correct. A company that enters into a finance lease reports the value of 
both the leased asset and lease payable as the lower of the present value of 
future lease payments and the fair value of the leased asset. The present value 
of the future lease payments, €47,250,188, is lower than the fair market value of 
the leased asset, €49,000,000. The company will record a lease payable on the 
balance sheet of €47,250,188. 
30 B is correct. An operating lease is economically similar to renting an asset. A

company that enters into an operating lease as a lessee reports a lease expense 
on its income statement during the period it uses the asset and reports no asset 
or liability on its balance sheet. The operating lease is disclosed in notes to the 
financial statements. 
31 C is correct. The current debt-  to- total-  capital ratio is $840/($840 + $520) = 
0.62. To adjust for the lease commitments, an analyst should add $100 to both 
the numerator and denominator: $940/($940 + $520) = 0.64.
32 C is correct. The financial leverage ratio is calculated as follows:
Average shareholder' s equity m=$,45 981 i illion
 million million$,$.18 7522 452=
33 B is correct. Company B has the lowest debt-  to- equity ratio, indicating the 
lowest financial leverage, and the highest interest coverage ratio, indicating the 
greatest number of times that EBIT covers interest payments.

Reading 30 ■ Non-  Current (Long-  Term) Liabilities 604
34 A is correct because the debt-  to- assets (total debt)/(total assets) ratio is (1,258 + 
321)/(8,750) = 1,579/8,750 = 0.18
35 B is correct. The company will report a net pension obligation of €1 million 
equal to the pension obligation (€10 million) less the plan assets (€9 million).
36 A is correct. A company that offers a defined benefit plan makes payments into 
a pension fund and the retirees are paid from the fund. The payments that a 
company makes into the fund are invested until they are needed to pay retir -
ees. If the fair value of the fund’s assets is higher than the present value of the 
estimated pension obligation, the plan has a surplus and the company’s balance 
sheet will reflect a net pension asset. Because the fair value of the fund’s assets 
is $1,500,000,000 and the present value of estimated pension obligations is 
$1,200,000,000, the company will present a net pension asset of $300,000,000 
on its balance sheet.

and Analysis (4)
This study session introduces the concept of financial reporting quality. The session 
examines the financial reporting quality differences that may exist between companies 
and the means for identifying them. Warning signs of poor or low quality reporting 
are covered. The application of financial analysis techniques to evaluate a company’s 
past and projected performance, assess credit risk, and screen for potential equity 
investments follows. Common adjustments to reported financials to facilitate cross-  
company comparisons conclude the session.
Reading 31 Financial Reporting Quality  
by Jack T. Ciesielski, CPA, CFA, Elaine Henry, PhD, CFA, and 
Thomas I. Selling, PhD, CPA
Reading 32 Financial Statement Analysis: Applications  
by Thomas R. Robinson, PhD, CFA, Jan Hendrik van Greuning, 
DCom, CFA, Elaine Henry, PhD, CFA, and Michael A. Broihahn, 
CPA, CIA, CFAFINANCIAL  REPORTIN g AN d A NALYSIS
9

9
readings.

Financial Reporting Quality
by Jack T. Ciesielski, CPA, CFA, Elaine Henry, PhD, CFA, and 
Thomas I. Selling, PhD, CPA
Jack T. Ciesielski, CPA, CFA, is at R.G. Associates, Inc., publisher of The Analyst’s 
Accounting Observer (USA). Elaine Henry, PhD, CFA, is at Stevens Institute of Technology 
(USA). Thomas I. Selling, PhD, CPA, is at the Cox School of Business, Southern Methodist 
University (USA).
a. distinguish between financial reporting quality and quality of 
reported results (including quality of earnings, cash flow, and 
balance sheet items);
b. describe a spectrum for assessing financial reporting quality;
c. distinguish between conservative and aggressive accounting;
d. describe motivations that might cause management to issue 
financial reports that are not high quality;
e. describe conditions that are conducive to issuing low-  quality, or 
even fraudulent, financial reports;

f. describe mechanisms that discipline financial reporting quality 
and the potential limitations of those mechanisms;
g. describe presentation choices, including non-  GAAP measures, 
that could be used to influence an analyst’s opinion;
h. describe accounting methods (choices and estimates) that could 
be used to manage earnings, cash flow, and balance sheet items;
i. describe accounting warning signs and methods for detecting 
manipulation of information in financial reports.REA dINg
31
© 2014 CFA Institute. All rights reserved.Note:  Changes in accounting 
analytical frameworks contained

readings.

Reading 31 ■ Financial Reporting Quality 608
Ideally, analysts would always have access to financial reports that are based on 
sound financial reporting standards, such as those from the International Accounting 
Standards Board (IASB) and the Financial Accounting Standards Board (FASB), and 
are free from manipulation. But, in practice, the quality of financial reports can vary 
greatly. High-  quality financial reporting provides information that is useful to analysts 
in assessing a company’s performance and prospects. Low-  quality financial reporting 
contains inaccurate, misleading, or incomplete information.
Extreme lapses in financial reporting quality have given rise to high-  profile scan -
dals that resulted not only in investor losses but also in reduced confidence in the 
financial system. Financial statement users who were able to accurately assess financial 
reporting quality were better positioned to avoid losses. These lapses illustrate the

challenges analysts face as well as the potential costs of failing to recognize practices 
that result in misleading or inaccurate financial reports.1 Examples of misreporting 
can provide an analyst with insight into various signals that may indicate poor-  quality 
It is important to be aware, however, that high-  profile financial scandals reflect 
only those instances of misreporting that were identified. Although no one can know 
the extent of undetected misreporting, some research suggests that it is relatively 
widespread. An Ernst & Young 2013 survey of more than 3,000 board members, 
executives, managers, and other employees in 36 countries across Europe, the Middle 
East, India, and Africa indicates that 20% of the respondents had seen manipulation 
(such as overstated sales and understated costs) occurring in their own companies, 
and 42% of board directors and senior managers were aware of some type of irregular

financial reporting in their own companies (Ernst & Young, 2013). Another survey 
of 169 chief financial officers of public US companies found that they believed, on 
average, that about 20% of companies intentionally distort earnings to misrepresent 
economic performance—even while adhering to US GAAP—and for such compa -
nies the magnitude of misrepresentation is about 10% of reported earnings (Dichev, 
Graham, Harvey, and Rajgopal, 2013 and 2015).
This reading addresses financial  reporting quality , which pertains to the quality of 
information in financial reports, including disclosures in notes. High-  quality reporting 
provides decision-  useful information, which is relevant and faithfully represents the 
economic reality of the company’s activities during the reporting period as well as the 
company’s financial condition at the end of the period. A separate but interrelated 
attribute of quality is quality of reported results  or earnings quality , which pertains

to the earnings and cash generated by the company’s actual economic activities and 
the resulting financial condition. The term “earnings quality” is commonly used in 
practice and will be used broadly to encompass the quality of earnings, cash flow, 
and/or balance sheet items. High-  quality earnings result from activities that a com -
pany will likely be able to sustain in the future and provide a sufficient return on 
the company’s investment. The concepts of earnings quality and financial reporting 
quality are interrelated because a correct assessment of earnings quality is possible 
only when there is some basic level of financial reporting quality. Beyond this basic 
level, as the quality of reporting increases, the ability of financial statement users to 
correctly assess earnings quality and to develop expectations for future performance 
arguably also increases.1
1 In this reading, the examples of misleading or inaccurate financial reports occurred in prior years— not

because there are no current examples of questionable financial reporting, but rather because it has been 
conclusively resolved that misreporting occurred in the historical examples.

Conceptual Overview 609
Section 2 provides a conceptual overview of reporting quality. Section 3 discusses 
motivations that might cause, and conditions that might enable, management to issue 
financial reports that are not high quality and mechanisms that aim to provide disci -
pline to financial reporting quality. Section 4 describes choices made by management 
that can affect financial reporting quality—presentation choices, accounting methods, 
and estimates—as well as warning signs of poor-  quality financial reporting.
CONCEPTUAL OVERVIEW
As indicated in the introduction, financial reporting quality and results or earnings 
quality are interrelated attributes of quality. Exhibit 1 illustrates this interrelationship 
and its implications.
Exhibit 1   Relationships between Financial Reporting Quality and Earnings 
Quality
Low High
Earnings 
(Results) 
QualityHigh
LOW financial reporting 
quality impedes assessment 
of earnings quality and

of earnings quality and 
impedes valuation.HIGH financial reporting  
quality enables assessment. 
HIGH earnings  quality 
increases company value.
LowHIGH financial reporting  
LOW earnings  quality 
decreases company value.
As can be seen in Exhibit 1, if financial reporting quality is low, the information 
provided is not useful to assess the company’s performance and thus to make invest -
ment and other decisions.
Financial reporting quality varies across companies. High-  quality reports contain 
information that is relevant, complete, neutral, and free from error. The lowest-  quality 
reports contain information that is pure fabrication. Earnings (results) quality can 
range from high and sustainable to low and unsustainable. Providers of resources pre -
fer high and sustainable earnings. Combining the two measures of quality—financial 
reporting and earnings—the overall quality of financial reports from a user perspective

can be thought of as spanning a continuum from the highest to the lowest. Exhibit 2 
presents a quality spectrum that provides a basis for evaluating better versus poorer 
quality reports. This spectrum ranges from reports that are of high financial reporting 
quality and reflect high and sustainable earnings quality to reports that are not useful 
because of poor financial reporting quality.2

Reading 31 ■ Financial Reporting Quality 610
Exhibit 2   Quality Spectrum of Financial Reports
GAAP ,
decision-useful,
sustainable, and
adequate returns
GAAP , decision-useful,
but sustainable? Low
“earnings quality”
Within GAAP , but
biased choices
“earnings management” (EM)
-Real EM
-Accounting EM
Non-compliant
Accounting
Fictitious
transactionsQuality Spectrum
2.1 GAAP , Decision-  Useful, Sustainable, and Adequate Returns
At the top of the spectrum, labeled in Exhibit 2 as “GAAP , decision-  useful, sustainable, 
and adequate returns” are high-  quality reports that provide useful information about 
high-  quality earnings.
■■High-  quality financial reports conform to the generally accepted accounting 
principles (GAAP) of the jurisdiction, such as International Financial Reporting 
Standards (IFRS), US GAAP , or other home-  country GAAP . The exhibit uses 
the term GAAP to refer generically to the accounting standards accepted in a 
company’s jurisdiction.

■■In addition to conforming to GAAP , high-  quality financial reports also embody 
the characteristics of decision-  useful information such as those defined in the 
Conceptual Framework .2 Recall that the fundamental characteristics of useful 
information are relevance and faithful representation. Relevant information is 
defined as information that can affect a decision and encompasses the notion 
of materiality. (Information is considered material if “omitting it or misstating it 
could influence decisions that users make on the basis of the financial informa -
tion of a specific reporting entity. ”3) Faithful representation of economic events 
is complete, neutral, and free from error.
2 The characteristics of decision-  useful information are identical under IFRS and US GAAP . In 
September  2010, the IASB adopted the Conceptual Framework for Financial Reporting  in place of the

Framework for the Preparation and Presentation of Financial Statements  (1989). The Conceptual Framework  
framework. The Conceptual Framework  (2010) contains two updated chapters: “The Objective of Financial 
Reporting” and “Qualitative Characteristics of Useful Financial Information. ” The remainder of the material 
in the Conceptual Framework  is from the Framework  (1989) and will be updated as the project is completed. 
Also in September 2010, the FASB issued Concepts Statement 8, “Conceptual Framework for Financial 
Reporting, ” to replace Concepts Statements 1 and 2.
3 Text from conceptual frameworks referenced in Note 4.

Conceptual Overview 611
The Conceptual Framework  also enumerates enhancing characteristics of useful 
information: comparability, verifiability, timeliness, and understandability. Of 
course, the desirable characteristics for financial information require trade-  offs. 
For example, financial reports must balance the aim of providing information 
that is produced quickly enough to be timely and thus relevant, and yet not so 
quickly that errors occur. Financial reports must balance the aim of providing 
information that is complete but not so exhaustive that immaterial information 
is included. High-  quality information results when these and other tradeoffs are 
made in an unbiased, skillful manner.
■■High-  quality earnings indicate an adequate level of return on investment and 
derive from activities that a company will likely be able to sustain in the future. 
An adequate level of return on investment exceeds the cost of the investment

and also equals or exceeds the expected return. Sustainable activities and sus -
tainable earnings are those expected to recur in the future. Sustainable earnings 
that provide a high return on investment contribute to higher valuation of a 
company and its securities.
2.2 GAAP , Decision-  Useful, but Sustainable?
The next level down in Exhibit 2, “GAAP , decision-  useful, but sustainable?” refers to 
circumstances in which high-  quality reporting provides useful information, but that 
information reflects results or earnings that are not sustainable (lower earnings quality). 
The earnings may not be sustainable because the company cannot expect earnings that 
generate the same level of return on investment in the future or because the earnings, 
although replicable, will not generate sufficient return on investment to sustain the 
company. Earnings quality is low in both cases. Reporting can be high quality even

when the economic reality being depicted is not of high quality. For example, consider 
a company that generates a loss, or earnings that do not provide an adequate return 
on investment, or earnings that resulted from non-  recurring activities. The relatively 
undesirable economic reality could nonetheless be depicted in financial reporting that 
provides high-  quality, decision-  useful information.
Exhibit 3 presents an excerpt from the fiscal year 2014 first-  quarter results of Toyota 
Motor Corporation, a Japanese automobile company. As highlighted by a Wall Street 
Journal  article,4 the company sold fewer cars but reported an 88% increase in operating 
profits compared with the prior year, primarily because of the change in exchange rates. 
The weaker yen benefited Toyota both because the company manufacturers more cars 
in Japan (compared with its competitors) and because the company sells a significant

number of cars outside of Japan. Exchange rate weakening is a less sustainable source 
of profits than manufacturing and selling cars. In summary, this example is a case of 
high-  quality financial reporting coupled with lower earnings quality.
Exhibit 3   Excerpt from Toyota Motor Corporation’s Consolidated Financial 
Results for FY2014 First Quarter Ending 30 June 2013
Consolidated vehicle unit sales in Japan and overseas decreased by 37 thousand 
units, or 1.6%, to 2,232 thousand units in FY2014 first quarter (the three months 
ended June 30, 2013) compared with FY2013 first quarter (the three months 
ended June 30, 2012). Vehicle unit sales in Japan decreased by 51 thousand units, 
or 8.8%, to 526 thousand units in FY2014 first quarter compared with FY2013 
4 Back (2013).

Reading 31 ■ Financial Reporting Quality 612
first quarter. Meanwhile, overseas vehicle unit sales increased by 14 thousand 
units, or 0.8%, to 1,706 thousand units in FY2014 first quarter compared with 
FY2013 first quarter.
As for the results of operations, net revenues increased by 753.7 billion yen, 
or 13.7%, to 6,255.3 billion yen in FY2014 first quarter compared with FY2013 
first quarter, and operating income increased by 310.2 billion yen, or 87.9%, to 
663.3 billion yen in FY2014 first quarter compared with FY2013 first quarter. 
The factors contributing to an increase in operating income were the effects of 
changes in exchange rates of 260.0 billion yen, cost reduction efforts of 70.0 billion 
yen, marketing efforts of 30.0 billion yen and other factors of 10.2 billion yen. 
On the other hand, the factors contributing to a decrease in operating income 
were the increase in expenses and others of 60.0 billion yen.
2.3 Biased Accounting Choices

The next level down in the spectrum in Exhibit 2 is “Within GAAP , but biased choices. ” 
Biased choices result in financial reports that do not faithfully represent economic 
phenomena. The problem with bias in financial reporting, as with other deficiencies 
in financial reporting quality, is that it impedes an investor’s ability to correctly assess 
a company’s past performance, to accurately forecast future performance, and thus, 
to appropriately value the company.
Choices are deemed to be “aggressive” if they increase a company’s reported 
performance and financial position in the current period. The choice can increase 
the amount of revenues, earnings, and/or operating cash flow reported in the period 
or decrease the amount of expenses reported in the period and/or the amount of 
debt reported on the balance sheet. Aggressive choices may decrease the company’s 
reported performance and financial position in later periods. In contrast, choices are

deemed “conservative” if they decrease a company’s reported performance and finan -
cial position in the current period. Conservative choices may decrease the amount 
of revenues, earnings, and/or operating cash flow reported in the period or increase 
the amount of expenses reported in the period and/or the amount of debt reported 
on the balance sheet. Conservative choices may increase the company’s reported 
performance and financial position in later periods.
Another type of bias is understatement of earnings volatility, so-  called earnings 
“smoothing. ” Earnings smoothing can result from conservative choices to understate 
earnings in periods when a company’s operations are performing well plus aggressive 
choices in periods when the company’s operations are struggling.
Biased choices can be made not only in the context of reported amounts but also 
in the context of how information is presented. For example, companies can disclose

information transparently and in a manner that facilitates analysis, or they can dis -
close information in a manner that aims to obscure unfavorable information and/or 
to emphasize favorable information.
EXAMPLE 1   
Quality of Financial Reports
PACCAR Inc. designs, manufactures, and distributes trucks and related after -
market parts that are sold worldwide under the Kenworth, Peterbilt, and DAF 
nameplates. In 2013, the US SEC charged PACCAR for various accounting 
deficiencies that “clouded their financial reporting to investors in the midst Exhibit 3   (Continued)

Conceptual Overview 613
of the financial crisis. ” The SEC complaint cites the company’s 2009 segment 
reporting. Exhibit 4A presents an excerpt from the notes to PACCAR’s financial 
statements, and Exhibit 4B presents an excerpt from the management’s discussion 
and analysis (MD&A) of PACCAR’s annual report.
Exhibit 4A   Excerpt from Notes to PACCAR’s 2009 Financial Statements
S. SEGMENT AND RELATED INFORMATION
PACCAR operates in two principal segments, Truck and Financial Services.
The Truck segment includes the manufacture of trucks and the distribution 
of related aftermarket parts, both of which are sold through a network 
of independent dealers... The Financial Services segment is composed of 
finance and leasing products and services provided to truck customers 
and dealers … Included in All Other is PACCAR’s industrial winch man -
ufacturing business. Also within this category are other sales, income and 
expenses not attributable to a reportable segment, including a portion of

corporate expense.
Business Segment Data ($ millions)
Income before Income Taxes
  Truck $25.9 $1,156.5 $1,352.8
  All other 42.2 6.0 32.0
68.1 1,162.5 1,384.8
Financial services 84.6 216.9 284.1
Investment income 22.3 84.6 95.4
$175.0 $1,464.0 $1,764.3
Exhibit 4B   Excerpt from MD&A of PACCAR’s 2009 Annual Report
Net sales and revenues and gross margins for truck units and aftermarket 
parts are provided below. The aftermarket parts gross margin includes 
direct revenues and costs, but excludes certain truck segment costs.
2009 2008 % Change
Net Sales and Revenues
Trucks $5,103.30 $11,281.30 −55
Aftermarket parts 1,890.70 2,266.10 −17
$6,994.00 $13,547.40 −48
Gross Margin    
Trucks −$46.6 $1,141.70 −104

Reading 31 ■ Financial Reporting Quality 614
Aftermarket parts 625.7 795.20 −21
$579.1 $1,936.90 −70
1 Based on the segment data excerpted from the notes to the financial state -
ments, was PACCAR’s truck segment profitable in 2009?
2 Based on the data about the truck’s gross margin presented in the MD&A, 
was PACCAR’s truck segment profitable in 2009?
3 What is the main difference between the note presentation and the 
MD&A presentation?
4 The SEC complaint stated that “PACCAR failed to report the operating 
results of its aftermarket parts business separately from its truck sales 
business as required under segment reporting requirements, which are in 
place to ensure that investors gain the same insight into a company as its 
executives. ” Is the PACCAR situation an example of issues with financial 
reporting quality, earnings quality, or both?
Yes, the segment data presented in the note to the financial statements indicates

that the Truck segment earned $25.9 million in 2009.
No, the segment data presented in the MD&A indicates that the Truck segment 
had a negative gross margin.
The main difference between the note presentation and the MD&A presentation 
is that the aftermarket parts business is combined with the trucks business in 
the notes but separated in the MD&A. Although the data are not exactly com -
parable in the two disclosures (because the note shows income before taxes and 
the MD&A shows gross profit), the two disclosures present a different picture 
of PACCAR’s profits from truck sales.
The PACCAR situation appears to be an example of issues with both financial 
reporting quality and earnings quality. The substantial decrease in truck sales and 
the negative gross margin reflect poor earnings quality. The failure to disclose 
clear segment information is an instance of poor financial reporting quality.

While choices exist within GAAP for the presentation of a desired economic picture, 
non-  GAAP reporting adds yet another dimension of management discretion. Non-  
GAAP reporting includes both non-  GAAP financial metrics and non-  GAAP operating 
metrics.5 Non-  GAAP financial metrics relate directly to the financial statements. A 
common non-  GAAP financial metric is “non-  GAAP earnings, ” which are earnings 
metrics created by reporting companies “that adjust standards-  compliant earnings to Exhibit 4B   (Continued)
5 The term “non-  GAAP” refers generally to all metrics that are non-  compliant with generally accepted 
accounting principles and thus includes “non-  IFRS” metrics.

Conceptual Overview 615
exclude items required  by accounting standards or to include items not permitted  by 
accounting standards” (Ciesielski and Henry, 2017). In contrast, non-  GAAP operating 
metrics do not relate directly to the financial statements and include metrics that 
are typically industry-  driven, such as subscribers, active users, and occupancy rates. 
Non-  GAAP financial reporting has become increasingly common; this development 
presents challenges to analysts. An important challenge is that non-  GAAP financial 
reporting diminishes comparability across financial statements. The adjustments that 
companies make to create non-  GAAP earnings, for example, are generally ad hoc 
and thus differ significantly across companies. When evaluating non-  GAAP financial 
metrics, investors must decide the extent to which specific adjustments should be 
incorporated into their analysis. In general, for all non-  GAAP metrics, investors need

to decide how such metrics should be incorporated into their analyses and forecasts.6
Management emphasis on non-  GAAP financial measures, such as pro forma 
earnings (also sometimes called “adjusted earnings”) to deflect attention from less-  
than-  desirable financial results is an example of an aggressive presentation choice. 
Since 2003, if a company uses a non-  GAAP financial measure7 in an SEC filing, 
it is required to display the most directly comparable GAAP measure with equal 
prominence and to provide a reconciliation between the non-  GAAP measure and the 
equivalent GAAP measure. In other words, a company is not allowed to give more 
prominence to a non-  GAAP financial measure in an SEC filing.
Similarly, the IFRS Practice Statement “Management Commentary, ” issued 
December  2010, requires disclosures when non-  IFRS measures are included in 
financial reports:
If information from the financial statements has been adjusted for inclusion

in management commentary, that fact should be disclosed. If financial per -
formance measures that are not required or defined by IFRSs are included 
within management commentary, those measures should be defined and 
explained, including an explanation of the relevance of the measure to 
users. When financial performance measures are derived or drawn from 
the financial statements, those measures should be reconciled to measures 
presented in the financial statements that have been prepared in accordance 
with IFRSs. (Page 17)
The reconciliation between as-  reported measures (GAAP financial measures 
presented in the financial statements) and as-  adjusted measures (non-  GAAP finan -
cial measures presented in places other than the financial statements) can provide 
important information.
EXAMPLE 2   
Presentation of Non-  GAAP Financial Measures
Nokia Corporation, a global telecommunications company headquartered in 
Finland, operates three businesses: Devices & Services, HERE (the new brand

for location and mapping services, formerly called Location & Commerce), and 
Nokia Siemens Networks. Exhibit 5 presents an excerpt from the company’s 
Interim Report for the second quarter ending June 2013.
6 A survey of non-  GAAP earnings in the S&P 500 is presented in Ciesielski and Henry (2017). Some 
observers even recommend that investors shift their focus from a company’s earnings to a company’s 
“strategic assets” and the contribution of these assets to its competitive edge (Gu and Lev, 2017).
7 Non-  domestic private issuers can file financial statements prepared in accordance with IFRS without 
reconciliation to US GAAP . The SEC recognizes US GAAP and IFRS as GAAP .

Reading 31 ■ Financial Reporting Quality 616
Exhibit 5   Excerpt from Summary Financial Information
Reported and Non-  IFRS second quarter 2013 
Results1,2,3
EUR million Q2/13 Q2/12Yo Y  
Change Q1/13QoQ 
Change
Nokia
Net sales 5,695 7,542 −24% 5,852 −3%
Operating profit −115 −824 −150
Operating profit 
(non-  IFRS) 303 −325 181 67%
EPS, EUR diluted −0.06 −0.38 −0.07
EPS, EUR diluted 
(non-  IFRS) 0.00 −0.08 −0.02
The following excerpt explains the term “Non-  IFRS. ”
Note 1 relating to non-  IFRS (also referred to as “underlying”) 
results:  In addition to information on our reported IFRS results, we 
provide certain information on a non-  IFRS, or underlying business 
performance, basis. Non-  IFRS results exclude all material special 
items for all periods. In addition, non-  IFRS results exclude intangible 
asset amortization, other purchase price accounting related items and 
inventory value adjustments arising from (i) the formation of Nokia

Siemens Networks and (ii) all business acquisitions completed after 
June 30, 2008. Nokia believes that our non-  IFRS results provide mean -
ingful supplemental information to both management and investors 
regarding Nokia’s underlying business performance by excluding the 
above-  described items that may not be indicative of Nokia’s business 
operating results. These non-  IFRS financial measures should not be 
viewed in isolation or as substitutes to the equivalent IFRS measure(s), 
but should be used in conjunction with the most directly compara -
ble IFRS measure(s) in the reported results. See note 2 below for 
information about the exclusions from our non-  IFRS results. More 
information, including a reconciliation of our Q2 2013 and Q2 2012 
non-  IFRS results to our reported results, can be found ….
In an excerpt from Note 2, the company also disclosed the following.
Note 2 relating to non-  IFRS exclusions:
Q2 2013—EUR 418 million (net) consisting of:

■■EUR 157 million restructuring charge and other associated 
items in Nokia Siemens Networks.
■■EUR 151 million losses related to divestments of businesses 
in Nokia Siemens Networks.
■■EUR 10 million restructuring charge in HERE
■■EUR 12 million of intangible asset amortization and other 
purchase price accounting related items arising from the 
acquisition of Motorola Solutions’ networks assets

Conceptual Overview 617
■■EUR 87 million of intangible asset amortization and other 
acquisition of NAVTEQ
■■EUR 1 million of intangible assets amortization and other 
acquisition of Novarra, MetaCarta and Motally in Devices 
& Services
Note 3 related to changes to historical comparative financial results due to 
revised IFRS accounting standard, IAS 19 Employee benefits.
1 Based on the information provided, explain the differences between the 
following two disclosures contained in Nokia’s interim statement:
A The first page of the interim report includes the following statement as 
a second-  quarter 2013 highlight: “Nokia Group achieved underlying 
operating profitability for the fourth consecutive quarter, with a Q2 
non-  IFRS operating margin of 5.3%.... ”
B Nokia’s Consolidated Income Statements (found on page 20 of the 
interim report) report a EUR278 million net loss.

2 How does the heading “Q2 2013—EUR418 million” from Nokia’s Note 
2 correspond with the excerpt from the company’s Summary Financial 
Information shown in Exhibit 5?
As shown in Note 1, the company uses the term “underlying” to refer to non-  IFRS 
metrics. The non-  IFRS metric disclosed in A, “non-  IFRS operating margin”—by 
definition—does not appear within financial statements prepared in accordance 
with IFRS. Here, it is referred to as a non-  IFRS metric because information on 
the company’s financial statements has been adjusted. In contrast, the IFRS 
metric disclosed in B, “net loss, ” is clearly presented on an income statement 
prepared in accordance with IFRS. Another difference between Disclosures A 
and B is that they refer to two different metrics: A refers to operating profit and 
B refers to net profit (loss). These two items appear on two different lines of

the income statement. In general, operating profit (or operating loss) is before 
deductions for non-  operating items, such as interest and taxes. The company’s 
operating profit in accordance with IFRS was a negative EUR115 million—in 
other words, a EUR115 million operating loss. Note that as shown in Exhibit 5, 
the second-  quarter non-  IFRS operating profit was EUR303 million and second-  
quarter net sales totaled EUR5,695 million. As indicated in Disclosure A, the 
non-  IFRS operating margin is 5.3% (= 303/5,695).
Overall, there are three key differences between Disclosures A and B: (1) A 
refers to a non-  IFRS metric rather than an IFRS metric; (2) A refers to operating 
profit, which was positive, rather than to net income, which was negative; and 
(3) A highlights a positive economic outcome. An analyst should be aware of 
the alternative means by which earnings announcements can paint a positive 
picture of companies’ results.

The heading “Q2 2013—EUR418 million” refers to the difference between the 
company’s non-  IFRS operating profit of EUR303  million and the company’s 
operating loss of EUR115 million calculated in accordance with IFRS. The next

Reading 31 ■ Financial Reporting Quality 618
lines indicate the components of the EUR418 million that were excluded when 
calculating the non-  IFRS operating profit but included when calculating the 
IFRS operating profit (loss).
Often, poor reporting quality occurs simultaneously with poor earnings quality; 
for example, aggressive accounting choices are made to obscure poor performance. 
It is also possible, of course, for poor reporting quality to occur with high-  quality 
earnings. Although a company with good performance would not require aggressive 
accounting choices to obscure poor performance, it might nonetheless produce poor-  
quality reports for other reasons. A company with good performance might be unable 
to produce high-  quality reports because of inadequate internal systems.
Another scenario in which poor reporting quality might occur simultaneously with 
high quality earnings is that a company with good performance might deliberately

produce reports based on “conservative” rather than aggressive accounting choices—
that is, choices that make current performance look worse. One motivation might 
be to avoid unwanted political attention. Another motivation could arise in a period 
in which management had already exceeded targets before the end of the period and 
thus made conservative accounting choices that would delay reporting profits until 
the following period (so-  called “hidden reserves”). Similar motivations might also 
contribute to accounting choices that create the appearance that the trajectory of 
future results would appear more attractive. For example, a company might make 
choices to accelerate losses in the first year of an acquisition or the first year of a new 
CEO’s tenure so that the trajectory of future results would appear more attractive.
Overall, unbiased  financial reporting is the ideal and the preference. Investors may

prefer conservative choices rather than aggressive ones, however, because a positive 
surprise is easier to tolerate than a negative surprise. Biased reporting, whether con -
servative or aggressive, adversely affects a user’s ability to assess a company.
The quality spectrum considers the more intuitive situation in which less-  than-  
desired underlying economics are the central motivation for poor reporting quality. In 
addition, it is necessary to have some degree of reporting quality in order to evaluate 
earnings quality. Proceeding down the spectrum, therefore, the concepts of reporting 
quality and earnings quality become progressively less distinguishable.
2.3.1  Within GAAP , but “Earnings Management”
The next level down on the spectrum in Exhibit  2 is labeled “Within GAAP , but 
‘earnings management. ’” The term “earnings management” is defined here as making 
intentional choices that create biased financial reports.8 The distinction between

earnings management and biased choices is subtle and, primarily, a matter of intent. 
Earnings management represents “deliberate actions to influence reported earnings 
and their interpretation” (Ronen and Yaari, 2008). Earnings can be “managed” upward 
(increased) by taking real actions, such as deferring research and development (R&D) 
expenses into the next reporting period. Alternatively, earnings can be increased by 
accounting  choices, such as changing accounting estimates. For example, the amount of 
estimated product returns, bad debt expense, or asset impairment could be decreased. 
Because it is difficult to determine intent, we include earnings management under 
the biased choices discussion.
8 Various definitions have appeared in academic research. Closest to the discussion here is Schipper (1989), 
which uses the term “earnings management” to mean “‘disclosure management’ in the sense of a purposeful

intervention in the external financial reporting process, with the intent of obtaining some private gain (as 
opposed to, say, merely facilitating the neutral operation of the process). ”

Conceptual Overview 619
2.4 Departures from GAAP
The next levels down on the spectrum in Exhibit  2 mark departures from GAAP . 
Financial reporting that departs from GAAP can generally be considered low quality. 
In such situations, earnings quality is likely difficult or impossible to assess because 
comparisons with earlier periods and/or other entities cannot be made. An example 
of improper accounting was Enron (accounting issues revealed in 2001), whose inap -
propriate use of off-  balance-  sheet structures and other complex transactions resulted 
in vastly understated indebtedness as well as overstated profits and operating cash 
flow. Another notorious example of improper accounting was WorldCom (accounting 
issues discovered in 2002), a company that by improperly capitalizing certain expen -
ditures dramatically understated its expenses and thus overstated its profits. More 
recently, New Century Financial (accounting issues revealed in 2007) issued billions

of dollars of subprime mortgages and improperly reserved only minimal amounts for 
loan repurchase losses. Each of these companies subsequently filed for bankruptcy.
In the 1980s, Polly Peck International (PPI) reported currency losses, incurred in 
the normal course of operations, directly through equity rather than in its profit and 
loss statements. In the 1990s, Sunbeam improperly reported revenues from “bill-  and-  
hold” sales and also manipulated the timing of expenses in an effort to falsely portray 
outstanding performance of its then-  new chief executive.
At the bottom of the quality spectrum, fabricated reports portray fictitious events, 
either to fraudulently obtain investments by misrepresenting the company’s per -
formance and/or to obscure fraudulent misappropriation of the company’s assets. 
Examples of fraudulent reporting are unfortunately easy to find, although they were 
not necessarily easy to identify at the time. In the 1970s, Equity Funding Corp. cre -

ated fictitious revenues and even fictitious policyholders. In the 1980s, Crazy Eddie’s 
reported fictitious inventory as well as fictitious revenues supported by fake invoices. 
In 2004, Parmalat reported fictitious bank balances.
EXAMPLE 3   
Spectrum for Assessing Quality of Financial Reports
Jake Lake, a financial analyst, has identified several items in the financial reports 
of several (hypothetical) companies. Describe each of these items in the context 
of the financial reporting quality spectrum.
1 ABC Co. ’s 2012 earnings totaled $233 million, including a $100 million 
gain from selling one of its less profitable divisions. ABC’s earnings for 
the prior three years totaled $120 million, $107 million, and $111 million. 
The company’s financial reports are extremely clear and detailed, and the 
company’s earnings announcement highlights the one-  time nature of the 
$100 million gain.
2 DEF Co. discloses that in 2012, it changed the depreciable life of its equip -

ment from 3 years to 15 years. Equipment represents a substantial compo -
nent of the company’s assets. The company’s disclosures indicate that the 
change is permissible under the accounting standards of its jurisdiction 
but provide only limited explanation of the change.
3 GHI Co. ’s R&D expenditures for the past five years have been approxi -
mately 3% of sales. In 2012, the company significantly reduced its R&D 
expenditures. Without the reduction in R&D expenditures, the company 
would have reported a loss. No explanation is disclosed.

Reading 31 ■ Financial Reporting Quality 620
ABC’s 2012 total earnings quality can be viewed as low because nearly half of 
the earnings are derived from a non-  sustainable activity, namely the sale of a 
division. ABC’s 2012 quality of earnings from continuing operations may be 
high because the amounts are fairly consistent from year to year, although an 
analyst would undertake further analysis to confirm earnings quality. In general, 
a user of financial reports should look beyond the bottom-  line net income. The 
description provided suggests that the company’s reporting quality is high; the 
reports are clear and detailed, and the one-  time nature of the $100 million gain 
is highlighted.
DEF’s accounting choice appears to be within permissible accounting standards, 
but its effect is to substantially lower depreciation expense and thus to increase 
earnings for the year. The quality of reported earnings is questionable. Although

the new level of earnings may be sustainable, similar increases in earnings for 
future periods might not be achievable, because increasing earnings solely by 
changing accounting estimates is likely not sustainable. In addition, the descrip -
tion provided suggests that the company’s reporting quality is low because it 
offers only a limited explanation for the change.
GHI’s operational choice to reduce its R&D may reflect real earnings management 
because the change enabled the company to avoid reporting a loss. In addition, 
the description provided suggests that the company’s reporting quality is low 
because it does not offer an explanation for the change.
2.5 Differentiate between Conservative and Aggressive 
This section returns to the implications of conservative and aggressive accounting 
choices. As mentioned earlier, unbiased  financial reporting is the ideal. But investors 
may prefer or be perceived to prefer conservative rather than aggressive accounting

choices because a positive surprise is acceptable. In contrast, management may prefer 
or be perceived to prefer aggressive accounting choices because they increase the 
company’s reported performance and financial position in the current period.
Aggressive accounting choices in the current period may decrease the company’s 
reported performance and financial position in later periods, which creates a sus -
tainability issue. Conservative choices do not typically create a sustainability issue, 
because they decrease the company’s reported performance and financial position in 
the current period and may increase its reported performance and financial position 
in later periods. In terms of establishing expectations for the future, however, financial 
reporting that is relevant and faithfully representative is the most useful.
A common presumption is that financial reports are typically biased upward, but 
that is not always the case. Although accounting standards ideally promote unbiased

financial reporting, some accounting standards may specifically require a conservative 
treatment of a transaction or an event. Also, managers may choose to take a conser -
vative approach when applying standards. It is important that an analyst consider the 
possibility of conservative choices and their effects.
At its most extreme, conservatism follows accounting practices that “anticipate no 
profit, but anticipate all losses” (Bliss, 1924). But in general, conservatism means that 
revenues may be recognized once a verifiable and legally enforceable receivable has 
been generated and that losses need not be recognized until it becomes “probable” that

Conceptual Overview 621
an actual loss will be incurred. Conservatism is not an absolute but is characterized by 
degrees, such as “the accountant’s tendency to require a higher degree of verification 
to recognize good news as gains than to recognize bad news as losses” (Basu, 1997). 
From this perspective, “verification” (e.g., physical existence of inventories, evidence 
of costs incurred or to be incurred, or establishment of rights and obligations on legal 
grounds) drives the degree of conservatism: For recognition of revenues, a higher 
degree of verification would be required than for expenses.
2.5.1  Conservatism in Accounting Standards
The Conceptual Framework  supports neutrality of information: “ A neutral depiction 
is without bias in the selection or presentation of financial information. ”9 Neutrality—
lack of upward or downward bias—is considered a desirable characteristic of financial 
reporting. Conservatism directly conflicts with the characteristic of neutrality because

the asymmetric nature of conservatism leads to bias in measuring assets and liabili -
ties—and ultimately, earnings.
Despite efforts to support neutrality in financial reporting, however, many con -
servatively biased standards remain. These standards result in downward-  biased 
pictures of earnings and financial position within financial reports. Without care, this 
biased portrayal can result in biased estimates of future prospects developed using 
Example 4 illustrates the issues posed by conservative accounting practices for 
analyzing financial reports of companies engaged in the exploration and production 
of underground natural resources—oil and gas, coal, precious metals, and so on.
EXAMPLE 4   
Accounting Conservatism in Extractive Industries
Exhibit 6 depicts the typical exploration and production operating cycle, begin -
ning with exploration activities, through realization of cash from customers, and

beyond, to the payment of royalties from cash collections that are often due to 
landowners and/or host governments.
9 IASB and FASB, The Conceptual Framework for Financial Reporting  (2010):QC 14 .

Reading 31 ■ Financial Reporting Quality 622
Exhibit 6   The Extractive Industries Production Cycle
Pay Royalties 
to Landowner
Collect Funds 
from Customer
Bill Customer
Ship ProductsReceive Order
from CustomerExtractionDiscoveryExploration
Under both IFRS and US GAAP , companies in the oil and gas industry 
recognize revenue after the product has been shipped. In addition, under both 
sets of standards, companies may capitalize some acquisition, exploration, and 
development costs, but extraction costs are expensed as they are incurred. 
Thus, extraction costs are expensed during the period between discovery and 
the time of sale.
1 Why is the revenue recognition accounting standard in the oil and gas 
industry characterized as conservative?
2 Why is the expense recognition accounting standard in the oil and gas 
The most significant “good news” events for an oil exploration and production

company, by far, are discoveries of oil and gas “reserves. ” Ironically, one could 
not possibly know this critical fact from looking at the company’s reported 
earnings, because conservative accounting standards delay recognition of sales 
revenue until the energy resources are extracted, a customer is identified, and 
product is shipped. Conservative accounting standards prohibit recognition of 
the first revenues from an oil and gas reserve until years after its actual discovery.
Because extraction costs must be expensed rather than capitalized, a company 
may report losses (or reduced profits) during the periods between discovery 
and the first sales from an oil field—even though the oil exists with certainty 
and possesses saleable value.
The unavoidable conclusion is that conservatism—which can now be characterized 
as a delay in the recognition in profits from when they are actually created until a point

at which they are subject to a sufficiently high level of verification—sometimes impairs 
the relevance of financial statements for external decision makers. In the particular 
case of oil and gas exploration and production, many jurisdictions require extensive 
supplemental disclosures about operations, which reduce the problem to a degree.

Conceptual Overview 623
Standards across jurisdictions may differ on the extent of conservatism embedded 
within the standards. An analyst should be aware of the implications of accounting 
standards on the financial reports.
An example is the different treatment by IFRS and US GAAP for the impairment of 
long-  lived assets.10 Both IFRS and US GAAP specify an impairment analysis protocol 
that begins with an assessment of whether recent events indicate that the economic 
benefit from an individual or group of long-  lived assets may be less than its carrying 
amount(s). From that point on, however, the two regimes diverge:
■■Under IFRS, if the “recoverable amount” (the higher of fair value less costs to 
sell and value in use) is less than the carrying amount, then an impairment 
charge will be recorded.
■■Under US GAAP , an impairment charge will be recorded only when the sum of 
the undiscounted future cash flows expected to be derived from the asset(s) is

less than the carrying amount(s). If the undiscounted future cash flows are less 
than the carrying amount, the asset is written down to fair value.
To illustrate the difference in application, assume that a factory is the unit of 
account eligible for impairment testing: Its carrying amount is $10,000,000; “fair 
value” and “recoverable amount” are both $6,000,000; and the undiscounted future 
net cash flows associated with the factory total $10,000,000. Under IFRS, an impair -
ment charge of $4,000,000 would be recorded; but under US GAAP , no impairment 
charge would be recognized.
Thus, on its face, IFRS would be regarded as more conservative than US GAAP 
because impairment losses would normally be recognized earlier under IFRS than 
under US GAAP . But, taking the analysis one step further, such a broad generalization 
may not hold up. For example, if an asset is impaired under both IFRS and US GAAP 
and the asset’s value in use exceeds its fair value, the impairment loss under US GAAP

will be greater. Also, IFRS permits the recognition of recoveries of the recoverable 
amount in subsequent periods if evidence indicates that the recoverable amount has 
subsequently increased. In contrast, US GAAP prohibits the subsequent write-  up of 
an asset after an impairment charge has been taken; it would recognize the asset’s 
increased value only when the asset is ultimately sold.
Other common examples of conservatism in accounting standards include the 
■■Research costs . Because the future benefit of research costs is uncertain at 
the time the costs are incurred, both US GAAP and IFRS require immediate 
expensing instead of capitalization.
■■Litigation losses . When it becomes “probable” that a cost will be incurred, both 
US GAAP and IFRS require expense recognition, even though a legal liability 
may not be incurred until a future date.
■■Insurance recoverables . Generally, a company that receives payment on an

insurance claim may not recognize a receivable until the insurance company 
acknowledges the validity of the claimed amount.
■■Commodity inventories . Increases in the market prices of commodity invento -
ries held may not be recognized unless they are sold, despite the fact that iden -
tifying a specific buyer is a relatively inconsequential activity from an economic 
standpoint.
10 See IAS 36 and FASB ASC Section 360-  10- 35.

Reading 31 ■ Financial Reporting Quality 624
Watts (2003) reviews empirical studies of conservatism, and identifies four potential 
benefits of conservatism:
■■Given asymmetrical information, conservatism may protect the contracting 
parties with less information and greater risk. This protection is necessary 
because the contracting party may be at a disadvantage. For example, corpo -
rations that access debt markets have limited liability, and lenders thus have 
limited recourse to recover their losses from shareholders. As another example, 
executives who receive earnings-  based bonuses might not be subject to hav -
ing those bonuses “clawed back” if earnings are subsequently discovered to be 
overstated.
■■Conservatism reduces the possibility of litigation and, by extension, litigation 
costs. Rarely, if ever, is a company sued because it understated good news or 
overstated bad news.
■■Conservative rules may protect the interests of regulators and politicians by

reducing the possibility that fault will be found with them if companies over -
state earnings or assets.
■■In many tax jurisdictions, financial and tax reporting rules are linked. For exam -
ple, in Germany and Japan, only deductions taken against reported income can 
be deducted against taxable income. Hence, companies can reduce the present 
value of their tax payments by electing conservative accounting policies for 
certain types of events.
Analysts should consider possible conservative and aggressive biases and their 
consequences when examining financial reports. Current-  period financial reports 
may be unbiased, upward biased through aggressive accounting choices, downward 
biased through conservative accounting choices, or biased through a combination of 
conservative and aggressive accounting choices.
2.5.2  Bias in the Application of Accounting Standards
Any application of accounting standards, whether the standard  itself is neutral or

not, often requires significant amounts of judgment. Characterizing the application 
of an accounting standard as conservative or aggressive is more a matter of intent 
rather than definition.
Careful analysis of disclosures, facts, and circumstances contributes to making an 
accurate inference of intent. Management seeking to manipulate earnings may take a 
longer view by sacrificing short-  term profitability in order to ensure higher profits in 
later periods. One example of biased accounting in the guise of conservatism is the 
so- called “big bath” restructuring charges. Both US GAAP and IFRS provide for accrual 
of future costs associated with restructurings, and these costs are often associated 
with and presented along with asset impairments. But in some instances, companies 
use the accounting provisions to estimate “big” losses in the current period so that 
performance in future periods will appear better. Having observed numerous instances

of manipulative practices in the late 1990s, in which US companies set up opportunities 
to report higher profits in future periods that were not connected with performance 
in those periods, the SEC staff issued rules that narrowed the circumstances under 
which costs can be categorized as part of a “non-  recurring” restructuring event and 
enhanced the transparency surrounding restructuring charges and asset impairments.11
A similar manifestation of “big bath” accounting is often referred to as “cookie jar 
reserve accounting. ” Both US GAAP and IFRS require accruals of estimates of future 
non-  payments of loans. In his 1998 speech “The ‘Numbers Game, ’” SEC chair Arthur 
11 SEC, “Restructuring and Impairment Charges, ” Staff Accounting Bulletin (SAB) No. 100 (1999): www.
sec.gov/interps/account/sab100.htm.

Context for Assessing Financial Reporting Quality 625
Levitt expressed the general concern that corporations were overstating loans and other 
forms of loss allowances for the purpose of smoothing income over time.12 In 2003, 
the SEC issued interpretive guidance that essentially requires a company to provide 
a separate section in management’s discussion and analysis (MD&A) titled “Critical 
Accounting Estimates. ”13 If the effects of subjective estimates and judgments of highly 
uncertain matters are material to stakeholders (investors, customers, suppliers, and 
other users of the financial statements), disclosures of their nature and exposure to 
uncertainty should be made in the MD&A. This requirement is in addition to required 
disclosures in the notes to the financial statements.
CONTEXT FOR ASSESSING FINANCIAL REPORTING 
QUALITY
In assessing financial reporting quality, it is useful to consider whether a company’s

managers may be motivated to issue financial reports that are not high quality. If 
motivation exists, an analyst should consider whether the reporting environment is 
conducive to managers’ misreporting. It is important to consider mechanisms within 
the reporting environment that discipline financial reporting quality, such as the 
regulatory regime.
3.1 Motivations
Managers may be motivated to issue financial reports that are not high quality to mask 
poor performance, such as loss of market share or lower profitability than competitors. 
Lewis (2012) stated, “ A firm experiencing performance problems, particularly those 
it considers transient, may induce a response that inflates current earnings numbers 
in exchange for lower future earnings. ”
■■Even when there is no need to mask poor performance, managers frequently 
have incentives to meet or beat market expectations as reflected in analysts’ 
forecasts and/or management’s own forecasts. Exceeding forecasts typically

increases stock price, if only temporarily. Additionally, exceeding forecasts can 
increase management compensation that is linked to increases in stock price 
or to reported earnings. Graham, Harvey, and Rajgopal (2005) found that the 
CFOs they surveyed view earnings as the most important financial metric to 
financial markets. Achieving (or exceeding) particular benchmarks, includ -
ing prior-  year earnings and analysts’ forecasts, is very important. The authors 
examined a variety of motivations for why managers might “exercise accounting 
discretion to achieve some desirable earnings goal. ” Motivations to meet earn -
ings benchmarks include equity market effects (for example, building credibility 
with market participants and positively affecting stock price) and trade effects 3
12 Arthur Levitt, “The ‘Numbers Game, ’” Remarks given at NYU Center for Law and Business (28 
September 1998): www.sec.gov/news/speech/speecharchive/1998/spch220.txt.

13 SEC, “Commission Guidance Regarding Management’s Discussion and Analysis of Financial Condition 
and Results of Operations, ” Financial Reporting Release (FRR) No. 72 (2003): www.sec.gov/rules/interp  
/33- 8350.htm.

Reading 31 ■ Financial Reporting Quality 626
(for example, enhancing reputation with customers and suppliers). Equity 
market effects are the most powerful incentives, but trade effects are important, 
particularly for smaller companies.
■■Career concerns and incentive compensation may motivate accounting choices. 
For example, managers might be concerned that working for a company that 
performs poorly will limit their future career opportunities or that they will not 
receive a bonus based on exceeding a particular earnings target. In both cases, 
management might be motivated to make accounting choices to increase earn -
ings. In a period of marginally poor performance, a manager might accelerate or 
inflate revenues and/or delay or under report expenses. Conversely, in a period 
of strong performance, a manager might delay revenue recognition or accelerate 
expense recognition to increase the probability of exceeding the next period’s

targets (i.e., to “bank” some earnings for the next period.) The surveyed manag -
ers indicated a greater concern with career implications of reported results than 
with incentive compensation implications.
Avoiding debt covenant violations can motivate managers to inflate earnings. 
Graham, Harvey, and Rajgopal’s survey indicates that avoidance of bond covenant 
violation is important to highly leveraged and unprofitable companies but relatively 
unimportant overall.
3.2 Conditions Conducive to Issuing Low-  Quality Financial 
Reports
As discussed, deviations from a neutral presentation of financial results could be 
driven by management choices or by a jurisdiction’s financial reporting standards. 
Ultimately, a decision to issue low-  quality, or even fraudulent, financial reports is 
made by an individual or individuals. Why individuals make such choices is not 
always immediately apparent. For example, why would the newly appointed CEO of

Sunbeam, who already had a net worth of more than $100 million, commit accounting 
fraud by improperly reporting revenues from “bill-  and-  hold” sales and manipulating 
the timing of expenses, rather than admit to lower-  than-  expected financial results?
Typically, three conditions exist when low-  quality financial reports are issued: 
opportunity, motivation, and rationalization. Opportunity can be the result of inter -
nal conditions, such as poor internal controls or an ineffective board of directors, or 
external conditions, such as accounting standards that provide scope for divergent 
choices or minimal consequences for an inappropriate choice. Motivation can result 
from pressure to meet some criteria for personal reasons, such as a bonus, or corporate 
reasons, such as concern about financing in the future. Rationalization is important 
because if an individual is concerned about a choice, he or she needs to be able to 
justify it to him- or herself.

Former Enron CFO Andrew Fastow, speaking at the 2013 Association of Certified 
Fraud Examiners Annual Fraud Conference, indicated that he knew at the time he was 
doing something wrong but followed procedure to justify his decision (Pavlo, 2013). 
He made sure to get management and board approval, as well as legal and accounting 
opinions, and to include appropriate disclosures. The incentive and corporate culture 
was to create earnings rather than focus on long-  term value. Clearly, as reflected in 
his prison sentence, he did something that was not only wrong but illegal.
3.3 Mechanisms That Discipline Financial Reporting Quality
Markets potentially discipline financial reporting quality. Companies and nations 
compete for capital, and the cost of capital is a function of perceived risk—including 
the risk that a company’s financial statements will skew investors’ expectations. Thus,

Context for Assessing Financial Reporting Quality 627
in the absence of other conflicting economic incentives, a company seeking to mini -
mize its long-  term cost of capital should aim to provide high-  quality financial reports. 
In addition to markets, other mechanisms that discipline financial reporting quality 
include market regulatory authorities, auditors, and private contracts.
3.3.1  Market Regulatory Authorities
Companies seeking to minimize the cost of capital should maximize reporting quality, 
but as discussed earlier, conflicting incentives often exist. For this reason, national 
regulations, and the regulators that establish and enforce rules, can play a significant 
role in financial reporting quality. Many of the world’s securities regulators are mem -
bers of the International Organization of Securities Commissions (IOSCO). IOSCO 
is recognized as the “global standard setter for the securities sector” although it does

not actually set standards but rather establishes objectives and principles to guide 
securities and capital market regulation. IOSCO’s membership includes more than 
120 securities regulators and 80 other securities market participants, such as stock 
exchanges.14
One member of IOSCO is the European Securities and Markets Authority (ESMA),15 
an independent EU authority with a mission to “enhance the protection of investors 
and reinforce stable and well-  functioning financial markets in the European Union. ”16 
ESMA organizes financial reporting enforcement activities through a forum consisting 
of European enforcers from European Economic Area countries. Direct supervision and 
enforcement activities are performed at the national level. For example, the Financial 
Conduct Authority (FCA) is the IOSCO member with primary responsibility for 
securities regulation in the United Kingdom. ESMA reported that European enforcers

performed 850 full and 1,100 partial reviews of companies’ accounts in 2011, which in 
turn led to enforcement actions with the following outcomes: 18 amended reports to 
restate financial statements, approximately 150 public corrective notes or announce -
ments, and approximately 420 required corrections in future financial statements.17
Another member of IOSCO is the US regulatory authority, the Securities and 
Exchange Commission. The SEC is responsible for overseeing approximately 9,100 
US public companies (along with investment advisers, broker/dealers, securities 
exchanges, and other entities) and reviews the disclosures of these companies at least 
once every three years with the aim of improving information available to investors 
and potentially uncovering possible violations of securities laws.18 In 2002, the SEC 
reported that it had filed 515 enforcement actions for financial reporting and disclosure

violations during the preceding five-  year period (along with around 2,000 other types 
of enforcement actions) in which 68% of the named parties were charged with fraud.19
Examples of regulatory bodies in Asia include the Financial Services Agency in 
Japan, the China Securities Regulatory Commission, and the Securities and Exchange 
Board of India. Examples of regulatory bodies in South America include the Comisión 
14 Visit www.iosco.org for more information.
15 ESMA is an associate member of IOSCO. The individual countries’ authorities are ordinary members 
of IOSCO. An ordinary member has primary responsibility for securities regulation in its jurisdiction and 
is the voting member of IOSCO. Some countries’ stock exchanges are ordinary or affiliate members. An 
affiliate member is a self-  regulatory body (SRO), or an international body, with an appropriate interest in 
securities regulation.
16 Text from ESMA’s mission statement on their website: www.esma.europa.eu.

17 ESMA, “ Activity Report on IFRS Enforcement in the European Economic Area in 2011, ” European 
Securities and Markets Authority (28 June 2012): www.esma.europa.eu.
18 SEC, “FY2013 Congressional Justification, ” Securities and Exchange Commission (February 2012): www.
sec.gov/about/secfy13congbudgjust.pdf
19 SEC, “Report Pursuant to Section 704 of the Sarbanes–Oxley Act of 2002, ” Securities and Exchange 
Commission (30 July 2002): www.sec.gov/news/studies/sox704report.pdf

Reading 31 ■ Financial Reporting Quality 628
Nacional de Valores in Argentina, Comissão de Valores Mobiliários in Brazil, and 
Superintendencia de Valores y Seguros in Chile. A full list of IOSCO members can 
be found on the organization’s website.
Typical features of a regulatory regime that most directly affect financial reporting 
quality include the following:
■■Registration requirements . Market regulators typically require publicly traded 
companies to register securities before offering the securities for sale to the 
public. A registration document typically contains current financial statements, 
other relevant information about the risks and prospects of the company issu -
ing the securities, and information about the securities being offered.
■■Disclosure requirements . Market regulators typically require publicly traded 
companies to make public periodic reports, including financial reports and 
management comments. Standard-  setting bodies, such as the IASB and FASB,

are typically private sector, self-  regulated organizations with board members 
who are experienced accountants, auditors, users of financial statements, and 
academics. Regulatory authorities, such as the Accounting and Corporate 
Regulatory Authority in Singapore, the Securities and Exchange Commission in 
the United States, the Securities and Exchange Commission in Brazil, and the 
Financial Reporting Council in the United Kingdom, have the legal authority to 
enforce financial reporting requirements and exert other controls over entities 
that participate in the capital markets within their jurisdiction. In other words, 
generally , standard-  setting bodies set the standards, and regulatory authorities 
recognize and enforce those standards. Without the recognition of standards 
by regulatory authorities, the private-  sector standard-  setting bodies would have 
no authority. Regulators often retain the legal authority to establish financial

reporting standards in their jurisdiction and can overrule the private-  sector 
standard-  setting bodies.
■■Auditing requirements . Market regulators typically require companies’ financial 
statements to be accompanied by an audit opinion attesting that the financial 
statements conform to the relevant set of accounting standards. Some regula -
tors, such as the SEC in the United States, require an additional audit opinion 
attesting to the effectiveness of the company’s internal controls over financial 
reporting.
■■Management commentaries.  Regulations typically require publicly traded com -
panies’ financial reports to include statements by management. For example, 
the FCA in the United Kingdom requires a management report containing “(1) 
a fair review of the issuer’s business; and (2) a description of the principal risks 
and uncertainties facing the issuer. ”
■■Responsibility statements . Regulations typically require a statement from the

person or persons responsible for the company’s filings. Such statements 
require the responsible individuals to explicitly acknowledge responsibility and 
to attest to the correctness of the financial reports. Some regulators, such as the 
SEC in the United States, require formal certifications that carry specific legal 
penalties for false certifications.
■■Regulatory review of filings . Regulators typically undertake a review process to 
ensure that the rules have been followed. The review process typically covers all 
initial registrations and a sample of subsequent periodic financial reports.
■■Enforcement mechanisms . Regulators are granted various powers to enforce the 
securities market rules. Such powers can include assessing fines, suspending or 
permanently barring market participants, and bringing criminal prosecutions. 
Public announcements of disciplinary actions are also a type of enforcement 
mechanism.

Context for Assessing Financial Reporting Quality 629
In summary, market regulatory authorities play a central role in encouraging 
high-  quality financial reporting.
3.3.2  Auditors
As noted, regulatory authorities typically require that publicly traded companies’ 
financial statements be audited by an independent auditor. Private companies also 
obtain audit opinions for their financial statements, either voluntarily or because audit 
reports are required by an outside party, such as providers of debt or equity capital.
Audit opinions provide financial statement users with some assurance that the 
information complies with the relevant set of accounting standards and presents the 
company’s information fairly. Exhibits 7, 8, and 9 provide excerpts from the indepen -
dent auditors’ reports for GlaxoSmithKline plc, Novartis Group, and the Nestlé Group, 
respectively. Note that for each company, the auditor issued an unqualified or clean

opinion that reflects the specific requirements of the company’s regulatory regime. 
For example, the audit opinions for Novartis include an SEC-  required opinion on the 
effectiveness of internal controls because Novartis’ securities trade in the United States. 
The SEC permits non-  US companies to report using US GAAP , IFRS as issued by the 
IASB, or home-  country GAAP . If a company reports using home-  country GAAP , a 
reconciliation to US GAAP must be provided. Regardless of the standards used by a 
non-  US company in preparing its financial statements, an opinion on internal controls’ 
effectiveness is required.
Exhibit 7   Excerpts from Audit Opinion of PricewaterhouseCoopers LLP 
from the 2012 Annual Report of GlaxoSmithKline plc
In our opinion the Group financial statements:
■■give a true and fair view of the state of the Group’s affairs as at 31 
December 2012 and of its profit and cash flows for the year then ended;

■■have been properly prepared in accordance with IFRS as adopted by the 
European Union; and
■■have been prepared in accordance with the requirements of the 
Companies Act 2006 and Article 4 of the IAS Regulation.
…
In our opinion the Group financial statements comply with IFRSs as issued by 
the IASB.
…
In our opinion the information given in the Directors’ Report for the financial 
year for which the Group financial statements are prepared is consistent with 
the Group financial statements.
Exhibit 8   Excerpts from Audit Opinion of PricewaterhouseCoopers AG from 
the 2012 Annual Report of Novartis Group
In our opinion, the consolidated financial statements for the year ended 
December 31, 2012 present fairly, in all material respects, the financial position, 
the results of operations and the cash flows in accordance with International 
Financial Reporting Standards (IFRS) as issued by the International Accounting 
Standards Board and comply with Swiss law.
…

Reading 31 ■ Financial Reporting Quality 630
In our opinion, Novartis Group maintained, in all material respects, effective 
internal control over financial reporting as of December 31, 2012, based on crite -
ria established in Internal Control – Integrated Framework issued by the COSO.
Exhibit 9   Excerpt from Audit Opinion of KPMG SA from the 2012 Annual 
Report of Nestlé Group
In our opinion, the consolidated financial statements [of the Nestlé Group] for the 
year ended 31 December 2012 give a true and fair view of the financial position, 
Financial Reporting Standards (IFRS) and comply with Swiss law.
Although audit opinions provide discipline for financial reporting quality, inherent 
limitations exist. First, an audit opinion is based on a review of information prepared 
by the company. If a company deliberately intends to deceive its auditor, a review of

information might not uncover misstatements. Second, an audit is based on sampling, 
and the sample might not reveal misstatements. Third, an “expectations gap” may 
exist between the auditor’s role and the public’s expectation of auditors. An audit 
is not typically intended to detect fraud; it is intended to provide assurance that the 
financial reports are fairly presented. Finally, the company being audited pays the audit 
fees, often established through a competitive process. This situation could provide an 
auditor with an incentive to show leniency to the company being audited, particularly 
if the auditor’s firm provides additional services to the company.
3.3.3  Private Contracting
Aspects of private contracts, such as loan agreements or investment contracts, can 
serve as mechanisms to discipline financial reporting quality. Many parties that have a 
contractual arrangement with a company have an incentive to monitor that company’s

performance and to ensure that the company’s financial reports are high quality. For 
example, loan agreements often contain loan covenants, which create specifically tai -
lored financial reporting requirements that are legally binding for the issuer. As noted 
earlier, avoidance of debt covenant violation is a potential motivation for managers to 
inflate earnings. As another example, an investment contract could contain provisions 
giving investors the option to recover all or part of their investment if certain financial 
triggers occur. Such provisions could motivate the investee’s managers to manipulate 
reported results to avoid the financial triggers.
Because the financial reports prepared by the investees or borrowers directly 
affect the contractual outcomes—potentially creating a motivation for misreport -
ing—investors and lenders are motivated to monitor financial reports and to ensure 
that they are high quality.Exhibit 8   (Continued)

Context for Assessing Financial Reporting Quality 631
EXAMPLE 5   
Financial Reporting Manipulation: Motivations and 
Disciplining Mechanisms
For each of the following two scenarios, identify (1) factors that might motivate 
the company’s managers to manipulate reported financial amounts and (2) 
applicable mechanisms that could discipline financial reporting quality.
1 ABC Co. is a private company. Bank NTBig has made a loan to ABC Co. 
ABC is required to maintain a minimum 2.0 interest coverage ratio. In 
its most recent financial reports, ABC reported earnings before interest 
and taxes of $1,200 and interest expense of $600. In the report’s notes, the 
company discloses that it changed the estimated useful life of its property, 
plant, and equipment during the year. Depreciation was approximately 
$150 lower as a result of this change in estimate.
2 DEF Co. is a publicly traded company. For the most recent quarter, the

average of analysts’ forecasts for earnings per share was $2.50. In its quar -
terly earnings announcement, DEF reported net income of $3,458,780. 
The number of common shares outstanding was 1,378,000. DEF’s main 
product is a hardware device that includes a free two-  year service con -
tract in the selling price. Based on management estimates, the company 
allocates a portion of revenues to the hardware device, which it recognizes 
immediately, and a portion to the service contract, which it defers and 
recognizes over the two years of the contract. Based on the disclosures, a 
higher percentage of revenue was allocated to hardware than in the past, 
with an estimated after-  tax impact on net income of $27,000.
The need to maintain a minimum interest coverage ratio of 2.0 might motivate 
ABC’s managers to manipulate reported financial amounts. The company’s 
coverage ratio based on the reported amounts is exactly equal to 2.0. If ABC’s

managers had not changed the estimated useful life of the property, plant, and 
equipment, the coverage ratio would have fallen below the required level.
EBIT, as reported $1,200
Impact on depreciation expense of changed 
assumptions about useful life 150
EBIT, as adjusted $1,050
Interest expense $600
Coverage ratio, as reported 2.00
Coverage ratio, as adjusted 1.75
The potential disciplining mechanisms include the auditors, who will assess 
the reasonableness of the depreciable lives estimates. In addition, the lenders 
will carefully scrutinize the change in estimate because the company only barely 
achieved the minimum coverage ratio and would not have achieved the minimum 
without the change in accounting estimate.

Reading 31 ■ Financial Reporting Quality 632
The desire to meet or exceed the average of analysts’ forecasts for earnings 
per share might motivate DEF Co. ’s managers to manipulate reported financial 
amounts. As illustrated in the following calculations, the impact of allocating a 
greater portion of revenue to hardware enabled the company to exceed analysts’ 
earnings per share forecasts by $0.01.
Net income, as reported $3,458,780
Impact on gross profit of changed revenue 
recognition, net of tax 27,000
Net income, as adjusted $3,431,780
Weighted average number of shares 1,378,000
Earnings per share, as reported $2.51
Earnings per share, as adjusted $2.49
The potential disciplining mechanisms include the auditors, market regula -
tors, financial analysts, and financial journalists.
DETECTION OF FINANCIAL REPORTING QUALITY 
ISSUES
Choices in the application of accounting standards abound, which is perhaps one

reason why accounting literature and texts are so voluminous. Compounding the 
complexity, measurement often depends on estimates of economic phenomena. Two 
estimates might be justifiable, but they may have significantly different effects on the 
company’s financial statements. As discussed earlier, the choice of a particular estimate 
may depend on the motivations of the reporting company’s managers. With many 
choices available, and the inherent flexibility of estimates in the accounting process, 
managers have many tools for managing and meeting analysts’ expectations through 
financial reporting.
An understanding of the choices that companies make in financial reporting is 
fundamental to evaluating the overall quality—both financial reporting and earnings 
quality—of the reports produced. Choices exist both in how information is presented 
(financial reporting quality) and in how financial results are calculated (earnings qual -

ity). Choices in presentation (financial reporting quality) may be fairly transparent to 
investors. Choices in the calculation of financial results (earnings quality), however, 
are more difficult to discern because they can be deeply embedded in the construction 
of reported financial results.
The availability of accounting choices enables managers to affect the reporting 
of financial results. Some choices increase performance and financial position in 
the current period (aggressive choices), and others increase them in later periods 
(conservative choices). A manager that wants to increase performance and financial 
position in the current period could:
■■Recognize revenue prematurely;
■■Use nonrecurring transactions to increase profits;
■■Defer expenses to later periods;4

Detection of Financial Reporting Quality Issues 633
■■Measure and report assets at higher values; and/or
■■Measure and report liabilities at lower values.
A manager that wants to increase performance and financial position in a later 
period could:
■■Defer current income to a later period (save income for a “rainy day”); and/or
■■Recognize future expenses in a current period, setting the table for improving 
The following sections describe some of the potential choices for how information 
is presented and how accounting elements [assets, liabilities, owners’ equity, revenue 
and gains (income), and expenses and losses] are recognized, measured, and reported. 
In addition to choices within GAAP , companies may prepare fraudulent reports. For 
example, these reports may include non-  existent revenue or assets. Section 4 con -
cludes with some of the warning signs that can indicate poor-  quality financial reports.
4.1 Presentation Choices

The technology boom of the 1990s and the internet bubble of the early 2000s featured 
companies, popular with investors, that often shared the same characteristic: They 
could not generate enough current earnings to justify their stock prices using the tra -
ditional price-  to- earnings ratio (P/E) approaches to valuation. Many investors chose 
to explain these apparent anomalies by rationalizing that the old focus on profits and 
traditional valuation approaches no longer applied to such companies. Strange new 
metrics for determining operating performance emerged. Website operators spoke 
of the “eyeballs” they had captured in a quarter, or the “stickiness” of their websites 
for web surfers’ visits. Various versions of “pro forma earnings”—that is, “non-  GAAP 
earnings measures”—became a financial reporting staple of the era.
Many technology companies were accomplished practitioners of pro forma report -

ing, but they were not the first to use it. In the early 1990s, downsizing of large com -
panies was a commonplace event, and massive restructuring charges obscured the 
operating performance at many established companies. For example, as it learned 
to cope in a world that embraced the personal computer rather than mainframe 
computing, International Business Machines (IBM) reported massive restructuring 
charges in 1991, 1992, and 1993: $3.7 billion, $11.6 billion, and $8.9 billion, respectively. 
IBM was not alone. Sears incurred $2.7 billion of restructuring charges in 1993, and 
AT&T reported restructuring charges of $7.7 billion in 1995. These events were not 
isolated; restructuring charges were a standard quarterly reporting event. To counter 
perceptions that their operations were floundering, and supposedly to assist investors 
in evaluating operating performance, companies often sanitized earnings releases

by excluding restructuring charges in pro forma measures of financial performance.
Accounting principles for reporting business combinations also played a role 
in boosting the popularity of pro forma earnings. Before 2001, acquisitions of one 
company by another often resulted in goodwill amortization charges that made sub -
sequent earnings reports look weak. Complicating matters, there were two accounting 
methods for recording acquisitions: pooling-  of- interests and purchase methods. The 
now-  extinct pooling-  of- interests treatment was difficult for companies to achieve 
because of the many restrictive criteria for its use, but it was greatly desired because 
it did not result in goodwill amortization charges. In the technology boom period, 
acquisitions were common and many were reported as purchases, with consequential 
goodwill amortization dragging down earnings for as long as 40 years under the then-

existing rules. Acquisitive companies reporting under purchase accounting standards 
perceived themselves to be at a reporting disadvantage compared with companies able

Reading 31 ■ Financial Reporting Quality 634
to apply pooling-  of- interests accounting. The companies reporting under purchase 
accounting began to present earnings adjusted for the exclusion of amortization of 
intangible assets and goodwill.
Because investors try to make intercompany comparisons on a consistent basis, 
earnings before interest, taxes, depreciation, and amortization has become an extremely 
popular performance measure. EBITDA is widely viewed as eliminating noisy reporting 
signals. That noise may be introduced by different accounting methods among com -
panies for depreciation, amortization of intangible assets, and restructuring charges. 
Companies may construct and report their own version of EBITDA, sometimes 
referring to it as “adjusted EBITDA, ” by adding to the list of items to exclude from 
net income. Items that analysts might encounter include the following:
■■Rental payments for operating leases, resulting in EBITDAR (earnings before

interest, taxes, depreciation, amortization, and rentals);
■■Equity-  based compensation, usually justified on the grounds that it is a non-  
cash expense;
■■Acquisition-  related charges;
■■Impairment charges for goodwill or other intangible assets;
■■Impairment charges for long-  lived assets;
■■Litigation costs; and
■■Loss/gain on debt extinguishments.
Among other incentives for the spread of non-  GAAP earnings measures are loan 
covenants. Lenders may make demands on a borrowing company that require achiev -
ing and maintaining performance criteria defined by using GAAP net income as a 
starting point but arriving at a measure suitable to the lender. The company may use 
this measure as its preferred non-  GAAP metric in earnings releases, and it also may 
use the measure in describing its liquidity or solvency situation in the management 
commentary (called management discussion and analysis in the United States).
As mentioned earlier, if a company uses a non-  GAAP financial measure in an

SEC filing, it must display the most directly comparable GAAP measure with equal 
prominence and provide a reconciliation of the non-  GAAP measure and the equivalent 
GAAP measure. Management must explain why it believes that the non-  GAAP finan -
cial measure provides useful information regarding the company’s financial condition 
and operations. Management must also disclose additional purposes, if material, for 
which it uses the non-  GAAP financial measures.
Similarly, IFRS requires a definition and explanation of any non-  IFRS measures 
included in financial reports, including why the measure is potentially relevant to 
users of the financial reports. Management must provide reconciliations of non-  IFRS 
measures with IFRS measures presented in the financial reports. There seems to be a 
general concern that management may use non-  GAAP measures to distract a user’s 
attention from GAAP measures.
The SEC intended that the definition of non-  GAAP financial measure capture all

measures that have the effect of depicting either
■■a measure of performance that differs from that presented in the financial state -
ments, such as income or loss before taxes or net income or loss, as calculated 
in accordance with GAAP; or
■■a measure of liquidity that differs from cash flow or cash flow from operations 
computed in accordance with GAAP .20
20 SEC, “Final Rule: Conditions for Use of Non-  GAAP Financial Measures, ” Securities and Exchange 
Commission (www.sec.gov/rules/final/33-  8176.htm).

Detection of Financial Reporting Quality Issues 635
The SEC prohibits the exclusion of charges or liabilities requiring cash settlement 
from any non-  GAAP liquidity measures, other than EBIT and EBITDA. Also prohib -
ited is the calculation of a non-  GAAP performance measure intended to eliminate or 
smooth items tagged as non-  recurring, infrequent, or unusual when such items are 
very likely to occur again. The SEC views the period within two years of either before 
or after the reporting date as the relevant time frame for considering whether a charge 
or gain is a recurring item. Example 6 describes a case of misuse and misreporting 
of non-  GAAP measures.
EXAMPLE 6   
Misuse and Misreporting of Non-  GAAP Measures
Groupon is an online discount merchant. In the company’s initial S-  1 registration 
statement in 2011, then-  CEO Andrew Mason gave prospective investors an up-  
front warning in a section entitled “We don’t measure ourselves in conventional

ways. ” He described Groupon’s adjusted consolidated segment operating income 
(adjusted CSOI) measure. Exhibit 10 provides excerpts from a section entitled 
“Non-  GAAP Financial Measures, ” which offered a more detailed explanation 
of the measure. Exhibit 11, also from the initial registration statement, shows a 
reconciliation of CSOI to the most comparable US GAAP measure. In its review, 
the SEC took the position that online marketing expenses were a recurring 
cost of business. Groupon responded that the marketing costs were similar to 
acquisition costs, not recurring costs, and that “we’ll ramp down marketing 
just as fast as we ramped it up, reducing the customer acquisition part of our 
marketing expenses” as time passes.21
Eventually, and after much negative publicity, Groupon changed its non-  
GAAP measure. Exhibit 12 shows an excerpt from the final prospectus filed in 
November, after the SEC’s review. Use the three exhibits to answer the questions 
that follow.

Exhibit 10   Groupon’s “Non-  GAAP Financial Measures”
Disclosures from June S-  1 Filing
Adjusted CSOI is operating income of our two segments, North America 
and International, adjusted for online marketing expense, acquisition-  
related costs and stock-  based compensation expense. Online marketing 
expense primarily represents the cost to acquire new subscribers and is 
dictated by the amount of growth we wish to pursue. Acquisition-  related 
costs are non-  recurring non-  cash items related to certain of our acquisi -
tions. Stock-  based compensation expense is a non-  cash item. We consider 
Adjusted CSOI to be an important measure of the performance of our busi -
ness as it excludes expenses that are non-  cash or otherwise not indicative 
of future operating expenses. We believe it is important to view Adjusted 
CSOI as a complement to our entire consolidated statements of operations.
Our use of Adjusted CSOI has limitations as an analytical tool, and you

should not consider this measure in isolation or as a substitute for analysis 
of our results as reported under GAAP . Some of these limitations are:
■■Adjusted CSOI does not reflect the significant cash investments that 
we currently are making to acquire new subscribers;
21 Correspondence between Groupon and SEC, filed in EDGAR on 16 September 2011.

Reading 31 ■ Financial Reporting Quality 636
■■Adjusted CSOI does not reflect the potentially dilutive impact of 
issuing equity-  based compensation to our management team and 
employees or in connection with acquisitions;
■■Adjusted CSOI does not reflect any interest expense or the cash 
requirements necessary to service interest or principal payments on 
any indebtedness that we may incur;
■■Adjusted CSOI does not reflect any foreign exchange gains and 
losses;
■■Adjusted CSOI does not reflect any tax payments that we might 
make, which would represent a reduction in cash available to us;
■■Adjusted CSOI does not reflect changes in, or cash requirements for, 
our working capital needs; and
■■Other companies, including companies in our industry, may calcu -
late Adjusted CSOI differently or may use other financial measures 
to evaluate their profitability, which reduces the usefulness of it as a 
comparative measure.
Because of these limitations, Adjusted CSOI should not be considered

as a measure of discretionary cash available to us to invest in the growth 
of our business. When evaluating our performance, you should consider 
Adjusted CSOI alongside other financial performance measures, including 
various cash flow metrics, net loss and our other GAAP results.
Exhibit 11   Groupon’s “Adjusted CSOI”
Excerpt from June S-  1 Filing
The following is a reconciliation of CSOI to the most comparable US 
GAAP measure, “loss from operations, ” for the years ended December 31, 
2008, 2009, and 2010 and the three months ended March 31, 2010 and 2011:
Y ear Ended  
December 31,Three Months 
Ended March 31,
(in $ thousands) 2008 2009 2010 2010 2011
(Loss) Income from 
operations (1,632) (1,077) (420,344) 8,571 (117,148)
Adjustments:
  Online marketing 162 4,446 241,546 3,904 179,903
  Stock-  based 
compensation 24 115 36,168 116 18,864
  Acquisition-  
related — — 203,183 — —
Total adjustments 186 4,561 480,897 4,020 198,767

Adjusted CSOI (1,446) 3,484 60,553 12,591 81,619Exhibit 10   (Continued)

Detection of Financial Reporting Quality Issues 637
Exhibit 12   Groupon’s “CSOI”
Excerpt from Revised S-  1 Filing
2008, 2009, and 2010 and the nine months ended September  30, 2010 
and 2011:
Y ear Ended  
December 31,Nine Months 
Ended 
September 30,
Loss from 
operations (1,632) (1,077) (420,344) (84,215) (218,414)
compensation 24 115 36,168 8,739 60,922
related — — 203,183 37,844 (4,793)
Total adjustments 24 115 239,351 46,583 56,129
CSOI (1,608) (962) (180,993) (37,632) (162,285)
1 What cautions did Groupon include along with its description of the 
“ Adjusted CSOI” metric?
2 Groupon excludes “online marketing” from “ Adjusted CSOI. ” How does 
the exclusion of this expense compare with the SEC’s limits on non-  GAAP 
performance measures?

3 In the first quarter of 2011, what was the effect of excluding online mar -
keting expenses on the calculation of “ Adjusted CSOI”?
4 For 2010, how did results under the revised non-  GAAP metric compare 
with the originally reported metric?
Groupon cautioned that the “ Adjusted CSOI” metric should not be considered 
in isolation, should not be considered as a substitute for analysis using GAAP 
results, and “should not be considered a measure of discretionary cash flow. ” 
The company lists numerous limitations, primarily citing items that adjusted 
CSOI did not reflect.
The SEC specifies that non-  GAAP measures should not eliminate items tagged 
as non-  recurring, infrequent, or unusual when such items may be very likely to 
occur again. Because the online marketing expense occurred in every period 
reported and is likely to occur again, exclusion of this item appears contrary to 
SEC requirements.

Reading 31 ■ Financial Reporting Quality 638
As shown in Exhibit 11, in the first quarter of 2011, the exclusion of the online 
marketing expense was enough to swing the company from a net loss under US 
GAAP reporting to a profit—at least, a profit as defined by adjusted CSOI. Using 
adjusted CSOI as a performance measure, the company showed results that were 
35% higher for the first quarter  of 2011 compared with the entire previous year .
As shown in Exhibit 12, the revised metric is now called “CSOI” and no longer 
refers to “ Adjusted CSOI. ” For 2010, results under the revised non-  GAAP metric, 
which includes online marketing costs, shows a loss of $180,993,000 instead of 
a profit of $60,553,000.
4.2 Accounting Choices and Estimates
Choices do not necessarily involve complex accounting standards. Something as simple 
as the shipping terms for goods delivered to customers can have a profound effect on

the timing of revenue. On the last day of the first quarter, suppose a company ships 
$10,000 of goods to a customer on the terms “free on board (FOB) shipping point, ” 
arriving the next day. This shipping term means that the customer takes title to the 
goods, and bears the risk of loss, at the time the goods leave the seller’s loading dock. 
Barring any issues with collectability of the receivable, or a likelihood of a return, the 
seller would be able to recognize revenue on the sale along with the associated profit. 
That revenue and profit would be recognized in the first quarter of the year. Change 
the point at which the goods’ title transfers to the customer to “FOB destination” and 
the revenue pattern will be completely different. Under these terms, the title—and 
risk of loss—transfers to the customer when the goods arrive at their destination, 
which is the customer’s address. The seller cannot recognize the sale and profit until

the shipment arrives the following day, which is the start of a new accounting period.
A simple change in shipping terms can make the difference between revenue and 
profits in the current period or postponing them until the next period. Shipping terms 
can also influence management behavior: To “make the numbers, ” managers might 
push product out the door prematurely under FOB shipping point arrangements in 
order to reflect as much revenue as possible in the current period. Alternatively, in 
the case of an overabundance of orders, the company could run the risk of exceeding 
analysts’ consensus estimates by a large margin. Management might be uncomfortable 
with this situation because investors might extrapolate too much from one reporting 
period in which expectations were exceeded. Management might want to prevent 
investors from becoming too optimistic and, if possible, delay revenue recognition 
until the next quarter. This result could be accomplished by fulfilling customer orders

by initiating delivery on the last day of the quarter, with shipping terms set as FOB 
destination. By doing so, title would transfer in the next accounting period. Another 
possibility in this scenario is that if the customers insisted on FOB shipping point terms, 
the selling company could simply delay shipment until after the close of the quarter.
This illustration also highlights a difficult distinction for investors to make. A 
company may use accounting as a tool to aggressively promote earnings growth—as 
in the example with the premature shipment of goods with FOB shipping point 
terms—but it may be aggressively managing the business flow by slacking off on 
shipping goods when business is “too good, ” as in the second example. In either case, 
a desired management outcome is obtained by a simple change in shipping terms. 
Yet, many investors might be inclined to say that the second example is a conservative

kind of earnings management and accept it, even though it artificially masks the actual 
economic activity that occurred at the time.

Detection of Financial Reporting Quality Issues 639
4.2.1  How Accounting Choices and Estimates Affect Earnings and Balance Sheets
Assumptions about inventory cost flows provide another example of how accounting 
choices can affect financial reporting. Companies may assume that their purchases 
of inventory items are sold to customers on a first-  in- first-  out (FIFO) basis, with 
the result that the remaining inventory reflects the most recent costs. Alternatively, 
they may assume that their purchases of inventory items are sold to customers on a 
weighted-  average cost basis. Example 7 makes the point that merely choosing a cost 
flow assumption can affect profitability.
EXAMPLE 7   
Effect of Cost Flow Assumption
A company starts operations with no inventory at the beginning of a fiscal 
year and makes purchases of a good for resale five times during the period at 
increasing prices. Each purchase is for the same number of units of the good. The

purchases, and the cost of goods available for sale, appear in the following table. 
Notice that the price per unit has increased by 140% by the end of the period.
Units Price Cost
Purchase 1 5 $100 $500
Purchase 2 5 150 750
Purchase 3 5 180 900
Purchase 4 5 200 1,000
Purchase 5 5 240 1,200
Cost of goods available for sale $4,350
During the period, the company sells, at $250 each, all of the goods purchased 
except for five of them. Although the ending inventory consists of five units, the 
cost attached to those units can vary greatly.
1 What are the ending inventory and cost of goods sold if the company uses 
the FIFO method of inventory costing?
2 What are the ending inventory and cost of goods sold if the company uses 
the weighted-  average method of inventory costing?
3 Compare cost of goods sold and gross profit calculated under the two 
methods.
The ending inventory and cost of goods sold if the company uses the FIFO 
method of inventory costing are $1,200 and $3,150.

The ending inventory and cost of goods sold if the company uses the weighted-  
average method of inventory costing are $870 and $3,480.
The following table shows how the choice of inventory costing methods—FIFO 
versus weighted average—affects the cost of goods sold and gross profit.

Reading 31 ■ Financial Reporting Quality 640
Cost Flow Assumption FIFO Weighted Average
Cost of goods available for sale $4,350 $4,350
Ending inventory (5 units) (1,200) (870)
Cost of goods sold $3,150 $3,480
Sales $5,000 $5,000
Cost of goods sold 3,150 3,480
Gross profit $1,850 $1,520
Gross profit margin 37.0% 30.4%
Note : Average inventory cost is calculated as Cost of goods available for sale/Units purchased = 
$4,350/25 = $174. There are five units in ending inventory, yielding an inventory value of $870.
Depending on which cost flow assumption the company uses, the end-  of- 
period inventory is either $870 (under the weighted-  average method) or $1,200 
(under FIFO). The choice of method results in a difference of $330 in gross profit 
and 6.6% in gross profit margin.
The previous example is simplified and extreme for purposes of illustration clarity, 
but the point is important: Management’s choice among acceptable inventory assump -

tions and methods affects profit. The selection of an inventory costing method is a 
policy decision, and companies cannot arbitrarily switch from one method to another 
at random. The selection does matter to profitability, however, and it also matters to 
the balance sheet.
In periods of changing prices, the FIFO cost assumption will provide a more current 
picture of ending inventory value, because the most recent purchases will remain in 
inventory. The balance sheet will be more relevant to investors. Under the weighted-  
average cost assumption, however, the balance sheet will display a blend of old and 
new costs. During inflationary periods, the value of the inventory will be understated: 
The company will not be able to replenish its inventory at the value shown. At the 
same time, the weighted-  average inventory cost method ensures that the more current 
costs are shown in cost of sales, making the income statement more relevant than

under the FIFO assumption. Trade-  offs exist, and investors should be aware of how 
accounting choices affect financial reports. High-  quality financial reporting provides 
users sufficient information to assess the effects of accounting choices.
Estimates abound in financial reporting because of the use of accrual accounting, 
which attempts to show the effects of all economic events on a company during a 
particular period. Accrual accounting stands in contrast to cash basis accounting, 
which shows only the cash transactions conducted by a company. Although a high 
degree of certainty exists with reporting only cash transactions, much information is 
hidden. For instance, a company with growing revenues that makes the majority of its 
sales on credit would be understating its revenues for each period if it reported only 
cash transactions. On an accrual basis, revenues reflect all transactions that occurred,

whether they transacted on a cash basis or credit-  extended basis. Estimates enter the 
process because some facts related to events occurring in a particular period might 
not yet be known. Estimates can be well grounded in reality and applied to present a 
complete picture of the events affecting a company, or they can be management tools 
for achieving a desired financial picture.
To illustrate how estimates affect financial reporting, consider revenues that include 
credit sales. A company sells $1,000,000 of merchandise on credit and records the sale 
just before year end. Under accrual accounting, that amount is included in revenues

Detection of Financial Reporting Quality Issues 641
and accounts receivable. The company’s managers know from experience that they 
will never collect every dollar of the accounts receivable. Past experience is that, on 
average, only 97% of accounts receivable is collected. The company would estimate 
an amount of the uncollectible accounts at the time the sales occur and record an 
uncollectible accounts expense of $30,000, lowering earnings. The other side of the 
entry would be to establish an allowance for uncollectible accounts of $30,000. This 
allowance would be a contra asset account, presented as an offset to accounts receiv -
able. The accounts receivable, net of the allowance for uncollectible accounts, would 
be stated at $970,000, which is the amount of cash the company ultimately expects to 
receive. If cash basis accounting had been used, no revenues or accounts receivable 
would have been reported even though sales of merchandise had occurred. Accrual

accounting, which contains estimates about future events, provides a much fuller 
picture of what transpired in the period than pure cash basis accounting.
Yet, accrual accounting poses temptations to managers to manage the numbers, 
rather than to manage the business. Suppose a company’s managers realize that the 
company will not meet analysts’ consensus estimates in a particular quarter, and further, 
their bonus pay is dependent on reaching specified earnings targets. By offering special 
payment terms, or discounts, the managers may induce customers to take delivery 
of products that they would normally not order so they could ship the products on 
FOB shipping point terms and recognize the revenues in the current quarter. They 
could even be so bold as to ship the goods under those terms even if the customer 
did not order them, in hopes that the customer would keep them or, at worst, return 
them in the next accounting period. Their focus would be to move the product off

the company’s property with FOB shipping point terms.
To further improve earnings in order to meet the consensus estimates, the compa -
ny’s managers might revise their estimate of the uncollectible accounts. The company’s 
collection history shows a typical non-  collection rate of 3% of sales, but the managers 
might rationalize the use of a 2% non-  collection rate. This change will reduce the 
allowance for uncollectible accounts and uncollectible accounts expense reported 
for the period. The managers might be able to justify the reduction on the grounds 
that the sales occurred in a part of the country that was experiencing an improved 
economic outlook, or that the company’s collection history had been biased by the 
inclusion of a prolonged period of economic downturn. Whatever the justification, it 
would be hard to prove that the new estimate is completely right or wrong until time 
has passed. Because proof of the reliability of estimates is rarely available at the time

the estimate is recorded, managers have a readily available means for manipulating 
earnings at their discretion.
ConAgra Foods, Inc. provides an example of how the allowance for uncollectible 
accounts may be manipulated in order to manage earnings.22 A subsidiary of ConAgra 
Foods, called United Agri-  Products (UAP), engaged in several improper accounting 
practices, one of them being the understatement of uncollectible accounts expense for 
several years. Exhibit 13 presents an excerpt from the SEC’s Accounting and Auditing 
Enforcement Release.
22 Accounting and Auditing Enforcement Release No. 2542, “SEC v. James Charles Blue, Randy Cook, and 
Victor Campbell,) United States District Court for the District of Colorado, Civ. Action No. 07-  CV-  00095 
REB-  MEH (17 January 2007).

Reading 31 ■ Financial Reporting Quality 642
Exhibit 13   SEC’s Accounting and Auditing Enforcement Release Regarding 
United Agri-  Products
… Generally, UAP’s policy required that accounts which were past due between 
90 days and one year should be reserved at 50%, and accounts over one year 
past due were to be reserved at 100%.
… In FY 1999 and continuing through FY 2000, UAP had substantial bad debt 
problems. In FY 2000, certain former UAP senior executives were informed that 
UAP needed to record an additional $50 million of bad debt expense. Certain 
former UAP senior executives were aware that in FY 1999 the size of the bad 
debt at certain IOCs had been substantial enough that it could have negatively 
impacted those IOC’s ability to achieve PBT (profits before taxes) targets. In 
addition, just prior to the end of UAP’s FY 2000, the Former UAP COO (chief 
operating officer), in the presence of other UAP employees, ordered that UAP’s

bad debt reserve be reduced by $7 million in order to assist the Company in 
meeting its PBT target for the fiscal year.
… At the end of FY 2000, former UAP senior executives reported financial 
results to ConAgra which they knew, or were reckless in not knowing, overstated 
UAP’s income before income taxes because UAP had failed to record sufficient 
bad debt expense. The misconduct with respect to bad debt expense caused 
ConAgra to overstate its reported income before income taxes by $7 million, or 
1.13%, in FY 2000. At the Agricultural Products’ segment level, the misconduct 
caused that segment’s reported operating profit to be overstated by 5.05%.
Deferred-  tax assets provide another example of choices in estimates that are very 
similar to the ones encountered in accrual accounting for credit sales. Deferred-  tax 
assets may arise when a company reports a net operating loss under tax accounting 
rules. A company may record a deferred-  tax asset based on the expectation that current

net tax operating losses will offset expected future profits and reduce the company’s 
future income tax liability. Accounting standards require that the deferred tax asset 
be reduced by a “valuation allowance” to account for the possibility that the company 
will be unable to generate enough profit to use all of the available tax benefits.23
Assume a company loses €1 billion in 2012, generating a net operating loss of the 
same amount for tax purposes. The company’s income tax rate is 25%, and it will be 
able to apply the net operating loss to its taxable income for the next 10 years. The 
net operating loss results in a deferred tax asset with a nominal value of €250 mil -
lion (25% × €1,000,000,000). Initial recognition would result in a deferred tax asset 
of €250 million and a credit to deferred tax expense of €250 million. The company 
must address the question of whether or not the €250 million will ever be completely

applied to future income. It may be experiencing increased competition and other 
circumstances that resulted in the €1 billion loss, and it may be unreasonable to assume 
that the company will have taxable income against which to apply the loss. In fact, the 
company’s managers might believe it is reasonable to assume only that it will survive 
for five years, and with marginal profitability. The €250 million deferred tax asset is 
thus overstated if no valuation allowance is recorded to offset it.
The managers believe that only €100 million of the net operating losses will actually 
be applied to the company’s taxable income. That belief implies that only €25 million of 
the tax benefits will ever be realized. The deferred tax assets reported on the balance 
sheet should not exceed this amount. The company should record a valuation allowance 
of €225 million, which would offset the deferred tax asset balance of €250 million,

23 See Accounting Standards Codification 740-  10- 30- 16 to 25, “Establishment of a Valuation Allowance 
for Deferred Tax Assets. ”

Detection of Financial Reporting Quality Issues 643
resulting in a net deferred tax asset balance of €25 million. There would also be a 
€225 million credit to the deferred tax provision. It is important to understand that 
the valuation allowance should be revised whenever facts and circumstances change.
The ultimate value of the deferred tax asset is driven by management’s outlook 
for the future—and that outlook may be influenced by other factors. If the company 
needs to stay in compliance with debt covenants and needs every euro of value that 
can be justified by the outlook, its managers may take a more optimistic view of 
the future and keep the valuation allowance artificially low (in other words, the net 
deferred tax asset high).
PowerLinx, Inc. provides an example of how over-  optimism about the realizabil -
ity of a deferred tax asset can lead to misstated financial reports. PowerLinx was a 
maker of security video cameras, underwater cameras, and accessories. Aside from

fraudulently reporting 90% of its fiscal year 2000 revenue, PowerLinx had problems 
with valuation of its deferred tax assets. Exhibit 14 provides an excerpt from the SEC’s 
Accounting and Auditing Enforcement Release with emphasis added.24
Exhibit 14   SEC’s Accounting and Auditing Enforcement Release Regarding 
PowerLinx
PowerLinx improperly recorded on its fiscal year 2000 balance sheet a deferred 
tax asset of $1,439,322 without any valuation allowance. The tax asset was mate -
rial, representing almost forty percent of PowerLinx’s total assets  of $3,841,944. 
PowerLinx also recorded deferred tax assets of $180,613, $72,907, and $44,921, 
respectively, in its financial statements for the first three quarters of 2000.
PowerLinx did not have a proper basis for recording the deferred tax assets. 
The company had accumulated significant losses in 2000 and had no historical 
operating basis from which to conclude that it would be profitable in future years.

Underwater camera sales had declined significantly and the company had devoted 
most of its resources to developing its SecureView product. The sole basis for 
PowerLinx’s “expectation” of future profitability was the purported $9 million 
backlog of SecureView orders, which management assumed would generate 
taxable income; however, this purported backlog, which predated Bauer’s hiring, 
did not reflect actual demand for SecureView cameras and, consequently, was 
not a reasonable or reliable indicator of future profitability. 
Another example of how choices and estimates can affect balance sheets is in the 
area of selecting a depreciation method for allocating the cost of long-  lived assets to 
accounting periods subsequent to their acquisition. A company’s managers may choose 
to depreciate long-  lived assets (1) on a straight-  line basis, with each year bearing the 
same amount of depreciation expense; (2) using an accelerated method, with greater

depreciation expense recognition in the earlier part of an asset’s life; or (3) using an 
activity-  based depreciation method, which allocates depreciation expense based on 
units of use or production. Depreciation expense is affected by another set of choices 
and estimates regarding the salvage value of the assets being depreciated. A salvage 
value of zero will always increase depreciation expense under any method compared 
with the choice of a non-  zero salvage value.
Assume a company invests $1,000,000 in manufacturing equipment and expects it 
to have a useful economic life of 10 years. During its expected life, the equipment will 
produce 400,000 units of product, or $2.50 depreciation expense per unit produced. 
24 Accounting and Auditing Enforcement Release No. 2448, “In the Matter of Douglas R. Bauer, Respondent, ” 
SEC (27 June 2006): www.sec.gov/litigation/admin/2006/34-  54049.pdf.

Reading 31 ■ Financial Reporting Quality 644
When it is disposed of at the end of its expected life, the company’s managers expect to 
realize no value for the equipment. The following table shows the differences in three 
alternative methods of depreciation: straight-  line, accelerated on a double-  declining 
balance basis, and units-  of- production method, with no salvage value assumed at the 
end of the equipment’s life.
Straight-  Line 
Method Double-  Declining Balance Method Units-  of- Production Method
Expense BalanceDeclining 
Balance 
Rate1Depreciation 
ExpenseUnits 
ProducedDepreciation 
Rate/UnitDepreciation 
Expense
1 $100,000 $1,000,000 20% $200,000 90,000 $2.50 $225,000
2 100,000 800,000 20% 160,000 80,000 $2.50 200,000
3 100,000 640,000 20% 128,000 70,000 $2.50 175,000
4 100,000 512,000 20% 102,400 60,000 $2.50 150,000
5 100,000 409,600 20% 81,920 50,000 $2.50 125,000
6 100,000 327,680 20% 65,536 10,000 $2.50 25,000
7 100,000 262,144 20% 52,429 10,000 $2.50 25,000

8 100,000 209,715 20% 41,943 10,000 $2.50 25,000
9 100,000 167,772 20% 33,554 10,000 $2.50 25,000
10 100,000 134,218 20% 26,844 10,000 $2.50 25,000
Total $1,000,000 $892,626 400,000 $1,000,000
1 Declining balance rate of 20% calculated as 10-  year life being equivalent to 10% annual depreciation rate, multiplied by 2 = 20%.
The straight-  line method allocates the cost of the equipment evenly to all 10 
years of the equipment’s life. The double-  declining balance method will have a higher 
allocation of cost to the earlier years of the equipment’s life, and as its name implies, 
the depreciation expense will decline in each succeeding year because it is based on 
a fixed rate applied to a declining balance. The rate used was double the straight-  line 
rate, but it could have been any other rate that the company’s managers believed was 
representative of the way the actual equipment depreciation occurred. Notice that

the double-  declining balance method also results in an incomplete depreciation of 
the machine at the end of 10 years; a balance of $107,374 (= $1,000,000 − $892,626) 
remains at the end of the expected life, which will result in a loss upon the retirement 
of the equipment if the company’s expectation of zero salvage value turns out to be 
correct. Some companies may choose to depreciate the equipment to its expected 
salvage, zero in this case, in its final year of use. Some companies may use a policy 
of switching to straight-  line depreciation after the mid-  life of its depreciable assets 
in order to fully depreciate them. That particular pattern is coincidentally displayed 
in the units-  of- production example, in which the equipment is used most heavily in 
the earliest part of its useful life, and then levels off to much less utilization in the 
second half of the expected life.
Exhibit 15 shows the different expense allocation patterns of the methods over

Detection of Financial Reporting Quality Issues 645
Exhibit 15   Expense Allocation Patterns of Different Depreciation Methods
US Dollars
250,000
200,000
150,000
100,000
50,000
0
3 1 2 4 6 7 9 10 5 8
YearUnits of Production
Double-Declining BalanceStraight Line
The company’s managers could justify any one of these methods. Each might fairly 
represent the way the equipment will be consumed over its expected economic life, 
which is a subjective estimate itself. The choices of methods and lives can profoundly 
affect reported income. These choices are not proven right or wrong until far into the 
future—but managers must estimate their effects in the present.
Exhibit 16 shows the effects of the three different methods on operating profit 
and operating profit margins, assuming that the production output of the equipment 
generates revenues of $500,000 each year and $200,000 of cash operating expenses 
are incurred, leaving $300,000 of operating profit before depreciation expense.

Exhibit 16   Effects of Depreciation Methods on Operating Profit
Straight Line
Y ear Depreciation Operating Profit Operating Profit Margin
1 $100,000 $200,000 40.0%
2 100,000 200,000 40.0%
3 100,000 200,000 40.0%
4 100,000 200,000 40.0%
5 100,000 200,000 40.0%
6 100,000 200,000 40.0%
7 100,000 200,000 40.0%
8 100,000 200,000 40.0%
9 100,000 200,000 40.0%
10 100,000 200,000 40.0%
Double Declining Balance
1 $200,000 $100,000 20.0%
2 160,000 140,000 28.0%
3 128,000 172,000 34.4%
4 102,400 197,600 39.5%
5 81,920 218,080 43.6%

Reading 31 ■ Financial Reporting Quality 646
6 65,536 234,464 46.9%
7 52,429 247,571 49.5%
8 41,943 258,057 51.6%
9 33,554 266,446 53.3%
10 134,218* 165,782 33.2%
Units of Production
1 $225,000 $75,000 15.0%
2 200,000 100,000 20.0%
3 175,000 125,000 25.0%
4 150,000 150,000 30.0%
5 125,000 175,000 35.0%
6 25,000 275,000 55.0%
7 25,000 275,000 55.0%
8 25,000 275,000 55.0%
9 25,000 275,000 55.0%
10 25,000 275,000 55.0%
* Includes $107,374 of undepreciated basis, treated as depreciation expense in final year of service.
The straight-  line method shows consistent operating profit margins, and the 
other two methods show varying degrees of increasing operating profit margins as 
the depreciation expense decreases over time.
The example above shows the differences among several alternative methods, but

even more depreciation expense variation is possible by changing estimated lives and 
assumptions about salvage value. For instance, change the expected life assumption 
to 5 years from 10 and add an expectation that the equipment will have a 10% salvage 
value at the end of its expected life. Exhibit 17 shows the revised depreciation calcu -
lations. Notice that under the double-  declining balance method, the depreciation rate 
is applied to the gross cost, unlike the other two methods. The straight-  line method 
and the units-  of- production method subtract the salvage value from the cost before 
depreciation expense is calculated. Also note that the assumption about the usage of 
the equipment is revised so that it is depreciated only to its salvage value of $100,000 
by the end of its estimated life. The total depreciation under each method is $900,000.Exhibit 16   (Continued)

Detection of Financial Reporting Quality Issues 647
Exhibit 17   Depreciation Calculations for Each Method in Changed Scenario
Balance 
Expense
1 $180,000 $1,000,000 40% $400,000 100,000 $2.25 $225,000
2 180,000 600,000 40% 240,000 90,000 $2.25 202,500
3 180,000 360,000 40% 144,000 80,000 $2.25 180,000
4 180,000 216,000 40% 86,400 70,000 $2.25 157,500
5 180,000 129,600 40% 29,600260,000 $2.25 135,000
Total $900,000 $900,000 400,000 $900,000
1 Declining balance rate of 40% calculated as 5-  year life being equivalent to 20% annual depreciation rate, multiplied by 2 = 40%.
2 Depreciation calculated as $29,600 instead of 40% × $129,600. Rote application of the declining-  balance rate would have resulted in $51,840 
of expense, which would have depreciated the asset below salvage value.

Exhibit 18 shows the different expense allocation patterns of the methods over the 
five-  year expected life, and assuming a 10% salvage value. Although each method is 
distinctly different in the timing of the cost allocation over time, the variation is less 
pronounced than over the longer life used in the previous example.
Exhibit 18   Expense Allocation Patterns of Depreciation Methods in 
Changed Scenario
US Dollars
200,000
150,000
100,000
50,000400,000450,000
350,000
300,000
250,000
0
3 1 2 4 5
YearUnits of ProductionDouble-Declining Balance
Perhaps one of the clearest examples of how choices affect both the balance 
sheet and income statement can be found in the area of capitalization practices. In 
classifying a payment made, management must determine whether the payment will 
benefit only the current period—making it an expense—or whether it will benefit 
future periods, leading to classification as a cost to be capitalized as an asset. This

management judgment embodies an implicit forecast of how the item acquired by 
the payment will be used, or not used, in the future.

Reading 31 ■ Financial Reporting Quality 648
That judgment can be biased by the powerful effect a capitalization policy can have 
on current earnings. Every amount capitalized on the balance sheet as a building, an 
item of inventory, a deferred cost, or any “other asset” is an amount that does not get 
recognized as an expense in the current period.
A real-  life example can be found in the case of WorldCom, Inc., a telecom concern 
that grew rapidly in the late 1990s. Much of WorldCom’s financial reporting was even -
tually found to be fraudulent, and one important part of the misreporting centered 
on its treatment of what is known in the telecom industry as “line costs. ” These are 
the costs of carrying a voice call or data transmission from its starting point to its 
ending point, and they represented WorldCom’s largest expense. WorldCom’s chief 
financial officer decided to capitalize such costs instead of treating them as an oper -

ating expense. As a consequence, from the second quarter of 1999 through the first 
quarter of 2002, WorldCom increased its operating income by $7 billion. In three of 
the five quarters in which the improper line cost capitalization took place, WorldCom 
would have recognized pretax losses instead of profits.25
Similarly, acquisitions are an area in which the managers charged with recording 
an acquisition must exercise judgment. An allocation of purchase price must be 
made to all of the different assets acquired based on their fair values, and those fair 
values are not always objectively verifiable. Management may have to make its own 
estimate of fair values for assets acquired, and management may be biased towards 
a low estimate for the values of depreciable assets in order to depress future depre -
ciation expense. Another benefit to keeping depreciable asset values low is that the 
amount of the purchase price that cannot be allocated to specific assets is classified

as goodwill, which is neither depreciated nor amortized in future reporting periods.
Goodwill reporting has choices of its own. Although goodwill has no effect on 
future earnings when unimpaired, annual testing of its fair value may reveal that the 
excess of price paid over the fair value of assets may not be recoverable, which should 
lead to a write-  down of goodwill. The estimation process for the fair value of goodwill 
may depend heavily on projections of future performance. Those projections may be 
biased upward in order to avoid a goodwill write-  down.
4.2.2  How Choices Affect the Cash Flow Statement
The cash flow statement consists of three sections: the operating section, which shows 
the cash generated or used by operations; the investing section, which shows the cash 
used for investments or provided by their disposal; and the financing section, which 
shows the cash transactions attributable to financing activities.

The operating section of the cash flow statement is often the portion most scruti -
nized by investors. Many of them consider the operating section to be a reality check 
on the reported earnings, on the grounds that significant earnings that are attribut -
able only to accrual accounting methods and unsupported by actual cash flows may 
indicate earnings manipulation. Such investors believe that amounts shown for cash 
generated by operations is more insulated from managerial manipulation than the 
income statement. Cash generated by operations can be managed to an extent, however.
The operating section of the cash flow statement can be shown either under the 
direct method or the indirect method. Under the direct method, “entities are encour -
aged to report major classes of gross cash receipts and gross cash payments and their 
arithmetic sum—the net cash flow from operating activities. ”26 In practice, companies

rarely use the direct method. Instead, they use the indirect method, which shows 
25 See Report of Investigation by the Special Investigative Committee of the Board of Directors of 
WorldCom, Inc., by Dennis R. Beresford, Nicholas deB. Katzenbach, & C.B. Rogers, Jr.PP 9-  11: www.sec.
gov/Archives/edgar/data/723527/000093176303001862/dex991.htm.
26 Accounting Standards Codification Section 230-  10- 45- 25, “Reporting Operating, Investing, and Financing 
Activities. ” The direct method and indirect method are similar in IFRS, as addressed in IAS 7, Paragraph 18.

Detection of Financial Reporting Quality Issues 649
a reconciliation of net income to cash provided by operations. The reconciliation 
shows the non-  cash items affecting net income along with changes in working capital 
accounts affecting cash provided by operations. Exhibit 19 provides an example of 
the indirect presentation method.
Exhibit 19   Indirect Presentation Method
Cash Flows from Operating Activities ($ millions) 2012
Net income $3,000
Adjustments to reconcile net income to net cash provided by operating 
activities:
Provision for doubtful receivables 10
Provision for depreciation and amortization 1,000
Goodwill impairment charges 35
Share-  based compensation expense 100
Provision for deferred income taxes 200
Changes in assets and liabilities:
Trade, notes and financing receivables related to sales (2,000)
Inventories (1,500)
Accounts payable 1,200
Accrued income taxes payable/receivable (80)
Retirement benefits 90
Other (250)
  Net cash provided by operating activities $1,805

Net cash provided by operating activities $1,805
Whether the indirect method or direct method is used, simple choices exist for 
managers to improve the appearance  of cash flow provided by operations without 
actually improving it. One such choice is in the area of accounts payable management, 
shaded in Exhibit 19. Assume that the accounts payable balance is $5,200 million at 
the end of the period, an increase of $1,200 million from its previous year-  end balance 
of $4,000 million. The $1,200 million increase in accounts payable matched increased 
expenses and/or assets but did not require cash. If the company’s managers had fur -
ther delayed paying creditors $500 million until the day after  the balance sheet date, 
they could have increased the cash provided by operating activities by $500 million. 
If the managers believe that the cash generated from operations is a metric of focus 
for investors, the managers could impress them with an artificially stronger cash flow

by simply stretching the accounts payable credit period.
What might alert investors to such machinations? They need to examine the 
composition of the operations section of the cash flow statement—if they do not, 
then nothing  will ever alert them. Studying changes in the working capital can reveal 
unusual patterns that may indicate manipulation of the cash provided by operations.
Another practice that might lead an investor to question the quality of cash provided 
by operations is to compare a company’s cash generation with an industry-  wide level 
or with the cash operating performance of one or more similar competitors. Cash 
generation performance can be measured several ways. One way is to compare the 
relationship between cash generated by operations and net income. Cash generated 
by operations in excess of net income signifies better quality of earnings, whereas a 
chronic excess of net income over cash generated by operations should be a cause for

concern; it may signal the use of accounting methods to simply raise net income instead

Reading 31 ■ Financial Reporting Quality 650
of depicting financial reality. Another way to measure cash generation performance is 
to compare cash generated by operations with debt service, capital expenditures, and 
dividends (if any). When there is a wide variance between the company’s cash gener -
ation performance and that of its benchmarks, investors should seek an explanation 
and carefully examine the changes in working capital accounts.
Because investors may focus on cash provided by operations as an important met -
ric, managers may resort to managing the working capital accounts as described in 
order to present the most favorable picture of cash provided by operations. But there 
are other means to improve the cash generation picture. A company may misclassify 
operating uses of cash into either the investing or financing sections of the cash flow 
statement, which enhances the appearance of cash generated by operating activities.

Dynegy Inc. provides an example of manipulation of cash from operations through 
clever construction of contracts and assistance from an unconsolidated special pur -
pose entity named ABG Gas Supply LLC (ABG). In April 2001, Dynegy entered into a 
contract for the purchase of natural gas from ABG. According to the contract, Dynegy 
would purchase gas at below-  market  rates from ABG for nine months and sell it at the 
current market rate. The nine-  month term coincided with Dynegy’s 2001 year end and 
would result in gains backed by cash flows. Dynegy also agreed to buy gas at above-  
market  rates from ABG for the following 51 months and sell it at the current market 
rate. The contract was reported at its fair value at the end of fiscal year 2001. It had 
no effect on net income for the year. The earlier portion of the contract resulted in 
a gain, supported by $300 million of cash flow, but the latter portion of the contract

resulted in non-  cash losses that offset the profit. The mark-  to- market rules required 
the recognition of both gains and losses from all parts of the contract, and hence the 
net effect on earnings was zero.
In April 2002, a Wall Street Journal  article exposed the chicanery, thanks to leaked 
documents. The SEC required Dynegy to restate the cash flow statement by reclassifying 
$300 million from the operating section of the cash flow statement to the financing 
section, on the grounds that Dynegy had used ABG as a conduit to effectively borrow 
$300 million from Citigroup. The bank had extended credit to ABG, which it used to 
finance its losses on the contract (Lee, 2012).
Another area of flexibility in cash flow statement reporting is found in the area of 
interest capitalization, which creates differences between total interest payments and 
total interest costs.27 Assume a company incurs total interest cost of $30,000, composed

of $3,000 of discount amortization and $27,000 of interest payments. Of the $30,000, 
two-  thirds of it ($20,000) is expensed; the remaining third ($10,000) is capitalized as 
plant assets. If the company uses the same interest expense/capitalization proportions 
to allocate the interest payments between operating and investing activities, then it 
will report $18,000 (2/3 × $27,000) as an operating outflow and $9,000 (1/3 × $27,000) 
as an investing outflow. The company might also choose to offset the entire $3,000 of 
non-  cash discount amortization against the $20,000 treated as expense, resulting in 
an operating outflow as low as $17,000, or as much as $20,000 if it allocated all of the 
non-  cash discount amortization to interest capitalized as investing activities. Similarly, 
the investing outflow could be as much as $10,000 or as little as $7,000, depending 
on the treatment of the non-  cash discount amortization. There are choices within

the choices, all in areas where investors believe choices do not even exist. Nurnberg 
and Largay (1998) note that companies apparently favor the method that reports the 
lowest operating outflow, presumably to maximize reported cash from operations.
27 See Nurnberg and Largay (1998) and Nurnberg (2006).

Detection of Financial Reporting Quality Issues 651
Investors and analysts need to be aware that presentation choices permitted in 
IAS 7, “Statement of Cash Flows, ” offer flexibility in classification of certain items 
in the cash flow statement. This flexibility can drastically change the results in the 
operating section of the cash flow statement. An excerpt from IAS 7, Paragraphs 33 
and 34, provides the background:
33. Interest paid and interest and dividends received are usually classified as 
operating cash flows for a financial institution. However, there is no consen -
sus on the classification of these cash flows for other entities. Interest paid 
and interest and dividends received may be classified as operating cash flows 
because they enter into the determination of profit or loss. Alternatively, 
interest paid and interest and dividends received may be classified as financ -
ing cash flows and investing cash flows respectively, because they are costs

of obtaining financial resources or returns on investments.
34. Dividends paid may be classified as a financing cash flow because 
they are a cost of obtaining financial resources. Alternatively, dividends paid 
may be classified as a component of cash flows from operating activities in 
order to assist users to determine the ability of an entity to pay dividends 
out of operating cash flows.  [Emphasis added.]
By allowing a choice of operating or financing for the placement of interest and 
dividends received or paid, IAS 7 gives a company’s managers the opportunities to 
select the presentation that gives the best-  looking picture of operating performance. 
An example is Norse Energy Corp. ASA, a Norwegian gas explorer and producer, 
which changed its classifications of interest paid and interest received in 2007 (Gordon, 
Henry, Jorgensen, and Linthicum, 2017). Interest paid was switched to financing 
instead of decreasing cash generated from operations. Norse Energy also switched its

classification of interest received to investing from operating cash flow. The net effect 
of these changes was to report positive, rather than negative, operating cash flows 
in both 2007 and 2008. With these simple changes, the company could also change 
the perception of its operations. The cash flow statement formerly presented the 
appearance of a company with operations that used more cash than it generated, and it 
possibly raised questions about the sustainability of operations. After the revision, the 
operating section of the cash flow statement depicted a much more viable operation.
Exhibit 20 shows the net effect of the reclassifications on Norse Energy’s cash flows.
Exhibit 20   Reclassification of Cash Flows
As Reported  
(following 2007 
reclassification)Adjustments, If No 
Reclassification*Pro-  forma  
(if no 
reclassification)
2008 2007 2008 2007 2008 2007
Operating $5.30 $2.80 ($13.70) ($14.40) ($8.40) ($11.60)
Investing $0.90 ($56.80) ($9.00) ($3.50) ($8.10) ($60.30)

Financing ($16.60) $34.50 $22.70 $17.90 $6.10 $52.40
Total ($10.40) ($19.50) $0 $0 ($10.40) ($19.50)
* The adjustments reverse the addition of interest received to investing and instead add it to 
operating. The adjustments also reverse the deduction of interest paid from financing and instead 
subtract it from operating.

Reading 31 ■ Financial Reporting Quality 652
4.2.3  Choices That Affect Financial Reporting
Exhibit  21 summarizes some of the areas where choices can be made that affect 
Exhibit 21   Areas Where Choices and Estimates Affect Financial Reporting
Area of Choice/
Estimate Analyst Concerns
Revenue recognition ■■How is revenue recognized: upon shipment or upon delivery 
of goods?
■■Is the company engaging in “channel stuffing”—the practice 
of overloading a distribution channel with more product 
than it is normally capable of selling? This can be accom -
plished by inducing customers to buy more through unusual 
discounts, the threat of near-  term price increases, or both—
or simply by shipping goods that were not ordered. These 
transactions may be corrected in a subsequent period and 
may even result in restated results. Are accounts receivable 
relative to revenues abnormally high for a company relative 
to its history or its peers? If so, channel stuffing may have 
occurred.

occurred.
■■Is there unusual activity in the allowance for sales returns 
relative to past history?
■■Does the company’s days sales outstanding indicate any 
collection issues that might indicate shipment of unneeded 
or unwanted goods to customers?
■■Does the company engage in “bill-  and-  hold” transactions? 
In such transactions, a customer purchases goods but 
requests that the goods remain with the seller until a later 
date. This kind of transaction makes it possible for a seller 
to manufacture fictitious sales by declaring end-  of- period 
inventory as “sold but held, ” with a minimum of effort and 
phony documentation.
■■Does the company use rebates as part of its marketing 
approach? If so, how significantly do the estimates of rebate 
fulfillment affect net revenues, and have any unusual breaks 
with history occurred?

Detection of Financial Reporting Quality Issues 653
■■Does the company separate its revenue arrangements into 
multiple deliverables of goods or services? This area is one 
of great revenue recognition flexibility, and also one that 
provides little visibility to investors. They simply cannot 
examine a company’s arrangements and decide for them -
selves as to the propriety of revenue allocation to different 
components of a contract. If a company uses multiple deliv -
erable arrangements with its customers as a routine matter, 
investors might be more sensitive to revenue reporting risks. 
In seeking a comfort level, investors might ask the follow -
ing questions: Does the company explain adequately how it 
determines the different allocations of deliverables and how 
revenue is recognized on each one? Do deferred revenues 
result? If not, does it seem reasonable that there are no 
deferred revenues for this kind of arrangement? Are there

unusual trends in revenues and receivables, particularly with 
regard to cash conversion? If an investor cannot be satisfied 
with the answers from these questions, he or she might be 
more comfortable with other investment choices.
Long-  lived assets: 
policies■■Do the estimated life spans of the associated assets make 
sense, or are they unusually low compared with others in 
the same industry?
■■Have there been changes in depreciable lives that have a 
positive effect on current earnings?
■■Do recent asset write-  downs indicate that company policy 
on asset lives might need to be reconsidered?
Intangibles: 
Capitalization 
policies■■Does the company capitalize expenditures related to 
intangibles, such as software? Does its balance sheet show 
any R&D capitalized as a result of acquisitions? Or, if the 
company is an IFRS filer, has it capitalized any internally 
generated development costs?
■■How do the company’s capitalization policies compare with 
the competition?

■■Are amortization policies reasonable?
Allowance for 
doubtful accounts/
loan loss reserves■■Are additions to such allowances lower or higher than in the 
past?
■■Does the collection experience justify any difference from 
historical provisioning?
■■Is there a possibility that any lowering of the allowance may 
be the result of industry difficulties along with the difficulty 
of meeting earnings expectations?
(continued)Exhibit 21   (Continued)

Reading 31 ■ Financial Reporting Quality 654
Inventory cost 
methods■■Does the company use a costing method that produces fair 
reporting results in view of its environment? How do its 
inventory methods compare with others in its industry? Are 
there differences that will make comparisons uneven if there 
are unusual changes in inflation?
■■Does the company use reserves for obsolescence in its 
inventory valuation? If so, are they subject to unusual 
fluctuations that might indicate adjusting them to arrive at a 
specified earnings result?
■■If a company reports under US GAAP and uses last-  in- first-  
out (LIFO) inventory accounting, does LIFO liquidation (the 
assumed sale of old, lower-  cost layers of inventory) occur 
through inventory reduction programs? This inventory 
reduction may generate earnings without supporting cash 
flow, and management may intentionally reduce the layers 
to produce specific earnings benefits.
Tax asset valuation

Tax asset valuation 
accounts■■Tax assets, if present, must be stated at the value at which 
management expects to realize them, and an allowance 
must be set up to restate tax assets to the level expected 
to eventually be converted into cash. Determining the 
allowance involves an estimate of future operations and tax 
payments. Does the amount of the valuation allowance seem 
reasonable, overly optimistic, or overly pessimistic?
■■Are there contradictions between the management com -
mentary and the allowance level, or the tax note and the 
allowance level? There cannot be an optimistic management 
commentary and a fully reserved tax asset, or vice versa. 
One of them has to be wrong.
■■Look for changes in the tax asset valuation account. It may 
be 100% reserved at first, and then “optimism” increases 
whenever an earnings boost is needed. Lowering the reserve 
decreases tax expense and increases net income.
Goodwill ■■Companies must annually assess goodwill balances for

impairment on a qualitative basis. If further testing appears 
necessary, it is based on estimates of the fair value of 
reporting units (US GAAP issuers) or cash-  generating units 
(IFRS issuers), which are associated with goodwill balances. 
The tests are based on subjective estimates, including future 
cash flows and the employment of discount rates.
■■Do the disclosures relating to the goodwill testing suggest 
that the testing was skewed to avoid goodwill impairment 
charges?Exhibit 21   (Continued)

Detection of Financial Reporting Quality Issues 655
Warranty reserves ■■Have additions to the reserves been reduced, perhaps to 
make earnings targets? Examine the trend in the charges of 
actual costs against the reserves: Do they support or contra -
dict the warranty provisioning activity? Do the actual costs 
charged against the reserve give the analyst any indication 
about the quality of the products sold?
Related-  party 
transactions■■Is the company engaged in transactions that disproportion -
ately benefit members of management? Does one company 
have control over another’s destiny through supply contracts 
or other dealings?
■■Do extensive dealings take place with non-  public  companies 
that are under management control? If so, non-  public com -
panies could absorb losses (through supply arrangements 
that are unfavorable to the private company, for example) in 
order to make the public company’s performance look good.

This scenario may provide opportunities for an owner to 
cash out.
The most important lesson is that choices exist among accounting methods and 
estimates, and an analyst needs a working knowledge of them in order to understand 
whether management may have made choices to achieve a desired result.
4.3 Warning Signs
The choices management makes to achieve desired results leave a trail, like tracks in 
sand or snow. The evidence or warning signs of information manipulation in finan -
cial reports are directly linked to the basic means of manipulation: biased revenue 
recognition and biased expense recognition. The bias may relate to timing and/or 
location of recognition. For example, a company may choose to defer expenses by 
capitalizing them, which relates to when an expense is recognized. In another example, 
a company may choose to recognize a loss in other comprehensive income or directly 
through equity rather than through the profit and loss statement, which relates to

where the loss is recognized. The alert investor or analyst should do the following to 
find warning signs.
1) Pay attention to revenue .  The single largest number on the income statement 
is revenue, and revenue recognition is a recurring source of accounting manipulation 
and even outright fraud. Answering the question, “Is revenue higher or lower than 
the previous comparable period?” is not sufficient. Many analytical procedures can be 
routinely performed to provide warning signals of accounting malfeasance:
■■Examine the accounting policies note for a company’s revenue recognition 
policies.
■●Consider whether the policies make it easier to prematurely recognize reve -
nue, such as recognizing revenue immediately upon shipment of goods, or if 
the company uses bill-  and-  hold arrangements whereby a sale is recognized 
before goods are actually shipped to the customer.
■●Barter transactions may exist, which can be difficult to value properly.Exhibit 21   (Continued)

Reading 31 ■ Financial Reporting Quality 656
■●Rebate programs involve many estimates, including forecasts of the amount 
of rebates that will ultimately be incurred. These estimates can have signifi -
cant effects on revenue recognition.
■●Multiple-  deliverable arrangements of goods and services are common, but 
clarity about the timing of revenue recognition for each item or service 
delivered is necessary for the investor to be comfortable with the reporting 
of revenues.
Although none of these decisions violates accounting standards, each can raise 
investor suspicions if other warning signs are present.
■■Look at revenue relationships.  Compare a company’s revenue growth with its 
primary competitors or its industry peer group.
■●If a company’s revenue growth is out of line with its competitors, its indus -
try, or the economy, the investor or analyst needs to understand the reasons 
for the outperformance. It may be a result of superior management or prod -

ucts and services, but not all management is superior, nor are the products 
and services of their companies. Revenue quality might be suspect, and the 
investor should take additional analytical steps.
■●Compare accounts receivable with revenues over several years.
 ■Examine the trend to determine whether receivables are increasing 
as a percentage of total revenues. If so, a company might be engag -
ing in channel-  stuffing activities, or worse, recording fictitious sales 
transactions.
 ■Calculate receivables turnover for several years:
 ●Examine the trend for unusual changes and seek an explanation if 
they exist.
 ●Compare a company’s days sales outstanding (DSO) or receivables 
turnover with that of relevant competitors or an industry peer group 
and determine whether the company is an outlier.
An increase in DSO or decrease in receivables turnover could suggest that 
some revenues are recorded prematurely or are even fictitious, or that the 
allowance for doubtful accounts is insufficient.

■●Examine asset turnover. If a company’s managers make poor asset alloca -
tion choices, revenues may not be sufficient to justify the investment. Be 
particularly alert when asset allocation choices involve acquisitions of entire 
companies. If post-  acquisition revenue generation is weak, managers might 
reach for revenue growth anywhere it can be found. That urge for growth 
might result in accounting abuses.
Revenues, divided by total assets, indicate the productivity of assets in gen -
erating revenues. If the company’s asset turnover is continually declining, or 
lagging the asset turnover of competitors or industry, it may portend future 
asset write-  downs, particularly in the area of goodwill balances for acquisi -
tive companies.
2) Pay attention to signals from inventories.  Although inventory is not a compo -
nent of every company’s asset base, its presence creates an opportunity for accounting 
manipulation.

■■Look at inventory relationships.  Because revenues involve items sold from 
inventory, the kind of examination an investor should perform on inventory is 
similar to that for revenues.

Detection of Financial Reporting Quality Issues 657
■●Compare growth in inventories with competitors and industry benchmarks. 
If a company’s inventory growth is out of line with its peers, without any 
concurrent sales growth, then it may be simply the result of poor inventory 
management—an operational inefficiency that might affect an investor’s 
view of a company. It may also signal obsolescence problems in the com -
pany’s inventory that have not yet been recognized through markdowns to 
the inventory’s net realizable value. Current gross and net profits could be 
overstated because of overstated inventory.
■●Calculate the inventory turnover ratio. This ratio is the cost of sales divided 
by the average ending inventory. Declining inventory turnover could also 
suggest obsolescence problems that should be recognized.
■●Companies reporting under US GAAP may use LIFO inventory cost flow 
assumptions. When this assumption is part of the accounting policies, and

a company operates in an inflationary environment, investors should note 
whether old, low-  cost inventory costs have been passed through current 
earnings and artificially improved gross, operating, and net profits.
3) Pay attention to capitalization policies and deferred costs.  In a study of enforce -
ment actions over a five-  year period, the SEC found that improper revenue recognition 
was the most prevalent accounting issue.28 Suppression of expenses was the next most 
prevalent problem noted. As the earlier discussion of WorldCom showed, improper 
capitalization practices can result in a significant misstatement of financial results.
■■Examine the company’s accounting policy note for its capitalization policy for 
long-  term assets, including interest costs, and for its handling of other deferred 
costs.  Compare the company’s policy with the industry practice. If the com -
pany is the only one capitalizing certain costs while other industry participants

treat them as expenses, a red flag is raised. If an outlier company of this type is 
encountered, it would be useful to cross-  check such a company’s asset turnover 
and profitability margins with others in its industry. An investor might expect 
such a company to be more profitable than its competitors, but the investor 
might also have lower confidence in the quality of the reported numbers.
4) Pay attention to the relationship of cash flow and net income.  Net income pro -
pels stock prices, but cash flow pays bills. Management can manipulate either one, but 
sooner or later, net income must be realized in cash if a company is to remain viable. 
When net income is higher than cash provided by operations, one possibility is that 
aggressive accrual accounting policies have shifted current expenses to later periods. 
Increasing earnings in the presence of declining cash generated by operations might 
signal accounting irregularities.

■■Construct a time series of cash generated by operations divided by net income.  
If the ratio is consistently below 1.0 or has declined repeatedly, there may be 
problems in the company’s accrual accounts.
5) Other potential warnings signs.  Other areas that might suggest further analysis 
■■Depreciation methods and useful lives.  As discussed earlier, depreciation meth -
ods and the useful lives selected can greatly influence profitability. An inves -
tor should compare a company’s policies with those of its peers to determine 
28 SEC, “Report Pursuant to Section 704 of the Sarbanes–Oxley Act of 2002” (www.sec.gov/news/studies/
sox704report.pdf): 5–6.

Reading 31 ■ Financial Reporting Quality 658
whether it is particularly lenient in its effects on earnings. Investors should 
likewise compare the length of depreciable lives used by a company with those 
used by its peers.
■■Fourth-  quarter surprises.  An investor should be suspicious of possible earnings 
management if a company routinely disappoints investors with poor earnings or 
overachieves in the fourth quarter of the year when no seasonality exists in the 
business. The company may be over- or under-  reporting profits in the first three 
quarters of the year.
■■Presence of related-  party transactions.  Related-  party transactions often arise 
when a company’s founders are still very active in managing the company, with 
much of their wealth tied to the company’s fortunes. They may be more biased 
in their view of a company’s performance because it relates directly to their 
own wealth and reputations, and they may be able to transact business with the

company in ways that may not be detected. For instance, they may purchase 
unsellable inventory from the company for disposal in another company of their 
own in order to avoid markdowns.
■■Non-  operating income or one-  time sales included in revenue.  To disguise weak -
ening revenue growth, or just to enhance revenue growth, a company might 
classify non-  operating income items into revenues or fail to clarify the nature of 
revenues. In the first quarter of 1997, Sunbeam Corporation included one-  time 
disposal of product lines in sales without indicating that such non-  recurring 
sales were included in revenues. This inclusion gave investors a false impression 
of the company’s sustainable revenue-  generating capability.
■■Classification of expenses as “non-  recurring. ”  To make operating performance 
look more attractive, managers might carve out “special items” in the income 
statement. Particularly when such special items appear period after period,

equity investors might find their interests best served by not giving serial 
“special items” such treatment and instead focusing on the net income line in 
evaluating performance over long periods.
■■Gross/operating margins out of line with competitors or industry.  This disparity 
is an ambivalent warning sign. It might signal superior management ability. But 
it might also signal the presence of accounting manipulations to add a veneer of 
superior management ability to the company’s reputation. Only the compilation 
and examination of other warning signals will enable an investor or analyst to 
decide which signal is being given.
Warning signals are just that: signals, not indisputable declarations of account -
ing manipulation guilt. Investors and analysts need to evaluate them cohesively, not 
on an isolated basis. When an investor finds a number of these signals, the subject 
investment should be viewed with caution or even discarded in favor of alternatives.

Furthermore, as discussed earlier, context is important in judging the value of warn -
ing signals. A few examples of facts and circumstances to be aware of are as follows.
■■Younger companies with an unblemished record of meeting growth projections.  
It is plausible, especially for a younger company with new and popular prod -
uct offerings, to generate above-  average returns for a period of time. But, as 
demand dissipates, products mature, and competitors challenge for market 
share, management may seek to extend its recent record of rapid growth in 
sales and profitability by unconventional means. At this point, the “earnings 
games” begin: aggressive estimates, drawing down “cookie jar” reserves, selling 
assets for accounting gains, taking on excess leverage, or entering into financial 
transactions with no apparent business purpose other than financial statement 
“window dressing. ”

Detection of Financial Reporting Quality Issues 659
■■Management has adopted a minimalist approach to disclosure.  Confidence in 
accounting quality depends on disclosure. For example, when large companies 
claim that they have only one reportable segment or that management’s com -
mentary is similar from period to period, there is cause for concern. If man -
agement does not seem to take seriously its obligation to provide information, 
one needs to be concerned. A plausible explanation for minimalist disclosure 
policies could be that management is protecting investors’ interests by with -
holding valuable information from competitors. But, this explanation is not 
necessarily the case. For example, after Sony Corporation acquired CBS Records 
and Columbia Pictures, it incurred substantial losses for a number of years. Yet, 
Sony chose to hide its negative trends and doubtful future prospects by aggre -
gating the results within a much larger “Entertainment Division. ” In 1998, after

Sony ultimately wrote off much of the goodwill associated with these ill-  fated 
acquisitions, the SEC sanctioned Sony and its CFO for failing to separately dis -
cuss them in MD&A in a balanced manner.29
■■Management fixation on earnings reports.  Beware of companies whose manage -
ment appears to be fixated on reported earnings, sometimes to the detriment 
of attending to real drivers of value. Indicators of excessive earnings fixation 
include the aggressive use of non-  GAAP measures of performance, special 
items, or non-  recurring charges. Another indicator of earnings fixation is highly 
decentralized operations in which division managers’ compensation packages 
are heavily weighted toward the attainment of reported earnings or non-  GAAP 
measures of performance.
A company’s culture is an intangible that investors should bear in mind when they 
are evaluating financial statements for the possibility of accounting manipulation.

A management’s highly competitive mentality may serve investors well when the 
company conducts business (assuming that actions taken are not unethical, illegal, or 
harmfully myopic), but that kind of thinking should not extend to communications 
with the owners of the company: the shareholders. That mentality can lead to the 
kind of accounting gamesmanship seen in the early part of the century. In examining 
financial statements for warning signs of manipulation, the investor should consider 
whether that mindset exists in the preparation of the financial statements.
One notable example of the mindset comes from one of the most recognized cor -
porate names in the world, General Electric. In the mid-  1980s, GE acquired Kidder 
Peabody, and it was ultimately determined that much of the earnings that Kidder had 
reported were bogus. As a consequence, GE would announce within two days that 
it would take a non-  cash write-  off of $350 million. Here is how former CEO/Chair

Jack Welsh described the ensuing meeting with senior management in his memoir, 
Straight from the Gut :
“The response of our business leaders to the crisis was typical of the GE 
culture  [emphasis added]. Even though the books had closed on the quarter, 
many immediately offered to pitch in to cover the Kidder gap. Some said 
they could find an extra $10 million, $20 million, and even $30 million from 
their businesses to offset the surprise. Though it was too late, their will -
ingness to help was a dramatic contrast to the excuses I had been hearing 
from the Kidder people. ” (p. 225)
It appears that the corporate governance apparatus fostered a GE culture that 
extended the concept of teamwork to the point of “sharing” profits to win one for 
the team as a whole, which is incompatible with the concept of neutral financial 
29 Accounting and Auditing Enforcement Release No. 1061, “In the Matter of Sony Corporation and 
Sumio Sano, Respondents, ” SEC (5 August 1998).

Reading 31 ■ Financial Reporting Quality 660
reporting. Although research is not conclusive on this question, it may also be worth 
considering that predisposition to earnings manipulation is more likely to be present 
when the CEO and board chair are one and the same, or when the audit committee of 
the board essentially serves at the pleasure of the CEO and lacks financial reporting 
sophistication. Finally, one could discuss whether the financial reporting environment 
today would reward or penalize a CEO who openly endorsed a view that he could 
legitimately exercise financial reporting discretion—albeit within limits—for the 
purpose of artificially smoothing earnings.
Restructuring and/or impairment charges.  At times, a company’s stock price has 
been observed to rise after it recognized a “big bath” charge to earnings of the current 
period. The conventional wisdom explaining the stock price rise is that accounting

recognition signals something positive: that management is now ready to part with 
the lagging portion of a company, so as to redirect its attention and talents to more-  
profitable activities. Consequently, the earnings charge should be disregarded for being 
solely related to past events.
The analyst should also consider, however, that the events leading ultimately to 
the big bath on the financial statements did not happen overnight, even though the 
accounting for those events occurs at a subsequent point. Management may want to 
communicate that the accounting adjustments reflect the company’s new path, but 
the restructuring charge also indicates that the old path of reported earnings was not 
real. In particular, expenses reported in prior years were very likely understated—even 
assuming that no improper financial statement manipulation had occurred. To extrap -
olate historical earnings trends, an analyst should consider making pro forma analytical

adjustments of prior years’ earnings to reflect in those prior years a reasonable share 
of the current period’s restructuring and impairment charges.
Management has a merger and acquisition orientation.  Tyco International Ltd. 
acquired more than 700 companies from 1996 to 2002. Even assuming the best of 
intentions regarding financial reporting, a growth-  at- any-  cost corporate culture poses 
a severe challenge to operational and financial reporting controls. In Tyco’s case, the 
SEC found that it consistently and fraudulently understated assets acquired (lower -
ing future depreciation and amortization charges) and overstated liabilities assumed 
(avoiding expense recognition and potentially increasing earnings in future periods).30
CONCLUSION
Financial reporting quality varies across companies. The ability to assess the quality of 
a company’s financial reporting is an important skill for analysts. Indications of low-

quality financial reporting can prompt an analyst to maintain heightened skepticism 
when reading a company’s reports, to review disclosures critically when undertaking 
financial statement analysis, and to incorporate appropriate adjustments in assessments 
of past performance and forecasts of future performance.
■■Financial reporting quality can be thought of as spanning a continuum from the 
highest (containing information that is relevant, correct, complete, and unbi -
ased) to the lowest (containing information that is not just biased or incomplete 
but possibly pure fabrication).5
30 Accounting and Auditing Enforcement Release No. 2414, “SEC Brings Settled Charges Against Tyco 
International Ltd. Alleging Billion Dollar Accounting Fraud, ” SEC (17 April 2006): www.sec.gov/litigation/
litreleases/2006/lr19657.htm.

Conclusion 661
■■Reporting quality , the focus of this reading, pertains to the information dis -
closed. High-  quality reporting represents the economic reality of the company’s 
activities during the reporting period and the company’s financial condition at 
the end of the period.
■■Results quality  (commonly referred to as earnings quality) pertains to the 
earnings and cash generated by the company’s actual economic activities and 
the resulting financial condition, relative to expectations of current and future 
financial performance.
■■An aspect of financial reporting quality is the degree to which accounting 
choices are conservative or aggressive. “ Aggressive” typically refers to choices 
that aim to enhance the company’s reported performance and financial posi -
tion by inflating the amount of revenues, earnings, and/or operating cash flow 
reported in the period; or by decreasing the amount of expenses reported in the 
period and/or the amount of debt reported on the balance sheet.

■■Conservatism in financial reports can result from either (1) accounting stan -
dards that specifically require a conservative treatment of a transaction or an 
event or (2) judgments necessarily made by managers when applying accounting 
standards that result in more- or less-  conservative results.
■■An example of conservatism in the oil and gas industry is the revenue recogni -
tion accounting standard. This standard permits recognition of revenue only at 
time of shipment rather than closer to the time of actual value creation, which 
is the time of discovery.
■■Managers may be motivated to issue less than high quality financial reports in 
order to mask poor performance, to boost the stock price, to increase personal 
compensation, and/or to avoid violation of debt covenants.
■■Conditions that are conducive to the issuance of low-  quality financial reports 
include cultural environment attributes that result in fewer or less transpar -

ent financial disclosures, book/tax conformity that shifts emphasis toward 
legal compliance and away from fair presentation, and limited capital markets 
regulation.
■■Mechanisms that discipline financial reporting quality include the free market 
and incentives for companies to minimize cost of capital, auditors, contract 
provisions specifically tailored to penalize misreporting, and enforcement by 
regulatory entities.
■■Pro forma earnings (also commonly referred to as non-  GAAP or non-  IFRS 
earnings) adjust earnings as reported on the income statement. Pro forma 
earnings that exclude negative items are a hallmark of aggressive presentation 
choices.
■■Companies are required to make additional disclosures when presenting any 
non-  GAAP or non-  IFRS metric.
■■Managers’ considerable flexibility in choosing their companies’ accounting 
policies and in formulating estimates provides opportunities for aggressive 
accounting.

■■Examples of accounting choices that affect earnings and balance sheets include 
inventory cost flow assumptions, estimates of uncollectible accounts receivable, 
estimated realizability of deferred tax assets, depreciation method, estimated 
salvage value of depreciable assets, and estimated useful life of depreciable 
assets.
■■Cash from operations is a metric of interest to investors that can be enhanced 
by operating choices, such as stretching accounts payable, and potentially by 
classification choices.

Reading 31 ■ Financial Reporting Quality 662
Back, Aaron. 2013. “Toyota, What a Difference the Yen Makes. ” 
Wall Street Journal  (4 August 2013).
Basu, Sudipta. 1997. “The Conservatism Principle and the 
Asymmetric Timeliness of Earnings. ” Journal of Accounting 
and Economics , vol. 24, no. 1 (December):3–37. 
Bliss, James Harris. 1924. Management through Accounts . New 
York: Ronald Press Company.
Ciesielski, Jack T, and Elaine Henry. 2017. “ Accounting’s Tower of 
Babel: Key Considerations in Assessing Non-  GAAP Earnings. ” 
Financial Analysts Journal , vol. 73, no. 2:34–50.
Dichev, Ilia, John Graham, Campbell Harvey, and Shivaram 
Rajgopal. 2013. “Earnings Quality: Evidence from the Field. ” 
Journal of Accounting and Economics , vol. 56, issues 2–3:1–33.
Ernst & Young. 2013. Navigating Today’s Complex Business Risks . 
Europe, Middle East, India and Africa Fraud Survey 2013 
(May): www.ey.com/Publication/vwLUAssets/Navigating_
todays_complex_business_risks/$FILE/Navigating_todays_

complex_business_risks.pdf.
Gordon, Elizabeth, Elaine Henry, Bjorn Jorgensen, and Cheryl 
Linthicum. 2017. “Flexibility in Cash-  Flow Classification 
under IFRS: Determinants and Consequences. ” Review of 
Accounting Studies , vol. 22, no. 2:839–872.
Graham, John, Campbell Harvey, and Shiva Rajgopal. 2005. 
“The Economic Implications of Corporate Financial 
Reporting. ” Journal of Accounting and Economics , vol. 40, no. 
1 (December):3–73. 
Gu, Feng, and Baruch Lev. 2017. “Time to Change Your 
Investment Model. ” Financial Analysts Journal , vol. 73, no. 
4:23–33.Lee, Lian Fen. 2012. “Incentives to Inflate Reported Cash from 
Operations Using Classification and Timing. ” Accounting 
Review , vol. 87, no. 1 (January):1–33. 
Lewis, Craig M. 2012. “Risk Modeling at the SEC: The Accounting 
Quality Model” Speech, the Financial Executives International 
Committee on Finance and Information Technology (13 
December): www.sec.gov/news/speech/2012/spch121312cml.
htm.

htm.
Nurnberg, H. 2006. “Perspectives on the Cash Flow Statement 
under FASB Statement No. 95. ” Center for Excellence in 
Accounting and Security Analysis Occasional Paper Series. 
Columbia Business School.
Nurnberg, H., and J. Largay. 1998. “Interest Payments in the 
Cash Flow Statement. ” Accounting Horizons , vol. 12, no. 4 
(December):407–418.
Pavlo, Walter. 2013. “Fmr Enron CFO Andrew Fastow Speaks 
At ACFE Annual Conference, ” Forbes  (26 June): www.forbes.
com/sites/walterpavlo/2013/06/26/fmr-  enron-  cfo- andrew-  
fastow-  speaks-  at- acfe-  annual-  conference/.
Ronen, Joshua, and Varda Yaari. 2008. Earnings Management: 
Emerging Insights in Theory, Practice, and Research . New York: 
Springer.
Schipper, Katherine. 1989. “Commentary on Earnings 
Management. ” Accounting Horizons , vol. 3, no. 4 
(December):91–102.
Watts, Ross. 2003. “Conservatism in Accounting Part I: 
Explanations and Implications. ” Accounting Horizons , vol. 17, 
no. 3 (September):207–221.

Practice Problems 663
1 In contrast to earnings quality, financial reporting quality most likely pertains 
to:
A sustainable earnings. 
B relevant information.
C adequate return on investment.
2 The information provided by a low-  quality financial report will most likely :
A decrease company value.
B indicate earnings are not sustainable.
C impede the assessment of earnings quality.
3 To properly assess a company’s past performance, an analyst requires:
A high earnings quality.
B high financial reporting quality.
C both high earnings quality and high financial reporting quality.
4 Low quality earnings most likely  reflect:
A low-  quality financial reporting.
B company activities which are unsustainable.
C information that does not faithfully represent company activities.
5 Earnings that result from non-  recurring activities most likely indicate:
A lower-  quality earnings.
B biased accounting choices.
C lower-  quality financial reporting.

6 Which attribute of financial reports would most likely  be evaluated as optimal 
in the financial reporting spectrum? 
A Conservative accounting choices
B Sustainable and adequate returns
C Emphasized pro forma earnings measures
7 Financial reports of the lowest level of quality reflect:
A fictitious events.
C accounting that is non-  compliant with GAAP .
8 When earnings are increased by deferring research and development (R&D) 
investments until the next reporting period, this choice is considered:
A non-  compliant accounting.
B earnings management as a result of a real action.
C earnings management as a result of an accounting choice.
9 A high-  quality financial report may reflect:
A earnings smoothing.
B low earnings quality.
C understatement of asset impairment.

Reading 31 ■ Financial Reporting Quality 664
10 If a particular accounting choice is considered aggressive in nature, then the 
financial performance for the current period would most likely :
A be neutral.
B exhibit an upward bias.
C exhibit a downward bias.
11 Which of the following is most likely  to reflect conservative accounting choices?
A Decreased reported earnings in later periods
B Increased reported earnings in the current period
C Increased debt reported on the balance sheet at the end of the current 
period
12 Which of the following is most likely  to be considered a potential benefit of 
accounting conservatism?
A A reduction in litigation costs
B Less biased financial reporting
C An increase in current period reported performance
13 Which of the following statements most likely  describes a situation that would 
motivate a manager to issue low-  quality financial reports?
A The manager’s compensation is tied to stock price performance.

B The manager has increased the market share of products significantly.
C The manager has brought the company’s profitability to a level higher than 
14 Which of the following concerns would most likely motivate a manager to make 
conservative accounting choices?
A Attention to future career opportunities
B Expected weakening in the business environment
C Debt covenant violation risk in the current period
15 Which of the following conditions best explains why a company’s manager 
would obtain legal, accounting, and board level approval prior to issuing low-  
quality financial reports?
A Motivation
B Opportunity
C Rationalization
16 A company is experiencing a period of strong financial performance. In order 
to increase the likelihood of exceeding analysts’ earnings forecasts in the next 
reporting period, the company would most likely undertake accounting choices 
that:
A inflate reported revenue in the current period.
B delay expense recognition in the current period.

C accelerate expense recognition in the current period.
17 Which of the following situations represents a motivation, rather than an 
opportunity, to issue low-  quality financial reports?
A Poor internal controls
B Search for a personal bonus
C Inattentive board of directors
18 Which of the following situations will most likely  motivate managers to inflate 
earnings in the current period?

Practice Problems 665
A Possibility of bond covenant violation
B Earnings in excess of analysts’ forecasts
C Earnings that are greater than the previous year
19 Which of the following best describes an opportunity for management to issue 
low-  quality financial reports?
A Ineffective board of directors
B Pressure to achieve some performance level
C Corporate concerns about financing in the future
20 An audit opinion of a company’s financial reports is most likely intended to:
A detect fraud.
B reveal misstatements.
C assure that financial information is presented fairly.
21 If a company uses a non-  GAAP financial measure in an SEC filing, then the 
company must:
A give more prominence to the non-  GAAP measure if it is used in earnings 
releases.
B provide a reconciliation of the non-  GAAP measure and equivalent GAAP 
measure.
C exclude charges requiring cash settlement from any non-  GAAP liquidity 
measures.
22 A company wishing to increase earnings in the current period may choose to:

A decrease the useful life of depreciable assets.
B lower estimates of uncollectible accounts receivables.
C classify a purchase as an expense rather than a capital expenditure.
23 Bias in revenue recognition would least likely  be suspected if:
A the firm engages in barter transactions.
B reported revenue is higher than the previous quarter.
C revenue is recognized before goods are shipped to customers.
24 Which technique most likely increases the cash flow provided by operations?
A Stretching the accounts payable credit period
B Applying all non-  cash discount amortization against interest capitalized
C Shifting classification of interest paid from financing to operating cash flows
25 Which of the following is an indication that a company may be recognizing 
revenue prematurely? Relative to its competitors, the company’s:
A asset turnover is decreasing.
B receivables turnover is increasing.
C days sales outstanding is increasing.

26 Which of the following would most likely  signal that a company may be using 
aggressive accrual accounting policies to shift current expenses to later periods? 
Over the last five-  year period, the ratio of cash flow to net income has:
A increased each year.
B decreased each year.
C fluctuated from year to year.
27 An analyst reviewing a firm with a large, current-  period restructuring charge to 
earnings should:

Reading 31 ■ Financial Reporting Quality 666
A view expenses reported in prior years as overstated. 
B disregard it because it is solely related to past events.
C consider making pro forma adjustments to prior years’ earnings.

Solutions 667
SOLUTIONS
1 B is correct. Financial reporting quality pertains to the quality of information 
in financial reports. High-  quality financial reporting provides decision-  useful 
information, which is relevant and faithfully represents the economic reality of 
the company’s activities. Earnings of high quality are sustainable and provide 
an adequate level of return. Highest-  quality financial reports reflect both high 
financial reporting quality and high earnings quality.
2 C is correct. Financial reporting quality  pertains to the quality of the infor -
mation contained in financial reports. High-  quality financial reports provide 
decision-  useful information that faithfully represents the economic reality of 
the company. Low-  quality financial reports impede assessment of earnings 
quality. Financial reporting quality is distinguishable from earnings quality, 
which pertains to the earnings and cash generated by the company’s actual eco -

nomic activities and the resulting financial condition. Low quality earnings are 
not sustainable and decrease company value.
3 B is correct. Financial reporting quality  pertains to the quality of the infor -
mation contained in financial reports. If financial reporting quality is low, 
the information provided is not useful to assess the company’s performance. 
Financial reporting quality is distinguishable from earnings quality, which 
pertains to the earnings and cash generated by the company’s actual economic 
activities and the resulting financial condition.
4 B is correct. Earnings quality pertains to the earnings and cash generated by the 
company’s actual economic activities and the resulting financial condition. Low-  
quality earnings are likely not sustainable over time because the company does 
not expect to generate the same level of earnings in the future or because earn -
ings will not generate sufficient return on investment to sustain the company in

the future. Earnings that are not sustainable decrease company value. Earnings 
quality is distinguishable from financial reporting quality, which pertains to the 
quality of the information contained in financial reports.
5 A is correct. Earnings that result from non-  recurring activities are unsus -
tainable. Unsustainable earnings are an example of lower-  quality earnings. 
Recognizing earnings that result from non-  recurring activities is neither a 
biased accounting choice or indicative of lower quality financial reporting 
because it faithfully represents economic events.
6 B is correct. At the top of the quality spectrum of financial reports are reports 
that conform to GAAP , are decision useful, and have earnings that are sustain -
able and offer adequate returns. In other words, these reports have both high 
7 A is correct. Financial reports span a quality continuum from high to low based

on decision-  usefulness and earnings quality (see Exhibit 2 of the reading). The 
lowest-  quality reports portray fictitious events, which may misrepresent the 
company’s performance and/or obscure fraudulent misappropriation of the 
company’s assets.
8 B is correct. Deferring research and development (R&D) investments into the 
next reporting period is an example of earnings management by taking a real 
action. 
9 B is correct. High-  quality financial reports offer useful information, mean -
ing information that is relevant and faithfully represents actual performance. 
Although low earnings quality may not be desirable, if the reported earnings

Reading 31 ■ Financial Reporting Quality 668
are representative of actual performance, they are consistent with high-  quality 
financial reporting. Highest-  quality financial reports reflect both high financial 
reporting quality and high earnings quality.
10 B is correct. Aggressive accounting choices aim to enhance the company’s 
reported performance by inflating the amount of revenues, earnings, and/or 
operating cash flow reported in the period. Consequently, the financial perfor -
mance for the current period would most likely exhibit an upward bias.
11 C is correct. Accounting choices are considered conservative if they decrease 
the company’s reported performance and financial position in the current 
period. Conservative choices may increase the amount of debt reported on the 
balance sheet. Conservative accounting choices may decrease the amount of 
revenues, earnings, and/or operating cash flow reported in the current period 
and increase those amounts in later periods.

12 A is correct. Conservatism reduces the possibility of litigation and, by exten -
sion, litigation costs. Rarely, if ever, is a company sued because it understated 
good news or overstated bad news. Accounting conservatism is a type of bias in 
financial reporting that decreases a company’s reported performance in the cur -
rent period. Conservatism directly conflicts with the characteristic of neutrality. 
13 A is correct. Managers often have incentives to meet or beat market expecta -
tions, particularly if management compensation is linked to increases in stock 
prices or to reported earnings.
14 B is correct. Managers may be motivated to understate earnings in the current 
period and increase the probability of meeting or exceeding the next period’s 
earnings target.
15 C is correct. Typically, conditions of opportunity, motivation, and rationaliza -
tion exist when individuals issue low-  quality financial reports. Rationalization

exists when an individual is concerned about a choice and needs to be able to 
justify it to herself or himself. If the manager is concerned about a choice in a 
financial reports, she or he may ask for other opinions to convince herself or 
himself that it is okay.
16 C is correct. In a period of strong financial performance, managers may pur -
sue accounting choices that increase the probability of exceeding next period’s 
earnings forecasts. By accelerating expense recognition or delaying revenue 
recognition, managers may increase earnings in the next period and increase 
the likelihood of exceeding next period’s earnings targets.
17 B is correct. Motivation can result from pressure to meet some criteria for 
personal reasons, such as a bonus, or corporate reasons, such as concern about 
financing in the future. Poor internal controls and an inattentive board of direc -
tors offer opportunities to issue low-  quality financial reports.

18 A is correct. The possibility of bond covenant violations may motivate managers 
to inflate earnings in the current period. By inflating earnings in the current 
period, the company may be able to avoid the consequences associated with 
violating bond covenants.
19 A is correct. Opportunities to issue low quality financial reports include inter -
nal conditions such as an ineffective board of directors and external conditions 
such as accounting standards that provide scope for divergent choices. Pressure 
to achieve some performance level and corporate concerns about financing in 
the future are examples of motivations to issue low-  quality financial reports. 
opportunity, motivation, and rationalization.

Solutions 669
20 C is correct. An audit is intended to provide assurance that the company’s 
financial reports are presented fairly, thus providing discipline regarding finan -
cial reporting quality. Regulatory agencies usually require that the financial 
statements of publicly traded companies be audited by an independent auditor 
to provide assurance that the financial statements conform to accounting stan -
dards. Privately held companies may also choose to obtain audit opinions either 
voluntarily or because an outside party requires it. An audit is not typically 
intended to detect fraud. An audit is based on sampling and it is possible that 
the sample might not reveal misstatements.
21 B is correct. If a company uses a non-  GAAP financial measure in an SEC filing, 
it is required to provide the most directly comparable GAAP measure with 
equivalent prominence in the filing. In addition, the company is required to 
provide a reconciliation between the non-  GAAP measure and the equivalent

GAAP measure. Similarly, IFRS require that any non-  IFRS measures included 
in financial reports must be defined and their potential relevance explained. The 
non-  IFRS measures must be reconciled with IFRS measures.
22 B is correct. If a company wants to increase reported earnings, the company’s 
managers may reduce the allowance for uncollected accounts and uncollected 
accounts expense reported in the period. Decreasing the useful life of depre -
ciable assets would increase depreciation expense and decrease earnings in 
the current period. Classifying a purchase as an expense rather than a capital 
expenditure would decrease earnings in the current period. The use of accrual 
accounting may result in estimates included in financial reports, because all 
facts associated with events may not be known at the time of recognition. These 
estimates can be grounded in reality or can be managed by the company to 
present a desired financial picture.

23 B is correct. Bias in revenue recognition can lead to manipulation of informa -
tion presented in financial reports. Addressing the question as to whether rev -
enue is higher or lower than the previous period is not sufficient to determine 
if there is bias in revenue recognition. Additional analytical procedures must 
be performed to provide warning signals of accounting malfeasance. Barter 
transactions are difficult to value properly and may result in bias in revenue 
recognition. Policies that make it easier to prematurely recognize revenue, such 
as revenue being recognized before goods are shipped to customers, may be a 
warning sign of accounting malfeasance.
24 A is correct. Managers can temporarily show a higher cash flow from oper -
ations by stretching the accounts payable credit period. In other words, the 
managers delay payments until the next accounting period. Applying all non-

cash discount amortization against interest capitalized causes reported interest 
expenses and operating cash outflow to be higher, resulting in a lower cash flow 
provided by operations. Shifting the classification of interest paid from financ -
ing to operating cash flows lowers the cash flow provided by operations.
25 C is correct. If a company’s days sales outstanding (DSO) is increasing relative 
to competitors, this may be a signal that revenues are being recorded prema -
turely or are even fictitious. There are numerous analytical procedures that can 
be performed to provide evidence of manipulation of information in financial 
reporting. These warning signs are often linked to bias associated with revenue 
recognition and expense recognition policies.
26 B is correct. If the ratio of cash flow to net income for a company is consistently 
below 1 or has declined repeatedly over time, this may be a signal of manipula -

tion of information in financial reports through aggressive accrual accounting

Reading 31 ■ Financial Reporting Quality 670
policies. When net income is consistently higher than cash provided by oper -
ations, one possible explanation is that the company may be using aggressive 
accrual accounting policies to shift current expenses to later periods.
27 C is correct. To extrapolate historical earnings trends, an analyst should con -
sider making pro forma analytical adjustments of prior years’ earnings to reflect 
in those prior years a reasonable share of the current period’s restructuring and 
impairment charges.

Financial Statement Analysis: Applications
by Thomas R. Robinson, PhD, CFA, Jan Hendrik van Greuning, DCom, CFA, 
Elaine Henry, PhD, CFA, and Michael A. Broihahn, CPA, CIA, CFA
Thomas R. Robinson, PhD, CFA, is at AACSB International (USA). Jan Hendrik van 
Greuning, DCom, CFA, is at BIBD (Brunei). Elaine Henry, PhD, CFA, is at Stevens Institute 
of Technology (USA). Michael A. Broihahn, CPA, CIA, CFA, is at Barry University (USA).
a. evaluate a company’s past financial performance and explain how 
a company’s strategy is reflected in past financial performance;
b. forecast a company’s future net income and cash flow;
c. describe the role of financial statement analysis in assessing the 
credit quality of a potential debt investment;
d. describe the use of financial statement analysis in screening for 
potential equity investments;
e. explain appropriate analyst adjustments to a company’s financial

statements to facilitate comparison with another company.REA dINg
32
International Financial Statement Analysis , by Thomas R. Robinson, CFA, Jan Hendrik van Greuning, CFA, 
Elaine Henry, CFA, and Michael A. Broihahn, CFA. © 2007 by CFA Institute. All rights reserved.Note:  Changes in accounting 
Finally, candidates should be

readings.

Reading 32 ■ Financial Statement Analysis: Applications 672
This reading presents several important applications of financial statement analysis. 
Among the issues we will address are the following:
■■What are the key questions to address in evaluating a company’s past financial 
performance?
■■How can an analyst approach forecasting a company’s future net income and 
cash flow?
■■How can financial statement analysis be used to evaluate the credit quality of a 
potential fixed-  income investment?
■■How can financial statement analysis be used to screen for potential equity 
investments?
■■How can differences in accounting methods affect financial ratio comparisons 
between companies, and what are some adjustments analysts make to reported 
financials to facilitate comparability among companies.
The reading “Financial Statement Analysis: An Introduction” described a frame -
work for conducting financial statement analysis. Consistent with that framework,

prior to undertaking any analysis, an analyst should explore the purpose and context 
of the analysis. The purpose and context guide further decisions about the approach, 
the tools, the data sources, and the format in which to report results of the analysis, 
and also suggest which aspects of the analysis are most important. Having identified 
the purpose and context, the analyst should then be able to formulate the key ques -
tions that the analysis must address. The questions will suggest the data the analyst 
needs to collect to objectively address the questions. The analyst then processes and 
analyzes the data to answer these questions. Conclusions and decisions based on the 
analysis are communicated in a format appropriate to the context, and follow-  up is 
undertaken as required. Although this reading will not formally present applications 
as a series of steps, the process just described is generally applicable.

Section 2 of this reading describes the use of financial statement analysis to evaluate 
a company’s past financial performance, and Section 3 describes basic approaches to 
projecting a company’s future financial performance. Section 4 presents the use of 
financial statement analysis in assessing the credit quality of a potential debt invest -
ment. Section 5 concludes the survey of applications by describing the use of finan -
cial statement analysis in screening for potential equity investments. Analysts often 
encounter situations in which they must make adjustments to a company’s reported 
financial results to increase their accuracy or comparability with the financials of 
other companies. Section 6 illustrates several common types of analyst adjustments. 
Section 7 presents a summary, and practice problems in the CFA Institute multiple-  
choice format conclude the reading.1

Application: Evaluating Past Financial Performance 673
APPLICATION: EVALUATING PAST FINANCIAL 
PERFORMANCE
Analysts examine a company’s past financial performance for a number of reasons. 
Cross-  sectional analysis of financial performance facilitates understanding of the 
comparability of companies for a market-  based valuation.1 Analysis of a company’s 
historical performance over time can provide a basis for a forward-  looking analysis 
of the company. Both cross-  sectional and trend analysis can provide information for 
evaluating the quality and performance of a company’s management.
An evaluation of a company’s past performance addresses not only what  happened 
(i.e., how the company performed) but also why it happened—the causes behind the 
performance and how the performance reflects the company’s strategy. Evaluative 
judgments assess whether the performance is better or worse than a relevant bench -
mark, such as the company’s own historical performance, a competitor’s performance,

or market expectations. Some key analytical questions include the following:
■■How and why have corporate measures of profitability, efficiency, liquidity, and 
solvency changed over the periods being analyzed?
■■How do the level and trend in a company’s profitability, efficiency, liquidity, and 
solvency compare with the corresponding results of other companies in the 
same industry? What factors explain any differences?
■■What aspects of performance are critical for a company to successfully com -
pete in its industry, and how did the company perform relative to those critical 
performance aspects?
■■What are the company’s business model and strategy, and how did they influ -
ence the company’s performance as reflected in, for example, its sales growth, 
efficiency, and profitability?
Data available to answer these questions include the company’s (and its competi -
tors’) financial statements, materials from the company’s investor relations department,

corporate press releases, and non-  financial-  statement regulatory filings, such as prox -
ies. Useful data also include industry information (e.g., from industry surveys, trade 
publications, and government sources), consumer information (e.g., from consumer 
satisfaction surveys), and information that is gathered by the analyst firsthand (e.g., 
through on-  site visits). Processing the data typically involves creating common-  size 
financial statements, calculating financial ratios, and reviewing or calculating industry-  
specific metrics. Example 1 illustrates the effects of strategy on performance and the 
use of basic economic reasoning in interpreting results.
EXAMPLE 1   
A Change in Strategy Reflected in Financial Performance
Apple Inc. is a company that has evolved and adapted over time. In its 1994 
Prospectus (Form 424B5) filed with the US SEC, Apple identified itself as 
“one of the world’s leading personal computer technology companies. ” At that

time, most of its revenue was generated by computer sales. In the prospectus, 
however, Apple stated, “The Company’s strategy is to expand its market share 2
1 Pinto et al. (2010) describe market-  based valuation as using price multiples—ratios of a stock’s market 
price to some measure of value per share (e.g., price-  to- earnings ratios). Although the valuation method 
may be used independently of an analysis of a company’s past financial performance, such an analysis may 
provide reasons for differences in companies’ price multiples.

Reading 32 ■ Financial Statement Analysis: Applications 674
in the personal computing industry while developing and expanding into new 
related business such as Personal Interactive Electronics and Apple Business 
Systems. ” Over time, products other than computers became significant gener -
ators of revenue and profit. In its 2010 Annual Report (Form 10-  K) filed with 
the SEC, Apple stated in Part I, Item 1, under Business Strategy, “The Company 
is committed to bringing the best user experience to its customers through its 
innovative hardware, software, peripherals, services, and Internet offerings. The 
Company's business strategy leverages its unique ability to design and develop 
. . . to provide its customers new products and solutions with superior ease-  of- 
use, seamless integration, and innovative industrial design. . . . The Company 
is therefore uniquely positioned to offer superior and well-  integrated digital

lifestyle and productivity solutions. ” Clearly, the company is no longer simply a 
personal computer technology company.
In analyzing the historical performance of Apple as of the beginning of 
2011, an analyst might refer to the information presented in Exhibit 1. Panel A 
presents selected financial data for the company from 2007 to 2010. Panels B 
and C present excerpts from the segment note. Panel B reports the net sales by 
product, in millions of dollars, and Panel C reports the unit sales by product, 
in thousands. [Because Apple manages its business on the basis of geographical 
segments, the more complete data required in segment reporting (i.e., segment 
operating income and segment assets) is available only by geographical segment, 
not by product.]
In 2005, an article in Barron’s  said, “In the last year, the iPod has become 
Apple’s best-  selling product, bringing in a third of revenues for the Cupertino,

Calif. firm . . . Little noticed by these iPod zealots, however is a looming threat 
. . . Wireless phone companies are teaming up with the music industry to make 
most mobile phones into music players” ( Barron’s  27 June 2005, p. 19). The threat 
noted by Barron’s  was not unnoticed or ignored by Apple.
In June 2007, Apple itself entered the mobile phone market with the launch 
of the original iPhone, followed in June 2008 by the second-  generation iPhone 
3G (a handheld device combining the features of a mobile phone, an iPod, and 
an internet connection device). Soon after, the company launched the iTunes 
App Store, which allows users to download third-  party applications onto their 
iPhones. As noted in a 2009 Business Week  article, Apple “is the world's largest 
music distributor, having passed Wal-  Mart Stores in early 2008. Apple sells 
around 90% of song downloads and 75% of digital music players in the United

States” ( Business Week , 28 September 2009, p. 34). Product innovations continue 
as evidenced by the introduction of the iPad in January 2010.
Exhibit 1   Selected Data for Apple Inc. (for the four years ended 25 September 2010)
Panel A: Data for Apple Inc. Fiscal Y ear
(dollars in millions) 2010 2009 2008 2007
Net sales $65,225 $42,905 $37,491 $24,578
Gross margin 25,684 17,222 13,197 8,152
Net income 14,013 8,235 6,119 3,495
Cash and marketable securities 51,011 33,992 24,490 15,386
Total current assets 41,678 31,555 30,006 21,956
Total assets 75,183 47,501 36,171 24,878
Total current liabilities 20,722 11,506 11,361 9,280

Application: Evaluating Past Financial Performance 675
Panel B: Net Sales by Product
Desktops $6,201 $4,324 $5,622 $4,023
Portables 11,278 9,535 8,732 6,313
Total Mac net sales 17,479 13,859 14,354 10,336
iPod 8,274 8,091 9,153 8,305
Other music related products and services 4,948 4,036 3,340 2,496
iPhone and related products and services 25,179 13,033 6,742 630
iPad and related products and services 4,958 0 0 0
Peripherals and other hardware 1,814 1,475 1,694 1,303
Software, service and other sales 2,573 2,411 2,208 1,508
Total net sales $65,225 $42,905 $37,491 $24,578
Panel C: Unit Sales by Product
(units in thousands) 2010 2009 2008 2007
Desktops 4,627 3,182 3,712 2,714
Portables 9,035 7,214 6,003 4,337
Total Mac unit sales 13,662 10,396 9,715 7,051
Net sales per Mac unit sold $1,279 $1,333 $1,478 $1,466
iPod unit sales 50,312 54,132 54,828 51,630
Net sales per iPod unit sold $164 $149 $167 $161
iPhone units sold 39,989 20,731 11,627 1,389

iPad units sold 7,458 0 0 0
Source:  Apple Inc. 2008 Form 10-  K, 2009 Form 10-  K/A, and 2010 Form 10-  K.
Using the information provided, address the following:
1 Typically, products that are differentiated either through recognizable 
brand names, proprietary technology, unique styling, or some combi -
nation of these features can be sold at a higher price than commodity 
products.
A In general, would the selling prices of differentiated products be more 
directly reflected in a company’s operating profit margin or gross 
profit margin?
B Does Apple’s financial data (Panel A) reflect a successful differentiation 
strategy?
2 How liquid is Apple at the end of fiscal 2009 and 2010? In general, what 
are some of the considerations that a company makes in managing its 
liquidity?
3 Based on the product segment data for 2007 (Panels B and C), Apple’s pri -
mary source of revenue was from sales of computers (the $10,336 million

in sales of Mac computers represented 42 percent of total net sales) and 
its secondary source of revenue was from iPods. How has the company’s 
product mix changed since 2007, and what might this change suggest for 
an analyst examining Apple relative to its competitors?Exhibit 1   (Continued)

Reading 32 ■ Financial Statement Analysis: Applications 676
A Sales of differentiated products at premium prices would generally be 
reflected more directly in the gross profit margin; such sales would 
have a higher gross profit margin, all else equal. The effect of premium 
pricing generally would also be reflected in a higher operating margin. 
Expenditures on advertising and/or research are required to support 
differentiation, however, which means that the effect of premium pricing 
on operating profit margins is often weaker than the effect on gross profit 
margins.
B Based on Apple’s financial data in Panel A, the company appears to have 
successfully implemented a differentiation strategy, with gross margin 
increasing from 33 percent of sales to 40 percent of sales, as shown in the 
following table:
2010 2009 2008 2007
$ 
MillionsPercent 
of Sales$ 
of Sales$ 
of Sales$ 
MillionsPercent of 
Sales

of Sales$ 
Sales
Net sales $65,225 100% $42,905 100% $37,491 100% $24,578 100%
Cost of sales 39,541 61% 25,683 60% 24,294 65% 16,426 67%
Gross 
margin$25,684 39% $17,222 40% $13,197 35% $8,152 33%
In general, in addition to a successful differentiation strategy, higher gross mar -
gins can result from lower input costs and/or a change in sales mix to include 
more product types with high gross margins.
Apple was very liquid at the end of fiscal 2009 and 2010, with current ratios of, 
respectively, 2.7 ($31,555/$11,506) and 2.0 (= $41,678/$20,722). In addition, the 
company had 71.6 and 67.8 percent of total assets invested in cash and market -
able securities at the end of, respectively, 2009 and 2010. In general, some of 
the considerations that a company makes in managing its liquidity include the 
following: (1) maintaining enough cash and other liquid assets to ensure that it

can meet near-  term operating expenditures and unexpected needs, (2) avoiding 
excessive amounts of cash because the return on cash assets is almost always less 
than the company’s costs of capital to finance its assets, and (3) accumulating 
cash that will be used for acquisitions (sometimes referred to as a “war chest, ” 
which is illustrated in Exhibit 2). Apple may be accumulating a war chest, but an 
analyst might, given point 2 above, question the amount of cash and marketable 
securities on hand.
In 2009, the proportion of Apple’s total sales from computers declined from 
42 percent to 32 percent and the proportion of total sales from iPods declined 
from 34 percent to 19 percent. The biggest shift in product sales was the increase 
in iPhone sales from 3 percent in 2007, the year of the product’s introduction, to 
30 percent in 2009. In 2010, the proportion of Apple’s total sales from computers 
and iPods continued to decline and the proportion from iPhones continued to

increase. These proportions in 2010 were, respectively, 27 percent, 13 percent, 
and 39 percent of total sales. The iPad introduced in fiscal 2010 represented 
8 percent of total sales that year. For an analyst examining Apple relative to its 
competitors, the relevant comparable companies clearly changed from 2007 
to 2010. Recently, the company may be more appropriately compared not only

Application: Evaluating Past Financial Performance 677
with other computer manufacturers but also with mobile phone manufacturers 
and companies developing competing software and systems for mobile internet 
devices. Apple’s product innovation has reshaped the competitive landscape.
To illustrate the use of a war chest, Exhibit  2 provides descriptions of several 
companies’ cash positions and potential uses of their funds. When a company has 
accumulated large amounts of cash, an analyst should consider the likely implications 
for a company’s strategic actions (i.e., potential acquisitions) or financing decisions 
(e.g., share buybacks, dividends, or debt repayment).
Exhibit 2   War Chests
The expression “war chest” is sometimes used to refer to large cash balances 
that a company accumulates prior to making acquisitions. Some examples are 
shown here:
Apple Inc.
Apple closed 2009 with nearly $40 billion in the bank, in the form

of cash, short-  term and long-  term marketable securities. That "war 
chest," as one shareholder described it [during Apple's annual share -
holder's meeting], has fueled speculation about what the company 
might do with the funds. Options could include large acquisitions or 
returning cash to shareholders in the form of a buyback or dividend.
Dan Gallagher, MarketWatch , 25 February 2010.
McLeod Russel India Ltd.
McLeod Russel India Ltd., the world’s biggest tea grower, plans 
to use rising prices to build a “war chest” of as much as $250 million 
to acquire companies. . . . The plantation company, based in Kolkata, 
may buy tea companies in India and Africa as it targets a 50 percent 
increase in production to 150 million kilograms in three to four years, 
said Aditya Khaitan, managing director of McLeod Russel.
Arijit Ghosh and Thomas Kutty Abraham, Bloomberg , 14 May 2010.
In calculating and interpreting financial statement ratios, an analyst needs to be

aware of the potential impact on the financial statements and related ratios of com -
panies reporting under different accounting standards, such as international financial 
reporting standards (IFRS), US generally accepted accounting principles (US GAAP), 
or other home-  country GAAP . Furthermore, even within a given set of accounting 
standards, companies still have discretion to choose among acceptable methods. A 
company also may make different assumptions and estimates even when applying 
the same method as another company. Therefore, making selected adjustments to a 
company’s financial statement data may be useful to facilitate comparisons with other 
companies or with the industry overall. Examples of such analyst adjustments will be 
discussed in Section 6.
Non-  US companies that use any acceptable body of accounting standards (other 
than IFRS or US GAAP) and file with the US SEC (because their shares or depositary

receipts based on their shares trade in the United States) are required to reconcile their 
net income and shareholders’ equity accounts to US GAAP . Note that in 2007, the 
SEC eliminated the reconciliation requirement for non-  US companies using IFRS and

Reading 32 ■ Financial Statement Analysis: Applications 678
filing with the SEC. Example 2 uses reconciliation data from SEC filings to illustrate 
how differences in accounting standards can affect financial ratio comparisons. The 
differences in the example are very large.
EXAMPLE 2   
The Effect of Differences in Accounting Standards on ROE 
Comparisons
In the process of comparing the 2009 performance of three telecommunication 
companies—Teléfonos de México, S.A.B. DE C.V. (TMX), Tele Norte Leste 
Participações S.A. (TNE), and Verizon Communications Inc. (VZ)—an analyst 
prepared Exhibit 3 to evaluate whether the differences in accounting standards 
affect the comparison of the three companies’ return on equity (ROE). Panel A 
presents selected data for TMX for 2008 and 2009 under Mexican GAAP and 
US GAAP . Panel B presents data for TNE under Brazilian GAAP and US GAAP . 
Panel C presents data for VZ under US GAAP .
Exhibit 3   Data for TMX, TNE, and VZ for a ROE Calculation (years

ended 31 December)
Panel A: Selected Data for Teléfonos de México (TMX)
(in millions of Mexican pesos) 2009 2008
Mexican GAAP
Net income 20,469 20,177
Shareholders’ equity 38,321 39,371
US GAAP
Net income 19,818 19,782
Shareholders’ equity 7,465 11,309
Panel B: Selected Data for Tele Norte Leste Participações S.A. (TNE)
(in millions of Brazilian reaisa) 2009 2008
Brazilian GAAP
Net income (1,056) 1,432
Shareholders’ equity 15,352 11,411
US GAAP
Net income 4,866 1,252
Shareholders’ equity 21,967 11,203
Panel C: Selected Data for Verizon Communications Inc.
(in millions of US dollars) 2009 2008
US GAAP
Net income 10,358 12,583
Shareholders’ equity 84,367 78,905
a “Reais” is the plural of “real. ”
Sources:  TMX’s and TME’s 2009 Form 20-  F; VZ’s 2009 10-  K.

Application: Evaluating Past Financial Performance 679
Based on TMX’s reconciliation note, the most significant adjustment for 
TMX between Mexican GAAP and US GAAP was an adjustment to shareholders’ 
equity for “Labor obligations (SFAS 158). ” The US accounting standard SFAS 158, 
Employers’ Accounting for Defined Benefit Pension and Other Postretirement Plans , 
now codified as Accounting Standards Codification (ASC) 715 (i.e., Expenses: 
Compensation–Retirement Benefits) requires companies to reflect on their bal -
ance sheets the funded status of pensions and other post-  employment benefits. 
(Funded status equals plan assets minus plan obligations.) For an underfunded 
plan—i.e., one in which assets that are held in trust to pay for the obligation are 
less than the amount of the obligation—the amount of underfunding is shown 
as a liability and as a reduction to shareholders’ equity. [The full reconciliation 
between shareholders’ equity under Mexican FRS and US GAAP (not presented

here) shows that the adjustment related to SFAS 158 reduced equity at TMX by 
50,028 million pesos and 46,637 million pesos in 2009 and 2008, respectively.]
Based on TNE’s reconciliation note, the most significant adjustment for 
TNE between Brazilian GAAP and US GAAP was an increase to net income to 
recognize a “bargain purchase gain on business combination. ” A bargain pur -
chase gain under US GAAP results when the purchase price of an acquisition 
is less than the fair value (as of the acquisition date) of the net identified assets 
acquired. The adjustment for the bargain purchase gain represented an increase 
of 6,591 million Brazilian reais to net income as reported under Brazilian GAAP .
Does the difference in accounting standards affect the ROE comparison?
Solution:
When ROE is compared under different standards, both of the non-  US compa -
nies report significantly higher ROE under US GAAP than under home-  country 
GAAP (Mexican GAAP for TMX and Brazilian GAAP for TNE).

When ROE is compared across companies, TMX’s ROE is higher than that 
of both of the other two companies regardless of whether the comparison is 
based on home-  country amounts or US GAAP amounts. For TNE, however, 
the company reported a loss and thus a negative ROE under home-  country 
(Brazilian) GAAP but a profit under US GAAP . The ROE for TNE is lower than 
VZ’s ROE when calculations are based on home-  country GAAP but higher than 
VZ’s ROE when calculations are based on US GAAP .
Results of the calculations are summarized in the following table, with the 
calculations based on TMX’s Mexican GAAP explained after the table:
Panel A: Teléfonos de México (TMX)
Return on average shareholders’ equity 52.69%
US GAAP
Return on average shareholders’ equity 211.12%
Panel B: Tele Norte Leste Participações S.A. (TNE)
Return on average shareholders’ equity –7.89%
US GAAP
Return on average shareholders’ equity 29.34%

Reading 32 ■ Financial Statement Analysis: Applications 680
Panel C: Verizon Communications Inc. (VZ)
US GAAP
Return on average shareholders’ equity 12.69%
For an illustration of the ROE calculation, we have calculated TMX’s ROE 
(with all numbers in thousands of Mexican pesos) as 20,468,983/[(38,320,773 + 
39,371,099)/2] = 52.69%. Note that TMX’s significantly higher ROE under US 
GAAP is the result of a much lower shareholders’ equity under US GAAP than 
under Mexican GAAP .
In Example 2, the 2009 ROE for both TMX and TNE differed substantially under 
home-  country GAAP and US GAAP . In general, because the reconciliation data are no 
longer required by the SEC, we cannot determine whether differences in net income, 
equity, and thus ROE also exist between IFRS and the companies’ home-  country GAAP 
(including US GAAP). Historically, research indicates that for most non-  US companies 
filing with the SEC, differences in net income between US GAAP and home-  country

GAAP average 1–2 percent of market value of equity, but large variations do occur.2 
Additionally, research indicates that for most non-  US companies filing with the SEC, 
ROE was historically higher under IFRS than under US GAAP .3
Comparison of the levels and trends in a company’s performance provide infor -
mation about how the company performed. The company’s management presents its 
view about causes underlying its performance in the management commentary or 
management discussion and analysis (MD&A) section of its annual report and during 
periodic conference calls with analysts and investors. To gain additional understanding 
of the causes underlying a company’s performance, an analyst can review industry 
information or seek information from additional sources, such as consumer surveys.
The results of an analysis of past performance provide a basis for reaching conclu -
sions and making recommendations. For example, an analysis undertaken as the basis

for a forward-  looking study might conclude that a company’s future performance is 
or is not likely to reflect continuation of recent historical trends. As another example, 
an analysis to support a market-  based valuation of a company might focus on whether 
the company’s profitability and growth outlook, which is better (worse) than the peer 
group median, justifies its relatively high (low) valuation. This analysis would con -
sider market multiples, such as price-  to- earnings ratio (P/E), price-  to- book ratio, and 
total invested capital to EBITDA (earnings before interest, taxes, depreciation, and 
amortization).4 As another example, an analysis undertaken as part of an evaluation 
of the management of two companies might result in conclusions about whether one 
company has grown as fast as another company, or as fast as the industry overall, and 
whether each company has maintained profitability while growing.
2 Pownall and Schipper (1999).

3 In a study of European companies’ reconciliations in the last year that reconciliations were required by 
the SEC, Henry, Lin, and Yang (2009) found that most of the companies reported IFRS net income higher 
than US GAAP net income and reported IFRS shareholders’ equity lower than US GAAP shareholders’ 
equity. The result was that 28 percent of the sample companies’ 2006 ROE under IFRS was more than 
5 percentage points higher than under US GAAP whereas fewer than 10 percent of the sample report ROE 
more than 5 percentage points lower.
4 Total invested capital  is the sum of market value of common equity, book value of preferred equity, 
and face value of debt.

Application: Projecting Future Financial Performance 681
APPLICATION: PROJECTING FUTURE FINANCIAL 
Projections of future financial performance are used in determining the value of a 
company or its equity component. Projections of future financial performance are 
also used in credit analysis—particularly in project finance or acquisition finance—to 
determine whether a company’s cash flows will be adequate to pay the interest and 
principal on its debt and to evaluate whether a company will likely remain in com -
pliance with its financial covenants.
Sources of data for analysts’ projections include some or all of the following: the 
company’s projections, the company’s previous financial statements, industry structure 
and outlook, and macroeconomic forecasts.
Evaluating a company’s past performance may provide a basis for forward-  looking 
analyses. An evaluation of a company’s business and economic environment and its

history may persuade the analyst that historical information constitutes a valid basis 
for such analyses and that the analyst’s projections may be based on the continuance 
of past trends, perhaps with some adjustments. Alternatively, in the case of a major 
acquisition or divestiture, for a start-  up company, or for a company operating in a 
volatile industry, past performance may be less relevant to future performance.
Projections of a company’s near-  term performance may be used as an input to 
market-  based valuation or relative valuation (i.e., valuation based on price multiples). 
Such projections may involve projecting next year’s sales and using the common-  size 
income statement to project major expense items or particular margins on sales (e.g., 
gross profit margin or operating profit margin). These calculations will then lead to the 
development of an income measure for a valuation calculation, such as net income,

earnings per share (EPS) or EBITDA. More complex projections of a company’s future 
performance involve developing a more detailed analysis of the components of per -
formance for multiple periods—for example, projections of sales and gross margin 
by product line, projection of operating expenses based on historical patterns, and 
projection of interest expense based on requisite debt funding, interest rates, and 
applicable taxes. Furthermore, a projection should include sensitivity analyses applied 
to the major assumptions.
3.1 Projecting Performance: An Input to Market-  Based 
Valuation
One application of financial statement analysis involves projecting a company’s near-  
term performance as an input to market-  based valuation. For example, an analyst 
might project a company’s sales and profit margin to estimate EPS and then apply a 
projected P/E to establish a target price for the company’s stock.
Analysts often take a top-  down approach to projecting a company’s sales.5 First,

industry sales are projected on the basis of their historical relationship with some 
macroeconomic indicator, such as growth in real gross domestic product (GDP). 
In researching the automobile industry, for example, the analyst may find that the 
industry’s annual domestic unit car sales (number of cars sold in domestic markets) 
bears a relationship to annual changes in real GDP . Regression analysis is often used 
to establish the parameters of such relationships. Other factors in projecting sales may 
include consumer income or tastes, technological developments, and the availability 
of substitute products or services. After industry sales are projected, a company’s 3
5 The discussion in this paragraph is indebted to Benninga and Sarig (1997).

Reading 32 ■ Financial Statement Analysis: Applications 682
market share is projected. Company-  level market share projections may be based on 
historical market share and a forward-  looking assessment of the company’s compet -
itive position. The company’s sales are then estimated as its projected market share 
multiplied by projected total industry sales.
After developing a sales forecast for a company, an analyst can choose among vari -
ous methods for forecasting income and cash flow. An analyst must decide on the level 
of detail to consider in developing forecasts. For example, separate forecasts may be 
made for individual expense items or for more aggregated expense items, such as total 
operating expenses. Rather than stating a forecast in terms of expenses, the forecast 
might be stated in terms of a forecasted profit margin (gross, operating, or net). The 
net profit margin, in contrast to the gross or operating profit margins, is affected by

financial leverage and tax rates, which are subject to managerial and legal/regulatory 
revisions; therefore, historical data may sometimes be more relevant for projecting 
gross or operating profit margins than for projecting net profit margins. Whatever 
the margin used, the forecasted amount of profit for a given period is the product of 
the forecasted amount of sales and the forecast of the selected profit margin.
As Example 3 illustrates, for relatively mature companies operating in non-  volatile 
product markets, historical information on operating profit margins can provide a useful 
starting point for forecasting future operating profits (at least over short forecasting 
horizons). Historical operating profit margins are typically less reliable for projecting 
future margins for a new or relatively volatile business or one with significant fixed 
costs (which can magnify the volatility of operating margins).
EXAMPLE 3   
Using Historical Operating Profit Margins to Forecast

Operating Profit
One approach to projecting operating profit is to determine a company’s average 
operating profit margin over the previous several years and apply that margin 
to a forecast of the company’s sales. Use the following information on three 
companies to answer Questions 1 and 2 below:
■■Johnson & Johnson (JNJ). This US health care conglomerate, founded in 
1887, had 2009 sales of around $61.9 billion from its three main busi -
nesses: pharmaceuticals, medical devices and diagnostics, and consumer 
products.
■■BHP Billiton (BHP). This company, with group headquarters in Australia 
and secondary headquarters in London, is the world’s largest natural 
resources company, reporting revenue of approximately US$50.2 billion 
for the fiscal year ended June 2009. The company mines, processes, and 
markets coal, copper, nickel, iron, bauxite, and silver and also has substan -
tial petroleum operations.
■■Baidu. This Chinese company, which was established in 2000 and went

public on NASDAQ in 2005, is the leading Chinese language search 
engine. The company’s revenues for 2009 were 4.4 billion renminbi 
(RMB), an increase of 40 percent from 2008 and more than 14 times 
greater than revenues in 2005.
1 For each of the three companies, state and justify whether the sug -
gested forecasting method (applying the average operating profit over 
the previous several years to a forecast of sales) would be a reasonable 
starting point for projecting future operating profit.

Application: Projecting Future Financial Performance 683
2 Assume that the 2009 forecast of sales was perfect and, therefore, 
equal to the realized sales by the company in 2009. Compare the 
forecast of 2009 operating profit, using an average of the previous four 
years’ operating profit margins, with the actual 2009 operating profit 
reported by the company given the following additional information:
■■JNJ: For the four years prior to 2009, JNJ’s average operating profit margin 
was approximately 25.0 percent. The company’s actual operating profit for 
2009 was $15.6 billion.
■■BHP: For the four years prior to the year ending June 2009, BHP’s average 
operating profit margin was approximately 38.5 percent. The company’s 
actual operating profit for the year ended June 2009 was US$12.2 billion.
■■Baidu: Over the four years prior to 2009, Baidu’s average operating profit 
margin was approximately 27.1 percent. The company’s actual operating 
profit for 2009 was RMB1.6 billion.

Using the additional information given, state and justify whether actual results 
support the usefulness of the stable operating margin assumption.
JNJ. Because JNJ is an established company with diversified operations 
in relatively stable businesses, the suggested approach to projecting the 
company’s operating profit would be a reasonable starting point.
BHP . Because commodity prices tend to be volatile and the mining indus -
try is relatively capital intensive, the suggested approach to projecting 
BHP’s operating profit would probably not be a useful starting point.
Baidu . A relatively new company such as Baidu has limited operating 
history on which to judge stability of margins. The company appears 
to have been in a period of rapid growth and is in an industry that has 
been changing rapidly in recent years. This important aspect about the 
company suggests that the broad approach to projecting operating profit

would not be a useful starting point for Baidu.
JNJ. JNJ’s actual operating profit margin for 2009 was 25.2 percent 
($15.6 billion divided by sales of $61.9 billion), which is very close to the 
company’s three-  year average operating profit margin of approximately 
25.0 percent. If the average operating profit margin had been applied to 
perfectly forecasted 2009 sales to obtain forecasted operating profit, the 
forecasting error would have been minimal.
BHP . BHP’s actual operating profit margin for the year ended June 2009 
was 24.3 percent ($12.2 billion divided by sales of $50.2 billion). If the 
company’s average profit margin of 38.5 percent had been applied to 
perfectly forecasted sales, the forecasted operating profit would have been 
approximately US$19.3 billion, around 58 percent higher than actual oper -
ating profit.
Baidu . Baidu’s actual operating profit margin for 2009 was 36.4 percent 
(RMB1.6 billion divided by sales of RMB4.4 billion). If the average profit

margin of 27.1 percent had been applied to perfectly forecasted sales, the 
forecasted operating profit would have been approximately RMB1.2 bil -
lion, or around 25 percent below Baidu’s actual operating profit.

Reading 32 ■ Financial Statement Analysis: Applications 684
Although prior years’ profit margins can provide a useful starting point in pro -
jections for companies with relatively stable business, the underlying data should, 
nonetheless, be examined to identify items that are not likely to occur again in the 
following year(s). Such non-  recurring (i.e., transitory) items should be removed from 
computations of any profit amount or profit margin that will be used in projections. 
Example 4 illustrates this principle.
EXAMPLE 4   
Issues in Forecasting
Following are excerpts from the annual reports of two global companies. Indicate 
the relevance of each disclosure in forecasting the company’s future net income. 
(Business descriptions are from the companies’ websites.)
1 Anheuser-  Busch InBev SA/NV, the world’s largest brewing company by 
volume, with brands such as Budweiser, Stella Artois, and Beck’s, dis -
closed the following items, which are primarily related to its acquisition of

Anheuser-  Busch.
1.1 “The 2009 restructuring charges of (153)m US dollar primarily 
relate to the Anheuser-  Busch integration, organizational alignments 
and outsourcing activities in the global headquarters, Western Europe 
and Asia Pacific. These changes aim to eliminate overlap or duplicated 
processes and activities across functions and zones. These one time 
expenses as a result of the series of decisions will provide the company 
with a lower cost base besides a stronger focus on AB InBev’s core 
activities, quicker decision-  making and improvements to efficiency, 
service and quality… ”
1.2 “2009 business and asset disposals resulted in an exceptional 
income of 1,541m US dollar mainly representing the sale of assets of 
InBev USA LLC (also doing business under the name Labatt USA) 
to an affiliate of KPS Capital Partners, L.P . (54m US dollar), the sale 
of the Korean subsidiary Oriental Brewery to an affiliate of Kohlberg

Kravis Roberts & Co. L.P . (428m US dollar) and the sale of the Central 
European operations to CVC Capital Partners (1,088m US dollar)... ”
Source:  2009 Annual Report, note 8.
2 Nestlé Group, the largest food and beverages manufacturer in the world, 
disclosed the following information about the sale of its holding in the eye 
care company Alcon Inc.
2.1 “The most significant divestment was announced on 4 
January 2010, with the agreement to sell our remaining holding in 
Alcon, for about USD 28 billion. The completion of this transaction 
will bring the total value realised from the three-  part disposal of Alcon 
to over USD 40 billion. Alcon was acquired by Nestlé in 1977 for USD 
280 million. ”
Source:  2009 Annual Report, Shareholder Letter, p. 4.
2.2 “On 7 July 2008, the Group sold 24.8% of Alcon outstanding 
capital to Novartis for a total amount of USD 10.4 billion, resulting in 
a profit on disposal of CHF 9208 million and in an increase of non-

controlling interests of CHF 1537 million. The agreement further 
included the option for Novartis to acquire Nestlé’s remaining share -
holding in Alcon at a price of USD 181.– per share from January 2010

Application: Projecting Future Financial Performance 685
until July 2011. During the same period, Nestlé had the option to 
sell its remaining shareholding in Alcon to Novartis at the lower of 
either the call price of USD 181.– per share or the average share price 
during the week preceding the exercise plus a premium of 20.5%. On 4 
January 2010, Novartis exercised its call option to acquire the remain -
ing 52% shareholding from Nestlé at a price of USD 181.– per share. 
The transaction is now pending regulatory approval which can be 
expected during the course of 2010. As IFRS 5 criteria were met on 31 
December 2009, Alcon’s related assets and liabilities are classified as 
a disposal group in Assets held for sale and Liabilities directly associ -
ated with assets held for sale. Moreover, Alcon operations are dis -
closed as discontinued operations in the 2009 Consolidated Financial 
Statements. The results of Alcon discontinued operations are disclosed 
separately in the income statement. ”

Source:  2009 Financial Statements, note 25
2.3 Excerpt from Nestlé’s consolidated income statement for the year 
ended 31 December 2009:
(CHF millions)
2009 2008
Sales
Continuing operations 100,579 103,086
Discontinued operations 7,039 6,822
Total 107,618 109,908
EBIT (earnings before interest, taxes, restruc -
turing and impairments)
Continuing operations 13,222 13,240
Discontinued operations 2,477 2,436
Total 15,699 15,676
Profit for the year
Continuing operations 9,551 7,656
Discontinued operations 2,242 11,395
Total 11,793 19,051
Source:  2009 Financial Statements.
Discussion of 1.1
This item relates to one-  time restructuring charges aimed at eliminating dupli -
cation between the pre-  acquisition operations of the two companies (InBev and 
Anheuser-  Busch). The restructuring charges themselves are not directly relevant 
in forecasting the future net income of the company. If the restructuring suc -

cessfully reduced the company’s cost base, however, the combined companies’ 
expenses in the future are likely to be less than the sum of the two individual 
companies’ expenses. Also, if the cost base was successfully reduced, the profit

Reading 32 ■ Financial Statement Analysis: Applications 686
margin for the combined company is likely to be higher than a profit margin 
calculated as the sum of the individual companies’ profits divided by the sum 
of the individual companies’ sales revenues.
Discussion of 1.2
Gains on sales of businesses and assets that result in exceptional income are not 
a core part of a company’s business. This item should typically not be viewed 
as an ongoing source of earnings and should not, therefore, be a component of 
forecasts of net income. Additionally, any portion of the company’s past income 
that had been generated by the businesses sold should be excluded from fore -
casted net income.
Discussion of 2.1
These disclosures pertain to Nestlé’s total USD40  billion return on the 
USD280 million investment in Alcon over 33 years (between 1977 and 2010). The 
information is not directly relevant to forecasting future net income. Although

forecasts of net income must exclude the income from the divested business, 
information about the amount of that income is disclosed elsewhere.
Discussion of 2.2
Gains on sales of businesses and assets that result in exceptional income are 
not a core part of a company’s business, so neither the CHF9,208 million gain 
in 2008 nor any further gains on the transaction should be included in ongoing, 
long-  term forecasts. An analyst can, however, use the disclosed information about 
the sale price and information about the net book value of the investment to 
estimate the gain that will be reported in 2010 net income. In addition, results 
of discontinued items should not be included when assessing past performance 
or when forecasting future net income. As noted, the results of the discontinued 
items are shown separately on the income statement, as shown in excerpt 2.3.
Discussion of 2.3
Results of discontinued items should not be included when assessing past per -

formance or when forecasting future net income. For example, the company’s 
EBIT margin (EBIT/sales) for continuing operations for 2009 of 13 percent should 
be included in an analysis (not the 15 percent for the combined continuing and 
discontinued operations).
In general, when earnings projections are used as a foundation for market-  based 
valuations, an analyst will make appropriate allowance for transitory components of 
past earnings.
3.2 Projecting Multiple-  Period Performance
Projections of future financial performance over multiple periods are needed in valu -
ation models that estimate the value of a company or its equity by discounting future 
cash flows. The value of a company or its equity developed in this way can then be 
compared with its current market price as a basis for investment decisions.
Projections of future performance are also used for credit analysis. These projec -
tions are important in assessing a borrower’s ability to repay interest and principal of

debt obligations. Investment recommendations depend on the needs and objectives 
of the client and on an evaluation of the risk of the investment relative to its expected 
return—both of which are a function of the terms of the debt obligation itself as well 
as financial market conditions. Terms of the debt obligation include amount, interest 
rate, maturity, financial covenants, and collateral.

Application: Projecting Future Financial Performance 687
Example 5 presents an elementary illustration of net income and cash flow fore -
casting to illustrate a format for analysis and some basic principles. In Example 5, 
assumptions are shown first; then, the period-  by- period abbreviated financial statement 
resulting from the assumptions is shown.
Depending on the use of the forecast, an analyst may choose to compute further, 
more specific cash flow metrics. For example, free cash flow to equity, which is used in 
discounted cash flow approaches to equity valuation, can be estimated as net income 
adjusted for noncash items, minus investment in net working capital and in net fixed 
assets, plus net borrowing.
EXAMPLE 5   
Basic Example of Financial Forecasting
Assume a company is formed with $100 of equity capital, all of which is imme -
diately invested in working capital. Assumptions are as follows:
Dividends Non-  dividend-  paying
First-  year sales $100
Sales growth 10% per year

Cost of goods sold/Sales 20%
Operating expense/Sales 70%
Interest income rate 5%
Tax rate 30%
Working capital as percent of sales 90%
Based on this information, forecast the company’s net income and cash flow 
for five years.
Solution:
Exhibit  4 shows the net income forecasts in Line 7 and cash flow forecasts 
(“Change in cash”) in Line 18.
Exhibit 4   Basic Financial Forecasting
Time Period
0 1 2 3 4 5
(1) Sales 100.0 110.0 121.0 133.1 146.4
(2) Cost of goods sold (20.0) (22.0) (24.2) (26.6) (29.3)
(3) Operating expenses (70.0) (77.0) (84.7) (93.2) (102.5)
(4) Interest income 0.0 0.9 0.8 0.8 0.7
(5) Income before tax 10.0 11.9 12.9 14.1 15.3
(6) Taxes (3.0) (3.6) (3.9) (4.2) (4.6)
(7) Net income 7.0 8.3 9.0 9.9 10.7
(8) Cash/Borrowing 0.0 17.0 16.3 15.4 14.4 13.1
(9) Working capital (non-  cash) 100.0 90.0 99.0 108.9 119.8 131.8
(10) Total assets 100.0 107.0 115.3 124.3 134.2 144.9
(11) Liabilities 0.0 0.0 0.0 0.0 0.0 0.0

Reading 32 ■ Financial Statement Analysis: Applications 688
0 1 2 3 4 5
(12) Equity 100.0 107.0 115.3 124.3 134.2 144.9
(13) Total liabilities + Equity 100.0 107.0 115.3 124.3 134.2 144.9
(14) Net income 7.0 8.3 9.0 9.9 10.7
(15) Plus: Non-  cash items 0.0 0.0 0.0 0.0 0.0
(16) Less: Investment in working capital –10.0 9.0 9.9 10.9 12.0
(17) Less: Investment in fixed capital 0.0 0.0 0.0 0.0 0.0
(18) Change in cash 17.0 –0.7 –0.9 –1.0 –1.3
(19) Beginning cash 0.0 17.0 16.3 15.4 14.4
(20) Ending cash 17.0 16.3 15.4 14.4 13.1
Exhibit 4 indicates that at time 0, the company is formed with $100 of equity 
capital (Line 12). All of the company’s capital is assumed to be immediately 
invested in working capital (Line 9). In future periods, because it is assumed 
that no dividends are paid, book equity increases each year by the amount of net 
income (Line 14). Future periods’ required working capital (Line 9) is assumed

to be 90 percent of annual sales (Line 1). Sales are assumed to be $100 in the 
first period and to grow at a constant rate of 10 percent per year (Line 1). The 
cost of goods sold is assumed to be constant at 20 percent of sales (Line 2), so 
the gross profit margin is 80 percent. Operating expenses are assumed to be 
70 percent of sales each year (Line 3). Interest income (Line 4) is calculated as 
5 percent of the beginning balance of cash/borrowing or the ending balance of 
the previous period (Line 8) and is an income item when there is a cash balance, 
as in this example. (If available cash is inadequate to cover required cash outflows, 
the shortfall is presumed to be covered by borrowing. This borrowing would be 
shown as a negative balance on Line 8 and an associated interest expense on 
Line 4. Alternatively, a forecast can be presented with separate lines for cash 
and borrowing.) Taxes of 30 percent are deducted to obtain net income (Line 7).

To calculate each period’s cash flow, begin with net income (Line 7 = Line 14), 
add back any noncash items, such as depreciation (Line 15), deduct investment 
in working capital in the period or change in working capital over the period 
(Line 16), and deduct investment in fixed capital in the period (Line 17).6 In this 
simple example, we are assuming that the company does not invest in any fixed 
capital (long-  term assets) but, rather, rents furnished office space. Therefore, 
there is no depreciation and noncash items are zero. Each period’s change in 
cash (Line 18) is added to the beginning cash balance (Line 19) to obtain the 
ending cash balance (Line 20 = Line 8).Exhibit 4   (Continued)
6 Working capital represents funds that must be invested in the daily operations of a business to, for 
example, carry inventory and accounts receivable. The term “investment” in this context means “addition

to” or “increase in. ” The “investment in fixed capital” is also referred to as “capital expenditure” (“capex”).

Application: Projecting Future Financial Performance 689
Example 5 is simplified to demonstrate some principles of forecasting. In practice, 
each aspect of a forecast presents a range of challenges. Sales forecasts may be very 
detailed, with separate forecasts for each year of each product line, each geographi -
cal, and/or each business segment. Sales forecasts may be based on past results (for 
relatively stable businesses), management forecasts, industry studies, and/or macro -
economic forecasts. Similarly, gross profit margins may be based on past results or 
forecasted relationships and may be detailed. Expenses other than cost of goods sold 
may be broken down into more detailed line items, each of which may be forecasted 
on the basis of its relationship with sales (if variable) or on the basis of its historical 
levels. Working capital requirements may be estimated as a proportion of the amount

of sales (as in Example 5) or the change in sales or as a compilation of specific forecasts 
for inventory, receivables, and payables. Most forecasts will involve some investment 
in fixed assets, in which case, depreciation amounts affect taxable income and net 
income but not cash flow. Example 5 makes the simplifying assumption that interest 
is paid on the beginning-  of- year cash balance.
Example 5 develops a series of point estimates for future net income and cash flow. 
In practice, forecasting generally includes an analysis of the risk in forecasts—in this 
case, an assessment of the impact on income and cash flow if the realized values of 
variables differ significantly from the assumptions used in the base case or if actual 
sales are much different from forecasts. Quantifying the risk in forecasts requires an 
analysis of the economics of the company’s businesses and expense structure and 
the potential impact of events affecting the company, the industry, and the economy

in general. When that investigation is completed, the analyst can use scenario anal -
ysis or Monte Carlo simulation to assess risk. Scenario analysis involves specifying 
assumptions that differ from those used as the base-  case assumptions. In Example 5, 
the projections of net income and cash flow could be recast in a more pessimistic 
scenario, with assumptions changed to reflect slower sales growth and higher costs. 
A Monte Carlo simulation involves specifying probability distributions of values for 
variables and random sampling from those distributions. In the analysis in Example 5, 
the projections would be repeatedly recast with the selected values for the drivers of 
net income and cash flow, thus permitting the analyst to evaluate a range of possible 
results and the probability of simulating the possible actual outcomes.
An understanding of financial statements and ratios can enable an analyst to 
make more detailed projections of income statement, balance sheet, and cash flow

statement items. For example, an analyst may collect information on normal inventory 
and receivables turnover and use this information to forecast accounts receivable, 
inventory, and cash flows based on sales projections rather than use a composite 
working capital investment assumption, as in Example 5.
As the analyst makes detailed forecasts, he or she must ensure that the forecasts are 
consistent with each other. For instance, in Example 6, the analyst’s forecast concerning 
days of sales outstanding (which is an estimate of the average time to collect payment 
from sales made on credit) should flow from a model of the company that yields a 
forecast of the change in the average accounts receivable balance. Otherwise, predicted 
days of sales outstanding and accounts receivable will not be mutually consistent.
EXAMPLE 6   
Consistency of Forecasts
Brown Corporation had an average days-  of- sales-  outstanding (DSO) period of 19

days in 2009. An analyst thinks that Brown’s DSO will decline in 2010 (because of 
expected improvements in the company’s collections department) to match the 
industry average of 15 days. Total sales (all on credit) in 2009 were $300 million,

Reading 32 ■ Financial Statement Analysis: Applications 690
and Brown expects total sales (all on credit) to increase to $320 million in 2010. 
To achieve the lower DSO, the change in the average accounts receivable balance 
from 2009 to 2010 that must occur is closest  to:
A –$3.51 million.
B –$2.46 million.
C $2.46 million.
D $3.51 million.
Solution:
B is correct. The first step is to calculate accounts receivable turnover from the 
DSO collection period. Receivable turnover equals 365/19 (DSO) = 19.2 for 
2009 and 365/15 = 24.3 in 2010. Next, the analyst uses the fact that the average 
accounts receivable balance equals sales/receivable turnover to conclude that 
for 2009, average accounts receivable was $300,000,000/19.2 = $15,625,000 and 
for 2010, it must equal $320,000,000/24.3  = $13,168,724. The difference is a 
reduction in receivables of $2,456,276.
The next section illustrates the application of financial statement analysis to credit 
risk analysis.
APPLICATION: ASSESSING CREDIT RISK

Credit risk  is the risk of loss caused by a counterparty’s or debtor’s failure to make 
a promised payment. For example, credit risk with respect to a bond is the risk that 
the obligor (the issuer of the bond) will not be able to pay interest and/or principal 
according to the terms of the bond indenture (contract). Credit analysis  is the eval -
uation of credit risk. Credit analysis may relate to the credit risk of an obligor in a 
particular transaction or to an obligor’s overall creditworthiness.
In assessing an obligor’s overall creditworthiness, one general approach is credit 
scoring, a statistical analysis of the determinants of credit default. Credit analysis for 
typically involves projections of period-  by- period cash flows.
Whatever the techniques adopted, the analytical focus of credit analysis is on

debt-  paying ability. Unlike payments to equity investors, payments to debt investors 
are limited by the agreed contractual interest. If a company experiences financial 
success, its debt becomes less risky but its success does not increase the amount of 
payments to its debtholders. In contrast, if a company experiences financial distress, 
it may be unable to pay interest and principal on its debt obligations. Thus, credit 
analysis has a special concern with the sensitivity of debt-  paying ability to adverse 
events and economic conditions—cases in which the creditor’s promised returns 
may be most at risk. Because those returns are generally paid in cash, credit analysis 
usually focuses on cash flow rather than accrual income. Typically, credit analysts use 
return measures related to operating cash flow because it represents cash generated 
internally, which is available to pay creditors.
These themes are reflected in Example 7, which illustrates the application to an

industry group of four groups of quantitative factors in credit analysis: (1) scale and 
diversification, (2) tolerance for leverage, (3) operational efficiency, and (4) margin 
stability.4

Application: Assessing Credit Risk 691
“Scale and diversification” relate to a company’s sensitivity to adverse events, adverse 
economic conditions, and other factors—such as market leadership, purchasing power 
with suppliers, and access to capital markets—that may affect debt-  paying ability.
Financial policies, or “tolerance for leverage, ” relate to the obligor’s ability to service 
its indebtedness (i.e., make the promised payments on debt). In Example 7, various 
solvency ratios are used to measure tolerance for leverage. One set of tolerance-  for- 
leverage measures is based on retained cash flow (RCF). RCF is defined by Moody’s 
Investors Service as operating cash flow before working capital changes less divi -
dends. For example, under the assumption of no capital expenditures, a ratio of RCF 
to total debt of 0.5 indicates that the company may be able to pay off debt from cash 
flow retained in the business in approximately 1/0.5 = 2 years (at current levels of

RCF and debt); a ratio adjusting for capital expenditures is also used. Other factors 
include interest coverage ratios based on EBITDA, which are also chosen by Moody’s 
in specifying factors for operational efficiency and margin stability.
“Operational efficiency” as defined by Moody’s relates to cost structure: Companies 
with lower costs are better positioned to deal with financial stress.
“Margin stability” relates to the past volatility of profit margins: Higher stability 
should be associated with lower credit risk.
EXAMPLE 7   
Moody’s Evaluation of Quantifiable Rating Factors for a 
Specific Industry7
Moody’s considers a number of items when assigning credit ratings for the global 
aerospace and defense industry, including quantitative measures of three broad 
factors: size and scale; business profile, revenue sustainability, and efficiency; and 
financial leverage and flexibility. A company’s ratings for each of these factors

are weighted and aggregated in determining the overall credit rating assigned. 
The broad factors, the sub-  factors, and weightings are as follows:
Broad Factor Sub-  factorsSub-  factor 
Weighting 
(%)Broad 
Factor 
Weighting 
(%)
Size and scale Total revenue 10 25
Operating profit 15
Business profile, 
revenue sus -
tainability and 
efficiencyExpected business profile 
(e.g., prime contractor versus 
easily replaced small supplier)10 25
Revenue visibility (backlog/
revenue)5
Revenue protection (compet -
itive factors; e.g., barriers to 
entry)5
EBITA/Average assets 5
7 “Rating Methodology: Global Aerospace and Defense” (Moody’s, 2010), p. 21.

Reading 32 ■ Financial Statement Analysis: Applications 692
Weighting 
(%)Broad 
Factor 
Weighting 
(%)
and flexibilityDebt/EBITDA 10 50
Free cash flow/Net debt 10
Retained cash flow/Debt 10
Cash and marketable securi -
ties/ Debt10
EBIT/Interest 10
Total 100 100
1 What are some reasons why Moody’s may have selected these three broad 
factors as being important in assigning a credit rating in the aerospace 
and defense industry?
2 Why might financial leverage and flexibility be weighted so heavily?
Size and scale:
■●Larger size can strengthen negotiating position with customers and 
suppliers, leading to better contract terms and potential cost savings.
■●Larger scale typically indicates prior success.
■●Larger scale can enhance a company’s ability to manage and react to 
variable market conditions.
■●Larger scale often indicates greater geographical, product, and cus -
tomer diversification.

Business profile, revenue sustainability, and efficiency:
■●A business profile that provides some protection from competition, 
a sustainable flow of revenues as indicated by a strong order backlog, 
and better operating efficiency should contribute to higher and more 
sustainable cash flows.
Financial leverage and flexibility:
■●Strong financial policies should increase the likelihood of cash flows 
being sufficient to service debt.
The level of debt relative to earnings and cash flow is a critical factor in assess -
ing creditworthiness. The higher the current level of debt, the higher the risk 
of default.
A point to note regarding Example 7 is that the rating factors and the metrics used 
to represent each can vary by industry group. For example, for heavy manufacturing 
(manufacturing of the capital assets used in other manufacturing and production 
processes), Moody’s distinguishes order trends and quality as distinctive credit factors

affecting future revenues, factory load, and profitability patterns.
Analyses of a company’s historical and projected financial statements are an inte -
gral part of the credit evaluation process. As noted by Moody’s, financial statement 
information is an important source of information for the rating process:

Application: Assessing Credit Risk 693
Much of the information used in assessing performance for the sub-  factors 
is found in or calculated using the company’s financial statements; others are 
derived from observations or estimates by the analysts. . . . Moody’s ratings 
are forward-  looking and incorporate our expectations for future financial 
and operating performance. We use both historical and projected financial 
results in the rating process. Historical results help us understand patterns 
and trends for a company’s performance as well as for peer comparison.8
As noted, Moody computes a variety of ratios in assessing creditworthiness. A 
comparison of a company’s ratios with the ratios of its peers is informative in evalu -
ating relative creditworthiness, as demonstrated in Example 8.
EXAMPLE 8   
Peer Comparison of Ratios
A credit analyst is assessing the efficiency and leverage of two aerospace com -
panies on the basis of certain sub-  factors identified by Moody’s. The analyst

collects the information from the companies’ annual reports and calculates the 
following ratios:9
Bombardier Inc. BAE Systems plc
EBITDA/Average assets 7.5% 10.1%
Debt/EBITDA 3.9 3.1
Retained cash flow to debt 6.1% 13.7%
Free cash flow to net debt –7.0% 7.7%
Based solely on the data given, which company is more likely to be assigned 
a higher credit rating, and why?
Solution:
The ratio comparisons are all in favor of BAE Systems plc. BAE has a higher 
level of EBITDA in relation to average assets, higher retained cash flow relative 
to debt, and higher free cash flow to net debt. BAE also has a lower level of 
debt relative to EBITDA. Based on the data given, therefore, BAE is likely to be 
assigned a higher credit rating.
Before calculating ratios such as those presented in Example 8, rating agencies 
make certain adjustments to reported financial statements, such as adjusting debt to 
include off-  balance-  sheet debt in a company’s total debt.10 We will describe in Section

6 some common adjustments.
Financial statement analysis, especially financial ratio analysis, can also be an 
important tool in selecting equity investments, as discussed in the next section.
8 Ibid., p. 7.
9 In calculating financial ratios (values not disclosed in the rating report), Moody’s makes various adjust -
ments to the financial data reported by companies in order to better reflect underlying obligations and/or 
to achieve greater comparability with other companies in the industry. The adjustments made in calculating 
ratios for this example do not necessarily correspond exactly to those calculated by Moody’s.
10 Ibid., p. 6.

Reading 32 ■ Financial Statement Analysis: Applications 694
APPLICATION: SCREENING FOR POTENTIAL EQUITY 
INVESTMENTS
Ratios constructed from financial statement data and market data are often used to 
screen for potential equity investments. Screening  is the application of a set of cri -
teria to reduce a set of potential investments to a smaller set having certain desired 
characteristics. Criteria involving financial ratios generally involve comparing one or 
more ratios with some pre-  specified target or cutoff values.
A security selection approach incorporating financial ratios may be applied whether 
the investor uses top-  down analysis or bottom-  up analysis. Top-  down analysis  involves 
identifying attractive geographical segments and/or industry segments, from which 
the investor chooses the most attractive investments. Bottom-  up analysis  involves 
selection of specific investments from all companies within a specified investment

universe. Regardless of the direction, screening for potential equity investments aims 
to identify companies that meet specific criteria. An analysis of this type may be used 
as the basis for directly forming a portfolio, or it may be undertaken as a preliminary 
part of a more thorough analysis of potential investment targets.
Fundamental to this type of analysis are decisions about which metrics to use as 
screens, how many metrics to include, what values of those metrics to use as cutoff  
points, and what weighting to give each metric. Metrics may include not only finan -
cial ratios but also characteristics such as market capitalization or membership as a 
component security in a specified index. Exhibit 5 presents a hypothetical example 
of a simple stock screen based on the following criteria: a valuation ratio (P/E) less 
than a specified value, a solvency ratio measuring financial leverage (total debt/assets)

not exceeding a specified value, positive net income, and dividend yield (dividends 
per share divided by price per share) greater than a specified value. Exhibit 5 shows 
the results of applying the screen in August 2010 to a set of 5,187 US companies with 
market capitalization greater than $100 million, which compose a hypothetical equity 
manager’s investment universe.
Exhibit 5   Example of a Stock Screen
Stocks Meeting Criterion
Criterion Number Percent of Total
P/E <15 1,471 28.36%
Total debt/Assets ≤ 0.5 880 16.97%
Net income/Sales > 0 2,907 56.04%
Dividend yield > 0.5% 1,571 30.29%
Meeting all four criteria simultaneously 101 1.95%
Source for data:  http://google.com/finance/.
Several points about the screen in Exhibit  5 are consistent with many screens 
used in practice:
■■Some criteria serve as checks on the results from applying other criteria. In 
this hypothetical example, the first criterion selects stocks that appear relatively

cheaply valued. The stocks might be cheap for a good reason, however, such as 
poor profitability or excessive financial leverage. So, the requirement for net 
income to be positive serves as a check on profitability, and the limitation on 5

Application: Screening for Potential Equity Investments 695
financial leverage serves as a check on financial risk. Of course, financial ratios 
or other statistics cannot generally control for exposure to certain other types of 
risk (e.g., risk related to regulatory developments or technological innovation).
■■If all the criteria were completely independent of each other, the set of stocks 
meeting all four criteria would be 42, equal to 5,187 times 0.82 percent—the 
product of the fraction of stocks satisfying the four criteria individually (i.e., 
0.2836 × 0.1697 × 0.5604 × 0.3029 = 0.0082, or 0.82 percent). As the screen 
illustrates, criteria are often not independent, and the result is that more 
securities pass the screening than if criteria were independent. In this example, 
101 (or 1.95 percent) of the securities pass all four screens simultaneously. For 
an example of the lack of independence, we note that dividend-  paying status

is probably positively correlated with the ability to generate positive earnings 
and the value of the third criterion. If stocks that pass one test tend to also pass 
another, few are eliminated after the application of the second test.
■■The results of screens can sometimes be relatively concentrated in a subset of 
the sectors represented in the benchmark. The financial leverage criterion in 
Exhibit 5 would exclude banking stocks, for example. What constitutes a high 
or low value of a measure of a financial characteristic can be sensitive to the 
industry in which a company operates.
Screens can be used by both growth investors  (focused on investing in high-  
earnings-  growth companies), value investors  (focused on paying a relatively low share 
price in relation to earnings or assets per share), and market-  oriented investors  (an 
intermediate grouping of investors whose investment disciplines cannot be clearly

categorized as value or growth). Growth screens would typically feature criteria related 
to earnings growth and/or momentum. Value screens, as a rule, feature criteria setting 
upper limits for the value of one or more valuation ratios. Market-  oriented screens 
would not strongly emphasize valuation or growth criteria. The use of screens involving 
financial ratios may be most common among value investors.
Many studies have assessed the most effective items of accounting information for 
screening equity investments. Some research suggests that certain items of accounting 
information can help explain (and potentially predict) market returns (e.g., Chan et 
al. 1991; Lev and Thiagarajan 1993; Lakonishok et al. 1994; Davis 1994; Abarbanell 
and Bushee 1998). Representative of such investigations is Piotroski (2000), whose 
screen uses nine accounting-  based fundamentals that aim to identify financially strong 
and profitable companies among those with high book value/market value ratios. For

example, the profitability measures relate to whether the company reported positive 
net income, positive cash flow, and an increase in return on assets (ROA).
An analyst may want to evaluate how a portfolio based on a particular screen 
would have performed historically. For this purpose, the analyst uses a process known 
as “back-  testing. ” Back-  testing  applies the portfolio selection rules to historical data 
and calculates what returns would have been earned if a particular strategy had been 
used. The relevance of back-  testing to investment success in practice, however, may 
be limited. Haugen and Baker (1996) described some of these limitations:
■■Survivorship bias: If the database used in back-  testing eliminates companies 
that cease to exist because of a bankruptcy or merger, then the remaining com -
panies collectively will appear to have performed better.

Reading 32 ■ Financial Statement Analysis: Applications 696
■■Look-  ahead bias: If a database includes financial data updated for restate -
ments (where companies have restated previously issued financial statements 
to correct errors or reflect changes in accounting principles),11 then there is a 
mismatch between what investors would have actually known at the time of the 
investment decision and the information used in the back-  testing.
■■Data-  snooping bias: If researchers build a model on the basis of previous 
researchers’ findings, then use the same database to test that model, they are 
not actually testing the model’s predictive ability. When each step is backward 
looking, the same rules may or may not produce similar results in the future. 
The predictive ability of the model’s rules can validly be tested only by using 
future data. One academic study has argued that the apparent ability of value

strategies to generate excess returns is largely explainable as the result of collec -
tive data snooping (Conrad, Cooper, and Kaul, 2003).
EXAMPLE 9   
Ratio-  Based Screening for Potential Equity Investments
Below are two alternative strategies under consideration by an investment firm:
Strategy A : Invest in stocks that are components of a global equity index, 
have a ROE above the median ROE of all stocks in the index, and have a 
P/E less than the median P/E.
Strategy B : Invest in stocks that are components of a broad-  based US 
equity index, have a ratio of price to operating cash flow in the lowest 
quartile of companies in the index, and have shown increases in sales for 
at least the past three years.
Both strategies were developed with the use of back-  testing.
1 How would you characterize the two strategies?
2 What concerns might you have about using such strategies?
Strategy A appears to aim for global diversification and combines a requirement

for high relative profitability with a traditional measure of value (low P/E). 
Strategy B focuses on both large and small companies in a single market and 
apparently aims to identify companies that are growing and have a lower price 
multiple based on cash flow from operations.
The use of any approach to investment decisions depends on the objectives and 
risk profile of the investor. With that crucial consideration in mind, we note that 
ratio-  based benchmarks may be an efficient way to screen for potential equity 
investments. In screening, however, many questions arise.
First, unintentional selections can be made if criteria are not specified care -
fully. For example, Strategy A might unintentionally select a loss-  making com -
pany with negative shareholders’ equity because negative net income divided by 
negative shareholders’ equity arithmetically results in a positive ROE. Strategy 
B might unintentionally select a company with negative operating cash flow

11 The US Government Accounting Office (2002) reported 919 restatements by 834 public companies 
from January 1997 to June 2002. The Wall Street Journal  has reported that the number of restatements 
increased from 613 in 2004 to 1,195 in 2005 ( Wall Street Journal , 2006).

Analyst Adjustments to Reported Financials 697
because price to operating cash flow will be negative and thus very low in the 
ranking. In both cases, the analyst can add additional screening criteria to avoid 
unintentional selections; these additional criteria could include requiring pos -
itive shareholders’ equity in Strategy A and requiring positive operating cash 
flow in Strategy B.
Second, the inputs to ratio analysis are derived from financial statements, 
and companies may differ in the financial standards they apply (e.g., IFRS ver -
sus US GAAP), the specific accounting method(s) they choose within those 
allowed by the reporting standards, and/or the estimates made in applying an 
accounting method.
Third, back-  testing may not provide a reliable indication of future performance 
because of survivorship bias, look-  ahead bias, or data-  snooping bias. Also, as 
suggested by finance theory and by common sense, the past is not necessarily 
indicative of the future.

Fourth, implementation decisions can dramatically affect returns. For exam -
ple, decisions about frequency and timing of portfolio re-  evaluation and changes 
affect transaction costs and taxes paid out of the portfolio.
ANALYST ADJUSTMENTS TO REPORTED FINANCIALS
When comparing companies that use different accounting methods or estimate key 
accounting inputs in different ways, analysts frequently adjust a company’s financials. 
In this section, we first provide a framework for considering potential analyst adjust -
ments to facilitate such comparisons and then provide examples of such adjustments. 
In practice, required adjustments vary widely. The examples presented here are not 
intended to be comprehensive but, rather, to illustrate the use of adjustments to 
facilitate a meaningful comparison.
6.1 A Framework for Analyst Adjustments
In this discussion of potential analyst adjustments to a company’s financial statements,

we use a framework focused on the balance sheet . Because the financial statements 
are interrelated, however, adjustments to items reported on one statement may also 
be reflected in adjustments to items on another financial statement. For example, an 
analyst adjustment to inventory on the balance sheet affects cost of goods sold on the 
income statement (and thus also affects net income and, subsequently, the retained 
earnings account on the balance sheet).
Regardless of the particular order in which an analyst considers the items that may 
require adjustment for comparability, the following aspects are appropriate:
■■Importance  (materiality ). Is an adjustment to this item likely to affect the 
conclusions? In other words, does it matter? For example, in an industry where 
companies require minimal inventory, does it matter that two companies use 
different inventory accounting methods?
■■Body of standards . Is there a difference in the body of standards being used

(US GAAP versus IFRS)? If so, in which areas is the difference likely to affect a 
comparison?
■■Methods . Is there a difference in accounting methods used by the companies 
being compared?
■■Estimates . Is there a difference in important estimates used by the companies 
being compared?6

Reading 32 ■ Financial Statement Analysis: Applications 698
The following sections illustrate analyst adjustments—first, those relating to the asset 
side of the balance sheet and then those relating to the liability side.
6.2 Analyst Adjustments Related to Investments
Accounting for investments in the debt and equity securities of other companies 
(other than investments accounted for under the equity method and investments in 
consolidated subsidiaries) depends on management’s intention (i.e., whether to actively 
trade the securities, make them available for sale, or in the case of debt securities, hold 
them to maturity). When securities are classified as “financial assets measured at fair 
value through profit or loss” (similar to “trading” securities in US GAAP), unrealized 
gains and losses are reported in the income statement. When securities are classified 
as “financial assets measured at fair value through other comprehensive income”

(similar to “available-  for- sale” securities in US GAAP), unrealized gains and losses are 
not reported in the income statement and, instead, are recognized in equity. If two 
otherwise comparable companies have significant differences in the classification of 
investments, analyst adjustments may be useful to facilitate comparison.
6.3 Analyst Adjustments Related to Inventory
With inventory, adjustments may be required for different accounting methods. As 
described in previous readings, a company’s decision about inventory method will 
affect the value of inventory shown on the balance sheet as well as the value of inven -
tory that is sold (cost of goods sold). If a company not reporting under IFRS12 uses 
LIFO (last-  in, first-  out) and another uses FIFO (first-  in, first-  out), comparability of 
the financial results of the two companies will suffer. Companies that use the LIFO 
method, must also, however, disclose the value of their inventory under the FIFO

method. To recast inventory values for a company using LIFO reporting on a FIFO 
basis, the analyst adds the ending balance of the LIFO reserve to the ending value of 
inventory under LIFO accounting. To adjust cost of goods sold to a FIFO basis, the 
analyst subtracts the change in the LIFO reserve from the reported cost of goods sold 
under LIFO accounting. Example 10 illustrates the use of a disclosure of the value 
of inventory under the FIFO method to make a more consistent comparison of the 
current ratios of two companies reporting in different methods.
EXAMPLE 10   
Adjustment for a Company Using LIFO Accounting for 
An analyst is comparing the financial performance of Carpenter Technology 
Corporation (CRS), a US company operating in the specialty metals industry, 
with the financial performance of a similar company that uses IFRS for report -
ing. Under IFRS, this company uses the FIFO method of inventory accounting.

Therefore, the analyst must convert results to a comparable basis. Exhibit  6 
provides balance sheet information on CRS.
12 IAS No. 2 does not permit the use of LIFO.

Analyst Adjustments to Reported Financials 699
Exhibit 6   Data for Carpenter Technology Corporation
30 June
2010 2009
Total current assets 820.2 749.7
Total current liabilities 218.1 198.5
NOTE 6. INVENTORIES
Inventories consist of the following ($ millions):
30 June
2010 2009
Raw materials $30.7 $29.5
Work in process 109.1 90.8
Finished goods 63.8 65.1
$203.6 $185.4
If the first-  in, first-  out method of inventory had been used instead of the LIFO method, 
inventories would have been $331.8 and $305.8 million higher as of June 30, 2010 and 2009, 
Source:  10- K for Carpenter Technology Corporation for the year ended 30 June 2010.
1 Based on the information in Exhibit 6, calculate CRS’s current ratio under 
FIFO and LIFO for 2009 and 2010.
2 CRS makes the following disclosure in the risk section of its MD&A. 
Assuming an effective tax rate of 35 percent, estimate the impact on CRS’s 
“We value most of our inventory using the LIFO method, which

could be repealed resulting in adverse affects on our cash flows 
and financial condition.
The cost of our inventories is primarily determined using the 
Last-  In First-  Out (“LIFO”) method. Under the LIFO inventory val -
uation method, changes in the cost of raw materials and production 
activities are recognized in cost of sales in the current period even 
though these materials and other costs may have been incurred at sig -
nificantly different values due to the length of time of our production 
cycle. Generally in a period of rising prices, LIFO recognizes higher 
costs of goods sold, which both reduces current income and assigns 
a lower value to the year-  end inventory. Recent proposals have been 
initiated aimed at repealing the election to use the LIFO method 
for income tax purposes. According to these proposals, generally 
taxpayers that currently use the LIFO method would be required to 
revalue their LIFO inventory to its first-  in, first-  out (“FIFO”) value.

As of June 30, 2010, if the FIFO method of inventory had been used 
instead of the LIFO method, our inventories would have been about 
$332 million higher. This increase in inventory would result in a one 
time increase in taxable income which would be taken into account

Reading 32 ■ Financial Statement Analysis: Applications 700
ratably over the first taxable year and the following several taxable 
years. The repeal of LIFO could result in a substantial tax liability 
which could adversely impact our cash flows and financial condition. ”
Source : 10-  K for Carpenter Technology Corporation for the year ended 30 
June 2010.
3 CRS reported cash flow from operations of $115.2 million for the year 
ended 30 June 2010. In comparison with the company’s operating cash 
flow, how significant is the additional potential tax liability?
The calculations of CRS’s current ratio (current assets divided by current lia -
bilities) are as follows:
2010 2009
I. Current ratio (unadjusted)
Total current assets $820.2 $749.7
Total current liabilities $218.1 $198.5
Current ratio (unadjusted) 3.8 3.8
II. Current ratio (adjusted)
Adjust inventory to FIFO, add: 331.8 305.8
Total current assets (adjusted) $1,152 $1,056

Current ratio (adjusted) 5.3 5.3
To adjust the LIFO inventory to FIFO, add the excess amounts of FIFO 
cost over LIFO cost to LIFO inventory and increase current assets by an equal 
amount. The effect of adjusting inventory on the current ratio is to increase the 
current ratio from 3.8 to 5.3 in both 2009 and 2010. CRS has greater liquidity 
according to the adjusted current ratio.
Assuming an effective tax rate of 35 percent, we find the total increase in CRS’s 
tax liability to be $116.1 million (0.35 × $331.8 million).
The additional tax liability would be greater than the entire amount of the com -
pany’s cash flow from operations of $115.2 million; the additional tax liability 
would be apportioned, however, over several years.
In summary, the information disclosed by companies that use LIFO allows an ana -

lyst to calculate the value of the company’s inventory as if the company were using the 
FIFO method. In Example 10, the portion of inventory valued under the LIFO method 
was a relatively small portion of total inventory; the LIFO reserve (excess of FIFO cost 
over LIFO) was also relatively small. If the LIFO method is used for a substantial part 
of a company’s inventory and the LIFO reserve is large relative to reported inventory, 
however, the adjustment to a FIFO basis can be important for comparison of the 
LIFO-  reporting company with a company that uses the FIFO method of inventory 
valuation. Example 11 illustrates a case in which such an adjustment would have a 
major impact on an analyst’s conclusions.

Analyst Adjustments to Reported Financials 701
EXAMPLE 11   
Analyst Adjustment to Inventory Value for Comparability 
in a Current Ratio Comparison
Company A reports under IFRS and uses the FIFO method of inventory account -
ing. Company B reports under US GAAP and uses the LIFO method. Exhibit 7 
gives data pertaining to current assets, LIFO reserves, and current liabilities of 
these companies.
Exhibit 7   Data for Companies Accounting for Inventory on Different 
Bases
Company A  
(FIFO)Company B  
(LIFO)
Current assets (includes inventory) $ 300,000 $ 80,000
LIFO reserve NA $ 20,000
Current liabilities $ 150,000 $ 45,000
NA = not applicable.
Based on the data given in Exhibit 7, compare the liquidity of the two com -
panies as measured by the current ratio.
Solution:
Company A’s current ratio is 2.0. Based on unadjusted balance sheet data, 
Company B’s current ratio is 1.78. Company A’s higher current ratio indicates 
that Company A appears to be more liquid than Company B; however, the use

of unadjusted data for Company B is not appropriate for making comparisons 
with Company A.
After adjusting Company B’s inventory to a comparable basis (i.e., to a FIFO 
basis), the conclusion changes. The following table summarizes the results when 
Company B’s inventory is left on a LIFO basis and when it is placed on a FIFO 
basis for comparability with Company A.
Company B
Company A  
(FIFO)Unadjusted  
(LIFO basis)Adjusted  
(FIFO basis)
Current assets (includes 
inventory)$ 300,000 $ 80,000 $ 100,000
Current liabilities $ 150,000 $ 45,000 $ 45,000
Current ratio 2.00 1.78 2.22
When both companies’ inventories are stated on a FIFO basis, Company B 
appears to be the more liquid, as indicated by its current ratio of 2.22 versus 
Company A’s ratio of 2.00.
The adjustment to place Company B’s inventory on a FIFO basis was signifi -
cant because Company B was assumed to use LIFO for its entire inventory and 
its inventory reserve was $20,000/$80,000 = 0.25, or 25 percent of its reported 

Reading 32 ■ Financial Statement Analysis: Applications 702
As mentioned earlier, an analyst can also adjust the cost of goods sold for a com -
pany using LIFO to a FIFO basis by subtracting the change in the amount of the LIFO 
reserve from cost of goods sold. Such an adjustment would be appropriate for making 
profitability comparisons with a company reporting on a FIFO basis and is important 
to make when the impact of the adjustment would be material.
6.4 Analyst Adjustments Related to Property, Plant, and 
Equipment
Management generally has considerable discretion in determination of depreciation 
expense. Depreciation expense affects the values of reported net income and reported 
net fixed assets. Analysts often consider management’s choices related to depreciation 
as a qualitative factor in evaluating the quality of a company’s financial reporting, 
and in some cases, analysts may adjust reported depreciation expense for a specific 
analytical purpose.

The amount of depreciation expense depends on both the accounting method and 
the estimates used in the calculations. Companies can use the straight-  line method, 
an accelerated method, or a usage method to depreciate fixed assets (other than land). 
The straight-  line method reports an equal amount of depreciation expense each period, 
and the expense is computed as the depreciable cost divided by the estimated useful 
life of the asset (when acquired, an asset’s depreciable cost is calculated as its total 
cost minus its estimated salvage value). Accelerated methods depreciate the asset 
more quickly; they apportion a greater amount of the depreciable cost to depreciation 
expense in the earlier periods. Usage-  based methods depreciate an asset in proportion 
to its usage. In addition to selecting a depreciation method, companies must estimate 
an asset’s salvage value and useful life to compute depreciation.

Disclosures required for depreciation often do not facilitate specific adjustments, so 
comparisons of companies concerning their decisions in depreciating assets are often 
qualitative and general. The accounts that are associated with depreciation include the 
balance sheet accounts for gross property, plant, and equipment (PPE) and accumu -
lated depreciation; the income statement amount for depreciation expense; and the 
statement of cash flows disclosure of capital expenditure (capex) and asset disposals. 
The relationships among these items can reveal various pieces of information. Note, 
however, that PPE typically includes a mix of assets with different depreciable lives 
and salvage values, so the items in the following list reflect general relationships in 
the total pool of assets.
■■Accumulated depreciation divided by gross PPE, from the balance sheet, sug -
gests how much of the useful life of the company’s overall asset base has passed.

■■Accumulated depreciation divided by depreciation expense suggests how many 
years’ worth of depreciation expense have already been recognized (i.e., the 
average age of the asset base).
■■Net PPE (net of accumulated depreciation) divided by depreciation expense is 
an approximate indicator of how many years of useful life remain for the com -
pany’s overall asset base.
■■Gross PPE divided by depreciation expense suggests the average life of the 
assets at installation.
■■Capex divided by the sum of gross PPE plus capex can suggest what percentage 
of the asset base is being renewed through new capital investment.
■■Capex in relation to asset disposal provides information on growth of the asset 
base.

Analyst Adjustments to Reported Financials 703
As Example 12 shows, these relationships can be evaluated for companies in an 
industry to suggest differences in their strategies for asset utilization or areas for 
further investigation.
EXAMPLE 12   
Differences in Depreciation
An analyst is evaluating the financial statements of two companies in the same 
industry. The companies have similar strategies with respect to the use of equip -
ment in manufacturing their products. The following information is provided 
(amounts in millions):
Net PPE $1,200 $750
Depreciation expense $120 $50
1 Based on the information given, estimate the average remaining useful 
lives of the asset bases of Company A and Company B.
2 Suppose that, based on a physical inspection of the companies’ plants and 
other industry information, the analyst believes that the actual remaining 
useful lives of Company A’s and Company B’s assets are roughly equal at

10 years. Based only on the facts given, what might the analyst conclude 
about Company B’s reported net income?
The estimated average remaining useful life of Company A’s asset base is 10 
years (calculated as net PPE divided by depreciation expense, or $1,200/$120 = 
10 years). For Company B, the average remaining useful life of the asset base 
appears to be far longer, 15 years ($750/$50).
If 10 years were used to calculate Company B’s depreciation expense, the expense 
would be $75 million (i.e., $25 million higher than reported) and higher depre -
ciation expense would decrease net income. The analyst might conclude that 
Company B’s reported net income reflects relatively more aggressive accounting 
estimates than estimates reflected in Company A’s reported net income.
6.5 Analyst Adjustments Related to Goodwill
Goodwill arises when one company purchases another for a price that exceeds the

fair value of the net identifiable assets acquired. Net identifiable assets include current 
assets, fixed assets, and certain intangible assets that have value and meet recognition 
criteria under accounting standards. A broad range of intangible assets might require 
valuation in the context of a business combination—for example, brands, technology, 
and customer lists. Goodwill is recorded as an asset and essentially represents the 
difference between the purchase price and the net identifiable assets. For example, 
assume ParentCo purchases TargetCo for a purchase price of $400 million and the fair 
value of TargetCo’s identifiable assets is $300 million (which includes the fair values of 
current assets, fixed assets, and a recognized brand). ParentCo will record total assets 
of $400  million consisting of $300  million in identifiable assets (including the fair

Reading 32 ■ Financial Statement Analysis: Applications 704
value of the brand) and $100 million of goodwill. The goodwill is tested annually for 
impairment and if the value of the goodwill is determined to be impaired, ParentCo will 
then reduce the amount of the asset and report a write-  off resulting from impairment.
One of the conceptual difficulties with goodwill arises in comparative financial 
statement analysis. Consider, for example, two hypothetical US companies, one of 
which has grown by making an acquisition and the other of which has grown inter -
nally. Assume that the economic value of the two companies is identical: Each has an 
identically valuable branded product, well-  trained workforce, and proprietary tech -
nology. The company that has grown by acquisition will have recorded the transaction 
to acquire the target company and its underlying net assets on the basis of the total 
consideration paid for the acquisition. The company that has grown internally will

have done so by incurring expenditures for advertising, staff training, and research, all 
of which are expensed as incurred under US GAAP . Given the immediate expensing, 
the value of the internally generated assets is not capitalized onto the balance sheet 
and is thus not directly reflected on the company’s balance sheet (revenues, income, 
and cash flows should reflect the benefits derived from the investment in the intangi -
ble assets). Ratios based on asset values and/or income, including profitability ratios 
(such as ROA) and market value to book value (MV/BV),13 will generally differ for the 
two companies because of differences in the accounting values of assets and income 
related to acquired intangibles and goodwill, although, by assumption, the economic 
value of the companies is identical.
EXAMPLE 13   
Ratio Comparisons for Goodwill
Miano Marseglia is an analyst who is evaluating the relative valuation of two

securities brokerage companies: TD Ameritrade Holding Corporation (AMTD) 
and the Charles Schwab Corporation (SCHW). As one part of an overall anal -
ysis, Marseglia would like to see how the two companies compare with each 
other and with the industry based on market value to book value. Because both 
companies are large players in the industry, Marseglia expects them to sell at a 
higher MV/BV than the industry median of 1.2. He collects the following data 
on the two companies.
SCHW AMTD
Market capitalization on January 2010 (mar -
ket price per share times the number of shares 
outstanding)$21,871 $11,525
Total shareholders’ equity as of most recent 
quarter$5,073 $3,551
Goodwill $528 $2,472
Other intangible assets $23 $1,225
Marseglia computes the MV/BV for the companies as follows:
SCHW $21,871/$5,073 = 4.3
AMTD $11,525/$3,551 = 3.2
13 MV/BV equals the total market value of the stock (the market capitalization) divided by total stock -

holders’ equity. It is also referred to as the price-  to- book ratio because it can also be calculated as price 
per share divided by stockholders’ equity per share.

Analyst Adjustments to Reported Financials 705
As expected, each company appears to be selling at a premium to the indus -
try average MV/BV of 1.2. The companies have similar MV/BVs (i.e., they are 
somewhat equally valued relative to the book value of shareholders’ equity), 
but based solely on MV/BV, AMTD appears to be a better value. Marseglia is 
concerned, however, because he notes that AMTD has significant amounts of 
goodwill and acquired intangible assets. He wonders what the relative value would 
be if the MV/BV were computed after adjusting book value, first, to remove 
goodwill and, second, to remove all intangible assets. Book value reduced by 
all intangible assets (including goodwill) is known as “tangible book value. ” The 
median price/tangible book value for the industry is 1.3.
1 Compute the MV/BV adjusted for goodwill and the price/tangible book 
value for each company.
2 Which company appears to be a better value based solely  on this data?

(Note that the MV/BV is only one part of a broader analysis. Much more 
evidence related to the valuations and the comparability of the companies 
would be required to reach a conclusion about whether one company is a 
better value.)
($ millions)
SCHW AMTD
Total stockholders’ equity $5,073 $3,551
Less: Goodwill $528 $2,472
Book value, adjusted $4,545 $1,079
Adjusted MV/BV 4.8 10.7
SCHW AMTD
Less: Other intangible assets $23 $1,225
Tangible book value $4,522 ($146)
MV/tangible book value 4.8 NM
NM = not meaningful.
After adjusting for goodwill, SCHW appears to be selling for a lower price relative 
to book value than does AMTD (4.8 versus 10.7). Both companies are selling 
at a premium to the industry, particularly AMTD, after adjusting for goodwill.
SCHW is also selling for a higher multiple than the industry (4.8 versus 1.3)

based on price/tangible book value. AMTD has a negative tangible book value 
and, therefore, its price/tangible book value is not meaningful. Based on this 
interpretation and based solely  on this information, Marseglia would conclude 
that AMTD is relatively more expensive than SCHW.

Reading 32 ■ Financial Statement Analysis: Applications 706
6.6 Analyst Adjustments Related to Off-  Balance-  Sheet 
Financing
A number of business activities give rise to obligations that, although they are eco -
nomically liabilities of a company, are not required to be reported on a company’s 
balance sheet. Including such off-  balance-  sheet obligations in a company’s liabilities 
can affect ratios and conclusions based on such ratios. In this section, we describe 
adjustments to financial statements related to one type of off-  balance-  sheet obliga -
tion, the operating lease. (Note that revised leasing standard IFRS 16 results in both 
operating and financing leases appearing on the lessee’s balance sheet. These standards 
are likely to change or even eliminate adjustments required for operating leases.)14
The rights of a lessee (the party that is leasing some asset) may be similar to 
the rights of an owner, but if the terms of the lease can be structured so it can be

accounted for as an operating lease, the lease is treated like a rental contract and 
neither the leased asset nor the associated liability is reported on the balance sheet.15 
The lessee simply records the periodic lease payment as a rental expense in its income 
statement. In contrast, when a company actually owns an asset, the asset is shown on 
the balance sheet, together with any corresponding liability, such as financing for the 
asset. Similarly, if a lease is accounted for as a capital lease—essentially equivalent 
to ownership—the leased asset and associated liability appear on the lessee’s balance 
sheet. Note that under IFRS 16, a company is required to account for most leases as 
capital leases, with both an asset and liability recorded on the balance sheet.
What is of concern to analysts is when a lease conveys to the lessee most of the 
benefits and risks of ownership but the lease is accounted for as an operating lease—

giving rise to off-  balance-  sheet financing. International accounting standard setters 
have stated that the entities should not avoid balance sheet recording of leases through 
artificial leasing structures.
A 2005 report by the US SEC on off-  balance-  sheet financing estimates that more 
than 63 percent of companies in the United States report having an operating lease. 
The SEC estimate of total future lease payments under operating leases was $1.2 tril -
lion over the remaining terms of the leases.
Because companies are required to disclose in their financial statements the 
amount and timing of lease payments, an analyst can use this information to answer 
the question: How would a company’s financial position look if operating lease obli -
gations were included in its total liabilities?
Exhibit 8 presents selected items from the balance sheet of AMR Corporation (the 
parent of American Airlines) and the text of the note from the financial statements

about the company’s leases. We use the information in this exhibit to illustrate analyst 
14 IFRS 16 [Leases] and FASB ASC Topic 842 [Leases] are effective 1 January 2019 and for fiscal years 
beginning after December 15, 2019, respectively.
15 A lessee classifies a lease as an operating lease if certain guidelines concerning the term of the lease, 
the present value of the lease payments, and the ownership of the asset at the end of the lease term are 
satisfied. Under US GAAP , FASB ASC 840-  10- 25 (Leases: Overall–Recognition)] specifies the criteria for 
classification.

Analyst Adjustments to Reported Financials 707
Exhibit 8   Lease Arrangements of AMR Corporation  
Selected Items from Balance Sheet  
2009 2008
    Total Assets $25,438 $25,175
Current maturities of long-  term debt $1,024 $1,845
Long-  term debt, less current maturities 9,984 8,423
Total long-  term debt 11,008 10,268
Current obligations under capital leases 90 107
Obligations under capital leases, less current 
obligations599 582
    Total long-  term debt and capital leases $11,697 $10,957
From Note 5. Leases
AMR's subsidiaries lease various types of equipment and property, primarily 
aircraft and airport facilities. The future minimum lease payments required 
under capital leases, together with the present value of such payments, and future 
minimum lease payments required under operating leases that have initial or 
remaining non-  cancelable lease terms in excess of one year as of December 31, 
2009, were (in millions):

Y ear Ending December 31, Capital Leases Operating Leases
2010 $181 $1,057
2011 184 1,032
2012 134 848
2013 119 755
2014 98 614
2015 and thereafter 436 5,021
$1,152 $9,327 (1)
Less amount representing interest 463
Present value of net minimum lease 
payments$689
(1) As of December  31, 2009, included in Accrued liabilities and Other liabilities and deferred 
credits on the accompanying consolidated balance sheet is approximately $1.2 billion relating to 
rent expense being recorded in advance of future operating lease payments.
Source:  AMR Corporation’s Form 10-  K for period ending 31 December 2009.
To evaluate the company’s solvency, we can calculate the debt-  to- assets ratio, 
defined as the ratio of total debt to total assets. When we include obligations under 
capital leases (amounting to $689 million in 2009), the debt-  to- assets ratio for 2009 
is 46.0 percent (total long-  term debt/total assets = $11,697/$25,438). The company’s

note on leases discloses a total of $9.3 billion of future payments for operating leases 
on an undiscounted basis. The note also indicates that of this amount, only $1.2 bil -
lion is shown on the balance sheet. To determine the impact of including operating 
lease obligations in total liabilities, we can calculate the present value of the future 
operating lease payments. Calculating the present value of these payments requires

Reading 32 ■ Financial Statement Analysis: Applications 708
a discount rate. We can estimate an appropriate discount rate from the information 
about the present value of the capital lease payments. Using the present value of the 
capital lease payments and the schedule of future payments, we can calculate the 
internal rate of return (i.e., the return that results in the discounted future payments 
equaling the present value). The internal rate of return from the capital lease informa -
tion can then be used as the discount rate to estimate the present value of the series 
of operating lease payments.
For AMR, the present value of the capital lease payments is $689 million. Exhibit 9 
shows different assumed streams of payments based on the information given in the 
note and illustrates the sensitivity of the analysis to assumptions about the timing of 
cash flows. Each assumed stream results in a different implied discount rate on the

lease or internal rate of return to the lease. Using the stream of payments shown in 
the note and assuming that all of the $436 million payments indicated for 2015 and 
thereafter are made in the year 2015 results in an internal rate of return of 15.04 percent. 
Based on the schedule of payments shown, a more reasonable assumption, however, 
is that the $436 million payments do not all occur in a single year. One approach to 
estimating the timing of these payments is to assume that the payments in 2015 and 
subsequent years equal the average annual payments in years 2010–2014 of $143 = 
($181 + $184 + $134 + $119 + $98)/5. Using this approach, we assume payments in 
2015 and the following three years that total the amount shown in the note for 2015 
and the internal rate of return of the capital lease is 13.90 percent. Given that lease 
payments have been generally declining over 2010–2015, another approach is to assume

that the amount of the lease payment after 2015 remains constant in subsequent years 
at an amount equal to the payment in 2014 until the total amount shown in the note 
for 2015 is reached. Using this assumption, we find the internal rate of return of the 
capital lease payments is 13.24 percent.16
Exhibit 9   Present Value of Operating Lease Payments Using a Discount Rate Derived from Present Value of 
Capital Lease Payments  
        Capital Lease     Operating Lease
Payments 
(as given 
in note)Payments 
Including 
Estimated Annual 
Payments for 2015 
and Thereafter  
(Through 2018)Payments Including 
(Through 2019)Payments 
As GivenPayments 
Including 
and Thereafter
Present value, given ($689) ($689) ($689)
2010 $181 $181 $181 $1,057 $1,057
2011 $184 $184 $184 $1,032 $1,032
2012 $134 $134 $134 $848 $848

16 If the term structure of the capital and operating leases can be assumed to be similar, an alternative, 
shortcut, way to estimate the present value of future operating lease payments that do not appear on the 
balance sheet is to assume that the relationship between the discounted and undiscounted operating lease 
payments is approximately the same as the relationship between the discounted and undiscounted capital 
lease payments. The discounted capital lease payments of $689 million as reported on the balance sheet are 
64.9 percent of the undiscounted noncurrent capital lease payments of $1,062 million ($1,152 million total 
minus $90 million current liabilities). Applying the same relationship to operating lease payments, we find 
that 64.9 percent of the undiscounted noncurrent operating lease payments of $8,127 million ($9,327 million 
total minus $1,200 million current) equals $5.3 billion, somewhat higher than the estimate of the present

value of future operating lease payments given in Exhibit 9 with a discount rate of 13.24 percent.

Analyst Adjustments to Reported Financials 709
Payments 
(as given 
Including 
Including 
2013 $119 $119 $119 $755 $755
2014 $98 $98 $98 $614 $614
2015 and thereafter $436 $143 $98 $5,021 $614
$143 $98 $614
$7 $98 $614
$44 $614
$614
$614
$614
$109
Internal rate of return 15.04% 13.90% 13.24%
Present value of operating lease payments with 15.04% discount rate $4,373
Present value of operating lease payments with 13.90% discount rate $4,575
Present value of operating lease payments with 13.24% discount rate $4,700
We developed discount rate estimates of 13.90 percent and 13.24 percent. Using 
a discount rate of 13.90 percent, the present value of future operating lease payments

would be roughly $4.6 billion, and using a discount rate of 13.24 percent, the present 
value would be around $4.7 billion. Because $1.2 billion of the amounts related to 
operating leases already appear on the balance sheet (as disclosed in the company’s 
lease note), the value of the future operating lease payments that do not appear on 
the balance sheet are estimated to be in the range of $4,575 million – $1,200 million 
= $3,375 million to $4,700 million – $1,200 million = $3,500 million. The lower the 
assumed discount rate, the higher the present value of the lease payments.
We now add the present value of the off-  balance-  sheet future operating lease pay -
ments to the company’s total assets and total debt. Making this adjustment increases 
the debt-  to- assets ratio to an amount between ($11,697 + $3,375)/($25,438 + $3,375) 
= 52.3 percent and ($11,697 + $3,500)/($25,438 + $3,500) = 52.5 percent. The discount

rates implied by the company’s capital lease structure are significantly higher, however, 
than yields on investment-  grade bonds as of the date of the example; therefore, an 
analyst might choose to examine the sensitivity of the lease obligation to alternative 
discount rates.Exhibit 9   (Continued)

Reading 32 ■ Financial Statement Analysis: Applications 710
EXAMPLE 14   
Analyst Adjustment to Debt for Operating Lease 
Payments
An analyst is evaluating the capital structure of two (hypothetical) companies, 
Koller Semiconductor and MacRae Manufacturing, as of the beginning of 2010. 
Koller Semiconductor makes somewhat less use of operating leases than MacRae 
Manufacturing. The analyst has the additional information in Exhibit 10.
Exhibit 10   
Koller  
SemiconductorMacRae  
Manufacturing
Total debt $1,200 $2,400
Total equity $2,000 $4,000
Average interest rate on debt 10% 8%
Lease payments on operating leases:
  2010 10 90
  2011 18 105
  2012 22 115
  2013 25 128
  2014 and thereafter 75 384
Based on the information given in Exhibit 10 and assuming no adjustment to 
equity, discuss how adjusting for operating leases affects the companies’ solvency 
on the basis of debt/debt-  plus-  equity. (Assume payments after 2013 occur at the

same rate as for 2013. For example, for Koller Semiconductor, the payments for 
2014 through 2016 would be assumed to be $25 each year.)
Solution:
Before the adjustment is made, the companies’ debt/debt-  plus-  equity are identi -
cal, both at 37.5 percent. To make the adjustment for operating leases, the first 
step is to calculate the present value of the operating lease payments. Assuming 
that payments after 2013 occur at the same rate as for 2013, the analyst finds 
Koller’s payment would be $25 in 2014, 2015, and 2016. The present value of $25 
discounted for five years at 10 percent is $15.52. MacRae’s payment is assumed 
to be $128 in each of 2014, 2015, and 2016. The present value of $128 discounted 
for five years at 8 percent is $87.11. Calculations for 2015 and 2016 are made in 
the same manner, resulting in the present values shown in Exhibit 11.
Exhibit 11   
Koller Semiconductor MacRae Manufacturing
2010 $9.09 $83.33
2011 $14.88 $90.02
2012 $16.53 $91.29
2013 $17.08 $94.08

Analyst Adjustments to Reported Financials 711
2015 $14.11 $80.66
2016 $12.83 $74.69
Total present value $100.04 $601.18
After the present value of capitalized lease obligations is added to total 
debt, MacRae Manufacturing’s debt/debt-  plus-  equity is significantly higher, at 
42.9 percent, than the debt/debt-  plus-  equity of Koller Semiconductor, as shown 
in Exhibit 12. The higher ratio reflects the impact of lease obligations on MacRae’s 
solvency, as measured by debt/debt-  plus-  equity.
Exhibit 12   
Before 
CapitalizingAfter 
CapitalizingBefore 
Capitalizing
Total debt $1,200 $1,300 $2,400 $3,001
Total equity $2,000 $2,000 $4,000 $4,000
Debt/(Debt + 
Equity)37.5% 39.4% 37.5% 42.9%
The adjustment for operating leases essentially treats the transaction as if the asset 
subject to the operating lease had been purchased rather than leased. The present

value of the capitalized lease obligations is the amount owed and the amount at which 
the asset is valued. Further adjustments reflect the reduction of rent expenses (if the 
asset is owned, rent would not be paid), the related interest expense on the amount 
owed, and a depreciation expense for the asset. The reduction of rent expense can be 
estimated as the average of two years of rent expense. Interest expense is estimated 
as the interest rate times the present value of the lease payments. Depreciation is 
estimated on a straight-  line basis for the number of years of future lease payments. 
As mentioned previously, IFRS 16 requires companies to recognize operating leases 
similar to that of capital leases, including recording the lease on the balance sheet.
EXAMPLE 15   
Effect on Coverage Ratio for Operating Lease Adjustment
The analyst is also evaluating the interest coverage ratio of the companies in the

previous example, Koller Semiconductor and MacRae Manufacturing.Exhibit 11   (Continued)

Reading 32 ■ Financial Statement Analysis: Applications 712
Koller 
SemiconductorMacRae 
EBIT before adjustment $850 $1,350
Interest expense before 
adjustment$120 $192
The prior-  year (2009) rent expense was $11 for Koller Semiconductor and 
$90 for MacRae Manufacturing.
Using the information in Example 14 and the additional information given 
here, discuss how adjustment for operating leases affects the companies’ solvency 
as measured by their coverage ratios.
Solution:
Interest coverage is calculated as EBIT divided by interest. For the adjustments, 
rent expense is the average of two years of rent. For Koller Semiconductor, rent 
expense is calculated as ($11 + $10)/2. The cost of interest on lease obligations 
is estimated as the interest rate multiplied by the present value of the lease 
payments. For Koller Semiconductor, this interest expense is calculated as 10% 
× $100.04, and for MacRae Manufacturing, it is calculated as 8% × $601.18.

Depreciation is estimated on a straight-  line basis by dividing the present value 
of lease payments by the number of years of lease payments (seven years). 
After the adjustment, both companies show a decline in interest coverage ratio, 
reflecting the increased obligation associated with the operating leases. Also the 
apparent difference in the coverage between the two companies is larger than 
it was in Example 14.
Exhibit 13   
Koller  
Interest coverage before adjustment 7.1 7.0
EBIT before adjustment $850.0 $1,350.0
Rent expense (an add-  back to EBIT) 10.5 90.0
Depreciation (a deduction from EBIT) (14.3) (85.9)
EBIT after adjustment $846.2 $1354.1
Interest expense before adjustment $120.0 $192.0
Assumed cost of interest on lease obliga -
tion (to add to interest)10.0 48.1
Interest expense after adjustment $130.0 $240.1
Interest coverage after adjustment 6.5     5.6

Summary 713
In summary, adjusting a company’s financial statements to include amounts of lease 
payments provides a more complete picture of the company’s financial condition and 
enables the comparison of companies with varying arrangements for financing assets 
and liabilities. The analyst may also need to adjust for amounts associated with other 
off- balance-  sheet financing arrangements.
SUMMARY
This reading described selected applications of financial statement analysis, including 
the evaluation of past financial performance, the projection of future financial perfor -
mance, the assessment of credit risk, and the screening of potential equity investments. 
In addition, the reading introduced analyst adjustments to reported financials. In all 
cases, the analyst needs to have a good understanding of the financial reporting stan -
dards under which the financial statements were prepared. Because standards evolve

over time, analysts must stay current in order to make good investment decisions.
The main points in the reading are as follows:
■■Evaluating a company’s historical performance addresses not only what hap -
pened but also the causes behind the company’s performance and how the 
performance reflects the company’s strategy.
■■The projection of a company’s future net income and cash flow often begins 
with a top-  down sales forecast in which the analyst forecasts industry sales and 
the company’s market share. By projecting profit margins or expenses and the 
level of investment in working and fixed capital needed to support projected 
sales, the analyst can forecast net income and cash flow.
■■Projections of future performance are needed for discounted cash flow valu -
ation of equity and are often needed in credit analysis to assess a borrower’s 
ability to repay interest and principal of a debt obligation.
■■Credit analysis uses financial statement analysis to evaluate credit-  relevant fac -

tors, including tolerance for leverage, operational stability, and margin stability.
■■When ratios constructed from financial statement data and market data are 
used to screen for potential equity investments, fundamental decisions include 
which metrics to use as screens, how many metrics to include, what values of 
those metrics to use as cutoff points, and what weighting to give each metric.
■■Analyst adjustments to a company’s reported financial statements are some -
times necessary (e.g., when comparing companies that use different accounting 
methods or assumptions). Adjustments include those related to investments; 
inventory; property, plant, and equipment; goodwill; and off-  balance-  sheet 
financing.

Reading 32 ■ Financial Statement Analysis: Applications 714
Chan, L.K.C., Y. Hamao, and J. Lakonishok. 1991. “Fundamentals 
and Stock Returns in Japan. ” Journal of Finance , vol. 46, no. 
5:1739–1764. doi:10.2307/2328571
Conrad, J., M. Cooper, and G. Kaul. 2003. “Value versus Glamour. ” 
Journal of Finance , vol. 58, no. 5:1969–1996. 
Davis, J. L. 1994. “The Cross-  Section of Realized Stock Returns: 
The Pre-  COMPUSTAT Evidence. ” Journal of Finance , vol. 49, 
no. 5:1579–1593. 
Haugen, R.A., and N.L. Baker. 1996. “Commonality in the 
Determinants of Expected Stock Returns. ” Journal of Financial 
Economics , vol. 41, no. 3:401–439. Henry, Elaine, Stephen Lin, and Ya-  wen Yang. 2009. “The

European-  U.S. ‘GAAP Gap’: IFRS to U.S. GAAP Form 20-  F 
Reconciliations. ” Accounting Horizons , vol. 23, no. 2:121–150. 
Lakonishok, J., A. Shleifer, and R.W. Vishny. 1994. “Contrarian 
Investment, Extrapolation and Risk. ” Journal of Finance , vol. 
49, no. 5:1541–1578. 
Piotroski, J.D. 2000. “Value Investing: The Use of Historical 
from Losers. ” Journal of Accounting Research , vol. 38, 
Pownall, G., and K. Schipper. 1999. “Implications of Accounting 
Research for the SEC’s Consideration of International 
Accounting Standards for U.S. Securities Offerings. ” 
Accounting Horizons , vol. 13, no. 3:259–280.

Practice Problems 715
1 Projecting profit margins into the future on the basis of past results would be 
most  reliable when the company:
A is in the commodities business.
B operates in a single business segment.
C is a large, diversified company operating in mature industries.
2 Galambos Corporation had an average receivables collection period of 19 days 
in 2003. Galambos has stated that it wants to decrease its collection period 
in 2004 to match the industry average of 15 days. Credit sales in 2003 were 
$300 million, and analysts expect credit sales to increase to $400 million in 
2004. To achieve the company’s goal of decreasing the collection period, the 
change in the average accounts receivable balance from 2003 to 2004 that must 
occur is closest  to:
A –$420,000.
B $420,000.
C $836,000.
3 Credit analysts are likely to consider which of the following in making a rating 
recommendation?
A Business risk but not financial risk
B Financial risk but not business risk

C Both business risk and financial risk
4 When screening for potential equity investments based on return on equity, to 
control risk, an analyst would be most likely  to include a criterion that requires:
A positive net income.
B negative net income.
C negative shareholders’ equity.
5 One concern when screening for stocks with low price-  to- earnings ratios is 
that companies with low P/Es may be financially weak. What criterion might an 
analyst include to avoid inadvertently selecting weak companies?
A Net income less than zero
B Debt-  to- total assets ratio below a certain cutoff point
C Current-  year sales growth lower than prior-  year sales growth
6 When a database eliminates companies that cease to exist because of a merger 
or bankruptcy, this can result in:
A look-  ahead bias.
B back-  testing bias.
C survivorship bias.
7 In a comprehensive financial analysis, financial statements should be:
A used as reported without adjustment.

B adjusted after completing ratio analysis.
C adjusted for differences in accounting standards, such as international finan -
cial reporting standards and US generally accepted accounting principles.

Reading 32 ■ Financial Statement Analysis: Applications 716
8 When comparing a US company that uses the last in, first out (LIFO) method 
of inventory with companies that prepare their financial statements under 
international financial reporting standards (IFRS), analysts should be aware that 
according to IFRS, the LIFO method of inventory:
A is never acceptable.
B is always acceptable.
C is acceptable when applied to finished goods inventory only.
9 An analyst is evaluating the balance sheet of a US company that uses last in, 
first out (LIFO) accounting for inventory. The analyst collects the following 
data:
31 Dec 05 31 Dec 06
Inventory reported on balance sheet $500,000 $600,000
LIFO reserve $ 50,000 $70,000
Average tax rate 30% 30%
 After adjusting the amounts to convert to the first in, first out (FIFO) method, 
inventory at 31 December 2006 would be closest to:
B $620,000.
C $670,000.
10 An analyst gathered the following data for a company ($ millions):
31 Dec 2000 31 Dec 2001

Gross investment in fixed assets $2.8 $2.8
Accumulated depreciation $1.2 $1.6
 The average age and average depreciable life of the company’s fixed assets at the 
end of 2001 are closest  to:
Average Age Average Depreciable Life
A    1.75 years 7 years
B    1.75 years 14 years
C    4.00 years 7 years
11 To compute tangible book value, an analyst would:
A add goodwill to stockholders’ equity.
B add all intangible assets to stockholders’ equity.
C subtract all intangible assets from stockholders’ equity.
12 Which of the following is an off-  balance-  sheet financing technique? The use of:
A capital leases.
B operating leases.
C the last in, first out inventory method.
13 To better evaluate the solvency of a company, an analyst would most likely add 
to total liabilities:
A the present value of future capital lease payments.
B the total amount of future operating lease payments.
C the present value of future operating lease payments.

Solutions 717
SOLUTIONS
1 C is correct. For a large, diversified company, margin changes in different busi -
ness segments may offset each other. Furthermore, margins are most likely to be 
stable in mature industries.
2 C is correct. Accounts receivable turnover is equal to 365/19 (collection period 
in days) = 19.2 for 2003 and needs to equal 365/15 = 24.3 in 2004 for Galambos 
to meet its goal. Sales/turnover equals the accounts receivable balance. For 
2003, $300,000,000/19.2 = $15,625,000, and for 2004, $400,000,000/24.3 = 
$16,460,905. The difference of $835,905 is the increase in receivables needed for 
Galambos to achieve its goal.
3 C is correct. Credit analysts consider both business risk and financial risk.
4 A is correct. Requiring that net income be positive would eliminate companies 
that report a positive return on equity only because both net income and share -
holders’ equity are negative.
5 B is correct. A lower value of debt/total assets indicates greater financial

strength. Requiring that a company’s debt/total assets be below a certain cutoff 
point would allow the analyst to screen out highly leveraged and, therefore, 
potentially financially weak companies.
6 C is correct. Survivorship bias exists when companies that merge or go bank -
rupt are dropped from the database and only surviving companies remain. 
Look-  ahead bias involves using updated financial information in back-  testing 
that would not have been available at the time the decision was made. Back-  
testing involves testing models in prior periods and is not, itself, a bias.
7 C is correct. Financial statements should be adjusted for differences in account -
ing standards (as well as accounting and operating choices). These adjustments 
should be made prior to common-  size and ratio analysis.
8 A is correct. LIFO is not permitted under IFRS.
9 C is correct. To convert LIFO inventory to FIFO inventory, the entire LIFO 
reserve must be added back: $600,000 + $70,000 = $670,000.

10 C is correct. The company made no additions to or deletions from the fixed 
asset account during the year, so depreciation expense is equal to the difference 
in accumulated depreciation at the beginning of the year and the end of the 
year, or $0.4 million. Average age is equal to accumulated depreciation/depreci -
ation expense, or $1.6/$0.4 = 4 years. Average depreciable life is equal to ending 
gross investment/depreciation expense = $2.8/$0.4 = 7 years.
11 C is correct. Tangible book value removes all intangible assets, including good -
will, from the balance sheet.
12 B is correct. Operating leases can be used as an off-  balance-  sheet financing 
technique because neither the asset nor liability appears on the balance sheet. 
Inventory and capital leases are reported on the balance sheet.
13 C is correct. The present value of future operating lease payments would be 
added to total assets and total liabilities.

GlossaryG-1
A priori probability   A probability based on logical analysis 
rather than on observation or personal judgment.
Abnormal return   The amount by which a security’s actual 
return differs from its expected return, given the security’s 
risk and the market’s return.
Absolute advantage   A country’s ability to produce a good 
or service at a lower absolute cost than its trading partner.
Absolute dispersion   The amount of variability present 
without comparison to any reference point or benchmark.
Absolute frequency   The number of observations in a given 
interval (for grouped data).
Accelerated book build   An offering of securities by an invest -
ment bank acting as principal that is accomplished in only 
one or two days.
Accelerated methods   Depreciation methods that allocate 
a relatively large proportion of the cost of an asset to the 
early years of the asset’s useful life.
Accounting costs   Monetary value of economic resources

used in performing an activity. These can be explicit, out-  
of- pocket, current payments, or an allocation of historical 
payments (depreciation) for resources. They do not include 
implicit opportunity costs.
Accounting profit   Income as reported on the income state -
ment, in accordance with prevailing accounting standards, 
before the provisions for income tax expense. Also called 
income before taxes  or pretax income .
Accounts payable   Amounts that a business owes to its vendors 
for goods and services that were purchased from them but 
which have not yet been paid.
Accounts receivable turnover   Ratio of sales on credit to the 
average balance in accounts receivable.
Accrued expenses   Liabilities related to expenses that have 
been incurred but not yet paid as of the end of an account -
ing period—an example of an accrued expense is rent that 
has been incurred but not yet paid, resulting in a liability 
“rent payable. ” Also called accrued liabilities .

Accrued interest   Interest earned but not yet paid.
Acid-  test ratio   A stringent measure of liquidity that indicates 
a company’s ability to satisfy current liabilities with its most 
liquid assets, calculated as (cash + short-  term marketable 
investments + receivables) divided by current liabilities.
Acquisition method   A method of accounting for a busi -
ness combination where the acquirer is required to mea -
sure each identifiable asset and liability at fair value. This 
method was the result of a joint project of the IASB and 
FASB aiming at convergence in standards for the account -
ing of business combinations.
Action lag   Delay from policy decisions to implementation.
Active investment   An approach to investing in which the 
investor seeks to outperform a given benchmark.
Active return   The return on a portfolio minus the return on 
the portfolio’s benchmark.
Active strategy   In reference to short-  term cash management,

an investment strategy characterized by monitoring and 
attempting to capitalize on market conditions to optimize 
the risk and return relationship of short-  term investments.Activity ratios   Ratios that measure how efficiently a com -
pany performs day-  to- day tasks, such as the collection of 
receivables and management of inventory. Also called asset 
utilization ratios  or operating efficiency ratios .
Add-  on rates   Bank certificates of deposit, repos, and indexes 
such as Libor and Euribor are quoted on an add-  on rate 
basis (bond equivalent yield basis).
Addition rule for probabilities   A principle stating that the 
probability that A or B occurs (both occur) equals the 
probability that A occurs, plus the probability that B occurs, 
minus the probability that both A and B occur.
Agency bonds   See quasi-  government bond .
Agency RMBS   In the United States, securities backed by 
residential mortgage loans and guaranteed by a federal

agency or guaranteed by either of the two GSEs (Fannie 
Mae and Freddie Mac).
Aggregate demand   The quantity of goods and services that 
households, businesses, government, and foreign customers 
want to buy at any given level of prices.
Aggregate demand curve   Inverse relationship between the 
price level and real output.
Aggregate income   The value of all the payments earned by 
the suppliers of factors used in the production of goods 
and services.
Aggregate output   The value of all the goods and services 
produced in a specified period of time.
Aggregate supply   The quantity of goods and services pro -
ducers are willing to supply at any given level of price.
Aggregate supply curve   The level of domestic output that 
companies will produce at each price level.
Aging schedule   A breakdown of accounts into categories of 
days outstanding.
All-  or- nothing (AON) orders   An order that includes the 
instruction to trade only if the trade fills the entire quantity 
(size) specified.

Allocationally efficient   Said of a market, a financial system, 
or an economy that promotes the allocation of resources 
to their highest value uses.
Alternative data   Non-  traditional data types generated by the 
use of electronic devices, social media, satellite and sensor 
networks, and company exhaust.
Alternative investment markets   Market for investments 
other than traditional securities investments (i.e., tradi -
tional common and preferred shares and traditional fixed 
income instruments). The term usually encompasses direct 
and indirect investment in real estate (including timber -
land and farmland) and commodities (including precious 
metals); hedge funds, private equity, and other investments 
requiring specialized due diligence.
Alternative trading systems   Trading venues that function 
like exchanges but that do not exercise regulatory authority 
over their subscribers except with respect to the conduct 
of the subscribers’ trading in their trading systems. Also

called electronic communications networks  or multilateral 
trading facilities .
American depository receipt   A US dollar-  denominated secu -
rity that trades like a common share on US exchanges.

G-2 Glossary
American depository share   The underlying shares on which 
American depository receipts are based. They trade in the 
issuing company’s domestic market.
American-  style   Said of an option contract that can be exer -
cised at any time up to the option’s expiration date.
Amortisation   The process of allocating the cost of intangible 
long-  term assets having a finite useful life to accounting 
periods; the allocation of the amount of a bond premium 
or discount to the periods remaining until bond maturity.
Amortised cost   The historical cost (initially recognised cost) 
of an asset, adjusted for amortisation and impairment.
Amortizing bond   Bond with a payment schedule that calls for 
periodic payments of interest and repayments of principal.
Amortizing loan   Loan with a payment schedule that calls for 
Annual percentage rate   The cost of borrowing expressed 
as a yearly rate.

Annuity   A finite set of level sequential cash flows.
Annuity due   An annuity having a first cash flow that is paid 
immediately.
Anticipation stock   Excess inventory that is held in anticipation 
of increased demand, often because of seasonal patterns 
of demand.
Antidilutive   With reference to a transaction or a security, one 
that would increase earnings per share (EPS) or result in 
EPS higher than the company’s basic EPS—antidilutive 
securities are not included in the calculation of diluted EPS.
Arbitrage   1) The simultaneous purchase of an undervalued 
asset or portfolio and sale of an overvalued but equivalent 
asset or portfolio, in order to obtain a riskless profit on the 
price differential. Taking advantage of a market inefficiency 
in a risk-  free manner. 2) The condition in a financial market 
in which equivalent assets or combinations of assets sell for 
two different prices, creating an opportunity to profit at no

risk with no commitment of money. In a well-  functioning 
financial market, few arbitrage opportunities are possible. 
3) A risk-  free operation that earns an expected positive net 
profit but requires no net investment of money.
Arbitrage-  free pricing   The overall process of pricing deriv -
atives by arbitrage and risk neutrality. Also called the 
principle of no arbitrage .
Arbitrageurs   Traders who engage in arbitrage. See arbitrage .
Arithmetic mean   The sum of the observations divided by the 
number of observations.
Arms index   A flow of funds indicator applied to a broad stock 
market index to measure the relative extent to which money 
is moving into or out of rising and declining stocks.
Artificial intelligence   Computer systems that exhibit cognitive 
and decision-  making ability comparable (or superior) to 
that of humans.
Asian call option   A European-  style option with a value at 
maturity equal to the difference between the stock price

at maturity and the average stock price during the life of 
the option, or $0, whichever is greater.
Ask  The price at which a dealer or trader is willing to sell 
an asset, typically qualified by a maximum quantity (ask 
size). See offer .
Ask size   The maximum quantity of an asset that pertains to a 
specific ask price from a trader. For example, if the ask for 
a share issue is $30 for a size of 1,000 shares, the trader is 
offering to sell at $30 up to 1,000 shares.
Asset allocation   The process of determining how investment 
funds should be distributed among asset classes.Asset-  backed securities   A type of bond issued by a legal 
entity called a special purpose entity  (SPE) on a collection 
of assets that the SPE owns. Also, securities backed by 
receivables and loans other than mortgages.
Asset-  based loan   A loan that is secured with company assets.
Asset-  based valuation models   Valuation based on estimates 
of the market value of a company’s assets.

Asset beta   The unlevered beta; reflects the business risk of 
the assets; the asset’s systematic risk.
Asset class   A group of assets that have similar characteristics, 
attributes, and risk/return relationships.
Asset swap   Converts the periodic fixed coupon of a specific 
bond to a Libor plus or minus a spread.
Asset utilization ratios   Ratios that measure how efficiently a 
company performs day-  to- day tasks, such as the collection 
of receivables and management of inventory.
Assets   Resources controlled by an enterprise as a result of 
past events and from which future economic benefits to 
the enterprise are expected to flow.
Assignment of accounts receivable   The use of accounts 
receivable as collateral for a loan.
At the money   An option in which the underlying’s price 
equals the exercise price.
Auction   A type of bond issuing mechanism often used for 
sovereign bonds that involves bidding.

Autarkic price   The price of a good or service in an autarkic 
economy.
Autarky   A state in which a country does not trade with other 
countries.
Automated Clearing House (ACH)   An electronic payment 
network available to businesses, individuals, and finan -
cial institutions in the United States, US Territories, and 
Canada.
Automatic stabilizer   A countercyclical factor that automat -
ically comes into play as an economy slows and unem -
ployment rises.
Available-  for-  sale   Debt and equity securities not classified 
as either held-  to- maturity or held-  for- trading securities. 
The investor is willing to sell but not actively planning to 
sell. In general, available-  for- sale securities are reported 
at fair value on the balance sheet.
Average fixed cost   Total fixed cost divided by quantity 
produced.
Average life   See weighted average life .
Average product   Measures the productivity of inputs on

average and is calculated by dividing total product by 
the total number of units for a given input that is used to 
generate that output.
Average revenue   Total revenue divided by quantity sold.
Average total cost   Total cost divided by quantity produced.
Average variable cost   Total variable cost divided by quantity 
produced.
Back simulation   Another term for the historical method of 
estimating VaR. This term is somewhat misleading in that 
the method involves not a simulation  of the past but rather 
what actually happened  in the past, sometimes adjusted to 
reflect the fact that a different portfolio may have existed 
in the past than is planned for the future.
Back-  testing   With reference to portfolio strategies, the appli -
cation of a strategy’s portfolio selection rules to historical 
data to assess what would have been the strategy’s historical 

G-3 Glossary
Backup lines of credit   A type of credit enhancement provided 
by a bank to an issuer of commercial paper to ensure that 
the issuer will have access to sufficient liquidity to repay 
maturing commercial paper if issuing new paper is not a 
viable option.
Balance of payments   A double-  entry bookkeeping system that 
summarizes a country’s economic transactions with the 
rest of the world for a particular period of time, typically 
a calendar quarter or year.
Balance of trade deficit   When the domestic economy is 
spending more on foreign goods and services than foreign 
economies are spending on domestic goods and services.
Balance sheet   The financial statement that presents an entity’s 
current financial position by disclosing resources the entity 
controls (its assets) and the claims on those resources (its 
liabilities and equity claims), as of a particular point in 
time (the date of the balance sheet). Also called statement

of financial position  or statement of financial condition .
Balance sheet ratios   Financial ratios involving balance sheet 
items only.
Balanced   With respect to a government budget, one in which 
spending and revenues (taxes) are equal.
Balloon payment   Large payment required at maturity to retire 
a bond’s outstanding principal amount.
Bank discount basis   A quoting convention that annualizes, on 
a 360-  day year, the discount as a percentage of face value.
Bar chart   A price chart with four bits of data for each time 
interval—the high, low, opening, and closing prices. A 
vertical line connects the high and low. A cross-  hatch 
left indicates the opening price and a cross-  hatch right 
indicates the close.
Barter economy   An economy where economic agents as 
house-  holds, corporations, and governments “pay” for 
goods and services with another good or service.
Base rates   The reference rate on which a bank bases lending 
rates to all other customers.

Basic EPS   Net earnings available to common shareholders 
(i.e., net income minus preferred dividends) divided by the 
weighted average number of common shares outstanding.
Basis point   Used in stating yield spreads, one basis point 
equals one-  hundredth of a percentage point, or 0.01%.
Basket of listed depository receipts   An exchange-  traded fund 
(ETF) that represents a portfolio of depository receipts.
Bearer bonds   Bonds for which ownership is not recorded; 
only the clearing system knows who the bond owner is.
Behavioral finance   A field of finance that examines the 
psychological variables that affect and often distort the 
investment decision making of investors, analysts, and 
portfolio managers.
Behind the market   Said of prices specified in orders that 
are worse than the best current price; e.g., for a limit buy 
order, a limit price below the best bid.
Benchmark   A comparison portfolio; a point of reference or 
comparison.

Benchmark issue   The latest sovereign bond issue for a given 
maturity. It serves as a benchmark against which to com -
pare bonds that have the same features but that are issued 
by another type of issuer.
Benchmark rate   Typically the yield-  to- maturity on a gov -
ernment bond having the same, or close to the same, 
time-  to- maturity.
Benchmark spread   The yield spread over a specific bench -
mark, usually measured in basis points.Bermuda-  style   Said of an option contract that can be exer -
cised on specified dates up to the option’s expiration date.
Bernoulli random variable   A random variable having the 
outcomes 0 and 1.
Bernoulli trial   An experiment that can produce one of two 
outcomes.
Best bid   The highest bid in the market.
Best effort offering   An offering of a security using an invest -
ment bank in which the investment bank, as agent for the 
issuer, promises to use its best efforts to sell the offering 
but does not guarantee that a specific amount will be sold.

Best-  in- class   An ESG implementation approach that seeks 
to identify the most favorable companies in an industry 
based on ESG considerations.
Best offer   The lowest offer (ask price) in the market.
Beta   A measure of the sensitivity of a given investment or 
portfolio to movements in the overall market.
Bid  The price at which a dealer or trader is willing to buy an 
asset, typically qualified by a maximum quantity.
Bid–ask spread   The difference between the prices at which 
dealers will buy from a customer (bid) and sell to a cus -
tomer (offer or ask). It is often used as an indicator of 
Bid–offer spread   The difference between the prices at which 
Bid size   The maximum quantity of an asset that pertains to 
a specific bid price from a trader.
Big Data   The vast amount of data being generated by industry,

governments, individuals, and electronic devices that arises 
from both traditional and non-  traditional data sources.
Bilateral loan   A loan from a single lender to a single borrower.
Binomial model   A model for pricing options in which the 
underlying price can move to only one of two possible 
new prices.
Binomial random variable   The number of successes in n 
Bernoulli trials for which the probability of success is 
constant for all trials and the trials are independent.
Binomial tree   The graphical representation of a model of asset 
price dynamics in which, at each period, the asset moves 
up with probability p or down with probability (1 – p).
Bitcoin   A cryptocurrency using blockchain technology that 
was created in 2009.
Block brokers   A broker (agent) that provides brokerage ser -
vices for large-  size trades.
Blockchain   A type of digital ledger in which information is 
recorded sequentially and then linked together and secured 
using cryptographic methods.

Blue chip   Widely held large market capitalization companies 
that are considered financially sound and are leaders in 
their respective industry or local stock market.
Bollinger Bands   A price-  based technical analysis indicator 
consisting of a moving average plus a higher line repre -
senting the moving average plus a set number of standard 
deviations from average price (for the same number of 
periods as used to calculate the moving average) and a 
lower line that is a moving average minus the same number 
of standard deviations.
Bond   Contractual agreement between the issuer and the 
bondholders.

G-4 Glossary
Bond equivalent yield   A calculation of yield that is annualized 
using the ratio of 365 to the number of days to maturity. 
Bond equivalent yield allows for the restatement and com -
parison of securities with different compounding periods.
Bond indenture   The governing legal credit agreement, typ -
ically incorporated by reference in the prospectus. Also 
called trust deed .
Bond market vigilantes   Bond market participants who might 
reduce their demand for long-  term bonds, thus pushing 
up their yields.
Bond yield plus risk premium approach   An estimate of the 
cost of common equity that is produced by summing the 
before-  tax cost of debt and a risk premium that captures the 
additional yield on a company’s stock relative to its bonds. 
The additional yield is often estimated using historical 
spreads between bond yields and stock yields.
Bonus issue of shares   A type of dividend in which a com -
pany distributes additional shares of its common stock to

shareholders instead of cash.
Book building   Investment bankers’ process of compiling a 
“book” or list of indications of interest to buy part of an 
offering.
Book value   The net amount shown for an asset or liability 
on the balance sheet; book value may also refer to the 
company’s excess of total assets over total liabilities. Also 
called carrying value .
Boom   An expansionary phase characterized by economic 
growth “testing the limits” of the economy.
Bottom-  up analysis   With reference to investment selec -
tion processes, an approach that involves selection from 
all securities within a specified investment universe, i.e., 
without prior narrowing of the universe on the basis of 
macroeconomic or overall market considerations.
Break point   In the context of the weighted average cost of 
capital (WACC), a break point is the amount of capital 
at which the cost of one or more of the sources of capital 
changes, leading to a change in the WACC.

Breakeven point   The number of units produced and sold at 
which the company’s net income is zero (Revenues = Total 
cost); in the case of perfect competition, the quantity at 
which price, average revenue, and marginal revenue equal 
average total cost.
Bridge financing   Interim financing that provides funds until 
permanent financing can be arranged.
Broad money   Encompasses narrow money plus the entire 
range of liquid assets that can be used to make purchases.
Broker   1) An agent who executes orders to buy or sell secu -
rities on behalf of a client in exchange for a commission. 
2) See futures commission merchants .
Broker–dealer   A financial intermediary (often a company) 
that may function as a principal (dealer) or as an agent 
(broker) depending on the type of trade.
Brokered market   A market in which brokers arrange trades 
among their clients.
Budget surplus/deficit   The difference between government

revenue and expenditure for a stated fixed period of time.
Business risk   The risk associated with operating earnings. 
Operating earnings are uncertain because total revenues 
and many of the expenditures contributed to produce those 
revenues are uncertain.
Buy-  side firm   An investment management company or other 
investor that uses the services of brokers or dealers (i.e., 
the client of the sell side firms).Buyback   A transaction in which a company buys back its 
own shares. Unlike stock dividends and stock splits, share 
repurchases use corporate cash.
Buyout fund   A fund that buys all the shares of a public 
company so that, in effect, the company becomes private.
Call  An option that gives the holder the right to buy an under -
lying asset from another party at a fixed price over a specific 
period of time.
Call market   A market in which trades occur only at a particular 
time and place (i.e., when the market is called).
Call money rate   The interest rate that buyers pay for their

margin loan.
Call option   An option that gives the holder the right to buy 
an underlying asset from another party at a fixed price 
over a specific period of time.
Call protection   The time during which the issuer of the bond 
is not allowed to exercise the call option.
Callable bond   A bond containing an embedded call option 
that gives the issuer the right to buy the bond back from 
the investor at specified prices on pre-  determined dates.
Callable common shares   Shares that give the issuing company 
the option (or right), but not the obligation, to buy back 
the shares from investors at a call price that is specified 
when the shares are originally issued.
Candlestick chart   A price chart with four bits of data for each 
time interval. A candle indicates the opening and closing 
price for the interval. The body of the candle is shaded if 
the opening price was higher than the closing price, and 
the body is clear if the opening price was lower than the

closing price. Vertical lines known as wicks or shadows 
extend from the top and bottom of the candle to indicate 
the high and the low prices for the interval.
Cannibalization   Cannibalization occurs when an investment 
takes customers and sales away from another part of the 
company.
Capacity   The ability of the borrower to make its debt pay -
ments on time.
Capital account   A component of the balance of payments 
account that measures transfers of capital.
Capital allocation line   (CAL) A graph line that describes the 
combinations of expected return and standard deviation of 
return available to an investor from combining the optimal 
portfolio of risky assets with the risk-  free asset.
Capital asset pricing model   (CAPM) An equation describing 
the expected return on any asset (or portfolio) as a linear 
function of its beta relative to the market portfolio.
Capital budgeting   The allocation of funds to relatively long-  
range projects or investments.

Capital consumption allowance   A measure of the wear and 
tear (depreciation) of the capital stock that occurs in the 
production of goods and services.
Capital deepening investment   Increases the stock of capital 
relative to labor.
Capital expenditure   Expenditure on physical capital (fixed 
assets).
Capital-  indexed bonds   Type of index-  linked bond. The cou -
pon rate is fixed but is applied to a principal amount that 
increases in line with increases in the index during the 
bond’s life.
Capital lease   See finance lease .
Capital market expectations   An investor’s expectations 
concerning the risk and return prospects of asset classes.

G-5 Glossary
Capital market line   (CML) The line with an intercept point 
equal to the risk-  free rate that is tangent to the efficient 
frontier of risky assets; represents the efficient frontier 
when a risk-  free asset is available for investment.
Capital market securities   Securities with maturities at issu -
ance longer than one year.
Capital markets   Financial markets that trade securities of 
longer duration, such as bonds and equities.
Capital rationing   A capital rationing environment assumes 
that the company has a fixed amount of funds to invest.
Capital restrictions   Controls placed on foreigners’ ability to 
own domestic assets and/or domestic residents’ ability to 
own foreign assets.
Capital stock   The accumulated amount of buildings, machin -
ery, and equipment used to produce goods and services.
Capital structure   The mix of debt and equity that a company 
uses to finance its business; a company’s specific mixture 
of long-  term financing.

Captive finance subsidiary   A wholly-  owned subsidiary of 
a company that is established to provide financing of the 
sales of the parent company.
Carry   The net of the costs and benefits of holding, storing, or 
“carrying” an asset.
Carrying amount   The amount at which an asset or liability 
is valued according to accounting principles.
Carrying value   The net amount shown for an asset or liabil -
ity on the balance sheet; book value may also refer to the 
company’s excess of total assets over total liabilities. For 
a bond, the purchase price plus (or minus) the amortized 
amount of the discount (or premium).
Cartel   Participants in collusive agreements that are made 
openly and formally.
Cash collateral account   Form of external credit enhance -
ment whereby the issuer immediately borrows the credit-  
enhancement amount and then invests that amount, usually 
in highly rated short-  term commercial paper.
Cash conversion cycle   A financial metric that measures the

length of time required for a company to convert cash 
invested in its operations to cash received as a result of 
its operations; equal to days of inventory on hand + days 
of sales outstanding – number of days of payables. Also 
called net operating cycle .
Cash flow additivity principle   The principle that dollar 
amounts indexed at the same point in time are additive.
Cash flow from operating activities   The net amount of cash 
provided from operating activities.
Cash flow from operations   The net amount of cash provided 
from operating activities.
Cash flow yield   The internal rate of return on a series of 
Cash market securities   Money market securities settled on 
a “same day” or “cash settlement” basis.
Cash markets   See spot markets .
Cash prices   See spot prices .
Cash-  settled forwards   See non-  deliverable forwards .
CBOE Volatility Index   A measure of near-  term market vol -
atility as conveyed by S&P 500 stock index option prices.

CD equivalent yield   A yield on a basis comparable to the 
quoted yield on an interest-  bearing money market instru -
ment that pays interest on a 360-  day basis; the annualized 
holding period yield, assuming a 360-  day year.Central bank funds market   The market in which deposit-  
taking banks that have an excess reserve with their national 
central bank can loan money to banks that need funds for 
maturities ranging from overnight to one year. Called the 
Federal or Fed funds market in the United States.
Central bank funds rates   Interest rates at which central bank 
funds are bought (borrowed) and sold (lent) for maturities 
ranging from overnight to one year. Called Federal or Fed 
funds rates in the United States.
Central banks   The dominant bank in a country, usually with 
official or semi-  official governmental status.
Certificate of deposit   An instrument that represents a speci -
fied amount of funds on deposit with a bank for a specified

maturity and interest rate. It is issued in small or large 
denominations, and can be negotiable or non-  negotiable.
Change in polarity principle   A tenet of technical analysis 
that once a support level is breached, it becomes a resis -
tance level. The same holds true for resistance levels; once 
breached, they become support levels.
Change of control put   A covenant giving bondholders the 
right to require the issuer to buy back their debt, often at 
par or at some small premium to par value, in the event 
that the borrower is acquired.
Character   The quality of a debt issuer’s management.
Classified balance sheet   A balance sheet organized so as 
to group together the various assets and liabilities into 
subcategories (e.g., current and noncurrent).
Clawback   A requirement that the general partner return 
any funds distributed as incentive fees until the limited 
partners have received back their initial investment and a 
percentage of the total profit.

Clearing   The process by which the exchange verifies the 
execution of a transaction and records the participants’ 
identities.
Clearing instructions   Instructions that indicate how to 
arrange the final settlement (“clearing”) of a trade.
Clearinghouse   An entity associated with a futures market 
that acts as middleman between the contracting parties 
and guarantees to each party the performance of the other.
Closed economy   An economy that does not trade with other 
countries; an autarkic economy .
Closed-  end fund   A mutual fund in which no new investment 
money is accepted. New investors invest by buying existing 
shares, and investors in the fund liquidate by selling their 
shares to other investors.
Code of ethics   An established guide that communicates an 
organization’s values and overall expectations regarding 
member behavior. A code of ethics serves as a general 
guide for how community members should act.

Coefficient of variation   (CV) The ratio of a set of observa -
tions’ standard deviation to the observations’ mean value.
Coincident economic indicators   Turning points that are usu -
ally close to those of the overall economy; they are believed 
to have value for identifying the economy’s present state.
Collateral manager   Buys and sells debt obligations for and 
from the CDO’s portfolio of assets (i.e., the collateral) to 
generate sufficient cash flows to meet the obligations to 
the CDO bondholders.
Collateral trust bonds   Bonds secured by securities such as 
common shares, other bonds, or other financial assets.
Collateralized bond obligations   A structured asset-  backed 
security that is collateralized by a pool of bonds.

G-6 Glossary
Collateralized debt obligation   Generic term used to describe 
a security backed by a diversified pool of one or more debt 
Collateralized loan obligations   A structured asset-  backed 
security that is collateralized by a pool of loans.
Collateralized mortgage obligation   A security created 
through the securitization of a pool of mortgage-  related 
products (mortgage pass-  through securities or pools of 
loans).
Collaterals   Assets or financial guarantees underlying a debt 
obligation that are above and beyond the issuer’s promise 
to pay.
Combination   A listing in which the order of the listed items 
does not matter.
Commercial paper   A short-  term, negotiable, unsecured prom -
issory note that represents a debt obligation of the issuer.
Committed capital   The amount that the limited partners have 
agreed to provide to the private equity fund.
Committed lines of credit   A bank commitment to extend 
credit up to a pre-  specified amount; the commitment is

considered a short-  term liability and is usually in effect for 
364 days (one day short of a full year).
Commodity swap   A swap in which the underlying is a com -
modity such as oil, gold, or an agricultural product.
Common market   Level of economic integration that incor -
porates all aspects of the customs union and extends it by 
allowing free movement of factors of production among 
members.
Common shares   A type of security that represent an owner -
ship interest in a company.
Common-  size analysis   The restatement of financial statement 
items using a common denominator or reference item 
that allows one to identify trends and major differences; 
an example is an income statement in which all items are 
expressed as a percent of revenue.
Common stock   See common shares .
Company analysis   Analysis of an individual company.
Comparable company   A company that has similar business 
risk; usually in the same industry and preferably with a 
single line of business.

Comparative advantage   A country’s ability to produce a 
good or service at a lower relative cost, or opportunity 
cost, than its trading partner.
Competitive strategy   A company’s plans for responding to 
the threats and opportunities presented by the external 
environment.
Complements   Goods that tend to be used together; techni -
cally, two goods whose cross-  price elasticity of demand 
is negative.
Complete markets   Informally, markets in which the variety 
of distinct securities traded is so broad that any desired 
payoff in a future state-  of- the- world is achievable.
Completed contract   A method of revenue recognition in 
which the company does not recognize any revenue until 
the contract is completed; used particularly in long-  term 
Component cost of capital   The rate of return required by 
suppliers of capital for an individual source of a company’s 
funding, such as debt or equity.

Compounding   The process of accumulating interest on 
interest.
Comprehensive income   The change in equity of a busi -
ness enterprise during a period from nonowner sources; 
includes all changes in equity during a period except those resulting from investments by owners and distributions to 
owners; comprehensive income equals net income plus 
other comprehensive income.
Conditional expected value   The expected value of a stated 
event given that another event has occurred.
Conditional probability   The probability of an event given 
(conditioned on) another event.
Conditional variances   The variance of one variable, given 
the outcome of another.
Consistent   With reference to estimators, describes an esti -
mator for which the probability of estimates close to the 
value of the population parameter increases as sample 
size increases.
Constant-  yield price trajectory   A graph that illustrates the 
change in the price of a fixed-  income bond over time

assuming no change in yield-  to- maturity. The trajectory 
shows the “pull to par” effect on the price of a bond trading 
at a premium or a discount to par value.
Constituent securities   With respect to an index, the individual 
securities within an index.
Consumer surplus   The difference between the value that a 
consumer places on units purchased and the amount of 
money that was required to pay for them.
Contingency provision   Clause in a legal document that allows 
for some action if a specific event or circumstance occurs.
Contingent claims   Derivatives in which the payoffs occur if 
a specific event occurs; generally referred to as options.
Contingent convertible bonds   Bonds that automatically 
convert into equity if a specific event or circumstance 
occurs, such as the issuer’s equity capital falling below 
the minimum requirement set by the regulators. Also 
called CoCos .
Continuation patterns   A type of pattern used in technical

analysis to predict the resumption of a market trend that 
was in place prior to the formation of a pattern.
Continuous random variable   A random variable for which 
the range of possible outcomes is the real line (all real num -
bers between −∞ and +∞ or some subset of the real line).
Continuous time   Time thought of as advancing in extremely 
small increments.
Continuous trading market   A market in which trades can 
be arranged and executed any time the market is open.
Continuously compounded return   The natural logarithm of 1 
plus the holding period return, or equivalently, the natural 
logarithm of the ending price over the beginning price.
Contra account   An account that offsets another account.
Contract rate   See mortgage rate .
Contraction   The period of a business cycle after the peak and 
before the trough; often called a recession  or, if exceptionally 
severe, called a depression .
Contraction risk   The risk that when interest rates decline, the

security will have a shorter maturity than was anticipated 
at the time of purchase because borrowers refinance at the 
new, lower interest rates.
Contractionary   Tending to cause the real economy to contract.
Contractionary fiscal policy   A fiscal policy that has the objec -
tive to make the real economy contract.
Contracts for differences   See non-  deliverable forwards .
Contribution margin   The amount available for fixed costs and 
profit after paying variable costs; revenue minus variable 
costs.
Controlling shareholders   A particular shareholder or block 
of shareholders holding a percentage of shares that gives 
them significant voting power.

G-7 Glossary
Convenience yield   A non-  monetary advantage of holding 
an asset.
Conventional bond   See plain vanilla bond .
Conventional cash flow   A conventional cash flow pattern is 
one with an initial outflow followed by a series of inflows.
Convergence   The tendency for differences in output per 
capita across countries to diminish over time; in technical 
analysis, a term that describes the case when an indicator 
moves in the same manner as the security being analyzed.
Conversion price   For a convertible bond, the price per share 
at which the bond can be converted into shares.
Conversion ratio   For a convertible bond, the number of 
common shares that each bond can be converted into.
Conversion value   For a convertible bond, the current share 
price multiplied by the conversion ratio.
Convertible bond   Bond that gives the bondholder the right 
to exchange the bond for a specified number of common 
shares in the issuing company.

Convertible preference shares   A type of equity security that 
entitles shareholders to convert their shares into a specified 
number of common shares.
Convexity adjustment   For a bond, one half of the annual or 
approximate convexity statistic multiplied by the change 
in the yield-  to- maturity squared.
Core inflation   The inflation rate calculated based on a price 
index of goods and services except food and energy.
Corporate governance   The system of internal controls and 
procedures by which individual companies are managed.
Correlation   A number between −1 and +1 that measures the 
comovement (linear association) between two random 
variables.
Correlation coefficient   A number between −1 and +1 that 
measures the consistency or tendency for two investments 
to act in a similar way. It is used to determine the effect on 
portfolio risk when two assets are combined.
Cost averaging   The periodic investment of a fixed amount 
of money.

of money.
Cost of capital   The rate of return that suppliers of capital 
require as compensation for their contribution of capital.
Cost of carry   See carry .
Cost of debt   The cost of debt financing to a company, such as 
when it issues a bond or takes out a bank loan.
Cost of preferred stock   The cost to a company of issuing 
preferred stock; the dividend yield that a company must 
commit to pay preferred stockholders.
Cost-  push   Type of inflation in which rising costs, usually 
wages, compel businesses to raise prices generally.
Cost recovery method   A method of revenue recognition 
in which the seller does not report any profit until the 
cash amounts paid by the buyer—including principal and 
interest on any financing from the seller—are greater than 
all the seller’s costs for the merchandise sold.
Cost structure   The mix of a company’s variable costs and 
fixed costs.
Counterparty risk   The risk that the other party to a contract 
will fail to honor the terms of the contract.

Coupon rate   The interest rate promised in a contract; this is 
the rate used to calculate the periodic interest payments.
Cournot assumption   Assumption in which each firm deter -
mines its profit-  maximizing production level assuming 
that the other firms’ output will not change.
Covariance   A measure of the co-  movement (linear association) 
between two random variables.Covariance matrix   A matrix or square array whose entries are 
covariances; also known as a variance–covariance matrix.
Covenants   The terms and conditions of lending agreements 
that the issuer must comply with; they specify the actions 
that an issuer is obligated to perform (affirmative covenant) 
or prohibited from performing (negative covenant).
Covered bond   Debt obligation secured by a segregated pool of 
assets called the cover pool. The issuer must maintain the 
value of the cover pool. In the event of default, bondholders

have recourse against both the issuer and the cover pool.
Credit analysis   The evaluation of credit risk; the evaluation 
of the creditworthiness of a borrower or counterparty.
Credit curve   A curve showing the relationship between time 
to maturity and yield spread for an issuer with comparable 
bonds of various maturities outstanding, usually upward 
sloping.
Credit default swap (CDS)   A type of credit derivative in 
which one party, the credit protection buyer who is seeking 
credit protection against a third party, makes a series of 
regularly scheduled payments to the other party, the credit 
protection seller. The seller makes no payments until a 
credit event occurs.
Credit derivatives   A contract in which one party has the right 
to claim a payment from another party in the event that 
a specific credit event occurs over the life of the contract.
Credit enhancements   Provisions that may be used to reduce 
the credit risk of a bond issue.

Credit-  linked coupon bond   Bond for which the coupon 
changes when the bond’s credit rating changes.
Credit-  linked note (CLN)   Fixed-  income security in which the 
holder of the security has the right to withhold payment 
of the full amount due at maturity if a credit event occurs.
Credit migration risk   The risk that a bond issuer’s creditwor -
thiness deteriorates, or migrates lower, leading investors 
to believe the risk of default is higher. Also called down -
grade risk .
Credit risk   The risk of loss caused by a counterparty’s or 
debtor’s failure to make a promised payment. Also called 
default risk .
Credit scoring model   A statistical model used to classify 
borrowers according to creditworthiness.
Credit spread option   An option on the yield spread on a bond.
Credit tranching   A structure used to redistribute the credit 
risk associated with the collateral; a set of bond classes 
created to allow investors a choice in the amount of credit

risk that they prefer to bear.
Credit-  worthiness   The perceived ability of the borrower to 
pay what is owed on the borrowing in a timely manner; it 
represents the ability of a company to withstand adverse 
impacts on its cash flows.
Cross-  default provisions   Provisions whereby events of default 
such as non-  payment of interest on one bond trigger 
default on all outstanding debt; implies the same default 
probability for all issues.
Cross-  price elasticity of demand   The percentage change in 
quantity demanded for a given percentage change in the 
price of another good; the responsiveness of the demand 
for Product A that is associated with the change in price 
of Product B.
Cross-  sectional analysis   Analysis that involves comparisons 
across individuals in a group over a given time period or 
at a given point in time.
Cross-  sectional data   Observations over individual units at a 
point in time, as opposed to time-  series data.

G-8 Glossary
Crossing networks   Trading systems that match buyers and 
sellers who are willing to trade at prices obtained from 
other markets.
Crowding out   The thesis that government borrowing may 
divert private sector investment from taking place.
Cryptocurrency   An electronic medium of exchange that lacks 
physical form.
Cryptography   An algorithmic process to encrypt data, mak -
ing the data unusable if received by unauthorized parties.
Cumulative distribution function   A function giving the 
probability that a random variable is less than or equal to 
a specified value.
Cumulative preference shares   Preference shares for which 
any dividends that are not paid accrue and must be paid 
in full before dividends on common shares can be paid.
Cumulative relative frequency   For data grouped into inter -
vals, the fraction of total observations that are less than 
the value of the upper limit of a stated interval.
Cumulative voting   A voting process whereby each shareholder

can accumulate and vote all his or her shares for a single 
candidate in an election, as opposed to having to allocate 
their voting rights evenly among all candidates.
Currencies   Monies issued by national monetary authorities.
Currency option bonds   Bonds that give the bondholder the 
right to choose the currency in which he or she wants to 
receive interest payments and principal repayments.
Currency swap   A swap in which each party makes interest 
payments to the other in different currencies.
Current account   A component of the balance of payments 
account that measures the flow of goods and services.
Current assets   Assets that are expected to be consumed or 
converted into cash in the near future, typically one year 
or less. Also called liquid assets .
Current cost   With reference to assets, the amount of cash or 
cash equivalents that would have to be paid to buy the same 
or an equivalent asset today; with reference to liabilities,

the undiscounted amount of cash or cash equivalents that 
would be required to settle the obligation today.
Current government spending   With respect to government 
expenditures, spending on goods and services that are 
provided on a regular, recurring basis including health, 
education, and defense.
Current liabilities   Short-  term obligations, such as accounts 
payable, wages payable, or accrued liabilities, that are 
expected to be settled in the near future, typically one 
year or less.
Current ratio   A liquidity ratio calculated as current assets 
divided by current liabilities.
Current yield   The sum of the coupon payments received over 
the year divided by the flat price; also called the income  or 
interest yield  or running yield .
Curve duration   The sensitivity of the bond price (or the 
market value of a financial asset or liability) with respect 
to a benchmark yield curve.
Customs union   Extends the free trade area (FTA) by not only

allowing free movement of goods and services among 
members, but also creating a common trade policy against 
nonmembers.
CVaR   Conditional VaR, a tail loss measure. The weighted 
average of all loss outcomes in the statistical distribution 
that exceed the VaR loss.
Cyclical   See cyclical companies .Cyclical companies   Companies with sales and profits that 
regularly expand and contract with the business cycle or 
state of economy.
Daily settlement   See mark to market  and marking to market .
Dark pools   Alternative trading systems that do not display 
the orders that their clients send to them.
Data mining   The practice of determining a model by extensive 
searching through a dataset for statistically significant 
patterns. Also called data snooping .
Data science   An interdisciplinary field that brings computer 
science, statistics, and other disciplines together to analyze 
and produce insights from Big Data.
Data snooping   See data mining .

Day order   An order that is good for the day on which it is 
submitted. If it has not been filled by the close of business, 
the order expires unfilled.
Day’s sales outstanding   Estimate of the average number of 
days it takes to collect on credit accounts.
Days in receivables   Estimate of the average number of days 
it takes to collect on credit accounts.
Days of inventory on hand   An activity ratio equal to the 
number of days in the period divided by inventory turnover 
Dead cross   A technical analysis term that describes a situation 
where a short-  term moving average crosses from above a 
longer-  term moving average to below it; this movement 
is considered bearish.
Dealers   A financial intermediary that acts as a principal in 
trades.
Dealing securities   Securities held by banks or other financial 
intermediaries for trading purposes.
Debentures   Type of bond that can be secured or unsecured.

Debt incurrence test   A financial covenant made in conjunc -
tion with existing debt that restricts a company’s ability to 
incur additional debt at the same seniority based on one 
or more financial tests or conditions.
Debt-  rating approach   A method for estimating a company’s 
before-  tax cost of debt based upon the yield on comparably 
rated bonds for maturities that closely match that of the 
company’s existing debt.
Debt-  to- assets ratio   A solvency ratio calculated as total debt 
divided by total assets.
Debt-  to- capital ratio   A solvency ratio calculated as total 
debt divided by total debt plus total shareholders’ equity.
Debt-  to- equity ratio   A solvency ratio calculated as total debt 
divided by total shareholders’ equity.
Declaration date   The day that the corporation issues a state -
ment declaring a specific dividend.
Decreasing returns to scale   When a production process leads 
to increases in output that are proportionately smaller than 
the increase in inputs.

Deductible temporary differences   Temporary differences 
that result in a reduction of or deduction from taxable 
income in a future period when the balance sheet item is 
recovered or settled.
Deep learning   Machine learning using neural networks with 
many hidden layers.
Deep learning nets   Machine learning using neural networks 
with many hidden layers.
Default probability   The probability that a borrower defaults 
or fails to meet its obligation to make full and timely pay -
ments of principal and interest, according to the terms of 
the debt security. Also called default risk .

G-9 Glossary
Default risk   The probability that a borrower defaults or fails 
to meet its obligation to make full and timely payments of 
principal and interest, according to the terms of the debt 
security. Also called default probability .
Default risk premium   An extra return that compensates 
investors for the possibility that the borrower will fail to 
make a promised payment at the contracted time and in 
the contracted amount.
Defensive companies   Companies with sales and profits that 
have little sensitivity to the business cycle or state of the 
economy.
Defensive interval ratio   A liquidity ratio that estimates the 
number of days that an entity could meet cash needs 
from liquid assets; calculated as (cash + short-  term mar -
ketable investments + receivables) divided by daily cash 
Deferred coupon bond   Bond that pays no coupons for its first 
few years but then pays a higher coupon than it otherwise 
normally would for the remainder of its life. Also called

split coupon bond .
Deferred income   A liability account for money that has been 
collected for goods or services that have not yet been 
delivered; payment received in advance of providing a 
good or service.
Deferred revenue   A liability account for money that has 
been collected for goods or services that have not yet 
been delivered; payment received in advance of providing 
a good or service.
Deferred tax assets   A balance sheet asset that arises when an 
excess amount is paid for income taxes relative to account -
ing profit. The taxable income is higher than accounting 
profit and income tax payable exceeds tax expense. The 
company expects to recover the difference during the 
course of future operations when tax expense exceeds 
income tax payable.
Deferred tax liabilities   A balance sheet liability that arises 
when a deficit amount is paid for income taxes relative 
to accounting profit. The taxable income is less than the 
accounting profit and income tax payable is less than tax

expense. The company expects to eliminate the liability over 
the course of future operations when income tax payable 
exceeds tax expense.
Defined benefit pension plans   Plans in which the company 
promises to pay a certain annual amount (defined benefit) 
to the employee after retirement. The company bears the 
investment risk of the plan assets.
Defined contribution pension plans   Individual accounts 
to which an employee and typically the employer makes 
contributions, generally on a tax-  advantaged basis. The 
amounts of contributions are defined at the outset, but 
the future value of the benefit is unknown. The employee 
bears the investment risk of the plan assets.
Deflation   Negative inflation.
Degree of confidence   The probability that a confidence inter -
val includes the unknown population parameter.
Degree of financial leverage   (DFL) The ratio of the per -
centage change in net income to the percentage change in 
operating income; the sensitivity of the cash flows available

to owners when operating income changes.
Degree of operating leverage   (DOL) The ratio of the per -
centage change in operating income to the percentage 
change in units sold; the sensitivity of operating income 
to changes in units sold.Degree of total leverage   The ratio of the percentage change 
in net income to the percentage change in units sold; the 
sensitivity of the cash flows to owners to changes in the 
number of units produced and sold.
Degrees of freedom (df)   The number of independent obser -
vations used.
Delta   The sensitivity of the derivative price to a small change 
in the value of the underlying asset.
Demand curve   Graph of the inverse demand function. A 
graph showing the demand relation, either the highest 
quantity willingly purchased at each price or the highest 
price willingly paid for each quantity.
Demand function   A relationship that expresses the quantity 
demanded of a good or service as a function of own-  price 
and possibly other variables.

Demand-  pull  Type of inflation in which increasing demand 
raises prices generally, which then are reflected in a busi -
ness’s costs as workers demand wage hikes to catch up 
with the rising cost of living.
Demand shock   A typically unexpected disturbance to 
demand, such as an unexpected interruption in trade or 
transportation.
Dependent   With reference to events, the property that the 
probability of one event occurring depends on (is related 
to) the occurrence of another event.
Depository bank   A bank that raises funds from depositors 
and other investors and lends it to borrowers.
Depository institutions   Commercial banks, savings and loan 
banks, credit unions, and similar institutions that raise 
funds from depositors and other investors and lend it to 
borrowers.
Depository receipt   A security that trades like an ordinary 
share on a local exchange and represents an economic 
interest in a foreign company.

Depreciation   The process of systematically allocating the cost 
of long-  lived (tangible) assets to the periods during which 
the assets are expected to provide economic benefits.
Depression   See contraction .
Derivative pricing rule   A pricing rule used by crossing net -
works in which a price is taken (derived) from the price 
that is current in the asset’s primary market.
Derivatives   A financial instrument whose value depends on 
the value of some underlying asset or factor (e.g., a stock 
price, an interest rate, or exchange rate).
Descriptive statistics   The study of how data can be summa -
rized effectively.
Development capital   Minority equity investments in more-  
mature companies that are seeking capital to expand or 
restructure operations, enter new markets, or finance 
major acquisitions.
Diffuse prior   The assumption of equal prior probabilities.
Diffusion index   Reflects the proportion of the index’s com -

ponents that are moving in a pattern consistent with the 
overall index.
Diluted EPS   The EPS that would result if all dilutive securities 
were converted into common shares.
Diluted shares   The number of shares that would be outstand -
ing if all potentially dilutive claims on common shares (e.g., 
convertible debt, convertible preferred stock, and employee 
stock options) were exercised.
Diminishing balance method   An accelerated depreciation 
method, i.e., one that allocates a relatively large propor -
tion of the cost of an asset to the early years of the asset’s 
useful life.

G-10 Glossary
Diminishing marginal productivity   Describes a state in 
which each additional unit of input produces less output 
than previously.
Direct debit program   An arrangement whereby a customer 
authorizes a debit to a demand account; typically used by 
companies to collect routine payments for services.
Direct financing leases   A type of finance lease, from a lessor 
perspective, where the present value of the lease payments 
(lease receivable) equals the carrying value of the leased 
asset. The revenues earned by the lessor are financing in 
nature.
Direct format   With reference to the cash flow statement, a 
format for the presentation of the statement in which cash 
flow from operating activities is shown as operating cash 
receipts less operating cash disbursements. Also called 
direct method .
Direct method   See direct format .
Direct taxes   Taxes levied directly on income, wealth, and 
corporate profits.
Direct write-  off method   An approach to recognizing credit

losses on customer receivables in which the company waits 
until such time as a customer has defaulted and only then 
recognizes the loss.
Disbursement float   The amount of time between check issu -
ance and a check’s clearing back against the company’s 
account.
Discount   To reduce the value of a future payment in allowance 
for how far away it is in time; to calculate the present value 
of some future amount. Also, the amount by which an 
instrument is priced below its face (par) value.
Discount interest   A procedure for determining the interest 
on a loan or bond in which the interest is deducted from 
the face value in advance.
Discount margin   See required margin.
Discount rates   In general, the interest rate used to calculate 
a present value. In the money market, however, discount 
rate is a specific type of quoted rate.
Discounted cash flow models   Valuation models that estimate 
the intrinsic value of a security as the present value of the

future benefits expected to be received from the security.
Discouraged worker   A person who has stopped looking for 
a job or has given up seeking employment.
Discrete random variable   A random variable that can take 
on at most a countable number of possible values.
Discriminatory pricing rule   A pricing rule used in continuous 
markets in which the limit price of the order or quote that 
first arrived determines the trade price.
Diseconomies of scale   Increase in cost per unit resulting 
from increased production.
Dispersion   The variability around the central tendency.
Display size   The size of an order displayed to public view.
Distressed investing   Investing in securities of companies in 
financial difficulties. Private equity funds that specialize 
in distressed investing typically buy the debt of mature 
companies in financial difficulties.
Distributed ledger   A type of database that may be shared 
among entities in a network.
Distributed ledger technology   Technology based on a dis -

tributed ledger.
Divergence   In technical analysis, a term that describes the 
case when an indicator moves differently from the security 
being analyzed.Diversification ratio   The ratio of the standard deviation of 
an equally weighted portfolio to the standard deviation of 
a randomly selected security.
Dividend   A distribution paid to shareholders based on the 
number of shares owned.
Dividend discount model   (DDM) A present value model that 
estimates the intrinsic value of an equity share based on 
the present value of its expected future dividends.
Dividend discount model based approach   An approach for 
estimating a country’s equity risk premium. The market rate 
of return is estimated as the sum of the dividend yield and 
the growth rate in dividends for a market index. Subtracting 
the risk-  free rate of return from the estimated market 
return produces an estimate for the equity risk premium.
Dividend payout ratio   The ratio of cash dividends paid to 
earnings for a period.

Divisor   A number (denominator) used to determine the value 
of a price return index. It is initially chosen at the incep -
tion of an index and subsequently adjusted by the index 
provider, as necessary, to avoid changes in the index value 
that are unrelated to changes in the prices of its constit -
uent securities.
Domestic content provisions   Stipulate that some percentage 
of the value added or components used in production 
should be of domestic origin.
Double bottoms   In technical analysis, a reversal pattern that 
is formed when the price reaches a low, rebounds, and 
then sells off back to the first low level; used to predict a 
change from a downtrend to an uptrend.
Double coincidence of wants   A prerequisite to barter trades, 
in particular that both economic agents in the transaction 
want what the other is selling.
Double declining balance depreciation   An accelerated 
depreciation method that involves depreciating the asset

at double the straight-  line rate. This rate is multiplied by 
the book value of the asset at the beginning of the period 
(a declining balance) to calculate depreciation expense.
Double top   In technical analysis, a reversal pattern that is 
formed when an uptrend reverses twice at roughly the 
same high price level; used to predict a change from an 
uptrend to a downtrend.
Down transition probability   The probability that an asset’s 
value moves down in a model of asset price dynamics.
Downgrade risk   The risk that a bond issuer’s creditworthiness 
deteriorates, or migrates lower, leading investors to believe 
the risk of default is higher. Also called credit migration risk .
Drag on liquidity   When receipts lag, creating pressure from 
the decreased available funds.
Drawdown   A percentage peak-  to- trough reduction in net 
asset value.
Dual-  currency bonds   Bonds that make coupon payments in 
one currency and pay the par value at maturity in another 
currency.

currency.
DuPont analysis   An approach to decomposing return on 
investment, e.g., return on equity, as the product of other 
Duration   A measure of the approximate sensitivity of a secu -
rity to a change in interest rates (i.e., a measure of interest 
rate risk).
Duration gap   A bond’s Macaulay duration minus the invest -
ment horizon.
Dutch Book theorem   A result in probability theory stating 
that inconsistent probabilities create profit opportunities.
Early repayment option   See prepayment option .

G-11 Glossary
Earnings per share   The amount of income earned during a 
period per share of common stock.
Earnings surprise   The portion of a company’s earnings that 
is unanticipated by investors and, according to the efficient 
market hypothesis, merits a price adjustment.
Economic costs   All the remuneration needed to keep a pro -
ductive resource in its current employment or to acquire 
the resource for productive use; the sum of total accounting 
costs and implicit opportunity costs.
Economic indicator   A variable that provides information on 
the state of the overall economy.
Economic loss   The amount by which accounting profit is less 
than normal profit.
Economic order quantity–reorder point (EOQ–ROP)   An 
approach to managing inventory based on expected 
demand and the predictability of demand; the ordering 
point for new inventory is determined based on the costs 
of ordering and carrying inventory, such that the total cost 
associated with inventory is minimized.

Economic profit   Equal to accounting profit less the implicit 
opportunity costs not included in total accounting costs; 
the difference between total revenue (TR) and total cost 
(TC). Also called abnormal profit  or supernormal profit .
Economic stabilization   Reduction of the magnitude of eco -
nomic fluctuations.
Economic union   Incorporates all aspects of a common market 
and in addition requires common economic institutions 
and coordination of economic policies among members.
Economies of scale   Reduction in cost per unit resulting from 
increased production.
Effective annual rate   The amount by which a unit of currency 
will grow in a year with interest on interest included.
Effective annual yield (EAY)   An annualized return that 
accounts for the effect of interest on interest; EAY is com -
puted by compounding 1 plus the holding period yield 
forward to one year, then subtracting 1.
Effective convexity   A curve convexity  statistic that measures

the secondary effect of a change in a benchmark yield curve 
on a bond’s price.
Effective duration   The sensitivity of a bond’s price to a change 
in a benchmark yield curve.
Effective interest rate   The borrowing rate or market rate 
that a company incurs at the time of issuance of a bond.
Efficient market   A market in which asset prices reflect new 
information quickly and rationally.
Elastic   Said of a good or service when the magnitude of elas -
ticity is greater than one.
Elasticity   The percentage change in one variable for a per -
centage change in another variable; a general measure of 
how sensitive one variable is to a change in the value of 
another variable.
Elasticity of demand   A measure of the sensitivity of quan -
tity demanded to a change in a product’s own price: 
%∆QD/%∆P.
Elasticity of supply   A measure of the sensitivity of quantity 
supplied to a change in price: %∆ QS/%∆P.
Electronic communications networks   See alternative trading 
systems .

systems .
Electronic funds transfer (EFT)   The use of computer networks 
to conduct financial transactions electronically.
Elliott wave theory   A technical analysis theory that claims 
that the market follows regular, repeated waves or cycles.Embedded option   Contingency provisions that provide the 
issuer or the bondholders the right, but not the obligation, 
to take action. These options are not part of the security 
and cannot be traded separately.
Empirical probability   The probability of an event estimated 
as a relative frequency of occurrence.
Employed   The number of people with a job.
Enterprise risk management   An overall assessment of a 
company’s risk position. A centralized approach to risk 
management sometimes called firmwide risk management.
Enterprise value   A measure of a company’s total market value 
from which the value of cash and short-  term investments 
have been subtracted.
Equal weighting   An index weighting method in which an

equal weight is assigned to each constituent security at 
inception.
Equipment trust certificates   Bonds secured by specific types 
of equipment or physical assets.
Equity   Assets less liabilities; the residual interest in the assets 
after subtracting the liabilities.
Equity risk premium   The expected return on equities minus 
the risk-  free rate; the premium that investors demand for 
investing in equities.
Equity swap   A swap transaction in which at least one cash 
flow is tied to the return to an equity portfolio position, 
often an equity index.
ESG   An acronym that encompasses environmental, social 
and governance.
ESG incorporation   The integration of qualitative and quanti -
tative environmental, social, and governance factors into 
traditional security and industry analysis; also known as 
ESG integration .
ESG integration   The integration of qualitative and quanti -
traditional security and industry analysis; also known as

ESG incorporation .
ESG investing   The consideration of environmental, social, and 
governance factors in the investment process.
Estimate   The particular value calculated from sample obser -
vations using an estimator.
Estimation   With reference to statistical inference, the sub -
division dealing with estimating the value of a population 
parameter.
Estimator   An estimation formula; the formula used to com -
pute the sample mean and other sample statistics are 
examples of estimators.
Ethical principles   Beliefs regarding what is good, acceptable, 
or obligatory behavior and what is bad, unacceptable, or 
forbidden behavior.
Ethics   The study of moral principles or of making good choices. 
Ethics encompasses a set of moral principles and rules of 
conduct that provide guidance for our behavior.
Eurobonds   Type of bond issued internationally, outside the 
jurisdiction of the country in whose currency the bond is 
denominated.
European option   An option that can only be exercised on

its expiration date.
European-  style   Said of an option contract that can only be 
exercised on the option’s expiration date.
Event   Any outcome or specified set of outcomes of a random 
variable.
Ex- dividend date   The first date that a share trades without 
(i.e., “ex”) the dividend.

G-12 Glossary
Excess kurtosis   Degree of kurtosis (fatness of tails) in excess 
of the kurtosis of the normal distribution.
Exchanges   Places where traders can meet to arrange their 
trades.
Exclusionary screening   An ESG implementation approach 
that excludes certain sectors or companies that deviate 
from an investor’s accepted standards. Also called negative 
screening  or norms-  based screening .
Execution instructions   Instructions that indicate how to fill 
an order.
Exercise   The process of using an option to buy or sell the 
underlying.
Exercise price   The fixed price at which an option holder can 
buy or sell the underlying. Also called strike price , striking 
price , or strike .
Exercise value   The value obtained if an option is exercised 
based on current conditions. Also known as intrinsic value .
Exhaustive   Covering or containing all possible outcomes.
Expansion   The period of a business cycle after its lowest point 
and before its highest point.

Expansionary   Tending to cause the real economy to grow.
Expansionary fiscal policy   Fiscal policy aimed at achieving 
real economic growth.
Expected inflation   The level of inflation that economic agents 
expect in the future.
Expected loss   Default probability times Loss severity given 
default.
Expected value   The probability-  weighted average of the pos -
sible outcomes of a random variable.
Expenses   Outflows of economic resources or increases in 
liabilities that result in decreases in equity (other than 
decreases because of distributions to owners); reductions 
in net assets associated with the creation of revenues.
Experience curve   A curve that shows the direct cost per unit 
of good or service produced or delivered as a typically 
declining function of cumulative output.
Export subsidy   Paid by the government to the firm when it 
exports a unit of a good that is being subsidized.
Exports   Goods and services that an economy sells to other 

Extension risk   The risk that when interest rates rise, fewer 
prepayments will occur because homeowners are reluctant 
to give up the benefits of a contractual interest rate that 
now looks low. As a result, the security becomes longer in 
maturity than anticipated at the time of purchase.
Externality   An effect of a market transaction that is borne by 
parties other than those who transacted.
Extra dividend   A dividend paid by a company that does not 
pay dividends on a regular schedule, or a dividend that 
supplements regular cash dividends with an extra payment.
Extreme value theory   A branch of statistics that focuses 
primarily on extreme outcomes.
Face value   The amount of cash payable by a company to 
the bondholders when the bonds mature; the promised 
payment at maturity separate from any coupon payment.
Factor   A common or underlying element with which several 
variables are correlated.
Fair value   The amount at which an asset could be exchanged,

or a liability settled, between knowledgeable, willing parties 
in an arm’s-  length transaction; the price that would be 
received to sell an asset or paid to transfer a liability in an 
orderly transaction between market participants.
Fed funds rate   The US interbank lending rate on overnight 
borrowings of reserves.Federal funds rate   The US interbank lending rate on overnight 
borrowings of reserves.
Fiat money   Money that is not convertible into any other 
commodity.
Fibonacci sequence   A sequence of numbers starting with 0 
and 1, and then each subsequent number in the sequence 
is the sum of the two preceding numbers. In Elliott Wave 
Theory, it is believed that market waves follow patterns that 
are the ratios of the numbers in the Fibonacci sequence.
Fiduciary call   A combination of a European call and a risk-  free 
bond that matures on the option expiration day and has a 
face value equal to the exercise price of the call.
FIFO method   The first in, first out, method of accounting

for inventory, which matches sales against the costs of 
items of inventory in the order in which they were placed 
Fill or kill   See immediate or cancel order .
Finance lease   Essentially, the purchase of some asset by the 
buyer (lessee) that is directly financed by the seller (lessor). 
Also called capital lease .
Financial account   A component of the balance of payments 
account that records investment flows.
Financial flexibility   The ability to react and adapt to financial 
adversities and opportunities.
Financial leverage   The extent to which a company can effect, 
through the use of debt, a proportional change in the return 
on common equity that is greater than a given proportional 
change in operating income; also, short for the financial 
leverage ratio.
Financial leverage ratio   A measure of financial leverage calcu -
lated as average total assets divided by average total equity.
Financial risk   The risk that environmental, social, or gover -

nance risk factors will result in significant costs or other 
losses to a company and its shareholders; the risk arising 
from a company’s obligation to meet required payments 
under its financing agreements.
Financing activities   Activities related to obtaining or repaying 
capital to be used in the business (e.g., equity and long-  
term debt).
Fintech   Technological innovation in the design and delivery 
of financial services and products in the financial industry.
Firm commitment offering   See underwritten offering .
First-  degree price discrimination   Where a monopolist is able 
to charge each customer the highest price the customer 
is willing to pay.
First lien debt   Debt secured by a pledge of certain assets that 
could include buildings, but may also include property and 
equipment, licenses, patents, brands, etc.
First mortgage debt   Debt secured by a pledge of a specific 
property.
Fiscal multiplier   The ratio of a change in national income to 
a change in government spending.

Fiscal policy   The use of taxes and government spending to 
affect the level of aggregate expenditures.
Fisher effect   The thesis that the real rate of interest in an 
economy is stable over time so that changes in nominal 
interest rates are the result of changes in expected inflation.
Fisher index   The geometric mean of the Laspeyres index.
Fixed charge coverage   A solvency ratio measuring the num -
ber of times interest and lease payments are covered by 
operating income, calculated as (EBIT + lease payments) 
divided by (interest payments + lease payments).
Fixed costs   Costs that remain at the same level regardless of 
a company’s level of production and sales.

G-13 Glossary
Fixed-  for-  floating interest rate swap   An interest rate swap 
in which one party pays a fixed rate and the other pays 
a floating rate, with both sets of payments in the same 
currency. Also called plain vanilla swap  or vanilla swap .
Fixed rate perpetual preferred stock   Nonconvertible, non -
callable preferred stock that has a fixed dividend rate and 
no maturity date.
Flags   A technical analysis continuation pattern formed by 
parallel trendlines, typically over a short period.
Flat price   The full price of a bond minus the accrued interest; 
also called the quoted  or clean  price.
Float   In the context of customer receipts, the amount of money 
that is in transit between payments made by customers and 
the funds that are usable by the company.
Float-  adjusted market-  capitalization weighting   An index 
weighting method in which the weight assigned to each 
constituent security is determined by adjusting its market 
capitalization for its market float.

Float factor   An estimate of the average number of days it 
takes deposited checks to clear; average daily float divided 
by average daily deposit.
Floaters   See floating-  rate notes .
Floating-  rate notes   A note on which interest payments are 
not fixed, but instead vary from period to period depending 
on the current level of a reference interest rate.
Flotation cost   Fees charged to companies by investment 
bankers and other costs associated with raising new capital.
Foreclosure   Allows the lender to take possession of a mort -
gaged property if the borrower defaults and then sell it to 
recover funds.
Foreign currency reserves   Holding by the central bank of 
non-  domestic currency deposits and non-  domestic bonds.
Foreign direct investment   Direct investment by a firm in 
one country (the source country) in productive assets in 
a foreign country (the host country).
Foreign exchange gains (or losses)   Gains (or losses) that

occur when the exchange rate changes between the inves -
tor’s currency and the currency that foreign securities are 
denominated in.
Foreign portfolio investment   Shorter-  term investment by 
individuals, firms, and institutional investors (e.g., pension 
funds) in foreign financial instruments such as foreign 
stocks and foreign government bonds.
Forward commitments   Class of derivatives that provides 
the ability to lock in a price to transact in the future at a 
previously agreed-  upon price.
Forward contract   An agreement between two parties in which 
one party, the buyer, agrees to buy from the other party, 
the seller, an underlying asset at a later date for a price 
established at the start of the contract.
Forward curve   A series of forward rates, each having the 
same timeframe.
Forward market   For future delivery, beyond the usual settle -
ment time period in the cash market.
Forward price   The fixed price or rate at which the transaction

scheduled to occur at the expiration of a forward contract 
will take place. This price is agreed on at the initiation date 
of the contract.
Forward rate   The interest rate on a bond or money market 
instrument traded in a forward market. A forward rate 
can be interpreted as an incremental, or marginal, return 
for extending the time-  to- maturity for an additional time 
period.Forward rate agreements   A forward contract calling for 
one party to make a fixed interest payment and the other 
to make an interest payment at a rate to be determined at 
the contract expiration.
Fractile   A value at or below which a stated fraction of the 
data lies.
Fractional reserve banking   Banking in which reserves con -
stitute a fraction of deposits.
Free cash flow   The actual cash that would be available to the 
company’s investors after making all investments necessary 
to maintain the company as an ongoing enterprise (also 
referred to as free cash flow to the firm); the internally

generated funds that can be distributed to the company’s 
investors (e.g., shareholders and bondholders) without 
impairing the value of the company.
Free cash flow to equity (FCFE)   The cash flow available to 
a company’s common shareholders after all operating 
expenses, interest, and principal payments have been made, 
and necessary investments in working and fixed capital 
have been made.
Free-  cash-  flow-  to- equity models   Valuation models based 
on discounting expected future free cash flow to equity.
Free cash flow to the firm (FCFF)   The cash flow available 
to the company’s suppliers of capital after all operating 
expenses have been paid and necessary investments in 
working capital and fixed capital have been made.
Free float   The number of shares that are readily and freely 
tradable in the secondary market.
Free trade   When there are no government restrictions on a 
country’s ability to trade.
Free trade areas   One of the most prevalent forms of regional

integration, in which all barriers to the flow of goods and 
services among members have been eliminated.
Frequency distribution   A tabular display of data summarized 
into a relatively small number of intervals.
Frequency polygon   A graph of a frequency distribution 
obtained by drawing straight lines joining successive points 
representing the class frequencies.
Full price   The price of a security with accrued interest; also 
called the invoice  or dirty  price.
Fundamental analysis   The examination of publicly available 
information and the formulation of forecasts to estimate 
the intrinsic value of assets.
Fundamental value   The underlying or true value of an asset 
based on an analysis of its qualitative and quantitative 
characteristics. Also called intrinsic value .
Fundamental weighting   An index weighting method in which 
the weight assigned to each constituent security is based 
on its underlying company’s size. It attempts to address

the disadvantages of market-  capitalization weighting by 
using measures that are independent of the constituent 
security’s price.
Funds of funds   Funds that hold a portfolio of hedge funds.
Funds of hedge funds   Funds that hold a portfolio of hedge 
funds.
Future value (FV)   The amount to which a payment or series 
of payments will grow by a stated future date.
Futures contract   A variation of a forward contract that has 
essentially the same basic definition but with some addi -
tional features, such as a clearinghouse guarantee against 
credit losses, a daily settlement of gains and losses, and an 
organized electronic or floor trading facility.
Futures price   The agreed-  upon price of a futures contract.

G-14 Glossary
FX swap   The combination of a spot and a forward FX 
transaction.
G- spread   The yield spread in basis points over an actual or 
interpolated government bond.
Gains   Asset inflows not directly related to the ordinary activ -
ities of the business.
Game theory   The set of tools decision makers use to incorpo -
rate responses by rival decision makers into their strategies.
Gamma   A numerical measure of how sensitive an option’s 
delta (the sensitivity of the derivative’s price) is to a change 
in the value of the underlying.
GDP deflator   A gauge of prices and inflation that measures 
the aggregate changes in prices across the overall economy.
General partner   (GP) The partner that runs the business and 
theoretically bears unlimited liability.
Geometric mean   A measure of central tendency computed by 
taking the nth root of the product of n non-  negative values.
Giffen goods   Goods that are consumed more as the price 
of the good rises because it is a very inferior good whose

income effect overwhelms its substitution effect when 
price changes.
Gilts   Bonds issued by the UK government.
Giro system   An electronic payment system used widely in 
Europe and Japan.
Global depository receipt   A depository receipt that is issued 
outside of the company’s home country and outside of the 
United States.
Global minimum-  variance portfolio   The portfolio on the 
minimum-  variance frontier with the smallest variance 
of return.
Global registered share   A common share that is traded on 
different stock exchanges around the world in different 
currencies.
Gold standard   With respect to a currency, if a currency is on 
the gold standard a given amount can be converted into a 
prespecified amount of gold.
Golden cross   A technical analysis term that describes a situa -
tion where a short-  term moving average crosses from below 
a longer-  term moving average to above it; this movement 
is considered bullish.
Good-  on- close   An execution instruction specifying that an

order can only be filled at the close of trading. Also called 
market on close .
Good-  on- open   An execution instruction specifying that an 
order can only be filled at the opening of trading.
Good-  till-  cancelled order   An order specifying that it is valid 
until the entity placing the order has cancelled it (or, com -
monly, until some specified amount of time such as 60 days 
has elapsed, whichever comes sooner).
Goodwill   An intangible asset that represents the excess of the 
purchase price of an acquired company over the value of 
the net assets acquired.
Government equivalent yield   A yield that restates a yield-  
to- maturity based on 30/360 day-  count to one based on 
actual/actual.
Green bonds   A bond used in green finance whereby the 
proceeds are earmarked towards environmental-  related 
products.
Green finance   A type of finance that addresses environmental 
concerns while achieving economic growth.
Grey market   The forward market for bonds about to be issued.

Also called “when issued” market.Gross domestic product   The market value of all final goods 
and services produced within the economy in a given 
period of time (output definition) or, equivalently, the 
aggregate income earned by all households, all companies, 
and the government within the economy in a given period 
of time (income definition).
Gross margin   Sales minus the cost of sales (i.e., the cost of 
goods sold for a manufacturing company).
Gross profit   Sales minus the cost of sales (i.e., the cost of 
Gross profit margin   The ratio of gross profit to revenues.
Grouping by function   With reference to the presentation of 
expenses in an income statement, the grouping together 
of expenses serving the same function, e.g. all items that 
are costs of goods sold.
Grouping by nature   With reference to the presentation of 
expenses in an income statement, the grouping together of 
expenses by similar nature, e.g., all depreciation expenses.

Growth cyclical   A term sometimes used to describe companies 
that are growing rapidly on a long-  term basis but that still 
experience above-  average fluctuation in their revenues and 
profits over the course of a business cycle.
Growth investors   With reference to equity investors, investors 
who seek to invest in high-  earnings-  growth companies.
Guarantee certificate   A type of structured financial instru -
ment that provides investors capital protection. It combines 
a zero-  coupon bond and a call option on some underlying 
asset.
Haircut   See repo margin .
Harmonic mean   A type of weighted mean computed by 
averaging the reciprocals of the observations, then taking 
the reciprocal of that average.
Head and shoulders pattern   In technical analysis, a rever -
sal pattern that is formed in three parts: a left shoulder, 
head, and right shoulder; used to predict a change from 
an uptrend to a downtrend.
Headline inflation   The inflation rate calculated based on

the price index that includes all goods and services in an 
economy.
Hedge funds   Private investment vehicles that typically use 
leverage, derivatives, and long and short investment 
strategies.
Hedge portfolio   A hypothetical combination of the derivative 
and its underlying that eliminates risk.
Held for trading   Debt or equity financial assets bought with 
the intention to sell them in the near term, usually less 
than three months; securities that a company intends to 
trade. Also called trading securities .
Held-  to- maturity   Debt (fixed-  income) securities that a com -
pany intends to hold to maturity; these are presented at 
their original cost, updated for any amortization of dis -
counts or premiums.
Herding   Clustered trading that may or may not be based on 
Hidden order   An order that is exposed not to the public but 
only to the brokers or exchanges that receive it.
High-  frequency trading   A form of algorithmic trading that

makes use of vast quantities of data to execute trades on 
ultra-  high-  speed networks in fractions of a second.
High-  water marks   The highest value, net of fees, that a fund 
has reached in history. It reflects the highest cumulative 
return used to calculate an incentive fee.
Histogram   A bar chart of data that have been grouped into 
a frequency distribution.

G-15 Glossary
Historical cost   In reference to assets, the amount paid to 
purchase an asset, including any costs of acquisition and/
or preparation; with reference to liabilities, the amount 
of proceeds received in exchange in issuing the liability.
Historical equity risk premium approach   An estimate of a 
country’s equity risk premium that is based upon the his -
torical averages of the risk-  free rate and the rate of return 
on the market portfolio.
Historical simulation   Another term for the historical method 
of estimating VaR. This term is somewhat misleading in that 
Holder-  of- record date   The date that a shareholder listed on 
the corporation’s books will be deemed to have owner -
ship of the shares for purposes of receiving an upcoming 
dividend.

dividend.
Holding period return   The return that an investor earns 
during a specified holding period; a synonym for total 
return.
Holding period yield (HPY)   The return that an investor earns 
during a specified holding period; holding period return 
with reference to a fixed-  income instrument.
Homogeneity of expectations   The assumption that all inves -
tors have the same economic expectations and thus have 
the same expectations of prices, cash flows, and other 
investment characteristics.
Horizon yield   The internal rate of return between the total 
return (the sum of reinvested coupon payments and the 
sale price or redemption amount) and the purchase price 
of the bond.
Horizontal analysis   Common-  size analysis that involves com -
paring a specific financial statement with that statement in 
prior or future time periods; also, cross-  sectional analysis 
of one company with another.
Horizontal demand schedule   Implies that at a given price,

the response in the quantity demanded is infinite.
Hostile takeover   An attempt by one entity to acquire a com -
pany without the consent of the company’s management.
Household   A person or a group of people living in the same 
residence, taken as a basic unit in economic analysis.
Human capital   The accumulated knowledge and skill that 
workers acquire from education, training, or life experience 
and the corresponding present value of future earnings to 
be generated by said skilled individual.
Hurdle rate   The rate of return that must be met for a project 
to be accepted.
Hypothesis   With reference to statistical inference, a statement 
about one or more populations.
Hypothesis testing   With reference to statistical inference, the 
subdivision dealing with the testing of hypotheses about 
one or more populations.
I- spread   The yield spread of a specific bond over the standard 
swap rate in that currency of the same tenor.
Iceberg order   An order in which the display size is less than

the order’s full size.
If- converted method   A method for accounting for the effect 
of convertible securities on earnings per share (EPS) that 
specifies what EPS would have been if the convertible secu -
rities had been converted at the beginning of the period, 
taking account of the effects of conversion on net income 
and the weighted average number of shares outstanding.Immediate or cancel order   An order that is valid only upon 
receipt by the broker or exchange. If such an order can -
not be filled in part or in whole upon receipt, it cancels 
immediately. Also called fill or kill .
Impact investing   Investing that seeks to achieve targeted 
social or environmental objectives along with measurable 
financial returns through engagement with a company or 
by direct investment in projects or companies.
Impact lag   The lag associated with the result of actions affect -
ing the economy with delay.
Implicit price deflator for GDP   A gauge of prices and inflation

that measures the aggregate changes in prices across the 
overall economy.
Implied forward rates   Calculated from spot rates, an implied 
forward rate is a break-  even reinvestment rate that links 
the return on an investment in a shorter-  term zero-  coupon 
bond to the return on an investment in a longer-  term 
zero-  coupon bond.
Implied volatility   The volatility that option traders use to 
price an option, implied by the price of the option and a 
particular option-  pricing model.
Import license   Specifies the quantity of a good that can be 
imported into a country.
Imports   Goods and services that a domestic economy (i.e., 
house-  holds, firms, and government) purchases from other 
In the money   Options that, if exercised, would result in 
the value received being worth more than the payment 
required to exercise.
Incentive fee   Fees paid to the general partner from the limited 
partner(s) based on realized profits.

Income   Increases in economic benefits in the form of inflows 
or enhancements of assets, or decreases of liabilities that 
result in an increase in equity (other than increases result -
ing from contributions by owners).
Income elasticity of demand   A measure of the responsiveness 
of demand to changes in income, defined as the percentage 
change in quantity demanded divided by the percentage 
change in income.
Income tax paid   The actual amount paid for income taxes in 
the period; not a provision, but the actual cash outflow.
Income tax payable   The income tax owed by the company 
on the basis of taxable income.
Income trust   A type of equity ownership vehicle established 
as a trust issuing ownership shares known as units.
Increasing marginal returns   When the marginal product 
of a resource increases as additional units of that input 
are employed.
Increasing returns to scale   When a production process leads

to increases in output that are proportionately larger than 
Incremental cash flow   The cash flow that is realized because 
of a decision; the changes or increments to cash flows 
resulting from a decision or action.
Indenture   Legal contract that describes the form of a bond, the 
obligations of the issuer, and the rights of the bondholders. 
Also called the trust deed .
Independent   With reference to events, the property that the 
occurrence of one event does not affect the probability of 
another event occurring.
Independent projects   Independent projects are projects 
whose cash flows are independent of each other.

G-16 Glossary
Independently and identically distributed (IID)   With respect 
to random variables, the property of random variables 
that are independent of each other but follow the identical 
probability distribution.
Index-  linked bond   Bond for which coupon payments and/
or principal repayment are linked to a specified index.
Index of Leading Economic Indicators   A composite of eco -
nomic variables used by analysts to predict future economic 
conditions.
Indexing   An investment strategy in which an investor con -
structs a portfolio to mirror the performance of a specified 
index.
Indifference curve   A curve representing all the combinations 
of two goods or attributes such that the consumer is entirely 
indifferent among them.
Indirect format   With reference to cash flow statements, a 
format for the presentation of the statement which, in the 
operating cash flow section, begins with net income then 
shows additions and subtractions to arrive at operating

cash flow. Also called indirect method .
Indirect method   See indirect format .
Indirect taxes   Taxes such as taxes on spending, as opposed 
to direct taxes.
Industry   A group of companies offering similar products 
and/or services.
Industry analysis   The analysis of a specific branch of manu -
facturing, service, or trade.
Inelastic   Said of a good or service when the magnitude of 
elasticity is less than one. Insensitive to price changes.
Inferior goods   A good whose consumption decreases as 
income increases.
Inflation   The percentage increase in the general price level 
from one period to the next; a sustained rise in the overall 
level of prices in an economy.
Inflation-  linked bond   Type of index-  linked bond that offers 
investors protection against inflation by linking the bond’s 
coupon payments and/or the principal repayment to an 
index of consumer prices. Also called linkers .
Inflation premium   An extra return that compensates investors 
for expected inflation.

Inflation rate   The percentage change in a price index—that 
is, the speed of overall price level movements.
Inflation Reports   A type of economic publication put out by 
many central banks.
Inflation uncertainty   The degree to which economic agents 
view future rates of inflation as difficult to forecast.
Information cascade   The transmission of information from 
those participants who act first and whose decisions influ -
ence the decisions of others.
Information-  motivated traders   Traders that trade to profit 
from information that they believe allows them to predict 
future prices.
Informationally efficient market   A market in which asset 
prices reflect new information quickly and rationally.
Initial coin offering   An unregulated process whereby com -
panies raise capital by selling crypto tokens to inves -
tors in exchange for fiat money or another agreed-  upon 
cryptocurrency.
Initial margin   The amount that must be deposited in a clear -

inghouse account when entering into a futures contract.
Initial margin requirement   The margin requirement on the 
first day of a transaction as well as on any day in which 
additional margin funds must be deposited.Initial public offering   (IPO) The first issuance of common 
shares to the public by a formerly private corporation.
Input productivity   The amount of output produced by work -
ers in a given period of time—for example, output per hour 
worked; measures the efficiency of labor.
Installment method   With respect to revenue recognition, a 
method that specifies that the portion of the total profit of 
the sale that is recognized in each period is determined by 
the percentage of the total sales price for which the seller 
has received cash.
Installment sales   With respect to revenue recognition, a 
the percentage of the total sales price for which the seller

Intangible assets   Assets lacking physical substance, such as 
patents and trademarks.
Interbank market   The market of loans and deposits between 
banks for maturities ranging from overnight to one year.
Interbank money market   The market of loans and deposits 
between banks for maturities ranging from overnight to 
one year.
Interest   Payment for lending funds.
Interest coverage   A solvency ratio calculated as EBIT divided 
by interest payments.
Interest-  only mortgage   A loan in which no scheduled prin -
cipal repayment is specified for a certain number of years.
Interest rate   A rate of return that reflects the relationship 
between differently dated cash flows; a discount rate.
Interest rate swap   A swap in which the underlying is an 
interest rate. Can be viewed as a currency swap in which 
both currencies are the same and can be created as a 
combination of currency swaps.
Intergenerational data mining   A form of data mining that

applies information developed by previous researchers 
using a dataset to guide current research using the same 
or a related dataset.
Intermarket analysis   A field within technical analysis that 
combines analysis of major categories of securities—
namely, equities, bonds, currencies, and commodities—to 
identify market trends and possible inflections in a trend.
Internal rate of return   (IRR) The discount rate that makes 
net present value equal 0; the discount rate that makes the 
present value of an investment’s costs (outflows) equal to 
the present value of the investment’s benefits (inflows).
Internet of Things   A network arrangement of structures and 
devices whereby the objects on the network are able to 
interact and share information.
Interpolated spread   The yield spread of a specific bond over 
the standard swap rate in that currency of the same tenor.
Interquartile range   The difference between the third and first 
quartiles of a dataset.

Interval   With reference to grouped data, a set of values within 
which an observation falls.
Interval scale   A measurement scale that not only ranks data 
but also gives assurance that the differences between scale 
values are equal.
Intrinsic value   See exercise value .
Inventory blanket lien   The use of inventory as collateral for 
a loan. Though the lender has claim to some or all of the 
company’s inventory, the company may still sell or use the 
inventory in the ordinary course of business.
Inventory investment   Net change in business inventory.

G-17 Glossary
Inventory turnover   An activity ratio calculated as cost of 
goods sold divided by average inventory.
Inverse demand function   A restatement of the demand 
function in which price is stated as a function of quantity.
Inverse floater   A type of leveraged structured financial instru -
ment. The cash flows are adjusted periodically and move 
in the opposite direction of changes in the reference rate.
Investing activities   Activities which are associated with the 
acquisition and disposal of property, plant, and equipment; 
intangible assets; other long-  term assets; and both long-  
term and short-  term investments in the equity and debt 
(bonds and loans) issued by other companies.
Investment banks   Financial intermediaries that provide 
advice to their mostly corporate clients and help them 
arrange transactions such as initial and seasoned securities 
offerings.
Investment opportunity schedule   A graphical depiction of a 
company’s investment opportunities ordered from highest

to lowest expected return. A company’s optimal capital 
budget is found where the investment opportunity schedule 
intersects with the company’s marginal cost of capital.
Investment policy statement   (IPS) A written planning doc -
ument that describes a client’s investment objectives and 
risk tolerance over a relevant time horizon, along with 
constraints that apply to the client’s portfolio.
Investment property   Property used to earn rental income 
or capital appreciation (or both).
IRR rule   An investment decision rule that accepts projects or 
investments for which the IRR is greater than the oppor -
tunity cost of capital.
January effect   Calendar anomaly that stock market returns 
in January are significantly higher compared to the rest of 
the months of the year, with most of the abnormal returns 
reported during the first five trading days in January. Also 
called turn-  of- the- year effect .
Joint probability   The probability of the joint occurrence of 
stated events.

Joint probability function   A function giving the probability 
of joint occurrences of values of stated random variables.
Just-  in- time (JIT) method   Method of managing inventory 
that minimizes in-  process inventory stocks.
Key rate duration   A method of measuring the interest rate 
sensitivities of a fixed-  income instrument or portfolio to 
shifts in key points along the yield curve.
Keynesians   Economists who believe that fiscal policy can 
have powerful effects on aggregate demand, output, and 
employment when there is substantial spare capacity in 
an economy.
Kondratieff wave   A 54-  year long economic cycle postulated 
by Nikolai Kondratieff.
Kurtosis   The statistical measure that indicates the combined 
weight of the tails of a distribution relative to the rest of 
the distribution.
Labor force   The portion of the working age population (over 
the age of 16) that is employed or is available for work but 
not working (unemployed).

Labor productivity   The quantity of goods and services (real 
GDP) that a worker can produce in one hour of work.
Laddering strategy   A form of active strategy which entails 
scheduling maturities on a systematic basis within the 
investment portfolio such that investments are spread out 
equally over the term of the ladder.Lagging economic indicators   Turning points that take place 
later than those of the overall economy; they are believed 
to have value in identifying the economy’s past condition.
Laspeyres index   A price index created by holding the com -
position of the consumption basket constant.
Law of demand   The principle that as the price of a good rises, 
buyers will choose to buy less of it, and as its price falls, 
they will buy more.
Law of diminishing marginal returns   The observation that 
a variable factor’s marginal product must eventually fall as 
more of it is added to a fixed amount of the other factors.

Law of diminishing returns   The smallest output that a 
firm can produce such that its long run average costs are 
minimized.
Law of one price   The condition in a financial market in which 
two equivalent financial instruments or combinations of 
financial instruments can sell for only one price. Equivalent 
to the principle that no arbitrage opportunities are possible.
Lead underwriter   The lead investment bank in a syndicate 
of investment banks and broker–dealers involved in a 
securities underwriting.
Leading economic indicators   Turning points that usually 
precede those of the overall economy; they are believed 
to have value for predicting the economy’s future state, 
usually near-  term.
Legal tender   Something that must be accepted when offered 
in exchange for goods and services.
Lender of last resort   An entity willing to lend money when 
no other entity is ready to do so.
Leptokurtic   Describes a distribution that has fatter tails than 
a normal distribution.

Lessee   The party obtaining the use of an asset through a lease.
Lessor   The owner of an asset that grants the right to use the 
asset to another party.
Letter of credit   Form of external credit enhancement whereby 
a financial institution provides the issuer with a credit 
line to reimburse any cash flow shortfalls from the assets 
backing the issue.
Level of significance   The probability of a Type I error in 
testing a hypothesis.
Leverage   In the context of corporate finance, leverage refers 
to the use of fixed costs within a company’s cost structure. 
Fixed costs that are operating costs (such as depreciation or 
rent) create operating leverage. Fixed costs that are financial 
costs (such as interest expense) create financial leverage.
Leveraged buyout   (LBO) A transaction whereby the target 
company management team converts the target to a pri -
vately held company by using heavy borrowing to finance 
the purchase of the target company’s outstanding shares.

Liabilities   Present obligations of an enterprise arising from 
past events, the settlement of which is expected to result 
in an outflow of resources embodying economic benefits; 
creditors’ claims on the resources of a company.
Life-  cycle stage   The stage of the life cycle: embryonic, growth, 
shakeout, mature, declining.
LIFO layer liquidation   With respect to the application of the 
LIFO inventory method, the liquidation of old, relatively 
low-  priced inventory; happens when the volume of sales 
rises above the volume of recent purchases so that some 
sales are made from relatively old, low-  priced inventory. 
Also called LIFO liquidation .

G-18 Glossary
LIFO method   The last in, first out, method of accounting for 
inventory, which matches sales against the costs of items 
of inventory in the reverse order the items were placed 
in inventory (i.e., inventory produced or acquired last are 
assumed to be sold first).
LIFO reserve   The difference between the reported LIFO inven -
tory carrying amount and the inventory amount that would 
have been reported if the FIFO method had been used 
(in other words, the FIFO inventory value less the LIFO 
inventory value).
Likelihood   The probability of an observation, given a partic -
ular set of conditions.
Limit down   A limit move in the futures market in which the 
price at which a transaction would be made is at or below 
the lower limit.
Limit order   Instructions to a broker or exchange to obtain the 
best price immediately available when filling an order, but 
in no event accept a price higher than a specified (limit) 
price when buying or accept a price lower than a specified

(limit) price when selling.
Limit order book   The book or list of limit orders to buy and 
sell that pertains to a security.
Limit up   A limit move in the futures market in which the 
price at which a transaction would be made is at or above 
the upper limit.
Limitations on liens   Meant to put limits on how much secured 
debt an issuer can have.
Limited partners   Partners with limited liability. Limited part -
nerships in hedge and private equity funds are typically 
restricted to investors who are expected to understand 
and to be able to assume the risks associated with the 
investments.
Line chart   In technical analysis, a plot of price data, typically 
closing prices, with a line connecting the points.
Linear interpolation   The estimation of an unknown value 
on the basis of two known values that bracket it, using a 
straight line between the two known values.
Linear scale   A scale in which equal distances correspond 
to equal absolute amounts. Also called arithmetic scale .

Linker   See inflation-  linked bond .
Liquid market   Said of a market in which traders can buy or sell 
with low total transaction costs when they want to trade.
Liquidation   To sell the assets of a company, division, or 
subsidiary piecemeal, typically because of bankruptcy; the 
form of bankruptcy that allows for the orderly satisfaction 
of creditors’ claims after which the company ceases to exist.
Liquidity   The ability to purchase or sell an asset quickly and 
easily at a price close to fair market value. The ability to 
meet short-  term obligations using assets that are the most 
readily converted into cash.
Liquidity premium   An extra return that compensates inves -
tors for the risk of loss relative to an investment’s fair value 
if the investment needs to be converted to cash quickly.
Liquidity ratios   Financial ratios measuring the company’s 
ability to meet its short-  term obligations.
Liquidity risk   The risk that a financial instrument cannot be

purchased or sold without a significant concession in price 
due to the size of the market.
Liquidity trap   A condition in which the demand for money 
becomes infinitely elastic (horizontal demand curve) so 
that injections of money into the economy will not lower 
interest rates or affect real activity.Load fund   A mutual fund in which, in addition to the annual 
fee, a percentage fee is charged to invest in the fund and/
or for redemptions from the fund.
Loan-  to- value ratio   The ratio of a property’s purchase price 
to the amount of its mortgage.
Lockbox system   A payment system in which customer pay -
ments are mailed to a post office box and the banking 
institution retrieves and deposits these payments several 
times a day, enabling the company to have use of the fund 
sooner than in a centralized system in which customer 
payments are sent to the company.
Locked limit   A condition in the futures markets in which a 
transaction cannot take place because the price would be

beyond the limits.
Lockup period   The minimum period before investors are 
allowed to make withdrawals or redeem shares from a fund.
Logarithmic scale   A scale in which equal distances represent 
equal proportional changes in the underlying quantity.
London interbank offered rate (Libor)   Collective name for 
multiple rates at which a select set of banks believe they 
could borrow unsecured funds from other banks in the 
London interbank market for different currencies and 
different borrowing periods ranging from overnight to 
one year.
Long   The buyer of a derivative contract. Also refers to the 
position of owning a derivative.
Long-  lived assets   Assets that are expected to provide eco -
nomic benefits over a future period of time, typically 
greater than one year. Also called long-  term assets .
Long position   A position in an asset or contract in which 
one owns the asset or has an exercisable right under the 
contract.
Long-  run average total cost   The curve describing average

total cost when no costs are considered fixed.
Long-  term contract   A contract that spans a number of 
accounting periods.
Longitudinal data   Observations on characteristic(s) of the 
same observational unit through time.
Look-  ahead bias   A bias caused by using information that was 
unavailable on the test date.
Loss aversion   The tendency of people to dislike losses more 
than they like comparable gains.
Loss severity   Portion of a bond’s value (including unpaid 
interest) an investor loses in the event of default.
Losses   Asset outflows not directly related to the ordinary 
activities of the business.
Lower bound   The lowest possible value of an option.
M2  A measure of what a portfolio would have returned if it 
had taken on the same total risk as the market index.
Macaulay duration   The approximate amount of time a bond 
would have to be held for the market discount rate at pur -
chase to be realized if there is a single change in interest

rate. It indicates the point in time when the coupon rein -
vestment and price effects of a change in yield-  to- maturity 
offset each other.
Machine learning   Diverse approaches by which computers 
are programmed to improve performance in specified 
tasks with experience.
Macroeconomics   The branch of economics that deals with 
aggregate economic quantities, such as national output 
and national income.
Maintenance covenants   Covenants in bank loan agreements 
that require the borrower to satisfy certain financial ratio 
tests while the loan is outstanding.

G-19 Glossary
Maintenance margin   The minimum amount that is required 
by a futures clearinghouse to maintain a margin account 
and to protect against default. Participants whose margin 
balances drop below the required maintenance margin 
must replenish their accounts.
Maintenance margin requirement   The margin requirement 
on any day other than the first day of a transaction.
Management buy-  ins  Leveraged buyout in which the current 
management team is being replaced and the acquiring team 
will be involved in managing the company.
Management buyout   (MBO) A leveraged buyout event in 
which a group of investors consisting primarily of the com -
pany’s existing management purchase at least controlling 
interest of its outstanding shares. They may purchase all 
shares and take the company private.
Management fee   A fee based on assets under management 
or committed capital, as applicable, also called a base fee .
Manufacturing resource planning (MRP)   The incorporation

of production planning into inventory management. A 
MRP analysis provides both a materials acquisition sched -
ule and a production schedule.
Margin   The amount of money that a trader deposits in a 
margin account. The term is derived from the stock mar -
ket practice in which an investor borrows a portion of the 
money required to purchase a certain amount of stock. In 
futures markets, there is no borrowing so the margin is 
more of a down payment or performance bond.
Margin bond   A cash deposit required by the clearinghouse 
from the participants to a contract to provide a credit 
guarantee. Also called a performance bond .
Margin call   A request for the short to deposit additional funds 
to bring their balance up to the initial margin.
Margin loan   Money borrowed from a broker to purchase 
Marginal cost   The cost of producing an additional unit of 
a good.
Marginal probability   The probability of an event not condi -
tioned on another event.

Marginal product   Measures the productivity of each unit 
of input and is calculated by taking the difference in total 
product from adding another unit of input (assuming other 
resource quantities are held constant).
Marginal propensity to consume   The proportion of an addi -
tional unit of disposable income that is consumed or spent; 
the change in consumption for a small change in income.
Marginal propensity to save   The proportion of an additional 
unit of disposable income that is saved (not spent).
Marginal revenue   The change in total revenue divided by 
the change in quantity sold; simply, the additional revenue 
from selling one more unit.
Marginal value curve   A curve describing the highest price 
consumers are willing to pay for each additional unit of 
a good.
Mark to market   The revaluation of a financial asset or liability 
to its current market value or fair value.
Market   A means of bringing buyers and sellers together to 
exchange goods and services.

Market anomaly   Change in the price or return of a security 
that cannot directly be linked to current relevant infor -
mation known in the market or to the release of new 
information into the market.
Market bid–ask spread   The difference between the best bid 
and the best offer.Market-  capitalization weighting   An index weighting method 
in which the weight assigned to each constituent security is 
determined by dividing its market capitalization by the total 
market capitalization (sum of the market capitalization) 
of all securities in the index. Also called value weighting .
Market discount rate   The rate of return required by investors 
given the risk of the investment in a bond; also called the 
required yield  or the required rate of return .
Market float   The number of shares that are available to the 
investing public.
Market liquidity risk   The risk that the price at which investors 
can actually transact—buying or selling—may differ from

the price indicated in the market.
Market model   A regression equation that specifies a linear 
relationship between the return on a security (or portfolio) 
and the return on a broad market index.
Market multiple models   Valuation models based on share 
price multiples or enterprise value multiples.
Market-  on- close   An execution instruction specifying that an 
order can only be filled at the close of trading.
Market order   Instructions to a broker or exchange to obtain 
the best price immediately available when filling an order.
Market-  oriented investors   With reference to equity investors, 
investors whose investment disciplines cannot be clearly 
categorized as value or growth.
Market rate of interest   The rate demanded by purchases of 
bonds, given the risks associated with future cash payment 
obligations of the particular bond issue.
Market risk   The risk that arises from movements in interest 
rates, stock prices, exchange rates, and commodity prices.

Market value   The price at which an asset or security can 
currently be bought or sold in an open market.
Marketable limit order   A buy limit order in which the limit 
price is placed above the best offer, or a sell limit order in 
which the limit price is placed below the best bid. Such 
orders generally will partially or completely fill right away.
Markowitz efficient frontier   The graph of the set of portfolios 
offering the maximum expected return for their level of 
risk (standard deviation of return).
Matching principle   The accounting principle that expenses 
should be recognized when the associated revenue is 
Matching strategy   An active investment strategy that includes 
intentional matching of the timing of cash outflows with 
investment maturities.
Matrix pricing   Process of estimating the market discount rate 
and price of a bond based on the quoted or flat prices of 
more frequently traded comparable bonds.
Maturity premium   An extra return that compensates investors

for the increased sensitivity of the market value of debt to 
a change in market interest rates as maturity is extended.
Maturity structure   A factor explaining the differences in yields 
on similar bonds; also called term structure .
Mean absolute deviation   With reference to a sample, the 
mean of the absolute values of deviations from the sample 
mean.
Mean excess return   The average rate of return in excess of 
the risk-  free rate.
Mean–variance analysis   An approach to portfolio analysis 
using expected means, variances, and covariances of asset 
returns.
Measure of central tendency   A quantitative measure that 
specifies where data are centered.

G-20 Glossary
Measure of value   A standard for measuring value; a function 
of money.
Measurement scales   A scheme of measuring differences. The 
four types of measurement scales are nominal, ordinal, 
interval, and ratio.
Measures of location   A quantitative measure that describes 
the location or distribution of data; includes not only 
measures of central tendency but also other measures 
such as percentiles.
Median   The value of the middle item of a set of items that 
has been sorted into ascending or descending order; the 
50th percentile.
Medium of exchange   Any asset that can be used to purchase 
goods and services or to repay debts; a function of money.
Medium-  term note   A corporate bond offered continuously to 
investors by an agent of the issuer, designed to fill the fund -
ing gap between commercial paper and long-  term bonds.
Menu costs   A cost of inflation in which businesses constantly 
have to incur the costs of changing the advertised prices 
of their goods and services.

Mesokurtic   Describes a distribution with kurtosis identical 
to that of the normal distribution.
Mezzanine financing   Debt or preferred shares with a rela -
tionship to common equity resulting from a feature such 
as attached warrants or conversion options. Mezzanine 
financing is subordinate to both senior and high-  yield 
debt. It is referred to as mezzanine because of its location 
on the balance sheet.
Microeconomics   The branch of economics that deals with 
markets and decision making of individual economic units, 
including consumers and businesses.
Minimum efficient scale   The smallest output that a firm 
can produce such that its long-  run average total cost is 
Minimum-  variance portfolio   The portfolio with the minimum 
variance for each given level of expected return.
Minority shareholders   A particular shareholder or block of 
shareholders holding a small proportion of a company’s

outstanding shares, resulting in a limited ability to exercise 
control in voting activities.
Minsky moment   Named for Hyman Minksy: A point in a 
business cycle when, after individuals become overextended 
in borrowing to finance speculative investments, people 
start realizing that something is likely to go wrong and a 
panic ensues leading to asset sell-  offs.
Mismatching strategy   An active investment strategy whereby 
the timing of cash outflows is not matched with investment 
maturities.
Modal interval   With reference to grouped data, the most 
frequently occurring interval.
Mode   The most frequently occurring value in a set of 
observations.
Modern portfolio theory   (MPT) The analysis of rational 
portfolio choices based on the efficient use of risk.
Modified duration   A measure of the percentage price change 
of a bond given a change in its yield-  to- maturity.
Momentum oscillators   A graphical representation of market 
sentiment that is constructed from price data and calcu -

lated so that it oscillates either between a high and a low 
or around some number.
Monetarists   Economists who believe that the rate of growth 
of the money supply is the primary determinant of the 
rate of inflation.Monetary policy   Actions taken by a nation’s central bank to 
affect aggregate output and prices through changes in bank 
reserves, reserve requirements, or its target interest rate.
Monetary transmission mechanism   The process whereby 
a central bank’s interest rate gets transmitted through 
the economy and ultimately affects the rate of increase 
of prices.
Monetary union   An economic union in which the members 
adopt a common currency.
Money   A generally accepted medium of exchange and unit 
of account.
Money convexity   For a bond, the annual or approximate 
convexity multiplied by the full price.
Money creation   The process by which changes in bank 
reserves translate into changes in the money supply.
Money duration   A measure of the price change in units of

the currency in which the bond is denominated given a 
change in its yield-  to- maturity.
Money market   The market for short-  term debt instruments 
(one-  year maturity or less).
Money market securities   Fixed-  income securities with matur -
ities at issuance of one year or less.
Money market yield   A yield on a basis comparable to the 
holding period yield, assuming a 360-  day year.
Money multiplier   Describes how a change in reserves is 
expected to affect the money supply; in its simplest form, 
1 divided by the reserve requirement.
Money neutrality   The thesis that an increase in the money 
supply leads in the long-  run to an increase in the price 
level, while leaving real variables like output and employ -
ment unaffected.
Money-  weighted return   The internal rate of return on a 
portfolio, taking account of all cash flows.

Moneyness   The relationship between the price of the under -
lying and an option’s exercise price.
Monopolistic competition   Highly competitive form of imper -
fect competition; the competitive characteristic is a notably 
large number of firms, while the monopoly aspect is the 
result of product differentiation.
Monopoly   In pure monopoly markets, there are no substi -
tutes for the given product or service. There is a single 
seller, which exercises considerable power over pricing 
and output decisions.
Monte Carlo simulation   An approach to estimating a prob -
ability distribution of outcomes to examine what might 
happen if particular risks are faced. This method is widely 
used in the sciences as well as in business to study a variety 
of problems.
Moral principles   Beliefs regarding what is good, acceptable, 
Mortgage-  backed securities   Debt obligations that represent

claims to the cash flows from pools of mortgage loans, 
most commonly on residential property.
Mortgage loan   A loan secured by the collateral of some 
specified real estate property that obliges the borrower to 
make a predetermined series of payments to the lender.
Mortgage pass-  through security   A security created when one 
or more holders of mortgages form a pool of mortgages 
and sell shares or participation certificates in the pool.
Mortgage rate   The interest rate on a mortgage loan; also 
called contract rate  or note rate .

G-21 Glossary
Moving average   The average of the closing price of a security 
over a specified number of periods. With each new period, 
the average is recalculated.
Moving-  average convergence/divergence oscilla -
tor  (MACD) A momentum oscillator that is constructed 
based on the difference between short-  term and long-  term 
moving averages of a security’s price.
Multi-  factor model   A model that explains a variable in terms 
of the values of a set of factors.
Multi-  market indexes   Comprised of indexes from different 
countries, designed to represent multiple security markets.
Multi-  step format   With respect to the format of the income 
statement, a format that presents a subtotal for gross profit 
(revenue minus cost of goods sold).
Multilateral trading facilities   See alternative trading systems .
Multinational corporation   A company operating in more 
than one country or having subsidiary firms in more than 
one country.

Multiplication rule for probabilities   The rule that the joint 
probability of events A and B equals the probability of A 
given B times the probability of B.
Multiplier models   Valuation models based on share price 
multiples or enterprise value multiples.
Multivariate distribution   A probability distribution that 
specifies the probabilities for a group of related random 
Multivariate normal distribution   A probability distribution 
for a group of random variables that is completely defined 
by the means and variances of the variables plus all the 
correlations between pairs of the variables.
Muni   A type of non-  sovereign bond issued by a state or local 
government in the United States. It very often (but not 
always) offers income tax exemptions.
Municipal bonds   A type of non-  sovereign bond issued by a 
state or local government in the United States. It very often 
(but not always) offers income tax exemptions.

Mutual fund   A professionally managed investment pool in 
which investors in the fund typically each have a pro-  rata 
claim on the income and value of the fund.
Mutually exclusive projects   Mutually exclusive projects com -
pete directly with each other. For example, if Projects A 
and B are mutually exclusive, you can choose A or B, but 
you cannot choose both.
n Factorial   For a positive integer n, the product of the first 
n positive integers; 0 factorial equals 1 by definition. n 
factorial is written as n!.
Narrow money   The notes and coins in circulation in an econ -
omy, plus other very highly liquid deposits.
Nash equilibrium   When two or more participants in a non-  
coop-  erative game have no incentive to deviate from their 
respective equilibrium strategies given their opponent’s 
National income   The income received by all factors of produc -
tion used in the generation of final output. National income

equals gross domestic product (or, in some countries, gross 
national product) minus the capital consumption allowance 
and a statistical discrepancy.
Natural language processing   Computer programs developed 
to analyze and interpret human language.
Natural rate of unemployment   Effective unemployment rate, 
below which pressure emerges in labor markets.Negative screening   An ESG implementation approach that 
excludes certain sectors or companies that deviate from 
an investor’s accepted standards. Also called exclusionary 
Neo-  Keynesians   A group of dynamic general equilibrium 
models that assume slow-  to- adjust prices and wages.
Net book value   The remaining (undepreciated) balance of 
an asset’s purchase cost. For liabilities, the face value of 
a bond minus any unamortized discount, or plus any 
unamortized premium.
Net exports   The difference between the value of a country’s 
exports and the value of its imports (i.e., value of exports

minus imports).
Net income   The difference between revenue and expenses; 
what remains after subtracting all expenses (including 
depreciation, interest, and taxes) from revenue.
Net operating cycle   An estimate of the average time that 
elapses between paying suppliers for materials and col -
lecting cash from the subsequent sale of goods produced.
Net present value   (NPV) The present value of an investment’s 
cash inflows (benefits) minus the present value of its cash 
outflows (costs).
Net profit margin   An indicator of profitability, calculated as 
net income divided by revenue; indicates how much of 
each dollar of revenues is left after all costs and expenses. 
Also called profit margin  or return on sales .
Net realisable value   Estimated selling price in the ordinary 
course of business less the estimated costs necessary to 
make the sale.
Net revenue   Revenue after adjustments (e.g., for estimated 
returns or for amounts unlikely to be collected).

Net tax rate   The tax rate net of transfer payments.
Neural networks   Computer programs based on how our own 
brains learn and process information.
Neutral rate of interest   The rate of interest that neither spurs 
on nor slows down the underlying economy.
New classical macroeconomics   An approach to macroeco -
nomics that seeks the macroeconomic conclusions of 
individuals maximizing utility on the basis of rational 
expectations and companies maximizing profits.
New Keynesians   A group of dynamic general equilibrium 
No-  load fund   A mutual fund in which there is no fee for 
investing in the fund or for redeeming fund shares, 
although there is an annual fee based on a percentage of 
the fund’s net asset value.
Node   Each value on a binomial tree from which successive 
moves or outcomes branch.
Nominal GDP   The value of goods and services measured at 
current prices.

Nominal rate   A rate of interest based on the security’s face 
value.
Nominal risk-  free interest rate   The sum of the real risk-  free 
interest rate and the inflation premium.
Nominal scale   A measurement scale that categorizes data 
but does not rank them.
Non-  accelerating inflation rate of unemployment   Effective 
unemployment rate, below which pressure emerges in 
labor markets.
Non-  agency RMBS   In the United States, securities issued 
by private entities that are not guaranteed by a federal 
agency or a GSE.

G-22 Glossary
Non-  cumulative preference shares   Preference shares for 
which dividends that are not paid in the current or subse -
quent periods are forfeited permanently (instead of being 
accrued and paid at a later date).
Non-  current assets   Assets that are expected to benefit the 
company over an extended period of time (usually more 
than one year).
Non-  current liabilities   Obligations that broadly represent a 
probable sacrifice of economic benefits in periods generally 
greater than one year in the future.
Non-  cyclical   A company whose performance is largely inde -
pendent of the business cycle.
Non-  deliverable forwards   Cash-  settled forward contracts, 
used predominately with respect to foreign exchange for -
wards. Also called contracts for differences .
Non-  financial risks   Risks that arise from sources other than 
changes in the external financial markets, such as changes 
in accounting rules, legal environment, or tax rates.

Non-  participating preference shares   Preference shares that 
do not entitle shareholders to share in the profits of the 
company. Instead, shareholders are only entitled to receive 
a fixed dividend payment and the par value of the shares 
in the event of liquidation.
Non-  recourse loan   Loan in which the lender does not have a 
shortfall claim against the borrower, so the lender can look 
only to the property to recover the outstanding mortgage 
balance.
Non-  renewable resources   Finite resources that are depleted 
once they are consumed, such as oil and coal.
Non-  sovereign bonds   A bond issued by a government below 
the national level, such as a province, region, state, or city.
Non-  sovereign government bonds   A bond issued by a gov -
ernment below the national level, such as a province, 
region, state, or city.
Nonconventional cash flow   In a nonconventional cash flow 
pattern, the initial outflow is not followed by inflows only,

but the cash flows can flip from positive (inflows) to nega -
tive (outflows) again (or even change signs several times).
Nonparametric test   A test that is not concerned with a 
parameter, or that makes minimal assumptions about the 
population from which a sample comes.
Nonsystematic risk   Unique risk that is local or limited to 
a particular asset or industry that need not affect assets 
outside of that asset class.
Normal distribution   A continuous, symmetric probability 
distribution that is completely described by its mean and 
its variance.
Normal goods   Goods that are consumed in greater quantities 
as income increases.
Normal profit   The level of accounting profit needed to just 
cover the implicit opportunity costs ignored in accounting 
costs.
Norms-  based screening   An ESG implementation approach 
screening  or exclusionary screening .

Notching   Ratings adjustment methodology where specific 
issues from the same borrower may be assigned different 
credit ratings.
Note rate   See mortgage rate .
Notes payable   Amounts owed by a business to creditors as 
a result of borrowings that are evidenced by (short-  term) 
loan agreements.Notice period   The length of time (typically 30 to 90 days) in 
advance that investors may be required to notify a fund 
of their intent to redeem.
Notional principal   An imputed principal amount.
NPV rule   An investment decision rule that states that an 
investment should be undertaken if its NPV is positive 
but not undertaken if its NPV is negative.
Number of days of inventory   An activity ratio equal to the 
number of days in a period divided by the inventory ratio 
for the period; an indication of the number of days a com -
pany ties up funds in inventory.
Number of days of payables   An activity ratio equal to the

number of days in a period divided by the payables turnover 
ratio for the period; an estimate of the average number of 
days it takes a company to pay its suppliers.
Number of days of receivables   Estimate of the average num -
ber of days it takes to collect on credit accounts.
Objective probabilities   Probabilities that generally do not 
vary from person to person; includes a priori and objective 
probabilities.
Off-  the-  run  Seasoned government bonds are off-  the- run 
securities; they are not the most recently issued or the 
most actively traded.
Offer   The price at which a dealer or trader is willing to sell an 
asset, typically qualified by a maximum quantity (ask size).
Official interest rate   An interest rate that a central bank sets 
and announces publicly; normally the rate at which it is 
willing to lend money to the commercial banks. Also called 
official policy rate  or policy rate .
Official policy rate   An interest rate that a central bank sets

willing to lend money to the commercial banks.
Oligopoly   Market structure with a relatively small number 
of firms supplying the market.
On-  the-  run  The most recently issued and most actively traded 
sovereign securities.
One-  sided hypothesis test   A test in which the null hypothesis 
is rejected only if the evidence indicates that the population 
parameter is greater than (smaller than) θ0. The alternative 
hypothesis also has one side.
One-  tailed hypothesis test   A test in which the null hypothesis 
Open economy   An economy that trades with other countries.
Open-  end fund   A mutual fund that accepts new investment 
money and issues additional shares at a value equal to 
the net asset value of the fund at the time of investment.

Open interest   The number of outstanding contracts in a 
clearinghouse at any given time. The open interest figure 
changes daily as some parties open up new positions, while 
other parties offset their old positions.
Open market operations   The purchase or sale of bonds by 
the national central bank to implement monetary policy. 
The bonds traded are usually sovereign bonds issued by 
the national government.
Operating activities   Activities that are part of the day-  to- day 
business functioning of an entity, such as selling inventory 
and providing services.
Operating breakeven   The number of units produced and sold 
at which the company’s operating profit is zero (revenues 
= operating costs).
Operating cash flow   The net amount of cash provided from 
operating activities.

G-23 Glossary
Operating cycle   A measure of the time needed to convert raw 
materials into cash from a sale; it consists of the number 
of days of inventory and the number of days of receivables.
Operating efficiency ratios   Ratios that measure how effi -
ciently a company performs day-  to- day tasks, such as the 
collection of receivables and management of inventory.
Operating lease   An agreement allowing the lessee to use some 
asset for a period of time; essentially a rental.
Operating leverage   The use of fixed costs in operations.
Operating profit   A company’s profits on its usual business 
activities before deducting taxes. Also called operating 
income .
Operating profit margin   A profitability ratio calculated as 
operating income (i.e., income before interest and taxes) 
divided by revenue. Also called operating margin .
Operating risk   The risk attributed to the operating cost struc -
ture, in particular the use of fixed costs in operations; the

risk arising from the mix of fixed and variable costs; the 
risk that a company’s operations may be severely affected 
by environmental, social, and governance risk factors.
Operational independence   A bank’s ability to execute mon -
etary policy and set interest rates in the way it thought 
would best meet the inflation target.
Operational risk   The risk of loss from failures in a company’s 
systems and procedures.
Operationally efficient   Said of a market, a financial system, 
or an economy that has relatively low transaction costs.
Opportunity cost   The value that investors forgo by choosing 
a particular course of action; the value of something in its 
best alternative use.
Option   A financial instrument that gives one party the right, 
but not the obligation, to buy or sell an underlying asset 
from or to another party at a fixed price over a specific 
period of time. Also referred to as contingent claim  or 
option contract .
Option-  adjusted price   The value of the embedded option

plus the flat price of the bond.
Option-  adjusted spread   OAS = Z-  spread – Option value (in 
basis points per year).
Option-  adjusted yield   The required market discount rate 
whereby the price is adjusted for the value of the embed -
ded option.
Option contract   See option .
Option premium   The amount of money a buyer pays and 
seller receives to engage in an option transaction.
Order   A specification of what instrument to trade, how much 
to trade, and whether to buy or sell.
Order-  driven markets   A market (generally an auction market) 
that uses rules to arrange trades based on the orders that 
traders submit; in their pure form, such markets do not 
make use of dealers.
Order precedence hierarchy   With respect to the execution 
of orders to trade, a set of rules that determines which 
orders execute before other orders.
Ordinal scale   A measurement scale that sorts data into cat -
egories that are ordered (ranked) with respect to some 
characteristic.

Ordinary annuity   An annuity with a first cash flow that is 
paid one period from the present.
Ordinary shares   Equity shares that are subordinate to all 
other types of equity (e.g., preferred equity). Also called 
common stock  or common shares .
Organized exchange   A securities marketplace where buyers 
and seller can meet to arrange their trades.Other comprehensive income   Items of comprehensive 
income that are not reported on the income statement; 
comprehensive income minus net income.
Out-  of- sample test   A test of a strategy or model using a 
sample outside the time period on which the strategy or 
model was developed.
Out of the money   Options that, if exercised, would require 
the payment of more money than the value received and 
therefore would not be currently exercised.
Outcome   A possible value of a random variable.
Over-  the-  counter (OTC) markets   A decentralized market 
where buy and sell orders initiated from various locations

are matched through a communications network.
Overbought   A market condition in which market sentiment 
is thought to be unsustainably bullish.
Overcollateralization   Form of internal credit enhancement 
that refers to the process of posting more collateral than 
needed to obtain or secure financing.
Overfitting   An undesirable result from fitting a model so 
closely to a dataset that it does not perform well on new 
data.
Oversold   A market condition in which market sentiment is 
thought to be unsustainably bearish.
Own price   The price of a good or service itself (as opposed 
to the price of something else).
Own-  price elasticity of demand   The percentage change in 
quantity demanded for a percentage change in good’s own 
price, holding all other things constant.
Owners’ equity   The excess of assets over liabilities; the resid -
ual interest of shareholders in the assets of an entity after 
deducting the entity’s liabilities. Also called shareholders’ 
equity .

equity .
Paasche index   An index formula using the current compo -
sition of a basket of products.
Paired comparisons test   A statistical test for differences 
based on paired observations drawn from samples that 
are dependent on each other.
Paired observations   Observations that are dependent on 
each other.
Pairs arbitrage trade   A trade in two closely related stocks 
involving the short sale of one and the purchase of the 
other.
Panel data   Observations through time on a single character -
istic of multiple observational units.
Par curve   A sequence of yields-  to- maturity such that each 
bond is priced at par value. The bonds are assumed to 
have the same currency, credit risk, liquidity, tax status, 
and annual yields stated for the same periodicity.
Par value   The amount of principal on a bond.
Parallel shift   A parallel yield curve shift implies that all rates 
change by the same amount in the same direction.
Parameter   A descriptive measure computed from or used to

describe a population of data, conventionally represented 
by Greek letters.
Parametric test   Any test (or procedure) concerned with 
parameters or whose validity depends on assumptions 
concerning the population generating the sample.
Pari passu   On an equal footing.
Partial duration   See key rate duration .
Participating preference shares   Preference shares that entitle 
shareholders to receive the standard preferred dividend 
plus the opportunity to receive an additional dividend if 
the company’s profits exceed a pre-  specified level.

G-24 Glossary
Pass-  through rate   The coupon rate of a mortgage pass-  
through security.
Passive investment   A buy and hold approach in which 
an investor does not make portfolio changes based on 
short-  term expectations of changing market or security 
Passive strategy   In reference to short-  term cash management, 
it is an investment strategy characterized by simple decision 
rules for making daily investments.
Payable date   The day that the company actually mails out (or 
electronically transfers) a dividend payment.
Payment date   The day that the company actually mails out 
(or electronically transfers) a dividend payment.
Payments system   The system for the transfer of money.
Peak   The highest point of a business cycle.
Peer group   A group of companies engaged in similar business 
activities whose economics and valuation are influenced 
by closely related factors.
Pennants   A technical analysis continuation pattern formed

by trendlines that converge to form a triangle, typically 
over a short period.
Per capita real GDP   Real GDP divided by the size of the pop -
ulation, often used as a measure of the average standard 
of living in a country.
Per unit contribution margin   The amount that each unit sold 
contributes to covering fixed costs—that is, the difference 
between the price per unit and the variable cost per unit.
Percentage-  of- completion   A method of revenue recogni -
tion in which, in each accounting period, the company 
estimates what percentage of the contract is complete and 
then reports that percentage of the total contract revenue 
in its income statement.
Percentiles   Quantiles that divide a distribution into 100 equal 
parts.
Perfect competition   A market structure in which the individ -
ual firm has virtually no impact on market price, because 
it is assumed to be a very small seller among a very large 
number of firms selling essentially identical products.

Perfectly elastic   When the quantity demanded or supplied of 
a given good is infinitely sensitive to a change in the value 
of a specified variable (e.g., price).
Perfectly inelastic   When the quantity demanded or supplied 
of a given good is completely insensitive to a change in the 
value of a specified variable (e.g., price).
Performance appraisal   The evaluation of risk-  adjusted per -
formance; the evaluation of investment skill.
Performance bond   See margin bond .
Performance evaluation   The measurement and assessment 
of the outcomes of investment management decisions.
Performance fee   Fees paid to the general partner from the 
limited partner(s) based on realized profits.
Performance measurement   The calculation of returns in a 
logical and consistent manner.
Period costs   Costs (e.g., executives’ salaries) that cannot be 
directly matched with the timing of revenues and which 
are thus expensed immediately.
Periodicity   The assumed number of periods in the year, typ -

ically matches the frequency of coupon payments.
Permanent differences   Differences between tax and financial 
reporting of revenue (expenses) that will not be reversed 
at some future date. These result in a difference between 
the company’s effective tax rate and statutory tax rate and 
do not result in a deferred tax item.Permissioned networks   Networks that are fully open only 
to select participants on a DLT network.
Permissionless networks   Networks that are fully open to any 
user on a DLT network.
Permutation   An ordered listing.
Perpetual bonds   Bonds with no stated maturity date.
Perpetuity   A perpetual annuity, or a set of never-  ending level 
sequential cash flows, with the first cash flow occurring one 
period from now. A bond that does not mature.
Personal consumption expenditures   All domestic personal 
consumption; the basis for a price index for such consump -
tion called the PCE price index.
Personal disposable income   Equal to personal income less 
personal taxes.

Personal income   A broad measure of household income 
that includes all income received by households, whether 
earned or unearned; measures the ability of consumers to 
make purchases.
Plain vanilla bond   Bond that makes periodic, fixed coupon 
payments during the bond’s life and a lump-  sum payment 
of principal at maturity. Also called conventional bond .
Platykurtic   Describes a distribution that has relatively less 
weight in the tails than the normal distribution.
Point and figure chart   A technical analysis chart that is con -
structed with columns of X’s alternating with columns of 
O’s such that the horizontal axis represents only the num -
ber of changes in price without reference to time or volume.
Point estimate   A single numerical estimate of an unknown 
quantity, such as a population parameter.
Point of sale (POS)   Systems that capture transaction data at 
the physical location in which the sale is made.
Policy rate   An interest rate that a central bank sets and

announces publicly; normally the rate at which it is willing 
to lend money to the commercial banks.
Population   All members of a specified group.
Population mean   The arithmetic mean value of a population; 
the arithmetic mean of all the observations or values in 
the population.
Population standard deviation   A measure of dispersion 
relating to a population in the same unit of measurement 
as the observations, calculated as the positive square root 
of the population variance.
Population variance   A measure of dispersion relating to a 
population, calculated as the mean of the squared devia -
tions around the population mean.
Portfolio company   In private equity, the company in which 
the private equity fund is investing.
Portfolio demand for money   The demand to hold specula -
tive money balances based on the potential opportunities 
or risks that are inherent in other financial instruments.
Portfolio planning   The process of creating a plan for building

a portfolio that is expected to satisfy a client’s investment 
objectives.
Position   The quantity of an asset that an entity owns or owes.
Positive screening   An ESG implementation approach that 
seeks to identify companies that embrace desired ESG-  
related principles.
Posterior probability   An updated probability that reflects or 
comes after new information.
Potential GDP   The level of real GDP that can be produced 
at full employment; measures the productive capacity of 
the economy.
Power of a test   The probability of correctly rejecting the 
null—that is, rejecting the null hypothesis when it is false.

G-25 Glossary
Precautionary money balances   Money held to provide a 
buffer against unforeseen events that might require money.
Precautionary stocks   A level of inventory beyond anticipated 
needs that provides a cushion in the event that it takes 
longer to replenish inventory than expected or in the case 
of greater than expected demand.
Preference shares   A type of equity interest which ranks above 
common shares with respect to the payment of dividends 
and the distribution of the company’s net assets upon 
liquidation. They have characteristics of both debt and 
equity securities. Also called preferred stock .
Preferred stock   See preference shares .
Premium   In the case of bonds, premium refers to the amount 
by which a bond is priced above its face (par) value. In the 
case of an option, the amount paid for the option contract.
Prepaid expense   A normal operating expense that has been 
paid in advance of when it is due.
Prepayment option   Contractual provision that entitles the

borrower to prepay all or part of the outstanding mortgage 
principal prior to the scheduled due date when the prin -
cipal must be repaid. Also called early repayment option .
Prepayment penalty mortgages   Mortgages that stipulate a 
monetary penalty if a borrower prepays within a certain 
time period after the mortgage is originated.
Prepayment risk   The uncertainty that the timing of the actual 
cash flows will be different from the scheduled cash flows 
as set forth in the loan agreement due to the borrowers’ 
ability to alter payments, usually to take advantage of 
interest rate movements.
Present value (PV)   The present discounted value of future 
cash flows: For assets, the present discounted value of 
the future net cash inflows that the asset is expected to 
generate; for liabilities, the present discounted value of the 
future net cash outflows that are expected to be required 
to settle the liabilities.
Present value models   Valuation models that estimate the

intrinsic value of a security as the present value of the 
future benefits expected to be received from the security. 
Also called discounted cash flow models .
Pretax margin   A profitability ratio calculated as earnings 
before taxes divided by revenue.
Price elasticity of demand   Measures the percentage change 
in the quantity demanded, given a percentage change in 
the price of a given product.
Price index   Represents the average prices of a basket of goods 
Price limits   Limits imposed by a futures exchange on the price 
change that can occur from one day to the next.
Price multiple   A ratio that compares the share price with 
some sort of monetary flow or value to allow evaluation 
of the relative worth of a company’s stock.
Price priority   The principle that the highest priced buy orders 
and the lowest priced sell orders execute first.
Price relative   A ratio of an ending price over a beginning price; 
it is equal to 1 plus the holding period return on the asset.

Price return   Measures only the price appreciation or percent -
age change in price of the securities in an index or portfolio.
Price return index   An index that reflects only the price appre -
ciation or percentage change in price of the constituent 
securities. Also called price index .
Price stability   In economics, refers to an inflation rate that is 
low on average and not subject to wide fluctuation.
Price takers   Producers that must accept whatever price the 
market dictates.Price to book value   A valuation ratio calculated as price per 
share divided by book value per share.
Price to cash flow   A valuation ratio calculated as price per 
share divided by cash flow per share.
Price to earnings ratio   (P/E ratio or P/E) The ratio of share 
price to earnings per share.
Price to sales   A valuation ratio calculated as price per share 
divided by sales per share.
Price value of a basis point   A version of money duration, it is 
an estimate of the change in the full price of a bond given

a 1 basis point change in the yield-  to- maturity.
Price weighting   An index weighting method in which the 
weight assigned to each constituent security is determined 
by dividing its price by the sum of all the prices of the 
constituent securities.
Priced risk   Risk for which investors demand compensation 
for bearing (e.g. equity risk, company-  specific factors, 
macroeconomic factors).
Primary bond markets   Markets in which issuers first sell 
bonds to investors to raise capital.
Primary capital markets (primary markets)   The market 
where securities are first sold and the issuers receive the 
proceeds.
Primary dealers   Financial institutions that are authorized 
to deal in new issues of sovereign bonds and that serve 
primarily as trading counterparties of the office responsible 
for issuing sovereign bonds.
Primary market   The market where securities are first sold 
and the issuers receive the proceeds.
Prime brokers   Brokers that provide services including custody,

administration, lending, short borrowing, and trading.
Principal   The amount of funds originally invested in a project 
or instrument; the face value to be paid at maturity.
Principal–agent relationship   A relationship in which a prin -
cipal hires an agent to perform a particular task or service; 
also known as an agency relationship .
Principal amount   Amount that an issuer agrees to repay the 
debt holders on the maturity date.
Principal business activity   The business activity from which a 
company derives a majority of its revenues and/or earnings.
Principal value   Amount that an issuer agrees to repay the 
Principle of no arbitrage   See arbitrage-  free pricing .
Prior probabilities   Probabilities reflecting beliefs prior to the 
arrival of new information.
Priority of claims   Priority of payment, with the most senior 
or highest ranking debt having the first claim on the cash 
flows and assets of the issuer.

Private equity securities   Securities that are not listed on 
public exchanges and have no active secondary market. 
They are issued primarily to institutional investors via 
non-  public offerings, such as private placements.
Private investment in public equity   An investment in the 
equity of a publicly traded firm that is made at a discount 
to the market value of the firm’s shares.
Private placement   Typically a non-  underwritten, unregis -
tered offering of securities that are sold only to an inves -
tor or a small group of investors. It can be accomplished 
directly between the issuer and the investor(s) or through 
an investment bank.
Probability   A number between 0 and 1 describing the chance 
that a stated event will occur.

G-26 Glossary
Probability density function   A function with non-  negative 
values such that probability can be described by areas 
under the curve graphing the function.
Probability distribution   A distribution that specifies the 
probabilities of a random variable’s possible outcomes.
Probability function   A function that specifies the probability 
that the random variable takes on a specific value.
Producer price index   Reflects the price changes experienced 
by domestic producers in a country.
Production function   Provides the quantitative link between 
the level of output that the economy can produce and the 
inputs used in the production process.
Productivity   The amount of output produced by workers 
in a given period of time—for example, output per hour 
Profit   The return that owners of a company receive for the use 
of their capital and the assumption of financial risk when 
making their investments.

Profit and loss (P&L) statement   A financial statement that 
provides information about a company’s profitability over 
a stated period of time.
Profit margin   An indicator of profitability, calculated as net 
income divided by revenue; indicates how much of each 
dollar of revenues is left after all costs and expenses.
Profitability ratios   Ratios that measure a company’s ability 
to generate profitable sales from its resources (assets).
Project sequencing   To defer the decision to invest in a future 
project until the outcome of some or all of a current 
project is known. Projects are sequenced through time, 
so that investing in a project creates the option to invest 
in future projects.
Promissory note   A written promise to pay a certain amount 
of money on demand.
Property, plant, and equipment   Tangible assets that are 
expected to be used for more than one period in either the 
production or supply of goods or services, or for admin -
istrative purposes.

Prospectus   The document that describes the terms of a new 
bond issue and helps investors perform their analysis on 
the issue.
Protective put   An option strategy in which a long position in 
an asset is combined with a long position in a put.
Proxy contest   Corporate takeover mechanism in which 
shareholders are persuaded to vote for a group seeking 
a controlling position on a company’s board of directors.
Proxy voting   A process that enables shareholders who are 
unable to attend a meeting to authorize another individual 
to vote on their behalf.
Pseudo-  random numbers   Numbers produced by random 
number generators.
Public offer   See public offering .
Public offering   An offering of securities in which any member 
of the public may buy the securities. Also called public offer .
Pull on liquidity   When disbursements are paid too quickly 
or trade credit availability is limited, requiring companies 
to expend funds before they receive funds from sales that

could cover the liability.
Pure discount bonds   See zero-  coupon bonds .
Pure discount instruments   Instruments that pay interest 
as the difference between the amount borrowed and the 
amount paid back.
Pure-  play method   A method for estimating the beta for a 
company or project; it requires using a comparable compa -
ny’s beta and adjusting it for financial leverage differences.Put  An option that gives the holder the right to sell an under -
lying asset to another party at a fixed price over a specific 
Put–call–forward parity   The relationship among puts, calls, 
and forward contracts.
Put–call parity   An equation expressing the equivalence (par -
ity) of a portfolio of a call and a bond with a portfolio of 
a put and the underlying, which leads to the relationship 
between put and call prices.
Put/call ratio   A technical analysis indicator that evaluates 
market sentiment based upon the volume of put options 
traded divided by the volume of call options traded for a

particular financial instrument.
Put option   An option that gives the holder the right to sell 
an underlying asset to another party at a fixed price over 
a specific period of time.
Putable bonds   Bonds that give the bondholder the right to 
sell the bond back to the issuer at a predetermined price 
on specified dates.
Putable common shares   Common shares that give investors 
the option (or right) to sell their shares (i.e., “put” them) 
back to the issuing company at a price that is specified 
Quantile   A value at or below which a stated fraction of the 
data lies. Also called fractile .
Quantitative easing   An expansionary monetary policy based 
on aggressive open market purchase operations.
Quantity equation of exchange   An expression that over 
a given period, the amount of money used to purchase 
all goods and services in an economy, M × V, is equal to 
monetary value of this output, P × Y.
Quantity theory of money   Asserts that total spending (in

money terms) is proportional to the quantity of money.
Quartiles   Quantiles that divide a distribution into four equal 
parts.
Quasi-  fixed cost   A cost that stays the same over a range of 
production but can change to another constant level when 
production moves outside of that range.
Quasi-  government bonds   A bond issued by an entity that 
is either owned or sponsored by a national government. 
Also called agency bond .
Quick assets   Assets that can be most readily converted to cash 
(e.g., cash, short-  term marketable investments, receivables).
Quick ratio   A stringent measure of liquidity that indicates a 
company’s ability to satisfy current liabilities with its most 
Quintiles   Quantiles that divide a distribution into five equal 
parts.
Quota rents   Profits that foreign producers can earn by raising 
the price of their goods higher than they would without 
a quota.

a quota.
Quotas   Government policies that restrict the quantity of a 
good that can be imported into a country, generally for a 
specified period of time.
Quote-  driven market   A market in which dealers acting as 
principals facilitate trading.
Quoted interest rate   A quoted interest rate that does not 
account for compounding within the year. Also called 
stated annual interest rate .
Quoted margin   The specified yield spread over the reference 
rate, used to compensate an investor for the difference 
in the credit risk of the issuer and that implied by the 
reference rate.

G-27 Glossary
Random number   An observation drawn from a uniform 
distribution.
Random number generator   An algorithm that produces 
uniformly distributed random numbers between 0 and 1.
Random variable   A quantity whose future outcomes are 
uncertain.
Range   The difference between the maximum and minimum 
values in a dataset.
Ratio scales   A measurement scale that has all the character -
istics of interval measurement scales as well as a true zero 
point as the origin.
Real GDP   The value of goods and services produced, measured 
at base year prices.
Real income   Income adjusted for the effect of inflation on the 
purchasing power of money. Also known as the purchasing 
power of income . If income remains constant and a good’s 
price falls, real income is said to rise, even though the num -
ber of monetary units (e.g., dollars) remains unchanged.
Real interest rate   Nominal interest rate minus the expected 
rate of inflation.
Real risk-  free interest rate   The single-  period interest rate for

a completely risk-  free security if no inflation were expected.
Realizable (settlement) value   With reference to assets, the 
amount of cash or cash equivalents that could currently 
be obtained by selling the asset in an orderly disposal; 
with reference to liabilities, the undiscounted amount of 
cash or cash equivalents expected to be paid to satisfy the 
Rebalancing   Adjusting the weights of the constituent secu -
rities in an index.
Rebalancing policy   The set of rules that guide the process of 
restoring a portfolio’s asset class weights to those specified 
in the strategic asset allocation.
Recession   A period during which real GDP decreases (i.e., 
negative growth) for at least two successive quarters, or 
a period of significant decline in total output, income, 
employment, and sales usually lasting from six months 
to a year.
Recognition lag   The lag in government response to an eco -
nomic problem resulting from the delay in confirming a

change in the state of the economy.
Recourse loan   Loan in which the lender has a claim against 
the borrower for any shortfall between the outstanding 
mortgage balance and the proceeds received from the 
sale of the property.
Redemption yield   See yield to maturity .
Redemptions   Withdrawals of funds by investors.
Refinancing rate   A type of central bank policy rate.
Registered bonds   Bonds for which ownership is recorded by 
either name or serial number.
Relative dispersion   The amount of dispersion relative to a 
reference value or benchmark.
Relative frequency   With reference to an interval of grouped 
data, the number of observations in the interval divided by 
the total number of observations in the sample.
Relative price   The price of a specific good or service in com -
parison with those of other goods and services.
Relative strength analysis   A comparison of the performance 
of one asset with the performance of another asset or a

benchmark based on changes in the ratio of the securities’ 
respective prices over time.
Relative strength index   A technical analysis momentum 
oscillator that compares a security’s gains with its losses 
over a set period.Renewable resources   Resources that can be replenished, 
such as a forest.
Rent   Payment for the use of property.
Reorganization   Agreements made by a company in bank -
ruptcy under which a company’s capital structure is altered 
and/or alternative arrangements are made for debt repay -
ment; US Chapter 11 bankruptcy. The company emerges 
from bankruptcy as a going concern.
Replication   The creation of an asset or portfolio from another 
asset, portfolio, and/or derivative.
Repo   A form of collateralized loan involving the sale of a 
security with a simultaneous agreement by the seller to 
buy the same security back from the purchaser at an 
agreed-  on price and future date. The party who sells the 
security at the inception of the repurchase agreement and

buys it back at maturity is borrowing money from the other 
party, and the security sold and subsequently repurchased 
represents the collateral.
Repo margin   The difference between the market value of the 
security used as collateral and the value of the loan. Also 
called haircut .
Repo rate   The interest rate on a repurchase agreement.
Repurchase agreement   A form of collateralized loan involv -
ing the sale of a security with a simultaneous agreement by 
the seller to buy the same security back from the purchaser 
at an agreed-  on price and future date. The party who sells 
the security at the inception of the repurchase agreement 
and buys it back at maturity is borrowing money from 
the other party, and the security sold and subsequently 
repurchased represents the collateral.
Repurchase date   The date when the party who sold the secu -
rity at the inception of a repurchase agreement buys the 
security back from the cash lending counterparty.

Repurchase price   The price at which the party who sold the 
security at the inception of the repurchase agreement 
buys the security back from the cash lending counterparty.
Required margin   The yield spread over, or under, the ref -
erence rate such that an FRN is priced at par value on a 
rate reset date.
Required rate of return   See market discount rate .
Required yield   See market discount rate .
Required yield spread   The difference between the yield-  to- 
maturity on a new bond and the benchmark rate; additional 
compensation required by investors for the difference in 
risk and tax status of a bond relative to a government bond. 
Sometimes called the spread over the benchmark .
Reserve accounts   Form of internal credit enhancement that 
relies on creating accounts and depositing in these accounts 
cash that can be used to absorb losses. Also called reserve 
funds .
Reserve funds   See reserve accounts .

funds .
Reserve requirement   The requirement for banks to hold 
reserves in proportion to the size of deposits.
Resistance   In technical analysis, a price range in which selling 
activity is sufficient to stop the rise in the price of a security.
Responsible investing   The practice of identifying companies 
that can efficiently manage their financial, environmental, 
and human capital resoruces to generate attractive long-  
term profitability; often synonymous with sustainable 
investing .
Restricted payments   A bond covenant meant to protect 
creditors by limiting how much cash can be paid out to 
shareholders over time.

G-28 Glossary
Retail method   An inventory accounting method in which 
the sales value of an item is reduced by the gross margin 
to calculate the item’s cost.
Retracement   In technical analysis, a reversal in the movement 
of a security’s price such that it is counter to the prevailing 
longerterm price trend.
Return-  generating model   A model that can provide an esti -
mate of the expected return of a security given certain 
parameters and estimates of the values of the independent 
variables in the model.
Return on assets (ROA)   A profitability ratio calculated as net 
income divided by average total assets; indicates a compa -
ny’s net profit generated per dollar invested in total assets.
Return on equity (ROE)   A profitability ratio calculated as net 
income divided by average shareholders’ equity.
Return on sales   An indicator of profitability, calculated as 
each dollar of revenues is left after all costs and expenses.

Return on total capital   A profitability ratio calculated as EBIT 
divided by the sum of short- and long-  term debt and equity.
Revaluation model   The process of valuing long-  lived assets at 
fair value, rather than at cost less accumulated depreciation. 
Any resulting profit or loss is either reported on the income 
statement and/or through equity under revaluation surplus.
Revenue   The amount charged for the delivery of goods or 
services in the ordinary activities of a business over a stated 
period; the inflows of economic resources to a company 
over a stated period.
Reversal patterns   A type of pattern used in technical analysis 
to predict the end of a trend and a change in direction of 
the security’s price.
Reverse repo   A repurchase agreement viewed from the per -
spective of the cash lending counterparty.
Reverse repurchase agreement   A repurchase agree -
ment viewed from the perspective of the cash lending 
counterparty.
Reverse stock split   A reduction in the number of shares

outstanding with a corresponding increase in share price, 
but no change to the company’s underlying fundamentals.
Revolving credit agreements   The strongest form of short-  
term bank borrowing facilities; they are in effect for multi -
ple years (e.g., 3–5 years) and may have optional medium-  
term loan features.
Rho   The sensitivity of the option price to the risk-  free rate.
Ricardian equivalence   An economic theory that implies that 
it makes no difference whether a government finances a 
deficit by increasing taxes or issuing debt.
Risk   Exposure to uncertainty. The chance of a loss or adverse 
outcome as a result of an action, inaction, or external event.
Risk averse   The assumption that an investor will choose the 
least risky alternative.
Risk aversion   The degree of an investor’s inability and unwill -
ingness to take risk.
Risk budgeting   The establishment of objectives for individ -
uals, groups, or divisions of an organization that takes

into account the allocation of an acceptable level of risk.
Risk exposure   The state of being exposed or vulnerable to a 
risk. The extent to which an entity is sensitive to under -
lying risks.
Risk governance   The top-  down process and guidance that 
directs risk management activities to align with and support 
the overall enterprise.Risk management   The process of identifying the level of 
risk an entity wants, measuring the level of risk the entity 
currently has, taking actions that bring the actual level of 
risk to the desired level of risk, and monitoring the new 
actual level of risk so that it continues to be aligned with 
the desired level of risk.
Risk management framework   The infrastructure, process, 
and analytics needed to support effective risk management 
in an organization.
Risk-  neutral pricing   Sometimes said of derivatives pricing, 
uses the fact that arbitrage opportunities guarantee that 
a risk-  free portfolio consisting of the underlying and the

derivative must earn the risk-  free rate.
Risk-  neutral probabilities   Weights that are used to compute 
a binomial option price. They are the probabilities that 
would apply if a risk-  neutral investor valued an option.
Risk premium   An extra return expected by investors for 
bearing some specified risk.
Risk shifting   Actions to change the distribution of risk 
outcomes.
Risk tolerance   The amount of risk an investor is willing and 
able to bear to achieve an investment goal.
Risk transfer   Actions to pass on a risk to another party, often, 
but not always, in the form of an insurance policy.
Robo-  adviser   A machine-  based analytical tool or service that 
provides technology-  driven investment solutions through 
online platforms.
Robust   The quality of being relatively unaffected by a violation 
of assumptions.
Rule of 72   The principle that the approximate number of years 
necessary for an investment to double is 72 divided by the 
stated interest rate.

Running yield   See current yield .
Safety-  first rules   Rules for portfolio selection that focus on 
the risk that portfolio value will fall below some minimum 
acceptable level over some time horizon.
Safety stock   A level of inventory beyond anticipated needs 
that provides a cushion in the event that it takes longer to 
replenish inventory than expected or in the case of greater 
than expected demand.
Sales   Generally, a synonym for revenue; “sales” is generally 
understood to refer to the sale of goods, whereas “revenue” 
is understood to include the sale of goods or services.
Sales risk   Uncertainty with respect to the quantity of goods 
and services that a company is able to sell and the price 
it is able to achieve; the risk related to the uncertainty of 
revenues.
Sales-  type leases   A type of finance lease, from a lessor per -
spective, where the present value of the lease payments 
(lease receivable) exceeds the carrying value of the leased

asset. The revenues earned by the lessor are operating 
(the profit on the sale) and financing (interest) in nature.
Sample   A subset of a population.
Sample excess kurtosis   A sample measure of the degree of 
a distribution’s kurtosis in excess of the normal distribu -
tion’s kurtosis.
Sample kurtosis   A sample measure of the degree of a distri -
bution’s peakedness.
Sample mean   The sum of the sample observations, divided 
by the sample size.

G-29 Glossary
Sample selection bias   Bias introduced by systematically 
excluding some members of the population according to 
a particular attribute—for example, the bias introduced 
when data availability leads to certain observations being 
excluded from the analysis.
Sample skewness   A sample measure of degree of asymmetry 
of a distribution.
Sample standard deviation   The positive square root of the 
sample variance.
Sample statistic   A quantity computed from or used to 
describe a sample.
Sample variance   A sample measure of the degree of dis -
persion of a distribution, calculated by dividing the sum 
of the squared deviations from the sample mean by the 
sample size minus 1.
Sampling   The process of obtaining a sample.
Sampling distribution   The distribution of all distinct possible 
values that a statistic can assume when computed from 
samples of the same size randomly drawn from the same 
population.
Sampling error   The difference between the observed value

of a statistic and the quantity it is intended to estimate.
Sampling plan   The set of rules used to select a sample.
Say on pay   A process whereby shareholders may vote on 
executive remuneration (compensation) matters.
Say’s law   Named for French economist J.B. Say: All that is pro -
duced will be sold because supply creates its own demand.
Scenario analysis   Analysis that shows the changes in key 
financial quantities that result from given (economic) 
events, such as the loss of customers, the loss of a sup -
ply source, or a catastrophic event; a risk management 
technique involving examination of the performance of 
a portfolio under specified situations. Closely related to 
stress testing.
Screening   The application of a set of criteria to reduce a set 
of potential investments to a smaller set having certain 
desired characteristics.
Seasoned offering   An offering in which an issuer sells addi -
tional units of a previously issued security.

Second-  degree price discrimination   When the monopolist 
charges different per-  unit prices using the quantity pur -
chased as an indicator of how highly the customer values 
the product.
Second lien   A secured interest in the pledged assets that 
ranks below first lien debt in both collateral protection 
and priority of payment.
Secondary bond markets   Markets in which existing bonds 
are traded among investors.
Secondary market   The market where securities are traded 
among investors.
Secondary precedence rules   Rules that determine how to 
rank orders placed at the same time.
Sector   A group of related industries.
Sector indexes   Indexes that represent and track different eco -
nomic sectors—such as consumer goods, energy, finance, 
health care, and technology—on either a national, regional, 
or global basis.
Secured bonds   Bonds secured by assets or financial guaran -
tees pledged to ensure debt repayment in case of default.

Secured debt   Debt in which the debtholder has a direct 
claim—a pledge from the issuer—on certain assets and 
their associated cash flows.Securitization   A process that involves moving assets into a 
special legal entity, which then uses the assets as guarantees 
to secure a bond issue.
Securitized assets   Assets that are typically used to create 
asset-  backed bonds; for example, when a bank securitizes 
a pool of loans, the loans are said to be securitized.
Security characteristic line   A plot of the excess return of a 
security on the excess return of the market.
Security market index   A portfolio of securities representing 
a given security market, market segment, or asset class.
Security market line   (SML) The graph of the capital asset 
pricing model.
Security selection   The process of selecting individual secu -
rities; typically, security selection has the objective of 
generating superior risk-  adjusted returns relative to a 
portfolio’s benchmark.

Self-  investment limits   With respect to investment limitations 
applying to pension plans, restrictions on the percentage 
of assets that can be invested in securities issued by the 
pension plan sponsor.
Sell-  side firm   A broker or dealer that sells securities to and 
provides independent investment research and recommen -
dations to investment management companies.
Semi-  strong-  form efficient market   A market in which 
security prices reflect all publicly known and available 
Semiannual bond basis yield   An annual rate having a peri -
odicity of two; also known as a semiannual bond equiv -
alent yield .
Semiannual bond equivalent yield   See semiannual bond 
basis yield .
Semideviation   The positive square root of semivariance 
(sometimes called semistandard deviation ).
Semilogarithmic   Describes a scale constructed so that equal 
intervals on the vertical scale represent equal rates of 
change, and equal intervals on the horizontal scale repre -

sent equal amounts of change.
Semivariance   The average squared deviation below the mean.
Seniority ranking   Priority of payment of various debt 
Sensitivity analysis   Analysis that shows the range of possible 
outcomes as specific assumptions are changed.
Separately managed account   (SMA) An investment port -
folio managed exclusively for the benefit of an individual 
or institution.
Serial maturity structure   Structure for a bond issue in which 
the maturity dates are spread out during the bond’s life; a 
stated number of bonds mature and are paid off each year 
before final maturity.
Settlement   The process that occurs after a trade is completed, 
the securities are passed to the buyer, and payment is 
received by the seller.
Settlement date   Date when the buyer makes cash payment 
and the seller delivers the security.
Settlement price   The official price, designated by the clearing -
house, from which daily gains and losses will be determined 
and marked to market.

Share repurchase   A transaction in which a company buys 
back its own shares. Unlike stock dividends and stock 
splits, share repurchases use corporate cash.
Shareholder activism   Strategies used by shareholders to 
attempt to compel a company to act in a desired manner.
Shareholder engagement   The process whereby companies 
engage with their shareholders.

G-30 Glossary
Shareholders’ equity   Assets less liabilities; the residual inter -
est in the assets after subtracting the liabilities.
Sharpe ratio   The average return in excess of the risk-  free rate 
divided by the standard deviation of return; a measure 
of the average excess return earned per unit of standard 
deviation of return.
Shelf registration   Type of public offering that allows the 
issuer to file a single, all-  encompassing offering circular 
that covers a series of bond issues.
Short   The seller of an asset or derivative contract. Also refers to 
the position of being short an asset or derivative contract.
Short position   A position in an asset or contract in which 
one has sold an asset one does not own, or in which a 
right under a contract can be exercised against oneself.
Short-  run average total cost   The curve describing average 
total cost when some costs are considered fixed.
Short selling   A transaction in which borrowed securities are

sold with the intention to repurchase them at a lower price 
at a later date and return them to the lender.
Shortfall risk   The risk that portfolio value will fall below 
some minimum acceptable level over some time horizon.
Shutdown point   The point at which average revenue is equal 
to the firm’s average variable cost.
Simple interest   The interest earned each period on the orig -
inal investment; interest calculated on the principal only.
Simple random sample   A subset of a larger population cre -
ated in such a way that each element of the population 
has an equal probability of being selected to the subset.
Simple random sampling   The procedure of drawing a sample 
to satisfy the definition of a simple random sample.
Simple yield   The sum of the coupon payments plus the 
straight-  line amortized share of the gain or loss, divided 
by the flat price.
Simulation   Computer-  generated sensitivity or scenario anal -
ysis that is based on probability models for the factors that 
drive outcomes.

Simulation trial   A complete pass through the steps of a 
simulation.
Single-  step format   With respect to the format of the income 
statement, a format that does not subtotal for gross profit 
Sinking fund arrangement   Provision that reduces the credit 
risk of a bond issue by requiring the issuer to retire a por -
tion of the bond’s principal outstanding each year.
Situational influences   External factors, such as environmental 
or cultural elements, that shape our behavior.
Skewed   Not symmetrical.
Skewness   A quantitative measure of skew (lack of symmetry); 
a synonym of skew.
Small country   A country that is a price taker in the world 
market for a product and cannot influence the world 
market price.
Smart contract   A computer program that is designed to self-  
execute on the basis of pre-  specified terms and conditions 
agreed to by parties to a contract.
Socially responsible investing   An investment approach that

excludes investments in companies or industries that devi -
ate from an organization’s beliefs and sometimes includes 
investments with favorable environmental or social profiles.
Solvency   With respect to financial statement analysis, the 
ability of a company to fulfill its long-  term obligations.
Solvency ratios   Ratios that measure a company’s ability to 
meet its long-  term obligations.Solvency risk   The risk that an entity does not survive or 
succeed because it runs out of cash, even though it might 
otherwise be solvent.
Sovereign bonds   A bond issued by a national government.
Sovereign yield spread   An estimate of the country spread 
(country equity premium) for a developing nation that is 
based on a comparison of bonds yields in country being 
analyzed and a developed country. The sovereign yield 
spread is the difference between a government bond yield 
in the country being analyzed, denominated in the currency 
of the developed country, and the Treasury bond yield on

a similar maturity bond in the developed country.
Sovereigns   A bond issued by a national government.
Spearman rank correlation coefficient   A measure of cor -
relation applied to ranked data.
Special dividend   A dividend paid by a company that does 
not pay dividends on a regular schedule, or a dividend that 
Special purpose entity   A non-  operating entity created to 
carry out a specified purpose, such as leasing assets or 
securitizing receivables; can be a corporation, partnership, 
trust, limited liability, or partnership formed to facilitate a 
specific type of business activity. Also called special purpose 
vehicle  or variable interest entity .
Special purpose vehicle   See special purpose entity .
Specific identification method   An inventory accounting 
method that identifies which specific inventory items were 
sold and which remained in inventory to be carried over 
to later periods.

Speculative demand for money   The demand to hold specu -
lative money balances based on the potential opportunities 
or risks that are inherent in other financial instruments. 
Also called portfolio demand for money .
Speculative money balances   Monies held in anticipation 
that other assets will decline in value.
Split coupon bond   See deferred coupon bond .
Sponsored   A type of depository receipt in which the foreign 
company whose shares are held by the depository has a 
direct involvement in the issuance of the receipts.
Spot curve   A sequence of yields-  to- maturity on zero-  coupon 
bonds. Sometimes called zero or strip curve  because coupon 
payments are “stripped” off of the bonds.
Spot markets   Markets in which assets are traded for imme -
diate delivery.
Spot prices   The price of an asset for immediately delivery.
Spot rates   A sequence of market discount rates that cor -
respond to the cash flow dates; yields-  to- maturity on

zero-  coupon bonds maturing at the date of each cash flow.
Spread   In general, the difference in yield between different 
fixed income securities. Often used to refer to the differ -
ence between the yield-  to- maturity and the benchmark.
Spread over the benchmark   See required yield spread .
Spread risk   Bond price risk arising from changes in the yield 
spread on credit-  risky bonds; reflects changes in the mar -
ket’s assessment and/or pricing of credit migration (or 
downgrade) risk and market liquidity risk.
Stackelberg model   A prominent model of strategic deci -
sionmaking in which firms are assumed to make their 
decisions sequentially.
Stagflation   When a high inflation rate is combined with a high 
level of unemployment and a slowdown of the economy.
Staggered boards   Election process whereby directors are 
typically divided into multiple classes that are elected sep -
arately in consecutive years—that is, one class every year.

G-31 Glossary
Stakeholder management   The identification, prioritization, 
and understanding of the interests of stakeholder groups, 
and managing the company’s relationships with these 
groups.
Stakeholders   Individuals or groups of individuals who may 
be affected either directly or indirectly by a decision and 
thus have an interest, or stake, in the decision.
Standard cost   With respect to inventory accounting, the 
planned or target unit cost of inventory items or services.
Standard deviation   The positive square root of the variance; a 
measure of dispersion in the same units as the original data.
Standard normal distribution   The normal density with mean 
(μ) equal to 0 and standard deviation (σ) equal to 1.
Standardizing   A transformation that involves subtracting the 
mean and dividing the result by the standard deviation.
Standards of conduct   Behaviors required by a group; estab -
lished benchmarks that clarify or enhance a group’s code 
of ethics.

of ethics.
Standing limit orders   A limit order at a price below market 
and which therefore is waiting to trade.
Stated annual interest rate   A quoted interest rate that does 
not account for compounding within the year. Also called 
quoted interest rate .
Statement of changes in equity   (statement of owners’ equity) 
A financial statement that reconciles the beginning-  of- 
period and end-  of- period balance sheet values of share -
holders’ equity; provides information about all factors 
affecting shareholders’ equity. Also called statement of 
owners’ equity .
Statement of financial condition   The financial statement that 
presents an entity’s current financial position by disclosing 
resources the entity controls (its assets) and the claims on 
those resources (its liabilities and equity claims), as of a 
particular point in time (the date of the balance sheet).
Statement of financial position   The financial statement that 
presents an entity’s current financial position by disclosing

Statement of operations   A financial statement that provides 
information about a company’s profitability over a stated 
Statistic   A quantity computed from or used to describe a 
sample of data.
Statistical inference   Making forecasts, estimates, or judg -
ments about a larger group from a smaller group actually 
observed; using a sample statistic to infer the value of an 
unknown population parameter.
Statistically significant   A result indicating that the null 
hypothesis can be rejected; with reference to an estimated 
regression coefficient, frequently understood to mean a 
result indicating that the corresponding population regres -
sion coefficient is different from 0.
Statutory voting   A common method of voting where each 
share represents one vote.

Step-  up coupon bond   Bond for which the coupon, which 
may be fixed or floating, increases by specified margins 
at specified dates.
Stock dividend   A type of dividend in which a company distrib -
utes additional shares of its common stock to shareholders 
instead of cash.
Stock-  out losses   Profits lost from not having sufficient inven -
tory on hand to satisfy demand.Stock split   An increase in the number of shares outstanding 
with a consequent decrease in share price, but no change 
to the company’s underlying fundamentals.
Stop-  loss order   See stop order .
Stop order   An order in which a trader has specified a stop 
price condition. Also called stop-  loss order .
Store of value   The quality of tending to preserve value.
Store of wealth   Goods that depend on the fact that they 
do not perish physically over time, and on the belief that 
others would always value the good.
Straight-  line method   A depreciation method that allocates

evenly the cost of a long-  lived asset less its estimated 
residual value over the estimated useful life of the asset.
Straight voting   A shareholder voting process in which share -
holders receive one vote for each share owned.
Strategic analysis   Analysis of the competitive environment 
with an emphasis on the implications of the environment 
for corporate strategy.
Strategic asset allocation   The set of exposures to IPS-  
permissible asset classes that is expected to achieve the 
client’s long-  term objectives given the client’s investment 
constraints.
Strategic groups   Groups sharing distinct business models 
or catering to specific market segments in an industry.
Street convention   Yield measure that neglects weekends and 
holidays; the internal rate of return on cash flows assuming 
payments are made on the scheduled dates, even when the 
scheduled date falls on a weekend or holiday.
Stress testing   A specific type of scenario analysis that esti -

mates losses in rare and extremely unfavorable combina -
tions of events or scenarios.
Strong-  form efficient market   A market in which security 
prices reflect all public and private information.
Structural (or cyclically adjusted) budget deficit   The deficit 
that would exist if the economy was at full employment 
(or full potential output).
Structural subordination   Arises in a holding company struc -
ture when the debt of operating subsidiaries is serviced by 
the cash flow and assets of the subsidiaries before funds 
can be passed to the holding company to service debt at 
the parent level.
Structured financial instruments   Financial instruments 
that share the common attribute of repackaging risks. 
Structured financial instruments include asset-  backed 
securities, collateralized debt obligations, and other struc -
tured financial instruments such as capital protected, yield 
enhancement, participation and leveraged instruments.

Subjective probability   A probability drawing on personal or 
subjective judgment.
Subordinated debt   A class of unsecured debt that ranks 
below a firm’s senior unsecured obligations.
Subordination   Form of internal credit enhancement that 
relies on creating more than one bond tranche and ordering 
the claim priorities for ownership or interest in an asset 
between the tranches. The ordering of the claim priorities is 
called a senior/subordinated structure, where the tranches 
of highest seniority are called senior followed by subor -
dinated or junior tranches. Also called credit tranching .
Substitutes   Said of two goods or services such that if the price 
of one increases the demand for the other tends to increase, 
holding all other things equal (e.g., butter and margarine).
Sunk cost   A cost that has already been incurred.
Supervised learning   A machine learning approach that makes 
use of labeled training data.

G-32 Glossary
Supply shock   A typically unexpected disturbance to supply.
Support   In technical analysis, a price range in which buying 
activity is sufficient to stop the decline in the price of a 
security.
Support tranche   A class or tranche in a CMO that protects 
the PAC tranche from prepayment risk.
Supranational bonds   A bond issued by a supranational agency 
such as the World Bank.
Surety bond   Form of external credit enhancement whereby 
a rated and regulated insurance company guarantees to 
reimburse bondholders for any losses incurred up to a 
maximum amount if the issuer defaults.
Survey approach   An estimate of the equity risk premium 
that is based upon estimates provided by a panel of finance 
experts.
Survivorship bias   The bias resulting from a test design that 
fails to account for companies that have gone bankrupt, 
merged, or are otherwise no longer reported in a database.
Sustainable growth rate   The rate of dividend (and earnings)

growth that can be sustained over time for a given level 
of return on equity, keeping the capital structure constant 
and without issuing additional common stock.
Sustainable investing   The practice of identifying companies 
that can efficiently manage their financial, environmen -
tal, and human capital resources to generate attractive 
long-  term profitability; often synonymous with responsible 
Sustainable rate of economic growth   The rate of increase 
in the economy’s productive capacity or potential GDP .
Swap contract   An agreement between two parties to exchange 
a series of future cash flows.
Syndicated loans   Loans from a group of lenders to a single 
borrower.
Syndicated offering   A bond issue that is underwritten by a 
group of investment banks.
Synthetic lease   A lease that is structured to provide a com -
pany with the tax benefits of ownership while not requir -
ing the asset to be reflected on the company’s financial 

Systematic risk   Risk that affects the entire market or econ -
omy; it cannot be avoided and is inherent in the overall 
market. Systematic risk is also known as non-  diversifiable 
or market risk.
Systematic sampling   A procedure of selecting every kth 
member until reaching a sample of the desired size. The 
sample that results from this procedure should be approx -
imately random.
t-Test   A hypothesis test using a statistic ( t-statistic) that follows 
a t-distribution.
Tactical asset allocation   The decision to deliberately deviate 
from the strategic asset allocation in an attempt to add 
value based on forecasts of the near-  term relative perfor -
mance of asset classes.
Target balance   A minimum level of cash to be held avail -
able—estimated in advance and adjusted for known funds 
transfers, seasonality, or other factors.
Target capital structure   A company’s chosen proportions 
of debt and equity.
Target independent   A bank’s ability to determine the defi -

nition of inflation that they target, the rate of inflation 
that they target, and the horizon over which the target is 
to be achieved.
Target semideviation   The positive square root of target 
semivariance.Target semivariance   The average squared deviation below 
a target value.
Tariffs   Taxes that a government levies on imported goods.
Tax base   The amount at which an asset or liability is valued 
for tax purposes.
Tax expense   An aggregate of an entity’s income tax payable (or 
recoverable in the case of a tax benefit) and any changes in 
deferred tax assets and liabilities. It is essentially the income 
tax payable or recoverable if these had been determined 
based on accounting profit rather than taxable income.
Tax loss carry forward   A taxable loss in the current period 
that may be used to reduce future taxable income.
Taxable income   The portion of an entity’s income that is sub -
ject to income taxes under the tax laws of its jurisdiction.

Taxable temporary differences   Temporary differences that 
result in a taxable amount in a future period when deter -
mining the taxable profit as the balance sheet item is 
Technical analysis   A form of security analysis that uses price 
and volume data, which is often displayed graphically, in 
decision making.
Technology   The process a company uses to transform inputs 
into outputs.
Tender offer   Corporate takeover mechanism which involves 
shareholders selling their interests directly to the group 
seeking to gain control.
Tenor   The time-  to- maturity for a bond or derivative contract. 
Also called term to maturity .
Term maturity structure   Structure for a bond issue in which 
the bond’s notional principal is paid off in a lump sum at 
maturity.
Term structure   See maturity structure .
Term structure of credit spreads   The relationship between 
the spreads over the “risk-  free” (or benchmark) rates and 
times-  to- maturity.

Term structure of yield volatility   The relationship between the 
volatility of bond yields-  to- maturity and times-  to- maturity.
Terminal stock value   The expected value of a share at the end 
of the investment horizon—in effect, the expected selling 
price. Also called terminal value .
Terminal value   The expected value of a share at the end of the 
investment horizon—in effect, the expected selling price.
Terms of trade   The ratio of the price of exports to the price 
of imports, representing those prices by export and import 
price indexes, respectively.
Text analytics   The use of computer programs to analyze and 
derive meaning from typically large, unstructured text- or 
voice-  based datasets.
Thematic investing   An ESG implementation approach that 
focuses on investing in companies within a specific sector 
or industry theme.
Third-  degree price discrimination   When the monopolist 
segregates customers into groups based on demographic

or other characteristics and offers different pricing to 
each group.
Time-  period bias   The possibility that when we use a time-  
series sample, our statistical conclusion may be sensitive 
to the starting and ending dates of the sample.
Time-  series data   Observations of a variable over time.
Time tranching   The creation of classes or tranches in an ABS/
MBS that possess different (expected) maturities.
Time value   The difference between the market price of the 
option and its intrinsic value.

G-33 Glossary
Time value decay   Said of an option when, at expiration, 
no time value remains and the option is worth only its 
exercise value.
Time value of money   The principles governing equivalence 
relationships between cash flows with different dates.
Time-  weighted rate of return   The compound rate of growth 
of one unit of currency invested in a portfolio during a 
stated measurement period; a measure of investment per -
formance that is not sensitive to the timing and amount 
of withdrawals or additions to the portfolio.
Tokenization   The process of representing ownership rights 
to physical assets on a blockchain or distributed ledger.
Top-  down analysis   With reference to investment selection 
processes, an approach that starts with macro selection 
(i.e., identifying attractive geographic segments and/or 
industry segments) and then addresses selection of the 
most attractive investments within those segments.
Total comprehensive income   The change in equity during a

period resulting from transaction and other events, other 
than those changes resulting from transactions with owners 
in their capacity as owners.
Total cost   The summation of all costs, for which costs are 
classified as fixed or variable.
Total factor productivity   A scale factor that reflects the por -
tion of growth that is not accounted for by explicit factor 
inputs (e.g. capital and labor).
Total fixed cost   The summation of all expenses that do not 
change as the level of production varies.
Total invested capital   The sum of market value of common 
equity, book value of preferred equity, and face value of 
debt.
Total probability rule   A rule explaining the unconditional 
probability of an event in terms of probabilities of the event 
conditional on mutually exclusive and exhaustive scenarios.
Total probability rule for expected value   A rule explain -
ing the expected value of a random variable in terms of 
expected values of the random variable conditional on

mutually exclusive and exhaustive scenarios.
Total return   Measures the price appreciation, or percentage 
change in price of the securities in an index or portfolio, 
plus any income received over the period.
Total return index   An index that reflects the price appreciation 
or percentage change in price of the constituent securities 
plus any income received since inception.
Total return swap   A swap in which one party agrees to pay the 
total return on a security. Often used as a credit derivative, 
in which the underlying is a bond.
Total variable cost   The summation of all variable expenses.
Tracking error   The standard deviation of the differences 
between a portfolio’s returns and its benchmark’s returns; 
a synonym of active risk.
Tracking risk   The standard deviation of the differences 
a synonym of active risk. Also called tracking error .
Trade creation   When regional integration results in the

replacement of higher cost domestic production by lower 
cost imports from other members.
Trade credit   A spontaneous form of credit in which a pur -
chaser of the goods or service is financing its purchase by 
delaying the date on which payment is made.
Trade diversion   When regional integration results in lower-  
cost imports from non-  member countries being replaced 
with higher-  cost imports from members.Trade payables   Amounts that a business owes to its vendors 
Trade protection   Government policies that impose restric -
tions on trade, such as tariffs and quotas.
Trade surplus (deficit)   When the value of exports is greater 
(less) than the value of imports.
Trading securities   Securities held by a company with the 
intent to trade them. Also called held-  for- trading securities .
Traditional investment markets   Markets for traditional 
investments, which include all publicly traded debts and

equities and shares in pooled investment vehicles that hold 
publicly traded debts and/or equities.
Transactions money balances   Money balances that are held 
to finance transactions.
Transactions motive   In the context of inventory management, 
the need for inventory as part of the routine production–
sales cycle.
Transfer payments   Welfare payments made through the social 
security system that exist to provide a basic minimum level 
of income for low-  income households.
Transparency   Said of something (e.g., a market) in which infor -
mation is fully disclosed to the public and/or regulators.
Treasury Inflation-  Protected Securities   A bond issued by 
the United States Treasury Department that is designed 
to protect the investor from inflation by adjusting the 
principal of the bond for changes in inflation.
Treasury stock method   A method for accounting for the effect 
of options (and warrants) on earnings per share (EPS) that 
specifies what EPS would have been if the options and

warrants had been exercised and the company had used 
the proceeds to repurchase common stock.
Tree diagram   A diagram with branches emanating from nodes 
representing either mutually exclusive chance events or 
mutually exclusive decisions.
Trend   A long-  term pattern of movement in a particular 
direction.
Treynor ratio   A measure of risk-  adjusted performance that 
relates a portfolio’s excess returns to the portfolio’s beta.
Triangle patterns   In technical analysis, a continuation chart 
pattern that forms as the range between high and low 
prices narrows, visually forming a triangle.
Trimmed mean   A mean computed after excluding a stated 
small percentage of the lowest and highest observations.
TRIN   A flow of funds indicator applied to a broad stock market 
index to measure the relative extent to which money is 
moving into or out of rising and declining stocks.
Triple bottoms   In technical analysis, a reversal pattern that 
is formed when the price forms three troughs at roughly

the same price level; used to predict a change from a 
downtrend to an uptrend.
Triple tops   In technical analysis, a reversal pattern that is 
formed when the price forms three peaks at roughly the 
same price level; used to predict a change from an uptrend 
to a downtrend.
Trough   The lowest point of a business cycle.
True yield   The internal rate of return on cash flows using the 
actual calendar including weekends and bank holidays.
Trust deed   The governing legal credit agreement, typically 
incorporated by reference in the prospectus. Also called 
bond indenture .

G-34 Glossary
Trust receipt arrangement   The use of inventory as collateral 
for a loan. The inventory is segregated and held in trust, 
and the proceeds of any sale must be remitted to the lender 
Turn-  of- the-  year effect   Calendar anomaly that stock mar -
ket returns in January are significantly higher compared 
to the rest of the months of the year, with most of the 
abnormal returns reported during the first five trading 
days in January.
Two-  fund separation theorem   The theory that all investors 
regardless of taste, risk preferences, and initial wealth will 
hold a combination of two portfolios or funds: a risk-  free 
asset and an optimal portfolio of risky assets.
Two-  sided hypothesis test   A test in which the null hypoth -
esis is rejected in favor of the alternative hypothesis if the 
evidence indicates that the population parameter is either 
smaller or larger than a hypothesized value.
Two-  tailed hypothesis test   A test in which the null hypoth -

Two-  week repo rate   The interest rate on a two-  week repur -
chase agreement; may be used as a policy rate by a central 
bank.
Type I error   The error of rejecting a true null hypothesis.
Type II error   The error of not rejecting a false null hypothesis.
Unanticipated (unexpected) inflation   The component of 
inflation that is a surprise.
Unconditional probability   The probability of an event not 
conditioned on another event.
Underemployed   A person who has a job but has the qualifi -
cations to work a significantly higher-  paying job.
Underlying   An asset that trades in a market in which buyers 
and sellers meet, decide on a price, and the seller then 
delivers the asset to the buyer and receives payment. The 
underlying is the asset or other derivative on which a par -

ticular derivative is based. The market for the underlying 
is also referred to as the spot market .
Underwriter   A firm, usually an investment bank, that takes 
the risk of buying the newly issued securities from the 
issuer, and then reselling them to investors or to dealers, 
thus guaranteeing the sale of the securities at the offering 
price negotiated with the issuer.
Underwritten offering   A type of securities issue mechanism 
in which the investment bank guarantees the sale of the 
securities at an offering price that is negotiated with the 
issuer. Also known as firm commitment offering .
Unearned revenue   A liability account for money that has 
been collected for goods or services that have not yet been 
delivered; payment received in advance of providing a good 
or service. Also called deferred revenue  or deferred income .
Unemployed   People who are actively seeking employment 
but are currently without a job.
Unemployment rate   The ratio of unemployed to the labor 
force.

force.
Unexpected inflation   The component of inflation that is a 
surprise.
Unit elastic   An elasticity with a magnitude of negative one. 
Also called unitary elastic .
Unit labor cost   The average labor cost to produce one unit 
of output.
Unit normal distribution   The normal density with mean (μ) 
equal to 0 and standard deviation (σ) equal to 1.Units-  of- production method   A depreciation method that 
allocates the cost of a long-  lived asset based on actual 
usage during the period.
Univariate distribution   A distribution that specifies the prob -
abilities for a single random variable.
Universal owners   Long-  term investors, such as pension funds, 
that have significant assets invested in globally diversified 
portfolios.
Unlimited funds   An unlimited funds environment assumes 
that the company can raise the funds it wants for all prof -
itable projects simply by paying the required rate of return.
Unsecured debt   Debt which gives the debtholder only a

general claim on an issuer’s assets and cash flow.
Unsponsored   A type of depository receipt in which the foreign 
company whose shares are held by the depository has no 
involvement in the issuance of the receipts.
Unsupervised learning   A machine learning approach that 
does not make use of labeled training data.
Up transition probability   The probability that an asset’s 
value moves up.
Validity instructions   Instructions which indicate when the 
order may be filled.
Valuation allowance   A reserve created against deferred tax 
assets, based on the likelihood of realizing the deferred 
tax assets in future accounting periods.
Valuation ratios   Ratios that measure the quantity of an asset 
or flow (e.g., earnings) in relation to the price associated 
with a specified claim (e.g., a share or ownership of the 
enterprise).
Value at risk   (VaR) A money measure of the minimum value 
of losses expected during a specified time period at a given 
level of probability.

Value investors   With reference to equity investors, investors 
who are focused on paying a relatively low share price in 
relation to earnings or assets per share.
VaR  See value at risk .
Variable costs   Costs that fluctuate with the level of produc -
tion and sales.
Variable-  rate note   Similar to a floating-  rate note, except that 
the spread is variable rather than constant.
Variance   The expected value (the probability-  weighted 
average) of squared deviations from a random variable’s 
expected value.
Variation margin   Additional margin that must be deposited in 
an amount sufficient to bring the balance up to the initial 
margin requirement.
Veblen goods   Goods that increase in desirability with increas -
ing price.
Vega   A measure of the sensitivity of an option’s price to 
changes in the underlying’s volatility.
Venture capital   Investments that provide “seed” or start-  up 
capital, early-  stage financing, or later-  stage financing

(including mezzanine-  stage financing) to companies that 
are in early development stages and require additional 
capital for expansion or preparation for an initial public 
offering.
Venture capital fund   A fund for private equity investors 
that provides financing for development-  stage companies.
Vertical analysis   Common-  size analysis using only one report -
ing period or one base financial statement; for example, 
an income statement in which all items are stated as per -
centages of sales.
Vertical demand schedule   Implies that some fixed quantity 
is demanded, regardless of price.

G-35 Glossary
Volatility   As used in option pricing, the standard deviation 
of the continuously compounded returns on the under -
lying asset.
Voluntarily unemployed   A person voluntarily outside the 
labor force, such as a jobless worker refusing an available 
vacancy.
Voluntary export restraint   A trade barrier under which the 
exporting country agrees to limit its exports of the good 
to its trading partners to a specific number of units.
Vote by proxy   A mechanism that allows a designated party—
such as another shareholder, a shareholder representative, 
or management—to vote on the shareholder’s behalf.
Warehouse receipt arrangement   The use of inventory as 
collateral for a loan; similar to a trust receipt arrangement 
except there is a third party (i.e., a warehouse company) 
that supervises the inventory.
Warrant   Attached option that gives its holder the right to 
buy the underlying stock of the issuing company at a fixed 
exercise price until the expiration date.

Weak-  form efficient market hypothesis   The belief that secu -
rity prices fully reflect all past market data, which refers 
to all historical price and volume trading information.
Wealth effect   An increase (decrease) in household wealth 
increases (decreases) consumer spending out of a given 
level of current income.
Weighted average cost method   An inventory accounting 
method that averages the total cost of available inventory 
items over the total units available for sale.
Weighted average cost of capital   A weighted average of the 
aftertax required rates of return on a company’s common 
stock, preferred stock, and long-  term debt, where the 
weights are the fraction of each source of financing in the 
company’s target capital structure.
Weighted average coupon rate   Weighting the mortgage rate 
of each mortgage loan in the pool by the percentage of the 
mortgage outstanding relative to the outstanding amount

of all the mortgages in the pool.Weighted average life   A measure that gives investors an 
indication of how long they can expect to hold the MBS 
before it is paid off; the convention-  based average time to 
receipt of all principal repayments. Also called average life .
Weighted average maturity   Weighting the remaining num -
ber of months to maturity for each mortgage loan in the 
pool by the amount of the outstanding mortgage balance.
Weighted mean   An average in which each observation is 
weighted by an index of its relative importance.
Wholesale price index   Reflects the price changes experienced 
Winsorized mean   A mean computed after assigning a stated 
percent of the lowest values equal to one specified low 
value, and a stated percent of the highest values equal to 
one specified high value.
Working capital   The difference between current assets and 
current liabilities.
Working capital management   The management of a compa -

ny’s short-  term assets (such as inventory) and short-  term 
liabilities (such as money owed to suppliers).
World price   The price prevailing in the world market.
Yield   The actual return on a debt security if it is held to 
maturity.
Yield duration   The sensitivity of the bond price with respect 
to the bond’s own yield-  to- maturity.
Yield to maturity   Annual return that an investor earns on a 
bond if the investor purchases the bond today and holds it 
until maturity. It is the discount rate that equates the pres -
ent value of the bond’s expected cash flows until maturity 
with the bond’s price. Also called yield-  to- redemption  or 
redemption yield .
Yield to redemption   See yield to maturity .
Yield-  to- worst   The lowest of the sequence of yields-  to- call 
and the yield-  to- maturity.
Zero-  coupon bonds   Bonds that do not pay interest during 
the bond’s life. It is issued at a discount to par value and 
redeemed at par. Also called pure discount bonds .

Zero volatility spread (Z-  spread)   Calculates a constant yield 
spread over a government (or interest rate swap) spot curve.

Index I-1
A
ABG Gas Supply LLC, 650
AbitibiBowater Inc., 462–464
accelerated methods of depreciation, 
122–124, 435
accounting
accrual, 640–641
acquisition method of, 422
“big bath, ” 624
cash-basis, 640–641
“cookie jar” reserve, 624–625
Accounting and Auditing Enforcement 
Release (SEC), 641–643
Accounting and Corporate Regulatory 
Authority, 47, 59, 628
accounting choices
aggressive
and bias in application of accounting 
standards, 624–625
conservative vs., 620–625
defined, 612
biased, 612–620
conservative, 620–625
aggressive vs., 620–625
benefits of, 624
bias in application of accounting 
in extractive industries, 621–622
losses in, 620–621
and deferred-tax assets, 642–643
earnings management with, 618
financial reporting issues, 638–655
cash flow statements, 648–651
earnings and balance sheets, 639–648
accounting equation, 12
accounting estimates, 640–641
Accounting for Income Taxes  (SFAS 109), 
508
Accounting for the Costs of Computer 
Software to be Sold, Leased, or

Software to be Sold, Leased, or 
Otherwise Marketed  (SFAS 86), 431
accounting goodwill, 184
accounting policies
changes in, 81–83
disclosures relating to, 79–83
retrospective application of, 128
accounting profit
defined, 508
taxable income vs., 508–513
and current tax assets/liabilities, 
509–510
and deferred tax assets/liabilities, 
510–513
taxable profit vs., 518–523
and business combinations/deferred 
taxes, 523
and investments in subsidiaries, 
branches, associates, and 
interests, 523
temporary differences, 519–522
Accounting Regulatory Committee, 55accounting scandals, 608
accounting standards. see also  specific 
standards
biased application of, 624–625
convergence of, 99–100, 112
for revenue recognition, 112–116
and ROE, 678–680
Accounting Standards Board of Japan, 
57
accounting standards boards, 48–50
attributes of, 50
Financial Accounting Standards Board, 
49–50
International Accounting Standards 
Board, 48–49
Accounting Standards Codification  
(FASB), 49–50
Accounting Standards Updates, 82, 114

Business Combinations (ASC 805), 
422n.9
Expenses: Compensation–Retirement 
Benefits (ASC 715), 679
Fair Value Measurements and 
Disclosures (ASC 820), 417n.2
General Electric disclosures, 82
Income Taxes (ASC 740), 508
Interest (ASC 835), 428n.11
Leases (ASC 840), 467n.29, 577n.14
Leases (ASC 842), 468
Revenue from Contracts with 
Customers (ASC 606), 112n.25, 
114
Statement of Cash Flows (ASC 230), 
471n.32
Accounting Standards Updates (ASUs), 
82, 114
accounts (on financial statements)
contra, 169
doubtful, 120, 653
tax asset valuation, 654
uncollectible, 641–642
accounts payable, as current liability, 
176
accounts receivable
as current assets, 169–171
and financial reporting quality, 656
and taxable/deductible temporary 
differences, 521
and tax bases of assets, 514, 515
accrual accounting, cash-basis vs., 
640–641
accrued expenses, as current liability, 
176
accumulated other comprehensive 
income, 193
Acer Inc., 275–277
acquisition
of businesses, 535

of long-lived assets, 417–435
accounting for, 417
capitalisation of interest costs, 
428–431capitalisation of internal development 
costs, 431–435
capitalising vs. expensing costs, 
423–428
and financial reporting issues, 648
intangible assets, 420–423
property, plant, and equipment, 
417–420
acquisition method of accounting, 422
activity ratios, 291–298
calculation of, 292–294
defined, 292–293
evaluation of, 295–298
interpretation of, 294–298
fixed asset turnover, 297
inventory turnover and DOH, 294–295
payables turnover and number of 
days of payables, 296
receivables turnover and DSO, 
295–296
total asset turnover, 297
working capital turnover, 297
adjusted consolidated segment operating 
income (adjusted CSOI), 635–638
adjusted EBITDA, 634
adjustments
financial statement, 698–713
to debt, 710–712
framework for, 698
for goodwill, 704–706
for inventory, 699–702
and current ratio, 701–702
with LIFO accounting, 699–701
for investments, 698
for off-balance-sheet financing,

for off-balance-sheet financing, 
706–713
for plant, property, and equipment, 
703–704
inventory, 368–375
declines and recoveries of inventory 
value, 369–370
inventory write-downs and financial 
ratios, 370–375
adverse audit opinion, 28
affirmative covenants, 559
Afghanistan, 59
Africa, 59. see also  specific countries and 
regions
age ratios, asset, 460–464
aggressive accounting choices
and biased application of standards, 
624–625
and non-GAAP measures in reports, 
612, 615
Alcatel-Lucent, 383–388
consolidated balance sheet, 384
consolidated income statement, 383–384
notes to consolidated financial 
statements, 385–386
solvency ratio evaluation, 306

I-2 Index
Alcon, 685
allowance
for doubtful accounts, 653
for loan loss reserves, 653
alternative inventory costing, 118–120, 
654
Altria Group Inc., 453
amortisation
of bonds, 550–554
amortisation of discounts, 551–553
amortisation of premiums, 553–554
and interest expense/interest 
payments, 550–554
defined, 121
and expense recognition on income 
statements, 124
of intangible assets, 121, 181
of long-lived assets, 443–444
amortisation expenses, 444
amortised costs, 66, 168–169, 186, 188
AMR Corporation, 707–710
analyst adjustments, 698–713
706–713
703–704
analysts, 652–655
Anheuser-Busch, 423
Anheuser-Busch InBev SA/NV, 684–686
annual reports, 53, 613–614
Annual Statement Studies (Risk 
Management Association), 282
antidilutive securities, 139–140
Apple Inc.
accounts receivable, 169–170

Apple Inc.
balance sheet components, 164
cash flow analysis of comparables, 
256–257
change in accounting standards, 
129–130
cross-sectional common-size analysis, 
200, 203–204
current assets, 168
current liabilities, 175
deferred revenue, 176–178
deferred tax assets, 174
deferred tax liabilities, 192
earnings announcements, 8–9
equity, 194–195
financial assets, 189
goodwill, 186
inventory valuation, 171, 172
marketable securities, 169
non-current assets, 179
non-current liabilities, 190–191
and revenue recognition on income 
statements, 111–112
statement of changes in equity, 
195–196
strategy and financial performance, 
273–274, 673–677
war chests, 677Apple TV, 129–130
applications of financial statement 
analysis, 671–717
706–713
703–704
credit risk assessments, 691–694

703–704
Moody’s rating factors, 692–693
peer comparison ratios, 694
equity screening, 694–697
example, 695
ratio-based, 697
financial performance evaluations, 
673–681
accounting standards and ROE, 
678–680
and changes in business strategy, 
673–677
and war chests, 677
financial performance projections, 
681–690
consistency of forecasts, 690
example, 687–689
forecasting operating profit, 683–684
issues with, 684–687
with market-based valuation, 
682–687
for multiple periods, 687–690
practice problems, 715–716
solutions to problems, 717
appraisals, asset revaluation, 446
Argentina, 58, 628
Armenia, 59
Arngrove Group Holdings, 127
ASA, 651
Asahi Breweries, 677
Asia, 59, 627. see also  specific countries 
and regions
asset age ratios, 460–464
assets
average age of depreciable, 462–464
on balance sheets, 162, 186–189
in Conceptual Framework,  64
current
and accounting profit vs. taxable 
income, 509–510
on balance sheets, 165, 167–174
debt-to-assets ratio, 304, 305, 586, 587
deferred tax

accounting choices about, 642–643
accounting profit vs. taxable income 
for, 510–513
changes in tax rates, 517–518
current assets, 174
defined, 509
and timing, 508
unused tax losses/credits, 523–524
defined, 9, 162
income tax bases of, 513–515
intangible
acquisition of, 420–423
on balance sheets, 181–186from business combinations, 
422–423
capitalization of, 647–648, 653
depreciation/amortisation of, 121, 
181
identifiable, 182–183
impairment of, 181, 450–451
on income statements, 124
internally-developed, 420–422
long-lived, 416
not from business combinations, 420
and research, 182, 421
lease versus buy decision for, 467–470
liquid asset requirement, 322
long-lived ( see long-lived assets)
non-current, on balance sheets, 165, 
178–189
recoverable amount of, 449
return on, 280, 308–309, 363
asset turnover
fixed, 293, 297, 462–464
total, 293, 297
asset utilization ratios, 292. see also  
activity ratios
associate businesses, investments in, 
523

523
assumptions, for financial reports, 65
ASUs. see Accounting Standards 
Updates
AT&T, 633
auditors, financial reporting quality and, 
629–630
audits
adverse opinions, 28
auditor’s reports, 27–29
qualified and unqualified opinions, 
27–28
standards for, 27
Australia, 15, 59
available-for-sale securities
defined, 187
as financial assets, 187–189
on income statements, 146
average age of depreciable assets, 
462–464
average daily rate, 323
average inventory days outstanding. 
see days of inventory on hand 
(DOH)
Azerbaijan, 59
B
back-testing, 696
Baidu, 683, 684
balance sheet equation, 12
balance sheet ratios, 204–206
balance sheets, 161–216
about, 162
analysis of, 13–16, 196–206
common-size, 196–204, 282–283, 
285–287
and capitalising vs. expensing of costs, 
423
and cash flow statements, 169, 
232–233
classified, 166
components of, 163–165

Index  I-3
consolidated
Alcatel-Lucent, 384
Micron Technology, Inc., 529–530
Volvo Group, 371–372
current assets, 167–174
Apple Inc., 168
cash and cash equivalents, 168–169
inventories, 171–173
other, 173–174
SAP Group, 167–168
trade receivables, 169–171
current liabilities, 174–178
Apple Inc., 175
deferred revenue analysis, 176–178
SAP Group, 175
defined, 12, 162
equity, 192–196
components of, 192–195
195–196
financial assets on, 186–189
format of, 165–167
interest costs, 428
leases, 471
LIFO liquidation, 364–365
non-current assets, 165, 178–189
Apple Inc., 179
financial assets, 186–189
goodwill, 183–186
intangible assets, 181–186
investment property, 180–181
179–180
SAP Group, 178–179
non-current liabilities, 190–192
Apple Inc., 190–191
deferred tax liabilities, 191–192
long-term financial liabilities, 191
SAP Group, 190
practice problems, 209–213
quality of reporting on, 639–648
solutions to problems, 214–216

vertical common-size, 282–283
Banco Central del Uruguay, 51n.10
banks
capital adequacy ratios, 322
regulation of, 47
barter transactions, revenue recognition 
for, 109, 655
Basel Accords, 47
Basel Committee on Banking 
Supervision, 47, 48, 51
Baseline (database), 293
BASF Group, 570–572
basic earnings per share, 132–134, 319, 
320
benchmarks, 625
B+H Ocean Carriers, 558–561
BHP Billiton, 683, 684
biased accounting choices, 612–620
biases
in accounting standard application, 
624–625
in equity screening, 696
“big bath” accounting, 624
bill-and-hold transactions, 652
Bloomberg, 281, 293, 316Bolivia, 58
bonds
amortisation, 550–554
at discount, 549–553
at face value, 546–549
interest expense for, 550–554
interest payments for, 550–554
issuance, 546–550
at premium, 553–554
with warrants, 563–564
bonds payable, 546–564
and amortisation of bonds, 550–554
debt covenants, 559–561
derecognition of debt, 557–559
disclosure of long-term debt, 561–564
fair value reporting, 554–557

and interest expense, 550–554
and interest payments, 550–554
and issuance of bonds, 546–550
presentation of long-term debt, 
561–564
Borrowing Costs  (IAS 23), 428n.11
borrowing costs, for property, plant, and 
equipment, 419–420
Botswana, 59
bottom line, income statement, 97
bottom-up analysis, 694–695
branches of businesses, investments in, 
523
Brazil, 58, 628
Brazilian GAAP , 58, 678–680
business combinations
IFRS vs. US GAAP on, 535
intangible assets from, 422–423
intangible assets not from, 420
and quality of financial reporting, 
633–634
taxable vs. accounting profit for, 523
422n.9
Business Combinations  (IFRS 3), 422n.9
business segments, financial analysis for, 
327–329
business strategy, financial performance 
and, 673–677
C
Cameroon, 59
Canada
bank regulation, 47
IFRS adoption, 58
liquidity representations on balance 
sheets, 15
Canadian GAAP , 58
capacity, productive, 461
capital
capital structure vs., 198
debt-to-capital ratio, 304, 305, 586–587

return on, 308, 309, 325
total invested, 681n.4
working, 166, 297, 689n.6
capital adequacy ratios, for banks, 322
capital expenditures
net cash flow to, 325
property, plant, and equipment as, 417, 
418
capitalization
of costs, 423–435
expensing of costs vs., 423–428on financial statements, 423–428
of interest costs, 428–431
of internal development costs, 
431–435
for ongoing purchases, 427
and financial reporting issues, 
647–648, 657
of intangibles, 653
of interest, 650–651
capital leases. see finance leases
capital markets, regulation of, 55
capital structure, 132, 198
Carpenter Technology Corporation, 
699–701
carrying amount, 444–447, 509
CAS. see Chinese accounting standards
cash
on balance sheets, 168–169
from customers, 235–236
to employees, 237–238
generation of, 649–650
for income taxes, 239
for interest, 238–239
for other operating expenses, 238
from sale of equipment, 239–240
sources and uses of, 246–249
to suppliers, 236–237
cash-basis accounting, 640–641

cash conversion cycle, 299–301
cash equivalents, 168–169
cash flow(s)
and capitalisation of interest costs, 
428–430
on cash flow statements, 219–221
discretionary cash flow to debt, 325
and financial reporting issues, 657
financing, 221
free cash flow to equity, 254–255
free cash flow to the firm, 254–255
net, 220, 325
net income and, 657
operating, 221–232
and capitalising vs. expensing of 
costs, 427–428
direct-format statement under IFRS, 
226–228
financing vs., 221
free operating cash flow to debt, 325
indirect-format statement under 
IFRS, 223–226
and leases, 471
under US GAAP , 228–232
price to cash flow ratio, 319, 320
profits vs., 7–8
retained, 691
cash flow per share, 319
cash flow ratios, 255–256
cash flow statements, 217–267
about, 218
analysis of, 20, 22–23, 246–257
common-size, 250–254
for comparables, 256–257
sources and uses of cash, 246–249
and balance sheets, 169, 232–233

and capitalising vs. expensing costs, 
423–424

I-4 Index
cash flow statements ( Continued )
components and format, 219–232
cash flows and non-cash activities, 
219–221
cash flows from operating activities, 
222–232
and IFRS vs. US GAAP , 221–222
defined, 12
disclosures about long-lived assets on, 
455
effects of reporting quality on, 
648–651
financing activities on, 219–220, 240
and income statements, 232–233
investing activities on, 219, 239–240
leases on, 471
operating activities on, 219, 235–239
cash for income taxes, 239
cash for interest, 238–239
cash for other operating expenses, 
238
cash from customers, 235–236
cash to employees, 237–238
cash to suppliers, 236–237
overall statement of cash flows, 
241–246
direct method, 23, 222, 241–242
indirect method, 23, 222–223, 
242–245
practice problems, 259–264
preparation of, 232–246
financing activities, 240
investing activities, 239–240
operating activities, 235–239
241–246
solutions to problems, 265–267
cash ratio, 299, 300
cash reserve ratio, 322
Caterpillar Inc.

consolidated financial position, 
359–360
consolidated results of operation, 
358–359
inventories of Volvo Group and, 
378–381
LIFO to FIFO conversion for, 358–363
statements, 360
CBS Records, 659
CEC Entertainment, Inc., 476–480
Central America, 58. see also  specific 
countries
CESR. see Committee of European 
Securities Regulators
CFA Institute
monitoring of financial reporting 
standards, 78–79
standards for communicating 
recommendations, 34
channel stuffing, 652
Charles Schwab Corporation, 705–706
Chile, 58, 628
China, 59, 627
China Construction Bank, 166–167
China Petroleum & Chemical 
Corporation, 563–564
China Securities Regulatory 
Commission, 51n.10Chinese accounting standards (CAS), 59
Cisco Systems, 172–173
Citigroup, 650
classified balance sheet, 166
Codification. see Accounting Standards 
Codification  (FASB)
coefficient of variation of net income, 
322
coefficient of variation of operating 
income, 322

coefficient of variation of revenues, 322
Colombia, 58
Columbia Pictures, 659
combined ratio, 279
Committee of European Securities 
Regulators (CESR), 55
commodity inventories, 623
common shares, 132, 192, 241
common-size analysis
for balance sheets, 196–204
analysis of ratios, 282–283, 285–287
cross-sectional, 200, 203–204
for S&P 500, 201–202
for cash flow statements, 250–254
horizontal, 141n.50, 282, 285–287
for income statements, 141–143, 
283–285
of ratios, 282–288
vertical, 141n.50, 197, 282–285
common stock, 132, 192, 241
comparability, of accounting choices, 24
comparables, 256–257
comparable store sales ratio, 322
comparative growth information, 288
compensation, 625–626
completed contract method of revenue 
recognition, 104–105, 107
complex capital structures, 132
component method of depreciation for 
long-lived assets, 441–443
A Comprehensive Business Reporting 
Model  (CFA Institute), 78–79
comprehensive income
defined, 193n.20
IFRS on, 145, 148

on income statements, 145–148
other
accumulated, 193
defined, 145
on income statements, 147–148
on statement of comprehensive 
income, 19–20
statement of, 12, 16–20
total, 145
US GAAP on, 145, 148
Compustat, 281
computations, financial analysis vs., 
272–274
ConAgra Foods, Inc., 641–642
“Conceptual Framework for Financial 
Reporting” (Concepts Statement 
8), 610n.2
Conceptual Framework for Financial 
Reporting 2010  (IFRS), 60–72
and barriers to single standards 
framework, 73–74
conservatism in, 621
constraints on financial reports, 63–64
convergence of US GAAP and, 70–72and effective standards frameworks, 
72–73
elements of financial reports, 64–66
objective of financial reporting/
reports, 44–46, 61–62
qualitative characteristics of financial 
reports, 62–63
610–611
requirements of Presentation of 
Financial Statements (IAS No. 1), 
66–70
conclusions, from financial statement 
analysis, 33–34
conservative accounting choices 
(conservatism)

biased application of standards, 
624–625
consistency, of financial performance 
forecasts, 690
consolidated balance sheets
consolidated financial position, 359–360
consolidated financial statements, notes 
to
Alcatel-Lucent, 385–386
Caterpillar Inc., 360
Micron Technology, Inc., 530–531
Volvo Group, 372–373
consolidated income statements
Alcatel-Lucent, 383–384
Volvo Group, 371
358–359
consolidated statements of operations, 
528–529
contra accounts, 169
contracts
and discipline for financial reporting 
quality, 630
modifications of, 115
and revenue recognition, 104–107, 
112–116
convertible debt, 136–137
“cookie jar” reserve accounting, 624–625
corporate culture, financial reporting 
issues and, 659–660
cost(s)
amortised, 66, 168–169, 186, 188
borrowing, 419–420

capitalisation of, 423–435
current, 66
deferred, 657
development, 431–435, 514–515, 521
expensing of, 423–428
fixed, 303–304, 347n.7
historical, 66
incremental, 115
interest, 428–431
internal development, 431–435
inventory, 117–118, 346–348
line, 648

Index  I-5
period, 117
production, 347n.7
research, 514, 515, 521, 623
software development, 422, 431–434
standard, 171
variable, 303, 347n.7
weighted average, 172
Costa Rica, 58
cost flow assumptions, 639–640
cost of goods sold
and activity ratio, 294
in inventory valuation, 172
cost of sales
and inflation, 355–356
and inventory valuation method, 346, 
350–352
and LIFO reserve, 357–358
in periodic vs. perpetual inventory 
systems, 352–354
cost recovery method of revenue 
recognition, 108–109
Cote D’Ivoire, 59
Council of the European Union, 55
coupon rate, 547
covenants, debt, 559–561, 626
coverage ratios, 305
for capitalised interest, 429–431
fixed charge, 305–306, 587
interest, 305, 325, 587
for operating lease adjustment, 
712–713
and solvency ratios, 587–589
CRA International Inc., 99
Crazy Eddie’s, 619
credit analysis, 324–326
credit rating process, 324–326
defined, 691
research on ratios in, 326
credit analysts, 30
credit risk
assessing, 691–694
defined, 324, 691
credits, unused tax, 523–524

credit sales, revenues and, 640–641
“Critical Accounting Estimates” 
(MD&A), 625
cross-sectional ratio analysis, 284–285, 
292
culture, corporate, 659–660
current assets
current cost, 66
current liabilities
of Apple Inc., 175
on balance sheets, 165–166, 174–178
deferred revenue analysis of,  
176–178
of SAP Group, 175current ratio
and conversion from LIFO to FIFO, 363
defined, 299
interpretation of, 300
inventory value in comparison of, 
701–702
current tax, 524–527
tax charged to equity, 525–527
and valuation allowance, 525
current tax liabilities, 509–510
customers, cash from, 235–236
CVC Capital Partners, 685
Czech Republic, 58
D
Daejan Holdings PLC, 465–466
Daimler AG, 309–311

D
DaimlerChrysler, 102
Danone. see Groupe Danone
data, financial statement
analysis, 33
collection, 32
interpretation, 33
processing, 33
data-snooping bias, 696
days of inventory on hand (DOH)
and activity ratios, 292–294
and conversion from LIFO to FIFO, 362
inventory management with, 376–377
and inventory turnover, 294–295
and inventory write-downs, 374–375
days of sales outstanding (DSO)
in activity ratio definition, 292
and quality of financial reporting, 656
and receivables turnover, 295–296
dealing securities, 219
debt
analyst adjustments to, 710–712
convertible, 136–137
in credit ratios, 325–326
derecognition of, 557–559
discretionary cash flow to, 325
extinguishment of, 557–559
forgiveness of, 127
long-term
on cash flow statement, 241
disclosure of, 561–564
and lease disclosure, 572–577
presentation of, 561–564
segment debt ratio, 328
debt covenants, 559–561, 626
debt ratios, 304, 305

debt to EBITDA ratio, 326
debt-to-equity ratio, 304, 305, 587
decision-useful information, in financial 
reports, 610–612
declining balance depreciation method, 
436
decomposition, of ROE, 313–318
deductible temporary differences, in 
taxable/accounting profit, 519–522
defensive internal ratio, 299, 300
deferred costs, 657
deferred income, 176
deferred method of tax recognition, 518n.3
deferred revenue (unearned revenue)
analysis of, 176–178as current liability, 176
on income statements, 100
deferred tax, 524–527
IFRS vs. US GAAP on, 533–536
and taxable vs. accounting profit, 522
deferred tax assets
current assets as, 174
deferred tax liabilities
on balance sheets, 191–192

defined-benefit pension plans, 583–584
defined-contribution pension plans, 583
Dell Inc.
business strategy and financial 
performance, 273–274
256–257
common-size cash flow statement, 
252–254
evaluation of liquidity measures, 301
depletion (term), 435n.12
depreciation
accelerated, 122–124, 435
462–464
component method, 441–443
declining balance, 436
defined, 24, 121
diminishing balance, 123–124
double-declining balance, 123, 
436–440, 644–647
statements, 122–124
of long-lived assets, 435–443
calculation of depreciation expense, 
441–443
financial reporting quality issues, 
643–647, 653
methods, 435–441
plant, property, and equipment, 180, 
703–704
657–658
straight-line
and balance sheet, 644–647
bond premium/discount 
amortisation, 551
calculation, 436

defined, 435
depreciation/amortisation, 121–122
double-declining and units-of-
production methods vs., 436–440
units-of-production, 435–440, 
644–647
useful life and residual value in, 121–124

I-6 Index
depreciation expenses, 441–443, 454
derecognition
of debt, 557–559
of long-lived assets, 451–453
derivatives, 186
detection of financial reporting issues, 
632–660
accounting choices and estimates, 
638–655
cash flow statement effects, 648–651
earnings and balance sheet effects, 
639–648
areas of choice/estimate and analyst 
concerns, 652–655
presentation choices, 633–638
warning signs, 655–660
capitalization policies, 657
cash flow and net income 
relationship, 657
company culture, 659–660
context for judging signs,  
658–659
inventories, 656–657
revenue, 655–656
development costs
internal, 431–435
and tax bases of assets, 514–515
development phase (intangible assets), 
182
diluted earnings per share, 134–140
with antidilutive securities, 139–140
defined, 132
if-converted method, 134–136
for stock options, 139
treasury stock method, 137–139
in valuation ratios, 319–321
diluted shares, 18
diminishing balance depreciation, 
123–124

123–124
direct financing leases
defined, 484, 578
and financial statements, 480–485, 
582–583
initial recognition and measurement 
of, 578–580
US GAAP on, 577, 578
direct-format statements
benefits of, 223
under IFRS, 226–228
for Telefónica Group, 226–228
direct method for cash flow from 
operating activities, 648
direct method for overall statement of 
cash flows, 241–242
adjustments to net income, 241–242
converting indirect and, 245–246
defined, 23, 222
direct write-off method, 120
disciplining mechanisms for financial 
reporting quality, 626–632
auditors, 629–630
market regulatory authorities, 627–629
and motivation for manipulation, 
631–632
private contracts, 630
disclaimer of opinion, 28disclosure(s)
of bonds with warrants, 563–564
of debt and financial instruments, 
555–557
of debt covenants, 560–561
of debt extinguishment, 558–559
and financial reporting quality, 659
and financial reporting standards, 
79–83
disclosures relating to accounting 
policies, 79–81

disclosures relating to changes in 
accounting policies, 81–83
at General Electric, 82
at Volkswagen, 80–81
of income tax information, 528–533
and financial analysis, 532–533
Micron Technology, Inc., 528–533
interim period, 115n.26
of inventory information, 376
of investment property, 466–467
of leases, 570–577
of LIFO liquidations, 364–366
of long-term debt, 561–564
market regulators’ requirements of, 628
and monitoring of financial reporting 
standards, 79–83
in notes to financial statements, 70
of pension plans, 585–586
and presentation of long-lived assets, 
453–466
fixed asset turnover and average age 
of depreciable assets, 462–464
Vodafone Group Plc, 455–460
of revaluation model for long-lived 
assets, 447–448
of revenue recognition, 115–116
disclosure management, 618n.8
discontinued operations, on income 
statements, 126
discount, bonds at, 549–553
disposal, of long-lived assets, 452–453

diversification, as credit analysis factor, 691
dividend-payout ratio, 319, 321
dividends, on cash flow statement, 241
dividends per share, 319
dividends receivable, 514, 521
DOH. see days of inventory on hand
donations, 516, 521, 522
double-declining balance depreciation
acceleration factor in, 123
on financial statements, 644–647
of long-lived assets, 436–440
other depreciation methods vs., 
doubtful accounts, 120, 653
DSO. see days of sales outstanding
Dun & Bradstreet, 282
DuPont analysis, 313–318
Dynegy Inc., 650
E
earnings
accounting choices/estimates and, 
639–648
announcements of, 8–11
price to earnings ratio, 319–320quality of, 608, 609, 618
retained, 193
sustainability of, 610–612
earnings before interest, taxes, 
depreciation, and amortization 
(EBITDA), adjusted, 634
earnings before interest and taxes 
(EBIT), 18, 99
earnings management, 618
earnings per share (EPS)
basic, 132–134, 319, 320
changes in, 140–141
defined, 18
diluted, 134–140

EBITDA per share, 319, 320
on income statements, 95n.5, 131–141
interpretation of, 320–321
and simple vs. complex capital 
structure, 132
earnings reports, 659
earnings smoothing, 612
earnings statements, 96
EBIT. see earnings before interest and 
taxes
EBITDA. see earnings before interest, 
taxes, depreciation, and 
amortization
EBITDA interest coverage, 325
EBIT interest coverage, 325
economic goodwill, 184
Ecuador, 58
EDGAR. see Electronic Data Gathering, 
Analysis, and Retrieval System
effective interest rate, 547, 551
Egypt, 59
Egyptian Financial Supervisory 
Authority, 51n.10
Electronic Data Gathering, Analysis, and 
Retrieval System (EDGAR), 52
El Salvador, 58
Employee Benefits  (IAS 19), 584n.17
employees
cash to, 237–238
net income/revenue per employee, 322

Employers’ Accounting for Defined Benefit 
Pension and Other Postretirement 
Plans  (SFAS 158), 679
ending inventory
350–352
enforcement, by market regulators, 628
Enron, 619, 626
EPS. see earnings per share
Equatorial Guinea, 59
equity
on balance sheets, 162, 192–196
195–196

Index  I-7
Conceptual Framework  on, 64
defined, 162
and financial position, 9
owners’ , 12, 162
return on equity, 309
and accounting standards, 678–680
decomposition of, 313–318
defined, 308
and ratio analysis, 280
shareholders’ , 162, 427
195–196
Apple Inc., 195–196
and balance sheet, 195–196
for financial statement analysis, 20, 
21
tax charged to, 525–527
total debt to total debt plus equity 
ratio, 326
total liabilities-to-equity ratio, 363
equity analysts, 30
Equity Funding Corp., 619
equity investments
analysis, 318–323
actions based on, 33
industry-specific ratios, 321–323
research on ratios in, 323
valuation ratios, 319–321
screening, 694–697
Ernst & Young, 608
ESC. see European Securities Committee
ESMA. see European Securities and 
Market Authority
estimates
and earnings/balance sheets, 640–641
in financial reporting, 45–46
EU. see European Union

Europe, 55, 58. see also  specific countries 
European Commission, 48, 55
European Financial Reporting Advisory 
Group, 55
European Parliament, 55
European Securities and Market 
Authority (ESMA), 55, 627
European Securities Committee (ESC), 55
European Union (EU), 55, 74
Evian, 329
expected loss impairment method, 187
expenditures, capital, 325, 417, 418
expense recognition on income 
statements, 16, 96–97, 116–125
and amortisation, 124
applications, 120–124
for doubtful accounts, 120
and financial analysis, 125
general principles, 117–120
and inventory costs, 117–118
for warranties, 120–121
expenses
accrued, 176
amortisation, 444
Conceptual Framework  on, 65
depreciation, 441–443, 454income tax, 368
interest, 471n.32, 550–554
other operating, 238
prepaid, 173–174
tax, 368, 509
and warranties, 120–121
expensing of costs
capitalisation of costs vs., 423–428
on financial statements, 423–428

eXtensible Business Reporting Language 
(XBRL), 282
external sources of information, for 
financial statement analysis, 29–30
extractive industries, 621–622
extraordinary items, on income 
statements, 126–127
F
face value, 546–549
FactSet, 281
fair value
of bonds payable, 554–557
Conceptual Framework  on, 66
defined, 162n.1, 169, 417n.2
financial assets at, 187–188
of financial liabilities, 554–555
and long-term asset acquisition, 417
Fair Value Measurement  (IFRS 13), 417n.2
fair value reporting, for bonds payable, 
554–557
FASB. see Financial Accounting 
Standards Board
Fastow, Andrew, 626
FCA. see Financial Conduct Authority
FCFE. see free cash flow to equity
FCFF. see free cash flow to the firm
Federal Financial Supervisory 
Authority, 47
FFO interest coverage. see funds from 
operations interest coverage
FFO to debt. see funds from operations 
to debt
FIFO method. see first-in, first-out 
method
finance leases

method
accounting/reporting by lessee, 
566–577
accounting/reporting by lessor, 
577–583
defined, 468
582–583
financial statement impact of, 580–583
operating leases vs.
for lessees, 471–480, 566–577, 
582–583
for lessors, 480–485, 577–583
on long-lived assets, 467–485
on non-current liabilities, 564–583recognition and measurement of, 
567–569, 578–580
sales-type leases
financial statement impact of, 485, 
580–583
US GAAP on, 577
treating operating leases as, 476–480
Financial Accounting Foundation, 49
Financial Accounting Standards 
Advisory Council, 49
Financial Accounting Standards Board 
and convergence of global reporting 
standards, 56–57
development of standards, 45, 46
disclosure requirements of, 628
evolving standards, 78
revenue recognition standards, 
99–100, 112
as standard-setting body, 47
financial analysis, 269–341

about, 270
for business/geographic segments, 
327–329
reporting requirements, 327–328
segment ratios, 328–329
common ratios, 290–318
activity ratios, 292–298
categories, 291
integrated analysis with, 311–318
interpretation and context, 291–292
liquidity ratios, 298–303
profitability ratios, 307–311
solvency ratios, 303–307
computations vs., 272–274
disclosure of income tax information, 
532–533
equity analysis, 318–323
statements, 125
framework for, 271–272
inventory management in, 377–388
model building and forecasting with, 330
objectives of, 271–272
practice problems, 333–338
process, 271–274
solutions to problems, 339–341
272–274
tools and techniques, 274–290
graphs, 288–290
regression analysis, 290
financial assets, on balance sheets, 
186–189

186–189
financial condition, statements of, 162. 
see also  balance sheets
Financial Conduct Authority (FCA), 627, 
628
financial flexibility, 20
Financial Instruments  (IFRS 9), 146, 187
financial leverage, 303–304
financial leverage ratio, 304, 305, 587

I-8 Index
financial performance
evaluating, 673–681
678–680
673–677
integrated analysis of, 312–313
projecting, 681–690
with market-based valuation, 682–687
financial position, statements of, 12, 162. 
financial ratios
financial analysis with, 278–282
and inventory write-downs, 370–375
financial reporting, for business 
segments, 327–328
Financial Reporting Council, 628
financial reporting quality, 607–670
about, 608–609
assessing, 625–632
conditions conducive to low-quality 
reports, 626
disciplining mechanism, 626–632
motivations for issuing low-quality 
reports, 625–626
conservative vs. aggressive accounting, 
620–625
detection of issues, 632–660
638–655

638–655
disciplining mechanisms, 626–632
market regulatory authorities, 
627–629
631–632
and earnings quality, 609, 618
practice problems, 663–666
solutions to problems, 667–670
spectrum of quality for financial 
reports, 609–620
and aggressive presentation, 612, 615
and biased accounting choices, 612–618
departures from GAAP , 619–620
“GAAP , decision-useful, but 
sustainable?” level, 611–612
“GAAP , decision-useful, sustainable, 
and adequate returns” level, 
610–611
presentation of non-GAAP financial 
measures, 614–618
“Within GAAP , but biased choices” 
level, 612–618
“Within GAAP , but ‘earnings 
management’” level, 618financial reporting standards, 43–89
about, 44
Reporting 2010,  60–72

constraints on financial reports, 
63–64
convergence of US GAAP and, 70–72
and effective standards frameworks, 
72–73
objective of financial reports, 61–62
requirements for financial 
statements, 66–70
global, 56–59
of IFRS vs. US GAAP , 74–77
monitoring developments in, 77–83
by CFA Institute, 78–79
with company disclosures, 79–83
for new products/types of 
transactions, 77–78
and objectives of financial reporting, 
44–46
practice problems, 85–87
reports based on, 608
solutions to problems, 88–89
standard-setting bodies, 47–55
for industry-specific regulation, 
47–48
regulatory authorities, 50–55
financial reports
constraints, 63–64
elements, 64–66
high-quality, 609–612
low-quality
conditions conducive to, 626
motivations for, 625–626
on spectrum of quality, 619–620
manipulation of
motivation for, 631–632

prevalence of, 608
objectives, 61–62
qualitative characteristics, 62–63
spectrum of quality, 609–620
and biased accounting choices, 
612–620
610–611
management’” level, 618
Financial Services Agency, 47, 48, 57
financial statement analysis, 5–41. see 
also applications of financial 
statement analysis
about, 6asset revaluations in, 445–446
framework, 30–34
conclusions and recommendations, 
33–34
data analysis and interpretation, 33
data collection, 32
data processing, 33
follow-up, 34
purpose and context of analysis, 
31–32
information sources, 11–30
balance sheet, 12–16
cash flow statement, 20, 22–23
financial notes, 24–25

financial statements, 11–30
internal and external sources of 
information, 29–30
management commentary/MD&A, 26
statement of changes in equity, 20, 21
statement of comprehensive income, 
16–20
supplementary information, 11–12
supplementary schedules, 24–25
practice problems, 37–39
scope of, 6–11
and earnings announcements, 8–11
and profit vs. cash flow, 7–8
solutions to problems, 40–41
financial statements. see also  specific 
statements
capitalisation vs. expensing of costs on, 
423–428
and direct financing leases, 480–485
finance vs. operating leases on, 
471–484
leases on, 580–583
LIFO liquidation on, 364–366
long-lived assets on, 454–455
notes to financial statements
disclosures, 70
financial statement analysis, 24–25
LIFO liquidation, 365
PACCAR, 613
relationships of, 287–288
requirements of IFRS framework, 
66–70
for disclosures in notes, 70
from IAS No. 1, 68–70
required statements, 67
statement features, 67–68

for structure and content, 68–70
and sales-type leases, 485
financing activities
cash flow from, 221
on cash flow statements, 219–220, 240
defined, 22
financing cash flow, 221
finished goods inventory, 346, 377
finite lives, intangible assets with, 450
Finland, 58
first-in, first-out (FIFO) method
analyst adjustments related to, 
699–702

Index  I-9
and earnings/balance sheets, 639–640
of inventory valuation
assigning costs in, 349
conversion from LIFO to FIFO, 
358–363
and cost of goods sold, 172
defined, 118–119
inflation and LIFO vs., 354–356
other valuation methods vs., 
349–352
systems, 352
five-way decomposition of ROE, 
316–318
fixed asset turnover ratio
and average age of depreciable assets, 
462–464
calculating, 293
interpreting, 297, 460
fixed charge coverage ratio, 305–306, 
587
fixed costs, leverage and, 303–304
fixed production costs, 347n.7
FOB shipping. see free on board 
shipping
follow-up, financial statement analysis, 
34
Ford Motor Company, 102–103
forecasts
consistency of, 690
and financial analysis, 330
of financial performance, 681–690
of operating profit, 683–684
and quality of financial reports, 625
ForgeHouse, Inc., 127
Form 3 (SEC), 54–55
Form 4 (SEC), 54–55
Form 5 (SEC), 54–55
Form 6-K (SEC), 53
Form 8-K (SEC), 54
Form 10-K (SEC), 53, 364–365
Form 10-Q (SEC), 53
Form 11-K (SEC), 55

Form 20-F (SEC), 53
Form 40-F (SEC), 53
Form 144 (SEC), 54
format
of balance sheets, 165–167
of cash flow statements, 219–232
219–221
222–232
of income statements, 95–99
Form DEF-14A (SEC), 53
fourth-quarter surprises, 658
Framework for the Preparation and 
Presentation of Financial 
Statements  (IASB), 45, 116
FRC. see UK Financial Reporting 
Council
free cash flow to equity (FCFE), 
254–255
free cash flow to the firm (FCFF), 
254–255
free on board (FOB) shipping, 638
function of expense method, 454–455funds from operations (FFO) interest 
coverage, 325
funds from operations (FFO) to debt, 
325
G
GAAP . see generally accepted accounting 
principles
sustainable?” financial reports, 
611–612
and adequate returns” financial 
reports, 610–611
gains
on debt forgiveness, 127

gains
extraordinary, 127
on income statement, 97
on marketable securities, 188–189
GDP . see gross domestic product
General Electric, 82, 659
generally accepted accounting 
principles (GAAP). see also  entries 
for specific countries and regions, 
e.g.: US GAAP
convergence of IFRS and, 57–59
financial reports with departures from, 
619–620
611–612
non-GAAP measures in financial 
reports, 614–618, 633–638
financial reports, 612–618
management’” financial reports, 
618
geographic segments, financial analysis 
for, 327–329
Georgia, 58
Germany
conservatism in, 624
management reporting requirements, 
26
Ghana, 59
GICS. see S&P/MSCI Global Industrial 
Classification System
GlaxoSmithKline plc, 629
global financial crisis (2008-2009), 56

global financial reporting standards, 
56–59. see also  International 
Financial Reporting Standards 
(IFRS)
Goldman Sachs, 555
goodwill
accounting, 184
analyst adjustments for, 704–706
on balance sheets, 183–186
from business combinations,  
422–423
defined, 420
economic, 184
and financial reporting issues, 648financial reporting issues with, 654
ratio comparisons for, 705–706
valuation of, 181–182
goodwill impairment, 185–186
Google, 54
graphs, for financial analysis, 288–290
gross domestic product (GDP), 682
gross margin, financial reporting quality 
and, 658
gross profit, 98
and inventory valuation method, 
350–352
and LIFO liquidation, 364, 366–367
gross profit margin, 307, 308
calculating, 356
and conversion from LIFO to FIFO, 
362–363
and income statement ratios, 144
on income statements, 98
inventory management with, 376, 377
and inventory write-downs, 375

in ratio analysis, 277
gross reporting of revenue, 109–110
Groupe Danone
cash flow statement, 248–249
income statement, 95–98, 131
segment ratio evaluation, 328–329
grouping by function (term), 98
grouping by nature (term), 98
Groupon, 635–638
growth investors, 696
Guatemala, 58
H
held-for-sale assets, impairment of,  
451
held for trading (term), 187
held-to-maturity (term), 186
HERE, 615, 616
Hewlett-Packard
256–257
high-quality financial reports
and earnings quality, 609
on spectrum of quality, 610–612
historical cost, 66
Honduras, 58
Hong Kong SAR, 59
horizontal common-size analysis, 
141n.50, 282, 285–287
I
IAS. see International Accounting 
Standards
IASB. see International Accounting 
IBM. see International Business 
Machines
identifiable intangible assets, 182–183
if-converted method for diluted earnings 
per share, 134–136

I-10  Index
IFRS. see International Financial 
Reporting Standards
IFRS Foundation, 48–49
impairment(s)
expected loss method of, 187
financial reporting quality and, 660
of goodwill, 185–186
of intangible assets, 181, 450–451
of long-lived assets, 448–451, 623
of PPE, 180, 449
Impairment of Assets  (IAS 36), 448
implicit interest rate, 478–479
InBev USA LLC, 423, 685, 686
incentives, for low-quality financial 
income
adjusted CSOI, 635–638
comprehensive
deferred, 176
net, 242–245
and asset revaluations, 445–446
coefficient of variation of, 322
defined, 98
and direct method for overall 
statement of cash flows,  
241–242
on income statement, 98
and indirect method for overall 
statement of cash flows, 242–245
per employee, 322
relationship of cash flow and, 657
operating, 322
other comprehensive

taxable, 508–513
total comprehensive, 145
income statement method of tax 
recognition, 518n.3
income statement ratios, 143–145
income statements, 93–159
analysis of, 16–19, 141–145
common-size, 141–143, 283–285
income statement ratios,  
143–145
and cash flow statements, 232–233
common-size analysis of, 141–143, 
283–285
components and format, 95–99
for CRA International Inc., 99
for Groupe Danone, 95–98
for Kraft Foods, 96–97
comprehensive income on, 145–148
of Alcatel-Lucent, 383–384
of Volvo Group, 371
disclosures about long-lived assets in, 
454–455earnings per share, 95n.5, 131–141
basic, 132–134
expense recognition, 116–125
and depreciation/amortisation, 
121–124

function, 94–95
interest costs on, 428
LIFO liquidation on, 365
non-operating items, 130–131
non-recurring items, 125–131
and changes in accounting policies, 
128–130
discontinued operations, 126
extraordinary items, 126–127
unusual and infrequent items, 
127–128
practice problems, 151–155
revenue recognition, 99–116
accounting standards issued May 
2014, 112–116
for barter transactions, 109
and financial statements, 111–112
general principles, 100–103
and gross vs. net reporting of 
revenues, 109–110
for installment sales, 108–109
for long-term contracts, 104–107
in special cases, 103–110
solutions to problems, 156–159
vertical common-size, 283–285
income taxes, 507–544
income, 508–513
cash for, 239
current and deferred tax, 524–527
disclosure of tax information, 528–533
IFRS vs. US GAAP , 508, 533–536
and inventory method changes, 368
practice problems, 538–542
presentation, 528–533
solutions to problems, 543–544

and taxable vs. accounting profit, 
518–523
tax bases, 513–518
of assets, 513–515
and changes in tax rates, 517–518
of liabilities, 515–517
unused tax losses and credits, 523–524
Income Taxes  (IAS 12), 508, 515, 518n.3, 
520, 522, 523
income tax paid, 509
income tax payable, 174, 177, 509
incremental costs, 115
indefinite lives, intangible assets with, 
451
India, 59, 627
indirect-format statements, 223–226indirect method for cash flow from 
operating activities, 648–649
indirect method for overall statement of 
cash flows, 242–245
adjustments to net income, 242–245
converting direct method and, 
245–246
defined, 23, 222–223
Indonesia, 59
industry-specific ratios, for equity 
analysis, 321–323
industry-specific regulation, of financial 
statements, 47–48
inflation, LIFO vs. FIFO and, 354–356
information
comparative growth, 288
decision-useful, 610–612
for financial statement analysis, 11–30

management commentary/MD&A, 
26
16–20
income tax, 528–533
from SEC forms, 52–55
supplementary, 11–12
infrequent items, 127–128
initial recognition, taxable and 
accounting profit at, 522
installment method of revenue 
installment sales, revenue recognition 
for, 108–109
Insurance Medical Group, Ltd., 127
insurance recoverables, 623
intangible assets
on balance sheets, 181–186
from business combinations, 422–423
depreciation/amortisation of, 121, 181
Intangible Assets  (IAS 38), 444

integrated analysis with ratios, 311–318
liquidity of company, 311–312
performance of company, 312–313
ROE decomposition, 313–318
interest
capitalization of, 419, 428–431, 
650–651
cash for, 238–239
interest coverage ratio, 305, 325, 587

Index  I-11
interest expenses, 471n.32, 550–554
interest payments, 550–554
interest rate
effective, 547, 551
implicit, 478–479
market, 547
interest received in advance, 516–517, 
521, 522
interests (in businesses)
as investments, 523
minority/noncontrolling, 17, 193
interim period disclosures, 115n.26
internal control systems, 29
internal development costs, 431–435
internally-developed intangible assets, 
420–422
internal sources of information, for 
financial statement analysis, 
29–30
(IAS), 66–70
Income Taxes  (IAS 12), 508, 515, 
518n.3, 520, 522, 523
Inventories,  369
Leases  (IAS 17), 467n.29
Presentation of Financial Statements  
(IAS 1), 68–70, 94n.1
Statement of Cash Flows  (IAS 7), 
471n.32
Board (IASB), 48–49
disclosure requirements, 628
development of standards, 45, 46, 78

Framework for the Preparation 
and Presentation of Financial 
Statements,  45, 116
and GAAP , 70–72
and global reporting standards, 
56–57
on income, 100
income statement standards, 94n.1
management reporting framework 
of, 26
on objective of financial reporting, 44
International Business Machines (IBM), 
633
International Federation of Accountants, 
27
International Financial Reporting 
Standards (IFRS). see also  
Conceptual Framework for 
Financial Reporting 2010
adoption of, 58–59
on amortisation, 121, 550, 551
on available-for-sale classification, 
146–147
for balance sheets, 14–15
on barter transactions, 109
on bond cost reporting, 555
on borrowed funds, 419
on capitalisation of interest costs, 
428n.11, 430for cash flow statements, 22, 220
on comprehensive income, 145, 148
on debt issuance costs, 557
on decision-useful information, 610n.2
on deferred tax assets/liabilities, 510, 
511, 525

511, 525
on depreciation, 121, 441
on diluted earnings per share, 139
on direct-format statements, 226–228
disclosure requirements, 79–81, 
453–454
for EU capital markets, 55
fair value definition, 417n.2
on financial statement ratios, 677–678
and global reporting standards, 56–59
on impairments, 180, 181, 448–451, 
454
income definition, 100
for income statements, 94, 98
on income taxes, 508
for indirect-format statements, 
223–226
for intangible assets, 420–422
on interest, 238, 419, 471n.32, 554
on inventory valuation, 346–348, 
367–369, 377
on investment property, 464
and IOSCO, 51
on leases, 468, 476, 480, 484n.36, 565, 
566, 570, 572, 577–578, 582–583
non-IFRS measures in financial 
reports, 634
on pension plans, 584
on percentage-of-completion method, 
104
on residual value, 121
on revaluation, 435, 444, 445, 447–448
on revenue recognition, 101, 112, 113, 
622
SEC’s adoption of, 357
on segment reporting, 327
and Swiss financial statements, 50

on taxable profit vs. accounting profit, 
518–520
on tax issues, 515
and US GAAP
conservatism in, 622–624
on financial reporting standards, 
74–77
frameworks of, 70–72
on income taxes, 508, 533–536
International Organization of Securities 
Commissions (IOSCO), 26, 48, 51, 
627–628
International Paper Company, 462–464
international standards for auditing 
(ISAs), 27
introductory paragraph, audit report, 27
Inventories  (IAS 2), 369
inventory(-ies), 345–414
adjustments to, 368–375
with LIFO reserve, 357
analyst adjustments for, 699–702
on balance sheets, 171–173
commodity, 623cost of, 347–348
days of inventory on hand
362
inventory management with, 
376–377
ending, 346, 350–356
and financial reporting issues, 656–657
finished goods, 346, 377

growth in, 656–657
inventory management, 375–388
comparisons of companies, 378–381
in financial analysis, 377–388
inventory ratios, 376–377
in MD&A of annual report, 381–382
presentation and disclosure of 
inventories, 376
for single company, 383–388
of manufacturing and merchandising 
companies, 346
practice problems, 391–406
presentation and disclosure of, 376
raw materials, 346, 377
solutions to problems, 407–414
valuation, 118–120, 172, 348–368
changes in, 367–368
comparison of, 354–356
cost of sales, gross profit, and ending 
inventory, 350–352
first-in, first-out, 118–119, 172, 
349–352
last-in, first-out, 119, 172, 349–352, 
357–367
LIFO liquidation, 363–367
LIFO reserve, 357–363
periodic vs. perpetual inventory 
retail method, 171
specific identification, 118, 349–352
specific identification methods, 172
weighted average cost, 172, 349–352
weighted average cost method, 119
work-in-progress, 346, 377
inventory costing, alternative methods, 
118–120, 654

inventory costs, 117–118, 346–348
inventory revenues, 117–118
inventory turnover ratio, 293–295
and activity ratio, 293–294
activity ratio definition, 292
362
and DOH, 294–295
inventory ratios, 657
and inventory write-downs, 374

I-12  Index
inventory value, 369–370
inventory write-downs
in financial analysis, 378
and financial ratios, 370–375
US GAAP vs. IFRS on, 368–369
investing activities
on cash flow statement, 219, 239–240
defined, 20, 22
net cash flow from, 220
investment property, 180–181, 464–467
analyst adjustments for, 698
in business subsidiaries, branches, 
associates, or interests, 523
IOSCO. see International Organization 
of Securities Commissions
iPad, 674–676
iPhone, 9, 129–130, 274, 674–676
iPod, 9, 674–676
Ireland, 58
Irving, Bryan, 127
ISAs. see international standards for 
auditing
Israel, 59
issuance, bond, 546–550
iTunes, 273–274, 674
Izumiya, Naoki, 677
J
Japan
benefits of conservatism in, 624
discipline for financial reporting 
quality in, 627
regulatory body of, 47
use of IFRS vs. GAAP in, 59
Japanese Business Accounting Council, 
57
Japanese GAAP , 57, 59
Jobs, Steve, 9
Johnson & Johnson, 561–563, 683, 684
K
Kazakhstan, 59
Kenya, 59
Khaitan, Aditya, 677
Kidder Peabody, 659
Kingdom of Saudi Arabia Capital Market

Kingdom of Saudi Arabia Capital Market 
Kohlberg Kravis Roberts & Co. L.P ., 
685
Koninklijke KPN N.V., 447–448
Korea, 59
KPMG SA, 630
KPS Capital Partners, L.P ., 685
Kraft Foods
derecognition of long-lived assets, 453
income statement, 97–98
statement of earnings, 96
Kyrgyz Republic, 59
L
last-in, first-out (LIFO) method
699–702
financial reporting issues with, 654, 
657
of inventory valuation, 349–367
assigning costs in, 350conversion from LIFO to FIFO, 
358–363
defined, 119, 350
inflation and FIFO vs., 354–356
and inventory write-downs, 370
LIFO liquidations, 363–367
other valuation methods vs.,  
349–352
leases, 564–583
advantages of, 564–565
analyst adjustments for, 707–713
direct financing, 480–485, 577–580, 
582–583
finance
566–577
577–583

577–583
direct financing leases, 480–485, 
577–580, 582–583
financial statement impact of, 
580–583
operating leases vs., 467–485, 
565–583
operating vs., 565–583
recognition and measurement of, 
sales-type, 577, 578, 580–583
sales-type leases, 484, 485, 577, 578, 
580–583
for long-lived assets, 467–485
finance vs. operating leases, 467–485
lease versus buy decision, 467–470
operating
566–567, 570–577
accounting/reporting by lessor, 577, 
582–583
707–713
and analyst adjustments to debt, 
710–712
coverage ratio for analyst adjustment, 
712–713
finance vs., 467–485, 565–583
582–583
sales-type, 484, 485, 577, 578, 
580–583
synthetic, 467, 565
Leases  (IFRS 16), 78, 220, 468, 566
Lebanon, 59
Lenovo Group Limited
activity ratios, 294–296

liquidity measures, 301
ratio analysis, 275–277
lessees
defined, 467, 564finance vs. operating leases for
financial statement impact of leases, 
471–480
leases on long-lived assets, 471–480
leases on non-current liabilities, 
566–577
treating operating leases as finance 
leases, 476–480
lessors
defined, 467, 564
finance vs. operating leases for
direct financing leases, 480–485
480–485
leases on long-term assets, 480–485
577–583
sales-type leases, 485
leverage, 303–304, 445
leverage ratios, 305, 587–589
Levitt, Arthur, 624–625
liabilities. see also  non-current liabilities
on balance sheets, 162, 165–166, 
174–178, 191
current
of SAP Group, 175
current tax, 509–510

income tax bases of, 515–517
long-term, 191
LIFO conformity rule, 357
disclosure of, 364–366
example, 366–367
on financial statements, 364–366
and LIFO reserve, 363–364
LIFO method. see last-in, first-out 
method
converting LIFO to FIFO inventory 
with, 358–363
defined, 357
and LIFO liquidations, 363–364
Lindsay, Don, 10–11
line costs, 648
line graphs, 290
liquidations, LIFO, 363–367
liquidity
on balance sheet, 15, 165–167
defined, 8, 164–165, 196
evaluation of measures, 301
integrated analysis of, 311–312

Index  I-13
bounds and context of, 302–303
calculations, 299
defined, 204, 291, 299
evaluation, 301
interpretation, 300–301
cash conversion cycle, 301
cash ratio, 300
current ratio, 300
defensive internal ratio, 300
quick ratio, 300
Lithuania, 58
litigation losses, 623
LM Ericsson Telephone Company, 
588–589
loan covenants, 634
loan loss reserves, allowances for, 653
loans
differences, 521, 522
and tax bases of liabilities, 516, 517
long-lived assets, 415–506. see also  non-
acquisition of, 417–435
capitalisation of costs, 423–435
417–420
amortisation of, 443–444
defined, 121, 416
depreciation of, 435–443, 643–647, 653
derecognition of, 451–453
disclosures for, 453–466
impairment of, 448–451, 623

investment property as, 464–467
leases on, 467–485
practice problems, 489–500
presentation of, 453–466
comparing fixed asset turnover and 
462–464
revaluation model for, 444–448
solutions to problems, 501–506
long-term contracts, revenue 
recognition for, 104–107
long-term debt
look-ahead bias, 696
losses
in conservative accounting choices, 
620–621
expected, as impairment method, 187
impairment, 449
litigation, 623on marketable securities, 188–189
tax loss carry forward, 509
unused tax, 523–524
Lotte Group, 677
low-quality financial reports
M

M
Macedonia, 58
Macintosh® computers, 9
McLeod Russel India Ltd., 677
Malawi, 59
Malaysia, 59
Malaysian GAAP , 59
management commentary, 26, 628
“Management Commentary” (IFRS 
Practice Statement), 615
management discussion and analysis 
(MD&A), 12
“Critical Accounting Estimates, ” 625
on derecognition, 557
in financial statement analysis, 26
information in, 564
inventory management in, 381–382
LIFO liquidation in, 364
of Microsoft, 431
of PACCAR, 613–614
policy disclosure requirements, 79
as SEC requirement, 557n.5
of Volvo Group, 381–382
managers
financial reporting quality and 
disclosure by, 659
fixation on earnings reports by, 659
merger and acquisition orientation of, 
660
reports by, 625–626
manipulation, of financial reports, 608, 
631–632
manufacturing companies, inventories 
of, 346
margin stability, 691
marketable securities, 169, 187–189
market-based valuation, 682–687
market-oriented investors, 696
market rate(s)
for bonds payable, 554–555

of interest, 547
market value to book value (MV/BV) 
ratio, 705–706
mark-to-market, 187
Mason, Andrew, 635
matching principle, 117
Mauritius, 59
MD&A. see management discussion and 
analysis
merchandising companies, inventories 
of, 346
merger and acquisition orientation, 660
MetaCarta, 617
Mexico, 58, 678–680
consolidated balance sheet, 529–530
consolidated statement of operations, 
528–529notes to consolidated financial 
statement, 530–531
Microsoft, 431
Middle East, 59. see also  specific 
countries
minimalist disclosure approach, 659
minority interests, 17, 193
model building, financial analysis for, 
330
Moldova, 58
monetary reserve requirement, 322
monitoring, of financial reporting 
standards, 77–83
for new products/types of transactions, 
77–78
Monte Carlo simulation, for risk 
assessment, 690
Moody’s Investor Service, 692–693
Morl, Ian, 127
Morocco, 59
Motally, 617
motivation

for manipulating financial reports, 
631–632
for producing low-quality financial 
reports, 618, 625–626
Motorola Solutions, 616
Mozambique, 59
MTR Gaming Group, Inc., 429–430
multiple-delivery arrangements, 656
multiple-period financial performance, 
projecting, 687–690
multi-step format, income statement, 98
MV/BV ratio. see market value to book 
value ratio
N
Namibia, 59
National Datacomputer Inc., 302–303
nature of expense method, 454–455
NAVTEQ, 617
negative covenants, 559
Nestlé Group, 630, 685–687
net book value, 123
net cash flow, 220, 325
Netherlands, 58
net income
cash flow and, 657
coefficient of variation for, 322
statement of cash flows, 241–242
net interest margin, 322
net profit margin, 307, 308
calculation of, 278

363
and income statement ratios, 143

I-14  Index
net realisable value (NRV), 171–172, 368
net reporting of revenues, 109–110
neutrality, in financial reporting, 621
New Century Financial, 619
new products, financial reporting 
standards for, 77–78
New Zealand, 59
Nicaragua, 58
Nigeria, 59
Nigerian Federal Executive Council, 59
Nokia Corporation, 588–589, 615–618
Nokia Siemens Networks, 615, 616
non-cash activities, on cash flow 
statements, 219–221
noncontrolling interest, 17, 193
non-current assets. see also  long-lived 
assets
on balance sheets, 165, 178–189
179–180
non-current liabilities, 545–604
balance sheets, 190–192
of Apple Inc., 190–191
of SAP Group, 190
on balance sheets, 166
amortisation of bonds, 550–554
disclosure of long-term debt,

disclosure of long-term debt, 
561–564
interest expense, 550–554
interest payment, 550–554
issuance of bonds, 546–550
561–564
defined, 546
finance vs. operating, 565–583
pension plans, 583–586
practice problems, 592–597
solutions to problems, 598–604
solvency of, 586–589
non-operating items
financial reporting quality issues with, 
658
on income statements, 130–131
non-public companies, related-party 
transactions with, 655
non-recurring items
658
on income statements, 125–131
128–130
127–128non-recurring restructuring events, 624
no par shares, 192
Norse Energy Corp., 651
North America, 58. see also  specific 
countries and regions
Norwalk Agreement, 56
Norway, 58
notes payable, 176
by Alcatel-Lucent, 385–386

by Caterpillar Inc., 360
disclosures in, 70
in financial statement analysis, 24–25
LIFO liquidation in, 365
by PACCAR, 613
by Volvo Group, 372–373
Novarra, 617
Novartis Group, 629–630, 685
Novo Nordisk, 585–586
NRV. see net realisable value
number of days of payables, 292, 296
O
objectives
of financial analysis, 271–272
of financial reporting, 44–46
of financial reports, 61–62
Objectives and Principles of Securities 
Regulation  (IOSCO), 51
obligations
in contracts, 113
performance, 114
occupancy rate, 323
OCI. see other comprehensive income
off-balance-sheet financing, 706–713
Office of the Comptroller of the 
Currency, 47
oil and gas industry, 621–622
one-time sales, 658
ongoing purchases, 427
operating activities
on cash flow statement, 219, 235–239
238
and cash generation activities, 
649–650

direct vs. indirect reporting method, 
648–649
defined, 20
operating cash flows (cash flows from 
operating activities), 221–232
427–428
226–228
direct method for calculating, 648
indirect-format statement under IFRS, 
223–226
indirect method for calculating, 
648–649
under US GAAP , 228–232operating efficiency ratios, 292. see also  
operating income
adjusted consolidated segment, 
635–638
operating leases
582–583
and adjustments to debt, 710–712
coverage ratio for, 712–713
finance leases vs.
582–583
on non-current liabilities, 565–583
financial statement impact of, 582–583

treating, as finance leases, 476–480
operating leverage, 303
operating margins, 658
operating profit
and depreciation method, 645–646
EBIT vs., 99
forecasts of, 683–684
on income statement, 99
operating profit margin, 307, 308
operating ROA, 308
operational efficiency, 691
operations, statement of, 17, 528–529. 
see also  income statements
opinion paragraph, audit report, 27
opinions, audit, 27–28
Oppenheimer, Peter, 9
ordinary shares, 132
Organization for the Harmonization of 
Business Law, 59
Oriental Brewery, 685
other comprehensive income (OCI)
other current assets, on balance sheets, 
173–174
other operating expenses, 238
overall statement of cash flows, 241–246
direct method, 241–242

indirect method, 242–245
converting direct and, 245–246
owners’ equity, 12, 162. see also  equity
P
PACCAR, 612–614
Pakistan, 59

Index  I-15
Panama, 58
Paraguay, 58
parent companies, on income 
statements, 17
Parmalat, 619
par value, 192
payables
accounts payable, as current liability, 176
561–564
561–564
payables turnover, 292, 296
payments, interest, 550–554
P/B ratio. see price to book value ratio
PCAOB. see Public Company 
Accounting Oversight Board
P/CF ratio. see price to cash flow ratio
pension plans
defined-benefit, 583–584
defined-contribution, 583
disclosure of, 585–586
as non-current liabilities, 583–586
pension trust fund, 584
P/E ratio. see price to earnings ratio
percentage-of-completion method of

percentage-of-completion method of 
revenue recognition, 104–106, 114
performance obligation, 114
period costs, 117
periodic inventory systems, 352–354
permanent differences, in taxable and 
accounting profit, 518–519
perpetual inventory systems, 352–354
Peru, 58
Philippines, 59
P&L statements. see profit and loss 
Poland, 58
Polly Peck International (PPI), 619
PowerLinx, Inc., 643
PPE. see property, plant, and equipment
PPI. see Polly Peck International
preferred stock, 134–136, 192–193
premiums, bond, 553–554
prepaid expenses, 173–174
presentation
aggressive, 612, 615
of deferred tax, 535–536
and detection of financial reporting 
issues, 633–638
of long-lived assets, 453–466
Vodafone Group Plc, 455–460of long-term debt, 561–564
of non-GAAP financial measures, 
614–618
present value, 66

pretax margin, 144, 307, 308
price, transaction, 113, 115
price to book value (P/B) ratio, 319, 320
price to cash flow (P/CF) ratio, 319, 320
price to earnings (P/E) ratio, 319–320
price to sales (P/S) ratio, 319, 320
PricewaterhouseCoopers, 28, 629
production costs, 347n.7
productive capacity, 461
products, new, 77–78
profit
cash flow vs., 7–8
gross, 98
350–352
operating
taxable, 518–523
profitability
426, 428
cost flow assumptions and, 639–640
calculation, 307–308
defined, 291
evaluation, 309–311
and income statement ratios, 145
interpretation, 308–311

profit and loss (P&L) statements, 17. see 
also income statements
profit margin
gross, 307, 308
362–363
net, 307, 308
363
in ratio analysis, 277operating, 307, 308
pretax, 144, 307, 308
pro forma reporting, 633
property, plant, and equipment (PPE), 
416. see also  long-lived assets
acquisition of, 417–420
analyst adjustments for, 703–704
on balance sheets, 179–180
on cash flow statements, 239–240
depreciation of, 703–704
impairment of, 448–450
sale of, 240
prorated revenue recognition, 104, 105
proxy statements, 53

P/S ratio. see price to sales ratio
Public Company Accounting Oversight 
Board (PCAOB), 27, 52
Q
Qatar, 59
qualified audit opinion, 28
quality
of earnings, 608, 609, 618
of financial reporting ( see financial 
reporting quality)
of reported results, 608
quick ratio, 299, 300
R
ratio analysis, 275–288
for Acer Inc., 275–277
classes of ratios, 278–279
common-size, 282–288
of balance sheet, 282–283, 285–287
of income statement, 283–285
cross-sectional, 284–285, 292
for equity investments, 697
for goodwill, 705–706
interpreting financial ratios, 279
for Lenovo Group Limited, 275–277
and relationships of financial 
statements, 287–288
and sources of ratios, 281–282
for Toshiba Corporation, 275–277
trend, 285–287
value, purpose, and limitations, 
280–281
raw materials inventory, 346, 377
RCF. see retained cash flow
realizable value, 66
rebate programs, 656
receivables
dividends, 514, 521
trade, 169–171
receivables turnover, 292, 295–296
recognition. see also  revenue 
recognition

and derecognition, 451–453, 557–559
expense, 16, 96–97, 116–125
of finance leases, 567–569, 578–580
of financial report elements, 65
tax, 518n.3
taxable and accounting profit at, 522

I-16  Index
recommendations, from financial 
statement analysis, 33–34
recoverable amount, 449, 623
registration requirements, of market 
regulators, 628
Regulation FD (SEC), 54n.14
regulatory authorities, 50–55. see also  
US Securities and Exchange 
Commission (SEC)
for capital markets in Europe, 55
quality from, 627–629
International Organization of 
Securities Commissions, 51
S-1 registration statements for, 54
related-party transactions, 655, 658
remaining useful life, 461–464
remeasurements, pension plan, 584
rent received in advance
research and development, 182, 184, 421
research costs, 514, 515, 521, 623
reserve, LIFO, 357–363
residual value, 121–124
responsibility statements, 628
restructuring events, 624, 660
results, quality of, 608

retail method for inventory valuation, 
171
retained cash flow (RCF), 691
retained earnings, 193
retention rate, 319, 321
retrospective application, of accounting 
policies, 128
return on assets (ROA), 280, 308–309
operating, 308
segment, 328–329
return on capital, 308, 309, 325
return on common equity, 308
return on equity (ROE), 309
return on investment, 308
return on sales. see net profit margin
return on total capital, 308, 309
revaluation model for long-lived assets, 
435, 444–448
revenue(s)
and accounts receivable, 656
and credit sales, 640–641
deferred/unearned
analysis of, 176–178
as current liability, 176
gross vs. net reporting of, 109–110
on income statements, 16, 95
inventory, 117–118
outsized growth of, 656Revenue from Contracts with Customers 
(ASC 606), 112n.25, 114

Revenue from Contracts with Customers  
(ASU 2014-09), 114
(IFRS 15), 112n.25, 114
revenue per employee, 322
revenue recognition
completed contract method, 104–105, 
107
and financial reporting issues, 640–
641, 652–653, 655–656
on income statements, 99–116
installment method, 108–109
in oil and gas industry, 622
percentage-of-completion method, 
104–106
prorated, 104, 105
reversal, impairment, 451
reviews, by market regulators, 628
rights, in contracts, 113
risk
credit, 324, 691–694
Monte Carlo simulation for assessing, 
690
Risk Management Association, 282
ROA. see return on assets
“ A Roadmap for Convergence between 
IFRSs and US GAAP” (IASB/
FASB), 56
Roche Group, 128

FASB), 56
ROE. see return on equity
Royal Dutch Shell PLC, 317–318, 
572–577
Royal Numico N. V., 328
Rule 144 (SEC), 54
S
S-1 registration statements, 54
Safeway, Inc., 185–186
sale(s)
available-for-sale securities, 146, 
187–189
cost of
adjusting, with LIFO reserve, 
357–358
350–352
in perpetual vs. periodic inventory 
credit, 640–641
days of sales outstanding, 292, 
295–296, 656
and finished goods inventory, 377–378
on income statements, 95n.4
installment, 108–109
of long-lived assets
cash from, 240and derecognition of assets, 451–452
impairment of assets held for sale, 
451
one-time, 658
price to sales ratio, 319, 320
return on ( see net profit margin)
sales per square meter (sales per square 
foot) ratio, 322
580–583
salvage value, 122
same store sales ratio, 321–322
SAP Group
accounts receivable, 169, 170

SAP Group
balance sheet components, 163–164
common-size analysis, 199
current assets, 167–168
equity, 193–194
inventories, 171
non-current assets, 178–179
non-current liabilities, 190
Sarbanes-Oxley Act (2002)
auditing standards, 27
internal control systems requirements, 
29
and SEC authority, 52
Saudi Arabia, 59
Saudi Arabian Monetary Agency, 59
scale, as credit analysis factor, 691
Scania AB, 18
scenario analysis, 330
scope paragraph, of audit report, 27
screening, of equity investments, 
694–697
Sears, 633
SEC. see US Securities and Exchange 
Commission
securities
antidilutive, 139–140
available-for-sale, 146, 187–189
dealing, 219
marketable, 169, 187–189
trading, 146, 219
Securities Act (1933), 52
Securities and Exchange Board of India, 
51n.10
Securities and Exchange Commission 
(Brazil), 47
Securities Exchange Act (1934), 52

Securities Offerings Registration 
Statement, 52
segment margin, 328–329
segment ROA, 328–329
segment turnover, 328–329
Self-Regulatory Organizations 
(SROs), 51
sensitivity analysis, 330

Index  I-17
Serbia, 58
settlement value, 66
SFAS. see Statement of Financial 
Accounting Standards
shareholders’ equity, 162, 427. see also  
equity
shares. see also  earnings per  
share (EPS)
common, 132, 192, 241
diluted, 18
no par, 192
ordinary, 132
treasury, 193
shipping, financial reporting quality and, 
638
simple capital structures, 132
simulations, 330, 690
Singapore, 59, 628
single-step format, for income 
statements, 98
Small, Medium, and Micro Enterprises 
(SMME), 522
software development costs, 422, 
431–434
solvency
defined, 8, 196, 303, 586
of non-current liabilities, 586–589
calculation, 304–305
defined, 204, 291, 304–305, 587
evaluation, 306–307, 588–589
interpretation, 305–307
leverage/coverage ratios, 587–589
Sony Corporation, 555–557, 659
South Africa, 59, 95n.4
South America, 58, 627–628. see also  
specific countries and regions
S&P 500, common-size analysis of, 
142–143, 201–202
specific identification method of

specific identification method of 
inventory valuation, 118, 172, 
349–352
spin-offs, 452–453
S&P/MSCI Global Industrial 
Classification System (GICS), 
142–143, 200
SROs. see Self-Regulatory Organizations
stacked column graphs, 289
standard costs, 171
Standard & Poor’s Corporation
coverage ratios for capitalized interest, 
430
credit rating process, 325
Standards Advice Review Group, 55
Standards and Financial Marketing 
Integrity Division, 78
Standards of Practice Handbook  (CFA 
Institute), 34
“Statement in Support of Convergence 
and Global Accounting Standards” 
(SEC), 57
statement of cash flows. see cash flow 
471n.32
471n.32, 651statement of changes in equity
of Apple Inc., 195–196
in financial statement analysis, 20, 21
statement of comprehensive income, 12, 
16–20
Statement of Financial Accounting 
Standards (SFAS)
Accounting for the Costs of Computer

Otherwise Marketed  (SFAS 86), 
431
Employers’ Accounting for Defined 
Benefit Pension and Other 
Postretirement Plans  (SFAS 158), 
679
statement of operations, 17, 528–529. 
see also  income statement
statements of financial condition, 162. 
statements of financial position, 12, 162. 
stock. see also  equity investments
preferred, 134–136, 192–193
treasury stock method for diluted EPS, 
137–139
stock options, diluted earnings per share 
for, 139
Straight from the Gut  (Welsh), 659
straight-line depreciation method
bond premium/discount amortisation, 
551
Strum Ruger & Co., Inc.
Form 10-K, 364–365
LIFO liquidation for, 364–366
subscription accounting, 129–130
subsidiaries, 17, 523
Sunbeam, 288, 619, 626, 658

supplementary information, for financial 
statement analysis, 11–12
suppliers, cash to, 236–237
survivorship bias, 696
sustainability, of earnings, 610–612
sustainable growth rate, 319, 321
Swaziland, 59
Swiss Exchange, 50, 58
Swiss GAAP , 50, 58
Switzerland, 50, 58
Syngenta, 75
synthetic leases, 467, 565
T
Tanzania, 59
taxable income, 508–513
taxable profit, accounting profit vs., 
518–523
taxable temporary differences, in 
taxable/accounting profit, 
519–522
tax asset valuation accounts, 654tax bases, 513–518
taxes
current, 524–527
deferred, 524–527, 533–536
income, 507–544
518–523
tax bases for, 513–518

518–523
unused tax losses and credits, 
523–524
in lease versus buy decision, 467
and LIFO method, 357
reporting of depreciation methods, 441
tax expense, 368, 509
tax rates, changes in, 517–518
tax recognition, 518n.3
TD Ameritrade Holding Corporation, 
705–706
Tech Data Corporation, 228–230
Teck Resources Ltd., 10–11
Telefónica Group, 226–228
Teléfonos de México, S.A.B. DE C.V., 
678–680
Tele Norte Leste Participações S.A., 
678–680
temporary differences, in accounting/
taxable profit, 508, 519–522
deductible differences, 519–522
examples, 520–522
at initial recognition, 522
taxable differences, 519–522
10-K, Form. see Form 10-K
Thailand, 59
Thomson Reuters, 281
Tokyo Agreement, 57
tolerance for leverage, 691
top-down analysis, 694
TORM A/S, 560–561
Toshiba Corporation, 275–277
total asset turnover, 293, 297
total comprehensive income, 145
total debt to total debt plus equity ratio, 
326
total invested capital, 681n.4

326
Toyota Motor Corporation, 611–612
trade payables. see accounts payable
trading securities, 146, 219
trailing twelve months (TTM) ratio, 281
transaction price, 113, 115
transactions, new, 77–78
treasury shares, 193
trend analysis, 285–287

I-18  Index
Tsingtao Brewery, 677
TTM ratio. see trailing twelve months 
ratio
Turkey, 59
turnover
asset, 293, 297, 462–464, 656
462–464
inventory turnover ratio, 294–295
calculation, 356
362
376–377
payables, 292, 296
receivables, 292, 295–296
total asset, 297
working capital, 292, 297
Tyco International Ltd., 660
U
Uganda, 59
uncollectible accounts, 641–642
unearned revenue
Unilever Group, 223–226
United Agri-Products (UPI), 641–642
United Kingdom, disclosure 
requirements, 628
UK Financial Reporting Council (FRC), 
26
United States
depreciation methods in, 428

LIFO method and taxes, 357
sheets, 15
manipulation of financial reporting, 
608
OCI statement format, 19
tax and financial regulations, 467
US GAAP
for bonds, 550, 551, 554, 555
for borrowed funds, 419
for capitalisation of interest costs, 
428n.11, 430
for cash flows, 22, 220, 223, 228–232
and completed contract method, 
104–105
for comprehensive income, 145, 148
for debt issuance costs, 557
for deferred tax assets/liabilities, 510, 
511, 525
for depreciation, 441fair value definition, 417n.2
and FASB, 50
for financial statement ratios, 677–678
and global reporting standards, 57, 
70–72, 74–75
for gross vs. net reporting, 110
and IFRS
74–77
for impairments, 448–451, 454
income statement standards, 94
income taxes, 508
for intangible assets, 420n.4, 421, 422

for interest, 238, 419, 471n.32, 554
for inventory valuation, 346–350, 
368–370, 377
for investment property, 467
for leases, 468, 476, 480, 484, 566, 570, 
577, 578, 582–583
for LIFO reserve, 357
for long-lived assets, 454
manipulation of financial reporting 
under, 608
for pension plans, 584–585
for revaluation, 435, 444, 447–448
for revenue recognition, 101–102, 112, 
113, 622
and ROE comparisons, 678–680
SEC on reconciliations with, 447n.17
for segment reporting, 327
and Syngenta, 75
and taxable profit v. accounting profit, 
518–520
on tax-related issues, 515, 523
Release, 641–643
adoption of IFRS, 357
standards, 57, 58
on “cookie jar” reserve accounting, 
625
discipline for financial reporting by, 
627, 628
financial reporting standards of, 51–55
Form 3, 54–55
Form 4, 54–55
Form 5, 54–55
Form 6-K, 53
Form 8-K, 54

Form 10-K, 53, 364–365
Form 10-Q, 53
Form 11-K, 55
Form 20-F, 53
Form 40-F, 53
Form 144, 54
Form DEF-14A, 53
and GAAP , 50, 72, 74–75
and Groupon, 635
and IASB, 48
on management reporting, 26
MD&A requirements, 26, 557n.5
on non-GAAP measures in financial 
reports, 615, 635on non-recurring restructuring events, 
624
and PACCAR, 612–613
on reconciliations with US GAAP , 
447n.17
Regulation FD, 54n.14
as regulatory body, 47
reporting requirements, 629
101–102
Rule 144, 54
units-of-production depreciation 
method, 435–440, 644–647
unqualified audit opinion, 27–28
unused tax credits, 523–524
unused tax losses, 523–524
unusual items, on income statements, 
127–128
UPI. see United Agri-Products
UPM-Kymmene Corporation, 462–464
Uruguay, 58
useful life, 121–124
Uzbekistan, 59
V
valuation
inventory, 348–368
349–352

349–352
357–367
weighted average cost, 349–352
market-based, 682–687
valuation allowance, 509, 525, 642
calculation, 319–320
defined, 291, 319–320
dividend-related quantities, 321
interpretation of EPS, 320–321
value
face, 546–549
fair
inventory, 369–370
market value to book value ratio, 
705–706
net book, 123
net realisable, 171–172, 368
par, 192
present, 66
price to book value ratio, 319, 320
realizable, 66
residual, 121–124

Index  I-19
salvage, 122
settlement, 66
value investors, 696
variable consideration, 114–115
variable costs, 303, 347n.7
variable production costs, 347n.7
variation, coefficient of, 322
Venezuela, 58
verification, conservatism and, 621
Verizon Communications Inc., 678–680
vertical common-size balance sheet, 
282–283
vertical common-size income statement, 
283–285
vertical common-size ratio analysis, 
141n.50, 197, 282–285
Vietnam, 59
Volkswagen Group
auditor’s reports, 28–29
balance sheets, 13–15
cash flow statements, 22–23
disclosures, 80–81
financial notes, 25
income statements, 17–18
MD&A, 26statement of changes in equity,  
20, 21
19–20
Volvic, 329
Volvo Group
consolidated balance sheet, 371–372
consolidated income statement, 371
inventories of Caterpillar Inc. and, 
378–381
inventory write-downs, 370–375
MD&A, 381–382
statements, 372–373
W
Wal-Mart Stores
balance sheets, 15–16
231–233

231–233
war chests, 677
warranties, expense recognition for, 
120–121
warrants, bonds with, 563–564
warranty reserves, 655
weighted average cost, 172weighted average cost method, 119, 
349–352
Welsh, Jack, 659
management’” financial reports, 618
working capital, 166, 297, 689n.6
working capital turnover, 292, 297
work-in-progress inventory, 346, 377
WorldCom
capitalization policies, 648
financial reporting quality, 619
write-downs, inventory
X
XBRL. see eXtensible Business Reporting 
Language
Z
Zambia, 59
Zimbabwe, 59
Z-score, 326

Corporate Finance
STUDY SESSION
Study Session 10 Corporate Finance (1)
Study Session 11 Corporate Finance (2)
The candidate should be able to evaluate a company’s corporate governance; to ana -
lyze a capital budgeting problem; to estimate a company’s cost of capital; to evaluate 
a company’s operating and financial leverage and its working capital management.
Some academic studies have shown that well governed companies may perform 
better in financial terms. Increasingly, investment approaches that consider envi -
ronmental, social, and governance factors, known as ESG, are being adopted. In 
addition to good governance practices, management decisions regarding investment 
and financing also play a central role in corporate profitability and performance. To 
remain in business as a going concern and to increase shareholder value over time, 
management must consistently identify and invest in profitable long-  term capital

projects relative to cost of capital (financing) and make optimal use of leverage and 
working capital in day to day operations.
© 2018 CFA Institute. All rights reserved.

Corporate Finance (1)
This study session provides an introduction to corporate governance and investing 
and financing decisions. An overview of corporate governance is presented along with 
a framework for understanding and analyzing corporate governance and stakeholder 
management. The growing impact of environmental and social considerations in invest -
ing is also highlighted. Capital budgeting and the assessment of capital investments 
are covered next. The session ends with practical techniques to estimate a company’s 
or project’s cost of capital. 
Reading 33  Corporate Governance and ESG: An Introduction  
by Assem Safieddine, PhD, Young Lee, CFA, Donna F. 
Anderson, CFA, and Deborah Kidd, CFA
Reading 34 Capital Budgeting  
by John D. Stowe, PhD, CFA, and Jacques R. Gagné, 
FSA, CFA, CIPM
Reading 35 Cost of Capital  
by Yves Courtois, CMT, MRICS, CFA, Gene C. Lai, 
PhD, and Pamela Peterson Drake, PhD, CFACOrPO rATE  FINANCE
10

Corporate Governance and 
ESG: An Introduction
by Assem Safieddine, PhD, Young Lee, CFA, Donna F. Anderson, CFA, and 
Deborah Kidd, CFA
Assem Safieddine, PhD, is at Suliman Olayan Business School, American University of 
Beirut (Lebanon). Young Lee, CFA, is at MacKay Shields LLC (USA) and MacKay Shields 
UK LLP (United Kingdom). Donna F. Anderson, CFA (USA). Deborah Kidd, CFA, is at 
Boyd Watterson Asset Management, LLC (USA).
a. describe corporate governance;
b. describe a company’s stakeholder groups and compare interests of 
stakeholder groups;
c. describe principal–agent and other relationships in corporate 
governance and the conflicts that may arise in these relationships;
d. describe stakeholder management;
e. describe mechanisms to manage stakeholder relationships and 
mitigate associated risks;
f. describe functions and responsibilities of a company’s board of 
directors and its committees;

g. describe market and non-  market factors that can affect 
stakeholder relationships and corporate governance;
h. identify potential risks of poor corporate governance and 
stakeholder management and identify benefits from effective 
corporate governance and stakeholder management;
i. describe factors relevant to the analysis of corporate governance 
and stakeholder management;
j. describe environmental and social considerations in investment 
analysis;
k. describe how environmental, social, and governance factors may 
be used in investment analysis.rEADING
33

Reading 33 ■ Corporate Governance and ESG: An Introduction 6
Weak corporate governance is a common thread found in many company failures. A 
lack of proper oversight by the board of directors, inadequate protection for minority 
shareholders, and incentives at companies that promote excessive risk taking are 
just a few of the examples that can be problematic for a company. Poor corporate 
governance practices resulted in several high-  profile accounting scandals and corpo -
rate bankruptcies over the past several decades and have been cited as significantly 
contributing to the 2008–2009 global financial crisis.
In response to these company failures, regulations have been introduced to 
promote stronger governance practices and protect financial markets and investors. 
Academics, policy makers, and other groups have published numerous works dis -
cussing the benefits of good corporate governance and identifying core corporate

governance principles believed to be essential to ensuring sound capital markets and 
the stability of the financial system.
The investment community has also demonstrated a greater appreciation for the 
importance of good corporate governance. The assessment of a company’s corporate 
governance system, including consideration of conflicts of interest and transparency 
of operations, has increasingly become an essential factor in the investment decision-  
making process. Additionally, investors have become more attentive to environment 
and social issues related to a company’s operations. Collectively, these areas often are 
referred to as environmental, social, and governance ( ESG ).
Section 2 of this reading provides an overview of corporate governance, including 
its underlying principles and theories. Section 3 discusses the various stakeholders of 
a company and conflicts of interest that exist among stakeholder groups. Section 4

describes stakeholder management, reflecting how companies manage their relation -
ships with stakeholders. Section 5 focuses on the role of the board of directors and its 
committees as overseers of the company. Section 6 explores certain key factors that 
affect corporate governance. Section 7 highlights the risks and benefits that underlie 
a corporate governance structure. Section 8 provides an overview of corporate gov -
ernance issues relevant for investment professionals. Finally, Section 9 discusses the 
growing effect of environmental and social considerations in the investment process.
CORPORATE GOVERNANCE OVERVIEW
Corporate governance  can be defined as “the system of internal controls and proce -
dures by which individual companies are managed. It provides a framework that defines 
the rights, roles and responsibilities of various groups . . . within an organization. At 
its core, corporate governance is the arrangement of checks, balances, and incentives

a company needs in order to minimize and manage the conflicting interests between 
insiders and external shareowners. ”1
Corporate governance practices differ among countries and jurisdictions, and even 
within countries different corporate governance systems may co-  exist. The corporate 
governance systems adopted in most of the world typically reflect the influences of 
either shareholder theory  or stakeholder theory  to a varying extent, as well as historical, 
cultural, legal, political, and other influences specific to a region.1
2
1 CFA Institute Centre for Financial Market Integrity, The Corporate Governance of Listed Companies: A 
Manual for Investors , 2nd ed. (Charlottesville, VA: CFA Institute, 2009).

Corporate Governance Overview 7
Shareholder theory takes the view that the most important responsibility of a 
company’s managers is to maximize shareholder returns. Stakeholder theory broad -
ens a company’s focus beyond the interests of only its shareholders to its customers, 
suppliers, employees, and others who have an interest in the company. The approach 
to corporate governance in a given country typically places greater emphasis on one 
of the two theories but can also exhibit a combination of the two. Notwithstanding the 
system of corporate governance used, nearly all companies depend on contributions 
from a number of stakeholders for their long-  term success. The company’s strategy 
is set by the board of directors, which also oversees management; in turn, the com -
pany’s strategy is executed by its managers; financial capital to fund the company’s 
activities and operations is supplied by shareholders, creditors, and suppliers; human

capital is provided by employees; and demand for goods and services comes from 
customers. Other stakeholders include governments and regulators, which seek to 
protect the interests and well-  being of their citizens. Certain external forces, such as 
the legal environment and competition, affect the way a company operates and the 
relationships among its stakeholders.
Two reports issued during the 1990s, the Cadbury Report and the Principles of 
Corporate Governance, were particularly influential in shaping the global corporate 
governance landscape. In 1991, the Committee on the Financial Aspects of Corporate 
Governance was established in the United Kingdom by the Financial Reporting 
Council, the London Stock Exchange, and the accountancy profession to examine 
corporate governance. In the following year, the report of the committee—commonly 
referred to as the Cadbury Report, after its chairman—defined corporate governance

simply as “the system by which companies are directed and controlled. ” The report 
focused on the responsibilities of a company’s board of directors, shareholders, and 
auditors, with shareholders implicitly identified as the primary stakeholder. In 1999, 
the Organisation for Economic Co-  operation and Development (OECD) produced 
the Principles of Corporate Governance , which expanded the scope of corporate 
governance to consider the interests of other stakeholders—notably employees, cred -
itors, and suppliers. According to the OECD, “Corporate governance includes a set 
of relationships between a company’s management, its board, its shareholders, and 
other stakeholders. ” The Principles of Corporate Governance , which was revised in 
2004 and again in 2015, also discusses potential positive outcomes of good corporate 
governance practices (including financial market stability and economic growth) and 
includes standards and guidelines designed to evaluate and improve the corporate

governance framework throughout the world.
There is evidence that some movement toward global convergence of corporate 
governance systems is underway. One trend is the increased acceptance and adoption 
of corporate governance regulations with similar principles from one jurisdiction 
to another. For example, a number of countries implemented regulations similar to 
those of the US Sarbanes–Oxley Act of 2002 (SOX) in response to corporate and 
accounting scandals of the early 2000s. Although these regulations are not identical, 
they share the same objective of improving internal controls and restoring investor 
confidence in financial disclosures. Another trend is initiatives by international agen -
cies to build greater consensus on important corporate governance principles. The 
Principles of Corporate Governance , for example, has been ratified by more than 30 
member countries, representing a broad range of corporate governance models. The

Principles of Corporate Governance  do not mandate, or even promote, the adoption 
of a single corporate governance regime; rather, the principles were designed to serve 
as a framework that can be adopted by any number of corporate governance systems.

Reading 33 ■ Corporate Governance and ESG: An Introduction 8
EXAMPLE 1   
Corporate Governance Overview
Which statement regarding corporate governance is most  accurate?
A Most countries have similar corporate governance regulations.
B A single definition of corporate governance is widely accepted in practice.
C Both shareholder theory and stakeholder theory consider the needs of a 
company’s shareholders.
Solution:
C is correct. Both shareholder and stakeholder theories consider the needs of 
shareholders, with the latter extending to a broader group of stakeholders. A 
is incorrect because corporate governance regulations differ across countries, 
although there is a trend toward convergence. B is incorrect because a universally 
accepted definition of corporate governance remains elusive.
COMPANY STAKEHOLDERS
A corporate governance system is likely to be influenced by several stakeholder groups. 
These groups do not necessarily share similar goals or needs; in fact, the interests of any

one group may conflict with the interests of another group. The varying influences of 
these groups are important considerations for investment professionals when analyzing 
a corporate governance system. This section provides an overview of a corporation’s 
primary stakeholder groups, followed by a discussion of principal–agent considerations 
and the conflicts that may arise among the groups.
3.1 Stakeholder Groups
The primary stakeholder groups of a corporation consist of shareholders, creditors, 
managers (or executives), other employees, board of directors, customers, suppliers, 
and governments/regulators (and, by extension, affected individuals and community 
groups). The interests of each of these groups are discussed in the following sections.
3.1.1  Shareholders
Shareholders own shares of stock in a corporation and are entitled to certain rights, 
such as the right to receive dividends and to vote on certain corporate issues.2 In terms

of capital structure, shareholders are the most junior class of capital providers; in 
case of a company bankruptcy, shareholders receive proceeds only after all creditors’ 
claims are paid. Shareholder interests are, therefore, typically focused on growth in 
corporate profitability that maximizes the value of a company’s equity.
As a company grows in size and its operations and structure become more com -
plex, most individual shareholders have little involvement in the company’s activities. 
Shareholders maintain control over the company through their power to elect the board 
of directors and vote for specified resolutions. The board of directors is expected to 
represent shareholders—protecting their interests, appointing senior management, 
providing strategic direction, and monitoring company and management performance. 3
2 https://themoderncorporation.wordpress.com/company-  law-  memo/

Company Stakeholders 9
In publicly traded companies that have dispersed ownership, the voting power in 
general meetings is distributed among a large number of shareholders. But in some 
companies, a particular shareholder or block of shareholders may hold a percentage 
of shares that gives them sufficient voting power to control the election of the board 
of directors and to influence the approval or blockage of a company resolution; these 
shareholders are known as controlling shareholders . In contrast, non-  controlling 
shareholders ( minority shareholders ) hold a much smaller proportion of a company’s 
outstanding shares, resulting in a more limited ability to exercise control in voting 
activities.
3.1.2  Creditors
Creditors, most commonly bondholders and banks, are a company’s lenders and the 
providers of debt financing. Creditors do not hold voting power (unlike common 
shareholders) and typically have limited influence over a company’s operations.

Creditors may protect themselves and exert some control over a company by using 
covenants, which restrict activities of the borrower. In return for capital provided, 
creditors expect to receive interest and principal payments. These payments are 
pre- determined from the terms of a debt contract and are typically not contingent 
on the company’s performance. Creditors usually do not participate in a company’s 
superior performance beyond receiving promised interest and principal payments. 
The company’s ability to generate cash flows, mainly through its operations, is the 
primary source of payments for creditors. Consequently, creditors generally prefer 
stability in company operations and performance, which contrasts with the interests 
of shareholders, who generally are inclined to tolerate higher risks in return for higher 
return potential from strong company performance.
3.1.3  Managers and Employees
Senior executives and other high-  level managers are normally compensated through

salary, bonuses, equity-  based remuneration (or compensation),3 and certain perqui -
sites. As a result, managers may be motivated to maximize the value of their total 
remuneration while also protecting their employment positions. Lower-  level employ -
ees normally seek fair remuneration, good working conditions, access to promotions, 
career development opportunities, training and development, job security, and a safe 
and healthy work environment.
As with shareholders and creditors, managers and employees have a significant 
interest in the company’s viability. Managers and employees tend to benefit if the 
company performs well and are among the most adversely affected stakeholders if 
a company’s financial position weakens. Despite some similarities, the interests of 
managers and employees and other stakeholders can conflict. For example, a company 
may be presented with a takeover offer that is attractive to shareholders but would

jeopardize the interests of managers in preserving their employment at the company.
3.1.4  Board of Directors
A company’s board of directors is elected by shareholders to protect shareholders’ 
interests, provide strategic direction, and monitor company and management perfor -
mance. A board is typically structured as either one-  tier or two-  tier.
A one-  tier structure consists of a single board of directors, composed of executive 
and non-  executive directors. Executive (sometimes called “internal”) directors are 
employees, typically senior managers, of the company. Non-  executive (sometimes 
3 The terms “remuneration” and “compensation” are typically interchangeable, with compensation generally 
used in North America and remuneration generally used outside North America. In this reading, unless 
specifically identified with North America, we primarily use “remuneration” .

Reading 33 ■ Corporate Governance and ESG: An Introduction 10
called “external”) directors are not employees of the company. Countries in which one-  
tier boards are common include the United States, the United Kingdom, and India. 
A two-  tier structure consists of two separate boards: (1) a supervisory board , which 
is primarily composed of non-  executive directors, and (2) a management (executive) 
board , which is composed of executive directors. The supervisory board oversees the 
management board. Two-  tier boards are common in such countries as Germany, the 
Netherlands, Finland, and China.
In this reading, unless specified otherwise, the term “board” refers to the single 
board of directors in a one-  tier structure and the supervisory board in a two-  tier struc -
ture. Directors, both internal and external, are typically experienced individuals who 
are focused on fulfilling their responsibilities toward shareholders and the company

while maintaining a good reputation in the business community. Directors are also 
typically concerned with their exposure to liability for breach of duty. Directors can 
mitigate this exposure by exercising appropriate levels of control over the company’s 
operations and its management. A company’s board of directors is discussed in more 
detail in Section 5 of this reading.
3.1.5  Customers
Customers expect a company’s products or services to satisfy their needs and provide 
appropriate benefits given the price paid, as well as to meet applicable standards of 
safety. Depending on the type of product or service and the duration of their relation -
ship with the company, customers may desire ongoing support, product guarantees, 
and after-  sale service. Companies are concerned with customer satisfaction given its 
potential correlation with sales revenues and profit. Compared with other stakeholder 
groups, customers tend to be less concerned with, and affected by, a company’s finan -

cial performance. However, customers, particularly those with long-  term relationships 
with the company, typically have an interest in a company’s stability.
3.1.6  Suppliers
A company’s suppliers have a primary interest in being paid as contracted or agreed 
on, and in a timely manner, for products or services delivered to the company. 
Suppliers often seek to build long-  term relationships with companies for the benefit 
of both parties and aim for these relationships to be fair and transparent. Suppliers, 
like creditors, are concerned with a company’s ability to generate sufficient cash flows 
to meet its financial obligations.
3.1.7  Governments/Regulators
Governments and regulators seek to protect the interests of the general public and 
ensure the well-  being of their nations’ economies. Because corporations have a sig -
nificant effect on a nation’s economic output, capital flows, employment, and social

welfare, among other factors, regulators have an interest in ensuring that corporations 
behave in a manner that is consistent with applicable laws. As the collector of tax rev -
enues, a government can also be considered one of the company’s major stakeholders.
 
Stakeholders in Non-  profit Organizations
The stakeholders of a non-  profit organization tend to differ from those of for-  profit 
companies. Non-  profit organizations do not have shareholders. Their stakeholders most 
commonly include board directors or trustees, employees, regulators, society, patrons of

Company Stakeholders 11
the organization, donors, and volunteers. The stakeholders of non-  profit organizations 
are generally focused on ensuring that the organization is serving the intended cause 
and that the donated funds are used as promised.
EXAMPLE 2   
Stakeholder Groups
Which stakeholders would most likely  realize the greatest benefit from a signif -
icant increase in the market value of the company?
A Creditors
B Customers
C Shareholders
Solution:
C is correct. Shareholders own shares of stock in the company, and their wealth 
is directly related to the market value of the company. A is incorrect because 
creditors are usually not entitled to any additional cash flows (beyond interest 
and debt repayment) if the company’s value increases. B is incorrect because 
customers may have an interest in the company’s stability and long-  term viability 
but they do not benefit directly from an increase in a company’s value.
3.2 Principal–Agent and Other Relationships in Corporate 
Governance

A principal–agent relationship  (also known as an agency relationship) is created 
when a principal hires an agent to perform a particular task or service. The principal–
agent relationship involves obligations, trust, and expectations of loyalty; the agent 
is expected to act in the best interests of the principal. In a company, agency theory 
stipulates that principal–agent relationships often lead to conflicts—for example, when 
managers do not act in the best interests of shareholders.4 Examples of principal–agent 
relationships and potential conflicts between the principal and agent are discussed in 
the following sections. Conflicts among stakeholder groups are also discussed but do 
not involve principal–agent relationships.
3.2.1  Shareholder and Manager/Director Relationships
In shareholder-  owned companies, shareholders typically grant directors and man -
agers the responsibility to make most corporate decisions. According to traditional

shareholder theory discussed earlier, the central duty of directors and managers is 
to act in the best interests of shareholders. In certain circumstances, managers may 
seek to maximize their personal benefits (e.g., remuneration and perquisites) to the 
detriment of shareholders’ interests.
4 Agency theory considers the problems that can arise in a business relationship when one person delegates 
decision-  making authority to another. The traditional view in the investment community is that directors 
and managers are agents of shareholders. More recently, however, many legal experts have argued that in 
several countries, corporations are separate “legal persons” and thus directors and managers are agents of 
the corporations rather than shareholders (or a subset of shareholders). See https://themoderncorporation.
wordpress.com/company-  law-  memo.

Reading 33 ■ Corporate Governance and ESG: An Introduction 12
Shareholder and manager (or shareholder and director) interests can also diverge 
with respect to risk tolerance. In some cases, shareholders with diversified investment 
portfolios may have a relatively high risk tolerance because the risk undertaken by a 
specific company can be diversified across the shareholders’ investments. Managers 
and directors, however, are typically more risk averse in their corporate decision 
making so they can better protect their employment status. Such behavior may differ 
from the company’s value creation objective. In addition, compared with sharehold -
ers, managers typically have greater access to information about the business and 
are more knowledgeable about its operations. Such “information asymmetry” (that 
is, unequal access to information) makes it easier for managers to make strategic 
decisions that are not necessarily in the best interest of shareholders and weakens

the ability of shareholders to exercise control. Another conflict of interest might arise 
between shareholders and directors when the board is influenced by insiders. In this 
case, the ability of the board to properly perform its monitoring and control role may 
be hindered. Finally, a conflict between the two groups may occur if directors favor 
certain influential shareholders over other shareholders.
3.2.2  Controlling and Minority Shareholder Relationships
In companies in which a particular shareholder holds a controlling stake, conflicts 
of interest may arise among the controlling and minority shareholders. In such 
ownership structures, the opinions of minority shareholders are often outweighed 
or overshadowed by the influence of the controlling shareholders. Minority share -
holders often have limited or no control over management and limited or no voice 
in director appointments or in major transactions that could have a direct effect on

the value of their shares. For instance, in companies that adopt straight voting  (that 
is, one vote for each share owned), controlling shareholders clearly wield the most 
influence in board of director elections, leaving minority shareholders with much less 
representation on the board.
The decisions made by controlling shareholders, or their board representatives, 
could also have an effect on corporate performance and, consequently, on minority 
shareholders’ wealth. Takeover transactions are notable situations in which controlling 
shareholders typically have greater influence than do minority shareholders with 
regard to the consideration received and other deal terms. An example of this situation 
occurred in 2007 when Qtel, Qatar’s largest telecommunications company, executed a 
deal with a consortium of the shareholders of Wataniya, Kuwait’s telecommunications 
company, to acquire the consortium’s shares in Wataniya (representing a 51% stake

in the target). The consortium of Wataniya’s shareholders sold their shares to Qtel 
at a premium of 48% on the stock price to the exclusion of minority shareholders.
Related-  party transactions are another example for which controlling shareholders 
may place their interests ahead of minority shareholders’ interests. Such a situation 
could occur when a controlling shareholder maintains a financial interest in a trans -
action between the company and a third party and that transaction conflicts with 
the company’s best interests. Consider, for example, a controlling shareholder that 
arranges a deal between the company and a third-  party supplier that is owned by the 
shareholder’s spouse whereby the supplier provides the company with inventory at 
above market prices. Such a transaction would benefit the controlling shareholder 
and the spouse’s interests but could harm the profitability of the company and the 
interests of minority shareholders.

Lastly, an equity structure with multiple share classes in which one class is non-  
voting or has limited voting rights creates a divergence between the ownership and 
control rights of different classes of shareholders. Under a multiple-  class structure 
(traditionally called a dual-  class structure  when there are two share classes), the com -
pany’s founders, executives, and other key insiders control the company by virtue of 
ownership of a share class with superior voting powers. The multiple-  class structure

Company Stakeholders 13
enables controlling shareholders to mitigate dilution of their voting power when new 
shares are issued. Examples of companies that have adopted multiple-  class stock 
structures are Alibaba and Facebook (each with two share classes), as well as Comcast 
and Google (each with three share classes).
3.2.3  Manager and Board Relationships
Given that a board of directors typically relies on management to operate the company, 
the board’s monitoring role can be compromised in the event of limited information 
provided to the board. This conflict is particularly pronounced for non-  executive 
directors who are typically not involved in the day-  to- day operations of a company.
3.2.4  Shareholder versus Creditor Interests
Shareholders typically seek growth in corporate profitability because of the residual 
nature of equity returns. However, the pre-  determined returns of debt obligations 
normally prevent creditors from receiving any cash flows beyond principal and interest

payments, but do expose creditors to default risk in case of extremely poor corporate 
performance. From an investment perspective, shareholders would likely prefer riskier 
projects with a strong likelihood of higher return potential, whereas creditors would 
likely prefer stable performance and lower-  risk activities. A divergence in risk tolerance 
regarding the company’s investments thus exists between shareholders and creditors.
Creditors may also find their interests jeopardized when the company attempts 
to increase its borrowings to a level that would increase default risk. If the company’s 
operations and investments fail to generate sufficient returns required to repay the 
increased interest and debt obligations, creditors will be increasingly exposed to default 
risk. The distribution of excessive dividends to shareholders might also conflict with 
creditors’ interests if it impairs the company’s ability to pay interest and principal.
3.2.5  Other Stakeholder Conflicts

In a corporation, interests can also conflict among other stakeholders. Some of these 
situations are as follows:
■■Conflict between customers and shareholders : For example, a company decides 
to charge a high price for its products or reduces product safety features to 
reduce costs.
■■Conflict between customers and suppliers : A company offers overly lenient 
credit terms to its customers, whereby the company’s ability to repay suppliers 
on time may be affected.
■■Conflict between shareholders and governments or regulators : Examples of such 
conflicts may include a company adopting accounting and reporting practices 
that reduce its tax burden, thus potentially benefiting shareholders, or a bank’s 
shareholders preferring a lower equity capital base while regulators prefer 
a higher capital position. This last conflict is fairly common in the banking 
industry and has been increasingly in focus since the global financial crisis of 
2008–2009.
EXAMPLE 3

EXAMPLE 3   
Stakeholder Relationships
A controlling shareholder of XYZ Company owns 55% of XYZ’s shares, and 
the remaining shares are spread among a large group of shareholders. In this 
situation, conflicts of interest are most likely  to arise between:
A shareholders and regulators.

Reading 33 ■ Corporate Governance and ESG: An Introduction 14
B the controlling shareholder and managers.
C the controlling shareholder and minority shareholders.
Solution:
C is correct. In this ownership structure, the controlling shareholder’s power is 
likely more influential than that of minority shareholders. Thus, the controlling 
shareholder may be able to exploit its position to the detriment of the interests 
of the remaining shareholders. Choices A and B are incorrect because the own -
ership structure in and of itself is unlikely to create material conflicts between 
shareholders and regulators or shareholders and managers.
STAKEHOLDER MANAGEMENT
Because interests among stakeholder groups differ, companies often adopt mechanisms 
to more efficiently manage stakeholder relationships. Stakeholder management  
involves identifying, prioritizing, and understanding the interests of stakeholder 
groups, and, on that basis, managing the company’s relationships with these groups.

4.1 Overview of Stakeholder Management
Effective communication and active engagement with the various stakeholders form 
the basis of stakeholder management. Although the practices underlying stakeholder 
management may vary, companies typically seek to balance the interests of their 
various stakeholders and thus limit the effect of conflicts.
To help balance these interests, corporate governance and stakeholder manage -
ment frameworks reflect a legal, contractual, organizational, and governmental infra -
structure that defines the rights, responsibilities, and powers of each group . The legal 
infrastructure  defines the framework for rights established by law and the availability 
or ease of legal recourse for any violation of these rights. The contractual infrastruc -
ture is shaped by the contractual arrangements entered into by the company and its 
stakeholders that help define and secure the rights of both parties. The organizational

infrastructure  refers to internal systems, governance procedures, and practices adopted 
and controlled by the company in managing its stakeholder relationships. Lastly, the 
governmental infrastructure  refers to regulations imposed on companies.
The corporate governance systems in such countries as France, Germany, and 
Japan focus on a broader range of stakeholders relative to the more shareholder-  driven 
Anglo-  American systems. Globally, there is a growing movement among regulators 
and practitioners to more effectively balance the interests of all stakeholders. For 
instance, the Companies Act 2006 in the United Kingdom introduced “enlightened 
shareholder value, ” which requires directors to consider the interests of all stakehold -
ers—not just shareholders. Several regulators, such as those in the United Kingdom 
and Japan, have adopted stewardship codes that encourage more active engagement 
of institutional investors with companies.4

Stakeholder Management 15
EXAMPLE 4   
Stakeholder Management
The component of stakeholder management in which a corporation has the 
most  control is:
A legal infrastructure.
B contractual infrastructure.
C governmental infrastructure.
Solution:
B is correct. A corporation’s contractual infrastructure refers to the contractual 
arrangements between the corporation and stakeholders. As such, the corpo -
ration has control over these arrangements. A is incorrect because the legal 
infrastructure is established by law, which is outside the corporation’s own 
control. Similarly, C is incorrect because a corporation’s governmental structure 
is largely imposed by regulators.
4.2 Mechanisms of Stakeholder Management
Stakeholder management and governance practices attempt to manage the interests 
of all stakeholders. As mentioned earlier, a prescribed or standard set of rights and 
practices does not exist across all companies, and the principles vary across countries

and jurisdictions. Still, there are some common control elements and governance 
mechanisms among companies.
4.2.1  General Meetings
Corporate laws grant shareholders certain powers and controls. The participation of 
shareholders in general meetings, also known as general assemblies, and the exercise 
of their voting rights are among the most influential tools available. General meet -
ings enable shareholders to participate in discussions and to vote on major corporate 
matters and transactions that are not delegated to the board of directors.
Companies are ordinarily required to hold an annual general meeting (AGM) 
within a certain period following the end of their fiscal year. The main purpose of those 
meetings is to present shareholders with the annual audited financial statements of 
the company, provide an overview of the company’s performance and activities, and 
address shareholder questions. Shareholders also elect the directors at the AGM and,

in some countries, may be required to approve the financial statements, discharge 
directors of their duties, appoint external auditors, or vote on the remuneration of 
the board and/or top management. Extraordinary general meetings can be called by 
the company or by shareholders throughout the year when significant resolutions 
requiring shareholder approval are proposed. These resolutions might relate to pro -
posed material corporate changes, such as amendments to the company’s bylaws or 
rights attached to a class of shares, mergers and acquisitions, or the sale of significant 
corporate assets or businesses.
All shareholders typically have the right to attend, speak at, and vote at general 
meetings. Regulations, particularly corporate laws, specify conditions for inviting 
shareholders to general meetings and circulating information to shareholders. These 
conditions vary across regulations but generally aim at ensuring the participation

of a large number of shareholders in general meetings without imposing excessive 
restrictions on the ability of the company to hold a meeting. By engaging in general 
meetings, shareholders can exercise their voting rights on major corporate issues

Reading 33 ■ Corporate Governance and ESG: An Introduction 16
and better monitor the performance of the board and senior management. General 
meetings and the underlying voting procedures are among the most widely adopted 
practices by companies in mitigating agency problems and their associated risks.
Some resolutions, such as the approval of financial statements and the election 
of directors and auditors, are considered ordinary at general meetings because they 
require only a simple majority of votes to be passed. Decisions that are more material 
in nature may require a supermajority vote, such as two-  thirds or 75% of votes, to 
be passed. Such special resolutions may include amendments to bylaws, voting on 
a merger or takeover transaction, or waiving pre-  emptive rights. Depending on the 
ownership structure, supermajority requirements may make it harder for majority 
shareholders to influence corporate decisions at the expense of minority shareholders.

Proxy voting  is a process that enables shareholders who are unable to attend a 
meeting to authorize another individual (for example, another shareholder or director) 
to vote on their behalf. Proxy voting is the most common form of investor participa -
tion in general meetings. Although most resolutions at most companies pass without 
controversy, sometimes minority shareholders attempt to strengthen their influence at 
companies via proxy voting. Several shareholders sometimes use this process to collec -
tively vote their shares in favor of or in opposition to a certain resolution. Cumulative 
voting  (as opposed to straight voting) enables each shareholder to accumulate and 
vote all his or her shares for a single candidate in an election involving more than 
one director. This voting process raises the likelihood that minority shareholders are 
represented by at least one director on the board, but it may not be compatible with

majority voting standards for director elections in which share ownership is widely 
dispersed. In terms of worldwide practice, the existence of cumulative voting varies; 
for example, it is mandated in Spain but not allowed in several countries, such as 
Germany, Japan, Singapore, and Turkey.
Minority shareholders are often granted rights to protect their interests in acqui -
sitions. For example, companies in European Union member states are required to 
adopt sell-  out rights. These rights allow minority shareholders who have voted against 
a merger offer to force a bidder with more than 90% of the target’s voting rights to 
buy their shares at a fair price upon the deal’s approval.
EXAMPLE 5   
General Meetings
Which of the statements about extraordinary general meetings (EGMs) of 
shareholders is true?
A The appointment of external auditors occurs during the EGM.
B A corporation provides an overview of corporate performance at the 
EGM.

EGM.
C An amendment to a corporation’s bylaws typically occurs during the 
EGM.
Solution:
C is correct. An amendment to corporate bylaws would normally take place 
during an EGM, which covers significant changes to a company, such as bylaw 
amendments. A and B are incorrect because the appointment of external audi -
tors and a corporate performance overview would typically take place during 
the AGM.

Stakeholder Management 17
4.2.2  Board of Director Mechanisms
In companies with complex ownership structures and operations, it is impractical 
for shareholders to be involved in strategy formulation and day-  to- day activities. 
Shareholders thus elect a board of directors to provide broad oversight of the company. 
Shareholders monitor the board’s performance through exercise of voting power and 
participation in general meetings. The board, in turn, appoints the top management of 
the company. The board is accountable primarily to shareholders and is responsible for 
the proper governance of the company; in this regard, the board is the link between 
shareholders and managers. The board guides managers on the company’s strategic 
direction, oversees and monitors management’s actions in implementing the strategy, 
and evaluates and rewards or disciplines management performance. The board also 
supervises the company’s audit, control, and risk management functions and ensures

the adoption of proper governance systems and compliance with all applicable laws 
and regulations. In Section 5 of this reading, we provide more detail regarding the 
functions and responsibilities of the board of directors and its committees.
4.2.3  The Audit Function
The audit function is an integral component of any governance structure. The func -
tion represents the systems, controls, and policies/procedures in place to examine 
the company’s operations and financial records. Internal audits are conducted by an 
independent internal audit function or department. External auditors are independent 
from the company and conduct an annual audit of the company’s financial records to 
provide reasonable and independent assurance of the accuracy of financial statements 
and their fair representation of the financial position of the company. External audi -
tors are typically recommended by an audit committee (which we discuss later in the

reading) for appointment by shareholders or, in some jurisdictions, by the board. The 
board of directors is generally required to receive and review the financial statements 
and auditors’ reports and confirm their accuracy before they are presented to share -
holders for approval at the AGM. Senior management of publicly traded companies 
is also required to review and provide assurance of the effectiveness of the internal 
control systems to the board of directors or to shareholders. Overall, a company’s audit 
function limits insiders’ discretion with regard to the use of company resources and 
to its financial reporting. The audit function is also designed to mitigate incidents of 
fraud or misstatements of accounting and financial information.
4.2.4  Reporting and Transparency
Shareholders have access to a range of financial and non-  financial information con -
cerning the company, typically through annual reports, proxy statements, disclosures

on the company’s website, the investor relations department, and other means of 
communication (e.g., social media). This information may relate to the company’s 
operations, its strategic direction or objectives, audited financial statements, governance 
structure, ownership structure, remuneration policies, related-  party transactions, and 
risk factors. Such information is essential for shareholders to
■■reduce the extent of information asymmetry between shareholders and 
managers;
■■assess the performance of the company and of its directors and managers;
■■make informed decisions in valuing the company and deciding to purchase, sell, 
or transfer shares; and
■■vote on key corporate matters or changes.

Reading 33 ■ Corporate Governance and ESG: An Introduction 18
4.2.5  Policies on Related-  Party Transactions
The development and implementation of policies for related-  party transactions and 
other conflicts of interest is an increasingly common practice among companies. These 
policies establish the procedures for mitigating, managing, and disclosing such cases. 
Typically, directors and managers are required to disclose any actual or potential, 
or direct or indirect, conflict of interest they have with the company, as well as any 
material interests in a transaction that may affect the company. Often, these policies 
require such transactions or matters to be voted on by the board (or shareholders) 
excluding the director (or shareholder) holding the interest. The adoption of these 
policies and procedures aims at ensuring that related-  party transactions are handled 
fairly and that they do not advance the interests of the related party at the expense of

the interests of the company or other shareholders.
4.2.6  Remuneration Policies
Executive remuneration plans have gained significant attention in the investment world, 
with a primary goal of aligning the interests of managers with those of shareholders. 
For this purpose, incentive plans increasingly include a variable component—typically 
profit sharing, stocks, or stock options—that is contingent on corporate or stock price 
performance. However, the granting of stock-  based remuneration does not serve its 
purpose if managers can improve their personal gains at the expense of the company 
while limiting their exposure to weak stock performance. As a result, companies 
are increasingly designing incentive plans that discourage either “short-  termism” 
or excessive risk taking by managers. Some incentive plans include granting shares, 
rather than options, to managers and restricting their vesting or sale for several years

or until retirement. A long-  term incentive plan delays the payment of remuneration, 
either partially or in total, until company strategic objectives (typically performance 
targets) are met.
Regulators across the world are also increasingly focused on remuneration policies. 
In some cases, regulators require companies to base remuneration specifically on 
long-  term performance measures. A number of regulators are requiring companies, 
including many in the financial industry, to adopt clawback provisions. These pro -
visions allow a company to recover previously paid remuneration if certain events, 
such as financial restatements, misconduct, breach of the law, or risk management 
deficiencies, are uncovered.
4.2.7  Say on Pay
Given the role of remuneration plans in aligning the interests of executives with those 
of shareholders, regulators and companies are increasingly seeking shareholder views 
on pay. The concept of say on pay  enables shareholders to vote on executive remu -

neration matters. Say on pay was first introduced in the United Kingdom in the early 
2000s. As one early example, in 2003 the shareholders of GlaxoSmithKline rejected 
the company’s remuneration report because of opposition to the proposed executive 
pay. This was the first such rejection by the shareholders of a large UK-  based com -
pany. Shortly thereafter, the practice of say on pay spread to other parts of the world 
and was implemented in the United States as part of the Dodd–Frank Act in 2011.
The scope and effect of say on pay varies across countries and companies. Some 
countries, such as Canada, have a non-  mandatory and advisory (non-  binding) say on 
pay system in which shareholders signal, rather than impose, their views on proposed 
remuneration. In other countries, such as the United States, France, and South Africa, 
say on pay is mandatory but non-  binding. In these countries, the board is required to

enable shareholders to vote on remuneration plans or packages, but the board does not 
have to abide by the result of the vote. Conversely, countries in which shareholder votes 
on say on pay are binding include the Netherlands, the United Kingdom, and China.

Stakeholder Management 19
Say on pay has been subject to criticism because of the fact that shareholders often 
have limited involvement in a company’s strategy and operations. These opponents 
argue that the board is better suited to determine remuneration matters. Conversely, 
by allowing shareholders to express their views on remuneration-  related matters, 
companies can limit the discretion of directors and managers in granting themselves 
excessive or inadequate remuneration. This approach could thus reduce a critical 
agency conflict in stakeholder management by better aligning the interests of prin -
cipals and agents.
4.2.8  Contractual Agreements with Creditors
The rights of creditors are established by laws and according to contracts executed with 
the company. Laws vary by jurisdiction but commonly contain provisions to protect 
creditors’ interests and provide legal recourse. One such provision is an indenture ,

which is a legal contract that describes the structure of a bond, the obligations of the 
issuer, and the rights of the bondholders. To limit creditors’ risk during the term of 
a bond (or loan), debtholders may choose to impose covenants  within indentures or 
contracts. Covenants are the terms and conditions of lending agreements, enabling 
creditors to specify the actions an issuer is obligated to perform or prohibited from 
performing. Collaterals  are another tool often used by creditors to guarantee repay -
ment, representing assets or financial guarantees that are above and beyond an issuer’s 
promise to repay its obligations.
To further protect their rights, creditors usually require the company to provide 
periodic information (including financial statements) to ensure that covenants are not 
violated and thus potential default risk is not increased. Because it is usually imprac -
tical and costly for individual bondholders to fully scrutinize a bond issue, companies

often hire a financial institution to act as a trustee and monitor the issue on behalf of a 
class of bondholders. In some countries, credit committees, particularly for unsecured 
bondholders, are established once a company files for bankruptcy. Such committees 
are expected to represent bondholders throughout the bankruptcy proceedings and 
protect bondholder interests in any restructuring or liquidation.
4.2.9  Employee Laws and Contracts
Employee rights are primarily secured through labor laws, which define the standards 
for employees’ rights and responsibilities and cover such matters as labor hours, 
pension and retirement plans, hiring and firing, and vacation and leave. In most 
countries, employees have the right to create unions. Unions seek to influence certain 
matters affecting employees. In the European Union, companies meeting specific size 
and geographic criteria are required to establish European Works Councils that are

composed of employees who meet with management at least annually. Although not 
a common practice in the United States and many other parts of the world, employ -
ees are sometimes represented on the board of directors—or supervisory boards—of 
companies meeting certain size or ownership criteria (e.g., in Germany, Austria, and 
Luxembourg). In Japan, the employee model stresses reaching a consensus between 
management and employees in decision making.
At the individual level, employment contracts specify an employee’s various rights 
and responsibilities. Employment contracts typically do not cover every situation 
between employees and employers, and thus there is some area of discretion in the 
employment relationship. Human resources policies also help companies manage their 
relationships with employees. Effective human resources policies seek to attract and 
recruit high-  quality employees while providing remuneration, training/development,

and career growth to improve employee retention. Some companies have employee 
stock ownership plans (ESOPs) to help retain and motivate employees. As part of an 
ESOP , a company establishes a fund consisting of cash and/or company shares. The 
shares, which have designated vesting periods, are granted to employees.

Reading 33 ■ Corporate Governance and ESG: An Introduction 20
Codes of ethics and business conduct also serve an important role in the relationship 
between employees and the company. Such codes establish the company’s values and 
the standards of ethical and legal behavior that employees must follow. Companies 
typically assign a compliance or corporate governance officer (or a board committee) 
to implement these codes, receive violation reports, and resolve ethical matters.
By managing its relationships with its employees, a company seeks to comply with 
employees’ rights and mitigate legal or reputational risks in violation of these rights. 
Employee relationship management also helps ensure that employees are fulfilling 
their responsibilities toward the company and are qualified and motivated to act in 
the company’s best interests.
4.2.10  Contractual Agreements with Customers and Suppliers
Both customers and suppliers enter into contractual agreements with a company that

specify the products and services underlying the relationship, the prices or fees and 
the payment terms, the rights and responsibilities of each party, the after-  sale rela -
tionship, and any guarantees. Contracts also specify actions to be taken and recourse 
available if either party breaches the terms of the contract.
4.2.11  Laws and Regulations
As part of their public service roles, governments and regulatory authorities develop 
laws that companies must follow and monitor companies’ compliance with these laws. 
Such laws may address or protect the rights of a specific group, such as consumers or 
the environment. Some industries or sectors whose services, products, or operations 
are more likely to endanger the public or specific stakeholders’ interests are usually 
subject to a more rigorous regulatory framework. Examples of these industries are 
banks, food manufacturers, and health care companies.
Many regulatory authorities have also adopted corporate governance codes that

consist of guiding principles for publicly traded companies. Publicly traded com -
panies, in turn, are generally required to annually publish corporate governance 
reports describing their governance structure and explain any deviations from guiding 
principles. Companies normally seek to adopt internal governance and compliance 
procedures and adhere to the relevant financial reporting and transparency require -
ments imposed by regulators.
EXAMPLE 6   
Which of the following is not typically used to protect creditors’ rights?
A Proxy voting
B Collateral to secure debt obligations
C The imposition of a covenant to limit a company’s debt level
Solution:
A is correct. Proxy voting is a practice adopted by shareholders, not creditors. B 
and C are incorrect because both collateral and covenants are used by creditors 
to help mitigate the default risk of a company.

Board of Directors and Committees 21
BOARD OF DIRECTORS AND COMMITTEES
As discussed earlier in the reading, the board of directors is a central component of a 
company’s governance structure. The board serves as the link between shareholders 
and managers and acts as the shareholders’ monitoring tool within the company. As 
the relevance of corporate governance has grown within the investment field, the 
responsibilities of the board of directors have also increased in importance.
5.1 Composition of the Board of Directors
The structure and composition of a board of directors vary by company and geogra -
phy. There is no single or optimal structure, and the number of directors may differ 
depending on the company size, structure, and complexity of operations. Most cor -
porate governance codes require that the board include a diverse mix of expertise, 
backgrounds, and competencies. Such qualifications may include specialized knowledge

of the company’s industry as well as experience in certain functions, such as strategy, 
finance/audit, risk management, human resources, or legal. Moreover, many companies 
seek age, gender, and racial diversity in board composition.
Boards with one-  tier structures comprise a mix of executive and non-  executive 
directors. Executive (or internal) directors are employed by the company and are typ -
ically members of senior management. Non-  executive (or external) directors provide 
objective decision making, monitoring, and performance assessment. Additionally, 
non-  executive directors can serve an important role in challenging management and 
using past expertise in strategy and board issues. An independent director  is a specific 
type of non-  executive director that does not have a material relationship with the 
company with regard to employment, ownership, or remuneration.
In two-  tier structures, the supervisory and management boards are independent

from each other. Regulators generally prohibit members of the management board from 
serving on the supervisory board or limit the number of individuals serving on both 
boards. Employee representatives are typically elected by the company’s employees 
and could make up half of the supervisory board in large companies.
In many countries, the chief executive officer (CEO) and chairperson roles are 
increasingly separated. In the United States, many companies have historically had 
“CEO duality, ” in which the CEO also serves as chairperson of the board. Nevertheless, 
the percentage of companies separating the two roles, particularly in the United States, 
has increased considerably in recent years. The appointment of a lead independent 
director is an alternative that is sometimes practiced by boards of companies without 
CEO duality. The lead independent director generally has the authority to request 
and oversee meetings of all independent directors. Duality is not applicable in two-

tier structures that prohibit the members of the management board from serving on 
the supervisory board. In these models, the chairperson of the supervisory board is 
typically external and the CEO usually chairs the management board.
 
Staggered Boards
The general practice for boards is that elections occur simultaneously and for specified 
terms (three years, for example). Some companies, however, have staggered boards  
whereby directors are typically divided into three classes that are elected separately 
in consecutive years—that is, one class every year. Because shareholders would need 
several years to replace a full board, this election process limits their ability to effect a 5

Reading 33 ■ Corporate Governance and ESG: An Introduction 22
major change of control at the company. This staggered board model was historically 
prevalent in the United States but has been generally replaced by regular board election 
terms. In contrast, the practice is common in Australia.
5.2 Functions and Responsibilities of the Board
As mentioned earlier, a company’s board of directors is elected by shareholders to act 
on their behalf. In fulfilling their functions, directors have a responsibility to consider 
the interests of all stakeholders. The duties of directors are mandated by law in many 
countries but vary across jurisdictions. Two widely established elements of directors’ 
responsibilities are the duty of care  and the duty of loyalty . According to the OECD’s 
Principles of Corporate Governance , duty of care “requires board members to act on 
a fully informed basis, in good faith, with due diligence and care. ” The OECD further

notes that duty of loyalty “is the duty of the board member to act in the interest of 
the company and shareholders. The duty of loyalty should prevent individual board 
members from acting in their own interest, or the interest of another individual or 
group, at the expense of the company and all shareholders. ”
A board of directors does not typically engage in the company’s day-  to- day activities; 
rather, those activities are delegated to management. The board guides and approves 
the company’s strategic direction, taking into consideration the company’s risk profile. 
It delegates the implementation of the company’s strategy to senior management, 
oversees the execution of the strategy, and establishes milestones to monitor the 
progress in reaching the objectives. The board also reviews corporate performance 
and determines relevant courses of action accordingly. In doing so, the board can 
monitor and evaluate management’s performance and determine whether senior

executive remuneration is aligned with the long-  term interests of the company. The 
board is also responsible for selecting, appointing, and terminating the employment 
of senior managers (or the management board in case of a two-  tier structure). One of 
the board’s main responsibilities is to ensure leadership continuity though succession 
planning for the CEO and other key executives.
The board plays a central role in ensuring the effectiveness of the company’s audit 
and control systems. It sets the overall structure of these systems and oversees their 
implementation, including oversight of the financial reporting practices and the review 
of the financial statements for fairness and accuracy. The board also oversees reports 
by internal audit, the audit committee, and the external auditors and proposes and 
follows up on remedial actions. The board has the ultimate responsibility to ensure 
that the company adopts and implements proper corporate governance principles

and complies with all applicable internal and external laws and regulations, including 
ethical standards.
In addition, the board typically ensures that the company has an appropriate 
enterprise risk management system in place, whereby risks are identified, mitigated, 
assessed, and managed appropriately. The board monitors the effectiveness of these 
systems through regular reviews and reports received from both management and 
the company’s risk function. The board also has the responsibility to review any 
proposals for corporate transactions or changes, such as major capital acquisitions, 
divestures, mergers, and acquisitions, before they are referred to shareholders for 
approval, if applicable.
5.3 Board of Directors Committees
A company’s board of directors typically establishes committees that focus on specific 
functions. Such committees, in turn, provide recommendations that are reported to 
the board on a regular basis. Despite the delegation of responsibilities to committees,

Board of Directors and Committees 23
the overall board remains ultimately responsible to shareholders and is not discharged 
of its liabilities to shareholders. Although board committees may vary by organiza -
tion, some of the most common committees are discussed in the following sections.
5.3.1  Audit Committee
The audit committee is perhaps the most common board committee among companies 
worldwide. The audit committee plays a key role in overseeing the audit and control 
systems at the company and ensuring their effectiveness. In this regard, the commit -
tee monitors the financial reporting process, including the application of accounting 
policies; ensures the integrity of financial statements; supervises the internal audit 
function and ensures its independence and competence; and presents an annual audit 
plan to the board and monitors its implementation by the internal audit function. 
The audit committee is also responsible for recommending the appointment of an

independent external auditor and proposing the auditor’s remuneration. Both inter -
nal and external auditors report their findings to the audit committee, which in turn 
proposes remedial action for highlighted issues or matters.
5.3.2  Governance Committee
The primary role of the governance (or corporate governance) committee is to ensure 
that the company adopts good corporate governance practices. In doing so, the 
committee develops and oversees the implementation of the corporate governance 
code, the charters of the board and its committees, and the company’s code of ethics 
and conflict of interest policy. The governance committee reviews these policies on 
a regular basis to incorporate any regulatory requirements or relevant developments 
in the field. Most importantly, the committee monitors the implementation of the 
governance policies and standards as well as the compliance with the applicable laws 
and regulations throughout the company. Remedial actions are recommended if any

flaws or breaches of laws or regulations are identified. In some companies, the gover -
nance committee may be responsible for overseeing an annual evaluation of the board 
to ensure that its structure and activities are aligned with the governance principles.
5.3.3  Remuneration or Compensation Committee
The remuneration (or compensation) committee of the board specializes in remu -
neration matters. This committee develops and proposes remuneration policies for 
the directors and key executives and presents them for approval by the board or 
by shareholders. The committee may also be involved in handling the contracts of 
managers and directors as well as in setting performance criteria and evaluating the 
performance of managers. The responsibilities of the remuneration committee may 
extend to establishing human resources policies for the company when remuneration 
matters are involved. In some companies, the remuneration committee also sets and

oversees the implementation of employee benefit plans, including insurance, pension, 
severance benefits, and retirement plans (including monitoring investment perfor -
mance of benefit plan funds).
5.3.4  Nomination Committee
The nomination committee identifies candidates who are qualified to serve as directors 
and recommends their nomination for election by shareholders. The committee also 
establishes the nomination procedures and policies, including the criteria for board 
directors, the search process, and the identification of qualified candidates for director 
positions. Director independence, including what constitutes an independent director, 
is also a function of the nomination committee. Through these roles, the nomination 
committee can help ensure that the board’s composition is well balanced and aligned 
with the company’s governance principles.

Reading 33 ■ Corporate Governance and ESG: An Introduction 24
5.3.5  Risk Committee
The risk committee assists the board in determining the risk policy, profile, and 
appetite of the company. Accordingly, the committee oversees establishing enterprise 
risk management plans and monitors their implementation. It also supervises the risk 
management functions in the company, receives regular reports, and reports on its 
findings and recommendations to the board.
5.3.6  Investment Committee
The investment committee of the board reviews material investment opportuni -
ties proposed by management and considers their viability for the company. Such 
opportunities may include large projects, acquisitions, and expansion plans, as well 
as divestures or major asset disposals. The committee often challenges, when nec -
essary, management assumptions underlying investment prospects, monitors the 
performance of investments, and reports its findings to the board. The committee

also is typically responsible for establishing and revising the investment strategy and 
policies of the company.
The specific board committees discussed in previous sections are the most com -
monly used, although the composition and number of committees may vary depending 
on the jurisdiction or on company-  specific factors (e.g., company size, industry, com -
plexity of operations, or regulatory requirements). An audit committee, for instance, 
is a regulatory requirement in a large number of jurisdictions. For banks and other 
financial institutions, a risk committee is strongly recommended by some regulators 
and required by others. In Brazil, the Central Bank of Brazil requires financial insti -
tutions to establish a remuneration committee at the board level. Some companies 
choose to combine two or more committees into one—for example, a nomination and 
remuneration (or compensation) committee or an audit and risk committee. Companies

may also find it valuable to establish committees with other specializations, such as 
a compliance committee, an ethics committee, a human resources committee, or a 
health/environmental/safety committee.
The composition of a board committee is normally aligned with its scope of respon -
sibilities. For instance, many regulators request that executive (internal) directors do 
not rule on matters underlying conflicts of interest or on matters requiring an unbiased 
judgment (such as audit, remuneration, or related-  party transaction matters). As such, 
a large number of rules, including those adopted by the London Stock Exchange and 
the New York Stock Exchange, require that the audit and the compensation commit -
tees be composed of independent directors only. Less stringent regulations, such as 
those of the Gulf Cooperation Council, require the audit committee to be composed 
of external (non-  executive) directors, the majority of which should be independent 
(including the chairperson).

EXAMPLE 7   
Responsibilities of Board Committees
A primary responsibility of a board’s audit committee does not include the:
A proper application of accounting policies.
B adoption of proper corporate governance.
C recommendation of remuneration for the external auditor(s).

Factors Affecting Stakeholder Relationships and Corporate Governance 25
Solution:
B is correct. The adoption of proper corporate governance is the responsibility 
of a corporation’s governance committee. Both A and C are incorrect because 
proper application of accounting policies and the remuneration of external 
auditors fall under the domain of the audit committee.
FACTORS AFFECTING STAKEHOLDER RELATIONSHIPS 
AND CORPORATE GOVERNANCE
This section explores ways in which certain factors, both market and non-  market 
related, can affect stakeholder relationships and corporate governance. For this sec -
tion, market factors include those that relate to capital markets whereas non-  market 
factors do not.
6.1 Market Factors
This section focuses on shareholder engagement, shareholder activism, and competitive 
forces, all of which are influential market factors for a company. Shareholder engage -
ment involves a company’s interactions with its shareholders, whereas shareholder

activism describes the efforts by shareholders to create a change within a corporation 
or modify a corporation’s behavior. Meanwhile, competitive dynamics can help align 
managerial interests with those of its stakeholders.
6.1.1  Shareholder Engagement
The engagement of companies with shareholders—called shareholder engagement —
has traditionally involved certain events, such as the annual shareholder meeting 
and analyst calls, the scope of which was limited to financial and strategic matters. 
There is a growing trend, however, for greater engagement between companies and 
their shareholders beyond these venues and topics. Companies have increasingly 
recognized the benefits that frequent, year-  round engagement with shareholders can 
provide, such as building support against short-  term activist investors, countering 
negative recommendations from proxy advisory firms, and receiving greater support 
for management’s position.
6.1.2  Shareholder Activism

Shareholder activism  refers to strategies used by shareholders to attempt to compel 
a company to act in a desired manner. Although shareholder activism can focus on 
a range of issues, including those involving social or political considerations, the 
primary motivation of activist shareholders is to increase shareholder value. Activist 
shareholders often pressure management through such tactics as initiating proxy 
battles (fights), proposing shareholder resolutions, and publicly raising awareness on 
issues of contention.
Shareholder activists may pursue additional tactics, such as shareholder derivative 
lawsuits, which are legal proceedings initiated by one or more shareholders against 
board directors, management, and/or controlling shareholders of the company. 
The theory behind this type of lawsuit is that the plaintiff shareholder is deemed to 
be acting on behalf of the company in place of its directors and officers who have

failed to adequately act for the benefit of the company and its shareholders. In many 
countries, however, the law restricts shareholders from pursuing legal action via the 6

Reading 33 ■ Corporate Governance and ESG: An Introduction 26
court system—in some cases, by imposing thresholds that enable only shareholders 
with interests above a minimum amount to pursue legal actions or by denying legal 
action altogether.
Hedge funds are among the most predominant shareholder activists. Compared 
with most traditional institutional investors, the fee structure of hedge funds often pro -
vides a significant stake in the financial success of any activist campaign. Furthermore, 
unlike regulated investment entities that are typically subject to restrictions on 
their investments (e.g., limitations on leverage or ownership of distressed or illiquid 
securities), hedge funds are loosely regulated and can thus pursue a greater range of 
activist opportunities.
6.1.3  Competition and Takeovers
Metrics that measure a company’s success, such as market share or earnings growth, 
provide information that is useful for shareholders to judge the performance of a

company’s management team or board of directors and compare such performance 
with that of competitors. Senior managers risk their employment status in the event 
of underperformance, and directors, in turn, can be voted out by shareholders.
The traditional view of the market for corporate control (often known as the take -
over market) is one in which shareholders of a company hire and fire management 
to achieve better resource utilization. Corporate takeovers can be pursued in several 
different ways. One mechanism is the proxy contest  (or proxy fight). In a proxy 
contest, shareholders are persuaded to vote for a group seeking a controlling position 
on a company’s board of directors. Managerial teams can also be displaced through a 
tender offer , which involves shareholders selling their interests directly to the group 
seeking to gain control. A contest for corporate control may attract arbitrageurs and

takeover specialists, who facilitate transfers of control by accumulating long positions 
from existing shareholders in the target company and later selling the positions to 
the highest bidder. Finally, a hostile takeover  is an attempt by one entity to acquire 
a company without the consent of the company’s management.
Preservation of their employment status serves as an incentive for board members 
and managers to focus on shareholder wealth maximization. This threat of removal, 
however, can also have negative implications for a company’s corporate governance 
practices if the company chooses to adopt anti-  takeover measures, such as a stag -
gered board or a shareholder rights plan (also known as a poison pill) to reduce the 
likelihood of an unwanted takeover. Staggering director elections can dilute the value 
of shareholder voting rights by extending the term that each director serves and elim -
inating the ability of shareholders to replace the entire board at any given election.

Shareholder rights plans enable shareholders to buy additional shares at a discount if 
another shareholder purchases a certain percentage of the company’s shares. These 
plans are designed to increase the cost to any bidder seeking to take over a company.
EXAMPLE 8   
Shareholder Activism
Which of the following is true of shareholder activism?
A Shareholder activists rarely include hedge funds.
B Regulators play a prominent role in shareholder activism.
C A primary goal of shareholder activism is to increase shareholder value.

Factors Affecting Stakeholder Relationships and Corporate Governance 27
Solution:
C is correct. Although the subject of shareholder activism may involve social 
and political issues, activist shareholders’ primary motivation is to increase 
shareholder value. A is incorrect because hedge funds commonly serve as 
shareholder activists. B is incorrect because regulators play a prominent role 
in standard setting, not shareholder activism.
6.2 Non-  market Factors
This section focuses on certain non-  market factors, such as a company’s legal envi -
ronment, the role of the media, and the corporate governance industry, that can have 
an effect on stakeholder relationships and corporate governance.
6.2.1  Legal Environment
The legal environment in which a company operates can significantly influence the 
rights and remedies of stakeholders. Countries that have a common law system (such 
as the United Kingdom, the United States, India, and Canada) are generally considered

to offer superior protection of the interests of shareholders and creditors relative to 
those that have adopted a civil law system (such as France, Germany, Italy, and Japan). 
The key difference between the two systems lies in the ability of a judge to create laws. 
In civil law systems, laws are created primarily through statutes and codes enacted by 
the legislature. The role of judges is generally limited to rigidly applying the statutes 
and codes to the specific case brought before the court. In contrast, in common law 
systems, laws are created both from statutes enacted by the legislature and by judges 
through judicial opinions. In common law systems, shareholders and creditors have 
the ability to appeal to a judge to rule against management actions and decisions 
that are not expressly forbidden by statute or code, whereas in civil law systems, this 
option is generally not possible.
Regardless of a country’s legal system, creditors are generally more successful in

seeking remedies in court to enforce their rights than shareholders are because share -
holder disputes often involve complex legal theories, such as whether a manager or 
director breached a duty owed to shareholders. In contrast, disputes involving creditors, 
such as whether the terms of an indenture or other debt contract have been breached, 
are more straightforward and therefore are more easily determinable by a court.
6.2.2  The Media
The media can affect corporate governance and influence stakeholder relationships 
through its ability to spread information quickly and shape public opinion. As an 
example, negative media attention can adversely affect the reputation or public per -
ception of a company or its managers and directors. Senior management’s concern 
over reputational risk can thus reduce the cost of monitoring management activities 
by stakeholders. Media attention can motivate politicians and regulators to introduce

corporate governance reforms or enforce laws that protect stakeholders and society 
at large. This influence was evident in the aftermath of the 2008–2009 financial crisis, 
when significant media attention was a factor in the adoption of new laws and regu -
lations designed to address perceived deficiencies in corporate governance.
Social media has become a powerful tool that stakeholders have increasingly 
used to protect their interests or enhance their influence on corporate matters. Prior 
to the advent of social media, companies typically had an advantage in distributing 
information because of their considerable resources as well as relationships with 
traditional media organizations. Through social media, stakeholders can instantly 
broadcast information with little cost or effort and are better able to compete with 
company management in influencing public sentiment.

Reading 33 ■ Corporate Governance and ESG: An Introduction 28
6.2.3  The Corporate Governance Industry
An important catalyst for the rise of the corporate governance industry occurred in 
2003, when the Securities and Exchange Commission (SEC) required US-  registered 
mutual funds to disclose their proxy voting records annually. The same rule also 
required US mutual funds to adopt policies and procedures designed to reasonably 
ensure that proxies would be voted in the best interests of their clients. In the years 
following the SEC’s 2003 mutual fund rule, institutional investors have, to varying 
degrees, committed additional resources to monitor and vote proxies for the large 
number of companies in which they invest.
With the increased importance and relevance of corporate governance among inves -
tors, the demand for external corporate governance services has grown considerably. 
In particular, some institutional investors have retained outside experts to assist with

corporate governance monitoring and proxy voting. In response to this demand, an 
industry that provides corporate governance services, including governance ratings and 
proxy advice, has developed. Because the corporate governance industry is relatively 
concentrated, these vendors have considerable influence in corporate governance 
practices, and in turn, corporations are generally compelled to pay attention to ratings 
and recommendations produced by the corporate governance industry.
CORPORATE GOVERNANCE AND STAKEHOLDER 
MANAGEMENT RISKS AND BENEFITS
As illustrated thus far, good corporate governance and stakeholder management can 
have a meaningfully positive effect on a company. A company will likely not meet the 
expectations of all stakeholders if one group is able to extract private benefits at the 
expense of another group. Depending on their nature and magnitude, unmanaged 
conflicts of interest and weak control over a company’s operations may expose the

company to various risks, such as legal, regulatory, reputational, or default risks. By 
adopting effective guidelines for managing the interests of stakeholder groups and 
instituting adequate levels of control, corporate governance can be reflected in bet -
ter company relationships, superior levels of efficiency in operations, and improved 
7.1 Risks of Poor Governance and Stakeholder Management
Weaknesses in stakeholder management mechanisms or the adoption of poor gover -
nance structures can create various risks for a company and its stakeholders. A weak 
control environment can encourage misconduct and hinder the ability of the company 
to identify and manage risks.
7.1.1  Weak Control Systems
In a company with weak control systems or inefficient monitoring tools, such as poor 
audit procedures or insufficient scrutiny by the board, one stakeholder group may 
benefit at the expense of the company or other stakeholders. This could consequently

have an adverse effect on the company’s resources, performance, and value. The audit 
deficiencies at Enron, for instance, prevented the uncovering of the acts of fraud, 
erroneous accounting records, and other related issues that led to one of the largest 
corporate bankruptcies in US history.7

Corporate Governance and Stakeholder Management Risks and Benefits 29
7.1.2  Ineffective Decision Making
When the quality and quantity of information available to managers are superior to 
those available to the board or shareholders, in the absence of sufficient monitoring 
tools, managers have an opportunity to make decisions that benefit themselves rela -
tive to the company or shareholders. Without proper scrutiny, such practices might 
go unnoticed. Deficient decisions could include managing the company with a lower 
risk profile relative to shareholders’ tolerance, thus avoiding investment opportunities 
that could create value for the company. Conversely, manager overconfidence may 
result in poor investment decisions without proper examination of their effect on the 
company or on shareholders’ wealth.
Remuneration policies for management could also have significant implications for 
the company. Outsized remuneration packages for executives could have an adverse

effect on shareholders’ wealth, constitute a burden on corporate performance, and 
affect the interests of other stakeholders, such as employees, customers, or creditors. 
Remuneration policies that are not carefully designed may also encourage managers 
to seek immediate personal gains by taking excessive risks or focusing on creating 
short-  term performance or stock price increases. Related-  party transactions that 
underlie unfair terms for the company are another example of activities that are not 
aligned with the objective of value creation and that could be facilitated by a poor 
governance system.
7.1.3  Legal, Regulatory, and Reputational Risks
Compliance weaknesses in the implementation of regulatory requirements or lack 
of proper reporting practices may expose the company to legal, regulatory, or rep -
utational risks. In such cases, the company may become subject to investigation by 
government or regulatory authorities for violation of applicable laws. A company

could also be exposed to lawsuits filed by shareholders, employees, creditors, or other 
parties for breach of contractual agreements or company bylaws or for violation of 
stakeholders’ legal rights. In today’s markets, information flows rapidly. Improperly 
managed conflicts of interest or governance failures could bring reputational damage 
to the company, and its associated costs could be significant. Such risks are partic -
ularly acute for publicly listed companies subject to scrutiny by investors, analysts, 
and other market participants.
7.1.4  Default and Bankruptcy Risks
Poor corporate governance, including weak management of creditors’ interests, can 
affect the company’s financial position and may hinder its ability to honor its debt 
obligations. To the extent that the deterioration of corporate performance results in 
a debt default, the company may be exposed to bankruptcy risk if creditors choose

to take legal action. The adverse consequences of corporate failures are not limited 
to the company’s shareholders; they extend to other stakeholders, such as managers 
and employees and even society and the environment.
7.2 Benefits of Effective Governance and Stakeholder 
Management
The development of good governance practices can play a vital role in aligning the 
interests of managers and the board of directors with those of shareholders, while 
balancing the interests of the company’s stakeholders. A good governance structure 
can be reflected in operational efficiency, improved control processes, better financial 
performance, and lower levels of risk.

Reading 33 ■ Corporate Governance and ESG: An Introduction 30
7.2.1  Operational Efficiency
As part of a good governance structure, an organization clarifies the delegation of 
responsibilities and reporting lines across the company and ensures that all employees 
have a clear understanding of their respective duties. When balanced with adequate 
internal control mechanisms, the governance structure can ensure that corporate 
decisions and activities are properly monitored and controlled to mitigate risk and 
help improve the operational efficiency of the company.
7.2.2  Improved Control
Governance practices seek to institute more effective control exercised at all corporate 
levels, from shareholders to the board of directors and management. These practices 
can help identify and manage risk at early stages that can otherwise hinder corporate 
performance and/or damage reputation. Control can be enhanced by the proper func -

tioning of a company’s audit committee and the effectiveness of its audit systems. By 
adopting procedures for monitoring compliance with internal policies and external 
regulations and for reporting any violations, the company can better mitigate regu -
latory or legal risks and their associated costs. Additionally, the adoption of formal 
procedures with regard to conflicts of interest and related-  party transactions allows 
the company to ensure fairness in its relationships with those parties.
7.2.3  Better Operating and Financial Performance
Good governance and stakeholder management can help a company improve its 
operating performance and reduce the costs associated with weak control systems. 
The costs of poor investments, legal proceedings against the company, and excessive 
perquisites are just a few examples that could be mitigated by well-  functioning gov -
ernance systems. Enhanced corporate governance could also allow the company to

improve its decision-  making process and respond faster to market factors. Proper 
remuneration policies are another governance tool that can motivate managers to 
make decisions with the objective of creating corporate value.
7.2.4  Lower Default Risk and Cost of Debt
Good corporate governance can lower business and investment risk. Governance 
arrangements that manage conflicts of interest with creditors, and that help protect 
creditor rights, can reduce a company’s cost of debt and default risk. Default risk can 
also often be mitigated by proper functioning of audit systems, improved transparency 
(e.g., reporting of earnings), and the control of information asymmetries between the 
company and its capital providers. With regard to credit risk, corporate governance 
mechanisms have become increasingly relevant criteria among credit rating agencies 
when assessing a company’s creditworthiness.
EXAMPLE 9   
Benefits of Corporate Governance

EXAMPLE 9   
Which of the following is not a benefit of an effective corporate governance 
structure?
A Operating performance can be improved.
B A corporation’s cost of debt can be reduced.
C Corporate decisions and activities require less control.

Analyst Considerations in Corporate Governance and Stakeholder Management 31
Solution:
C is correct. A benefit of an effective corporate governance system is to enable 
adequate scrutiny and control over operations. B is incorrect because an effective 
governance structure can reduce investors’ perceived credit risk of a corpo -
ration, thus potentially lowering the corporation’s cost of debt. A is incorrect 
because operating efficiency may indeed be a benefit of an effective corporate 
governance structure.
ANALYST CONSIDERATIONS IN CORPORATE 
GOVERNANCE AND STAKEHOLDER MANAGEMENT
In the past, analysts may have considered corporate governance and stakeholder 
management issues to be only peripherally related to traditional fundamental analysis. 
Generally, these issues were seen as obscure and unlikely to be material drivers of 
performance. Following the aforementioned governance failures in the early 2000s, 
the global financial crisis, and the rise of shareholder activism around the world,

there is little doubt that governance and stakeholder issues have become increasingly 
important topics for analysts.
Some key questions that analysts may consider when assessing a company’s cor -
porate governance or stakeholder management system are as follows:
■■What is the company’s ownership and voting structure among shareholders?
■■Who represents shareholders on this company’s board?
■■What are the main drivers of the management team’s remuneration and incen -
tive structure?
■■Who are the significant investors in the company?
■■How robust are the shareholder rights at the company, including relative to 
peers?
■■How effectively is the company managing long-  term risks, such as securing 
access to necessary resources, managing human capital, exhibiting integrity and 
leadership, and strengthening the long-  term sustainability of the enterprise?
A qualitative analysis of these issues—typically provided by a company’s proxy

statements, annual reports, and sustainability reports, if available—can provide 
important insights about the quality of management and sources of potential risk.
8.1 Economic Ownership and Voting Control
Generally speaking, corporations with publicly traded equity have a voting structure 
that involves one vote for each share. That is, any shareholder’s voting power is equal 
to the percentage of the company’s outstanding shares owned by that shareholder. 
When there are exceptions to this norm and economic ownership becomes separated 
from control, investors can face significant potential risks.
In a small number of markets, dual-  class structures are allowed under the local 
regulatory framework or exchange rules, which is the most common way that voting 
power is decoupled from ownership. In these cases, common shares may be divided 
into two classes, one of which has superior voting rights to the other. A common

arrangement is when a share class (for example, Class A) carries one vote per share 
and is publicly traded whereas another share class (for example, Class B) carries several 
votes per share and is held exclusively by company insiders or family members. This 8

Reading 33 ■ Corporate Governance and ESG: An Introduction 32
structure is used by Facebook, for example. In this way, the founders and/or insiders 
of a company may continue to control board elections, strategic decisions, and all 
other significant voting matters for a long period—even once their ownership level 
declines to less than 50% of the company’s shares.
Another mechanism used to separate voting control from economic ownership 
is when one class of stock (held by insiders) elects a majority of the board; outside 
shareholders who hold a different share class would then be entitled to elect only a 
minority of the board. Technically, each share carries equal voting rights, but with 
this structure, the insiders retain substantial power over the affairs of the corporation 
because they control a majority of the board. Alibaba’s partnership structure is one 
example of this type of control.
Proponents of dual share systems, such as those just mentioned, argue that the

systems promote company stability and enable management to make long-  term strate -
gic investments, insulated from the short-  term pressures of outside investors. Critics 
of these structures believe they create conflicts of interest between the providers of 
capital and the management of the business.
It is virtually impossible for outside investors to dismantle dual-  class structures 
because of the inherent design of their unequal voting rights. Therefore, these struc -
tures can remain in place even through generational changes within a founding family. 
Investors with long time horizons may want to consider the motivations of the con -
trolling stockholders, generational dynamics, succession planning, and the relationship 
between the board and management. In addition, there may be potential valuation 
implications because dual-  class companies tend to trade at a discount to their peers.
8.2 Board of Directors Representation

In most markets, investors have access to basic biographical information about the 
non-  executive members of corporate boards. Analysts can assess the available infor -
mation to determine whether the experience and skill sets on the board match the 
current and future needs of the company.
In particular, questions regarding directors’ independence, tenure, experience, and 
diversity may bring useful investment insights. For example, if the board has multiple 
directors engaging in related-  party transactions with the company, investors may 
have cause for concern about any conflicts of interest that arise. The issue of board 
tenure can also be a useful tool for investors. Directors with long periods of service 
to a company clearly offer valuable experience and expertise, but if the board com -
position is dominated by such long-  tenured members, it may have a negative effect 
on the board’s diversity and adaptability.

An example in which board composition had a significant effect on company 
performance occurred at a European pharmaceutical company. At one point in its 
history, the company had become overleveraged and faced significant financial distress. 
In response, non-  executive directors with banking and turnaround experience were 
added to the board. With the help of these directors, the company recovered. Seven 
years later, the most promising product in the company’s pharmaceutical portfolio 
began to cause serious side effects in its patient population. The situation required 
both a meaningful understanding of the medical issues involved and a rapid response 
from the company. However, the board was still composed of directors with financial 
expertise rather than medical training. The company struggled with its response to 
the crisis, and its stock price fell sharply. This situation was one in which the board’s

composition had been ideal for a certain point in the company’s history, but ultimately 
the directors failed to refresh the board’s membership as the needs of the business 
changed.

Analyst Considerations in Corporate Governance and Stakeholder Management 33
8.3 Remuneration and Company Performance
The availability and quality of information about executive remuneration plans varies 
widely across markets. In those markets where such disclosures are available, analysts 
can assess the elements of the remuneration program to determine whether they 
support or conflict with the key drivers of performance for the company.
Generally speaking, current executive remuneration programs consist of a base 
salary, a short-  term bonus usually delivered in the form of cash, and a multi-  year 
incentive plan delivered in one or more forms of equity (options, time-  vested shares, 
and/or performance-  vested shares). Often, these short-  term and long-  term plans are 
contingent on achieving financial or operational objectives, and often these objectives 
are disclosed. In these situations, an analyst can assess whether the primary drivers

of the remuneration plan are the same factors that, in the analyst’s view, drive overall 
company results.
Assessment of the suitability of a remuneration plan for a particular company is 
a subjective exercise and is highly dependent on industry and geographic norms. But 
there are some warning signs that may warrant particular scrutiny:
■■Plans offering little alignment with shareholders.  As an example, if a plan 
offers only cash-  based payouts and no equity, there may be a misalignment of 
incentives between executives and investors unless management already owns a 
significant stake in the company.
■■Plans exhibiting little variation in results over multiple years.  If an award is 
described as performance-  based but still pays in full every year regardless of the 
company’s results, investors may have concerns about the rigor of the perfor -
mance hurdles underlying the awards.
■■Plans with excessive payouts relative to comparable companies with

comparable performance.  Investors may want to understand the cause of the 
anomaly and whether it is a temporary issue or a result of flawed remuneration 
plan design.
■■Plans that may have specific strategic implications.  As an example, some 
remuneration plans contain payouts tied to specific milestones, such as regu -
latory approval of a product, completion of an acquisition, or achievement of 
specific cost reductions. In addition, some companies offer particularly high 
post-  employment pay arrangements tied to the sale of the company, whereas 
others offer no such arrangements. These factors are not necessarily negative 
features, but investors may want to understand whether the milestones driving 
the incentive plan align with the company’s objectives.
■■Plans based on incentives from an earlier period in the company’s life 
cycle.  A frequent example of such a plan relates to a company that has matured 
beyond its fast growth phase. The company’s business may have matured, and

competition may have limited the opportunity for market share gains. Investors 
may believe the company should become more focused on both returns and 
disciplined capital allocation. Even after the company communicates to the 
investor community a more returns-  oriented strategy, the financial incentives in 
the remuneration plan may still be based purely on revenue growth. Investors 
may want to understand such potential misalignment of interests.
8.4 Investors in the Company
Examining the composition of investors in a company can be another source of useful 
insight for analysts. The behavior of these investors can result in both limitations and 
catalysts with regard to changes in the corporation. For example, cross-  shareholdings

Reading 33 ■ Corporate Governance and ESG: An Introduction 34
are still prevalent in a number of markets. This situation occurs when a company, 
particularly a publicly listed one, holds a large, passive, minority stake in another 
company. Such holdings generally help to protect management from shareholder 
pressures because implicit in a cross-  shareholding arrangement is the guarantee that 
the owner of the shares will support management on all voting issues. In effect, these 
shareholdings act as takeover defenses.
Similarly, the presence of a sizable affiliated stockholder (such as an individual, 
family trust, endowment, or private equity fund) can shield a company from the effects 
of voting by outside shareholders. As an example, a US consumer goods company 
has an affiliated charitable foundation that owns more than 20% of the outstanding 
shares. The company also has a provision in its corporate charter requiring that any

changes to the charter must be approved by two-  thirds of outstanding shares. As a 
result, it is virtually impossible for any measure to pass without the support of the 
foundation. The interests of the foundation thus conflict with the interests of the 
overall shareholder base. In effect, this single minority shareholder most likely holds 
the power to block the votes of the majority.
Analysts should note that market context is important in assessing the potential 
effects of affiliated stockholders. In certain countries, the presence of such shareholders 
is common, viewed by local market participants as a means of enhancing stability, 
strengthening the relationship between companies and their business partners, and 
fostering a long-  term perspective by protecting the company against hostile takeover 
bids.
A final aspect of investor composition that has become increasingly relevant 
relates to activist shareholders, which we discussed earlier. The presence of activist

shareholders can meaningfully and rapidly change the investment thesis for a company. 
Experienced activists, together with short-  term-  oriented investors who follow their 
activities, can create substantial turnover in a company’s shareholder composition in 
a short amount of time. This is because an activist often serves as a catalyst for new 
strategic alternatives at a company and can attract new investors and/or arbitrageurs.
8.5 Strength of Shareholders’ Rights
Within a framework of regional regulations and corporate governance codes, analysts 
may want to understand whether the shareholder rights of a particular company are 
strong, weak, or average compared with other companies. For example, if an ana -
lyst’s viewpoint includes the possibility that a company will merge in the future, he 
or she may want to understand whether there are significant structural obstacles to 
transactions that are embedded in the company’s charter or bylaws. Similarly, if the

thesis involves an outside catalyst, such as an activist shareholder who will introduce 
change at the company and improve performance, the analyst must take a position 
on whether shareholders are sufficiently empowered to advance such a change. If it is 
impossible for shareholders to remove directors from the board or to convene special 
stockholder meetings, it will be difficult for external initiatives to be successful.
In a number of developed markets, including the United Kingdom, the Netherlands, 
and Japan, regulatory agencies or stock exchanges have adopted governance codes, 
which are standards of governance reflecting local investors’ expectations with regard 
to disclosure, board composition, shareholder rights, and other related issues. Often, 
these governance codes are implemented on a “comply or explain” basis, which indi -
cates that standards are voluntary in nature. However, any deviation from the code

must be explained by the company in a public disclosure. If a company has elected 
to deviate from the locally accepted governance practice, the analyst may want to 
understand the reasoning behind the decision.

Analyst Considerations in Corporate Governance and Stakeholder Management 35
8.6 Managing Long-  Term Risks
Analysts may uncover useful insights regarding how a company manages various 
issues, such as long-  term environmental risks, management of human capital, trans -
parency, and treatment of investors and other stakeholders. Of particular note, the 
academic evidence linking these and other management quality issues to share price 
performance remains mixed, in part because indicators of management quality are 
often correlated with each other and, therefore, difficult to isolate. However, poor 
stakeholder relations and inadequate management of long-  term risks have indeed had 
an enormous negative effect on share value in certain instances. Therefore, analysts 
may consider the assessment of such issues to be a useful component of their overall 
risk assessment of the company.
One way to approach management quality issues is to assess whether the company

demonstrates a persistent pattern of fines, accidents, regulatory penalties, investiga -
tions, and the like. A notable example was US coal mining company Massey Energy, 
which was penalized by environmental and worker-  safety agencies numerous times 
over multiple years for accidents, safety violations, and repeated breaches of regu -
lations. In 2010, an explosion at one of the company’s sites resulted in the deaths of 
29 workers and, ultimately, the sale of the company and criminal charges against its 
executives. Even in the absence of circumstances as extreme as these, poor manage -
ment of stakeholder interests can have a significant effect on company operations, 
reputation, and valuation.
8.7 Summary of Analyst Considerations
The analysis of corporate governance, stakeholder management, and other non-  
financial (often termed “extra-  financial”) considerations is inherently a subjective 
exercise. Governance practices that may raise the risk profile of one company may be

perfectly acceptable in a different context, depending on geographic norms, mitigating 
circumstances, or the investor’s risk tolerance and investment thesis. In this section, 
we have provided a basic framework for investors interested in uncovering incremental 
insights about a company by analyzing its governance standards, practices, and risks.
EXAMPLE 10   
Analyst Considerations
1 Which of the following best describes dual-  class share structures?
A Dual-  class share structures can be easily changed over time.
B Company insiders can maintain significant power over the 
organization.
C Conflicts of interest between management and stakeholder groups are 
less likely than with single share structures.
2 An investment analyst would likely be most  concerned with an executive 
remuneration plan that:
A varies each year.
B is consistent with a company’s competitors.
C is cash-  based only, without an equity component.
3 Which of the following best describes activist shareholders? Activist

Reading 33 ■ Corporate Governance and ESG: An Introduction 36
B have little effect on the company’s long-  term investors.
C can alter the composition of a company’s shareholder base.
B is correct. Under dual-  class share systems, company founders or insiders may 
control board elections, strategic decisions, and other significant voting matters. 
A is incorrect because dual share systems are virtually impossible to dismantle 
once adopted. C is incorrect because conflicts of interest between management 
and stakeholders are more likely than with single share structures because of 
the potential control element under dual systems.
C is correct. If an executive remuneration plan offers cash only, the incentives 
between management and investors and other stakeholders may be misaligned. 
A is incorrect because a plan that varies over time would typically be of less 
concern to an analyst compared with one that did not change. B is incorrect

because an analyst would likely be concerned if a company’s executives were 
excessively compensated relative to competitors.
C is correct. The presence of activist shareholders can create substantial turnover 
in the company’s shareholder composition. A is incorrect because the presence 
of activist shareholders can materially change a company’s strategic direction. 
B is incorrect because long-  term investors in a company need to consider how 
activist shareholders affect the company.
ESG CONSIDERATIONS FOR INVESTORS
The inclusion of governance factors in investment analysis has evolved considerably. 
Management and accountability structures are relatively transparent, and informa -
tion regarding them is widely available. Also, the risks of poor corporate governance 
have long been understood by analysts and shareholders. In contrast, the practice 
of considering environmental and social factors, which collectively with governance

form the commonly used acronym “ESG, ” has evolved more slowly. A large number of 
environmental and social issues exist, and identifying which factors are likely to affect 
company performance is not an easy task. Issues driving the inclusion of environmental 
and social information in the investment process include scarcity of natural resources, 
climate change, global economic and demographic trends, and societal evolution. 
Although ESG factors were once regarded as intangible or qualitative information, 
refinements in the identification and analysis of such factors, as well as increased 
corporate disclosures, have resulted in increasingly quantifiable information. Still, 
the process of reflecting quantitative ESG-  related information and data in financial 
valuation is evolving. 
9.1 ESG Terminology
Several ESG-  related terms exist, and distinguishing among them can be challenging 
because of the lack of definitive terminology in the investment community. Among the

most common—and broadest—terms are sustainable investing  (SI) and responsible 
investing  (RI). Both of these terms refer to identifying companies that, in an investor’s 
view, efficiently manage their financial, environmental, and human capital resources 9

ESG Considerations for Investors 37
to generate attractive long-  term profitability; that is, the companies are deemed to 
have “sustainable” business models. Sustainable investing and responsible investing, 
along with the term ESG investing , generally refer to the consideration of ESG factors 
in the investment process. 
Socially responsible investing  (SRI) is a related term that tends to have multiple 
meanings, creating confusion among investors. Socially responsible investing has tra -
ditionally referred to the practice of excluding investments in companies or industries, 
such as weapons and defense, that deviate from an investor’s beliefs. The term has 
evolved to include investment objectives that promote positive social attributes, often 
by investing in companies with favorable environmental or social profiles.
9.2 ESG Implementation Approaches
Implementation approaches to ESG range from value -based to values -based. The

objective of a value -based approach is to mitigate risks and identify opportunities by 
analyzing ESG considerations in addition to traditional financial metrics. Conversely, 
the objective of a values -based approach is to express the moral or ethical beliefs of 
an investor. Between the value-  based and values-  based approaches lie a continuum 
of approaches that strives for value creation through values investing.
Specific implementation approaches to ESG include negative screening (sometimes 
also referred to as exclusionary screening  or norms-  based screening ), positive 
screening, best-  in- class approach, ESG integration, thematic investing, and impact 
investing. Negative screening  refers to the practice of excluding certain sectors, such 
as companies engaged in fossil fuel extraction or production, or excluding companies 
that deviate from accepted standards in areas such as human rights or environmental

concerns. Many of these negative screens use specific standards, such as the UN Global 
Compact’s Ten Principles on human rights, labor, the environment, and corruption.
In contrast to negative screening, positive screening  or best-  in- class  approach 
focuses on investments with favorable ESG aspects. Positive screening, typically 
implemented through an ESG ranking or scoring approach, aims to identify companies 
that successfully manage ESG risks and may benefit from ESG-  related opportunities 
in their sector. For example, positive screening may include seeking companies that 
promote employee rights, workplace well-  being, and customer safety. The best-  in- class 
approach seeks to identify companies within each industry that rank (or score) most 
favorably based on ESG considerations. The best-  in- class approach does not exclude 
any industries but instead focuses on finding the best representation within each

sector. This approach typically maintains sector weightings comparable to a relative 
benchmark index to avoid overweighting or underweighting risk exposures.
ESG integration , or ESG incorporation , refers to the integration of qualitative and 
quantitative environmental, social, and governance factors into traditional security and 
industry analysis. The focus of ESG integration is to identify risks and opportunities 
arising from ESG factors and to determine whether a company is properly managing 
its environmental, social, and governance resources in accordance with a sustainable 
business model.
Thematic investing  focuses on investing in companies within a specific sector or 
following a specific theme, such as energy efficiency or climate change. This approach 
is often based on needs arising from economic or social trends. Two common ESG-  
related trends are increased demand for energy and water, as well as the availability

of alternative sources of each. Global economic development has raised the demand 
for energy, whereas increased carbon emissions are believed to negatively affect the 
earth’s climate. Similarly, rising global living standards and heightened industrial needs 
have created a greater demand for water along with the need to prevent drought or 
limited access to clean drinking water in certain regions of the world.

Reading 33 ■ Corporate Governance and ESG: An Introduction 38
Impact investing  seeks to achieve targeted social or environmental objectives 
along with measurable financial returns through engagement with a company or by 
direct investment in projects or companies. It has evolved through greater accep -
tance that positive social and environmental impact can be consistent with economic 
profit generation. Impact investing can be executed through various asset classes and 
investment vehicles, often through direct transactions, such as venture capital invest -
ing. Another example of impact investing relates to green finance . According to the 
Organisation for Economic Co-  operation and Development (OECD), green finance 
relates to “achieving economic growth while reducing pollution and greenhouse gas 
emissions, minimising waste and improving efficiency in the use of natural resources. ”5 
As with other previously mentioned ESG terms, there are several definitions for green

finance in practice. The primary investment vehicles used in green finance are green 
bonds , in which issuers earmark the proceeds towards environmental-  related projects. 
Green bond issuance has grown significantly in recent years. According to the Climate 
Bond Initiative, total worldwide green bond issuance for the first ten months of 2017 
totaled USD 95 billion, compared to USD 37 billion for all of 2014. 
9.3 Catalysts for ESG Growth
ESG considerations have become increasingly relevant over the past several years 
after many investors suffered substantial losses from environmental disasters, social 
controversies, or governance deficiencies. In one notable example, the 2010 explo -
sion of the Deepwater Horizon oil rig in the Gulf of Mexico caused a massive oil 
spill, resulting in loss of life, widespread destruction of marine and wildlife habitats, 
and economic damage to surrounding tourism destinations. As a result of BP plc’s

economic interest in the rig, the company incurred tens of billions of dollars in fines, 
remuneration claims, and clean-  up costs. 
In addition to environmental issues, investors have become increasingly conscious 
of workplace, human rights, and governance issues—and the costs associated with 
them. For example, Walmart lost a 2011 appeals court ruling on a US$187 million 
class action lawsuit over wage and hour discrimination. Over the years, Walmart 
has faced numerous employee strikes and lawsuits over labor and human rights 
violations and the company has paid a significant amount of money to settle claims 
and lawsuits. An example of investor loss related to corporate governance occurred 
in 2015 at German automaker Volkswagen. Specifically, many investors believed that 
inadequate governance oversight at Volkswagen permitted more than 11 million of 
its diesel cars to pass emissions tests yet emit unlawful amounts of nitrogen oxide.

Many investors attributed their losses to internal audit and compliance shortcomings, 
as well as a lack of independence in Volkswagen’s board of directors. The company 
ultimately incurred several billion dollars of civil and criminal penalties.
Another investor development that has supported ESG growth is the adoption 
of more sophisticated views about sustainable growth and its effect on investment 
performance. To this end, some large institutional asset owners embrace the con -
cept of being “universal owners. ” Universal owners  are long-  term investors, such as 
pension funds, that have significant assets invested in globally diversified portfolios. 
Given their size and scope, the investment portfolios of universal owners are linked 
to economic growth and unavoidably exposed to costs resulting from external factors, 
such as environmental damages. Because their funds’ long-  term performance and the

interests of their beneficiaries are at stake, some universal owners strive to positively 
5 http://www.oecd-  ilibrary.org/environment/green-  finance-  and-  investment_24090344

ESG Considerations for Investors 39
influence the way companies conduct business to minimize exposure to ESG-  related 
costs. Institutions that adhere to the universal owner philosophy believe that sus -
tainable global economic growth is essential to successful investment performance.
9.4 ESG Market Overview
Reflecting the growth of ESG-  related information in the marketplace, the amount 
of global assets under management (AUM) dedicated to the consideration of ESG 
factors in portfolio selection and management has increased substantially. According 
to the Global Sustainable Investing Alliance (GSIA), a collaboration of organizations 
dedicated to advancing sustainable investing in the financial markets, about US$23 tril -
lion of AUM were dedicated toward sustainable investment mandates as of year-  end 
2016. Europe (53%) and the United States (38%) accounted for the vast majority of 
these AUM. Determining the true size of the ESG investment universe is difficult,

however, because managers and investors define and implement ESG mandates in 
many different ways. There are often differences regarding which ESG factors should 
be considered—as well as how they are considered—in the investment process. 
The increased interest in sustainable investing has led to increased corporate 
disclosures of ESG issues, as well as a growing number of companies that collect and 
analyze ESG data. In addition to the GSIA, several organizations have been formed 
to monitor and advance the mission of sustainable investing. For example, the Global 
Reporting Initiative (GRI), a non-  profit organization formed in 1997, produces a 
sustainability reporting framework that measures and reports sustainability-  related 
issues and performance. In 2006, the United Nations and a consortium of institutional 
investors launched the Principles of Responsible Investment (PRI) to support investors 
committed to including ESG issues into their investment decision-  making and own -

ership practices. In 2011, the non-  profit Sustainability Accounting Standards Board 
(SASB) was formed to develop sustainability accounting standards for companies when 
disclosing material ESG information. In addition to these key organizations, several 
others exist that promote the advancement of sustainable investing. To help educate 
investors, CFA Institute published “Environmental, Social, and Governance Issues in 
Investing: A Guide for Investment Professionals” in November 2015.6
9.5 ESG Factors in Investment Analysis
The materiality of ESG factors in investment analysis, particularly environmental and 
social factors, often differ meaningfully among sectors. An ESG factor is considered to 
be material when it is believed to have an impact on a company’s long-  term business 
model. For example, environmental factors such as emissions and water usage will 
likely be significant for utilities or mining companies, yet are relatively inconsequential 
for financial institutions.

Overall, environmental factors that are generally considered material in invest -
ment analysis include natural resource management, pollution prevention, water 
conservation, energy efficiency and reduced emissions, the existence of carbon assets, 
and adherence to environmental safety and regulatory standards. A specific concern 
among investors of energy companies is also the existence of “stranded assets, ” i.e., 
carbon-  intensive assets that are at risk of no longer being economically viable because 
of changes in regulation or investor sentiment. Analysts may find it difficult to assess 
potentially significant financial risks of energy companies because of limited infor -
mation on the existence of these companies’ carbon assets, as well as the difficulty in 
determining political and regulatory risks. Material environmental effects can arise 
6 https://www.cfapubs.org/doi/pdf/10.2469/ccb.v2015.n11.1

Reading 33 ■ Corporate Governance and ESG: An Introduction 40
from strategic or operational decisions based on inadequate governance processes 
or errors in judgment. For example, oil spills, industrial waste contamination events, 
and local resource depletion can result from poor environmental standards, breaches 
in safety standards, or unsustainable business models. Such events can be costly in 
terms of regulatory fines, litigation, clean-  up costs, reputational risk, and resource 
Social factors considered in ESG implementation generally pertain to the man -
agement of the human capital of a business, including human rights and welfare 
concerns in the workplace; product development; and, in some cases, community 
impact. Staff turnover, worker training and safety, employee morale, ethics policies, 
employee diversity, and supply chain management can all affect a company’s ability 
to sustain its competitive advantage. In addition, minimizing social risks can lower a

company’s costs (e.g., through higher employee productivity, lower employee turnover, 
and reduced litigation potential) and reduce its reputational risk.
As mentioned earlier, governance factors have long been recognized in investment 
analysis. Many performance indicators can help evaluate risks arising from gover -
nance issues such as ownership structure, board independence and composition, and 
compensation. Although several governance factors may apply across industries and 
geographic regions, other factors are unique (such as systemic risk management for 
financial services companies).
One area of debate is whether the consideration of ESG factors is consistent with 
fiduciary duty—particularly when overseeing and managing pension fund assets. 
Pension fund regulation regarding ESG considerations varies globally. In the United 
States, the Employee Retirement Income Security Act of 1974 (ERISA) sets the stan -

dards for the protection of private pension plan beneficiaries. A fiduciary must act 
solely in the interest of pension plan participants and beneficiaries. Accepting lower 
returns or assuming greater risk in a private pension plan to promote environmen -
tal, social, or public policy causes would violate fiduciary duty and is prohibited by 
ERISA. However, in October 2015, the US Department of Labor (DOL) determined 
that certain ESG-  related investment considerations do not violate ERISA or fiduciary 
duty. These considerations include the addition of ESG factors in investment policy 
statements; the integration of ESG factors in the evaluation of an investment’s risk or 
return; and using ESG considerations as determining factors when choosing among 
investments that are otherwise financially or economically equivalent. 
EXAMPLE 11   
ESG Implementation Methods
The ESG implementation method that is most  associated with excluding certain 
sectors or companies is:
A best-  in- class.

B thematic investing.
C negative screening.
Solution:
C is correct. Negative screening entails excluding certain companies or sectors, 
such as fossil fuel extraction, from a portfolio. B is incorrect because thematic 
investing typically focuses on investing in companies within a specific sector 
or following a specific theme, such as energy efficiency or climate change, as

Summary 41
opposed to merely excluding a set of companies or industries from a portfolio. 
Likewise, A is incorrect because best-  in- class focuses on companies that rank 
(or score) most favorably with regard to ESG factors.
SUMMARY
The investment community has increasingly recognized the importance of corporate 
governance, as well as environmental and social considerations. Although practices 
concerning corporate governance (and ESG overall) will undoubtedly continue to 
evolve, investment analysts who have a good understanding of these concepts can 
better appreciate the implications of ESG considerations in investment decision 
making. The core concepts covered in this reading are as follows:
■■Corporate governance can be defined as a system of controls and procedures by 
which individual companies are managed.
■■There are many systems of corporate governance, most reflecting the influences 
of either shareholder theory or stakeholder theory, or both. Current trends,

however, point to increasing convergence.
■■A corporation’s governance system is influenced by several stakeholder groups, 
and the interests of the groups often diverge or conflict.
■■The primary stakeholder groups of a corporation consist of shareholders, credi -
tors, managers and employees, the board of directors, customers, suppliers, and 
government/regulators.
■■A principal–agent relationship (or agency relationship) entails a principal hiring 
an agent to perform a particular task or service. In a corporate structure, such 
relationships often lead to conflicts among various stakeholders.
■■Stakeholder management involves identifying, prioritizing, and understanding 
the interests of stakeholder groups and on that basis managing the company’s 
relationships with stakeholders. The framework of corporate governance and 
stakeholder management reflects a legal, contractual, organizational, and gov -
ernmental infrastructure.

■■Mechanisms of stakeholder management may include general meetings, a board 
of directors, the audit function, company reporting and transparency, related-  
party transactions, remuneration policies (including say on pay), and other 
mechanisms to manage the company’s relationship with its creditors, employ -
ees, customers, suppliers, and regulators.
■■A board of directors is the central pillar of the governance structure, serves 
as the link between shareholders and managers, and acts as the shareholders’ 
internal monitoring tool within the company.
■■The structure and composition of a board of directors vary across countries and 
companies. The number of directors may vary, and the board typically includes 
a mix of expertise levels, backgrounds, and competencies.
■■Executive (internal) directors are employed by the company and are typically 
members of senior management. Non-  executive (external) directors have lim -

ited involvement in daily operations but serve an important oversight role.
■■Two primary duties of a board of directors are duty of care and duty of loyalty.

Reading 33 ■ Corporate Governance and ESG: An Introduction 42
■■A company’s board of directors typically has several committees that are 
responsible for specific functions and report to the board. Although the types 
of committees may vary across organization, the most common are the audit 
committee, governance committee, remuneration (compensation) committee, 
nomination committee, risk committee, and investment committee.
■■Stakeholder relationships and corporate governance are continually shaped and 
influenced by a variety of market and non-  market factors.
■■Shareholder engagement by a company can provide benefits that include 
building support against short-  term activist investors, countering negative 
recommendations from proxy advisory firms, and receiving greater support for 
management’s position.
■■Shareholder activism encompasses a range of strategies that may be used by 
shareholders when seeking to compel a company to act in a desired manner.

■■From a corporation’s perspective, risks of poor governance include weak control 
systems; ineffective decision making; and legal, regulatory, reputational, and 
default risk. Benefits include better operational efficiency, control, and operat -
ing and financial performance, as well as lower default risk (or cost of debt).
■■Key analyst considerations in corporate governance and stakeholder man -
agement include economic ownership and voting control, board of directors 
representation, remuneration and company performance, investor composition, 
strength of shareholders’ rights, and the management of long-  term risks.
■■Several terms—sometimes interchangeable—and investment approaches have 
evolved in relation to ESG: sustainable investing; responsible investing; ESG 
investing; and socially responsible investing.
■■Negative screening is an approach to ESG implementation that excludes certain 
companies or sectors from investment consideration because of their under -

lying business activities or other environmental or social concerns. Positive 
screening and best-  in- class strategies focus on investments with favorable ESG 
aspects. Thematic investing focuses on investing in companies within a specific 
sector or industry theme, such as energy efficiency or climate change. Impact 
investing seeks to achieve targeted social or environmental objectives along 
with measurable financial returns.
■■ESG integration (or ESG incorporation) integrates qualitative and quantitative 
environmental, social, and governance factors into traditional security and 
industry analysis.

Practice Problems 43
1 Corporate governance:
A complies with a set of global standards.
B is independent of both shareholder theory and stakeholder theory.
C seeks to minimize and manage conflicting interests between insiders and 
external shareholders.
2 Which group of company stakeholders would be least affected if the firm’s 
financial position weakens?
A Suppliers
C Managers and employees
3 Which of the following represents a principal–agent conflict between share -
holders and management?
A Risk tolerance
B Multiple share classes
C Accounting and reporting practices
4 Which of the following issues discussed at a shareholders’ general meeting 
would most likely  require only a simple majority vote for approval?
A Voting on a merger
B Election of directors
C Amendments to bylaws
5 Which of the following statements regarding stakeholder management is most  
accurate?
A Company management ensures compliance with all applicable laws and 
regulations.

B Directors are excluded from voting on transactions in which they hold 
material interest.
C The use of variable incentive plans in executive remuneration is decreasing.
6 Which of the following represents a responsibility of a company’s board of 
directors?
A Implementation of strategy
B Enterprise risk management
C Considering the interests of shareholders only
7 Which of the following statements about non-  market factors in corporate gov -
ernance  is most  accurate?
A Stakeholders can spread information quickly and shape public opinion.
B A civil law system offers better protection of shareholder interests than does 
a common law system.
C Vendors providing corporate governance services have limited influence on 
corporate governance practices.
8 Which of the following statements regarding corporate shareholders is most  
accurate?
A Cross-  shareholdings help promote corporate mergers.

Reading 33 ■ Corporate Governance and ESG: An Introduction 44
B Dual-  class structures are used to align economic ownership with control.
C Affiliated shareholders can protect a company against hostile takeover bids.
9 Which of the following statements about environmental, social, and governance 
(ESG) in investment analysis is correct?
A ESG factors are strictly intangible in nature.
B ESG terminology is easily distinguishable among investors.
C Environmental and social factors have been adopted in investment analysis 
more slowly than governance factors.
10 Which of the following statements regarding ESG implementation methods is 
most accurate ?
A Negative screening is the most commonly applied method.
B Thematic investing considers multiple factors.
C The best-  in- class strategy excludes industries with unfavorable ESG aspects.

Solutions 45
SOLUTIONS
1 C is correct. Corporate governance is the arrangement of checks, balances, and 
incentives a company needs to minimize and manage the conflicting interests 
between insiders and external shareholders.
2 B is correct. Compared with other stakeholder groups, customers tend to be 
less concerned with, and affected by, a company’s financial performance.
3 A is correct. Shareholder and manager interests can diverge with respect to risk 
tolerance. In some cases, shareholders with diversified investment portfolios 
can have a fairly high risk tolerance because specific company risk can be diver -
sified away. Managers are typically more risk averse in their corporate decision 
making to better protect their employment status.
4 B is correct. The election of directors is considered an ordinary resolution and, 
therefore, requires only a simple majority of votes to be passed.
5 B is correct. Often, policies on related-  party transactions require that such

transactions or matters be voted on by the board (or shareholders), excluding 
the director holding the interest.
6 B is correct. The board typically ensures that the company has an appropriate 
enterprise risk management system in place.
7 A is correct. Social media has become a powerful tool for stakeholders to 
instantly broadcast information with little cost or effort and to compete with 
8 C is correct. The presence of a sizable affiliated stockholder (such as an indi -
vidual, family trust, endowment, or private equity fund) can shield a company 
from the effects of voting by outside shareholders.
9 C is correct. The risks of poor corporate governance have long been understood 
by analysts and shareholders. In contrast, the practice of considering environ -
mental and social factors has been slower to take hold.
10 A is correct. Negative screening, which refers to the practice of excluding

certain sectors or companies that violate accepted standards in such areas as 
human rights or environmental concerns, is the most common ESG investment 
strategy (implementation method).

Capital Budgeting
by John D. Stowe, PhD, CFA, and Jacques R. Gagné, FSA, CFA, CIPM
John D. Stowe, PhD, CFA, is at Ohio University (USA). Jacques R. Gagné, FSA, CFA, CIPM, 
is at ENAP (Canada).
a. describe the capital budgeting process and distinguish among the 
various categories of capital projects;
b. describe the basic principles of capital budgeting;
c. explain how the evaluation and selection of capital projects is 
affected by mutually exclusive projects, project sequencing, and 
capital rationing;
d. calculate and interpret net present value (NPV), internal rate of 
return (IRR), payback period, discounted payback period, and 
profitability index (PI) of a single capital project;
e. explain the NPV profile, compare the NPV and IRR methods 
when evaluating independent and mutually exclusive projects, 
and describe the problems associated with each of the evaluation 
methods;

methods;
f. describe expected relations among an investment’s NPV, company 
value, and share price.
Capital budgeting is the process that companies use for decision making on capital 
projects—those projects with a life of a year or more. This is a fundamental area of 
knowledge for financial analysts for many reasons.
■■First, capital budgeting is very important for corporations. Capital projects, 
which make up the long-  term asset portion of the balance sheet, can be so large 
that sound capital budgeting decisions ultimately decide the future of many 
corporations. Capital decisions cannot be reversed at a low cost, so mistakes are 1rEADING
34
© 2007 CFA Institute. All rights reserved.

Reading 34 ■ Capital Budgeting 48
very costly. Indeed, the real capital investments of a company describe a com -
pany better than its working capital or capital structures, which are intangible 
and tend to be similar for many corporations.
■■Second, the principles of capital budgeting have been adapted for many other 
corporate decisions, such as investments in working capital, leasing, mergers 
and acquisitions, and bond refunding.
■■Third, the valuation principles used in capital budgeting are similar to the 
valuation principles used in security analysis and portfolio management. Many 
of the methods used by security analysts and portfolio managers are based on 
capital budgeting methods. Conversely, there have been innovations in secu -
rity analysis and portfolio management that have also been adapted to capital 
budgeting.
■■Finally, although analysts have a vantage point outside the company, their inter -
est in valuation coincides with the capital budgeting focus of maximizing share -

holder value. Because capital budgeting information is not ordinarily available 
outside the company, the analyst may attempt to estimate the process, within 
reason, at least for companies that are not too complex. Further, analysts may 
be able to appraise the quality of the company’s capital budgeting process—for 
example, on the basis of whether the company has an accounting focus or an 
economic focus.
This reading is organized as follows: Section 2 presents the steps in a typical 
capital budgeting process. After introducing the basic principles of capital budgeting 
in Section 3, in Section 4 we discuss the criteria by which a decision to invest in a 
project may be made.
THE CAPITAL BUDGETING PROCESS
The specific capital budgeting procedures that a manager uses depend on the manag -
er’s level in the organization, the size and complexity of the project being evaluated, 
and the size of the organization. The typical steps in the capital budgeting process 

■■Step One: Generating Ideas—Investment ideas can come from anywhere, from 
the top or the bottom of the organization, from any department or functional 
area, or from outside the company. Generating good investment ideas to con -
sider is the most important step in the process.
■■Step Two: Analyzing Individual Proposals—This step involves gathering the 
information to forecast cash flows for each project and then evaluating the 
project’s profitability.
■■Step Three: Planning the Capital Budget—The company must organize the 
profitable proposals into a coordinated whole that fits within the company’s 
overall strategies, and it also must consider the projects’ timing. Some projects 
that look good when considered in isolation may be undesirable strategically. 
Because of financial and real resource issues, the scheduling and prioritizing of 
projects is important.
■■Step Four: Monitoring and Post-  auditing—In a post-  audit, actual results

are compared to planned or predicted results, and any differences must be 
explained. For example, how do the revenues, expenses, and cash flows realized 
from an investment compare to the predictions? Post-  auditing capital proj -
ects is important for several reasons. First, it helps monitor the forecasts and 2

The Capital Budgeting Process 49
analysis that underlie the capital budgeting process. Systematic errors, such as 
overly optimistic forecasts, become apparent. Second, it helps improve business 
operations. If sales or costs are out of line, it will focus attention on bringing 
performance closer to expectations if at all possible. Finally, monitoring and 
post-  auditing recent capital investments will produce concrete ideas for future 
investments. Managers can decide to invest more heavily in profitable areas and 
scale down or cancel investments in areas that are disappointing.
Planning for capital investments can be very complex, often involving many persons 
inside and outside of the company. Information about marketing, science, engineering, 
regulation, taxation, finance, production, and behavioral issues must be systematically 
gathered and evaluated. The authority to make capital decisions depends on the size

and complexity of the project. Lower-  level managers may have discretion to make 
decisions that involve less than a given amount of money, or that do not exceed a given 
capital budget. Larger and more complex decisions are reserved for top management, 
and some are so significant that the company’s board of directors ultimately has the 
decision-  making authority.
Like everything else, capital budgeting is a cost–benefit exercise. At the margin, 
the benefits from the improved decision making should exceed the costs of the capital 
budgeting efforts.
Companies often put capital budgeting projects into some rough categories for 
analysis. One such classification would be as follows:
1 Replacement projects. These are among the easier capital budgeting decisions. 
If a piece of equipment breaks down or wears out, whether to replace it may not 
require careful analysis. If the expenditure is modest and if not investing has

significant implications for production, operations, or sales, it would be a waste 
of resources to overanalyze the decision. Just make the replacement. Other 
replacement decisions involve replacing existing equipment with newer, more 
efficient equipment, or perhaps choosing one type of equipment over another. 
These replacement decisions are often amenable to very detailed analysis, and 
you might have a lot of confidence in the final decision.
2 Expansion projects. Instead of merely maintaining a company’s existing busi -
ness activities, expansion projects increase the size of the business. These 
expansion decisions may involve more uncertainties than replacement deci -
sions, and these decisions will be more carefully considered.
3 New products and services. These investments expose the company to even 
more uncertainties than expansion projects. These decisions are more complex 
and will involve more people in the decision-  making process.

4 Regulatory, safety, and environmental projects. These projects are frequently 
required by a governmental agency, an insurance company, or some other 
external party. They may generate no revenue and might not be undertaken by a 
company maximizing its own private interests. Often, the company will accept 
the required investment and continue to operate. Occasionally, however, the 
cost of the regulatory/safety/environmental project is sufficiently high that the 
company would do better to cease operating altogether or to shut down any 
part of the business that is related to the project.
5 Other. The projects above are all susceptible to capital budgeting analysis, and 
they can be accepted or rejected using the net present value (NPV) or some 
other criterion. Some projects escape such analysis. These are either pet proj -
ects of someone in the company (such as the CEO buying a new aircraft) or 
so risky that they are difficult to analyze by the usual methods (such as some

Reading 34 ■ Capital Budgeting 50
BASIC PRINCIPLES OF CAPITAL BUDGETING
Capital budgeting has a rich history and sometimes employs some pretty sophisticated 
procedures. Fortunately, capital budgeting relies on just a few basic principles. Capital 
budgeting usually uses the following assumptions:
1 Decisions are based on cash flows. The decisions are not based on accounting 
concepts, such as net income. Furthermore, intangible costs and benefits are 
often ignored because, if they are real, they should result in cash flows at some 
other time.
2 Timing of cash flows is crucial. Analysts make an extraordinary effort to detail 
precisely when cash flows occur.
3 Cash flows are based on opportunity costs. What are the incremental cash flows 
that occur with an investment compared to what they would have been without 
the investment?
4 Cash flows are analyzed on an after-  tax basis. Taxes must be fully reflected in 
all capital budgeting decisions.

5 Financing costs are ignored. This may seem unrealistic, but it is not. Most of 
the time, analysts want to know the after-  tax operating cash flows that result 
from a capital investment. Then, these after-  tax cash flows and the investment 
outlays are discounted at the “required rate of return” to find the net present 
value (NPV). Financing costs are reflected in the required rate of return. If we 
included financing costs in the cash flows and in the discount rate, we would be 
double-  counting the financing costs. So even though a project may be financed 
with some combination of debt and equity, we ignore these costs, focusing on 
the operating cash flows and capturing the costs of debt (and other capital) in 
the discount rate.
6 Capital budgeting cash flows are not accounting net income. Accounting 
net income is reduced by noncash charges such as accounting depreciation. 
Furthermore, to reflect the cost of debt financing, interest expenses are also

subtracted from accounting net income. (No subtraction is made for the cost of 
equity financing in arriving at accounting net income.) Accounting net income 
also differs from economic income, which is the cash inflow plus the change in 
the market value of the company. Economic income does not subtract the cost 
of debt  financing, and it is based on the changes in the market value of the 
company, not changes in its book value (accounting depreciation). 
In assumption 5 above, we referred to the rate used in discounting the cash flows 
as the “required rate of return. ” The required rate of return is the discount rate that 
investors should require given the riskiness of the project. This discount rate is fre -
quently called the “opportunity cost of funds” or the “cost of capital. ” If the company 
can invest elsewhere and earn a return of r, or if the company can repay its sources 
of capital and save a cost of r, then r is the company’s opportunity cost of funds. If

the company cannot earn more than its opportunity cost of funds on an investment, 
it should not undertake that investment. Unless an investment earns more than the 
cost of funds from its suppliers of capital, the investment should not be undertaken. 
The cost-  of- capital concept is discussed more extensively elsewhere. Regardless of 
what it is called, an economically sound discount rate is essential for making capital 
budgeting decisions.3

Basic Principles of Capital Budgeting 51
Although the principles of capital budgeting are simple, they are easily confused in 
practice, leading to unfortunate decisions. Some important capital budgeting concepts 
that managers find very useful are given below.
■■A sunk cost  is one that has already been incurred. You cannot change a sunk 
cost. Today’s decisions, on the other hand, should be based on current and 
future cash flows and should not be affected by prior, or sunk, costs.
■■An opportunity cost  is what a resource is worth in its next-  best use. For 
example, if a company uses some idle property, what should it record as the 
investment outlay: the purchase price several years ago, the current market 
value, or nothing? If you replace an old machine with a new one, what is the 
opportunity cost? If you invest $10 million, what is the opportunity cost? The 
answers to these three questions are, respectively: the current market value, the

cash flows the old machine would generate, and $10 million (which you could 
invest elsewhere).
■■An incremental cash flow  is the cash flow that is realized because of a deci -
sion: the cash flow with  a decision minus the cash flow without  that decision. If 
opportunity costs are correctly assessed, the incremental cash flows provide a 
sound basis for capital budgeting.
■■An externality  is the effect of an investment on other things besides the invest -
ment itself. Frequently, an investment affects the cash flows of other parts of the 
company, and these externalities can be positive or negative. If possible, these 
should be part of the investment decision. Sometimes externalities occur out -
side of the company. An investment might benefit (or harm) other companies 
or society at large, and yet the company is not compensated for these benefits 
(or charged for the costs). Cannibalization  is one externality. Cannibalization

occurs when an investment takes customers and sales away from another part 
of the company.
■■Conventional cash flows  versus nonconventional cash flows —A conventional 
cash flow pattern is one with an initial outflow followed by a series of inflows. 
In a nonconventional cash flow pattern, the initial outflow is not followed by 
inflows only, but the cash flows can flip from positive to negative again (or even 
change signs several times). An investment that involved outlays (negative cash 
flows) for the first couple of years that were then followed by positive cash flows 
would be considered to have a conventional pattern. If cash flows change signs 
once, the pattern is conventional. If cash flows change signs two or more times, 
the pattern is nonconventional.
Several types of project interactions make the incremental cash flow analysis 
challenging. The following are some of these interactions:
■■Independent projects  versus mutually exclusive projects —Independent

projects are projects whose cash flows are independent of each other. Mutually 
exclusive projects compete directly with each other. For example, if Projects A 
and B are mutually exclusive, you can choose A or B, but you cannot choose 
both. Sometimes there are several mutually exclusive projects, and you can 
choose only one from the group.
■■Project sequencing —Many projects are sequenced through time, so that 
investing in a project creates the option to invest in future projects. For exam -
ple, you might invest in a project today and then in one year invest in a second

Reading 34 ■ Capital Budgeting 52
project if the financial results of the first project or new economic conditions 
are favorable. If the results of the first project or new economic conditions are 
not favorable, you do not invest in the second project.
■■Unlimited funds  versus capital rationing —An unlimited funds environment 
assumes that the company can raise the funds it wants for all profitable proj -
ects simply by paying the required rate of return. Capital rationing exists when 
the company has a fixed amount of funds to invest. If the company has more 
profitable projects than it has funds for, it must allocate the funds to achieve the 
maximum shareholder value subject to the funding constraints.
INVESTMENT DECISION CRITERIA
Analysts use several important criteria to evaluate capital investments. The two most 
comprehensive measures of whether a project is profitable or unprofitable are the 
net present value (NPV) and internal rate of return (IRR). In addition to these, we

present four other criteria that are frequently used: the payback period, discounted 
payback period, average accounting rate of return (AAR), and profitability index (PI). 
An analyst must fully understand the economic logic behind each of these investment 
decision criteria as well as its strengths and limitations in practice.
4.1 Net Present Value
For a project with one investment outlay, made initially, the net present value (NPV) 
is the present value of the future after-  tax cash flows minus the investment outlay, or
NPVCFOutlay =
+()−
=∑t
t
tn
r11
where
 CFt = after-  tax cash flow at time t
 r = required rate of return for the investment
 Outlay = investment cash flow at time zero
To illustrate the net present value criterion, we will take a look at a simple example. 
Assume that Gerhardt Corporation is considering an investment of €50 million in a 
capital project that will return after-  tax cash flows of €16 million per year for the next

four years plus another €20 million in Year 5. The required rate of return is 10 percent.
For the Gerhardt example, the NPV would be1
NPV
NPV=+ ++ +−
=+16
11016
11016
11016
11020
11050
14 545 11 2345.. .. .
.3 3 223 12 021 10 928 12 418 50
63 136 50 13 136.. ..
.¬ .+ ++−
=− = NPV milli on n.4
(1)
1 Occasionally, you will notice some rounding errors in our examples. In this case, the present values of 
the cash flows, as rounded, add up to €63.135. Without rounding, they add up to €63.13627, or €63.136. We 
will usually report the more accurate result, the one that you would get from your calculator or computer 
without rounding intermediate results.

Investment Decision Criteria 53
The investment has a total value, or present value of future cash flows, of 
€63.136 million. Since this investment can be acquired at a cost of €50 million, the 
investing company is giving up €50 million of its wealth in exchange for an investment 
worth €63.136 million. The investor’s wealth increases by a net of €13.136 million.
Because the NPV is the amount by which the investor’s wealth increases as a result 
of the investment, the decision rule for the NPV is as follows:
Invest if NPV > 0
Do not invest if NPV < 0
Positive NPV investments are wealth-  increasing, whereas negative NPV invest -
ments are wealth-  decreasing.
Many investments have cash flow patterns in which outflows may occur not only 
at time zero, but also at future dates. It is useful to consider the NPV to be the present 
value of all cash flows:
NPVC FCF CF CF, or
NPVCF01=+
+()+
+()++
+()
=
+()=11 1
112
2rr r
rn
n
t
t
t
0 0n
∑

NPVCF01=+
+()+
+()++
+()
=
+()=11 1
112
2rr r
rn
n
t
t
t
0 0n
∑
In Equation 2, the investment outlay, CF0, is simply a negative cash flow. Future 
cash flows can also be negative.
4.2 Internal Rate of Return
The internal rate of return (IRR) is one of the most frequently used concepts in capital 
budgeting and in security analysis. The IRR definition is one that all analysts know by 
heart. For a project with one investment outlay, made initially, the IRR is the discount 
rate that makes the present value of the future after-  tax cash flows equal that invest -
ment outlay. Written out in equation form, the IRR solves this equation:
CF
IRROutlayt
t
tn
11+()=
=∑
where IRR is the internal rate of return. The left-  hand side of this equation is the 
present value of the project’s future cash flows, which, discounted at the IRR, equals 
the investment outlay. This equation will also be seen rearranged as
CF
IRROutlay 0t
t
tn
11+()−=
=∑
In this form, Equation 3 looks like the NPV equation, Equation 1, except that the

discount rate is the IRR instead of r (the required rate of return). Discounted at the 
IRR, the NPV is equal to zero.
In the Gerhardt Corporation example, we want to find a discount rate that makes 
the total present value of all cash flows, the NPV, equal zero. In equation form, the 
IRR is the discount rate that solves this equation:
−+
+()+
+()+
+()+
+()+
+()5016
116
116
116
120
11 2345IRRI RR IRRI RR IRR= =0
Algebraically, this equation would be very difficult to solve. We normally resort to 
trial and error, systematically choosing various discount rates until we find one, the 
IRR, that satisfies the equation. We previously discounted these cash flows at 10 per -
cent and found the NPV to be €13.136 million. Since the NPV is positive, the IRR is (2)
(3)

Reading 34 ■ Capital Budgeting 54
probably greater than 10 percent. If we use 20 percent as the discount rate, the NPV 
is −€0.543 million, so 20 percent is a little high. One might try several other discount 
rates until the NPV is equal to zero; this approach is illustrated in Table 1.
Table 1   Trial and Error Process for Finding IRR
Discount Rate (%) NPV
10 13.136
20 −0.543
19 0.598
19.5 0.022
19.51 0.011
19.52 0.000
The IRR is 19.52 percent. Financial calculators and spreadsheet software have routines 
that calculate the IRR for us, so we do not have to go through this trial and error 
procedure ourselves. The IRR, computed more precisely, is 19.5197 percent.
The decision rule for the IRR is to invest if the IRR exceeds the required rate of 
return for a project:
Invest if IRR > r
Do not invest if IRR < r
In the Gerhardt example, since the IRR of 19.52 percent exceeds the project’s required 
rate of return of 10 percent, Gerhardt should invest.

Many investments have cash flow patterns in which the outlays occur at time zero 
and at future dates. Thus, it is common to define the IRR as the discount rate that 
makes the present values of all cash flows sum to zero:
CF
IRRt
t
tn
10
0+()=
=∑
Equation 4 is a more general version of Equation 3.
4.3 Payback Period
The payback period is the number of years required to recover the original investment 
in a project. The payback is based on cash flows. For example, if you invest $10 million 
in a project, how long will it be until you recover the full original investment? Table 2 
below illustrates the calculation of the payback period by following an investment’s 
cash flows and cumulative cash flows.
Table 2   Payback Period Example
Y ear 0 1 2 3 4 5
Cash flow −10,000 2,500 2,500 3,000 3,000 3,000
Cumulative 
cash flow−10,000 −7,500 −5,000 −2,000 1,000 4,000(4)

Investment Decision Criteria 55
In the first year, the company recovers 2,500 of the original investment, with 7,500 still 
unrecovered. You can see that the company recoups its original investment between 
Year 3 and Year 4. After three years, 2,000 is still unrecovered. Since the Year 4 cash 
flow is 3,000, it would take two-  thirds of the Year 4 cash flow to bring the cumulative 
cash flow to zero. So, the payback period is three years plus two-  thirds of the Year 4 
cash flow, or 3.67 years.
The drawbacks of the payback period are transparent. Since the cash flows are not 
discounted at the project’s required rate of return, the payback period ignores the time 
value of money and the risk of the project. Additionally, the payback period ignores 
cash flows after the payback period is reached. In the table above, for example, the 
Year 5 cash flow is completely ignored in the payback computation!
Example 1 is designed to illustrate some of the implications of these drawbacks

of the payback period.
EXAMPLE 1   
Drawbacks of the Payback Period
The cash flows, payback periods, and NPVs for Projects A through F are given 
in Table 3. For all of the projects, the required rate of return is 10 percent.
Table 3   Examples of Drawbacks of the Payback Period
Cash Flows
Y earProject  
AProject  
BProject  
CProject  
DProject  
EProject  
F
0 −1,000 −1,000 −1,000 −1,000 −1,000 −1,000
1 1,000 100 400 500 400 500
2 200 300 500 400 500
3 300 200 500 400 10,000
4 400 100 400
5 500 500 400
Payback 
period 1.0 4.0 4.0 2.0 2.5 2.0
NPV −90.91 65.26 140.60 243.43 516.31 7,380.92
Comment on why the payback period provides misleading information 
about the following:
1 Project A.
2 Project B versus Project C.
3 Project D versus Project E.
4 Project D versus Project F.
Project A does indeed pay itself back in one year. However, this result is mis -
leading because the investment is unprofitable, with a negative NPV.

Reading 34 ■ Capital Budgeting 56
Although Projects B and C have the same payback period and the same cash 
flow after the payback period, the payback period does not detect the fact that 
Project C’s cash flows within the payback period occur earlier and result in a 
higher NPV.
Projects D and E illustrate a common situation. The project with the shorter 
payback period is the less profitable project. Project E has a longer payback and 
Solution to 4: 
Projects D and F illustrate an important flaw of the payback period—that the 
payback period ignores cash flows after the payback period is reached. In this 
case, Project F has a much larger cash flow in Year 3, but the payback period 
does not recognize its value.
The payback period has many drawbacks—it is a measure of payback and not a 
measure of profitability. By itself, the payback period would be a dangerous criterion

for evaluating capital projects. Its simplicity, however, is an advantage. The payback 
period is very easy to calculate and to explain. The payback period may also be used 
as an indicator of project liquidity. A project with a two-  year payback may be more 
liquid than another project with a longer payback.
Because it is not economically sound, the payback period has no decision rule like 
that of the NPV or IRR. If the payback period is being used (perhaps as a measure of 
liquidity), analysts should also use an NPV or IRR to ensure that their decisions also 
reflect the profitability of the projects being considered.
4.4 Discounted Payback Period
The discounted payback period is the number of years it takes for the cumulative 
discounted cash flows from a project to equal the original investment. The discounted 
payback period partially addresses the weaknesses of the payback period. Table 4 gives 
an example of calculating the payback period and discounted payback period. The

example assumes a discount rate of 10 percent.
Table 4   Payback Period and Discounted Payback Period
Cash flow (CF) −5,000 1,500.00 1,500.00 1,500.00 1,500.00 1,500.00
Cumulative CF −5,000 −3,500.00 −2,000.00 −500.00 1,000.00 2,500.00
Discounted CF −5,000 1,363.64 1,239.67 1,126.97 1,024.52 931.38
Cumulative discounted CF −5,000 −3,636.36 −2,396.69 −1,269.72 −245.20 686.18
The payback period is three years plus 500/1,500 = 1/3 of the fourth year’s cash flow, 
or 3.33 years. The discounted payback period is between four and five years. The 
discounted payback period is four years plus 245.20/931.38 = 0.26 of the fifth year’s 
discounted cash flow, or 4.26 years.

Investment Decision Criteria 57
The discounted payback period relies on discounted cash flows, much as the NPV 
criterion does. If a project has a negative NPV, it will usually not have a discounted 
payback period since it never recovers the initial investment.
The discounted payback does account for the time value of money and risk within 
the discounted payback period, but it ignores cash flows after the discounted payback 
period is reached. This drawback has two consequences. First, the discounted payback 
period is not a good measure of profitability because it ignores these cash flows. Second, 
another idiosyncrasy of the discounted payback period comes from the possibility of 
negative cash flows after the discounted payback period is reached. It is possible for a 
project to have a negative NPV but to have a positive cumulative discounted cash flow 
in the middle of its life and, thus, a reasonable discounted payback period. The NPV

and IRR, which consider all of a project’s cash flows, do not suffer from this problem.
4.5 Average Accounting Rate of Return
The average accounting rate of return (AAR) can be defined as
AARAverage net income
Average book value=
To understand this measure of return, we will use a numerical example.
Assume a company invests $200,000 in a project that is depreciated straight-  line 
over a five-  year life to a zero salvage value. Sales revenues and cash operating expenses 
for each year are as shown in Table 5. The table also shows the annual income taxes 
(at a 40 percent tax rate) and the net income.
Table 5   Net Income for Calculating an Average Accounting Rate of Return
Y ear 1 Y ear 2 Y ear 3 Y ear 4 Y ear 5
Sales $100,000 $150,000 $240,000 $130,000 $80,000
Cash expenses 50,000 70,000 120,000 60,000 50,000
Depreciation 40,000 40,000 40,000 40,000 40,000
Earnings before taxes 10,000 40,000 80,000 30,000 −10,000
Taxes (at 40 percent) 4,000 16,000 32,000 12,000 −4,000a

Net income 6,000 24,000 48,000 18,000 −6,000
a Negative taxes occur in Year 5 because the earnings before taxes of −$10,000 can be deducted against earnings on other projects, thus 
reducing the tax bill by $4,000.
For the five-  year period, the average net income is $18,000. The initial book value 
is $200,000, declining by $40,000 per year until the final book value is $0. The average 
book value for this asset is ($200,000 − $0) / 2 = $100,000. The average accounting 
rate of return is
Average book value= = =18 000
100 00018,
,%
The advantages of the AAR are that it is easy to understand and easy to calculate. 
The AAR has some important disadvantages, however. Unlike the other capital bud -
geting criteria discussed here, the AAR is based on accounting numbers and not based 
on cash flows. This is an important conceptual and practical limitation. The AAR also 
does not account for the time value of money, and there is no conceptually sound

cutoff for the AAR that distinguishes between profitable and unprofitable investments. 
The AAR is frequently calculated in different ways, so the analyst should verify the

Reading 34 ■ Capital Budgeting 58
formula behind any AAR numbers that are supplied by someone else. Analysts should 
know the AAR and its potential limitations in practice, but they should rely on more 
economically sound methods like the NPV and IRR.
4.6 Profitability Index
The profitability index (PI) is the present value of a project’s future cash flows divided 
by the initial investment. It can be expressed as
PIPV of  future cash f lows
Initial investment1NPV
Initial == +iinvestment
You can see that the PI is closely related to the NPV. The PI is the ratio  of the PV of 
future cash flows to the initial investment, whereas an NPV is the difference  between 
the PV of future cash flows and the initial investment. Whenever the NPV is positive, 
the PI will be greater than 1.0; conversely, whenever the NPV is negative, the PI will 
be less than 1.0. The investment decision rule for the PI is as follows:
Invest if PI > 1.0
Do not invest if PI < 1.0

Because the PV of future cash flows equals the initial investment plus the NPV, the 
PI can also be expressed as 1.0 plus the ratio of the NPV to the initial investment, as 
shown in Equation 5 above. Example 2 illustrates the PI calculation.
EXAMPLE 2   
Example of a PI Calculation
The Gerhardt Corporation investment (discussed earlier) had an outlay of 
€50 million, a present value of future cash flows of €63.136 million, and an NPV 
of €13.136 million. The profitability index is
Initial investment 50.000= = =63 136 .1126 .
The PI can also be calculated as
PINPV
Initial investment=+ =+ = 1113 136
50 000126.
..
Because the PI > 1.0, this is a profitable investment.
The PI indicates the value you are receiving in exchange for one unit of currency 
invested. Although the PI is used less frequently than the NPV and IRR, it is sometimes 
used as a guide in capital rationing. The PI is usually called the profitability index in

corporations, but it is commonly referred to as a “benefit–cost ratio” in governmental 
and not-  for- profit organizations.
4.7 NPV Profile
The NPV profile shows a project’s NPV graphed as a function of various discount 
rates. Typically, the NPV is graphed vertically (on the y-axis), and the discount rates 
are graphed horizontally (on the x-axis). The NPV profile for the Gerhardt capital 
budgeting project is shown in Example 3.(5)

Investment Decision Criteria 59
EXAMPLE 3   
NPV Profile
For the Gerhardt example, we have already calculated several NPVs for differ -
ent discount rates. At 10 percent the NPV is €13.136 million; at 20 percent the 
NPV is −€0.543 million; and at 19.52 percent (the IRR), the NPV is zero. What 
is the NPV if the discount rate is 0 percent? The NPV discounted at 0 percent 
is €34 million, which is simply the sum of all of the undiscounted cash flows. 
Table 6 and Figure 1 show the NPV profile for the Gerhardt example for discount 
rates between 0 percent and 30 percent.
Table 6   Gerhardt NPV Profile
Discount Rate (%) NPV (€ Millions)
0 34.000
5.00 22.406
10.00 13.136
15.00 5.623
20.00 −0.543
25.00 −5.661
30.00 −9.954
Figure 1   Gerhardt NPV Profile
NPV
40
30
20
20 25 3010
100
_1035
25
15
155
5_5
_15
Discount Rate (%)
Three interesting points on this NPV profile are where the profile goes through 
the vertical axis (the NPV when the discount rate is zero), where the profile goes

through the horizontal axis (where the discount rate is the IRR), and the NPV 
for the required rate of return (NPV is €13.136 million when the discount rate 
is the 10 percent required rate of return).

Reading 34 ■ Capital Budgeting 60
The NPV profile in Figure 1 is very well-  behaved. The NPV declines at a decreas -
ing rate as the discount rate increases. The profile is convex from the origin (convex 
from below). You will shortly see some examples in which the NPV profile is more 
complicated.
4.8 Ranking Conflicts between NPV and IRR
For a single conventional project, the NPV and IRR will agree on whether to invest or 
to not invest. For independent, conventional projects, no conflict exists between the 
decision rules for the NPV and IRR. However, in the case of two mutually exclusive 
projects, the two criteria will sometimes disagree. For example, Project A might have 
a larger NPV than Project B, but Project B has a higher IRR than Project A. In this 
case, should you invest in Project A or in Project B?
Differing cash flow patterns can cause two projects to rank differently with the 
NPV and IRR. For example, suppose Project A has shorter-  term payoffs than Project

B. This situation is presented in Example 4.
EXAMPLE 4   
Ranking Conflict Due to Differing Cash Flow Patterns
Projects A and B have similar outlays but different patterns of future cash flows. 
Project A realizes most of its cash payoffs earlier than Project B. The cash flows, 
as well as the NPV and IRR for the two projects, are shown in Table 7. For both 
projects, the required rate of return is 10 percent.
Table 7   Cash Flows, NPV, and IRR for Two Projects with Different Cash 
Flow Patterns
Cash Flows
Y ear 0 1 2 3 4 NPV IRR (%)
Project A −200 80 80 80 80 53.59 21.86
Project B −200 0 0 0 400 73.21 18.92
If the two projects were not mutually exclusive, you would invest in both because 
they are both profitable. However, you can choose either A (which has the higher 
IRR) or B (which has the higher NPV).
Table 8 and Figure 2 show the NPVs for Project A and Project B for various 
discount rates between 0 percent and 30 percent.
Table 8   NPV Profiles for Two Projects with Different Cash Flow 
Patterns

Patterns
Discount Rate (%) NPV for Project A NPV for Project B
0 120.00 200.00
5.00 83.68 129.08
10.00 53.59 73.21
15.00 28.40 28.70
15.09 27.98 27.98

Investment Decision Criteria 61
18.92 11.41 0.00
20.00 7.10 −7.10
21.86 0.00 −18.62
25.00 −11.07 −36.16
30.00 −26.70 −59.95
Figure 2   NPV Profiles for Two Projects with Different Cash Flow 
Patterns
NPV
250
150200
100
50
0
_50
_100
Discount Rate (%)20 25 30 10 15 5
Project B (broken line) has the higher NPV for discount rates between 0 per -
cent and 15.09 percent. Project A (solid line) has the higher NPV for discount 
rates exceeding 15.09 percent. The crossover point of 15.09 percent in Figure 2 
corresponds to the discount rate at which both projects have the same NPV (of 
27.98). Project B has the higher NPV below the crossover point, and Project A 
has the higher NPV above it.
Whenever the NPV and IRR rank two mutually exclusive projects differently, as 
they do in the example above, you should choose the project based on the NPV. Project 
B, with the higher NPV, is the better project because of the reinvestment assumption.

Mathematically, whenever you discount a cash flow at a particular discount rate, you 
are implicitly assuming that you can reinvest a cash flow at that same discount rate.2 
In the NPV calculation, you use a discount rate of 10 percent for both projects. In the 
IRR calculation, you use a discount rate equal to the IRR of 21.86 percent for Project 
A and 18.92 percent for Project B.Table 8   (Continued)
2 For example, assume that you are receiving $100 in one year discounted at 10  percent. The present 
value is $100/$1.10 = $90.91. Instead of receiving the $100 in one year, invest it for one additional year at 
10 percent, and it grows to $110. What is the present value of $110 received in two years discounted at 
10 percent? It is the same $90.91. Because both future cash flows are worth the same, you are implicitly 
assuming that reinvesting the earlier cash flow at the discount rate of 10 percent has no effect on its value.

Reading 34 ■ Capital Budgeting 62
Can you reinvest the cash inflows from the projects at 10 percent, or 21.86 percent, 
or 18.92 percent? When you assume the required rate of return is 10 percent, you are 
assuming an opportunity cost of 10 percent—that you can either find other projects 
that pay a 10 percent return or pay back your sources of capital that cost you 10 per -
cent. The fact that you earned 21.86 percent in Project A or 18.92 percent in Project 
B does not mean that you can reinvest future cash flows at those rates. (In fact, if you 
can reinvest future cash flows at 21.86 percent or 18.92 percent, these should have 
been used as your required rate of return instead of 10 percent.) Because the NPV 
criterion uses the most realistic discount rate—the opportunity cost of funds—the 
NPV criterion should be used for evaluating mutually exclusive projects.
Another circumstance that frequently causes mutually exclusive projects to be

ranked differently by NPV and IRR criteria is project scale—the sizes of the projects. 
Would you rather have a small project with a higher rate of return or a large project 
with a lower rate of return? Sometimes, the larger, low rate of return project has the 
better NPV. This case is developed in Example 5.
EXAMPLE 5   
Ranking Conflicts due to Differing Project Scale
Project A has a much smaller outlay than Project B, although they have similar 
future cash flow patterns. The cash flows, as well as the NPVs and IRRs for 
the two projects, are shown in Table 9. For both projects, the required rate of 
return is 10 percent.
Table 9   Cash Flows, NPV, and IRR for Two Projects of Differing Scale
Cash Flows
Project A −100 50 50 50 50 58.49 34.90
Project B −400 170 170 170 170 138.88 25.21
If they were not mutually exclusive, you would invest in both projects because 
they are both profitable. However, you can choose either Project A (which has

the higher IRR) or Project B (which has the higher NPV).
Table 10 and Figure 3 show the NPVs for Project A and Project B for various 
Table 10   NPV Profiles for Two Projects of Differing Scale
0 100.00 280.00
5.00 77.30 202.81
10.00 58.49 138.88
15.00 42.75 85.35
20.00 29.44 40.08
21.86 25.00 25.00
25.00 18.08 1.47
25.21 17.65 0.00

Investment Decision Criteria 63
30.00 8.31 −31.74
34.90 0.00 −60.00
35.00 −0.15 −60.52
Figure 3   NPV Profiles for Two Projects of Differing Scale
NPV
300
150200250
100
50
0
_50
_100
Discount Rate (%)30 20 25 35 10 15 5
Project B (broken line) has the higher NPV for discount rates between 
0 percent and 21.86 percent. Project A has the higher NPV for discount rates 
exceeding 21.86 percent. The crossover point of 21.86 percent in Figure 3 cor -
responds to the discount rate at which both projects have the same NPV (of 
25.00). Below the crossover point, Project B has the higher NPV, and above it, 
Project A has the higher NPV. When cash flows are discounted at the 10 percent 
required rate of return, the choice is clear—Project B, the larger project, which 
has the superior NPV.
The good news is that the NPV and IRR criteria will usually indicate the same 
investment decision for a given project. They will usually both recommend acceptance

or rejection of the project. When the choice is between two mutually exclusive projects 
and the NPV and IRR rank the two projects differently, the NPV criterion is strongly 
preferred. There are good reasons for this preference. The NPV shows the amount of 
gain, or wealth increase, as a currency amount. The reinvestment assumption of the 
NPV is the more economically realistic. The IRR does give you a rate of return, but the 
IRR could be for a small investment or for only a short period of time. As a practical 
matter, once a corporation has the data to calculate the NPV, it is fairly trivial to go 
ahead and calculate the IRR and other capital budgeting criteria. However, the most 
appropriate and theoretically sound criterion is the NPV.Table 10   (Continued)

Reading 34 ■ Capital Budgeting 64
4.9 The Multiple IRR Problem and the No IRR Problem
A problem that can arise with the IRR criterion is the “multiple IRR problem. ” We 
can illustrate this problem with the following nonconventional cash flow pattern:3
Time 0 1 2
Cash flow −1,000 5,000 −6,000
The IRR for these cash flows satisfies this equation:
−+
+()+−
+()= 1 0005 000 6 00002,,,
1I RR 1I RR1
It turns out that there are two values of IRR that satisfy the equation: IRR = 1 = 100% 
and IRR = 2 = 200%. To further understand this problem, consider the NPV profile 
for this investment, which is shown in Table 11 and Figure 4.
As you can see in the NPV profile, the NPV is equal to zero at IRR = 100% and IRR 
= 200%. The NPV is negative for discount rates below 100 percent, positive between 
100 percent and 200 percent, and then negative above 200 percent. The NPV reaches 
its highest value when the discount rate is 140 percent.

It is also possible to have an investment project with no IRR. The “no-  IRR problem” 
occurs with this cash flow pattern:4
Time 0 1 2
Cash flow 100 −300 250
10000
1IRR 1IRR1+−
+()+
+()=3 25002
For these cash flows, no discount rate exists that results in a zero NPV. Does that mean 
this project is a bad investment? In this case, the project is actually a good investment. 
As Table 12 and Figure 5 show, the NPV is positive for all discount rates. The lowest 
NPV, of 10, occurs for a discount rate of 66.67 percent, and the NPV is always greater 
than zero. Consequently, no IRR exists.
Table 11   NPV Profile for a Multiple IRR Example
0 −2,000.00
25 −840.00
50 −333.33
75 −102.04
100 0.00
125 37.04
140 41.67
150 40.00
175 24.79
200 0.00
225 −29.59
3 This example is adapted from Hirschleifer (1958).
4 This example is also adapted from Hirschleifer.

Investment Decision Criteria 65
250 −61.22
300 −125.00
350 −185.19
400 −240.00
500 −333.33
1,000 −595.04
2,000 −775.51
3,000 −844.95
4,000 −881.62
10,000 −951.08
1,000,000 −999.50
Figure 4   NPV Profile for a Multiple IRR Example
NPV
100
_150_1000
_5050
_200
_300_250
_350
_400
50 400 250 200 300 350 100 150
Table 12   NPV Profile for a Project with No IRR
0 50.00
25 20.00
50 11.11
66.67 10.00
75 10.20
100 12.50
125 16.05
150 20.00
175 23.97
200 27.78
225 31.36
(continued)Table 11   (Continued)

Reading 34 ■ Capital Budgeting 66
250 34.69
275 37.78
300 40.63
325 43.25
350 45.68
375 47.92
400 50.00
Figure 5   NPV Profile for a Project with No IRR
NPV
60
1020304050
0
450 250 0 200 300 350 400 100 50 150
For conventional projects that have outlays followed by inflows—negative cash flows 
followed by positive cash flows—the multiple IRR problem cannot occur. However, 
for nonconventional projects, as in the example above, the multiple IRR problem can 
occur. The IRR equation is essentially an nth degree polynomial. An nth degree poly -
nomial can have up to n solutions, although it will have no more real solutions than 
the number of cash flow sign changes. For example, a project with two sign changes 
could have zero, one, or two IRRs. Having two sign changes does not mean that you 
will have multiple IRRs; it just means that you might . Fortunately, most capital bud -
geting projects have only one IRR. Analysts should always be aware of the unusual

cash flow patterns that can generate the multiple IRR problem.
4.10  Popularity and Usage of the Capital Budgeting Methods
Analysts need to know the basic logic of the various capital budgeting criteria as well 
as the practicalities involved in using them in real corporations. Before delving into 
the many issues involved in applying these models, we would like to present some 
feedback on their popularity.
The usefulness of any analytical tool always depends on the specific application. 
Corporations generally find these capital budgeting criteria useful. Two surveys by 
Graham and Harvey (2001) and Brounen, De Jong, and Koedijk (2004) report on the 
frequency of their use by US and European corporations. Table 13 gives the mean Table 12   (Continued)

Investment Decision Criteria 67
responses of executives in five countries to the question “How frequently does your 
company use the following techniques when deciding which projects or acquisitions 
to pursue?”
Table 13   Mean Responses about Frequency of Use of Capital Budgeting Techniques
United 
StatesUnited 
Kingdom Netherlands Germany France
Internal rate of returna3.09 2.31 2.36 2.15 2.27
Net present valuea3.08 2.32 2.76 2.26 1.86
Payback perioda2.53 2.77 2.53 2.29 2.46
Hurdle rate 2.13 1.35 1.98 1.61 0.73
Sensitivity analysis 2.31 2.21 1.84 1.65 0.79
Earnings multiple approach 1.89 1.81 1.61 1.25 1.70
Discounted payback perioda1.56 1.49 1.25 1.59 0.87
Real options approach 1.47 1.65 1.49 2.24 2.20
Accounting rate of returna1.34 1.79 1.40 1.63 1.11
Value at risk 0.95 0.85 0.51 1.45 1.68
Adjusted present value 0.85 0.78 0.78 0.71 1.11
Profitability indexa0.85 1.00 0.78 1.04 1.64
a These techniques were described in this section of the reading. You will encounter the others elsewhere.

Note : Respondents used a scale ranging from 0 (never) to 4 (always).
Although financial textbooks preach the superiority of the NPV and IRR tech -
niques, it is clear that several other methods are heavily used.5 In the four European 
countries, the payback period is used as often as, or even slightly more often than, the 
NPV and IRR. In these two studies, larger companies tended to prefer the NPV and 
IRR over the payback period. The fact that the US companies were larger, on aver -
age, partially explains the greater US preference for the NPV and IRR. Other factors 
influence the choice of capital budgeting techniques. Private corporations used the 
payback period more frequently than did public corporations. Companies managed 
by an MBA had a stronger preference for the discounted cash flow techniques. Of 
course, any survey research also has some limitations. In this case, the persons in 
these large corporations responding to the surveys may not have been aware of all of

the applications of these techniques.
These capital budgeting techniques are essential tools for corporate managers. 
Capital budgeting is also relevant to external analysts. Because a corporation’s investing 
decisions ultimately determine the value of its financial obligations, the corporation’s 
investing processes are vital. The NPV criterion is the criterion most directly related 
to stock prices. If a corporation invests in positive NPV projects, these should add to 
the wealth of its shareholders. Example 6 illustrates this scenario.
5 Analysts often refer to the NPV and IRR as “discounted cash flow techniques” because they accurately 
account for the timing of all cash flows when they are discounted.

Reading 34 ■ Capital Budgeting 68
EXAMPLE 6   
NPVs and Stock Prices
Freitag Corporation is investing €600  million in distribution facilities. The 
present value of the future after-  tax cash flows is estimated to be €850 million. 
Freitag has 200 million outstanding shares with a current market price of €32.00 
per share. This investment is new information, and it is independent of other 
expectations about the company. What should be the effect of the project on 
the value of the company and the stock price?
Solution: 
The NPV of the project is €850 million − €600 million = €250 million. The total 
market value of the company prior to the investment is €32.00 × 200 million 
shares = €6,400 million. The value of the company should increase by €250 million 
to €6,650 million. The price per share should increase by the NPV per share, 
or €250 million/200 million shares = €1.25 per share. The share price should 
increase from €32.00 to €33.25.

The effect of a capital budgeting project’s positive or negative NPV on share price 
is more complicated than Example 6 above, in which the value of the stock increased 
by the project’s NPV. The value of a company is the value of its existing investments 
plus the net present values of all of its future investments. If an analyst learns of an 
investment, the impact of that investment on the stock price will depend on whether 
the investment’s profitability is more or less than expected. For example, an analyst 
could learn of a positive NPV project, but if the project’s profitability is less than 
expectations, this stock might drop in price on the news. Alternatively, news of a 
particular capital project might be considered as a signal about other capital projects 
underway or in the future. A project that by itself might add, say, €0.25 to the value of 
the stock might signal the existence of other profitable projects. News of this project

might increase the stock price by far more than €0.25.
The integrity of a corporation’s capital budgeting processes is important to ana -
lysts. Management’s capital budgeting processes can demonstrate two things about 
the quality of management: the degree to which management embraces the goal of 
shareholder wealth maximization, and its effectiveness in pursuing that goal. Both of 
these factors are important to shareholders.
SUMMARY
projects—those projects with a life of a year or more. This reading developed the 
principles behind the basic capital budgeting model, the cash flows that go into the 
model, and several extensions of the basic model.
■■Capital budgeting undergirds the most critical investments for many corpora -
tions—their investments in long-  term assets. The principles of capital budget -
ing have been applied to other corporate investing and financing decisions and

to security analysis and portfolio management.
■■The typical steps in the capital budgeting process are: 1) generating ideas, 2) 
analyzing individual proposals, 3) planning the capital budget, and 4) monitor -
ing and post-  auditing.

Summary 69
■■Projects susceptible to capital budgeting process can be categorized as: 1) 
replacement, 2) expansion, 3) new products and services, and 4) regulatory, 
safety and environmental.
■■Capital budgeting decisions are based on incremental after-  tax cash flows dis -
counted at the opportunity cost of funds. Financing costs are ignored because 
both the cost of debt and the cost of other capital are captured in the discount 
rate.
■■The net present value (NPV) is the present value of all after-  tax cash flows, or
NPVCF=
+()=∑t
t
tn
r10
where the investment outlays are negative cash flows included in the CFts and 
where r is the required rate of return for the investment.
■■The IRR is the discount rate that makes the present value of all future cash flows 
sum to zero. This equation can be solved for the IRR:
CF
IRRt
t
tn
10
0+()=
=∑
■■The payback period is the number of years required to recover the original 
investment in a project. The payback is based on cash flows.

■■The discounted payback period is the number of years it takes for the cumula -
tive discounted cash flows from a project to equal the original investment.
■■The average accounting rate of return (AAR) can be defined as follows:
■■The profitability index (PI) is the present value of a project’s future cash flows 
divided by the initial investment:
Initial investmentNPV
Initial == +1iinvestment
■■The capital budgeting decision rules are to invest if the NPV > 0, if the IRR > r, 
or if the PI > 1.0 There are no decision rules for the payback period, discounted 
payback period, and AAR because they are not always sound measures.
■■The NPV profile is a graph that shows a project’s NPV graphed as a function of 
various discount rates.
■■For mutually exclusive projects that are ranked differently by the NPV and IRR, 
it is economically sound to choose the project with the higher NPV.

■■The “multiple IRR problem” and the “no IRR problem” can arise for a project 
with nonconventional cash flows—cash flows that change signs more than once 
during the project’s life.
■■The fact that projects with positive NPVs theoretically increase the value of the 
company and the value of its stock could explain the popularity of NPV as an 
evaluation method.

Reading 34 ■ Capital Budgeting 70
1 Given the following cash flows for a capital project, calculate the NPV and IRR. 
The required rate of return is 8 percent.
Cash flow −50,000 15,000 15,000 20,000 10,000 5,000
 
NPV IRR
A $1,905 10.9%
B $1,905 26.0%
C $3,379 10.9%
2 Given the following cash flows for a capital project, calculate its payback period 
and discounted payback period. The required rate of return is 8 percent.
 The discounted payback period is:
A 0.16 years longer than the payback period.
B 0.51 years longer than the payback period.
C 1.01 years longer than the payback period.
3 An investment of $100 generates after-  tax cash flows of $40 in Year 1, $80 in 
Year 2, and $120 in Year 3. The required rate of return is 20 percent. The net 
present value is closest  to:
A $42.22.
B $58.33.
C $68.52.
4 An investment of $150,000 is expected to generate an after-  tax cash flow of

$100,000 in one year and another $120,000 in two years. The cost of capital is 
10 percent. What is the internal rate of return?
A 28.39 percent.
B 28.59 percent.
C 28.79 percent.
5 Kim Corporation is considering an investment of 750 million won with 
expected after-  tax cash inflows of 175 million won per year for seven years. The 
required rate of return is 10 percent. What is the project’s:
NPV? IRR? 
A 102 million won 14.0%
B 157 million won 23.3%
C 193 million won 10.0%

Practice Problems 71
6 Kim Corporation is considering an investment of 750 million won with 
required rate of return is 10 percent. Expressed in years, the project’s payback 
period and discounted payback period, respectively, are closest  to:
A 4.3 years and 5.4 years.
B 4.3 years and 5.9 years.
C 4.8 years and 6.3 years.
7 An investment of $20,000 will create a perpetual after-  tax cash flow of $2,000. 
The required rate of return is 8 percent. What is the investment’s profitability 
index?
A 1.08.
B 1.16.
C 1.25.
8 Hermann Corporation is considering an investment of €375 million with 
expected after-  tax cash inflows of €115 million per year for seven years and an 
additional after-  tax salvage value of €50 million in Year 7. The required rate of 
return is 10 percent. What is the investment’s PI?
A 1.19.
B 1.33.
C 1.56.
9 Erin Chou is reviewing a profitable investment project that has a conventional

cash flow pattern. If the cash flows for the project, initial outlay, and future 
after-  tax cash flows all double, Chou would predict that the IRR would:
A increase and the NPV would increase.
B stay the same and the NPV would increase.
C stay the same and the NPV would stay the same.
10 Shirley Shea has evaluated an investment proposal and found that its payback 
period is one year, it has a negative NPV, and it has a positive IRR. Is this com -
bination of results possible?
A Yes .
B No, because a project with a positive IRR has a positive NPV.
C No, because a project with such a rapid payback period has a positive NPV.
11 An investment has an outlay of 100 and after-  tax cash flows of 40 annually for 
four years. A project enhancement increases the outlay by 15 and the annual 
after-  tax cash flows by 5. As a result, the vertical intercept of the NPV profile of 
the enhanced project shifts:
A up and the horizontal intercept shifts left.
B up and the horizontal intercept shifts right.

C down and the horizontal intercept shifts left.
12 Projects 1 and 2 have similar outlays, although the patterns of future cash flows 
are different. The cash flows as well as the NPV and IRR for the two projects are 
shown below. For both projects, the required rate of return is 10 percent.
Cash Flows
Project 1 −50 20 20 20 20 13.40 21.86
Project 2 −50 0 0 0 100 18.30 18.92

Reading 34 ■ Capital Budgeting 72
 The two projects are mutually exclusive. What is the appropriate investment 
decision?
A Invest in both projects.
B Invest in Project 1 because it has the higher IRR.
C Invest in Project 2 because it has the higher NPV.
13 Consider the two projects below. The cash flows as well as the NPV and IRR 
for the two projects are given. For both projects, the required rate of return is 
10 percent.
Cash Flows
Project 1 −100 36 36 36 36 14.12 16.37
Project 2 −100 0 0 0 175 19.53 15.02
 What discount rate would result in the same NPV for both projects?
A A rate between 0.00 percent and 10.00 percent.
B A rate between 10.00 percent and 15.02 percent.
C A rate between 15.02 percent and 16.37 percent.
14 Wilson Flannery is concerned that this project has multiple IRRs.
Y ear 0 1 2 3
Cash flows −50 100 0 −50
 How many discount rates produce a zero NPV for this project?
A One, a discount rate of 0 percent.
B Two, discount rates of 0 percent and 32 percent.

C Two, discount rates of 0 percent and 62 percent.
15 With regard to the net present value (NPV) profiles of two projects, the cross -
over rate is best described as the discount rate at which:
A two projects have the same NPV.
B two projects have the same internal rate of return.
C a project’s NPV changes from positive to negative.
16 With regard to net present value (NPV) profiles, the point at which a profile 
crosses the vertical axis is best described as:
A the point at which two projects have the same NPV.
B the sum of the undiscounted cash flows from a project.
C a project’s internal rate of return when the project’s NPV is equal to zero.
17 With regard to net present value (NPV) profiles, the point at which a profile 
crosses the horizontal axis is best described as:

18 With regard to capital budgeting, an appropriate estimate of the incremental 
cash flows from a project is least likely  to include:
A externalities.
B interest costs.
C opportunity costs.

Solutions 73
SOLUTIONS
1 C is correct.
NPV=− +++ + 50 00015 000
10815 000
10820 000
10810 000
10823 4,,
.,
.,
.,
.+ +
=− + +++5 000
108
50 000 13 888 89 12 860 08 15 876 64 7355,
.
,, ., ., ., NPV0 030
3 402 92
50 000 53 378 83 3 378 83.
,.
,, ., .+
=− += NPV
 The IRR, found with a financial calculator, is 10.88 percent.
2 C is correct.
Cumulative cash flow −50,000 −35,000 −20,000 0 10,000 15,000
Discounted cash flow −50,000 13,888.89 12,860.08 15,876.64 7,350.30 3,402.92
Cumulative DCF −50,000 −36,111.11 −23,251.03 −7,374.38 −24.09 3,378.83
 As the table shows, the cumulative cash flow offsets the initial investment in 
exactly three years. The payback period is 3.00 years. The discounted payback 
period is between four and five years. The discounted payback period is 4 years 
plus 24.09/3,402.92 = 0.007 of the fifth year cash flow, or 4.007 = 4.01 years. The 
discounted payback period is 4.01 − 3.00 = 1.01 years longer than the payback 
period.

period.
3 B is correct.
NPVCF=
+()=− ++ +=
=∑t
t
t r110040
12080
120120
12058 33
03
23 . ... $
4 C is correct. The IRR can be found using a financial calculator or with trial and 
error. Using trial and error, the total PV is equal to zero if the discount rate is 
28.79 percent.
Y ear Cash Flow 28.19% 28.39% 28.59% 28.79%
0 −150,000 −150,000 −150,000 −150,000 −150,000
1 100,000 78,009 77,888 77,767 77,646
2 120,000 73,025 72,798 72,572 72,346
Total 1,034 686 338 −8
 A more precise IRR of 28.7854 percent has a total PV closer to zero.
5 A is correct.
The NP V million won =− += −+ =
=∑ 750175
110750 851 97 101 97
17
... .t
t
 The IRR, found with a financial calculator, is 14.02 percent. (The PV is −750, N 
= 7, and PMT = 175.)
6 B is correct.

Reading 34 ■ Capital Budgeting 74
Y ear 0 1 2 3 4 5 6 7
Cash flow −750 175 175 175 175 175 175 175
Cumulative cash flow −750 −575 −400 −225 −50 125 300 475
 The payback period is between four and five years. The payback period is four 
years plus 50/175 = 0.29 of the fifth year cash flow, or 4.29 years.
Discounted cash flow −750 159.09 144.63 131.48 119.53 108.66 98.78 89.80
Cumulative DCF −750 −590.91 −446.28 −314.80 −195.27 −86.61 12.17 101.97
 The discounted payback period is between five and six years. The discounted 
payback period is five years plus 86.61/98.78 = 0.88 of the sixth year cash flow, 
or 5.88 years.
7 C is correct. 
The present value of future cash f lows is PV= =2 000
00825,
.,0 000
25 000
20 00The profitabil ity index is PIPV
Investment= =,
,0 0125=.
8 C is correct.
PV  million euros
PI=+ =
===∑115
11050
110585 53
585 53
37517
7...
.t
t
1156 .
9 B is correct. The IRR would stay the same because both the initial outlay and

the after-  tax cash flows double, so that the return on each dollar invested 
remains the same. All of the cash flows and their present values double. The 
difference between total present value of the future cash flows and the initial 
outlay (the NPV) also doubles.
10 A is correct. If the cumulative cash flow in one year equals the outlay and 
additional cash flows are not very large, this scenario is possible. For example, 
assume the outlay is 100, the cash flow in Year 1 is 100 and the cash flow in Year 
2 is 5. The required return is 10 percent. This project would have a payback of 
1.0 years, an NPV of −4.96, and an IRR of 4.77 percent.
11 A is correct. The vertical intercept changes from 60 to 65 (NPV when cost 
of capital is 0%), and the horizontal intercept (IRR, when NPV equals zero) 
changes from 21.86 percent to 20.68 percent.
12 C is correct. When valuing mutually exclusive projects, the decision should 
be made with the NPV method because this method uses the most realistic

discount rate, namely the opportunity cost of funds. In this example, the rein -
vestment rate for the NPV method (here 10 percent) is more realistic than the 
reinvestment rate for the IRR method (here 21.86 percent or 18.92 percent).
13 B is correct. For these projects, a discount rate of 13.16 percent would yield the 
same NPV for both (an NPV of 6.73).
14 C is correct. Discount rates of 0 percent and approximately 61.8 percent both 
give a zero NPV.

Solutions 75
Rate 0% 20% 40% 60% 61.8% 80% 100%
NPV 0.00 4.40 3.21 0.29 0.00 −3.02 −6.25
15 A is correct. The crossover rate is the discount rate at which the NPV profiles 
for two projects cross; it is the only point where the NPVs of the projects are 
the same.
16 B is correct. The vertical axis represents a discount rate of zero. The point 
where the profile crosses the vertical axis is simply the sum of the cash flows.
17 C is correct. The horizontal axis represents an NPV of zero. By definition, the 
project’s IRR equals an NPV of zero.
18 B is correct. Costs to finance the project are taken into account when the cash 
flows are discounted at the appropriate cost of capital; including interest costs 
in the cash flows would result in double-  counting the cost of debt.

Cost of Capital
by Yves Courtois, CMT, MRICS, CFA, Gene C. Lai, PhD, and 
Pamela Peterson Drake, PhD, CFA
Yves Courtois, CMT, MRICS, CFA, is at KPMG (Luxembourg). Gene C. Lai, PhD (USA). 
Pamela Peterson Drake, PhD, CFA, is at James Madison University (USA).
a. calculate and interpret the weighted average cost of capital 
(WACC) of a company;
b. describe how taxes affect the cost of capital from different capital 
sources;
c. describe the use of target capital structure in estimating WACC 
and how target capital structure weights may be determined;
d. explain how the marginal cost of capital and the investment 
opportunity schedule are used to determine the optimal capital 
budget;
e. explain the marginal cost of capital’s role in determining the net 
present value of a project;
f. calculate and interpret the cost of debt capital using the yield-  to- 
maturity approach and the debt-  rating approach;

g. calculate and interpret the cost of noncallable, nonconvertible 
preferred stock;
h. calculate and interpret the cost of equity capital using the capital 
asset pricing model approach, the dividend discount model 
approach, and the bond-  yield-  plus risk-  premium approach;
i. calculate and interpret the beta and cost of capital for a project;
j. describe uses of country risk premiums in estimating the cost of 
equity;
k. describe the marginal cost of capital schedule, explain why it 
may be upward-  sloping with respect to additional capital, and 
calculate and interpret its break-  points;
l. explain and demonstrate the correct treatment of flotation costs.rEADING
35

Reading 35 ■ Cost of Capital 78
A company grows by making investments that are expected to increase revenues and 
profits. The company acquires the capital or funds necessary to make such investments 
by borrowing or using funds from owners. By applying this capital to investments 
with long-  term benefits, the company is producing value today. But, how much value? 
The answer depends not only on the investments’ expected future cash flows but also 
on the cost of the funds. Borrowing is not costless. Neither is using owners’ funds.
The cost of this capital is an important ingredient in both investment decision 
making by the company’s management and the valuation of the company by investors. 
If a company invests in projects that produce a return in excess of the cost of capital, 
the company has created value; in contrast, if the company invests in projects whose 
returns are less than the cost of capital, the company has actually destroyed value.

Therefore, the estimation of the cost of capital is a central issue in corporate financial 
management. For the analyst seeking to evaluate a company’s investment program 
and its competitive position, an accurate estimate of a company’s cost of capital is 
important as well.
Cost of capital estimation is a challenging task. As we have already implied, the 
cost of capital is not observable but, rather, must be estimated. Arriving at a cost of 
capital estimate requires a host of assumptions and estimates. Another challenge is 
that the cost of capital that is appropriately applied to a specific investment depends 
on the characteristics of that investment: The riskier the investment’s cash flows, the 
greater its cost of capital. In reality, a company must estimate project-  specific costs of 
capital. What is often done, however, is to estimate the cost of capital for the company 
as a whole and then adjust this overall corporate cost of capital upward or downward

to reflect the risk of the contemplated project relative to the company’s average project.
This reading is organized as follows: In the next section, we introduce the cost 
of capital and its basic computation. Section 3 presents a selection of methods for 
estimating the costs of the various sources of capital. Section 4 discusses issues an 
analyst faces in using the cost of capital. A summary concludes the reading.
COST OF CAPITAL
The cost of capital  is the rate of return that the suppliers of capital—bondholders 
and owners—require as compensation for their contribution of capital. Another 
way of looking at the cost of capital is that it is the opportunity cost of funds for the 
suppliers of capital: A potential supplier of capital will not voluntarily invest in a 
company unless its return meets or exceeds what the supplier could earn elsewhere 
in an investment of comparable risk.
A company typically has several alternatives for raising capital, including issuing

equity, debt, and instruments that share characteristics of debt and equity. Each source 
selected becomes a component of the company’s funding and has a cost (required rate 
of return) that may be called a component cost of capital . Because we are using the 
cost of capital in the evaluation of investment opportunities, we are dealing with a 
marginal  cost—what it would cost to raise additional funds for the potential invest -
ment project. Therefore, the cost of capital that the investment analyst is concerned 
with is a marginal cost.
Let us focus on the cost of capital for the entire company (later we will address how 
to adjust that for specific projects). The cost of capital of a company is the required 
rate of return that investors demand for the average-  risk investment of a company. 
The most common way to estimate this required rate of return is to calculate the 1
2

Cost of Capital 79
marginal cost of each of the various sources of capital and then calculate a weighted 
average of these costs. This weighted average is referred to as the weighted average 
cost of capital  (WACC). The WACC is also referred to as the marginal cost of capital 
(MCC) because it is the cost that a company incurs for additional capital. The weights 
in this weighted average are the proportions of the various sources of capital that the 
company uses to support its investment program. Therefore, the WACC, in its most 
general terms, is
WACC = wdrd(1 – t) + wprp + were  
where
 wd = the proportion of debt that the company uses when it raises new funds
 rd = the before-  tax marginal cost of debt
 t = the company’s marginal tax rate
 wp = the proportion of preferred stock the company uses when it raises new 
funds
 rp = the marginal cost of preferred stock
 we = the proportion of equity that the company uses when it raises new funds
 re = the marginal cost of equity
EXAMPLE 1

re = the marginal cost of equity
EXAMPLE 1   
Computing the Weighted Average Cost of Capital
Assume that ABC Corporation has the following capital structure: 30 percent 
debt, 10 percent preferred stock, and 60 percent equity. ABC Corporation wishes 
to maintain these proportions as it raises new funds. Its before-  tax cost of debt 
is 8 percent, its cost of preferred stock is 10 percent, and its cost of equity is 
15  percent. If the company’s marginal tax rate is 40  percent, what is ABC’s 
weighted average cost of capital?
Solution:
The weighted average cost of capital is
 WACC = (0.3)(0.08)(1 – 0.40) + (0.1)(0.1) + (0.6)(0.15)
  = 11.44 percent
There are important points concerning the calculation of the WACC as shown in 
Equation 1 that the analyst must be familiar with. The next two sections address two 
key issues: taxes and the selection of weights.
2.1 Taxes and the Cost of Capital
Notice that in Equation 1 we adjust the expected before-  tax cost on new debt financ -

ing, rd, by a factor of (1 − t). In the United States and many other tax jurisdictions, 
the interest on debt financing is a deduction to arrive at taxable income. Taking the 
tax- deductibility of interest as the base case, we adjust the pre-  tax cost of debt for this 
tax shield. Multiplying rd by (1 − t) results in an estimate of the after-  tax cost of debt.
For example, suppose a company pays €1 million in interest on its €10 million of 
debt. The cost of this debt is not €1 million because this interest expense reduces tax -
able income by €1 million, resulting in a lower tax. If the company is subject to a tax 
rate of 40 percent, this €1 million of interest costs the company (€1 million) (1 − 0.4) (1)

Reading 35 ■ Cost of Capital 80
= €0.6 million because the interest reduces the company’s tax bill by €0.4 million. In 
this case, the before-  tax cost of debt is 10 percent, whereas the after-  tax cost of debt 
is (€0.6 million)/(€10 million) = 6 percent.
Estimating the cost of common equity capital is more challenging than estimating 
the cost of debt capital. Debt capital involves a stated legal obligation on the part of 
the company to pay interest and repay the principal on the borrowing. Equity entails 
no such obligation. Estimating the cost of conventional preferred equity is rather 
straightforward because the dividend is generally stated and fixed, but estimating 
the cost of common equity is challenging. There are several methods available for 
estimating the cost of common equity, and we discuss two in this reading. The first 
method uses the capital asset pricing model, and the second method uses the dividend

discount model, which is based on discounted cash flows. No matter the method, 
there is no need to make any adjustment in the cost of equity for taxes because the 
payments to owners, whether in the form of dividends or the return on capital, are 
not tax-  deductible for the company.
EXAMPLE 2   
Incorporating the Effect of Taxes on the Costs of Capital
Jorge Ricard, a financial analyst, is estimating the costs of capital for the Zeale 
Corporation. In the process of this estimation, Ricard has estimated the before-  tax 
costs of capital for Zeale’s debt and equity as 4 percent and 6 percent, respectively. 
What are the after-  tax costs of debt and equity if Zeale’s marginal tax rate is:
1 30 percent?
2 48 percent?
Marginal Tax Rate After-  Tax Cost of Debt After-  Tax Cost of Equity
Solution to 1: 30 percent 0.04(1 − 0.30) = 2.80 percent 6 percent
Solution to 2: 48 percent 0.04(1 − 0.48) = 2.08 percent 6 percent

Note : There is no adjustment for taxes in the case of equity; the before-  tax cost of equity is equal to the after-  tax cost of equity.
2.2 Weights of the Weighted Average
How do we determine what weights to use? Ideally, we want to use the proportion of 
each source of capital that the company would use in the project or company. If we 
assume that a company has a target capital structure and raises capital consistent with 
this target, we should use this target capital structure. The target capital structure  is 
the capital structure that a company is striving to obtain. If we know the company’s 
target capital structure, then, of course, we should use this in our analysis. Someone 
outside the company, however, such as an analyst, typically does not know the target 
capital structure and must estimate it using one of several approaches:
1 Assume the company’s current capital structure, at market value weights for the 
components, represents the company’s target capital structure.

2 Examine trends in the company’s capital structure or statements by manage -
ment regarding capital structure policy to infer the target capital structure.
3 Use averages of comparable companies’ capital structures as the target capital 
structure.

Cost of Capital 81
In the absence of knowledge of a company’s target capital structure, we may take 
Method 1 as the baseline. Note that in applying Method 3, we use an unweighted, 
arithmetic average, as is often done for simplicity. An alternative is to calculate a 
weighted average, which would give more weight to larger companies.
Suppose we are using the company’s current capital structure as a proxy for the 
target capital structure. In this case, we use the market value of the different capital 
sources in the calculation of these proportions. For example, if a company has the 
following market values for its capital
Bonds outstanding $5 million
Preferred stock 1 million
Common stock 14 million
Total capital $20 million
the weights that we apply would be
wd = 0.25
wp = 0.05
we = 0.70
Example 3 illustrates the estimation of weights. Note that a simple way of transforming a 
debt-  to- equity ratio D/E into a weight—that is, D/(D + E)—is to divide D/E by 1 + D/E.
EXAMPLE 3

EXAMPLE 3   
Estimating the Proportions of Capital
Fin Anziell is a financial analyst with Analytiker Firma. Anziell is in the process 
of estimating the cost of capital of Gewicht GmbH. The following information 
is provided:
Gewicht GmbH
  Market value of debt €50 million
  Market value of equity €60 million
Primary competitors and their capital structures (in millions):
Competitor Market Value of Debt Market Value of Equity
A €25 €50
B €101 €190
C £40 £60
What are Gewicht’s proportions of debt and equity that Anziell would use if 
estimating these proportions using the company’s: 
1 current capital structure?
2 competitors’ capital structure?
3 Suppose Gewicht announces that a debt-  to- equity ratio of 0.7 reflects its 
target capital structure. What weights should Anziell use in the cost of 
capital calculations?

Reading 35 ■ Cost of Capital 82
Current capital structure
w
wd
e==
=¬
¬500 4545
60 million
¬50 mi llion + ¬60 mi llion
 million.
¬¬¬50 600 5454 million  mi llion +=.
Competitors’ capital structure:1
wd=+

++

++


=¬
¬¬¬
¬¬25
25 50101
101 19040
40 60
3£
££0 0 3601
50
25 50190
101 19060
40 60.
£
££we=+

++

++ ¬
¬¬¬
¬¬  

=30 6399 .
A debt-  to- equity ratio of 0.7 represents a weight on debt of 0.7/1.7 = 0.4118 so 
that wd = 0.4118 and we = 1 − 0.4118 = 0.5882. These would be the preferred 
weights to use in a cost of capital calculation.
2.3 Applying the Cost of Capital to Capital Budgeting and 
Security Valuation
With some insight now into the calculation of the cost of capital, let us continue to 
improve our understanding of the roles it plays in financial analysis. A chief use of the 
marginal cost of capital estimate is in capital-  budgeting decision making. What role

does the marginal cost of capital play in a company’s investment program, and how 
do we adapt it when we need to evaluate a specific investment project?
A company’s marginal cost of capital (MCC) may increase as additional capital 
is raised, whereas returns to a company’s investment opportunities are generally 
believed to decrease as the company makes additional investments, as represented 
by the investment opportunity schedule  (IOS).2 We show this relation in Figure 1, 
graphing the upward-  sloping marginal cost of capital schedule against the downward-  
sloping investment opportunity schedule. In the context of a company’s investment 
decision, the optimal capital budget is that amount of capital raised and invested at 
which the marginal cost of capital is equal to the marginal return from investing. In 
other words, the optimal capital budget occurs when the marginal cost of capital 
intersects with the investment opportunity schedule as seen in Figure 1.

The relation between the MCC and the IOS provides a broad picture of the basic 
decision-  making problem of a company. However, we are often interested in valuing 
an individual project or even a portion of a company, such as a division or product 
line. In these applications, we are interested in the cost of capital for the project, 
product, or division as opposed to the cost of capital for the company overall. The 
1 These weights represent the arithmetic average of the three companies’ debt proportion and equity 
proportion, respectively.
2 The investment opportunity schedule originates with Fisher’s production opportunities [Irving Fisher, 
The Theory of Interest  (New York: MacMillan Co.), 1930] and was adapted to capital budgeting by John 
Hirshleifer [“On the Theory of Optimal Investment Decision, ” Journal of Political Economy , Vol. 66, No. 
4 (August 1958), pp. 329–352.]

Cost of Capital 83
cost of capital in these applications should reflect the riskiness of the future cash flows 
of the project, product, or division. For an average-  risk project, the opportunity cost 
of capital is the company’s WACC. If the systematic risk of the project is above or 
below average relative to the company’s current portfolio of projects, an upward or 
downward adjustment, respectively, is made to the company’s WACC. Companies may 
take an ad hoc  or a systematic approach to making such adjustments. The discussion 
of a systematic approach is a somewhat advanced topic that we defer to Section 4.1.
Figure 1   Optimal Investment Decision
Optimal capital
budget Margina l
cost of capital  Investmen t
opportunity
schedul e
Amount of New Capital Cost or Return
The WACC or MCC corresponding to the average risk of the company, adjusted 
appropriately for the risk of a given project, plays a role in capital-  budgeting decision

making based on the net present value  (NPV) of that project. Recall from the reading 
on capital budgeting that the NPV is the present value of all the project cash flows. It 
is useful to think of it as the difference between the present value of the cash inflows, 
discounted at the opportunity cost of capital applicable to the specific project, and 
the present value of the cash outflows, discounted using that same opportunity cost 
of capital:
NPV = Present value of inflows − Present value of outflows
If an investment’s NPV is positive, the company should undertake the project. If we 
choose to use the company’s WACC in the calculation of the NPV of a project, we 
are assuming that the project:
■■has the same risk as the average-  risk project of the company, and
■■will have a constant target capital structure throughout its useful life.3
These may not be realistic or appropriate assumptions and are potential drawbacks

to using the company’s WACC in valuing projects. However, alternative approaches 
are subject to drawbacks as well, and the approach outlined has wide acceptance.4
3 WACC is estimated using fixed proportions of equity and debt. The NPV method assumes a constant 
required rate of return, whereas a fluctuating capital structure would cause WACC to fluctuate. The impor -
tance of this issue is demonstrated by James A. Miles and John R. Ezzell, “The Weighted Average Cost of 
Capital, Perfect Capital Markets, and Project Life: A Clarification, ” Journal of Financial and Quantitative 
Analysis , Vol. 15, No. 3 (September 1980), pp. 719–730.
4 See the reading on capital budgeting for a discussion.

Reading 35 ■ Cost of Capital 84
For the analyst, the second key use of the marginal cost of capital is in security 
valuation using any one of several discounted cash flow valuation models available.5 
For a particular valuation model, if these cash flows are cash flows to the company’s 
suppliers of capital (that is, free cash flow to the firm), the analyst uses the weighted 
average cost of capital of the company in the valuation.6 If these cash flows are strictly 
those belonging to the company’s owners, such as the free cash flow to equity, or divi -
dends, the analyst uses the cost of equity capital to find the present value of these flows.7
In the next section, we discuss how an analyst may approach the calculation of the 
component costs of capital, focusing on debt, preferred stock, and common equity.
COSTS OF THE DIFFERENT SOURCES OF CAPITAL
Each source of capital has a different cost because of the differences among the sources,

such as seniority, contractual commitments, and potential value as a tax shield. We 
focus on the costs of three primary sources of capital: debt, preferred equity, and 
common equity.
3.1 Cost of Debt
The cost of debt  is the cost of debt financing to a company when it issues a bond 
or takes out a bank loan. We discuss two methods to estimate the before-  tax cost of 
debt, rd: the yield-  to- maturity approach and debt-  rating approach.
3.1.1  Yield-  to- Maturity Approach
The yield to maturity  (YTM) is the annual return that an investor earns on a bond 
if the investor purchases the bond today and holds it until maturity. In other words, 
it is the yield, rd, that equates the present value of the bond’s promised payments to 
its market price:
PPMT
rPMT
rFV
rPMT
dn
dn
dnt
01
1212121=
+

+… +
+

+
+

=
+ +









+
+

=∑
rFV
rdt
tn
dn
2121
where
 P0 = the current market price of the bond
 PMTt = the interest payment in period t
 rd = the yield to maturity

rd = the yield to maturity
 n = the number of periods remaining to maturity
 FV = the maturity value of the bond3
(2)
5 Such models are discussed thoroughly at Level II of the CFA Program.
6 Free cash flow to the firm (FCFF)  is the cash flow available to the company’s suppliers of capital after 
all operating expenses (including taxes) have been paid and necessary investments in working capital (e.g., 
inventory) and fixed capital (e.g., plant and equipment) have been made.
7 Free cash flow to equity (FCFE)  is the cash flow available to holders of the company’s common equity 
after all operating expenses, interest, and principal payments have been paid and necessary investments 
in working capital and fixed capital have been made.

Costs of the Different Sources of Capital 85
This valuation equation assumes the bond pays semi-  annual interest and that any 
intermediate cash flows (in this case the interest prior to maturity) are reinvested at 
the rate rd/2.8
Example 4 illustrates the calculation of the after-  tax cost of debt.
EXAMPLE 4   
Calculating the After-  Tax Cost of Debt
Valence Industries issues a bond to finance a new project. It offers a 10-  year, 
$1,000 face value, 5 percent semi-  annual coupon bond. Upon issue, the bond 
sells at $1,025. What is Valence’s before-  tax cost of debt? If Valence’s marginal 
tax rate is 35 percent, what is Valence’s after-  tax cost of debt?
Solution:
Given:
PV
FV
PMT
n=
=
=÷ =
=× =$,
$,
,$
$,1 025
1 000
51 000 22 5
10 22 0
1 025percen tof
= =
+()



+
+() =∑$$ , 25
11 000
1 120
20iit
t
Use a financial calculator to solve for i, the six-  month yield. Because i = 
2.342 percent, the before-  tax cost of debt is rd = 2.342 percent × 2 = 4.684 per -

cent, and Valence’s after-  tax cost of debt is rd (1 − t) = 0.04684 (1 − 0.35) = 
0.03045 or 3.045 percent.
3.1.2  Debt-  Rating Approach
When a reliable current market price for a company’s debt is not available, the debt-  
rating approach  can be used to estimate the before-  tax cost of debt. Based on a 
company’s debt rating, we estimate the before-  tax cost of debt by using the yield 
on comparably rated bonds for maturities that closely match that of the company’s 
existing debt.
Suppose a company’s capital structure includes debt with an average maturity 
(or duration) of 10 years and the company’s marginal tax rate is 35 percent. If the 
company’s rating is AAA and the yield on debt with the same debt rating and similar 
maturity is 4 percent, the company’s after-  tax cost of debt is
rd(1 – t) = 4 percent(1 – 0.35) = 2.6 percent
A consideration when using this approach is that debt ratings are ratings of the debt

issue itself, with the issuer being only one of the considerations. Other factors, such 
as debt seniority and security, also affect ratings and yields, so care must be taken 
to consider the likely type of debt to be issued by the company in determining the 
comparable debt rating and yield. The debt-  rating approach is a simple example of 
pricing on the basis of valuation-  relevant characteristics, which in bond markets has 
been known as evaluated pricing or matrix pricing .
8 rd is expressed as an annual rate and is divided by the number of payment periods per year. Because most 
corporate bonds pay semi-  annual interest, we divided rd by 2 in this calculation. The interest payment for 
each period thus corresponds with the bond’s semi-  annual coupon payment.

Reading 35 ■ Cost of Capital 86
3.1.3  Issues in Estimating the Cost of Debt
3.1.3.1  Fixed-  Rate Debt versus Floating-  Rate Debt  Up to now, we have assumed 
that the interest on debt is a fixed amount each period. We can observe market yields 
of the company’s existing debt or market yields of debt of similar risk in estimating 
the before-  tax cost of debt. However, the company may also issue floating-  rate debt 
in which the interest rate adjusts periodically according to a prescribed index, such as 
the prime rate or Libor, over the life of the instrument.
Estimating the cost of a floating-  rate security is difficult because the cost of this 
form of capital over the long term depends not only on the current yields but also on 
the future yields. The analyst may use the current term structure of interest rates and 
term structure theory to assign an average cost to such instruments.
3.1.3.2  Debt with Optionlike Features  How should an analyst determine the cost of

debt when the company used debt with optionlike features, such as call, conversion, or 
put provisions? Clearly, options affect the value of debt. For example, a callable bond 
would have a yield greater than a similar noncallable bond of the same issuer because 
bondholders want to be compensated for the call risk associated with the bond. In a 
similar manner, the put feature of a bond, which provides the investor with an option 
to sell the bond back to the issuer at a predetermined price, has the effect of lowering 
the yield on a bond below that of a similar nonputable bond.
If the company already has debt outstanding incorporating optionlike features that 
the analyst believes are representative of the future debt issuance of the company, the 
analyst may simply use the yield to maturity on such debt in estimating the cost of debt.
If the analyst believes that the company will add or remove option features in

future debt issuance, the analyst can make market value adjustments to the current 
YTM to reflect the value of such additions and/or deletions. The technology for such 
adjustments is an advanced topic that is outside the scope of this reading.
3.1.3.3  Nonrated Debt  If a company does not have any debt outstanding or if the 
yields on the company’s existing debt are not available, the analyst may not always be 
able to use the yield on similarly rated debt securities. It may be the case that the com -
pany does not have rated bonds. Though researchers offer approaches for estimating a 
company’s “synthetic” debt rating based on financial ratios, these methods are imprecise 
because debt ratings incorporate not only financial ratios but also information about 
the particular bond issue and the issuer that are not captured in financial ratios.
3.1.3.4  Leases  A lease is a contractual obligation that can substitute for other forms

of borrowing. This is true whether the lease is an operating lease  or a capital lease  
(finance lease ). If the company uses leasing as a source of capital, the cost of these 
leases should be included in the cost of capital. The cost of this form of borrowing is 
similar to that of the company’s other long-  term borrowing.
3.2 Cost of Preferred Stock
The cost of preferred stock  is the cost that a company has committed to pay pre -
ferred stockholders as a preferred dividend when it issues preferred stock. In the case 
of nonconvertible, noncallable preferred stock that has a fixed dividend rate and no 
maturity date ( fixed rate perpetual preferred stock ), we can use the formula for the 
value of a preferred stock:
PD
rpp
p=

Costs of the Different Sources of Capital 87
where
 Pp = the current preferred stock price per share
 Dp = the preferred stock dividend per share
 rP = the cost of preferred stock
We can rearrange this equation to solve for the cost of preferred stock: 
rD
Ppp
p=
Therefore, the cost of preferred stock is the preferred stock’s dividend per share 
divided by the current preferred stock’s price per share. Unlike interest on debt, the 
dividend on preferred stock is not tax-  deductible by the company; therefore, there is 
no adjustment to the cost for taxes.9
A preferred stock may have a number of features that affect the yield and hence 
the cost of preferred stock. These features include a call option, cumulative dividends, 
participating dividends, adjustable-  rate dividends, or convertibility into common 
stock. When estimating a yield based on current yields of the company’s preferred 
stock, we must make appropriate adjustments for the effects of these features on the

yield of an issue. For example, if the company has callable, convertible preferred stock 
outstanding, yet it is expected that the company will issue only noncallable, noncon -
vertible preferred stock in the future, we would have to either use the current yields 
on comparable companies’ noncallable, nonconvertible preferred stock or estimate 
the yield on preferred equity using methods outside the scope of this reading.
EXAMPLE 5   
Calculating the Cost of Preferred Equity
Alcoa has one class of preferred stock outstanding, a $3.75 cumulative preferred 
stock, for which there are 546,024 shares outstanding.10 If the price of this stock 
is $72, what is the estimate of Alcoa’s cost of preferred equity?
Solution:
Cost of Alcoa’s preferred stock = $3.75/$72.00 = 5.21 percent.
EXAMPLE 6   
Choosing the Best Estimate of the Cost of Preferred Equity
Wim Vanistendael is finance director of De Gouden Tulip N.V., a leading Dutch

flower producer and distributor. He has been asked by the CEO to calculate the 
cost of preferred equity and has recently obtained the following information:
■■The issue price of preferred stock was €3.5 million and the preferred divi -
dend is 5 percent.(3)
9 This is not to be confused, however, with the dividends-  received deduction, which reduces the effective 
tax on intercorporate preferred dividends received.
10 Alcoa Annual Report 2004, Footnote R, p. 56.

Reading 35 ■ Cost of Capital 88
■■If the company issued new preferred stock today, the preferred coupon 
rate would be 6.5 percent.
■■The company’s marginal tax rate is 30.5 percent.
What is the cost of preferred equity for De Gouden Tulip N.V.? 
Solution:
If De Gouden Tulip were to issue new preferred stock today, the coupon rate 
would be close to 6.5 percent. The current terms thus prevail over the past terms 
when evaluating the actual cost of preferred stock. The cost of preferred stock 
for De Gouden Tulip is, therefore, 6.5 percent. Because preferred dividends offer 
no tax shield, there is no adjustment made based upon the marginal tax rate.
3.3 Cost of Common Equity
The cost of common equity, ( re), usually referred to simply as the cost of equity, is the 
rate of return required by a company’s common shareholders. A company may increase 
common equity through the reinvestment of earnings—that is, retained earnings—or 
through the issuance of new shares of stock.

As we discussed earlier, the estimation of the cost of equity is challenging because 
of the uncertain nature of the future cash flows in terms of the amount and timing. 
Commonly used approaches for estimating the cost of equity include the capital asset 
pricing model, the dividend discount model, and the bond yield plus risk premium 
method.
3.3.1  Capital Asset Pricing Model Approach
In the capital asset pricing model (CAPM) approach, we use the basic relationship 
from the capital asset pricing model theory that the expected return on a stock, E(Ri), 
is the sum of the risk-  free rate of interest, RF, and a premium for bearing the stock’s 
market risk, βi(RM − RF):
ER RE RRiF iM F () =+ () − β
where
 βi = the return sensitivity of stock i to changes in the market return
 E(RM) = the expected return on the market
 E(RM) − RF = the expected market risk premium
A risk-  free asset is defined here as an asset that has no default risk. A common

proxy for the risk-  free rate is the yield on a default-  free government debt instrument. In 
general, the selection of the appropriate risk-  free rate should be guided by the duration 
of projected cash flows. If we are evaluating a project with an estimated useful life of 
10 years, we may want to use the rate on the 10-  year Treasury bond.
EXAMPLE 7   
Using the CAPM to Estimate the Cost of Equity
Valence Industries wants to know its cost of equity. Its CFO believes the risk-  free 
rate is 5 percent, equity risk premium is 7 percent, and Valence’s equity beta is 
1.5. What is Valence’s cost of equity using the CAPM approach?
Solution:
Cost of common stock = 5 percent + 1.5(7 percent) = 15.5 percent.(4)

Costs of the Different Sources of Capital 89
The expected market risk premium, or E(RM − RF), is the premium that investors 
demand for investing in a market portfolio relative to the risk-  free rate. When using 
the CAPM to estimate the cost of equity, in practice we typically estimate beta relative 
to an equity market index. In that case, the market premium estimate we are using is 
actually an estimate of the equity risk premium  (ERP).
An alternative to the CAPM to accommodate risks that may not be captured by 
the market portfolio alone is a multifactor model that incorporates factors that may 
be other sources of priced risk  (risk for which investors demand compensation for 
bearing), including macroeconomic factors and company-  specific factors. In general
ER RiF i
i() =+ ()
+ (β
β1 1
2Factor risk prem ium
Factor risk prem ium) )+
+ ()2
βij jFactor risk prem ium
where
 βij = stock i’s sensitivity to changes in the jth factor
 (Factor risk premium)j = expected risk premium for the jth factor

The basic idea behind these multifactor models is that the CAPM beta may not capture 
all the risks, especially in a global context, which include inflation, business-  cycle, 
interest rate, exchange rate, and default risks.11,12
There are several ways to estimate the equity risk premium, though there is no 
general agreement as to the best approach. The three we discuss are the historical 
equity risk premium approach, the dividend discount model approach, and the survey 
approach.
The historical equity risk premium approach  is a well-  established approach 
based on the assumption that the realized equity risk premium observed over a long 
period of time is a good indicator of the expected equity risk premium. This approach 
requires compiling historical data to find the average rate of return of a country’s mar -
ket portfolio and the average rate of return for the risk-  free rate in that country. For 
example, an analyst might use the historical returns to the TOPIX Index to estimate

the risk premium for Japanese equities. The exceptional bull market observed during 
the second half of the 1990s, and the bursting of the technology bubble that followed 
during the years 2000–2002, reminds us that the time period for such estimates should 
cover complete market cycles.
Elroy Dimson, Paul Marsh, and Mike Staunton conducted an analysis of the equity 
risk premiums observed in markets located in 16 countries, including the United 
States, over the period 1900–2002.13 These researchers found that the annualized US 
equity risk premium relative to US Treasury bills was 5.3 percent (geometric mean) 
and 7.2 percent (arithmetic mean). They also found that the annualized US equity 
risk premium relative to bonds was 4.4 percent (geometric mean) and 6.4 percent (5)
11 An example of the multi-  factor model is the three-  factor Fama and French model [Eugene Fama and 
Kenneth French, “The Cross-  Section of Expected Stock Returns, ” Journal of Finance , Vol. 47, No. 2 (1992),

pp. 427–465], which includes factors for the market, equity capitalization, and the ratio of book value of 
equity to the market value of equity.
12 These models are discussed in more detail by Robert F. Bruner, Robert M. Conroy, Wei Li, Elizabeth 
O’Halloran, and Miquel Palacios Lleras [ Investing in Emerging Markets , AIMR Research Foundation 
monograph (August 2003)] and by Eugene F. Fama and Kenneth R. French, “The Capital Asset Pricing 
Model: Theory and Evidence, ” Journal of Economic Perspectives , Vol. 18, No. 3 (Summer 2004), pp. 3–24.
13 Elroy Dimson, Paul Marsh, and Mike Staunton, “Global Evidence on the Equity Risk Premium, ” Journal 
of Applied Corporate Finance  (Fall 2003), pp. 27–38.

Reading 35 ■ Cost of Capital 90
(arithmetic mean).14 Note that the arithmetic mean is greater than the geometric 
mean as a result of the significant volatility of the observed market rate of return and 
of the observed risk-  free rate. Under the assumption of an unchanging distribution of 
returns through time, the arithmetic mean is the unbiased estimate of the expected 
single-  period equity risk premium, but the geometric mean better reflects growth 
rate over multiple periods.15 In Table 1 we provide historical estimates of the equity 
risk premium for 16 developed markets from Dimson, Marsh, and Staunton’s study.
Table 1   Equity Risk Premiums Relative to Bonds (1900 to 
2002) 
Mean
Country Geometric Arithmetic
Australia 6.3% 7.9%
Belgium 2.8 4.7
Canada 4.2 5.7
Denmark 1.8 3.1
France 4.6 6.7
Germany 6.3 9.6
Ireland 3.1 4.5
Italy 4.6 8.0
Japan 5.9 10.0
The Netherlands 4.4 6.4
South Africa 5.4 7.1
Spain 2.2 4.1
Sweden 4.9 7.1
Switzerland 2.4 3.9
United Kingdom 4.2 5.5
United States 4.8 6.7
World 4.3 5.4

Note : Germany excludes 1922–23. Switzerland commences in 1911.
Source:  Dimson, Marsh, and Staunton (2003).
To illustrate the historical method as applied in the CAPM, suppose that we use 
the historical geometric mean for US equity of 4.8 percent to value Citibank Inc. as 
of early January 2006. According to Standard & Poor’s, Citibank had a beta of 1.32 
at that time. Using the 10-  year US Treasury bond yield of 4.38 percent to represent 
the risk-  free rate, the estimate of the cost of equity for Citibank is 4.38 percent + 
1.32(4.8 percent) = 10.72 percent.
14 Jeremy Siegel presents a longer time series of market returns, covering the period from 1802 through 
2004, and observes an equity return of 6.82 percent and an equity risk premium in the range of 3.31 to 
5.36 percent. See Jeremy J. Siegel, “Perspectives on the Equity Risk Premium, ” Financial Analysts Journal ,

Vol. 61, No. 6 (November/December 2005), pp. 61–73. The range depends on the method of calculation 
(compounded or arithmetic) and the benchmark (bonds or bills).
15 Aside from the method of averaging (geometric versus arithmetic), estimates of the historical equity 
risk premium differ depending on the assumed investment horizon (short versus intermediate versus long), 
whether conditional on some variable or unconditional, whether US or global markets are examined, the 
source of the data, the period observed, and whether nominal or real returns are estimated.

Costs of the Different Sources of Capital 91
The historical premium approach has several limitations. One limitation is that 
the level of risk of the stock index may change over time. Another is that the risk 
aversion of investors may change over time. And still another limitation is that the 
estimates are sensitive to the method of estimation and the historical period covered.
EXAMPLE 8   
Estimating the Equity Risk Premium Using Historical Rates 
of Return
Suppose that the arithmetic average T-  bond rate observed over the last 100 
years is an unbiased estimator for the risk-  free rate and amounts to 5.4 percent. 
Likewise, suppose the arithmetic average of return on the market observed 
over the last 100 years is an unbiased estimator for the expected return for the 
market. The average rate of return of the market was 9.3 percent. Calculate the 
equity risk premium.
Solution:
ERP9 3 percen t5 4 percen t3 9 percen t =- =- = RRMF .. .

A second approach for estimating the equity risk premium is the dividend discount 
model based approach  or implied risk premium approach, which is implemented 
using the Gordon growth model (also known as the constant-  growth dividend discount 
model). For developed markets, corporate earnings often meet, at least approximately, 
the model’s assumption of a long-  run trend growth rate. We extract the premium by 
analyzing how the market prices an index. That is, we use the relationship between the 
value of an index and expected dividends, assuming a constant growth in dividends:
PD
rge01=−
where P0 is the current market value of the equity market index, D1 are the dividends 
expected next period on the index, re is the required rate of return on the market, and 
g is the expected growth rate of dividends. We solve for the required rate of return 
on the market as
rD
Pge=+1
0
Therefore, the expected return on the market is the sum of the dividend yield and the

growth rate in dividends.16 The equity risk premium thus is the difference between 
the expected return on the equity market and the risk-  free rate.
Suppose the expected dividend yield on an equity index is 5  percent and the 
expected growth rate of dividends on the index is 2 percent. The expected return on 
the market according to the Gordon growth model is
E(Rm) = 5 percent + 2 percent = 7 percent
A risk-  free rate of interest of 3.8 percent implies an equity risk premium of 7 percent 
− 3.8 percent = 3.2 percent.(6)
16 We explain Equation 6 in more detail in Section 3.3.2.

Reading 35 ■ Cost of Capital 92
Another approach to estimate the equity risk premium is quite direct: Ask a panel 
of finance experts for their estimates and take the mean response. This is the survey 
approach . For example, one set of US surveys found that the expected US equity risk 
premium over the next 30 years was 5.5 percent to 7 percent forecasting from 2001 
as the baseline year and 7.1 percent using 1998 as the baseline year.
Once we have an estimate of the equity risk premium, we fine-  tune this estimate 
for the particular company or project by adjusting it for the specific systematic risk 
of the project. We adjust for the specific systematic risk by multiplying the market 
risk premium by beta to arrive at the company’s or project’s risk premium, which we 
then add to the risk-  free rate to determine the cost of equity within the framework 
of the CAPM.17
3.3.2  Dividend Discount Model Approach
Earlier we used the Gordon growth model to develop an estimate of the equity risk

premium for use in the CAPM. We can also use the Gordon growth model directly 
to obtain an estimate of the cost of equity. To review, the dividend discount model 
in general states that the intrinsic value of a share of stock is the present value of the 
share’s expected future dividends:
VD
rD
rD
rt
et tee0 112
21 1 1=
+()



=+()+
+()+=∞∑ 
where
 V0 = the intrinsic value of a share
 Dt = the share’s dividend at the end of period t
 re = the cost of equity
Based on Gordon’s constant growth formulation, we assume dividends are expected 
to grow at a constant rate, g.18 Therefore, if we assume that price reflects intrinsic 
value ( V0 = P0), we can rewrite the valuation of the stock as
PD
rge01=−
We can then rewrite the above equation and estimate the cost of equity as we did for 
Equation 6 in Section 3.3.1:
rD
Pge=+1
0
Therefore, to estimate re, we need to estimate the dividend in the next period and 
the assumed constant dividend growth rate. The current stock price, P0, is known,

and the dividend of the next period, D1, can be predicted if the company has a stable 
dividend policy. (The ratio D1/P0 may be called the forward annual dividend yield.) 
The challenge is estimating the growth rate.
There are at least two ways to estimate the growth rate. The first is to use a fore -
casted growth rate from a published source or vendor. A second is to use a relationship 
between the growth rate, the retention rate, and the return on equity. In this context, 
this is often referred to as the sustainable growth rate  and is interpretable as the 
17 Some researchers argue that the equity risk premium should reflect a country risk premium. For 
example, a multinational company or project may have a higher cost of capital than a comparable domestic 
company because of political risk, foreign exchange risk, or higher agency costs. In most cases, this risk is 
unsystematic and hence does not affect the cost of capital estimate.

18 Myron J. Gordon, The Investment, Financing, and Valuation of the Corporation , Homewood, IL: Irwin, 
1962.

Topics in Cost of Capital Estimation 93
rate of dividend (and earnings) growth that can be sustained over time for a given 
level of return on equity, keeping the capital structure constant and without issuing 
additional common stock. The relationship is given in Equation 7:
g = (1 – D/EPS)ROE
where D/EPS represents the assumed stable dividend payout ratio and ROE is the his -
torical return on equity. The term (1 – D/EPS) is the company’s earnings retention rate.
Consider Citigroup, Inc. Citigroup has an earnings retention rate of 59 percent. As 
of early January 2006, Citigroup had a forward annual dividend yield of 3.9 percent, a 
trailing return on equity of approximately 20 percent, but an estimated average return 
on equity going forward of approximately 16.6  percent. According to Equation  7, 
Citigroup’s sustainable growth rate is 0.59(16.6 percent) = 9.79 percent. The dividend 
discount model estimate of the cost of equity is, therefore, 9.79 percent + 3.9 percent 
= 13.69 percent.

3.3.3  Bond Yield plus Risk Premium Approach
The bond yield plus risk premium approach  is based on the fundamental tenet in 
financial theory that the cost of capital of riskier cash flows is higher than that of less 
risky cash flows. In this approach, we sum the before-  tax cost of debt, rd, and a risk 
premium that captures the additional yield on a company’s stock relative to its bonds. 
The estimate is, therefore,
re = rd + Risk premium
The risk premium compensates for the additional risk of equity compared with 
debt.19 Ideally, this risk premium is forward looking, representing the additional risk 
associated with the stock of the company as compared with the bonds of the same 
company. However, we often estimate this premium using historical spreads between 
bond yields and stock yields. In developed country markets, a typical risk premium 
added is in the range of 3 to 5 percent.
Looking again at Citigroup, as of early January 2006, the yield to maturity of the

Citigroup 5.3s bonds maturing in 2016 was approximately 4.95 percent. Adding an 
arbitrary risk premium of 3.5  percent produces an estimate of the cost of equity 
of 4.95  + 3.5  = 8.45  percent. This estimate contrasts with the higher estimates of 
10.72  percent, under the CAPM approach, and 13.69  percent, under the dividend 
discount model approach. Such disparities are not uncommon and reflect the difficulty 
of cost of equity estimation.
TOPICS IN COST OF CAPITAL ESTIMATION
When calculating a company’s weighted average cost of capital (WACC), it is essential 
to understand the risk factors that have been considered in determining the risk-  free 
rate, the equity risk premium, and beta to ensure a consistent calculation of WACC 
and avoid the double counting or omission of pertinent risk factors.(7)
(8)
4
19 This risk premium is not to be confused with the equity risk premium. The equity risk premium is the

difference between the cost of equity and the risk-  free rate of interest . The risk premium in the bond yield 
plus risk premium approach is the difference between the cost of equity and the company’s cost of debt .

Reading 35 ■ Cost of Capital 94
4.1 Estimating Beta and Determining a Project Beta
When the analyst uses the CAPM to estimate the cost of equity, he or she must estimate 
beta. The estimation of beta presents many choices as well as challenges.
One common method of estimating the company’s stock beta is to use a market 
model regression of the company’s stock returns ( Ri) against market returns ( Rm) 
over T periods:20
RR tTit mt =+ = ab   /circumflexnosp/circumflexnosp…12,,
where  a is the estimated intercept and  b is the estimated slope of the regression that 
is used as an estimate of beta. However, beta estimates are sensitive to the method of 
estimation and data used. Consider some of the issues:
■■Estimation period . The estimated beta is sensitive to the length of the estima -
tion period, with beta commonly estimated using data over two to nine years. 
Selection of the estimation period is a trade-  off between data richness captured

by longer estimation periods and company-  specific changes that are better 
reflected with shorter estimation periods. In general, longer estimation periods 
are applied to companies with a long and stable operating history, and shorter 
estimation periods are used for companies that have undergone significant 
structural changes in the recent past (such as restructuring, recent acquisition, 
or divestiture) or changes in financial and operating leverage.
■■Periodicity of the return interval  (e.g., daily, weekly, or monthly). Researchers 
have observed smaller standard error in beta estimated using smaller return 
intervals, such as daily returns.21
■■Selection of an appropriate market index . The choice of market index affects the 
estimate of beta.
■■Use of a smoothing technique . Some analysts adjust historical betas to reflect the 
tendency of betas to revert to 1.22 As an example, the expression βi,adj = 0.333 + 
0.667βi adjusts betas above and below 1.0 toward 1.0.

■■Adjustments for small-  capitalization stocks . Small-  capitalization stocks have 
generally exhibited greater risks and greater returns than large-  capitalization 
stocks over the long run. Roger Ibbotson, Paul Kaplan, and James Peterson 
argue that betas for small-  capitalization companies be adjusted upward.23
Arriving at an estimated beta for publicly traded companies is generally not a 
problem because of the accessibility of stock return data, the ease of use of estimating 
beta using simple regression, and the availability of estimated betas on publicly traded 
companies from financial analysis vendors, such as Barra, Bloomberg, Thompson 
Financial’s Datastream, Reuters, and Value Line. The challenge is to estimate a beta 
for a company that is not publicly traded or to estimate a beta for a project that is 
not the average or typical project of a publicly traded company. Estimating a beta in 
these cases requires proxying for the beta by using the information on the project or

company combined with a beta of a publicly traded company.
20 This equation is commonly referred to as the market model  and was first introduced by Michael C. 
Jensen in “The Performance of Mutual Funds in the Period 1945–1964, ” Journal of Finance , Vol. 23, No. 2 
(1969), pp. 389–416.
21 Phillip R. Daves, Michael C. Ehrhardt, and Robert A. Kunkel, “Estimating Systematic Risk: The Choice 
of Return Interval and Estimation Period, ” Journal of Financial and Strategic Decisions , Vol. 13, No. 1 
(Spring 2000), pp. 7–13.
22 Marshall Blume, “On the Assessment of Risk, ” Journal of Finance , Vol. 26, No. 1 (March 1971), pp. 1–10.
23 Roger G. Ibbotson, Paul D. Kaplan, and James D. Peterson, “Estimates of Small Stock Betas Are Much 
Too Low, ” Journal of Portfolio Management  (Summer 1997), pp. 104–110.

Topics in Cost of Capital Estimation 95
The beta of a company or project is affected by the systematic components of 
business risk and by financial risk. Both of these factors affect the uncertainty of the 
cash flows of the company or project. The business risk  of a company or project is the 
risk related to the uncertainty of revenues, referred to as sales risk , and to operating 
risk, which is the risk attributed to the company’s operating cost structure. Sales risk 
is affected by the elasticity of the demand of the product, the cyclicality of the reve -
nues, and the structure of competition in the industry. Operating risk is affected by 
the relative mix of fixed and variable operating costs: the greater the fixed operating 
costs, relative to variable operating costs, the greater the uncertainty of income and 
cash flows from operations.
Financial risk  is the uncertainty of net income and net cash flows attributed to

the use of financing that has a fixed cost, such as debt and leases. The greater the 
use of fixed-  financing sources of capital, relative to variable sources, the greater the 
financial risk. In other words, a company that relies heavily on debt financing instead 
of equity financing is assuming a great deal of financial risk.
How does a financial analyst estimate a beta for a company or project that is not 
publicly traded? One common method is the pure-  play method , which requires using 
a comparable publicly traded company’s beta and adjusting it for financial leverage 
differences.
A comparable company  is a company that has similar business risk. The reason 
it is referred to as the pure-  play  method is that one of the easiest ways of identifying 
a comparable for a project is to find a company in the same industry that is in that 
single  line of business. For example, if the analyst is examining a project that involves

drug stores, appropriate comparables in the United States may be Walgreens, CVS 
Corporation, and Rite Aid Corporation.
In estimating a beta in this way, the analyst must make adjustments to account 
for differing degrees of financial leverage. This requires a process of “unlevering” 
and “levering” the beta. The beta of the comparable is first “unlevered” by removing 
the effects of its financial leverage.24 The unlevered beta is often referred to as the 
asset beta  because it reflects the business risk of the assets. Once we determine the 
unlevered beta, we adjust it for the capital structure of the company or project that 
is the focus of our analysis. In other words, we “lever” the asset beta to arrive at an 
estimate of the equity beta for the project or company of interest.
For a given company, we can unlever its equity beta to estimate its asset beta. To 
do this, we must determine the relationship between a company’s asset beta and its

equity beta. Because the company’s risk is shared between creditors and owners, we 
can represent the company’s risk, βasset, as the weighted average of the company’s 
creditors’ market risk, βdebt, and the market risk of the owners, βequity :
βasset = βdebtwd + βequity we
or
ββ βasse td ebte quity=+

++

D
DEE
DE
where
 E = market value of equity
 D = market value of debt
 wd = proportion of debt = D/(D + E)
 we = proportion of equity = E/(D + E)
24 The process of unlevering and levering a beta was developed by Robert S. Hamada [“The Effect of the 
Firm’s Capital Structure on the Systematic Risk of Common Stocks, ” Journal of Finance  (May 1972), pp. 
435–452] and is based on the capital structure theories of Franco Modigliani and Merton Miller.

Reading 35 ■ Cost of Capital 96
But interest on debt is deducted by the company to arrive at taxable income, so the 
claim that creditors have on the company’s assets does not cost the company the full 
amount but, rather, the after-  tax claim; the burden of debt financing is actually less 
due to interest deductibility. We can represent the asset beta of a company as the 
weighted average of the betas of debt and equity after considering the effects of the 
tax- deductibility of interest: 
ββ βasse td ebte quity=−()
−() ++−() +1
11tD
tD EE
tD E
where t is the marginal tax rate.
We generally assume that a company’s debt does not have market risk, so βdebt = 
0. This means that the returns on debt do not vary with the returns on the market, 
which we generally assume to be true for most large companies. If βdebt = 0, then25
ββasse te quity =
+−()









1
11 tD
E
Therefore, the market risk of a company’s equity is affected by both the asset’s market

risk, βasset, and a factor representing the nondiversifiable portion of the company’s 
financial risk,  11+−()



tD
E:
ββequity asse t =+ −()



11 tD
E
Suppose a company has an equity beta of 1.5, a debt-  to- equity ratio of 0.4, and a 
marginal tax rate of 30 percent. Using Equation 9, the company’s asset beta is 1.1719:
βasset 1.5 1.1719 =
+−() () ()



= [] = 151
11 03 040 7813 .
...
In other words, if the company did not have any debt financing, its βasset = βequity  = 
1.1719; however, the use of debt financing increases its βequity  from 1.1719 to 1.5. What 
would the company’s equity beta be if the company’s debt-  to- equity ratio were 0.5 
instead of 0.4? In this case, we apply Equation 10, using the debt-  to- equity ratio of 0.5:
βequity 1.5821 =+ −() () () = 1 1719 11 03 05 .. .
Therefore, the unlevering calculation produces a measure of market risk for the 
assets of the company—ignoring the company’s capital structure. We use the levering

calculation in Equation 10 to estimate the market risk of a company given a specific 
asset risk, marginal tax rate, and capital structure.
We can use the same unlevering and levering calculations to estimate the asset 
risk and equity risk for a project. We start with the equity beta of the comparable 
company, which is the levered beta, βL,comparable , and then convert it into the equiv -
alent asset beta for the unlevered company, βU,comparable . Once we have the estimate 
of the unlevered beta, which is the company’s asset risk, we then can use the project’s 
capital structure and marginal tax rate to convert this asset beta into an equity beta 
for the project, βL,project .(9)
(10)
25 The first step is ββasse te quity =−() +

E
tD E 1, which we simplify to arrive at Equation 9.

Topics in Cost of Capital Estimation 97
Estimating a Beta Using the Pure-  Play Method
Step 1: Select the comparable      Determine comparable company or companies. 
These are companies with similar business risk.
↓
Step 2: Estimate comparable’s beta      Estimate the equity beta of the comparable 
company or companies.
↓
Step 3: Unlever the comparable’s beta      Unlever the beta of the comparable com -
pany or companies, removing the financial risk component of the equity beta, leaving 
the business risk component of the beta.
↓
Step 4: Lever the beta for the project’s financial risk      Lever the beta of the proj -
ect by adjusting the asset beta for the financial risk of the project.
We begin by estimating the levered beta of the comparable company, βL,comparable . 
Using the capital structure and tax rate of the levered company, we estimate the asset 
beta for the comparable company, βU,comparable :
ββ
U,comparableL,comparable
comparablecomparable
coD
E=
+−() 11 t
mmparable







coD
E=
+−() 11 t






We then consider the financial leverage of the project or company and calculate its 
equity risk, βL,project :
ββL,project U,comparable projectproject
projectD
E=+ −()
11 t 





To illustrate the use of these equations, suppose we want to evaluate a project 
that will be financed with debt and equity in a ratio of 0.4:1 [a debt-  to- equity ratio of 
0.4, corresponding to approximately 0.4/(0.4 + 1.0) = €0.286 for each euro of capital 
needed]. We find a comparable company operating in the same line of business as 
the project. The marginal tax rate for the company sponsoring the project and the 
comparable company is 35 percent. The comparable company has a beta of 1.2 and a 
debt-  to- equity ratio of 0.125. The unlevered beta of the comparable is 1.1098:
βU,comparable =
+−()() =12
11 03501251 1098.
...
The levered beta for the project is 1.3983:
βL,project =+ −()() = 1 1098 11 035041 3983 .. ..

We then use the 1.3983 as the beta in our CAPM estimate of the component cost 
of equity for the project and, combined with the cost of debt in a weighted average, 
provide an estimate of the cost of capital for the project.26(11)
(12)
26 In this example, the weights are wd = 0.4/1.4 = 0.2857 and we = 1/1.4 = 0.7143.

Reading 35 ■ Cost of Capital 98
EXAMPLE 9   
Inferring an Asset Beta
Suppose that the beta of a publicly traded company’s stock is 1.3 and that the 
market value of equity and debt are, respectively, C$540 million and C$720 mil -
lion. If the marginal tax rate of this company is 40 percent, what is the asset 
beta of this company?
Solution:
βU=
+−()



=13
11 04720
540072.
..
EXAMPLE 10   
Calculating a Beta Using the Pure-  Play Method
Raymond Cordier is the business development manager of Aerotechnique S.A., 
a private Belgian subcontractor of aerospace parts. Although Aerotechnique is 
not listed on the Belgian stock exchange, Cordier needs to evaluate the levered 
beta for the company. He has access to the following information:
■■The average levered and average unlevered betas for the group of compa -
rable companies operating in different European countries are 1.6 and 1.0, 
■■Aerotechnique’s debt-  to- equity ratio, based on market values, is 1.4.

■■Aerotechnique’s corporate tax rate is 34 percent.
Solution:
The beta for Aerotechnique is estimated on the basis of the average unlevered beta 
extracted from the group of comparable companies. On that basis, and applying 
the financing structure of Aerotechnique, the estimated beta for Aerotechnique is
βAerotechnique =+ −() () () = 1011 0341 41 924 .. ..
EXAMPLE 11   
Estimating the Weighted Average Cost of Capital
Georg Schrempp is the CFO of Bayern Chemicals KgaA, a large German man -
ufacturer of industrial, commercial, and consumer chemical products. Bayern 
Chemicals is privately owned, and its shares are not listed on an exchange. The 
CFO has appointed Markus Meier, CFA, of Crystal Clear Valuation Advisors, a 
third-  party valuator, to perform a stand-  alone valuation of Bayern Chemicals. 
Meier had access to the following information to calculate Bayern Chemicals’ 
weighted average cost of capital:
■■The nominal risk-  free rate is represented by the yield on the long-  term 10-

Topics in Cost of Capital Estimation 99
■■The average long-  term historical equity risk premium in Germany is 
assumed at 5.7 percent.27
■■Bayern Chemicals’ corporate tax rate is 38 percent.
■■Bayern Chemicals’ target debt-  to- equity ratio is 0.7. Bayern is operating at 
its target debt-  to- equity ratio.
■■Bayern Chemicals’ cost of debt has an estimated spread of 225 basis 
points over the 10-  year bund.
■■Table 2 supplies additional information on comparables for Bayern 
Chemicals.
Table 2   Information on Comparables
Comparable 
Companies CountryTax 
Rate 
(%)Market 
in MillionsNet 
Debt in 
Millions D/E Beta
British 
Chemicals 
Ltd.United 
Kingdom30.0 4,500 6,000 1.33 1.45
Compagnie 
Petrochimique 
S.A.France 30.3 9,300 8,700 0.94 0.75
Rotterdam 
Chemie N.V.Netherlands 30.5 7,000 7,900 1.13 1.05
Average 1.13 1.08
Based only on the information given, calculate Bayern Chemicals’ WACC.
Solution:
To calculate the cost of equity, the first step is to “unlever” the betas of the

comparable companies and calculate an average for a company with business 
risk similar to the average of these companies:
Comparable Companies Unlevered Beta
British Chemicals Ltd. 0.75
Compagnie Petrochimique S.A. 0.45
Rotterdam Chemie N.V. 0.59
Average* 0.60
* An analyst must apply judgment and experience to determine a representative average for 
the comparable companies. This example uses a simple average, but in some situations a 
weighted average based on some factor such as market capitalization may be more appropriate.
Levering the average unlevered beta for the peer group average, applying Bayern 
Chemicals’ target debt-  to- equity ratio and marginal tax rate, results in a beta 
of 0.86: 
βBayern Che mical=+ −() {} = 0601 10 3807 08 6 .. ..
27 Dimson, Marsh, and Staunton, op. cit .

Reading 35 ■ Cost of Capital 100
The cost of equity of Bayern Chemicals ( re) can be calculated as follows: 
re = 4.5 percent + (0.86)(5.7 percent) = 9.4 percent
The weights for the cost of equity and cost of debt may be calculated as follows: 
wDE
D
E
wwd
ed=
+

==
=− =− =107
17041
11 0410 59.
..
..
The before-  tax cost of debt of Bayern Chemicals ( rd) is 6.75 percent: 
rd = 4.5 percent + 2.25 percent = 6.75 percent
As a result, Bayern Chemicals’ WACC is 7.27 percent: 
 WACC = [(0.41)(0.0675)(1 – 0.38)] + [(0.59)(0.094)]
  = 0.0726 or 7.26 percent
4.2 Country Risk
The use of a stock’s beta to capture the country risks of a project is well supported in 
empirical studies that examine developed nations. However, beta does not appear to 
adequately capture country risk for companies in developing nations.28 A common 
approach for dealing with this problem is to adjust the cost of equity estimated using 
the CAPM by adding a country spread to the market risk premium.29 The country

spread is also referred to as a country risk premium.
Perhaps the simplest estimate of the country spread is the sovereign yield spread , 
which is the difference between the government bond yield in that country, denomi -
nated in the currency of a developed country, and the Treasury bond yield on a similar 
maturity bond in the developed country.30 However, this approach may be too coarse 
for the purposes of risk premium estimation.
28 Campbell R. Harvey, “The International Cost of Capital and Risk Calculator, ” Duke University working 
paper (July 2001).
29 Adding the country spread to the market risk premium for a developing country and then multiplying 
this sum by the market risk of the project is making the assumption that the country risk premium varies 
according to market risk. An alternative method calculates the cost of equity as the sum of three terms: 1) 
the risk-  free rate of interest, 2) the product of the beta and the developed market risk premium, and 3) the

country risk premium. This latter method assumes that the country risk premium is the same, regardless 
of the project’s market risk.
30 Jorge O. Mariscal and Rafaelina M. Lee, “The Valuation of Mexican Stocks: An Extension of the Capital 
Asset Pricing Model, ” New York: Goldman Sachs (1993).

Topics in Cost of Capital Estimation 101
Another approach is to calculate the country risk premium as the product of the 
sovereign yield spread and the ratio of the volatility of the developing country equity 
market to that of the sovereign bond market denominated in terms of the currency 
of a developed country:31
Country  equity  prem ium
Sovereign y ield spreadAnnua lized s t
=a andard de viation
of equity  index
Annua lized standard deviat i ion of the
sovereign bond market in terms
of the de veloped mmark et currenc y
















The logic of this calculation is that the sovereign yield spread captures the general 
risk of the country, which is then adjusted for the volatility of the stock market relative 
to the bond market. This country risk premium is then used in addition to the equity 
premium estimated for a project in a developed country. Therefore, if the equity risk 
premium for a project in a developed country is 4.5  percent and the country risk

premium is 3 percent, the total equity risk premium used in the CAPM estimation is 
7.5 percent. If the appropriate beta is 1.2 and the risk-  free rate of interest is 4 percent, 
the cost of equity is
Cost of equity = 0.04 + 1.2(0.045 + 0.03) = 0.13 or 13 percent
EXAMPLE 12   
Estimating the Country Risk Premium
Miles Avenaugh, an analyst with the Global Company, is estimating a country 
risk premium to include in his estimate of the cost of equity capital for Global’s 
investment in Argentina. Avenaugh has researched yields in Argentina and 
observed that the Argentinean government’s 10-  year bond is 9.5  percent. A 
similar maturity US Treasury bond has a yield of 4.5 percent. The annualized 
standard deviation of the Argentina Merval stock index, a market value index 
of stocks listed on the Buenos Aires Stock Exchange, during the most recent 
year is 40 percent. The annualized standard deviation of the Argentina dollar-

denominated 10-  year government bond over the recent period was 28 percent.
What is the estimated country risk premium for Argentina based on 
Avenaugh’s research?
Solution:
Country risk prem ium=

= () = 005040
02800514286 0 071 ..
... .4 4 or 7 14 percen t . 
Still another approach is to use country credit ratings to estimate the expected rates 
of returns for countries that have credit ratings but no equity markets.32 This method 
requires estimating reward to credit risk measures for a large sample of countries for 
which there are both credit ratings and equity markets and then applying this ratio to 
those countries without equity markets based on the country’s credit rating.(13)
31 Aswath Damodaran, “Estimating Equity Risk Premiums, ” New York University working paper (1999) 
and Aswath Damodaran, “Measuring Company Exposure to Country Risk: Theory and Practice, ” New York 
University working paper (September 2003).

32 Claude Erb, Campbell R. Harvey, and Tadas Viskanta, “Expected Returns and Volatility in 135 Countries, ” 
Journal of Portfolio Management  (Spring 1996), pp. 46–58.

Reading 35 ■ Cost of Capital 102
4.3 Marginal Cost of Capital Schedule
As we noted in Section 2.3, as a company raises more funds, the costs of the different 
sources of capital may change, resulting in a change in the weighted average cost of 
capital for different levels of financing. The result is the marginal cost of capital (MCC) 
schedule, which we often depict in graphical form as the weighted average cost of 
capital for different amounts of capital raised, as we showed earlier in Figure 1.33
Why would the cost of capital change as more capital is raised? One source of a 
difference in cost depending on the amount of capital raised is that a company may 
have existing debt with a bond covenant that restricts the company from issuing 
debt with similar seniority as existing debt. Or, a debt incurrence test  may restrict a 
company’s ability to incur additional debt at the same seniority based on one or more

financial tests or conditions. For example, if a company issues senior debt such that 
any additional debt at that seniority violates the debt incurrence test of an existing 
bond covenant, the company may have to issue less senior debt or even equity, which 
would have a higher cost.
Another source of increasing marginal costs of capital is a deviation from the 
target capital structure. In the ideal, theoretical world, a company has a target capital 
structure and goes to the market each period and raises capital in these proportions. 
However, as a practical matter, companies do not necessarily tap the market in these 
ideal proportions because of considerations for economies of scale in raising new cap -
ital and market conditions. Because of such perceived economies of scale, companies 
tend to issue new securities such that in any given period, it may deviate from the 
proportions dictated by any target or optimal capital structure. In other words, these

short-  run deviations are due to the “lumpiness” of security issuance. As the company 
experiences deviations from the target capital structure, the marginal cost of capital 
may increase, reflecting these deviations.
The amount of capital at which the weighted average cost of capital changes—
which means that the cost of one of the sources of capital changes—is referred to as a 
break point . The reality of raising capital is that the marginal cost of capital schedule 
is not as smooth as we depicted in Figure 1 but, rather, is a step-  up cost schedule as 
shown in Figure 2.
33 Later in this section, we will discuss cases where a company’s WACC may actually decrease as addi -
tional capital is raised. For example, if a company financed solely with common equity raises additional 
capital via debt, then the tax advantages provided by debt will result in a lower WACC under the new 
capital structure. For this discussion, we are assuming that the company is already operating at or near its

Topics in Cost of Capital Estimation 103
Figure 2   Marginal Cost of Capital Schedule
0%1%2%3%4%5%6%7%
$0.5 $2.5 $4.5 $6.5 $8.5 $10.5 $12.5 $14.5 $16.5 $18.5
Amount of New CapitalWACC
Consider the case of a company facing the costs of capital given in Table 3.
Table 3   Schedule of the Costs of Debt and Equity
Amount of New Debt 
(in Millions)After-  Tax 
Cost of DebtAmount of New Equity 
(in Millions) Cost of Equity
new debt ≤ €2 2.0 percent new equity ≤ €6 5.0 percent
€2 < new debt ≤ €5 2.5 percent €6 < new equity ≤ €8 7.0 percent
€5 < new debt 3.0 percent €8 < new equity 9.0 percent
If the company raises capital according to its target capital structure proportions 
of 40 percent debt and 60 percent equity, this company faces a marginal cost of capital 
schedule that is upward sloping, with break points at €5 million, €10 million, €12.5 mil -
lion, and €13.3 million, as depicted in Figure 2. These break points are determined 
from the amounts of capital at which the cost changes, calculated as

Brea k pointAmount of capita l at which the source's cost o=ff capital change s
Proportion of new capita l raised from th ee source
For example, the first break point for debt financing is reached with €2 million/0.4 = 
€5 million of new capital raised. The first break point attributed to a change in equity 
cost occurs at €6 million/0.6 = €10 million. Example 13 illustrates a marginal cost of 
capital schedule with break points and also how the WACC figures in the choice of 
an optimal capital structure.(14)

Reading 35 ■ Cost of Capital 104
EXAMPLE 13   
Marginal Cost of Capital Schedule
Alan Conlon is the CFO of Allied Canadian Breweries Ltd. He wants to deter -
mine the capital structure that will result in the lowest cost of capital for Allied. 
He has access to the following information:
■■The minimum rate at which the company can borrow is the 12-  month 
Libor rate plus a premium that varies with the debt-  to- capital ratio [ D/(D 
+ E)] as given in Table 4.
Table 4   Spreads over Libor for Alternative Debt-  to- 
Capital Ratios
D
DE+  Spread (bps)
Less than 0.40 200
0.40 to 0.49 300
0.50 to 0.59 400
0.60 to 0.69 600
0.70 to 0.79 800
0.80 to 0.89 1,000
0.90 or higher 1,200
■■The current 12-  month Libor is 4.5 percent.
■■The market risk premium is 4 percent, and unleveraged beta is 0.9.
■■The risk-  free rate is 4.25 percent.
■■The company’s tax rate is 36 percent.
1 Determine the WACC for 10 percent intervals of the debt-  to- capital ratio

(i.e., 0.1, 0.2, etc.) based on the information given in Table 4.
2 Recommend a target capital structure based on 10 percent intervals of the 
debt-  to- capital ratio, recommend a target capital structure.
The WACC expressed as a function of the capital structure is shown in Table 5.
Table 5   WACC for Alternative Capital Structures
D
DE+ β rd (Percent) re (Percent) WACC (Percent)
0.1 0.96 6.5 8.1 7.7
0.2 1.04 6.5 8.4 7.6
0.3 1.15 6.5 8.8 7.4
0.4 1.28 7.5 9.4 7.6

Topics in Cost of Capital Estimation 105
D
0.5 1.48 8.5 10.2 7.8
0.6 1.76 10.5 11.3 8.6
0.7 2.24 12.5 13.2 9.6
0.8 3.20 14.5 17.1 10.8
0.9 6.08 16.5 28.6 12.4
The optimal capital structure is 30 percent debt; based on 10 percent intervals 
of the debt-  to- capital ratio, this will achieve the lowest possible cost of capital.
4.4 Flotation Costs
When a company raises new capital, it generally seeks the assistance of investment 
bankers. Investment bankers charge the company a fee based on the size and type of 
offering. This fee is referred to as the flotation cost . In the case of debt and preferred 
stock, we do not usually incorporate flotation costs in the estimated cost of capital 
because the amount of these costs is quite small, often less than 1 percent.34
However, with equity issuance, the flotation costs may be substantial, so we should 
consider these when estimating the cost of external equity capital. For example, Inmoo

Lee, Scott Lochhead, Jay Ritter, and Quanshui Zhao observe average flotation costs for 
new equity in the United States of 7.11 percent.35 The flotation costs in other coun -
tries differ from the US experience: Thomas Bühner and Christoph Kaserer observe 
flotation costs around 1.65 percent in Germany, Seth Armitage estimates an average 
issuance cost of 5.78  percent in the United Kingdom, and Christoph Kaserer and 
Fabian Steiner observe an average cost of 4.53 for Swiss capital offerings.36 A large 
part of the differences in costs among these studies is likely attributed to the type of 
offering; cash underwritten offers, typical in the United States, are generally more 
expensive than rights offerings, which are common in Europe.
Should we incorporate flotation costs into the cost of capital? There are two views 
on this topic. One view, which you can find often in textbooks, is to incorporate the 
flotation costs into the cost of capital. The other view is that flotation costs should not

be included in the cost of capital but, rather, incorporated into any valuation analysis 
as an additional cost of the project.Table 5   (Continued)
34 We can incorporate them for these sources by simply treating the flotation costs as an outlay, hence 
reducing proceeds from the source.
35 Inmoo Lee, Scott Lochhead, Jay R. Ritter, and Quanshui Zhao, “The Costs of Raising Capital, ” Journal 
of Financial Research , Vol. 19 (Spring, 1996), pp. 59–71.
36 Thomas Bühner and Christoph Kaserer, “External Financing Costs and Economies of Scale in Investment 
Banking: The Case of Seasoned Equity Offerings in Germany, ” European Financial Management , Vol. 9 
(June 2002), pp. 249; Seth Armitage, “The Direct Costs of UK Rights Issues and Open Offers, “ European 
Financial Management , Vol. 6 (2000), pp. 57–68; Christoph Kaserer and Fabian Steiner, “The Cost of Raising 
Capital—New Evidence from Seasoned Equity Offerings in Switzerland, ” Technische Universität München 
working paper (February 2004).

Reading 35 ■ Cost of Capital 106
Consistent with the first view, we can specify flotation costs in monetary terms, 
as an amount per share or as a percentage of the share price. With flotation costs in 
monetary terms on a per share basis, F, the cost of external equity is
rD
PFge=−

+1
0
As a percentage applied against the price per share, the cost of external equity is
rD
Pfge=−()

+1
01
where f is the flotation cost as a percentage of the issue price.
Suppose a company has a current dividend of $2 per share, a current price of $40 
per share, and an expected growth rate of 5 percent. The cost of internally generated 
equity would be 10.25 percent:
re=+()

+= +=$.
$.. .. ,.21 005
400050 0525 0050 1025 10 25  or  pe ercen t
If the flotation costs are 4 percent of the issuance, the cost of externally generated 
equity would be slightly higher at 10.469 percent:
re=+()
−()

+= +=$.
$... .. ,21 005
4010 040050 05469 0050 1047   or  percen t 10 47 .

The problem with this approach is that the flotation costs are a cash flow at the 
initiation of the project and affect the value of any project by reducing the initial cash 
flow. Adjusting the cost of capital for flotation costs is incorrect because by doing so, 
we are adjusting the present value of the future cash flows by a fixed percentage—in 
the above example, a difference of 22 basis points, which does not necessarily equate 
to the present value of the flotation costs.37
The alternative and recommended approach is to make the adjustment to the cash 
flows in the valuation computation. For example, consider a project that requires a 
€60,000 initial cash outlay and is expected to produce cash flows of €10,000 each 
year for 10 years. Suppose the company’s marginal tax rate is 40 percent and that 
the before-  tax cost of debt is 5 percent. Furthermore, suppose that the company’s

dividend next period is €1, the current price of the stock is €20, and the expected 
growth rate is 5 percent so that the cost of equity using the dividend discount model 
is (€1/€20) + 0.05 = 0.10 or 10 percent. Assume the company will finance the project 
with 40 percent debt and 60 percent equity. Table 6 summarizes the information on 
the component costs of capital.
Table 6   After-  Tax Costs of Debt and Equity
Source of CapitalAmount 
Raised (€) Proportion Marginal After-  Tax Cost
Debt 24,000 0.40 0.05(1 − 0.4) = 0.03
Equity 36,000 0.60 0.10(15)
(16)
37 This argument is made by John R. Ezzell and R. Burr Porter [“Flotation Costs and the Weighted 
Average Cost of Capital, ” Journal of Financial and Quantitative Analysis , Vol. 11, No. 3 (September 1976), 
pp. 403–413]. They argue that the correct treatment is to deduct flotation costs as part of the valuation as 
one of the initial-  period cash flows.

Topics in Cost of Capital Estimation 107
The weighted average cost of capital is 7.2 percent calculated as 0.40(3 percent) + 
0.60(10 percent). Ignoring flotation costs for the moment, the net present value (NPV) 
of this project is
NPV = €69,591 – €60,000 = €9,591
If the flotation costs are, say, 5 percent of the new equity capital, the flotation costs 
are €1,800. The net present value considering flotation costs is
NPV = €69,591 – €60,000 – €1,800 = €7,791
If flotation costs are not tax deductible, or €69,591 − €60,000 − €1,800(0.6) = €8,511, 
if flotation costs are tax deductible.
 
If, instead of considering the flotation costs as part of the cash flows, we adjust the 
cost of equity, the cost of capital is 7.3578 percent and the NPV is
NPV = €69,089 – €60,000 = €9,089
As you can see, we arrive at different assessments of value using these two methods.
So, if it is preferred to deduct the flotation costs as part of the net present value

calculation, why do we see the adjustment in the cost of capital so often in textbooks? 
The first reason is that it is often difficult to identify particular financing associated 
with a project. Using the adjustment for the flotation costs in the cost of capital may 
be useful if specific project financing cannot be identified. Second, by adjusting the 
cost of capital for the flotation costs, it is easier to demonstrate how costs of financing 
a company change as a company exhausts internally generated equity (i.e., retained 
earnings) and switches to externally generated equity (i.e., a new stock issue).
4.5 What Do CFOs Do?
In this reading, we have introduced you to methods that may be used to estimate 
the cost of capital for a company or a project. What do companies actually use when 
making investment decisions? In a survey of a large number of US company CFOs, 
John Graham and Campbell Harvey asked about the methods that companies actually 
use.38 Their survey revealed the following:

■■The most popular method for estimating the cost of equity is the capital asset 
■■Few companies use the dividend cash flow model to estimate a cost of equity.
■■Publicly traded companies are more likely to use the capital asset pricing model 
than are private companies.
■■In evaluating projects, the majority use a single company cost of capital, but a 
large portion apply some type of risk adjustment for individual projects.
The survey also reveals that the single-  factor capital asset pricing model is the most 
popular method for estimating the cost of equity, though the next most popular 
methods, respectively, are average stock returns and multifactor return models. The 
lack of popularity of the dividend discount model indicates that this approach, which 
was once favored, has lost its following in practice.39
38 John Graham and Campbell Harvey, “How Do CFOs Make Capital Budgeting and Capital Structure

Decisions, ” Journal of Applied Corporate Finance , Vol. 15, No. 1 (Spring 2002), pp. 8–23.
39 A survey published in 1982 by Lawrence Gitman and V. Mercurio [“Cost of Capital Techniques Used 
by Major US Firms: Survey and Analysis of Fortune’s 1000, ” Financial Management , Vol. 14, No. 4 (Winter 
1982), pp. 21–29] indicated that fewer than 30 percent used the CAPM model in the estimation of the 
cost of equity.

Reading 35 ■ Cost of Capital 108
In a survey of publicly traded multinational European companies, Franck Bancel 
and Usha Mittoo provide evidence consistent with the Graham and Harvey survey.40 
They find that over 70 percent of companies use the CAPM to determine the cost 
of equity; this compares with the 73.5 percent of US companies that use the CAPM. 
In a survey of both publicly traded and private European companies, Dirk Brounen, 
Abe de Jong, and Kees Koedijk confirm the result of Graham and Harvey that larger 
companies are more likely to use the more sophisticated methods, such as CAPM, in 
estimating the cost of equity.41 Brounen, Jong, and Koedijk find that the popularity 
of the use of CAPM is less for their sample (ranging from 34 percent to 55.6 percent, 
depending on the country) than for the other two surveys, which may reflect the 
inclusion of smaller, private companies in the latter sample.
We learn from the survey evidence that the CAPM is a popular method for esti -

mating the cost of equity capital and that it is used less by smaller, private companies. 
This latter result is not surprising because of the difficulty in estimating systematic 
risk in cases in which the company’s equity is not publicly traded.
SUMMARY
In this reading, we provided an overview of the techniques used to calculate the cost of 
capital for companies and projects. We examined the weighted average cost of capital, 
discussing the methods commonly used to estimate the component costs of capital 
and the weights applied to these components. The international dimension of the cost 
of capital, as well as key factors influencing the cost of capital, were also analyzed.
■■The weighted average cost of capital is a weighted average of the after-  tax mar -
ginal costs of each source of capital: WACC = wdrd(1 – t) + wprp + were
■■An analyst uses the WACC in valuation. For example, the WACC is used to 
value a project using the net present value method:

NPV = Present value of inflows – Present value of the outflows
■■The before-  tax cost of debt is generally estimated by means of one of the two 
methods: yield to maturity or bond rating.
■■The yield-  to- maturity method of estimating the before-  tax cost of debt uses the 
familiar bond valuation equation. Assuming semi-  annual coupon payments, the 
equation is
PPMT
rPMT
rFV
rPMT
dn
dn
dnt
01
1212121=
+

+… +
+

+
+

=
+ +









+
+

=∑
rFV
rdt
tn
dn
2121
We solve for the six-  month yield ( rd/2) and then annualize it to arrive at the 
before-  tax cost of debt, rd.
40 Franck Bancel and Usha Mittoo, “The Determinants of Capital Structure Choice: A Survey of European 
Firms, ” Financial Management , Vol. 44, No. 4 (Winter 2004).
41 Dirk Brounen, Abe de Jong, and Kees Koedijk, “Corporate Finance in Europe: Confronting Theory with 
Practice, ” Financial Management , Vol. 44, No. 4 (Winter 2004).

Summary 109
■■Because interest payments are generally tax-  deductible, the after-  tax cost is the 
true, effective cost of debt to the company. If a current yield or bond rating is 
not available, such as in the case of a private company without rated debt or a 
project, the estimate of the cost of debt becomes more challenging.
■■The cost of preferred stock is the preferred stock dividend divided by the cur -
rent preferred stock price:
rD
Ppp
p=
■■The cost of equity is the rate of return required by a company’s common stock -
holders. We estimate this cost using the CAPM (or its variants) or the dividend 
discount method.
■■The CAPM is the approach most commonly used to calculate the cost of 
common stock. The three components needed to calculate the cost of common 
stock are the risk-  free rate, the equity risk premium, and beta:
■■When estimating the cost of equity capital using the CAPM when we do not

have publicly traded equity, we may be able to use the pure-  play method in 
which we estimate the unlevered beta for a company with similar business risk, 
βU,
ββ
coD
E=
+−() 11 t






and then lever this beta to reflect the financial risk of the project or company:
projectD
E=+ −()
11 t 





■■It is often the case that country and foreign exchange risk are diversified so 
that we can use the estimated β in the CAPM analysis. However, in the case 
in which these risks cannot be diversified away, we can adjust our measure of 
systematic risk by a country equity premium to reflect this nondiversified risk:

































■■The dividend discount model approach is an alternative approach to calculating 
the cost of equity, whereby the cost of equity is estimated as follows:
rD
Pge=+1
0
■■We can estimate the growth rate in the dividend discount model by using pub -
lished forecasts of analysts or by estimating the sustainable growth rate:
gD=−()1E PSROE

Reading 35 ■ Cost of Capital 110
■■In estimating the cost of equity, an alternative to the CAPM and dividend 
discount approaches is the bond yield plus risk premium approach. In this 
approach, we estimate the before-  tax cost of debt and add a risk premium that 
reflects the additional risk associated with the company’s equity.
■■The marginal cost of capital schedule is a graph plotting the new funds raised 
by a company on the x-axis and the cost of capital on the y-axis. The cost of 
capital is level to the point at which one of the costs of capital changes, such 
as when the company bumps up against a debt covenant, requiring it to use 
another form of capital. We calculate a break point using information on when 
the different sources’ costs change and the proportions that the company uses 
when it raises additional capital:
Brea k pointAmount of capita l at which the source' s cost o=ff capital change s

■■Flotation costs are costs incurred in the process of raising additional capital. 
The preferred method of including these costs in the analysis is as an initial 
cash flow in the valuation analysis.
■■Survey evidence tells us that the CAPM method is the most popular method 
used by companies in estimating the cost of equity. The CAPM is more popular 
with larger, publicly traded companies, which is understandable considering the 
additional analyses and assumptions required in estimating systematic risk for a 
private company or project.

Practice Problems 111
1 The cost of equity is equal to the:
A expected market return.
B rate of return required by stockholders.
C cost of retained earnings plus dividends.
2 Which of the following statements is correct?
A The appropriate tax rate to use in the adjustment of the before-  tax cost of 
debt to determine the after-  tax cost of debt is the average tax rate because 
interest is deductible against the company's entire taxable income.
B For a given company, the after-  tax cost of debt is generally less than both 
the cost of preferred equity and the cost of common equity.
C For a given company, the investment opportunity schedule is upward slop -
ing because as a company invests more in capital projects, the returns from 
investing increase.
3 Using the dividend discount model, what is the cost of equity capital for Zeller 
Mining if the company will pay a dividend of C$2.30 next year, has a payout

ratio of 30 percent, a return on equity (ROE) of 15 percent, and a stock price of 
C$45?
A 9.61 percent.
B 10.50 percent.
C 15.61 percent.
4 Dot.Com has determined that it could issue $1,000 face value bonds with an 
8 percent coupon paid semi-  annually and a five-  year maturity at $900 per bond. 
If Dot.Com’s marginal tax rate is 38 percent, its after-  tax cost of debt is closest  
to:
A 6.2 percent.
B 6.4 percent.
C 6.6 percent.
5 The cost of debt can be determined using the yield-  to- maturity and the bond 
rating approaches. If the bond rating approach is used, the:
A coupon is the yield.
B yield is based on the interest coverage ratio.
C company is rated and the rating can be used to assess the credit default 
spread of the company's debt.
6 Morgan Insurance Ltd. issued a fixed-  rate perpetual preferred stock three years 
ago and placed it privately with institutional investors. The stock was issued 
at $25 per share with a $1.75 dividend. If the company were to issue preferred

stock today, the yield would be 6.5 percent. The stock's current value is:
A $25.00.
B $26.92.
C $37.31.
7 A financial analyst at Buckco Ltd. wants to compute the company's weighted 
average cost of capital (WACC) using the dividend discount model. The analyst 
has gathered the following data:

Reading 35 ■ Cost of Capital 112
Before-  tax cost of new debt 8 percent
Tax rate 40 percent
Target debt-  to- equity ratio 0.8033
Stock price $30
Next year's dividend $1.50
Estimated growth rate 7 percent
 Buckco’s WACC is closest  to:
A 8 percent.
B 9 percent.
C 12 percent.
8 The Gearing Company has an after-  tax cost of debt capital of 4 percent, a cost 
of preferred stock of 8 percent, a cost of equity capital of 10 percent, and a 
weighted average cost of capital of 7 percent. Gearing intends to maintain its 
current capital structure as it raises additional capital. In making its capital-  
budgeting decisions for the average-  risk project, the relevant cost of capital is:
A 4 percent.
B 7 percent.
C 8 percent.
9 Fran McClure of Alba Advisers is estimating the cost of capital of Frontier 
Corporation as part of her valuation analysis of Frontier. McClure will be using 
this estimate, along with projected cash flows from Frontier's new projects, to

estimate the effect of these new projects on the value of Frontier. McClure has 
gathered the following information on Frontier Corporation:
Current Y ear ($)Forecasted for 
Next Y ear ($)
Book value of debt 50 50
Market value of debt 62 63
Book value of shareholders' equity 55 58
Market value of shareholders' equity 210 220
 The weights that McClure should apply in estimating Frontier's cost of capital 
for debt and equity are, respectively:
A wd = 0.200; we = 0.800.
B wd = 0.185; we = 0.815.
C wd = 0.223; we = 0.777.
10 Wang Securities had a long-  term stable debt-  to- equity ratio of 0.65. Recent 
bank borrowing for expansion into South America raised the ratio to 0.75. 
The increased leverage has what effect on the asset beta and equity beta of the 
company?
A The asset beta and the equity beta will both rise.
B The asset beta will remain the same and the equity beta will rise.
C The asset beta will remain the same and the equity beta will decline.

11 Brandon Wiene is a financial analyst covering the beverage industry. He is 
evaluating the impact of DEF Beverage’s new product line of flavored waters. 
DEF currently has a debt-  to- equity ratio of 0.6. The new product line would be 
financed with $50 million of debt and $100 million of equity. In estimating the 
valuation impact of this new product line on DEF's value, Wiene has estimated

Practice Problems 113
the equity beta and asset beta of comparable companies. In calculating the 
equity beta for the product line, Wiene is intending to use DEF's existing capital 
structure when converting the asset beta into a project beta. Which of the fol -
lowing statements is correct?
A Using DEF’s debt-  to- equity ratio of 0.6 is appropriate in calculating the new 
product line's equity beta.
B Using DEF’s debt-  to- equity ratio of 0.6 is not appropriate, but rather the 
debt-  to- equity ratio of the new product, 0.5, is appropriate to use in calcu -
lating the new product line’s equity beta.
C Wiene should use the new debt-  to- equity ratio of DEF that would result 
from the additional $50 million debt and $100 million equity in calculating 
the new product line's equity beta.
12 Trumpit Resorts Company currently has 1.2 million common shares of stock 
outstanding and the stock has a beta of 2.2. It also has $10 million face value

of bonds that have five years remaining to maturity and 8 percent coupon with 
semi-  annual payments, and are priced to yield 13.65 percent. If Trumpit issues 
up to $2.5 million of new bonds, the bonds will be priced at par and have a yield 
of 13.65 percent; if it issues bonds beyond $2.5 million, the expected yield on 
the entire issuance will be 16 percent. Trumpit has learned that it can issue new 
common stock at $10 a share. The current risk-  free rate of interest is 3 percent 
and the expected market return is 10 percent. Trumpit’s marginal tax rate is 
30 percent. If Trumpit raises $7.5 million of new capital while maintaining the 
same debt-  to- equity ratio, its weighted average cost of capital is closest  to:
A 14.5 percent.
B 15.5 percent.
C 16.5 percent.
13–181
Jurgen Knudsen has been hired to provide industry expertise to Henrik Sandell, CFA, 
an analyst for a pension plan managing a global large-  cap fund internally. Sandell is

concerned about one of the fund's larger holdings, auto parts manufacturer Kruspa 
AB. Kruspa currently operates in 80 countries, with the previous year's global revenues 
at €5.6 billion. Recently, Kruspa’s CFO announced plans for expansion into Trutan, a 
country with a developing economy. Sandell worries that this expansion will change 
the company's risk profile and wonders if he should recommend a sale of the position.
Sandell provides Knudsen with the basic information. Kruspa’s global annual free 
cash flow to the firm is €500 million and earnings are €400 million. Sandell estimates 
that cash flow will level off at a 2 percent rate of growth. Sandell also estimates that 
Kruspa’s after-  tax free cash flow to the firm on the Trutan project for next three years 
is, respectively, €48 million, €52 million, and €54.4 million. Kruspa recently announced 
a dividend of €4.00 per share of stock. For the initial analysis, Sandell requests that

Knudsen ignore possible currency fluctuations. He expects the Trutanese plant to 
sell only to customers within Trutan for the first three years. Knudsen is asked to 
evaluate Kruspa’s planned financing of the required €100 million with a €80 million 
public offering of 10-  year debt in Sweden and the remainder with an equity offering.
1 The Level I exam uses only independent questions. This minicase is intended as a learning exercise.

Reading 35 ■ Cost of Capital 114
Equity risk premium, Sweden 4.82 percent
Risk-  free rate of interest, Sweden 4.25 percent
Industry debt-  to- equity ratio 0.3
Market value of Kruspa’s debt €900 million
Market value of Kruspa’s equity €2.4 billion
Kruspa’s equity beta 1.3
Kruspa’s before-  tax cost of debt 9.25 percent
Trutan credit A2 country risk premium 1.88 percent
Corporate tax rate 37.5 percent
Interest payments each year Level
13 Using the capital asset pricing model, Kruspa’s cost of equity capital for its typi -
cal project is closest  to:
A 7.62 percent.
B 10.52 percent.
C 12.40 percent.
14 Sandell is interested in the weighted average cost of capital of Kruspa AB prior 
to its investing in the Trutan project. This weighted average cost of capital 
(WACC) is closest  to:
A 7.65 percent.
B 9.23 percent.
C 10.17 percent.
15 In his estimation of the project’s cost of capital, Sandell would like to use the

asset beta of Kruspa as a base in his calculations. The estimated asset beta of 
Kruspa prior to the Trutan project is closest  to:
A 1.053.
B 1.110.
C 1.327.
16 Sandell is performing a sensitivity analysis of the effect of the new project on 
the company's cost of capital. If the Trutan project has the same asset risk 
as Kruspa, the estimated project beta for the Trutan project, if it is financed 
80 percent with debt, is closest  to:
A 1.300.
B 2.635.
C 3.686.
17 As part of the sensitivity analysis of the effect of the new project on the compa -
ny's cost of capital, Sandell is estimating the cost of equity of the Trutan project 
considering that the Trutan project requires a country equity premium to 
capture the risk of the project. The cost of equity for the project in this case is 
closest  to:
A 10.52 percent.
B 19.91 percent.
C 28.95 percent.

Practice Problems 115
18 In his report, Sandell would like to discuss the sensitivity of the project’s net 
present value to the estimation of the cost of equity. The Trutan project’s net 
present value calculated using the equity beta without and with the country risk 
premium are, respectively:
A €26 million and €24 million.
B €28 million and €25 million.
C €30 million and €27 million.
19–222
Boris Duarte, CFA, covers initial public offerings for Zellweger Analytics, an inde -
pendent research firm specializing in global small-  cap equities. He has been asked to 
evaluate the upcoming new issue of TagOn, a US-  based business intelligence software 
company. The industry has grown at 26 percent per year for the previous three years. 
Large companies dominate the market, but sizable “pure-  play” companies such as 
Relevant, Ltd., ABJ, Inc., and Opus Software Pvt. Ltd also compete. Each of these com -

petitors is domiciled in a different country, but they all have shares of stock that trade 
on the US NASDAQ. The debt ratio of the industry has risen slightly in recent years.
CompanySales in 
Millions ($)Market Value 
Equity in 
Debt in 
Millions ($)Equity 
Beta Tax RateShare Price 
($)
Relevant Ltd. 752 3,800 0.0 1.702 23 percent 42
ABJ, Inc. 843 2,150 6.5 2.800 23 percent 24
Opus Software Pvt. Ltd. 211 972 13.0 3.400 23 percent 13
Duarte uses the information from the preliminary prospectus for TagOn’s initial 
offering. The company intends to issue 1 million new shares. In his conversation with 
the investment bankers for the deal, he concludes the offering price will be between 
$7 and $12. The current capital structure of TagOn consists of a $2.4 million five-  
year non-  callable bond issue and 1 million common shares. Other information that 
Duarte has gathered:
Currently outstanding bonds $2.4 million five-  year bonds, coupon 
of 12.5 percent, with a market value of

of 12.5 percent, with a market value of 
$2.156 million
Risk-  free rate of interest 5.25 percent
Estimated equity risk premium 7 percent
Tax rate 23 percent
19 The asset betas for Relevant, ABJ, and Opus, respectively, are:
A 1.70, 2.52, and 2.73.
B 1.70, 2.79, and 3.37.
C 1.70, 2.81, and 3.44.
2 The Level I exam uses only independent questions. This minicase is intended as a learning exercise.

Reading 35 ■ Cost of Capital 116
20 The average asset beta for the pure players in this industry, Relevant, ABJ, and 
Opus, weighted by market value of equity is closest  to:
A 1.67.
B 1.97.
C 2.27.
21 Using the capital asset pricing model, the cost of equity capital for a company 
in this industry with a debt-  to- equity ratio of 0.01, asset beta of 2.27, and a mar -
ginal tax rate of 23 percent is closest  to:
A 17 percent.
B 21 percent.
C 24 percent.
22 The marginal cost of capital for TagOn, based on an average asset beta of 2.27 
for the industry and assuming that new stock can be issued at $8 per share, is 
A 20.5 percent.
B 21.0 percent.
C 21.5 percent.
23 Two years ago, a company issued $20 million in long-  term bonds at par value 
with a coupon rate of 9 percent. The company has decided to issue an addi -
tional $20 million in bonds and expects the new issue to be priced at par value 
with a coupon rate of 7 percent. The company has no other debt outstanding

and has a tax rate of 40 percent. To compute the company's weighted average 
cost of capital, the appropriate after-  tax cost of debt is closest  to:
A 4.2%.
B 4.8%.
C 5.4%.
24 An analyst gathered the following information about a company and the 
market:
Current market price per share of common stock $28.00
Most recent dividend per share paid on common stock ( D0) $2.00
Expected dividend payout rate 40%
Expected return on equity (ROE) 15%
Beta for the common stock 1.3
Expected rate of return on the market portfolio 13%
Risk-  free rate of return 4%
 Using the discounted cash flow (DCF) approach, the cost of retained earnings 
for the company is closest  to:
A 15.7%.
B 16.1%.
C 16.8%.
25 An analyst gathered the following information about a company and the 
market:

Practice Problems 117
 Using the Capital Asset Pricing Model (CAPM) approach, the cost of retained 
earnings for the company is closest  to:
A 13.6%.
B 15.7%.
C 16.1%.
26 An analyst gathered the following information about a private company and its 
publicly traded competitor:
Comparable Companies Tax Rate (%) Debt/Equity Equity Beta
Private company 30.0 1.00 N.A.
Public company 35.0 0.90 1.75
 Using the pure-  play method, the estimated equity beta for the private company 
is closest  to:
A 1.029.
B 1.104.
C 1.877.
27 An analyst gathered the following information about the capital markets in the 
United States and in Paragon, a developing country.
Selected Market Information (%)

Yield on US 10-  year Treasury bond 4.5
Yield on Paragon 10-  year government bond 10.5
Annualized standard deviation of Paragon stock index 35.0
Annualized standard deviation of Paragon dollar-  denominated govern -
ment bond 25.0
 Based on the analyst’s data, the estimated country equity premium for Paragon 
A 4.29%.
B 6.00%.
C 8.40%.

Reading 35 ■ Cost of Capital 118
SOLUTIONS
1 B is correct. The cost of equity is defined as the rate of return required by 
stockholders.
2 B is correct. Debt is generally less costly than preferred or common stock. The 
cost of debt is further reduced if interest expense is tax deductible.
3 C is correct. First calculate the growth rate using the sustainable growth cal -
culation, and then calculate the cost of equity using the rearranged dividend 
discount model:
g = (1 – Dividend payout ratio)(Return on equity) = (1 – 0.30)(15%) = 10.5%
re = (D1/P0) + g = ($2.30/$45) + 10.50% = 15.61%
4 C is correct. FV = $1,000; PMT  = $40; N = 10; PV = $900
Solve for i. The six-  month yield, i, is 5.3149%
YTM = 5.3149% × 2 = 10.62985%
rd(1 − t) = 10.62985%(1 − 0.38) = 6.5905%
5 C is correct. The bond rating approach depends on knowledge of the company's 
rating and can be compared with yields on bonds in the public market.
6 B is correct. The company can issue preferred stock at 6.5%. 
Pp = $1.75/0.065 = $26.92

7 B is correct.
Cost of equity = D1/P0 + g = $1.50/$30 + 7% = 5% + 7% = 12%
D/(D + E) = 0.8033/1.8033 = 0.445
WACC = [(0.445) (0.08)(1 − 0.4)] + [(0.555)(0.12)] = 8.8%
8 B is correct. The weighted average cost of capital, using weights derived from 
the current capital structure, is the best estimate of the cost of capital for the 
average-  risk project of a company.
9 C is correct.
wd = $63/($220 + 63) = 0.223
we = $220/($220 + 63) = 0.777
10 B is correct. Asset risk does not change with a higher debt-  to- equity ratio. 
Equity risk rises with higher debt.
11 B is correct. The debt-  to- equity ratio of the new product should be used when 
making the adjustment from the asset beta, derived from the comparables, to 
the equity beta of the new product.
12 B is correct.
Capital structure:
Market value of debt : FV = $10,000,000, PMT  = $400,000, N = 10,
I/YR = 13.65%. Solving for PV gives the answer $7,999,688.

Market value of equity:  1.2 million shares outstanding at $10 = $12,000,000

Solutions 119
Market value of debt $7,999,688 40%
Market value of equity 12,000,000 60%
Total capital $19,999,688 100%
 To raise $7.5 million of new capital while maintaining the same capital struc -
ture, the company would issue $7.5 million × 40% = $3.0 million in bonds, 
which results in a before-  tax rate of 16 percent.
rd(1 − t) = 0.16(1 − 0.3) = 0.112 or 11.2%
re = 0.03 + 2.2 (0.10 − 0.03) = 0.184 or 18.4%
WACC = [0.40(0.112)] + [0.6(0.184)] = 0.0448 + 0.1104 = 0.1552 or 15.52%
13 B is correct.
re = 0.0425 + (1.3)(0.0482) = 0.1052 or 10.52%
14 B is correct.
 WACC =  [(€900/€3300) .0925 (1 − 0.375)] + [(€2400/€3300)(0.1052)]
  = 0.0923 or 9.23%
15 A is correct.
Asset beta = Unlevered beta = 1.3/(1 + [(1−0.375)(€900/€2400)] = 1.053
16 C is correct.
Project beta = 1.053 {1 + [(1 − 0.375)(€80/€20)]} = 1.053 {3.5} = 3.686
17 C is correct.
re = 0.0425 + 3.686(0.0482 + 0.0188) = 0.2895 or 28.95%
18 C is correct.
 Cost of equity without the country risk premium:

Cost of equity without the country risk premium:
re = 0.0425 + 3.686 (0.0482) = 0.2202 or 22.02%
 Cost of equity with the country risk premium:
re = 0.0425 + 3.686 (0.0482 + 0.0188) = 0.2895 or 28.95%
 Weighted average cost of capital without the country risk premium:
 WACC =  [0.80 (0.0925) (1 − 0.375) ] + [0.20 (0.2202)] = 0.04625 + 0.04404
  = 0.09038 or 9.03 percent
 Weighted average cost of capital with the country risk premium:
 WACC =  [0.80 (0.0925) (1 − 0.375) ] + [0.20 (0.2895)] = 0.04625 + 0.0579
  = 0.1042 or 10.42 percent
 NPV without the country risk premium:
NPV48 mi llion  mi llion  mi=
+()+
+()+¬¬ ¬
10 090352
10 090354 4
12... lllion million
 million  mi llio10 0903100
44 03 43 743+()−
=+.
..¬
¬n n 41.97 mi llion  mi llion
 million+−
=¬
¬100
29 74 .

Reading 35 ■ Cost of Capital 120
 NPV with the country risk premium:
+()+
+()+¬¬ ¬
10 104252
10 104254 4
 million  mi llio10 1042100
43 47 42 653+()−
=+.
..¬
¬n n 40.41 mi llion  mi llion
 million+−
=¬
¬100
26 53 .
19 B is correct.
Asset betas: βequity /[1 + (1 − t)(D/E)]
Relevant = 1.702/[1 + (0.77)(0)] = 1.702
ABJ = 2.8/[1 + (0.77)(0.003)] = 2.7918
Opus = 3.4/1 + [(0.77)(0.013)] = 3.3663
20 C is correct.
 Weights are determined based on relative market values:
Pure-  PlayMarket Value of 
Equity in MillionsProportion of 
Total
Relevant $3,800 0.5490
ABJ 2,150 0.3106
Opus 972 0.1404
Total $6,922 1.0000
Weighted average beta (0.5490)(1.702) + (0.3106)(2.7918) + (0.1404)(3.3572) 
= 2.27.
21 B is correct.
Asset beta = 2.27
Levered beta = 2.27 {1 + [(1 − 0.23)(0.01)]} = 2.2875
Cost of equity capital = 0.0525 + (2.2875)(0.07) = 0.2126 or 21.26%
22 C is correct.
For debt: FV = 2,400,000; PV = 2,156,000; n = 10; PMT  = 150,000
Solve for i. i = 0.07748. YTM = 15.5%

Before-  tax cost of debt = 15.5%
Market value of equity = 1 million shares outstanding + 1 million newly 
issued shares = 2 million shares at $8 = $16 million
Total market capitalization = $2.156 million + $16 million = $18.156 million
Levered beta = 2.27 {1 + [(1 − 0.23)(2.156/16)]} = 2.27 (1.1038) = 2.5055
Cost of equity = 0.0525 + 2.5055 (0.07) = 0.2279 or 22.79%
Debt weight = $2.156/$18.156 = 0.1187
Equity weight = $16/$18.156 = 0.8813
 TagOn’s MCC =  [(0.1187)(0.155)(1 − 0.23)] + [(0.8813)(0.2279)]
  = 0.01417 + 0.20083
  = 0.2150 or 21.50%

Solutions 121
23 A is correct. The relevant cost is the marginal cost of debt. The before-  tax 
marginal cost of debt can be estimated by the yield to maturity on a comparable 
outstanding. After adjusting for tax, the after-  tax cost is 7(1 − 0.4) = 7(0.6) = 
4.2%.
24 C is correct. The expected return is the sum of the expected dividend yield plus 
expected growth. The expected growth is (1 − 0.4)15% = 9%. The expected divi -
dend yield is $2.18/$28 = 7.8%. The sum is 16.8%.
25 B is correct. Using the CAPM approach, 4% + 1.3(9%) = 15.7%.
26 C is correct. Inferring the asset beta for the public company: unlevered beta = 
1.75/[1 + (1 − 0.35) (0.90)] = 1.104. Relevering to reflect the target debt ratio of 
the private firm: levered beta = 1.104 × [1 + (1 − 0.30) (1.00)] = 1.877.
27 C is correct. The country equity premium can be estimated as the sovereign 
yield spread times the volatility of the country’s stock market relative to its

bond market. Paragon’s equity premium is (10.5% – 4.5%) × (35%/25%) = 6% × 
1.4 = 8.40%.

Corporate Finance (2)
This study session covers how companies make use of leverage and manage their 
working capital to meet short-  term operational needs. The various types of leverage 
(operating, financial, total), measures of leverage, and how leverage affects a com -
pany’s earnings and financial ratios are examined. A discussion then follows on the 
different types of working capital and the management issues associated with each. 
The session concludes with techniques for assessing the effectiveness of working 
capital management.
Reading 36  Measures of Leverage  
by Pamela Peterson Drake, PhD, CFA, Raj Aggarwal, PhD, 
CFA, Cynthia Harrington, CFA, and Adam Kobor, PhD, 
CFA
Reading 37 Working Capital Management  
by Edgar A. Norton, Jr., PhD, CFA, Kenneth L. Parkinson, 
MBA, CCM, and Pamela Peterson Drake, PhD, CFACOrPO rATE  FINANCE
11

Measures of Leverage
by Pamela Peterson Drake, PhD, CFA, Raj Aggarwal, PhD, CFA, 
Cynthia Harrington, CFA, and Adam Kobor, PhD, CFA
Pamela Peterson Drake, PhD, CFA, is at James Madison University (USA). Raj 
Aggarwal, PhD, CFA (USA). Cynthia Harrington, CFA, is at teamyou.co (USA). Adam 
Kobor, PhD, CFA, is at New York University (USA).
a. define and explain leverage, business risk, sales risk, operating 
risk, and financial risk and classify a risk;
b. calculate and interpret the degree of operating leverage, the 
degree of financial leverage, and the degree of total leverage;
c. analyze the effect of financial leverage on a company’s net income 
and return on equity;
d. calculate the breakeven quantity of sales and determine the 
company's net income at various sales levels;
e. calculate and interpret the operating breakeven quantity of sales.

This reading presents elementary topics in leverage. Leverage  is the use of fixed costs 
in a company’s cost structure. Fixed costs that are operating costs (such as depreciation 
or rent) create operating leverage. Fixed costs that are financial costs (such as interest 
expense) create financial leverage.
Analysts refer to the use of fixed costs as leverage because fixed costs act as a ful -
crum for the company’s earnings. Leverage can magnify earnings both up and down. 
The profits of highly leveraged companies might soar with small upturns in revenue. 
But the reverse is also true: Small downturns in revenue may lead to losses.
Analysts need to understand a company’s use of leverage for three main reasons. 
First, the degree of leverage is an important component in assessing a company’s risk 
and return characteristics. Second, analysts may be able to discern information about 
a company’s business and future prospects from management’s decisions about the use

of operating and financial leverage. Knowing how to interpret these signals also helps 
the analyst evaluate the quality of management’s decisions. Third, the valuation of a 1rEADING
36
© 2010 CFA Institute. All rights reserved.

Reading 36 ■ Measures of Leverage 126
company requires forecasting future cash flows and assessing the risk associated with 
those cash flows. Understanding a company’s use of leverage should help in forecasting 
cash flows and in selecting an appropriate discount rate for finding their present value.
The reading is organized as follows: Section 2 introduces leverage and defines 
important terms. Section 3 illustrates and discusses measures of operating leverage 
and financial leverage, which combine to define a measure of total leverage that gauges 
the sensitivity of net income to a given percent change in units sold. This section also 
covers breakeven points in using leverage and corporate reorganization (a possible 
consequence of using leverage inappropriately). A summary and practice problems 
conclude this reading.
LEVERAGE
Leverage increases the volatility of a company’s earnings and cash flows and increases

the risk of lending to or owning a company. Additionally, the valuation of a company 
and its equity is affected by the degree of leverage: The greater a company’s leverage, 
the greater its risk and, hence, the greater the discount rate that should be applied in 
its valuation. Further, highly leveraged (levered) companies have a greater chance of 
incurring significant losses during downturns, thus accelerating conditions that lead 
to financial distress and bankruptcy.
Consider the simple example of two companies, Impulse Robotics, Inc., and 
Malvey Aerospace, Inc. These companies have the following performance for the 
period of study:1
Exhibit 1   Impulse Robotics and Malvey Aerospace
Impulse Robotics Malvey Aerospace
Revenues $1,000,000 $1,000,000
Operating costs 700,000 750,000
Operating income $300,000 $250,000
Financing expense 100,000 50,000
Net income $200,000 $200,000
These companies have the same net income, but are they identical in terms of

operating and financial characteristics? Would we appraise these two companies at 
the same value? Not necessarily.
The risk associated with future earnings and cash flows of a company are affected 
by the company’s cost structure. The cost structure  of a company is the mix of vari -
able and fixed costs. Variable costs  fluctuate with the level of production and sales. 
Some examples of variable costs are the cost of goods purchased for resale, costs of 
materials or supplies, shipping charges, delivery charges, wages for hourly employees, 
sales commissions, and sales or production bonuses. Fixed costs  are expenses that are 
the same regardless of the production and sales of the company. These costs include 
depreciation, rent, interest on debt, insurance, and wages for salaried employees.2
1 We are ignoring taxes for this example, but when taxes are included, the general conclusions remain 
the same.

Leverage 127
Suppose that the cost structures of the companies differ in the manner shown in 
Exhibit 2.
Exhibit 2   Impulse Robotics and Malvey Aerospace
Number of units produced and sold 100,000 100,000
Sales price per unit $10 $10
Variable cost per unit $2 $6
Fixed operating cost $500,000 $150,000
Fixed financing expense $100,000 $50,000
The risk associated with these companies is different, although, as we saw in 
Exhibit 1, they have the same net income. They have different operating and financing 
cost structures, resulting in differing volatility of net income.
For example, if the number of units produced and sold is different from 100,000, 
the net income of the two companies diverges. If 50,000 units are produced and sold, 
Impulse Robotics has a loss of $200,000 and Malvey Aerospace has $0 earnings. If, on 
the other hand, the number of units produced and sold is 200,000, Impulse Robotics

earns $1 million whereas Malvey Aerospace earns $600,000. In other words, the vari -
ability in net income is greater for Impulse Robotics, which has higher fixed costs in 
terms of both fixed operating costs and fixed financing costs.
Impulse Robotics’ cost structure results in more leverage than that of Malvey 
Aerospace. We can see this effect when we plot the net income of each company 
against the number of units produced and sold, as in Exhibit 3. The greater leverage of 
Impulse Robotics is reflected in the greater slope of the line representing net income. 
This means that as the number of units sold changes, Impulse Robotics experiences 
a greater change in net income than does Malvey Aerospace for the same change in 
units sold.

Reading 36 ■ Measures of Leverage 128
Exhibit 3   Net Income for Different Numbers of Units Produced and Sold10,00050,000
30,00070,00090,000110,000130,000150,000170,000190,000210,000230,000250,000Impulse Robotics Net Income
Malvey Aerospace Net Income e
Number of Units Produced and SoldNet Income
$1,500,000
$1,000,000
$500,000
$0
–$500,000
–$1,000,000
Companies that have more fixed costs relative to variable costs in their cost struc -
tures have greater variation in net income as revenues fluctuate and, hence, more risk.
BUSINESS RISK AND FINANCIAL RISK
Risk arises from both the operating and financing activities of a company. In the 
following, we address how that happens and the measures available to the analyst to 
gauge the risk in each case.
3.1 Business Risk and Its Components
Business risk  is the risk associated with operating earnings. Operating earnings are 
risky because total revenues are risky, as are the costs of producing revenues. Revenues

are affected by a large number of factors, including economic conditions, industry 
dynamics (including the actions of competitors), government regulation, and demo -
graphics. Therefore, prices of the company’s goods or services or the quantity of sales 
may be different from what is expected. We refer to the uncertainty with respect to 
the price and quantity of goods and services as sales risk .
Operating risk  is the risk attributed to the operating cost structure, in particular 
the use of fixed costs in operations. The greater the fixed operating costs relative to 
variable operating costs, the greater the operating risk. Business risk is therefore the 
combination of sales risk and operating risk. Companies that operate in the same line 
of business generally have similar business risk.3

Business Risk and Financial Risk 129
3.2 Sales Risk
Consider Impulse Robotics once again. Suppose that the forecasted number of units 
produced and sold in the next period is 100,000 but that the standard deviation of the 
number of units sold is 20,000. And suppose the price that the units sell for is expected 
to be $10 per unit but the standard deviation is $2. Contrast this situation with that 
of a company named Tolley Aerospace, Inc., which has the same cost structure but a 
standard deviation of units sold of 40,000 and a price standard deviation of $4.
If we assume, for simplicity’s sake, that the fixed operating costs are known with 
certainty and that the units sold and price per unit follow a normal distribution, we 
can see the impact of the different risks on the operating income of the two companies 
through a simulation; the results are shown in Exhibit 4. Here, we see the differing 
distributions of operating income that result from the distributions of units sold and

price per unit. So, even if the companies have the same cost structure, differing sales 
risk affects the potential variability of the company’s profitability. In our example, 
Tolley Aerospace has a wider distribution of likely outcomes in terms of operating 
profit. This greater volatility in operating earnings means that Tolley Aerospace has 
more sales risk than Impulse Robotics.
Exhibit 4   Operating Income Simulations for Impulse Robotics and Tolley 
Aerospace
Panel A: Impulse Robotics
0100200300400–$400,000$0$400,000$800,000$1,200,000$1,600,000$2,000,000$2,400,000$2,800,000
Operating ProfitFrequency

Reading 36 ■ Measures of Leverage 130
Panel B: Tolley Aerospace
3.3 Operating Risk
The greater the fixed component of costs, the more difficult it is for a company to adjust 
its operating costs to changes in sales. The mixture of fixed and variable costs depends 
largely on the type of business. Even within the same line of business, companies can 
vary their fixed and variable costs to some degree. We refer to the risk arising from 
the mix of fixed and variable costs as operating risk . The greater the fixed operating 
costs relative to variable operating costs, the greater the operating risk.
Next, we look at how operating risk affects the variability of cash flows. A concept 
taught in microeconomics is elasticity , which is simply a measure of the sensitivity 
of changes in one item to changes in another. We can apply this concept to examine

how sensitive a company’s operating income is to changes in demand, as measured by 
unit sales. We will calculate the operating income elasticity, which we refer to as the 
degree of operating leverage  (DOL). DOL is a quantitative measure of operating 
risk as it was defined earlier.
The degree of operating leverage is the ratio of the percentage change in operating 
income to the percentage change in units sold. We will simplify things and assume 
that the company sells all that it produces in the same period. Then,
DOLPercentage change in operating incom e
Percentage change=  in units sol d
For example, if DOL at a given level of unit sales is 2.0, a 5 percent increase in unit 
sales from that level would be expected to result in a (2.0)(5%) = 10 percent increase 
in operating income. As illustrated later in relation to Exhibit 6, a company’s DOL is 
dependent on the level of unit sales being considered.(1)Exhibit 4   (Continued)

Business Risk and Financial Risk 131
Returning to Impulse Robotics, the price per unit is $10, the variable cost per unit 
is $2, and the total fixed operating costs are $500,000. If Impulse Robotics’ output 
changes from 100,000 units to 110,000 units—an increase of 10 percent in the number 
of units sold—operating income changes from $300,000 to $380,000:2
Exhibit 5   Operating Leverage of Impulse Robotics
ItemSelling 100,000 
UnitsSelling 110,000 
UnitsPercentage 
Change
Revenues $1,000,000 $1,100,000 +10.00
Less variable costs 200,000 220,000 +10.00
Less fixed costs 500,000 500,000 0.00
Operating income $300,000 $380,000 +26.67
Operating income increases by 26.67 percent when units sold increases by 10 per -
cent. What if the number of units decreases  by 10 percent, from 100,000 to 90,000? 
Operating income is $220,000, representing a decline  of 26.67 percent.
What is happening is that for a 1 percent change in units sold, the operating income

changes by 2.67 times that percentage, in the same direction. If units sold increases 
by 10 percent, operating income increases by 26.7 percent; if units sold decreased by 
20 percent, operating income would decrease by 53.3 percent.
We can represent the degree of operating leverage as given in Equation 1 in terms 
of the basic elements of the price per unit, variable cost per unit, number of units 
sold, and fixed operating costs. Operating income is revenue minus total operating 
costs (with variable and fixed cost components):
Operatin g
incomePrice
per unitNumber of
units sol d=



 


−


Variable cos t
units sol d 


−

Fixed operating
costs
or
Operatin g
incomeNumber of
units sol dPrice
per unit=



 −



Variable cos t
per unit




 −



per unit
Contribution m argin/dncurlybracketleft/dncurlybracketmid/horizcurlybracketext/horizcurlybracketext/horizcurlybracketext/horizcurlybracketext/horizcurlybracketext/horizcurlybracketext/horizcurlybracketext/horizcurlybracketext /horizcurlybracketext/dncurlybracketright/horizcurlybracketext/horizcurlybracketext/horizcurlybracketext/horizcurlybracketext/horizcurlybracketext/horizcurlybracketext/horizcurlybracketext/horizcurlybracketext−

costs
The per unit contribution margin  is the amount that each unit sold contributes 
to covering fixed costs—that is, the difference between the price per unit and the vari -
able cost per unit. That difference multiplied by the quantity sold is the contribution 
margin , which equals revenue minus variable costs.
2 We provide the variable and fixed operating costs for our sample companies used in this reading to

illustrate the leverage and breakeven concepts. In reality, however, the financial analyst does not have these 
breakdowns but rather is faced with interpreting reported account values that often combine variable and 
fixed costs and costs for different product lines.

Reading 36 ■ Measures of Leverage 132
How much does operating income change when the number of units sold changes? 
Fixed costs do not change; therefore, operating income changes by the contribution 
margin. The percentage change in operating income for a given change in units sold 
simplifies to
DOL =−()
−() −QP V
QP VF
where Q is the number of units, P is the price per unit, V is the variable operating cost 
per unit, and F is the fixed operating cost. Therefore, P – V is the per unit contribution 
margin and Q(P − V) is the contribution margin.
Applying the formula for DOL using the data for Impulse Robotics, we can cal -
culate the sensitivity to change in units sold from 100,000 units:
DOL
1 units11 2
11 25@
,,$ $
,$ $$ , 00 00000 000 0
00 000 00 0 0002 =− ()
− () −=. .67
A DOL of 2.67 means that a 1 percent change in units sold results in a 1% × 2.67 = 
2.67% change in operating income; a DOL of 5 means that a 1 percent change in units

sold results in a 5 percent change in operating income, and so on.
Why do we specify that the DOL is at a particular quantity sold (in this case, 
100,000 units)? Because the DOL is different at different numbers of units produced 
and sold. For example, at 200,000 units,
DOL
2 units12
12 5@
,,$ $
,$ $$ , 00 000200 000 0
200 000 00 0 0001 =− ()
− () −=. .45
We can see the sensitivity of the DOL for different numbers of units produced and 
sold in Exhibit 6. When operating profit is negative, the DOL is negative. At positions 
just below and just above the point where operating income is $0, operating income is 
at its most sensitive on a percentage basis to changes in units produced and sold. At 
the point at which operating income is $0 (at 62,500 units produced and sold in this 
example), the DOL is undefined because the denominator in the DOL calculation is 
$0. After this point, the DOL gradually declines as more units are produced and sold.(2)

Business Risk and Financial Risk 133
Exhibit 6   Impulse Robotics’ Degree of Operating Leverage for Different 
Number of Units Produced and Sold
051015
–20–15–10–5
–30–2510,00030,00050,00070,00090,000110,000130,000150,000170,000190,000210,000230,000250,000270,000290,000
Units Produced and SoldDOL
P = $10; V = $2; F = $500,000
We will now look at a similar situation in which the company has shifted some of 
the operating costs away from fixed costs and into variable costs. Malvey Aerospace 
has a unit sales price of $10, a variable cost of $6 a unit, and $150,000 in fixed costs. A 
change in units sold from 100,000 to 110,000 (a 10 percent change) changes operating 
profit from $250,000 to $290,000, or 16 percent. The DOL in this case is 1.6:
DOL
1 units1
1@
,,$ $
,$ $$ , 00 000100 000 06
100 000 06 150 0001 =− ()
− () −=..6
and the change in operating income is 16 percent:
Percentage change
in operating incomeDOLPercentage chang=()ee 
in units sold

=() () = 1610 16.% %


We can see the difference in leverage in the case of Impulse Robotics and Malvey 
Aerospace companies in Exhibit 7. In Panel A, we see that Impulse Robotics has higher 
operating income than Malvey Aerospace when both companies produce and sell more 
than 87,500 units, but lower operating income than Malvey when both companies 
produce and sell less than 87,500 units.3
Exhibit 7   Profitability and the DOL for Impulse Robotics and Malvey 
Aerospace
Impulse Robotics: P = $10; V = $2; F = $500,000
Malvey Aerospace: P = $10; V = $6; F = $150,000
3 We can calculate the number of units that produce the same operating income for these two companies 
by equating the operating incomes and solving for the number of units. Let X be the number of units. 
The X at which Malvey Aerospace and Impulse Robotics generate the same operating income is the X that 
solves the following: 10 X − 2X − 500,000 = 10 X − 6X − 150,000; that is, X = 87,500.

Reading 36 ■ Measures of Leverage 134
Panel A: Operating Income and Number of Units Produced 
and Sold
–$800,000–$400,000$0$400,000$800,000$1,200,00010,00030,00050,00070,00090,000110,000130,000150,000170,000190,000
Units Produced and SoldOperating Income
Impulse Robotics
Malvey  Aerospace
Panel B: Degree of Operating Leverage (DOL)
–30–20–10010203010,00030,00050,00070,00090,000110,000130,000150,000170,000190,000
Malvey Aerospace
This example confirms what we saw earlier in our reasoning of fixed and variable 
costs: The greater the use of fixed, relative to variable, operating costs, the more sen -
sitive operating income is to changes in units sold and, therefore, the more operating 
risk. Impulse Robotics has more operating risk because it has more operating leverage. 
However, as Panel B of Exhibit 7 shows, the degrees of operating leverage are similar 
for the two companies for larger numbers of units produced and sold.

Both sales risk and operating risk influence a company’s business risk. And both 
sales risk and operating risk are determined in large part by the type of business the 
company is in. But management has more opportunity to manage and control oper -
ating risk than sales risk.Exhibit 7   (Continued)

Business Risk and Financial Risk 135
Suppose a company is deciding which equipment to buy to produce a particular 
product. The sales risk is the same no matter what equipment is chosen to produce 
the product. But the available equipment may differ in terms of the fixed and variable 
operating costs of producing the product. Financial analysts need to consider how the 
operating cost structure of a company affects the company’s risk.
EXAMPLE 1   
Calculating the Degree of Operating Leverage
Arnaud Kenigswald is analyzing the potential impact of an improving economy 
on earnings at Global Auto, one of the world’s largest car manufacturers. Global 
is headquartered in Berlin. Two Global Auto divisions manufacture passenger 
cars and produce combined revenues of €93 billion. Kenigswald projects that 
sales will improve by 10 percent due to increased demand for cars. He wants to 
see how Global’s earnings might respond given that level of increase in sales. He

first looks at the degree of leverage at Global, starting with operating leverage.
Global sold 6 million passenger cars in 2009. The average price per car was 
€24,000, fixed costs associated with passenger car production total €15 billion 
per year, and variable costs per car are €14,000. What is the degree of operating 
leverage of Global Auto?
Solution:
DOL  
6 mi llion units6 mi llion 24 14
6 mi llion @ (¬ ,¬ ,)=−000 000
((¬ ,¬ ,) ¬.24 14 15 bi llion 000 0001 333−−=
For a 10 percent increase in cars sold, operating income increases by 1.333 × 
10% = 13.33%.
Industries that tend to have high operating leverage are those that invest up front 
to produce a product but spend relatively little on making and distributing it. Software 
developers and pharmaceutical companies fit this description. Alternatively, retailers 
have low operating leverage because much of the cost of goods sold is variable.
Because most companies produce more than one product, the ratio of variable

to fixed costs is difficult to obtain. We can get an idea of the operating leverage of a 
company by looking at changes in operating income in relation to changes in sales for 
the entire company. This relation can be estimated by regressing changes in operating 
income (the variable to be explained) on changes in sales (the explanatory variable) 
over a recent time period.4 Although this approach does not provide a precise mea -
sure of operating risk, it can help provide a general idea of the amount of operating 
leverage present. For example, compare the relation between operating earnings and 
revenues for Abbott Laboratories, a pharmaceutical company, and Wal-  Mart Stores, 
a discount retailer, as shown in Exhibit 8. Note that the slope of the least-  squares 
regression line is greater for Abbott (with a slope coefficient of 0.1488) than for Wal-  
Mart (with a slope coefficient of 0.0574). (A visual comparison of slopes should not

be relied upon because the scales of the x- and y-axes are different in diagrams for the 
two regressions.) We can see that operating earnings are more sensitive to changes 
in revenues for the higher-  operating-  leveraged Abbott Laboratories as compared to 
the lower-  operating-  leveraged Wal-  Mart Stores.
4 A least-  squares regression is a procedure for finding the best-  fitting line (called the least squares regression 
line) through a set of data points by minimizing the squared deviations from the line.

Reading 36 ■ Measures of Leverage 136
Exhibit 8   Relation between Operating Earnings and Revenues
Panel A: Abbott Laboratories Operating Earnings and 
Revenues, 1990–2004
Estimated regression: Operating earnings = $754.77 + 0.1488 Revenues 
R2 = 66.25%
$0$500$1,000$1,500$2,000$2,500$3,000$3,500$4,000$4,500
$0 $5,000 $10,000 $15,000 $20,000 $25,000
Revenues in MillionsOperating Earnings in Millions
Panel B: Wal-  Mart Stores Operating Earnings and 
Estimated regression: Operating earnings = $152.762 + 0.0574 Revenues 
R2 = 99.38%
$0$2,000$4,000$6,000$8,000$10,000$12,000$14,000$16,000$18,000
$0 $50,000 $100,000 $150,000 $200,000 $250,000 $300,000
Sources:  Abbott Laboratories 10-  K filings and Wal-  Mart Stores 10-  K filings, various years.
3.4 Financial Risk
We can expand on the concept of risk to accommodate the perspective of owning a 
security. A security represents a claim on the income and assets of a business; therefore,

the risk of the security goes beyond the variability of operating earnings to include 
how the cash flows from those earnings are distributed among the claimants—the 
creditors and owners of the business. The risk of a security is therefore affected by 
both business risk and financial risk.

Business Risk and Financial Risk 137
Financial risk  is the risk associated with how a company finances its operations. 
If a company finances with debt, it is legally obligated to pay the amounts that make 
up its debts when due. By taking on fixed obligations, such as debt and long-  term 
leases, the company increases its financial risk. If a company finances its business 
with common equity, generated either from operations (retained earnings) or from 
issuing new common shares, it does not incur fixed obligations. The more fixed-  cost 
financial obligations (e.g., debt) incurred by the company, the greater its financial risk.
We can quantify this risk in the same way we did for operating risk, looking at the 
sensitivity of the cash flows available to owners when operating income changes. This 
sensitivity, which we refer to as the degree of financial leverage  (DFL), is
DFLPercentage change in net inco me
Percentage change in op=eerating incom e

For example, if DFL at a given level of operating income is 1.1, a 5 percent increase 
in operating income would be expected to result in a (1.1)(5%) = 5.5 percent increase 
in net income. A company’s DFL is dependent on the level of operating income being 
considered.
Net income is equal to operating income, less interest and taxes.5 If operating 
income changes, how does net income change? Consider Impulse Robotics. Suppose 
the interest payments are $100,000 and, for simplicity, the tax rate is 0 percent: If 
operating income changes from $300,000 to $360,000, net income changes from 
$200,000 to $260,000:
Exhibit 9   Financial Risk of Impulse Robotics (1) 
Operating Income 
of $300,000Operating Income 
of $360,000Percentage 
Change
Operating income $300,000 $360,000 +20
Less interest 100,000 100,000 0
Net income $200,000 $260,000 +30
A 20 percent increase in operating income increases net income by $60,000, or

30 percent. What if the fixed financial costs are $150,000? A 20 percent change in 
operating income results in a 40 percent change in the net income, from $150,000 
to $210,000:
Exhibit 10   Financial Risk of Impulse Robotics (2) 
Change
Less interest 150,000 150,000 0
Net income $150,000 $210,000 +40(3)
5 More complex entities than we have been using for our examples may also need to account for other 
income (losses) and extraordinary income (losses) together with operating income as the basis for earnings 
before interest and taxes.

Reading 36 ■ Measures of Leverage 138
Using more debt financing, which results in higher fixed costs, increases the sensi -
tivity of net income to changes in operating income. We can represent the sensitivity 
of net income to a change in operating income, continuing the notation from before 
and including the fixed financial cost, C, and the tax rate, t, as
DFL1
1=−() − −()
−() −− −()=−() − 
−(QP VF t
QP VF CtQP VF
QP V) )−− FC
As you can see in Equation 4, the factor that adjusts for taxes, (1 – t), cancels out 
of the equation. In other words, the DFL is not affected by the tax rate.
In the case in which operating income is $300,000 and fixed financing costs are 
$100,000, the degree of financial leverage is
DFL
3  operating income3
31@
$,$,
$, $,.00 00000 000
00 000 00 0001 =−=5 5
If, instead, fixed financial costs are $150,000, the DFL is equal to 2.0:
DFL
31 5@
$,$,
00 000 0 0002 =−=0 0

31 5@
$,$,
Again, we need to qualify our degree of leverage by the level of operating income 
because DFL is different at different levels of operating income.
The greater the use of financing sources that require fixed obligations, such as 
interest, the greater the sensitivity of net income to changes in operating income.
EXAMPLE 2   
Calculating the Degree of Financial Leverage
Global Auto also employs debt financing. If Global can borrow at 8 percent, the 
interest cost is €40 billion. What is the degree of financial leverage of Global 
Auto if 6 million cars are produced and sold?
Solution: 
At 6 million cars produced and sold, operating income = €45 billion. Therefore:
¬¬
¬¬4545
45 billion operating incomeDFL @ billion
 billion=−4 4090 billion=.
For every 1 percent change in operating income, net income changes 9 percent 
due to financial leverage. 
Unlike operating leverage, the degree of financial leverage is most often a choice

by the company’s management. Whereas operating costs are very similar among com -
panies in the same industry, competitors may decide on differing capital structures.
Companies with relatively high ratios of tangible assets to total assets may be able 
to use higher degrees of financial leverage than companies with relatively low ratios 
because the claim on the tangible assets that lenders would have in the event of a 
default may make lenders more confident in extending larger amounts of credit. In 
general, businesses with plants, land, and equipment that can be used to collateralize 
borrowings and businesses whose revenues have below-  average business cycle sensi -
tivity may be able to use more financial leverage than businesses without such assets 
and with relatively high business cycle sensitivity.
Using financial leverage generally increases the variability of return on equity (net 
income divided by shareholders’ equity). In addition, its use by a profitable company

may increase the level of return on equity. Example 3 illustrates both effects.(4)

Business Risk and Financial Risk 139
EXAMPLE 3   
The Leveraging Role of Debt
Consider the Capital Company, which is expected to generate $1,500,000 in 
revenues and $500,000 in operating earnings next year. Currently, the Capital 
Company does not use debt financing and has assets of $2,000,000.
Suppose Capital were to change its capital structure, buying back $1,000,000 
of stock and issuing $1,000,000 in debt. If we assume that interest on debt is 
5 percent and income is taxed at a rate of 30 percent, what is the effect of debt 
financing on Capital’s net income and return on equity if operating earnings 
may vary as much as 40 percent from expected earnings?
Exhibit 11   Return on Equity of Capital Company
No Debt 
(Shareholders’ 
Equity = $2 million)Expected 
Operating 
Earnings,  
Less 40%Expected 
Operating 
EarningsExpected 
Operating 
Earnings,  
Plus 40%
Earnings before 
interest and taxes $300,000 $500,000 $700,000
Interest expense 0 0 0
taxes $300,000 $500,000 $700,000

Taxes 90,000 150,000 210,000
Net income $210,000 $350,000 $490,000
Return on equity110.5% 17.5% 24.5%
Debt to Total 
Assets = 50%; 
Equity = $1 million)Expected 
Operating 
Earnings,  
Operating 
Operating 
Earnings,  
Plus 40%
Interest expense 50,000 50,000 50,000
taxes $250,000 $450,000 $650,000
Taxes 75,000 135,000 195,000
Net income $175,000 $315,000 $455,000
Return on equity 17.5% 31.5% 45.5%
1 Recall that ROE is calculated as net income/shareholders’ equity.
Depicting a broader array of capital structures and operating earnings, ranging 
from an operating loss of $500,000 to operating earnings of $2,000,000, Exhibit 12 
shows the effect of leverage on the return on equity for Capital Company:

Reading 36 ■ Measures of Leverage 140
Exhibit 12   Return on Equity of Capital Company for Different Levels 
of Operating Earnings and Different Financing Choices
–100%–50%50%
0%100%150%200%250%300%
–$500,00 0– $100,00 0$ 300,000 $700,00 0$ 1,100,000 $1,500,000 $1,900,000
Earnings before Interest and TaxesReturn on Equity
Debt to total assets = 0%
Debt to total assets = 33.33%
Debt to total assets = 50%
Debt to total assets = 67%
Business is generally an uncertain venture. Changes in the macroeconomic and 
competitive environments that influence sales and profitability are typically difficult 
to discern and forecast. The larger the proportion of debt in the financing mix of a 
business, the greater is the chance that it will face default. Similarly, the greater the 
proportion of debt in the capital structure, the more earnings are magnified upward 
in improving economic times. The bottom line? Financial leverage tends to increase 
the risk of ownership for shareholders.
3.5 Total Leverage

The degree of operating leverage gives us an idea of the sensitivity of operating income 
to changes in revenues. And the degree of financial leverage gives us an idea of the 
sensitivity of net income to changes in operating income. But often we are concerned 
about the combined effect of both operating leverage and financial leverage. Owners 
are concerned about the combined effect because both factors contribute to the risk 
associated with their future cash flows. And financial managers, making decisions 
intended to maximize owners’ wealth, need to be concerned with how investment 
decisions (which affect the operating cost structure) and financing decisions (which 
affect the capital structure) affect lenders’ and owners’ risk.
Look back at the example of Impulse Robotics. The sensitivity of owners’ cash flow 
to a given change in units sold is affected by both operating and financial leverage.

Consider using 100,000 units as the base number produced and sold. A 10 percent 
increase in units sold results in a 27  percent increase in operating income and a 
40 percent increase in net income; a like decrease in units sold results in a similar 
decrease in operating income and net income.

Business Risk and Financial Risk 141
Exhibit 13   Total Leverage of Impulse Robotics
Units Produced and Sold:
90,000 100,000 110,000
Revenues $900,000 $1,000,000 $1,100,000
Less variable costs 180,000 200,000 220,000
Less fixed costs 500,000 500,000 500,000
Operating income $220,000 $300,000 $380,000
Less interest 100,000 100,000 100,000
Net income $120,000 $200,000 $280,000
Relative to 100,000 units produced and sold
   Percentage change in units sold −10% +10%
   Percentage change in operating profit −27% +27%
   Percentage change in net income −40% +40%
Combining a company’s degree of operating leverage with its degree of financial 
leverage results in the degree of total leverage  (DTL), a measure of the sensitivity of 
net income to changes in the number of units produced and sold. We again make the 
simplifying assumption that a company sells all that it produces in the same period:
DTLPercentage change in net inco me
Percentage change in t h=e e num ber of units sol d
or
DTL
DOL DFL=−()

or
DTL
−() −×−() − 
−() −− 
×
=−(QP V
QP VFQP VF
QP VF C
QP V) )
−() −− QP VF C
Suppose
Number of units sold = Q =100,000
Price per unit = P =$10
Variable cost per unit = V =$2
Fixed operating cost = F =$500,000
Fixed financing cost = C =$100,000
Then,
DTL=− ()
− () −−=100,000 $$
100,000 $$ $$10 2
10 2 500 000 100 00040,,.
which we could also have determined by multiplying the DOL, 2.67, by the DFL, 1.5. 
This means that a 1 percent increase in units sold will result in a 4 percent increase in 
net income; a 50 percent increase in units produced and sold results in a 200 percent 
increase in net income; a 5 percent decline in units sold results in a 20 percent decline 
in income to owners; and so on.(5)
(6)

Reading 36 ■ Measures of Leverage 142
Because the DOL is relative to the base number of units produced and sold and 
the DFL is relative to the base level of operating earnings, DTL is different depending 
on the number of units produced and sold. We can see the DOL, DFL, and DTL for 
Impulse Robotics for different numbers of units produced and sold, beginning at the 
number of units for which the degrees are positive, in Exhibit 14.
Exhibit 14   DOL, DFL, and DTL for Different Numbers of Units Produced and 
Sold
P = $10, V = $2, F = $500,000, C = $100,000
02468101214161880,000100,000120,000140,000160,000180,000200,000220,000240,000
Number of Units Produced and SoldDegree of Leverage
 DOL
DFL
DTL
In the case of operating leverage, the fixed operating costs act as a fulcrum. The 
greater the proportion of operating costs that are fixed, the more sensitive operating 
income is to changes in sales. In the case of financial leverage, the fixed financial costs,

such as interest, act as a fulcrum. The greater the proportion of financing with fixed 
cost sources, such as debt, the more sensitive cash flows available to owners are to 
changes in operating income. Combining the effects of both types of leverage, we see 
that fixed operating and financial costs together increase the sensitivity of earnings 
to owners.

Business Risk and Financial Risk 143
EXAMPLE 4   
Calculating the Degree of Total Leverage
Continuing from Example 2, Global Auto’s total leverage is
DTL @
 million unitsDOL  @
 million unitsDFL @
 billion 66 45=×¬  operating income
DTL @
 million units million
662 4 000 1=− ¬¬, 4 4 000
62 4 000 14 000 15
45,
,,()
− () −
× million  billion
 billion¬¬ ¬
¬
¬¬¬45 40
61 333 9 01 2 billion  bi llion
DTL @
 million units−
=× = ..
Given Global Auto’s operating and financial leverage, a 1 percent change in unit 
sales changes net income by 12 percent. 
3.6 Breakeven Points and Operating Breakeven Points
Looking back at Exhibit 3, we see that there is a number of units at which the com -
pany goes from being unprofitable to being profitable—that is, the number of units 
at which the net income is zero. This number is referred to as the breakeven point. 
The breakeven point , QBE, is the number of units produced and sold at which the 
company’s net income is zero—the point at which revenues are equal to costs.

Plotting revenues and total costs against the number of units produced and sold, as 
in Exhibit 15, indicates that the breakeven is at 75,000 units. At this number of units 
produced and sold, revenues are equal to costs and, hence, profit is zero.
Exhibit 15   Impulse Robotics Breakeven
$0$500,000$1,000,000$1,500,000$2,000,000$2,500,000$3,000,00010,00030,00050,00070,00090,000110,000130,000150,000170,000190,000210,000230,000250,000
Number of Units Produced and SoldRevenues or Expenses
Breakeven at 
75,000 units
Profit
LossTotal costs Revenues

Reading 36 ■ Measures of Leverage 144
We can calculate this breakeven point for Impulse Robotics and Malvey Aerospace. 
Consider that net income is zero when the revenues are equal to the expenses. We 
can represent this equality of revenues and costs (summing variable operating costs, 
fixed operating costs, and fixed financing costs) by the following equation:
PQ = VQ + F + C
where
 P = the price per unit
 Q = the number of units produced and sold
 V = the variable cost per unit
 F = the fixed operating costs
 C = the fixed financial cost
Therefore, 
PQBE = VQBE + F + C
and the breakeven number of units, QBE, is6
QFC
PVBE=+
−
In the case of Impulse Robotics and Malvey Aerospace, Impulse Robotics has a 
higher breakeven point. Using numbers taken from Exhibit 2:
Impulse Robotics:   unitsBEQ =+
−=$$
$$500 000 100 000
10 275 000,,,
MMalvey Aerospace:  unitsBEQ =+
−=$1 $5
$$ 650 000 0 000
1050 000,,,
This means that Impulse Robotics must produce and sell more units to achieve a

profit. So, while the higher-  leveraged Impulse Robotics has a greater breakeven point 
relative to Malvey Aerospace, the profit that Impulse Robotics generates beyond this 
breakeven point is greater than that of Malvey Aerospace. Therefore, leverage has its 
rewards in terms of potentially greater profit, but it also increases risk.
In addition to the breakeven point specified in terms of net income, QBE, we can 
also specify the breakeven point in terms of operating profit, which we refer to as the 
operating breakeven  point, QOBE. Revenues at the operating breakeven point are set 
equal to operating costs at the operating breakeven point to solve for the operating 
breakeven number of units, QOBE. The expression shows QOBE as equal to fixed oper -
ating costs divided by the difference between price per unit and variable cost per unit:
PQ VQ F
QF
PVOBEO BE
OBE=+
=−
For the two companies in our example, Impulse Robotics and Malvey Aerospace, the

operating breakevens are 62,500 and 37,500 units, respectively:
Impulse Robotics:   units
Malvey AOBEQ =−=$500,000
$$10 262 500 ,
eerospace:  unitsOBEQ =−=$150,000
$$ 6 1037 500 ,
Impulse Robotics has a higher operating breakeven point in terms of the number of 
units produced and sold.(7)
6 You will notice that we did not consider taxes in our calculation of the breakeven point. This is because 
at the point of breakeven, taxable income is zero.

Business Risk and Financial Risk 145
EXAMPLE 5   
Calculating Operating Breakeven and Breakeven Points
Continuing with his analysis, Kenigswald considers the effect of a possible 
downturn on Global Auto’s earnings. He divides the fixed costs of €15 billion 
by the per unit contribution margin:
QOBE billion cars =−=¬
¬¬15
24 000 14 0001 500 000,,,,
The operating breakeven for Global is 1,500,000 cars, or €36 billion in revenues. 
We calculate the breakeven point by dividing fixed operating costs, plus interest 
costs, by the contribution margin:
QBE billion  bi llion  bi llion=+
−=¬¬
¬¬¬
¬15 40
24 000 14 00055
10 ,, ,0 0005 500 000=,,  cars
Considering the degree of total leverage, Global’s breakeven is 5.5 million cars, 
or revenues of €132 billion. 
We can verify these calculations by constructing an income statement for 
the breakeven sales (in € billions):
1,500,000 Cars 5,500,000 Cars
Revenues ( = P × Q) €36 €132
Variable operating costs ( = V × Q) 21 77
Fixed operating costs ( F) 15 15

Operating income € 0 € 40
Fixed financial costs ( C) 40 40
Net income −€40 € 0
As business expands or contracts beyond or below breakeven points, fixed costs 
do not change. The breakeven points for companies with low operating and financial 
leverage are less important than those for companies with high leverage. Companies 
with greater total leverage must generate more revenue to cover fixed operating and 
financing costs. The farther unit sales are from the breakeven point for high-  leverage 
companies, the greater the magnifying effect of this leverage.
3.7 The Risks of Creditors and Owners
As we discussed earlier, business risk refers to the effect of economic conditions as 
well as the level of operating leverage. Uncertainty about demand, output prices, and 
costs are among the many factors that affect business risk. When conditions change 
for any of these factors, companies with higher business risk experience more volatile

earnings. Financial risk is the additional risk that results from the use of debt and 
preferred stock. The degree of financial risk grows with greater use of debt. Who 
bears this risk?
The risk for providers of equity and debt capital differs because of the relative 
rights and responsibilities associated with the use of borrowed money in a business. 
Lenders have a prior claim on assets relative to shareholders, so they have greater 
security. In return for lending money to a business, lenders require the payment of 
interest and principal when due. These contractual payments to lenders must be made

Reading 36 ■ Measures of Leverage 146
regardless of the profitability of the business. A business must satisfy these claims in 
a timely fashion or face the pain of bankruptcy should it default. In return for their 
higher priority in claims, lenders get predefined yet limited returns.
In contrast, equity providers claim whatever is left over after all expenses, includ -
ing debt service, have been paid. So, unlike the fixed and known commitments to the 
lenders, what is left over for the owners may be a great deal or may be nothing. In 
exchange for this risk, providers of equity capital exercise the decision-  making power 
over the business, including the right to hire, guide, and if necessary, fire managers. In 
public companies, ownership rights are usually exercised through an elected board of 
directors. They undertake the decisions over what portion of the business’s earnings 
should be paid out as dividends for common shareholders.

Legal codes in most countries provide for these rights, as well as conditions for 
companies to file for bankruptcy (with reference to businesses, often called insol -
vency). A number of bankruptcy codes provide in some form for two categories of 
bankruptcies. One form provides for a temporary protection from creditors so that 
a viable business may reorganize. In the United States, the US Bankruptcy Code sets 
the terms for the form of negotiated reorganization  of a company’s capital structure 
that allows it to remain a going concern in Chapter 11.7 For businesses that are not 
viable, the second form of bankruptcy process allows for the orderly satisfaction of 
the creditors’ claims. In the United States, this form of bankruptcy is referred to as 
liquidation .8 Whereas both types of bankruptcy lead to major dislocations in the 
rights and privileges of owners, lenders, employees, and managers, it is in this latter 
category of bankruptcy that the original business ceases to exist.

The difference between a company that reorganizes and emerges from bankruptcy 
and one that is liquidated is often the difference between operating and financial lever -
age. Companies with high operating leverage have less flexibility in making changes, 
and bankruptcy protection does little to help reduce operating costs. Companies with 
high financial leverage use bankruptcy laws and protection to change their capital 
structure and, once the restructuring is complete, can emerge as ongoing concerns.
EXAMPLE 6   
Chapter 11 Reorganization and Owens Corning
The world’s largest manufacturer of glass fiber insulation, Owens Corning 
Corporation of Toledo, Ohio, filed for Chapter 11 bankruptcy on 5 October 2000, 
as it faced growing asbestos liability claims. With revenues exceeding $6 billion 
per year, Owens Corning was one of the largest corporations ever afforded 
bankruptcy protection by the US courts.
From 1952 to 1972, Owens Corning produced an asbestos-  containing high-

temperature pipe coating called Kaylo, and at the time of its bankruptcy filing, it 
had received more than 460,000 asbestos personal injury claims and had paid or 
agreed to pay more than $5 billion for asbestos-  related awards and settlements, 
legal expenses, and claims processing fees. While the company had assets of 
$7 billion and liabilities of $5.7 billion, the trust fund it set aside to pay those 
claims appeared inadequate.
7 US Code, Title 11—Bankruptcy, Chapter 11—Reorganization. Companies filing for bankruptcy under 
this code are referred to as having filed for Chapter 11 bankruptcy.
8 US Code, Title 11—Bankruptcy, Chapter 7—Liquidation.

Summary 147
The company’s stock traded at between $15 and $25 per share in the year 
prior to the announcement; the price fell to $1 per share when Owens Corning 
declared bankruptcy and admitted that it had been overwhelmed by the asbestos 
EXAMPLE 7   
Chapter 7 and Webvan Do Not Deliver
Since the peak of the NASDAQ in March of 2000, many technology companies 
have found either that they cannot raise enough capital to implement their 
business plans or that they have an untenable business plan. Some have simply 
shut their doors and gone out of business, while others have filed for bankruptcy. 
Either way, these companies have left many unsatisfied creditors.
For example, Webvan.com was a start-  up company in the late 1990s that 
raised over $1.2 billion in equity, $375 million of which came from an IPO in 
November 1999. It had very ambitious business plans to build a series of ware -
houses and deliver groceries to fulfill customer orders placed over the internet.

Webvan.com, however, faced a number of challenges, including a downturn in 
the economy, and quickly ran through its capital.
Webvan.com filed for Chapter 11 bankruptcy protection in July 2001 and 
reported that it owed $106 million to creditors. By the time it began liquidation 
under Chapter 7 in January 2002, it reported that the value of its liquidated assets 
totaled only $25 million, leaving its creditors to receive pennies on the dollar 
and its investors to receive little or nothing for their $1.2 billion investment in 
Whereas the ability to file for bankruptcy is important to the economy, the goal 
of most investors is to avoid ownership of companies that are heading toward this 
extreme step, as well as to be able to evaluate opportunities among companies already 
in bankruptcy. Under both Chapter 7 and Chapter 11, providers of equity capital gen -
erally lose all value during the bankruptcy. On the other hand, debtholders typically

receive at least a portion of their capital, but the payments of principal and interest 
are delayed during the period of bankruptcy protection.
SUMMARY
In this reading, we have reviewed the fundamentals of business risk, financial risk, 
and measures of leverage.
■■Leverage is the use of fixed costs in a company’s cost structure. Business risk is 
the risk associated with operating earnings and reflects both sales risk (uncer -
tainty with respect to the price and quantity of sales) and operating risk (the 
risk related to the use of fixed costs in operations). Financial risk is the risk 
associated with how a company finances its operations (i.e., the split between 
equity and debt financing of the business).

Reading 36 ■ Measures of Leverage 148
■■The degree of operating leverage (DOL) is the ratio of the percentage change in 
operating income to the percentage change in units sold. We can use the follow -
ing formula to measure the degree of operating leverage:
DOL =−()
−() −QP V
QP VF
■■The degree of financial leverage (DFL) is the percentage change in net income 
for a one percent change in operating income. We can use the following for -
mula to measure the degree of financial leverage:
DFL=−() − −()
−(QP VF t
QP V1
1 ) )−− FC
■■The degree of total leverage (DTL) is a measure of the sensitivity of net income 
to changes in unit sales, which is equivalent to DTL = DOL × DFL.
■■The breakeven point, QBE, is the number of units produced and sold at which 
the company’s net income is zero, which we calculate as
QFC
PVBE=+
−
■■The operating breakeven point, QOBE, is the number of units produced and sold

at which the company’s operating income is zero, which we calculate as
QF
PVOBE=−

Practice Problems 149
1 If two companies have identical unit sales volume and operating risk, they are 
most likely  to also have identical:
A sales risk.
B business risk.
C sensitivity of operating earnings to changes in the number of units produced 
and sold.
2 Degree of operating leverage is best described as a measure of the sensitivity of:
A net earnings to changes in sales.
B fixed operating costs to changes in variable costs.
C operating earnings to changes in the number of units produced and sold.
3 The Fulcrum Company produces decorative swivel platforms for home televi -
sions. If Fulcrum produces 40 million units, it estimates that it can sell them 
for $100 each. Variable production costs are $65 per unit and fixed production 
costs are $1.05 billion. Which of the following statements is most accurate ? 
Holding all else constant, the Fulcrum Company would:
A generate positive operating income if unit sales were 25 million.

B have less operating leverage if fixed production costs were 10 percent 
greater than $1.05 billion.
C generate 20 percent more operating income if unit sales were 5 percent 
greater than 40 million.
4 The business risk of a particular company is most accurately  measured by the 
company’s:
A debt-  to- equity ratio.
B efficiency in using assets to generate sales.
C operating leverage and level of uncertainty about demand, output prices, 
and competition.
5 Consider two companies that operate in the same line of business and have the 
same degree of operating leverage: the Basic Company and the Grundlegend 
Company. The Basic Company and the Grundlegend Company have, respec -
tively, no debt and 50 percent debt in their capital structure. Which of the 
following statements is most accurate ? Compared to the Basic Company, the 
Grundlegend Company has:
A a lower sensitivity of net income to changes in unit sales.
B the same sensitivity of operating income to changes in unit sales.

C the same sensitivity of net income to changes in operating income.
6 Myundia Motors now sells 1 million units at ¥3,529 per unit. Fixed operating 
costs are ¥1,290 million and variable operating costs are ¥1,500 per unit. If 
the company pays ¥410 million in interest, the levels of sales at the operating 
breakeven and breakeven points are, respectively:
A ¥1,500,000,000 and ¥2,257,612,900.
B ¥2,243,671,760 and ¥2,956,776,737.
C ¥2,975,148,800 and ¥3,529,000,000.

Reading 36 ■ Measures of Leverage 150
7 Juan Alavanca is evaluating the risk of two companies in the machinery indus -
try: The Gearing Company and Hebelkraft, Inc. Alavanca used the latest fiscal 
year’s financial statements and interviews with managers of the respective com -
panies to gather the following information:
The Gearing Company Hebelkraft, Inc.
Number of units produced and sold 1 million 1.5 million
Sales price per unit $200 $200
Variable cost per unit $120 $100
Fixed operating cost $40 million $90 million
Fixed financing expense $20 million $20 million
 Based on this information, the breakeven points for The Gearing Company and 
Hebelkraft, Inc. are:
A 0.75 million and 1.1 million units, respectively.
B 1 million and 1.5 million units, respectively.
C 1.5 million and 0.75 million units, respectively.
8–16
Mary Benn, CFA, is a financial analyst for Twin Fields Investments, located in Storrs,

Connecticut, USA. She has been asked by her supervisor, Bill Cho, to examine two 
small Japanese cell phone component manufacturers: 4G, Inc. and Qphone Corp. 
Cho indicates that his clients are most interested in the use of leverage by 4G and 
Qphone. Benn states, “I will have to specifically analyze each company’s respective 
business risk, sales risk, operating risk, and financial risk. ” “Fine, I’ll check back with 
you shortly, ” Cho, answers.
Benn begins her analysis by examining the sales prospects of the two firms. The 
results of her sales analysis appear in Exhibit 1. She also expects very little price vari -
ability for these cell phones. She next gathers more data on these two companies to 
assist her analysis of their operating and financial risk.
When Cho inquires as to her progress Benn responds, “I have calculated Qphone’s 
degree of operating leverage (DOL) and degree of financial leverage (DFL) at Qphone’s

2009 level of unit sales. I have also calculated Qphone’s breakeven level for unit sales. 
I will have 4G’s leverage results shortly. ”
Cho responds, “Good, I will call a meeting of some potential investors for tomorrow. 
Please help me explain these concepts to them, and the differences in use of leverage 
by these two companies. In preparation for the meeting, I have a number of questions”:
■■“You mentioned business risk; what is included in that?”
■■“How would you classify the risk due to the varying mix of variable and fixed 
costs?”
■■“Could you conduct an analysis and tell me how the two companies will fare 
relative to each other in terms of net income if their unit sales increased by 
10 percent above their 2009 unit sales levels?”
■■“Finally, what would be an accurate verbal description of the degree of total 
leverage?”

The relevant data for analysis of 4G is contained in Exhibit 2, and Benn’s analysis of 
the Qphone data appears in Exhibit 3:
Exhibit 1   Benn’s Unit Sales Estimates for 4G, Inc. and Qphone Corp. 
Company 2009 Unit SalesStandard 
Deviation of Unit 
Sales2010 Expected Unit 
Sales Growth Rate 
(%)
4G, Inc. 1,000,000 25,000 15
Qphone Corp. 1,500,000 10,000 15
Exhibit 2   Sales, Cost, and Expense Data for 4G, Inc. (At Unit Sales of 
1,000,000) 
Number of units produced and sold 1,000,000
Sales price per unit ¥108
Variable cost per unit ¥72
Fixed operating cost ¥22,500,000
Fixed financing expense ¥9,000,000
Exhibit 3   Benn’s Analysis of Qphone (At Unit Sales of 1,500,000) 
Degree of operating leverage 1.40
Degree of financial leverage 1.15
Breakeven quantity (units) 571,429
8 Based on Benn’s analysis, 4G’s sales risk relative to Qphone’s is most likely  to be:
A lower.
B equal.
C higher.
9 What is the most appropriate  response to Cho’s question regarding the compo -
nents of business risk?

A Sales risk and financial risk.
B Operating risk and sales risk.
C Financial risk and operating risk.
10 The most appropriate  response to Cho’s question regarding the classification of 
risk arising from the mixture of variable and fixed costs is:
B financial risk.
C operating risk.

Reading 36 ■ Measures of Leverage 152
11 Based on the information in Exhibit 2, the degree of operating leverage (DOL) 
of 4G, Inc., at unit sales of 1,000,000, is closest  to:
A 1.60.
B 2.67.
C 3.20.
12 Based on the information in Exhibit 2, 4G, Inc. ’s degree of financial leverage 
(DFL), at unit sales of 1,000,000, is closest  to:
A 1.33.
B 2.67.
C 3.00.
13 Based on the information in Exhibit 1 and Exhibit 3, Qphone’s expected per -
centage change in operating income for 2010 is closest  to:
A 17.25%.
B 21.00%.
C 24.30%.
14 4G’s breakeven quantity of unit sales is closest  to:
A 437,500 units.
B 625,000 units.
C 875,000 units.
15 In response to Cho’s question regarding an increase in unit sales above 2009 
unit sales levels, it is most likely  that 4G’s net income will increase at:
A a slower rate than Qphone’s.
B the same rate as Qphone’s.
C a faster rate than Qphone’s.
16 The most appropriate  response to Cho’s question regarding a description of the

degree of total leverage is that degree of total leverage is:
A the percentage change in net income divided by the percentage change in 
B the percentage change in operating income divided by the percentage 
change in units sold.
C the percentage change in net income divided by the percentage change in 
operating income.

Solutions 153
SOLUTIONS
1 C is correct. The companies’ degree of operating leverage should be the same, 
consistent with C. Sales risk refers to the uncertainty of the number of units 
produced and sold and the price at which units are sold. Business risk is the 
joint effect of sales risk and operating risk.
2 C is correct. The degree of operating leverage is the elasticity of operating earn -
ings with respect to the number of units produced and sold. As an elasticity, the 
degree of operating leverage measures the sensitivity of operating earnings to a 
change in the number of units produced and sold.
3 C is correct. Because DOL is 4, if unit sales increase by 5 percent, Fulcrum’s 
operating earnings are expected to increase by 4 × 5% = 20%. The calculation 
for DOL is:
DOL million
 million=() − ()
() − () −40 100
40 100$ $65
$ $65 $1.05   billion
 billion
 billion  bi llion=−=$1.
$1. $1.$
$400
400 0514.
00354.=
4 C is correct. Business risk reflects operating leverage and factors that affect

sales (such as those given).
5 B is correct. Grundlegend’s degree of operating leverage is the same as Basic 
Company’s, whereas Grundlegend’s degree of total leverage and degree of finan -
cial leverage are higher.
Operating breakev en units million=− ()=¥,
¥, ,1 290
3 529 1 50063¥5 5 781 173
3 529 635 781 1,.
¥, ,. units
Operating breakev en sal es=× 7 73 2 243 671 760 units =¥, ,,
 or
Operating breakev en sal es million=−()=¥,
¥, ¥,¥1 290
11 500 3 5292 2 243 671 760,, ,
Total breakev en million  mi llion=+
− ()¥, ¥
¥, ¥,1 290 410
3 529 1 500= =
=
=¥,
¥,
,.
¥1 700
2 029
837 851 1582 million
 units
Break even sales 3 3 529 837 851 1582 2 956 776 737,, .¥ ,, , ×=  units
 or
Break even sales million=−()=¥,
¥, ¥,¥, ,,1 700
11 500 3 5292 956 776 7 737
7 A is correct. For The Gearing Company, 
QFC
PVBE million  mi llion=+
−=+
−=$$
$$,40 20
200 120750 000
 For Hebelkraft, Inc.,
QFC
−=+
−=$$
$$,,90 20
200 1001100 000

Reading 36 ■ Measures of Leverage 154
8 C is correct. Sales risk is defined as uncertainty with respect to the price or 
quantity of goods and services sold. 4G has a higher standard deviation of unit 
sales than Qphone; in addition, 4G’s standard deviation of unit sales stated as a 
fraction of its level of unit sales, at 25,000/1,000,000 = 0.025, is greater than the 
comparable ratio for Qphone, 10,000/1,500,000 = 0.0067. 
9 B is correct. Business risk is associated with operating earnings. Operating 
earnings are affected by sales risk (uncertainty with respect to price and quan -
tity), and operating risk (the operating cost structure and the level of fixed 
costs).
10 C is correct. Operating risk refers to the risk arising from the mix of fixed and 
variable costs.
11 B is correct.  DOL =−()
−() −QP V
QP VF
DOL  @
 units 1000 0001 000 000 108 72
1 000 000 108 72 ,,,, ¥¥
,, ¥¥=− ()
− ( ) )−=¥, ,.22 500 000267
12 C is correct. Degree of financial leverage is
DFL=−() − 
−() −− 
=− () −QP VF
QP VF C

−() −− 
=− () −QP VF
QP VF C
1 000 000 108 72 22 500,, ¥¥ ¥, ,,
,, ¥¥ ¥, ,¥ ,,.000
1 000 000 108 72 22 500 000 9 000 000300− () −−=
13 B is correct. The degree of operating leverage of Qphone is 1.4. The percentage 
change in operating income is equal to the DOL times the percentage change in 
units sold, therefore:
in operating incomeDOLPercentage chang=()e e

=() () = 1415 21.% %
14 C is correct. The breakeven quantity is computed
QFC
PVBE=+
−=+ ()
− ()=¥, ,¥ ,,
¥¥,22 500 000 9 000 000
108 72875 000
15 C is correct. 4G, Inc. ’s degree of total leverage can be shown to equal 8, whereas 
Qphone Corp. ’s degree of total leverage is only DOL × DFL = 1.4 × 1.15 = 1.61. 
Therefore, a 10 percent increase in unit sales will mean an 80 percent increase 
in net income for 4G, but only a 16.1 percent increase in net income for 
Qphone Corp. The calculation for 4G, Inc. ’s DTL is
DTL=−()
−() −−
=− ()
− (QP V
QP VF C
1 000 000 108 72
1 000 000 108 72,,
,,¥¥

QP VF C
,,¥¥
¥¥ ) )−−=¥¥22 500 000 9 000 000800,, ,,.
16 A is correct. Degree of total leverage is defined as the percentage change in net 
income divided by the percentage change in units sold.

Working Capital Management
by Edgar A. Norton, Jr., PhD, CFA, Kenneth L. Parkinson, MBA, CCM, and 
Edgar A. Norton, Jr., PhD, CFA, is at Illinois State University (USA). Kenneth L. Parkinson, 
MBA, CCM, is at Treasury Information Services, LLC (USA). Pamela Peterson Drake, PhD, 
CFA, is at James Madison University (USA).
a. describe primary and secondary sources of liquidity and factors 
that influence a company’s liquidity position;
b. compare a company’s liquidity measures with those of peer 
companies;
c. evaluate working capital effectiveness of a company based on its 
operating and cash conversion cycles and compare the company’s 
effectiveness with that of peer companies;
d. describe how different types of cash flows affect a company’s net 
daily cash position;
e. calculate and interpret comparable yields on various securities, 
compare portfolio returns against a standard benchmark, and

evaluate a company’s short-  term investment policy guidelines;
f. evaluate a company’s management of accounts receivable, 
inventory, and accounts payable over time and compared to peer 
g. evaluate the choices of short-  term funding available to a company 
and recommend a financing method.
The focus of this reading is on the short-  term aspects of corporate finance activities 
collectively referred to as working capital management . The goal of effective work -
ing capital management is to ensure that a company has adequate ready access to the 
funds necessary for day-  to- day operating expenses, while at the same time making 
sure that the company’s assets are invested in the most productive way. Achieving this 
goal requires a balancing of concerns. Insufficient access to cash could ultimately lead 1rEADING
37

Reading 37 ■ Working Capital Management 156
to severe restructuring of a company by selling off assets, reorganization via bank -
ruptcy proceedings, or final liquidation of the company. On the other hand, excessive 
investment in cash and liquid assets may not be the best use of company resources.
Effective working capital management encompasses several aspects of short-  term 
finance: maintaining adequate levels of cash, converting short-  term assets (i.e., accounts 
receivable and inventory) into cash, and controlling outgoing payments to vendors, 
employees, and others. To do this successfully, companies invest short-  term funds in 
working capital portfolios of short-  dated, highly liquid securities, or they maintain 
credit reserves in the form of bank lines of credit or access to financing by issuing 
commercial paper or other money market instruments.
Working capital management is a broad-  based function. Effective execution requires

managing and coordinating several tasks within the company, including managing 
short-  term investments, granting credit to customers and collecting on this credit, 
managing inventory, and managing payables. Effective working capital management 
also requires reliable cash forecasts, as well as current and accurate information on 
transactions and bank balances.
Both internal and external factors influence working capital needs; we summarize 
them in Exhibit 1.
Exhibit 1   Internal and External Factors That Affect Working Capital Needs
Internal Factors External Factors
■■Company size and growth rates
■■Organizational structure
■■Sophistication of working capital 
management
■■Borrowing and investing positions/
activities/capacities■■Banking services
■■Interest rates
■■New technologies and new products
■■The economy
■■Competitors
The scope of working capital management includes transactions, relations, anal -
yses, and focus:
■■Transactions include payments for trade, financing, and investment.

■■Relations with financial institutions and trading partners must be maintained to 
ensure that the transactions work effectively.
■■Analyses of working capital management activities are required so that appro -
priate strategies can be formulated and implemented.
■■Focus requires that organizations of all sizes today must have a global viewpoint 
with strong emphasis on liquidity.
In this reading, we examine the different types of working capital and the man -
agement issues associated with each. We also look at methods of evaluating the 
effectiveness of working capital management.
MANAGING AND MEASURING LIQUIDITY
Liquidity  is the extent to which a company is able to meet its short-  term obligations 
using assets that can be readily transformed into cash. When we evaluate the liquidity 
of an asset, we focus on two dimensions: the type of asset and the speed at which the 2

Managing and Measuring Liquidity 157
asset can be converted to cash, either by sale or financing. Unlike many aspects of 
corporate finance, corporate liquidity management does not involve a great deal of 
theory or generally accepted principles. For companies that have the luxury of large 
excesses of cash, liquidity is typically taken for granted, and the focus is on putting the 
excess liquidity to its most productive use. On the other hand, when a company faces 
tighter financial situations, it is important to have effective liquidity management to 
ensure solvency. Unfortunately, this recognition comes too late for some companies, 
with bankruptcy and possible liquidation representing the company’s final choice.
2.1 Defining Liquidity Management
Liquidity management refers to the ability of an organization to generate cash when 
and where it is needed. Liquidity refers to the resources available for an entity to tap

into cash balances and to convert other assets or extend other liabilities into cash for 
use in keeping the entity solvent (i.e., being able to pay bills and continue in opera -
tion). For the most part, we associate liquidity with short-  term assets and liabilities, 
yet longer-  term assets can be converted into cash to provide liquidity. In addition, 
longer-  term liabilities can also be renegotiated to reduce the drain on cash, thereby 
providing liquidity by preserving the limited supply of cash. Of course, the last two 
methods may come at a price as they tend to reduce the company’s overall financial 
strength.
The challenges of managing liquidity include developing, implementing, and 
maintaining a liquidity policy. To do this effectively, a company must manage all of 
its key sources of liquidity efficiently. These key sources may vary from company to 
company, but they generally include the primary sources of liquidity, such as cash

balances, and secondary sources of liquidity, such as selling assets.
2.1.1  Primary Sources of Liquidity
Primary sources of liquidity represent the most readily accessible resources available. 
They may be held as cash or as near-  cash securities. Primary sources include:
■■Ready cash balances, which is cash available in bank accounts, resulting from 
payment collections, investment income, liquidation of near-  cash securities (i.e., 
those with maturities of less than 90 days), and other cash flows.
■■Short-  term funds, which may include items such as trade credit, bank lines of 
credit, and short-  term investment portfolios.
■■Cash flow management, which is the company’s effectiveness in its cash man -
agement system and practices, and the degree of decentralization of the collec -
tions or payments processes. The more decentralized the system of collections, 
for example, the more likely the company will be to have cash tied up in the 
system and not available for use.

These sources represent liquidity that is typical for most companies. They represent 
funds that are readily accessible at relatively low cost.
2.1.2  Secondary Sources of Liquidity
The main difference between the primary and secondary sources of liquidity is that 
using a primary source is not likely to affect the normal operations of the company, 
whereas using a secondary source may result in a change in the company’s financial 
and operating positions. Secondary sources include:
■■negotiating debt contracts, relieving pressures from high interest payments or 
principal repayments;

Reading 37 ■ Working Capital Management 158
■■liquidating assets, which depends on the degree to which short-  term and/or 
long-  term assets can be liquidated and converted into cash without substantial 
loss in value; and
■■filing for bankruptcy protection and reorganization.
Use of secondary sources may signal a company’s deteriorating financial health 
and provide liquidity at a high price—the cost of giving up a company asset to pro -
duce emergency cash. The last source, reorganization through bankruptcy, may also 
be considered a liquidity tool because a company under bankruptcy protection that 
generates operating cash will be liquid and generally able to continue business oper -
ations until a restructuring has been devised and approved.
2.1.3  Drags and Pulls on Liquidity
Cash flow transactions—that is, cash receipts and disbursements—have significant 
effects on a company’s liquidity position. We refer to these effects as drags and pulls

on liquidity. A drag on liquidity  is when receipts lag, creating pressure from the 
decreased available funds; a pull on liquidity  is when disbursements are paid too 
quickly or trade credit availability is limited, requiring companies to expend funds 
before they receive funds from sales that could cover the liability.
Major drags on receipts involve pressures from credit management and deterio -
ration in other assets and include:
■■Uncollected receivables . The longer these are outstanding, the greater the risk 
that they will not be collected at all. They are indicated by the large number of 
days of receivables and high levels of bad debt expenses. Just as the drags on 
receipts may cause increased pressures on working capital, pulls on outgoing 
payments may have similar effects.
■■Obsolete inventory . If inventory stands unused for long periods, it may be an 
indication that it is no longer usable. Slow inventory turnover ratios can also

indicate obsolete inventory. Once identified, obsolete inventory should be 
attended to as soon as possible in order to minimize storage and other costs.
■■Tight credit.  When economic conditions make capital scarcer, short-  term debt 
becomes more expensive to arrange and use. Attempting to smooth out peak 
borrowings can help blunt the impact of tight credit as can improving the com -
pany’s collections.
In many cases, drags may be alleviated by stricter enforcement of credit and collection 
practices.1
However, managing the cash outflows may be as important as managing the 
inflows. If suppliers and other vendors who offer credit terms perceive a weakened 
financial position or are unfamiliar with a company, they may restrict payment terms 
so much that the company’s liquidity reserves are stretched thin. Major pulls on 
payments include:
■■Making payments early.  By paying vendors, employees, or others before the due 
dates, companies forgo the use of funds. Effective payment management means

not making early payments. Payables managers typically hold payments until 
they can be made by the due date.
1 In a survey of CFOs, companies have become more efficient in working capital management, with 
US companies in 2005 reducing their investment in working capital by 2.5 percent from 2004 levels and 
European companies reducing their investment by 3.3 percent (REL 2005 CFO Survey, www.relconsult.com).

Managing and Measuring Liquidity 159
■■Reduced credit limits.  If a company has a history of making late payments, 
suppliers may cut the amount of credit they will allow to be outstanding at 
any time, which can squeeze the company’s liquidity. Some companies try to 
extend payment periods as long as possible, disregarding the possible impact of 
reduced credit limits.
■■Limits on short-  term lines of credit . If a company’s bank reduces the line of 
credit it offers the company, a liquidity squeeze may result. Credit line restric -
tions may be government-  mandated, market-  related, or simply company-  
specific. Many companies try to avert this situation by establishing credit lines 
far in excess of what they are likely to need. This “over-  banking” approach is 
often commonplace in emerging economies or even in more-  developed coun -
tries where the banking system is not sound and the economy is shaky.
■■Low liquidity positions . Many companies face chronic liquidity shortages, often

because of their particular industry or from their weaker financial position. The 
major remedy for this situation is, of course, to improve the company’s financial 
position, or else the company will be heavily affected by interest rates and credit 
availability. Most companies facing this situation have to deal with secured bor -
rowing to obtain any working capital funds. Therefore, it is important for these 
companies to identify assets that can be used to help support the company’s 
short-  term borrowing activities.
It is critical that these drags and pulls be identified as soon as possible, often when 
they have not yet happened or have just arisen.
2.2 Measuring Liquidity
Liquidity contributes to a company’s credit-  worthiness. Credit-  worthiness  is the 
perceived ability of the borrower to pay what is owed on the borrowing in a timely 
manner and represents the ability of a company to withstand adverse impacts on its

cash flows. Credit-  worthiness allows the company to obtain lower borrowing costs and 
better terms for trade credit and contributes to the company’s investment flexibility, 
enabling it to exploit profitable opportunities.
The less liquid the company, the greater the risk it will suffer financial distress 
or, in the extreme case, insolvency or bankruptcy. Because debt obligations are paid 
with cash, the company’s cash flows ultimately determine solvency. The immediate 
source of funds for paying bills is cash on hand, proceeds from the sale of marketable 
securities, or the collection of accounts receivable. Additional liquidity also comes 
from inventory that can be sold and thus converted into cash either directly through 
cash sales or indirectly through credit sales (i.e., accounts receivable).
There is, however, some point at which a company may have too much invested 
in low- and non-  earning assets. Cash, marketable securities, accounts receivable,

and inventory represent a company’s liquidity. However, these investments are low 
earning relative to the long-  term, capital investment opportunities that companies 
may have available.
Various financial ratios can be used to assess a company’s liquidity as well as its 
management of assets over time. Here we will look at some of these ratios in a little 
more detail.
We calculate liquidity ratios  to measure a company’s ability to meet short-  term 
obligations to creditors as they mature or come due. This form of liquidity analysis 
focuses on the relationship between current assets and current liabilities and the 
rapidity with which receivables and inventory can be converted into cash during 
normal business operations.

Reading 37 ■ Working Capital Management 160
In short-  term financial management, a great deal of emphasis is placed on the 
levels of and changes in current assets and liabilities. The two most common mea -
surements are the current ratio and the quick ratio. The current ratio  is the ratio of 
current assets to current liabilities:
Curre nt ratioCurre nt assets
Curre nt liabil ities=
The quick ratio  (also known as the acid-  test ratio ) is the ratio of the quick assets 
to current liabilities. Quick assets  are those assets that can be most readily converted 
to cash. In most situations, the least liquid of the current assets is inventory. Hence, 
we typically exclude inventory when calculating the quick ratio:
Quick ratioCash Short- term  marketable investment sR eceiva=++ b bles
Curre nt liabilities
The greater the current ratio or the quick ratio (that is, the greater the potential ability 
to cover current liabilities), the higher a company’s liquidity. Whether a given current

or quick ratio is good or bad, however, depends on a number of factors, including 
the trend in these ratios, the comparability of these ratios with competitors, and the 
available opportunities in more-  profitable, long-  lived, capital investments.
In addition to looking at the relations among these balance sheet accounts, we 
can also form ratios that measure how well key current assets are managed over time. 
The key ratios for asset management are turnover ratios. For example, the accounts 
receivable turnover  is the ratio of sales on credit to the average balance in accounts 
receivable:2
Accounts receivable turnoverCredit sale s
Average receivabl=ees
This ratio is a measure of how many times, on average, accounts receivable are created 
by credit sales and collected on during the fiscal period. As another example, the 
inventory turnover  is the ratio of the cost of goods sold to the balance in inventory:
Inventory turnov erCost of goods sol d
Average inventor y=

This ratio is a measure of how many times, on average, inventory is created or acquired 
and sold during the fiscal period.
Another perspective on the activity within the current accounts is to estimate 
the number of days of the current asset or liability that are on hand. For example, 
the number of days of receivables , also referred to as the day’s sales outstanding  
and days in receivables , gives us an idea of the management of the extension and 
collection of credit to customers:
Number of da ys of recei vablesAccounts receivabl e
Average d=aays sales on credi t
Accounts receivabl e
Sales on credi t36'
=5 5
2 You will notice that we use credit sales instead of total revenue; the difference lies in the context. Within 
the context of working capital management, the corporate financial analyst would have access to details 
regarding the company’s credit versus cash sales. For some companies, sales may be for cash or be some

combination of cash sales and credit sales. For the analyst who is looking at the company without benefit 
of internal information regarding how much of sales is in the form of credit sales, an approximation is 
generally used based on industry norms for credit practices.

Managing and Measuring Liquidity 161
For example, if this number of days is 35.5, this tells us that it takes, on average, 35.5 
days to collect on the credit accounts. Whether this is good or bad depends on credit 
terms that are offered to customers and the relation between sales and the extension 
of credit, which is often dictated by industry customs and competitive pressures.
The number of days of inventory  gives us an indication of how well the inventory 
acquisition, process, and distribution is managed:
Number of da ys of inv entoryInventory
Average da ys cost of='   goods sold
Inventory
Cost of goods sol d 365=
The number of days of inventory, also known as the average inventory period, day’s 
sales in ending inventory, and the inventory holding period, is the length of time, 
on average, that the inventory remains within the company during the fiscal period. 
We expect variation in the number of days of inventory among industries because

of differences in the production cycle of different types of inventory. For example, 
we expect a grocery store to have a lower number of days of inventory than, say, an 
aircraft manufacturer.
We can also look at the disbursement side of cash flows with the number of days 
of payables , which provides a measure of how long it takes the company to pay its 
own suppliers:
Number of da ys of pa yablesAccounts pa yable
Average da ys p='uurchasesAccounts pa yable
Purchases 365=
The number of days of payables is also referred to as the day’s payables outstanding 
and the average days payable. Purchases are not an item on published financial state -
ments, so if you are evaluating a company’s payables, you can estimate the purchases 
by using what you know about the company’s cost of goods sold and beginning and 
ending balances in inventory.3
Each of these turnover ratios and numbers of days helps tell a story of how the 
company is managing its liquid assets. Like all ratios, the numbers themselves do

not indicate much, but when we put these together with trends, information on 
the company’s profitability, and information about competitors, we develop a good 
understanding of a company’s performance.4
Some of the major applications of this type of analysis include performance eval -
uation, monitoring, credit-  worthiness, and financial projections. But ratios are useful 
only when they can be compared. The comparison should be done in two ways—com -
parisons over time for the same company and over time for the company compared 
with its peer group. Peer groups can include competitors from the same industries as 
the company as well as other companies with comparable size and financial situations.
Consider Wal-  Mart Stores, Inc. We can see the change in the current ratio and 
quick ratio over the fiscal years 1992 through 2005 in Exhibit 2, Panel A. Here, we see 
that the current ratio has declined, yet the quick ratio has increased slightly. We can

see what is driving these trends in Panel B of this exhibit. One driver is the efficiency 
in the management of inventory, which results in holding on to inventory fewer days, 
as indicated by the downward trend in the number of days of inventory. Putting it in 
3 We know that Beginning inventory + Purchases − Cost of goods sold = Ending inventory. Therefore, if we 
know the inventory balances (from the balance sheet) and the cost of goods sold (from the income statement), 
we can determine the purchases: Purchases = Cost of goods sold + Ending inventory − Beginning inventory.
4 For example, if we see a small number of days of inventory, it could mean that the company is managing 
its production very efficiently or it could mean that the company is at significant risk of a shortage of inven -
tory. We don’t know more until we look at what is needed or usual for companies in the industry, trends in

turnover for the company, and the company’s profitability in relation to the number of days of inventory.

Reading 37 ■ Working Capital Management 162
perspective, this trend may be because of, in part, the product shift when Wal-  Mart 
Stores increased its presence in the grocery line of business. Another driver is the 
increasing number of days of payables, which means that company is taking longer 
to pay what it owes suppliers.
Exhibit 2   Liquidity Analysis of Wal-  Mart Stores
Panel A: Current and Quick Ratios, 1992–2005
0.00.20.40.60.81.01.21.41.61.8
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
Fiscal yearNumber of times
Curren t ratio
Quick rati o
Panel B: Number of Days of Inventory and Number of Days of 
Payables
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
Fiscal yearNumber of days
Number of days of inventory
Number of days of payables
Source:  Wal-  Mart Stores, Inc., 10-  K filings, various years.
Comparing Wal-  Mart with Target Inc. and Kohl’s in the 2005 fiscal year, as shown

in Exhibit  3, we see differences among these three competitors. These differences 
may be explained, in part, by the different product mixes (e.g., Wal-  Mart has more 
sales from grocery lines than the others), as well as different inventory management 
systems and different inventory suppliers. The different need for liquidity may also be 
explained, in part, by the different operating cycles of the companies.

Managing and Measuring Liquidity 163
Exhibit 3   Liquidity Ratios among Discount Retailers
Company
Ratio for 2005 Fiscal Y ear Wal-  Mart Target Kohl’s
Current ratio 0.9 1.5 2.4
Quick ratio 0.2 0.9 1.2
Number of days of inventory 48.9 61.0 94.5
Number of days of payables 38.1 64.7 33.9
Source:  Company 10-  K filings with Securities and Exchange Commission for fiscal year 2005.
EXAMPLE 1   
Measuring Liquidity
Given the following ratios, how well has the company been managing its liquidity 
for the past two years?
Current Y ear Past Y ear
Ratio Company Industry Company Industry
Current ratio 1.9 2.5 1.1 2.3
Quick ratio 0.7 1.0 0.4 0.9
Number of days of 
receivables39.0 34.0 44.0 32.5
Number of days of inventory 41.0 30.3 45.0 27.4
Number of days of payables 34.3 36.0 29.4 35.5
Solution: 
The ratios should be compared in two ways—over time (there would typically 
be more than two years’ worth of data) and against the industry averages. In all

ratios shown here, the current year shows improvement over the previous year 
in terms of increased liquidity. In each case, however, the company remains 
behind the industry average in terms of liquidity. A brief snapshot such as this 
example could be the starting point to initiate or encourage more improvements 
with the goal of reaching or beating the industry standards.
We can combine the number of days of inventory, number of days of receivables, 
and number of days of payables to get a sense of the company’s operating cycle and 
net operating cycle. The operating cycle  is a measure of the time needed to convert 
raw materials into cash from a sale. It consists of the number of days of inventory and 
the number of days of receivables:
Operating c ycleNumber of da ys
of inv entoryNumber of da ys
o=+ff recei vables
The operating cycle does not take everything into account, however, because the 
available cash flow is increased by deferring payment to suppliers. This deferral is

considered in the net operating cycle , also called the cash conversion cycle . The

Reading 37 ■ Working Capital Management 164
net operating cycle is a measure of the time from paying suppliers for materials to 
collecting cash from the subsequent sale of goods produced from these supplies. It 
consists of the operating cycle minus the number of days of payables:
Net operating c ycleNumber of da ys
of inv entoryNumber of d=+aays
of recei vablesNumber of da ys
of pa yables−
In general, the shorter these cycles the greater a company’s cash-  generating ability 
and the less its need for liquid assets or outside finance. For many companies, the 
cash conversion cycle represents a period of time that requires financing—that is, the 
company offsets some of the financing need by deferring payments through payables 
terms, but the remainder must be financed.
MANAGING THE CASH POSITION
Although the mix or magnitude of data items may change from day to day, the goal is 
the same: ensuring that the net cash position is not negative. Ideally, the company’s

daily cash inflows and outflows would be equal, but this is rarely the case. Without the 
reliability of matching these flows, companies must take other steps to ensure that the 
flows net out each day. Most companies try to avoid negative balances because the cost 
of garnering daily funds by issuing debt or by drawing on bank overdraft facilities is 
very costly, although the cost of maintaining a small short-  term investment portfolio, 
in terms of an opportunity cost, is regarded as an acceptable cost of doing business.
In addition, it is difficult to borrow the exact amount needed, so many companies 
borrow a little extra to be safe and invest any small excesses overnight at lower rates 
than if they could invest them earlier or in securities with higher rates. To manage 
the cash position effectively, the treasury function, which is usually responsible for 
this activity, must gather information from various sources at all times during the day,

making decisions based on the latest information.
Several critical factors help determine how a company can establish an efficient 
cash flow system. In most cases, the central treasury function may not be able to 
dictate how the company collects from customers or pays its vendors. What it can 
do, however, is use the best services and techniques associated with the company’s 
payment configuration.
As an example of a typical cycle of cash management information that occurs 
daily, consider the process outlined in Exhibit 4. This hypothetical schedule shows 
how important it is to have an efficient, smooth-  flowing information system that can 
meet the time requirements.
Exhibit 4   An Example of the Daily Cycle of Cash Management
Information from bank reporting systems is gathered and analyzed. Morning
↓
The cash manager receives information from company sources.
↓
The cash manager receives updates from the company’s bank(s) on 
current-  day transactions.
↓

↓
The cash management staff is arranging short-  term investments and/
or loans, as necessary, through broker–dealers from their banks or 
investment banks.3

Managing the Cash Position 165
↓
The cash management staff makes funds transfers. Midday
↓
The cash movements for the day are completed or are scheduled for 
completion, and the company’s cash position is finalized.
↓
Necessary paperwork for all transactions is completed. Also, the 
running cash worksheet is updated and set for the next business day.Close of the 
business day
3.1 Forecasting Short-  Term Cash Flows
Forecasting cash flows is necessary to allow effective management of working capital 
accounts. For cash forecasting to be effective, it has to be relatively precise. However, 
a forecast that is precise may not be accurate . There are many factors that are outside 
of the company’s control, such as the general economy, unexpected raw material 
shortages, and changing interest rates. The uncertainty in forecasting encourages 
companies to maintain some minimum level of cash on hand as a buffer.
3.1.1  Minimum Cash Balances

Most companies want a cash buffer as protection from unexpected cash needs or to 
provide the financial flexibility to take advantage of attractive opportunities, such as 
procuring raw material inventory at a discount. This buffer is often expressed as a 
minimum desired cash balance. The size of this buffer depends on several influences, 
including the variation in the levels of the company’s cash inflows and outflows, the 
company’s ability to access other liquidity sources, and the company’s ability to access 
borrowing facilities with little lead time.
3.1.2  Identifying Typical Cash Flows
Having an accurate forecast can help a financial manager make better use of the 
company’s financial history. Many product lines, especially those that are not in high-  
growth stages but rather are in steadier, mature stages, will have similar cash flows 
from year to year or season to season. If an extensive database has been established,

it will be possible to draw reasonable projections for the current period or longer.
Even in cases of heavy growth through mergers and acquisitions, companies should 
try to transfer the acquired company’s cash flow history to be used as a starting point 
for consolidating the new operation into the rest of the company. The cash manager 
must identify cash flow elements to build a reliable forecast. These elements are not 
difficult to identify in general terms, but it is much harder to define them more spe -
cifically to be able to collect data regularly.
The cash elements that comprise a total forecast vary from company to company. 
However, it is good practice to identify the elements that pertain to any one individual 
company. Exhibit 5 shows typical elements arranged as inflows and outflows. It may 
be more useful to try to arrange the elements in this manner—i.e., show matching 
elements by the direction of their flow (in or out). In most cases, a company’s data

elements can be arranged this way to facilitate data gathering, reviewing variances, 
and presenting final reports to management and other cash users or providers.Exhibit 4   (Continued)

Reading 37 ■ Working Capital Management 166
Exhibit 5   Examples of Cash Inflows and Outflows
Inflows Outflows
■■Receipts from operations, broken 
down by operating unit, departments, 
etc.
■■Funds transfers from subsidiaries, 
joint ventures, third parties
■■Maturing investments
■■Debt proceeds (short and long term)
■■Other income items (interest, etc.)
■■Tax refunds■■Payables and payroll disbursements, 
broken down by operating unit, depart -
ments, etc.
■■Funds transfers to subsidiaries
■■Investments made
■■Debt repayments
■■Interest and dividend payments
■■Tax payments
These elements should reflect real cash flows, excluding such items as deprecia -
tion or accruals that are paid at a later date (these should be included when they are 
to be paid).
3.1.3  Cash Forecasting Systems
Cash forecasting should be structured as a system in order to be effective, and to do 
this, several aspects of the forecast must be considered. We provide some examples

of these aspects in Exhibit 6, which highlights each aspect for three different forecast 
horizons. In some cases, one aspect may be more important than others. For instance, 
if daily cash is being handled fairly easily, it may be more critical to spend time and 
resources to ensure that the medium-  term forecasting part of the overall system is 
functioning at the highest levels of reliability. In addition, some factors, such as format 
or time horizon, should not be changed arbitrarily because change may affect their 
accuracy and reliability levels.
Exhibit 6   Examples of Cash Forecasting Aspects over Different Forecast Horizons
Short Term Medium Term Long Term
Data frequency Daily/weekly for 4–6 weeks Monthly for one year Annually for 3–5 years
Format Receipts and disbursements Receipts and disbursements Projected financial statements
Techniques Simple projections Projection models and averages Statistical models
Accuracy Very high Moderate Lowest

Reliability Very high Fairly high Not as high
Uses Daily cash management Planning financial transactions Long-  range financial position
3.2 Monitoring Cash Uses and Levels
Another facet of cash forecasting is monitoring and control. Managing the cash posi -
tion essentially means keeping a “running score” on daily cash flows. Monitoring daily 
cash flows is a key aspect of a company’s cash forecasting system in that the financial 
manager in charge of managing the cash position must know the company’s cash 
balance in the bank on virtually a real-  time basis. However, it really is not forecasting  
as such, because most of the transactions are actually known; the challenge lies in the

Investing Short-  Term Funds 167
collection of this known information in time to do something with that information. 
For example, receiving information about a deposit too late to transfer the funds 
renders the information valueless.
To receive the appropriate information on a timely basis, information should be 
gathered from principal users and providers of cash, supplemented by short-  term 
cash projections in days or even throughout the current day. The minimum level of 
cash available is estimated in advance, adjusted for known funds transfers, seasonal -
ity, or other factors, and is used as a target balance  figure for each bank. Note that 
most companies use one major bank as their lead bank (or concentration bank) and 
control the balances for the bank through one main concentration account, with the 
target balance applied to the main account. For larger companies, more than one 
concentration bank is possible, but managing the cash positions in multiple concen -

tration banks quickly makes the system complex and requires an efficient information 
processing system.
For most companies, it is necessary to manage a cash position with the assistance 
of short-  term investments and borrowings. These short-  term liquidity sources help 
counter the excesses and deficits that typically occur in a company’s cash flow. The 
short-  term investments are usually kept in a portfolio that is very liquid, with short 
maturities. In this way, funds are available whenever they are needed, but the company 
gives up the extra yield that might have been earned if the investments were made 
for longer periods of time or with securities with less liquidity. Short-  term borrowing 
is for very short periods of time, but a borrower may find more economies in bor -
rowing for regular periods, such as thirty days, to reduce the number of transactions 
and associated paperwork. Also, by extending the borrowing period, companies can

usually obtain better rates and availabilities of funds than if they continually borrow 
very short maturities.
Many companies face predictable peaks and valleys in their business throughout 
the year. For instance, manufacturers of consumer electronics products achieve the 
bulk of their sales during the holiday shopping season (from late November through 
the end of the year), which means that they have build-  up of products that are shipped 
well before they receive payment. Thus, they have to finance this inventory roll-  out 
before they receive any cash. During this period, they are likely to use up most or 
all of the temporary excess funds they set aside or to tap into the credit lines they 
arranged for this purpose. When sales roll in during the busy shopping season, they 
use the proceeds to pay down the borrowing and then invest any excess.
Other influencing factors on a company’s cash needs may be associated with

non-  operating activities, such as major capital expenditure programs, mergers and 
acquisitions, sales or disposition of company assets, and the timing of long-  term 
financial transactions, such as bond issues, private placements of debt or equity, and 
equity issues.
Predicting the peak need caused by seasonality or other non-  operating activities 
is important if the company is going to have to borrow funds to cover the need. If a 
company sets aside too much, it will incur excess costs that are unjustified. If it sets 
aside too little, it will have to pay a penalty to raise funds quickly. Either case is a 
costly error. A reliable forecast can help avoid this situation.
INVESTING SHORT-  TERM FUNDS
Short-  term investments represent a temporary store of funds that are not necessar -
ily needed in a company’s daily transactions. If a substantial portion of a company’s 
working capital portfolio is not needed for short-  term transactions, it should be sep -

arated from a working capital portfolio and placed in a longer-  term portfolio. Such 4

Reading 37 ■ Working Capital Management 168
longer-  term portfolios are often handled by another area or are handled by an outside 
money manager under the company’s supervision. In this way, the risks, maturities, 
and portfolio management of longer-  term portfolios can be managed independently 
of the working capital portfolio.
Short-  term working capital portfolios consist of securities that are highly liquid, 
less risky, and shorter in maturity than other types of investment portfolios. Thus, a 
company’s working capital portfolio may consist of short-  term debt securities, such as 
short-  term US government securities and short-  term bank and corporate obligations. 
This type of portfolio changes almost constantly, as cash is needed or more excess 
cash is available for investments.
4.1 Short-  Term Investment Instruments
We describe examples of the major instruments for short-  term investments in Exhibit 7.

The relative amounts of each security can vary from one company to another, depending 
on the company’s risk tolerance and how quickly the invested funds will be needed.
Exhibit 7   Examples of Short-  Term Investment Instruments
InstrumentsTypical 
Maturities Features Risks
US Treasury Bills 
(T- bills)13, 26, and 52 
weeks■■Obligations of US government (guaranteed), issued at 
a discount
■■Active secondary market
■■Lowest rates for traded securitiesVirtually no risk
Federal agency 
securities5–30 days ■■Obligations of US federal agencies (e.g., Fannie Mae, 
Federal Home Loan Board) issued as interest-  bearing
■■Slightly higher yields than T-  billsSlight liquidity risk; 
insignificant credit 
risk
Bank certificates of 
deposit (CDs)14–365 days ■■Bank obligations, issued interest-  bearing in $100,000 
increments
■■“Yankee” CDs offer slightly higher yieldsCredit and liquidity 
risk (depending on 
bank’s credit)
Banker’s acceptances 
(BAs)30–180 days ■■Bank obligations for trade transactions (usually for -

eign), issued at a discount
■■Investor protected by underlying company and trade 
flow itself
■■Small secondary marketCredit and liquidity 
Eurodollar time 
deposits1–180 days ■■Time deposit with bank off-  shore (outside United 
States, such as Bahamas)
■■Can be CD or straight time deposit (TD)
■■Interest-  bearing investment
■■Small secondary market for CDs, but not TDsCredit risk (depend -
ing on bank) Very 
high liquidity risk for 
TDs
Bank sweep services 1 day ■■Service offered by banks that essentially provides 
interest on checking account balance (usually over a 
minimum level)
■■Large number of sweeps are for overnightCredit and liquidity 
bank)
Repurchase agree -
ments (Repos)1 day + ■■Sale of securities with the agreement of the dealer 
(seller) to buy them back at a future time
■■Typically over-  collateralized at 102 percent
■■Often done for very short maturities (< 1 week)Credit and liquidity 
dealer)

Investing Short-  Term Funds 169
Commercial paper 
(CP)1–270 days ■■Unsecured obligations of corporations and financial 
institutions, issued at discount
■■Secondary market for large issuers
■■CP issuers obtain short-  term credit ratingsCredit and liquidity 
credit rating)
Mutual funds and 
money market mutual 
fundsVaries ■■Money market mutual funds commonly used by 
smaller businesses
■■Low yields but high liquidity for money market funds; 
mutual fund liquidity dependent on underlying secu -
rities in fund
■■Can be linked with bank sweep arrangementCredit and liquidity 
fund manager)
Tax-  advantaged 
securities7, 28, 35, 49, 
and 90 days■■Preferred stock in many forms, including adjustable 
rate preferred stocks (ARPs), auction rate preferred 
stocks (AURPs), and convertible adjustable preferred 
stocks (CAPs)
■■Dutch auction often used to set rate
■■Offer higher yieldsCredit and liquidity 
risk (depending on

issuer’s credit)
4.1.1  Computing Yields on Short-  Term Investments
Some securities, such as T-  bills and banker’s acceptances, are issued at a discount. 
Thus, the investor invests less than the face value of the security and receives the 
face value back at maturity. For instance, a $1 million security that pays 5 percent in 
interest with one month remaining to maturity would be purchased at:
Purchase price 1,000,000 1,000,000 995 =− () () () = $. $$ 0051 12 , ,833.33
Proceeds (face valu e) 1,000,000=$
The difference between the purchase price and the face value, $4,166.67, is the dis-
count interest .
Interest-  bearing securities differ from discounted securities in that the investor 
pays the face amount and receives back that same face amount plus the interest on the 
security. For example, a 5 percent, 30-  day, $1 million security would return $1 million 
face value plus interest earned:
Purchase price (face valu e)
Proceeds 1,000,000=
=+$, ,
$1 000 000

=+$, ,
$1 000 000
00051 12 .$ $ () () () = 1,000,000 1,004,166.67
Rates on securities may be quoted as nominal rates or as yields. A nominal rate  is a 
rate of interest based on the security’s face value. In the previous two examples, the 
nominal rate in each instance was 5 percent. A yield , on the other hand, is the actual 
return on the investment if it is held to maturity. For example, if you buy the discount 
security for $995,833.33 and hold it for one month until it matures for $1 million, 
your yield on this investment is
Yield1,000,000 995,833.33
995,833.330.004184 =− 

() =()$12 1 12() =5.0209%Exhibit 7   (Continued)

Reading 37 ■ Working Capital Management 170
where the second factor, 12, annualizes the monthly yield of 0.4184 percent. The factor 
that is used to annualize the yield depends on the type of security and the traditions 
for quoting yields. For example, the money market yield  is typically annualized using 
the ratio of 360 to the number of days to maturity:
Mone y mark et yieldFace valueP urchase pric e
Purchase price=−  



360
Number of da ys to maturity
On the other hand, the bond equivalent yield  is typically annualized using the 
ratio of 365 to the number of days to maturity:
Bond equi valent yieldFace valueP urchase pric e
Purchase pr=−
iiceN umber of da ys to maturity



365
One source of confusion is that the yield on US T-  bills may be quoted on the basis 
of the discount basis or the bond equivalent basis (also referred to as the investment 
yield basis). The yield on a T-  bill using the discount basis is calculated using the face

value as the basis for the yield and then using a 360-  day year:
Discount -basis y ieldFace valueP urchase pric e
Face value=− 
 


360
Although the relevant yield for investment decision purposes is the bond equivalent 
yield, it is important to understand the discount basis because it is often quoted in 
the context of these securities.
EXAMPLE 2   
Computing Investment Yields
For a 91-  day $100,000 US T-  bill sold at a discounted rate of 7.91 percent, cal -
culate the following:
1 Money market yield.
2 Bond equivalent yield.
Purchase price 100,000 .0791 100,000
98,0=− () () () 
=$$
$91 360
0 00.53
Money market yield = [1,999.47/98,000.53] × [360/91] = 8.07 percent
Bond equivalent yield = [1,999.47/98,000.53] × [365/91] = 8.18 percent
4.1.2  Investment Risks
Investors face several types of risks. We list a number of these in Exhibit 8. In this 
exhibit, we list the types of risk—credit, market, liquidity, and foreign exchange—and

the attributes and safety measures associated with each type. The attributes describe 
the conditions that contribute to the type of risk, and the safety measures describe the 
steps that investors usually take to prevent losses from the risk. With the exception 
of foreign exchange risk, the key safety measures taken are to shift to “safety” (i.e., 
government securities, such as US T-  bills) or to shorten maturities so that securities 
will mature quicker, allowing an investor to shift funds to a safer type of security.

Investing Short-  Term Funds 171
Exhibit 8   Types of Investment Risks and Safety Measures
Type of Risk Key Attributes Safety Measures
Credit (or 
default)■■Issuer may default
■■Issuer could be adversely 
affected by economy, market
■■Little secondary market■■Minimize amount
■■Keep maturities short
■■Watch for “questionable” 
names
■■Emphasize government 
Market (or 
interest rate)■■Price or rate changes may 
adversely affect return
■■There is no market to sell the 
maturity to, or there is only a 
small secondary market■■Keep maturities short
■■Keep portfolio diverse in terms 
of maturity, issuers
Liquidity ■■Security is difficult or impossi -
ble to (re)sell
■■Security must be held to 
maturity and cannot be liqui -
dated until then■■Stick with government 
■■Look for good secondary 
market
Foreign 
exchange■■Adverse general market move -
ment against your currency■■Hedge regularly
■■Keep most in your currency 
and domestic market (avoid 
foreign exchange)
4.2 Strategies

Short-  term investment strategies are fairly simple because the securities in a working 
capital portfolio are limited in type and are much shorter in maturity than a longer-  
term portfolio. Most short-  term investors seek “reasonable” returns and do not want 
to take on substantial risk. Short-  term investment strategies can be grouped into two 
types: passive and active. A passive strategy  is characterized by one or two decision 
rules for making daily investments, whereas an active strategy  involves constant 
monitoring and may involve matching, mismatching, or laddering strategies.
Passive strategies are less aggressive than active ones and place top priority on 
safety and liquidity. Yet, passive strategies do not have to offer poor returns, especially 
if companies have reliable cash forecasts. Often, companies with good cash forecasts 
can combine a passive strategy with an active matching strategy to enhance the yield

of a working capital portfolio without taking on substantially greater risks.
The major problem associated with passive strategies is complacency, which can 
cause the company to roll over the portfolio mechanically, with little attention paid to 
yields and more focus on simply reinvesting funds as they mature. Passive strategies 
must be monitored, and the yield from investment portfolios should be benchmarked 
regularly against a suitable standard, such as a T-  bill with comparable maturity.
Active strategies require more daily involvement and possibly a wider choice of 
investments. Although investments are rolled over with an active strategy, just as they 
are with a passive strategy, this type of strategy calls for more shopping around, better 
forecasts, and a more flexible investment policy/guideline.
Active strategies can include intentional matching or mismatching the timing of 
cash outflows with investment maturities. A matching strategy  is the more con -

servative of the two and uses many of the same investment types as are used with 
passive strategies. A mismatching strategy  is riskier and requires very accurate and

Reading 37 ■ Working Capital Management 172
reliable cash forecasts. These strategies usually use securities that are more liquid, 
such as T-  bills, so that securities can be liquidated if adverse market conditions arise. 
Mismatching strategies may also be accomplished using derivatives, which may pose 
additional risks to a company unaccustomed to buying and selling derivatives.
A laddering strategy  is another form of active strategy, which entails scheduling 
maturities on a systematic basis within the investment portfolio such that investments 
are spread out equally over the term of the ladder. A laddering strategy falls some -
where between a matching and a passive strategy. Laddering strategies have been used 
effectively in managing longer-  term investment portfolios, but laddering also should 
be an effective short-  term strategy.
Managing a working capital portfolio involves handling and safeguarding assets

of the company. Accordingly, companies with investment portfolios should have a 
formal, written policy/guideline that protects the company and the investment man -
agers. Investment policy/guidelines should not be very lengthy, especially because 
they must be understood by the company’s investment managers and communicated 
to the company’s investment dealers.
Although the investment policy/guideline should be customized for an individual 
company, the basic structure of such a policy is provided in Exhibit 9.
Exhibit 9   Sample Format of an Investment Policy
Purpose List and explain the reasons that the portfolio exists and also 
describe the general attributes of the portfolio, such as a summary of 
the strategy that will be used and the general types of securities that 
are acceptable investments.
Authorities Identify the executives who oversee the portfolio managers who 
make the investments that compose the portfolio and the outside

managers that could be used and how they would be managed. Also 
describe procedures that must be performed if the policy is not 
followed.
Limitations 
and/or 
restrictionsDescribe, in general terms, the types of investments that should be 
considered for inclusion in the portfolio. The list should not consist 
of specific securities; it should describe the general types  of secu -
rities, such as commercial paper, US T-  bills, or bank CDs. In this 
manner, the policy retains more flexibility than if specific issuers 
or securities are listed. In the latter case, the policy would require 
change every time an issuer was no longer issuing any securities. 
This section should also include any restrictions as to the relative 
amount of each security that is allowable in the overall portfolio. 
This section may also include procedures when a maximum has been 
exceeded or must be exceeded under special circumstances, such as 
when the portfolio is temporarily inflated prior to using the funds

Investing Short-  Term Funds 173
Quality May be in a separate section or may be included with the previous 
one. Investments with working capital funds must be safe, so many 
companies include credit standards for potential investments in their 
policy statements. Reference may be made to long-  term ratings or, 
more frequently, to short-  term credit ratings. The ratings cited are 
usually those from the major rating agencies: Standard & Poor’s and 
Moody’s.
Other items Other items are sometimes included in a policy/guideline, such as 
statements that require the portfolio to be included in the financial 
audit or that regular reports will be generated by the investment 
manager. Some companies also define the types of securities that 
are “eligible, ” but this does not seem necessary if the policy is well 
written.
EXAMPLE 3   
Evaluating an Investment Policy
A sample investment policy is shown below. Review the client’s investment

policy, considering the basic investment policy structure shown in Exhibit 9. 
The average portfolio size is $100 million, with no significant peaks or valleys 
throughout the year. After reviewing the policy, answer the following questions:
1 Is the policy an effective one?
2 What shortcomings or potential problem areas, if any, does it have?
3 How would you change this policy, if at all?
Working Capital Portfolio Investment Policy/Guidelines
■■Purpose: This is a working capital portfolio with emphasis on safety and 
liquidity. We will sacrifice return for either of these two goals.
■■Authorities: The treasurer, with agreement from the CFO, will be in 
charge of managing short-  term investments. Authority and control to 
execute can be delegated by the treasurer or CFO to another treasury 
manager if documented.
■■Maximum maturity: Securities may not be made for longer than three (3) 
years.
■■Types/amounts of investments permitted: no more than 10 percent of the

portfolio or $50 million with any issuer, subject to the credit limitation 
that any eligible issuer must be rated A-  1, P-  1 by Standard & Poor’s and 
Moody’s.
■■Repurchase agreements must be equal to, or preferably exceed, the PSA 
Standard Investment Agreement, which requires 102 percent collateral for 
repurchases.
■■All investments must be held in safekeeping by XYZ Bank.
■■The investment manager can execute exception transactions but must 
document them in writing.Exhibit 9   (Continued)

Reading 37 ■ Working Capital Management 174
The policy is fairly effective in that it tries to provide simple, understandable 
rules. It calls for credit quality, limits the possible position with any single issuer, 
accepts market standards (such as the PSA), and calls for safekeeping. It also 
has an exception procedure that is straightforward.
The credit ratings may be too restrictive. Many investment securities may 
not be rated by both S&P and Moody’s, which is implied, if not stated, in the 
policy. Also, the 10 percent limitation apparently is to be applied to all securi -
ties. However, most investment managers do not consider securities issued by 
governmental agencies or the government itself to be so risky that a limitation 
needs to be applied.
The words “or equivalent” should be added to the credit quality of the types of 
investments. Also, there should be no limitation to highly rated governmental

securities, such as US Treasury-  bills and the equivalent from the major devel -
oped countries. A credit rating reference could be applied to determine eligible 
governmental securities.
4.3 Evaluating Short-  Term Funds Management
Tracking tools can range from simple spreadsheets to more expensive treasury 
workstations. If both portfolios are not too large or diversified, a spreadsheet may be 
sufficient to be able to compare effective yields and borrowing costs on an ongoing 
basis and to generate periodic performance reports.
Investment returns should be expressed as bond equivalent yields, to allow com -
parability among investment alternatives. In addition, the overall portfolio return 
should be weighted according to the currency size of the investment. We provide 
an abbreviated example of a portfolio report in Exhibit 10. The report provides the 
weighted average returns of the different investments. The yields are all calculated on 
a bond equivalent yield basis.

Exhibit 10   Short-  Term Investment Portfolio Report
Security/Loan Dealer/Bank€ Amt 
(000) Weight (%)Yield 
(%) Maturity
US T-  bills ABC Bank 23,575 39.8 3.50 90 days
Finco CP XYZ Co. 20,084 33.9 4.65 45 days
Megabank CD Megabank 15,560 26.3 5.05 30 days
Weighted average yield from investments 4.30
Short-  term benchmark ratea4.25
a Benchmark rate = independent source, such as synthetic portfolio maintained independently or 
rate provided by third party, such as a money manager or other empirical source (e.g., a financial 
institution, trade association, or central bank).

Managing Accounts Receivable 175
MANAGING ACCOUNTS RECEIVABLE
Credit accounts vary by type of customer and the industry, and granting credit involves 
a tradeoff between increasing sales and uncollectible accounts. There are three primary 
activities in accounts receivable management: granting credit and processing transac -
tions, monitoring credit balances, and measuring performance of the credit function.
Processing accounts receivable transactions requires recording credit sales to 
create a record and posting customer payments—or at least monitoring the posting—
to the accounts receivable account by applying the payment against the customer’s 
outstanding credit balance. Monitoring the outstanding accounts receivable requires 
a regular reporting of outstanding receivable balances and notifying the collection 
managers of past due situations. Monitoring is an ongoing activity. Measuring the 
performance of the credit functions entails preparing and distributing key performance

measurement reports, including an accounts receivable aging schedule and day’s sales 
outstanding reports.
Essentially, the accounts receivable management function is a go-  between for the 
credit manager, treasury manager, and accounting manager. This role is an important 
one because it can slow up the recording of payments, which may, in turn, prevent 
customers from purchasing more of the company’s products or, worse yet, could 
prevent the treasury manager from depositing the check and converting the check 
to available funds.
The accounts receivable management function is also considered to be a derivative 
activity from credit granting because it helps in providing information needed by the 
credit management function. It depends on the source of the sale for its records, on 
the credit manager for additional information on the status of the accounts receivable 
record, and possibly on the treasury manager to establish an efficient system of getting

the payment information to the accounts receivable manager for cash application 
(e.g., from a bank lockbox).
The goals for the accounts receivable management system include the following:
■■efficient processing and maintaining accurate, up-  to- date records that are avail -
able to credit managers and other interested parties as soon as possible after 
payments have been received;
■■control of accounts receivable and ensuring that accounts receivable records 
are current and that no unauthorized entry into the accounts receivable file has 
occurred;
■■collection on accounts and coordination with the treasury management 
function;
■■coordination and notification with the credit managers frequently; and
■■preparation of regular performance measurement reports.
Companies may achieve scale economies by centralizing the accounts receivable 
function by using a captive finance subsidiary.5 A captive finance subsidiary  is a

wholly owned subsidiary of the company that is established to provide financing of 
the sales of the parent company.5
5 As pointed out by Shehzad L. Mian and Clifford W. Smith [“ Accounts Receivable Management Policy: 
Theory and Evidence, ” Journal of Finance , vol. 47, no. 1 (March 1992) pp. 169–200], companies that have 
highly variable accounts receivable (for example, from seasonality) may find the use of a captive finance 
subsidiary attractive because it may allow the subsidiary’s debt indentures to differ from those of the 
parent company.

Reading 37 ■ Working Capital Management 176
One of the challenges in accounts receivable management is monitoring receiv -
ables and collecting on accounts. Many companies resort to outsourcing the accounts 
receivable function, primarily to increase the collection on accounts, provide credit 
evaluation services, and to apply the most recent technology. Also, some companies 
may invest in credit insurance, which reduces the risk of bad debts and shifts some 
of the evaluation of credit-  worthiness to the insurer.
5.1 Key Elements of the Trade Credit Granting Process
Credit management is an integral part of the collection process. It sets the frame -
work for sales in that it can restrict sales by rejecting credit or expand it by loosening 
acceptance criteria. It also links the collection and cash application processes and has 
a profound effect on the method of collection as well. In addition, credit management

techniques incorporate fundamental financial analysis methods in setting credit policy, 
granting credit, and managing existing credit customers.
A weak, ineffective credit management function may enhance sales, but many 
of those sales may become bad debts. On the other hand, a strong, active credit 
management function can work in tandem with sales and marketing on one side and 
accounting and treasury on the other. To establish an effective credit management 
function a company must have a well-  conceived strategy customized to the company’s 
needs and reflecting the company’s goals.
Credit management policies are usually established as a set of basic guidelines to 
be used by credit managers. A company’s credit policy sets the boundaries for the 
credit management function. It lays out procedures as part of the policy and offers 
guidance for each typical situation. The policy shows the steps in the granting process

and provides decision rules for specific situations. The policy can also influence the 
sales level by making it easy or difficult for customers to buy on credit.
Customers may start out with one type of credit account that is restrictive, such 
as cash on delivery, and may eventually demonstrate that they are regular payers and 
can be given open book credit accounts.
The major types of credit accounts include the following:
■■open book, which is the most common for company to company;
■■documentary, with or without lines of credit, most common for cross-  border 
transactions;
■■installment credit, with regular timed payments; and
■■revolving credit.
The types of credit terms offered vary by type of customer, the relative financial 
strength of the customer, and the type of credit terms the competition is offering. 
The different forms of terms of credit other than cash, which generally implies 7 to 
10 days, include the following:

■■Ordinary terms . Terms are set forth in a standard format— net t  or d/t1 net t2, 
where t in the first example refers to the length of time a customer has to pay 
the invoice before becoming past due. In the second example, t1 is the time 
period for taking discounts, and t2 is the same as t in the first example. For 
example, net 60  means that the full amount of the invoice is due in 60 days. 
Most trade credit customers will take the full 60 days. Terms of 1/10 net 30  
mean that the customer can take a 1 percent discount if the invoice is paid 
within 10 days or else pay the full amount of the invoice by 30 days from the 
invoice date.

Managing Accounts Receivable 177
■■Cash before delivery (CBD)  terms require that the amount of the invoice must 
be paid in advance before delivery will be scheduled. Checks must clear before 
any shipment is made.
■■Cash on delivery (COD)  terms require that payment must be made (usually in 
the form of a bank check) when the product is delivered; otherwise, no delivery 
will be made.
■■Bill-  to- bill. These terms require that each prior bill must be paid before new 
shipments are possible.
■■Monthly billing . These terms require payment monthly. They have a different 
format; for example, 2/10th Prox net 30th  means that the customer can take a 
2 percent discount if it pays within the first 10 days of the next month or else it 
must pay the full amount of the invoice by the 30th day of the next month.
Credit managers may evaluate customers’ credit-  worthiness using a credit scoring 
model. A credit scoring model  is a statistical model used to classify borrowers accord -

ing to credit-  worthiness. These models were first designed for assisting in making 
consumer credit decisions. Major credit card issuers needed a tool they could use to 
make mass credit decisions. It was also used for small business loans after many larger 
banks discovered that their costs of reviewing and deciding whether to grant loans 
were such that they could not efficiently make loans of the smaller sizes required by 
smaller businesses. To overcome this problem, they adopted credit scoring models.
Credit scoring models offer an opportunity for a company to make fast decisions 
on the basis of simple data, not requiring a great deal of paperwork. The scoring 
models give greater weight to such factors as:
■■ready cash (e.g., high checking account balances);
■■organization type, with corporations rated higher than sole proprietorships or 
partnership; and
■■being current in supplier payments, as indicated by financial services such as 
Dun & Bradstreet.

The models penalize the potential borrower for:
■■prior late payment behavior or defaults: payment patterns are habitual;
■■heavy use of personal credit cards: no reserves or reduced reserves available;
■■previous personal  bankruptcy or tax liens: carries over from person to com -
pany; and
■■high-  risk categories: food services, hospitality industries.
Credit scoring can also be used to predict late payers.
5.2 Managing Customers’ Receipts
Cash collections systems are a function of the types of customers a company has and 
the methods of payment that the customers use. For instance, if a company’s sales 
are made at retail locations, it cannot take advantage of the benefits offered by bank 
lockbox services. Instead, it must deal with organizing and controlling local deposits 
and concentrating these deposits efficiently and economically. On the other hand, if 
a company manufactures and sells products to other businesses, it can use a bank

lockbox services to expedite processing and clearing of check payments.
We illustrate a typical network for a company with both electronic and check 
payments in Exhibit 11. Checks from one type of customer are directed to a bank 
lockbox, while electronic payments from another type of customer are transmitted 
via electronic funds transfer (EFT)  through one of the available networks, such as

Reading 37 ■ Working Capital Management 178
the Automated Clearing House (ACH)  system or the Giro system . The ACH system 
is an electronic payment network available to businesses, individuals, and financial 
institutions in the United States, US Territories, and Canada. The Giro systems are 
postal-  based systems in Europe and elsewhere.
Exhibit 11   Cash Collections and Concentration
Buyersending
bankACH
Buyercheck
bank
lockbox
Sellerelectronic
payment
instructions
remittance informationInformation
reporting
Direct EDI
transmission
Paper
advicespayment data EC/EDI
system
In most cases, the best practice for collections involves the establishment of a system 
that accelerates payments as well as their information content, such as the customer’s 
name and identification number and which invoices are being paid. From the collect -
ing company’s point of view, the way to achieve this best practice is to establish an 
electronic collection network. This can apply to either retail or wholesale companies.

Retail payments can be made by credit/debit cards or electronic checks, which 
are converted to electronic debits or digitized images, or by direct debit. These pay -
ments clear electronically and can be facilitated through point of sale (POS)  systems, 
which are systems that capture the transaction data at the physical location in which 
the sale is made. A direct debit program  is an arrangement whereby the customer 
authorizes a debit to a demand account and is used by companies—such as utilities, 
telecommunications service providers, cable companies, insurance companies, and 
credit card companies—to collect routine payments for services.
If payments cannot be converted to electronic payments, the next best practice 
is to use a bank lockbox service. A lockbox system  is coordinated with the banking 
institution in which customer payments are mailed to a post office box and the banking 
institution retrieves and deposits these payments several times a day, enabling the

company to have use of the fund sooner than in a centralized system in which customer 
payments are sent to the company. An acceptable bank lockbox arrangement is one 
in which the checks deposited today are available tomorrow or the next business day. 
This one-  day availability lays the groundwork for best practices in cash concentration.

Managing Accounts Receivable 179
A good performance measure for check deposits is a calculated float factor . The 
float  in this context is the amount of money that is in transit between payments made 
by customers and the funds that are usable by the company. We compute the float 
factor by dividing the average daily deposit in dollars into the average daily float:6
Float factorAverage dail y float
Average daily  deposit
Aver=
=aage dail y float
Total amount of checks deposite dNumber of d days
This calculation gives the average number of days it took deposited checks to 
clear. If the float factor is very small (e.g., less than 1.0), it is probably worthwhile to 
investigate further to determine whether same-  day wire transfers from the deposi -
tory account are warranted, assuming the depository account is with a bank other 
than the company’s lead bank. The float factor only measures how long it takes for 
checks to clear, not how long it takes to receive the checks, deposit them, and then

have them clear. However, it is still very useful and can be computed easily for any 
depository accounts.
EXAMPLE 4   
Calculating Float Factors
Given the following data, compute a float factor for this company bank account.
Total deposits for the month: $3,360,900
Number of days in month: 30 days
Average daily float: $154,040
Solution:
Average daily deposit = ($3,360,900)/30 = $112,030
 Float factor = Average daily float/Average daily deposit
  = $154,040/$112,030 = 1.375
Cash concentration involves two major activities: consolidating deposits and 
moving funds between company accounts or to outside points. The best practice for 
cash concentration may be different for consolidating deposits than for moving funds, 
depending on the timing required and the availability of the funds being transferred.
For bank lockbox concentration, assuming that the checks clear in one business 
day (on average), the concentration technique of choice is the electronic funds transfer

method. In this method, bank lockbox personnel call in the deposit via a reporting 
service or directly to the concentration bank. The concentration bank creates an 
electronic funds transfer debit that clears overnight, giving the company available 
funds in its concentration account. This system can be set up to run with or without 
intervention by the company’s cash manager. In most cases, the best practice does 
not involve any intervention.
Electronic funds transfers offer distinct advantages to companies that use them 
for concentration of funds. First, they are substantially cheaper than the alternative, 
the wire transfer. In addition, they are reliable in that the transfer can be made part 
6 We determine the average daily float from an analysis of cash accounts.

Reading 37 ■ Working Capital Management 180
of a routine that can be performed daily without exception. Even small payments that 
would not be economical to transfer out by wire can be transferred economically by 
electronic funds transfer.
5.3 Evaluating Accounts Receivable Management
There are numerous ways of measuring accounts receivable performance. Most of them 
deal with how effectively outstanding accounts receivable items can be converted into 
cash. Measures can be derived from general financial reports as well as more detailed 
internal financial records.
Many measures, such as number of days of receivables, can be calculated easily 
from financial statements. The standard number of days of receivables evaluates the 
total receivables outstanding but does not consider the age distribution within this 
outstanding balance.
5.3.1  Accounts Receivable Aging Schedule
One key report that accounts receivable managers should use is the aging schedule ,

which is a breakdown of the accounts into categories of days outstanding. We pro -
vide an example of an aging schedule in Exhibit 12, Panel A. As you can see in this 
example, the report shows the total sales and receivables for each reporting period 
(typically 30 days). It is handier to convert the aging schedule to percentages, as we 
show in this exhibit. Note that in the exhibit, it is easy to spot a change in April’s aging: 
Accounts receivable have not been collected and converted to cash as rapidly as in 
previous months. In this case, the April change should be scrutinized. For example, 
the extension of credit terms may have been increased as part of a special program. 
This change could also signal a change in payments by the company’s customers.
Exhibit 12   An Accounts Receivable Aging Schedule
Panel A: The Aging Schedule
($ Millions) January February March April
Sales 530 450 560 680
Total accounts receivable 600 560 650 720
Current (1–30 days old) 330 290 360 280

1–30 days past due 90 120 160 250
31–60 days past due 80 60 60 110
61–90 days past due 70 50 40 50
>90 days past due 30 40 30 30
Aging Expressed as Percent January February March April
Current (1–30 days old) 55.0 51.8 55.4 38.9
1–30 days past due 15.0 21.4 24.6 34.7
31–60 days past due 13.3 10.7 9.2 15.3
61–90 days past due 11.7 8.9 6.2 6.9
>90 days past due 5.0 7.1 4.6 4.2

Managing Accounts Receivable 181
Panel B: Calculation of the Weighted Average Collection Period
March April
Aging GroupCollection 
DaysaWeightb 
(%)Weighted 
DayscCollection 
DaysWeight 
Days
Current (1–30 days) 20 55.4 11.1 29 38.9 11.3
31–60 days 48 24.6 11.8 55 34.7 19.1
61–90 days 80 9.2 7.4 88 15.3 13.5
91–120 days 110 6.2 6.8 115 6.9 7.9
121+ days 130 4.6 6.0 145 4.2 6.1
Weighted average collection daysd43.0 57.9
a The average days for collecting receivables in each grouping.
b The weighting from the aging schedule.
c This figure, expressed in days, is the product of the previous two columns.
d The sum of each grouping’s product equals the overall days.
5.3.2  The Number of Days of Receivables
The number of days of receivables gives us the overall picture of accounts receivable 
collection. We can compare the number of days with the credit policy to give us an 
idea of how well the company is collecting on its accounts, relative to the terms that

it grants credit. But we can take this a step further by calculating a weighted average 
of the collection period, or weighted average day’s sales outstanding. By focusing on 
the time it takes to collect receivables, the weighted average collection period is a good 
measure of how long it is taking to collect from the company’s customers regardless 
of the sales level or the changes in sales.
The calculation of the weighted average collection period requires data on the 
number of days it takes to collect accounts of each age grouping. For example, we could 
group receivables in regular increments, such as 30-  day periods, and then weight the 
collection period in each group by the monetary amount of accounts in the group.
Using the data provided in Exhibit 12, Panel A, it is possible to compute number 
of days of receivables for March and April, as shown in Panel B of this exhibit. As 
you can see in this example, we can get a better idea of why the number of days of

receivables changed from one month to the next. The weighted average collection days 
increased from March to April, primarily because of the large representation in receiv -
able accounts in the 31–60 and 61–90 day ranges, which made up only 24.6 percent + 
9.2 percent = 33.8 percent of accounts in March, but 50 percent of accounts in April.
The primary drawback to this measure is that it requires more information than 
number of days of receivables, and this information is not readily available, especially 
for comparisons among companies.Exhibit 12   (Continued)

Reading 37 ■ Working Capital Management 182
MANAGING INVENTORY
The primary goal for an inventory system is to maintain the level of inventory so that 
production management and sales management can make and sell the company’s 
products without more than necessary invested in this asset. Like cash and accounts 
receivable management, inventory management involves balancing: having sufficient 
inventory, but not too much.
Inventory is a current asset that is created by purchasing, paid by accounts payable, 
and funded by the treasury. The investment in inventory does not produce cash until 
it is sold or otherwise disposed of. Excessive levels of inventory can possibly overstate 
the value of inventory because the more that is on hand, the greater the potential for 
obsolete inventory, which can be sold off, but at a discount. Shortages of inventory 
result in lost sales.
The amount of inventory that a company holds or feels it has to hold creates a

financial requirement for the company. If the company’s product lines are more diverse 
or if its production processes are more involved in using inventory to make final 
products and then store the products, the company may have a significant financial 
investment in inventory.
The investment in inventory has been quite staggering for many companies, which 
has caused them to look for new inventory management techniques. New techniques 
in inventory control, aided by improved technology, have enabled substantial reduction 
of the inventory levels a company must maintain and still be able to make products and 
have them available for sale as needed. For instance, newer just-  in- time approaches 
to inventory management have lowered required inventory balances and cemented 
major trading partner relationships.
The motives for holding inventory, which dictate how much inventory will be held 
and, in turn, how much working capital will be tied up in inventory, are very similar

to the need for holding cash. The major motives include the transactions motive, the 
precautionary motives, and the speculative motive.
The transactions motive  reflects the need for inventory as part of the routine 
production–sales cycle. Inventory need is equal to the planned manufacturing activity, 
and the approach to inventory will be dictated by the manufacturing plan.
Precautionary stocks  also may be desirable to avoid any stock-  out losses , which 
are profits lost from not having sufficient inventory on hand to satisfy demand. 
Managing inventory well means keeping extra inventory, especially if it could become 
obsolete quickly, at a minimum. To do this, a company must have a reliable forecast 
and a flexible inventory approach. In addition, many companies that do not have a 
reliable forecast maintain a reserve as a precaution for shortfalls in the plan. Of course, 
how much stock is determined by the lead time for additional inventory purchases,

the length of time it takes to deliver final products to the market, and how much can 
be spent on extra inventory.
In certain industries, managers may acquire inventory for speculative reasons, 
such as ensuring the availability and pricing of inventory. Inventory managers working 
together with purchasing managers can benefit from out-  of- the- ordinary purchases. 
For instance, if a publisher is certain that paper costs will be increasing for the next 
year, it can buy more paper in the current year and store it for future use. This decision 
assumes that the storage costs are not greater than the savings.
Companies usually attempt to strike a balance in managing their inventory levels. 
Overinvestment can result in liquidity squeezes or related problems with an increase 
in debt without an increase in cash. Overinvestment can also lead to the misuse of 
facilities as more storage is required for the built-  up inventory. Having large amounts 6

Managing Inventory 183
of inventory on hand can result in losses from shrinkage, spoilage, and so on. Finally, 
overinvestment can reduce the company’s competitiveness as it may not be able to 
match pricing because of its large inventory costs.
On the other hand, underinvestment in inventory can create problems from losing 
customers who could not purchase a product, or gaining their ill-  will from long delays 
in delivery. Plant shutdowns and expensive special runs can also be costly. Finally, a risk 
with underinvestment is the company’s inability to avoid price increases by suppliers.
6.1 Approaches to Managing Levels of Inventory
To control inventory costs, a company should adopt the appropriate approach for its 
inventory. The two basic approaches are the economic order quantity and just-  in- time.
Many companies use the classical approach, economic order quantity–reorder 
point (EOQ–ROP) , at least for some portion of their inventory. This method is based

on expected demand and the predictability of demand, and it requires determining 
the level of inventory at which new inventory is ordered. This ordering point is deter -
mined based on the costs of ordering and carrying inventory, such that the total cost 
associated with inventory is minimized. The demand and lead times determine the 
inventory level. For EOQ–ROP to work well, there must be a reliable short-  term fore -
cast. Often, a company may use EOQ–ROP for smaller items that have low unit costs.
Use of the EOQ–ROP method may involve safety stocks and anticipation stocks. A 
safety stock  is a level of inventory beyond anticipated needs that provides a cushion 
in the event that it takes longer to replenish inventory than expected or in the case of 
greater than expected demand. A company may consider the number of days of inven -
tory on hand and the lead time in replenishing stock in determining the appropriate

level of the safety stock. An anticipation stock  is inventory in excess of that needed 
for anticipated demand, which may fluctuate with the company’s sales or production 
seasonality. We illustrate the EOQ–ROP method in Exhibit 13.
Exhibit 13   EOQ–ROP Inventory Method
Inventory Level
Economic order quantity
Safety stock
Timeorder
orderorderorder
The just-  in- time (JIT) method  is a system that minimizes in-  process inventory 
stocks—raw materials and in production—by evaluating the entire system of the 
delivery of materials and production. Materials are ordered, for example, at a point at 
which current stocks of material reach a reorder point, a point determined primarily 
by historical demand. Materials or manufacturing resource planning (MRP)  systems 
incorporate production planning into inventory management. The analysis of pro -
duction and materials needed for production are incorporated into an analysis that

Reading 37 ■ Working Capital Management 184
provides both a materials acquisition schedule and a production schedule. Combining 
the JIT and MRP methods can provide a broader base for integrating inventory into 
the company’s supply chain management and effectively reduce inventory levels.7
In most instances, companies will have several types of inventory that can be 
managed effectively using one or more of these approaches. Obviously, a company 
should select the method that allows the most cost-  beneficial investment in inventory.
6.2 Inventory Costs
There are several component costs of inventory. Some components represent oppor -
tunity costs, whereas others may be real costs. The component costs include:
■■Ordering . Procurement or replenishment costs, both of which may be fixed or 
variable. These costs depend on the number of orders placed. Examples: freight, 
labor and handling, paperwork, machine setup.
■■Carrying . Financing and holding costs, which are opportunity or real costs.

These costs depend on average inventory levels and the type of goods. 
Examples: storage, capital costs, obsolescence, insurance, and taxes.
■■Stock-  out. Opportunity or real costs, which are affected by level of inventory, 
item mix, processing time versus term of sale. These costs might vary greatly 
depending on how they are estimated. Examples: lost sales, back-  order costs, 
substitution costs.
■■Policy . Costs of gathering data and general operating costs, which may be real 
costs or “soft” costs. These costs depend on inventory mix and complexity. 
Examples: data processing, labor charges, overtime, training.
6.3 Evaluating Inventory Management
The most common way to measure the company’s investment in inventory and 
evaluate its inventory management is to compute the inventory turnover ratio and 
the number of days of inventory. The inventory turnover is a rough measure, but it 
is simple to calculate and compare with other standards or past history. Inventory

turnover will vary among industries, as you can see in Exhibit 14, which provides a 
calculated inventory turnover and number of days of inventory for various industries.
Further, the inventory turnover may differ among companies within an industry 
because of different product mixes. For example, in fiscal year 2005, Wal-  Mart Stores 
had an inventory turnover of 7.5 times compared with Target’s 5.7 times. This differ -
ence may be because of Wal-  Mart’s greater foothold in the higher turnover grocery 
business, as compared with Target.
Although the analysis of trends is important, care should be taken when inter -
preting changes. For example, a decrease in the inventory turnover may mean that 
more inventory is on hand and is not moving through manufacturing and being 
sold. On the other hand, a decrease in inventory turnover may indicate a change in 
the company’s product mix, or it may mean that the company is reducing its risk of 
inventory stock-  outs.

7 Some companies have integrated cash management and inventory management. For example, the moment 
a customer orders and pays for a computer with Dell Corporation, the production process begins. This effi -
ciency results in a negative operating cycle; that is, Dell Corporation is collecting on accounts as it invests in 
the inventory production. Because it uses trade credit for its supplies, it has little need for working capital.

Managing Accounts Payable 185
Exhibit 14   Inventory Turnover and Number of Days of Inventory for US 
Corporations in Different Industries, 2002
IndustryInventory 
Turnover 
(Times)Number 
of Days of 
Inventory
Apparel manufacturing 4.9 74.0
Chemical manufacturing 5.7 64.4
Electronics and appliances stores 7.3 50.2
Food manufacturing 8.1 44.9
Food, beverage, and liquor stores 11.2 32.7
Machinery manufacturing 5.6 65.2
Mining 10.4 35.2
Motor vehicle dealers and parts dealers 5.6 65.2
Paper manufacturing 6.8 53.8
Transportation equipment manufacturing 9.7 37.7
Source:  Statistics of Income, 2002,  Corporation Returns with Net Income, Table 7, www.irs.gov.
EXAMPLE 5   
Financial Impact of Inventory Methods
If a company’s inventory turnover ratio is 6.1 times (annually) and the industry 
average number of days of inventory is 52 days, how does the company compare 
with the industry average?
Solution: 
Convert the turnover ratio to a number of days of inventory:
 Number of days of inventory = 365/Inventory turnover

= 365/6.1 = 59.84 days
Comparing this answer with the industry average, 52.0 days, it appears that the 
company’s inventory turnover is slower than the industry average. 
MANAGING ACCOUNTS PAYABLE
Accounts payable are amounts due suppliers of goods and services that have not been 
paid. They arise from trade credit , which is a spontaneous form of credit in which 
a purchaser of the goods or service is, effectively, financing its purchase by delaying 
the date on which payment is made. Trade credit may involve a delay of payment, 
with a discount for early payment. The terms of the latter form of credit are generally 
stated in the discount form: A discount from the purchase price is allowed if payment 
is received within a specified number of days; otherwise the full amount is due by a 
specified date. For example, the terms “2/10, net 30” indicate that a 2 percent discount 
is available if the account is paid within 10 days; otherwise the full amount is due by

the 30th day. The terms will differ among industries, influenced by tradition within 
the industry, terms of competitors, and current interest rates.7

Reading 37 ■ Working Capital Management 186
A key working capital link is the purchasing–inventory–payables process. This 
process is concerned with the procurement of goods—finished or not—that become 
the company’s items for sale. Handled efficiently, the process minimizes excess funds 
“in the pipeline. ” Handled inefficiently, the process can create a severe drain on a 
company’s liquidity, tying up funds and reducing the company’s financial reserves.
Inefficiencies may arise in managing purchasing, inventory, and payables. Each 
area has to be organized and efficiently linked with the other areas. Purchasing can 
often influence how payments are to be made and the terms of credit. Here again, 
purchasing management needs to be kept informed as to the types of payment mech -
anisms the company can handle to avoid agreeing with suppliers to make payments 
in a medium that the company does not yet support.
The effective management of accounts payable is an important working capital

management activity because inefficient payables management may result in oppor -
tunity costs from payments made too early, lost opportunities to take advantage of 
trade discounts, and failure to use the benefits of technologies offered by e-  commerce 
and other web-  based activities.
Accounts payable is the final step in the procurement cycle because it combines 
the paperwork, approvals, and disbursements of funds. An effective accounts payable 
function helps integrate the components of the cycle and does not require the uneco -
nomical outlay of the company’s funds until the outlay is due.
A company may not believe that it needs a formal guideline or policy to manage the 
function well. However, there must be some method to ensure that payables practices 
are organized, consistent, and cost-  effective. For example, if payables management 
is decentralized and more than one operating entity deals with the same supplier,

the credit terms offered to each entity should be the same unless there are special 
circumstances, such as volume constraints, that warrant different terms. To handle 
payables effectively, a company needs rules to ensure that company assets are not 
being depleted unnecessarily.
There are several factors that a company should consider as guidelines for effec -
tively managing its accounts payable, including:
■■Financial organization’s centralization.  The degree to which the company’s core 
financial function is centralized or decentralized affects how tightly payables 
can be controlled.
■■Number, size, and location of vendors.  The composition of the company’s supply 
chain and how dependent the company is on its trading partners (and vice 
versa) determines how sophisticated a payables system it needs.
■■Trade credit and cost of borrowing or alternative cost.  The importance of credit 
to the company and its ability to evaluate trade credit opportunities, such as

trade discounts, encourages standardized payables procedures and enhanced 
information management throughout the company.
■■Control of disbursement float.  Many companies still pay suppliers by check and 
create disbursement float —the amount of time between check issuance and 
a check’s clearing back against the company’s account. This float has value to 
many companies because it allows them to use their funds longer than if they 
had to fund their checking account on the day the checks were mailed.
■■Inventory management.  Newer inventory control techniques, such as MRP 
and JIT, increase the number of payments that must be processed by accounts 
payable. Many older systems cannot accommodate this extra volume, so newer 
management techniques and systems are required.
■■E- commerce and electronic data interchange (EDI).  Global developments to 
use the internet and other direct connections between customer and supplier 
are revolutionizing the supply chain for many companies. Because payments

Managing Accounts Payable 187
for many of these activities should be considered as part of the overall process, 
many companies have determined that paying electronically offers a more 
efficient, cost-  effective alternative to checks, which only are more valuable when 
the disbursement float value is large and interest rates (which provide value to 
float) are also high.
Stretching payables, also known as pushing on payables when it stretches beyond 
the due date, is sometimes done by corporate cash managers and other financial 
managers.8 Stretching payables is taking advantage of vendor grace periods. The 
evaluation of payables stretching opportunities is fairly straightforward. The number 
of additional days that payments can be extended or stretched is determined and 
valued by applying the company’s opportunity cost for the additional days times the 
amount of the payable.
For example, if a payable that averaged $100,000 can be stretched for an addi -

tional seven days, the company gains an additional seven days’ use of the funds. This 
opportunity can be valued by multiplying the amount, $100,000, by the company’s 
opportunity cost for short-  term funds. For example, if the company’s estimated cost 
for short-  term funds is 8 percent annually (0.02191 percent daily), then the value of 
stretching a $100,000 payment for seven days is $153.42. The values for each opportunity 
(throughout a year’s activity) can be valued in this way to determine the overall benefit, 
which can then be weighed against the costs (both financial and nonfinancial ones).
There are basically two countering forces: paying too early is costly unless the 
company can take advantage of discounts, and paying late affects the company’s 
perceived credit-  worthiness.
7.1 The Economics of Taking a Trade Discount
One key activity that companies should review from time to time is the evaluation of

trade discounts. Trade discounts should be evaluated using the formula shown below, 
which computes the implicit rate (of return) that is represented by the trade discount 
offer; that is, it is the equivalent return to the customer of an alternative investment.
The implicit rate is calculated as follows:
Cost of tra de credi tDiscount
1D iscountNumber o
=+−

 1365f f days 
beyond discount period

−1
The cost of funds during the discount period is 0 percent, so it is beneficial for the 
customer to pay close to the end of the discount period. Once the discount period 
ends, the cost of the credit to the customer jumps up and then declines as the net day 
is approached. For example, if the terms are 2/10, net 30, which means that there is a 
2 percent discount for paying within 10 days and the net amount is due by the 30th 
day, the cost of trade credit is 109 percent if the credit is paid on the 20th day, but it 
is only 44.6 percent if paid on the 30th day.

If the customer’s cost of funds or short-  term investment rate is less than the 
calculated rate, the discount offers a better return or incremental return over the 
company’s short-  term borrowing rate.
8 Keep in mind that stretching payments beyond their due dates might be considered unethical and may 
draw retaliation from suppliers in the form of tighter credit terms in the future.

Reading 37 ■ Working Capital Management 188
EXAMPLE 6   
Evaluating Trade Discounts
Compute the cost of trade credit if terms are 1/10, net 30 and the account is 
paid on:
■■the 20th day, and
■■the 30th day.
Solution:
Cost of trade credit if paid on day 20 =+−

 1001
10 013.
.6 65 10
1
44 32()
−
= . percen t
Cost of trade credit if paid on day 30 =+−

 1001
10 013.
.6 65 20
1()
−
=20.13 percen t
As you can see, the cost of the credits is much lower when the company pays 
on the net day than any day prior to the net day. 
7.2 Managing Cash Disbursements
Handling cash disbursements effectively is a common goal for most companies. To 
accomplish this, companies use best practices that include the ability to delay funding 
bank accounts until the day checks clear, to erect safeguards against check fraud, to 
pay electronically when it is cost-  effective to do so, and to manage bank charges for 
disbursement services. Best practices in cash disbursements, like check collections,

depend on the nature of the payments—i.e., whether they are made electronically or 
by check.
Banks offer controlled disbursement services to optimize the funding of checks 
on the same day they clear against the company’s account. When combined with a 
positive pay service, which provides a filter against check fraud, this method provides 
the best practice in handling paper-  based (check) disbursements.
7.3 Evaluating Accounts Payable Management
The number of days of payables, which is also referred to as the average age of pay -
ables, is a useful measure in evaluating a company’s credit extension and collection.
If the accounts payable balance from the company’s balance sheet is €450 million 
and the amount of purchases is €4,100 million, the number of days of payables is
Average da ys p='uurchases
40.06 da ys=
=450
4100 365
Comparing the number of days of payables with the credit terms under which

credit was granted to the company is important; paying sooner than necessary is costly 
in terms of the cost of credit, and paying later than the net day is costly in terms of 
relations with suppliers.
In some cases, treasurers will manage the company’s payables closely, comparing 
the number of days of payables with the number of days of inventory because in some 
industries these two numbers of days are similar to one another.

Managing Short-  Term Financing 189
MANAGING SHORT-  TERM FINANCING
An overall short-  term financial strategy should focus on ensuring that the company 
maintains a sound liquidity position. It should also reflect the degree of risk the com -
pany believes can be managed without affecting the company’s stability. It is common 
to consider short-  term financial strategies as applying mostly to investments. However, 
they should include other financial activities as well. In many cases, a company will 
only be an investor or borrower, but it is common for large multinational corporations 
to have both short-  term investments and short-  term borrowing.
A short-  term policy should include guidelines for managing investment, borrow -
ing, foreign exchange, and risk management activities and should encompass all the 
company’s operations, including foreign subsidiaries and other domestic subsidiaries 
that are self-  financing. These guidelines accomplish several things.

Too often companies do not explore their options sufficiently, and as a result, they 
do not take advantage of cost savings that some forms of borrowing offer. This lack of 
awareness usually indicates that a company’s treasurer may not be familiar with the 
common forms of short-  term borrowing and has not factored them into an effective 
borrowing strategy.
8.1 Sources of Short-  Term Financing
The main types of short-  term borrowing alternatives that borrowers should consider 
include bank sources as well as money market sources. The main types of bank 
short-  term borrowing include uncommitted and committed bank lines of credit and 
revolving credit agreements ("revolvers"). The latter two types can be unsecured or 
secured, depending on the company’s financial strength and the general credit situation, 
which may vary from country to country. Two of these types—uncommitted lines and 
revolvers—are more common in the United States, whereas regular lines are more

common in other parts of the world. We provide examples of several types of short-  
term borrowing options in Exhibit 15, with bank sources in Panel A of this exhibit and 
nonbank sources in Panel B. In this exhibit, we provide the primary features for each 
type of borrowing, including the typical users, source(s) for the alternative, the base 
rate for computing interest, type of compensation required, and any other comments.
Exhibit 15   Short-  Term Financing Instruments
Panel A: Bank Sources
Source/Type Users Rate Base Compensation Other
Uncommitted line Large corporations None Mainly in United 
States; limited 
reliability
Regular line All sizes Prime (US) or base 
rate (other coun -
tries), money market, 
Libor +Commitment fee Common everywhere
Overdraft line All sizes Commitment fee Mainly outside United 
States
Revolving credit 
agreementLarger corporations Commitment fee+ extra 
feesMost reliable (primar -
ily in United States)
Collateralized loan Small, weak

Collateralized loan Small, weak 
borrowersBase + Collateral Common everywhere8

Reading 37 ■ Working Capital Management 190
Discounted receivables Large companies Varies Extra fees More overseas, but 
some in United States
Banker’s acceptances International 
companiesSpread over commer -
cial paperNone Small volume
Factoring Smaller Prime + + Service fees Special industries
Panel B: Nonbank Sources
Nonbank finance 
companiesSmall, weak 
borrowersPrime + + + Service fees Less reliable
Commercial paper Largest corporations Money market sets 
rateBackup line of credit, 
commissions +Lowest rates for short-  
term funds
Uncommitted lines of credit are, as the name suggests, the least reliable form of 
bank borrowing. A bank may offer an uncommitted line of credit for an extended 
period of time, but it reserves the right to refuse to honor any request for use of the 
line. In other words, an uncommitted line is very unstable and is only as good as the

bank’s desire to offer it. Therefore, companies should not rely very much on uncom -
mitted lines. In fact, banks will not “officially” acknowledge that an uncommitted 
line is usable, which means that uncommitted lines cannot be shown as a financial 
reserve in a footnote to the company’s financial statements. The primary attraction of 
uncommitted lines is that they do not require any compensation other than interest.
Committed lines of credit  are the form of bank line of credit that most companies 
refer to as regular lines of credit. They are more reliable than uncommitted because 
of the bank’s formal commitment, which can be verified through an acknowledgment 
letter as part of the annual financial audit and can be footnoted in the company’s 
annual report. These lines of credit are in effect for 364 days (one day short of a full 
year). This effectively makes sure that they are short-  term liabilities, usually classified 
as notes payable or the equivalent, on the financial statements.

Regular lines are unsecured and are pre-  payable without any penalties. The 
borrowing rate is a negotiated item. The most common interest rates negotiated are 
borrowing at the bank’s prime rate or at a money market rate plus a spread. The most 
common money market rate is an offshore rate—the London interbank offered rate 
(Libor) , which is a Eurodollar rate—plus a spread. The spread varies depending on 
the borrower’s credit-  worthiness. Regular lines, unlike uncommitted lines, require 
compensation, usually in the form of a commitment fee. The fee is typically a frac -
tional percent (e.g., ½ percent) of the full amount or the unused amount of the line, 
depending on bank–company negotiations.
Revolving credit agreements , which are often referred to as revolvers, are the 
most reliable form of short-  term bank borrowing facilities. They have formal legal 
agreements that define the aspects of the agreement. These agreements are similar

to regular lines with respect to borrowing rates, compensation, and being unsecured. 
Revolvers differ in that they are in effect for multiple years (e.g., 3–5 years) and may 
have optional medium-  term loan features. In addition, they are often done for much 
larger amounts than a regular line, and these larger amounts are spread out among 
more than one bank.Exhibit 15   (Continued)

Managing Short-  Term Financing 191
For companies with weak financial positions, such as those facing financial distress 
or that have deteriorated profitability, and many smaller companies that do not have 
sufficient capital, banks or other lenders (see nonbank sources in Exhibit 15) require 
that the company (or individual for much smaller companies) provide collateral in 
the form of an asset, such as a fixed asset that the company owns or high-  quality 
receivables and inventory. These assets are pledged against the loans, and banks or 
other lenders file a lien against them with the state in which the loan is made. This 
lien becomes part of the borrower’s financial record and is shown on its credit report.
8.2 Short-  Term Borrowing Approaches
Given the various forms of short-  term borrowing, it is essential that a borrower have a 
planned strategy before getting stuck in an uneconomical situation. Many borrowing

companies spend too little time establishing a sound strategy for their short-  term 
borrowing beyond making sure that they are able to borrow at all, from any source.
The major objectives of a short-  term borrowing strategy include the following:
■■Ensuring that there is sufficient capacity to handle peak cash needs.
■■Maintaining sufficient sources of credit to be able to fund ongoing cash needs.
■■Ensuring that rates obtained are cost-  effective and do not substantially exceed 
market averages.
In addition, there are several factors that borrowers should consider as part of their 
short-  term borrowing strategies, including the following:
■■Size and credit-  worthiness . There is no doubt that the size of the borrower dic -
tates the options available. Larger companies can take advantage of economies 
of scale to access commercial paper, banker’s acceptances, and so on. The size 
of the borrower often reflects a manufacturing company’s need for short-  term

financing. The size of lender is also an important criterion, as larger banks have 
higher house or legal lending limits. Credit-  worthiness of the borrower will 
determine the rate, compensation, or even whether the loan will be made at all.
■■Sufficient access . Borrowers should diversify to have adequate alternatives 
and not be too reliant on one lender or form of lending if the amount of their 
lending is very large. Even so, it is typical for borrowers to use one alternative 
primarily, but often with more than one provider. Borrowers should be ready to 
go to other sources and know how to. Borrowers should not stay too long with 
just one source or with lowest rates. Many borrowers are usually prepared to 
trade off rates (somewhat) for certainty.
■■Flexibility of borrowing options . Flexibility means the ability to manage matur -
ities efficiently; that is, there should not be any “big” days, when significant 
amounts of loans mature. To do this successfully, borrowers need active matu -

rity management, awareness of the market conditions (e.g., knowing when the 
market or certain maturities should be avoided), and the ability to prepay loans 
when unexpected cash receipts happen.
Borrowing strategies, like investment strategies, can be either passive or active. 
Passive strategies usually involve minimal activity with one source or type of bor -
rowing and with little (if any) planning. This “take what you can get” strategy is often 
reactive in responding to immediate needs or “panic attacks. ” Passive strategies are 
characterized by steady, often routine rollovers of borrowings for the same amount 
of funds each time, without much comparison shopping. Passive strategies may also 
arise when borrowing is restricted, such as instances where borrowers are limited to 
one or two lenders by agreement (e.g., in a secured loan arrangement).

Reading 37 ■ Working Capital Management 192
Active strategies are usually more flexible, reflecting planning, reliable forecasting, 
and seeking the best deal. With active strategies, borrowers are more in control and 
do not fall into the rollover “trap” that is possible with passive strategies.
Many active strategies are matching strategies. Matching borrowing strategies 
function in a manner similar to matching investment strategies—loans are scheduled 
to mature when large cash receipts are expected. These receipts can pay back the loan, 
so the company does not have to invest the funds at potentially lower rates than the 
borrowing cost, thereby creating unnecessary costs.
8.3 Asset-  Based Loans
Many companies that do not have the credit quality sufficient to qualify for unsecured 
bank loans may borrow from financial institutions by arranging for a secured loan, 
where the loan is secured using assets of the company. These secured loans are often

referred to as asset-  based loans . Often the assets used in short-  term secured loans 
are the current assets of receivables and inventory. Unlike the collateral that may be 
used in longer-  term borrowing, asset-  based loans secured by accounts receivable and 
inventory present a challenge for the lender because the cash flows from accounts 
receivable depend on the amount and timing of collections and are influenced by the 
business risk of the company and its customers.
Lenders of these short-  term asset-  based loans are protected by the existence of 
the collateral and by provisions in the law that may provide them with a blanket lien 
on current and future assets of the company. The downside of a blanket lien is that 
even if the asset-  based loan was secured by, say, accounts receivable, the lender may 
have a legal interest in other assets of the company until the loan is repaid.
Besides using working capital as the security for a loan, a company can use other

means to generate cash flow from these working capital accounts. For example, a com -
pany can use its accounts receivable to generate cash flow through the assignment 
of accounts receivable , which is the use of these receivables as collateral for a loan, 
or a company can factor  its accounts receivable, which is selling the receivables to 
the factor. In an assignment arrangement, the company remains responsible for the 
collection of the accounts, whereas in a factoring arrangement the company is shifting 
the credit granting and collection process to the factor. The cost of this credit depends 
on the credit quality of the accounts and the costs of collection.
Like accounts receivables, inventory may be a source of cash flow through the use 
of the inventory as collateral, with different types of arrangements possible:
■■An inventory blanket lien , in which the lender has a claim on some or all of 
the company’s inventory, but the company can sell the inventory in the ordinary

course of business.
■■A trust receipt arrangement , in which the lender requires the company to 
certify that the goods are segregated and held in trust, with proceeds of any sale 
remitted to the lender immediately.
■■A warehouse receipt arrangement  is similar to the trust receipt arrange -
ment, but there is a third party (i.e., a warehouse company) that supervises the 
The cost of asset-  based loans security by inventory depends on the length of time it 
takes to sell the goods.

Managing Short-  Term Financing 193
8.4 Computing the Costs of Borrowing
In carrying out a sound short-  term borrowing strategy, one of the key decisions is 
selecting the most cost-  effective form of short-  term loan. However, this selection is 
often not a simple task, because each of the major forms has to be adjusted to be on 
a common basis for comparability. The fundamental rule is to compute the total cost 
of the form of borrowing and divide that number by the total amount of loan you 
received (i.e., net proceeds), adjusted for any discounting or compensating balances.
For example, in the case of a line of credit that requires a commitment fee,9 the 
cost of the line of credit is
CostInterest Commitment fe e
Loan amount=+
On the other hand, if the interest rate is stated as “all inclusive” such that the amount 
borrowed includes the interest, as may be the case in a banker’s acceptance, the interest 
is compared with the net proceeds when determining the cost:
CostInterest

Net proceed sInterest
Loan amount Interest==−
If there are dealer’s fees and other fees, the expenses beyond the interest must be 
considered when determining the cost. For example, if a borrowing involves a dealer’s 
fee and a backup fee and is quoted as all inclusive, the cost is
CostInterest Dealer s commi ssion Backup costs
Loan amount=++
−'
IInterest
The key is to compare the interest and fees paid with the net proceeds of the loan. If 
the loan is for a period less than a year, then we annualize accordingly.
EXAMPLE 7   
Computing the Effective Cost of Short-  Term Borrowing 
Alternatives
You are asked to select one of the following choices as the best offer for bor -
rowing $5,000,000 for one month:
1 Drawing down on a line of credit at 6.5 percent with a 1/2 percent com -
mitment fee on the full amount. Note:  One-  twelfth of the cost of the 
commitment fee (which gives an option to borrow any time during the 
year) is allocated to the first month.

2 A banker’s acceptance at 6.75 percent, an all-  inclusive rate.
3 Commercial paper at 6.15 percent with a dealer’s commission of 1/8 per -
cent and a backup line cost of 1/4 percent, both of which would be 
assessed on the $5 million of commercial paper issued.
9 A commitment fee is a fee paid to the lender in return for the legal commitment to lend funds in the future.

Reading 37 ■ Working Capital Management 194
Solution:
Line of credit cost:
Line costInterest Commitment fe e
Usable loan amount
0.0=+×
=12
6 65 $5,000,000 1 0.005 $5,000,000 1
5,000,000
$×× () +× × ()×
=12 1212$
2 27,083.33 2,083.33
$5,000,0000.07 or 7 percen t+×=12
Banker’s acceptance cost:
BA costInterest
Net proceed s
0.0675 $5,000,000 1
5,00=×
=××12
12
$ 0 0,000 0.0675 $5,000,000 1
$28,125
$4,971,8750.0−× × ()×
=× =1212
12 6 679 or 6.79 percen t
Commercial paper cost (quoted as nominal rate at a discount):
CP c ost
Interest Dealer s commi ssions Backup costs
Net proc=++ '
eeeds
0.0615 $5,000,000 1 0.00125 $5,000,000 1×
=×× () +× × () +12
12 12 0 0.0025 $5,000,000 1
5,000,000 0.0615 $5,000,000 1×× ()
−× × ()12
12 $× ×
=++
−×=12
12$25,625 520.83 1041.67
$5,000,000 25,6250.0656 or 6 6.56 percen t
We have simplified this cost analysis by assuming a loan for one month, 
using a factor of 1/12 to determine the interest and a factor of 12 to annualize.

For specific arrangements for which the cost is determined using a 365-  day or 
360-  day year, the appropriate adjustment would be required.
As the results show, the commercial paper alternative comes out with the 
lowest effective cost, and the line of credit has the highest effective cost. The 
commitment fee that was payable on the full line added more additional costs 
than the additional fees and discounting effects added in the other two options.
Line cost 7.00 percent
Banker’s acceptance cost 6.79 percent
Commercial paper cost 6.56 percent
SUMMARY
In this reading, we considered a key aspect of financial management: the management 
of a company’s working capital. This aspect of finance is a critical one in that it ensures, 
if done effectively, that the company will stay solvent and remain in business. If done 
improperly, the results can be disastrous for the company.

Summary 195
Working capital management covers a wide range of activities, most of which are 
focused on or involve the company’s cash levels. Competing uses for the company’s 
cash, which is often a scarce resource, create the need for an efficient method of 
handling the short-  term financing of company activities.
Major points that were covered in this reading:
■■Understanding how to evaluate a company’s liquidity position.
■■Calculating and interpreting operating and cash conversion cycles.
■■Evaluating overall working capital effectiveness of a company and comparing it 
with other peer companies.
■■Identifying the components of a cash forecast to be able to prepare a short-  term 
(i.e., up to one year) cash forecast.
■■Understanding the common types of short-  term investments, and computing 
comparable yields on securities.
■■Measuring the performance of a company’s accounts receivable function.
■■Measuring the financial performance of a company’s inventory management 
function.

function.
■■Measuring the performance of a company’s accounts payable function.
■■Evaluating the short-  term financing choices available to a company and recom -
mending a financing method.
Working capital management is an integral part of the financial management of 
a company because many short-  term activities have effects on long-  term financial 
decisions. Having an effective short-  term financial strategy, for example, allows a 
company to plan ahead with the confidence that its short-  term concerns are being 
handled properly. Perhaps unlike other areas of finance, short-  term finance has more 
qualitative features, making each company’s case somewhat different from another’s. 
This unique nature, combined with the short time frame associated with this aspect 
of finance, makes short-  term finance a dynamic, challenging activity.

Reading 37 ■ Working Capital Management 196
1 Suppose a company has a current ratio of 2.5 times and a quick ratio of 1.5 
times. If the company’s current liabilities are €100 million, the amount of inven -
tory is closest  to:
A €50 million.
B €100 million.
C €150 million.
2 Given the following financial statement data, calculate the operating cycle for 
this company.
In Millions ($)
Credit sales 25,000
Cost of goods sold 20,000
Accounts receivable 2,500
Inventory—Beginning balance 2,000
Inventory—Ending balance 2,300
Accounts payable 1,700
 The operating cycle for this company is closest  to:
A 42.0 days.
B 47.9 days.
C 78.5 days.
3 Given the following financial statement data, calculate the net operating cycle 
for this company.
Credit sales 40,000
Cost of goods sold 30,000
Accounts receivable 3,000
Inventory—Beginning balance 1,500
Inventory—Ending balance 2,000
Accounts payable 4,000
 The net operating cycle of this company is closest  to:
A 3.8 days.
B 24.3 days.
C 51.7 days.

A 3.8 days.
4 The bond equivalent yield for a 182-  day US Treasury bill that has a price of 
$9,725 per $10,000 face value is closest  to:
A 5.44%.
B 5.53%.
C 5.67%.
5 A company increasing its credit terms for customers from 1/10, net 30 to 1/10, 
net 60 will most likely  experience:

Practice Problems 197
A an increase in cash on hand.
B a higher level of uncollectible accounts.
C an increase in the average collection period.
6 Suppose a company uses trade credit with the terms of 2/10, net 50. If the com -
pany pays its account on the 50th day, the effective borrowing cost of skipping 
the discount on day 10 is closest  to:
A 14.9%.
B 15.0%.
C 20.2%.
7 William Jones is evaluating three possible means of borrowing $1 million for 
one month:
■●Drawing down on a line of credit at 7.2 percent with a 1/2 percent commit -
ment fee on the full amount with no compensating balances.
■●A banker’s acceptance at 7.1 percent, an all-  inclusive rate.
■●Commercial paper at 6.9 percent with a dealer’s commission of 1/4 percent 
and a backup line cost of 1/3 percent, both of which would be assessed on 
the $1 million of commercial paper issued.
 Which of these forms of borrowing results in the lowest cost of credit?
A Line of credit.
B Banker’s acceptance.
C Commercial paper.

8–12
Mary Gonzales is evaluating companies in the office supply industry and has compiled 
the following information:
20X1 20X2
CompanyCredit 
Sales ($)Average 
Receivables 
Balance ($)Credit 
Balance ($)
A 5.0 million 1.0 million 6.0 million 1.2 million
B 3.0 million 1.2 million 4.0 million 1.5 million
C 2.5 million 0.8 million 3.0 million 1.0 million
D 0.5 million 0.1 million 0.6 million 0.2 million
Industry 25.0 million 5.0 million 28.0 million 5.4 million
8 Which of the companies had the highest number of days of receivables for the 
year 20X1? 
9 Which of the companies has the lowest accounts receivable turnover in the year 
20X2?

Reading 37 ■ Working Capital Management 198
C Company D.
10 The industry average receivables collection period:
A increased from 20X1 to 20X2.
B decreased from 20X1 to 20X2.
C did not change from 20X1 to 20X2.
11 Which of the companies reduced the average time it took to collect on accounts 
receivable from 20X1 to 20X2?
A Company B.
B Company C.
12 Mary determined that Company A had an operating cycle of 100 days in 20X2, 
whereas Company D had an operating cycle of 145 days for the same fiscal year. 
This means that:
A Company D’s inventory turnover is less than that of Company A.
B Company D’s inventory turnover is greater than that of Company A.
C Company D’s cash conversion cycle is shorter than that of Company A.

Solutions 199
SOLUTIONS
1 B is correct.
Current ratio = Current assets/Current Liabilities = Current assets/ 
€100 million = 2.5
 Therefore, current assets = €250 million
Quick ratio = (Current assets − Inventory)/ Current Liabilities = (€250 mil -
lion − Inventory)/€100 million = 1.5
 Therefore, Inventory = €100 million
Number of days of inventory = $2,300/($20,000/365) = 41.975 days
Number of days of receivables = $2,500/($25,000/365) = 36.5 days
Operating cycle = 41.975 + 36.5 days = 78.475 days
Note: The net operating cycle is 47.9 days.
Purchases = $20,000 + $2,300 − $2,000 = $20,300
Number of days of payables = $1,700/($20,300/365) = 30.567 days
The net operating cycle is 78.475 − 30.567 = 47.908 days
3 A is correct.
Number of days of inventory = $2,000/($30,000/365) = 24.333 days
Number of days of receivables = $3,000/($40,000/365) = 27.375 days
Operating cycle = 24.333 + 27.375 days = 51.708 days
Purchases = $30,000 + $2,000 − $1,500 = $30,500

Number of days of payables = $4,000/($30,500/365) = 47.869 days
The net operating cycle is 51.708 − 47.869 = 3.839 days
4 C is correct.
Bond equivalent yield = [($10,000 − 9,725)/$9,725 ] × (365/182) = 
5.671 percent
5 C is correct. A higher level of uncollectible accounts may occur, but a longer 
average collection period will certainly occur. 
6 C is correct.
Cost  percen t =+

 −= 1002
09812 024365 40.
..

Reading 37 ■ Working Capital Management 200
7 B is correct. 
Net Proceed=+×
=×12
0 072 10 ., $0 00 000 1120 005 1 000 000 112
1 000 00012,. ,,
,,×+ ×××
=+() () $
$
$6,000 4 1 16.67
$1 000 00012 0 077
,,. ×=  or 7.7 percen t
Bankers acceptance costInterest
Net Proceed' =×
=×12
0 071 10 ., $ 0 00 000 112
1 000 000 0 071 1 000 000 11212,
,, ., ,×
−× ××
=()
() $$
$5,916.6 7 7
$994,083.33×=12 0 0714 .  or 7.14 percen t
Commerc ial
paper costInterest Dealer s commi ssion B ackup c=++ ' oosts
Net proceed×
=×× +× ()12
0 069 1 000 000 1120 0025 1 000 0 ., ,. ,, $$ 0 00 1120 003333 1 000 000 112
1 000 000 0 069 1 000×+ ××
−×() ()., ,
,, .,$
$$ ,,
,.000 11212
5 75012 00××
=++
−×=()
$5,750 208.33 277.78
$1,000,0007753 or 7.53 percen t
8 B is correct.
Company A: $1.0 million/($5.0 million/365) = 73.0 days
Company B: $1.2 million/($3.0 million/365) = 146.0 days
Company C: $0.8 million/($2.5 million/365) = 116.8 days
Company D: $0.1 million/($0.5 million/365) = 73.0 days
9 B is correct.

Company A: $6.0 million/$1.2 million = 5.00
Company B: $4.0 million/$1.5 million = 2.67
Company C: $3.0 million/$1.0 million = 3.00
Company D: $0.6 million/$0.2 million = 3.00
10 B is correct.
20X1: 73 days
20X2:  70.393
 Note : If the number of days decreased from 20X1 to 20X2, the receivable turn -
over increased.
11 A is correct.
 Company B increased its accounts receivable (A/R) turnover and reduced its 
number of days of receivables between 20X1 and 20X2.

Solutions 201
20X1 20X2
Company A/R 
TurnoverNumber of Days 
of ReceivablesA/R 
of Receivables
A 5.000 73.000 5.000 73.000
B 2.500 146.000 2.667 136.875
C 3.125 116.800 3.000 121.667
D 5.000 73.000 3.000 121.667
Company A number of days of inventory = 100 − 73 = 27 days
Company D number of days of inventory = 145 − 121.67 = 23.33 days
Company A’s turnover = 365/27 = 13.5 times
Company D’s inventory turnover = 365/23.3 = 15.6 times

Portfolio Management 
Study Session 12 Portfolio Management (1)
Study Session 13 Portfolio Management (2)
The candidate should be able to explain and demonstrate the use of fundamentals of 
portfolio and risk management, including return and risk measurement, and portfolio 
planning and construction.

Portfolio Management (1)
This study session introduces the concept of a portfolio approach to investments. 
The needs of individual and institutional investors are each examined, along with 
the range of available investment solutions. The three main steps in the portfolio 
management process (planning, execution, and feedback) are outlined. Common 
measures of portfolio risk and return and the introduction of modern portfolio the -
ory—a quantitative framework for asset pricing and portfolio selection—then follow.
Reading 38 Portfolio Management: An Overview  
by Robert M. Conroy, DBA, CFA, and Alistair Byrne, 
PhD, CFA
Reading 39 Portfolio Risk and Return: Part I  
by Vijay Singal, PhD, CFA
Reading 40 Portfolio Risk and Return: Part II  
by Vijay Singal, PhD, CFAPOrTFOLIO  MANAGEMENT  
12

Portfolio Management: An Overview
by Robert M. Conroy, DBA, CFA, and Alistair Byrne, PhD, CFA
Robert M. Conroy, DBA, CFA, is at the Darden School of Business, University of Virginia 
(USA). Alistair Byrne, PhD, CFA, is at State Street Global Advisors (United Kingdom).
a. describe the portfolio approach to investing;
b. describe types of investors and distinctive characteristics and 
needs of each;
c. describe defined contribution and defined benefit pension plans;
d. describe the steps in the portfolio management process;
e. describe mutual funds and compare them with other pooled 
investment products.
In this reading we explain why the portfolio approach is important to all types of 
investors in achieving their financial goals. We compare the financial needs of different 
types of individual and institutional investors. After we outline the steps in the portfolio

management process, we compare and contrast the types of investment management 
products that are available to investors and how they apply to the portfolio approach.
A PORTFOLIO PERSPECTIVE ON INVESTING
One of the biggest challenges faced by individuals and institutions is to decide how to 
invest for future needs. For individuals, the goal might be to fund retirement needs. 
For such institutions as insurance companies, the goal is to fund future liabilities in 
the form of insurance claims, whereas endowments seek to provide income to meet 
the ongoing needs of such institutions as universities. Regardless of the ultimate 
goal, all face the same set of challenges that extend beyond just the choice of what 
asset classes to invest in. They ultimately center on formulating basic principles that 1
2rEADING
38

Reading 38 ■ Portfolio Management: An Overview 208
determine how to think about investing. One important question is: Should we invest 
in individual securities, evaluating each in isolation, or should we take a portfolio 
approach? By “portfolio approach, ” we mean evaluating individual securities in rela -
tion to their contribution to the investment characteristics of the whole portfolio. In 
the following section, we illustrate a number of reasons why a diversified portfolio 
perspective is important.
2.1 Portfolio Diversification: Avoiding Disaster
Portfolio diversification helps investors avoid disastrous investment outcomes. This 
benefit is most convincingly illustrated by examining what may happen when indi -
viduals have not diversified.
We are usually not able to observe how individuals manage their personal invest -
ments. However, in the case of US 401(k) individual retirement portfolios,1 it is pos -

sible to see the results of individuals’ investment decisions. When we examine their 
retirement portfolios, we find that some individual participants make sub-  optimal 
investment decisions.
During the 1990s, Enron Corporation was one of the most admired corporations 
in the United States. A position in Enron shares returned over 27 percent per year 
from 1990 to September 2000, compared to 13 percent for the S&P 500 Index for the 
same time period.
Exhibit 1   Value of US$1 Invested from January 1990 to September 2000 
Enron vs. S&P 500 Composite Index (01/01/1990 = US$1.00) 
$18.00
$16.00
$14.00
$12.00
$10.00
$8.00
$6.00
$4.00
$2.00
$0.00Enron
S&P 500Jan-90
Oct-90
Jul-91
Apr-92
Jan-93
Oct-93
Jul-94
Apr-95
Jan-96
Oct-96
Jul-97
Apr-98
Jan-99
Oct-99
Jul-00
Source:  Thomson Reuters Datastream.
During this time period, thousands of Enron employees participated in the com -
pany’s 401(k) retirement plan. The plan allowed employees to set aside some of their

earnings in a tax-  deferred account. Enron participated by matching the employees’ 
1 In the United States, 401(k) plans are employer-  sponsored individual retirement savings plans. They allow 
individuals to save a portion of their current income and defer taxation until the time when the savings and 
earnings are withdrawn. In some cases, the sponsoring firm will also make matching contributions in the 
form of cash or shares. Individuals within certain limits have control of the invested funds and consequently 
can express their preferences as to which assets to invest in.

A Portfolio Perspective on Investing 209
contributions. Enron made the match by depositing required amounts in the form of 
Enron shares. Enron restricted the sale of its contributed shares until an employee 
turned 50 years old. In January 2001, the employees’ 401(k) retirement accounts were 
valued at over US$2 billion, of which US$1.3 billion (or 62 percent) was in Enron shares. 
Although Enron restricted the sale of shares it contributed, less than US$150 million 
of the total of US$1.3 billion in shares had this restriction. The implication was that 
Enron employees continued to hold large amounts of Enron shares even though they 
were free to sell them and invest the proceeds in other assets.
A typical individual was Roger Bruce,2 a 67-  year-  old Enron retiree who held all of 
his US$2 million in retirement funds in Enron shares. Unlike most stories, this one 
does not have a happy ending. Between January 2001 and January 2002, Enron’s share 
price fell from about US$90 per share to zero.

Exhibit 2   Value of US$1 Invested from January 1990 to January 2002 Enron vs. S&P 500 Composite Index 
(1/1/1990 = US$1.00)
18
16
14
12
10
8
6
4
2
0Enron
S&P 50001/01/1990
01/09/1990
01/05/1991
01/01/1992
01/09/1992
01/05/1993
01/01/1994
01/09/1994
01/05/1995
01/01/1996
01/09/1996
01/05/1997
01/01/1998
01/09/1998
01/05/1999
01/01/2000
01/09/2000
01/05/2001
01/01/2002
Employees and retirees who had invested all or most of their retirement savings 
in Enron shares, just like Mr. Bruce, experienced financial ruin. The hard lesson that 
the Enron employees learned from this experience was to “not put all your eggs in one 
basket. ”3 Unfortunately, the typical Enron employee did have most of his or her eggs 
in one basket. Most employees’ wages and financial assets were dependent on Enron’s 
continued viability; hence, any financial distress on Enron would have a material impact

on an employee’s financial health. The bankruptcy of Enron resulted in the closing 
of its operations, the dismissal of thousands of employees, and its shares becoming 
worthless. Hence, the failure of Enron was disastrous to the typical Enron employee.
Enron employees were not the only ones to be victims of over-  investment in a single 
company’s shares. Another form of pension arrangement in many corporations is the 
defined contribution plan, in which the employer makes periodic cash contributions 
to a retirement fund managed by the employees themselves instead of guaranteeing a 
certain pension at retirement. In the defined contribution retirement plans at Owens 
Corning, Northern Telecom, Corning, and ADC Telecommunications, employees 
2 Singletary (2001).
3 This expression, which most likely originated in England in the 1700s, has a timeless sense of wisdom.

Reading 38 ■ Portfolio Management: An Overview 210
all held more than 25 percent of their assets in the company’s shares during a time 
(March 2000 to December 2001) in which the share prices in these companies fell by 
almost 90 percent. The good news in this story is that the employees participating in 
employer-  matched 401(k) plans since 2001 have significantly reduced their holdings 
of their employers’ shares.
Thus, by taking a diversified portfolio approach, investors can spread away some 
of the risk. All rational investors are concerned about the risk–return trade-  off of 
their investments. The portfolio approach provides investors with a way to reduce 
the risk associated with their wealth without necessarily decreasing their expected 
rate of return.
2.2 Portfolios: Reduce Risk
In addition to avoiding a potential disaster associated with over investing in a single 
security, portfolios also generally offer equivalent expected returns with lower over -

all volatility  of returns—as represented by a measure such as standard deviation. 
Consider this simple example: Suppose you wish to make an investment in companies 
listed on the Hong Kong Stock Exchange (HKSE) and you start with a sample of five 
companies.4 The cumulative returns for the five companies from Q2 2004 through 
Q2 2008 are shown in Exhibit 3.
Exhibit 3   Cumulative Wealth Index of Sample of Shares Listed on HKSE (Q2 
2004 = US$1.00) 
$4.00
$3.50
$3.00
$2.50
$2.00
$1.50
$1.00
$0.50
$0.00Cumulative Wealth Index
Q2
2004Q4
2004Q2
2005Q4
2005Q2
2006Q4
2006Q2
2007Q4
2007Q2
2008
Cathay Pacific Airways
Hutchison WhampoaYue Yuen Industrial
Li & Fung
COSCO Pacific
The individual quarterly returns for each of the five shares are shown in Exhibit 4. 
The annualized means and annualized standard deviations for each are also shown.5
4 A sample of five companies from a similar industry group was arbitrarily selected for illustration purposes.

5 Mean quarterly returns are annualized by multiplying the quarterly mean by 4. Quarterly standard 
deviations are annualized by taking the quarterly standard deviation and multiplying it by 2.

A Portfolio Perspective on Investing 211
Exhibit 4   Quarterly Returns (in Percent) for Sample of HKSE Listed Shares End of Q2 2004–End of Q2 2008
Yue Yuen 
IndustrialCathay 
Pacific 
AirwaysHutchison 
Whampoa Li & FungCOSCO 
PacificEqually 
Weighted 
Portfolio
Q3 2004 –11.1% –2.3% 0.6% –13.2% –1.1% –5.4%
Q4 2004 –0.5 –5.4 10.8 1.7 21.0 5.5
Q1 2005 5.7 6.8 19.1 13.8 15.5 12.2
Q2 2005 5.3 4.6 –2.1 16.9 12.4 7.4
Q3 2005 17.2 2.4 12.6 14.5 –7.9 7.8
Q4 2005 –17.6 –10.4 –0.9 4.4 –16.7 –8.2
Q1 2006 12.6 7.4 4.2 –10.9 15.4 5.7
Q2 2006 7.5 –0.4 –3.6 29.2 21.9 10.9
Q3 2006 –7.9 1.3 –5.1 –2.0 –1.6 –3.1
Q4 2006 8.2 27.5 0.1 26.0 –10.1 10.3
Q1 2007 18.3 24.3 16.5 22.8 25.7 21.5
Q2 2007 0.1 –2.6 –6.7 –0.4 0.3 –1.8
Q3 2007 –6.2 –4.2 16.7 11.9 11.1 5.8
Q4 2007 –8.0 17.9 –1.8 12.4 8.4 5.8
Q1 2008 3.5 –20.1 –8.5 –20.3 –31.5 –15.4
Q2 2008 2.1 –11.8 –2.6 24.2 –6.1 1.2
Mean annual return 7.3% 8.7% 12.3% 32.8% 14.2% 15.1%
Annual standard 
deviation20.2% 25.4% 18.1% 29.5% 31.3% 17.9%
Diversification ratio 71.0%

Suppose you want to invest in one of these five securities next year. There is a 
wide variety of risk–return trade-  offs for the five shares selected. If you believe that 
the future will replicate the past, then choosing Li & Fung would be a good choice. 
For the prior four years, Li & Fung provided the best trade-  off between return and 
risk. In other words, it provided the most return per unit of risk. However, if there 
is no reason to believe that the future will replicate the past, it is more likely that the 
risk and return on the one security selected will be more like selecting one randomly. 
When we randomly selected one security each quarter, we found an average annualized 
return of 15.1 percent and an average annualized standard deviation of 24.9 percent, 
which would now become your expected return and standard deviation, respectively.

Alternatively, you could invest in an equally weighted portfolio of the five shares, 
which means that you would invest the same dollar amount in each security for each 
quarter. The quarterly returns on the equally weighted portfolio are just the average 
of the returns of the individual shares. As reported in Exhibit 4, the equally weighted 
portfolio has an average return of 15.1 percent and a standard deviation of 17.9 percent. 
As expected, the equally weighted portfolio’s return is the same as the return on the 
randomly selected security. However, the same does not hold true for the portfolio 
standard deviation. That is, the standard deviation of an equally weighted portfolio is 
not simply the average of the standard deviations of the individual shares. In a more 
advanced reading we will demonstrate in greater mathematical detail how such a 
portfolio offers a lower standard deviation of return than the average of its individual

components due to the correlations or interactions between the individual securities.

Reading 38 ■ Portfolio Management: An Overview 212
Because the mean return is the same, a simple measure of the value of diversification 
is calculated as the ratio of the standard deviation of the equally weighted portfolio to 
the standard deviation of the randomly selected security. This ratio may be referred 
to as the diversification ratio . In this case, the equally weighted portfolio’s standard 
deviation is approximately 71 percent of that of a security selected at random. The 
diversification ratio of the portfolio’s standard deviation to the individual asset’s stan -
dard deviation measures the risk reduction benefits of a simple portfolio construction 
method, equal weighting. Even though the companies were chosen from a similar 
industry grouping, we see significant risk reduction. An even greater portfolio effect 
(i.e., lower diversification ratio) could have been realized if we had chosen companies 
from completely different industries.

This example illustrates one of the critical ideas about portfolios: Portfolios affect 
risk more than returns. In the prior section portfolios helped avoid the effects of 
downside risk associated with investing in a single company’s shares. In this section we 
extended the notion of risk reduction through portfolios to illustrate why individuals 
and institutions should hold portfolios.
2.3 Portfolios: Composition Matters for the Risk–Return 
Trade-  off
In the previous section we compared an equally weighted portfolio to the selection of 
a single security. In this section we examine additional combinations of the same set of 
shares and observe the trade-  offs between portfolio volatility of returns and expected 
return (for short, their risk–return trade-  offs). If we select the portfolios with the best 
combination of risk and return (taking historical statistics as our expectations for the 
future), we produce the set of portfolios shown in Exhibit 5.

Exhibit 5   Optimal Portfolios for Sample of HKSE Listed Shares
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0.12
Standard DeviationExpected Return
0.17Cathay Pacific AirwaysCOSCO PacificEqually weighted portfolio
Hutchison Whampoa
Yue Yuen IndustrialLi & Fung
0.22 0.27 0.32 0.37
In addition to illustrating that the diversified portfolio approach reduces risk, 
Exhibit 5 also shows that the composition of the portfolio matters. For example, an 
equally weighted portfolio (20 percent of the portfolio in each security) of the five 
shares has an expected return of 15.1 percent and a standard deviation of 17.9 per -
cent. Alternatively, a portfolio with 25  percent in Yue Yuen Industrial (Holdings), 
3 percent in Cathay Pacific, 52 percent in Hutchison Whampoa, 20 percent in Li & 
Fung, and 0 percent in COSCO Pacific produces a portfolio with an expected return

A Portfolio Perspective on Investing 213
of 15.1 percent and a standard deviation of 15.6 percent. Compared to a simple equally 
weighted portfolio, this provides an improved trade-  off between risk and return because 
a lower level of risk was achieved for the same level of return.
2.4 Portfolios: Not Necessarily Downside Protection
A major reason that portfolios can effectively reduce risk is that combining securities 
whose returns do not move together provides diversification. Sometimes a subset of 
assets will go up in value at the same time that another will go down in value. The 
fact that these may offset each other creates the potential diversification benefit we 
attribute to portfolios. However, an important issue is that the co-  movement or 
correlation pattern of the securities’ returns in the portfolio can change in a manner 
unfavorable to the investor. We use historical return data from a set of global indexes 
to show the impact of changing co-  movement patterns.

When we examine the returns of a set of global equity indexes over the last 15 years, 
we observe a reduction in the diversification benefit due to a change in the pattern of 
co- movements of returns. Exhibits 6 and 7 show the cumulative returns for a set of 
five global indexes6 for two different time periods. Comparing the first time period, 
from Q4 1993 through Q3 2000 (as shown in Exhibit 6), with the last time period, 
from Q1 2006 through Q1 2009 (as shown in Exhibit 7), we show that the degree to 
which these global equity indexes move together has increased over time.
Exhibit 6   Returns to Global Equity Indexes Q4 1993–Q3 2000
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0Cumulative Return (Q4 1993 = US$1.00)
Q4 1993 Q4 1995 Q4 1997 Q4 1999
S&P 500 MSCI EAFE US$ Hang Seng Nikkei 500 MSCI AC EAFE + EM US$
6 The S&P 500, Hang Seng, and Nikkei 500 are broad-  based composite equity indexes designed to mea -

sure the performance of equities in the United States, Hong Kong, and Japan. MSCI stands for Morgan 
Stanley Capital International. EAFE refers to developed markets in Europe, Australasia, and the Far East. 
AC indicates all countries, and EM is emerging markets. All index returns are in US dollars.

Reading 38 ■ Portfolio Management: An Overview 214
Exhibit 7   Returns to Global Equity Indexes Q1 2006–Q1 2009
2.5
2.0
1.5
1.0
0.5
0Cumulative Returns (Q1 2006 = US$1.00)
Q1 2006 Q3 2007 Q1 2009
The latter part of the second time period, from Q4 2007 to Q1 2009, was a period 
of dramatic declines in global share prices. Exhibit 8 shows the mean annual returns 
and standard deviation of returns for this time period.
Exhibit 8   Returns to Global Equity Indexes
Q4 1993–Q3 2000 Q1 2006–Q1 2009 Q4 2007–Q1 2009
Global Index MeanStand. 
Dev. MeanStand. 
Dev.
S&P 500 20.5% 13.9% –6.3% 21.1% –40.6% 23.6%
MSCI EAFE US$ 10.9 14.2 –3.5 29.4 –48.0 35.9
Hang Seng 20.4 35.0 5.1 34.2 –53.8 34.0
Nikkei 500 3.3 18.0 –13.8 27.6 –48.0 30.0
MSCI AC EAFE + EM US$ 7.6 13.2 –4.9 30.9 –52.0 37.5
Randomly selected index 12.6% 18.9% –4.7% 28.6% –48.5% 32.2%

Equally weighted portfolio 12.6% 14.2% –4.7% 27.4% –48.5% 32.0%
Diversification ratio 75.1% 95.8% 99.4%
During the period Q4 2007 through Q1 2009, the average return for the equally 
weighted portfolio, including dividends, was −48.5 percent. Other than reducing the 
risk of earning the return of the worst performing market, the diversification bene -
fits were small. Exhibit 9 shows the cumulative quarterly returns of each of the five 
indexes over this time period. All of the indexes declined in unison. The lesson is that 
although portfolio diversification generally does reduce risk, it does not necessarily 
provide the same level of risk reduction during times of severe market turmoil as it 
does when the economy and markets are operating ‘normally’ . In fact, if the economy

A Portfolio Perspective on Investing 215
or markets fail totally (which has happened numerous times around the world), then 
diversification is a false promise. In the face of a worldwide contagion, diversification 
was ineffective, as illustrated at the end of 2008.
Exhibit 9   Return to Global Equity Indexes Q4 2007–Q1 2009
1.01.2
0.8
0.6
0.4
0.2
0Cumulative Returns (Q4 2007 = US$1.00)
Q4 2007 Q1 2008 Q2 2008 Q3 2008 Q4 2008 Q1 2009
 
Portfolios are most likely  to provide: 
A risk reduction.
B risk elimination.
C downside protection.
Solution: 
A is correct. Combining assets into a portfolio should reduce the portfolio’s volatility. 
However, the portfolio approach does not necessarily provide downside protection or 
eliminate all risk. 
2.5 Portfolios: The Emergence of Modern Portfolio Theory
The concept of diversification has been around for a long time and has a great deal

of intuitive appeal. However, the actual theory underlying this basic concept and 
its application to investments only emerged in 1952 with the publication of Harry 
Markowitz’s classic article on portfolio selection.7 The article provided the foundation 
for what is now known as modern portfolio theory  (MPT). The main conclusion of 
MPT is that investors should not only hold portfolios but should also focus on how 
individual securities in the portfolios are related to one another. In addition to the 
7 Markowitz (1952).

Reading 38 ■ Portfolio Management: An Overview 216
diversification benefits of portfolios to investors, the work of William Sharpe (1964), 
John Lintner (1965), and Jack Treynor (1961) demonstrated the role that portfolios 
play in determining the appropriate individual asset risk premium (i.e., the return in 
excess of the risk-  free return expected by investors as compensation for the asset’s 
risk). According to capital market theory, the priced risk of an individual security is 
affected by holding it in a well-  diversified portfolio. The early research provided the 
insight that an asset’s risk should be measured in relation to the remaining systematic 
or non-  diversifiable risk, which should be the only risk that affects the asset’s price. 
This view of risk is the basis of the capital asset pricing model, or CAPM, which is 
discussed in greater detail in other readings. Although MPT has limitations, the

concepts and intuitions illustrated in the theory continue to be the foundation of 
knowledge for portfolio managers.
INVESTMENT CLIENTS
Portfolio managers are employed or contracted by a wide variety of investment clients. 
We can group the clients into categories based on their distinctive characteristics 
and needs. Our initial distinction is between management of the private wealth of 
individual investors and investment management for institutional investors.
3.1 Individual Investors
Individual investors have a variety of motives for investing and constructing port -
folios. Short-  term goals can include providing for children’s education, saving for a 
major purchase (such as a vehicle or a house), or starting a business. The retirement 
goal—investing to provide for an income in retirement—is a major part of the invest -
ment planning of most individuals. Many employees of public and private companies 
invest for retirement through defined contribution pension plans  (DC plans). A DC

plan is a pension plan in which contributions rather than benefits are specified, such 
as 401(k) plans in the United States, group personal pension schemes in the United 
Kingdom, and superannuation plans in Australia. Individuals will invest part of their 
wages while working, expecting to draw on the accumulated funds to provide income 
during retirement or to transfer some of their wealth to their heirs. The key to a DC 
plan is that the employee accepts the investment risk and is responsible for ensuring 
that there are enough funds in the plan to meet their needs upon retirement.
Some individuals will be investing for growth and will therefore seek assets that 
have the potential for capital gains. Others, such as retirees, may need to draw an 
income from their assets and may therefore choose to invest in fixed-  income and 
dividend-  paying shares. The investment needs of individuals will depend in part on

their broader financial circumstances, such as their employment prospects and whether 
or not they own their own residence. They may also need to consider such issues as 
building up a cash reserve and the purchase of appropriate insurance policies before 
undertaking longer-  term investments.
3.2 Institutional Investors
There are many different types of institutional investors. Examples include defined ben -
efit pensions plans, university endowments, charitable foundations, banks, insurance 
companies, investment companies, and sovereign wealth funds (SWFs). Institutional 
investors are major participants in the investment markets. Exhibit 10 shows the rela -
tive size and growth rates of the key categories across the Organisation for Economic 3

Investment Clients 217
Co- operation and Development (OECD) countries. Investment funds are the largest 
category, with insurance companies and pension funds not far behind. The relative 
importance of these categories does vary significantly across the individual OECD 
Exhibit 10   Institutional Assets (in US$ billions) 1995 to 2005
1995 2005 Average annual growth (second axis)Investment
FundsInsurance
CompaniesPension Funds Other Forms of
Institutional
SavingsUS$ (billions)
16,000
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0 0%2%4%6%8%10%12%14%16%
Source:  OECD, “Recent Trends in Institutional Investors Statistics” (2008): www.oecd.org/dataoecd/53/49/42143444.pdf.
3.2.1  Defined Benefit Pension Plans
In defined benefit pension plans  (DB plans), an employer has an obligation to pay 
a certain annual amount to its employees when they retire. In other words, the future 
benefit is defined because the DB plan requires the plan sponsor to specify the obliga -

tion stated in terms of the retirement income benefits owed to participants. DB plans 
need to invest the assets that will provide cash flows that match the timing of the future 
pension payments (i.e., liabilities). Plans are committed to paying pensions to members, 
and the assets of these plans are there to fund those payments. Plan managers need 
to ensure that sufficient assets will be available to pay pension benefits as they come 
due. The plan may have an indefinitely long time horizon if new plan members are 
being admitted or a finite time horizon if the plan has been closed to new members. 
Even a plan closed to new members may still have a time horizon of 70 or 80 years. For 
example, a plan member aged 25 may not retire for another 40 years and may live 30 
years in retirement. Hence, pension plans can be considered long-  term investors. In 
some cases, the plan managers attempt to match the fund’s assets to its liabilities by,

for example, investing in bonds that will produce cash flows corresponding to expected 
future pension payments. There may be many different investment philosophies for 
pension plans, depending on funded status and other variables.

Reading 38 ■ Portfolio Management: An Overview 218
3.2.2  Endowments and Foundations
University endowments are established to provide continuing financial support to 
a university and its students (e.g., scholarships). Endowments vary in size (assets 
under management), but many are major investors. It is common for US universities 
to have large endowments, but it is somewhat less common elsewhere in the world. 
Exhibit 11 shows the top ten US university endowments by assets as of the end of 
2008. In terms of non-  US examples, the University of Oxford, United Kingdom, and 
its various colleges were estimated to have a total endowment of £4.8 billion as of 
2004 and the University of Cambridge, United Kingdom, and its colleges, £5.3 billion. 
These were by far the largest endowments in the United Kingdom. The third largest, 
University of Edinburgh, was £156 million.8 The French business school INSEAD’s 
endowment was valued at €105 million as of 2008.

Exhibit 11   Top Ten US University Endowments by Asset Value
Rank Institution StateEndowment 
Funds 2008 
(US$000)
1 Harvard University MA $36,556,284
2 Yale University CT 22,869,700
3 Stanford University CA 17,200,000
4 Princeton University NJ 16,349,329
5 University of Texas System TX 16,111,184
6 Massachusetts Institute of Technology MA 10,068,800
7 University of Michigan MI 7,571,904
8 Northwestern University IL 7,243,948
9 Columbia University NY 7,146,806
10 Texas A&M University System and 
foundationsTX 6,659,352
Source:  NACUBO, “2008 NACUBO Endowment Study” (January 2009): www.nacubo.org/
Research/NACUBO_Endowment_Study.html.
Charitable foundations invest donations made to them for the purpose of funding 
grants that are consistent with the charitable foundation’s objectives. Similar to uni -
versity endowments, many charitable foundations are substantial investors. Exhibit 12

lists US grant-  making foundations ranked by the market value of their assets based 
on the most current audited financial data in the Foundation Center’s database as of 5 
February 2009. Again, large foundations are most common in the United States, but they 
also exist elsewhere. For example, the Wellcome Trust is a UK-  based medical charity 
that had approximately £13 billion of assets as of 2008.9 The Li Ka Shing Foundation 
is a Hong Kong-  based education and medical charity with grants, sponsorships, and 
commitments amounting to HK$10.7 billion.
8 Acharya and Dimson (2007).
9 See www.wellcome.ac.uk/Investments/History-  and-  objectives/index.htm.

Investment Clients 219
Exhibit 12   Top Ten US Foundation Endowments by Asset Value
Rank FoundationAssets 
(US$000)As of Fiscal Y ear-  
End Date
1 Bill & Melinda Gates Foundation $38,921,022 12/31/07
2 J. Paul Getty Trust 11,187,007 06/30/07
3 Ford Foundation 11,045,128 09/30/08
4 Robert Wood Johnson Foundation 10,722,296 12/31/07
5 William and Flora Hewlett 
Foundation9,284,917 12/31/07
6 W.K. Kellogg Foundation 8,402,996 08/31/07
7 Lilly Endowment 7,734,860 12/31/07
8 John D. and Catherine T. MacArthur 
Foundation7,052,165 12/31/07
9 David and Lucile Packard Foundation 6,594,540 12/31/07
10 Andrew W. Mellon Foundation 6,539,865 12/31/07
Source:  Foundation Center (2009): http://foundationcenter.org.
A typical investment objective of an endowment or a foundation is to maintain 
the real (inflation-  adjusted) capital value of the fund while generating income to fund 
the objectives of the institution. Most foundations and endowments are established

with the intent of having perpetual lives. Example 1 describes the US$22 billion Yale 
University endowment’s approach to balancing short-  term spending needs with 
ensuring that future generations also benefit from the endowment, and it also shows 
the £13  billion Wellcome Trust’s approach. The investment approach undertaken 
considers the objectives and constraints of the institution (for example, no tobacco 
investments for a medical endowment).
EXAMPLE 1   
Spending Rules
The following examples of spending rules are from the Yale University endowment 
(in the United States) and from the Wellcome Trust (in the United Kingdom).
Y ale University Endowment
The spending rule is at the heart of fiscal discipline for an endowed 
institution. Spending policies define an institution’s compromise 
between the conflicting goals of providing substantial support for 
current operations and preserving purchasing power of Endowment 
assets. The spending rule must be clearly defined and consistently

applied for the concept of budget balance to have meaning.
Yale’s policy is designed to meet two competing objectives. The 
first goal is to release substantial current income to the operating 
budget in a stable stream, since large fluctuations in revenues are 
difficult to accommodate through changes in University activities 
or programs. The second goal is to protect the value of Endowment 
assets against inflation, allowing programs to be supported at today’s 
level far into the future.

Reading 38 ■ Portfolio Management: An Overview 220
Yale’s spending rule attempts to achieve these two objectives 
by using a long-  term spending rate of 5.25 percent combined with 
a smoothing rule that adjusts spending gradually to changes in 
Endowment market value. The amount released under the spending 
rule is based on a weighted average of prior spending adjusted for 
inflation (80 percent weight) and an amount determined by applying 
the target rate to the current Endowment market value (20 percent 
weight) with an adjustment factor based on inflation and the expected 
growth of the Endowment net of spending.
(“2007 Yale Endowment Annual Report” (p.15): [www.yale.edu/investments/
Yale_Endowment_07.pdf]).
Wellcome Trust
Our overall investment objective is to generate 6 percent real return 
over the long term. This is to provide for real increases in annual 
expenditure while preserving at least the Trust’s capital base in real

terms in order to balance the needs of both current and future ben -
eficiaries. We use this absolute return strategy because it aligns asset 
allocation with funding requirements and it provides a competitive 
framework in which to judge individual investments.
(Wellcome Trust, “History and Objectives: Investment Goals” [www.wellcome.
ac.uk/Investments/History-  and-  objectives/index.htm])
3.2.3  Banks
Banks typically accept deposits and extend loans. In some cases, banks need to invest 
their excess reserves, (i.e., when deposits have not been used to make loans). The 
investments of excess reserves need to be conservative, emphasizing fixed-  income 
and money market instruments rather than equities and other riskier assets. In some 
countries, including the United States, there are legal restrictions on banks owning 
equity investments.10 In addition to low risk, the investments also need to be relatively

liquid so that they can be sold quickly if depositors wish to withdraw their funds. The 
bank’s objective is to earn a return on its reserves that exceeds the rate of interest it 
pays on its deposits.
3.2.4  Insurance Companies
Insurance companies receive premiums for the policies they write, and they need 
to invest these premiums in a manner that will allow them to pay claims. Similar 
to banks, such investments need to be relatively conservative given the necessity of 
paying claims when due. Life insurance companies and non-  life insurance companies 
(for example, auto and home insurance) differ in their purpose and objectives and 
hence in their investment time horizons. Life insurance companies have longer time 
horizons than non-  life insurance companies as a result of different expectations of 
when payments will be required under policies.
10 See, for example, www.minneapolisfed.org/publications_papers/pub_display.cfm?id=3518.

Investment Clients 221
3.2.5  Investment Companies
Investment companies that manage mutual funds are also institutional investors. The 
mutual fund is a collective financial institution in which investors pool their capital 
to have it invested by a professional manager. The investors own shares or units in 
the fund. For many investment managers, the mutual fund is, in effect, their client. 
However, mutual funds are slightly different in that they can also be considered a 
financial product. For many individual investors, the mutual fund is an efficient means 
to benefit from portfolio diversification and the skill of a professional manager. The 
mutual fund is likely to invest in a particular category of investments, such as US small 
capitalization equities. Mutual funds may also have certain limits and restrictions 
that apply to their investments, either as set by regulation and law or as decided by 
the board of directors of the investment company. We will revisit these investment

vehicles in greater detail when we discuss pooled investments in Section 5.
3.2.6  Sovereign Wealth Funds
Sovereign wealth funds (SWFs) are government-  owned investment funds, of which 
many are very sizable. Exhibit 13 provides a listing of the top 10 sovereign wealth 
funds as of March 2018.
Exhibit 13   Sovereign Wealth Funds by Asset Value
FundAssets as of 
March 2018  
(US$ bns) Inception Date Country
Government Pension Fund – Global $1,033 1990 Norway
China Investment Corporation 900 2007 Peoples’ Republic of China
Abu Dhabi Investment Corporation 828 1976 UAE – Abu Dhabi
Kuwait Investment Authority 524 1953 Kuwait
SAMA Foreign Holdings 494 1952 Saudi Arabia
Hong Kong Monetary Authority Investment 
Portfolio457 1993 Peoples’ Republic of China
SAFE Investment Company 441 1997 Peoples’ Republic of China
Government of Singapore Investment Authority 390 1981 Singapore
Qatar Investment Authority 320 2005 Qatar
National Social Security Fund 295 2000 Peoples’ Republic of China
Total of top 10 SWFs $5,682

Total of all SWFs $7,677
Source:  SWF Institute (www.swfinstitute.org).
Some funds have been established to invest revenues from finite natural resources 
(e.g., oil) for the benefit of future generations of citizens. Others manage foreign 
exchange reserves or other assets of the state. Some funds are quite transparent in 
nature—disclosing their investment returns and their investment holdings—whereas 
relatively little is known about the investment operations of others.
Exhibit 14 summarizes how investment needs vary across client groups. In some 
cases, generalizations are possible. In others, needs vary by client.

Reading 38 ■ Portfolio Management: An Overview 222
Exhibit 14   Summary of Investment Needs by Client Type
Client Time Horizon Risk Tolerance Income Needs Liquidity Needs
Individual investors Varies by individual Varies by individual Varies by individual Varies by individual
Defined benefit pen -
sion plansTypically long term Typically quite high High for mature 
funds; low for grow -
ing fundsTypically quite low
Endowments and 
foundationsVery long term Typically high To meet spending 
commitmentsTypically quite low
Banks Short term Quite low To pay interest on 
deposits and opera -
tional expensesHigh to meet repay -
ment of deposits
Insurance companies Short term for prop -
erty and casualty; long 
term for life insurance 
companiesTypically quite low Typically low High to meet claims
Investment companies Varies by fund Varies by fund Varies by fund High to meet 
redemptions
STEPS IN THE PORTFOLIO MANAGEMENT PROCESS
In the previous section we discussed the different types of investment management

clients and the distinctive characteristics and needs of each. The following steps in 
the investment process are critical in the establishment and management of a client’s 
■■The Planning Step
■●Understanding the client’s needs
■●Preparation of an investment policy statement (IPS)
■■The Execution Step
■●Asset allocation
■●Security analysis
■●Portfolio construction
■■The Feedback Step
■●Portfolio monitoring and rebalancing
■●Performance measurement and reporting
4.1 Step One: The Planning Step
The first step in the investment process is to understand the client’s needs (objectives 
and constraints) and develop an investment policy statement  (IPS). A portfolio 
manager is unlikely to achieve appropriate results for a client without a prior under -
standing of the client’s needs. The IPS is a written planning document that describes 
the client’s investment objectives and the constraints that apply to the client’s portfolio.

The IPS may state a benchmark—such as a particular rate of return or the perfor -
mance of a particular market index—that can be used in the feedback stage to assess 4

Steps in the Portfolio Management Process 223
the performance of the investments and whether objectives have been met. The IPS 
should be reviewed and updated regularly (for example, either every three years or 
when a major change in a client’s objectives, constraints, or circumstances occurs).
4.2 Step Two: The Execution Step
The next step is for the portfolio manager to construct a suitable portfolio based on 
the IPS of the client. The portfolio execution step consists of first deciding on a target 
asset allocation, which determines the weighting of asset classes to be included in the 
portfolio. This step is followed by the analysis, selection, and purchase of individual 
investment securities.
4.2.1  Asset Allocation
The next step in the process is to assess the risk and return characteristics of the 
available investments. The analyst forms economic and capital market expectations 
that can be used to form a proposed allocation of asset classes suitable for the client.

Decisions that need to be made in the asset allocation  of the portfolio include the 
distribution between equities, fixed-  income securities, and cash; sub-  asset classes, 
such as corporate and government bonds; and geographical weightings within asset 
classes. Alternative assets—such as real estate, commodities, hedge funds, and private 
equity—may also be included.
Economists and market strategists may set the top down view on economic con -
ditions and broad market trends. The returns on various asset classes are likely to be 
affected by economic conditions; for example, equities may do well when economic 
growth has been unexpectedly strong whereas bonds may do poorly if inflation 
increases. The economists and strategists will attempt to forecast these conditions.
 
Top down —A top-  down analysis  begins with consideration of macroeconomic con -
ditions. Based on the current and forecasted economic environment, analysts evaluate

markets and industries with the purpose of investing in those that are expected to perform 
well. Finally, specific companies within these industries are considered for investment.
 
Bottom up —rather than emphasizing economic cycles or industry analysis, a bottom-  up 
analysis  focuses on company-  specific circumstances, such as management quality and 
business prospects. It is less concerned with broad economic trends than is the case for 
top-  down analysis, but instead focuses on company specifics. 
4.2.2  Security Analysis
The top-  down view can be combined with the bottom-  up insights of security analysts 
who are responsible for identifying attractive investments in particular market sectors. 
They will use their detailed knowledge of the companies and industries they cover to 
assess the expected level and risk of the cash flows that each security will produce. 
This knowledge allows the analysts to assign a valuation to the security and identify 
preferred investments.

4.2.3  Portfolio Construction
The portfolio manager will then construct the portfolio, taking account of the target 
asset allocation, security analysis, and the client’s requirements as set out in the IPS. 
A key objective will be to achieve the benefits of diversification (i.e., to avoid putting 
all the eggs in one basket). Decisions need to be taken on asset class weightings, sector 
weightings within an asset class, and the selection and weighting of individual securities

Reading 38 ■ Portfolio Management: An Overview 224
or assets. The relative importance of these decisions on portfolio performance depends 
at least in part on the investment strategy selected; for example, consider an investor 
that actively adjusts asset sector weights in relation to forecasts of sector performance 
and one who does not. Although all decisions have an effect on portfolio performance, 
the asset allocation decision is commonly viewed as having the greatest impact.
Exhibit  15 shows the broad portfolio weights of the endowment funds of Yale 
University and the University of Virginia as of June 2008. As you can see, the portfolios 
have a heavy emphasis on such alternative assets as hedge funds, private equity, and 
real estate—Yale University particularly so.
Exhibit 15   Endowment Portfolio Weights, June 2008
Asset ClassYale University 
EndowmentUniversity of Virginia 
Endowment
Public equity 25.3% 53.6%
Fixed income 4.0 15.0
Private equity 20.2 19.6

Real assets (e.g., real estate) 29.3 10.1
Absolute return (e.g., hedge funds) 25.1 8.1
Cash –3.9 –6.5
Portfolio value US$22.9bn US$5.1bn
Note : The negative cash position indicates that at the point the figures were taken, the funds had 
net borrowing rather than net cash.
Sources:  “2008 Yale Endowment Annual Report” (p. 2): www.yale.edu/investments/Yale_
Endowment_08.pdf; “University of Virginia Investment Management Company Annual Report 
2008” (p. 16): http://uvm-  web.eservices.virginia.edu/public/reports/FinancialStatements_2008.
pdf.
Risk management is an important part of the portfolio construction process. The 
client’s risk tolerance will be set out in the IPS, and the portfolio manager must make 
sure the portfolio is consistent with it. As noted above, the manager will take a diver -
sified portfolio perspective: What is important is not the risk of any single investment, 
but rather how all the investments perform as a portfolio.

The endowments shown above are relatively risk tolerant investors. Contrast 
the asset allocation of the endowment funds with the portfolio mix of the insurance 
companies shown in Exhibit 16. You will notice that the majority of the insurance 
assets are invested in fixed-  income investments, typically of high quality. Note that 
the Yale University portfolio has only 4 percent invested in fixed income, with the 
remainder invested in such growth assets as equity, real estate, and hedge funds. This 
allocation is in sharp contrast to the Massachusetts Mutual Life Insurance Company 
(MassMutual) portfolio, which is over 80 percent invested in bonds, mortgages, loans, 
and cash—reflecting the differing risk tolerance and constraints (life insurers face 
regulatory constraints on their investments).

Steps in the Portfolio Management Process 225
Exhibit 16   Insurance Company Portfolios, December 200811
Asset Classes MassMutual Portfolio MetLife Portfolio
Bonds 56.4% 58.7%
Preferred and common shares 2.2 1.0
Mortgages 15.1 15.9
Real estate 1.3 2.4
Policy loans 10.6 3.0
Partnerships 6.4 1.9
Other assets 4.5 5.3
Cash 3.5 11.8
Note : MetLife is the Metropolitan Life Insurance Company.
Sources:  “MassMutual Financial Group 2008 Annual Report” (p. 26): www.massmutual.com/
mmfg/docs/annual_report/index.html, “MetLife 2008 Annual Report” (p. 83): http://investor.
metlife.com/phoenix.zhtml?c=121171&p=irol-  reportsannual.
The portfolio construction phase also involves trading. Once the portfolio man -
ager has decided which securities to buy and in what amounts, the securities must be 
purchased. In many investment firms, the portfolio manager will pass the trades to a 
buy-  side trader—a colleague who specializes in securities trading—who will contact 
a stockbroker or dealer to have the trades executed.

Sell-  side firm —A broker or dealer that sells securities to and provides independent 
investment research and recommendations to investment management companies.
 
Buy-  side firm —Investment management companies and other investors that use the 
services of brokers or dealers (i.e., the clients of the sell-  side firms). 
4.3 Step Three: The Feedback Step
Finally, the feedback step assists the portfolio manager in rebalancing the portfolio 
due to a change in, for example, market conditions or the circumstances of the client.
4.3.1  Portfolio Monitoring and Rebalancing
Once the portfolio has been constructed, it needs to be monitored and reviewed and 
the composition revised as the security analysis changes because of changes in security 
prices and changes in fundamental factors. When security and asset weightings have 
drifted from the intended levels as a result of market movements, some rebalancing 
may be required. The portfolio may also need to be revised if it becomes apparent

that the client’s needs or circumstances have changed.
11 Asset class definitions: Bonds—Debt instruments of corporations and governments as well as various 
types of mortgage- and asset-  backed securities; Preferred and Common Shares—Investments in preferred 
and common equities; Mortgages—Mortgage loans secured by various types of commercial property as 
well as residential mortgage whole loan pools; Real Estate—Investments in real estate; Policy Loans—Loans 
by policyholders that are secured by insurance and annuity contracts; Partnerships—Investments in part -
nerships and limited liability companies; Cash—Cash, short-  term investments, receivables for securities, 
and derivatives. Cash equivalents have short maturities (less than one year) or are highly liquid and able 
to be readily sold.

Reading 38 ■ Portfolio Management: An Overview 226
4.3.2  Performance Evaluation and Reporting
Finally, the performance of the portfolio must be evaluated, which will include assessing 
whether the client’s objectives have been met. For example, the investor will wish to 
know whether the return requirement has been achieved and how the portfolio has 
performed relative to any benchmark that has been set. Analysis of performance may 
suggest that the client’s objectives need to be reviewed and perhaps changes made to 
the IPS. As we will discuss in the next section, there are numerous investment prod -
ucts that clients can use to meet their investment needs. Many of these products are 
diversified portfolios that an investor can purchase.
POOLED INVESTMENTS
The challenge faced by all investors is finding the right set of investment products to 
meet their needs. Just as there are many different types of investment management

clients, there is a diverse set of investment products available to investors. These vary 
from a simple brokerage account in which the individual creates her own portfolio 
by assembling individual securities, to large institutions that hire individual portfolio 
managers for all or part of their investment management needs. Although the array of 
products is staggering, there are some general categories of pooled investment products 
that represent the full range of what is available. At one end are mutual funds and 
exchange traded funds in which investors can participate with a small initial invest -
ment. At the other end are hedge funds and private equity funds, which might require 
a minimum investment of US$1 million or more. In this context, the amount of funds 
that an individual or institution can commit to a particular product has a significant 
impact on which products are available. Exhibit 17 provides a general breakdown of

what investment products are available to investors based on investable funds.
Exhibit 17   Investment Products by Minimum Investment
■■Mutual funds
■■Exchange traded funds■■Mutual funds
■■Exchange traded funds
■■Separately managed accounts■■Mutual funds
■■Separately managed accounts
■■Hedge funds
■■Private equity funds
As little as US$50 US$100,000 US$1,000,000 +
5.1 Mutual Funds
Rather than assemble a portfolio on their own, individual investors and institutions 
can turn over the selection and management of their investment portfolio to a third 
party. One alternative is a mutual fund . This type of fund is a comingled investment 
pool in which investors in the fund each have a pro-  rata claim on the income and 
value of the fund. The value of a mutual fund is referred to as the “net asset value. ” It 
is computed daily based on the closing price of the securities in the portfolio. At the 
end of the third quarter of 2008,12 the Investment Company Institute reported over 5

Pooled Investments 227
48,000 mutual funds in over 23 countries with a total net asset value of approximately 
US$20 trillion. Exhibit 18 shows the breakdown of mutual fund assets across the major 
regions of the world as of the end of 2007.
Exhibit 18   Global Allocation of Mutual Fund Assets: 2007
Europe
34%
Africa & 
Asia/Pacific
15%
Other Americas
5%United States
46%
Source:  2008 Investment Company Fact Book , 48th ed. (p. 20): (www.ici.org/pdf/2008_factbook.
pdf).
Mutual funds are one of the most important investment vehicles for individuals 
and institutions. The best way to understand how a mutual fund works is to consider 
a simple example. Suppose that an investment firm wishes to start a mutual fund with 
a target amount of US$10 million. It is able to reach this goal through investments 
from five individuals and two institutions. The investment of each is as follows:
InvestorAmount 
Invested (US$)Percent of 
Total Number of Shares
Individuals
A $1.0 million 10% 10,000
B 1.0 10 10,000
C 0.5 5 5,000

D 2.0 20 20,000
E 0.5 5 5,000
Institutions
X 2.0 20 20,000
Y 3.0 30 30,000
Totals $10.0 million 100% 100,000

Reading 38 ■ Portfolio Management: An Overview 228
Based on the US$10 million value (net asset value), the investment firm sets a total 
of 100,000 shares at an initial value of US$100 per share (US$10 million/100,000 = 
US$100). The investment firm will appoint a portfolio manager to be responsible for 
the investment of the US$10 million. Going forward, the total value of the fund or 
net asset value will depend on the value of the assets in the portfolio.
The fund can be set up as an open-  end fund or a closed-  end fund. If it is an 
open-  end fund , it will accept new investment money and issue additional shares at a 
value equal to the net asset value of the fund at the time of investment. For example, 
assume that at a later date the net asset value of the fund increases to US$12.0 mil -
lion and the new net asset value per share is US$120. A new investor, F, wishes to 
invest US$0.96 million in the fund. If the total value of the assets in the fund is now

US$12 million or US$120 per share, in order to accommodate the new investment the 
fund would create 8,000 (US$0.96 million/US$120) new shares. After this investment, 
the net asset value of the fund would be US$12.96 million and there would be a total 
of 108,000 shares.
Funds can also be withdrawn at the net asset value per share. Suppose on the same 
day Investor E wishes to withdraw all her shares in the mutual fund. To accommo -
date this withdrawal, the fund will have to liquidate US$0.6 million in assets to retire 
5,000 shares at a net asset value of US$120 per share (US$0.6 million/US$120). The 
combination of the inflow and outflow on the same day would be as follows:
Type Investment (US$) Shares
Inflow (Investor F buys) $960,000 8,000
Outflow (Investor E sells) –$600,000 –5,000
Net $360,000 3,000
The net of the inflows and outflows on that day would be US$360,000 of new 
funds to be invested and 3,000 new shares created. However, the number of shares

held and the value of the shares of all remaining investors, except Investor E, would 
remain the same.
An alternative to setting the fund up as an open-  end fund would be to create a 
closed-  end fund  in which no new investment money is accepted into the fund. New 
investors invest by buying existing shares, and investors in the fund liquidate by 
selling their shares to other investors. Hence, the number of outstanding shares does 
not change. One consequence of this fixed share base is that, unlike open-  end funds 
in which new shares are created and sold at the current net asset value per share, 
closed-  end funds can sell for a premium or discount to net asset value depending on 
the demand for the shares.
There are advantages and disadvantages to each type of fund. The open-  end fund 
structure makes it easy to grow in size but creates pressure on the portfolio manager 
to manage the cash inflows and outflows. One consequence of this structure is the

need to liquidate assets that the portfolio manager might not want to sell at the time 
to meet redemptions. Conversely, the inflows require finding new assets in which to 
invest. As such, open-  end funds tend not to be fully invested but rather keep some 
cash for redemptions not covered by new investments. Closed-  end funds do not 
have these problems, but they do have a limited ability to grow. Of the total net asset 
value of all US mutual funds at the end of 2008 (US$9.6 trillion), only approximately 
2 percent were in the form of closed-  end funds.
In addition to open-  end or closed-  end funds, mutual funds can be classified as 
load or no-  load funds. The primary difference between the two is whether the investor 
pays a sales charge (a “load”) to purchase, hold, or redeem shares in the fund. In the 
case of the no- load fund , there is no fee for investing in the fund or for redemption 
but there is an annual fee based on a percentage of the fund’s net asset value. Load

funds  are funds in which, in addition to the annual fee, a percentage fee is charged

Pooled Investments 229
to invest in the fund and/or for redemptions from the fund. In addition, load funds 
are usually sold through retail brokers who receive part of the upfront fee. Overall, 
the number and importance of load funds has declined over time.
Mutual funds also differ in terms of the type of assets that they invest in. Broadly 
speaking, there are four different types of funds that are differentiated by broad asset 
type: stock funds (domestic and international), bond funds (taxable and non-  taxable), 
hybrid or balanced funds (combination of stocks and bonds), and money market funds 
(taxable and non-  taxable). The approximately US$9.6 trillion in US mutual fund net 
asset value by asset type as of the end of 2008 is shown in Exhibit 19. A breakdown 
for the European mutual fund market is shown in Exhibit 20.
Exhibit 19   Mutual Funds Net Asset Value by Asset Type End of 2007 and 
2008
2007
200860%
50%
40%
30%
20%
10%
0%
Stock Funds Money Market Hybrid Bond Funds

20%
10%
0%
Source:  Investment Company Institute (2009a).

Reading 38 ■ Portfolio Management: An Overview 230
Exhibit 20   European Mutual Fund (UCITS) Assets
Recent Trends in Assets by UCITS Type
(EUR billion) 
2,400
2,000
1,600
1,200
800
400
0
2004 Q4 2005 Q4 2006 Q4 2007 Q4 2008 Q4Equity
Money Market
Balanced
Other (Incl. FoF)Bond
Note : UCITS (Undertakings for Collective Investments in Transferable Securities) are a set of regulations designed to help the European 
Union achieve a single funds market across Europe.
Source:  EFAMA Quarterly Statistical Release No. 36 (Fourth Quarter of 2008) . EFAMA is the European Fund and Asset Management 
Association.
Stock and money market funds make up the largest segments of the US mutual 
fund industry. Between 2007 and 2008, however, there was a dramatic shift in the rel -
ative proportion of net asset value in stock funds and money market funds. Although 
there was a significant increase in the total value of assets in money market funds

(24 percent, or approximately US$700 billion), the biggest change was in the value of 
total assets of stock funds, which fell by 43 percent or approximately US$2.8 trillion. 
Close to 10 percent of this drop, or US$280 billion, was the result of redemptions 
exceeding new investments, with the remaining of the decline attributed to the dra -
matic fall in share prices during 2008.13 A similar drop in equity assets is evident in 
the European data.
5.2 Types of Mutual Funds
The following section introduces the major types of mutual funds differentiated by the 
asset type that they invest in: money market funds, bond mutual funds, stock mutual 
funds, and hybrid or balanced funds.
5.2.1  Money Market Funds
Although money market funds have been a substitute for bank savings accounts since 
the early 1980s, they are not insured in the same way as bank deposits. At the end of 
2008, the total net asset value of US money market funds was in excess of US$3.8 tril -

lion, with a further €1 trillion in European money market funds. In the United States, 
13 These figures were extracted from data in Investment Company Institute (2009a).

Pooled Investments 231
there are two basic types of money market funds: taxable and tax-  free. Taxable money 
market funds invest in high-  quality, short-  term corporate debt and federal government 
debt. Tax-  free money market funds invest in short-  term state and local government 
debt. At the end of 2008 in the United States, there were approximately 540 taxable 
funds with about US$3.3 trillion in net asset value and approximately 250 tax-  free 
money market funds with a total net asset value of about US$490 billion. From an 
investor’s point of view, these funds are essentially cash holdings. As such, the pre -
sumption of investors is that the net asset value of a money market fund is always 
US$1.00 per share.
In September 2008 two large money market funds “broke the buck”; that is, the 
net asset value of the shares fell below US$1.00 per share. This drop in value caused 
investors to question the safety of money market funds and resulted in a massive out -

flow of funds from money market funds. This outflow continued until the US Federal 
Reserve intervened to provide short-  term insurance for some money market funds. 
This insurance, although similar to bank deposits, was limited in scope and time.
5.2.2  Bond Mutual Funds
A bond mutual fund is an investment fund consisting of a portfolio of individual 
bonds and, occasionally, preferred shares. The net asset value of the fund is the sum 
of the value of each bond in the portfolio divided by the number of shares. Investors 
in the mutual fund hold shares, which account for their pro-  rata share or interest 
in the portfolio. The advantage is that an investor can invest in a bond fund for as 
little as US$100, which provides a stake in a diversified bond portfolio in which each 
individual bond may cost between US$10,000 and US$100,000. The major difference 
between a bond mutual fund and a money market fund is the maturity of the under -

lying assets. In a money market fund the maturity is as short as overnight and rarely 
longer than 90 days. A bond mutual fund, however, holds bonds with maturities as 
short as one year and as long as 30 years. Exhibit 21 illustrates the general categories 
of bond mutual funds.14
Exhibit 21   Bond Mutual Funds
Type of Bond Mutual Fund Securities Held
Global Domestic and non-  domestic government, corpo -
rate, and securitized debt
Government Government bonds and other government-  affiliated 
bonds
Corporate Corporate debt
High yield Below investment-  grade corporate debt
Inflation protected Inflation-  protected government debt
National tax-  free bonds National tax-  free bonds (e.g., US municipal bonds)
An example of a typical bond mutual fund is the T. Rowe Price Corporate Income 
Fund. Exhibit 22 shows the asset composition, credit quality, and maturity diversifi -
cation for this bond mutual fund.

14 In the United States, judicial rulings on federal powers of taxation have created a distinction between 
(federally) taxable and (federally) tax-  exempt bonds and a parallel distinction for US bond mutual funds.

Reading 38 ■ Portfolio Management: An Overview 232
Exhibit 22   Asset Composition of T. Rowe Price Corporate Income Fund As of 31 March 2009
Asset Composition Credit Quality Diversification Maturity Diversification
Assets % of Total Bond Ratinga% of Total Maturity (years) % of Total
US corporate 78.7 AAA 7.1 0–1 year 3.7
Foreign bonds 18.4 AA 7.4 1–5 years 31.3
Cash 2.4 A 28.1 5–10 years 46.2
Other 0.5 BBB 48.8 10+ years 18.7
BB 5.8
Other and not rated 0.3
Cash 2.4
a Bond rating is from Standard & Poor’s. AAA represents the highest credit quality. Bonds rated BBB and above are considered to be 
investment-  grade bonds. Bonds rated below BBB are non-  investment-  grade bonds and are also known as high-  yield or junk bonds.
Source:  T. Rowe Price (www.troweprice.com).
5.2.3  Stock Mutual Funds
Historically, the largest types of mutual funds based on market value of assets under 
management are stock or equity funds. At the end of the third quarter of 2008, the

worldwide investment in stock mutual funds totaled around US$8.6  trillion, with 
approximately US$4 trillion of that in US stock mutual funds.
There are two types of stock mutual funds. The first is an actively managed fund 
in which the portfolio manager seeks outstanding performance through the selec -
tion of the appropriate stocks to be included in the portfolio. Passive management is 
followed by index funds that are very different from actively managed funds. Their 
goal is to match or track the performance of different indexes. The first index fund 
was introduced in 1976 by the Vanguard Group. At the end of 2008, index funds held 
approximately 13 percent of the total net asset value of stock mutual funds.15
There are several major differences between actively managed funds and index 
funds. First, management fees for actively managed funds are higher than for index 
funds. The higher fees for actively managed funds reflect its goal to outperform an

index, whereas the index fund simply aims to match the return on the index. Higher 
fees are required to pay for the research conducted to actively select securities. A 
second difference is that the level of trading in an actively managed fund is much 
higher than in an index fund, which has obvious tax implications. Mutual funds are 
required to distribute all income and capital gains realized in the portfolio, so the 
actively managed fund tends to have more opportunity to realize capital gains. This 
results in higher taxes relative to an index fund, which uses a buy-  and-  hold strategy. 
Consequently, there is less buying and selling in an index fund and less likelihood of 
realizing capital gains distributions.
5.2.4  Hybrid/Balanced Funds
Hybrid or balanced funds are mutual funds that invest in both bonds and shares. 
These types of funds represent a small fraction of the total investment in US mutual 
funds but are more common in Europe. (See Exhibits 19 and 20.) These types of funds,

however, are gaining popularity with the growth of lifecycle funds. These are funds that 
manage the asset mix based on a desired retirement date. For example, if an investor 
was 40 years old in 2008 and planned to retire at the age of 67, he could invest in a 
mutual fund with a target date of 2035 and the fund would manage the appropriate 
15 Mamudi (2009).

Pooled Investments 233
asset mix over the next 27 years. In 2008 it might be 90 percent invested in shares and 
10 percent in bonds. As time passes, however, the fund would gradually change the 
mix of shares and bonds to reflect the appropriate mix given the time to retirement.
5.3 Other Investment Products
In addition to mutual funds, a number of pooled investment products are increasingly 
popular in meeting the individual needs of clients. The following section introduces 
these products: exchange traded funds, separately managed accounts, hedge funds, 
and buyout and venture capital funds .
5.3.1  Exchange Traded Funds16
Exchange traded funds (ETFs) combine features of closed-  end and open-  end mutual 
funds. ETFs trade like closed-  end mutual funds; however, like open-  end funds, ETFs’ 
prices track net asset value due to an innovative redemption procedure. ETFs are 
created by fund sponsors who determine which securities will be included in the

basket of securities. To obtain the basket, the fund sponsors contact an institutional 
investor who deposits the securities with the fund sponsor. In return, the institutional 
investor receives creation units that typically represent between 50,000 and 100,000 
ETF shares. These shares can then be sold to the public by the institutional investor. 
The institutional investor can redeem the securities held in the ETF by returning 
the number of shares in the original creation unit. This process prevents meaningful 
premiums or discounts from net asset value. Closed-  end mutual funds are predomi -
nantly actively managed stock or bond funds whereas ETFs are typically index funds. 
The first ETF was created in the United States in 1993 and in 1999 in Europe. At the 
end of 2017, there were nearly 1,800 ETFs available in the United States with a total 
net asset value of over US$3 trillion. A breakdown of the types of ETFs traded in the 
United States is shown in Exhibit 23.

The major difference between an index mutual fund and an ETF is that an investor 
investing in an index mutual fund buys the fund shares directly from the fund and all 
investments are settled at the net asset value. In the case of an ETF, however, investors 
buy the shares from other investors just as if they were buying or selling shares of 
stock. This setup includes the opportunity to short the shares or even purchase the 
shares on margin. The price an investor pays is based on the prevailing price at the 
time the transaction was made. This price may or may not be equal to the net asset 
value at the time, but it represents the price at that time for a willing buyer and seller. 
In practice, the market price of the ETF is likely to be close to the net asset value of 
the underlying investments.
Other main differences between an index mutual fund and an index ETF are trans -

action costs, transaction price, treatment of dividends, and the minimum investment 
amount. Expenses are lower for ETFs but, unlike mutual funds, investors do incur 
brokerage costs. Also as noted above, all purchases and redemptions in a mutual 
fund take place at the same price at the close of business. ETFs are constantly traded 
throughout the business day, and as such each purchase or sale takes place at the 
prevailing market price at that time. In the case of the ETF, dividends are paid out to 
the shareholders whereas index mutual funds usually reinvest the dividends. Hence, 
there is a direct cash flow from the ETF that is not there with the index mutual fund. 
Depending on the investor, this cash flow may or may not be desirable. Note that the 
tax implications are the same with either fund type. Finally, the minimum required 
investment in an ETF is usually smaller. Investors can purchase as little as one share 
in an ETF, which is usually not the case with an index mutual fund.

16 For more detailed information on ETFs, see Hill, Nadig, and Hougan (2015).

Reading 38 ■ Portfolio Management: An Overview 234
Exhibit 23   Types of Exchange Traded Funds (ETFs) October 2017
Type of ETF October 2017Totals 
(in US$ 
trillions) Asset Class by Type of ETF as a Percentage of Total ETF Assets under Management
Broad-  based equity Total Market Large Cap Mid-  Cap Broad-  Based, 
Other
46.6% $1,508.6 4.5% 26.7% 5.1% 5.2%
Sector Commodities Consumer Financial Natural 
ResourcesReal Estate Technology Utilities Other 
Sectors
13.1% 423.9 2.1% 0.9% 1.8% 1.7% 1.7% 2.0% 1.6% 1.4%
Global/intern. Global International Regional Single Country Emerging 
Markets
23.3% 753.4 2.4% 10.2% 2.3% 1.6% 6.8%
Hybrid Hybrid
0.2% 7.4 0.2%
Bond Government 
BondMunicipal 
BondCorporate 
BondHigh Yield 
BondsInternational 
Bond
16.8% 543.0 3.6% 0.9% 8.9% 2.0% 1.3%
Totals 100.0% $3,236.3
Source:  Investment Company Institute, “ETF Assets and Net Issuance, October 2017. ”

Pooled Investments 235
ETFs are often cited as having tax advantages over index mutual funds. The advan -
tage is not related to the dividends but rather to capital gains. As long as there is no 
sale of assets in either fund, no taxable capital gains would be realized by investors. 
It is possible, however, that because of the flow of funds into and out of index mutual 
funds, these funds would have a greater likelihood of generating taxable capital gains 
for investors. Overall, it is not clear how much of an advantage there is or if there is 
any advantage at all.
5.3.2  Separately Managed Accounts
A fund management service for institutions or individual investors with substantial 
assets is the separately managed account  (SMA), which is also commonly referred 
to as a “managed account, ” “wrap account, ” or “individually managed account” . An 
SMA is an investment portfolio managed exclusively for the benefit of an individual or

institution. The account is managed by an individual investment professional to meet 
the specific needs of the client in relation to investment objectives, risk tolerance, and 
tax situation. In an SMA, the individual shares are held directly by the investor; and 
in return for annual fees, an individual can receive personalized investment advice.
The key difference between an SMA and a mutual fund is that the assets are owned 
directly by the individual. Therefore, unlike a mutual fund, the investor has control 
over which assets are bought and sold and the timing of the transactions. Moreover, 
in a mutual fund, there is no consideration given to the tax position of the individual 
asset. In an SMA, the transactions can take into account the specific tax needs of the 
investor. The main disadvantage of an SMA is that the required minimum investment 
is usually much higher than is the case with a mutual fund. Usually, the minimum 
investment is between US$100,000 and US$500,000.

Large institutions often use segregated accounts, which means their investments are 
held in an account on their behalf and managed by a portfolio manager or team. They 
can also use mutual funds. The decision on which approach to take often depends on 
the value of assets involved. Larger amounts of assets are more likely to be managed 
on a segregated basis.
5.3.3  Hedge Funds
The origin of hedge funds17 can be traced back as far as 1949 to a fund managed by 
A.W. Jones & Co. It offered a strategy of a non-  correlated offset to the “long-  only” 
position typical of most portfolios. From this start emerged a whole new industry 
of hedge funds. Hedge fund strategies generally involve a significant amount of risk, 
driven in large measure by the liberal use of leverage and complexity. They also often 
involve the extensive use of derivatives.
A key difference between hedge funds and mutual funds is that the vast majority

of hedge funds are exempt from many of the reporting requirements for the typical 
public investment company. In the United States, investment companies do not have 
to register with the US Securities and Exchange Commission (SEC) if they have 100 
or fewer investors [Section 3(c)1 of the Investment Company Act of 1940] or if the 
investor base is greater than 100 but less than 500 “qualified purchasers”18 [Section 
3(c)7 of the Investment Company Act of 1940]. In order to qualify for the exemption, 
hedge funds cannot be offered for sale to the general public; they can only be sold via 
private placement. In addition, Regulation D of the Securities Act of 1933 requires 
17 For more information on hedge funds, see the Level I CFA Program curriculum reading “Introduction 
to Alternative Investments. ”
18 A “qualified purchaser” is an individual with over US$5 million in investment assets.

Reading 38 ■ Portfolio Management: An Overview 236
that hedge funds be offered solely to “accredited investors. ”19 The net effect of these 
regulations is that the hedge fund investor base is generally very different from that 
of the typical mutual fund.
From its start in 1955 to the end of 2008, the hedge fund industry has grown to 
over 9,200 hedge funds with approximately US$1.4 trillion in assets.20 Not all hedge 
funds are the same, however. Many different strategies are employed. A few exam -
ples21 include:
■■Convertible Arbitrage —Buying such securities as convertible bonds that can 
be converted into shares at a fixed price and simultaneously selling the stock 
short.
■■Dedicated Short Bias —Taking more short positions than long positions.
■■Emerging Markets —Investing in companies in emerging markets by purchas -
ing corporate or sovereign securities.
■■Equity Market Neutral —Attempting to eliminate the overall market move -

ment by going short overvalued securities and going long a nearly equal value 
of undervalued securities.
■■Event Driven —Attempting to take advantage of specific company events. 
Event-  driven strategies take advantage of transaction announcements and other 
one-  time events.
■■Fixed-  Income Arbitrage —Attempting to profit from arbitrage opportunities in 
interest rate securities. When using a fixed-  income arbitrage strategy, the inves -
tor assumes opposing positions in the market to take advantage of small price 
discrepancies while limiting interest rate risk.
■■Global Macro —Trying to capture shifts between global economies, usually 
using derivatives on currencies or interest rates.
■■Long/Short —Buying long equities that are expected to increase in value and 
selling short equities that are expected to decrease in value. Unlike the equity 
market neutral strategy, this strategy attempts to profit from market move -
ments, not just from identifying overvalued and undervalued equities.

The list above is not all-  inclusive; there are many other strategies. Hedge funds 
are not readily available to all investors. They require a minimum investment that is 
typically US$250,000 for new funds and US$1 million or more for well-  established 
funds. In addition, they usually have restricted liquidity that could be in the form of 
allowing only quarterly withdrawals or having a fixed-  term commitment of up to five 
years. Management fees are not only a fixed percentage of the funds under manage -
ment; managers also collect fees based on performance. A typical arrangement would 
include a 1 percent to 2 percent fee on assets under management and 20 percent of 
the outperformance as compared to a stated benchmark.
19 An “accredited individual” investor must have a minimum net worth of US$1 million or a minimum 
individual income of US$200,000 in each of the two most recent years with the expectation of having

the same income in the current year. An accredited institution must have a minimum of US$5 million in 
invested assets.
20 Both the number of hedge funds and the value of assets under management fell dramatically in the 
second half of 2008. According to Hedge Fund Research, Inc., during 2008 the total number of funds 
fell by 8  percent and the value of assets under management fell from approximately US$1.9  trillion to 
US$1.4 trillion at the end of 2008.
21 In the examples, “long” refers to owning the security and “selling short” refers to a strategy of borrowing 
shares and converting them to cash with the intention of repaying the shares at a later date by buying them 
back at a lower price. Long positions have a positive return when the price of the security increases, and 
short positions have a positive return when the price of the security falls.

Summary 237
5.3.4  Buyout and Venture Capital Funds
Two areas that have grown considerably over the last 15 years have been buyout and 
venture capital funds. Both take equity positions but in different types of companies. 
An essential feature of both is that they are not passive investors, and as such, they 
play a very active role in the management of the company. Furthermore, the equity 
they hold is private rather than traded on public markets. In addition, neither intends 
to hold the equity for the long term; from the beginning, both plan for an exit strategy 
that will allow them to liquidate their positions. Both venture capital funds and private 
equity funds operate in a manner similar to hedge funds. A minimum investment is 
required, there is limited liquidity during some fixed time period, and management 
fees are based not only on funds under management but also on the performance of 
the fund.
Buyout Funds  The essence of a buyout fund  is that it buys all the shares of a public

company and, by holding all the shares, the company becomes private. The early lev-
eraged buyouts  (LBOs) of the mid-  1960s through the early 1990s created the modern 
private equity firm. These were highly levered transactions that used the company’s 
cash flow to pay down the debt and build the equity position. In its current form, pri -
vate equity firms raise money specifically for the purpose of buying public companies, 
converting them to private companies, and simultaneously restructuring the com -
pany. The purchase is usually financed through a significant increase in the amount of 
debt issued by the company. A typical financing would include 25 percent equity and 
75 percent debt in one form or another. The high level of debt is also accompanied by 
a restructuring of the operations of the company. The key is to increase the cash flow. 
Most private equity funds do not intend to hold the company for the long run because

their goal is to exit the investment in three to five years either through an initial public 
offering (IPO) or a sale to another company. Generally, a private equity firm makes a 
few very large investments.
Venture Capital Funds  Venture capital differs from a buyout fund in that a venture 
capital firm does not buy established companies but rather provides financing for 
companies in their start-  up phase. Venture capital funds play a very active role in the 
management of the companies in which they invest; beyond just providing money, 
they provide close oversight and advice. Similar to buyout funds, venture capital funds 
typically have a finite investment horizon and, depending on the type of business, make 
the investment with the intent to exit in three to five years. These funds make a large 
number of small investments with the expectation that only a small number will pay 
off. The assumption is that the one that does pay off pays off big enough to compensate

for the ones that do not pay off.
SUMMARY
■■In this reading we have discussed how a portfolio approach to investing could 
be preferable to simply investing in individual securities.
■■The problem with focusing on individual securities is that this approach may 
lead to the investor “putting all her eggs in one basket. ”
■■Portfolios provide important diversification benefits, allowing risk to be reduced 
without necessarily affecting or compromising return.

Reading 38 ■ Portfolio Management: An Overview 238
Acharya, Shanta, and Elroy Dimson. 2007. Endowment Asset 
Management: Investment Strategies in Oxford and Cambridge . 
New York: Oxford University Press.
Hill, Joanne M., Dave Nadig, and Matt Hougan. 2015. A 
Comprehensive Guide to Exchange-  Traded Funds (ETFs) . 
Charlottesville, VA: The CFA Institute Research Foundation.
Investment Company Institute. 2007. “ A Guide to Exchange-
Traded Funds”: (www.ici.org/investor_ed/brochures/bro_etf).
Investment Company Institute. 2009a. “Trends in Mutual Fund 
Investing, December 2008” (20 March).
Investment Company Institute. 2009b. “Worldwide Mutual Fund 
Assets and Flows, Third Quarter 2008” (5 May).
Lintner, John. 1965. “The Valuation of Risk Assets and the 
Selection of Risky Investments in Stock Portfolios and Capital 
Budgets. ” Review of Economics and Statistics , vol. 47, no. 1 
(February):13–37. Mamudi, Sam. 2009. “More Investors Ditch Market-Beating

Attempts, Embrace Index Funds. ” FiLife  (in partnership with 
the Wall Street Journal ; 27 February): http://www.filife.com/
stories/more-  investors-  ditch-  market-  beating-  attempts-  
embrace-  index-  funds.
Markowitz, Harry M. 1952. “Portfolio Selection. ” Journal of 
Finance , vol. 7, no. 1 (March):77–91. 
Sharpe, William F. 1964. “Capital Asset Prices: A Theory of 
Market Equilibrium under Conditions of Risk. ” Journal of 
Finance , vol. 19, no. 3 (September):425–442. 
Singletary, Michelle. 2001. “Cautionary Tale of an Enron 
Employee Who Went for Broke. ” Seattlepi.com (10 December): 
http://www.seattlepi.com/money/49894_singletary10.shtml.
Treynor, J. L. 1961. “Toward a Theory of Market Value of Risky 
Assets. ” Unpublished manuscript.■■We have outlined the differing investment needs of various types of individual 
and institutional investors. Institutional clients include defined benefit pension 
plans, endowments and foundations, banks, insurance companies, investment

companies, and sovereign wealth funds.
■■Understanding the needs of your client and creating an investment policy 
statement represent the first steps of the portfolio management process. Those 
steps are followed by security analysis, portfolio construction, monitoring, and 
performance measurement stages.
■■We also discussed the different types of investment products that investors can 
use to create their portfolio. These range from mutual funds, to exchange traded 
funds, to hedge funds, to private equity funds.

Practice Problems 239
1 Investors should use a portfolio approach to:
A reduce risk.
B monitor risk.
C eliminate risk.
2 Which of the following is the best reason for an investor to be concerned with 
the composition of a portfolio?
A Risk reduction.
B Downside risk protection.
C Avoidance of investment disasters.
3 With respect to the formation of portfolios, which of the following statements is 
A Portfolios affect risk less than returns.
B Portfolios affect risk more than returns.
C Portfolios affect risk and returns equally.
4 Which of the following institutions will on average  have the greatest need for 
A Banks.
B Investment companies.
C Non-  life insurance companies.
5 Which of the following institutional investors will most likely  have the longest 
time horizon?
A Defined benefit plan.
B University endowment.
C Life insurance company.
6 A defined benefit plan with a large number of retirees is likely  to have a high 
need for
A income.
B liquidity.

need for
A income.
C insurance.
7 Which of the following institutional investors is most likely  to manage invest -
ments in mutual funds?
A Insurance companies.
C University endowments.
8 With respect to the portfolio management process, the asset allocation is deter -
mined in the:
A planning step.
B feedback step.
C execution step.
9 The planning step of the portfolio management process is least likely  to include 
an assessment of the client’s

Reading 38 ■ Portfolio Management: An Overview 240
A securities.
B constraints.
C risk tolerance.
10 With respect to the portfolio management process, the rebalancing of a portfo -
lio’s composition is most likely  to occur in the:
11 An analyst gathers the following information for the asset allocations of three 
portfolios:
Portfolio Fixed Income (%) Equity (%) Alternative Assets (%)
1 25 60 15
2 60 25 15
3 15 60 25
 Which of the portfolios is most likely  appropriate for a client who has a high 
degree of risk tolerance?
A Portfolio 1.
B Portfolio 2.
C Portfolio 3.
12 Which of the following investment products is most likely  to trade at their net 
asset value per share?
A Exchange traded funds.
B Open-  end mutual funds.
C Closed-  end mutual funds.
13 Which of the following financial products is least likely  to have a capital gain 
distribution?

14 Which of the following forms of pooled investments is subject to the least  
amount of regulation?
A Hedge funds.
B Exchange traded funds.
15 Which of the following pooled investments is most likely  characterized by a few 
large investments?
B Buyout funds.
C Venture capital funds.

Solutions 241
SOLUTIONS
1 A is correct. Combining assets into a portfolio should reduce the portfolio’s vol -
atility. Specifically, “individuals and institutions should hold portfolios to reduce 
risk. ” As illustrated in the reading, however, risk reduction may not be as great 
during a period of dramatic economic change.
2 A is correct. Combining assets into a portfolio should reduce the portfolio’s vol -
atility. The portfolio approach does not necessarily provide downside protection 
or guarantee that the portfolio always will avoid losses.
3 B is correct. As illustrated in the reading, portfolios reduce risk more than they 
increase returns.
4 A is correct. The excess reserves invested by banks need to be relatively liquid. 
Although investment companies and non-  life insurance companies have high 
liquidity needs, the liquidity need for banks is on average the greatest.
5 B is correct. Most foundations and endowments are established with the intent

of having perpetual lives. Although defined benefit plans and life insurance 
companies have portfolios with a long time horizon, they are not perpetual.
6 A is correct. Income is necessary to meet the cash flow obligation to retirees. 
Although defined benefit plans have a need for income, the need for liquidity 
typically is quite low. A retiree may need life insurance; however, a defined ben -
efit plan does not need insurance.
7 B is correct. Investment companies manage investments in mutual funds. 
Although endowments and insurance companies may own mutual funds, they 
do not issue or redeem shares of mutual funds.
8 C is correct. The client’s objectives and constraints are established in the invest -
ment policy statement and are used to determine the client’s target asset alloca -
tion, which occurs in the execution step of the portfolio management process.
9 A is correct. Securities are analyzed in the execution step. In the planning step,

a client’s objectives and constraints are used to develop the investment policy 
10 B is correct. Portfolio monitoring and rebalancing occurs in the feedback step 
of the portfolio management process.
11 C is correct. Portfolio 3 has the same equity exposure as Portfolio 1 and has a 
higher exposure to alternative assets, which have greater volatility (as discussed 
in the section of the reading comparing the endowments from Yale University 
and the University of Virginia).
12 B is correct. Open-  end funds trade at their net asset value per share, whereas 
closed-  end funds and exchange traded funds can trade at a premium or a 
discount.
13 A is correct. Exchange traded funds do not have capital gain distributions. If an 
investor sells shares of an ETF (or open-  end mutual fund or closed-  end mutual 
fund), the investor may have a capital gain or loss on the shares sold; however, 
the gain (or loss) from the sale is not a distribution.

14 A is correct. Hedge funds are currently exempt from the reporting require -
ments of a typical public investment company.
15 B is correct. Buyout funds or private equity firms make only a few large invest -
ments in private companies with the intent of selling the restructured compa -
nies in three to five years. Venture capital funds also have a short time horizon; 
however, these funds consist of many small investments in companies with the 
expectation that only a few will have a large payoff (and that most will fail).

Portfolio Risk and Return: Part I
by Vijay Singal, PhD, CFA
Vijay Singal, PhD, CFA, is at Virginia Tech (USA).
a. calculate and interpret major return measures and describe their 
appropriate uses;
b. describe characteristics of the major asset classes that investors 
consider in forming portfolios;
c. calculate and interpret the mean, variance, and covariance (or 
correlation) of asset returns based on historical data;
d. explain risk aversion and its implications for portfolio selection;
e. calculate and interpret portfolio standard deviation;
f. describe the effect on a portfolio’s risk of investing in assets that 
are less than perfectly correlated;
g. describe and interpret the minimum-  variance and efficient 
frontiers of risky assets and the global minimum-  variance 
portfolio;
h. explain the selection of an optimal portfolio, given an investor’s 
utility (or risk aversion) and the capital allocation line.

Construction of an optimal portfolio is an important objective for an investor. In this 
reading, we will explore the process of examining the risk and return characteristics of 
individual assets, creating all possible portfolios, selecting the most efficient portfolios, 
and ultimately choosing the optimal portfolio tailored to the individual in question.
During the process of constructing the optimal portfolio, several factors and invest -
ment characteristics are considered. The most important of those factors are risk and 
return of the individual assets under consideration. Correlations among individual 
assets along with risk and return are important determinants of portfolio risk. Creating 
a portfolio for an investor requires an understanding of the risk profile of the investor. 1rEADING
39

Reading 39 ■ Portfolio Risk and Return: Part I 244
Although we will not discuss the process of determining risk aversion for individuals 
or institutional investors, it is necessary to obtain such information for making an 
informed decision. In this reading, we will explain the broad types of investors and 
how their risk–return preferences can be formalized to select the optimal portfolio 
from among the infinite portfolios contained in the investment opportunity set.
The reading is organized as follows: Section 2 discusses the investment charac -
teristics of assets. In particular, we show the various types of returns and risks, their 
computation and their applicability to the selection of appropriate assets for inclusion 
in a portfolio. Section 3 discusses risk aversion and how indifference curves, which 
incorporate individual preferences, can be constructed. The indifference curves are 
then applied to the selection of an optimal portfolio using two risky assets. Section 4

provides an understanding and computation of portfolio risk. The role of correlation 
and diversification of portfolio risk are examined in detail. Section 5 begins with the 
risky assets available to investors and constructs a large number of risky portfolios. It 
illustrates the process of narrowing the choices to an efficient set of risky portfolios 
before identifying the optimal risky portfolio. The risky portfolio is combined with 
investor risk preferences to generate the optimal risky portfolio. A summary concludes 
this reading.
INVESTMENT CHARACTERISTICS OF ASSETS
Financial assets are generally defined by their risk and return characteristics. Comparison 
along these two dimensions simplifies the process of selecting from millions of assets 
and makes financial assets substitutable. These characteristics distinguish financial 
assets from physical assets, which can be defined along multiple dimensions. For

example, wine is characterized by its grapes, aroma, sweetness, alcohol content, 
and age, among other factors. The price of a television depends on picture quality, 
manufacturer, screen size, number and quality of speakers, and so on, none of which 
are similar to the characteristics for wine. Therein lies one of the biggest differences 
between financial and physical assets. Although financial assets are generally claims 
on real assets, their commonality across two dimensions (risk and return) simplifies 
the issue and makes them easier to value than real assets. In this section, we will 
compute, evaluate, and compare various measures of return and risk.
2.1 Return
Financial assets normally generate two types of return for investors. First, they may 
provide periodic income through cash dividends or interest payments. Second, the 
price of a financial asset can increase or decrease, leading to a capital gain or loss.

Certain financial assets, through design or choice, provide return through only 
one of these mechanisms. For example, investors in non-  dividend-  paying stocks, 
such as Google or Baidu, obtain their return from capital appreciation only. Similarly, 
you could also own or have a claim to assets that only generate periodic income. For 
example, defined benefit pension plans, retirement annuities, and reverse mortgages1 
make income payments as long as you live.2
1 A reverse mortgage is a type of loan that allows individuals to convert part of their home equity into 
cash. The loan is usually disbursed in a stream of payments made to the homeowner by the lender. As long 
as the homeowner lives in the home, they need not be repaid during the lifetime of the homeowner. The 
loan, however, can be paid off at any time by the borrower not necessarily by selling the home.

Investment Characteristics of Assets 245
You should be aware that returns reported for stock indexes are sometimes mis -
leading because most index levels only capture price appreciation and do not adjust 
for cash dividends unless the stock index is labeled “total return” or “net dividends 
reinvested. ” For example, as reported by Yahoo! Finance, the S&P 500 Index of US 
stocks was at 903.25 on 31 December 2008. Similarly, Yahoo! Finance reported that 
the index closed on 30 July 2002 at 902.78, implying a return of close to 0 percent 
over the approximately six-  and-  a-half-  year period. The results are very different, 
however, if the total return S&P 500 Index is considered. The index was at 1283.62 
on 30 July 2002 and had risen 13.2 percent to 1452.98 on 31 December 2008, giving 
an annual return of 1.9 percent. The difference in the two calculations arises from 
the fact that index levels reported by Yahoo! Finance and other reporting agencies do

not include cash dividends, which are an important part of the total return. Thus, it 
is important to recognize and account for income from investments.
In the following subsection, we consider various types of returns, their computa -
tion, and their application.
2.1.1  Holding Period Return
Returns can be measured over a single period or over multiple periods. Single period 
returns are straightforward because there is only one way to calculate them. Multiple 
period returns, however, can be calculated in various ways and it is important to be 
aware of these differences to avoid confusion.
A holding period return  is the return earned from holding an asset for a single 
specified period of time. The period may be 1 day, 1 week, 1 month, 5 years, or any 
specified period. If the asset (bond, stock, etc.) is bought now, time ( t – 1), at a price 
of 100 and sold later, say at time t, at a price of 105 with no dividends or other income,

then the holding period return is 5 percent [(105 – 100)/100)]. If the asset also pays 
an income of 2 units at time t, then the total return is 7 percent. This return can be 
generalized and shown as a mathematical expression:
RPP D
PPP
PD
Ptt t
ttt
tt
t=−+=−+=−
−−
−−1
11
11Capital  gain + Div idend d yield
=+−PD
PTT
01
In the above expression, P is the price and D is the dividend. The subscript indi -
cates the time of that price or dividend, t – 1, is the beginning of the period and t is 
the end of the period. The following two observations are important.
■■We computed a capital gain of 5 percent and a dividend yield of 2 percent in the 
above example. For ease of illustration, we assumed that the dividend is paid at 
time t. If the dividend was received any time before t, our holding period return 
would have been higher because we would have earned a return by putting the 
dividend in the bank for the remainder of the period.

■■Return can be expressed in decimals (0.07), fractions (7/100), or as a percent 
(7%). They are all equivalent.
The holding period return can be computed for a period longer than one year. For 
example, you may need to compute a three-  year holding period return from three 
annual returns. In that case, the holding period return is computed by compounding 
the three annual returns: R = [(1 + R1) × (1 + R2) × (1 + R3)] – 1, where R1, R2, and 
R3 are the three annual returns.
In this and succeeding parts of Section 2.1, we consider the aggregation of several 
single period returns.

Reading 39 ■ Portfolio Risk and Return: Part I 246
2.1.2  Arithmetic or Mean Return
When assets have returns for multiple holding periods, it is necessary to aggregate 
those returns into one overall return for ease of comparison and understanding. It 
is also possible to compute the return for a long or an unusual holding period. Such 
returns, however, may be difficult to interpret. For example, a return of 455 percent 
earned by AstraZeneca PLC over the last 16 years (1993 to 2008) may not be meaningful 
unless all other returns are computed for the same period. Therefore, most holding 
period returns are reported as daily, monthly, or annual returns.
Aggregating returns across several holding periods becomes a challenge and can 
lead to different conclusions depending on the method of aggregation. The remainder 
of this section is designed to present various ways of computing average returns as 
well as discussing their applicability.

The simplest way to compute the return is to take the simple average of all holding 
period returns. Thus, three annual returns of –50 percent, 35 percent, and 27 percent 
will give us an average of 4 percent per year =−+ + 

50 35 27
3%% %. The arithmetic 
return is easy to compute and has known statistical properties, such as standard 
deviation. We can calculate the arithmetic return and its standard deviation to deter -
mine how dispersed the observations are around the mean or if the mean return is 
statistically different from zero.
In general, the arithmetic or mean return is denoted by  Ri and given by the fol -
lowing equation for asset i, where Rit is the return in period t and T is the total number 
of periods:
RRR RR
TTRiii iT iT
it
tT
=++ ++=−
=∑12 1
11 ...,
2.1.3  Geometric Mean Return
The arithmetic mean return is the average of the returns earned on a unit of invest -

ment at the beginning of each holding period. It assumes that the amount invested 
at the beginning of each period is the same, similar to the concept of calculating 
simple interest. However, because the base amount changes each year (the previous 
year’s earnings needs to be added to or “compounded” to the beginning value of the 
investment), a holding or geometric period return may be quite different from the 
return implied by the arithmetic return. The geometric mean return assumes that the 
investment amount is not reset at the beginning of each year and, in effect, accounts 
for the compounding of returns. Basically, the geometric mean reflects a “buy-  and-  
hold” strategy, whereas the arithmetic reflects a constant dollar investment at the 
beginning of each time period.2
2 A buy-  and-  hold strategy assumes that the money invested initially grows or declines with time depend -
ing on whether a particular period’s return is positive or negative. On the one hand, a geometric return

compounds the returns and captures changes in values of the initial amount invested. On the other hand, 
arithmetic return assumes that we start with the same amount of money every period without compounding 
the return earned in a prior period.

Investment Characteristics of Assets 247
A geometric mean return provides a more accurate representation of the growth 
in portfolio value over a given time period than does an arithmetic mean return. In 
general, the geometric mean return is denoted by  RGi and given by the following 
equation for asset i:
RR RR R
RGi ii iT iTT
it
tT
T=+() ×+() ×× +() ×+() −
=+ () −−
=∏11 11 1
112 1
1,
1 1
where Rit is the return in period t and T is the total number of periods.
In the example in Section 2.1.2, we calculated the arithmetic mean to be 4 percent. 
Exhibit 1 shows the actual return for each year and the actual amount at the end of 
each year using actual returns. Beginning with an initial investment of €1.0000, we 
will have €0.8573 at the end of the three-  year period as shown in the third column. 
Note that we compounded the returns because, unless otherwise stated, we receive 
return on the amount at the end of the prior year. That is, we will receive a return of

35 percent in the second year on the amount at the end of the first year, which is only 
€0.5000, not the initial amount of €1.0000. Let us compare the actual amount at the end 
of the three-  year period, €0.8573, with the amount we get using an annual arithmetic 
mean return of 4 percent calculated above. The year-  end amounts are shown in the 
fourth column using the arithmetic return of 4 percent. At the end of the three-  year 
period, €1 will be worth €1.1249 (=1.0000 × 1.043). This ending amount of €1.1249 
is much larger than the actual amount of €0.8573. Clearly, the calculated arithmetic 
return is greater than the actual return. In general, the arithmetic return is biased 
upward unless the actual holding period returns are equal. The bias in arithmetic mean 
returns is particularly severe if holding period returns are a mix of both positive and 
negative returns, as in the example.
For our example and using the above formula, the geometric mean return per

year is –5.0 percent, compared with an arithmetic mean return of 4.0 percent. The 
last column of Exhibit 1 shows that using the geometric return of –5.0 percent gener -
ates a value of €0.8574 at the end of the three-  year period, which is very close to the 
actual value of €0.8573. The small difference in ending values is the result of a slight 
approximation used in computing the geometric return of –5.0 percent. Because of 
the effect of compounding, the geometric mean return is always less than or equal to 
the arithmetic mean return,  RRGi i   <, unless there is no variation in returns, in which 
case they are equal.
Exhibit 1   
Actual Return 
for the Y ear 
(%)Y ear-  End 
Actual 
AmountY ear-  End Amount 
Using Arithmetic 
Return of 4%Y ear-  End 
Amount Using 
Geometric 
Return of –5%
Year 0 €1.0000 €1.0000 €1.0000
Year 1 –50 0.5000 1.0400 0.9500
Year 2 35 0.6750 1.0816 0.9025
Year 3 27 0.8573 1.1249 0.8574

Reading 39 ■ Portfolio Risk and Return: Part I 248
2.1.4  Money-  Weighted Return or Internal Rate of Return
The above return computations do not account for the amount of money invested 
in different periods. It matters to an investor how much money was invested in each 
of the three years. If she had invested €10,000 in the first year, €1,000 in the second 
year, and €1,000 in the third year, then the return of –50  percent in the first year 
significantly hurts her. On the other hand, if she had invested only €100 in the first 
year, the effect of the –50 percent return is drastically reduced.
The money-  weighted return  accounts for the money invested and provides the 
investor with information on the return she earns on her actual investment. The 
money-  weighted return and its calculation are similar to the internal rate of return  
and the yield to maturity. Just like the internal rate of return, amounts invested are

cash outflows from the investor’s perspective and amounts returned or withdrawn by 
the investor, or the money that remains at the end of an investment cycle, is a cash 
inflow for the investor.
The money-  weighted return can be illustrated most effectively with an example. In 
this example, we use the actual returns from the previous example. Assume that the 
investor invests €100 in a mutual fund at the beginning of the first year, adds another 
€950 at the beginning of the second year, and withdraws €350 at the end of the second 
year. The cash flows are shown in Exhibit 2.
Exhibit 2   
Y ear 1 2 3
Balance from previous year €0 €50 €1,000
New investment by the investor (cash 
inflow for the mutual fund) at the start of 
the year100 950 0
Net balance at the beginning of year 100 1,000 1,000
Investment return for the year –50% 35% 27%
Investment gain (loss) –50 350 270
Withdrawal by the investor (cash outflow 
for the mutual fund) at the end of the year0 –350 0

Balance at the end of year €50 €1,000 €1,270
The internal rate of return is the discount rate at which the sum of present values 
of these cash flows will equal zero. In general, the equation may be expressed as fol -
lows, where T is the number of periods, CFt is the cash flow at time t, and IRR is the 
internal rate of return or the money-  weighted rate of return:
 
IRRCFt
t
tT
10
0+()=
=∑
A cash flow can be positive or negative; a positive cash flow is an inflow where 
money flows to the investor, whereas a negative cash flow is an outflow where money 
flows away from the investor. We can compute the internal rate of return by using the 
above equation. The flows are expressed as follows, where each cash inflow or outflow 
occurs at the end of each year. Thus, CF0 refers to the cash flow at the end of Year 0

Investment Characteristics of Assets 249
or beginning of Year 1, and CF3 refers to the cash flow at end of Year 3 or beginning 
of Year 4. Because cash flows are being discounted to the present—that is, end of Year 
0 or beginning of Year 1—the period of discounting CF0 is zero.
CF 1
CF 95
CF 35
CF 127
CF
IRRCF
IRR1
2
30
0
01
100
0
0
0
11=−
=−
=+
=+
+()+
+()+,
CCF
IRRCF
IRR
IRRI RR2
23
3
1211
100
1950
1350
1+()+
+()
=−+−
+()++
+()++1 1270
10
26 113+()=
=IRR
IRR. %
IRR = 26.11% is the internal rate of return, or the money-  weighted rate of return, 
which tells the investor what she earned on the actual euros invested for the entire 
period. This return is much greater than the arithmetic and geometric mean returns 
because only a small amount was invested when the mutual fund’s return was 
–50 percent.
Although the money-  weighted return is an accurate measure of what the inves -
tor actually earned on the money invested, it is limited in its applicability to other

situations. For example, it does not allow for return comparison between different 
individuals or different investment opportunities. Two investors in the same  mutual 
fund may have different money-  weighted returns because they invested different 
amounts in different years.
2.1.5  Comparison of Returns
The previous subsections have introduced a number of return measures. The following 
example illustrates the computation, comparison, and applicability of each measure.
EXAMPLE 1   
Computation of Returns
Ulli Lohrmann and his wife, Suzanne Lohrmann, are planning for retirement 
and want to compare the past performance of a few mutual funds they are con -
sidering for investment. They believe that a comparison over a five-  year period 
would be appropriate. They are given the following information about the Rhein 
Valley Superior Fund that they are considering.
Y earAssets Under Management at the 
Beginning of Y ear (€) Net Return (%)
1 30 million 15
2 45 million –5
3 20 million 10
4 25 million 15

5 35 million 3
The Lohrmanns are interested in aggregating this information for ease of 
comparison with other funds.
1 Compute the holding period return for the five-  year period.
2 Compute the arithmetic mean annual return.

Reading 39 ■ Portfolio Risk and Return: Part I 250
3 Compute the geometric mean annual return. How does it compare with 
the arithmetic mean annual return?
4 The Lohrmanns want to earn a minimum annual return of 5 percent. Is 
the money-  weighted annual return greater than 5 percent?
The holding period return is R = (1 + R1)(1 + R2)(1 + R3)(1 + R4)(1 + R5) –1 = 
(1.15)(0.95)(1.10)(1.15)(1.03) –1 = 0.4235 = 42.35% for the five-  year period.
The arithmetic mean annual return can be computed as an arithmetic mean of 
the returns given by this equation: 
Ri=− +++=15 51 01 53
5760% %%% %.%
The geometric mean annual return can be computed using this equation:
RR RR RGi ii iT iTT=+() ×+() ×× +() ×+() −
=× ×− 11 11 1
1150 95 11012 1 ,
.. .××× −
=− ==1151 03 1
1 4235 10 0732 7325
5..
.. .%
Thus, the geometric mean annual return is 7.32 percent, slightly less than the 
arithmetic mean return.

To calculate the money-  weighted rate of return, tabulate the annual returns 
and investment amounts to determine the cash flows, as shown in Exhibit 3. 
All amounts are in millions of euros.
Exhibit 3   
Y ear 1 2 3 4 5
Balance from previous year 0 34.50 42.75 22.00 28.75
New investment by the 
investor (cash inflow for 
the Rhein fund) 30.00 10.50 0 3.00 6.25
Withdrawal by the investor 
(cash outflow for the Rhein 
fund) 0 0 –22.75 0 0
Net balance at the begin -
ning of year 30.00 45.00 20.00 25.00 35.00
Investment return for the 
year 15% –5% 10% 15% 3%
Investment gain (loss) 4.50 –2.25 2.00 3.75 1.05
Balance at the end of year 34.50 42.75 22.00 28.75 36.05
CF0 = –30.00, CF1 = –10.50, CF2 = +22.75, CF3 = –3.00, 
CF4 = –6.25, CF5 = +36.05.

Investment Characteristics of Assets 251
For clarification, it may be appropriate to explain the notation for cash flows. 
Each cash inflow or outflow occurs at the end of each year. Thus, CF0 refers to 
the cash flow at the end of Year 0 or beginning of Year 1, and CF5 refers to the 
cash flow at end of Year 5 or beginning of Year 6. Because cash flows are being 
discounted to the present—that is, end of Year 0 or beginning of Year 1—the 
period of discounting CF0 is zero whereas the period of discounting for CF5 is 
5 years.
To get the exact money-  weighted rate of return (IRR), the following equation 
would be equal to zero. Instead of calculating, however, use the 5 percent return 
to see whether the value of the expression is positive or not. If it is positive, then 
the money-  weighted rate of return is greater than 5 percent, because a 5 percent 
discount rate could not reduce the value to zero.
−
()+−
()+
()+−
()+− 30 00
10510 50
10522 75
105300
10562
01 23.
..
..
..
..5 5
10536 05
1051 147145..
..
()+

10562
01 23.
..
..
..
..5 5
10536 05
..
()+
()=
Because the value is positive, the money-  weighted rate of return is greater 
than 5 percent. Using a financial calculator, the exact money-  weighted rate of 
return is 5.86 percent.
2.1.6  Annualized Return
The period during which a return is earned or computed can vary and often we have 
to annualize a return that was calculated for a period that is shorter (or longer) than 
one year. You might buy a short-  term treasury bill with a maturity of 3 months, or you 
might take a position in a futures contract that expires at the end of the next quarter. 
How can we compare these returns? In many cases, it is most convenient to annualize 
all available returns. Thus, daily, weekly, monthly, and quarterly returns are converted 
to an annual return. In addition, many formulas used for calculating certain values 
or prices may require all returns and periods to be expressed as annualized rates of

return. For example, the most common version of the Black–Scholes option-  pricing 
model requires annualized returns and periods to be in years.
To annualize any return for a period shorter than one year, the return for the 
period must be compounded by the number of periods in a year. A monthly return is 
compounded 12 times, a weekly return is compounded 52 times, and a quarterly return 
is compounded 4 times. Daily returns are normally compounded 365 times. For an 
uncommon number of days, we compound by the ratio of 365 to the number of days.
If the weekly return is 0.2 percent, then the compound annual return is computed 
as shown because there are 52 weeks in a year:
rrannual weekl y =+() −= +() −
=() −= =11 10 21
1 002 10 1095 1052 52
52.%
.. ..% 95
If the return for 15 days is 0.4 percent, the annualized return is computed assuming 
365 days in a year. Thus,
rrannual =+() −= +() −
=() −=11 10 41
1 004 10 1015365 15 365 15
365 15.%
.. 2 20 10 20=.%

365 15.%
A general equation to annualize returns is given, where c is the number of periods 
in a year. For a quarter, c = 4 and for a month, c = 12:
rrannual periodc=+() −  1 1

Reading 39 ■ Portfolio Risk and Return: Part I 252
How can we annualize a return when the holding period return is more than one 
year? For example, how do we annualize an 18-  month holding period return? Because 
one year contains two-  thirds of 18-  month periods, c = 2/3 in the above equation. An 
18- month return of 20 percent can be annualized, as shown:
rrannual month =+() −= +() −= = 11 10 20 10 1292 12 921823 23.. .%
Similar expressions can be constructed when quarterly or weekly returns are 
needed for comparison instead of annual returns. In such cases, c is equal to the 
number of holding periods in a quarter or in a week. For example, assume that you 
want to convert daily returns to weekly returns or annual returns to weekly returns for 
comparison between weekly returns. For converting daily returns to weekly returns, c 
= 5, assuming that there are five trading days in a week. For converting annual returns

to weekly returns, c = 1/52. The expressions for annual returns can then be rewritten 
as expressions for weekly returns, as shown:
rr rrweekly daily weekly annual =+() −= +() − 11 115 152; 
One major limitation of annualizing returns is the implicit assumption that returns 
can be repeated precisely, that is, money can be reinvested repeatedly while earning 
a similar return. This type of return is not always possible. An investor may earn a 
return of 5 percent during a week because the market went up that week or he got 
lucky with his stock, but it is highly unlikely that he will earn a return of 5 percent 
every week for the next 51 weeks, resulting in an annualized return of 1,164.3 per -
cent (= 1.0552 – 1). Therefore, it is important to annualize short-  term returns with 
this limitation in mind. Annualizing returns, however, allows for comparison among 
different assets and over different time periods.
EXAMPLE 2   
Annualized Returns

EXAMPLE 2   
London Arbitrageurs, PLC employs many analysts who devise and implement 
trading strategies. Mr. Brown is trying to evaluate three trading strategies that 
have been used for different periods of time.
■■Keith believes that he can predict share price movements based on 
earnings announcements. In the last 100 days he has earned a return of 
6.2 percent.
■■Thomas has been very successful in predicting daily movements of the 
Australian dollar and the Japanese yen based on the carry trade. In the 
last 4 weeks, he has earned 2 percent after accounting for all transactions 
costs.
■■Lisa follows the fashion industry and luxury retailers. She has been invest -
ing in these companies for the last 3 months. Her return is 5 percent.
Mr. Brown wants to give a prize to the best performer but is somewhat confused 
by the returns earned over different periods. Annualize returns in all three cases 
and advise Mr. Brown.
Solution:

Solution:
Annualized return for Keith: RKeith  = (1 + 0.062)365/100 – 1 = 0.2455 = 24.55%
Annualized return for Thomas: RThomas  = (1 + 0.02)52/4 – 1 = 0.2936 = 
29.36%
Annualized return for Lisa: RLisa = (1 + 0.05)4 – 1 = 0.2155 = 21.55%

Investment Characteristics of Assets 253
Thomas earned the highest return and deserves the reward, assuming the per -
formance of all traders is representative of what they can achieve over the year.
2.1.7  Portfolio Return
When several individual assets are combined into a portfolio, we can compute the 
portfolio return as a weighted average of the returns in the portfolio. The portfolio 
return is simply a weighted average of the returns of the individual investments, or 
assets. If Asset 1 has a return of 20 percent and constitutes 25 percent of the portfo -
lio’s investment, then the contribution to the portfolio return is 5 percent (= 25% of 
20%). In general, if Asset i has a return of Ri and has a weight of wi in the portfolio, 
then the portfolio return, RP, is given as:
Rw RwPi i
iN
i
iN
==
==∑∑
111 ,   
Note that the weights must add up to 1 because the assets in a portfolio, includ -
ing cash, must account for 100 percent of the investment. Also, note that these are

single period returns, so there are no cash flows during the period and the weights 
remain constant.
A two-  asset portfolio is easier to work with, so we will use only two assets to 
illustrate most concepts. Extending the analysis to multiple assets, however, is easily 
achieved and covered in later sections. With only two assets in the portfolio, the port -
folio return can be written as shown, where w1 and w2 are weights in assets 1 and 2.
RP = w1R1 + w2R2
Because the portfolio consists of only two assets, the sum of the two weights should 
equal 100 percent. Therefore, w1 + w2 = 1 or w2 = (1 – w1). By substituting, we can 
rewrite the above equation as follows:
RP = w1R1 + (1 – w1)R2
2.2 Other Major Return Measures and their Applications
The statistical measures of return discussed in the previous section are generally 
applicable across a wide range of assets and time periods. Special assets, however, 
such as mutual funds, and other considerations, such as taxes or inflation, may require

return measures that are specific to a particular application.
Although it is not possible to consider all types of special applications, we will dis -
cuss the effect of fees (gross versus net returns), taxes (pre-  tax and after-  tax returns), 
inflation (nominal and real returns), and leverage . Many investors use mutual funds 
or other external entities (i.e., investment vehicles) for investment. In those cases, 
funds charge management fees and expenses to the investors. Consequently, gross and 
net- of- fund-  expense returns should also be considered. Of course, an investor may be 
interested in the net-  of- expenses after-  tax real return, which is in fact what an investor 
truly receives. We consider these additional return measures in the following sections.
2.2.1  Gross and Net Return
A gross return is the return earned by an asset manager prior to deductions for manage -
ment expenses, custodial fees, taxes, or any other expenses that are not directly related

to the generation of returns but rather related to the management and administration 
of an investment. These expenses are not deducted from the gross return because 
they may vary with the amount of assets under management or may vary because 
of the tax status of the investor. Trading expenses, however, such as commissions, 
are accounted for in (i.e., deducted from) the computation of gross return because

Reading 39 ■ Portfolio Risk and Return: Part I 254
trading expenses contribute directly to the return earned by the manager. Thus, gross 
return is an appropriate measure for evaluating and comparing the investment skill of 
asset managers because it does not include any fees related to the management and 
administration of an investment.
Net return is a measure of what the investment vehicle (mutual fund, etc.) has 
earned for the investor. Net return accounts for (i.e., deducts) all managerial and 
administrative expenses that reduce an investor’s return. Because individual investors 
are most concerned about the net return (i.e., what they actually receive), small mutual 
funds with a limited amount of assets under management are at a disadvantage com -
pared with the larger funds that can spread their largely fixed administrative expenses 
over a larger asset base. As a result, many small-  sized mutual funds waive part of the 
expenses to keep the funds competitive.

2.2.2  Pre-  tax and After-  tax Nominal Return
All return measures discussed previously are pre-  tax nominal returns—that is, no 
adjustment has been made for taxes or inflation. In general, all returns are pre-  tax 
nominal returns unless they are otherwise designated.
Investors are concerned about the tax liability of their returns because taxes reduce 
the actual return that they receive. The two types of returns, capital gains (change in 
price) and income (such as dividends or interest), are usually taxed differently. Capital 
gains come in two forms: short-  term capital gains and long-  term capital gains. Long-  
term capital gains typically receive preferential tax treatment in a number of countries. 
Interest income is taxed as ordinary income in most countries. Dividend income may 
be taxed as ordinary income, may have a lower tax rate, or may be exempt from taxes

depending on the country and the type of investor. The after-  tax nominal return is 
computed as the total return minus any allowance for taxes on realized gains.3
Because taxes are paid on realized capital gains and income, the investment manager 
can minimize the tax liability by selecting appropriate securities (e.g., those subject 
to more favorable taxation, all other investment considerations equal) and reducing 
trading turnover. Therefore, many investors evaluate investment managers based on 
the after-  tax nominal return.
2.2.3  Real Returns
A nominal return ( r) consists of three components: a real risk-  free return as com -
pensation for postponing consumption ( rrF), inflation as compensation for loss of 
purchasing power (π), and a risk premium  for assuming risk ( RP). Thus, nominal 
return and real return can be expressed as:
11 11
11 1
1+() =+() ×+() ×+()
+() =+() ×+()
+rr RP
rr RP
rrF
real rF
reπ
 or
a al r () =+() ÷+() 11 π

rr RP
rrF
real rF
reπ
 or
Often the real risk-  free return and the risk premium are combined to arrive at the 
real “risky” rate as given in the second equation above, simply referred to as the real 
return. Real returns are particularly useful in comparing returns across time periods 
because inflation rates may vary over time. Real returns are also useful in comparing 
returns among countries when returns are expressed in local currencies instead of 
a constant investor currency in which inflation rates vary between countries (which 
are usually the case). Finally, the after-  tax real return is what the investor receives as 
compensation for postponing consumption and assuming risk after paying taxes on 
investment returns. As a result, the after-  tax real return becomes a reliable benchmark 
3 Bonds issued at a discount to the par value may be taxed based on accrued gains instead of realized gains.

Investment Characteristics of Assets 255
for making investment decisions. Although it is a measure of an investor’s bench -
mark return, it is not commonly calculated by asset managers because it is difficult 
to estimate a general tax component applicable to all investors. For example, the tax 
component depends on an investor’s specific taxation rate (marginal tax rate), how 
long the investor holds an investment (long-  term versus short-  term), and the type of 
account the asset is held in (tax-  exempt, tax-  deferred, or normal).
2.2.4  Leveraged Return
In the previous calculations, we have assumed that the investor’s position in an asset 
is equal to the total investment made by an investor using his or her own money. This 
section differs in that the investor creates a leveraged position. There are two ways 
of creating a claim on asset returns that are greater than the investment of one’s own 
money. First, an investor may trade futures contracts in which the money required

to take a position may be as little as 10 percent of the notional value of the asset. In 
this case, the leveraged return, the return on the investor’s own money, is 10 times 
the actual return of the underlying security. Note that both the gains and losses are 
amplified by a factor of 10.
Investors can also invest more than their own money by borrowing money to pur -
chase the asset. This approach is easily done in stocks and bonds, and very common 
when investing in real estate. If half (50 percent) of the money invested is borrowed, 
then the asset return to the investor is doubled but the investor must account for 
interest to be paid on borrowed money.
EXAMPLE 3   
Computation of Special Returns
Let’s return to Example 1. After reading this section, Mr. Lohrmann decided 
that he was not being fair to the fund manager by including the asset manage -
ment fee and other expenses because the small size of the fund would put it at

a competitive disadvantage. He learns that the fund spends a fixed amount of 
€500,000 every year on expenses that are unrelated to the manager’s performance.
Mr. Lohrmann has become concerned that both taxes and inflation may 
reduce his return. Based on the current tax code, he expects to pay 20 percent 
tax on the return he earns from his investment. Historically, inflation has been 
around 2 percent and he expects the same rate of inflation to be maintained.
1 Estimate the annual gross return for the first year by adding back the fixed 
expenses.
2 What is the net return that investors in the Rhein Valley Superior Fund 
earned during the five-  year period?
3 What is the after-  tax net return for the first year that investors earned 
from the Rhein Valley Superior Fund? Assume that all gains are realized at 
the end of the year and the taxes are paid immediately at that time.
4 What is the anticipated after-  tax real return that investors would have 
earned in the fifth year?

The gross return for the first year is higher by 1.67 percent (= €500,000/€30,000,000) 
than the investor return reported by the fund. Thus, the gross return is 16.67 per -
cent (= 15% + 1.67%).

Reading 39 ■ Portfolio Risk and Return: Part I 256
The investor return reported by the mutual fund is the net return of the fund 
after accounting for all direct and indirect expenses. The net return is also the 
pre-  tax nominal return because it has not been adjusted for taxes or inflation. 
The net return for the five-  year holding period was 42.35 percent.
The net return earned by investors during the first year was 15 percent. Applying 
a 20 percent tax rate, the after-  tax return that accrues to the investors is 12 per -
cent [= 15% – (0.20 × 15%)].
As in Part 3, the after-  tax return earned by investors in the fifth year is 2.4 percent 
[= 3% – (0.20 × 3%)]. Inflation reduces the return by 2 percent so the after-  tax 
real return earned by investors in the fifth year is 0.39 percent, as shown:
12 40
12 00110 0240
10 020011 0039 10 003+()
+()−=+()
+()−= −=.%
.%.
... 990 39=.%
Note that taxes are paid before adjusting for inflation.

2.3 Variance and Covariance of Returns
Having discussed the various kinds of returns in considerable detail, we now turn to 
measures of riskiness of those returns. Just like return, there are various kinds of risk. 
For now, we will consider the total risk of an asset or a portfolio of assets as measured 
by its standard deviation, which is the square root of variance.
2.3.1  Variance of a Single Asset
Variance , or risk, is a measure of the volatility or the dispersion of returns. Variance is 
measured as the average squared deviation from the mean. Higher variance suggests 
less predictable returns and therefore a more risky investment. The variance (σ2) of 
asset returns is given by the following equation,
σµ
22
1=−()
=∑R
Tt
tT
where Rt is the return for period t, T is the total number of periods, and μ is the mean 
of T returns, assuming T is the population of returns.
If only a sample of returns is available instead of the population of returns (as is

usually the case in the investment world), then the above expression underestimates 
the variance. The correction for sample  variance is made by replacing the denominator 
with ( T – 1), as shown next, where  R is the mean return of the sample observations 
and s2 is the sample variance:
sRR
Tt
tT
22
1
1=−()
−=∑

Investment Characteristics of Assets 257
2.3.2  Standard Deviation of an Asset
The standard deviation  of returns of an asset is the square root of the variance of 
returns. The population  standard deviation (σ) and the sample  standard deviation ( s) 
are given below.
σµ
=−()
=−()
−==∑∑R
TsRR
Tt
tT
t
tT2
12
1
1;
Standard deviation is another measure of the risk of an asset, which may also be 
referred to as its volatility. In a later section, we will decompose this risk measure 
into its separate components.
2.3.3  Variance of a Portfolio of Assets
Like a portfolio’s return, we can calculate a portfolio’s variance. When computing 
the variance of portfolio returns, standard statistical methodology can be used by 
finding the variance of the full expression of portfolio return. Although the return 
of a portfolio is simply a weighted average of the returns of each security, this is not 
the case with the standard deviation of a portfolio (unless all securities are perfectly

correlated—that is, correlation equals one). Variance can be expressed more generally 
for N securities in a portfolio using the notation from section 2.1.7 of this reading:
w
Rw Ri
iN
PP ii
iN=
= () =

=
=∑
∑1
1
2
1σ VarV ar  
The right side of the equation is the variance of the weighted average returns 
of individual securities. Weight is a constant, but the returns are variables whose 
variance is shown by Var( Ri). We can rewrite the equation as shown next. Because 
the covariance of an asset with itself is the variance of the asset, we can separate the 
variances from the covariances in the second equation:
σ
σPi ji j
ijN
Pi i
iN
ij ijww RR
wR ww RR2
1
22
1= ()
= ()+ (=
=∑
∑Cov
VarC ov,
,,
) )
=≠∑
ij ijN
,,1
Cov( Ri,Rj) is the covariance of returns, Ri and Rj, and can be expressed as the 
product of the correlation between the two returns (ρ1,2) and the standard deviations 
of the two assets. Thus, Cov( Ri,Rj) = ρijσiσj.
For a two asset portfolio, the expression for portfolio variance simplifies to the

following using covariance and then using correlation:
σσ σ
σσ σρP
Pww ww RR
ww ww2
12
12
22
22
12 12
2
12
12
22
22
12 12
2=+ + ()
=+ +Cov,
221 2σσ
The standard deviation of a two asset portfolio is given by the square root of the 
portfolio’s variance:
σσ σP ww ww RR =+ + () 12
12
22
22
12 12 2C ov ,
or,
σσ σρ σσP ww ww =+ +12
12
22
22
12 1212 2

Reading 39 ■ Portfolio Risk and Return: Part I 258
EXAMPLE 4   
Return and Risk of a Two-  Asset Portfolio
Assume that as a US investor, you decide to hold a portfolio with 80 percent 
invested in the S&P 500 US stock index and the remaining 20 percent in the 
MSCI Emerging Markets index. The expected return is 9.93  percent for the 
S&P 500 and 18.20 percent for the Emerging Markets index. The risk (standard 
deviation) is 16.21 percent for the S&P 500 and 33.11 percent for the Emerging 
Markets index. What will be the portfolio’s expected return and risk given 
that the covariance between the S&P 500 and the Emerging Markets index is 
0.5 percent or 0.0050? Note that units for covariance and variance are written 
as %2 when not expressed as a fraction. These are units of measure like squared 
feet and the numbers themselves are not actually squared.
Solution:
Portfolio return, RP = w1R1 + (1 – w1), R2 = (0.80 × 0.0993) + (0.20 × 0.1820) 
= 0.1158 = 11.58%.
Portfolio ris k== ++ () σσ σP ww wwCovRR12

12
22
22
12 12 2,
σσ σ
σpU SUSE ME MU SEMU SEM
pww ww Cov22 22 2
22 22
0800 1621 0=+ +
=×() +,
.. .. .
...
..20 0 3311
20 80 0200 0050
0 01682 0 00439 022
2× ()
+ ×××()
=+ + 
σp .. .
.. %00160 0 02281
0 15103 15 10=
==σp
The portfolio’s expected return is 11.58 percent and the portfolio’s risk is 
15.10 percent. Look at this example closely. It shows that we can take the port -
folio of a US investor invested only in the S&P 500, combine it with a riskier  
portfolio consisting of emerging markets securities, and the return of the US 
investor increases from 9.93 percent to 11.58 percent while the risk of the port -
folio actually falls from 16.21 percent to 15.10 percent. Exhibit 4 depicts how 
the combination of the two assets results in a superior risk–return trade-  off. 
Not only does the investor get a higher return, but he also gets it at a lower risk. 
That is the power of diversification as you will see later in this reading.

Investment Characteristics of Assets 259
Exhibit 4   Combination of Two Assets
S&P 500PortfolioEmerging
Markets
10%20%Expected Portfolio Return E (Rp)
20% 30% 10%
Standard Deviation of Portfolio σpρ = 0.093
2.4 Historical Return and Risk
At this time, it is beneficial to look at historical risk and returns for the three main 
asset categories: stocks, bonds, and Treasury bills. Stocks refer to corporate owner -
ship, bonds refer to long-  term fixed-  income securities, and Treasury bills refer to 
short-  term government debt securities. Although there is generally no expectation 
of default on government securities, long-  term government bond prices are volatile 
(risky) because of possible future changes in interest rates. In addition, bondholders 
also face the risk that inflation will reduce the purchasing power of their cash flows.
2.4.1  Historical Mean Return and Expected Return
Before examining historical data, it is useful to distinguish between the historical mean

return and expected return, which are very different concepts but easy to confuse. 
Historical return is what was actually earned in the past , whereas expected return is 
what an investor anticipates to earn in the future .
Expected return is the nominal return that would cause the marginal investor 
to invest in an asset based on the real risk-  free interest rate ( rrF), expected inflation 
[E(π)], and expected risk premium for the risk of the asset [ E(RP)]. The real risk-  free 
interest rate is expected to be positive as compensation for postponing consumption. 
Similarly, the risk premium is expected to be positive in most cases.4 The expected 
inflation rate is generally positive, except when the economy is in a deflationary state 
4 There are exceptions when an asset reduces overall risk of a portfolio. We will consider those exceptions 
in section 4.3.

Reading 39 ■ Portfolio Risk and Return: Part I 260
and prices are falling. Thus, expected return is generally positive. The relationship 
between the expected return and the real risk-  free interest rate, inflation rate, and 
risk premium can be expressed by the following equation:
1 + E(R) = (1 + rrF) × [1 + E(π)] × [1 + E(RP)]
The historical mean return for investment in a particular asset, however, is obtained 
from the actual return that was earned by an investor. Because the investment is 
risky, there is no guarantee that the actual return will be equal to the expected return. 
In fact, it is very unlikely that the two returns are equal for a specific time period 
being considered. Given a long enough period of time, we can expect  that the future 
(expected) return will equal the average historical return. Unfortunately, we do not 
know how long that period is—10 years, 50 years, or 100 years. As a practical matter,

we often assume that the historical mean return is an adequate representation of the 
expected return, although this assumption may not be accurate. For example, Exhibit 5 
shows that the historical equity returns in the last nine years (2000–2008) for large 
US company stocks were negative whereas the expected return was nearly always 
positive. Nonetheless, longer-  term returns (1926–2008) were positive and could be 
consistent with expected return. Though it is unknown if the historical mean returns 
accurately represent expected returns, it is an assumption that is commonly made.
Exhibit 5   Risk and Return for US Asset Classes by Decade (%)
1930s 1940s 1950s 1960s 1970s 1980s 1990s 2000s* 1926–2008
Large company 
stocksReturn –0.1 9.2 19.4 7.8 5.9 17.6 18.2 –3.6 9.6
Risk 41.6 17.5 14.1 13.1 17.2 19.4 15.9 15.0 20.6
Small company 
stocksReturn 1.4 20.7 16.9 15.5 11.5 15.8 15.1 4.1 11.7
Risk 78.6 34.5 14.4 21.5 30.8 22.5 20.2 24.5 33.0
Long-  term corpo -

rate bondsReturn 6.9 2.7 1.0 1.7 6.2 13.0 8.4 8.2 5.9
Risk 5.3 1.8 4.4 4.9 8.7 14.1 6.9 11.3 8.4
Long-  term govern -
ment bondsReturn 4.9 3.2 –0.1 1.4 5.5 12.6 8.8 10.5 5.7
Risk 5.3 2.8 4.6 6.0 8.7 16.0 8.9 11.7 9.4
Treasury bills Return 0.6 0.4 1.9 3.9 6.3 8.9 4.9 3.1 3.7
Risk 0.2 0.1 0.2 0.4 0.6 0.9 0.4 0.5 3.1
Inflation Return –2.0 5.4 2.2 2.5 7.4 5.1 2.9 2.5 3.0
Risk 2.5 3.1 1.2 0.7 1.2 1.3 0.7 1.6 4.2
* Through 31 December 2008.
Note : Returns are measured as annualized geometric mean returns.
Risk is measured by annualizing monthly standard deviations.
Source:  2009 Ibbotson SBBI Classic Yearbook (Tables 2-  1, 6-  1, C-  1 to C-  7).
Going forward, be sure to distinguish between expected return and historical 
mean return. We will alert the reader whenever historical returns are used to estimate 
expected returns.
2.4.2  Nominal Returns of Major US Asset Classes
We focus on three major asset categories in Exhibit  5: stocks, bonds, and T-  bills.

The mean nominal returns for US asset classes are reported decade by decade since 
the 1930s. The total for the 1926–2008 period is in the last column. All returns are 
annual geometric mean returns. Large company stocks had an overall annual return of 
9.6 percent during the 83-  year period. The return was negative in the 1930s and 2000s,

Investment Characteristics of Assets 261
and positive in all remaining decades. The 1950s and 1990s were the best decades for 
large company stocks. Small company stocks fared even better. The nominal return 
was never negative for any decade, and had double-  digit growth in all decades except 
two, leading to an overall 83-  year annual return of 11.7 percent.
Long-  term corporate bonds and long-  term government bonds earned overall 
returns of 5.9 percent and 5.7 percent, respectively. The corporate bonds did not have 
a single negative decade, although government bonds recorded a negative return in 
the 1950s when stocks were doing extremely well. Bonds also had some excellent 
decades, earning double-  digit returns in the 1980s and 2000s.
Treasury bills (short-  term government securities) did not earn a negative return 
in any decade. In fact, Treasury bills earned a negative return only in 1938 (–0.02 per -

cent) when the inflation rate was –2.78  percent. Consistently positive returns for 
Treasury bills are not surprising because nominal interest rates are almost never 
negative and the Treasury bills suffer from little interest rate or inflation risk. Since 
the Great Depression, there has been no deflation in any decade, although inflation 
rates were highly negative in 1930 (–6.03 percent), 1931 (–9.52 percent), and 1932 
(–10.30  percent). Conversely, inflation rates were very high in the late 1970s and 
early 1980s, reaching 13.31 percent in 1979. Inflation rates have fallen since then to 
a negligible level of 0.09 percent in 2008. Overall, the inflation rate was 3.0 percent 
for the 83-  year period.
2.4.3  Real Returns of Major US Asset Classes
Because inflation rates can vary greatly, from –10.30 percent to +13.31 percent in the 
last 83 years, comparisons across various time periods is difficult and misleading using

nominal returns. Therefore, it is more effective to rely on real returns. Real returns on 
stocks, bonds, and T-  bills are reported from 1900 in Exhibits 6 and 7.
Exhibit 6   Cumulative Returns on US Asset Classes in Real Terms, 1900–2011
834
9.3
2.8
01101001,000
1900 10 20 30 40 50 60 70 80 90 2000 10
Equities  6.2%  p.a. Bonds 2.0%  p.a. Bills 0.9%  p.a.0.1
Source:  E. Dimson, P . Marsh, and M. Staunton, Credit Suisse Global Investment Returns Yearbook 2012 , Credit Suisse Research Institute 
(February 2009). This chart is updated annually and can be found at www.tinyurl.com/DMSsourcebook.

Reading 39 ■ Portfolio Risk and Return: Part I 262
Exhibit 6 shows that $1 would have grown to $834 if invested in stocks, to only 
$9.30 if invested in bonds, and to $2.80 if invested in T-  bills. The difference in growth 
among the three asset categories is huge, although the difference in real returns does 
not seem that large: 6.2 percent per year for equities compared with 2.0 percent per 
year for bonds. This difference represents the effect of compounding over a 112-  year 
period. 
Exhibit 7 reports both the nominal and real rates of return. As we discussed earlier 
and as shown in the table, geometric mean is never greater than the arithmetic mean. 
Our analysis of returns focuses on the geometric mean because it is a more accurate 
representation of returns for multiple holding periods than the arithmetic mean. We 
observe that the real returns for US stocks are higher than the real returns for US

bonds, and that the real returns for bonds are higher than the real returns for US T-  bills.
Exhibit 7   Nominal Returns, Real Returns and Risk Premiums for Asset Classes (1900–2008)
United States WorldWorld excluding  
Asset GM (%) AM (%) SD (%) GM (%) AM (%) SD (%) GM (%) AM (%) SD (%)
Nominal 
ReturnsEquities 9.2 11.1 20.2 8.4 9.8 17.3 7.9 9.7 20.1
Bonds 5.2 5.5 8.3 4.8 5.2 8.6 4.2 5.0 13.0
Bills 4.0 4.0 2.8 — — — — — —
Inflation 3.0 3.1 4.9 — — — — — —
Real Returns Equities 6.0 8.0 20.4 5.2 6.7 17.6 4.8 6.7 20.2
Bonds 2.2 2.6 10.0 1.8 2.3 10.3 1.2 2.2 14.1
Bills 1.0 1.1 4.7 — — — — — —
Premiums Equities vs. 
bills5.0 7.0 19.9 — — — — — —
Equities vs. 
bonds3.8 5.9 20.6 3.4 4.6 15.6 3.5 4.7 15.9
Bonds vs. bills 1.1 1.4 7.9 — — — — — —
Note : All returns are in percent per annum measured in US$. GM = geometric mean, AM = arithmetic mean, SD = standard deviation.

“World” consists of 17 developed countries: Australia, Belgium, Canada, Denmark, France, Germany, Ireland, Italy, Japan, the Netherlands, 
Norway, South Africa, Spain, Sweden, Switzerland, United Kingdom, and the United States. Weighting is by each country’s relative market 
capitalization size.
Sources:  Credit Suisse Global Investment Returns Sourcebook, 2009. Compiled from tables 62, 65, and 68. T-  bills and inflation rates are 
not available for the world and world excluding the United States.
2.4.4  Nominal and Real Returns of Asset Classes in Major Countries
Along with US returns, returns of major asset classes for a 17-  country world and the 
world excluding the United States are also presented in Exhibit 7. Equity returns are 
weighted by each country’s GDP before 1968 because of a lack of reliable market cap -
italization data. Returns are weighted by a country’s market capitalization beginning 
with 1968. Similarly, bond returns are defined by a 17-  country bond index, except GDP

is used to create the weights because equity market capitalization weighting is inap -
propriate for a bond index and bond market capitalizations were not readily available.
The nominal mean return for the world stock index over the last 109 years was 
8.4 percent, and bonds had a nominal geometric mean return of 4.8 percent. The nom -
inal geometric mean returns for the world excluding the United States are 7.9 percent 
for stocks and 4.2 percent for bonds. For both stocks and bonds, the United States 
has earned higher returns than the world excluding the United States. Similarly, real

Investment Characteristics of Assets 263
returns for stocks and bonds in the United States are higher than the real returns for 
rest of the world. No separate information is available for Treasury bills for non-  US 
2.4.5  Risk of Major Asset Classes
Risk for major asset classes in the United States is reported for 1926–2008 in Exhibit 5, 
and the risk for major asset classes for the United States, the world, and the world 
excluding the United States are reported for 1900–2008 in Exhibit 7. Exhibit 5 shows 
that US small company stocks had the highest risk, 33.0 percent, followed by US large 
company stocks, 20.6 percent. Long-  term government bonds and long-  term corporate 
bonds had lower risk at 9.4 percent and 8.4 percent, with Treasury bills having the 
lowest risk at about 3.1 percent.
Exhibit 7 shows that the risk for world stocks is 17.3 percent and for world bonds 
is 8.6 percent. The world excluding the United States has risks of 20.1 percent for

stocks and 13.0 percent for bonds. The effect of diversification is apparent when world 
risk is compared with US risk and world excluding US risk. Although the risk of US 
stocks is 20.2 percent and the risk of world excluding US stocks is 20.1 percent, the 
combination gives a risk of only 17.3 percent for world stocks. We can see a similar 
impact for world bonds when compared with US bonds and world bonds excluding 
US bonds. We observe a similar pattern in the risk levels of real returns.
2.4.6  Risk–Return Trade-  off
The expression “risk–return trade-  off” refers to the positive relationship between 
expected risk and return. In other words, a higher return is not possible to attain in 
efficient markets and over long periods of time without accepting higher risk. Expected 
returns should be greater for assets with greater risk.
The historical data presented above show the risk–return trade-  off. Exhibit 5 shows

for the United States that small company stocks had higher risk and higher return 
than large company stocks. Large company stocks had higher returns and higher 
risk than both long-  term corporate bonds and government bonds. Bonds had higher 
returns and higher risk than Treasury bills. Uncharacteristically, however, long-  term 
government bonds had higher total risk than long-  term corporate bonds, although 
the returns of corporate bonds were slightly higher. These factors do not mean that 
long-  term government bonds had greater default risk, just that they were more variable 
than corporate bonds during this historic period.
Turning to real returns, we find the same pattern: Higher returns were earned 
by assets with higher risk. Exhibit 7 reveals that the risk and return for stocks were 
the highest of the asset classes, and the risk and return for bonds were lower than 
stocks for the United States, the world, and the world excluding the United States. US

Treasury bills had the lowest return and lowest risk among T-  bills, bonds, and stocks.
Another way of looking at the risk–return trade-  off is to focus on the risk pre -
mium , which is the extra return investors can expect for assuming additional risk, 
after accounting for the nominal risk-  free interest rate (includes both compensation 
for expected inflation and the real risk-  free interest rate). Worldwide equity risk pre -
miums reported at the bottom of Exhibit 7 show that equities outperformed bonds 
and bonds outperformed T-  bills. Investors in equities earned a higher return than 
investors in T-  bills because of the higher risk in stocks. Conversely, investors in T-  bills 
cannot expect to earn as high a return as equity investors because the risk of their 
holdings is much lower.
A more dramatic representation of the risk–return trade-  off is shown in Exhibit 6, 
which shows the cumulative returns of US asset classes in real terms. The line rep -

resenting T-  bills is much less volatile than the other lines. Adjusted for inflation, the 
average real return on T-  bills was 0.9 percent per year. The line representing bonds 
is more volatile than the line for T-  bills but less volatile than the line representing

Reading 39 ■ Portfolio Risk and Return: Part I 264
stocks. The total return for equities including dividends and capital gains shows how 
$1 invested at the beginning of 1900 grows to $834, generating an annualized return 
of 6.2 percent in real terms.
Over long periods of time, we observe that higher risk does result in higher mean 
returns. Thus, it is reasonable to claim that, over the long term, market prices reward 
higher risk with higher returns, which is a characteristic of a risk-  averse investor, a 
topic that we discuss in Section 3.
2.5 Other Investment Characteristics
In evaluating investments using mean (expected return) and variance (risk), we make 
two important assumptions. First, we assume that the returns are normally distributed 
because a normal distribution can be fully characterized by its mean and variance. 
Second, we assume that markets are not only informationally efficient but that they

are also operationally efficient. To the extent that these assumptions are violated, we 
need to consider additional investment characteristics. These are discussed below.
2.5.1  Distributional Characteristics
As explained in an earlier reading, a normal distribution  has three main characteris -
tics: its mean and median are equal; it is completely defined by two parameters, mean 
and variance; and it is symmetric around its mean with:
■■68 percent of the observations within ±1σ of the mean,
■■95 percent of the observations within ±2σ of the mean, and
■■99 percent of the observations within ±3σ of the mean.
Using only mean and variance would be appropriate to evaluate investments if returns 
were distributed normally. Returns, however, are not normally distributed; deviations 
from normality occur both because the returns are skewed, which means they are not 
symmetric around the mean, and because the probability of extreme events is signifi -

cantly greater than what a normal distribution would suggest. The latter deviation is 
referred to as kurtosis or fat tails in a return distribution. The next sections discuss 
these deviations more in-  depth.
Skewness  Skewness  refers to asymmetry of the return distribution, that is, returns 
are not symmetric around the mean. A distribution is said to be left skewed or nega -
tively skewed if most of the distribution is concentrated to the right, and right skewed 
or positively skewed if most is concentrated to the left. Exhibit  8 shows a typical 
representation of negative and positive skewness, whereas Exhibit 9 demonstrates the 
negative skewness of stock returns by plotting a histogram of US large company stock 
returns for 1926–2008.

Investment Characteristics of Assets 265
Exhibit 8   Skewness
Distribution Skewed to the Right (Positively Skewed) Distribution Skewed to the Left (Negatively Skewed)
Source:  Reprinted from Fixed Income Readings for the Chartered Financial Analyst ® Program.  Copyright CFA Institute.
Exhibit 9   Histogram of US Large Company Stock Returns, 1926–2008 (Percent)
19312008
19372002
1974
19392001
1973
1966
1957
19412000
1990
1981
1977
1969
1962
1953
1946
1940
1939
1934
1932
19292007
2005
1994
1993
1992
1987
1984
1978
1970
1960
1956
1948
19472006
2004
1988
1986
1979
1972
1971
1968
1965
1964
1959
1952
1949
1944
19262003
1999
1998
1996
1983
1982
1976
1967
1963
1961
1951
1943
19421997
1995
1991
1989
1985
1980
1975
1955
1950
1945
1938
1936
19271958
1935
19281954
1933
–60 –50 –40 –30 –20 0 –10 10 20 30 40 50 60 70
Source:  2009 Ibbotson SBBI Classic Yearbook (Table 2.2)
Kurtosis  Kurtosis  refers to fat tails or higher than normal probabilities for extreme 
returns and has the effect of increasing an asset’s risk that is not captured in a mean–

variance framework, as illustrated in Exhibit 10. Investors try to evaluate the effect of 
kurtosis by using such statistical techniques as value at risk (VaR) and conditional tail 
expectations.5 Several market participants note that the probability and the magnitude 
5 Value at risk is a money measure of the minimum losses expected on a portfolio during a specified time 
period at a given level of probability. It is commonly used to measure the losses a portfolio can suffer under 
normal market conditions. For example, if a portfolio’s one-  day 10 percent VaR is £200,000, it implies that 
there is a 10 percent probability that the value of the portfolio will decrease by more than £200,000 over 
a single one-  day period (under normal market conditions). This probability implies that the portfolio will 
experience a loss of at least £200,000 on one out of every ten days.

Reading 39 ■ Portfolio Risk and Return: Part I 266
of extreme events is underappreciated and was a primary contributing factor to the 
financial crisis of 2008.6 The higher probability of extreme negative outcomes among 
stock returns can also be observed in Exhibit 9.
Exhibit 10   Kurtosis
0 1 2 3 4 5
Standard DeviationsFat Tails Distribution
Normal Distribution
–1 –2 –3 –4 –5
Source:  Reprinted from Fixed Income Readings for the Chartered Financial Analyst® Program.  
Copyright CFA Institute.
2.5.2  Market Characteristics
In the previous analysis, we implicitly assumed that markets are both informationally 
and operationally efficient. Although informational efficiency of markets is a topic 
beyond the purview of this reading, we should highlight certain operational limitations 
of the market that affect the choice of investments. One such limitation is liquidity .
The cost of trading has three main components—brokerage commission, bid–ask

spread, and price impact—of which liquidity affects the latter two. Brokerage commis -
sion is usually negotiable and does not constitute a large fraction of the total cost of 
trading except in small-  sized trades. Stocks with low liquidity can have wide bid–ask 
spreads. The bid–ask spread, which is the difference between the buying price and 
the selling price, is incurred as a cost of trading a security. The larger the bid–ask 
spread, the higher is the cost of trading. If a $100 stock has a spread of 10 cents, the 
bid–ask spread is only 0.1 percent ($0.10/$100). On the other hand, if a $10 stock has 
a spread of 10 cents, the bid–ask spread is 1 percent. Clearly, the $10 stock is more 
expensive to trade and an investor will need to earn 0.9 percent extra to make up the 
higher cost of trading relative to the $100 stock.
Liquidity also has implications for the price impact of trade. Price impact refers 
to how the price moves in response to an order in the market. Small orders usually

have little impact, especially for liquid stocks. For example, an order to buy 100 shares 
of a $100 stock with a spread of 1 cent may have no effect on the price. On the other 
hand, an order to buy 100,000 shares may have a significant impact on the price as the 
6 For example, see Bogle (2008) and Taleb (2007).

Risk Aversion and Portfolio Selection 267
buyer has to induce more and more stockholders to tender their shares. The extent of 
the price impact depends on the liquidity of the stock. A stock that trades millions of 
shares a day may be less affected than a stock that trades only a few hundred thou -
sand shares a day. Investors, especially institutional investors managing large sums of 
money, must keep the liquidity of a stock in mind when making investment decisions.
Liquidity is a bigger concern in emerging markets than in developed markets 
because of the smaller volume of trading in those markets. Similarly, liquidity is a 
more important concern in corporate bond markets and especially for bonds of lower 
credit quality than in equity markets because an individual corporate bond issue may 
not trade for several days or weeks. This certainly became apparent during the global 
financial crisis.
There are other market-  related characteristics that affect investment decisions

because they might instill greater confidence in the security or might affect the costs 
of doing business. These include analyst coverage, availability of information, firm 
size, etc. These characteristics about companies and financial markets are essential 
components of investment decision making.
RISK AVERSION AND PORTFOLIO SELECTION
As we have seen, stocks, bonds, and T-  bills provide different levels of returns and have 
different levels of risk. Although investment in equities may be appropriate for one 
investor, another investor may not be inclined to accept the risk that accompanies a 
share of stock and may prefer to hold more cash. In the last section, we considered 
investment characteristics of assets in understanding their risk and return. In this 
section, we consider the characteristics of investors, both individual and institutional, 
in an attempt to pair the right kind of investors with the right kind of investments.

First, we discuss risk aversion and utility theory. Later we discuss their implications 
for portfolio selection.
3.1 The Concept of Risk Aversion
The concept of risk aversion  is related to the behavior of individuals under uncer -
tainty. Assume that an individual is offered two alternatives: one where he will get 
£50 for sure and the other is a gamble with a 50 percent chance that he gets £100 and 
50 percent chance that he gets nothing. The expected value in both cases is £50, one 
with certainty and the other with uncertainty. What will an investor choose? There 
are three possibilities: an investor chooses the gamble, the investor chooses £50 with 
certainty, or the investor is indifferent. Let us consider each in turn. However, please 
understand that this is only a representative example, and a single choice does not 
determine the risk aversion of an investor.
Risk Seeking
If an investor chooses the gamble, then the investor is said to be risk loving or risk

seeking. The gamble has an uncertain outcome, but with the same expected value 
as the guaranteed outcome. Thus, an investor choosing the gamble means that the 
investor gets extra “utility” from the uncertainty associated with the gamble. How 
much is that extra utility worth? Would the investor be willing to accept a smaller 
expected value because he gets extra utility from risk? Indeed, risk seekers will accept 
less return because of the risk that accompanies the gamble. For example, a risk seeker 
may choose a gamble with an expected value of £45 in preference to a guaranteed 
outcome of £50.3

Reading 39 ■ Portfolio Risk and Return: Part I 268
There is a little bit of gambling instinct in many of us. People buy lottery tickets 
although the expected value is less than the money they pay to buy it. Or people 
gamble at casinos in Macau or Las Vegas with the full knowledge that the expected 
return is negative, a characteristic of risk seekers. These or any other isolated actions, 
however, cannot be taken at face value except for compulsive gamblers.
Risk Neutral
If an investor is indifferent about the gamble or the guaranteed outcome, then the 
investor may be risk neutral. Risk neutrality means that the investor cares only about 
return and not about risk, so higher return investments are more desirable even if they 
come with higher risk. Many investors may exhibit characteristics of risk neutrality 
when the investment at stake is an insignificant part of their wealth. For example, a 
billionaire may be indifferent about choosing the gamble or a £50 guaranteed outcome.
Risk Averse

If an investor chooses the guaranteed outcome, he/she is said to be risk averse  because 
the investor does not want to take the chance of not getting anything at all. Depending 
on the level of aversion to risk, an investor may be willing to accept a guaranteed 
outcome of £45 instead of a gamble with an expected value of £50.
In general, investors are likely to shy away from risky investments for a lower, but 
guaranteed return. That is why they want to minimize their risk for the same amount 
of return, and maximize their return for the same amount of risk. The risk–return 
trade-  off discussed earlier is an indicator of risk aversion. A risk-  neutral investor would 
maximize return irrespective of risk and a risk-  seeking investor would maximize both 
risk and return.
Data presented in the last section illustrate the historically positive relationship 
between risk and return, which demonstrates that market prices were based on trans -

actions and investments by risk-  averse investors and reflect risk aversion. Therefore, 
for all practical purposes and for our future discussion, we will assume that the repre -
sentative investor is a risk-  averse investor. This assumption is the standard approach 
taken in the investment industry globally.
Risk Tolerance
Risk tolerance  refers to the amount of risk an investor can tolerate to achieve an 
investment goal. The higher the risk tolerance, the greater is the willingness to take 
risk. Thus, risk tolerance is negatively related to risk aversion.
3.2 Utility Theory and Indifference Curves
Continuing with our previous example, a risk-  averse investor would rank the guar -
anteed outcome of £50 higher than the uncertain outcome with an expected value 
of £50. We can say that the utility that an investor or an individual derives from the 
guaranteed outcome of £50 is greater than the utility or satisfaction or happiness he/

she derives from the alternative. In general terms, utility is a measure of relative satis -
faction from consumption of various goods and services or in the case of investments, 
the satisfaction that an investor derives from different portfolios.
Because individuals are different in their preferences, all risk-  averse individuals 
may not rank investment alternatives in the same manner. Consider the £50 gamble 
again. All risk-  averse individuals will rank the guaranteed outcome of £50 higher than 
the gamble. What if the guaranteed outcome is only £40? Some risk-  averse investors 
might consider £40 inadequate, others might accept it, and still others may now be 
indifferent about the uncertain £50 and the certain £40.

Risk Aversion and Portfolio Selection 269
A simple implementation of utility theory allows us to quantify the rankings of 
investment choices using risk and return. There are several assumptions about indi -
vidual behavior that we make in the definition of utility given in the equation below. 
We assume that investors are risk averse. They always prefer more to less (greater 
return to lesser return). They are able to rank different portfolios in the order of their 
preference and that the rankings are internally consistent. If an individual prefers X 
to Y and Y to Z, then he/she must prefer X to Z. This property implies that the indif -
ference curves (see Exhibit 11) for the same individual can never touch or intersect. 
An example of a utility function is given below
UE rA =()−1
22σ
where, U is the utility of an investment, E(r) is the expected return, and σ2 is the 
variance of the investment.
In the above equation, A is a measure of risk aversion, which is measured as the

marginal reward that an investor requires to accept additional risk. More risk-  averse 
investors require greater compensation for accepting additional risk. Thus, A is higher 
for more risk-  averse individuals. As was mentioned previously, a risk-  neutral investor 
would maximize return irrespective of risk and a risk-  seeking investor would maxi -
mize both risk and return.
We can draw several conclusions from the utility function. First, utility is unbounded 
on both sides. It can be highly positive or highly negative. Second, higher return 
contributes to higher utility. Third, higher variance reduces the utility but the reduc -
tion in utility gets amplified by the risk aversion coefficient, A. Utility can always be 
increased, albeit marginally, by getting higher return or lower risk. Fourth, utility does 
not indicate or measure satisfaction. It can be useful only in ranking various invest -
ments. For example, a portfolio with a utility of 4 is not necessarily two times better

than a portfolio with a utility of 2. The portfolio with a utility of 4 could increase our 
happiness 10 times or just marginally. But we do prefer a portfolio with a utility of 
4 to a portfolio with a utility of 2. Utility cannot be compared among individuals or 
investors because it is a very personal concept. From a societal point of view, by the 
same argument, utility cannot be summed among individuals.
Let us explore the utility function further. The risk aversion coefficient, A, is greater 
than zero for a risk-  averse investor. So any increase in risk reduces his/her utility. The 
risk aversion coefficient for a risk-  neutral investor is 0, and changes in risk do not 
affect his/her utility. For a risk lover, the risk aversion coefficient is negative, creating 
an inverse situation so that additional risk contributes to an increase in his/her utility. 
Note that a risk-  free asset (σ2 = 0) generates the same utility for all individuals.
3.2.1  Indifference Curves

An indifference curve  plots the combinations of risk–return pairs that an investor 
would accept to maintain a given level of utility (i.e., the investor is indifferent about 
the combinations on any one curve because they would provide the same level of 
overall utility). Indifference curves are thus defined in terms of a trade-  off between 
expected rate of return and variance of the rate of return. Because an infinite number 
of combinations of risk and return can generate the same utility for the same investor, 
indifference curves are continuous at all points.

Reading 39 ■ Portfolio Risk and Return: Part I 270
Exhibit 11   Indifference Curves for Risk-  Averse InvestorsExpected  ReturnE(Ri)Low
Utility
xx
0
Standard Deviatio nModerate
UtilityHigh
Utility
σi12 3
ab
cx
A set of indifference curves is plotted in Exhibit 11. By definition, all points on any 
one of the three curves have the same utility. An investor does not care whether he/
she is at Point a or Point b on indifference Curve 1. Point a has lower risk and lower 
return than Point b, but the utility of both points is the same because the higher return 
at Point b is offset by the higher risk.
Like Curve 1, all points on Curve 2 have the same utility and an investor is indif -
ferent about where he/she is on Curve 2. Now compare Point c with Point b. Point c 
has the same risk but significantly lower return than Point b, which means that the 
utility at Point c is less than the utility at Point b. Given that all points on Curve 1 have

the same utility and all points on Curve 2 have the same utility and Point b has higher 
utility than Point c, Curve 1 has higher utility than Curve 2. Therefore, risk-  averse 
investors with indifference Curves 1 and 2 will prefer Curve 1 to Curve 2. The utility 
of risk-  averse investors always increases as you move northwest—higher return with 
lower risk. Because all investors prefer more utility to less, investors want to move 
northwest to the indifference curve with the highest utility.
The indifference curve for risk-  averse investors runs from the southwest to the 
northeast because of the risk–return trade-  off. If risk increases (going east) then it 
must be compensated by higher return (going north) to generate the same utility. The 
indifference curves are convex because of diminishing marginal utility of return (or 
wealth). As risk increases, an investor needs greater return to compensate for higher

risk at an increasing rate (i.e., the curve gets steeper). The upward-  sloping convex 
indifference curve has a slope coefficient closely related to the risk aversion coeffi -
cient. The greater the slope, the higher is the risk aversion of the investor as a greater 
increment in return is required to accept a given increase in risk.
Indifference curves for investors with different levels of risk aversion are plotted in 
Exhibit 12. The most risk-  averse investor has an indifference curve with the greatest 
slope. As volatility increases, this investor demands increasingly higher returns to 
compensate for risk. The least risk-  averse investor has an indifference curve with the 
least slope and so the demand for higher return as risk increases is not as acute as for 
the more risk-  averse investor. The risk-  loving investor’s indifference curve, however, 
exhibits a negative slope, implying that the risk-  lover is happy to substitute risk for

Risk Aversion and Portfolio Selection 271
return. For a risk lover, the utility increases both with higher risk and higher return. 
Finally, the indifference curves of risk-  neutral investors are horizontal because the 
utility is invariant with risk.
Exhibit 12   Indifference Curves for Various Types of Investors
0High Risk
AversionModerate Risk
Aversion
Low Risk
Aversion
Risk Lover12
3
4
5Expected Return
Standard DeviationE(Ri)
σi
In the remaining parts of this reading, all investors are assumed to be risk averse 
unless stated otherwise.
EXAMPLE 5   
Comparing a Gamble with a Guaranteed Outcome
Assume that you are given an investment with an expected return of 10 percent 
and a risk (standard deviation) of 20 percent, and your risk aversion coefficient 
is 3.
1 What is your utility of this investment?
2 What must be the minimum risk-  free return you should earn to get the 
same utility?
U = 0.10 – 0.5 × 3 × 0.202 = 0.04.

A risk-  free return’s σ is zero, so the second term disappears. To get the same 
utility (0.04), the risk-  free return must be at least 4 percent. Thus, in your mind, 
a risky return of 10 percent is equivalent to a risk-  free return or a guaranteed 
outcome of 4 percent.

Reading 39 ■ Portfolio Risk and Return: Part I 272
EXAMPLE 6   
Computation of Utility
Based on investment information given below and the utility formula U = E(r) 
– 0.5 Aσ2, answer the following questions. Returns and standard deviations are 
both expressed as percent per year. When using the utility formula, however, 
returns and standard deviations must be expressed in decimals.
InvestmentExpected Return 
E(r)Standard 
Deviation σ
1 12% 30%
2 15 35
3 21 40
4 24 45
1 Which investment will a risk-  averse investor with a risk aversion coeffi -
cient of 4 choose?
2 Which investment will a risk-  averse investor with a risk aversion coeffi -
cient of 2 choose?
3 Which investment will a risk-  neutral investor choose?
4 Which investment will a risk-  loving investor choose?
Solutions to 1 and 2:
The utility for risk-  averse investors with A = 4 and A = 2 for each of the four invest -
ments are shown in the following table. Complete calculations for Investment

1 with A = 4 are as follows: U = 0.12 – 0.5 × 4 × 0.302= –0.06.
InvestmentExpected 
Return E(r)Standard 
Deviation σ Utility A = 4 Utility A = 2
1 12% 30% –0.0600 0.0300
2 15 35 –0.0950 0.0275
3 21 40 –0.1100 0.0500
4 24 45 –0.1650 0.0375
The risk-  averse investor with a risk aversion coefficient of 4 should choose 
Investment 1. The risk-  averse investor with a risk aversion coefficient of 2 should 
choose Investment 3.
A risk-  neutral investor cares only about return. In other words, his risk aver -
sion coefficient is 0. Therefore, a risk-  neutral investor will choose Investment 4 
because it has the highest return.
A risk-  loving investor likes both higher risk and higher return. In other words, 
his risk aversion coefficient is negative. Therefore, a risk-  loving investor will 
choose Investment 4 because it has the highest return and highest risk among 
the four investments.

Risk Aversion and Portfolio Selection 273
3.3 Application of Utility Theory to Portfolio Selection
The simplest application of utility theory and risk aversion is to a portfolio of two 
assets, a risk-  free asset and a risky asset. The risk-  free asset has zero risk and a return 
of Rf. The risky asset has a risk of σi (> 0) and an expected return of E(Ri). Because 
the risky asset has risk that is greater than that of the risk-  free asset, the expected 
return from the risky asset will be greater than the return from the risk-  free asset, 
that is, E(Ri) > Rf.
We can construct a portfolio of these two assets with a portfolio expected return, 
E(Rp), and portfolio risk, σp, based on sections 2.1.7 and 2.3.3. In the equations given 
below, w1 is the weight in the risk-  free asset and (1 – w1) is the weight in the risky 
asset. Because σf = 0 for the risk-  free asset, the first and third terms in the formula

for variance are zero leaving only the second term. We arrive at the last equation by 
taking the square root of both sides, which shows the expression for standard deviation 
for a portfolio of two assets when one asset is the risk-  free asset:
ER wR wE R
ww wwpf i
Pf if() =+ −() ()
=+ −() +− ()11
2
122
122
11 121
12 1 σσ σρ σσσσ
σσii
piw
w=−()
=−()1
1122
1
The two-  asset portfolio is drawn in Exhibit 13 by varying w1 from 0 percent to 
100 percent. The portfolio standard deviation is on the horizontal axis and the port -
folio return is on the vertical axis. If only these two assets are available in the economy 
and the risky asset represents the market, the line in Exhibit 13 is called the capital 
allocation line . The capital allocation line represents the portfolios available to an 
investor. The equation for this line can be derived from the above two equations by 
rewriting the second equation as  wp
i11=−σ
σ. Substituting the value of w1 in the

i11=−σ
σ. Substituting the value of w1 in the 
equation for expected return, we get the following equation for the capital allocation 
line:
ER RE Rpp
ifp
ii () =−

+ () 1σ
σσ
σ
This equation can be rewritten in a more usable form:
ER RER R
pfif
ip () =+()− ()
σσ
The capital allocation line has an intercept of Rf, and a slope of  ER Rif
i() − ()
σ, which 
is the additional required return for every increment in risk, and is sometimes referred 
to as the market price of risk.

Reading 39 ■ Portfolio Risk and Return: Part I 274
Exhibit 13   Capital Allocation Line with Two Assets
0Expected Return
RfE(Ri) x
Portfolio Standard DeviationE(Rp)
σiσp
Because the equation is linear, the plot of the capital allocation line is a straight 
line. The line begins with the risk-  free asset as the leftmost point with zero risk and a 
risk-  free return, Rf. At that point, the portfolio consists of only the risk-  free asset. If 
100 percent is invested in the portfolio of all risky assets, however, we have a return 
of E(Ri) with a risk of σi.
We can move further along the line in pursuit of higher returns by borrowing 
at the risk-  free rate and investing the borrowed money in the portfolio of all risky 
assets. If 50 percent is borrowed at the risk-  free rate, then w1 = –0.50 and 150 per -
cent is placed in the risky asset, giving a return = 1.50 E(Ri) – 0.50 Rf, which is > E(Ri) 
because E(Ri) > Rf.
The line plotted in Exhibit 13 is comprised of an unlimited number of risk–return

pairs or portfolios. Which one of these portfolios should be chosen by an investor? 
The answer lies in combining indifference curves from utility theory with the capital 
allocation line from portfolio theory. Utility theory gives us the utility function or 
the indifference curves for an individual, as in Exhibit 11, and the capital allocation 
line gives us the set of feasible investments. Overlaying each individual’s indifference 
curves on the capital allocation line will provide us with the optimal portfolio for that 
investor. Exhibit 14 illustrates this process of portfolio selection.

Risk Aversion and Portfolio Selection 275
Exhibit 14   Portfolio Selection Expected Portfolio ReturnE(Rp)
0
Portfolio Standard Deviation  xl
m
n
xx
ba
σpxx12 3
The capital allocation line consists of the set of feasible portfolios. Points under 
the capital allocation line may be attainable but are not preferred by any investor 
because the investor can get a higher return for the same risk by moving up to the 
capital allocation line. Points above the capital allocation line are desirable but not 
achievable with available assets.
Three indifference curves for the same individual are also shown in Exhibit 14. 
Curve 1 is above the capital allocation line, Curve 2 is tangential to the line, and 
Curve 3 intersects the line at two points. Curve 1 has the highest utility and Curve 
3 has the lowest utility. Because Curve 1 lies completely above the capital allocation 
line, points on Curve 1 are not achievable with the available assets on the capital

allocation line. Curve 3 intersects the capital allocation line at two Points, a and b. 
The investor is able to invest at either Point a or b to derive the risk–return trade-  off  
and utility associated with Curve 3. Comparing points with the same risk, observe 
that Point n on Curve 3 has the same risk as Point m on Curve 2, yet Point m has the 
higher expected return. Therefore, all investors will choose Curve 2 instead of Curve 
3. Curve 2 is tangential to the capital allocation line at Point m. Point m is on the 
capital allocation line and investable. Point m and the utility associated with Curve 
2 is the best that the investor can do because he/she cannot move to a higher utility 
indifference curve. Thus, we have been able to select the optimal portfolio for the 
investor with indifference Curves 1, 2, and 3. Point m, the optimal portfolio for one 
investor, may not be optimal for another investor. We can follow the same process,

however, for finding the optimal portfolio for other investors: the optimal portfolio is 
the point of tangency between the capital allocation line and the indifference curve for 
that investor. In other words, the optimal portfolio maximizes the return per unit of 
risk (as it is on the capital allocation line), and it simultaneously supplies the investor 
with the most satisfaction (utility).
As an illustration, Exhibit 15 shows two indifference curves for two different inves -
tors: Kelly with a risk aversion coefficient of 2 and Jane with a risk aversion coefficient 
of 4. The indifference curve for Kelly is to the right of the indifference curve for Jane 
because Kelly is less risk averse than Jane and can accept a higher amount of risk, 
i.e. has a higher tolerance for risk. Accordingly, their optimal portfolios are different: 
Point k is the optimal portfolio for Kelly and Point j is the optimal portfolio for Jane.

Reading 39 ■ Portfolio Risk and Return: Part I 276
In addition, for the same return, the slope of Jane’s curve is higher than Kelly’s sug -
gesting that Jane needs greater incremental return as compensation for accepting an 
additional amount of risk compared with Kelly.
Exhibit 15   Portfolio Selection for Two Investors with Various Levels of Risk Aversion Expected Portfolio ReturnE(Rp)
0A = 4A = 2Indifference Curves
Capital Allocation
Line
jk
Portfolio Standard Deviation  σpxx
PORTFOLIO RISK
We have seen before that investors are risk averse and demand a higher return for a 
riskier investment. Therefore, ways of controlling portfolio risk without affecting return 
are valuable. As a precursor to managing risk, this section explains and analyzes the 
components of portfolio risk. In particular, it examines and describes how a portfolio 
consisting of assets with low correlations have the potential of reducing risk without 
necessarily reducing return.
4.1 Portfolio of Two Risky Assets

The return and risk of a portfolio of two assets was introduced in Section 2 of this 
reading. In this section, we briefly review the computation of return and extend the 
concept of portfolio risk and its components.
4.1.1  Portfolio Return
When two individual assets are combined in a portfolio, we can compute the port -
folio return as a weighted average of the returns of the two assets. Consider Assets 
1 and 2 with weights of 25 percent and 75 percent in a portfolio. If their returns are 
20 percent and 5 percent, the weighted average return = (0.25 × 20%) + (0.75 × 5%) 
= 8.75%. More generally, the portfolio return can be written as below, where Rp is 
return of the portfolio and R1, R2 are returns on the two assets:
Rw Rw RP=+ −() 11 12 14

Portfolio Risk 277
4.1.2  Portfolio Risk
Portfolio risk or variance measures the amount of uncertainty in portfolio returns. 
Portfolio variance can be calculated by taking the variance of both sides of the return 
equation as below, where Cov (R1,R2) is the covariance of returns, R1 and R2, w1 is the 
weight in Asset 1, w2 (= 1 – w1) is the weight in Asset 2, and  σ12, σ22 are the variances 
of the two assets:
σPP Rw Rw R
wR wR ww R2
11 22
12
122
21 2 2= () =+ ()
= () + () +VarV ar
VarV ar Cov112
12
12
22
22
12 12 2,
,R
ww ww RR()
=+ + () σσ Cov
The standard deviation, or risk, of a portfolio of two assets is given by the square 
root of the portfolio’s variance:
12
22
22
12 12 2C ov ,
4.1.3  Covariance and Correlation
The covariance  in the formula for portfolio standard deviation can be expanded as 
Cov( R1,R2) = ρ12σ1σ2 where ρ12 is the correlation between returns, R1, R2. Although 
covariance is important, it is difficult to interpret because it is unbounded on both

sides. It is easier to understand the correlation coefficient  (ρ12), which is bounded 
but provides similar information.
Correlation is a measure of the consistency or tendency for two investments to 
act in a similar way. The correlation coefficient, ρ12, can be positive or negative and 
ranges from –1 to +1. Consider three different values of the correlation coefficient:
■■ρ12 = +1: Returns of the two assets are perfectly positively  correlated. Assets 1 
and 2 move together 100 percent of the time.
■■ρ12 = –1: Returns of the two assets are perfectly negatively  correlated. Assets 1 
and 2 move in opposite directions 100 percent of the time.
■■ρ12 = 0: Returns of the two assets are uncorrelated . Movement of Asset 1 pro -
vides no prediction regarding the movement of Asset 2.
The correlation coefficient between two assets determines the effect on portfolio 
risk when the two assets are combined. To see how this works, consider two different

values of ρ12. You will find that portfolio risk is unaffected when the two assets are 
perfectly correlated (ρ12 = +1). In other words, the portfolio’s standard deviation is 
simply a weighted average of the standard deviations of the two assets and as such a 
portfolio’s risk is unchanged with the addition of assets with the same risk parameters. 
Portfolio risk falls, however, when the two assets are not perfectly correlated (ρ12 < 
+1). Sufficiently low values of the correlation coefficient can make the portfolio riskless 
under certain conditions.
First, let ρ12 = +1
σσ σρ σσ σσ σσ
σpww ww ww ww
w2
12
12
22
22
12 1212 12
12
22
22
12 12
122 =+ += ++
=112 22
11 22+ ()
=+w
wwpσ
σσ σ
The first set of terms on the right side of the first equation contain the usual terms 
for portfolio variance. Because the correlation coefficient is equal to +1, the right 
side can be rewritten as a perfect square. The third row shows that portfolio risk is a

weighted average of the risks of the individual assets’ risks. In Subsection 4.1.1., the

Reading 39 ■ Portfolio Risk and Return: Part I 278
portfolio return was shown always to be a weighted average of returns. Because both 
risk and return are just weighted averages of the two assets in the portfolio there is 
no reduction in risk when ρ12 = +1.
Now let ρ12 < +1
The above analysis showed that portfolio risk is a weighted average of asset risks when 
ρ12 = + 1. When ρ12 < +1, the portfolio risk is less than the weighted average of the 
individual assets’ risks.
To show this, we begin by reproducing the general formula for portfolio risk, which 
is expressed by the terms to the left of the “<” sign below. The term to the right of “<” 
shows the portfolio risk when ρ12 = + 1:
σp ww ww ww ww
w=+ +< ++
=12
12
22
22
12 1212 12
12
22
22
12 12
1122
+ + ()
<+()w
wwp22
11 22σ
σσ σ
The left side is smaller than the right side because the correlation coefficient on the 
left side for the new portfolio is <1. Thus, the portfolio risk is less than the weighted

average of risks while the portfolio return is still a weighted average of returns.
As you can see, we have achieved diversification by combining two assets that are 
not perfectly correlated. For an extreme case in which ρ12 = –1 (that is, the two asset 
returns move in opposite directions), the portfolio can be made risk free.
EXAMPLE 7   
Effect of Correlation on Portfolio Risk
Two stocks have the same return and risk (standard deviation): 10 percent return 
with 20 percent risk. You form a portfolio with 50 percent each of Stock 1 and 
Stock 2 to examine the effect of correlation on risk.
1 Calculate the portfolio return and risk if the correlation is 1.0.
2 Calculate the portfolio return and risk if the correlation is 0.0.
3 Calculate the portfolio return and risk if the correlation is –1.0.
4 Compare the return and risk of portfolios with different correlations.
RR ww12 12 12
110 0102 00 20 50
050== == == ==
=%. %. %
.; ; 
. Case 1:  σσ
ρ2 2
2
12
121
05 01 05 01 01 01 0=+
=+
=×() +×() ==

ρ2 2
2
12
121
=+
=Rw Rw R
R
wp
p
p11 22
.. .. .%
σσ +++
=×() +×() +× ×ww w
p22
22
12 12 12
22 22 22
05 02 05 02 20 50 5σσ σρ
σ .. .. .. ×××× () =
== =02 02 10 04
0040 20 20.. .
.. % σp
This equation demonstrates the earlier point that with a correlation of 1.0 the 
risk of the portfolio is the same as the risk of the individual assets.

Portfolio Risk 279
ρ
σσ σσ σρ
σ12
11 22
2
12
12
22
22
12 12 120
0101 0
2=
=+ ==
=+ +Rw Rw R
ww wwp
p
p.%
222 22 205 02 05 02
20 50 50 20 20 002
0=×() +×()
+×× ××× () =
=.. ..
... ..
. σp 0 02 0141 4 ==.%
This equation demonstrates the earlier point that, when assets have correlations 
of less than 1.0, they can be combined in a portfolio that has less risk than either 
of the assets individually.
ρ
σσ σσ σρ
σ12
2
12
12
22
22
12 12 121
00 0
2=−
=+ ==
=+ +Rw Rw R
ww wwp
p11 22 11.%
p p
p22 22 205 02 05 02
20 50 50 20 21 0
0=×() +×()
+×× ××× − () =
=.. ..
... .
% σ
This equation demonstrates the earlier point that, if the correlation of assets 
is low enough, in this case 100 percent negative correlation or –1.00 (exactly 
inversely related), a portfolio can be designed that eliminates risk. The individual 
assets retain their risk characteristics, but the portfolio is risk free.
The expected return is 10 percent in all three cases; however, the returns will

be more volatile in Case 1 and least volatile in Case 3. In the first case, there 
is no diversification of risk (same risk as before of 20 percent) and the return 
remains the same. In the second case, with a correlation coefficient of 0, we have 
achieved diversification of risk (risk is now 14 percent instead of 20 percent), 
again with the same return. In the third case with a correlation coefficient of 
–1, the portfolio is risk free, although we continue to get the same return of 
10 percent. This example shows the power of diversification that we expand on 
further in Section 4.3.
4.1.4  Relationship between Portfolio Risk and Return
The previous example illustrated the effect of correlation on portfolio risk while keeping 
the weights in the two assets equal and unchanged. In this section, we consider how 
portfolio risk and return vary with different portfolio weights and different correla -
tions. Formulas for computation are in Subsections 4.1.1 and 4.1.2.

Asset 1 has an annual return of 7 percent and annualized risk of 12 percent, whereas 
Asset 2 has an annual return of 15 percent and annualized risk of 25 percent. The 
relationship is tabulated in Exhibit 16 for the two assets and graphically represented 
in Exhibit 17.

Reading 39 ■ Portfolio Risk and Return: Part I 280
Exhibit 16   Relationship between Risk and Return
Weight in 
Asset 1 (%)Portfolio 
ReturnPortfolio Risk with Correlation of
1.0 0.5 0.2 –1.0
0 15.0 25.0 25.0 25.0 25.0
10 14.2 23.7 23.1 22.8 21.3
20 13.4 22.4 21.3 20.6 17.6
30 12.6 21.1 19.6 18.6 13.9
40 11.8 19.8 17.9 16.6 10.2
50 11.0 18.5 16.3 14.9 6.5
60 10.2 17.2 15.0 13.4 2.8
70 9.4 15.9 13.8 12.3 0.9
80 8.6 14.6 12.9 11.7 4.6
90 7.8 13.3 12.2 11.6 8.3
100 7.0 12.0 12.0 12.0 12.0
Exhibit 17   Relationship between Risk and Return
14
11
Standard Deviation of Portfolio  σpExpected Portfolio Return E(Rp)
10 51 5 20 258ρ = –1ρ = .2
ρ = 1
ρ = .5
The table shows the portfolio return and risk for four correlation coefficients ranging 
from +1.0 to –1.0 and 11 weights ranging from 0 percent to 100 percent. The portfolio 
return and risk are 15 percent and 25 percent, respectively, when 0 percent is invested 
in Asset 1, versus 7 percent and 12 percent when 100 percent is invested in Asset 1.

The portfolio return varies with weights but is unaffected by the correlation coefficient.
Portfolio risk becomes smaller with each successive decrease in the correlation 
coefficient, with the smallest risk when ρ12 = –1. The graph in Exhibit  17 shows 
that the risk–return relationship is a straight line when ρ12 = +1. As the correlation

Portfolio Risk 281
falls, the risk becomes smaller and smaller as in the table. The curvilinear nature of 
a portfolio of assets is recognizable in all investment opportunity sets (except at the 
extremes where ρ12 = –1 or +1).
EXAMPLE 8   
Portfolio of Two Assets
An investor is considering investing in a small-  cap stock fund and a general bond 
fund. Their returns and standard deviations are given below and the correlation 
between the two fund returns is 0.10.
Expected Annual 
Return (%)Standard Deviation of 
Returns (%)
Small-  cap fund, S 19 33
Bond fund, B 8 13
1 If the investor requires a portfolio return of 12 percent, what should the 
proportions in each fund be?
2 What is the standard deviation of the portfolio constructed in Part 1?
We can calculate the weights by setting the portfolio return equal to 12 percent. 
12% = w1 × 19% + (1 – w1) × 8%; w1 = 36.4%, (1 – w1) = 63.6%. Thus, 36.4 percent 
should be invested in the small-  cap fund and 63.6 percent should be invested

in the bond fund.
σσ σρ σσp ww ww =+ +
×× =+() (12
12
22
22
12 1212
22 222
0 364 0330 636 013 .. .. ) )()+ ××× ××
=20 364 0 636 0100 33 013
15 23... ..
.%
The portfolio risk is 15.23 percent, which is much less than a weighted average 
of risks of 20.28% (63.6% × 13% + 36.4% × 33%).
4.2 Portfolio of Many Risky Assets
In the previous section, we discussed how the correlation between two assets can 
affect the risk of a portfolio and the smaller the correlation the lower is the risk. The 
above analysis can be extended to a portfolio with many risky assets ( N). Recall the 
following equations from Sections 2.1.7 and 2.3.3 for portfolio return and variance:
ER wERw ww ijpi i
iN
Pi i
iN
ij
ij ijN
() = () =+
== =≠∑∑ ∑
122 2
11,,
,,  Cov σσ (()



=
=∑, wi
iN
1
1
To examine how a portfolio with many risky assets works and the ways in which 
we can reduce the risk of a portfolio, assume that the portfolio has equal weights (1/ N)

for all N assets. In addition, assume that  σ2 and  Cov are the average variance and

Reading 39 ■ Portfolio Risk and Return: Part I 282
average covariance. Given equal weights and average variance/covariance, we can 
rewrite the portfolio variance as below (intermediate steps are omitted to focus on 
the main result):
 C ov σσ
σσPi i
iN
ij
ij ijN
Pww wi j
NN22 2
11
22=+ ()




=+−== ≠∑∑
,,,
1 1 ()
NCov
The equation in the second line shows that as N becomes large, the first term on 
the right side with the denominator of N becomes smaller and smaller, implying that 
the contribution of one asset’s variance to portfolio variance gradually becomes neg -
ligible. The second term, however, approaches the average covariance as N increases. 
It is reasonable to say that for portfolios with a large number of assets, covariance 
among the assets accounts for almost all of the portfolio’s risk.
4.2.1  Importance of Correlation in a Portfolio of Many Assets
The analysis becomes more instructive and interesting if we assume that all assets in

the portfolio have the same variance and the same correlation among assets. In that 
case, the portfolio risk can then be rewritten as:
σσρσpNN
N=+−()22 1
The first term under the root sign becomes negligible as the number of assets in 
the portfolio increases leaving the second term (correlation) as the main determining 
factor for portfolio risk. If the assets are unrelated to one another, the portfolio can 
have close to zero risk. In the next section, we review these concepts to learn how 
portfolios can be diversified.
4.3 The Power of Diversification
Diversification is one of the most important and powerful concepts in investments. 
Because investors are risk averse, they are interested in reducing risk preferably without 
reducing return. In other cases, investors may accept a lower return if it will reduce 
the chance of catastrophic losses. In previous sections of this reading, you learned 
the importance of correlation and covariance in managing risk. This section applies

those concepts to explore ways for risk diversification. We begin with a simple but 
intuitive example.
EXAMPLE 9   
Diversification with Rain and Shine
Assume a company Beachwear rents beach equipment. The annual return from 
the company’s operations is 20 percent in years with many sunny days but falls 
to 0 percent in rainy years with few sunny days. The probabilities of a sunny year 
and a rainy year are equal at 50 percent. Thus, the average return is 10 percent, 
with a 50 percent chance of 20 percent return and a 50 percent chance of 0 per -
cent return. Because Beachwear can earn a return of 20 percent or 0 percent, 
its average return of 10 percent is risky.

Portfolio Risk 283
You are excited about investing in Beachwear but do not like the risk. Having 
heard about diversification, you decide to add another business to the portfolio 
to reduce your investment risk.
■■There is a snack shop on the beach that sells all the healthy food you like. 
You estimate that the annual return from the Snackshop is also 20 percent 
in years with many sunny days and 0 percent in other years. As with the 
Beachwear shop, the average return is 10 percent.
You decide to invest 50  percent each in Snackshop and Beachwear. The 
average return is still 10 percent, with 50 percent of 10 percent from Snackshop 
and 50 percent of 10 percent from Beachwear. In a sunny year, you would earn 
20 percent (= 50% of 20% from Beachwear + 50% of 20% from Snackshop). In 
a rainy year, you would earn 0 percent (=50% of 0% from Beachwear + 50% of 
0% from Snackshop). The results are tabulated in Exhibit 18.
Exhibit 18   
Type CompanyPercent 
InvestedReturn 
in Sunny 
Y ear (%)Return in

in Sunny 
Y ear (%)Return in 
Rainy Y ear 
(%)Average 
Return (%)
Single stock Beachwear 100 20 0 10
Single stock Snackshop 100 20 0 10
Portfolio of two stocksBeachwear 50 20 0 10
Snackshop 50 20 0 10
Total 100 20 0 10
These results seem counterintuitive. You thought that by adding another 
business you would be able to diversify and reduce your risk, but the risk is 
exactly the same as before. What went wrong? Note that both businesses do 
well when it is sunny and both businesses do poorly when it rains. The correla -
tion between the two businesses is +1.0. No reduction in risk occurs when the 
correlation is +1.0.
■■To reduce risk, you must consider a business that does well in a rainy year. 
You find a company that rents DVDs. DVDrental company is similar to 
the Beachwear company, except that its annual return is 20 percent in a 
rainy year and 0 percent in a sunny year, with an average return of 10 per -
cent. DVDrental’s 10 percent return is also risky just like Beachwear’s

return. 
If you invest 50 percent each in DVDrental and Beachwear, then the aver -
age return is still 10 percent, with 50 percent of 10 percent from DVDrental 
10 percent (= 50% of 20% from Beachwear + 50% of 0% from DVDrental). In 
a rainy year also, you would earn 10 percent (=50% of 0% from Beachwear + 
50% of 20% from DVDrental). You have no risk because you earn 10 percent 
in both sunny and rainy years. Thus, by adding DVDrental to Beachwear, you 
have reduced (eliminated) your risk without affecting your return. The results 
are tabulated in Exhibit 19.

Reading 39 ■ Portfolio Risk and Return: Part I 284
Exhibit 19   
in Sunny 
Rainy Y ear 
Return (%)
Single stock DVDrental 100 0 20 10
DVDrental 50 0 20 10
Total 100 10 10 10
In this case, the two businesses have a correlation of –1.0. When two busi -
nesses with a correlation of –1.0 are combined, risk can always be reduced to zero.
4.3.1  Correlation and Risk Diversification
Correlation is the key in diversification of risk. Notice that the returns from Beachwear 
and DVDRental always go in the opposite direction. If one of them does well, the 
other does not. Therefore, adding assets that do not behave like other assets in your 
portfolio is good and can reduce risk. The two companies in the above example have 
a correlation of –1.0.
Even when we expand the portfolio to many assets, correlation among assets

remains the primary determinant of portfolio risk. Lower correlations are associated 
with lower risk. Unfortunately, most assets have high positive correlations. The chal -
lenge in diversifying risk is to find assets that have a correlation that is much lower 
than +1.0.
4.3.2  Historical Risk and Correlation
When we discussed asset returns in section 2.4.1, we were careful to distinguish 
between historical or past returns and expected or future returns because historical 
returns may not be a good indicator of future returns. Returns may be highly positive 
in one period and highly negative in another period depending on the risk of that 
asset. Exhibit 5 showed that returns for large US company stocks were high in the 
1990s but have been very low in the 2000s.
Risk for an asset class, however, does not usually change dramatically from one 
period to the next. Stocks have been risky even in periods of low returns. T-  bills are

always less risky even when they earn high returns. From Exhibit 5, we can see that 
risk has typically not varied much from one decade to the next, except that risk for 
bonds has been much higher in recent decades when compared with earlier decades. 
Therefore, it is not unreasonable to assume that historical risk can work as a good 
proxy for future risk.
As with risk, correlations are quite stable among assets of the same country. 
Intercountry correlations, however, have been on the rise in the last few decades 
as a result of globalization and the liberalization of many economies. A correlation 
above 0.90 is considered high because the assets do not provide much opportunity 
for diversification of risk, such as the correlations that exist among large US company 
stocks on the NYSE, NASDAQ, S&P 500 Index, and Dow Jones Industrial Average. 
Correlations below 0.30 are considered attractive for portfolio diversification.

Portfolio Risk 285
4.3.3  Historical Correlation among Asset Classes
Correlations among major US asset classes and international stocks are reported in 
Exhibit 20 for 1970–2008. The highest correlation is between US large company stocks 
and US small company stocks at about 70 percent, whereas the correlation between US 
large company stocks and international stocks is approximately 66 percent. Although 
these are the highest correlations, they still provide diversification benefits because 
the correlations are less than 100  percent. The correlation between international 
stocks and US small company stocks is lower, at 49 percent. The lowest correlations 
are between stocks and bonds, with some correlations being negative, such as that 
between US small company stocks and US long-  term government bonds. Similarly, 
the correlation between T-  bills and stocks is close to zero and is marginally negative 
for international stocks.7

Exhibit 20   Correlation Among US Assets and International Stocks (1970–2008)
SeriesInternational 
StocksUS Large 
Company 
StocksUS Small 
Company 
StocksUS Long-  Term 
Corporate 
BondsUS Long-  
Term 
Treasury 
BondsUS 
T- BillsUS 
Inflation
International stocks 1.00
US large company stocks 0.66 1.00
US small company 
stocks0.49 0.71 1.00
US long-  term corporate 
bonds0.07 0.31 0.13 1.00
US long-  term Treasury 
bonds–0.04 0.13 –0.05 0.92 1.00
US T-  bills –0.02 0.15 0.07 0.02 0.90 1.00
US inflation –0.09 –0.09 0.06 –0.40 –0.40 0.65 1.00
Source:  2009 Ibbotson SBBI Classic Yearbook (Table 13-  5).
The low correlations between stocks and bonds are attractive for portfolio diver -
sification. Similarly, including international securities in a portfolio can also control 
portfolio risk. It is not surprising that most diversified portfolios of investors contain 
domestic stocks, domestic bonds, foreign stocks, foreign bonds, real estate, cash, and 
other asset classes.

4.3.4  Avenues for Diversification
The reason for diversification is simple. By constructing a portfolio with assets that 
do not move together, you create a portfolio that reduces the ups and downs in the 
short term but continues to grow steadily in the long term. Diversification thus makes 
a portfolio more resilient to gyrations in financial markets.
7 In any short period, T-  bills are riskless and uncorrelated with other asset classes. For example, a 3-  month 
US Treasury bill is redeemable at its face value upon maturity irrespective of what happens to other assets. 
When we consider multiple periods, however, returns on T-  bills may be related to other asset classes 
because short-  term interest rates vary depending on the strength of the economy and outlook for inflation.

Reading 39 ■ Portfolio Risk and Return: Part I 286
We describe a number of approaches for diversification, some of which have been 
discussed previously and some of which might seem too obvious. Diversification, 
however, is such an important part of investing that it cannot be emphasized enough, 
especially when we continue to meet and see many investors who are not properly 
diversified.
■■Diversify with asset classes.  Correlations among major asset classes8 are 
not usually high, as can be observed from the few US asset classes listed in 
Exhibit 20. Correlations for other asset classes and other countries are also typ -
ically low, which provides investors the opportunity to benefit from diversifying 
among many asset classes to achieve the biggest benefit from diversification. A 
partial list of asset classes includes domestic large caps, domestic small caps, 
growth stocks, value stocks, domestic corporate bonds, long-  term domestic

government bonds, domestic Treasury bills (cash), emerging market stocks, 
emerging market bonds, developed market stocks (i.e., developed markets 
excluding domestic market), developed market bonds, real estate, and gold and 
other commodities. In addition, industries and sectors are used to diversify 
portfolios. For example, energy stocks may not be well correlated with health 
care stocks. The exact proportions in which these assets should be included in a 
portfolio depend on the risk, return, and correlation characteristics of each and 
the home country of the investor.
■■Diversify with index funds.  Diversifying among asset classes can become costly 
for small portfolios because of the number of securities required. For example, 
creating exposure to a single category, such as a domestic large company asset 
class, may require a group of at least 30 stocks. Exposure to 10 asset classes 
may require 300 securities, which can be expensive to trade and track. Instead,

it may be effective to use exchange-  traded funds or mutual funds that track the 
respective indexes, which could bring down the costs associated with building 
a well-  diversified portfolio. Therefore, many investors should seriously consider 
index mutual funds as an investment vehicle as opposed to individual securities.
■■Diversification among countries.  Countries are different because of different 
economic fundamentals, industry focus, economic policy, and political cli -
mate. Thus, securities of issuers domiciled in different countries provide an 
opportunity for diversification. Country returns may also be different because 
of different currencies. In other words, the return on a foreign investment may 
be different when translated to the home country’s currency. Because currency 
returns are uncorrelated with stock returns, they may help reduce the risk of 
investing in a foreign country even when that country, in isolation, is a very

risky emerging market from an equity investment point of view. Investment in 
foreign countries is an essential part of a well-  diversified portfolio.
■■Diversify by  not owning your employer’s stock.  Companies encourage their 
employees to invest in company stock through employee stock plans and 
retirement plans. You should evaluate investing in your company, however, just 
as you would evaluate any other investment. In addition, you should consider 
the nonfinancial investments that you have made, especially the human capi -
tal you have invested in your company. Because you work for your employer, 
you are already heavily invested in it because your earnings depend on your 
employer. The level of your earnings, whether your compensation improves or 
whether you get a promotion, depends on how well your employer performs. If 
8 Major asset classes are distinguished from sub-  classes, such as US value stocks and US growth stocks.

Portfolio Risk 287
a competitor drives your employer out of the market, you will be out of a job. 
Additional investments in your employer will concentrate your wealth in one 
asset even more so and make you less diversified.
■■Evaluate each asset before adding to a portfolio.  Every time you add a security 
or an asset class to the portfolio, recognize that there is a cost associated with 
diversification. There is a cost of trading an asset as well as the cost of tracking a 
larger portfolio. In some cases, the securities or assets may have different names 
but belong to an asset class in which you already have sufficient exposure. A 
general rule to evaluate whether a new asset should be included to an existing 
portfolio is based on the following risk–return trade-  off relationship:
ER RE RRnewfnewnewp
ppf () =+ ×() − σρ
σ,
where E(R)  is the return from the asset, Rf is the return on the risk-  free asset, 
σ is the standard deviation, ρ is the correlation coefficient, and the subscripts

new and p refer to the new stock and existing portfolio. If the new asset’s risk-  
adjusted return benefits the portfolio, then the asset should be included. The 
condition can be rewritten using the Sharpe ratio on both sides of the equation 
as:
ER R ER Rnewf
newpf
pnewp() −
>() −
×σσρ,
If the Sharpe ratio of the new asset is greater than the Sharpe ratio of the cur -
rent portfolio times the correlation coefficient, it is beneficial to add the new 
asset.
■■Buy insurance for risky portfolios.  It may come as a surprise, but insurance is 
an investment asset—just a different kind of asset. Insurance has a negative 
correlation with your assets and is thus very valuable. Insurance gives you a 
positive return when your assets lose value, but pays nothing if your assets 
maintain their value. Over time, insurance generates a negative average return. 
Many individuals, however, are willing to accept a small negative return because

insurance reduces their exposure to an extreme loss. In general, it is reasonable 
to add an investment with a negative return if that investment significantly 
reduces risk (an example of a classic case of the risk–return trade-  off).
Alternatively, investments with negative correlations also exist. Historically, 
gold has a negative correlation with stocks; however, the expected return is usu -
ally small and sometimes even negative. Investors often include gold and other 
commodities in their portfolios as a way of reducing their overall portfolio risk, 
including currency risk and inflation risk.
Buying put options is another way of reducing risk. Because put options pay 
when the underlying asset falls in value (negative correlation), they can protect 
an investor’s portfolio against catastrophic losses. Of course, put options cost 
money, and the expected return is zero or marginally negative.

Reading 39 ■ Portfolio Risk and Return: Part I 288
EFFICIENT FRONTIER AND INVESTOR’S OPTIMAL 
PORTFOLIO
In this section, we formalize the effect of diversification and expand the set of invest -
ments to include all available risky assets in a mean–variance framework. The addition 
of a risk-  free asset generates an optimal risky portfolio and the capital allocation line. 
We can then derive an investor’s optimal portfolio by overlaying the capital allocation 
line with the indifference curves of investors.
5.1 Investment Opportunity Set
If two assets are perfectly correlated, the risk–return opportunity set is represented 
by a straight line connecting those two assets. The line contains portfolios formed 
by changing the weight of each asset invested in the portfolio. This correlation was 
depicted by the straight line (with ρ = 1) in Exhibit 17. If the two assets are not per -
fectly correlated, the portfolio’s risk is less than the weighted average risk of the com -

ponents, and the portfolio formed from the two assets bulges on the left as shown by 
curves with the correlation coefficient (ρ) less than 1.0 in Exhibit 17. All of the points 
connecting the two assets are achievable (or feasible). The addition of new assets to 
this portfolio creates more and more portfolios that are either a linear combination 
of the existing portfolio and the new asset or a curvilinear combination, depending 
on the correlation between the existing portfolio and the new asset.
As the number of available assets increases, the number of possible combinations 
increases rapidly. When all investable assets are considered, and there are hundreds 
and thousands of them, we can construct an opportunity set of investments. The 
opportunity set will ordinarily span all points within a frontier because it is also pos -
sible to reach every possible point within that curve by judiciously creating a portfolio 
from the investable assets.

We begin with individual investable assets and gradually form portfolios that can 
be plotted to form a curve as shown in Exhibit 21. All points on the curve and points 
to the right of the curve are attainable by a combination of one or more of the invest -
able assets. This set of points is called the investment opportunity set. Initially, the 
opportunity set consists of domestic assets only and is labeled as such in Exhibit 21.5

Efficient Frontier and Investor’s Optimal Portfolio 289
Exhibit 21   Investment Opportunity SetPortfolio  Expected  ReturnE(Rp)
Portfolio Standard DeviationIndividual Assets
0Domestic assets onlyWith international assets
σ
5.1.1  Addition of Asset Classes
Exhibit 21 shows the effect of adding a new asset class, such as international assets. 
As long as the new asset class is not perfectly correlated with the existing asset class, 
the investment opportunity set will expand out further to the northwest, providing a 
superior risk–return trade-  off.
The investment opportunity set with international assets dominates the opportunity 
set that includes only domestic assets. Adding other asset classes will have the same 
impact on the opportunity set. Thus, we should continue to add asset classes until 
they do not further improve the risk–return trade-  off. The benefits of diversification 
can be fully captured in this way in the construction of the investment opportunity

set, and eventually in the selection of the optimal portfolio.
In the discussion that follows in this section, we will assume that all investable 
assets available to an investor are included in the investment opportunity set and no 
special attention needs to be paid to new asset classes or new investment opportunities.
5.2 Minimum-  Variance Portfolios
The investment opportunity set consisting of all available investable sets is shown in 
Exhibit 22. There are a large number of portfolios available for investment, but we 
must choose a single optimal portfolio. In this subsection, we begin the selection 
process by narrowing the choice to fewer portfolios.

Reading 39 ■ Portfolio Risk and Return: Part I 290
Exhibit 22   Minimum-  Variance FrontierPortfolio  Expected  ReturnE(Rp)
Portfolio Standard DeviationMinimum-Variance
Frontier
Global
Minimum-
Variance
Portfolio (Z)Efficient Frontier
X
0A B
CD
σ
5.2.1  Minimum-  Variance Frontier
Risk-  averse investors seek to minimize risk for a given return. Consider Points A, B, and 
X in Exhibit 22 and assume that they are on the same horizontal line by construction. 
Thus, the three points have the same expected return, E(R1), as do all other points on 
the imaginary line connecting A, B, and X. Given a choice, an investor will choose 
the point with the minimum risk, which is Point X. Point X, however, is unattainable 
because it does not lie within the investment opportunity set. Thus, the minimum risk 
that we can attain for E(R1) is at Point A. Point B and all points to the right of Point 
A are feasible but they have higher risk. Therefore, a risk-  averse investor will choose

only Point A in preference to any other portfolio with the same return.
Similarly, Point C is the minimum variance point for the return earned at C. Points 
to the right of C have higher risk. We can extend the above analysis to all possible 
returns. In all cases, we find that the minimum-  variance portfolio  is the one that 
lies on the solid curve drawn in Exhibit 22. The entire collection of these minimum-  
variance portfolios is referred to as the minimum-  variance frontier. The minimum-  
variance frontier defines the smaller set of portfolios in which investors would want 
to invest. Note that no risk-  averse investor will choose to invest in a portfolio to the 
right of the minimum-  variance frontier because a portfolio on the minimum-  variance 
frontier can give the same return but at a lower risk.
5.2.2  Global Minimum-  Variance Portfolio
The left-  most point on the minimum-  variance frontier is the portfolio with the min -

imum variance among all portfolios of risky assets, and is referred to as the global 
minimum-  variance portfolio . An investor cannot hold a portfolio consisting of risky  
assets that has less risk than that of the global minimum-  variance portfolio. Note the 
emphasis on “risky” assets. Later, the introduction of a risk-  free asset will allow us 
to relax this constraint.

Efficient Frontier and Investor’s Optimal Portfolio 291
5.2.3  Efficient Frontier of Risky Assets
The minimum-  variance frontier gives us portfolios with the minimum variance for a 
given return. However, investors also want to maximize return for a given risk. Observe 
Points A and C on the minimum-  variance frontier shown in Exhibit 22. Both of them 
have the same risk. Given a choice, an investor will choose Portfolio A because it 
has a higher return. No one will choose Portfolio C. The same analysis applies to all 
points on the minimum-  variance frontier that lie below the global minimum-  variance 
portfolio. Thus, portfolios on the curve below the global minimum-  variance portfolio 
and to the right of the global minimum-  variance portfolio are not beneficial and are 
inefficient portfolios for an investor.
The curve that lies above and to the right of the global minimum-  variance portfolio 
is referred to as the Markowitz efficient frontier  because it contains all portfolios of

risky assets that rational, risk-  averse investors will choose.
An important observation that is often ignored is the slope at various points on 
the efficient frontier. As we move right from the global minimum-  variance portfolio 
(Point Z) in Exhibit 22, there is an increase in risk with a concurrent increase in return. 
The increase in return with every unit increase in risk, however, keeps decreasing as 
we move from left to the right because the slope continues to decrease. The slope at 
Point D is less than the slope at Point A, which is less than the slope at Point Z. The 
increase in return by moving from Point Z to Point A is the same as the increase in 
return by moving from Point A to Point D. It can be seen that the additional risk in 
moving from Point A to Point D is 3 to 4 times more than the additional risk in mov -
ing from Point Z to Point A. Thus, investors obtain decreasing increases in returns 
as they assume more risk.
5.3 A Risk-  Free Asset and Many Risky Assets

Until now, we have only considered risky assets in which the return is risky or uncertain. 
Most investors, however, have access to a risk-  free asset, most notably from securities 
issued by the government. The addition of a risk-  free asset makes the investment 
opportunity set much richer than the investment opportunity set consisting only of 
risky assets.
5.3.1  Capital Allocation Line and Optimal Risky Portfolio
By definition, a risk-  free asset has zero risk so it must lie on the y-axis in a mean-  
variance graph. A risk-  free asset with a return of Rf is plotted in Exhibit 23. This asset 
can now be combined with a portfolio of risky assets. The combination of a risk-  free 
asset with a portfolio of risky assets is a straight line, such as in Section 3.3 (see 
Exhibit 13). Unlike in Section 3.3, however, we have many risky portfolios to choose 
from instead of a single risky portfolio.

Reading 39 ■ Portfolio Risk and Return: Part I 292
Exhibit 23   Optimal Risky PortfolioE(Rp)
Portfolio Standard DeviationEfficient Frontier
of Risky Assets
P
RfCAL(P)
CAL(A)
AOptimal Risky
PortfolioXY
σp
All portfolios on the efficient frontier are candidates for being combined with the 
risk-  free asset. Two combinations are shown in Exhibit 23: one between the risk-  free 
asset and efficient Portfolio A and the other between the risk-  free asset and efficient 
Portfolio P . Comparing capital allocation line A and capital allocation line P reveals 
that there is a point on CAL(P) with a higher return and same risk for each point 
on CAL(A). In other words, the portfolios on CAL(P) dominate the portfolios on 
CAL(A). Therefore, an investor will choose CAL(P) over CAL(A). We would like to 
move further northwest to achieve even better portfolios. None of those portfolios, 
however, is attainable because they are above the efficient frontier.

What about other points on the efficient frontier? For example, Point X is on 
the efficient frontier and has the highest return of all risky portfolios for its risk. 
However, Point Y on CAL(P), achievable by leveraging Portfolio P as seen in Section 
3.3, lies above Point X and has the same risk but higher return. In the same way, we 
can observe that not only does CAL(P) dominate CAL(A) but it also dominates the 
Markowitz efficient frontier of risky assets.
CAL(P) is the optimal capital allocation line and Portfolio P is the optimal risky 
portfolio. Thus, with the addition of the risk-  free asset, we are able to narrow our 
selection of risky portfolios to a single optimal risky portfolio, P , which is at the tan -
gent of CAL(P) and the efficient frontier of risky assets.
5.3.2  The Two-  Fund Separation Theorem
The two-  fund separation theorem  states that all investors regardless of taste, risk 
preferences, and initial wealth will hold a combination of two portfolios or funds: a

risk-  free asset and an optimal portfolio of risky assets.9
The separation theorem allows us to divide an investor’s investment problem into 
two distinct steps: the investment decision and the financing decision. In the first 
step, as in the previous analysis, the investor identifies the optimal risky portfolio. The 
optimal risky portfolio is selected from numerous risky portfolios without considering 
the investor’s preferences. The investment decision at this step is based on the optimal 
risky portfolio’s (a single portfolio) return, risk, and correlations.
9 In the next reading, you will learn that the optimal portfolio of risky assets is the market portfolio.

Efficient Frontier and Investor’s Optimal Portfolio 293
The capital allocation line connects the optimal risky portfolio and the risk-  free 
asset. All optimal investor portfolios must be on this line. Each investor’s optimal 
portfolio on the CAL(P) is determined in the second step. Considering each individual 
investor’s risk preference, using indifference curves, determines the investor’s allocation 
to the risk-  free asset (lending) and to the optimal risky portfolio. Portfolios beyond the 
optimal risky portfolio are obtained by borrowing at the risk-  free rate (i.e., buying on 
margin). Therefore, the individual investor’s risk preference determines the amount 
of financing (i.e., lending to the government instead of investing in the optimal risky 
portfolio or borrowing to purchase additional amounts of the optimal risky portfolio).
EXAMPLE 10   
Choosing the Right Portfolio
In Exhibit 24, the risk and return of the points marked are as follows:

Point Return (%) Risk (%) Point (%) Return (%) Risk (%)
A 15 10 B 11 10
C 15 30 D 25 30
F 4 0 G (gold) 10 30
P 16 17
Exhibit 24   
25.00
20.00
15.00
10.00
5.00
0.00ADOptimal CAL
Stocks
GoldCP
GB
F
Standard Deviation (%)Expected Return (%)
01 02 03 04 0
Answer the following questions with reference to the points plotted on Exhibit 24 
and explain your answers. The investor is choosing one portfolio based on the 
graph.
1 Which of the above points is not achievable?
2 Which of these portfolios will not be chosen by a rational, risk-  averse 
investor?
3 Which of these portfolios is most suitable for a risk-  neutral investor?

Reading 39 ■ Portfolio Risk and Return: Part I 294
4 Gold is on the inefficient part of the feasible set. Nonetheless, gold is 
owned by many rational investors as part of a larger portfolio. Why?
5 What is the utility of an investor at point P with a risk aversion coefficient 
of 3?
Portfolio A is not attainable because it lies outside the feasible set and not on 
the capital allocation line.
Portfolios G and C will not be chosen because D provides higher return for the 
same risk. G and C are the only investable points that do not lie on the capital 
allocation line.
Portfolio D is most suitable because a risk-  neutral investor cares only about 
return and portfolio D provides the highest return. A = 0 in the utility formula.
Gold may be owned as part of a portfolio (not as the portfolio) because gold 
has low or negative correlation with many risky assets, such as stocks. Being

part of a portfolio can thus reduce overall risk even though its standalone risk 
is high and return is low. Note that gold’s price is not stable—its return is very 
risky (30 percent). Even risk seekers will choose D over G, which has the same 
risk but higher return.
U = E(r) – 0.5Aσ2 = 0.16 – 0.5 × 3 × 0.0289 = 0.1167 = 11.67%.
5.4 Optimal Investor Portfolio
The CAL(P) in Exhibits 23 and 25 contains the best possible portfolios available to 
investors. Each of those portfolios is a linear combination of the risk-  free asset and 
the optimal risky portfolio. Among the available portfolios, the selection of each 
investor’s optimal portfolio depends on the risk preferences of an investor. In Section 
3, we discussed that the individual investor’s risk preferences are incorporated into 
their indifference curves. These can be used to select the optimal portfolio.
Exhibit 25 shows an indifference curve that is tangent to the capital allocation

line, CAL(P). Indifference curves with higher utility than this one lie above the cap -
ital allocation line, so their portfolios are not achievable. Indifference curves that lie 
below this one are not preferred because they have lower utility. Thus, the optimal 
portfolio for the investor with this indifference curve is portfolio C on CAL(P), which 
is tangent to the indifference curve.

Efficient Frontier and Investor’s Optimal Portfolio 295
Exhibit 25   Optimal Investor PortfolioExpected Return (%)E(Rp)
0Indifference curve 
Standard Deviation (%)PC
AEfficient frontier
of risky assets
Optimal risky
portfolio
Optimal investor
portfolioCAL(P)
Rf
σp
EXAMPLE 11   
Comprehensive Example on Portfolio Selection
This comprehensive example reviews many concepts learned in this reading. 
The example begins with simple information about available assets and builds 
an optimal investor portfolio for the Lohrmanns.
Suppose the Lohrmanns can invest in only two risky assets, A and B. The 
expected return and standard deviation for asset A are 20 percent and 50 percent, 
and the expected return and standard deviation for asset B are 15 percent and 
33 percent. The two assets have zero correlation with one another.
1 Calculate portfolio expected return and portfolio risk (standard deviation) 
if an investor invests 10 percent in A and the remaining 90 percent in B.

The subscript “ rp” means risky portfolio.
Rrp
rp AA B ww=×[] +−() × ==
=+0102 01 0101 50 155 15 50
22 2.% .% .. %
σ σ σσρ σσBA BABA B ww2
22 222
0100 50 0900 33 20 10 090+
× () +×() + ××× = .. .. .. 000 05 00 33
0 3012 30 12.. .
.. %×× ()
==
Note that the correlation coefficient is 0, so the last term for standard deviation 
is zero.
2 Generalize the above calculations for portfolio return and risk by assum -
ing an investment of wA in Asset A and an investment of (1 – wA) in Asset 
B.

Reading 39 ■ Portfolio Risk and Return: Part I 296
Rw ww
wwrp AA A
rp AA=× +−() ×= +
=× +−() ×20 11 50 05 015
05 10 3322 2%% ..
.. σ222 2
20250 1089 12
0 3589 0 2178 0 1089=+ −+()
=− +..
.. .ww w
wwAA A
AA
The investment opportunity set can be constructed by using different weights 
in the expressions for E(Rrp) and σrp in Part 1 of this example. Exhibit 26 shows 
the combination of Assets A and B.
Exhibit 26   
B = 15% return, 33% riskA = 20% return, 50% risk25%
20%
15%
10%
5%
0%Expected Portfolio Return E(Rp)
Standard Deviation of Portfolio σp0% 10% 20% 30% 40% 50% 60%
3 Now introduce a risk-  free asset with a return of 3 percent. Write an 
equation for the capital allocation line in terms of wA that will connect the 
risk-  free asset to the portfolio of risky assets. (Hint: use the equation in 
Section 3.3 and substitute the expressions for a risky portfolio’s risk and 
return from Part 2 above).

Efficient Frontier and Investor’s Optimal Portfolio 297
The equation of the line connecting the risk-  free asset to the portfolio of risky 
assets is given below (see Section 3.3), where the subscript “ rp” refers to the 
risky portfolio instead of “ i, ” and the subscript “ p” refers to the new portfolio of 
two risky assets and one risk-  free asset.
ER RER R
ER RER Rpfif
ip
pfrp f
rpp() =+()−
() =+() −σσ
σσ, 
Rewritten a s
==++−
−+
=+0030050 15 003
0 3589 0 2178 0 1089
00302... .
.. .
..w
wwA
AApσ
0 05 012
0 3589 0 2178 0 10892w
wwA
AAp+
−+.
.. .σ
The capital allocation line is the line that has the maximum slope because it is 
tangent to the curve formed by portfolios of the two risky assets. Exhibit 27 shows 
the capital allocation line based on a risk-  free asset added to the group of assets.
Exhibit 27   
B = 15% return, 33% riskA = 20% return, 50% risk
Capital Allocation Line
Standard Deviation of Portfolio σp25%
20%
15%
10%
5%
0%Expected Portfolio Return  E(Rp)
0% 10% 20% 30% 40% 50% 60%

4 The slope of the capital allocation line is maximized when the weight in 
Asset A is 38.20 percent.10 What is the equation for the capital allocation 
line using wA of 38.20 percent? 
10 You can maximize0050 12
0 3589 0 2178 0 10892..
.. .w
wwA
AA+
−+ by taking the first derivative of the slope with respect 
to wA and setting it to 0.

Reading 39 ■ Portfolio Risk and Return: Part I 298
By substituting 38.20 percent for wA in the equation in Part 3, we get E(Rp) = 
0.03 + 0.4978σp as the capital allocation line.
5 Having created the capital allocation line, we turn to the Lohrmanns. 
What is the standard deviation of a portfolio that gives a 20 percent 
return and is on the capital allocation line? How does this portfolio com -
pare with asset A? 
Solve the equation for the capital allocation line to get the standard deviation: 
0.20 = 0.03 + 0.4978σp. σp = 34.2%. The portfolio with a 20 percent return has 
the same return as Asset A but a lower standard deviation, 34.2 percent instead 
of 50.0 percent.
6 What is the risk of portfolios with returns of 3 percent, 9 percent, 15 per -
cent, and 20 percent? 
You can find the risk of the portfolio using the equation for the capital allocation 
line: E(Rp) = 0.03 + 0.4978σp.

For a portfolio with a return of 15 percent, write 0.15 = 0.03 + 0.4978σp. 
Solving for σp gives 24.1  percent. You can similarly calculate risks of other 
portfolios with the given returns.
The risk of the portfolio for a return of 3 percent is 0.0 percent, for a return 
of 9 percent is 12.1 percent, for a return of 15 percent is 24.1 percent, and for a 
return of 20 percent is 34.2 percent. The points are plotted in Exhibit 28.
Exhibit 28   
B = 15% return, 33% riskA = 20% return, 50% ris k
3%9%15%20%
20%
15%
10%
0% 10% 20% 30% 40% 50%5%
7 What is the utility that the Lohrmanns derive from a portfolio with a 
return of 3 percent, 9 percent, 15 percent, and 20 percent? The risk aver -
sion coefficient for the Lohrmanns is 2.5.

Efficient Frontier and Investor’s Optimal Portfolio 299
To find the utility, use the utility formula with a risk aversion coefficient of 2.5:
Utility
Utility  
Utility  =() −×
() =
() =ERpp 05 25
30 0300
902..
%.
%.σ
0 09 05 25 0 121 0 0717
15 0150 52 50 2412−× ×= +
() =− ××.. ..
%. .. . Utility  2 2
20 0774
20 0200 52 50 341 0 0546=+
() =− ×× =+.
%. .. .. Utility  
Based on the above information, the Lohrmanns choose a portfolio with a return 
of 15 percent and a standard deviation of 24.1 percent because it has the highest 
utility: 0.0774. Finally, Exhibit 29 shows the indifference curve that is tangent 
to the capital allocation line to generate Lohrmanns’ optimal investor portfolio.
Exhibit 29   
Lohrmanns’ Optimal portfolio
Capital Allocation LineLohrmanns’ Utility Curve
(not to scale)
Standard Deviation of Portfolio σp20%
15%
10%
5%
0% 10% 20% 30% 40% 50%
5.4.1  Investor Preferences and Optimal Portfolios

The location of an optimal investor portfolio depends on the investor’s risk prefer -
ences. A highly risk-  averse investor may invest a large proportion, even 100 percent, 
of his/her assets in the risk-  free asset. The optimal portfolio in this investor’s case 
will be located close to the y-axis. A less risk-  averse investor, however, may invest a 
large portion of his/her wealth in the optimal risky asset. The optimal portfolio in 
this investor’s case will lie closer to Point P in Exhibit 25.
Some less risk-  averse investors (i.e., with a high risk tolerance) may wish to accept 
even more risk because of the chance of higher return. Such an investor may borrow 
money to invest more in the risky portfolio. If the investor borrows 25 percent of 
his wealth, he/she can invest 125 percent in the optimal risky portfolio. The optimal 
investor portfolio for such an investor will lie to the right of Point P on the capital 

Reading 39 ■ Portfolio Risk and Return: Part I 300
Thus, moving from the risk-  free asset along the capital allocation line, we encounter 
investors who are willing to accept more risk. At Point P , the investor is 100 percent 
invested in the optimal risky portfolio. Beyond Point P , the investor accepts even more 
risk by borrowing money and investing in the optimal risky portfolio.
Note that we are able to accommodate all types of investors with just two portfolios: 
the risk-  free asset and the optimal risky portfolio. Exhibit 25 is also an illustration 
of the two-  fund separation theorem. Portfolio P is the optimal risky portfolio that 
is selected without regard to investor preferences. The optimal investor portfolio 
is selected on the capital allocation line by overlaying the indifference curves that 
incorporate investor preferences.
SUMMARY
This reading provides a description and computation of investment characteristics,

such as risk and return, that investors use in evaluating assets for investment. This 
was followed by sections about portfolio construction, selection of an optimal risky 
portfolio, and an understanding of risk aversion and indifference curves. Finally, 
the tangency point of the indifference curves with the capital allocation line allows 
identification of the optimal investor portfolio. Key concepts covered in the reading 
■■Holding period return is most appropriate for a single, predefined holding 
period.
■■Multiperiod returns can be aggregated in many ways. Each return computation 
has special applications for evaluating investments.
■■Risk-  averse investors make investment decisions based on the risk–return 
trade-  off, maximizing return for the same risk, and minimizing risk for the 
same return. They may be concerned, however, by deviations from a normal 
return distribution and from assumptions of financial markets’ operational 
efficiency.

■■Investors are risk averse, and historical data confirm that financial markets price 
assets for risk-  averse investors.
■■The risk of a two-  asset portfolio is dependent on the proportions of each asset, 
their standard deviations and the correlation (or covariance) between the asset’s 
returns. As the number of assets in a portfolio increases, the correlation among 
asset risks becomes a more important determinate of portfolio risk.
■■Combining assets with low correlations reduces portfolio risk.
■■The two-  fund separation theorem allows us to separate decision making into 
two steps. In the first step, the optimal risky portfolio and the capital alloca -
tion line are identified, which are the same for all investors. In the second step, 
investor risk preferences enable us to find a unique optimal investor portfolio 
for each investor.
■■The addition of a risk-  free asset creates portfolios that are dominant to portfo -

lios of risky assets in all cases except for the optimal risky portfolio.
By successfully understanding the content of this reading, you should be comfortable 
calculating an investor’s optimal portfolio given the investor’s risk preferences and 
universe of investable assets available.

References 301
2009 Ibbotson Stocks, Bonds, Bills, and Inflation (SBBI) Classic 
Yearbook . 2009. Chicago, IL: Morningstar.
Bogle, John C. 2008. “Black Monday and Black Swans. ” Financial 
Analysts Journal , vol. 64, no. 2: 30–40. Dimson, Elroy, Paul Marsh, and Mike Staunton. 2009. Credit 
Suisse Global Investment Returns Sourcebook . 2009. Zurich, 
Switzerland: Credit Suisse Research Institute.
Taleb, Nassim N. 2007. The Black Swan: The Impact of the Highly 
Improbable . New York: Random House Inc.

Reading 39 ■ Portfolio Risk and Return: Part I 302
1 An investor purchased 100 shares of a stock for $34.50 per share at the begin -
ning of the quarter. If the investor sold all of the shares for $30.50 per share 
after receiving a $51.55 dividend payment at the end of the quarter, the holding 
period return is closest  to:
A −13.0%.
B −11.6%.
C −10.1%.
2 An analyst obtains the following annual rates of return for a mutual fund:
Y ear Return (%) 
2008 14
2009 −10
2010 −2
 The fund’s holding period return over the three-  year period is closest  to:
A 0.18%.
B 0.55%.
C 0.67%.
3 An analyst observes the following annual rates of return for a hedge fund:
2008 22
2009 −25
2010 11
 The hedge fund’s annual geometric mean return is closest  to:
A 0.52%.
B 1.02%.
C 2.67%.
4 Which of the following return calculating methods is best for evaluating the 
annualized returns of a buy-  and-  hold strategy of an investor who has made

annual deposits to an account for each of the last five years?
A Geometric mean return.
B Arithmetic mean return.
C Money-  weighted return.
5 An investor evaluating the returns of three recently formed exchange-  traded 
funds gathers the following information:
ETF Time Since Inception Return Since Inception (%) 
1     146 days 4.61
2     5 weeks 1.10
3     15 months 14.35
 The ETF with the highest annualized rate of return is:

Practice Problems 303
A ETF 1.
B ETF 2.
C ETF 3.
6 With respect to capital market theory, which of the following asset charac -
teristics is least likely  to impact the variance of an investor’s equally weighted 
portfolio?
A Return on the asset.
B Standard deviation of the asset.
C Covariances of the asset with the other assets in the portfolio.
7 A portfolio manager creates the following portfolio:
Security Security Weight (%)Expected  
Standard Deviation (%)
1 30 20
2 70 12
 If the correlation of returns between the two securities is 0.40, the expected 
standard deviation of the portfolio is closest  to:
A 10.7%.
B 11.3%.
C 12.1%.
8 A portfolio manager creates the following portfolio:
1 30 20
2 70 12
 If the covariance of returns between the two securities is −0.0240, the expected 
A 2.4%.
B 7.5%.
C 9.2%.
9–10

9–10
A portfolio manager creates the following portfolio:
1 30 20
2 70 12
9 If the standard deviation of the portfolio is 14.40%, the correlation between the 
two securities is equal to:
A −1.0.

Reading 39 ■ Portfolio Risk and Return: Part I 304
B 0.0.
C 1.0.
10 If the standard deviation of the portfolio is 14.40%, the covariance between the 
A 0.0006.
B 0.0240.
C 1.0000.
11–14
An analyst observes the following historic geometric returns:
Asset Class Geometric Return (%)
Equities 8.0
Corporate Bonds 6.5
Treasury bills 2.5
Inflation 2.1
11 The real rate of return for equities is closest  to:
A 5.4%.
B 5.8%.
C 5.9%.
12 The real rate of return for corporate bonds is closest  to:
A 4.3%.
B 4.4%.
C 4.5%.
13 The risk premium for equities is closest  to:
A 3.2%.
B 3.4%.
C 3.6%.
14 The risk premium for corporate bonds is closest  to:
A 1.5%.
B 1.8%.
C 2.1%.
15 With respect to trading costs, liquidity is least likely  to impact the:
A stock price.
B bid–ask spreads.
C brokerage commissions.
16 Evidence of risk aversion is best illustrated by a risk–return relationship that is:
A negative.

Practice Problems 305
B neutral.
C positive.
17 With respect to risk-  averse investors, a risk-  free asset will generate a numerical 
utility that is:
A the same for all individuals.
B positive for risk-  averse investors.
C equal to zero for risk seeking investors.
18 With respect to utility theory, the most risk-  averse investor will have an indif -
ference curve with the:
A most convexity.
B smallest intercept value.
C greatest slope coefficient.
19 With respect to an investor’s utility function expressed as:  UE rA =()−1
22σ, 
which of the following values for the measure for risk aversion has the least  
amount of risk aversion?
A −4.
B 0.
C 4.
20–23
A financial planner has created the following data to illustrate the application of utility 
theory to portfolio selection:
InvestmentExpected  
Return (%)Expected  
1 18 2
2 19 8
3 20 15
4 18 30
20 A risk-  neutral investor is most likely  to choose:
A Investment 1.
B Investment 2.

C Investment 3.
21 If an investor’s utility function is expressed as  UE rA =()−1
22σ and the 
measure for risk aversion has a value of −2, the risk-  seeking investor is most 
likely  to choose:
A Investment 2.
B Investment 3.
C Investment 4.

Reading 39 ■ Portfolio Risk and Return: Part I 306
22 If an investor’s utility function is expressed as  UE rA=− ()1
22σ and the 
measure for risk aversion has a value of 2, the risk-  averse investor is most likely  
to choose:
23 If an investor’s utility function is expressed as  UE rA =()−1
22σ and the 
measure for risk aversion has a value of 4, the risk-  averse investor is most likely  
to choose:
24 With respect to the mean–variance portfolio theory, the capital allocation line, 
CAL, is the combination of the risk-  free asset and a portfolio of all:
A risky assets.
B equity securities.
C feasible investments.
25 Two individual investors with different levels of risk aversion will have optimal 
portfolios that are:
A below the capital allocation line.
B on the capital allocation line.
C above the capital allocation line.
26–28

26–28
Security Expected Annual Return (%) Expected Standard Deviation (%)
1 16 20
2 12 20
26 If the portfolio of the two securities has an expected return of 15%, the propor -
tion invested in Security 1 is:
A 25%.
B 50%.
C 75%.
27 If the correlation of returns between the two securities is −0.15, the expected 
standard deviation of an equal-  weighted portfolio is closest  to:
A 13.04%.
B 13.60%.

Practice Problems 307
C 13.87%.
28 If the two securities are uncorrelated, the expected standard deviation of an 
equal-  weighted portfolio is closest  to:
A 14.00%.
B 14.14%.
C 20.00%.
29 As the number of assets in an equally-  weighted portfolio increases, the contri -
bution of each individual asset’s variance to the volatility of the portfolio:
A increases.
B decreases.
C remains the same.
30 With respect to an equally-  weighted portfolio made up of a large number 
of assets, which of the following contributes the most  to the volatility of the 
A Average variance of the individual assets.
B Standard deviation of the individual assets.
C Average covariance between all pairs of assets.
31 The correlation between assets in a two-  asset portfolio increases during a 
market decline. If there is no change in the proportion of each asset held in the 
portfolio or the expected standard deviation of the individual assets, the volatil -
ity of the portfolio is most likely  to:

32–34
An analyst has made the following return projections for each of three possible out -
comes with an equal likelihood of occurrence:
AssetOutcome 1  
(%) Outcome 2  
(%) Outcome 3  
(%) Expected Return  
(%) 
1 12 0 6 6
2 12 6 0 6
3 0 6 12 6
32 Which pair of assets is perfectly negatively correlated?
A Asset 1 and Asset 2.
B Asset 1 and Asset 3.
C Asset 2 and Asset 3.
33 If the analyst constructs two-  asset portfolios that are equally-  weighted, which 
pair of assets has the lowest  expected standard deviation?

Reading 39 ■ Portfolio Risk and Return: Part I 308
34 If the analyst constructs two-  asset portfolios that are equally weighted, which 
pair of assets provides the least  amount of risk reduction?
35 Which of the following statements is least  accurate? The efficient frontier is the 
set of all attainable risky assets with the:
A highest expected return for a given level of risk.
B lowest amount of risk for a given level of return.
C highest expected return relative to the risk-  free rate.
36 The portfolio on the minimum-  variance frontier with the lowest standard devi -
ation is:
A unattainable.
B the optimal risky portfolio.
C the global minimum-  variance portfolio.
37 The set of portfolios on the minimum-  variance frontier that dominates all sets 
of portfolios below the global minimum-  variance portfolio is the:
A capital allocation line.
B Markowitz efficient frontier.

C set of optimal risky portfolios.
38 The dominant capital allocation line is the combination of the risk-  free asset 
and the:
A optimal risky portfolio.
B levered portfolio of risky assets.
C global minimum-  variance portfolio.
39 Compared to the efficient frontier of risky assets, the dominant capital alloca -
tion line has higher rates of return for levels of risk greater than the optimal 
risky portfolio because of the investor’s ability to:
A lend at the risk-  free rate.
B borrow at the risk-  free rate.
C purchase the risk-  free asset.
40 With respect to the mean–variance theory, the optimal portfolio is determined 
by each individual investor’s:
A risk-  free rate.
B borrowing rate.
C risk preference.

Solutions 309
SOLUTIONS
1 C is correct. −10.1% is the holding period return, which is calculated as: (3,050 
− 3,450 + 51.55)/3,450, which is comprised of a dividend yield of 1.49% = 51.55/
(3,450) and a capital loss yield of −11.59% = –400/(3,450).
2 B is correct. [(1 + 0.14)(1 − 0.10)(1 − 0.02)] – 1 = 0.0055 = 0.55%.
3 A is correct. [(1 + 0.22)(1 − 0.25)(1 + 0.11)](1/3) − 1 = 1.0157(1/3) − 1 = 0.0052 = 
0.52%
4 A is correct. The geometric mean return compounds the returns instead of the 
amount invested.
5 B is correct. The annualized rate of return for ETF 2 is 12.05% = (1.011052/5) − 
1, which is greater than the annualized rate of ETF 1, 11.93% = (1.0461365/146) 
− 1, and ETF 3, 11.32% = (1.143512/15) − 1. Despite having the lowest value for 
the periodic rate, ETF 2 has the highest annualized rate of return because of the 
reinvestment rate assumption and the compounding of the periodic rate.
6 A is correct. The asset’s returns are not used to calculate the portfolio’s variance

[only the assets’ weights, standard deviations (or variances), and covariances (or 
correlations) are used].
7 C is correct.
σσ σρ σσport ww ww =+ +
=() () +() ()12
12
22
22
12 12 12
22 22
03 20 07 12,
.% .%2 2
02030 70 40 20 12
0 3600 0 7056 0 4032+()()() () ()
=+ + ().. .% %
.% .% .% .. ..% .%50 51 4688 12 11=() =
8 A is correct.
σσ σport ww ww CovRR =+ + ()
=() () +() (12
12
22
22
12 12
22 22
03 20 07 12 .% .% ) )+()() −()
=+ − () =2
05203070 0240
0 3600 0 7056 1 008 0 057.. .
.% .% .% ..662 4005%. %.() =
9 C is correct. A portfolio standard deviation of 14.40% is the weighted average, 
which is possible only if the correlation between the securities is equal to 1.0.
10 B is correct. A portfolio standard deviation of 14.40% is the weighted average, 
which is possible only if the correlation between the securities is equal to 1.0. 
If the correlation coefficient is equal to 1.0, then the covariance must equal 
0.0240, calculated as: Cov(R1,R2) = ρ12σ1σ2 = (1.0)(20%)(12%) = 2.40% = 0.0240.

11 B is correct. (1 + 0.080)/(1 + 0.0210) – 1 = 5.8%
12 A is correct. (1 + 0.065)/(1 + 0.0210) – 1 = 4.3%
13 A is correct. (1 + 0.058)/(1 + 0.0250) – 1 = 3.2%
14 B is correct. (1 + 0.043)/(1 + 0.0250) – 1 = 1.8%
15 C is correct. Brokerage commissions are negotiated with the brokerage firm. 
A security’s liquidity impacts the operational efficiency of trading costs. 
Specifically, liquidity impacts the bid–ask spread and can impact the stock price 
(if the ability to sell the stock is impaired by the uncertainty associated with 
being able to sell the stock).

Reading 39 ■ Portfolio Risk and Return: Part I 310
16 C is correct. Historical data over long periods of time indicate that there exists 
a positive risk–return relationship, which is a reflection of an investor’s risk 
aversion.
17 A is correct. A risk-  free asset has a variance of zero and is not dependent on 
whether the investor is risk neutral, risk seeking or risk averse. That is, given 
that the utility function of an investment is expressed as  UE rA =()−1
22σ, 
where A is the measure of risk aversion, then the sign of A is irrelevant if the 
variance is zero (like that of a risk-  free asset).
18 C is correct. The most risk-  averse investor has the indifference curve with the 
greatest slope.
19 A is correct. A negative value in the given utility function indicates that the 
investor is a risk seeker.
20 C is correct. Investment 3 has the highest rate of return. Risk is irrelevant to 
a risk-  neutral investor, who would have a measure of risk aversion equal to 0.

Given the utility function, the risk-  neutral investor would obtain the greatest 
amount of utility from Investment 3.
Return (%) Expected  
Standard Deviation (%)Utility  
A = 0
1 18 2 0.1800
2 19 8 0.1900
3 20 15 0.2000
4 18 30 0.1800
21 C is correct. Investment 4 provides the highest utility value (0.2700) for a risk-  
seeking investor, who has a measure of risk aversion equal to −2.
Standard Deviation 
(%)Utility  
A = –2
1 18 2 0.1804
2 19 8 0.1964
3 20 15 0.2225
4 18 30 0.2700
22 B is correct. Investment 2 provides the highest utility value (0.1836) for a risk-  
averse investor who has a measure of risk aversion equal to 2.
Standard Deviation (%) Utility  
A = 2
1 18 2 0.1796
2 19 8 0.1836
3 20 15 0.1775
4 18 30 0.0900
23 A is correct. Investment 1 provides the highest utility value (0.1792) for a risk-  
averse investor who has a measure of risk aversion equal to 4.

Solutions 311
A = 4
1 18 2 0.1792
2 19 8 0.1772
3 20 15 0.1550
4 18 30 0.0000
24 A is correct. The CAL is the combination of the risk-  free asset with zero risk 
and the portfolio of all risky assets that provides for the set of feasible invest -
ments. Allowing for borrowing at the risk-  free rate and investing in the portfo -
lio of all risky assets provides for attainable portfolios that dominate risky assets 
below the CAL.
25 B is correct. The CAL represents the set of all feasible investments. Each inves -
tor’s indifference curve determines the optimal combination of the risk-  free 
asset and the portfolio of all risky assets, which must lie on the CAL.
26 C is correct.
Rw Rw R
Rw wp
p=× +−() ×
=× +−() ×
= () +11 12
111
16 11 2
15 075160 25 1 
%%
%. %. 2 2%()
27 A is correct.
12
22
22
12 12 12
22 22
05 20 05 20,
.%.%2 2
02050 50 15 20 20
1 0000 1 0000 0 3000+() () −() () ()
=+ − ().. .% %

.% .% .%.. ..% .%50 51 7000 13 04=() =
28 B is correct.
=() () +()(12
12
22
22
12 12 12
22 2 22
05 20 05 20,
.%.% ) )+() () () () ()
=+ + ()2050 50 00 20 20
1 0000 1 0000 0 00000... %%
.% .% .%.550 52 0000 14 14=() = .% .%.
29 B is correct. The contribution of each individual asset’s variance (or standard 
deviation) to the portfolio’s volatility decreases as the number of assets in the 
equally weighted portfolio increases. The contribution of the co-  movement 
measures between the assets increases (i.e., covariance and correlation) as the 
number of assets in the equally weighted portfolio increases. The following 
equation for the variance of an equally weighted portfolio illustrates these 
points:  σσσρσpNN
NCOVNN
N2222 11=+−=+−.
30 C is correct. The co-  movement measures between the assets increases (i.e., 
covariance and correlation) as the number of assets in the equally weighted

portfolio increases. The contribution of each individual asset’s variance (or

Reading 39 ■ Portfolio Risk and Return: Part I 312
standard deviation) to the portfolio’s volatility decreases as the number of assets 
in the equally weighted portfolio increases. The following equation for the vari -
ance of an equally weighted portfolio illustrates these points:
σσσρσpNN
NCOVNN
N2222 11=+−=+−
31 A is correct. Higher correlations will produce less diversification benefits 
provided that the other components of the portfolio standard deviation do not 
change (i.e., the weights and standard deviations of the individual assets).
32 C is correct. Asset 2 and Asset 3 have returns that are the same for Outcome 
2, but the exact opposite returns for Outcome 1 and Outcome 3; therefore, 
because they move in opposite directions at the same magnitude, they are per -
fectly negatively correlated.
33 C is correct. An equally weighted portfolio of Asset 2 and Asset 3 will have the 
lowest portfolio standard deviation, because for each outcome, the portfolio has

the same expected return (they are perfectly negatively correlated).
34 A is correct. An equally weighted portfolio of Asset 1 and Asset 2 has the high -
est level of volatility of the three pairs. All three pairs have the same expected 
return; however, the portfolio of Asset 1 and Asset 2 provides the least amount 
of risk reduction.
35 C is correct. The efficient frontier does not account for the risk-  free rate. The 
efficient frontier is the set of all attainable risky assets with the highest expected 
return for a given level of risk or the lowest amount of risk for a given level of 
return.
36 C is correct. The global minimum-  variance portfolio is the portfolio on the 
minimum-  variance frontier with the lowest standard deviation. Although 
the portfolio is attainable, when the risk-  free asset is considered, the global 
minimum-  variance portfolio is not the optimal risky portfolio.
37 B is correct. The Markowitz efficient frontier has higher rates of return for

a given level of risk. With respect to the minimum-  variance portfolio, the 
Markowitz efficient frontier is the set of portfolios above the global minimum-  
variance portfolio that dominates the portfolios below the global minimum-  
variance portfolio.
38 A is correct. The use of leverage and the combination of a risk-  free asset and 
the optimal risky asset will dominate the efficient frontier of risky assets (the 
Markowitz efficient frontier).
39 B is correct. The CAL dominates the efficient frontier at all points except for 
the optimal risky portfolio. The ability of the investor to purchase additional 
amounts of the optimal risky portfolio by borrowing (i.e., buying on margin) at 
the risk-  free rate makes higher rates of return for levels of risk greater than the 
optimal risky asset possible.
40 C is correct. Each individual investor’s optimal mix of the risk-  free asset and the 
optimal risky asset is determined by the investor’s risk preference.

Portfolio Risk and Return: Part II
a. describe the implications of combining a risk-  free asset with a 
portfolio of risky assets;
b. explain the capital allocation line (CAL) and the capital market 
line (CML);
c. explain systematic and nonsystematic risk, including why an 
investor should not expect to receive additional return for bearing 
nonsystematic risk;
d. explain return generating models (including the market model) 
and their uses;
e. calculate and interpret beta;
f. explain the capital asset pricing model (CAPM), including its 
assumptions, and the security market line (SML);
g. calculate and interpret the expected return of an asset using the 
CAPM;
h. describe and demonstrate applications of the CAPM and the 
SML;
i. calculate and interpret the Sharpe ratio, Treynor ratio, M2, and 
Jensen’s alpha.

Our objective in this reading is to identify the optimal risky portfolio for all investors 
by using the capital asset pricing model (CAPM). The foundation of this reading is 
the computation of risk and return of a portfolio and the role that correlation plays 
in diversifying portfolio risk and arriving at the efficient frontier. The efficient frontier 
and the capital allocation line consist of portfolios that are generally acceptable to all 1rEADING
40

Reading 40 ■ Portfolio Risk and Return: Part II 314
investors. By combining an investor’s individual indifference curves with the market-  
determined capital allocation line, we are able to illustrate that the only optimal risky 
portfolio for an investor is the portfolio of all risky assets (i.e., the market).
Additionally, we discuss the capital market line, a special case of the capital allo -
cation line that is used for passive investor portfolios. We also differentiate between 
systematic and nonsystematic risk, and explain why investors are compensated for 
bearing systematic risk but receive no compensation for bearing nonsystematic risk. 
We discuss in detail the CAPM, which is a simple model for estimating asset returns 
based only on the asset’s systematic risk. Finally, we illustrate how the CAPM allows 
security selection to build an optimal portfolio for an investor by changing the asset 
mix beyond a passive market portfolio.

The reading is organized as follows. In Section 2, we discuss the consequences of 
combining a risk-  free asset with the market portfolio and provide an interpretation 
of the capital market line. Section 3 decomposes total risk into systematic and non -
systematic risk and discusses the characteristics of and differences between the two 
kinds of risk. We also introduce return-  generating models, including the single-  index 
model, and illustrate the calculation of beta by using formulas and graphically by using 
the security characteristic line. In Section 4, we introduce the capital asset pricing 
model and the security market line. We discuss many applications of the CAPM and 
the SML throughout the reading, including the use of expected return in making cap -
ital budgeting decisions, the evaluation of portfolios using the CAPM’s risk-  adjusted 
return as the benchmark, security selection, and determining whether adding a new

security to the current portfolio is appropriate. Our focus on the CAPM does not 
suggest that the CAPM is the only viable asset pricing model. Although the CAPM 
is an excellent starting point, more advanced readings expand on these discussions 
and extend the analysis to other models that account for multiple explanatory factors. 
A preview of a number of these models is given in Section 5, and a summary and 
CAPITAL MARKET THEORY
You have learned how to combine a risk-  free asset with one risky asset and with many 
risky assets to create a capital allocation line. In this section, we will expand our dis -
cussion of multiple risky assets and consider a special case of the capital allocation 
line, called the capital market line. While discussing the capital market line, we will 
define the market and its role in passive portfolio management. Using these concepts, 
we will illustrate how leveraged portfolios can enhance both risk and return.

2.1 Portfolio of Risk-  Free and Risky Assets
Although investors desire an asset that produces the highest return and carries the 
lowest risk, such an asset does not exist. As the risk–return capital market theory 
illustrates, one must assume higher risk in order to earn a higher return. We can 
improve an investor’s portfolio, however, by expanding the opportunity set of risky 
assets because this allows the investor to choose a superior mix of assets.
Similarly, an investor’s portfolio improves if a risk-  free asset is added to the mix. 
In other words, a combination of the risk-  free asset and a risky asset can result in a 
better risk–return trade-  off than an investment in only one type of asset because the 
risk-  free asset has zero correlation with the risky asset. The combination is called the 
capital allocation line  (and is depicted in Exhibit 2). Superimposing an investor’s indif -
ference curves on the capital allocation line will lead to the optimal investor portfolio.2

Capital Market Theory 315
Investors with different levels of risk aversion will choose different portfolios. 
Highly risk-  averse investors choose to invest most of their wealth in the risk-  free asset 
and earn low returns because they are not willing to assume higher levels of risk. Less 
risk-  averse investors, in contrast, invest more of their wealth in the risky asset, which 
is expected to yield a higher return. Obviously, the higher return cannot come without 
higher risk, but the less risk-  averse investor is willing to accept the additional risk.
2.1.1  Combining a Risk-  Free Asset with a Portfolio of Risky Assets
We can extend the analysis of one risky asset to a portfolio of risky assets. For con -
venience, assume that the portfolio contains all available risky assets,1 although an 
investor may not wish to include all of these assets in the portfolio because of the 
investor’s specific preferences. If an asset is not included in the portfolio, its weight

will be zero. The risk–return characteristics of a portfolio of N risky assets are given 
by the following equations:
ER wE Rw wi jpi i
iN
pi j
ijN
() = () = ()



== =∑∑
12
11,, ,
,  Cov an σ d d wi
iN
=
=∑ 1
1
The expected return on the portfolio, E(Rp), is the weighted average of the expected 
returns of individual assets, where wi is the fractional weight in asset i and Ri is the 
expected return of asset i. The risk of the portfolio (σp), however, depends on the 
weights of the individual assets, the risk of the individual assets, and their interrela -
tionships. The covariance  between assets i and j, Cov( i,j), is a statistical measure of the 
interrelationship between each pair of assets in the portfolio and can be expressed as 
follows, where ρij is the correlation  between assets i and j and σi is the risk of asset i:
Cov( i,j) = ρijσiσj
Note from the equation below that the correlation of an asset with itself is 1; therefore:
Cov( i,i) = ρiiσiσi = σi2

By substituting the above expressions for covariance, we can rewrite the portfolio 
variance equation as
σσ ρσ σpi i
iN
ij
ij ijN
ijij ww w22 2
11=+



== ≠∑∑
,,
The suggestion that portfolios have lower risk than the assets they contain may 
seem counterintuitive. These portfolios can be constructed, however, as long as the 
assets in the portfolio are not perfectly correlated. As an illustration of the effect 
of asset weights on portfolio characteristics, consider a simple two-  asset portfolio 
with zero weights in all other assets. Assume that Asset 1 has a return of 10 percent 
and a standard deviation (risk) of 20 percent. Asset 2 has a return of 5 percent and 
a standard deviation (risk) of 10 percent. Furthermore, the correlation between the 
two assets is zero. Exhibit 1 shows risks and returns for Portfolio X with a weight of 
25 percent in Asset 1 and 75 percent in Asset 2, Portfolio Y with a weight of 50 per -

cent in each of the two assets, and Portfolio Z with a weight of 75 percent in Asset 1 
and 25 percent in Asset 2.
1 N risky assets.

Reading 40 ■ Portfolio Risk and Return: Part II 316
Exhibit 1   Portfolio Risk and Return
PortfolioWeight in  
Asset 1  
(%)Weight in  
Asset 2  
(%)Portfolio  
Return  
Standard  
Deviation (%)
X 25.0 75.0 6.25 9.01
Y 50.0 50.0 7.50 11.18
Z 75.0 25.0 8.75 15.21
Return 10.0 5.0
Standard deviation 20.0 10.0
Correlation between 
Assets 1 and 2 0.0
From this example we observe that the three portfolios are quite different in terms 
of their risk and return. Portfolio X has a 6.25 percent return and only 9.01 percent 
standard deviation, whereas the standard deviation of Portfolio Z is more than two-  
thirds higher (15.21 percent), although the return is only slightly more than one-  third 
higher (8.75 percent). These portfolios may become even more dissimilar as other 
assets are added to the mix.
Consider three portfolios of risky assets, A, B, and C, as in Exhibit 2, that may have 
been presented to a representative investor by three different investment advisers.

Each portfolio is combined with the risk-  free asset to create three capital allocation 
lines, CAL(A), CAL(B), and CAL(C). The exhibit shows that Portfolio C is superior to 
the other two portfolios because it has a greater expected return for any given level of 
risk. As a result, an investor will choose the portfolio that lies on the capital allocation 
line for Portfolio C. The combination of the risk-  free asset and the risky Portfolio C 
that is selected for an investor depends on the investor’s degree of risk aversion.
Exhibit 2   Risk-  Free Asset and Portfolio of Risky Assets
Indifference
Curve
Portfolio Standard Deviation ( σp)Expected Portfolio Retu rn E(Rp) CAL(C)
CAL(B)
CAL(A)C
B
A
Rf

Capital Market Theory 317
2.1.2  Does a Unique Optimal Risky Portfolio Exist?
We assume that all investors have the same economic expectation and thus have the 
same expectations of prices, cash flows, and other investment characteristics. This 
assumption is referred to as homogeneity of expectations . Given these investment 
characteristics, everyone goes through the same calculations and should arrive at 
the same optimal risky portfolio. Therefore, assuming homogeneous expectations, 
only one optimal portfolio exists. If investors have different expectations, however, 
they might arrive at different optimal risky portfolios. To illustrate, we begin with an 
expression for the price of an asset:
P
rt
tt
tT
=
+()=∑CF
10
where CFt is the cash flow at the end of period t and rt is the discount rate or the 
required rate of return for that asset for period t. Period t refers to all periods begin -
ning from now until the asset ceases to exist at the end of time T. Because the current

time is the end of period 0, which is the same as the beginning of period 1, there are 
(T + 1) cash flows and ( T + 1) required rates of return. These conditions are based 
on the assumption that a cash flow, such as an initial investment, can occur now ( t = 
0). Ordinarily, however, CF0 is zero.
We use the formula for the price of an asset to estimate the intrinsic value of an 
asset. For ease of reference, assume that the asset we are valuing is a share of HSBC 
Holdings (parent of HSBC Bank), a British company that also trades on the Hong 
Kong Stock Exchange. In the case of corporate stock, there is no expiration date, so 
T could be extremely large, meaning we will need to estimate a large number of cash 
flows and rates of return. Fortunately, the denominator reduces the importance of 
distant cash flows, so it may be sufficient to estimate, say, 20 annual cash flows and 20 
rates of returns. How much will HSBC earn next year and the year after next? What

will the banking sector look like in five years’ time? Different analysts and investors 
will have their own estimates that may be quite different from one another. Also, as 
we delve further into the future, more serious issues in estimating future revenue, 
expenses, and growth rates arise. Therefore, to assume that cash flow estimates for 
HSBC will vary among these investors is reasonable. In addition to the numerator 
(cash flows), it is also necessary to estimate the denominator, the required rates of 
return. We know that riskier companies will require higher returns because risk and 
return are positively correlated. HSBC stock is riskier than a risk-  free asset, but by 
how much? And what should the compensation for that additional risk be? Again, 
it is evident that different analysts will view the riskiness of HSBC differently and, 
therefore, arrive at different required rates of return.
HSBC closed at HK$89.40 on 31 December 2009 on the Hong Kong Stock Exchange.

The traded price represents the value that a marginal investor attaches to a share of 
HSBC, say, corresponding to Analyst A’s expectation. Analyst B may think that the 
price should be HK$50, however, and Analyst C may think that the price should be 
HK$150. Given a current price of HK$89.40, the expected returns of HSBC are quite 
different for the three analysts. Analyst B, who believes the price should be HK$50, 
concludes that HSBC is overvalued and may assign a weight of zero to HSBC in the 
recommended portfolio even though the market capitalization of HSBC is in excess 
of HK$1 trillion. In contrast, Analyst C, with a valuation of HK$150, thinks HSBC is 
undervalued and will significantly overweight HSBC in a portfolio.
Our discussion illustrates that analysts can arrive at different valuations that 
necessitate the assignment of different asset weights in a portfolio. Given the existence 
of many asset classes and numerous assets in each asset class, one can visualize that

Reading 40 ■ Portfolio Risk and Return: Part II 318
each investor will have his or her own optimal risky portfolio depending on his or her 
assumptions underlying the valuation computations. Therefore, market participants 
will have their own and possibly different optimal risky portfolios.
If investors have different valuations of assets, then the construction of a unique 
optimal risky portfolio is not possible. If we make a simplifying assumption of homoge -
neity in investor expectations, we will have a single optimal risky portfolio as previously 
mentioned. Even if investors have different expectations, market prices are a proxy 
of what the marginal, informed investor expects, and the market portfolio becomes 
the base case, the benchmark, or the reference portfolio that other portfolios can be 
judged against. For HSBC, the market price is HK$89.40 per share and the market 
capitalization is HK$1.08 trillion. In constructing the market portfolio, HSBC’s weight

in the market portfolio will be equal to its market value divided by the value of all 
other assets included in the market portfolio.
2.2 The Capital Market Line
In the previous section, we discussed how the risk-  free asset could be combined with 
a risky portfolio to create a capital allocation line. In this section, we discuss a specific 
CAL that uses the market portfolio as the optimal risky portfolio and is known as 
the capital market line. We also discuss the significance of the market portfolio and 
applications of the capital market line.
2.2.1  Passive and Active Portfolios
In the above subsection, we arrived at three possible valuations for each share of 
HSBC: HK$50, HK$89.40, and HK$150. Which one is correct?
If the market is an informationally efficient market , the price in the market, 
HK$89.40, is an unbiased estimate of all future discounted cash flows (recall the for -
mula for the price of an asset). In other words, the price aggregates and reflects all

information that is publicly available, and investors cannot expect to earn a return that 
is greater than the required rate of return for that asset. If, however, the price reflects 
all publicly available information and there is no way to outperform the market, then 
there is little point in investing time and money in evaluating HSBC to arrive at your 
price using your own estimates of cash flows and rates of return.
In that case, a simple and convenient approach to investing is to rely on the prices 
set by the market. Portfolios that are based on the assumption of unbiased market prices 
are referred to as passive portfolios. Passive portfolios most commonly replicate and 
track market indexes, which are passively constructed on the basis of market prices 
and market capitalizations. Examples of market indexes are the S&P 500 Index, the 
Nikkei 300, and the CAC 40. Passive portfolios based on market indexes are called

index funds and generally have low costs because no significant effort is expended in 
valuing securities that are included in an index.
In contrast to passive investors’ reliance on market prices and index funds, active 
investors may not rely on market valuations. They have more confidence in their own 
ability to estimate cash flows, growth rates, and discount rates. Based on these esti -
mates, they value assets and determine whether an asset is fairly valued. In an actively 
managed portfolio, assets that are undervalued, or have a chance of offering above-  
normal returns, will have a positive weight (i.e., overweight compared to the market 
weight in the benchmark index), whereas other assets will have a zero weight, or even 
a negative weight if short selling is permitted (i.e., some assets will be underweighted 
compared with the market weight in the benchmark index). This style of investing 
is called active investment management, and the portfolios are referred to as active

portfolios. Most open-  end mutual funds and hedge funds practice active investment 
management, and most analysts believe that active investing adds value. Whether 
these analysts are right or wrong is the subject of continuing debate.

Capital Market Theory 319
2.2.2  What Is the “Market”?
In the previous discussion, we referred to the “market” on numerous occasions without 
actually defining the market. The optimal risky portfolio and the capital market line 
depend on the definition of the market. So what is the market?
Theoretically, the market  includes all risky assets or anything that has value, which 
includes stocks, bonds, real estate, and even human capital. Not all assets are tradable, 
however, and not all tradable assets are investable. For example, the Taj Mahal in India 
is an asset but is not a tradable asset. Similarly, human capital is an asset that is not 
tradable. Moreover, assets may be tradable but not investable because of restrictions 
placed on certain kinds of investors. For example, all stocks listed on the Shanghai 
Stock Exchange are tradable. Class A shares, however, are available only to domestic 
investors, whereas Class B shares are available to both domestic and foreign investors.

For investors not domiciled in China, Class A shares are not investable—that is, they 
are not available for investment.
If we consider all stocks, bonds, real estate assets, commodities, etc., probably 
hundreds of thousands of assets are tradable and investable. The “market” should 
contain as many assets as possible; we emphasize the word “possible” because it is not 
practical to include all assets in a single risky portfolio. Even though advancements in 
technology and interconnected markets have made it much easier to span the major 
equity markets, we are still not able to easily invest in other kinds of assets like bonds 
and real estate except in the most developed countries.
For the rest of this reading, we will define the “market” quite narrowly because it is 
practical and convenient to do so. Typically, a local or regional stock market index is 
used as a proxy for the market because of active trading in stocks and because a local

or regional market is most visible to the local investors. For our purposes, we will use 
the S&P 500 Index as the market’s proxy. The S&P 500 is commonly used by analysts 
as a benchmark for market performance throughout the United States. It contains 
500 of the largest stocks that are domiciled in the United States, and these stocks are 
weighted by their market capitalization (price times the number of outstanding shares).
The stocks in the S&P 500 account for approximately 80 percent of the total equity 
market capitalization in the United States, and because the US stock markets represent 
about 32 percent of the world markets, the S&P 500 represents roughly 25 percent 
of worldwide publicly traded equity. Our definition of the market does not include 
non-  US stock markets, bond markets, real estate, and many other asset classes, and 
therefore, “market” return and the “market” risk premium refer to US equity return and

the US equity risk premium, respectively. The use of this proxy, however, is sufficient 
for our discussion, and is relatively easy to expand to include other tradable assets.
2.2.3  The Capital Market Line (CML)
A capital allocation line includes all possible combinations of the risk-  free asset and 
an investor’s optimal risky portfolio. The capital market line  is a special case of the 
capital allocation line, where the risky portfolio is the market portfolio. The risk-  free 
asset is a debt security with no default risk, no inflation risk, no liquidity risk, no 
interest rate risk, and no risk of any other kind. US Treasury bills are usually used as 
a proxy of the risk-  free return, Rf.
The S&P 500 is a proxy of the market portfolio, which is the optimal risky portfolio. 
Therefore, the expected return on the risky portfolio is the expected market return, 
expressed as E(Rm). The capital market line is shown in Exhibit 3, where the standard

deviation (σp), or total risk, is on the x-axis and expected portfolio return, E(Rp), is on 
the y-axis. Graphically, the market portfolio is the point on the Markowitz efficient 
frontier where a line from the risk-  free asset is tangent to the Markowitz efficient 
frontier. All points on the interior of the Markowitz efficient frontier are inefficient 
portfolios in that they provide the same level of return with a higher level of risk or

Reading 40 ■ Portfolio Risk and Return: Part II 320
a lower level of return with the same amount of risk. When plotted together, the 
point at which the CML is tangent to the Markowitz efficient frontier is the optimal 
combination of risky assets, on the basis of market prices and market capitalizations. 
The optimal risky portfolio is the market portfolio.
Exhibit 3   Capital Market Line
M
RfExpected Portfolio Return E(Rp) 
Standard Devi ation of Po rtfolio σpCML
Points above the
CML are not
achievable 
Effic ient
frontierE(Rm)
Individual
Securities
The CML’s intercept on the y-axis is the risk-  free return ( Rf) because that is the 
return associated with zero risk. The CML passes through the point represented by 
the market return, E(Rm). With respect to capital market theory, any point above the 
CML is not achievable and any point below the CML is dominated by and inferior to 
any point on the CML.
Note that we identify the CML and CAL as lines even though they are a combi -

nation of two assets. Unlike a combination of two risky assets, which is usually not 
a straight line, a combination of the risk-  free asset and a risky portfolio is a straight 
line, as illustrated below by computing the combination’s risk and return.
Risk and return characteristics of the portfolio represented by the CML can be 
computed by using the return and risk expressions for a two-  asset portfolio:
E(Rp) = w1Rf + (1 – w1)E(Rm),
and
σσ σpf mf m ww ww RR =+ −() +− () () 122
122
11 12 1C ov ,
The proportion invested in the risk-  free asset is given by w1, and the balance is 
invested in the market portfolio, (1 – w1). The risk of the risk-  free asset is given by 
σf, the risk of the market is given by σm, the risk of the portfolio is given by σp, and 
the covariance between the risk-  free asset and the market portfolio is represented 
by Cov( Rf,Rm).

Capital Market Theory 321
By definition, the standard deviation of the risk-  free asset is zero. Because its risk 
is zero, the risk-  free asset does not co-  vary or move with any other asset. Therefore, 
its covariance with all other assets, including the market portfolio, is zero, making the 
first and third terms under the square root sign zero. As a result, the portfolio return 
and portfolio standard deviation can be simplified and rewritten as:
and
σp = (1 – w1)σm
By substitution, we can express E(Rp) in terms of σp. Substituting for w1, we get:
ER RER R
pfmf
mp () =+() − 

×σσ
Note that the expression is in the form of a line, y = a + bx. The y-intercept is 
the risk-  free rate, and the slope of the line referred to as the market price of risk is 
[E(Rm) – Rf]/σm. The CML has a positive slope because the market’s risky return is 
larger than the risk-  free return. As the amount of the total investment devoted to the

market increases—that is, as we move up the line—both standard deviation (risk) and 
expected return increase.
EXAMPLE 1   
Risk and Return on the CML
Mr. Miles is a first time investor and wants to build a portfolio using only US 
T- bills and an index fund that closely tracks the S&P 500 Index. The T-  bills have 
a return of 5 percent. The S&P 500 has a standard deviation of 20 percent and 
an expected return of 15 percent.
1 Draw the CML and mark the points where the investment in the market is 
0 percent, 25 percent, 75 percent, and 100 percent.
2 Mr. Miles is also interested in determining the exact risk and return at 
each point.
We calculate the equation for the CML as E(Rp) = 5% + 0.50 × σp by substituting 
the given information into the general CML equation. The intercept of the line 
is 5 percent, and its slope is 0.50. We can draw the CML by arbitrarily taking 
any two points on the line that satisfy the above equation.

Alternatively, the CML can be drawn by connecting the risk-  free return of 
5 percent on the y-axis with the market portfolio at (20 percent, 15 percent). 
The CML is shown in Exhibit 4.

Reading 40 ■ Portfolio Risk and Return: Part II 322
Exhibit 4   Risk and Return on the CML
100% in market
Standard Deviation of Portfolio σpExpected Portfolio Return E(Rp)
0% in market
Slope = .575%
25%Rm = 15%
σm = 20Rf = 5%CML
M
Return with 0 percent invested in the market = 5 percent, which is the risk-  
free return.
Standard deviation with 0 percent invested in the market = 0 percent 
because T-  bills are not risky.
Return with 25 percent invested in the market = (0.75 × 5%) + (0.25 × 15%) = 
7.5%.
Standard deviation with 25 percent invested in the market = 0.25 × 20% = 
5%.
Return with 75 percent invested in the market = (0.25 × 5%) + (0.75 × 15%) = 
12.50%.
Standard deviation with 75 percent invested in the market = 0.75 × 20% = 
15%.
Return with 100 percent invested in the market = 15 percent, which is the 
return on the S&P  500.
Standard deviation with 100 percent invested in the market = 20 percent, 
which is the risk of the S&P  500.
2.2.4  Leveraged Portfolios

In the previous example, Mr. Miles evaluated an investment of between 0 percent and 
100 percent in the market and the balance in T-  bills. The line connecting Rf and M 
(market portfolio) in Exhibit 4 illustrates these portfolios with their respective levels 
of investment. At Rf, an investor is investing all of his or her wealth into risk-  free 
securities, which is equivalent to lending 100 percent at the risk-  free rate. At Point M 
he or she is holding the market portfolio and not lending any money at the risk-  free 
rate. The combinations of the risk-  free asset and the market portfolio, which may be 
achieved by the points between these two limits, are termed “lending” portfolios. In 
effect, the investor is lending part of his or her wealth at the risk-  free rate.

Capital Market Theory 323
If Mr. Miles is willing to take more risk, he may be able to move to the right of the 
market portfolio (Point M in Exhibit 4) by borrowing money and purchasing more 
of Portfolio M. Assume that he is able to borrow money at the same risk-  free rate of 
interest, Rf, at which he can invest. He can then supplement his available wealth with 
borrowed money and construct a borrowing portfolio. If the straight line joining Rf 
and M is extended to the right of Point M, this extended section of the line represents 
borrowing portfolios. As one moves further to the right of Point M, an increasing 
amount of borrowed money is being invested in the market. This means that there is 
negative  investment in the risk-  free asset, which is referred to as a leveraged position  
in the risky portfolio. The particular point chosen on the CML will depend on the 
individual’s utility function, which, in turn, will be determined by his risk and return 
preferences.
EXAMPLE 2

EXAMPLE 2   
Risk and Return of a Leveraged Portfolio with Equal 
Lending and Borrowing Rates
Mr. Miles decides to set aside a small part of his wealth for investment in a 
portfolio that has greater risk than his previous investments because he antic -
ipates that the overall market will generate attractive returns in the future. He 
assumes that he can borrow money at 5 percent and achieve the same return 
on the S&P 500 as before: an expected return of 15 percent with a standard 
deviation of 20 percent.
Calculate his expected risk and return if he borrows 25 percent, 50 percent, 
and 100 percent of his initial investment amount.
Solution:
The leveraged portfolio’s standard deviation and return can be calculated in the 
same manner as before with the following equations:
E(Rp) = w1Rf + (1 – w1)E(Rm)
and
The proportion invested in T-  bills becomes negative instead of positive because 
Mr. Miles is borrowing money. If 25 percent of the initial investment is borrowed,

w1 = –0.25, and (1 – w1) = 1.25, etc.
Return with –25 percent invested in T-  bills = (–0.25 × 5%) + (1.25 × 15%) = 
17.5%.
Standard deviation with –25 percent invested in T-  bills = 1.25 × 20% = 25%.
Return with –50 percent invested in T-  bills = (–0.50 × 5%) + (1.50 × 15%) = 
20.0%.
Standard deviation with –50 percent invested in T-  bills = 1.50 × 20% = 30%.
Return with –100 percent invested in T-  bills = (–1.00 × 5%) + (2.00 × 15%) = 
25.0%.
Standard deviation with –100 percent invested in T-  bills = 2.00 × 20% = 40%.
Note that negative investment (borrowing) in the risk-  free asset provides a 
higher expected return for the portfolio but that higher return is also associated 
with higher risk.

Reading 40 ■ Portfolio Risk and Return: Part II 324
Leveraged Portfolios with Different Lending and Borrowing Rates  Although we 
assumed that Mr. Miles can borrow at the same rate as the US government, it is more 
likely that he will have to pay a higher interest rate than the government because his 
ability to repay is not as certain as that of the government. Now consider that although 
Mr. Miles can invest (lend) at Rf, he can borrow at only Rb, a rate that is higher than 
With different lending and borrowing rates, the CML will no longer be a single 
straight line. The line will have a slope of [ E(Rm) – Rf]/σm between Points Rf and M, 
where the lending rate is Rf, but will have a smaller slope of [ E(Rm) – Rb]/σm at points 
to the right of M, where the borrowing rate is Rb. Exhibit 5 illustrates the CML with 
different lending and borrowing rates.
Exhibit 5   CML with Different Lending and Borrowing Rates
Borrowing
RfExpected  Portfolio  Return E(Rp)

Borrowing
Standard Devi ation of Po rtfolio σpLendingMarket
portfolio, M 
Slope  =E(Rm) – Rf
σmE(Rm) – Rb
σm
The equations for the two lines are given below.
wE RRER R
pfmf
mp 1 0≥ () =+() − 

× : σσ
and
wE RRER R
pbmb
mp 1 0< () =+() − 

× : σσ
The first equation is for the line where the investment in the risk-  free asset is zero 
or positive—that is, at M or to the left of M in Exhibit 5. The second equation is for 
the line where borrowing, or negative investment in the risk-  free asset, occurs. Note 
that the only difference between the two equations is in the interest rates used for 
borrowing and lending.
All passive portfolios will lie on the kinked CML, although the investment in the 
risk-  free asset may be positive (lending), zero (no lending or borrowing), or negative 
(borrowing). Leverage allows less risk-  averse investors to increase the amount of risk 
they take by borrowing money and investing more than 100 percent in the passive

Capital Market Theory 325
EXAMPLE 3   
Leveraged Portfolio with Different Lending and 
Borrowing Rates
Mr. Miles approaches his broker to borrow money against securities held in 
his portfolio. Even though Mr. Miles’ loan will be secured by the securities in 
his portfolio, the broker’s rate for lending to customers is 7 percent. Assuming 
a risk-  free rate of 5 percent and a market return of 15 percent with a standard 
deviation of 20 percent, estimate Mr. Miles’ expected return and risk if he invests 
25 percent and 75 percent in the risk-  free asset and if he decides to borrow 
25 percent and 75 percent of his initial investment and invest the money in the 
market.
Solution:
The unleveraged portfolio’s standard deviation and return are calculated using 
the same equations as before:
and
The results are unchanged. The slope of the line for the unleveraged portfolio 
is 0.50, just as before:

7.5%.
5%.
12.5%.
15%.
For the leveraged portfolio, everything remains the same except that Rf is 
replaced with Rb.
E(Rp) = w1Rb + (1 – w1)E(Rm),
and
σp = (1 – w1)σm.
Return with –25 percent invested in T-  bills = (–0.25 × 7%) + (1.25 × 15%) = 
17.0%.
Return with –75 percent invested in T-  bills = (–0.75 × 7%) + (1.75 × 15%) = 
21.0%.
Standard deviation with –75 percent invested in T-  bills = 1.75 × 20% = 35%.
The risk and return of the leveraged portfolio is higher than that of the unlev -
eraged portfolio. As Mr. Miles borrows more money to invest in the market, the

expected return increases but so does the standard deviation of the portfolio. 
The slope of the line for the leveraged portfolio is 0.40, compared with 0.50 for 
the unleveraged portfolio, which means that for every 1 percent increase in risk, 
the investor gets a 0.40 percent increase in expected return in the leveraged

Reading 40 ■ Portfolio Risk and Return: Part II 326
part of the portfolio, compared with a 0.50 percent increase in expected return 
in the unleveraged part of the portfolio. Only investors who are less risk averse 
will choose leveraged portfolios.
PRICING OF RISK AND COMPUTATION OF EXPECTED 
RETURN
In constructing a portfolio, it is important to understand the concept of correlation 
and how less than perfect correlation can diversify the risk of a portfolio. As a conse -
quence, the risk of an asset held alone may be greater than the risk of that same asset 
when it is part of a portfolio. Because the risk of an asset varies from one environment 
to another, which kind of risk should an investor consider and how should that risk 
be priced? This section addresses the question of pricing of risk by decomposing 
the total risk of a security or a portfolio into systematic and nonsystematic risk. The 
meaning of these risks, how they are computed, and their relevance to the pricing of

assets are also discussed.
3.1 Systematic Risk and Nonsystematic Risk
Systematic risk, also known as non-  diversifiable or market risk, is the risk that affects 
the entire market or economy. In contrast, nonsystematic risk is the risk that pertains 
to a single company or industry and is also known as company-  specific, industry-  
specific, diversifiable, or idiosyncratic risk.
Systematic risk  is risk that cannot be avoided and is inherent in the overall market. 
It is non-  diversifiable because it includes risk factors that are innate within the market 
and affect the market as a whole. Examples of factors that constitute systematic risk 
include interest rates, inflation, economic cycles, political uncertainty, and widespread 
natural disasters. These events affect the entire market, and there is no way to avoid 
their effect. Systematic risk can be magnified through selection or by using leverage, 
or diminished by including securities that have a low correlation with the portfolio,

assuming they are not already part of the portfolio.
Nonsystematic risk  is risk that is local or limited to a particular asset or industry 
that need not affect assets outside of that asset class. Examples of nonsystematic risk 
could include the failure of a drug trial, major oil discoveries, or an airliner crash. All 
these events will directly affect their respective companies and possibly industries, 
but have no effect on assets that are far removed from these industries. Investors are 
capable of avoiding nonsystematic risk through diversification by forming a portfolio 
of assets that are not highly correlated with one another.
We will derive expressions for each kind of risk later in this reading. You will 
see that the sum of systematic variance and nonsystematic variance equals the total 
variance of the security or portfolio:
Total variance = Systematic variance + Nonsystematic variance
Although the equality relationship is between variances, you will find frequent

references to total risk as the sum of systematic risk and nonsystematic risk. In those 
cases, the statements refer to variance, not standard deviation.3

Pricing of Risk and Computation of Expected Return 327
3.1.1  Pricing of Risk
Pricing or valuing an asset is equivalent to estimating its expected rate of return. If 
an asset has a known terminal value, such as the face value of a bond, then a lower 
current price implies a higher future return and a higher current price implies a lower 
future return. The relationship between price and return can also be observed in the 
valuation expression shown in Section 2.1.2. Therefore, we will occasionally use price 
and return interchangeably when discussing the price of risk.
Consider an asset with both systematic and nonsystematic risk. Assume that both 
kinds of risk are priced—that is, you receive a return for both systematic risk and non -
systematic risk. What will you do? Realizing that nonsystematic risk can be diversified 
away, you would buy assets that have a large amount of nonsystematic risk. Once you 
have bought those assets with nonsystematic risk, you would diversify, or reduce that

risk, by including other assets that are not highly correlated. In the process, you will 
minimize nonsystematic risk and eventually eliminate it altogether from your portfolio. 
Now, you would have a diversified portfolio with only systematic risk, yet you would 
be compensated for nonsystematic risk that you no longer have. Just like everyone else, 
you would have an incentive to take on more and more diversifiable risk because you 
are compensated for it even though you can get rid of it. The demand for diversifiable 
risk will keep increasing until its price becomes infinite and its expected return falls 
to zero. This means that our initial assumption of a non-  zero return for diversifiable 
risk was incorrect and that the correct assumption is zero return for diversifiable risk. 
Therefore, we can assume that in an efficient market, no incremental reward can be 
earned for taking on diversifiable risk.
In the previous exercise we illustrated why investors should not be compensated

for taking on nonsystematic risk. Therefore, investors who have nonsystematic risk 
must diversify it away by investing in many industries, many countries, and many 
asset classes. Because future returns are unknown and it is not possible to pick only 
winners, diversification helps in offsetting poor returns in one asset class by garnering 
good returns in another asset class, thereby reducing the overall risk of the portfolio. 
In contrast, investors must be compensated for accepting systematic risk because that 
risk cannot be diversified away. If investors do not receive a return commensurate with 
the amount of systematic risk they are taking, they will refuse to accept systematic risk.
In summary, systematic or non-  diversifiable risk is priced and investors are com -
pensated for holding assets or portfolios based only on that investment’s systematic 
risk. Investors do not receive any return for accepting nonsystematic or diversifiable

risk. Therefore, it is in the interest of risk-  averse investors to hold only well-  diversified 
EXAMPLE 4   
Systematic and Nonsystematic Risk
1 Describe the systematic and nonsystematic risk components of the follow -
ing assets:
A A risk-  free asset, such as a three-  month Treasury bill
B The market portfolio, such as the S&P 500, with total risk of 
20 percent
2 Consider two assets, A and B. Asset A has total risk of 30 percent, half 
of which is nonsystematic risk. Asset B has total risk of 17 percent, all of 
which is systematic risk. Which asset should have a higher expected rate 
of return?

Reading 40 ■ Portfolio Risk and Return: Part II 328
By definition, a risk-  free asset has no risk. Therefore, a risk-  free asset has zero 
systematic risk and zero nonsystematic risk.
As we mentioned earlier, a market portfolio is a diversified portfolio, one in which 
no more risk can be diversified away. We have also described it as an efficient 
portfolio. Therefore, a market portfolio does not contain any nonsystematic risk. 
All of its total risk, 20 percent, is systematic risk.
The amount of systematic risk in Asset A is 15  percent, and the amount of 
systematic risk in Asset B is 17 percent. Because only systematic risk is priced 
or receives a return, the expected rate of return must be higher for Asset B.
3.2 Calculation and Interpretation of Beta
As previously mentioned, in order to form the market portfolio, you should combine 
all available risky assets. Knowledge of the correlations among those assets allows us

to estimate portfolio risk. You also learned that a fully diversified portfolio will include 
all asset classes and essentially all assets in those asset classes. The work required for 
construction of the market portfolio is formidable. For example, for a portfolio of 
1,000 assets, we will need 1,000 return estimates, 1,000 standard deviation estimates, 
and 499,500 (1,000 × 999 ÷ 2) correlations. Other related questions that arise with 
this analysis are whether we really need all 1,000 assets and what happens if there are 
errors in these estimates.
An alternate method of constructing an optimal portfolio is simpler and easier to 
implement. An investor begins with a known portfolio, such as the S&P 500, and then 
adds other assets one at a time on the basis of the asset’s standard deviation, expected 
return, and impact on the portfolio’s risk and return. This process continues until the 
addition of another asset does not have a significant impact on the performance of

the portfolio. The process requires only estimates of systematic risk for each asset 
because investors will not be compensated for nonsystematic risk. Expected returns 
can be calculated by using return-  generating models, as we will discuss in this sec -
tion. In addition to using return-  generating models, we will also decompose total 
variance into systematic variance and nonsystematic variance and establish a formal 
relationship between systematic risk and return. In the next section, we will expand 
on this discussion and introduce the CAPM as the preferred return-  generating model.
3.2.1  Return-  Generating Models
A return-  generating model  is a model that can provide an estimate of the expected 
return of a security given certain parameters. If systematic risk is the only relevant 
parameter for return, then the return-  generating model will estimate the expected 
return for any asset given the level of systematic risk.

As with any model, the quality of estimates of expected return will depend on 
the quality of input estimates and the accuracy of the model. Because it is difficult to 
decide which factors are appropriate for generating returns, the most general form 
of a return-  generating model is a multi-  factor model. A multi-  factor model  allows 
more than one variable to be considered in estimating returns and can be built using 
different kinds of factors, such as macroeconomic, fundamental, and statistical factors.
Macroeconomic factor models use economic factors that are correlated with 
security returns. These factors may include economic growth, the interest rate, the 
inflation rate, productivity, employment, and consumer confidence. Past relationships

Pricing of Risk and Computation of Expected Return 329
with returns are estimated to obtain parameter estimates, which are, in turn, used 
for computing expected returns. Fundamental factor models analyze and use rela -
tionships between security returns and the company’s underlying fundamentals, 
such as, for example, earnings, earnings growth, cash flow generation, investment 
in research, advertising, and number of patents. Finally, in a statistical factor model, 
historical and cross-  sectional return data are analyzed to identify factors that explain 
variance or covariance in observed returns. These statistical factors, however, may or 
may not have an economic or fundamental connection to returns. For example, the 
conference to which the American football Super Bowl winner belongs, whether the 
American Football Conference or the National Football Conference, may be a factor 
in US stock returns, but no obvious economic connection seems to exist between the

winner’s conference and US stock returns. Moreover, data mining may generate many 
spurious factors that are devoid of any economic meaning. Because of this limitation, 
analysts prefer the macroeconomic and fundamental factor models for specifying and 
estimating return-  generating models.
A general return-  generating model is expressed in the following manner:
ER RE FE RR EFif ij j
jk
im fi jj
jk
() −= () = () − + ()
==∑∑ββ β
11
2
The model has k factors, E(F1), E(F2), ... E(Fk). The coefficients, βij, are called factor 
weights or factor loadings associated with each factor. The left-  hand side of the model 
has excess return, or return over the risk-  free rate. The right-  hand side provides the 
risk factors that would generate the return or premium required to assume that risk. 
We have separated out one factor, E(Rm), which represents the market return. All 
models contain return on the market portfolio as a key factor.

Three-  Factor and Four-  Factor Models  Eugene Fama and Kenneth French2 suggested 
that a return-  generating model for stock returns should include relative size of the 
company and relative book-  to- market value of the company in addition to beta. Fama 
and French found that past returns could be explained better with their model than 
with other models available at that time, most notably, the capital asset pricing model. 
Mark Carhart (1997) extended the Fama and French model by adding another factor: 
momentum, defined as relative past stock returns. We will discuss these models further 
in Section 5.3.2.
The Single-  Index Model  The simplest form of a return-  generating model is a single-  
factor linear model, in which only one factor is considered. The most common imple -
mentation is a single-  index model, which uses the market factor in the following form: 
E(Ri) – Rf = βi[E(Rm) – Rf].
Although the single-  index model is simple, it fits nicely with the capital market line.

Recall that the CML is linear, with an intercept of Rf and a slope of [ E(Rm) – Rf]/σm. 
We can rewrite the CML by moving the intercept to the left-  hand side of the equation, 
rearranging the terms, and generalizing the subscript from p to i, for any security:
ER RE RRifi
mmf () −=

() − σ
σ
The factor loading or factor weight, σi/σm, refers to the ratio of total security risk to total 
market risk. To obtain a better understanding of factor loading and to illustrate that the 
CML reduces to a single-  index model, we decompose total risk into its components.
2 Fama and French (1992).

Reading 40 ■ Portfolio Risk and Return: Part II 330
3.2.2  Decomposition of Total Risk for a Single-  Index Model
With the introduction of return-  generating models, particularly the single-  index 
model, we are able to decompose total variance into systematic and nonsystematic 
variances. Instead of using expected returns in the single index, let us use realized 
returns. The difference between expected returns and realized returns is attributable 
to non-  market changes, as an error term, ei, in the second equation below:
E(Ri) – Rf = βi[E(Rm) – Rf]
and
Ri – Rf = βi(Rm – Rf) + ei
The variance of realized returns can be expressed in the equation below (note that 
Rf is a constant). We can further drop the covariance term in this equation because, 
by definition, any non-  market return is uncorrelated with the market. Thus, we are 
able to decompose total variance into systematic and nonsystematic variances in the 
second equation below:
σβ σσii me miRe22 222 =+ + ()Cov,

Total variance = Systematic variance + Nonsystematic variance, which can be written as
σβ σσii me22 22=+
Total risk can be expressed as
σβ σσii me =+22 2
Because nonsystematic risk is zero for well-  diversified portfolios, such as the 
market portfolio, the total risk of a market portfolio and other similar portfolios is 
only systematic risk, which is βiσm. We can now return to the CML discussed in the 
previous subsection and replace σi with βiσm because the CML assumes that the 
market is a diversified portfolio. By making this substitution for the above equation, 
we get the following single-  index model:
ER RE RR ER Rifi
mmfim
mmf () −=

× () − =

× () − σ
σβσ
σ,,
Thus, the CML, which is only for well-  diversified portfolios, is fully consistent with 
a single-  index model.
In this section, you have learned how to decompose total variance into systematic

and nonsystematic variances and how the CML is the same as a single-  index model 
for diversified portfolios.
3.2.3  Return-  Generating Models: The Market Model
The most common implementation of a single-  index model is the market model , in 
which the market return is the single factor or single index. In principle, the market 
model and the single-  index model are similar. The difference is that the market model 
is easier to work with and is normally used for estimating beta risk and computing 
abnormal returns. The market model is
Ri = αi + βiRm + ei
To be consistent with the previous section, αi = Rf(1 – β). The intercept, αi, and 
slope coefficient, βi, can be estimated by using historical security and market returns. 
These parameter estimates are then used to predict company-  specific returns that a 
security may earn in a future period. Assume that a regression of Wal-  Mart’s histor -
ical daily returns on S&P 500 daily returns gives an αi of 0.0001 and a βi of 0.9. Thus,

Pricing of Risk and Computation of Expected Return 331
Wal-  Mart’s expected daily return = 0.0001 + 0.90 × Rm. If on a given day the market 
rises by 1 percent and Wal-  Mart’s stock rises by 2 percent, then Wal-  Mart’s company-  
specific return ( ei) for that day = Ri − E(Ri) = Ri – (αi + βiRm) = 0.02 – (0.0001 + 0.90 × 
0.01) = 0.0109, or 1.09%. In other words, Wal-  Mart earned an abnormal return of 
1.09 percent on that day.
3.2.4  Calculation and Interpretation of Beta
We begin with the single-  index model introduced in Section 3.2.2 using realized 
returns and rewrite it as
Ri = (1 – βi)Rf + βi × Rm + ei
Because systematic risk depends on the correlation between the asset and the market, 
we can arrive at a measure of systematic risk from the covariance between Ri and Rm, 
where Ri is defined using the above equation. Note that the risk-  free rate is a constant, 
so the first term in Ri drops out.
Cov  Cov
Cov  CovRR Re R
RR eRim im im
im mi m
i,,
,,() =× + ()
= () + ()
=β
β
βσσm20+

im mi m
i,,
,,() =× + ()
= () + ()
=β
β
βσσm20+
The first term is beta multiplied by the variance of Rm. Because the error term is 
uncorrelated with the market, the second term drops out. Then, we can rewrite the 
equation in terms of beta as follows:
β
σρσ σ
σρσ
σiim
mim im
mim i
mRR=()==Cov, ,,
22
The above formula shows the expression for beta, βi, which is similar to the fac -
tor loading in the single-  index model presented in Section 3.2.1. For example, if the 
correlation between an asset and the market is 0.70 and the asset and market have 
standard deviations of return of 0.25 and 0.15, respectively, the asset’s beta would 
be (0.70)(0.25)/0.15  = 1.17. If the asset’s covariance with the market and market 
variance were given as 0.026250 and 0.02250, respectively, the calculation would be 
0.026250/0.02250 = 1.17. The beta in the market model includes an adjustment for 
the correlation between asset i and the market because the market model covers all

assets whereas the CML works only for fully diversified portfolios.
As shown in the above equation, beta  is a measure of how sensitive an asset’s 
return is to the market as a whole and is calculated as the covariance of the return 
on i and the return on the market divided by the variance of the market return; that 
expression is equivalent to the product of the asset’s correlation with the market with 
a ratio of standard deviations of return (i.e., the ratio of the asset’s standard deviation 
to the market’s). As we have shown, beta captures an asset’s systematic risk, or the 
portion of an asset’s risk that cannot be eliminated by diversification. The variances and 
correlations required for the calculation of beta are usually based on historical returns.
A positive beta indicates that the return of an asset follows the general market 
trend, whereas a negative beta shows that the return of an asset generally follows a

trend that is opposite to that of the market. In other words, a positive beta indicates 
that the return of an asset moves in the same direction of the market, whereas a 
negative beta indicates that the return of an asset moves in the opposite direction of 
the market. A risk-  free asset’s beta is zero because its covariance with other assets is 
zero. In other words, a beta of zero indicates that the asset’s return has no correlation

Reading 40 ■ Portfolio Risk and Return: Part II 332
with movements in the market. The market’s beta can be calculated by substituting 
σm for σi in the numerator. Also, any asset’s correlation with itself is 1, so the beta of 
the market is 1:
βρσ
σρσ
σiim i
mmm m
m== =,,1
Because the market’s beta is 1, the average beta of stocks in the market, by defini -
tion, is 1. In terms of correlation, most stocks, especially in developed markets, tend 
to be highly correlated with the market, with correlations in excess of 0.70. Some US 
broad market indexes, such as the S&P 500, the Dow Jones 30, and the NASDAQ 
100, have even higher correlations that are in excess of 0.90. The correlations among 
different sectors are also high, which shows that companies have similar reactions to 
the same economic and market changes. As a consequence and as a practical matter, 
finding assets that have a consistently negative beta because of the market’s broad 
effects on all assets is unusual.
EXAMPLE 5

EXAMPLE 5   
Calculation of Beta
Assuming that the risk (standard deviation) of the market is 25 percent, calculate 
the beta for the following assets:
1 A short-  term US Treasury bill.
2 Gold, which has a standard deviation equal to the standard deviation of 
the market but a zero correlation with the market.
3 A new emerging market that is not currently included in the definition of 
“market”—the emerging market’s standard deviation is 60 percent, and 
the correlation with the market is –0.1.
4 An initial public offering or new issue of stock with a standard deviation 
of 40 percent and a correlation with the market of 0.7 (IPOs are usually 
very risky but have a relatively low correlation with the market).
We use the formula for beta in answering the above questions:  βρσ
σiim i
m=,
By definition, a short-  term US Treasury bill has zero risk. Therefore, its beta 
is zero.

is zero.
Because the correlation of gold with the market is zero, its beta is zero.
Beta of the emerging market is –0.1 × 0.60 ÷ 0.25 = –0.24.
Beta of the initial public offering is 0.7 × 0.40 ÷ 0.25 = 1.12.
3.2.5  Estimation of Beta
An alternative and more practical approach is to estimate beta directly by using the 
market model described above. The market model, Ri = αi + βiRm + ei, is estimated by 
using regression analysis, which is a statistical process that evaluates the relationship

Pricing of Risk and Computation of Expected Return 333
between a given variable (the dependent variable) and one or more other (indepen -
dent) variables. Historical security returns ( Ri) and historical market returns ( Rm) are 
inputs used for estimating the two parameters αi and βi.
Regression analysis is similar to plotting all combinations of the asset’s return 
and the market return ( Ri, Rm) and then drawing a line through all points such that it 
minimizes the sum of squared linear deviations from the line. Exhibit 6 illustrates the 
market model and the estimated parameters. The intercept, αi (sometimes referred 
to as the constant), and the slope term, βi, are all that is needed to define the security 
characteristic line and obtain beta estimates.
Exhibit 6   Beta Estimation Using a Plot of Security and Market ReturnsSecurity Return
Market ReturnRi
RmSlope = βi [Beta]
Although beta estimates are important for forecasting future levels of risk, there

is much concern about their accuracy. In general, shorter periods of estimation (e.g., 
12 months) represent betas that are closer to the asset’s current level of systematic 
risk. Shorter period beta estimates, however, are also less accurate than beta estimates 
measured over three to five years because they may be affected by special events in that 
short period. Although longer period beta estimates are more accurate, they may be 
a poor representation of future expectations, especially if major changes in the asset 
have occurred. Therefore, it is necessary to recognize that estimates of beta, whether 
obtained through calculation or regression analysis, may or may not represent current 
or future levels of an asset’s systematic risk.
3.2.6  Beta and Expected Return
Although the single-  index model, also called the capital asset pricing model  (CAPM), 
will be discussed in greater detail in the next section, we will use the CAPM in this

section to estimate returns, given asset betas. The CAPM is usually written with the 
risk-  free rate on the right-  hand side:
E(Ri) = Rf + βi[E(Rm) – Rf]

Reading 40 ■ Portfolio Risk and Return: Part II 334
The model shows that the primary determinant of expected return for a security is 
its beta, or how well the security correlates with the market. The higher the beta of 
an asset, the higher its expected return will be. Assets with a beta greater than 1 have 
an expected return that is higher than the market return, whereas assets with a beta 
of less than 1 have an expected return that is less than the market return.
In certain cases, assets may require a return less than the risk-  free return. For 
example, if an asset’s beta is negative, the required return will be less than the risk-  
free rate. When combined with the market, the asset reduces the risk of the overall 
portfolio, which makes the asset very valuable. Insurance is one such asset. Insurance 
gives a positive return when the insured’s wealth is reduced because of a catastrophic 
loss. In the absence of such a loss or when the insured’s wealth is growing, the insured

is required to pay an insurance premium. Thus, insurance has a negative beta and a 
negative expected return, but helps in reducing overall risk.
EXAMPLE 6   
Calculation of Expected Return
1 Alpha Natural Resources (ANR), a coal producer, buys a large but pri -
vately held coal producer in China. As a result of the cross-  border acquisi -
tion of a private company, ANR’s standard deviation of returns is reduced 
from 50 percent to 30 percent and its correlation with the market falls 
from 0.95 to 0.75. Assume that the standard deviation and return of the 
market remain unchanged at 25 percent and 10 percent, respectively, and 
that the risk-  free rate is 3 percent.
A Calculate the beta of ANR stock and its expected return before the 
acquisition.
B Calculate the expected return after the acquisition.
Using the formula for βi, we can calculate βi and then the return.
βρσ
σiim i
m==×=, ..
..0950 50
025190
E(Ri) = Rf + βi[E(Rm) – Rf] = 0.03 + 1.90 × (0.10 – 0.03) = 0.163 = 16.3%

We follow the same procedure but with the after-  acquisition correlation and risk.
βρσ
σiim i
m==×=, ..
..0750 30
025090
E(Ri) = Rf + βi[E(Rm) – Rf] = 0.03 + 0.90 × (0.10 – 0.03) = 0.093 = 9.3%
The market risk premium is 7 percent (10% – 3%). As the beta changes, the 
change in the security’s expected return is the market risk premium multiplied 
by the change in beta. In this scenario, ANR’s beta decreased by 1.0, so the new 
expected return for ANR is 7 percentage points lower.
2 Mr. Miles observes the strong demand for iPods and iPhones and wants to 
invest in Apple stock. Unfortunately, Mr. Miles doesn’t know the return he 
should expect from his investment. He has been given a risk-  free rate of 
3 percent, a market return of 10 percent, and Apple’s beta of 1.5.

The Capital Asset Pricing Model 335
A Calculate Apple’s expected return.
B An analyst looking at the same information decides that the past per -
formance of Apple is not representative of its future performance. He 
decides that, given the increase in Apple’s market capitalization, Apple 
acts much more like the market than before and thinks Apple’s beta 
should be closer to 1.1. What is the analyst’s expected return for Apple 
stock?
Solution to 2A:
E(Ri) = Rf + βi[E(Rm) – Rf] = 0.03 + 1.5 × (0.10 – 0.03) = 0.135 = 13.5%
Solution to 2B:
E(Ri) = Rf + βi[E(Rm) – Rf] = 0.03 + 1.1 × (0.10 – 0.03) = 0.107 = 10.7%
This example illustrates the lack of connection between estimation of past returns 
and projection into the future. Investors should be aware of the limitations of 
using past returns for estimating future returns.
THE CAPITAL ASSET PRICING MODEL
The capital asset pricing model is one of the most significant innovations in portfolio

theory. The model is simple, yet powerful; is intuitive, yet profound; and uses only 
one factor, yet is broadly applicable. The CAPM was introduced independently by 
William Sharpe, John Lintner, Jack Treynor, and Jan Mossin and builds on Harry 
Markowitz’s earlier work on diversification and modern portfolio theory.3 The model 
provides a linear expected return–beta relationship that precisely determines the 
expected return given the beta of an asset. In doing so, it makes the transition from 
total risk to systematic risk, the primary determinant of expected return. Recall the 
following equation:
The CAPM asserts that the expected returns of assets vary only by their systematic 
risk as measured by beta. Two assets with the same beta will have the same expected 
return irrespective of the nature of those assets. Given the relationship between risk 
and return, all assets are defined only by their beta risk, which we will explain as the 
assumptions are described.

In the remainder of this section, we will examine the assumptions made in arriving 
at the CAPM and the limitations those assumptions entail. Second, we will implement 
the CAPM through the security market line to price any portfolio or asset, both effi -
cient and inefficient. Finally, we will discuss ways in which the CAPM can be applied 
to investments, valuation, and capital budgeting.
4.1 Assumptions of the CAPM
Similar to all other models, the CAPM ignores many of the complexities of financial 
markets by making simplifying assumptions. These assumptions allow us to gain 
important insights into how assets are priced without complicating the analysis. Once 4
3 See, for example, Markowitz (1952), Sharpe (1964), Lintner (1965a, 1965b), Treynor (1961, 1962), and 
Mossin (1966).

Reading 40 ■ Portfolio Risk and Return: Part II 336
the basic relationships are established, we can relax the assumptions and examine how 
our insights need to be altered. Some of these assumptions are constraining, whereas 
others are benign. And other assumptions affect only a particular set of assets or only 
marginally affect the hypothesized relationships.
1 Investors are risk-  averse, utility-  maximizing, rational individuals.
 Risk aversion means that investors expect to be compensated for accepting risk. 
Note that the assumption does not require investors to have the same degree of 
risk aversion; it only requires that they are averse to risk. Utility maximization 
implies that investors want higher returns, not lower returns, and that inves -
tors always want more wealth (i.e., investors are never satisfied). Investors are 
understood to be rational in that they correctly evaluate and analyze available 
information to arrive at rational decisions. Although rational investors may

use the same information to arrive at different estimates of expected risk and 
expected returns, homogeneity among investors (see Assumption 4) requires 
that investors be rational individuals. 
 Risk aversion and utility maximization are generally accepted as reflecting a 
realistic view of the world. Yet, rationality among investors has been questioned 
because investors may allow their personal biases and experiences to disrupt 
their decision making, resulting in suboptimal investments. Nonetheless, the 
model’s results are unaffected by such irrational behavior as long as it does not 
affect prices in a significant manner (i.e., the trades of irrational investors cancel 
each other or are dominated by the trades of rational investors).
2 Markets are frictionless, including no transaction costs and no taxes.
 Frictionless markets allow us to abstract the analysis from the operational 
characteristics of markets. In doing so, we do not allow the risk–return rela -

tionship to be affected by, for example, the trading volume on the New York 
Stock Exchange or the difference between buying and selling prices. Specifically, 
frictionless markets do not have transaction costs, taxes, or any costs or restric -
tions on short selling. We also assume that borrowing and lending at the risk-  
free rate is possible. 
 The transaction costs of many large institutions are negligible, and many 
institutions do not pay taxes. Even the presence of non-  zero transaction costs, 
taxes, or the inability to borrow at the risk-  free rate does not materially affect 
the general conclusions of the CAPM. Costs of short selling4 or restrictions on 
short selling, however, can introduce an upward bias in asset prices, potentially 
jeopardizing important conclusions of the CAPM.
3 Investors plan for the same single holding period.
 The CAPM is a single-  period model, and all investor decisions are made on the

basis of that one period. The assumption of a single period is applied for conve -
nience because working with multi-  period models is more difficult. A single-  
period model, however, does not allow learning to occur, and bad decisions can 
persist. In addition, maximizing utility at the end of a multi-  period horizon may 
require decisions in certain periods that may seem suboptimal when examined 
from a single-  period perspective. Nonetheless, the single holding period does 
not severely limit the applicability of the CAPM to multi-  period settings. 
4 Investors have homogeneous expectations or beliefs.
4 Short selling  shares involves selling shares that you do not own. Because you do not own the shares, 
you (or your broker) must borrow the shares before you can short sell. You sell the borrowed shares in the 
market hoping that you will be able to return the borrowed shares by buying them later in the market at a

lower price. Brokerage houses and securities lenders lend shares to you to sell in return for a portion (or 
all) of the interest earned on the cash you receive for the shares that are short sold.

The Capital Asset Pricing Model 337
 This assumption means that all investors analyze securities in the same way 
using the same probability distributions and the same inputs for future cash 
flows. In addition, given that they are rational individuals, the investors will 
arrive at the same valuations. Because their valuations of all assets are identical, 
they will generate the same optimal risky portfolio, which we call the market 
portfolio. 
 The assumption of homogeneous beliefs can be relaxed as long as the dif -
ferences in expectations do not generate significantly different optimal risky 
5 All investments are infinitely divisible.
 This assumption implies that an individual can invest as little or as much as he 
or she wishes in an asset. This supposition allows the model to rely on continu -
ous functions rather than on discrete jump functions. The assumption is made 
for convenience only and has an inconsequential impact on the conclusions of 
the model.

the model. 
6 Investors are price takers.
 The CAPM assumes that there are many investors and that no investor is large 
enough to influence prices. Thus, investors are price takers, and we assume that 
security prices are unaffected by investor trades. This assumption is generally 
true because even though investors may be able to affect prices of small stocks, 
those stocks are not large enough to affect the primary results of the CAPM. 
 
The main objective of these assumptions is to create a marginal investor who 
rationally chooses a mean–variance-  efficient portfolio in a predictable fashion. We 
assume away any inefficiency in the market from both operational and informational 
perspectives. Although some of these assumptions may seem unrealistic, relaxing most 
of them will have only a minor influence on the model and its results. Moreover, the 
CAPM, with all its limitations and weaknesses, provides a benchmark for comparison 
and for generating initial return estimates.

4.2 The Security Market Line
In this subsection, we apply the CAPM to the pricing of securities. The security market 
line (SML) is a graphical representation of the capital asset pricing model with beta, 
reflecting systematic risk, on the x-axis and expected return on the y-axis. Using the 
same concept as the capital market line, the SML intersects the y-axis at the risk-  free 
rate of return, and the slope of this line is the market risk premium, Rm – Rf. Recall 
that the capital market line (CML) does not apply to all securities or assets but only 
to portfolios on the efficient frontier. The efficient frontier gives optimal combinations 
of expected return and total risk. In contrast, the security market line applies to any 
security, efficient or not. Total risk and systematic risk are equal only for efficient 
portfolios because those portfolios have no diversifiable risk remaining.

Exhibit 7 is a graphical representation of the CAPM, the security market line. As 
shown earlier in this reading, the beta of the market is 1 ( x-axis) and the market earns 
an expected return of Rm (y-axis). Using this line, it is possible to calculate the expected 
return of an asset. The next example illustrates the beta and return calculations.

Reading 40 ■ Portfolio Risk and Return: Part II 338
Exhibit 7   The Security Market Line
MSML
BetaExpected Return
1.0RfSlope = Rm – RfE(Ri)
E(Rm)
βiβi = βm
EXAMPLE 7   
Security Market Line and Expected Return
1 Suppose the risk-  free rate is 3 percent, the expected return on the market 
portfolio is 13 percent, and its standard deviation is 23 percent. An Indian 
company, Bajaj Auto, has a standard deviation of 50 percent but is uncor -
related with the market. Calculate Bajaj Auto’s beta and expected return.
2 Suppose the risk-  free rate is 3 percent, the expected return on the mar -
ket portfolio is 13 percent, and its standard deviation is 23 percent. A 
German company, Mueller Metals, has a standard deviation of 50 percent 
and a correlation of 0.65 with the market. Calculate Mueller Metal’s beta 
and expected return.
βρσ
σiim i
m==×=, ..
.00 05 0
0230
E(Ri) = Rf + βi[E(Rm) – Rf] = 0.03 + 0 × (0.13 – 0.03) = 0.03 = 3.0%

Because of its zero correlation with the market portfolio, Bajaj Auto’s beta is 
zero. Because the beta is zero, the expected return for Bajaj Auto is the risk-  free 
rate, which is 3 percent.
βρσ
σiim i
m==×=, ..
..0650 50
023141

The Capital Asset Pricing Model 339
E(Ri) = Rf + βi[E(Rm) – Rf] = 0.03 + 1.41× (0.13 – 0.03) = 0.171 = 17.1%
Because of the high degree of correlation with the market, the beta for Mueller 
Metals is 1.41 and the expected return is 17.1 percent. Because Mueller Metals 
has systematic risk that is greater than that of the market, it has an expected 
return that exceeds the expected return of the market.
4.2.1  Portfolio Beta
As we stated above, the security market line applies to all securities. But what about 
a combination of securities, such as a portfolio? Consider two securities, 1 and 2, 
with a weight of wi in Security 1 and the balance in Security 2. The return for the two 
securities and return of the portfolio can be written as:
ER RE RR
ER RE RR
ER wERfm f
fm f
p11
22
11() =+ () − 
() =+ () − 
() = (β
β
) )+ ()
=+ () − ++ () − 
=+wE R
wR wE RR wR wE RR
Rfm ff mf
f22
11 12 22 ββ
www ER Rmf 11 22 ββ+ () () − 

f22
11 12 22 ββ
The last equation gives the expression for the portfolio’s expected return. From this 
equation, we can conclude that the portfolio’s beta = w1β1 + w2β2. In general, the port -
folio beta is a weighted sum of the betas of the component securities and is given by:
ββpi i
in
i
in
ww==
==∑∑
111 ; 
The portfolio’s return given by the CAPM is
E(Rp) = Rf + βp[E(Rm) – Rf]
This equation shows that a linear relationship exists between the expected return of 
a portfolio and the systematic risk of the portfolio as measured by βp.
EXAMPLE 8   
Portfolio Beta and Return
You invest 20 percent of your money in the risk-  free asset, 30 percent in the 
market portfolio, and 50 percent in RedHat, a US stock that has a beta of 2.0. 
Given that the risk-  free rate is 4 percent and the market return is 16 percent, 
what are the portfolio’s beta and expected return?
Solution:
The beta of the risk-  free asset = 0, the beta of the market = 1, and the beta of

RedHat is 2.0. The portfolio beta is
βp = w1β1 + w2β2 + w3β3 = (0.20 × 0.0) + (0.30 × 1.0) + (0.50 × 2.0) = 1.30
E(Ri) = Rf + βi[E(Rm) – Rf] = 0.04 + 1.30 × (0.16 – 0.04) = 0.196 = 19.6%
The portfolio beta is 1.30, and its expected return is 19.6 percent.

Reading 40 ■ Portfolio Risk and Return: Part II 340
Alternate Method:
Another method for calculating the portfolio’s return is to calculate individual 
security returns and then use the portfolio return formula (i.e., weighted average 
of security returns) to calculate the overall portfolio return.
Return of the risk-  free asset = 4 percent; return of the market = 16 percent
RedHat’s return based on its beta = 0.04 + 2.0 × (0.16 – 0.04) = 0.28
Portfolio return = (0.20 × 0.04) + (0.30 × 0.16) + (0.50 × 0.28) = 0.196 = 
19.6%
Not surprisingly, the portfolio return is 19.6 percent, as calculated in the first 
method.
4.3 Applications of the CAPM
The CAPM offers powerful and intuitively appealing predictions about risk and 
the relationship between risk and return. The CAPM is not only important from a 
theoretical perspective but is also used extensively in practice. In this section, we 
will discuss some common applications of the model. When applying these tools to

different scenarios, it is important to understand that the CAPM and the SML are 
functions that give an indication of what the return in the market should  be, given a 
certain level of risk. The actual return may be quite different from the expected return.
Applications of the CAPM include estimates of the expected return for capital 
budgeting, comparison of the actual return of a portfolio or portfolio manager with 
the CAPM return for performance appraisal, and the analysis of alternate return 
estimates and the CAPM returns as the basis for security selection. The applications 
are discussed in more detail in this section.
4.3.1  Estimate of Expected Return
Given an asset’s systematic risk, the expected return can be calculated using the 
CAPM. Recall that the price of an asset is the sum of all future cash flows discounted 
at the required rate of return, where the discount rate or the required rate of return

is commensurate with the asset’s risk. The expected rate of return obtained from 
the CAPM is normally the first estimate that investors use for valuing assets, such 
as stocks, bonds, real estate, and other similar assets. The required rate of return 
from the CAPM is also used for capital budgeting and determining the economic 
feasibility of projects. Again, recall that when computing the net present value of a 
project, investments and net revenues are considered cash flows and are discounted 
at the required rate of return. The required rate of return, based on the project’s risk, 
is calculated using the CAPM.
Because risk and return underlie almost all aspects of investment decision making, 
it is not surprising that the CAPM is used for estimating expected return in many sce -
narios. Other examples include calculating the cost of capital for regulated companies 
by regulatory commissions and setting fair insurance premiums. The next example

shows an application of the CAPM to capital budgeting.
EXAMPLE 9   
Application of the CAPM to Capital Budgeting
GlaxoSmithKline Plc is examining the economic feasibility of developing a new 
medicine. The initial investment in Year 1 is $500 million. The investment in 
Year 2 is $200 million. There is a 50 percent chance that the medicine will be

The Capital Asset Pricing Model 341
developed and will be successful. If that happens, GlaxoSmithKline must spend 
another $100 million in Year 3, but its income from the project in Year 3 will 
be $500 million, not including the third-  year investment. In Years 4, 5, and 6, 
it will earn $400 million a year if the medicine is successful. At the end of Year 
6, it intends to sell all rights to the medicine for $600 million. If the medicine is 
unsuccessful, none of GlaxoSmithKline’s investments can be salvaged. Assume 
that the market return is 12 percent, the risk-  free rate is 2 percent, and the beta 
risk of the project is 2.3. All cash flows occur at the end of each year.
1 Calculate the expected annual cash flows using the probability of success.
2 Calculate the expected return.
3 Calculate the net present value.
There is a 50 percent chance that the cash flows in Years 3–6 will occur. Taking 
that into account, the expected annual cash flows are:

Year 1: –$500 million (outflow)
Year 2: –$200 million (outflow)
Year 3: 50% of –$100 million (outflow) + 50% of $500 million = $200 million
Year 4: 50% of $400 million = $200 million
Year 5: 50% of $400 million = $200 million
Year 6: 50% of $400 million + 50% of $600 million = $500 million
The expected or required return for the project can be calculated using the 
CAPM, which is = 0.02 + 2.3 × (0.12 – 0.02) = 0.25.
The net present value is the discounted value of all cash flows:
NPVCF
rt
tt
tT
=
+()
=−
+()+−
+()+
+()=∑
1
500
10 25200
10 25200
10 250
2 . ..334
56200
10 25
200
10 25500
10 25
400 128 102 40+
+()
+
+()+
+()
=− −+ +.
..
.8 81 92 65 54 131 07 147 07.. .. . ++ =−
Because the net present value is negative (–$147.07 million), the project should 
not be accepted by GlaxoSmithKline.
4.3.2  Portfolio Performance Evaluation
Institutional money managers, pension fund managers, and mutual fund managers 
manage large amounts of money for other people. Are they doing a good job? How

does their performance compare with a passively managed portfolio—that is, one in 
which the investor holds just the market portfolio? Evaluating the performance of a 
portfolio is of interest to all investors and money managers. Because active manage -
ment costs significantly more than passive management, we expect active managers to 
perform better than passive managers or at least to cover the difference in expenses. 
For example, Fidelity’s passively managed Spartan 500 Index fund has an expense ratio

Reading 40 ■ Portfolio Risk and Return: Part II 342
of only 0.10 percent whereas Fidelity’s actively managed Contrafund has an expense 
ratio of 0.94 percent. Investors need a method for determining whether the manager 
of the Contrafund is worth the extra 0.84 percent in expenses.
In this reading, performance evaluation  is based only on the CAPM. However, 
it is easy to extend this analysis to multi-  factor models that may include industry 
or other special factors. Four ratios are commonly used in performance evaluation.
Sharpe and Treynor Ratios  Performance has two components, risk and return. 
Although return maximization is a laudable objective, comparing just the return of a 
portfolio with that of the market is not sufficient. Because investors are risk averse, they 
will require compensation for higher risk in the form of higher returns. A commonly 
used measure of performance is the Sharpe ratio , which is defined as the portfolio’s 
risk premium divided by its risk:

Sharpe ratio =−RRpf
pσ
Recalling the CAL from earlier in the reading, one can see that the Sharpe ratio, 
also called the reward-  to- variability ratio, is simply the slope of the capital allocation 
line; the greater the slope, the better the asset. Note, however, that the ratio uses the 
total risk  of the portfolio, not its systematic risk. The use of total risk is appropriate 
if the portfolio is an investor’s total portfolio—that is, the investor does not own any 
other assets. Sharpe ratios of the market and other portfolios can also be calculated in 
a similar manner. The portfolio with the highest Sharpe ratio has the best performance, 
and the one with the lowest Sharpe ratio has the worst performance, provided that 
the numerator is positive for all comparison portfolios. If the numerator is negative, 
the ratio will be less negative for riskier portfolios, resulting in incorrect rankings.

The Sharpe ratio, however, suffers from two limitations. First, it uses total risk as 
a measure of risk when only systematic risk is priced. Second, the ratio itself (e.g., 
0.2 or 0.3) is not informative. To rank portfolios, the Sharpe ratio of one portfolio 
must be compared with the Sharpe ratio of another portfolio. Nonetheless, the ease 
of computation makes the Sharpe ratio a popular tool.
The Treynor ratio  is a simple extension of the Sharpe ratio and resolves the Sharpe 
ratio’s first limitation by substituting beta risk for total risk. The Treynor ratio is
Treynor ratio =−RRpf
pβ
Just like the Sharpe ratio, the numerators must be positive for the Treynor ratio 
to give meaningful results. In addition, the Treynor ratio does not work for negative-  
beta assets—that is, the denominator must also be positive for obtaining correct esti -
mates and rankings. Although both the Sharpe and Treynor ratios allow for ranking

of portfolios, neither ratio gives any information about the economic significance of 
differences in performance. For example, assume the Sharpe ratio of one portfolio is 
0.75 and the Sharpe ratio for another portfolio is 0.80. The second portfolio is superior, 
but is that difference meaningful? In addition, we do not know whether either of the 
portfolios is better than the passive market portfolio. The remaining two measures, M2 
and Jensen’s alpha, attempt to address that problem by comparing portfolios while also 
providing information about the extent of the overperformance or underperformance.
M-Squared ( M2)  M2 was created by Franco Modigliani and his granddaughter, Leah 
Modigliani—hence the name M-squared. M2 is an extension of the Sharpe ratio in that it 
is based on total risk , not beta risk. The idea behind the measure is to create a portfolio 
(P′) that mimics the risk of a market portfolio—that is, the mimicking portfolio (P ′)

alters the weights in Portfolio P and the risk-  free asset until Portfolio P ′ has the same 
total risk as the market (i.e., σp′ = σm). Because the risks of the mimicking portfolio

The Capital Asset Pricing Model 343
and the market portfolio are the same, we can obtain the return on the mimicking 
portfolio and directly compare it with the market return. The weight in Portfolio P , wp, 
that makes the risks equal can be calculated as follows:
σσ σσ σ
σ
σ′=+ −= =
=pp pp Rf mp p
pm
pww w
w()1 , which gi ves
Because the correlation between the market and the risk-  free asset is zero, we get wp 
as the weight invested in Portfolio P and the balance invested in the risk-  free asset. 
The risk-  adjusted return for the mimicking portfolio is:
Rw Rw RR R
Rpp pp fm
ppm
pf
fm
p′=+ −=

+−


=+()11σ
σσ
σ
σ
σ 
−() =+− 

RR RRR
pf fmpf
pσσ
The return of the mimicking portfolio based on excess returns is  RRpfm
p−()σ
σ.5 The 
difference in the return of the mimicking portfolio and the market return is M2, which 
can be expressed as a formula:
MR RR Rpfm
pmf2=−() −−()σ
σ
M2 gives us rankings that are identical to those of the Sharpe ratio. They are easier

to interpret, however, because they are in percentage terms. A portfolio that matches 
the performance of the market will have an M2 of zero, whereas a portfolio that out -
performs the market will have an M2 that is positive. By using M2, we are not only 
able to determine the rank of a portfolio but also which, if any, of our portfolios beat 
the market on a risk-  adjusted basis.
Jensen’s Alpha  Like the Treynor ratio, Jensen’s alpha is based on systematic risk. We 
can measure a portfolio’s systematic risk by estimating the market model, which is done 
by regressing the portfolio’s daily return on the market’s daily return. The coefficient on 
the market return is an estimate of the beta risk of the portfolio (see Section 3.2.5 for 
more details). We can calculate the risk-  adjusted return of the portfolio using the beta 
of the portfolio and the CAPM. The difference between the actual portfolio return and

the calculated risk-  adjusted return is a measure of the portfolio’s performance relative 
to the market portfolio and is called Jensen’s alpha. By definition, αm of the market is 
zero. Jensen’s alpha is also the vertical distance from the SML measuring the excess 
return for the same risk as that of the market and is given by
αp = Rp – [Rf + βp(Rm – Rf)]
If the period is long, it may contain different risk-  free rates, in which case Rf 
represents the average risk-  free rate. Furthermore, the returns in the equation are all 
realized, actual returns. The sign of αp indicates whether the portfolio has outperformed 
the market. If αp is positive, then the portfolio has outperformed the market; if αp is 
negative, the portfolio has underperformed the market. Jensen’s alpha is commonly 
used for evaluating most institutional managers, pension funds, and mutual funds. 
Values of alpha can be used to rank different managers and the performance of their

5 Note that the last term within parentheses on the right-  hand side of the previous equation is the Sharpe 
ratio.

Reading 40 ■ Portfolio Risk and Return: Part II 344
portfolios, as well as the magnitude of underperformance or overperformance. For 
example, if a portfolio’s alpha is 2 percent and another portfolio’s alpha is 5 percent, 
the second portfolio has outperformed the first portfolio by 3 percentage points and 
the market by 5 percentage points. Jensen’s alpha is the maximum amount that you 
should be willing to pay the manager to manage your money.
EXAMPLE 10   
Portfolio Performance Evaluation
A British pension fund has employed three investment managers, each of whom is 
responsible for investing in one-  third of all asset classes so that the pension fund 
has a well-  diversified portfolio. Information about the managers is given below.
Manager Return σ β
X 10% 20% 1.1
Y 11 10 0.7
Z 12 25 0.6
Market (M) 9 19
Risk-  free rate ( Rf) 3
Calculate the expected return, Sharpe ratio, Treynor ratio, M2, and Jensen’s 
alpha. Analyze your results and plot the returns and betas of these portfolios.
Solution:

Solution:
In each case, the calculations are shown only for Manager X. All answers are 
tabulated below. Note that the β of the market is 1 and the σ and β of the risk-  
free rate are both zero.
Expected return:
 ER RE RRXf Xm f () =+ () − =+
×−β 0031 10
0090..
.. 0 03 0 096 96
0100 03
020035() ==
=−
=−=.. %
..
.. Sharpe ratio
TreRRXf
Xσ
y ynor ratio =−
=−=RRXf
Xβ0100 03
110 064..
..
MR RR RXfm
Xmf20100 03019
020
0090 03 00=−() −−() =−()
−−() =σ
σ...
.
.. .0065 065
0100 03 11 00 6
00=
=− +−()=− +× ()
=.%
.. ..
.αβXX fX mf RR RR  
0 04 040 =.%
Exhibit 8   Measures of Portfolio Performance Evaluation
Manager Ri σi βi E(Ri) Sharpe Ratio Treynor Ratio M2αi
X 10.0% 20.0% 1.10 9.6% 0.35 0.064 0.65% 0.40%
Y 11.0 10.0 0.70 7.2 0.80 0.114 9.20 3.80
Z 12.0 25.0 0.60 6.6 0.36 0.150 0.84 5.40

The Capital Asset Pricing Model 345
M 9.0 19.0 1.00 9.0 0.32 0.060 0.00 0.00
Rf 3.0 0.0 0.00 3.0 – – – 0.00
Let us begin with an analysis of the risk-  free asset. Because the risk-  free asset 
has zero risk and a beta of zero, calculating the Sharpe ratio, Treynor ratio, or 
M2 is not possible because they all require the portfolio risk in the denominator. 
The risk-  free asset’s alpha, however, is zero. Turning to the market portfolio, we 
see that the absolute measures of performance, the Sharpe ratio and the Treynor 
ratio, are positive for the market portfolio. These ratios are positive as long as 
the portfolio earns a return that is in excess of that of the risk-  free asset. M2 
and αi are performance measures relative to the market, so they are both equal 
to zero for the market portfolio.
All three managers have Sharpe and Treynor ratios greater than those of the

market, and all three managers’ M2 and αi are positive; therefore, the pension 
fund should be satisfied with their performance. Among the three managers, 
Manager X has the worst performance, irrespective of whether total risk or 
systematic risk is considered for measuring performance. The relative rankings 
are depicted in Exhibit 9.
Exhibit 9   Ranking of Portfolios by Performance Measure
Rank Sharpe Ratio Treynor Ratio M2αi
1 Y Z Y Z
2 Z Y Z Y
3 X X X X
4 M M M M
5 – – – Rf
Comparing Y and Z, we can observe that Y performs much better than Z 
when total risk is considered. Y has a Sharpe ratio of 0.80, compared with a 
Sharpe ratio of 0.36 for Z. Similarly, M2 is higher for Y (9.20 percent) than for Z 
(0.84 percent). In contrast, when systematic risk is used, Z outperforms Y. The 
Treynor ratio is higher for Z (0.150) than for Y (0.114), and Jensen’s alpha is also 
higher for Z (5.40 percent) than for Y (3.80 percent), which indicates that Z has

done a better job of generating excess return relative to systematic risk than Y.
Exhibit 10 confirms these observations in that all three managers outperform 
the benchmark because all three points lie above the SML. Among the three 
portfolios, Z performs the best when we consider risk-  adjusted returns because 
it is the point in Exhibit 10 that is located northwest relative to the portfolios 
X and Y.Exhibit 8   (Continued)

Reading 40 ■ Portfolio Risk and Return: Part II 346
Exhibit 10   Portfolios Along the SML
2.05%10%
1.0
Beta15%
Z
Y X
MReturn on InvestmentSMLRi
Rf = 3%
βi
When do we use total risk performance measures like the Sharpe ratio 
and M2, and when do we use beta risk performance measures like the Treynor 
ratio and Jensen’s alpha? Total risk is relevant for an investor when he or she 
holds a portfolio that is not fully diversified, which is not a desirable portfolio. 
In such cases, the Sharpe ratio and M2 are appropriate performance measures. 
Thus, if the pension fund were to choose only one fund manager to manage all 
its assets, it should choose Manager Y. Performance measures relative to beta 
risk—Treynor ratio and Jensen’s alpha—are relevant when the investor holds 
a well-  diversified portfolio with negligible diversifiable risk. In other words, if 
the pension fund is well diversified and only the systematic risk of the portfolio 
matters, the fund should choose Manager Z.

The measures of performance evaluation assume that the benchmark market 
portfolio is the correct portfolio. As a result, an error in the benchmark may cause 
the results to be misleading. For example, evaluating a real estate fund against the 
S&P 500 is incorrect because real estate has different characteristics than equity. In 
addition to errors in benchmarking, errors could occur in the measurement of risk 
and return of the market portfolio and the portfolios being evaluated. Finally, many 
estimates are based on historical data. Any projections based on such estimates assume 
that this level of performance will continue in the future.
4.3.3  Security Characteristic Line
Similar to the SML, we can draw a security characteristic line  (SCL) for a security. 
The SCL is a plot of the excess return of the security on the excess return of the market. 
In Exhibit 11, Jensen’s alpha is the intercept and the beta is the slope. The equation of

the line can be obtained by rearranging the terms in the expression for Jensen’s alpha 
and replacing the subscript p with i:
Ri – Rf = αi + βi(Rm – Rf)
As an example, the SCL is drawn in Exhibit 11 using Manager X’s portfolio from 
Exhibit  8. The security characteristic line can also be estimated by regressing the 
excess security return, Ri – Rf, on the excess market return, Rm – Rf.

The Capital Asset Pricing Model 347
Exhibit 11   The Security Characteristic LineExcess Security Return
Excess Market ReturnSlope = βi [Beta]Ri – Rf
Rm – Rfαi
4.3.4  Security Selection
When discussing the CAPM, we assumed that investors have homogeneous expecta -
tions and are rational, risk-  averse, utility-  maximizing investors. With these assump -
tions, we were able to state that all investors assign the same value to all assets and, 
therefore, have the same optimal risky portfolio, which is the market portfolio. In 
other words, we assumed that there is commonality among beliefs about an asset’s 
future cash flows and the required rate of return. Given the required rate of return, 
we can discount the future cash flows of the asset to arrive at its current value, or 
price, which is agreed upon by all or most investors.
In this section, we introduce heterogeneity in beliefs of investors. Because inves -
tors are price takers, it is assumed that such heterogeneity does not significantly

affect the market price of an asset. The difference in beliefs can relate to future cash 
flows, the systematic risk of the asset, or both. Because the current price of an asset 
is the discounted value of the future cash flows, the difference in beliefs could result 
in an investor-  estimated price that is different from the CAPM-  calculated price. The 
CAPM-  calculated price is the current market price because it reflects the beliefs of all 
other investors in the market. If the investor-  estimated current price is higher (lower) 
than the market price, the asset is considered undervalued (overvalued). Therefore, 
the CAPM is an effective tool for determining whether an asset is undervalued or 
overvalued and whether an investor should buy or sell the asset.
Although portfolio performance evaluation is backward looking and security selec -
tion is forward looking, we can apply the concepts of portfolio evaluation to security

selection. The best measure to apply is Jensen’s alpha because it uses systematic risk 
and is meaningful even on an absolute basis. A positive Jensen’s alpha indicates a 
superior security, whereas a negative Jensen’s alpha indicates a security that is likely 
to underperform the market when adjusted for risk.
Another way of presenting the same information is with the security market line. 
Potential investors can plot a security’s expected return and beta against the SML 
and use this relationship to decide whether the security is overvalued or undervalued

Reading 40 ■ Portfolio Risk and Return: Part II 348
in the market.6 Exhibit  12 shows a number of securities along with the SML. All 
securities that reflect the consensus market view are points directly on the SML (i.e., 
properly valued). If a point representing the estimated return of an asset is above 
the SML (Points A and C), the asset has a low level of risk relative to the amount of 
expected return and would be a good choice for investment. In contrast, if the point 
representing a particular asset is below the SML (Point B), the stock is considered 
overvalued. Its return does not compensate for the level of risk and should not be 
considered for investment. Of course, a short position in Asset B can be taken if short 
selling is permitted.
Exhibit 12   Security Selection Using SML
Beta15%25%
SMLReturn on InvestmentRi
Rf = 5%C (R = 20%, β = 1.2)
A (R = 11%, β = 0.5)B (R = 12%, β = 1.0)
βm = 1.0
4.3.5  Constructing a Portfolio

βm = 1.0
Based on the CAPM, investors should hold a combination of the risk-  free asset and the 
market portfolio. The true market portfolio consists of a large number of securities, 
and an investor would have to own all of them in order to be completely diversified. 
Because owning all existing securities is not practical, in this section, we will consider 
an alternate method of constructing a portfolio that may not require a large number 
of securities and will still be sufficiently diversified. Exhibit 13 shows the reduction 
in risk as we add more and more securities to a portfolio. As can be seen from the 
exhibit, much of the nonsystematic risk can be diversified away in as few as 30 secu -
rities. These securities, however, should be randomly selected and represent different 
asset classes for the portfolio to effectively diversify risk. Otherwise, one may be better 
off using an index (e.g., the S&P 500 for a diversified large-  cap equity portfolio and

other indexes for other asset classes).
6 In this reading, we do not consider transaction costs, which are important whenever deviations from 
a passive portfolio are considered. Thus, the magnitude of undervaluation or overvaluation should be 
considered in relation to transaction costs prior to making an investment decision.

The Capital Asset Pricing Model 349
Exhibit 13   Diversification with Number of Stocks
5 1Variance
Number of  StocksSystematic VarianceTotal
Variance Non-Systematic Variance
Varian ce of Market Portfolio
10 20 30
Let’s begin constructing the optimal portfolio with a portfolio of securities like 
the S&P 500. Although the S&P 500 is a portfolio of 500 securities, it is a good start -
ing point because it is readily available as a single security for trading. In contrast, it 
represents only the large corporations that are traded on the US stock markets and, 
therefore, does not encompass the global market entirely. Because the S&P 500 is the 
base portfolio, however, we treat it is as the market for the CAPM.
Any security not included in the S&P 500 can be evaluated to determine whether it 
should be integrated into the portfolio. That decision is based on the αi of the security, 
which is calculated using the CAPM with the S&P 500 as the market portfolio. Note

that security i may not necessarily be priced incorrectly for it to have a non-  zero αi; 
αi can be positive merely because it is not well correlated with the S&P 500 and its 
return is sufficient for the amount of systematic risk it contains. For example, assume 
a new stock market, ABC, opens to foreign investors only and is being considered for 
inclusion in the portfolio. We estimate ABC’s model parameters relative to the S&P 
500 and find an αi of approximately 3 percent, with a βi of 0.60. Because αi is positive, 
ABC should be added to the portfolio. Securities with a significantly negative αi may 
be short sold to maximize risk-  adjusted return. For convenience, however, we will 
assume that negative positions are not permitted in the portfolio.
In addition to the securities that are correctly priced but enter the portfolio because 
of their risk–return superiority, securities already in the portfolio (S&P 500) may be

undervalued or overvalued based on investor expectations that are incongruent with 
the market. Securities in the S&P 500 that are overvalued (negative αi) should be 
dropped from the S&P 500 portfolio, if it is possible to exclude individual securities, 
and positions in securities in the S&P 500 that are undervalued (positive αi) should 
be increased.
This brings us to the next question: What should the relative weight of securities 
in the portfolio be? Because we are concerned with maximizing risk-  adjusted return, 
securities with a higher αi should have a higher weight, and securities with greater 
nonsystematic risk should be given less weight in the portfolio. A complete analysis 
of portfolio optimization is beyond the scope of this reading, but the following prin -
ciples are helpful. The weight in each nonmarket security should be proportional

Reading 40 ■ Portfolio Risk and Return: Part II 350
to α
σi
ei2, where the denominator is the nonsystematic variance of security i. The total 
weight of nonmarket securities in the portfolio is proportional to  w
wii
iN
iei
iNα
σ=
=∑
∑1
22
1. The weight 
in the market portfolio is a function of  ERm
m()
σ2. The information ratio,  α
σi
ei (i.e., alpha 
divided by nonsystematic risk), measures the abnormal return per unit of risk added 
by the security to a well-  diversified portfolio. The larger the information ratio is, the 
more valuable the security.
EXAMPLE 11   
Optimal Investor Portfolio with Heterogeneous Beliefs
A Japanese investor is holding the Nikkei 225 index, which is her version of the 
market. She thinks that three stocks, P , Q, and R, which are not in the Nikkei 
225, are undervalued and should form a part of her portfolio. She has the fol -
lowing information about the stocks, the Nikkei 225, and the risk-  free rate (the 
information is given as expected return, standard deviation, and beta):

P: 15%, 30%, 1.5
Q: 18%, 25%, 1.2
R: 16%, 23%, 1.1
Nikkei 225: 12%, 18%, 1.0
Risk-  free rate: 2%, 0%, 0.0
1 Calculate Jensen’s alpha for P , Q, and R.
2 Calculate nonsystematic variance for P , Q, and R.
3 Should any of the three stocks be included in the portfolio? If so, which 
stock should have the highest weight in the portfolio?
Stock P’s α: Ri – [Rf + βi(Rm – Rf)] = 0.15 – (0.02 + 1.5 × 0.10) = –0.02
Stock Q’s α: Ri – [Rf + βi(Rm – Rf)] = 0.18 – (0.02 + 1.2 × 0.10) = 0.04
Stock R’s α: Ri – [Rf + βi(Rm – Rf)] = 0.16 – (0.02 + 1.1 × 0.10) = 0.03
Total variance = Systematic variance + Nonsystematic variance. From Section 
3.2.2, we write the equation as  σσ βσei ii m22 22=− .
Stock P’s nonsystematic variance = (0.30 × 0.30) – (1.5 × 1.5 × 0.18 × 0.18) = 
0.09 – 0.0729 = 0.0171
Stock Q’s nonsystematic variance = (0.25 × 0.25) – (1.2 × 1.2 × 0.18 × 0.18) = 
0.0625 – 0.0467 = 0.0158
Stock R’s nonsystematic variance = (0.23 × 0.23) – (1.1 × 1.1 × 0.18 × 0.18) =

Beyond the Capital Asset Pricing Model 351
Stock P has a negative α and should not be included in the portfolio, unless a 
negative position can be assumed through short selling. Stocks Q and R have 
a positive α; therefore, they should be included in the portfolio with positive 
weights.
The relative weight of Q is 0.04/0.0158 = 2.53.
The relative weight of R is 0.03/0.0137 = 2.19.
Stock Q will have the largest weight among the nonmarket securities to be added 
to the portfolio. In relative terms, the weight of Q will be 15.5 percent greater 
than the weight of R (2.53/2.19 = 1.155). As the number of securities increases, 
the analysis becomes more complex. However, the contribution of each addi -
tional security toward improvement in the risk–return trade-  off will decrease 
and eventually disappear, resulting in a well-  diversified portfolio. 
BEYOND THE CAPITAL ASSET PRICING MODEL
In general, return-  generating models allow us to estimate an asset’s return given its

characteristics, where the asset characteristics required for estimating the return 
are specified in the model. Estimating an asset’s return is important for investment 
decision making. These models are also important as a benchmark for evaluating 
portfolio, security, or manager performance. The return-  generating models were 
briefly introduced in Section 3.2.1, and one of those models, the capital asset pricing 
model, was discussed in detail in Section 4.
The purpose of this section is to make readers aware that, although the CAPM is 
an important concept and model, the CAPM is not the only return-  generating model. 
In this section, we revisit and highlight the limitations of the CAPM and preview 
return-  generating models that address some of those limitations.
5.1 The CAPM
The CAPM is a model that simplifies a complex investment environment and allows 
investors to understand the relationship between risk and return. Although the

CAPM affords us this insight, its assumptions can be constraining and unrealistic, 
as mentioned in Section 5.2. In Section 5.3, we discuss other models that have been 
developed along with their own limitations.
5.2 Limitations of the CAPM
The CAPM is subject to theoretical and practical limitations. Theoretical limitations 
are inherent in the structure of the model, whereas practical limitations are those that 
arise in implementing the model.5

Reading 40 ■ Portfolio Risk and Return: Part II 352
5.2.1  Theoretical Limitations of the CAPM
■■Single-  factor model: Only systematic risk or beta risk is priced in the CAPM. 
Thus, the CAPM states that no other investment characteristics should be con -
sidered in estimating returns. As a consequence, it is prescriptive and easy to 
understand and apply, although it is very restrictive and inflexible.
■■Single-  period model: The CAPM is a single-  period model that does not con -
sider multi-  period implications or investment objectives of future periods, 
which can lead to myopic and suboptimal investment decisions. For example, it 
may be optimal to default on interest payments in the current period to maxi -
mize current returns, but the consequences may be negative in the next period. 
A single-  period model like the CAPM is unable to capture factors that vary over 
time and span several periods.
5.2.2  Practical Limitations of the CAPM

In addition to the theoretical limitations, implementation of the CAPM raises several 
practical concerns, some of which are listed below.
■■Market portfolio: The true market portfolio according to the CAPM includes all 
assets, financial and nonfinancial, which means that it also includes many assets 
that are not investable, such as human capital and assets in closed economies. 
Richard Roll7 noted that one reason the CAPM is not testable is that the true 
market portfolio is unobservable.
■■Proxy for a market portfolio: In the absence of a true market portfolio, market 
participants generally use proxies. These proxies, however, vary among analysts, 
the country of the investor, etc. and generate different return estimates for the 
same asset, which is impermissible in the CAPM.
■■Estimation of beta risk: A long history of returns (three to five years) is required 
to estimate beta risk. The historical state of the company, however, may not be

an accurate representation of the current or future state of the company. More 
generally, the CAPM is an ex ante  model, yet it is usually applied using ex post  
data. In addition, using different periods for estimation results in different 
estimates of beta. For example, a three-  year beta is unlikely to be the same as 
a five-  year beta, and a beta estimated with daily returns is unlikely to be the 
same as the beta estimated with monthly returns. Thus, we are likely to estimate 
different returns for the same asset depending on the estimate of beta risk used 
in the model.
■■The CAPM is a poor predictor of returns: If the CAPM is a good model, its 
estimate of asset returns should be closely associated with realized returns. 
However, empirical support for the CAPM is weak.8 In other words, tests of the 
CAPM show that asset returns are not determined only by systematic risk. Poor 
predictability of returns when using the CAPM is a serious limitation because

return-  generating models are used to estimate future returns.
■■Homogeneity in investor expectations: The CAPM assumes that homogeneity 
exists in investor expectations for the model to generate a single optimal risky 
portfolio (the market) and a single security market line. Without this assump -
tion, there will be numerous optimal risky portfolios and numerous security 
market lines. Clearly, investors can process the same information in a rational 
manner and arrive at different optimal risky portfolios.
7 Roll (1977).
8 See, for example, Fama and French (1992).

Beyond the Capital Asset Pricing Model 353
5.3 Extensions to the CAPM
Given the limitations of the CAPM, it is not surprising that other models have been 
proposed to address some of these limitations. These new models are not without 
limitations of their own, which we will mention while discussing the models. We divide 
the models into two categories and provide one example of each type.
5.3.1  Theoretical Models
Theoretical models are based on the same principle as the CAPM but expand the 
number of risk factors. The best example of a theoretical model is the arbitrage pricing 
theory (APT), which was developed by Stephen Ross.9 Like the CAPM, APT proposes 
a linear relationship between expected return and risk:
E(Rp) = RF + λ1βp,1 + ... + λKβp,K
where
 E(Rp) = the expected return of portfolio p
 RF = the risk-  free rate
 λj = the risk premium (expected return in excess of the risk-  free rate) for 
factor j
 βp,j = the sensitivity of the portfolio to factor j
 K = the number of risk factors

K = the number of risk factors
Unlike the CAPM, however, APT allows numerous risk factors—as many as are 
relevant to a particular asset. Moreover, other than the risk-  free rate, the risk factors 
need not be common and may vary from one asset to another. A no-  arbitrage con -
dition in asset markets is used to determine the risk factors and estimate betas for 
the risk factors.
Although it is theoretically elegant, flexible, and superior to the CAPM, APT is 
not commonly used in practice because it does not specify any of the risk factors 
and it becomes difficult to identify risk factors and estimate betas for each asset in a 
portfolio. So from a practical standpoint, the CAPM is preferred to APT.
5.3.2  Practical Models
If beta risk in the CAPM does not explain returns, which factors do? Practical models 
seek to answer this question through extensive research. As mentioned in Section 
3.2.1, the best example of such a model is the four-  factor model proposed by Fama

and French (1992) and Carhart (1997).
Based on an analysis of the relationship between past returns and a variety of 
different factors, Fama and French (1992) proposed that three factors seem to explain 
asset returns better than just systematic risk. Those three factors are relative size, 
relative book-  to- market value, and beta of the asset. With Carhart’s (1997) addition 
of relative past stock returns, the model can be written as follows:
ER MKTS MB HMLU MDit ii MKTt iSMB ti HMLt iUMD t () =+ ++ + αβ ββ β,, ,,
9 Ross (1976).

Reading 40 ■ Portfolio Risk and Return: Part II 354
where
 E(Ri) = the return on an asset in excess of the one-  month T-  bill return
 MKT  = the excess return on the market portfolio
 SMB  = the difference in returns between small-  capitalization stocks and large-  
capitalization stocks (size)
 HML =  the difference in returns between high-  book-  to- market stocks and low-  
book-  to- market stocks (value versus growth)
 UMD  = the difference in returns of the prior year’s winners and losers 
(momentum)
Historical analysis shows that the coefficient on MKT  is not significantly different 
from zero, which implies that stock return is unrelated to the market. The factors that 
explain stock returns are size (smaller companies outperform larger companies), book-  
to- market ratio (value companies outperform glamour companies), and momentum 
(past winners outperform past losers).
The four-  factor model has been found to predict asset returns much better than the

CAPM and is extensively used in estimating returns for US stocks . Note the emphasis 
on US stocks; because these factors were estimated for US stocks, they have worked 
well for US stocks over the last several years.
Three observations are in order. First, no strong economic arguments exist for 
the three additional risk factors. Second, the four-  factor model does not necessarily 
apply to other assets or assets in other countries, and third, there is no expectation 
that the model will continue to work well in the future.
5.4 The CAPM and Beyond
The CAPM has limitations and, more importantly, is ineffective in modeling asset 
returns. However, it is a simple model that allows us to estimate returns and evaluate 
performance. The newer models provide alternatives to the CAPM, although they are 
not necessarily better in all situations or practical in their application in the real world.
SUMMARY
In this reading, we discussed the capital asset pricing model in detail and covered

related topics such as the capital market line. The reading began with an interpretation 
of the CML, uses of the market portfolio as a passive management strategy, and lever -
aging of the market portfolio to obtain a higher expected return. Next, we discussed 
systematic and nonsystematic risk and why one should not expect to be compensated 
for taking on nonsystematic risk. The discussion of systematic and nonsystematic risk 
was followed by an introduction to beta and return-  generating models. This broad 
topic was then broken down into a discussion of the CAPM and, more specifically, the 
relationship between beta and expected return. The final section included applications 
of the CAPM to capital budgeting, portfolio performance evaluation, and security 
selection. The highlights of the reading are as follows.
■■The capital market line is a special case of the capital allocation line, where the 
efficient portfolio is the market portfolio.

■■Obtaining a unique optimal risky portfolio is not possible if investors are per -
mitted to have heterogeneous beliefs because such beliefs will result in hetero -
geneous asset prices.

References 355
Carhart, Mark. 1997. “On Persistence in Mutual Fund 
Performance. ” Journal of Finance , vol. 52, no. 1:57–82. 
Fama, Eugene, and Kenneth French. 1992. “The Cross-  Section 
of Expected Stock Returns. ” Journal of Finance , vol. 47, no. 
2:427–466. 
Lintner, John. 1965a. “Security Prices, Risk, and Maximal 
Gains from Diversification. ” Journal of Finance , vol. 20, no. 
4:587–615. 
Lintner, John. 1965b. “The Valuation of Risk Assets and the 
Budgets. ” Review of Economics and Statistics , vol. 47, no. 
1:13–37. 
Markowitz, Harry. 1952. “Portfolio Selection. ” Journal of Finance , 
vol. 7, no. 1:77–91. Mossin, Jan. 1966. “Equilibrium in a Capital Asset Market. ” 
Econometrica , vol. 34, no. 4:768–783. 
Roll, Richard. 1977. “ A Critique of the Asset Pricing Theory’s 
Tests Part I: On Past and Potential Testability of the Theory. ” 
Journal of Financial Economics , vol. 4, no. 2:129–176.

Ross, Stephen A. 1976. “The Arbitrage Theory of Capital Asset 
Pricing. ” Journal of Economic Theory , vol. 13, no. 3:341–360. 
Sharpe, William F. 1964. “Capital Asset Prices: A Theory Of 
Finance , vol. 19, no. 3:425–442. 
Treynor, Jack L. 1961. Market Value, Time, and Risk . Unpublished 
manuscript.
Treynor, Jack L. 1962. Toward a Theory of Market Value of Risky 
Assets . Unpublished manuscript.■■Investors can leverage their portfolios by borrowing money and investing in the 
market.
■■Systematic risk is the risk that affects the entire market or economy and is not 
diversifiable.
■■Nonsystematic risk is local and can be diversified away by combining assets 
with low correlations.
■■Beta risk, or systematic risk, is priced and earns a return, whereas nonsystem -
atic risk is not priced.
■■The expected return of an asset depends on its beta risk and can be computed 
using the CAPM, which is given by E(Ri) = Rf + βi[E(Rm) – Rf].

■■The security market line is an implementation of the CAPM and applies to all 
securities, whether they are efficient or not.
■■Expected return from the CAPM can be used for making capital budgeting 
decisions.
■■Portfolios can be evaluated by several CAPM-  based measures, such as the 
Sharpe ratio, the Treynor ratio, M2, and Jensen’s alpha.
■■The SML can assist in security selection and optimal portfolio construction.
By successfully understanding the content of this reading, you should feel comfort -
able decomposing total variance into systematic and nonsystematic variance, analyzing 
beta risk, using the CAPM, and evaluating portfolios and individual securities.

Reading 40 ■ Portfolio Risk and Return: Part II 356
1 The line depicting the total risk and expected return of portfolio combinations 
of a risk-  free asset and any risky asset is the:
A security market line.
B capital allocation line.
C security characteristic line.
2 The portfolio of a risk-  free asset and a risky asset has a better risk-  return 
tradeoff than investing in only one asset type because the correlation between 
the risk-  free asset and the risky asset is equal to:
A −1.0.
B 0.0.
C 1.0.
3 With respect to capital market theory, an investor’s optimal portfolio is the 
combination of a risk-  free asset and a risky asset with the highest:
A expected return.
B indifference curve.
C capital allocation line slope.
4 Highly risk-  averse investors will most likely  invest the majority of their wealth 
in:
B risk-  free assets.
C the optimal risky portfolio.
5 The capital market line (CML) is the graph of the risk and return of portfolio

combinations consisting of the risk-  free asset and:
A any risky portfolio.
B the market portfolio.
C the leveraged portfolio.
6 Which of the following statements most accurately  defines the market portfolio 
in capital market theory? The market portfolio consists of all:
B tradable assets.
C investable assets.
7 With respect to capital market theory, the optimal risky portfolio:
A is the market portfolio.
B has the highest expected return.
C has the lowest expected variance.
8 Relative to portfolios on the CML, any portfolio that plots above the CML is 
considered:
A inferior.
B inefficient.
C unachievable.

Practice Problems 357
9 A portfolio on the capital market line with returns greater than the returns on 
the market portfolio represents a(n):
A lending portfolio.
B borrowing portfolio.
C unachievable portfolio.
10 With respect to the capital market line, a portfolio on the CML with returns 
less than the returns on the market portfolio represents a(n):
11 Which of the following types of risk is most likely  avoided by forming a diversi -
fied portfolio?
A Total risk.
B Systematic risk.
C Nonsystematic risk.
12 Which of the following events is most likely  an example of nonsystematic risk?
A A decline in interest rates.
B The resignation of chief executive officer.
C An increase in the value of the US dollar.
13 With respect to the pricing of risk in capital market theory, which of the follow -
ing statements is most accurate ?
A All risk is priced.
B Systematic risk is priced.
C Nonsystematic risk is priced.

14 The sum of an asset’s systematic variance and its nonsystematic variance of 
returns is equal to the asset’s:
A beta.
B total risk.
C total variance.
15 With respect to return-  generating models, the intercept term of the market 
model is the asset’s estimated:
A beta.
B alpha.
C variance.
16 With respect to return-  generating models, the slope term of the market model 
is an estimate of the asset’s:
A total risk.
B systematic risk.
C nonsystematic risk.
17 With respect to return-  generating models, which of the following statements is 
most accurate ? Return-  generating models are used to directly estimate the:
A expected return of a security.
B weights of securities in a portfolio.
C parameters of the capital market line.

Reading 40 ■ Portfolio Risk and Return: Part II 358
18–20
An analyst gathers the following information:
SecurityExpected  
Annual Return (%)Expected  
(%)Correlation between 
Security and the 
Market
Security 1 11 25 0.6
Security 2 11 20 0.7
Security 3 14 20 0.8
Market 10 15 1.0
18 Which security has the highest  total risk?
A Security 1.
B Security 2.
C Security 3.
19 Which security has the highest  beta measure?
20 Which security has the least  amount of market risk?
21 With respect to capital market theory, the average beta of all assets in the mar -
ket is:
A less than 1.0.
B equal to 1.0.
C greater than 1.0.
22 The slope of the security characteristic line is an asset’s:
A beta.
B excess return.
C risk premium.
23 The graph of the capital asset pricing model is the:
A capital market line.
B security market line.

24 With respect to capital market theory, correctly priced individual assets can be 
plotted on the:
C capital allocation line.

Practice Problems 359
25 With respect to the capital asset pricing model, the primary determinant of 
expected return of an individual asset is the:
A asset’s beta.
B market risk premium.
C asset’s standard deviation.
26 With respect to the capital asset pricing model, which of the following values 
of beta for an asset is most likely  to have an expected return for the asset that is 
less than the risk-  free rate?
A −0.5
B 0.0
C 0.5
27 With respect to the capital asset pricing model, the market risk premium is:
A less than the excess market return.
B equal to the excess market return.
C greater than the excess market return.
28–31
Standard Deviation (%) Beta
Security 1 25 1.50
Security 2 15 1.40
Security 3 20 1.60
28 With respect to the capital asset pricing model, if the expected market risk 
premium is 6% and the risk-  free rate is 3%, the expected return for Security 1 is 
A 9.0%.

A 9.0%.
B 12.0%.
C 13.5%.
29 With respect to the capital asset pricing model, if expected return for Security 2 
is equal to 11.4% and the risk-  free rate is 3%, the expected return for the market 
A 8.4%.
B 9.0%.
C 10.3%.
30 With respect to the capital asset pricing model, if the expected market risk pre -
mium is 6% the security with the highest  expected return is:
31 With respect to the capital asset pricing model, a decline in the expected mar -
ket return will have the greatest  impact on the expected return of:

Reading 40 ■ Portfolio Risk and Return: Part II 360
32 Which of the following performance measures is consistent with the CAPM?
A M-squared.
B Sharpe ratio.
C Jensen’s alpha.
33 Which of the following performance measures does not require the measure to 
be compared to another value?
A Sharpe ratio.
B Treynor ratio.
34 Which of the following performance measures is most  appropriate for an inves -
tor who is not fully diversified?
35 Analysts who have estimated returns of an asset to be greater than the expected 
returns generated by the capital asset pricing model should consider the asset 
to be:
A overvalued.
B undervalued.
C properly valued.
36 With respect to capital market theory, which of the following statements best 
describes the effect of the homogeneity assumption? Because all investors have 
the same economic expectations of future cash flows for all assets, investors will 
invest in:

invest in:
A the same optimal risky portfolio.
B the Standard and Poor’s 500 Index.
C assets with the same amount of risk.
37 With respect to capital market theory, which of the following assumptions 
allows for the existence of the market portfolio? All investors:
A are price takers.
B have homogeneous expectations.
C plan for the same, single holding period.
38 The intercept of the best fit line formed by plotting the excess returns of a man -
ager’s portfolio on the excess returns of the market is best described as Jensen’s:
A beta.
B ratio.
C alpha.
39 Portfolio managers who are maximizing risk-  adjusted returns will seek to invest 
more  in securities with:
A lower values of Jensen’s alpha.
B values of Jensen’s alpha equal to 0.

Practice Problems 361
C higher values of Jensen’s alpha.
40 Portfolio managers, who are maximizing risk-  adjusted returns, will seek to 
invest less in securities with:
A lower values for nonsystematic variance.
B values of nonsystematic variance equal to 0.
C higher values for nonsystematic variance.

Reading 40 ■ Portfolio Risk and Return: Part II 362
SOLUTIONS
1 B is correct. A capital allocation line (CAL) plots the expected return and total 
risk of combinations of the risk-  free asset and a risky asset (or a portfolio of 
risky assets).
2 B is correct. A portfolio of the risk-  free asset and a risky asset or a portfolio of 
risky assets can result in a better risk-  return tradeoff than an investment in only 
one type of an asset, because the risk-  free asset has zero correlation with the 
risky asset.
3 B is correct. Investors will have different optimal portfolios depending on their 
indifference curves. The optimal portfolio for each investor is the one with 
highest utility; that is, where the CAL is tangent to the individual investor’s 
highest possible indifference curve.
4 B is correct. Although the optimal risky portfolio is the market portfolio, highly 
risk-  averse investors choose to invest most of their wealth in the risk-  free asset.

5 B is correct. Although the capital allocation line includes all possible combina -
tions of the risk-  free asset and any risky portfolio, the capital market line is a 
special case of the capital allocation line, which uses the market portfolio as the 
optimal risky portfolio.
6 A is correct. The market includes all risky assets, or anything that has value; 
however, not all assets are tradable, and not all tradable assets are investable.
7 A is correct. The optimal risky portfolio is the market portfolio. Capital market 
theory assumes that investors have homogeneous expectations, which means 
that all investors analyze securities in the same way and are rational. That is, 
investors use the same probability distributions, use the same inputs for future 
cash flows, and arrive at the same valuations. Because their valuations of all 
assets are identical, all investors will invest in the same optimal risky portfolio 
(i.e., the market portfolio).

8 C is correct. Theoretically, any point above the CML is not achievable and any 
point below the CML is dominated by and inferior to any point on the CML.
9 B is correct. As one moves further to the right of point M on the capital market 
line, an increasing amount of borrowed money is being invested in the market 
portfolio. This means that there is negative investment in the risk-  free asset, 
which is referred to as a leveraged position in the risky portfolio.
10 A is correct. The combinations of the risk-  free asset and the market portfolio 
on the CML where returns are less than the returns on the market portfolio are 
termed ‘lending’ portfolios.
11 C is correct. Investors are capable of avoiding nonsystematic risk by forming 
a portfolio of assets that are not highly correlated with one another, thereby 
reducing total risk and being exposed only to systematic risk.
12 B is correct. Nonsystematic risk is specific to a firm, whereas systematic risk

affects the entire economy.
13 B is correct. Only systematic risk is priced. Investors do not receive any return 
for accepting nonsystematic or diversifiable risk.
14 C is correct. The sum of systematic variance and nonsystematic variance equals 
the total variance of the asset. References to total risk as the sum of systematic 
risk and nonsystematic risk refer to variance, not to risk.
15 B is correct. In the market model, Ri = αi + βiRm + ei, the intercept, αi, and 
slope coefficient, βi, are estimated using historical security and market returns.

Solutions 363
16 B is correct. In the market model, Ri = αi + βiRm + ei, the slope coefficient, βi, is 
an estimate of the asset’s systematic or market risk.
17 A is correct. In the market model, Ri = αi + βiRm + ei, the intercept, αi, and 
slope coefficient, βi, are estimated using historical security and market returns. 
These parameter estimates then are used to predict firm-  specific returns that a 
security may earn in a future period.
18 A is correct. Security 1 has the highest total variance; 0.0625 = 0.252 compared 
to Security 2 and Security 3 with a total variance of 0.0400.
19 C is correct. Security 3 has the highest beta value; 1.07 =  ρσ
σ33 08020
15, .%
%m
m=() () 
compared to Security 1 and Security 2 with beta values of 1.00 and 0.93, 
20 B is correct. Security 2 has the lowest beta value; 0.93 =  ρσ
σ22 07020
15, .%
%m
m=() () 
compared to Security 1 and 3 with beta values of 1.00 and 1.07, respectively.

21 B is correct. The average beta of all assets in the market, by definition, is equal 
to 1.0.
22 A is correct. The security characteristic line is a plot of the excess return of the 
security on the excess return of the market. In such a graph, Jensen’s alpha is 
the intercept and the beta is the slope.
23 B is correct. The security market line (SML) is a graphical representation of the 
capital asset pricing model, with beta risk on the x-  axis and expected return on 
the y-  axis.
24 B is correct. The security market line applies to any security, efficient or not. 
The CAL and the CML use the total risk of the asset (or portfolio of assets) 
rather than its systematic risk, which is the only risk that is priced.
25 A is correct. The CAPM shows that the primary determinant of expected return 
for an individual asset is its beta, or how well the asset correlates with the 
market.
26 A is correct. If an asset’s beta is negative, the required return will be less than

the risk-  free rate in the CAPM. When combined with a positive market return, 
the asset reduces the risk of the overall portfolio, which makes the asset very 
valuable. Insurance is an example of a negative beta asset.
27 B is correct. In the CAPM, the market risk premium is the difference between 
the return on the market and the risk-  free rate, which is the same as the return 
in excess of the market return.
28 B is correct. The expected return of Security 1, using the CAPM, is 12.0% = 3% 
+ 1.5(6%); E(Ri) = Rf + βi[E(Rm) – Rf].
29 B is correct. The expected risk premium for Security 2 is 8.4%, (11.4% − 3%), 
indicates that the expected market risk premium is 6%; therefore, since the 
risk-  free rate is 3% the expected rate of return for the market is 9%. That is, 
using the CAPM, E(Ri) = Rf + βi[E(Rm) – Rf], 11.4% = 3% + 1.4(X%), where X% = 
(11.4% − 3%)/1.4 = 6.0% = market risk premium.
30 C is correct. Security 3 has the highest beta; thus, regardless of the value for the

risk-  free rate, Security 3 will have the highest expected return:
E(Ri) = Rf + βi[E(Rm) – Rf] 
31 C is correct. Security 3 has the highest beta; thus, regardless of the risk-  free 
rate the expected return of Security 3 will be most sensitive to a change in the 
expected market return.

Reading 40 ■ Portfolio Risk and Return: Part II 364
32 C is correct. Jensen’s alpha adjusts for systematic risk, and M-squared and the 
Sharpe Ratio adjust for total risk.
33 C is correct. The sign of Jensen’s alpha indicates whether or not the portfolio 
has outperformed the market. If alpha is positive, the portfolio has outper -
formed the market; if alpha is negative, the portfolio has underperformed the 
market.
34 A is the correct. M-squared adjusts for risk using standard deviation (i.e., total 
risk).
35 B is correct. If the estimated return of an asset is above the SML (the expected 
return), the asset has a lower level of risk relative to the amount of expected 
return and would be a good choice for investment (i.e., undervalued).
36 A is correct. The homogeneity assumption refers to all investors having the 
same economic expectation of future cash flows. If all investors have the same 
expectations, then all investors should invest in the same optimal risky port -

folio, therefore implying the existence of only one optimal portfolio (i.e., the 
market portfolio).
37 B is correct. The homogeneous expectations assumption means that all inves -
tors analyze securities in the same way and are rational. That is, they use the 
same probability distributions, use the same inputs for future cash flows, and 
arrive at the same valuations. Because their valuation of all assets is identi -
cal, they will generate the same optimal risky portfolio, which is the market 
portfolio.
38 C is correct. This is because of the plot of the excess return of the security on 
the excess return of the market. In such a graph, Jensen’s alpha is the intercept 
and the beta is the slope.
39 C is correct. Since managers are concerned with maximizing risk-  adjusted 
returns, securities with a higher value of Jensen’s alpha, αi, should have a higher 
weight.
40 C is correct. Since managers are concerned with maximizing risk-  adjusted

returns, securities with greater nonsystematic risk should be given less weight 
in the portfolio.

Portfolio Management (2)
This study session introduces the portfolio planning and construction process, 
including the development of an investment policy statement (IPS). A discussion of 
risk management, including the various types and measures of risk, follows, and a risk 
management framework is provided. The session concludes with coverage on how 
financial technology (fintech) is impacting areas within the investment industry, such 
as investment analysis, automated advice, and risk management.
Reading 41 Basics of Portfolio Planning and Construction  
by Alistair Byrne, PhD, CFA, and Frank E. Smudde, 
CFA
Reading 42 Risk Management: An Introduction  
by Don M. Chance, PhD, CFA, and Michael E. 
Edleson, PhD, CFA
Reading 43 Fintech in Investment Management  
by Barbara J. Mack and Robert Kissell, PhDPOrTFOLIO  MANAGEMENT  
13

Basics of Portfolio Planning 
and Construction
by Alistair Byrne, PhD, CFA, and Frank E. Smudde, CFA
Alistair Byrne, PhD, CFA, is at State Street Global Advisors (United Kingdom). Frank E. 
Smudde, CFA (Netherlands).
a. describe the reasons for a written investment policy statement 
(IPS);
b. describe the major components of an IPS;
c. describe risk and return objectives and how they may be 
developed for a client; 
d. distinguish between the willingness and the ability (capacity) to 
take risk in analyzing an investor’s financial risk tolerance;
e. describe the investment constraints of liquidity, time horizon, tax 
concerns, legal and regulatory factors, and unique circumstances 
and their implications for the choice of portfolio assets;
f. explain the specification of asset classes in relation to asset 
allocation;
g. describe the principles of portfolio construction and the role of 
asset allocation in relation to the IPS.

To build a suitable portfolio for a client, investment advisers should first seek to 
understand the client’s investment goals, resources, circumstances, and constraints. 
Investors can be categorized into broad groups based on shared characteristics with 
respect to these factors (e.g., various types of individual investors and institutional 
investors). Even investors within a given type, however, will invariably have a number 
of distinctive requirements. In this reading, we consider in detail the planning for 
investment success based on an individualized understanding of the client.1rEADING
41

Reading 41 ■ Basics of Portfolio Planning and Construction 368
This reading is organized as follows: Section 2 discusses the investment policy 
statement, a written document that captures the client’s investment objectives and the 
constraints. Section 3 discusses the portfolio construction process, including the first 
step of specifying a strategic asset allocation for the client. A summary and practice 
problems conclude the reading.
PORTFOLIO PLANNING
Portfolio planning  can be defined as a program developed in advance of constructing 
a portfolio that is expected to satisfy the client’s investment objectives. The written 
document governing this process is the investment policy statement (IPS).
2.1 The Investment Policy Statement
The IPS is the starting point of the portfolio management process. Without a full 
understanding of the client’s situation and requirements, it is unlikely that success -
ful results will be achieved. “Success” can be defined as a client achieving his or her

important investment goals using means that he or she is comfortable with (in terms 
of risks taken and other concerns). The IPS essentially communicates a plan for 
achieving investment success.
The IPS will be developed following a fact finding discussion with the client. This 
fact finding discussion can include the use of a questionnaire designed to articulate 
the client’s risk tolerance as well as specific circumstances. In the case of institutional 
clients, the fact finding may involve asset–liability management studies, identification 
of liquidity needs, and a wide range of tax and legal considerations.
The IPS can take a variety of forms. A typical format will include the client’s 
investment objectives and the constraints that apply to the client’s portfolio.
The client’s objectives are specified in terms of risk tolerance and return require -
ments. These must be consistent with each other: a client is unlikely to be able to find

a portfolio that offers a relatively high expected return without taking on a relatively 
high level of risk.
The constraints section covers factors that need to be taken into account when 
constructing a portfolio for the client that meets the objectives. The typical constraint 
categories are liquidity requirements, time horizon, regulatory requirements, tax status, 
and unique needs. The constraints may be internal (i.e., set by the client), or external 
(i.e., set by law or regulation). These are discussed in detail below.
Having a well constructed IPS for all clients should be standard procedure for a 
portfolio manager. The portfolio manager should have the IPS close at hand and be 
able to refer to it to assess the suitability of a particular investment for the client. In 
some cases, the need for the IPS goes beyond simply being a matter of standard pro -
cedure. In some countries, the IPS (or an equivalent document) is a legal or regulatory

requirement. For example, UK pension schemes must have a statement of investment 
principles under the Pensions Act 1995 (Section 35), and this statement is in essence 
an IPS. The UK Financial Conduct Authority (FCA) also has requirements for invest -
ment firms to “know their customers. ” The European Union’s Markets in Financial 
Instruments Directive (“MiFID”) requires firms to assign clients to categories, such 
as professional clients and retail clients.
In the case of an institution, such as a pension plan or university endowment, the 
IPS may set out the governance arrangements that apply to the investment funds. 
For example, this information could cover the investment committee’s approach to 
appointing and reviewing investment managers for the portfolio, and the discretion 2

Portfolio Planning 369
that those managers have. The IPS could also set out the institution’s approach to 
corporate governance, in terms of how it will approach the use of shareholder voting 
rights and other forms of engagement with corporate management.
The IPS should be reviewed on a regular basis to ensure that it remains consistent 
with the client’s circumstances and requirements. For example, the UK Pensions 
Regulator suggests that a pension scheme’s statements of investment principles—a 
form of IPS—should be reviewed at least every three years. The IPS should also be 
reviewed if the manager becomes aware of a material change in the client’s circum -
stances, or on the initiative of the client when his or her objectives, time horizon, or 
liquidity needs change.
2.2 Major Components of an IPS
There is no single standard format for an IPS. Many IPS, however, include the fol -
lowing sections:
■■Introduction . This section describes the client.

■■Statement of Purpose . This section states the purpose of the IPS.
■■Statement of Duties and Responsibilities . This section details the duties and 
responsibilities of the client, the custodian of the client’s assets, and the invest -
ment managers.
■■Procedures . This section explains the steps to take to keep the IPS current and 
the procedures to follow to respond to various contingencies.
■■Investment Objectives . This section explains the client’s objectives in investing.
■■Investment Constraints . This section presents the factors that constrain the 
client in seeking to achieve the investment objectives.
■■Investment Guidelines . This section provides information about how policy 
should be executed (e.g., on the permissible use of leverage and derivatives) and 
on specific types of assets excluded from investment, if any.
■■Evaluation and Review . This section provides guidance on obtaining feedback 
on investment results.

■■Appendices : (A) Strategic Asset Allocation (B) Rebalancing Policy. Many inves -
tors specify a strategic asset allocation (SAA), also known as the policy portfo -
lio, which is the baseline allocation of portfolio assets to asset classes in view 
of the investor’s investment objectives and the investor’s policy with respect to 
rebalancing asset class weights.
The sections that are most closely linked to the client’s distinctive needs, and probably 
the most important from a planning perspective, are those dealing with investment 
objectives and constraints. An IPS focusing on these two elements has been called 
an IPS in an “objectives and constraints” format.
In the following sections, we discuss the investment objectives and constraints 
format of an IPS beginning with risk and return objectives. We follow a tradition of 
CFA Institute presentations in discussing risk objectives first. The process of develop -

ing the IPS is the basic mechanism for evaluating and trying to improve an investor’s 
overall expected return–risk stance. In a portfolio context, “investors have learned 
to appreciate that their objective is not to manage reward but to control and manage 
risk. ” Stated another way, return objectives and expectations must be tailored to be 
consistent with risk objectives. The risk and return objectives must also be consistent 
with the constraints that apply to the portfolio.

Reading 41 ■ Basics of Portfolio Planning and Construction 370
2.2.1  Risk Objectives
When constructing a portfolio for a client, it is important to ensure that the risk of 
the portfolio is suitable for the client. The IPS should state clearly the risk tolerance 
of the client.
Risk objectives are specifications for portfolio risk that reflect the risk tolerance 
of the client. Quantitative risk objectives can be absolute or relative or a combination 
of the two.
Examples of an absolute risk objective would be a desire not to suffer any loss of 
capital or not to lose more than a given percent of capital in any 12-  month period. 
Note that these objectives are not related to investment market performance, good 
or bad, and are absolute in the sense of being self-  standing. The fulfillment of such 
objectives could be achieved by not taking any risk; for example, by investing in an 
insured bank certificate of deposit at a credit-  worthy bank. If investments in risky assets

are undertaken, however, such statements would need to be restated as a probability 
statement to be operational (i.e., practically useful). For example, the desire not to 
lose more than 4 percent of capital in any 12-  month period might be restated as an 
objective that with 95 percent probability the portfolio not lose more than 4 percent 
in any 12-  month period. Measures of absolute risk include the variance or standard 
deviation of returns and value at risk.1
Some clients may choose to express relative risk objectives, which relate risk relative 
to one or more benchmarks perceived to represent appropriate risk standards. For 
example, investments in large-  cap UK equities could be benchmarked to an equity 
market index, such as the FTSE 100 Index. The S&P 500 Index could be used as a 
benchmark for large-  cap US equities, or for investments with cash-  like characteris -
tics, the benchmark could be an interest rate such as Libor or a Treasury bill rate. For

risk relative to a benchmark, the relevant measure is tracking risk, or tracking error.2
For institutional clients, the benchmark may be linked to some form of liability the 
institution has. For example, a pension plan must meet the pension payments as they 
come due and the risk objective will be to minimize the probability that it will fail to 
do so. (A related return objective might be to outperform the discount rate used in 
finding the present value of liabilities over a multi-  year time horizon.)
When a policy portfolio (that is, a specified set of long-  term asset class weight -
ings) is used, the risk objective may be expressed as a desire for the portfolio return 
to be within a band of plus or minus X percent of the benchmark return calculated 
by assigning an index or benchmark to represent each asset class present in the policy 
portfolio. Again, this objective has to be interpreted as a statement of probability; for

example, a 95 percent probability that the portfolio return will be within X percent 
of the benchmark return over a stated time period. Example 1 reviews this material.
EXAMPLE 1   
Types of Risk Objectives
A Japanese institutional investor has a portfolio valued at ¥10 billion. The inves -
tor expresses his first risk objective as a desire not to lose more than ¥1 billion 
in the coming 12-  month period. The investor specifies a second risk objective 
1 Value at risk  is a money measure of the minimum value of losses expected during a specified time 
period at a given level of probability.
2 Tracking risk  (sometimes called tracking error ) is the standard deviation of the differences between a 
portfolio’s returns and its benchmark’s returns.

Portfolio Planning 371
of achieving returns within 4 percent of the return to the TOPIX stock market 
index, which is the investor’s benchmark. Based on this information, address 
1 A Characterize the first risk objective as absolute or relative.
B Give an example of how the risk objective could be restated in a prac -
tical manner.
2 A Characterize the second risk objective as absolute or relative.
B Identify a measure for quantifying the risk objective.
A This is an absolute risk objective.
B This risk objective could be restated in a practical manner by specifying 
that the 12-  month 95 percent value at risk of the portfolio must not be 
more than ¥1 billion.
A This is a relative risk objective.
B This risk objective could be quantified using the tracking risk as a mea -
sure. For example, assuming returns follow a normal distribution, an 
expected tracking risk of 2 percent would imply a return within 4 percent

of the index return approximately 95 percent of the time. Remember that 
tracking risk is stated as a one standard deviation measure.
A client’s overall risk tolerance is a function of the client’s ability to bear (accept) 
risk and his or her “risk attitude, ” which might be considered as the client’s willingness 
to take risk. For ease of expression, from this point on we will refer to ability to bear 
risk and willingness to take risk as the two components of risk tolerance. Above average 
ability to bear risk and above average willingness to take risk imply above average risk 
tolerance. Below average ability to bear risk and below average willingness to take risk 
imply below average risk tolerance.
The ability to bear risk is measured mainly in terms of objective factors, such 
as time horizon, expected income, and the level of wealth relative to liabilities. For 
example, an investor with a 20-  year time horizon can be considered to have a greater

ability to bear risk, other things being equal, than an investor with a 2-  year horizon. 
This difference is because over 20 years there is more scope for losses to be recovered 
or other adjustments to circumstances to be made than there is over 2 years.
Similarly, an investor whose assets are comfortably in excess of their liabilities has 
more ability to bear risk than an investor whose wealth and expected future expen -
diture are more closely balanced. For example, a wealthy individual who can sustain 
a comfortable lifestyle after a very substantial investment loss has a relatively high 
ability to bear risk. A pension plan that has a large surplus of assets over liabilities 
has a relatively high ability to bear risk.
Risk attitude, or willingness to take risk, is a more subjective factor based on the 
client’s psychology and perhaps also his or her current circumstances. Although the 
list of factors that are related to an individual’s risk attitude remains open to debate,

it is believed that some psychological factors, such as personality type, self-  esteem, 
and inclination to independent thinking, are correlated with risk attitude. Some 
individuals are comfortable taking financial and investment risk, whereas others find 
it distressing. Although there is no single agreed-  upon method for measuring risk 
tolerance, a willingness to take risk may be gauged by discussing risk with the client or

Reading 41 ■ Basics of Portfolio Planning and Construction 372
by asking the client to complete a psychometric questionnaire. For example, financial 
planning academic John Grable and collaborators have developed 13-  item and 5-  item 
risk attitude questionnaires that have undergone some level of technical validation. 
The five-  item questionnaire is shown in Exhibit 1.
Exhibit 1   A Five-  Item Risk Assessment Instrument
1 Investing is too difficult to understand.
a Strongly agree
b Tend to agree
c Tend to disagree
d Strongly disagree
2 I am more comfortable putting my money in a bank account than in the 
stock market.
3 When I think of the word “risk” the term “loss” comes to mind 
4 Making money in stocks and bonds is based on luck.

5 In terms of investing, safety is more important than returns.
Source:  Grable and Joo (2004).
The responses, a), b), c), and d), are coded 1, 2, 3, and 4, respectively, and summed. 
The lowest score is 5 and the highest score is 20, with higher scores indicating greater 
risk tolerance. For two random samples drawn from the faculty and staff of large US 
universities ( n = 406), the mean score was 12.86 with a standard deviation of 3.01 
and a median score of 13.
Note that a question, such as the first one in Exhibit 1, indicates that risk attitude 
may be associated with non-  psychological factors (such as level of financial knowl -
edge and understanding and decision-  making style) as well as psychological factors.

Portfolio Planning 373
The adviser needs to examine whether a client’s ability to accept risk is consistent 
with the client’s willingness to take risk. For example, a wealthy investor with a 20-  
year time horizon, who is thus able to take risk, may also be comfortable taking risk; 
in this case the factors are consistent. If the wealthy investor has a low willingness to 
take risk, there would be a conflict.
In the institutional context, there could also be conflict between ability and will -
ingness to take risk. In addition, different stakeholders within the institution may 
take different views. For example, the trustees of a well-  funded pension plan may 
desire a low-  risk approach to safeguard the funding of the scheme and beneficiaries 
of the scheme may take a similar view. The sponsor, however, may wish a higher-  risk/
higher-  return approach in an attempt to reduce future funding costs. When a trustee

bears a fiduciary responsibility to pension beneficiaries and the interests of the pen -
sion sponsor and the pension beneficiaries conflict, the trustee should act in the best 
interests of the beneficiaries.
When ability to take risk and willingness to take risk are consistent, the investment 
adviser’s task is the simplest. When ability to take risk is below average and willingness 
to take risk is above average, the investor’s risk tolerance should be assessed as below 
average overall. When ability to take risk is above average but willingness is below 
average, the portfolio manager or adviser may seek to counsel the client and explain 
the conflict and its implications. For example, the adviser could outline the reasons 
why the client is considered to have a high ability to take risk and explain the likely 
consequences, in terms of reduced expected return, of not taking risk. The investment 
adviser, however, should not aim to change a client’s willingness to take risk that is not

a result of a miscalculation or misperception. Modification of elements of personality 
is not within the purview of the investment adviser’s role. The prudent approach is to 
reach a conclusion about risk tolerance consistent with the lower of the two factors 
(ability and willingness) and to document the decisions made.
Example 2 is the first of a set that follows the analysis of a private wealth manage -
ment client through the preparation of the major elements of an IPS.
EXAMPLE 2   
The Case of Henri Gascon: Risk Tolerance
Henri Gascon is an energy trader who works for a major French oil company 
based in Paris. He is 30-  years old and married with one son, aged 5. Gascon has 
decided that it is time to review his financial situation and consults a financial 
adviser. The financial adviser notes the following aspects of Gascon’s situation:
■■Gascon’s annual salary of €250,000 is more than sufficient to cover the 
family’s outgoings.

■■Gascon owns his apartment outright and has €1,000,000 of savings.
■■Gascon perceives that his job is reasonably secure.
■■Gascon has a good knowledge of financial matters and is confident that 
equity markets will deliver positive returns over the longer term.
■■In the risk tolerance questionnaire, Gascon strongly disagrees with the 
statements that “making money in stocks and bonds is based on luck” and 
that “in terms of investing, safety is more important than returns. ”
■■Gascon expects that most of his savings will be used to fund his retire -
ment, which he hopes to start at age 50.

Reading 41 ■ Basics of Portfolio Planning and Construction 374
Based only on the information given, which of the following statements is most  
accurate?
A Gascon has a low ability to take risk, but a high willingness to take risk.
B Gascon has a high ability to take risk, but a low willingness to take risk.
C Gascon has a high ability to take risk, and a high willingness to take risk.
Solution: 
C is correct. Gascon has a high income relative to outgoings, a high level of 
assets, a secure job, and a time horizon of 20 years. This information suggests 
a high ability  to take risk. At the same time, Gascon is knowledgeable and con -
fident about financial markets and responds to the questionnaire with answers 
that suggest risk tolerance. This result suggests he also has a high willingness  
to take risk.
EXAMPLE 3   
The Case of Jacques Gascon: Risk Tolerance
Henri Gascon is so pleased with the services provided by the financial adviser,

that he suggests to his brother Jacques that he should also consult the adviser. 
Jacques thinks it is a good idea. Jacques is a self-  employed computer consultant 
also based in Paris. He is 40-  years old and divorced with four children, aged 
between 12 and 16. The financial adviser notes the following aspects of Jacques’ 
situation:
■■Jacques’ consultancy earnings average €40,000 per annum, but are quite 
volatile.
■■Jacques is required to pay €10,000 per year to his ex-  wife and children.
■■Jacques has a mortgage on his apartment of €100,000 and €10,000 of 
savings.
■■Jacques has a good knowledge of financial matters and expects that equity 
markets will deliver very high returns over the longer term.
■■In the risk tolerance questionnaire, Jacques strongly disagrees with the 
statements “I am more comfortable putting my money in a bank account 
than in the stock market” and “When I think of the word “risk” the term 
“loss” comes to mind immediately. ”

■■Jacques expects that most of his savings will be required to support his 
children at university.
Based on the above information, which statement is correct?
A Jacques has a low ability to take risk, but a high willingness to take risk.
B Jacques has a high ability to take risk, but a low willingness to take risk.
C Jacques has a high ability to take risk, and a high willingness to take risk.
Solution: 
A is correct. Jacques does not have a particularly high income, his income is 
unstable, and he has reasonably high outgoings for his mortgage and mainte -
nance payments. His investment time horizon is approximately two to six years 
given the ages of his children and his desire to support them at university. This

Portfolio Planning 375
finely balanced financial situation and short time horizon suggests a low ability 
to take risk. In contrast, his expectations for financial market returns and risk 
tolerance questionnaire answers suggest a high willingness to take risk. The 
financial adviser may wish to explain to Jacques how finely balanced his financial 
situation is and suggest that, despite his desire to take more risk, a relatively 
cautious portfolio might be the most appropriate approach to take.
2.2.2  Return Objectives
A client’s return objectives can be stated in a number of ways. Similar to risk objectives, 
return objectives may be stated on an absolute or a relative basis.
As an example of an absolute objective, the client may want to achieve a particular 
percentage rate of return, for example, X percent. This could be a nominal rate of 
return or be expressed in real (inflation-  adjusted) terms.
Alternatively, the return objective can be stated on a relative basis, for example,

relative to a benchmark return. The benchmark could be an equity market index, 
such as the S&P 500 or the FTSE 100, or a cash rate of interest such as Libor. Libor 
might be appropriate when the investor has some liability that is linked to that rate; 
for example, a bank that has a particular cost of funding linked to Libor. A relative 
return objective might be stated as, for example, a desire to outperform the benchmark 
index by one percentage point per year.
Some institutions also set their return objective relative to a peer group or uni -
verse of managers; for example, an endowment aiming for a return that is in the top 
50 percent of returns of similar institutions, or a private equity mandate aiming for 
returns in the top quartile among the private equity universe. This objective can be 
problematic when limited information is known about the investment strategies or 
the returns calculation methodology being used by peers, and we must bear in mind

the impossibility of all institutions being “above average. ” Furthermore, a good bench -
mark should be investable—that is, able to be replicated by the investor—and a peer 
benchmark typically does not meet that criterion.
In each case, the return requirement can be stated before or after fees. Care should 
be taken that the fee basis used is clear and understood by both the manager and client. 
The return can also be stated on either a pre- or post-  tax basis when the investor is 
required to pay tax. For a taxable investor, the baseline is to state and analyze returns 
on an after-  tax basis.
The return objective could be a required return—that is, the amount the investor 
needs to earn to meet a particular future goal—such as a certain level of retirement 
income.
The manager or adviser must ensure that the return objective is realistic. Care 
should be taken that client and manager are in agreement on whether the return

objective is nominal (which is more convenient for measurement purposes) or real (i.e., 
inflation-  adjusted, which usually relates better to the objective). It must be consistent 
with the client’s risk objective (high expected returns are unlikely to be possible without 
high levels of risk) and also with the current economic and market environment. For 
example, 15 percent nominal returns might be possible when inflation is 10 percent, 
but will be unlikely when inflation is 3 percent.
When a client has unrealistic return expectations, the manager or adviser will 
need to counsel them about what is achievable in the current market environment 
and within the client’s tolerance for risk.

Reading 41 ■ Basics of Portfolio Planning and Construction 376
EXAMPLE 4   
The Case of Henri Gascon: Return Objectives
Having assessed his risk tolerance, Henri Gascon now begins to discuss his 
retirement income needs with the financial adviser. He wishes to retire at age 
50, which is 20 years from now. His salary meets current and expected future 
expenditure requirements, but he does not expect to be able to make any 
additional pension contributions to his fund. Gascon sets aside €100,000 of his 
savings as an emergency fund to be held in cash. The remaining €900,000 is 
invested for his retirement.
Gascon estimates that a before-  tax amount of €2,000,000 in today’s money 
will be sufficient to fund his retirement income needs. The financial adviser 
expects inflation to average 2 percent per year over the next 20 years. Pension 
fund contributions and pension fund returns in France are exempt from tax, 
but pension fund distributions are taxable upon retirement.

1 Which of the following is closest to the amount of money Gascon will 
have to accumulate in nominal terms by his retirement date to meet his 
retirement income objective (i.e., expressed in money of the day in 20 
years)?
A €900,000.
C €3,000,000.
2 Which of the following is closest to the annual rate of return that Gascon 
must earn on his pension portfolio to meet his retirement income 
objective?
A 2.0%.
B 6.2%.
C 8.1%.
C is correct. At 2 percent annual inflation, €2,000,000 in today’s money equates 
to €2,971,895 in 20 years measured in money of the day [2m × (1 + 2%)20].
B is correct. €900,000 growing at 6.2 percent per year for 20 years will accu -
mulate to €2,997,318, which is just above the required amount. [The solution 
of 6.2  percent comes from €2,997,318/€900,000  = (1  + X)20, where X is the 
required rate of return.]
In the following sections, we analyze five major types of constraints on portfolio

selection: liquidity, time horizon, tax concerns, legal and regulatory factors, and 
unique circumstances.
2.2.3  Liquidity
The IPS should state what the likely requirements are to withdraw funds from the 
portfolio. Examples for an individual investor would be outlays for covering healthcare 
payments or tuition fees. For institutions, it could be spending rules and requirements 
for endowment funds, the existence of claims coming due in the case of property and 
casualty insurance, or benefit payments for pension funds and life insurance companies.

Portfolio Planning 377
When the client does have such a requirement, the manager should allocate part of 
the portfolio to cover the liability. This part of the portfolio will be invested in assets 
that are liquid—that is, easily converted to cash—and low risk at the point in time 
the liquidity need is actually present (e.g., a bond maturing at the time when private 
education expenses will be incurred), so that their value is known with reasonable 
certainty. For example, the asset allocation in the insurance portfolios of Finnish insurer 
Sampo (see Exhibit 2) shows a large allocation to fixed-  income investments, some of 
which are either highly liquid or have a short maturity. These investments enable the 
company, in the case of property and casualty insurance, to pay out on potentially 
“lumpy” claims of which the timing is unpredictable, and in the case of life insurance, 
to pay out on life benefits, the size and timing of which are more predictable and can

therefore be matched with the maturity profile of the fixed-  income portfolio.
Exhibit 2   Asset Allocation of Sampo
Panel A: Allocation of Investment Assets, Sampo Group, 
31 December 2008
Sampo Group €16,502 Million 
Fixed Income 80.2%
Equities Nordea 9.7%
Equities Other 6.7%Private Equity 1.6%
Real Estate 1.2%
Hedge Funds 0.6%

Reading 41 ■ Basics of Portfolio Planning and Construction 378
Panel B: Fixed-  Income Investments by Type of Instrument, 
Sampo Group, 31 December 2008
Sampo Group €13,214 Million
Short-Term Fixed Income 22%
Scandinavian Governments 28%
Euro Govt/Credits 31%
US Govt/Credits 9%Other Currency Govt/Credits 2%
Swedish Index-Linked Bonds 6%
Global High Yield 1%
Other Fixed Income 1%
Source:  Sampo Group, 2008 Annual Report, pp. 59–61.
2.2.4  Time Horizon
The IPS should state the time horizon over which the investor is investing. It may 
be the period over which the portfolio is accumulating before any assets need to be 
withdrawn; it could also be the period until the client’s circumstances are likely to 
change. For example, a 50-  year old pension plan investor hoping to retire at age 60 has 
a 10-  year horizon. The portfolio may not be liquidated at age 60, but its structure may 
need to change, for example, as the investor begins to draw an income from the fund.

The time horizon of the investor will affect the nature of investments used in 
the portfolio. Illiquid or risky investments may be unsuitable for an investor with a 
short time horizon because the investor may not have enough time to recover from 
investment losses, for example. Such investments, however, may be suitable for an 
investor with a longer horizon, especially if the risky investments are expected to 
have higher returns.
EXAMPLE 5   
Investment Time Horizon
1 Frank Johnson is investing for retirement and has a 20-  year horizon. He 
has an average risk tolerance. Which investment is likely to be the least  
suitable for a major allocation in Johnson’s portfolio?
A Listed equities.
B Private equity.
C US Treasury bills.
2 Al Smith has to pay a large tax bill in six months and wants to invest the 
money in the meantime. Which investment is likely to be the least  suit -
able for a major allocation in Smith’s portfolio?Exhibit 2   (Continued)

Portfolio Planning 379
C is correct. With a 20-  year horizon and average risk tolerance, Johnson can 
accept the additional risk of listed equities and private equity compared with 
US Treasury bills.
B is correct. Private equity is risky, has no public market, and is the least liquid 
among the assets mentioned.
2.2.5  Tax Concerns
Tax status varies among investors. Some investors will be subject to taxation on 
investment returns and some will not. For example, in many countries returns to 
pension funds are exempt from tax. Some investors will face various rates of tax on 
income (dividends and interest payments) than they do on capital gains (associated 
with increases in asset prices). Typically, when there is a differential, income is taxed 
more highly than gains. Gains may be subject to a lower rate of tax or part or all of the

gain may be exempt from taxation. Furthermore, income may be taxed as it is earned, 
whereas gains may be taxed when they are realized. Hence, in such cases there is a 
time value of money benefit in the deferment of taxation of gains relative to income.
In many cases, the portfolio should reflect the tax status of the client. For exam -
ple, a taxable investor may wish to hold a portfolio that emphasizes capital gains 
and receives little income. A taxable investor based in the United States is also likely 
to consider including US municipal bonds (“munis”) in his or her portfolio because 
interest income from munis, unlike from treasuries and corporate bonds, is exempt 
from taxes. A tax-  exempt investor, such as a pension fund, will be relatively indifferent 
to the form of returns.
2.2.6  Legal and Regulatory Factors
The IPS should state any legal and regulatory restrictions that constrain how the 
portfolio is invested.

In some countries, such institutional investors as pension funds are subject to 
restrictions on the composition of the portfolio. For example, there may be a limit on 
the proportion of equities or other risky assets in the portfolio, or on the proportion 
of the portfolio that may be invested overseas. The United States has no limits on 
pension fund asset allocation but some countries do, examples of which are shown in 
Exhibit 3. Pension funds also often face restrictions on the percentage of assets that can 
be invested in securities issued by the plan sponsor, so called self-  investment limits .
Exhibit 3   Examples of Pension Fund Investment Restrictions
Country Listed Equity Real EstateGovernment 
BondsCorporate 
BondsForeign 
Assets
Switzerland 50% 50% No limits No limits 30%
Russia 65% Not allowed No limits 80% 10%

Reading 41 ■ Basics of Portfolio Planning and Construction 380
Assets
Japan No limits Not permitted No limits No limits No limits
India Minimum 25 percent in central government bonds; minimum 15 percent in state government 
bonds; minimum 30 percent invested in bonds of public sector enterprises
Source:  OECD “Survey of Investment Regulations of Pension Funds, ” July 2008.
When an individual has access to material nonpublic information about a particular 
security, this situation may also form a constraint. For example, the directors of a public 
company may need to refrain from trading the company’s stock at certain points of 
the year before financial results are published. The IPS should note this constraint so 
that the portfolio manager does not inadvertently trade the stock on the client’s behalf.
2.2.7  Unique Circumstances
This section of the IPS should cover any other aspect of the client’s circumstances

that is likely to have a material impact on the composition of the portfolio. A client 
may have considerations derived from his or her religion or ethical values that could 
constrain investment choices. For instance, a Muslim investor seeking compliance 
with Shari’a (the Islamic law) will avoid investing in businesses and financial instru -
ments inconsistent with Shari’a, such as casinos and bonds, because Shari’a prohibits 
gambling and lending money on interest. Similarly, a Christian investor may wish to 
avoid investments that he or she believes are inconsistent with their faith.
Whether rooted in religious beliefs or not, a client may have personal objections 
to certain products (e.g., pornography, weapons, tobacco, gambling) or practices (e.g., 
environmental impact of business activities, human impact of government policies, 
labour standards), which could lead to the exclusion of certain companies, countries,

or types of securities (e.g., interest-  bearing debt) from the investable universe as well 
as the client’s benchmark. Such considerations are often referred to as ESG (environ -
mental, social, governance), and investing in accordance with such considerations is 
referred to as SRI (socially responsible investing).
EXAMPLE 6   
Ethical Preferences
The £3 billion F&C Stewardship Growth Fund is designed for investors who 
wish to have ethical and environmental principles applied to the selection of 
their investments. The fund’s managers apply both positive (characteristics to 
be emphasized in the portfolio) and negative (characteristics to be avoided in 
the portfolio) screening criteria:
Positive Criteria
■■Supplies the basic necessities of life (e.g., healthy food, housing, clothing, 
water, energy, communication, healthcare, public transport, safety, per -
sonal finance, education)
■■Offers product choices for ethical and sustainable lifestyles (e.g. fair trade, 
organic)

organic)
■■Improves quality of life through the responsible use of new technologiesExhibit 3   (Continued)

Portfolio Planning 381
■■Shows good environmental management
■■Actively addresses climate change (e.g., renewable energy, energy 
efficiency)
■■Promotes and protects human rights
■■Supports good employment practices
■■Provides a positive impact on local communities
■■Maintains good relations with customers and suppliers
■■Applies effective anti-  corruption controls
■■Uses transparent communication
Negative Criteria
■■Tobacco production
■■Alcohol production
■■Gambling
■■Pornography or violent material
■■Manufacture and sale of weapons
■■Unnecessary exploitation of animals
■■Nuclear power generation
■■Poor environmental practices
■■Human rights abuses
■■Poor relations with employees, customers or suppliers
Source:  Excerpted from F&C documents; www.fandc.com/new/Advisor/Default.aspx?ID=79620.
When the portfolio represents only part of the client’s total wealth, there may 
be aspects or portions of wealth not under the control of the manager that have

implications for the portfolio. For example, an employee of a public company whose 
labour income and retirement income provision are reliant on that company and who 
may have substantial investment exposure to the company through employee share 
options and stock holdings, may decide that his or her portfolio should not invest 
additional amounts in that stock. An entrepreneur may be reluctant to see his or her 
portfolio invested in the shares of competing businesses or in any business that has 
risk exposures aligned with his or her entrepreneurial venture.
A client’s income may rely on a particular industry or asset class. Appropriate 
diversification requires that industry or asset class to be de-  emphasized in the cli -
ent’s investments. For example, a stockbroker should consider having a relatively 
low weighting in equities, as his skills and thus income-  generating ability are worth 
less when equities do not perform well. Employees should similarly be wary of hav -

ing concentrated share positions in the equity of the company they work for. If the 
employer encounters difficulties, not only may the employee lose his or her job, but 
their investment portfolio could also suffer a significant loss of value.
2.3 Gathering Client Information
As noted above, it is important for portfolio managers and investment advisers to 
know their clients. For example, Dutch securities industry practice requires financial 
intermediaries to undertake substantial fact finding. This is required not only in 
the case of full service wealth management or in the context of an IPS, but also in

Reading 41 ■ Basics of Portfolio Planning and Construction 382
“lighter” forms of financial intermediation, such as advisory relationships (in which 
clients make investment decisions after consultation with their investment adviser 
or broker) or execution-  only relationships (in which the client makes his investment 
decisions independently).
An exercise in fact finding about the customer should take place at the beginning 
of the client relationship. This will involve gathering information about the client’s 
circumstances as well as discussing the client’s objectives and requirements.
Important data to gather from a client should cover family and employment 
situation as well as financial information. If the client is an individual, it may also be 
necessary to know about the situation and requirements of the client’s spouse or other 
family members. The health of the client and his or her dependents is also relevant

information. In an institutional relationship, it will be important to know about key 
stakeholders in the organization and what their perspective and requirements are. 
Information gathering may be done in an informal way or may involve structured 
interviews or questionnaires or analysis of data. Many advisers will capture data elec -
tronically and use special systems that record data and produce customized reports.
Good record keeping is very important, and may be crucial in a case in which any 
aspect of the client relationship comes into dispute at a later stage.
EXAMPLE 7   
Henri Gascon: Description of Constraints
Henri Gascon continues to discuss his investment requirements with the financial 
adviser. The financial adviser begins to draft the constraints section of the IPS.
Gascon expects that he will continue to work for the oil company and that 
his relatively high income will continue for the foreseeable future. Gascon and

his wife do not plan to have any additional children, but expect that their son 
will go to a university at age 18. They expect that their son’s education costs can 
be met out of their salary income.
Gascon’s emergency reserve of €100,000 is considered to be sufficient as a 
reserve for unforeseen expenditures and emergencies. His retirement savings of 
€900,000 has been contributed to his defined-  contribution pension plan account 
to fund his retirement. Under French regulation, pension fund contributions 
are paid from gross income (i.e., income prior to deduction of tax) and pension 
fund returns are exempt from tax, but pension payments from a fund to retirees 
are taxed as income to the retiree.
With respect to Gascon’s retirement savings portfolio, refer back to Example 2 
as needed and address the following:
1 As concerns liquidity,
A a maximum of 50 percent of the portfolio should be invested in liquid 
assets.
B the portfolio should be invested entirely in liquid assets because of

high spending needs.
C the portfolio has no need for liquidity because there are no short-  term 
spending requirements.
2 The investment time horizon is closest  to:
A 5 years.
B 20 years.
C 40 years.
3 As concerns taxation, the portfolio:

Portfolio Planning 383
A should emphasize capital gains because income is taxable.
B should emphasize income because capital gains are taxable.
C is tax exempt and thus indifferent between income and capital gains.
4 The principle legal and regulatory factors applying to the portfolio are:
A US Securities laws.
B European banking laws.
C French pension fund regulations.
5 As concerns unique needs, the portfolio should:
A have a high weighting in oil and other commodity stocks.
B be invested only in responsible and sustainable investments.
C not have significant exposure to oil and other commodity stocks.
C is correct. The assets are for retirement use, which is 20 years away. Any short-  
term spending needs will be met from other assets or income.
B is correct. The relevant time horizon is to the retirement date, which is 20 
years away. The assets may not be liquidated at that point, but a restructuring

of the portfolio is to be expected as Gascon starts to draw an income from it.
C is correct. Because no tax is paid in the pension fund, it does not matter 
whether returns come in the form of income or capital gains.
C is correct. The management of the portfolio will have to comply with any rules 
relating the French pension funds.
C is correct. Gascon’s human capital (i.e., future labour income) is affected by 
the prospects of the oil industry. If his portfolio has significant exposure to oil 
stocks, he would be increasing a risk exposure he already has.
Example  8, the final one based on Henri Gascon, shows how the information 
obtained from the fact-  finding exercises might be incorporated into the objectives 
and constraints section of an IPS.
EXAMPLE 8   
Henri Gascon: Outline of an IPS
Following is a simplified excerpt from the IPS the adviser prepares for Henri 
Gascon, covering objectives and constraints.
Risk Objectives:

■■The portfolio may take on relatively high amounts of risk in seeking to 
meet the return requirements. With a 20-  year time horizon and signifi -
cant assets and income, the client has an above average ability to take risk.

Reading 41 ■ Basics of Portfolio Planning and Construction 384
The client is a knowledgeable investor, with an above average willingness 
to take risk. Hence, the client’s risk tolerance is above average, explaining 
the above portfolio risk objective.
■■The portfolio should be well diversified with respect to asset classes and 
concentration of positions within an asset class. Although the client has 
above average risk tolerance, his investment assets should be diversified to 
control the risk of catastrophic loss.
Return Objectives:
The portfolio’s long-  term return requirement is 6.2 percent per year, in nominal 
terms and net of fees, to meet the client’s retirement income goal.
Constraints:
■■Liquidity : The portfolio consists of pension fund assets and there is no 
need for liquidity in the short to medium term.
■■Time Horizon : The portfolio will be invested with a 20-  year time horizon. 
The client intends to retire in 20 years, at which time an income will be 
drawn from the portfolio.

■■Tax Status : Under French law, contributions to the fund are made gross 
of tax and returns in the fund are tax-  free. Hence, the client is indifferent 
between income and capital gains in the fund.
■■Legal and Regulatory Factors : The management of the portfolio must 
comply with French pension fund regulations.
■■Unique Needs : The client is an executive in the oil industry. The portfolio 
should strive to minimize additional exposures to oil and related stocks.
PORTFOLIO CONSTRUCTION
Once the IPS has been compiled, the investment manager can construct a suitable 
portfolio. Strategic asset allocation is a traditional focus of the first steps in portfolio 
construction. The strategic asset allocation is stated in terms of percent allocations to 
asset classes. An asset class  is a category of assets that have similar characteristics, 
attributes, and risk–return relationships. The strategic asset allocation  (SAA) is the

set of exposures to IPS-  permissible asset classes that is expected to achieve the client’s 
long-  term objectives given the client’s investment constraints.
The focus on the SAA is the result of a number of important investment princi -
ples. One principle is that a portfolio’s systematic risk accounts for most of its change 
in value over the long term. Systematic risk  is risk related to the economic system 
(e.g., risk related to business cycle) that cannot be eliminated by holding a diversified 
portfolio. This risk is different from the particular risks of individual securities, which 
may be avoided by holding other securities with offsetting risks. A second principle 
is that the returns to groups of similar assets (e.g., long-  term debt claims) predict -
ably reflect exposures to certain sets of systematic factors (e.g., for the debt claims, 
unexpected changes in the inflation rate). Thus, the SAA is a means of providing the

investor with exposure to the systematic risks of asset classes in proportions that meet 
the risk and return objectives.
The process of formulating a strategic asset allocation is based on the IPS, already 
discussed, and capital market expectations, introduced in Section 3.1. How to make 
the strategic asset allocation operational with a rebalancing policy and a translation 3

Portfolio Construction 385
into actual investment portfolios will be described in Section 3.3. Section 3.4 lists 
some alternatives to the approach chosen and describes some portfolio construction 
techniques.
3.1 Capital Market Expectations
Capital market expectations  are the investor’s expectations concerning the risk and 
return prospects of asset classes, however broadly or narrowly the investor defines 
those asset classes. When associated with the client’s investment objectives, the result 
is the strategic asset allocation that is expected to allow the client to achieve his or 
her investment objectives (at least under normal capital market conditions).
Traditionally, capital market expectations are quantified in terms of asset class 
expected returns, standard deviation of returns, and correlations among pairs of asset 
classes. Formally, the expected return of an asset class consists of the risk-  free rate

and one or more risk premium(s) associated with the asset class. Expected returns are 
in practice developed in a variety of ways, including the use of historical estimates, 
economic analysis, and various kinds of valuation models. Standard deviations and 
correlation estimates are frequently based on historical data.
3.2 The Strategic Asset Allocation
Traditionally, investors have distinguished cash, equities, bonds, and real estate as 
the major asset classes. This list has been expanded with private equity, hedge funds, 
and commodities. In addition, such assets as art and intellectual property rights may 
be considered asset classes for those investors prepared to take a more innovative 
approach and to accept some illiquidity. Combining such new asset classes as well 
as hedge funds and private equity under the header “alternative investments” has 
become accepted practice.
As the strategic asset allocation is built up by asset classes, the decision about

how to define those asset classes is an important one. Defining the asset classes also 
determines the extent to which the investor controls the risk and return character -
istics of the eventual investment portfolio. For example, separating bonds into gov -
ernment bonds and corporate bonds, and then further separating corporate bonds 
into investment grade and non-  investment grade (high yield) and government bonds 
into domestic and foreign government bonds, creates four bond categories for which 
risk–return expectations can be expressed and correlations with other asset classes 
(and, in an asset–liability management context, with the liabilities) can be estimated. 
An asset allocator who wants to explicitly consider the risk–return characteristics of 
those bond categories in the strategic asset allocation may choose to treat them as 
distinct asset classes. Similarly, in equities some investors distinguish between emerging

market and developed market equities, between domestic and international equities, 
or between large-  cap and small-  cap equities. In some regulatory environments for 
institutional investors, asset class definitions are mandatory, thereby forcing asset 
allocators to articulate risk–return expectations (and apply risk management) on the 
asset classes specified.
When defining asset classes, a number of criteria apply. Intuitively, an asset class 
should contain relatively homogeneous assets while providing diversification relative 
to other asset classes. In statistical terms, risk and return expectations should be 
similar and paired correlations of assets should be relatively high within an asset class 
but should be lower versus assets in other asset classes.3 Also, the asset classes, while 
3 A technically precise characterization other than one in terms of pairwise correlations is given by 
Kritzman (1999).

Reading 41 ■ Basics of Portfolio Planning and Construction 386
being mutually exclusive, should add up to a sufficient approximation of the relevant 
investable universe. Applying these criteria ensures that the strategic asset allocation 
process has considered all available investment alternatives.
EXAMPLE 9   
Specifying Asset Classes
The strategic asset allocations of many institutional investors make a distinction 
between domestic equities and international equities, or between developed 
market equities and emerging market equities. Often, equities are separated 
into different market capitalization brackets, resulting, for example, in an asset 
class such as domestic small-  cap equity.
The correlation matrix in Exhibit 4 shows the paired correlations between 
different equity asset classes and other asset classes. These correlations are 
measured over 10 years of monthly returns through February 2009. In addition, 
the exhibit shows the annualized volatility of monthly returns.

Exhibit 4   Asset Class Correlation Matrix
A B C D E F G H I J K L
A. MSCI Europe 1.00 0.77 0.95 0.97 0.88 0.20 0.59 −0.08 −0.35 0.10 −0.29 0.01
B. MSCI 
Emerging 
Markets0.77 1.00 0.82 0.83 0.76 0.35 0.63 0.18 −.25 0.22 −0.20 0.11
C. MSCI World 0.95 0.82 1.00 0.96 0.97 0.25 0.69 0.00 −0.31 0.18 −0.27 0.06
D. MSCI EAFE 0.97 0.83 0.96 1.00 0.88 0.27 0.65 −0.01 −0.34 0.15 −0.29 0.05
E. MSCI US 0.88 0.76 0.97 0.88 1.00 0.20 0.70 −0.01 −0.27 0.18 −0.24 0.06
F. Commodities 0.20 0.35 0.25 0.27 0.20 1.00 0.27 0.25 −0.04 0.14 −0.07 0.14
G. Real Estate 0.59 0.63 0.69 0.65 0.70 0.27 1.00 0.18 −0.01 0.40 0.02 0.32
H. Gold −0.08 0.18 0.00 −0.01 −0.01 0.25 0.18 1.00 0.21 0.30 0.12 0.14
I. US Treasuries −0.35 −0.25 −0.31 −0.34 −0.27 −0.04 −0.01 0.21 1.00 0.67 0.78 0.55
J. US Investment 
Grade0.10 0.22 0.18 0.15 0.18 0.14 0.40 0.30 0.67 1.00 0.61 0.79
K. European 
Government 
Bonds−0.29 −0.20 −0.27 −0.29 −0.24 −0.07 0.02 0.12 0.78 0.61 1.00 0.83
L. European 
Investment 
Grade

Grade 
Corporates0.01 0.11 0.06 0.05 0.06 0.14 0.32 0.14 0.55 0.79 0.83 1.00
Annualized 
Volatility16.6% 20.7% 15.0% 15.4% 15.7% 25.4% 18.9% 16.6% 5.0% 6.0% 3.1% 3.2%
Data based on monthly returns in local currencies from January 1999 to February 2009. Commodities, Real Estate, and Gold in USD.
Source:  MSCI, NAREIT, Bloomberg Barclays (formerly Bloomberg Capital), Standard and Poor’s.

Portfolio Construction 387
Based only on the information given, address the following:
1 Contrast the correlations between equity asset classes with the correla -
tions between equity asset classes and European government bonds.
2 Which equity asset class is most sharply distinguished from MSCI 
Europe?
The matrix reveals very strong correlation between the equity asset classes (MSCI 
Europe, MSCI Emerging Markets, MSCI EAFE, and MSCI US). For example, the 
correlation between European equities and US equities is 0.88. The correlation 
of equities with bonds, however, is much lower. For example, both asset classes 
have a similar negative correlation with European government bonds (–0.29 
and –0.24, respectively). It is worth noting, however, that correlations can vary 
through time, and the values shown may be specific to the sample period used. 
In this particular case, extreme market conditions in 2008 resulted in negative 
correlations between equities and bonds.

Correlations of emerging market equities with other categories of equities are 
0.76 or higher, whereas all groupings of equities share similar correlations with 
commodities (between 0.20 and 0.35), gold (between –0.08 and 0.18), and real 
estate (between 0.59 and 0.70). These high-  paired correlations between equity 
asset classes, combined with the similarity of the correlations between any of 
these asset classes and non-  equity asset classes, suggests that defining the equity 
asset class more narrowly has limited added value in providing diversification. 
The case for treatment as a separate asset class can best be made for emerging 
markets stocks, which usually have the lowest correlation of all equity asset 
classes with other asset classes and have a volatility of returns far in excess of 
the other equity groupings.
Using correlation as a metric, Example  9 tends to indicate that only emerging

markets were well differentiated from European equities. So, why do investors still 
often subdivide equities? Apart from any regulatory reasons, one explanation might 
be that this decomposition into smaller asset classes corresponds to the way the asset 
allocation is structured in portfolios. Many investment managers have expertise exclu -
sively in specific areas of the market, such as emerging market equities, US small-  cap 
equity, or international investment-  grade credit. Bringing the asset class definitions of 
the asset allocation in line with investment products actually available in the market 
may simplify matters from an organizational perspective.
The risk–return profile of the strategic asset allocation depends on the expected 
returns and risks of the individual asset classes, as well as the correlation between 
those asset classes. In general, adding assets classes with low correlation improves

the risk–return trade-  off (more return for similar risk), as long as the stand-  alone risk 
of such asset classes does not exceed its diversification effect. Typically, the strategic 
asset allocation for risk-  averse investors will have a large weight in government bonds 
and cash, whereas those with more willingness and ability to take risk will have more 
of their assets in risky asset classes, such as equities and many types of alternative 

Reading 41 ■ Basics of Portfolio Planning and Construction 388
EXAMPLE 10   
Objective of a Strategic Asset Allocation
ABP is a pension fund with approximately 2.6 million members. It manages a 
defined-  benefit scheme for civil servants in the Netherlands, and its goal is to 
pay out a “real” pension (i.e., one that will increase through time in line with 
consumer price inflation). With €173 billion under management at the end of 
2008, ABP is one of the world’s largest pension funds. It decides on its asset 
allocation in an investment plan that is reviewed every three years. The asset 
class terminology used by ABP is distinctive.4 Exhibit 5 shows ABP’s SAA under 
the plan for 2007–2009.
Exhibit 5   Strategic Asset Allocation for ABP
Real assets
Equities, developed countries 27%
Equities, emerging markets 5
Convertible bonds 2
Private Equity 5
Hedge Funds 5
Commodities 3
Real estate 9
Infrastructure 2
Innovation 2
Total real assets 60%
Fixed income securities
Inflation-  linked bonds 7%

Government bonds 10
Corporate bonds 23
Total fixed income securities 40%
Total 100%
1 Discuss the way the asset classes have been defined.
2 How does the asset allocation relate to the pension fund’s ambition to pay 
out a real (i.e., inflation-  adjusted) pension?
4 ABP defines an asset class category called “real assets, ” which contains asset classes (not fixed-  income 
securities) that are expected to perform well in times of inflation, but considered a major risk. The use of 
the term “real assets” differs from the use elsewhere in the CFA curriculum. The term “innovation” refers 
to alternative investments that are relatively new to ABP’s portfolio. An example of such an investment 
is music rights. “Infrastructure” is investments in non-  public equity of infrastructure projects such as 
toll roads. Inflation-  linked bonds are fixed-  income securities of which the payout depends on a measure

of inflation in the issuing country. Some major issuers of such bonds are the United States, the United 
Kingdom, and France.

Portfolio Construction 389
The asset allocation is fairly narrow in its definition of alternative asset classes, 
whereas the traditional asset classes, such as bonds and equities, are defined 
quite broadly. It appears that allocations within the broader groupings of gov -
ernment bonds, credits, and equities (developed and emerging) are not made 
on the strategic level.
This asset allocation seems to reflect an attempt to control the risk of inflation: 
only 33 percent of the strategic asset allocation is in nominal bonds, whereas 
7  percent is in inflation-  linked bonds and 60  percent in “real” assets (assets 
believed to have a positive correlation with inflation and, therefore, hedging 
inflation to some degree).
A strategic asset allocation results from combining the constraints and objec -
tives articulated in the IPS and long-  term capital market expectations regarding the

asset classes. The strategic asset allocation or policy portfolio will subsequently be 
implemented into real portfolios. Exhibit 6 illustrates conceptually how investment 
objectives and constraints and long-  term capital market expectations combine into 
a policy portfolio.
Exhibit 6   Strategic Asset Allocation Process
Long- term Capital Market
ExpectationsInvestment Objectives
and Constraints (IPS)
Optimization and/or
Simulatio n
Strategic Asse t
Allocation
In some frameworks used in practice, the asset allocation is an integral part of the 
investment policy statement. This presentation, however, keeps the asset allocation 
separate from the investment policy statement because clients’ investment objectives 
and constraints qualitatively differ in nature from capital market expectations, thus 
requiring different types of analysis, different sources of information, and different 
review cycles.
How will capital market expectations and investment objectives and constraints

eventually translate into a strategic asset allocation? In general, investors choosing 
from a range of asset allocations with similar returns would prefer those with lower 
risk. Choosing from allocations with similar levels of risk, investors would prefer 
those with the highest return. Formally, investors’ risk and return objectives can be 
described as a utility function, in which utility increases with higher expected returns

Reading 41 ■ Basics of Portfolio Planning and Construction 390
and lower risk. The assumption that expected utility is increasing in expected return 
and decreasing in variance of return could yield an expected utility equation, such as 
that shown in Equation 1.
UE Rpp p =() −λσ2
where
 Up = the investor’s expected utility from the portfolio
 E(Rp) = the expected return of the portfolio
 σp = the standard deviation of returns of the portfolio
 λ = a measure of the investor’s risk aversion
This utility function expresses a positive relationship between utility and expected 
portfolio return (i.e., higher expected return increases utility, all else equal) and a 
negative relationship between utility and volatility of portfolio return as measured by 
the variance of portfolio returns. The stronger the negative relationship, the greater 
the investor’s risk aversion. The portfolio is understood to represent a particular asset

allocation. The asset allocation providing the highest expected utility is the one that 
is optimal for the investor given his or her risk aversion. 
For different values of Up, a line can be plotted that links those combinations of 
risk and expected return that produces that level of utility: an indifference curve. An 
investor would attain equal utility from all risk/return combinations on that curve.
Capital market expectations, specified in asset classes’ expected returns, standard 
deviations of return, and correlations, translate into an efficient frontier of portfolios. 
A multi-  asset class portfolio’s expected return is given by
ER wE RPi i in() = ()=∑1
where wi equals the weight of asset class i in the portfolio, and its risk is given by
σpp i jn
in
pj ij ww RR = ()= =∑ ∑ ,, ,1 1Cov
The covariance between the returns on asset classes i and j is given by the product 
of the correlation between the two asset classes and their standard deviations of return:
CovRRij ij ij ,, () =ρ σσ
where

where
 Cov( Ri,Rj) = the covariance between the return of asset classes i and j
 ρi,j = the correlation between the returns of asset classes i and j
The resulting portfolios can be represented as a scatter of dots in a chart depicting 
their risk and expected return. As a portfolio’s risk is a positive function of the risk of 
its assets and the correlations among them, a portfolio consisting of lowly correlated 
risky assets has lower risk than one with similarly risky assets with high correlation. It 
is therefore possible to construct different portfolios with equal expected returns but 
with different levels of risk. The line that connects those portfolios with the minimal 
risk for each level of expected return (above that of the minimum variance portfolio) 
is the efficient frontier. Clearly, the efficient frontier will move “upward” as more 
lowly correlated assets with sufficient expected return are added to the mix because it

lowers the risk in the portfolios. Similarly, when return expectations increase for asset 
classes while volatility and correlation assumptions remain unchanged, the efficient 
frontier will move upward because each portfolio is able to generate higher returns 
for the same level of risk.(1)
(2)
(3)
(4)

Portfolio Construction 391
Both the efficient frontier and a range of indifference curves can be plotted in the 
risk–return space. In Exhibit 7, the downward curves that are concave from below 
represent efficient frontiers associated with different assumed expected returns. The 
upward or convex curves are indifference curves. The point where the efficient fron -
tier intersects with the indifference curve with the highest utility attainable (i.e., the 
point of tangency) represents the optimal asset allocation for the client/investor. In 
Exhibit 7, efficient frontier 1 has a point of tangency with indifference curve 1. Higher 
levels of utility, such as those associated with indifference curve 0, can apparently 
not be reached with the assets underlying the efficient frontier. It is clear that when 
capital market expectations change, this change moves the efficient frontier away from 
its original location. In the chart, this movement is illustrated by efficient frontier 2,

which incorporates different capital market expectations. This new efficient frontier 
has a point of tangency with indifference curve 2, which is associated with a lower 
level of expected utility. Because the point of tangency represents the strategic asset 
allocation, it implies the asset allocation should be adjusted. Similarly, should invest -
ment objectives or constraints change, the indifference curves will change their shape 
and location. This change will again move the point of tangency, and hence change 
the asset allocation.
Exhibit 7   Strategic Asset Allocation Efficient Frontier
20%
18%
16%
14%
12%
10%
8%
6%
4%
2%
0%
Standard Deviation of Portfolio Retu rnsExpected Portfolio Retu rns
0%
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
11%
12%
13%
14%
15%
16%
17%
18%
19%
20%
indifference cu rve 2
indifference cu rve 1
efficient frontier 2indifference cu rve 0
efficient frontier 1
This framework describes how investor objectives and capital market expectations

should theoretically be reconciled. It will, however, not be the exact procedure that 
in practice will be followed. First, an IPS does not necessarily translate the client’s 
investment objectives and constraint into a utility function. Rather, an IPS gives 
threshold levels for risk and expected return, combined with a number of additional 
constraints that cannot be captured in this model. Second, the model illustrated is a

Reading 41 ■ Basics of Portfolio Planning and Construction 392
single-  period model, whereas in practice, the constraints from the IPS will make it 
more appropriate to use multi-  period models. Multi-  period problems can be more 
effectively addressed using simulation.
EXAMPLE 11   
Approaching a SAA for a Private Investor
Rainer Gottschalk recently sold his local home construction company in the 
south of Germany to a large homebuilder with a nationwide reach. Upon sell -
ing his company, he accepted a job as regional manager for that nationwide 
homebuilder. He is now considering his and his family’s financial future. He 
looks forward to his new job, where he likes his new role, and which provides 
him with income to fulfill his family’s short-  term and medium-  term liquidity 
needs. He feels strongly that he should not invest the proceeds of the sale of his 
company in real estate because his income already depends on the state of the

real estate market. He consults a financial adviser from his bank about how to 
invest his money to retire in good wealth in 20 years.
The IPS they develop suggests a return objective of 6 percent, with a stan -
dard deviation of 12 percent. The bank’s asset management division provides 
Gottschalk and his adviser with the following data (Exhibit  8) on market 
expectations.
Exhibit 8   Risk, Return, and Correlation Estimates
Expected 
Return (%)Standard 
Deviation (%)Correlation Matrix
European 
EquitiesEmerging 
Mkt. 
EquitiesEuropean Govt. 
Bonds
European equities 8.40 24 1.00 0.86 –0.07
Emerging market equities 9.20 28 0.86 1.00 –0.07
European government bonds 3.50 7 –0.07 –0.07 1.00
Note : Standard deviation and correlation calculated over the period March 1999–December 2008. All data in unhedged euros.
Sources:  Barclay’s, MSCI, Bloomberg.
To illustrate the possibilities, the adviser presents Gottschalk with the fol -
lowing plot (Exhibit 9), in which the points forming the shaded curve outline

the risk–return characteristics of the portfolios that can be constructed out of 
the three assets. An imaginary line linking the points with the lowest standard 
deviation for each attainable level of return would be the efficient frontier. The 
two straight lines show the risk and return objectives. Gottschalk should aim 
for portfolios that offer an expected return of at least 6 percent (the straight 
horizontal line or above) and a standard deviation of return of 12 percent or 
lower (the straight vertical line to the left).

Portfolio Construction 393
Exhibit 9   Efficient Frontier
10%
9%
8%
7%
6%
5%
4%
3%
0% 5% 10% 15% 20% 25% 30%Expected Portfolio Return
Standard Deviation of Portfolio Return
Portfolio risk and expected return Return objective Risk objective
Exhibit 9 shows that a portfolio on the efficient frontier satisfies the two 
objectives. This portfolio consists of 28 percent European stocks, 20 percent 
emerging market equities, and 52 percent government bonds and gives a 6 per -
cent expected return and a 12 percent standard deviation. This combination is 
what the adviser recommends to Gottschalk as his strategic asset allocation.
3.3 Steps Toward an Actual Portfolio
The strategic asset allocation in itself does not yet represent an actual investment 
portfolio. It is the first step in implementing an investment strategy. For quantitatively 
oriented portfolio managers, the next step is often risk budgeting.
As used in this reading, risk budgeting  is the process of deciding on the amount

of risk to assume in a portfolio (the overall risk budget), and subdividing that risk 
over the sources of investment return (e.g., strategic asset allocation, tactical asset 
allocation, and security selection).5 Because the decision about the amount of risk 
to be taken is made in constructing the IPS, at this stage we are concerned about the 
subdivision of that risk.
Apart from the exposures to systematic risk factors specified in the strategic asset 
allocation, the returns of an investment strategy depend on two other sources: tac -
tical asset allocation and security selection. Tactical asset allocation  is the decision 
to deliberately deviate from the policy exposures to systematic risk factors (i.e., the 
policy weights of asset classes) with the intent to add value based on forecasts of 
5 Some writers use risk budgeting to refer to allocating an amount or budget of tracking risk to active 
portfolio managers on a given asset class. See Waring, Whitney, Pirone, Castille (2000).

Reading 41 ■ Basics of Portfolio Planning and Construction 394
the near-  term returns of those asset classes. For instance, an investor may decide to 
temporarily invest more of the portfolio in equities than the SAA prescribes if the 
investor anticipates that equities will deliver a higher return over the short term than 
other asset classes. Security selection  is an attempt to generate higher returns than 
the asset class benchmark by selecting securities with a higher expected return. For 
example, an investment manager may decide to add more IBM stock in his portfolio 
than the weight in his equity benchmark if he expects this stock to do better than the 
benchmark. To fund this purchase, he may sell another stock expected to do worse 
than either the benchmark or IBM. Obviously, deciding to deviate from policy weights 
or to select securities aiming to beat the benchmark creates additional uncertainty 
about returns. This risk is over and above the risk inherent in the policy portfolio.

Hence, an investment policy should set risk limits and desired payoffs for each of 
these three activities.
Risk budgeting implies that the portfolio manager has to choose, for every asset 
class, whether to deploy security selection as a return generator. This choice is generally 
referred to as the choice between active or passive management. Contrary to strategic 
asset allocation, where exposures to sources of systematic risk are selected and sized, 
security selection is not rewarded with a long-  run payoff to risk. Security selection is 
a zero-  sum game: All investors in an asset class are competing with each to identify a 
typically limited number of assets that are misvalued. In total, the gross returns of all 
market participants average out to the market return (the reward for taking systematic 
risk). This implies that the average active investor will match the market return, and 
that one investor’s gain versus the market return is the other investor’s loss versus the

market return. However, because active managers tend to trade more and have to pay 
people (including themselves) to generate investment ideas or information leading to 
such ideas, the average active manager will underperform the market, net of costs. 
This does not imply, however, that there are no skillful investment managers who, 
with some consistency, beat their benchmarks. Neither does it imply that all passive 
managers will be able to match the benchmark. The higher the turnover of an index, 
the more trading costs a passive manager will incur, making the task of effectively 
mimicking an index more difficult.
The likelihood of adding a significant amount of value from security selection 
depends on the skills of the manager and the informational efficiency of the market 
for the asset class his skill relates to. The more efficient an asset class or a subset of 
that asset class (such as a regional stock, bond, or real estate market or a size category

within the stock market), the more skillful an asset manager has to be to add value. 
Broadly speaking, an efficient market is a market in which prices, on average, very 
quickly reflect newly available information. That requires a sizeable participation of 
mean–variance optimizing investors, acting on rational expectations, using the same or 
similar pricing models, and having equal opportunities to access relevant information. 
Clearly, the market for US large-  capitalization equities would be quite efficient. By 
contrast, some regional bond and equity markets do not have the technical and regula -
tory systems for information dissemination that are sufficient to serve all investors on 
a timely basis. Skilled managers should be able to exploit the resulting inefficiencies.
Sometimes, however, the choice between active and passive management is actually 
made implicitly when the asset class is included in the asset allocation. The markets for

some assets—such as those for non-  listed real estate, art, and infrastructure assets—
are so illiquid that it is very difficult to buy a diversified exposure. As a result, there 
is no way of taking exposure to the asset class without engaging in security selection.
As the portfolio is constructed and its value changes with the returns of the asset 
classes and securities in which it is invested, the weights of the asset classes will grad -
ually deviate from the policy weights in the strategic asset allocation. This process is 
referred to as drift. Periodically, or when a certain threshold deviation from the policy 
weight (the bandwidth) has been breached, the portfolio should be rebalanced back to

Portfolio Construction 395
the policy weights. The set of rules that guide the process of restoring the portfolio’s 
original exposures to systematic risk factors is known as the rebalancing policy . 
Even absent a formal risk budget, formulating a rebalancing policy is an important 
element of risk management.
EXAMPLE 12   
Strategic Asset Allocation for a European Charity
A European charity has an asset allocation at the beginning of the year consisting 
of the asset classes and weights shown in Exhibit 10:
Exhibit 10   Asset Allocation of a European Charity (Beginning of Y ear) 
Asset ClassPolicy  
WeightCorridor  
(+/–)Upper  
LimitLower  
Limit
European equities 30.0% 2.0% 32.0% 28.0%
International equities 15.0 2.0 17.0 13.0
European government bonds 20.0 2.0 22.0 18.0
Corporate bonds 20.0 2.0 22.0 18.0
Cash and money market instruments 15.0 2.0 17.0 13.0
Total 100.0
As Exhibit 10 reveals, the charity has a policy that the asset class weights

cannot deviate from the policy weights by more than 2 percent (the corridor). 
The resulting upper and lower limits for the asset class weights are shown in 
the rightmost columns of the table. There are two reasons for asset class actual 
weights to deviate from policy weights: by deliberate choice (tactical asset 
allocation or market timing) and as a result of divergence of the returns of the 
different asset classes (drift). In this example, the asset class weights start the 
year exactly in line with policy weights.
After half a year, the investment portfolio is as shown in Exhibit 11.
Exhibit 11   Asset Allocation for a European Charity (6 Months Later) 
Asset ClassPolicy 
WeightCorridor 
(+/–)Upper 
LimitLower 
LimitPeriod 
ReturnEnding 
Weight
European equities 30.0% 2.0% 32.0% 28.0% 15.0% 32.4%
International equities 15.0 2.0 17.0 13.0 10.0 15.5
European government bonds 20.0 2.0 22.0 18.0 0.5 18.9
Corporate bonds 20.0 2.0 22.0 18.0 1.5 19.1
Cash and money market

Cash and money market 
instruments 15.0 2.0 17.0 13.0 1.0 14.2
Total 100.0% 6.6% 100.0%
1 Discuss the returns of the portfolio and comment on the main asset 
weight changes.

Reading 41 ■ Basics of Portfolio Planning and Construction 396
The investment portfolio generated a return calculated on beginning (policy) 
weights of 6.55 percent or 6.6 percent (= 0.30 × 15% + 0.15 × 10% + 0.20 × 0.5% 
+ 0.20 × 1.5% + 0.15 × 1.0%), mainly driven by a strong equity market. Bond 
returns were more subdued, leading to considerable drift in asset class weights. 
In particular, the European equity weight breached the upper limit of its allowed 
actual weight.
The investment committee decides against reducing European equities back 
to policy weight and adding to the fixed income and cash investments toward 
policy weights. Although this rebalancing would be prudent, the committee 
decides to engage in tactical asset allocation based on the view that this market 
will continue to be strong over the course of the year. It decides to just bring 
European equities back to within its bandwidth (a 32 percent portfolio weight) and

add the proceeds to cash. Exhibit 12 shows the outcome after another half year.
Exhibit 12   Asset Allocation for a European Charity (an Additional 6 Months Later) 
WeightStarting 
Weight
European equities 30.0% 32.0% 2.0% 32.0% 28.0% –9.0% 29.7%
International equities 15.0 15.5 2.0 17.0 13.0 –6.0 14.9
European government bonds 20.0 18.9 2.0 22.0 18.0 4.0 20.0
Corporate bonds 20.0 19.1 2.0 22.0 18.0 4.0 20.2
Cash and money market instruments 15.0 14.6 2.0 17.0 13.0 2.0 15.2
Total 100.0% –2.0% 100.0%
The prior decision not to rebalance to policy weights did not have a positive 
result. Contrary to the expectations of the investment committee, both European 
and international equities performed poorly while bonds recovered. The return 
of the portfolio was −2.0 percent.
2 How much of this return can be attributed to tactical asset allocation?

Because tactical asset allocation is the deliberate decision to deviate from policy 
weights, the return contribution from tactical asset allocation is equal to the 
difference between the actual return, and the return that would have been made 
if the asset class weights were equal to the policy weights. Exhibit 13 shows the 
difference to be −0.30 percent.
Exhibit 13   Returns to Tactical Asset Allocation
Weight IStarting 
Weight IIWeights 
Difference 
III (= II – I)Period 
Return IVTAA 
Contribution V 
(= III × IV)
European equities 30.0% 32.0% 2.0% –9.0% –0.18%
International equities 15.0 15.5 0.5 –6.0 –0.03
European government bonds 20.0 18.9 –1.1 4.0 –0.05
Corporate bonds 20.0 19.1 –0.9 4.0 –0.04

Portfolio Construction 397
(= III × IV)
instruments 15.0 14.6 –0.4 2.0 –0.01
Total 100.0% –2.0% –0.30%
The process of executing an investment strategy continues with selecting the appro -
priate manager(s) for each asset class and allocating funds to them. The investment 
portfolio management process is then well into the execution stage.
The investment managers’ performance will be monitored, as well as the results of 
the strategic asset allocation. When asset class weights move outside their corridors, 
money is transferred from the asset classes that have become too large compared with 
the SAA to those that fall short. Managers as well as the strategic asset allocation will 
be reviewed on the basis of the outcome of the monitoring process. In addition, cap -
ital market expectations may change, as may the circumstances and objectives of the

client. These changes could result in an adjustment of the strategic asset allocation.
3.4 Additional Portfolio Organizing Principles
The top-  down oriented framework laid out in earlier paragraphs is quite general. Other 
models of portfolio organization are also used in practice, and these are described 
briefly here. In addition, this section introduces some portfolio construction concepts 
in use to better capture the value of active management.
According to some practitioners, a top-  down investment process as described 
earlier has two drawbacks. They both result from the fact that in a top-  down process, 
a multitude of specialist managers may work for the same client within the same 
asset class. Each of these managers will manage risk versus the client’s benchmark, 
and because these benchmarks may be similar to or overlapping with those of other 
managers, the aggregate of all the portfolios within one asset class may be less active

than was intended. The resulting investment portfolio may underutilize its risk budget. 
Another drawback is that as the investment managers each engage in trading over the 
full extent (including the benchmark exposure) of their portfolio, the aggregate of all 
portfolios may not be efficient from a capital gains tax point of view. More trading 
results in more capital gains being realized, increasing the tax bill at the end of the 
year. To circumvent these issues, the core–satellite approach was developed. In this 
approach, a majority of the portfolio is invested on a passive or low active risk basis 
(usually a combination of a bond portfolio and an equity portfolio) while a minority 
of the assets is managed aggressively in smaller “satellite” portfolios. The aim of the 
satellite portfolios is to generate a high active return with little regard for benchmark 
exposure, whereas the core is managed with low turnover to capture the long-  term

systematic risk premium of its assets on a tax-  optimal basis. The aggressive manage -
ment in satellites can be executed with the objective of market timing (in which case 
tactical asset tilts are executed through long–short positions in asset class indexes or 
derivatives), as well as security selection (in which case, highly active security selection 
vehicles act as satellites). A drawback of the core–satellite approach is that the assign -
ment of asset class monies to actual portfolio managers—with their various expected Exhibit 13   (Continued)

Reading 41 ■ Basics of Portfolio Planning and Construction 398
alphas, risk surrounding those alphas, and correlations between those alphas—can 
be seen as an optimization process in its own right. The outcome of that process is 
not necessarily consistent with a core–satellite structure (Waring and Siegel, 2003).
SUMMARY
In this reading, we have discussed construction of a client’s investment policy state -
ment, including discussion of risk and return objectives and the various constraints 
that will apply to the portfolio. We have also discussed the portfolio construction 
process, with emphasis on the strategic asset allocation decisions that must be made.
■■The IPS is the starting point of the portfolio management process. Without a 
full understanding of the client’s situation and requirements, it is unlikely that 
successful results will be achieved.
■■The IPS can take a variety of forms. A typical format will include the client’s

investment objectives and also list the constraints that apply to the client’s 
■■The client’s objectives are specified in terms of risk tolerance and return 
requirements.
■■The constraints section covers factors that need to be considered when con -
structing a portfolio for the client that meets the objectives. The typical con -
straint categories are liquidity requirements, time horizon, regulatory require -
ments, tax status, and unique needs.
■■Risk objectives are specifications for portfolio risk that reflect the risk tolerance 
of the client. Quantitative risk objectives can be absolute or relative or a combi -
nation of the two.
■■The client’s overall risk tolerance is a function of the client’s ability to accept 
risk and their “risk attitude, ” which can be considered the client’s willingness to 
take risk.
■■The client’s return objectives can be stated on an absolute or a relative basis. As 
an example of an absolute objective, the client may want to achieve a particular

percentage rate of return. Alternatively, the return objective can be stated on a 
relative basis, for example, relative to a benchmark return.
■■The liquidity section of the IPS should state what the client’s requirements are 
to draw cash from the portfolio.
■■The time horizon section of the IPS should state the time horizon over which 
the investor is investing. This horizon may be the period during which the port -
folio is accumulating before any assets need to be withdrawn.
■■Tax status varies among investors and a client’s tax status should be stated in 
the IPS.
■■The IPS should state any legal or regulatory restrictions that constrain the 
investment of the portfolio.
■■The unique circumstances section of the IPS should cover any other aspect of 
a client’s circumstances that is likely to have a material impact on the composi -
tion of the portfolio; for example, any religious or ethical preferences.
■■Asset classes are the building blocks of an asset allocation. An asset class is a

category of assets that have similar characteristics, attributes, and risk–return 
relationships. Traditionally, investors have distinguished cash, equities, bonds, 
and real estate as the major asset classes.

References 399
Grable, John E., and Soo-  Hyun Joo. 2004. “Environmental and 
Biopsychosocial Factors Associated with Financial Risk 
Tolerance. ” Financial Counseling and Planning , vol. 15, no. 1: 
73–82.
Kritzman, Mark. 1999. “Toward Defining an Asset Class. ” Journal 
of Alternative Investments , vol. 2, no. 1: 79–82. Waring, M. Barton, and Laurence B. Siegel. 2003. “The 
Dimensions of Active Management. ” Journal of Portfolio 
Management , vol. 29, no. 3: 35–51. 
Waring, M. Barton, Duane Whitney, John Pirone, and Charles 
Castille. 2000. “Optimizing Manager Structure and Budgeting 
Manager Risk. ” Journal of Portfolio Management , vol. 26, no. 
3: 90–104. ■■A strategic asset allocation results from combining the constraints and objec -
tives articulated in the IPS and capital market expectations regarding the asset 
classes.
■■As time goes on, a client’s asset allocation will drift from the target allocation, 
and the amount of allowable drift as well as a rebalancing policy should be

formalized.
■■In addition to taking systematic risk, an investment committee may choose 
to take tactical asset allocation risk or security selection risk. The amount of 
return attributable to these decisions can be measured.

Reading 41 ■ Basics of Portfolio Planning and Construction 400
1 Which of the following is least  important as a reason for a written investment 
policy statement (IPS)?
A The IPS may be required by regulation.
B Having a written IPS is part of best practice for a portfolio manager.
C Having a written IPS ensures the client’s risk and return objectives can be 
achieved.
2 Which of the following best describes the underlying rationale for a written 
investment policy statement (IPS)?
A A written IPS communicates a plan for trying to achieve investment success.
B A written IPS provides investment managers with a ready defense against 
client lawsuits.
C A written IPS allows investment managers to instruct clients about the 
proper use and purpose of investments.
3 A written investment policy statement (IPS) is most  likely to succeed if:
A it is created by a software program to assure consistent quality.
B it is a collaborative effort of the client and the portfolio manager.

C it reflects the investment philosophy of the portfolio manager.
4 The section of the investment policy statement (IPS) that provides information 
about how policy may be executed, including investment constraints, is best 
described as the:
A Investment Objectives .
B Investment Guidelines .
C Statement of Duties and Responsibilities .
5 Which of the following is least  likely to be placed in the appendices to an 
A Rebalancing Policy .
B Strategic Asset Allocation .
6 Which of the following typical topics in an investment policy statement (IPS) is 
most  closely linked to the client’s “distinctive needs”?
A Procedures .
7 An investment policy statement that includes a return objective of outperform -
ing the FTSE 100 by 120 basis points is best characterized as having a(n):
A relative return objective.
B absolute return objective.

C arbitrage-  based return objective.
8 Risk assessment questionnaires for investment management clients are most  
useful in measuring:
A value at risk.

B ability to take risk.
C willingness to take risk.
9 Which of the following is best characterized as a relative risk objective?
A Value at risk for the fund will not exceed US$3 million.
B The fund will not underperform the DAX by more than 250 basis points.
C The fund will not lose more than €2.5 million in the coming 12-  month 
period.
10 In preparing an investment policy statement, which of the following is most  
difficult to quantify?
A Time horizon.
B Ability to accept risk.
C Willingness to accept risk.
11 After interviewing a client in order to prepare a written investment policy state -
ment (IPS), you have established the following:
■●The client has earnings that vary dramatically between £30,000 and £70,000 
(pre-  tax) depending on weather patterns in Britain.
■●In three of the previous five years, the after-  tax income of the client has 
been less than £20,000.
■●The client’s mother is dependent on her son (the client) for approximately 
£9,000 per year support.

■●The client’s own subsistence needs are approximately £12,000 per year.
■●The client has more than 10 years’ experience trading investments including 
commodity futures, stock options, and selling stock short.
■●The client’s responses to a standard risk assessment questionnaire suggest 
he has above average risk tolerance.
 The client is best described as having a:
A low ability to take risk, but a high willingness to take risk.
B high ability to take risk, but a low willingness to take risk.
C high ability to take risk and a high willingness to take risk.
12 After interviewing a client in order to prepare a written investment policy state -
■●The client has earnings that have exceeded €120,000 (pre-  tax) each year for 
the past five years.
■●She has no dependents.
■●The client’s subsistence needs are approximately €45,000 per year.
■●The client states that she feels uncomfortable with her lack of understanding

of securities markets.
■●All of the client’s current savings are invested in short-  term securities guar -
anteed by an agency of her national government.
she has low risk tolerance.

Reading 41 ■ Basics of Portfolio Planning and Construction 402
13 A client who is a 34-  year old widow with two healthy young children (aged 
5 and 7) has asked you to help her form an investment policy statement. She 
has been employed as an administrative assistant in a bureau of her national 
government for the previous 12 years. She has two primary financial goals—her 
retirement and providing for the college education of her children. This client’s 
time horizon is best described as being:
A long term.
B short term.
C medium term.
14 The timing of payouts for property and casualty insurers is unpredictable 
(“lumpy”) in comparison with the timing of payouts for life insurance compa -
nies. Therefore, in general, property and casualty insurers have:
A lower liquidity needs than life insurance companies.
B greater liquidity needs than life insurance companies.
C a higher return objective than life insurance companies.

15 A client who is a director of a publicly listed corporation is required by law to 
refrain from trading that company’s stock at certain points of the year when 
disclosure of financial results are pending. In preparing a written investment 
policy statement (IPS) for this client, this restriction on trading:
A is irrelevant to the IPS.
B should be included in the IPS.
C makes it illegal for the portfolio manager to work with this client.
16 Consider the pairwise correlations of monthly returns of the following asset 
classes:
Brazilian  
EquitiesEast Asian  
EquitiesEuropean  
EquitiesUS 
Equities
Brazilian equities 1.00 0.70 0.85 0.76
East Asian equities 0.70 1.00 0.91 0.88
European equities 0.85 0.91 1.00 0.90
US equities 0.76 0.88 0.90 1.00
 Based solely on the information in the above table, which equity asset class is 
most  sharply distinguished from US equities?
A Brazilian equities.
B European equities.
C East Asian equities.
17 Returns on asset classes are best described as being a function of:

A the failure of arbitrage.
B exposure to the idiosyncratic risks of those asset classes.
C exposure to sets of systematic factors relevant to those asset classes.
18 In defining asset classes as part of the strategic asset allocation decision, pair -
wise correlations within asset classes should generally be:
A equal to correlations among asset classes.
B lower than correlations among asset classes.
C higher than correlations among asset classes.
19 Tactical asset allocation is best described as:
A attempts to exploit arbitrage possibilities among asset classes.

B the decision to deliberately deviate from the policy portfolio.
C selecting asset classes with the desired exposures to sources of systematic 
risk in an investment portfolio.
20 Investing the majority of the portfolio on a passive or low active risk basis while 
a minority of the assets is managed aggressively in smaller portfolios is best 
described as:
A the core–satellite approach.
B a top-  down investment policy.
C a delta-  neutral hedge approach.

Reading 41 ■ Basics of Portfolio Planning and Construction 404
SOLUTIONS
1 C is correct. Depending on circumstances, a written IPS or its equivalent may 
be required by law or regulation and a written IPS is certainly consistent with 
best practices. The mere fact that a written IPS is prepared for a client, however, 
does not ensure  that risk and return objectives will in fact be achieved.
2 A is correct. A written IPS is best seen as a communication instrument allowing 
clients and portfolio managers to mutually establish investment objectives and 
3 B is correct. A written IPS, to be successful, must incorporate a full understand -
ing of the client’s situation and requirements. As stated in the reading, “The IPS 
will be developed following a fact finding discussion with the client. ”
4 B is correct. The major components of an IPS are listed in Section 2.2 of the 
reading. Investment Guidelines  are described as the section that provides infor -

mation about how policy may be executed, including investment constraints. 
Statement of Duties and Responsibilities  “detail[s] the duties and responsibilities 
of the client, the custodian of the client’s assets, the investment managers, and 
so forth. ” Investment Objectives  is “a section explaining the client’s objectives in 
investing. ”
5 C is correct. The major components of an IPS are listed in Section 2.2 of the 
reading. Strategic Asset Allocation (also known as the policy portfolio) and 
Rebalancing Policy are often included as appendices to the IPS. The Statement 
of Duties and Responsibilities , however, is an integral part of the IPS and is 
unlikely to be placed in an appendix.
6 B is correct. According to the reading, “The sections of an IPS that are most 
closely linked to the client’s distinctive needs are those dealing with invest -
ment objectives and constraints. ” Investment Guidelines  “[provide] informa -

tion about how policy may be executed, including investment constraints. ” 
Procedures  “[detail] the steps to be taken to keep the IPS current and the 
procedures to follow to respond to various contingencies. ” Statement of Duties 
and Responsibilities  “detail[s] the duties and responsibilities of the client, the 
custodian of the client’s assets, the investment managers, and so forth. ”
7 A is correct. Because the return objective specifies a target return relative to  the 
FTSE 100 Index, the objective is best described as a relative return objective.
8 C is correct. Risk attitude is a subjective factor and measuring risk attitude is 
difficult. Oftentimes, investment managers use psychometric questionnaires, 
such as those developed by Grable and Joo (2004), to assess a client’s willingness 
9 B is correct. The reference to the DAX marks this response as a relative risk 
objective. Value at risk establishes a minimum value of loss expected during a

specified time period at a given level of probability. A statement of maximum 
allowed absolute loss (€2.5 million) is an absolute risk objective.
10 C is correct. Measuring willingness to take risk (risk tolerance, risk aversion) 
is an exercise in applied psychology. Instruments attempting to measure risk 
attitudes exist, but they are clearly less objective than measurements of ability 
to take risk. Ability to take risk is based on relatively objective traits such as 
expected income, time horizon, and existing wealth relative to liabilities.

Solutions 405
11 A is correct. The volatility of the client’s income and the significant support 
needs for his mother and himself suggest that the client has a low ability to take 
risk. The client’s trading experience and his responses to the risk assessment 
questionnaire indicate that the client has an above average willingness to take 
risk.
12 B is correct. On the one hand, the client has a stable, high income and no 
dependents. On the other hand, she exhibits above average risk aversion. Her 
ability to take risk is high, but her willingness to take risk is low.
13 A is correct. The client’s financial objectives are long term. Her stable employ -
ment indicates that her immediate liquidity needs are modest. The children will 
not go to college until 10 or more years later. Her time horizon is best described 
as being long term.
14 B is correct. The unpredictable nature of property and casualty (P&C) claims 
forces P&C insurers to allocate a substantial proportion of their investments

into liquid, short maturity assets. This need for liquidity also forces P&C com -
panies to accept investments with relatively low expected returns. Liquidity is of 
less concern to life insurance companies given the greater predictability of life 
insurance payouts.
15 B is correct. When a client has a restriction in trading, such as this obligation to 
refrain from trading, the IPS “should note this constraint so that the portfolio 
manager does not inadvertently trade the stock on the client’s behalf. ”
16 A is correct. The correlation between US equities and Brazilian equities is 0.76. 
The correlations between US equities and East Asian equities and the cor -
relation between US equities and European equities both exceed 0.76. Lower 
correlations indicate a greater degree of separation between asset classes. 
Therefore, using solely the data given in the table, returns on Brazilian equities 
are most sharply distinguished from returns on US equities.

17 C is correct. Strategic asset allocation depends on several principles. As stated 
in the reading, “One principle is that a portfolio’s systematic risk accounts for 
most of its change in value over the long run. ” A second principle is that, “the 
returns to groups of like assets… predictably reflect exposures to certain sets of 
systematic factors. ” This latter principle establishes that returns on asset classes 
primarily reflect the systematic risks of the classes.
18 C is correct. As the reading states, “an asset class should contain homogeneous 
assets… paired correlations of securities would be high within an asset class, 
but should be lower versus securities in other asset classes. ”
19 B is correct. Tactical asset allocation allows actual asset allocation to deviate 
from that of the strategic asset allocation (policy portfolio) of the IPS. Tactical 
asset allocation attempts to take advantage of temporary dislocations from the

market conditions and assumptions that drove the policy portfolio decision.
20 A is correct. The core–satellite approach to constructing portfolios is defined 
as “investing the majority of the portfolio on a passive or low active risk basis 
while a minority of the assets is managed aggressively in smaller portfolios. ”

Risk Management: An Introduction
by Don M. Chance, PhD, CFA, and Michael E. Edleson, PhD, CFA
Don M. Chance, PhD, CFA, is at Louisiana State University (USA). Michael E. Edleson, 
PhD, CFA, is at the University of Chicago (USA).
a. define risk management;
b. describe features of a risk management framework;
c. define risk governance and describe elements of effective risk 
governance;
d. explain how risk tolerance affects risk management;
e. describe risk budgeting and its role in risk governance;
f. identify financial and non-  financial sources of risk and describe 
how they may interact;
g. describe methods for measuring and modifying risk exposures 
and factors to consider in choosing among the methods.
Risk—and risk management—is an inescapable part of economic activity. People gen -
erally manage their affairs in order to be as happy and secure as their environment and

resources will allow. But regardless of how carefully these affairs are managed, there is 
risk because the outcome, whether good or bad, is seldom predictable with complete 
certainty. There is risk inherent in nearly everything we do, but this reading will focus 
on economic and financial risk, particularly as it relates to investment management.
All businesses and investors manage risk, whether consciously or not, in the 
choices they make. At its core, business and investing are about allocating resources 
and capital to chosen risks. In their decision process, within an environment of 
uncertainty, these entities may take steps to avoid some risks, pursue the risks that 
provide the highest rewards, and measure and mitigate their exposure to these risks as 
necessary. Risk management processes and tools make difficult business and financial 
problems easier to address in an uncertain world. Risk is not just a matter of fate; it is 1rEADING
42
© 2015 CFA Institute. All rights reserved.

Reading 42 ■ Risk Management: An Introduction 408
something that organizations can actively control with their decisions, within a risk 
management framework. Risk is an integral part of the business or investment pro -
cess. Even in the earliest models of modern portfolio theory, such as mean–variance 
portfolio optimization and the capital asset pricing model, investment return is linked 
directly to risk but requires that risk be managed optimally. Proper identification and 
measurement of risk, and keeping risks aligned with the goals of the enterprise, are 
key factors in managing businesses and investments. Good risk management results 
in a higher chance of a preferred outcome—more value for the company or portfolio 
or more utility for the individual.
Portfolio managers need to be familiar with risk management not only to improve 
the portfolio’s risk–return outcome, but also because of two other ways in which

they use risk management at an enterprise level. First, they help to manage their own 
companies that have their own enterprise risk issues. Second, many portfolio assets 
are claims on companies that have risks. Portfolio managers need to evaluate the 
companies’ risks and how those companies are addressing them.
This reading takes a broad approach that addresses both the risk management 
of enterprises in general and portfolio risk management. The principles underlying 
portfolio risk management are generally applicable to the risk management of financial 
and non-  financial institutions as well.
The concept of risk management is also relevant to individuals. Although many 
large entities formally practice risk management, most individuals practice it more 
informally and some practice it haphazardly, oftentimes responding to risk events 
after they occur. Although many individuals do take reasonable precautions against

unwanted risks, these precautions are often against obvious risks, such as sticking a 
wet hand into an electrical socket or swallowing poison. The more subtle risks are 
often ignored. Many individuals simply do not view risk management as a formal, 
systematic process that would help them achieve not only their financial goals but 
also the ultimate end result of happiness, or maximum utility as economists like to 
call it, but they should.
Although the primary focus of this reading is on institutions, we will also cover 
risk management as it applies to individuals. We will show that many common themes 
underlie risk management—themes that are applicable to both organizations and 
individuals.
Although often viewed as defensive, risk management is a valuable offensive weapon 
in the manager’s arsenal. In the quest for preferred outcomes, such as higher profit, 
returns, or share price, management does not usually get to choose the outcomes but

does choose the risks it takes in pursuit of those outcomes. The choice of which risks 
to undertake through the allocation of its scarce resources is the key tool available 
to management. An organization with a comprehensive risk management culture in 
place, in which risk is integral to every key strategy and decision, should perform 
better in the long-  term, in good times and bad, as a result of better decision making.
The fact that all businesses and investors engage in risky activities (i.e., activities 
with uncertain outcomes) raises a number of important questions. The questions that 
this reading will address include the following:
■■What is risk management, and why is it important?
■■What risks does an organization (or individual) face in pursuing its objectives?
■■How are an entity’s goals affected by risk, and how does it make risk manage -
ment decisions to produce better results?
■■How does risk governance guide the risk management process and risk budget -

ing to integrate an organization’s goals with its activities?
■■How does an organization measure and evaluate the risks it faces, and what 
tools does it have to address these risks?

The Risk Management Process 409
The answers to these questions collectively help to define the process of risk manage -
ment. This reading is organized along the lines of these questions. Section 2 describes 
the risk management process, and Section 3 discusses risk governance and risk toler -
ance. Section 4 covers the identification of various risks, and Section 5 addresses the 
measurement and management of risks. Section 6 provides a summary.
THE RISK MANAGEMENT PROCESS
Risk , broadly speaking, is exposure to uncertainty. Risk is also the concept used to 
describe all of the uncertain environmental variables that lead to variation in and 
unpredictability of outcomes. More colloquially, risk is about the chance of a loss or 
adverse outcome as a result of an action, inaction, or external event.
This last view may make it sound as if risk is something to be avoided. But that 
is not at all the case. Risk is a key ingredient in the recipe for business or investment

success, and return without risk is generally a false hope and usually a prescription 
for falling short of one’s goals. Risks taken must be carefully chosen, understood, and 
well-  managed to have a chance at adding value through decisions. Risk and return 
are the interconnected forces of the financial universe. Many decision makers focus 
on return, which is not something that is easily controlled, as opposed to risk, or 
exposure to risk, which may actually be managed or controlled.
Risk exposure  is the extent to which the underlying environmental or market 
risks result in actual risk borne by a business or investor who has assets or liabilities 
that are sensitive to those risks. It is the state of being exposed or vulnerable to a 
risk. Risk exposure results from the decisions of an organization or investor to take 
on risk-  sensitive assets and liabilities.
Suppose there is an important announcement in Japan that will result in the yen

either appreciating or depreciating by 1%. The range of possible outcomes in real sit -
uations is clearly not as simple as the up-  or- down 1% case used here, but we will use 
a simplified example to make an important point. The risk is the uncertain outcome 
of this event, and the currency risk to a non-  Japanese business is the uncertain return 
or variation in return in domestic currency terms that results from the event. The risk 
can be described as the range of resulting outcomes and is often thought of in terms 
of a probability distribution of future returns. Suppose that the underlying amount is 
¥1,000,000. The risk exposure of a business may be zero or it could be sizable, depend -
ing on whether the business has assets or liabilities tied to this risk1—in this case, 
exposure to that currency. One million yen would, in this example, result in ¥10,000 
of risk exposure (1% of ¥1,000,000). Risk management would include, among other

things, quantifying and understanding this risk exposure, deciding how and why to 
have the exposure and how much risk the participant can bear, and possibly mitigating 
this risk by tailoring the exposure in a number of ways. The risk management process 
would inform the decision of whether to operate or invest in this risky currency.2
1 The word “risk” is confusing because it is used by different people at different times to mean so many 
different things. Even when used properly, the term has three related but different meanings, which this 
example illustrates well. Risk can mean, in turn, the underlying uncertainty, the extent of the risky action 
taken, or the resulting range of risky outcomes to the entity. In this example, the first meaning is the 
uncertain +1% or –1% movement of the currency. The second meaning is the ¥1,000,000 worth of risky 
currency, the position taken by the business. The third meaning is the +¥10,000 or –¥10,000 risky outcome

that might accrue to the business for having engaged in this risky activity. A common way of more precisely 
distinguishing among these three “risks” in usage is: risk driver  for the underlying risk, risk position  to 
describe or quantify the risky action taken, and risk exposure  for the potential valuation change that may 
result. In the oversimplified example above, the risk exposure is simply the risk position multiplied by the 
risk driver. In practice the term “risk” is used interchangeably for all three meanings.

Reading 42 ■ Risk Management: An Introduction 410
Risk management  is the process by which an organization or individual 
defines the level of risk to be taken, measures the level of risk being taken, 
and adjusts the latter toward the former, with the goal of maximizing the 
company’s or portfolio’s value or the individual’s overall satisfaction, or utility.
Said differently, risk management comprises all the decisions and actions needed 
to best achieve organizational or personal objectives while bearing a tolerable level 
of risk. Risk management is not about minimizing risk; it is about actively under -
standing and embracing those risks that best balance the achievement of goals with 
an acceptable chance of failure, quantifying the exposure, and continually monitoring 
and modifying it. A company that shied away from all risk would find that it could 
not operate. In trying to create wealth, all entities will find themselves “in the risk

business. ” Risk management is not about avoiding risks any more than a practical 
diet is about avoiding calories. Risk management is not even about predicting risks. 
“The Doctrine of No Surprises” is a key mantra among many risk managers, but it 
does not mean they are expected to predict what will happen. Instead, it means that 
if an unpredictable event, either positive or negative, happens in an uncertain world, 
the impact  of that event on the organization or portfolio would not be a surprise and 
would have been quantified and considered in advance.
For example, a risk manager of a bank would not have been expected to know that 
a real estate crisis was going to occur and cause significant defaults on the bank’s real 
estate securities. But a good risk manager would help the bank’s management decide 
how much exposure it should have in these securities by quantifying the potential 
financial impact of such a crisis destroying, say, 60% of the bank’s capital. A good risk

management process would include a deep discussion at the governance level about 
the balance between the likely returns and the unlikely—but sizable—losses and 
whether such losses are tolerable. Management would ensure that the risk analysis 
and discussion actively affects their investment decisions, that the potential loss is 
continuously quantified and communicated, and that it will take actions to mitigate or 
transfer any portion of the risk exposure that cannot be tolerated.2 The only surprise 
here should be the market shock itself; the risk manager should have prepared the 
organization through stress-  testing and scenario analysis, continuously reporting in 
advance on the potential impact of this sizable risk exposure.
A poor risk management process would have ignored the possibility, though small, 
of such a significant market event and not quantified the potential loss from exposure 
to a real estate crisis. As such, the bank’s management would have had no idea that

more than half of the bank’s capital could be at risk, not addressed this risk in any 
governance/risk appetite discussion, ignored these risks in its investment decisions, 
and not taken any action to mitigate this risk. In a good risk management process, 
most of the work is done before an adverse event happens; in a poor risk management 
process, perhaps just as much work gets done, but it all comes after the event, which 
is after the damage has been done.
Good risk management does not prevent losses, but provides a full top-  to- bottom 
framework that rigorously informs the decision-  making process—before, during, 
and after a risk event. Because risks and exposures are dynamic, risk management 
is a continuous process that is always being reevaluated and revised. If this process 
is done well, it provides management and staff with the knowledge to navigate as 
efficiently as possible toward the goals set by the governing body. In turn, this effort

increases ex ante  the value of the business or investment decisions undertaken. Good 
risk management may allow managers to more quickly or effectively act in the face 
2 For example, hedges may be used to limit loss of capital to 20%.

The Risk Management Process 411
of a crisis. But ex post , even the best risk management may not stop a portfolio from 
losing money in a market crash nor prevent a business from reduced profits in an 
economic downturn.
A risk management framework  flows logically from the definition of risk manage -
ment that was previously given: It is the infrastructure, process, and analytics needed 
to support effective risk management in an organization. This process should fully 
integrate the “risk” and “return” aspects of the enterprise into decisions in support of 
best achieving its goals within its tolerance for risk. Risk management is not a “one 
size fits all” solution; it is integral to the enterprise’s goals and needs. Thus, it is best 
achieved through a custom solution. Despite customization, every risk management 
system or framework should address the following key factors:
■■Risk governance
■■Risk identification and measurement
■■Risk infrastructure
■■Defined policies and processes

■■Risk monitoring, mitigation, and management
■■Communications
■■Strategic analysis or integration
Not surprisingly, these factors often overlap in practice. They are defined and dis -
cussed here.
Governance is the top-  level system of structures, rights, and obligations by which 
organizations are directed and controlled. Normally performed at the board level, 
governance is how goals are defined, authority is granted, and top-  level decisions are 
made. The foundation for risk management in the organization is set at the board 
level as well. Risk governance  is the top-  down process and guidance that directs risk 
management activities to align with and support the overall enterprise and is addressed 
in more detail in Section 3. Good governance should include defining an organization’s 
risk tolerance and providing risk oversight. Governance is often driven by regulatory 
concerns, as well as by the fiduciary role of the governing body. A risk management

committee is another facet of governance; it provides top decision makers with a forum 
for regularly considering risk management issues. To achieve the best results for an 
organization, risk governance should take an enterprise-  wide view. Enterprise risk 
management  is an overarching governance approach applied throughout the entity 
and consistent with its strategy, guiding the risk management framework to focus risk 
activities on the objectives, health, and value of the entire  organization.
Risk identification and measurement  is the main quantitative core of risk manage -
ment; but more than that, it must include the qualitative assessment and evaluation 
of all potential sources of risk and the organization’s risk exposures.3 This ongoing 
work involves analyzing the environment for relevant risk drivers, which is the com -
mon term used for any fundamental underlying factor that results in a risk that is

relevant or important to an entity,4 analyzing the business or portfolio to ascertain 
risk exposures, tracking changes in those risk exposures, and calculating risk metrics 
to size these risks under various scenarios and stresses.
Risks are not limited to what is going on in the financial markets. There are many 
types of risk that can potentially impact a business, portfolio, or individual. A fuller 
overview of the range of risks will be the focus of Section 4.
3 This material is covered in more detail in Section 4.
4 Risk drivers are covered in more detail in Section 5.1.

Reading 42 ■ Risk Management: An Introduction 412
The power of technology has allowed for risk management to be more quantita -
tive and timely. Management can measure and monitor risk, run scenarios, conduct 
statistical analysis, work with more complex models, and examine more dimensions 
and risk drivers as well as do it faster. This use of technology needs to be balanced 
with and supplement—not supplant—experienced business judgment. Technology 
has made risk infrastructure even more important and beneficial in managing risks.
Risk infrastructure  refers to the people and systems required to track risk expo -
sures and perform most of the quantitative risk analysis to allow an assessment of the 
organization’s risk profile. Infrastructure would include risk capture (the important 
operational process by which a risk exposure gets populated into a risk system), a 
database and data model, analytic models and systems, a stress or scenario engine,

and an ability to generate reports, as well as some amount of skilled and empowered 
personnel resources dedicated to building and executing the risk framework. With 
increased reliance on technology, more time and effort must be allotted to test data, 
models, and results in order to avoid the ironic outcome of the risk of errors coming 
from within risk systems.
Obviously, the scope of risk infrastructure will be related to the resources, or 
potential losses, of the organization. Individuals and smaller businesses may rely heavily 
on an external partner or provider for much of their risk infrastructure and analysis.
Policies and processes  are the extension of risk governance into both the day-  to- day 
operation and decision-  making processes of the organization. There may be limits, 
requirements, constraints, and guidelines—some quantitative, some procedural—to 
ensure risky activities are in line with the organization’s predetermined risk tolerance

and regulatory requirements. Much of this is just common sense business practice: 
updating and protecting data, controlling cash flows, conducting due diligence on 
investments, handling exceptions and escalations, and making checklists to support 
important decisions. In a good risk framework, processes would naturally evolve to 
consider risk at all key decision points, such as investment decisions and asset allo -
cation. Risk management should become an integrated part of the business and not 
just a policing or regulatory function.
The process of risk monitoring, mitigation, and management  is the most obvious 
facet of a risk framework, but also one of the most difficult. Actively monitoring 
and managing risk requires pulling together risk governance, identification and 
measurement, infrastructure, and policies and processes and continually reviewing 
and reevaluating in the face of changing risk exposures and risk drivers. It requires

recognizing when risk exposure is not aligned with risk tolerance and then taking 
action to bring them back into alignment.5
Communication  of critical risk issues must happen continually and across all levels 
of the organization. Governance parameters, such as risk tolerances and associated 
constraints, must be clearly communicated to, and understood by, managers. Risk 
metrics must be reported in a clear and timely manner. Risk issues must be reviewed 
and discussed as a standard part of decision making. Changes in exposure must be 
discussed so that action can be taken as appropriate. There should also be a feedback 
loop with the governance body so that top-  level risk guidance can be validated or 
updated and communicated back to the rest of the organization.
Strategic analysis and integration  help turn risk management into an offensive 
weapon to improve performance. Good risk management is a key to increasing the

value of the overall business or portfolio. A risk management framework should pro -
vide the tools to better understand the how and why of performance and help sort out 
which activities are adding value and which are not. In investing, rigorous analysis can 
support better investment decisions and improve strategy and risk-  adjusted returns.
5 Risk mitigation and management is discussed in more detail in Section 5.

The Risk Management Process 413
Exhibit 1   The Risk Management Framework in an Enterprise Context
Risk Drivers
Board Management
Goals Strategies
Risk 
Tolerance
Risk 
Budgeting
Policies & Processes(Allocate to) 
Risky Activities
Risk ExposuresIdentify Risks
Measure Risks
Monitor RisksRisk Mitigation
& Management Establish Risk
Infrastructure 
Risks
in
Line? 
Reports
(Communications) 
Strategic
Analysis MODIFYRisk Governance
YESNO
Exhibit 1 illustrates the process of risk management for an enterprise, pulling all 
the described elements of the risk framework together. Although there are a very high 
number of risks faced by every organization, most organizations are primarily affected 
by a small number of key risk drivers, or primary underlying factors that create risk. 
Along the left side is risk governance, which represents board-  level decisions and 
encompasses and affects the boxes immediately to its right. The governance body,

often called a board, defines the goals of the organization and, in turn, decides on 
its risk tolerance. It may additionally provide guidance on how or where that risk is 
taken (risk budgeting). The board is also involved in setting high-  level policies that 
will affect most risk management processes. These risk governance activities are a 
crucial keystone of the risk framework and will be discussed in detail in the next 
section. When the rest of the risk framework hinges off of these top-  down governance 
elements and is focused on the goals of the entire enterprise (as shown here), the end 
result is effective enterprise risk management.
The role of management, shown in the middle column, is to plan and execute value-  
maximizing strategies consistent with their governance guidance. Each management 
activity in the framework flows not only from management (shown with the arrows) 
but also from the governance activities on the left. Thus, not only are management’s

strategies designed to achieve the board’s goals, but management also allocates capital 
to risky activities (its business or investing choices) to execute its strategies consistent 
with the defined risk tolerance. The risk exposures that result from management’s 
choice of activities should also be aligned with the governing body’s risk budget. In

Reading 42 ■ Risk Management: An Introduction 414
addition, management participates actively in setting or implementing policies and 
establishing procedures that relate to when, how, how much, and by whom each of 
the other elements of the risk framework are performed.6
The rest of the risk management framework comprises a number of important 
risk activities to help the business achieve all of its strategic and governance goals 
and mandates. These other elements to implement risk management are shown in 
the far right column of the illustration. Driven by its need to establish a risk man -
agement program to support the enterprise’s goals, management would provide the 
requisite resources for risk management activities by establishing a risk management 
infrastructure. With risk processes defined and risk infrastructure in place, risks are 
then identified and measured, which is a regular and continual process of translat -

ing risk exposures (produced by the risky activities) into meaningful and generally 
quantitative risk metrics.
The next major steps—risk monitoring, mitigation, and management—are where 
much of a firm’s day-  to- day risk management activity is focused. These activities are split 
across three boxes in the illustration. Risk levels are continuously monitored, having 
just been measured.7 There is a major decision at the monitoring stage: Management 
must check that all the risks are in line and not outside the limits of the defined risk 
tolerance or budget.8 This process involves evaluating the actual risk exposures com -
pared with the organization’s risk policies and procedures to ensure that everything 
is in compliance. If the answer is “no, ” then risk mitigation and management actions 
need to be taken to modify risk levels and to bring them back into compliance. There 
are a variety of methods to accomplish this task, which are addressed in Section 5.

Whatever the method, management’s allocation of the risk budget to risky activities 
will be altered by this modification, which includes changing the entity’s risk expo -
sures, starting the circle again through the steps on the right, and re-  checking to see 
if risk levels are now consistent with risk policies.
When risks are in line with limits, policies, tolerances, mandates, and so on, then the 
process moves back to continuous monitoring followed by communicating risk levels.9 
This communication, at a minimum, includes reporting key risk metrics on a regular 
and timely basis across the organization to assist management in its decision-  making 
process and the board in fulfilling its governance duties. Finally, strategic analysis is 
supported by the risk measurement, reporting, and other steps of the enterprise risk 
management process. By analyzing all of the enterprise’s strategies and risky activities

via the risk measurement lens, management can improve its decision-  making process 
and ascertain where to invest its limited capital and risk budget most fruitfully. This 
step is generally underappreciated and is an inexpensive and beneficial by-  product 
of having built a risk framework. The last two boxes or steps (reports and strategic 
analysis) represent important feedback loops to inform and improve both governance 
and the portfolio of risky activities that make up the business.
6 In essence, there could be an arrow from policies and processes to every other box to the right, but 
these rather obvious relationships are intentionally omitted in the diagram to avoid clutter. Likewise, risk 
exposures inform nearly all the boxes to the right. Risk management is innately quite interrelated.
7 Continuous usually does not mean real-  time; the frequency of monitoring is based on the resources avail -

able, the level of systems support, and the need for risk information in the decision process. At large financial 
firms, this monitoring will generally be daily; for small businesses and individuals it might be quarterly.
8 This task is generally delegated to a risk manager; but whatever the title, someone must be accountable 
for this important check.
9 While not obvious in the illustration, communication and reporting should happen whether or not 
risk levels are in compliance; such communications are even more important when risk levels are out of 
alignment with tolerances.

The Risk Management Process 415
There are many feedback loops in properly executed risk management. In practice, 
most of these steps overlap most of the time and are being performed simultaneously. 
Good risk management ties together all these steps from the highest governance 
decisions to lower-  level specifics, such as models, reports, and operational checklists.
The risk environment is dynamic, and many of our notions of probabilities and 
likely risk outcomes change in ways we probably could not predict. The risk manage -
ment framework should be robust enough to anticipate this dynamism—to expect 
the unexpected. It should be evolutionary—flexible enough to grow with a company 
or individual and its new challenges.
The complexity of the risk management framework depends on the complexity 
of an entity’s risk exposures and their resources. But that does not mean that smaller 
organizations or individuals should skip the risk management process; they may simply

be able to do less, or have to work with external partners to assist with large portions 
of the framework, or be less formal about the process. Ultimately, the key principles 
just covered are still important even to the smallest entity, even if the specific com -
ponents do not get assembled as described.
THE RISK MANAGEMENT PROCESS FOR AN INDIVIDUAL
Although an individual has neither the resources nor the organizational overhead of 
a large business, the importance of risk management is not diminished and the risk 
management framework still applies, albeit most likely in a scaled-  down form. Though 
nearly all of the essential elements of the process illustrated in Exhibit 1 are still useful, 
the individual can reduce the recipe to six essential ingredients, consistent with the 
reduced scope of the individual’s risk exposures.
The first step for an individual is much like that shown in Exhibit 1 for the most complex

organization: the determination of goals or objectives. This step would include most of the 
elements associated with risk governance, just without all the organizational complexity.
The next functional step involves choosing investments (or other assets) and identi -
fying their risks. Lacking any risk infrastructure, the individual may at this stage already 
require the services of an investment professional or financial adviser. This step and 
subsequent steps will probably be executed by the adviser, although the individual 
principal still needs to stay knowledgeable and involved. In the context of the illustra -
tion in Exhibit 1, the individual is effectively their own governance body and the adviser 
serves the role of management.
The next steps for the individual are equivalent to the heart of the risk management 
process: risk monitoring and risk mitigation and management. The individual would 
first evaluate their risk exposure (like the diamond or decision step in the illustration),

then consider various alternative approaches to modify the risk if necessary, followed by 
implementing the risk management solution (insuring, hedging, trading, etc.).
The final functional step for an individual’s risk management process would be evalu -
ation and review. This step is parallel to the back-  end of the risk management illustration, 
the boxes at the bottom right. This process may occur with much less frequency for an 
individual—but it is no less important.
Each individual should simplify the risk management process as required so that they 
do not end up considering it “too esoteric and complicated to worry about” and thus 
ignoring risk management altogether. The potential costs of avoiding risk management 
are essentially the same for an individual as for a large corporation or a hedge fund, 
although perhaps with less money involved.
At its core, business and investing are about allocating resources and capital to

chosen risks. Understanding which risks drive better outcomes should be one of the 
goals of risk management, and it makes good risk management inextricably linked 
with good management generally. When effective risk management is truly integrated 
at all levels of the decision-  making process and the overall management process,

Reading 42 ■ Risk Management: An Introduction 416
the organization has developed an effective risk culture . This culture generally pro -
duces better results than just considering risk issues as a separate afterthought, and, 
in turn, it produces much  better results than ignoring risk issues altogether in the 
decision-  making process. For individuals, the adoption of a risk culture should result 
in a personal awareness of the many types of risks, their rewards, the costs, the rela -
tionships between them, and the methods of aligning the risks borne with the risks 
and outcomes desired. This awareness should lead to better investment return and/
or smaller losses for the risk taken, resulting in higher satisfaction.
There are a number of other benefits from establishing good risk management: 
(1) Most obvious is less frequent surprises and a better notion of what the damage 
would be in the event of a surprise; (2) more decision discipline leading to better con -

sideration of trade-  offs and better risk−return relationships; (3) better response and 
risk mitigation stemming from more awareness and active monitoring, which should 
trim some of the worst losses; (4) better efficiency and fewer operational errors from 
policies and procedures, transparency, and risk awareness; (5) better relations, with 
more trust, between the governing body and management, which generally results 
in more effective delegation; (6) a better image or reputation because analysts and 
investors perceive a company as prudent and value-  focused. Together, all these benefits 
should lead to higher value for the enterprise.
EXAMPLE 1   
Risk Management and Risk Management Framework
1 Which of the following is not a goal of risk management?
A Measuring risk exposures
B Minimizing exposure to risk
C Defining the level of risk appetite
2 Which element of a risk management framework sets the overall context 
for risk management in an organization?
A Governance
B Risk infrastructure

C Policies and processes
3 Which element of risk management makes up the analytical component of 
the process?
A Communication
B Risk governance
C Risk identification and measurement
4 Which element of risk management involves action when risk exposures 
are found to be out of line with risk tolerance?
A Risk governance
B Risk identification and measurement
C Risk monitoring, mitigation, and management
B is correct. The definition of risk management includes both defining the level 
of risk desired and measuring the level of risk taken. Risk management means 
taking risks actively and in the best, most value-  added way possible and is not 
about minimizing risks.

Risk Governance 417
A is correct. Governance is the element of the risk management framework that 
is the top-  level foundation for risk management. Although policies, procedures, 
and infrastructure are necessary to implement a risk management framework, 
it is governance that provides the overall context for an organization’s risk 
C is correct. Risk identification and measurement is the quantitative part of 
the process. It involves identifying the risks and summarizing their potential 
quantitative impact. Communication and risk governance are largely qualitative.
C is correct. Risk monitoring, mitigation, and management require recognizing 
and taking action when these (risk exposure and risk tolerance) are not in line, 
as shown in the middle of Exhibit 1. Risk governance involves setting the risk 
tolerance. Risk identification and measurement involves identifying and mea -
suring the risk exposures.
RISK GOVERNANCE

Risk governance is the foundation for risk management. As defined earlier, it is the 
top-  down process and guidance that directs risk management activities to align with 
and support the goals of the overall enterprise. It typically emanates from a board of 
directors with fiduciary obligations and risk oversight and who prescribe goals and 
authorities. Referring back to the definition of risk management, note that risk man -
agement is keenly focused on the risk and value of the overall enterprise.
3.1 An Enterprise View of Risk Governance
In addition to the responsibility for risk oversight, there are two other important 
areas in which the governing body drives the risk framework. First, it determines the 
organization’s goals, direction, and priorities, which combined serve as a key foun -
dation for enterprise risk management. Recall that enterprise risk management is an

overarching governance approach applied across the entity that focuses risk activities 
on the objectives, health, and value of the whole organization. Second, it spells out 
the risk appetite or tolerance, meaning which risks are acceptable, which risks are to 
be mitigated and to what extent, and which risks are unacceptable. Risk governance 
should also provide a sense of the worst losses that could be tolerated in various 
scenarios, and management should manage risk accordingly. These considerations 
should flow naturally into decisions about risk budgeting to guide implementation of 
an optimal program that is consistent with that risk tolerance.
Risk governance is the impact of the governing body of an organization on the 
risk management framework. It provides context for and clarity on an organization’s 
value drivers and risk appetite, specifies clear authority to management to execute 
risk management, and ensures risk oversight to continually determine whether

risk management is functioning well and consistent with the organization’s value 
maximization. It is the governing body’s job to tie the organizational goals and risk 
framework together; thus, risk governance happens within an enterprise context. Risk 3

Reading 42 ■ Risk Management: An Introduction 418
governance and risk oversight also entail compliance with regulatory requirements. 
Risk governance is a difficult and demanding discipline, and if it is going to flourish 
in an organization, it needs visible commitment from the top.
Providing clear guidance with sufficient leeway to execute strategy is often a dif -
ficult balance. Even more challenging is providing for advance discussion and a clear 
decision and statement of organizational risk appetite. There is usually substantial 
discussion about this risk appetite after  a crisis, but too often there is very little dis -
cussion during periods of normalcy, when it would be much more beneficial. Because 
risk is one of the main strategic tools that management can regulate, it is especially 
important for governing bodies to openly discuss risk, consider scenarios, understand 
the impact of negative outcomes on the organization, and make it clear where they

are not willing to venture. Much like an automobile that comes with a red zone on 
some dials to establish boundaries for safe operation, risk governance bodies should 
likewise establish hypothetical red zones to ensure the safe operation of their enterprise.
Enterprise risk management (focusing risk activities on the objectives, health, and 
value of the whole  organization) requires that the entire economic balance sheet of 
the business be considered, not just the assets or one part of the business in isolation. 
A narrower view of risk management is unlikely to meet the goal of maximizing the 
value of the entire enterprise.
Pension fund management provides a classic example of the importance of consid -
ering enterprise risk management: “Funds” are the assets and “pension” is the liability. 
But a true enterprise view requires an even broader outlook. A corporate pension 
fund’s manager might try to maximize only the fund’s assets, but this would generally

do a disservice to the corporation. The assets and liabilities of a pension fund are both 
sensitive to market variables, so ignoring the liabilities would be ignoring half the risk. 
With liabilities that are quite bond-  like, a pension fund manager using all equities 
for maximum growth would potentially make the overall fund insolvent in a market 
collapse with declining interest rates because, in such a situation, the liabilities would 
increase substantially in value while the assets fell. Risk tolerance for the assets in 
isolation would be far different from the risk tolerance of the entire enterprise. One 
should look beyond just the pension liabilities, which are likely to be a small part of 
the overall enterprise. Broader still, a true enterprise risk view in this case would also 
consider the parent corporation’s business risk profile and not just the pension assets 
and liabilities. In a market collapse, the overall business might be in a recessionary

phase, rendering increasing contributions from the corporation to its pension fund 
quite painful. Factoring the corporate risk profile into the pension fund investment 
strategy may cause the risk tolerance to be lower in this case.
Risk governance that focuses on the entire enterprise will result in risk manage -
ment that is much less likely to be at odds with the goals of the organization and more 
likely to enhance long-  run value. Likewise, consideration of a full spectrum of risks, 
and not just the most obvious quantitative risks, will result in better risk governance.
The enterprise view of risk management is equally applicable and important to an 
individual, even if the term “enterprise” is not often used in an individual context.10 
The appropriate set of risks for an individual must be viewed not in isolation, but in 
consideration of the goals and characteristics of the individual in a holistic view. For

example, an adviser may be designing an investment portfolio to maximize a client’s 
wealth and optimize the risk–return trade-  off at some perceived comfortable level 
of risk.11 But the client, whose wealth consists not only of financial assets but also 
10 Enterprise risk management is actually an easier concept for an individual; compared with an organi -
zation in which deciding, coordinating, and communicating goals can be a big challenge, the scope of risk 
management efforts for an individual is smaller and more manageable.
11 Here, the individual is the governing body, setting individual goals and risk appetite; the financial pro -
fessional or wealth manager is the “management team” executing much of the rest of the risk framework.

Risk Governance 419
of valuable human capital,12 might prefer that risk allocation decisions be made in 
view of both forms of capital, optimizing her total wealth. For example, a client with 
a career in real estate would most likely benefit if her financial portfolio is invested 
in a way that considers her earnings exposure to real estate related risks. Holdings of 
real estate securities above a certain level, even if optimal from an isolated portfolio 
perspective, might make this individual less than optimally diversified from a total 
wealth perspective. In another example, Investor X, who has substantial inflation-  
adjusted pension benefits, is different from Investor Y, who has a fixed pension benefit, 
and different still from Investor Z, who has no pension benefit and retires with solely 
his own investment portfolio. These three investors will require remarkably different 
investment solutions, not only to deal with inflation but also to deal with the uncer -

tainty surrounding lifespans. Individuals with different goals and characteristics will 
need differing investment and risk solutions that are best suited to their individual 
situations. In fact, because of the extremely variable life cycle of an individual and the 
discrete nature of many individuals’ goals, the enterprise view is even more important 
to risk management for individuals than it is for institutions.
Risk governance extends into management to include ways to ensure that the risk 
framework of an organization stays consistent with top-  level guidance. One useful 
approach is to provide a regular forum to discuss the risk framework and key risk issues 
at the management level. In other words, a risk management committee would be a 
key element of good risk governance. Its activities could parallel the governance body’s 
risk deliberations, but at an operational level as opposed to high-  level oversight. In

this forum, governance overlaps with many of the other aspects of the organization’s 
risk framework as discussed in Section 2. In fact, if done well, it integrates all of them.
In the same vein, another element of good risk governance is the formal appoint -
ment of a responsible executive as chief risk officer (CRO). This officer should be 
responsible for building and implementing the risk framework for the enterprise and 
managing the many activities therein. In the same manner that risks are inextrica -
bly linked with the core business activities, the CRO is likewise a key participant in 
the strategic decisions of the enterprise—this position is not solely a policing role. 
Although the chief executive is responsible for risk as well as all other aspects of an 
enterprise, it makes no more sense for the CEO to perform the role of the CRO than 
it would be for the CEO to perform the role of the CFO. Many financial firms now

have a CRO in executive management,13 which had become best practice even in the 
years prior to the 2008 crisis.
3.2 Risk Tolerance
Perhaps the most important element of good risk governance is the risk tolerance  
discussion and decision within the governing body. Business and investment strategy 
centers on selecting a portfolio of acceptable risk activities that will maximize value 
and produce the highest returns possible for the given risk level. At the governance 
level, the duty is generally not to select these activities—a job that usually falls to 
management—but to establish the organization’s risk appetite. Certain risks or levels of 
risks may be deemed acceptable, other risks deemed unacceptable, and in the middle 
12 Human capital  is a common term in economics and finance relating to the marketable skills of an 
individual and the corresponding present value of future earnings to be generated by said skilled individ -

ual. As with nearly any valuable asset, it is risky; for example, the present value of an architect’s lifetime 
earnings stream is quite sensitive to equity market and real estate valuations as well as to interest rates. 
Risk considerations related to human capital will be important later in the curriculum.
13 Although this is common for financial firms or other large organizations, many less-  complex companies 
will forgo a formal risk structure. The board still maintains its risk governance responsibilities; and it is 
up to them to work out with management as to how, and to what extent, to meet these responsibilities.

Reading 42 ■ Risk Management: An Introduction 420
are risks that may be pursued in a risk-  limited fashion. Said differently, risk tolerance 
identifies the extent to which the entity is willing to experience losses or opportunity 
costs and to fail in meeting its objectives.14
The enterprise risk management perspective is the right lens through which to 
view the risk appetite question. The risk tolerance decision begins with two different 
analyses that must be integrated—an “inside” view and an “outside” view. First, what 
shortfalls within an organization would cause it to fail, or at least fail to achieve some 
critical goals? Second, what uncertain forces is the organization exposed to? That is, 
what are its risk drivers? With the answers to these two difficult questions in hand, a 
board could begin defining dimensions and levels of risk that it finds too uncomfortable 
to take on. This risk tolerance should be formally chosen and communicated before  a

crisis, and will serve as the high-  level guidance for management in its strategic selection 
of risks. Many organizations will do this after  a crisis, which is better than not doing 
it at all but is much like buying insurance after the loss occurs. It is best to take care 
of it when there seems to be no particularly pressing reason to do so. Similarly, some 
individuals may not give much thought to their own risk tolerance until after a crisis 
occurs, when they belatedly decide that the risk was not worth taking.
For example, suppose a Spanish construction equipment manufacturing company’s 
board is determining its risk tolerance. From the inside perspective, it has two main 
concerns: revenue and liquidity. It determines that it can tolerate a 5%−10% drop in 
revenue, but that a 20% drop would trigger its debt covenants and put the launch of its 
new flagship product at risk. Related to this strategy, it needs €40 million of cash flow

annually for the next three years for critical capital expenditures and can leave almost 
none of this cash flow at risk. From the outside perspective, it realizes that there are 
three main uncertainties or risk drivers over which it has no control: changes in the 
value of the US dollar, interest rate changes, and market returns on industrial sector 
equities. Both its business results and its own stock price are strongly correlated with 
these three risks and could be adversely affected by any of them.
Rather than taking a passive approach as a risk observer, the board in this example 
uses a top-  level analysis to formulate its risk tolerance. In this case, it may decide to 
limit maximum cash flow variation to €10 million annually and revenue exposure to 
−10% in a global recession. In addition, it may specify other stated limits, such as the 
maximum exposure to currency or other risks. This guidance may affect the riskiness

of other product strategies that management may pursue. The company may require 
more expensive financing options to reduce cash flow uncertainty. The governance 
restrictions may drive risk mitigation programs, such as a hedging strategy, especially 
for the primary risk drivers that are stated areas of concern.
Governance guidance is important in helping an enterprise target where it should 
actively pursue risk and where it should mitigate or modify risk. Strategic goals centered 
on core competencies should be pursued, which leads the company into taking risks 
that best position the enterprise for success and value creation. Companies sometimes 
take risks in areas where they have no expertise, which puts their core value creation 
and their entire organization at peril. A well-  functioning risk program would limit 
or hedge those non-  core risks in areas where they have no comparative advantage. 
Modifying risk is covered in detail in Section 5.

14 The risk tolerance decision for an individual  is similar, but not identical, to that of a business enter -
prise. In traditional finance theory, the individual focuses on maximizing unobservable utility, whereas 
the business maximizes a generally observable value—the market value or equity price of the company. 
Although individuals are facing life and certain death on an uncertain timetable, most businesses tend to 
be relatively short-  lived entities, but with an expectation of immortality. The decisions about risk toler -
ance from those two very different viewpoints can be expected to differ—for example, risk tolerance in 
organizations often treats its continued existence as a major consideration. In many ways, the individual’s 
risk tolerance decision is the harder one.

Risk Governance 421
How does a company determine its risk tolerance? There is certainly no formula. 
Most importantly, a company’s goals, its expertise in certain areas, and its strategies 
will help a board determine which risks the company may pursue and with how much 
intensity. The ability of a company to respond dynamically to adverse events may 
allow for a higher risk tolerance. The amount of loss a company can sustain without 
impairing its status as a going concern should factor into its risk tolerance; some 
companies are more fragile than others. The competitive landscape matters because 
both the board’s and investors’ expectations are usually developed in the context of 
how a company is positioned in its industry. The government and regulatory land -
scape is important too, both in their ex ante  demands on how companies approach 
risk and in the likely ex post  reaction in the event of disasters. Quantitative analyses

such as scenario analysis, economic models, and sensitivities to macro risk drivers 
might be used to assess where a board’s zone of comfort is bounded. There are other 
factors that should not determine risk tolerance, but in many cases they do. Personal 
motivations, beliefs, and agendas of board members (the agency problem); company 
size; whether the market environment seems stable; short-  term pressures; and man -
agement compensation often affect risk tolerance in ways that might not be in line 
with the owners’ best interests.
Once risk tolerance is determined, the overall risk framework should be geared 
toward measuring, managing, and communicating compliance with this risk toler -
ance—getting the risk exposure in line with the enterprise’s risk appetite.
This sort of governance exercise not only helps ensure that the organization sur -
vives through the worst of times, but also helps ensure a strategic trade-  off between

risk and return in the decision process, which, in turn, improves potential returns 
for the given level of risk and value. It is quite easy to find business strategies and 
investment approaches that produce apparently outsized returns, but they might be 
at the cost of putting the organization at extreme risk. A somewhat extreme example 
would be a company selling put options on its own equity, which could produce higher 
short-  term profits but would dramatically increase the chance of the company failing 
in a steep market decline. Excessive leverage is another risky strategy for boosting 
short-  term profits that may actually decrease value or lead to failure in the long run. 
A formal risk governance process with a stated risk tolerance would naturally result 
in avoidance of many easier, less well-  reasoned strategies that entail excessive risk 
compared with the firm’s risk tolerance. Instead, it would lead the strategic discussion

into alternative strategies that are more likely to actually add value while taking rea -
sonable risk within the enterprise’s risk tolerance and not simply trade ruin for return. 
Sincere, good risk governance and risk culture can avoid excessively risky strategies 
that might put the long-  term enterprise value at risk. This approach should produce 
enhanced value for the enterprise.
3.3 Risk Budgeting
Risk budgeting  picks up where risk tolerance leaves off. Whereas risk tolerance focuses 
on the appetite for risk and what is and is not acceptable, risk budgeting has a more 
specific focus on how that risk is taken. Risk budgeting quantifies and allocates the 
tolerable risk by specific metrics; it extends and guides implementation of the risk 
tolerance decision.
Risk budgeting applies to both business management and portfolio management. Its 
foundation is the perspective that business or portfolio management involves assem -

bling a number of risk activities or securities, which can be collated into an assemblage 
of various risk characteristics. For example, a traditional view of a portfolio might 
be that it is allocated 20% to hedge funds, 30% to private equity, and the remaining 
50% is split between stocks and bonds. An alternative risk view of the same portfolio 
might be 70% driven by global equity returns, 20% by domestic equity returns, with

Reading 42 ■ Risk Management: An Introduction 422
the remaining 10% driven by interest rates. The equity component might be allocated 
65% to value and 35% to growth. The portfolio might also have 45% illiquid securities 
and the remainder liquid. Other allocations can be stated in terms of exposures to 
inflation, long-  term interest rates, currencies, and so on. These multiple dimensions 
for viewing the allocation of a portfolio are not mutually exclusive: they co-  exist. If 
one is evaluating the risk exposure of a portfolio and trying to keep it in line with a 
stated risk tolerance, one would be far more concerned with the risk characteristics 
of the investment assets and portfolio rather than their common classifications of 
stocks, hedge funds, real estate, private equity, and so on. These terms tell us a little 
about risk but not enough. Equity is traditionally riskier than hedge funds, but some 
equities are of quite low risk and some hedge funds are of quite high risk. The risk

view may be more meaningful and useful in understanding the portfolio risk than the 
traditional asset allocation view.
Risk budgeting is any means of allocating a portfolio based on some risk char -
acteristics of the investments. In the purest sense, the term “budget” implies that 
there is a total risk limit for the organization. Although this approach is not formally 
required,15 it would certainly be good practice to have a risk budget that is consistent 
with the organization’s risk tolerance. A risk budget provides a means of implementing 
the risk tolerance at a strategic level, or in other words, a means of bridging from the 
high-  level governance risk decision to the many management decisions, large and 
small, that result in the actual risk exposures.
A risk budget can be complex and multi-  dimensional or it can be a simple, one-  
dimensional risk measure. Even the simplest measure can provide significant benefits in

developing an effective risk culture. Four well-  known single-  dimension measures that 
are often used are standard deviation, beta, value at risk (VaR), and scenario loss, but 
there are many others. It is common for some hedge funds to budget risk using standard 
deviation, managing to a fixed-  risk fund target, and evaluating individual investments 
based on their returns and risks as they affect the ex ante  standard deviation.
More complex forms of risk budgeting use multiple dimensions of risk. One popular 
approach evaluates risks by their underlying risk classes, such as equity, fixed income, 
commodity risk, and so on, and then allocates investments by their risk class. Also 
common are risk factor approaches to risk budgeting, in which exposure to various 
factors is used to attempt to capture associated risk premiums. An example would be 
to budget an allocation to give greater emphasis to value stocks based on the belief

that they may provide a higher risk-  adjusted return than growth stocks. This tactic 
might be layered over a strategic budget with a certain “beta” as the overall equity 
risk, supplemented with value and additional factor tilts specified up to some level.
Risk budgeting, although a desirable element of risk governance, cuts across the 
entire risk management framework, providing a focal point for each of the facets of 
risk management described in Section 2. And although it is true that in practice many 
organizations operate without a risk budget, it is generally because there has been no 
specific declaration of their risk tolerance. If a board has a clear understanding of its 
risk appetite, both the board and management will want some means of implementing 
a strategic allocation that is consistent with it. Thus, the risk budget becomes a critical 
overarching construct for the organization’s risk framework.

Some individuals may, often through the assistance of a financial planner, engage 
in some form of risk budgeting, but many do not execute it well or carry it far enough. 
A classic example of this failure is the tendency of many individuals to invest their 
financial portfolios in their employers. The risk budget for their total wealth—financial 
15 One could do risk budgeting even if there were no other risk governance guidance.

Risk Governance 423
and human capital—is extremely concentrated in one firm and/or one industry. Not 
surprisingly, such risk budgets typically occur not through formal planning because 
most formal plans would recognize the problem, but through inaction or inattention.
One major benefit of even the most basic risk budgeting is that it forces risk trade-  
offs and supports a culture in which risk is considered as a part of all key decisions. 
Suppose that all the activities a business wants to pursue are in excess of the risk 
budget. The budgeting of risk should result in an approach, whether explicit or not, 
of choosing to invest where the return per unit of risk is the highest. Better still, it 
should also result in a market-  benchmarked choice of risk intensity, between possibly 
doing less of each risky investment or doing more, but with a risk-  mitigating hedge. 
This benefit is extremely important. By choosing between a market hedge or less of a

risky investment, one ends up evaluating the investment directly against the market 
risk–return benchmark. Thus, one is not only comparing risk–return relationships 
among one’s investment choices, but also comparing active versus passive strategies; 
that is, evaluating investment choices as a whole against the “market return” on a 
risk-  equivalent basis. In other words, one ends up attempting to add active value in 
each of one’s decisions while still staying within the confines of the organization’s risk 
tolerance. The result is even more powerful than merely ensuring that the business is 
compensated well for the risks they decide to accept. Just having a risk budget forces 
decision makers to try to add value to the enterprise in every risky decision they make. 
The risk-  budgeting framework makes this consideration innate to the decision process.
EXAMPLE 2   
Risk Governance
1 Which of the following approaches is most  consistent with an enterprise 
view of risk governance?

A Separate strategic planning processes for each part of the enterprise
B Considering an organization’s risk tolerance when developing its asset 
allocation
C Trying to achieve the highest possible risk-  adjusted return on a com -
pany’s pension fund’s assets
2 Which of the following statements about risk tolerance is most  accurate?
A Risk tolerance is best discussed after a crisis, when awareness of risk is 
heightened.
B The risk tolerance discussion is about the actions management will 
take to minimize losses.
C The organization’s risk tolerance describes the extent to which the 
organization is willing to experience losses.
3 Which of the following is not consistent with a risk-  budgeting approach to 
portfolio management?
A Limiting the beta of the portfolio to 0.75
B Allocating investments by their amount of underlying risk sources or 
factors
C Limiting the amount of money available to be spent on hedging strate -
gies by each portfolio manager

4 Who would be the least  appropriate for controlling the risk management 
function in a large organization?
A Chief risk officer

Reading 42 ■ Risk Management: An Introduction 424
B Chief financial officer
C Risk management committee
B is correct. The enterprise view is characterized by a focus on the organization 
as a whole—its goals, value, and risk tolerance. It is not about strategies or risks 
at the individual business line level.
C is correct. Risk tolerance identifies the extent to which the organization is 
willing to experience losses or opportunity costs and fail in meeting its objectives. 
It is best discussed before a crisis and is primarily a risk governance or oversight 
issue at the board level, not a management or tactical one.
C is correct. Risk budgeting is any means of allocating a portfolio by some risk 
characteristics of the investments. This approach could be a strict limit on beta 
or some other risk measure or an approach that uses risk classes or factors to 
allocate investments. Risk budgeting does not require nor prohibit hedging,

although hedging is available as an implementation tool to support risk budgeting 
and overall risk governance.
B is correct. A chief risk officer or a risk management committee is an individual 
or group that specializes in risk management. A chief financial officer may have 
considerable knowledge of risk management, may supervise a CRO, and would 
likely have some involvement in a risk management committee, but a CFO has 
broader responsibilities and cannot provide the specialization and attention to 
risk management that is necessary in a large organization.
IDENTIFICATION OF RISKS
Having laid the framework for understanding the concept of risk management and 
risk governance, we now move into the implementation of the process. One of the 
first important parts of the process is the identification of risks. In this reading, we 
identify two general categorizations of risks. The first is the set of risks that originate

from the financial markets. Accordingly, we refer to this type of risk as financial risks . 
The second group of risks includes those that emanate from outside the financial 
markets. As such, we refer to these as non-  financial risks . Although most risks ulti -
mately have monetary consequences, we reserve the term “financial risks” to refer to 
the risks that arise from events occurring in the financial markets, such as changes in 
prices or interest rates.16 Non-  financial risks arise from other sources, such as actions 
within an entity, or from external origins, such as the environment, the community, 
regulators, politicians, suppliers, and customers. In this reading, we will consider 
the types of financial and non-  financial risks faced by organizations and individuals.4
16 We use the term “financial markets” in a very broad sense. A company may also be exposed to com -
modity price risk, which we would include as a financial risk.

Identification of Risks 425
4.1 Financial Risks
The risk management industry has come to classify three types of risks as primarily 
financial in nature. The three primary types of financial risks are market risk, credit 
risk, and liquidity risk. Market risk  is the risk that arises from movements in interest 
rates, stock prices, exchange rates, and commodity prices. This categorization is not 
to say that these four main factors are the underlying drivers of market risks. Market 
risks typically arise from certain fundamental economic conditions or events in the 
economy or industry or developments in specific companies. These are the underlying 
risk drivers, which we will cover later.
Market risks are among the most obvious and visible risks faced by most organi -
zations and many individuals. The financial markets receive considerable attention 
in the media, and information on financial market activity is abundant. Institutional

investors and many corporations devote considerable resources to processing this 
information with the objective of optimizing performance. Many individuals also 
devote considerable attention to market risk, and financial publications and television 
and radio shows are widely followed in the general population. The state of knowledge 
in risk management is probably greatest in the area of market risk.
The second primary financial risk is credit risk. Credit risk  is the risk of loss if one 
party fails to pay an amount owed on an obligation, such as a bond, loan, or derivative, 
to another party. In a loan, only one party owes money to the other. In some types of 
derivatives, only one party owes money to the other, and in other types of derivatives, 
either party can owe the other. This type of risk is also sometimes called default risk 
and sometimes counterparty risk. As with market risk, the root source of the risk

can arise from fundamental conditions in the economy, industry, or weakness in the 
market for a company’s products. Ultimately, default is an asset-  specific risk. Bond 
and derivatives investors must consider credit risk as one of their primary decision 
tools.17 Similar to market risk, credit risk is also a highly visible risk with considerable 
attention paid to defaults, bankruptcies, and the stresses arising from inadequate 
cash flow in relation to leverage. Credit risk is a particularly significant risk in that 
although market prices can go down and bounce back up, defaults and bankruptcies 
have extremely long-  term implications for borrowers.
Although market and credit risk are extremely common risks to institutions, they 
are also assumed by individuals in their personal investments. One other financial 
risk, however, is much more common to institutions, although it can be faced by 
individuals, often unknowingly. This third risk is liquidity risk , which is the risk of a

significant downward valuation adjustment when selling a financial asset. In order to 
sell an asset, a party may need to reduce the price to a level that is less than the marked 
value or the seller’s assessment of the asset’s true value based on the fundamentals 
of the asset. In certain market conditions, the seller must make a significant price 
concession. Having to make price concessions is not necessarily unusual and does 
not imply a poorly functioning market. Indeed, given no shift in demand, a rightward 
shift of a supply curve in order to sell a larger quantity is entirely consistent with the 
notion that a seller must lower the price to sell a greater quantity.
All assets have transaction costs in the market, such as the bid–ask spread. The 
existence of a sell price that is less than a buy price, however, is not a risk but simply 
a cost. It is the uncertainty  of that valuation spread that creates this type of risk. Thus,

liquidity risk could also be called “transaction cost risk. ” The liquidity risk of a $10 
stock purchased for $10 is not the risk that one would receive the “bid” price of only 
$9.99 right after one bought it. That $0.01 spread is a known cost when the stock is 
17 With certain derivatives (swaps and forwards), either party could be forced to pay off to the other, 
so each party is concerned about whether its counterparty will pay off, meaning that for some products, 
credit risk is bilateral.

Reading 42 ■ Risk Management: An Introduction 426
purchased, so it is not a risk. The risk is that this spread cost might increase dramat -
ically as a result of either changing market conditions or attempting to maintain a 
position significantly larger than the normal trading volume for the stock. This problem 
becomes a serious issue for risk management when the liquidation price falls to less 
than the seller’s estimate of the fundamental value of the asset. Although this risk is 
often associated with illiquid assets,18 it really stems from a couple of sources. First, 
market liquidity varies over time and the market for specific assets may become less 
liquid; second, as the size of a position increases, the cost and uncertainty associated 
with liquidating it will increase. In some extreme cases, there may be no price above 
zero at which the seller can sell the asset.
Of course one might argue that the cost of illiquidity, and liquidity risk, should

thus be part of the investor’s assessment of fundamental value, and indeed it is for 
many analysts. If not, liquidity risk can sometimes be confused with a form of valu -
ation denial in which investors believe that they paid an appropriate price and that 
the market has not converged to its true value. But less liquidity means a thin market 
and a lack of investor interest, which may be fertile ground for investment opportu -
nities. Although lack of liquidity can offer benefits, such as the opportunity to buy an 
asset well before everyone else sees that it is an attractive investment, liquidity risk 
is generally considered to be a negative factor with which risk managers and indeed 
all investors must contend.
4.2 Non-  Financial Risks
Recall that we refer to financial risks as those arising primarily from changes in prices 
and rates in financial markets. Although most risks have monetary consequences, 
there are a number of risks that are typically classified as non-  financial in nature.

These risks arise from a variety of sources, such as the relationship between the entity 
and counterparties, regulators, governments, the environment, suppliers, customers, 
and employees.
One important risk of this type is closely related to default risk but deals more 
with the settling of payments that occur just before a default. This risk is called settle -
ment risk. As an example, suppose Party A enters into a forward contract to purchase 
¥200 million of Japanese government bonds from Party B. Now at expiration if all goes 
well, Party A would wire the money and Party B would transfer the bonds. Each party 
fulfills its obligation expecting that the other will do so as well. Now, suppose Party 
A wires the money but Party B does not send the bonds, and in fact, Party B declares 
bankruptcy. At this point, Party A cannot get the money back, except possibly much 
later through the potentially slow and cumbersome bankruptcy process.19 Although

the financial consequences are very high, the root source of this risk is the timing of 
the payment process itself.
Entities face two types of risks related to the law, and as such, this risk is referred 
to as legal risk. One risk is simply the risk of being sued over a transaction or for that 
matter, anything an entity does or fails to do. In financial risk management, however, 
the major legal concern is that the terms of a contract will not be upheld by the legal 
system. For example, suppose Bank E enters into a derivatives contract with Party F. 
18 The illiquid nature of an asset is not itself the risk because that is a direct cost borne immediately 
upon purchase. Still, uncertainty around the valuation of illiquid assets is a pervasive issue, so it is natural 
to associate liquidity risk with liquidity characteristics. More importantly, though, the term liquidity risk  
also commonly refers to a much broader set of risks for the entity, which are addressed in the next section.

19 This type of risk often arises because of significant time zone differences. Settlement risk is also called 
Herstatt risk; Herstatt was the name of a German bank that failed in 1974 after receiving “overnight” pay -
ments and then defaulting. More recently, in the case of Lehman Brothers in 2008, in addition to obvious 
and serious counterparty issues, there were settlement losses, especially related to overseas subsidiaries.

Identification of Risks 427
Assume that as the underlying changes in price, Party F incurs a loss, whereas there is 
a corresponding gain to Bank E. But suppose that Party F then identifies a legal issue 
that it interprets as giving it the right to refuse to pay. If the court upholds Party F’s 
position, Bank E could incur a loss. Litigation always involves uncertainty because 
even a seemingly weak case can prevail in court.
The following three non-  financial risks are related: regulatory risk, accounting risk, 
and tax risk. They could even be collectively referred to as compliance risk because 
they all deal with the matter of conforming to policies, laws, rules, and regulations 
as set forth by governments and authoritative bodies, such as accounting governing 
boards. Obviously the regulatory, accounting, and tax environment is always subject 
to change, but the rapid expansion of financial products and strategies in relation to

the relatively slow manner in which government and private regulators are able to 
respond means that laws and regulations are nearly always catching up with the finan -
cial world. When these laws and regulations are updated, it can result in significant 
unexpected costs, back taxes, financial restatements, and penalties.
Another type of non-  financial risk is model risk, which is the risk of a valuation 
error from improperly using a model. This risk arises when an organization uses the 
wrong model or uses the right model incorrectly. A simple example applicable to both 
a portfolio manager and a corporate analyst is the assumption of constant dividend 
growth in the dividend discount model when, in fact, growth is not constant.
Closely related to model risk is tail risk—more events in the tail of the distribution 
than would be expected by probability models. This risk is a facet of market risk, but 
it also infects valuations and models when it is ignored or mishandled. Tail risk is

known to be especially severe for the normal distribution, which tends to be overused 
in modeling. As an example, consider the monthly returns on the S&P 500 Index from 
1950 to 2013. The monthly average return was 0.7%, and the monthly standard devia -
tion was 4.18%. If we rank the monthly returns, we would find that the largest negative 
return was −21.76%, which occurred in the well-  known market crash of October 1987. 
With a normal distribution, we would find that a return that low would occur only 
once every 2,199,935 years.20 The second and third worst monthly returns of −16.94% 
(October 2008) and −14.58% (August 1998) would occur only once every 6,916 and 
654 years respectively. If the normal distribution is a realistic descriptor of returns, 
results of these magnitudes should never  have occurred in recorded market history, 
and yet we have seen three such instances. Interestingly, according to the normal

distribution, the largest positive return of 16.30% in October 1974 would occur only 
once every 888 years. Technically, one could argue that if we go another 2,199,935 
years and do not observe a monthly return as low as −21.76%, then the assumption of 
a normal distribution might seem reasonable, but it seems safe to reject the normal 
distribution for at least another two million years. Similar comments can apply to the 
second and third worst returns albeit over shorter periods.
Many quantitative models (e.g., option models) and decision models (e.g., port -
folio construction and asset allocation, relying on standard deviation in analysis and 
decisions) ignore the existence of fat tails in returns; as a result, market risk is often 
considered and dealt with in an oversimplified fashion.21 Tail risk, as the term is used 
in practice, is important and is discussed separately because financial professionals

realize the implicit failure of modeling market risk. More plainly, ignoring tail risk is 
20 This calculation and those that follow are based on determining the probability of the given return or less.
21 A related model risk normally lumped in with tail risk is that of unstable parameters or changing regimes 
because these are pathologies that can produce returns that appear fat-  tailed. A simple, recent, and realistic 
example is changing correlations. Suppose that everybody believes that the equity–commodity correlation 
is 0.1 and uses models for portfolio construction and diversification based on that relationship. If the true 
correlation suddenly changes to 0.9, such as during a financial crisis, then all the model prescriptions become 
not just useless but harmful. Portfolio diversification turns out far less than expected, risk is higher than 
expected, and the “optimal” allocation to commodities turns out to be very wrong.

Reading 42 ■ Risk Management: An Introduction 428
a form of model risk. And although tail risk might seem more of a financial risk than 
a non-  financial risk, the mistake occurs internally, arising from poor choices made 
in modeling.
Most of the internal risks faced by an organization are often grouped together and 
referred to as operational risk. Operational risk  is the risk that arises from the people 
and processes that combine to produce the output of an organization. Although the 
factors that give rise to such risks can arise externally, the risks themselves are largely 
internal to an organization because it would be expected to have its people and pro -
cesses functioning effectively regardless of pressures placed on it by external forces. 
For example, a hacker breaking into a company’s computer system and stealing credit 
cards is an external force. Hacking, however, is not simply a random act of mischief.

Companies are aware of the threat of hackers, and hackers can break in to a system 
only if that system is vulnerable. An organization is responsible for establishing suf -
ficiently tight computer security to deter hackers from breaking in and stealing or 
doing mischief. In addition to the threats posed by hackers and viruses, even secure 
computers themselves are a particular source of risk. Programming errors and bugs 
can create the possibility of costly mistakes.
Employees themselves are major sources of potential internal risks. Banks are 
keenly aware of the vulnerability to employee theft, given the ease with which so 
many employees have access to accounts and systems for making entries. But even 
perfectly honest employees make mistakes and some can be quite costly. The employee 
who credits someone’s account $100,000 for a $100 deposit may have made an hon -
est mistake, but it is a mistake that could quickly lead to the rapid disappearance of

money. In the past, employees up to senior management have been guilty of perpe -
trating accounting fraud, not necessarily for their own direct benefit but to make the 
company look better.
In banks and other companies that trade in the financial markets, there is the risk 
that a trader or portfolio manager will fail to follow laws, rules, or guidelines and 
put the company at great financial risk. This individual is commonly described as a 
“rogue trader. ” Personified by Nick Leeson of Barings Bank, who in 1995 destroyed the 
200-  year old company by engaging in a series of highly speculative trades to cover up 
losses, the rogue trader has become a standard concern of risk managers. Although 
it was never clear if Leeson’s trades were truly unauthorized, his legacy left the fear 
that institutions bear the risk that one trader can imperil the entire organization by 
making large and highly speculative trades that put the bank’s entire capital base at

risk.22 In essence, a rogue trader is a trader who engages in risky transactions without 
regard for the organization’s limits or conforming to its controls.
Companies are also threatened by business interruptions, such as the weather. Not 
only can weather temporarily shut down a company, but it can do serious long-  term 
damage. Although weather is an external force that is completely out of the control 
of an organization, it does not excuse the organization from having the appropriate 
internal procedures for managing weather-  related problems. Simple and fairly low-  
cost actions, such as having generators, sleeping quarters, and food available, can go 
a long way toward keeping employees around and working when roads are closed 
and electricity is off. Airlines are particularly experienced in quickly adjusting their 
schedules to the weather. Yet, some companies have not heeded inclement weather 
forecasts. Failing to react to the warnings of hurricanes and dangerous snowstorms

can result in considerable loss.
22 Although Leeson may have been the origin of the term “rogue trader, ” he has certainly not been the 
largest rogue trader. For example, the trading of Bruno Iksil, a credit default swaps trader in the London office 
of JPMorgan Chase, resulted in a $2 billion loss for one of Wall Street’s most stable financial institutions. 
Unlike Barings, however, JPMorgan Chase survived the financial loss but suffered great embarrassment 
and was fined almost a billion dollars by regulators.

Identification of Risks 429
Terrorism is another form of operational risks that poses a threat to organizations 
and individuals. The 1993 attacks on the World Trade Center led many companies to 
recognize that the New York City financial district was a major terrorist target and 
that, as such, their operations could be shut down by these acts of violence. When the 
more destructive attacks of 11 September 2001 occurred, many companies had already 
established backup operations sufficiently far away from that area. Of course, such 
risk is not confined to major financial centers, and indeed, organizations worldwide 
have begun to take security measures that address this operational risk.
Some of these operational risks are insurable, at least to a modest extent. We 
will briefly discuss insurance later, but most companies would much prefer to take 
proactive steps toward prevention than to incur the inconvenience of losses and then 
have an outside entity compensate them for their losses.

Solvency risk  is the risk that the entity does not survive or succeed because it 
runs out of cash, even though it might otherwise be solvent.23 This was probably the 
most underappreciated component of risk prior to the financial crisis of 2008.24 The 
collapse of Lehman Brothers was often associated with an excess of leverage, which 
was certainly a key factor in its failure. But it was solvency risk that forced the com -
pany into bankruptcy. Almost overnight, Lehman’s liquidity disappeared because most 
funding sources would no longer willingly bear Lehman’s counterparty risk. Even if 
it had experienced large market gains on the day it went under, it had already been 
destroyed by solvency risk. Across the entire financial industry, from hedge funds to 
pension funds, painful but valuable lessons were learned about the critical impor -
tance of funds availability and solvency risk, even if all other risks were well-  aligned.

Solvency risk is now viewed as one of the key factors in running a successful hedge 
fund because investors are extremely sensitive to not recovering their investment in 
the event of a “run on the fund. ”
Solvency, in the personal or institutional sense, is the availability of funding to 
continue to operate without liquidating—or at a less extreme level, to be able to 
make good on liabilities and meet one’s cash flow requirements. Solvency risk is the 
ultimate example of the importance of taking an enterprise view of risk management. 
For example, a university’s investment officer might have a perfectly well-  balanced 
set of risks in the endowment portfolio when viewed in isolation. But as a part of a 
university, the portfolio may be affected by a deep recession because the university’s 
professional degree revenue, grant money, and donations will fall at the same time as 
the portfolio’s investment value and cash distributions are in decline. Although the

endowment and university may survive, it might be necessary for the endowment to 
take many emergency actions that impair its value, simply attributable to the overall 
solvency risk and the ultimate need of the enterprise to not run out of cash.
Solvency risk is easily mitigated though never eliminated by a large number of 
possible safeguards, none of which is free. Many businesses produce short-  term higher 
returns by essentially ignoring solvency risk, but in doing so, they are not managing risk 
very well. Since the 2008 crisis, most businesses are keenly aware of the consequences 
of bad solvency management, and have taken such steps as using less leverage, securing 
more stable sources of financing, investing in models to provide more transparency 
on solvency risk, incorporating solvency risk at an enterprise level in risk governance, 
and holding more cash equivalents and assets with less liquidity risk.

23 Solvency risk is often referred to as liquidity risk by industry professionals, even though the expression 
liquidity risk  was used earlier to refer to the risk of valuation shock when selling a security. Although the 
term “liquidity risk” is used in practice in both contexts, in this reading we will refer to the risk relating to 
the cash position of an entity as “solvency risk. ”
24 Bank runs are perhaps the simplest example of solvency risk. An otherwise solvent bank can easily be 
ruined by a bank run that wipes out its ability to make good on short-  term liabilities. Bank runs are not 
uncommon occurrences in history, so solvency risk certainly long predates the 2008 crisis.

Reading 42 ■ Risk Management: An Introduction 430
Individuals can also face a number of risks of an operational nature. These include 
hackers breaking into one’s computer and the threat of burglary and robbery. One 
of the most commonly cited risks for individuals is identity theft. For individuals, 
however, we consider their primary non-  financial risks to be related to their life and 
health as well as other life-  changing events.
Obviously the health of an individual is an extremely important risk. Poor health 
can result from poor choices in life, but it can also arise from factors that are outside 
the control of the individual. These risks can result in direct health care expenses, 
reduced income because of disability, and reduced lifespan or quality of life. People 
vary widely in the risk management strategies they undertake to control their health, 
such as in their choices in diet, exercise, preventive health care, and avoidance of

undue health risks. Some individuals address only their financial exposure to health 
risks, and still others do not take proactive steps to address this risk at all.
Closely related to health risk is mortality risk—the risk of dying relatively young—
and longevity risk—the risk of outliving one’s financial resources. Not only are these 
risks a primary determinant of the quality of life, they are also critical factors in 
investment planning. Although it is probably desirable not to know when one will die, 
financial planning for one’s years in retirement is heavily dependent on one’s mortal -
ity assumption. Insurance companies, defined benefit pension plans, and vendors of 
retirement annuities need only know the group average mortality. Mortality tables 
are reasonably accurate, so these institutions have relatively precise estimates of death 
rates for groups as a whole. Individuals themselves, however, clearly do not know

how long they will live. People who use defined contribution plans must therefore 
build portfolios and control retirement distributions so that their assets outlive them, 
which is difficult to do when they do not know when they will die. No one wants to 
outlive their money, but with an increasingly aging population and good health care, 
this problem is becoming a greater concern.
There are a number of other major non-  financial risks that individuals face, which 
are generally involved with some sort of life-  changing disaster. The largest ones—fire, 
natural disaster, or massive liability stemming from harming others, such as in a car 
accident—are generally considered “property and casualty” risks and are insured as 
such.
Individuals also face another non-  financial risk that, although not common, does 
seem to be growing. This risk is the possibility that the individual will be cheated by 
a financial adviser. Whether an adviser simply charges too much for their services,

steals a small amount of money, or engages in a massive Ponzi scheme, individuals 
may face a high risk of loss from their advisers. Although the overwhelming majority 
of financial advisers are honest, the amount of money at stake has proven to be a 
significant temptation for an unscrupulous few.
4.3 Interactions between Risks
In some cases, a risk classified into one category could easily have been classified into 
another. Indeed, the interactions between risks are numerous. It has been said that 
market risk begets credit risk, which begets operational risk. That is, given unexpected 
market moves, one party then owes the other party money. Given the debtor–creditor 
nature of the relationship, the two parties must have internal operations that process 
the transactions and pay or collect the money. Thus, whenever there is credit risk, 
there is settlement risk. If there were no market risk, the other risks in the chain would

likely be relatively minor. Legal risk often arises from market or credit risk. Large 
market moves create losses for one party. There is a long history of parties searching 
for loopholes in contracts and suing to avoid incurring the loss.

Identification of Risks 431
One simple example of an adverse risk interaction is counterparty risk. When 
trading a derivative contract, it is important to consider the cost of counterparty 
risk. Suppose Party A buys an out-  of- the- money put option with a strike price of 
¥1000—a contract theoretically worth ¥100 entitling him to as much as ¥1000 from 
Counterparty C if an underlying equity index is down. But there is a 2% chance that 
C could default; and assume that the possibility of default is considered independent 
of the performance of the equity market. This transaction, with payoffs adjusted for 
the possibility of default, might price at, say, ¥98 to A. But in reality, the credit risk 
of C’s default is likely dependent on the equity market return. If the probability dis -
tribution of default risk overlaps substantially with that of the market being down, 
which is a likely scenario, then the risks interact and the cost of risk is higher. In this

example, perhaps the probability of C defaulting is 10% or more when the put option 
is in the money. So A’s expected payoff is lower as a result of facing a credit risk that 
is compounded by market risk. In fact, it is quite likely that in the extreme event—a 
deep decline in the equity market when A would presumably receive ¥1000—Party 
A will in all likelihood get nothing. Thus, the investor bears much more risk than 
initially thought as a result of the failure to consider the interaction of the two risks. 
And in doing so, Party A overpaid for the contract. This sort of risk interaction is so 
common in markets that practitioners have given it a very fitting term—“wrong-  way 
risk. ” In fact, it was extremely common in the financial crisis of 2008, when holders of 
many securities based on mortgage credit believed that the risks were well-  diversified 
when in truth, the risks were quite systematic.
Another example of interacting risks was experienced by many banks, funds, and

private investment partnerships in 2008, as well as the hedge fund Long-  Term Capital 
Management in 1998. Leverage, which manifested itself in higher market risk, inter -
acted in an extremely toxic manner with liquidity risk and solvency risk and impaired 
or shuttered many investment firms.25
In most adverse financial risk interactions, the whole is much worse than the sum 
of its parts; the combined risk compounds the individual risks in a non-  linear manner. 
For this example, a 2× levered entity might produce a 2% loss when its unlevered twin 
or baseline risk bears a 1% loss. If liquidity is a serious issue for the entity, then at a 10% 
baseline loss, the entity might face some moderate distress from liquidity or funding 
problems that it ends up losing 25% instead of 20%. It would not be surprising if this 
entity failed at a 30% baseline loss because of the toxic interplay between levered risk

and liquidity problems. This resulting non-  linear reaction to risk drivers exists across 
many risk interactions in many markets, making up-  front scenario planning even more 
valuable to the risk process, a point we will return to later.
Earlier, we briefly described a common example of interacting risks for individuals. 
Suppose an individual works for a publicly traded company and, through an incentive 
program, receives shares of the company in her company retirement portfolio or for 
her personal holdings. Company policies may require that employees hold on to these 
shares for a number of years. When that time has elapsed, however, many individuals 
fail to recognize the incredibly concentrated risk they are assuming, so they hold on 
to their shares. An employee’s reasoning for not selling the shares is often that the 
company she works for has been a solid performing company for many years, so she 
feels no reason to worry. Moreover, the team spirit often imbued in employees gen -

erates pride that can make employees believe that there is no better place in which 
to work and to invest their money. But if something goes wrong in the company or 
the industry, the employee may lose her job and her savings—an incredibly adverse 
25 This example illustrates yet another risk, systemic risk, that is a significant concern to regulators and 
governments. Stresses and failures in one sector transmit to stresses and failures in other sectors, which 
can ultimately impact an entire economy. Systemic risk is the ultimate example of interactions among risks.

Reading 42 ■ Risk Management: An Introduction 432
interaction between market risk and human capital risk. In 2003, Enron was a sad 
example, with many loyal and honest employees losing virtually all of their retirement 
savings by failing to recognize this risk.
In sum, it is important to recognize that risks do not usually arise independently, 
but generally interact with one another, a problem that is even more critical in stressed 
market conditions. The resulting combined risk is practically always non-  linear in that 
the total risk faced is worse than the sum of the risks of the separate components. 
Most risk models and systems do not directly account for risk interactions, which 
makes the consequences of the risk interaction even worse. Governance bodies, 
company management, and financial analysts should be keenly aware of the potential 
risk and damage of risks in combination, and be aware of the dangers of treating risks 
as separate and unrelated.
EXAMPLE 3

EXAMPLE 3   
Financial and Non-  Financial Sources of Risk
1 Which of the following is not a financial risk?
A Credit risk
B Market risk
C Operational risk
2 Which of the following best describes an example of interactions among 
risks?
A A stock in Russia declines at the same time as a stock in Japan 
declines.
B Political events cause a decline in economic conditions and an increase 
in credit spreads.
C A market decline makes a derivative counterparty less creditworthy 
while causing it to owe more money on that derivative contract.
3 Which of the following best describes a financial risk?
A The risk of an increase in interest rates.
B The risk that regulations will make a transaction illegal.
C The risk of an individual trading without limits or controls.
4 Which of the following is not an example of model risk?
A Assuming the tails of a returns distribution are thin when they are, in 
fact, fat.
B Using standard deviation to measure risk when the returns distribu -

tion is asymmetric.
C Using the one-  year risk-  free rate to discount the face value of a one-  
year government bond.
5 Which of the following is the risk that arises when it becomes difficult to 
sell a security in a highly stressed market?
A Liquidity risk
B Systemic risk
C Wrong-  way risk
6 The risks that individuals face based on mortality create which of the 
following problems?
A The risk of loss of income to their families.

Identification of Risks 433
B Covariance risk associated with their human capital and their invest -
ment portfolios.
C The interacting effects of solvency risk and the risk of being taken 
advantage of by an unscrupulous financial adviser.
C is correct. Operational risk is the only risk listed that is considered non-  
financial, even though it may have financial consequences. Credit and market 
risks derive from the possibility of default and market movements, respectively, 
and along with liquidity risk, are considered financial risks.
C is correct. Although most risks are likely to be interconnected in some way, 
in some cases the risks an entity is exposed to will interact  in such a way that 
a loss (or gain) in one exposure will lead directly to a loss in a different expo -
sure as well, such as with many counterparty contracts. Conditions in A and 
B are much more directly linked in that market participants fully expect what

follows—for example, in B, an outbreak of war in one region of the world could 
well cause widespread uncertainty; a flight to quality, such as to government-  
backed securities; and a widening in spreads for credit-  risky securities. In C, in 
contrast, the reduction in creditworthiness following the market decline may 
be expected, but owing more money on an already existing contract as a result 
comes from the interaction of risks.
A is correct because this risk arises from the financial markets.
C is correct. The risk-  free rate is generally the appropriate rate to use in dis -
counting government bonds. Although government bonds are generally default 
free, their returns are certainly risky. Assuming a returns distribution has thin 
tails when it does not and assuming symmetry in an asymmetric distribution 
are both forms of model risk.
A is correct. Securities vary highly in how liquid they are. Those with low liquidity

are those for which either the number of agents willing to invest or the amount 
of capital these agents are willing to invest is limited. When markets are stressed, 
these limited number of investors or small amount of capital dry up, leading to 
the inability to sell the security at any price the seller feels is reasonable. Systemic 
risk is the risk of failure of the entire financial system and a much broader risk 
than liquidity risk. Wrong-  way risk is the extent to which one’s exposure to a 
counterparty is positively related to the counterparty’s credit risk.
A is correct. The uncertainty about death creates two risks: mortality risk and 
longevity risk. The mortality risk (risk of dying relatively young) is manifested 
by a termination of the income stream generated by the person. In contrast, 
longevity risk is the risk of outliving one’s financial resources.

Reading 42 ■ Risk Management: An Introduction 434
MEASURING AND MODIFYING RISKS
The core element of risk management is the measurement and modification of risk. 
One cannot modify risk without measuring it. The primary purpose of measuring risk 
is to determine whether the risk being taken, or being considered, is consistent with 
the pre-  defined risk tolerance. To understand how risk is measured, it is important 
to understand the basic elements that drive risk.
5.1 Drivers
This section illustrates the origins of risk. Risk is a part of life itself. None of us knows 
from one day to the next everything that will happen to us in the next 24 hours, let 
alone over a longer period. We may get a phone call that a relative is extremely sick, 
or we may be contacted by a head-  hunter about an attractive job possibility. We may 
learn that we are going to be given an award from a prestigious organization, or we 
may find that our identity has been stolen. All of us can almost surely name something

that happened the previous day that was not anticipated. Most of these happenings 
are minor and often quickly forgotten. Others are serious. Some are good. Some are 
bad. Some are unpredictable outcomes of known events, such as whether we get an 
offer following a job interview or whether a medical test reveals that we are healthy 
or ill. Some events are completely unanticipated, such as getting a phone call from an 
old friend we have not talked to in many years or having a flat tire on the drive home. 
Fortunately, the vast majority of risks in life are minor. The ones that are not minor, 
however, have the potential to be highly unpredictable and financially, and sometimes 
physically and emotionally, quite costly.
In a conceptual sense, financial risks are no different from the other risks we face 
in life. All risks arise from the fact that the future is unknown. Financial risks largely 
emanate from economic risks, and economic risks emanate from the uncertainties 
of life.

of life.
Financial markets generate prices that fluctuate as investors absorb information 
about the global and domestic state of the economy, the company’s industry, and the 
idiosyncratic characteristics of the company itself. Global and domestic macroeco -
nomies are driven by the companies that operate within them, but much of the tone 
as well as the ground rules are set by governments and quasi-  governmental agencies, 
such as central banks. Taxes, regulations, laws, and monetary and fiscal policy establish 
a legal and economic environment and a set of ground rules that greatly affect the 
degree and quality of economic activity that takes place. Attempts by governments 
and central banks of different countries to coordinate economic policies can lead to 
some degrees of success if harmonized, but if not, they can create an environment in 
which companies engage in practices designed to seek favorable treatment in some 
countries and avoid unfavorable treatment in others.26

All economies, in turn, are composed of industries. Government policies also 
affect industries, in some cases encouraging economic activity in some industries 
while discouraging it in others. Some industries are stable, weathering macroeconomic 
storms quite well, whereas others are highly cyclical.5
26 This practice is sometimes called regulatory arbitrage. The policies of certain countries can be more 
conducive to establishing operations. Examples are the flow of money into countries whose banking laws 
are less restrictive and more conducive to secrecy and incorporation in or moving a company to a country 
with lighter regulations or more favorable tax treatment.

Measuring and Modifying Risks 435
The uncertainties of global and domestic macroeconomic and central bank policies 
create risks for economies and industries that we often treat as systematic. Seemingly 
minor events, such as filling the position of central bank chairperson, are often viewed 
by investors as major events, signaling possibly a change in policy that can greatly 
affect the macroeconomy and possibly certain industries.
Moving down to a more fundamental level, investors face the unsystematic or 
idiosyncratic risks of individual companies. Modern investment analysis prescribes 
that diversified portfolios bear no unsystematic risk. We are then led to believe that 
unsystematic risk does not matter in a well-  diversified portfolio. But unsystematic 
risk does matter to the management of a company. It also matters to poorly diver -
sified investors. And it certainly matters to the financial analysts who cover specific

companies. And what would appear to be unsystematic risk can oftentimes actually 
be systematic. For example, poor credit risk management by a major bank can turn 
into a global financial crisis if that bank is “too big to fail. ”
In sum, the basic drivers of risk arise from global and domestic macroeconomies, 
industries, and individual companies. Risk management can control some of this risk, 
but it cannot control all of it. For example, the risk manager of a company may be able 
to reduce the likelihood that his company will default, but he cannot control move -
ments in interest rates. For the latter risk, he must accept that interest rate volatility 
is a given and that he can only position the company to be able to ensure that its risk 
exposure is aligned with its objective and risk tolerance. In order to do so, he must 
first be able to measure the risk.
5.2 Metrics
The notion of metrics in the context of risk refers to the quantitative measures of risk

exposure. The most basic metric associated with risk is probability. Probability is a 
measure of the relative frequency with which one would expect an outcome, series 
of outcomes, or range of outcomes to occur. One can speak about the probability of 
rolling a six in one roll of a die as 1/6, the chance of rain in the next 24 hours as 20%, 
or the odds of a central bank taking actions to increase interest rates of 50%. These 
are all probabilities, differing in concept by the fact that the die roll is associated 
with an objective probability measure, whereas the other two examples are subjective 
probabilities. It is important to note that probability, in and of itself, is not a sufficient 
metric of risk. A chance of financial loss of 25% does not tell us everything we need 
to know. There are other measures of risk that incorporate probability but give us 
more information.
The standard deviation is a measure of the dispersion in a probability distribution.

Although there is a formal mathematical definition of standard deviation, at this point 
we need only understand the conceptual definition. Standard deviation measures a 
range over which a certain percentage of the outcomes would be expected to occur. 
For example, in a normal distribution, about 68% of the time the outcomes will lie 
within plus or minus one standard deviation of the expected value. Two standard 
deviations in both directions would cover about 95% of the outcomes, whereas three 
would encompass 99% of the outcomes. Although standard deviation, or volatility, 
is widely used in the financial world, it does have significant limitations. In partic -
ular, standard deviation may not be an appropriate measure of risk for non-  normal 
distributions. Standard deviation may not exist for return distributions with fat tails.
Moreover, according to modern portfolio theory, the risk captured by an asset’s

standard deviation overstates the risk of that asset’s returns in the context of a diver -
sified portfolio. Investors can easily diversify their holdings, thereby eliminating a 
portion of the risk in their portfolios by diversifying away the security-  specific risk. 
As a result, most financial valuation theories assert that the ability of investors to 
eliminate security-  specific risk, or non-  systematic risk, means that investors should

Reading 42 ■ Risk Management: An Introduction 436
not expect to earn a premium to compensate them for the assumption of this risk. 
As a consequence, the risk of a security may be better measured by its beta , a mea -
sure of the sensitivity of a security’s returns to the returns on the market portfolio. 
Beta measures relative risk, meaning how much market risk an asset contributes to 
a well-  diversified portfolio.27
Beta describes risk well for a portfolio of equities, but other sources of risk may 
require other descriptive risk metrics. The risk associated with derivatives is one 
example of this. Although derivatives are widely used to manage risk, they do so by 
assuming other risks. Even if the derivative is being used to establish a hedge of an 
existing exposure to risk, it would still result in the assumption of additional risk 
because the assumed risk is being used to offset an existing risk. For example, if one

purchases a call option denominated in euros to buy Russian rubles, one would be 
assuming the risk of the ruble/euro exchange rate. Because most derivatives exposures 
are highly leveraged, it is critical that the risk of derivatives be properly measured. 
There are several specialized measures of derivatives risk.
The sensitivity of the derivative price to a small change in the value of the under -
lying asset is called the delta . It is perhaps the most important measure of derivatives 
risk. Yet delta is limited to capturing only small changes in the value of the underlying. 
Large changes are captured by the concept of gamma . Whereas delta is a first-  order 
risk, gamma is considered a second-  order risk because it reflects the risk of changes 
in delta.28 Some derivatives, such as options, are also sensitive to changes in the 
volatility of the underlying. This risk is captured by a concept called vega , which is a

first-  order measure of the change in the derivative price for a change in the volatility 
of the underlying. Derivatives are also sensitive to changes in interest rates, which 
are reflected in a measure called rho. Most options have relatively low sensitivity to 
interest rates.29 These, and other mathematically derived derivatives metrics, are 
collectively referred to as “the Greeks. ”
Other asset classes may have their own special metrics to describe risk. One 
well-  known example, duration , is a measure of the interest rate sensitivity of a fixed-  
income instrument. Analogous to delta, it is a first-  order risk. The wide variety of 
financial instrument types and asset classes leads to a proliferation of terminology 
and risk measures, with most of them having no meaning outside their asset class. 
As financial organizations and asset risk modeling became more sophisticated and 
computer power increased, an approach was needed to measure and describe financial

risk across the broad spectrum of asset classes. Spurred by the onset of global bank 
capital regulation, this led to the development of value at risk.
Value at risk  or VaR is a measure of the size of the tail of the distribution of profits 
on a portfolio or for an entity. A VaR measure contains three elements: an amount 
stated in units of currency, a time period, and a probability. For example, assume a 
27 Earlier we discussed the fact that unsystematic risk matters to some parties. Here we seem to be saying 
that it should not matter to anyone. Capital market models almost always assume that investors can diversify 
quite easily and, as a result, they should not expect to earn a premium for bearing diversifiable risk. This 
assumption does not mean that everyone’s wealth is well-  diversified. Investors who do not diversify prob -
ably cannot expect to earn a return for bearing diversifiable risk, but it does not mean that these investors

should not care about measuring the risk they choose to assume by not diversifying.
28 The notion of a first-  order risk versus a second-  order risk can be seen by considering the following. 
Suppose A affects B and B, in turn, affects C. A does not affect C directly but does so only indirectly. A 
is a first-  order risk for B and a second-  order risk for C. In the case of options, small market movements 
affect an option price through the option’s delta. As long as the movements are small, the delta is relatively 
stable. If the movements are large, the delta itself will move, creating gamma risk that arises as a result 
of the non-  linear valuation function of the option. Of course, it is natural to wonder what it means to say 
that a movement passes from the notion of “small” to the notion of “large. ” Unfortunately, the passage from 
small to large does not cross an identifiable border.

29 Options on interest rates, however, have a high sensitivity to interest rates, but only because interest 
rates are the underlying, and thus, the source of market risk.

Measuring and Modifying Risks 437
London bank determines that its VaR is £3 million at 5% for one day. This statement 
means that the bank expects to lose a minimum of £3 million in one day 5% of the 
time. A critical, and often overlooked word, is minimum . In this example, the bank 
expects that its losses will be at least £3 million in one day with 5% probability. In a 
VaR measure, there is no ultimate maximum that one can state. VaR is thus a min -
imum extreme loss metric. With a probability of 5% and a measurement period of 
one day, we can interpret the bank’s VaR as expecting a minimum loss of £3 million 
once every 20 business days. VaR can also be used to measure credit losses, although 
the construction of the measure is considerably more difficult given the extreme 
asymmetry of the risk.
VaR is a simple but controversial measure. There are several ways to estimate VaR, 
each of which has its own advantages and disadvantages. The different measures can

lead to highly diverse estimates. Moreover, VaR is subject to the same model risk as 
derivative pricing models. VaR is based on a particular assumption about the probability 
distribution of returns or profits. If that assumption is incorrect, the VaR estimate will 
be incorrect. VaR also requires certain inputs. If those inputs are incorrect, the VaR 
estimate will be incorrect. Many critics of VaR have argued that naive users of VaR 
can be lulled into a false sense of security. A presumably tolerable VaR can give the 
illusion that the risk is under control, when in fact, it is not. Yet, VaR is accepted as 
a risk measure by most banking regulators and is approved for disclosure purposes 
in typical accounting standards. As with any risk measure, one should supplement it 
with other measures.
As emphasized earlier, VaR does not tell the maximum loss. The maximum loss is 
the entire equity of an organization or the entire value of a portfolio, but the statistics

used to estimate VaR can be used to gauge average extreme losses. Conditional VaR 
or CVaR  is a common tail loss measure, defined as the weighted average of all loss 
outcomes in the statistical distribution that exceed the VaR loss. Another tail risk 
metric in the credit risk space that is analogous to CVaR is expected loss given default, 
which answers the question for a debt security, “If the underlying company or asset 
defaults, how much do we lose on average?”
VaR focuses on the left tail of the distribution and purports to tell us the expected 
frequency of extreme negative returns, but it can understate the actual risk. For 
example, the normal distribution gives us a well-  defined measure of extreme negative 
returns, which are balanced by extreme positive returns. Yet, actual historical return 
distributions have shown that there are more extreme negative returns than would be 
expected under the normal distribution. We previously described this concern in the

form of tail risk. In response to this concern, statisticians have developed a branch 
of study that focuses primarily on extreme outcomes, which is called extreme value 
theory , and leads to measures of the statistical characteristics of outcomes that occur 
in the tails of the distribution. There are mathematical rules that define the statistical 
properties of such large outcomes, and these rules have been widely used for years 
in the insurance business. In the past 20 years or so, risk managers have taken to 
using them to help gauge the likelihood of outcomes that exceed those that would 
normally be expected.
Two measures in particular that are often used to complement VaR are scenario 
analysis  and stress testing . These are common sense approaches that ask “If this 
happens, then how are we affected?” Scenario analysis can be thought of as a package 
of stress tests, usually with some common underlying theme. A scenario defines a set

of conditions or market movements that could occur and would put some pressure 
on a portfolio. An example might be a sharp increase in interest rates coupled with 
a significant decline in the value of a currency. The portfolio is then evaluated to 
determine its expected loss under these scenarios. A different means of posing a sce -
nario analysis is stress testing, which is done by proposing specific asset price moves 
generally involving extremely large and high pressure scenarios that would occur only

Reading 42 ■ Risk Management: An Introduction 438
rarely but would have the potential for destabilizing the entire organization. The US 
Federal Reserve and other central banks have begun requiring major banks to stress 
test their portfolios. Although scenario analysis and stress testing can provide some 
information, they are, as noted previously for other measures, subject to model risk.
Of course, the measures just mentioned focus primarily on market risk. Credit 
risk, which is covered in more detail in readings on fixed-  income analysis, has long 
relied heavily on the credit ratings provided by private companies, such as Moody’s 
Analytics, Standard & Poor’s, and Fitch Ratings. In effect, a large part of credit analysis 
for many lenders has been outsourced since the early part of the 20th century. Most 
lenders, however, do not rely exclusively on these rating companies. They do their 
own analysis, which focuses on the creditor’s liquidity, profitability, and leverage.

Liquidity measures, such as the current ratio, may indicate how well a borrower can 
cover short-  term obligations. Solvency ratios, such as cash flow coverage or interest 
coverage, may reveal whether a borrower generates enough cash or earnings to make its 
promised interest payments. Profitability measures, such as return on assets, estimate 
whether a company is sufficiently profitable so that it can easily accommodate debt. 
Leverage measures, such as the ratio of debt to total assets, reflect whether a company 
has sufficient equity capital in relation to its debt to absorb losses and negative cash 
flows without defaulting. Credit analysis also examines the strength and cyclicality 
of the macroeconomy and the company’s industry. Other widely used measures of 
credit risk include credit VaR, probability of default, expected loss given default, and 
the probability of a credit rating change.
One of the problems of credit risk measurement is that credit events, such as a

ratings downgrade or a default, are relatively rare for a particular entity. Certainly in 
the aggregate there are many credit losses, but very few companies that default have 
a history of defaulting.30 Without a history to go by, estimating the likelihood of an 
event that has never actually occurred is extremely difficult. Imagine the challenge 
of assigning a default probability to Lehman Brothers in 2007. It had been in oper -
ation since 1850 and had never defaulted. Yet in 2008, Lehman Brothers, one of the 
most successful financial companies of all time, filed for bankruptcy. Because of the 
infrequency of default, risk managers normally attempt to assess default probability 
by aggregating companies with similar characteristics.31
Another useful source of information for risk managers about these rare events 
is the ex ante  risk cost that is implied by the market pricing of derivatives. A credit 
default swap (CDS) on an issuing company has an observable price that acts as a signal

to a bondholder of the risk cost of a default.32 Put options, exotic options, insurance 
contracts, and other financial instruments may contain valuable signals of the cost of 
rare adverse events, or at least the price of hedging them.
Operational risk is one of the most difficult risks to measure. Consider the oper -
ational risk event reported in 2014 in which hackers broke into Home Depot’s credit 
card data base. Assessing the likelihood of such an event and estimating the potential 
losses would be almost impossible. The threat of litigation alone for years afterward 
30 Hostess, Frontier Airlines, and Aloha Airlines have all filed for bankruptcy twice, and all are still oper -
ating today. Filing for bankruptcy, of course, does not necessarily imply default. Liberal bankruptcy laws 
in the United States have made bankruptcy filings more or less one of many common corporate strategies. 
Nonetheless, very few companies have defaulted or filed for bankruptcy more than once. Even two obser -

vations of bankruptcy for one firm is a very unreliable sample.
31 In some sense, aggregating companies with similar characteristics is what credit ratings do. Companies 
rated BAA/Baa+ can be quite diverse but all are considered similar with respect to their ability to pay 
their debts.
32 A credit default swap is a derivative contract between a credit protection buyer and a credit protection 
seller in which the buyer makes a series of payments to the seller in exchange for a promise of compen -
sation for losses resulting from a pre-  defined credit event, such as a default. If a bond issuer is perceived 
by market participants to be in a weakening credit position (at higher risk of default), its yield spread will 
widen. This risk is reflected quickly in the liquid CDS market.

Measuring and Modifying Risks 439
is difficult to quantify. As with credit risk, significant operational risk events are rare 
but usually quite costly if they do occur. Hence, attempts to quantify the risk usually 
involve a third party aggregating operational risk events across numerous companies 
and publishing the statistics.
As mentioned, there are numerous other risks that would likewise be difficult to 
measure. For example, there is always the possibility of changes in accounting rules, 
laws, tax rates, and regulatory requirements that can result in significant costs as 
companies adapt their policies and actions from one regulatory environment to a new 
one. How would one measure such risks? Moreover, the time period spanned by these 
risks is extremely long, and in fact, theoretically infinite. Changes in these rules and 
laws are often motivated by politics. How does one quantify such risks when there

are no real numeric measures? Analysis invariably reverts to subjective evaluation of 
the likelihood of such threats and their potential losses.
As we have described, many risks are measurable, at least on an ex post  basis. 
Market-  related risks are blessed with large quantities of data, so they are relatively 
measurable. Credit, operational, and other risks are somewhat rare events. Although 
it is probably a good thing that such events are indeed rare, their infrequency makes 
measurement more difficult. Nonetheless, virtually any risk manager will attempt to 
obtain at least a subjective sense of the expected frequency, likelihood, and cost of 
these events. With either objective or subjective measurements in mind, risk managers 
can then proceed to modify these risks accordingly.
5.3 Methods of Risk Modification
The notion of risk modification presumes that an analysis has been conducted in the 
risk governance stage that defines how much risk is acceptable. Coupled with mea -

surements of the actual risk, as discussed in the previous section, the risk manager 
then proceeds to align the actual risk with the acceptable risk.
It is important to understand, however, that risk modification is not strictly risk 
reduction. For example, a portfolio with the strategic objective of maintaining a 
50/50 split between equity and cash will naturally find that in a market in which cash 
outperforms equity, the split between equity and cash will tilt toward cash. Thus, 
the portfolio becomes less risky. Beyond a certain point, the risk of the portfolio is 
unacceptably low given the return target. Thus, risk modification would take the form 
of rebalancing by increasing the risk. For the most part, however, risk management 
focuses more on reducing the risk. Risk reduction is commonly referred to as hedging. 
A hedge is a transaction put in place to reduce risk. Some hedges are designed to 
lead to the ultimate in risk reduction—the complete elimination of risk. Others are

simply designed to lower the risk to an acceptable level.33 For some companies, risk 
management is primarily concerned with keeping the organization solvent. Regardless 
of the focus, much of what is done to manage risk is the same. In this section, we will 
examine four broad categories of risk modification: risk prevention and avoidance, 
risk acceptance, risk transfer, and risk shifting.
5.3.1  Risk Prevention and Avoidance
One method of managing risk is taking steps to avoid it altogether, but avoiding risk 
may not be as simple as it appears. It is difficult to completely avoid risk, but more 
importantly, it is unclear that every risk should be completely avoided. Consider, for 
example, the threat of a terrorist getting on a plane with a weapon. It might well be 
33 For example, in the case of the portfolio with a strategic target of 50/50 equity and cash, if equity 
outperforms cash, the portfolio will tilt toward equity. At some point, a risk-  reducing strategy would then

be in order. This type of hedge would reduce the risk but not eliminate it.

Reading 42 ■ Risk Management: An Introduction 440
possible to completely eliminate this risk. We could subject ourselves to extensive 
background checks, provide fingerprint and DNA samples, and permit complete 
searches of our bodies and baggage at airports. Clearly, there is a very high cost to 
eliminating this risk in terms of money, time, and freedom. Instead we choose a trade-  off 
between cost and benefits. The actual trade-  off may be subject to debate because risk 
assessment and risk management are subject to variation from one person to another.
We could nearly eliminate the risk of being injured or killed in an airplane crash if 
we choose to never fly.34 Like any risk-  avoidance strategy, however, there would more 
than likely be a trade-  off in terms of the loss of the benefits provided by the activity. 
We could try to protect our children from all harm, but that may come at the expense 
of preparing them poorly for adult life. We could invest our entire retirement savings

in cash, but would most likely give up protection against inflation and lose out on 
the opportunity to benefit from long-  term economic growth and the performance of 
investable assets that benefit from that growth.
Insurance companies rely heavily on the techniques of risk prevention and avoid -
ance. An automobile insurance company would prefer that their policyholders never 
drive their cars. Although it cannot prohibit them from doing so, it can reward them 
with lower premiums if they drive less and have safe driving records. A life insurance 
company would prefer that their policyholders do not smoke, and it can reward non-  
smokers with lower rates.
Nearly every risk we take has an upside, at least as perceived by the person taking 
the risk. Some counterexamples might seem to belie this point, but not if viewed from 
the point of view of the risk taker. One could argue that there are no benefits from 
smoking, but people who smoke may have the opinion that the pleasure they receive

exceeds the costs. Casino gambling incurs the risk of significant financial loss and 
addiction, but it is risk that is acceptable to the consumers who incur it relative to the 
perceived benefits they receive. The risks of extreme sports, such as skydiving, would 
seem to be exceeded by the benefits obtained by participants, and yet participants 
engage in them with apparently much enjoyment. People undertake all types of risky 
behaviors because they obtain commensurate benefits. These examples are simply 
cases in which the decision maker chooses to bear a certain degree of risk. They are 
conceptually the same as an investor who chooses to accept a relatively high degree 
of risk. Likewise, those who live their lives engaging in very few risky activities are 
conceptually the same as the investor who keeps only a modest exposure to risky assets.
In organizations, the decision to avoid risk is generally made at the governance

level as a part of setting the risk tolerance. Boards will often decide that there are some 
business or investment activities simply not worth pursuing based on either the goals 
of the organization or the perceived risk–return trade-  off. These are strategic decisions. 
Boards may exclude some areas or activities to allow management to focus on choos -
ing risks in other areas where they presumably have a better chance of adding value.
We recap this section by noting that risk prevention and avoidance is simply an 
element of the decision of how much risk to accept, given the trade-  off between the 
risk of loss and the benefit of gain. This could be a direct benefit or an indirect benefit 
of avoiding or eliminating a risk. Most decisions in life involve a trade-  off between 
benefits and costs, neither of which is necessarily easy to measure. Thus, risk man -
agement is an ongoing process of fine-  tuning exposure to achieve the level of risk that 
is desired in relation to the benefits.

In the event that the risk measurement process shows that the risk exceeds the 
acceptable level, there are three approaches to managing the risk: self-  insuring, risk 
transfer, and risk shifting.
34 Of course, it would still be possible to be hit by an airplane when it comes down, but that risk is 
extremely small.

Measuring and Modifying Risks 441
5.3.2  Risk Acceptance: Self-  Insurance and Diversification
In many cases, from both a risk tolerance and a strategic standpoint, it makes sense to 
keep a risk exposure—but to do so in the most efficient manner possible. Self-  insurance 
is the notion of bearing a risk that is considered undesirable but too costly to elimi -
nate by external means. In some cases, self-  insuring means simply to bear the risk. In 
other cases, it may involve the establishment of a reserve to cover losses. Choosing to 
not have health insurance can be an optimal choice for some young, healthy adults 
without responsibility for children. Setting aside some money to cover potential health 
costs completes the picture of an individual who completely self-  insures. Similarly, a 
young healthy individual who does not buy life insurance but engages in a systematic, 
well-  conceived savings and investment plan is engaging in self-  insurance.

One must be careful with this approach, however, because there is a fine line 
between self-  insurance and denial. To the extent that self-  insurance results in risks 
that are completely in line with the enterprise’s risk tolerance, it would be an example 
of good governance. But if there is a risk that is outside the enterprise’s risk tolerance, 
and management decides to bear that risk anyway, saying it is self-  insuring, manage -
ment is basically ignoring that risk, disregarding and violating its risk tolerance, and 
practicing bad risk governance. For example, an investment management firm, via its 
risk tolerance decision, may decide that it cannot bear any investment loss exceeding 
€1 billion and may apply a variety of risk management tools to limit its market and 
credit risk accordingly. But suppose that the firm makes no move to limit or insure 
its risks from fraud or a rogue trader on the grounds that it is “self-  insuring” this risk,

which could result in a loss as high as €3 billion. By leaving itself open to a loss that far 
exceeds its stated risk tolerance, management is violating the firm’s risk governance.
From the perspective of a business organization, self-  insurance is obtained by setting 
aside sufficient capital to cover losses. The banking industry is a classic example of 
self-  insurance. Although in many countries government insurance may protect depos -
itors, banks self-  insure to some extent by maintaining capital and loan loss reserves.
Another form of accepting risk, but doing so in the most efficient manner possible, 
is diversification. Technically, it is a risk-  mitigation technique. But diversification and 
“the efficient frontier” are so central to modern portfolio analysis that capturing the full 
benefits of diversification seems the obvious thing for all organizations to pursue—a 
starting point at which other risk modification could be appended. Although diversi -

fication is one form of risk management, it is usually not effective if used in isolation.
In the next two subsections, we discuss how undesired risk can be modified or 
eliminated by selling the risk to another party. We make two subtle classifications of 
these methods: risk transfer and risk shifting.
5.3.3  Risk Transfer
Risk transfer  is the process of passing on a risk to another party, often, but not always, 
in the form of an insurance policy. Insurance is a legal contract in which one party, 
the insurer, agrees to cover some percentage of a loss incurred by another party, the 
insured, from a specific event in return for the payment of a premium by the insured. 
Insurance as a method of risk modification has been in existence for very long time, 
and in fact, is even mentioned in the Code of Hammurabi almost 4,000 years ago. 
Insurance has been widely used in the commercial shipping and farming industries 
going back hundreds of years. Insurance is almost as old as commerce itself.35

35 It is worth noting that the insurance industry has for a long time referred to itself using the term “risk 
management. ” A department of risk management in a large organization is often the group that manages the 
organization’s insurance policies. But since around 1990 or so, the term “risk management” has increasingly 
come to refer to far more than insurance.

Reading 42 ■ Risk Management: An Introduction 442
From the point of view of the insurer, insurance almost always works on the basis 
of diversification or pooling of risks. An insurer attempts to sell many policies with 
risks that have low correlations. The insurer assesses the pooled risks and charges a 
premium that covers the expected aggregate losses and the insurer’s operating costs 
as well as leaves a profit. Insurers need accurate statistics on aggregate risks, but these 
are often not difficult to obtain. These actuarial data are widely available on accidents, 
illnesses, property and casualty damage, and death. In principle, a well-  diversified 
insurer does not care if a single insured party has significantly larger-  than-  average 
claims as long as there is no reason to believe that the claims are correlated. There 
will be other parties that have smaller-  than-  average claims.
Insurers do have to manage their risks carefully. Some risks can be correlated.

In the US Gulf Coast region, property insurance, which includes coverage for loss 
by hurricanes, is typically more expensive than property insurance in other regions. 
Even with a higher premium, an insurer has to avoid providing too much property 
coverage in an area where a systemic event, such as a hurricane, can occur in order 
to diversify its risk exposure.
Although insurers carefully assess their risk and charge premiums that they believe 
accurately reflect expected losses, they nonetheless remain responsible for potentially 
large claims. Insurers also manage their risk by avoiding writing too many policies 
with similar and potentially correlated risks and by selling some of the risk to another 
insurer, a practice known as reinsurance. A company that primarily insures property 
in the US Midwest, which is highly subject to tornado risk, might be willing to accept 
some Gulf Coast hurricane risk for a reasonable premium. Insurers often write pro -

visions into contracts to exclude coverage of special cases. For example, a war might 
nullify insurance coverage in an area. Most insurance policies also contain provisions 
to guard against moral hazards, such as suicide or destroying one’s own property. In 
the last 20 years or so, some insurance companies have issued bonds that permit them 
to legally avoid paying principal and/or interest if insurance claims exceed a certain 
amount. These instruments, known as catastrophe bonds, essentially pass some of 
the insurance risk on to the investors who buy the bonds.
Most insurance policies do not cover all of the risk that is insured. It is common 
for policies to contain a provision known as a deductible. A deductible is a monetary 
amount of the loss that will be covered by the insured before any claims are paid. Thus, 
both the insured and the insurer bear some of the risk, although the insurer usually 
bears the greater amount. Deductibles serve several purposes. Because insurers incur

fixed costs for each claim, deductibles reduce the number of small claims. Deductibles 
also encourage good risk management by the insured parties. Finally, deductibles offer 
the insured the opportunity to combine risk transfer with self-  insurance and thereby 
achieve a potentially better trade-  off of risk and reward.
As noted, the concept of insurance relies on the diversification or pooling of risks. 
In a few cases, however, the risks are not easy to pool. For example, suppose a volatile 
but extremely successful actor is signed to star in a movie. The production company 
knows that it runs the risk that the actor will engage in behavior that damages the 
ability of the company to finish the movie. The number of volatile and extremely suc -
cessful actors for whom policies could be written at the same time is somewhat limited. 
Thus, an insurer would have to bear that risk without the benefit of diversification.

For example, suppose a television network plans to cover the Olympics but is con -
cerned about a possible cancellation or boycott. It might want an insurance policy to 
cover it against loss. Specialized coverage is possible through such companies as Lloyd’s 
of London. The approximately 350-  year old Lloyd’s is famous for covering unusual 
risks. It does so by organizing groups of investors who are willing to bear a risk for 
a premium. These groups, called syndicates, are subject to the full extent of losses. 
In many cases, investors in these syndicates have been required to pay substantial

Measuring and Modifying Risks 443
amounts of money to cover losses.36 These examples illustrate how syndicates work. 
Although there is only one Olympics to insure, there may also be only one actor to 
insure. Because the two risks are uncorrelated, a company could write policies on both 
risks and would achieve some diversification. Moreover, there are other unusual risks 
that can be covered such that the aggregate pool would represent a highly diverse set 
of risks that have low correlations.37
A very slight variation of insurance is a surety bond. With a surety bond, an insurer 
promises to pay an insured a certain amount of money if a third party fails to fulfill 
its obligation. For example, if a party engages the services of another party, the first 
party is covered if the party obligated to provide the service fails to perform to a sat -
isfactory degree. Surety bonds are widely used in commercial activity when one party

bears the risk of the potentially high cost of non-  performance by another party. A 
slight variation of a surety bond is a fidelity bond, which is often used to cover against 
losses that result from employee dishonesty. Bonds of this type work very similarly to 
insurance and rely on the pooling of uncorrelated risks.38 Other similar arrangements 
include indemnity clauses and hold harmless arrangements, such as when two parties 
sign a contract and one party agrees to hold the other harmless and/or indemnify the 
other in the event of loss.
The use of insurance by so many as a risk management tool suggests that the cost 
of risk exceeds the actuarial cost to many individuals and enterprises. Ex ante  consid -
eration of the cost of a risk in terms of the entity’s value or utility ties risk mitigation 
back to the risk tolerance decision and the most fundamental governance decisions 
on which value-  added strategies to pursue. As an alternative to ignoring  the cost of

risk, the impact on enterprise value should be quite positive.
5.3.4  Risk Shifting
Whereas risk transfer refers to actions taken that pass the risk on to other parties, risk 
shifting  refers to actions that change the distribution of risk outcomes. Risk transfer is 
often associated with insurance, whereas risk shifting generally involves derivatives as 
the risk modification vehicle. Although insurance is a form of risk management based 
on the pooling or diversification of risks, risk shifting diverts some portion of the risk 
distribution to another market participant who either bears the risk or intermediates 
that risk by moving it to yet another party. The organization may want to adjust its 
probability distribution of returns, essentially adjusting the payoff diagram of its risk 
exposures. An example is a company that is willing to make slightly less profit than it 
otherwise would if the stock market is up to prevent it from losing too much money

if the stock market is down, for example, more than 20% next year. It is adjusting its 
potential economic outcomes by shifting the probability distribution of its profits 
conditional on market performance. Risk shifting represents the bulk of hedging and 
is the most common form of risk modification for financial organizations.
The principal device through which risk shifting is performed is a derivative. We 
briefly mentioned derivatives earlier in this reading. By definition, a derivative is a 
financial instrument that derives its price from the price of an underlying asset or 
rate. Because the price of the underlying and the price of the derivative are so closely 
related, derivatives can provide essentially the same exposure as the underlying but 
36 NBC insured the 1980 Summer Olympics in Moscow through Lloyd’s of London to the extent that if a 
US boycott occurred, Lloyd’s would pay NBC for losses that it incurred by prepaying the Soviet Union for

broadcasting rights. The United States did boycott the Olympics and NBC collected on its policy.
37 There are insurance policies to cover singers’ voices, athletes’ bodies, and even such bizarre possibilities 
as alien abductions and risks from paranormal activity.
38 In the context of surety and fidelity bonds, the word “bond” does not mean a debt obligation issued 
by one party, the borrower, and bought by another, the lender. In this context, the word refers to assuring 
one party that it bears no risk for the actions of a specific other party.

Reading 42 ■ Risk Management: An Introduction 444
can do so at lower cost and capital requirements. As such, derivatives permit the effi -
cient shifting of risk across the probability distribution and from one party to another. 
One can hold the underlying and take an offsetting position in the derivative or vice 
versa. Whereas insurance can be designed to perform similarly, insurance functions 
primarily through the pooling of diverse risks. With derivatives, risks are shifted across 
probability distributions or payoffs and across parties, to leave specific outcomes of 
the conditional probability distribution with the parties most willing to bear the risk.
There are several types of derivatives, and the manner in which they provide risk 
shifting varies by type. Derivatives are classified into two categories: forward com -
mitments or contingent claims. Forward commitments are agreements that obligate 
two parties to undertake a transaction at a future date at a price or rate agreed on

when the commitment is made. Forward commitments include such instruments 
as forward contracts, futures contracts, and swaps. Forward commitments can be 
used to lock in a future interest rate for a borrower or lender, the purchase or sale 
price of an asset, or an exchange rate for a currency. Parties who engage in forward 
commitments do not pay any money at the initiation of the contract. In lieu of any 
up- front payment from one party to the other, the two parties agree on the terms of 
the transaction that will be consummated at the end of the contract. Depending on 
movements in the price or rate of the underlying, one party will ultimately gain from 
the transaction while the other will lose or, in the less likely case, both parties could 
breakeven. For example, a corporate treasurer can use a forward contract to lock in 
the rate at which a foreign cash flow will be converted into the company’s domestic

currency. Regardless of movements in the exchange rate during the life of the contract, 
the foreign cash flow will convert to the domestic currency at a rate that is locked in 
when the contract is initiated. On the opposite side of the transaction, the party can 
be a speculator who simply bears the risk or it can be a dealer who intermediates the 
risk between the hedger and the speculator. We will discuss dealers in more detail in 
a few paragraphs.
The other type of derivative is a contingent claim, which is commonly known 
as an option. An option is a contract between two parties that gives one party the 
right to buy or sell an underlying asset or to pay or receive a known underlying rate. 
An option takes the form of either a call option, which provides the right to buy the 
underlying or to pay a known rate, or a put option, which provides the right to sell 
the underlying or to receive a known rate.
With a forward commitment, both parties are mutually obligated to each other.

Because an option grants the right, but not the obligation, to one party, that party has 
an advantage over the other. Consequently, that party, the buyer of the option, must 
pay cash, called the premium, to the seller of the option at the start of the contract. 
Once the premium is paid, the option buyer has no further obligation. He can either 
exercise the option or he can let the option expire unexercised. In the latter case, the 
option buyer incurs a loss equal to the premium. If the option is a call and it is exer -
cised, the buyer pays the fixed price or rate and receives the underlying. If the option 
is a put and it is exercised, the buyer receives the fixed price or rate and delivers the 
underlying.39 If the buyer of the option does exercise it, he may achieve a gain that 
exceeds the premium paid but the gain could also be less than the premium paid, 
thereby resulting in a net overall loss. An option buyer could be using the option to

speculate on an upward move in the underlying if a call or downward move if a put. 
Alternatively, the option buyer could be hedging. In the example used earlier for for -
ward commitments, the corporate treasurer anticipating an inflow of cash in a foreign 
currency could buy a put option to sell that currency, thereby converting it into his 
39 Instead of one party delivering the underlying, some options call for settlement in cash of an equivalent 
amount. Some forward commitments also settle in cash.

Measuring and Modifying Risks 445
domestic cash flow at a known fixed rate. The option gives the treasurer the flexibility 
to not exercise it if the underlying currency rises in value. This flexibility comes at 
the cost of having to pay a premium at the start of the transaction, thus shifting the 
financial outcome across the entire probability distribution of that uncertain currency 
rate. In contrast, with the forward contract, the treasurer does not have to pay cash 
at the start but is obligated to convert at the agreed-  upon rate.
Derivatives can be created in public forums, such as on derivatives exchanges, or 
privately between two parties. On derivatives exchanges, there are a large number 
of individual and institutional traders that make markets in derivatives. For private 
derivatives transactions, there is an extensive market of large bank and non-  bank deal -
ers willing to buy and sell derivatives. In both types of markets, these dealers assume

the risk being transferred from parties who originate the transactions. These dealers 
almost always restructure and transfer some portion if not all of the risk by finding 
other parties that are willing to take on that risk. Ultimately, the risk is assumed by 
some party willing to accept the risk, producing an economically efficient outcome 
for all parties.40
5.3.5  How to Choose Which Method for Modifying Risk
Choosing which risk mitigation method to use—risk prevention and avoidance, 
self-  insuring, risk transfer, or risk shifting—is a critical part of the risk management 
process. Fortunately, the methods are not mutually exclusive, and many organizations 
use all methods to some extent. No single method provides a clear-  cut advantage over 
the others. As with all decisions, the trade-  off is one of costs versus benefits that are 
weighed in light of the risk tolerance of the organization or individual.
For example, many companies that have extensive foreign operations and are,

therefore, highly exposed to exchange rate risk, hedge that risk using derivatives. 
Some companies prefer forwards, some prefer swaps, some prefer options, and some 
use multiple instruments. Some companies attempt to hedge currency risk by setting 
up operations in foreign countries rather than manufacturing domestically and ship -
ping the goods to foreign countries.41 Some companies manage their currency risk 
by attempting to balance currency assets and liabilities. Some airlines hedge the risk 
of oil price changes and others do not. Some airlines that do hedge this risk do so to 
a far greater degree than others. Additionally, some prefer the certainty of forwards 
and swaps, whereas others prefer the flexibility of options, even with the up-  front cost 
that options require. Most insurance companies rely on their actuarial knowledge but 
supplement it with proactive measures, such as selling risk to other parties.

To the extent possible, most organizations should avoid risks that provide few 
benefits and potentially extreme costs. Reasonable, low-  cost precautions against 
risks with few benefits should always be taken. Thus, risk prevention and avoidance 
is probably the first choice of measures, especially for risks that lie outside the core 
competencies of the organization and have little reasonable expectation of adding value. 
40 There is a potential exception to this statement. If the corporate treasurer wanting to lay off the foreign 
currency risk could be matched with a counterparty with the exact opposite risk, the ultimate risk could 
be extinguished. For example, suppose the treasurer of a South Korean company anticipates the inflow of 
£150 million in exactly three months and expects on that day to convert that money into Korean won. If 
there were another party who anticipated on that same day that it would take a certain amount of Korean

won and convert it to £150 million, the two parties could offset their risk by trading with each other, a 
process called novation. Of course, finding parties with the exact opposite needs is difficult. Dealers typically 
parcel out risk, sometimes in pieces to various parties. Also, through sophisticated modeling, dealers and 
speculators can offset the risk with similar but not precisely balanced positions.
41 Here is yet another example of the interactions of risks. A decision to manufacture products in a 
foreign country involves trade-  offs between exchange rate risk, political risk, and a variety of other risks 
germane to that country’s economy, not to mention a potentially different degree of operational risk, in 
the pursuit of higher profits.

Reading 42 ■ Risk Management: An Introduction 446
Nonetheless, avoidance may not be the best value for its cost. Moreover, avoiding risk 
may mean avoiding opportunity. Thus, an organization often cannot simply decide 
not to take a risk, at least not for all undesirable risks.
Organizations that have large amounts of free cash flow may choose to self-  insure 
some risks, but few organizations have so much cash that they can afford to self-  insure 
all risks. Some risks can potentially imperil the entire capital base. Most companies 
would, however, prefer to self-  insure to the extent possible because self-  insurance 
reduces the costs associated with external monitoring and gives the organization the 
greatest flexibility. Self-  insurance and avoidance should generally be clearly addressed 
at the governance level and be consistent with stated risk tolerance.
Risk transfer, or the use of insurance, is a widely used risk management tactic, but

it may not be suitable for many types of risks. Some risks simply are not insurable, at 
least not in a cost-  effective way. Insurance works best when risks can be pooled, and 
that is not the case for many types of risks, particularly those that can affect a large 
number of parties at the same time. The use of risk shifting tools, such as derivatives, 
may not be available for all types of risks, thus limiting their use in risk mitigation. 
For financial risks that exceed risk appetite, risk shifting is a very common choice.
The various risk management methods are not equal in terms of the risk reduction 
and the risk profile that remains. For example, contingent claims, such as insurance, 
provide the flexibility in the form of offering opportunity to profit in one direction 
and have a loss reduced in the other, but they require payment of cash up front. In 
contrast, forward commitments lock in an outcome. In other words, they provide little

flexibility, but they require no cash payment up front. The risk profile that exists when 
a contingent claim hedge is put in place differs significantly from the risk profile that 
exists when a forward commitment hedge is placed. This process requires significant 
understanding and discussion at all levels of the organization.
To recap, risk takers should identify risks that offer few rewards in light of poten -
tial costs and avoid those risks when possible. They should self-  insure where it makes 
sense and diversify to the extent possible. They should consider insurance when risks 
can be pooled effectively if the cost of the insurance is less than the expected benefit. 
If derivatives are used, they must consider the trade-  off of locking in outcomes with 
forward commitments versus the flexibility relative to cash cost of contingent claims, 
which can tailor the desired outcomes or payoffs by shifting the risk. Ultimately, the

decision is always one of balancing costs against benefits while producing a risk profile 
that is consistent with the risk management objectives of the organization.
EXAMPLE 4   
Measuring and Modifying Risk
1 From the perspective of an organization, which of the following best 
describes risk drivers?
A The probabilities of adverse events
B The statistical methods that measure risk
C Factors that influence macroeconomies and industries
2 Which of the following concepts directly measures the risk of derivatives?
A Probability
B Delta and gamma
C Beta and standard deviation
3 The best definition of value at risk is:
A the expected loss if a counterparty defaults.

Summary 447
B the maximum loss an organization would expect to incur over a hold -
ing period.
C the minimum loss expected over a holding period a certain percentage 
of the time.
4 Which of the following are methods commonly used to supplement VaR 
to measure the risk of extreme events?
A Standard deviation
B Loss given default
C Scenario analysis and stress testing
5 Which of the following is a true statement about insurable risks?
A Insurable risks are less costly.
B Insurable risks have smaller loss limits.
C Insurable risks are typically diversifiable by the insurer.
C is correct. Risks (and risk drivers) arise from fundamental factors in macro -
economies and industries.
B is correct. Delta and gamma are measures of the movement in an option 
price, given a movement in the underlying. The other answers can reflect some 
elements of derivatives risk, but they are not direct measures of the risk.

C is correct. VaR measures a minimum loss expected over a holding period a 
certain percentage of the time. It is not an expected loss nor does it reflect the 
maximum possible loss, which is the entire equity of the organization.
C is correct. Scenario analysis and stress testing both examine the performance 
of a portfolio subject to extreme events. The other two answers are metrics 
used in portfolio analysis but are not typically associated with extreme events.
C is correct. Insurance works by pooling risks. It is not necessarily less costly 
than derivatives nor does it have lower loss limits.
SUMMARY
Success in business and investing requires the skillful selection and management of 
risks. A well-  developed risk management process ties together an entity’s goals, strategic 
competencies, and tools to create value to help it both thrive and survive. Good risk 
management results in better decision making and a keener assessment of the many

important trade-  offs in business and investing, helping managers maximize value.
■■Risk and risk management are critical to good business and investing. Risk 
management is not only about avoiding risk.

Reading 42 ■ Risk Management: An Introduction 448
■■Taking risk is an active choice by boards and management, investment man -
agers, and individuals. Risks must be understood and carefully chosen and 
managed.
■■Risk exposure is the extent to which an entity’s value may be affected through 
sensitivity to underlying risks.
■■Risk management is a process that defines risk tolerance and measures, moni -
tors, and modifies risks to be in line with that tolerance.
■■A risk management framework is the infrastructure, processes, and analytics 
needed to support effective risk management; it includes risk governance, risk 
identification and measurement, risk infrastructure, risk policies and processes, 
risk mitigation and management, communication, and strategic risk analysis 
and integration.
■■Risk governance is the top-  level foundation for risk management, including risk 
oversight and setting risk tolerance for the organization.

■■Risk identification and measurement is the quantitative and qualitative assess -
ment of all potential sources of risk and the organization’s risk exposures.
■■Risk infrastructure comprises the resources and systems required to track and 
assess the organization’s risk profile.
■■Risk policies and processes are management’s complement to risk governance at 
the operating level.
■■Risk mitigation and management is the active monitoring and adjusting of risk 
exposures, integrating all the other factors of the risk management framework.
■■Communication includes risk reporting and active feedback loops so that the 
risk process improves decision making.
■■Strategic risk analysis and integration involves using these risk tools to rigor -
ously sort out the factors that are and are not adding value as well as incorpo -
rating this analysis into the management decision process, with the intent of 
improving outcomes.
■■Employing a risk management committee, along with a chief risk officer (CRO),

are hallmarks of a strong risk governance framework.
■■Governance and the entire risk process should take an enterprise risk manage -
ment perspective to ensure that the value of the entire enterprise is maximized.
■■Risk tolerance, a key element of good risk governance, delineates which risks 
are acceptable, which are unacceptable, and how much risk the overall organi -
zation can be exposed to.
■■Risk budgeting is any means of allocating investments or assets by their risk 
characteristics.
■■Financial risks are those that arise from activity in the financial markets.
■■Non-  financial risks arise from actions within an entity or from external origins, 
such as the environment, the community, regulators, politicians, suppliers, and 
customers.
■■Financial risks consist of market risk, credit risk, and liquidity risk.
■■Market risk arises from movements in stock prices, interest rates, exchange 
rates, and commodity prices.
■■Credit risk is the risk that a counterparty will not pay an amount owed.

■■Liquidity risk is the risk that, as a result of degradation in market conditions 
or the lack of market participants, one will be unable to sell an asset without 
lowering the price to less than the fundamental value.

Summary 449
■■Non-  financial risks consist of a variety of risks, including settlement risk, oper -
ational risk, legal risk, regulatory risk, accounting risk, tax risk, model risk, tail 
risk, and sovereign or political risk.
■■Operational risk is the risk that arises from within the operations of an organi -
zation and includes both human and system or process errors.
■■Solvency risk is the risk that the entity does not survive or succeed because it 
runs out of cash to meet its financial obligations.
■■Individuals face many of the same organizational risks outlined here but also 
face health risk, mortality or longevity risk, and property and casualty risk.
■■Risks are not necessarily independent because many risks arise as a result of 
other risks; risk interactions can be extremely non-  linear and harmful.
■■Risk drivers are the fundamental global and domestic macroeconomic and 
industry factors that create risk.

■■Common measures of risk include standard deviation or volatility; asset-  specific 
measures, such as beta or duration; derivative measures, such as delta, gamma, 
vega, and rho; and tail measures such as value at risk, CVaR and expected loss 
given default.
■■Risk can be modified by prevention and avoidance, risk transfer (insurance), or 
risk shifting (derivatives).
■■Risk can be mitigated internally through self-  insurance or diversification.
■■The primary determinants of which method is best for modifying risk are the 
benefits weighed against the costs, with consideration for the overall final risk 
profile and adherence to risk governance objectives.

Reading 42 ■ Risk Management: An Introduction 450
1 Risk management in the case of individuals is best described as concerned with:
A hedging risk exposures.
B maximizing utility while bearing a tolerable level of risk.
C maximizing utility while avoiding exposure to undesirable risks.
2 Which of the following may be controlled by an investor?
A Risk
B Raw  returns
C Risk-  adjusted returns
3 The process of risk management includes:
A minimizing risk.
B maximizing returns .
C defining and measuring risks being taken.
4 Risk governance:
A aligns risk management activities with the goals of the overall enterprise.
B defines the qualitative assessment and evaluation of potential sources of risk 
C delegates responsibility for risk management to all levels of the organiza -
tion’s hierarchy.
5 The factors a risk management framework should address include all of the 
following except :
A communications.
B policies and processes.
C names of responsible individuals.

6 Which of the following is the correct sequence of events for risk governance 
and management that focuses on the entire enterprise? Establishing:
A risk tolerance, then risk budgeting, and then risk exposures.
B risk exposures, then risk tolerance, and then risk budgeting.
C risk budgeting, then risk exposures, and then risk tolerance.
7 Which of the following best describes activities that are supported by a risk 
management infrastructure?
A Risk tolerance, budgeting, and reporting
B Risk tolerance, measurement, and monitoring
C Risk identification, measurement, and monitoring
8 Effective risk governance in an enterprise provides guidance on all of the fol -
lowing except :
A unacceptable risks.
B worst losses that may be tolerated.
C specific methods to mitigate risk for each subsidiary in the enterprise .
9 A firm’s risk management committee would be expected to do all of the follow -
ing except :
A approving the governing body’s proposed risk policies.

Practice Problems 451
B deliberating the governing body’s risk policies at the operational level.
C providing top decision-  makers with a forum for considering risk manage -
ment issues.
10 Once an enterprise’s risk tolerance is determined, the role of risk management 
is to:
A analyze risk drivers.
B align risk exposures with risk appetite.
C identify the extent to which the enterprise is willing to fail in meeting its 
11 Which factor should most  affect a company’s ability to tolerate risk?
A A stable market environment
B The beliefs of the individual board members
C The ability to dynamically respond to adverse events
12 Risk budgeting includes all of the following except :
A determining the target return.
B quantifying tolerable risk by specific metrics.
C allocating a portfolio by some risk characteristics of the investments.
13 A benefit of risk budgeting is that it:
A considers risk tradeoffs.
B establishes a firm’s risk tolerance.
C reduces uncertainty facing the firm.

14 Which of the following risks is best described as a financial risk?
A Credit
B Solvency
C Operational
15 Liquidity risk is most  associated with:
A the probability of default.
B a widening bid–ask spread.
C a poorly functioning market.
16 An example of a non-  financial risk is:
A market risk.
B liquidity risk.
C settlement risk.
17 If a company has a one-  day 5% Value at Risk of $1 million, this means:
A 5% of the time the firm is expected to lose at least $1 million in one day.
B 95% of the time the firm is expected to lose at least $1 million in one day.
C 5% of the time the firm is expected to lose no more than $1 million in one 
day.
18 An entity choosing to accept a risk exposure may:
A buy insurance.
B enter into a derivative contract.
C establish a reserve fund to cover losses.
19 The choice of risk-  modification method is based on:
A minimizing risk at the lowest cost.

Reading 42 ■ Risk Management: An Introduction 452
B maximizing returns at the lowest cost.
C weighing costs versus benefits in light of the entity’s risk tolerance.

Solutions 453
SOLUTIONS
1 B is correct. For individuals, risk management concerns maximizing utility 
while taking risk consistent with individual’s level of risk tolerance.
2 A is correct. Many decision makers focus on return, which is not something 
that is easily controlled, as opposed to risk, or exposure to risk, which may 
actually be managed or controlled
3 C is correct. Risks need to be defined and measured so as to be consistent 
with the entity’s chosen level of risk tolerance and target for returns or other 
outcomes.
4 A is correct. Risk governance is the top-  down process that defines risk toler -
ance, provides risk oversight and guidance to align risk with enterprise goals.
5 C is correct. While risk infrastructure, which a risk management framework 
must address, refers to the people and systems required to track risk exposures, 
there is no requirement to actually name the responsible individuals.
6 A is correct. In establishing a risk management system, determining risk tol -

erance must happen before specific risks can be accepted or reduced. Risk toler -
ance defines the appetite for risk. Risk budgeting determine how or where the 
risk is taken and quantifies the tolerable risk by specific metrics. Risk exposures 
can then be measured and compared against the acceptable risk.
7 C is correct.  Risk infrastructure  refers to the people and systems required to 
track risk exposures and perform most of the quantitative risk analysis to allow 
an assessment of the organization’s risk profile. The risk management infra -
structure identifies, measures, and monitors risks (among other things).
8 C is correct. Risk governance is not about specifying methods to mitigate risk 
at the business line level. Rather, it is about establishing an appropriate level of 
risk for the entire enterprise. Specifics of dealing with risk fall under risk man -
agement and the risk infrastructure framework.
9 A is correct. The risk management committee is a part of the risk governance

structure at the operational level—as such, it does not approve the governing 
body’s policies.
10 B is correct. When risk tolerance has been determined, the risk framework 
should be geared toward measuring, managing, and complying with the risk tol -
erance, or aligning risk exposure with risk tolerance. The risk tolerance decision 
begins by looking at what shortfalls within an organization would cause it to fail 
to achieve some critical goals and what are the organization’s risk drivers.
11 C is correct. If a company has the ability to adapt quickly to adverse events 
may allow for a higher risk tolerance. There are other factors, such as beliefs of 
board members and a stable market environment, which may but should not 
affect risk tolerance.
12 A is correct. Risk budgeting does not include determining the target return. 
Risk budgeting quantifies and allocates the tolerable risk by specific metrics.
13 A is correct. The process of risk budgeting forces the firm to consider risk

tradeoffs. As a result, the firm should choose to invest where the return per unit 
of risk is the highest.

Reading 42 ■ Risk Management: An Introduction 454
14 A is correct. A financial risk originates from the financial markets. Credit risk is 
one of three financial risks identified in the reading: Credit risk is the chance of 
loss due to an outside party defaulting on an obligation. Solvency risk depends 
at least in part on factors internal to the organization and operational risk is an 
internal  risk arising from the people and processes within the organization.
15 B is correct. Liquidity risk is also called transaction cost risk. When the bid–ask 
spread widens, purchase and sale transactions become increasingly costly. The 
risk arises from the uncertainty of the spread.
16 C is correct. Settlement risk is related to default risk, but deals with the timing 
of payments rather than the risk of default.
17 A is correct. The VaR measure indicates the probability of a loss of at least a 
certain level in a time period.

18 C is correct. Risk acceptance is similar to self-  insurance. An entity choosing 
to self-  insure may set up a reserve fund to cover losses. Buying insurance is a 
form of risk transfer and using derivatives is a form of risk-  shifting, not risk 
acceptance.
19 C is correct. Among the risk-  modification methods of risk avoidance, risk 
acceptance, risk transfer, and risk shifting none has a clear advantage. One must 
weigh benefits and costs in light of the firm’s risk tolerance when choosing the 
method to use.

Fintech in Investment Management
by Barbara J. Mack and Robert Kissell, PhD
Barbara J. Mack is at Pingry Hill Enterprises, Inc. (USA). Robert Kissell, PhD, is at Kissell 
Research Group (USA).
a. describe “fintech;”
b. describe Big Data, artificial intelligence, and machine learning;
c. describe fintech applications to investment management;
d. describe financial applications of distributed ledger technology.
The meeting of finance and technology, commonly known as fintech , is changing the 
landscape of investment management. Advancements include the use of Big Data, 
artificial intelligence, and machine learning to evaluate investment opportunities, 
optimize portfolios, and mitigate risks. These developments are affecting not only 
quantitative asset managers but also fundamental asset managers who make use of 
these tools and technologies to engage in hybrid forms of investment decision making.

Investment advisory services are undergoing changes with the growth of automated 
wealth advisers or “robo-  advisers. ” Robo-  advisers may assist investors without the 
intervention of a human adviser, or they may be used in combination with a human 
adviser. The desired outcome is the ability to provide tailored, actionable advice to 
investors with greater ease of access and at lower cost.
In the area of financial record keeping, blockchain and distributed ledger technol -
ogy (DLT) are creating new ways to record, track, and store transactions for financial 
assets. An early example of this trend is the cryptocurrency bitcoin, but the technology 
is being considered in a broader set of applications.
This reading is divided into seven main sections, which together define fintech 
and outline some of its key areas of impact in the field of investment management. 
Section 2 explains the concept of and areas of fintech. Sections 3 and 4 discuss Big 1rEADING
43

Reading 43 ■ Fintech in Investment Management 456
Data, artificial intelligence, and machine learning. Section 5 discusses data science, 
and Section 6 provides applications of fintech to investment management. Section 7 
examines DLT. A summary of key points completes the reading.
WHAT IS FINTECH?
In its broadest sense, the term “fintech” generally refers to technology-  driven innovation 
occurring in the financial services industry. For the purposes of this reading, fintech  
refers to technological innovation in the design and delivery of financial services and 
products. Note, however, that in common usage, fintech can also refer to companies 
(often new, startup companies) involved in developing the new technologies and their 
applications, as well as the business sector that comprises such companies. Many 
of these innovations are challenging the traditional business models of incumbent 
financial services providers.

Early forms of fintech included data processing and the automation of routine tasks. 
Then followed systems that provided execution of decisions according to specified 
rules and instructions. Fintech has since advanced into decision-  making applications 
based on complex machine-  learning logic, where computer programs are able to 
“learn” how to complete tasks over time. In some applications, advanced computer 
systems are performing tasks at levels far surpassing human capabilities. Fintech has 
changed the financial services industry in many ways, giving rise to new systems for 
investment advice, financial planning, business lending, and payments.
Whereas fintech covers a broad range of services and applications, areas of fintech 
development that are more directly relevant to the investment industry include the 
■■Analysis of large datasets.  In addition to growing amounts of traditional data,

such as security prices, corporate financial statements, and economic indica -
tors, massive amounts of alternative data generated from non-  traditional data 
sources, such as social media and sensor networks, can now be integrated into 
a portfolio manager’s investment decision-  making process and used to help 
generate alpha and reduce losses.
■■Analytical tools.  For extremely large datasets, techniques involving artificial 
intelligence  (AI)—computer systems capable of performing tasks that previ -
ously required human intelligence—may be better suited to identify complex, 
non-  linear relationships than traditional quantitative methods and statistical 
analysis. Advances in AI-  based techniques are enabling different data analysis 
approaches. For example, analysts are turning to artificial intelligence to sort 
through the enormous amounts of data from company filings, annual reports, 
and earnings calls to determine which data are most important and to help

uncover trends and generate insights relating to human sentiment and behavior.
■■Automated trading.  Executing investment decisions through computer algo -
rithms or automated trading applications may provide a number of benefits to 
investors, including more efficient trading, lower transaction costs, anonymity, 
and greater access to market liquidity.2

Big Data 457
■■Automated advice.  Robo-  advisers  or automated personal wealth management 
services provide investment services to a larger number of retail investors at 
lower cost than traditional adviser models can provide.
■■Financial record keeping.  New technology, such as DLT, may provide secure 
ways to track ownership of financial assets on a peer-  to- peer (P2P) basis. By 
allowing P2P interactions—in which individuals or firms transact directly with 
each other without mediation by a third party—DLT reduces the need for finan -
cial intermediaries.
Drivers underlying fintech development in these areas include extremely rapid 
growth in data—including their quantity, types, sources, and quality—and techno -
logical advances that enable the capture and extraction of information from them. 
The data explosion is addressed in Section 3, and selected technological advances and 
data science are addressed in Sections 4 and 5, respectively.
BIG DATA

BIG DATA
As noted, datasets are growing rapidly in terms of the size and diversity of data types 
that are available for analysis. The term Big Data  has been in use since the late 1990s 
and refers to the vast amount of data being generated by industry, governments, 
individuals, and electronic devices. Big Data includes data generated from traditional 
sources—such as stock exchanges, companies, and governments—as well as non-  
traditional data types, also known as alternative data , arising from the use of elec -
tronic devices, social media, sensor networks, and company exhaust (data generated 
in the normal course of doing business).
Traditional data sources include corporate data in the form of annual reports, 
regulatory filings, sales and earnings figures, and conference calls with analysts. 
Traditional data also include data that are generated in the financial markets, including 
trade prices and volumes. Because the world has become increasingly connected, we

can now obtain data from a wide range of devices, including smart phones, cameras, 
microphones, radio-  frequency identification (RFID) readers, wireless sensors, and 
satellites that are now in use all over the world. As the internet and the presence 
of such networked devices have grown, the use of non-  traditional data sources, or 
alternative data sources—including social media (posts, tweets, and blogs), email and 
text communications, web traffic, online news sites, and other electronic information 
sources—has risen.
The term Big Data  typically refers to datasets having the following characteristics:
■■Volume : The amount of data collected in files, records, and tables is very large, 
representing many millions, or even billions, of data points.
■■Velocity : The speed with which the data are communicated is extremely great. 
Real-  time or near-  real-  time data have become the norm in many areas.
■■Variety : The data are collected from many different sources and in a vari -

ety of formats, including structured data (e.g., SQL tables or CSV files), 
semi-  structured data (e.g., HTML code), and unstructured data (e.g., video 
messages).
Features relating to Big Data’s volume, velocity, and variety are shown in Exhibit 1.3

Reading 43 ■ Fintech in Investment Management 458
Exhibit 1   Big Data Characteristics: Volume, Velocity, and Variety
Data
MB
GB
TB
PBVolume Key
Megabyte
Gigabyte
Terabyte
PetabyteBytes of Information
One Million
One Billion
One Trillion
One QuadrillionData 
Volume
Social
Video
Unstructured
MobileDatabase
Photo
Web
AudioTableReal Time
Near Real Time
Periodic
BatchData 
Velocity
MB GB TB PB
Data 
Variety
Source:  http://whatis.techtarget.com/definition/3Vs.
Exhibit 1 shows that data volumes are growing from megabytes (MB) and gigabytes 
(GB) to far larger sizes, such as terabytes (TB) and petabytes (PB), as more data are 
being generated, captured, and stored. At the same time, more data, traditional and 
non-  traditional, are available on a real-  time or near-  real-  time basis with far greater 
variety in data types than ever before.
Big Data may be structured, semi-  structured, or unstructured data. Structured data 
items can be organized in tables and are commonly stored in a database where each

field represents the same type of information. Unstructured data may be disparate, 
unorganized data that cannot be represented in tabular form. Unstructured data, such 
as those generated by social media, email, text messages, voice recordings, pictures, 
blogs, scanners, and sensors, often require different, specialized applications or cus -
tom programs before they can be useful to investment professionals. For example, in 
order to analyze data contained in emails or texts, specially developed or customized 
computer code may be required to first process these files. Semi-  structured data may 
have attributes of both structured and unstructured data.
3.1 Sources of Big Data
Big Data, therefore, encompasses data generated by
■■financial markets (e.g., equity, fixed income, futures, options, and other 
derivatives),
■■businesses (e.g., corporate financials, commercial transactions, and credit card 
purchases),
■■governments (e.g., trade, economic, employment, and payroll data),

Big Data 459
■■individuals (e.g., credit card purchases, product reviews, internet search logs, 
and social media posts),
■■sensors (e.g., satellite imagery, shipping cargo information, and traffic patterns), 
and, in particular,
■■the Internet of Things, or IoT (e.g., data generated by “smart” buildings, where 
the building is providing a steady stream of information about climate control, 
energy consumption, security, and other operational details).
In gathering business intelligence, historically, analysts have tended to draw on 
traditional data sources, employing statistical methods to measure performance, 
predict future growth, and analyze sector and market trends. In contrast, the analysis 
of Big Data incorporates the use of alternative data sources.
From retail sales data to social media sentiment to satellite imagery that may 
reveal information about agriculture, shipping, and oil rigs, alternative datasets may

provide additional insights about consumer behavior, firm performance, trends, and 
other factors important for investment-  related activities. Such information is having 
a significant effect on the way that professional investors, particularly quantitative 
investors, approach financial analysis and decision-  making processes.
There are three main sources of alternative data:
■■data generated by individuals,
■■data generated by business processes, and
■■data generated by sensors.
Data generated by individuals are often produced in text, video, photo, and audio 
formats and may also be generated through such means as website clicks or time spent 
on a webpage. This type of data tends to be unstructured. The volume of this type 
of data is growing dramatically as people participate in greater numbers and more 
frequently in online activities, such as social media and e-  commerce, including online 
reviews of products, services, and entire companies, and as they make personal data

available through web searches, email, and other electronic trails.
Business process data include information flows from corporations and other public 
entities. These data tend to be structured data and include direct sales information, 
such as credit card data, as well as corporate exhaust. Corporate exhaust includes 
corporate supply chain information, banking records, and retail point-  of- sale scanner 
data. Business process data can be leading or real-  time indicators of business perfor -
mance, whereas traditional corporate metrics may be reported only on a quarterly or 
even yearly basis and are typically lagging indicators of performance.
Sensor data are collected from such devices as smart phones, cameras, RFID chips, 
and satellites that are usually connected to computers via wireless networks. Sensor 
data can be unstructured, and the volume of data is many orders of magnitude greater 
than that of individual or business process datastreams. This form of data is growing

exponentially because microprocessors and networking technology are increasingly 
present in a wide array of personal and commercial electronic devices. Extended to 
office buildings, homes, vehicles, and many other physical forms, this culminates in 
a network arrangement, known as the Internet of Things , that is formed by the vast 
array of physical devices, home appliances, smart buildings, vehicles, and other items 
that are embedded with electronics, sensors, software, and network connections that 
enable the objects in the system to interact and share information.
Exhibit 2 shows a classification of alternative data sources and includes examples 
for each.

Reading 43 ■ Fintech in Investment Management 460
Exhibit 2   Classification of Alternative Data Sources
Individuals Business Processes Sensors
Social media Transaction data Satellites
News, reviews Corporate data Geolocation
Web searches, personal data Internet of Things
Other sensors
In the search to identify new factors that may affect security prices, enhance asset 
selection, improve trade execution, and uncover trends, alternative data are being used 
to support data-  driven investment models and decisions. As interest in alternative 
data has risen, there has been a growth in the number of specialized firms that collect, 
aggregate, and sell alternative datasets.
While the marketplace for alternative data is expanding, investment professionals 
should understand potential legal and ethical issues related to information that is not 
in the public domain. For example, the scraping of web data could potentially capture

personal information that is protected by regulations or that may have been published 
or provided without the explicit knowledge and consent of the individuals involved. 
Best practices are still in development in many jurisdictions, and because of varying 
approaches taken by national regulators, there may be conflicting forms of guidance.
3.2 Big Data Challenges
Big Data poses several challenges when it is used in investment analysis, including 
the quality, volume, and appropriateness of the data. Key issues revolve around the 
following questions, among others: Does the dataset have selection bias, missing 
data, or data outliers? Is the volume of collected data sufficient? Is the dataset well 
suited for the type of analysis? In most instances, the data must be sourced, cleansed, 
and organized before analysis can occur. This process can be extremely difficult with 
alternative data owing to the unstructured characteristics of the data involved, which

are more often qualitative (e.g., texts, photos, and videos) than quantitative in nature.
Given the size and complexity of alternative datasets, traditional analytical meth -
ods cannot always be used to interpret and evaluate these datasets. To address this 
challenge, artificial intelligence and machine learning techniques have emerged that 
support work on such large and complex sources of information.
ADVANCED ANALYTICAL TOOLS: ARTIFICIAL 
INTELLIGENCE AND MACHINE LEARNING
Artificial intelligence computer systems are capable of performing tasks that have 
traditionally required human intelligence. AI technology has enabled the development 
of computer systems that exhibit cognitive and decision-  making ability comparable 
or superior to that of human beings.
An early example of AI was the “expert system, ” a type of computer programming 
that attempted to simulate the knowledge base and analytical abilities of human experts

in specific problem-  solving contexts. This was often accomplished through the use of 
“if- then” rules. By the late 1990s, faster networks and more powerful processors enabled 
AI to be deployed in logistics, data mining, financial analysis, medical diagnosis, and 4

Advanced Analytical Tools: Artificial Intelligence and Machine Learning 461
other areas. Since the 1980s, financial institutions have made use of AI—particularly, 
neural networks , programming based on how our brain learns and processes infor -
mation—to detect abnormal charges or claims in credit card fraud detection systems.
Machine learning  (ML) is a technology that has grown out of the wider AI field. 
ML algorithms are computer programs that are able to “learn” how to complete tasks, 
improving their performance over time with experience. As it is currently used in the 
investing context, ML requires massive amounts of data for “training, ” so although 
some ML techniques have existed for years, insufficient data have historically limited 
broader application. Previously, these algorithms lacked access to the large amounts of 
data needed to model relationships successfully. The growth in Big Data has provided

ML algorithms, such as neural networks, with sufficient data to improve modeling 
and predictive accuracy, and greater use of ML techniques is now possible.
In ML, the computer algorithm is given “inputs” (a set of variables or datasets) 
and may be given “outputs” (the target data). The algorithm “learns” from the data 
provided how best to model inputs to outputs (if provided) or how to identify or 
describe underlying data structure if no outputs are given. Training occurs as the 
algorithm identifies relationships in the data and uses that information to refine its 
learning process.
ML involves splitting the dataset into a training dataset and validation dataset 
(evaluation dataset). The training dataset allows the algorithm to identify relationships 
between inputs and outputs based on historical patterns in the data. These relation -
ships are then tested on the validation dataset. Once an algorithm has mastered the

training and validation datasets, the ML model can be used to predict outcomes based 
on other datasets.
ML still requires human judgement in understanding the underlying data and 
selecting the appropriate techniques for data analysis. Before they can be used, the 
data must be clean and free of biases and spurious data. As noted, ML models also 
require sufficiently large amounts of data and may not perform well where there may 
not be enough available data to train and validate the model.
Analysts must also be cognizant of errors that may arise from overfitting  the 
data, because models that overfit the data may discover “false” relationships or 
“unsubstantiated” patterns that will lead to prediction errors and incorrect output 
forecasts. Overfitting occurs when the ML model learns the input and target dataset 
too precisely. In such cases, the model has been “over-  trained” on the data and treats 
noise in the data as true parameters. An ML model that has been overfitted is not

able to accurately predict outcomes using a different dataset and may be too complex. 
When a model has been underfitted, the ML model treats true parameters as if they 
are noise and is not able to recognize relationships within the training data. In such 
cases, the model may be too simplistic. Underfitted models will typically fail to fully 
discover patterns that underlie the data.
In addition, since they are not explicitly programmed, ML techniques can appear 
to be opaque or “black box” approaches, which arrive at outcomes that may not be 
entirely understood or explainable.
4.1 Types of Machine Learning
ML approaches can help identify relationships between variables, detect patterns or 
trends, and create structure from data, including data classification. The main types 
of machine learning approaches include supervised and unsupervised learning.
In supervised learning , computers learn to model relationships based on labeled

training data. In supervised learning, inputs and outputs are labeled, or identified, 
for the algorithm. After learning how best to model relationships for the labeled 
data, the trained algorithms are used to model or predict outcomes for new datasets. 
Trying to identify the best signal, or variable, to forecast future returns on a stock or

Reading 43 ■ Fintech in Investment Management 462
trying to predict whether local stock market performance will be up, down, or flat 
during the next business day are problems that may be approached using supervised 
learning techniques.
In unsupervised learning , computers are not given labeled data but instead are 
given only data from which the algorithm seeks to describe the data and their struc -
ture. Trying to group companies into peer groups based on their characteristics rather 
than using standard sector or country groupings is a problem that may be approached 
using unsupervised learning techniques.
Underlying AI advances have been key developments relating to neural networks. 
In deep learning , (or deep learning nets ), computers use neural networks, often with 
many hidden layers, to perform multistage, non-  linear data processing to identify pat -
terns. Deep learning may use supervised or unsupervised machine learning approaches.

By taking a layered or multistage approach to data analysis, deep learning develops an 
understanding of simple concepts that informs analysis of more complex concepts. 
Neural networks have existed since 1958 and have been used for many applications, 
such as forecasting and pattern recognition, since the early 1990s. Improvements in the 
algorithms underlying neural networks are providing more accurate models that better 
incorporate and learn from data. As a result, these algorithms are now far better at 
such activities as image, pattern, and speech recognition. In many cases, the advanced 
algorithms require less computing power than the earlier neural networks, and their 
improved solution enables analysts to discover insights and identify relationships that 
were previously too difficult or too time consuming to uncover.
 
Advances in Artificial Intelligence outside Finance
Non-  finance-  related AI breakthroughs include victories in the general knowledge game -

show Jeopardy (by IBM’s Watson in 2011) and in the ancient Chinese board game Go (by 
Google’s DeepMind in 2016). Not only is AI providing solutions where there is perfect 
information (all players have equal access to the same information), such as checkers, 
chess, and Go, but AI is also providing insight in cases where information may be imperfect 
and players have hidden information; AI successes at the game of poker (by DeepStack) 
are an example. AI has also been behind the rise of virtual assistants, such as Siri (from 
Apple), Google’s Translate app, and Amazon’s product recommendation engine.
The ability to analyze Big Data using ML techniques, alongside more traditional 
statistical methods, represents a significant development in investment research, 
supported by the presence of greater data availability and advances in the algorithms 
themselves. Improvements in computing power and software processing speeds and 
falling storage costs have further supported this evolution.

ML techniques are being used for Big Data analysis to help predict trends or mar -
ket events, such as the likelihood of a successful merger or an outcome to a political 
election. Image recognition algorithms can now analyze data from satellite-  imaging 
systems to provide intelligence on the number of consumers in retail store parking 
lots, shipping activity and manufacturing facilities, and yields on agricultural crops, 
to name just a few examples.
Such information may provide insights into individual firms or at national or global 
levels and may be used as inputs into valuation or economic models.

Data Science: Extracting Information from Big Data 463
DATA SCIENCE: EXTRACTING INFORMATION FROM 
BIG DATA
Data science  can be defined as an interdisciplinary field that harnesses advances in 
computer science (including machine learning), statistics, and other disciplines for 
the purpose of extracting information from Big Data (or data in general). Companies 
rely on the expertise of data scientists/analysts to extract information and insights 
from Big Data for a wide variety of business and investment purposes.
An important consideration for the data scientist is the structure of the data. As 
noted in the discussion on Big Data, because of their unstructured nature, alternative 
data often require specialized treatment before they can be used for analysis.
5.1 Data Processing Methods
To help determine the best data management technique needed for Big Data analy -
sis, data scientists use various data processing methods, including capture, curation, 
storage, search, and transfer.

■■Capture—Data capture refers to how the data are collected and transformed 
into a format that can be used by the analytical process. Low-  latency systems—
systems that operate on networks that communicate high volumes of data with 
minimal delay (latency)—are essential for automated trading applications that 
make decisions based on real-  time prices and market events. In contrast, high-  
latency systems do not require access to real-  time data and calculations.
■■Curation—Data curation refers to the process of ensuring data quality and 
accuracy through a data cleaning exercise. This process consists of reviewing all 
data to detect and uncover data errors—bad or inaccurate data—and making 
adjustments for missing data when appropriate.
■■Storage—Data storage refers to how the data will be recorded, archived, and 
accessed and the underlying database design. An important consideration for

data storage is whether the data are structured or unstructured and whether 
analytical needs require low-  latency solutions.
■■Search—Search refers to how to query data. Big Data has created the need for 
advanced applications capable of examining and reviewing large quantities of 
data to locate requested data content.
■■Transfer—Transfer refers to how the data will move from the underlying data 
source or storage location to the underlying analytical tool. This could be 
through a direct data feed, such as a stock exchange’s price feed.
5.2 Data Visualization
Data visualization is an important tool for understanding Big Data. Visualization 
refers to how the data will be formatted, displayed, and summarized in graphical form. 
Traditional structured data can be visualized using tables, charts, and trends, whereas 
non-  traditional unstructured data require new techniques of data visualization. These 
visualization tools include, for example, interactive three-  dimensional (3D) graphics,

where users can focus in on specified data ranges and rotate the data across 3D axes 
to help identify trends and uncover relationships. Multidimensional data analysis 
consisting of more than three variables requires additional data visualization tech -
niques—for example, adding color, shapes, and sizes to the 3D charts. Further, a wide 5

Reading 43 ■ Fintech in Investment Management 464
variety of solutions exists to reflect the structure of the data through the geometry of 
the visualization, with interactive graphics allowing for especially rich possibilities. 
Examples include heat maps, tree diagrams, and network graphs.
Another valuable Big Data visualization technique that is applicable to textual data 
is a “tag cloud, ” where words are sized and displayed on the basis of the frequency 
of the word in the data file. For example, words that appear more often are shown 
with a larger font, and words that appear less often are shown with a smaller font. A 
“mind map” is another data visualization technique; it is a variation of the tag cloud, 
but rather than displaying the frequency of words, a mind map shows how different 
concepts are related to each other.
Exhibit 3 shows an example of a “tag cloud” based on a section of this reading. 
The more frequently a word is found within the text, the larger it becomes in the tag

cloud. As shown in the tag cloud, the words appearing most frequently in the section 
include “data, ” “ML, ” “learning, ” “ AI, ” “techniques, ” “model, ” and “relationships. ”
Exhibit 3   Data Visualization Tag Cloud: Section 4, Advanced Analytical 
Tools
insights
outcomes
analysis
help
solutioncomputer
Sidebar
providing
large
stock
types
over
morehuman
uncoverrelationshipsalgorithms MLoccurs
providemodel
learnsupervisedapproaches
players
enabled
other
programming
marketnow
previously
modelsusinginformation
structureunderlying
complex
training
detectnetworks
performancecomputers
understandingsince
tasks
identifycaseuse
target
processing
datasets
analyze
systemstruewhileerrorsprovided
patterns
advances
better
Machine
Big
algorithm
outputsdata
dataset
patternunsupervised
neural
possibleTrying
existed
predictGoogle’s
learns
approachedArtificialtechniques
learning
computing
deeplabelled
validationinputs
given basedimage
intelligencetreatingbest
variablesadvanced
amounts
describeused
concepts
abletrendsAI

amounts
concepts
Source:  https://worditout.com/word-  cloud/create.
 
Programming Languages and Databases
Some of the more common programming languages used in data science include the 
■■ Python:  Python is an open source, free programming language that does not 
require an in-  depth understanding of computer programming. Python allows 
individuals with little or no programming experience to develop computer appli -
cations for advanced analytical use and is the basis for many fintech applications.
■■ R: r is an open source, free programming language traditionally used for statisti -
cal analysis. r has mathematical packages for statistical analysis, machine learning, 
optimization, econometrics, and financial analysis.

Selected Applications of Fintech to Investment Management 465
■■ Java:  Java is a programming language that can run on different computers, 
servers, and operating systems. Java is the underlying program language used in 
many internet applications.
■■ C/C++:  C/C++ is a specialized programming language that provides the ability 
to optimize source code to achieve superior calculation speed and processing 
performance. C/C++ is used in applications for algorithmic and high-  frequency 
trading.
■■ Excel VBA:  Excel VBA helps bridge the gap between programming and man -
ual data processing by allowing users to run macros to automate tasks, such as 
updating data tables and formulas, running data queries and collecting data from 
different web locations, and performing calculations. Excel VBA allows users to 
develop customized reports and analyses that rely on data that are updated from 
different applications and databases.
Some of the more common databases in use include the following:

■■ SQL:  SQL is a database for structured data where the data can be stored in tables 
with rows and columns. SQL databases need to be run on a server that is accessed 
by users.
■■ SQLite:  SQLite is a database for structured data. SQLite databases are embedded 
into the program and do not need to be run on a server. It is the most common 
database for mobile apps that require access to data.
■■ NoSQL:  NoSQL is a database used for unstructured data where the data cannot 
be summarized in traditional tables with rows and columns.
SELECTED APPLICATIONS OF FINTECH TO 
INVESTMENT MANAGEMENT
Fintech is being used in numerous areas of investment management. Applications 
for investment management include text analytics and natural language processing, 
robo-  advisory services, risk analysis, and algorithmic trading.
6.1 Text Analytics and Natural Language Processing
Text analytics  involves the use of computer programs to analyze and derive meaning

typically from large, unstructured text- or voice-  based datasets, such as company fil -
ings, written reports, quarterly earnings calls, social media, email, internet postings, 
and surveys. Text analytics includes using computer programs to perform automated 
information retrieval from different, unrelated sources in order to aid the decision-  
making process. More analytical usage includes lexical analysis, or the analysis of word 
frequency in a document and pattern recognition based on key words and phrases. 
Text analytics may be used in predictive analysis to help identify indicators of future 
performance, such as consumer sentiment.
Natural language processing  (NLP) is a field of research at the intersection of 
computer science, artificial intelligence, and linguistics that focuses on developing 
computer programs to analyze and interpret human language. Within the larger 
field of text analytics, NLP is an important application. Automated tasks using NLP

include translation, speech recognition, text mining, sentiment analysis, and topic 
analysis. NLP may also be employed in compliance functions to review employee 
voice and electronic communications for adherence to company or regulatory policy, 
inappropriate conduct, or fraud or for ensuring private or customer information is 
kept confidential.6

Reading 43 ■ Fintech in Investment Management 466
Consider that all the public corporations worldwide generate millions of pages of 
annual reports and tens of thousands of hours of earnings calls each year. This is more 
information than any individual analyst or team of researchers can assess. NLP , espe -
cially when aided by ML algorithms, can analyze annual reports, call transcripts, news 
articles, social media posts, and other text- and audio-  based data to identify trends 
in shorter timespans and with greater scale and accuracy than is humanly possible.
For example, NLP may be used to monitor analyst commentary to aid investment 
decision making. Financial analysts may generate earnings-  per- share (EPS) forecasts 
reflecting their views on a company’s near-  term prospects. Focusing on forecasted 
EPS numbers could mean investors miss subtleties contained in an analyst’s written 
research report. Since analysts tend not to change their buy, hold, and sell recom -

mendations for a company frequently, they may instead offer nuanced commentary 
without making a change in their investment recommendation. After analyzing ana -
lyst commentary, NLP can assign sentiment ratings ranging from very negative to 
very positive for each. NLP can, therefore, be used to detect, monitor, and tag shifts 
in sentiment, potentially ahead of an analyst’s recommendation change. Machine 
capabilities enable this analysis to scale across thousands of companies worldwide, 
performing work previously done by humans.
Similarly, communications and transcripts from policymakers, such as the European 
Central Bank or the US Federal Reserve, offer an opportunity for NLP-  based analysis, 
because officials at these institutions may send subtle messages through their choice 
of topics, words, and inferred tone. NLP can help analyze nuances within text to 
provide insights around trending or waning topics of interest, such as interest rate

policy, aggregate output, or inflation expectations.
Models using NLP analysis may incorporate non-  traditional information to eval -
uate what people are saying—via their preferences, opinions, likes, or dislikes—in an 
attempt to identify trends and short-  term indicators about a company, a stock, or an 
economic event that might have a bearing on future performance. Past research has 
evaluated the predictive power of Twitter sentiment regarding IPO performance, for 
example.1 The effect of positive and negative news sentiment on stock returns has 
also been researched.2
6.2 Robo-  Advisory Services
Since their emergence in 2008, a number of startup firms, as well as large asset man -
agers, have introduced robo-  advisory services, which provide investment solutions 
through online platforms, reducing the need for direct interaction with financial 
advisers.
As robo-  advisers have been incorporated into the investment landscape, they

have drawn the attention of regulatory authorities. In the United States, robo-  advisers 
must be established as registered investment advisers, and they are regulated by the 
Securities and Exchange Commission. In the United Kingdom, they are regulated by 
the Financial Conduct Authority. In Australia, all financial advisers must obtain an 
Australian Financial Services license, with guidance on digital advisers coming from 
the Australian Securities and Investments Commission. Robo-  advisers are also on the 
rise in parts of Asia and the rest of the world. Although regulatory conditions vary, 
robo-  advisers are likely to be held to a similar level of scrutiny and code of conduct 
as other investment professionals in the given region.
1 Jim Kyung-  Soo Liew and Garrett Zhengyuan Wang, “Twitter Sentiment and IPO Performance: A Cross-  
Sectional Examination, ” Journal of Portfolio Management , vol. 42, no. 4 (Summer 2016): 129–135.

2 Steven L. Heston and Nitish Ranjan Sinha, “News vs. Sentiment: Predicting Stock Returns from News 
Stories, ” Financial Analysts Journal , vol. 73, no. 3 (Third Quarter 2017): 67–83. (https://www.cfapubs.org/
doi/abs/10.2469/faj.v73.n3.3).

Selected Applications of Fintech to Investment Management 467
Robo-  advice tends to start with an investor questionnaire, which may include 
many of the categories and subcategories shown in Exhibit 4. Exhibit 4 is a synthesis 
of questionnaires created by the researchers attributed in the source below. Once 
assets, liabilities, risk preferences, and target investment returns have been digitally 
entered by a client, the robo-  adviser software produces recommendations, based 
on algorithmic rules and historical market data, that incorporate the client’s stated 
investment parameters. According to research by Michael Tertilt and Peter Scholz, 
robo-  advisers do not seem to incorporate the full range of available information into 
their recommendations;3 further research will be necessary over time to see how this 
may affect performance and the evolution of digital advisory services. Nevertheless, 
current robo-  advisory services include automated asset allocation, trade execution,

portfolio optimization, tax-  loss harvesting, and rebalancing for investor portfolios.
Exhibit 4   Categories and Subcategories for Investor Questionnaires
General Information Risk Tolerance
  Income   Age
  Investment Amount   Association with Investing
  Job Description   Association with Risk
  Other   Choose Portfolio Risk Level
  Source of Income   Comfort Investing in Stock
  Spendings   Credit Based Investments
  Time to Retirement   Dealing with Financial Decisions
  Type of Account   Degree of Financial Risk Taken
  Working Status   Education
Risk Capacity   Ever Interested in Risky Asset for Thrill
  Dependence on Withdrawal  
of Investment Amount  Experience of Drop/Reaction on Drop/Max Drop before 
Selling
  Income Prediction   Family and Household Status
  Investment Amount/Savings Rate Ratio   Financial Knowledge
  Investment Amount/Total Capital Ratio   Gender
  Investment Horizon   Investment Experience
  Liabilities   Investment Goal

Liabilities   Investment Goal
  Savings Rate   Investor Type/Self-  Assessment Risk Tolerance
  Total Capital   Preference Return vs. Risk
Source:  Michael Tertilt and Peter Scholz, 2017 “To Advise, or Not to Advise—How Robo-  Advisors Evaluate the Risk Preferences of Private 
Investors, ” working paper (13 June): Table 1: Categories and Subcategories for Questionnaires.
Although their analyses and recommendations can cover both active and passive 
management styles, most robo-  advisers follow a passive investment approach. These 
robo-  advisers typically have low fees and low account minimums, implementing their 
recommendations with low-  cost, diversified index mutual funds or exchange-  traded 
funds (ETFs). A diverse range of asset classes can be managed in this manner, including 
3 Michael Tertilt and Peter Scholz, To Advise, or Not to Advise — How Robo-  Advisors Evaluate the Risk

Preferences of Private Investors (June 12, 2017). Available at SSRN: https://ssrn.com/abstract=2913178 or 
http://dx.doi.org/10.2139/ssrn.2913178

Reading 43 ■ Fintech in Investment Management 468
stocks, bonds, commodities, futures, and real estate. Because of their low-  cost struc -
ture, robo-  advisers can reach underserved populations, such as the mass affluent or 
mass market segments, which are less able to afford a traditional financial adviser.
Two types of wealth management services dominate the robo-  advice sector: fully 
automated digital wealth managers and adviser-  assisted digital wealth managers.
■■Fully Automated Digital Wealth Managers
The fully automated model does not rely on assistance from a human finan -
cial adviser. These services seek to offer a low-  cost solution to investing and 
recommend an investment portfolio, which is often composed of ETFs. The 
service package may include direct deposits, periodic rebalancing, and dividend 
reinvestment options.
■■Adviser-  Assisted Digital Wealth Managers
Adviser-  assisted digital wealth managers provide automated investment services

along with a virtual financial adviser, who is available to offer basic financial 
planning advice and periodic reviews by phone. Adviser-  assisted digital wealth 
managers are capable of providing additional services that may involve a more 
holistic analysis of a client’s assets and liabilities.
Wealthy and ultra-  wealthy individuals typically have had access to human advisory 
teams, but there has been a gap in the availability and quality of advisers to serve 
investors with less wealth. The advent of robo-  advisers offers a cost-  effective and 
easily accessible form of financial guidance. In following a typically passive investment 
approach, research suggests that robo-  advisers tend to offer fairly conservative advice.
However, critics of robo-  advisers have wondered what would happen in a time of 
crisis, when people most often look to human expertise for guidance. It may not always 
be completely transparent why a robo-  adviser chooses to make a recommendation or

take a trading action that it did, unlike a human adviser who can provide his or her 
rationale. And finally, there may be trust issues in allowing computers to make these 
decisions, including worries of instances where robo-  advisers might recommend 
inappropriate investments.
As the complexity and size of an investor’s portfolio grows, robo-  advisers may not 
be able to sufficiently address the particular preferences and needs of the investor. In 
the case of extremely affluent investors who may own a greater number of asset types—
including alternative investments (e.g., venture capital, private equity, hedge funds, 
and real estate)—in addition to global stocks and bonds and have greater demands 
for customization, the need for a team of human advisers, each with particular areas 
of investment or wealth-  management expertise, is likely to endure.
6.3 Risk Analysis
As mandated by regulators worldwide, the global investment industry has undertaken

major steps in stress testing and risk assessment that involve the analysis of vast 
amounts of quantitative and qualitative risk data. Required data include information 
on the liquidity of the firm and its trading partners, balance sheet positions, credit 
exposures, risk-  weighted assets, and risk parameters. Stress tests may also take qual -
itative information into consideration, such as capital planning procedures, expected 
business plan changes, business model sustainability, and operational risk.
There is increasing interest in monitoring risk in real time. To do so, relevant data 
must be taken by a firm, mapped to known risks, and identified as it moves within the 
firm. Data may be aggregated for reporting purposes or used as inputs to risk models. 
Big Data may provide insights into real-  time and changing market circumstances to 
help identify weakening market conditions and adverse trends in advance, allowing

managers to employ risk management techniques and hedging practices sooner to help

Distributed Ledger Technology 469
preserve asset value. For example, evaluation of alternative data using ML techniques 
may help foreshadow declining company earnings and future stock performance. 
Furthermore, analysis of real-  time market data and trading patterns may help analysts 
detect buying or selling pressure in the stock.
ML techniques may be used to help assess data quality. To help ensure accurate 
and reliable data that may originate from numerous alternative data sources, ML 
techniques can help validate data quality by identifying questionable data, potential 
errors, and data outliers before integration with traditional data for use in risk models 
and in risk management applications.
Portfolio risk management often makes use of scenario analysis—analyzing the 
likely performance of the portfolio and liquidation costs under a hypothetical stress 
scenario or the repeat of a historical stress event. For example, to understand the

implications of holding or liquidating positions during adverse or extreme market 
periods, such as the financial crisis, fund managers may perform “what-  if” scenario 
analysis and portfolio backtesting using point-  in- time data to understand liquidation 
costs and portfolio consequences under differing market conditions. These backtesting 
simulations are often computationally intense and may be facilitated through the use 
of advanced AI-  based techniques.
6.4 Algorithmic Trading
Algorithmic trading is the computerized buying and selling of financial instruments, 
in accordance with pre-  specified rules and guidelines. Algorithmic trading is often 
used to execute large institutional orders, slicing orders into smaller pieces and exe -
cuting across different exchanges and trading venues. Algorithmic trading provides 
investors with many benefits, including speed of execution, anonymity, and lower 
transaction costs. Over the course of a day, algorithms may continuously update and

revise their execution strategy on the basis of changing prices, volumes, and market 
volatility. Algorithms may also determine the best way to price the order (e.g., limit 
or market order) and the most appropriate trading venue (e.g., exchange or dark pool) 
to route for execution.
High-  frequency trading  (HFT) is a form of algorithmic trading that makes use 
of vast quantities of granular financial data (tick data, for example) to automatically 
place trades when certain conditions are met. Trades are executed on ultra-  high-  speed, 
low-  latency networks in fractions of a second. HFT algorithms decide what to buy 
or sell and where to execute on the basis of real-  time prices and market conditions, 
seeking to earn a profit from intraday market mispricings.
Global financial markets have undergone substantial change as markets have frag -
mented into multiple trading destinations consisting of electronic exchanges, alter -

native trading systems, and so-  called dark pools, and average trade sizes have fallen. 
In this environment, and with markets continuously reflecting real-  time information, 
algorithmic trading has been viewed as an important tool.
DISTRIBUTED LEDGER TECHNOLOGY
Distributed ledger technology —technology based on a distributed ledger (defined 
below)—represents a fintech development that offers potential improvements in the 
area of financial record keeping. DLT networks are being considered as an efficient 
means to create, exchange, and track ownership of financial assets on a peer-  to- peer 
basis. Potential benefits include greater accuracy, transparency, and security in record 
keeping; faster transfer of ownership; and peer-  to- peer interactions. However, the 7

Reading 43 ■ Fintech in Investment Management 470
technology is not fully secure, and breaches in privacy and data protection are pos -
sible. In addition, the processes underlying DLT generally require massive amounts 
of energy to verify transaction activity.
A distributed ledger  is a type of database that may be shared among entities 
in a network. In a distributed ledger, entries are recorded, stored, and distributed 
across a network of participants so that each participant has a matching copy of the 
digital database. Basic elements of a DLT network include a digital ledger, a consensus 
mechanism used to confirm new entries, and a participant network.
The consensus mechanism is the process by which the computer entities (or nodes) 
in a network agree on a common state of the ledger. Consensus generally involves 
two steps: transaction validation and agreement on ledger update by network parties. 
These features enable the creation of records that are, for the most part, considered

immutable, or unchangeable, yet they are transparent and accessible to network par -
ticipants on a near-  real-  time basis.
Features of DLT include the use of cryptography —an algorithmic process to 
encrypt data, making the data unusable if received by unauthorized parties—which 
enables a high level of network security and database integrity. For example, DLT 
uses cryptographic methods of proof to verify network participant identity and for 
data encryption.
DLT has the potential to accommodate “ smart contracts , ” which are computer 
programs that self-  execute on the basis of pre-  specified terms and conditions agreed 
to by the parties to a contract. Examples of smart contract use are the automatic exe -
cution of contingent claims for derivatives and the instantaneous transfer of collateral 
in the event of default.
Exhibit 5 illustrates a distributed ledger network in which all nodes are connected 
to one another, each having a copy of the distributed ledger. The term “Consensus”

is shown in the center of the network and represents the consensus mechanism in 
which the nodes agree on new transactions and ledger updates.
Exhibit 5   Distributed Ledger Network Setup
Node
NodeNode
NodeNode NodeLedger Ledger
Ledger
Ledger Ledger
LedgerConsensus
Source:  https://blockgeeks.com/guides/what-  is- hyperledger/.
Blockchain  is a type of digital ledger in which information, such as changes in 
ownership, is recorded sequentially within blocks that are then linked or “chained” 
together and secured using cryptographic methods. Each block contains a grouping 
of transactions (or entries) and a secure link (known as a hash) to the previous block.

Distributed Ledger Technology 471
New transactions are inserted into the chain only after validation via a consensus 
mechanism in which authorized members agree on the transaction and the preceding 
order, or history, in which previous transactions have occurred.
The consensus mechanism used to verify a transaction includes a cryptographic 
problem that must be solved by some computers on the network (known as miners) 
each time a transaction takes place. The process to update the blockchain can require 
substantial amounts of computing power, making it very difficult and extremely 
expensive for an individual third party to manipulate historical data. To manipulate 
historical data, an individual or entity would have to control the majority of nodes in the 
network. The success of the network, therefore, relies on broad network participation.
 
Blockchain (Distributed Ledger) Network—How Do 
Transactions Get Added?

Outlined below are the steps involved in adding a transaction to a blockchain distrib -
uted ledger.
1 Transaction takes place between buyer and seller
2 Transaction is broadcast to the network of computers (nodes)
3 Nodes validate the transaction details and parties to the transaction
4 Once verified, the transaction is combined with other transactions to form a new 
block (of predetermined size) of data for the ledger
5 This block of data is then added or linked (using a cryptographic process) to the 
previous block(s) containing data
6 Transaction is considered complete and ledger has been updated
7.1 Permissioned and Permissionless Networks
DLT can take the form of permissionless or permissioned networks. Permissionless 
networks  are open to any user who wishes to make a transaction, and all users within 
the network can see all transactions that exist on the blockchain. In a permissionless, 
or open, DLT system, network participants can perform all network functions.

The main benefit of a permissionless network is that it does not depend on a cen -
tralized authority to confirm or deny the validity of transactions, because this takes 
place through the consensus mechanism. This means no single point of failure exists, 
since all transactions are recorded on a single distributed database and every node 
stores a copy of the database. Once a transaction has been added to the blockchain, it 
cannot be changed, barring manipulation; the distributed ledger becomes a permanent 
and immutable record of all previous transactions. In a permissionless network, trust 
is not a requirement between transacting parties.
A well-  known example of an open, permissionless network is bitcoin . Using 
blockchain technology, Bitcoin was created in 2009 to serve as the public ledger for 
all transactions occurring on its virtual currency. Since the introduction of bitcoin, 
many more cryptocurrencies, or digital currencies, which use permissionless DLT

networks, have been created.
In permissioned networks , network members may be restricted from participating 
in certain network activities. Controls, or permissions, may be used to allow varying 
levels of access to the ledger, from adding transactions (e.g., a participant) to viewing 
transactions only (e.g., a regulator) to viewing selective details of the transactions but 
not the full record.

Reading 43 ■ Fintech in Investment Management 472
7.2 Applications of Distributed Ledger Technology to 
Investment Management
Potential applications of DLT to investment management include cryptocurrencies, 
tokenization, post-  trade clearing and settlement, and compliance.
7.2.1  Cryptocurrencies
A cryptocurrency , also known as a digital currency, operates as electronic currency and 
allows near-  real-  time transactions between parties without the need for an intermedi -
ary, such as a bank. As electronic mediums of exchange, cryptocurrencies lack physical 
form and are issued privately by individuals, companies, and other organizations. Most 
issued cryptocurrencies utilize open DLT systems in which a decentralized distributed 
ledger is used to record and verify all digital currency transactions. Cryptocurrencies 
have not traditionally been government backed or regulated. Central banks around 
the world, however, are recognizing potential benefits and examining use cases for

their own cryptocurrency versions.
Many cryptocurrencies have a self-  imposed limit on the total amount of currency 
they may issue. Although such limits could help maintain their store of value, it is 
important to note that many cryptocurrencies have experienced high levels of price 
volatility. A lack of clear fundamentals underlying these currencies has contributed 
to their volatility.
Cryptocurrencies have proven to be an attractive means for companies looking to 
raise capital. An initial coin offering  (ICO) is an unregulated process whereby com -
panies sell their crypto tokens to investors in exchange for fiat money or for another 
agreed upon cryptocurrency. An ICO is typically structured to issue digital tokens to 
investors that can be used to purchase future products or services being developed 
by the issuer. ICOs provide an alternative to traditional, regulated capital-  raising pro -
cesses, such as initial public offerings (IPOs). Compared to the regulated IPO market,

ICOs may have lower associated issuance costs and shorter capital raising time frames. 
However, most ICOs do not typically have attached voting rights. Regulation for ICOs 
is under consideration in a number of jurisdictions, and there have been numerous 
instances of investor loss resulting from fraudulent schemes.
7.2.2  Tokenization
Transactions involving physical assets, such as real estate, luxury goods, and com -
modities, often require substantial efforts in ownership verification and examination 
each time a transfer in ownership takes place. Through tokenization , the process of 
representing ownership rights to physical assets on a blockchain or distributed ledger, 
DLT has the potential to streamline this process by creating a single, digital record of 
ownership with which to verify ownership title and authenticity, including all historical 
activity. Real estate transactions that require ownership and identify verification may

be one area to benefit from tokenization, because these transactions are typically labor 
intensive and costly, involving decentralized, paper-  based records and multiple parties.
7.2.3  Post-  Trade Clearing and Settlement
In the financial securities markets, post-  trade processes to confirm, clear, and settle 
transactions are often complex and labor intensive, requiring multiple interactions 
between counterparties and financial intermediaries. DLT has the ability to streamline 
existing post-  trade processes by providing near-  real-  time trade verification, recon -
ciliation, and settlement, thereby reducing the complexity, time, and costs associated 
with processing transactions. A single distributed record of ownership between net -
work peers would eliminate the need for independent and duplicative reconciliation 
efforts between parties and reduce the need for third-  party facilitation. A shortened

Summary 473
settlement time frame could lessen the time exposed to counterparty risk and associated 
collateral requirements while increasing the potential liquidity of assets and funds. 
Additionally, the use of automated contracts may also help to reduce post-  trade time 
frames, lowering exposure to counterparty credit risk and trade fails.
7.2.4  Compliance
Regulators worldwide have imposed more stringent reporting requirements and 
demand greater transparency and access to data. To meet these requirements, many 
firms have added staff to their post-  trade and compliance groups. But these functions 
remain predominantly manual. To comply with regulations, firms need to maintain 
and process large amounts of risk-  related data. DLT may allow regulators and firms 
to maintain near-  real-  time review over transactions and other compliance-  related 
processes. Improved post-  trade reconciliation and automation through DLT could

lead to more accurate record keeping and create operational efficiencies for a firm’s 
compliance and regulatory reporting processes, while providing greater transparency 
and auditability for external authorities and regulators.
DLT-  based compliance may better support shared information, communications, 
and transparency within and between firms, exchanges, custodians, and regulators. 
Closed or permissioned networks could offer advantages in security and privacy. 
These platforms could store highly sensitive information in a way that is secure but 
easily accessible to internal and external authorities. DLT could help uncover fraud -
ulent activity and reduce compliance costs associated with know-  your-  customer and 
anti-  money-  laundering regulations, which entail verifying the identity of clients and 
business partners.
 
DLT Challenges
A number of challenges exist before DLT may be successfully adopted by the investment 
industry. These include the following:

■■ There is a lack of DLT network standardization, as well as difficulty integrating with 
legacy systems.
■■ DLT processing capabilities may not be financially competitive with existing 
solutions.
■■ Increasing the scale of DLT systems requires substantial (storage) resources.
■■ Immutability of transactions means accidental or “canceled” trades can be undone 
only by submitting an equal and offsetting trade.
■■ DLT requires huge amounts of computer power normally associated with high 
electricity usage.
■■ regulatory approaches may differ by jurisdiction.
SUMMARY
■■The term “fintech” refers to technological innovation in the design and delivery 
of financial services and products.

Reading 43 ■ Fintech in Investment Management 474
■■Areas of fintech development include the analysis of large datasets, analytical 
techniques, automated trading, automated advice, and financial record keeping.
■■Big Data is characterized by the three Vs—volume, velocity, and variety—and 
includes both traditional and non-  traditional (or alternative) datasets.
■■Among the main sources of alternative data are data generated by individuals, 
business processes, and sensors.
■■Artificial intelligence computer systems are capable of performing tasks that 
traditionally required human intelligence at levels comparable (or superior) to 
those of human beings.
■■Machine learning (ML) computer programs are able to “learn” how to complete 
tasks, improving their performance over time with experience. Main types of 
ML include supervised and unsupervised learning.
■■Natural language processing is an application of text analytics that uses insight

into the structure of human language to analyze and interpret text- and voice-  
based data.
■■Robo-  advisory services are providing automated advisory services to increasing 
numbers of retail investors. Services include asset allocation, portfolio optimi -
zation, trade execution, rebalancing, and tax strategies.
■■Big Data and ML techniques may provide insights into real-  time and changing 
market circumstances to help identify weakening or adverse trends in advance, 
allowing for improved risk management and investment decision making.
■■Algorithmic traders use automated trading programs to determine when, 
where, and how to trade an order on the basis of pre-  specified rules and mar -
ket conditions. Benefits include speed of executions, lower trading costs, and 
anonymity.
■■Blockchain and distributed ledger technology (DLT) may offer a new way 
to store, record, and track financial assets on a secure, distributed basis.

Applications include cryptocurrencies and tokenization. Additionally, DLT may 
bring efficiencies to post-  trade and compliance processes through automation, 
smart contracts, and identity verification.

Practice Problems 475
1 A correct description of fintech is that it:
A is driven by rapid growth in data and related technological advances.
B increases the need for intermediaries.
C is at its most advanced state using systems that follow specified rules and 
instructions.
2 A characteristic of Big Data is that:
A one of its traditional sources is business processes.
B it involves formats with diverse types of structures.
C real-  time communication of it is uncommon due to vast content.
3 In the use of machine learning (ML):
A some techniques are termed “black box” due to data biases.
B human judgment is not needed because algorithms continuously learn from 
data.
C training data can be learned too precisely, resulting in inaccurate predictions 
when used with different datasets.
4 Text Analytics is appropriate for application to:
A economic trend analysis.
B large, structured datasets.
C public but not private information.

5 In providing investment services, robo-  advisers are most likely  to:
A rely on their cost effectiveness to pursue active strategies.
B offer fairly conservative advice as easily accessible guidance.
C be free from regulation when acting as fully-  automated wealth managers.
6 Which of the following statements on fintech’s use of data as part of risk analy -
sis is correct?
A Stress testing requires precise inputs and excludes qualitative data.
B Machine learning ensures that traditional and alternative data are fully 
segregated.
C For real-  time risk monitoring, data may be aggregated for reporting and 
used as model inputs.
7 A factor associated with the widespread adoption of algorithmic trading is 
increased:
A market efficiency.
B average trade sizes.
C trading destinations.
8 A benefit of distributed ledger technology (DLT) favoring its use by the invest -
ment industry is its:
A scalability of underlying systems.

B ease of integration with existing systems.
C streamlining of current post-  trade processes.

Reading 43 ■ Fintech in Investment Management 476
9 What is a distributed ledger technology (DLT) application suited for physical 
assets?
A Tokenization
B Cryptocurrencies
C Permissioned networks

Solutions 477
SOLUTIONS
1 A is correct. Drivers of fintech include extremely rapid growth in data (includ -
ing their quantity, types, sources, and quality) and technological advances 
enabling the capture and extraction of information from it.
2 B is correct. Big Data is collected from many different sources and is in a 
variety of formats, including structured data (e.g., SQL tables or CSV files), 
3 C is correct. Overfitting occurs when the ML model learns the input and target 
dataset too precisely. In this case, the model has been “over trained” on the data 
and is treating noise in the data as true parameters. An ML model that has been 
overfitted is not able to accurately predict outcomes using a different dataset 
and may be too complex.
4 A is correct. Through the Text Analytics application of natural language pro -
cessing (NLP), models using NLP analysis may incorporate non-  traditional

information to evaluate what people are saying—via their preferences, opinions, 
likes, or dislikes—in the attempt to identify trends and short-  term indicators 
about a company, a stock, or an economic event that might have a bearing on 
5 B is correct. Research suggests that robo-  advisers tend to offer fairly conser -
vative advice, providing a cost-  effective and easily accessible form of financial 
guidance to underserved populations, such as the mass affluent and mass mar -
ket segments.
6 C is correct. There is increasing interest in monitoring risk in real-  time. To do 
so, relevant data must be taken by a firm, mapped to known risks, and identi -
fied while moving within the firm. Data may be aggregated for reporting pur -
poses or used as inputs to risk models.
7 C is correct. Global financial markets have undergone substantial change as 
markets have fragmented into multiple trading destinations consisting of elec -

tronic exchanges, alternative trading systems, and so-  called dark pools. In such 
an environment, when markets are continuously reflecting real-  time infor -
mation and continuously changing conditions, algorithmic trading has been 
viewed as an important tool.
8 C is correct. DLT has the potential to streamline the existing, often complex 
and labor intensive post-  trade processes in securities markets by providing 
close to real-  time trade verification, reconciliation, and settlement, thereby 
reducing related complexity, time, and costs.
9 A is correct. Through tokenization—the process of representing ownership 
rights to physical assets on a blockchain or distributed ledger—DLT has the 
potential to streamline this rights process by creating a single, digital record of 
ownership with which to verify ownership title and authenticity, including all 
historical activity.

Index I-1
A
AAR. see average accounting rate of 
return
Abbott Laboratories, 135–136
ability to take risk, investors’ , 371–373. 
see also  risk tolerance
ABP (pension fund), 388–389
absolute risk objectives, 370
Abu Dhabi Investment Authority, 221
access, short-term borrowing strategy 
and, 191
accounting risk, 427
accounts payable management,  
185–188
cash disbursements, 188
evaluating, 188
trade discounts, 187–188
accounts receivable aging schedule, 
180–181
accounts receivable management, 
175–181
customers’ receipts, 177–180
evaluating, 180–181
trade granting process, 176–177
accounts receivable turnover, 160
accredited individuals, 236n.20
ACH. see Automated Clearing House
acid-test ratio, 160
actively managed funds, 232
active portfolios, capital market line for, 
318
active strategies
borrowing, 192
short-term investing, 171–172
activist shareholders. see shareholder 
activism
ADC Telecommunications, 209–210
adviser-assisted digital wealth managers, 
468
affiliated stockholders, as takeover 
defense, 34

after-tax cost of debt, 85
after-tax nominal return, 254
agency relationship, 11. see also  
principal–agent relationship
aging schedule, 180–181
AGM. see annual general meeting
AI. see artificial intelligence
algorithmic trading, 469
algorithms, 462
Alibaba, 13, 32
Aloha Airlines, 438n.30
Alpha Natural Resources, 334–335
alternative data, 457, 460
analysts
corporate governance considerations, 
31–36
board of directors representation, 32
composition of investors, 33–34
economic ownership and voting 
control, 31–32
long-term risk management, 35remuneration and company 
performance, 32–33
shareholders’ rights, 34
estimates of value by, 48
natural language processing for 
monitoring, 466
analytical tools, 456
Andrew W. Mellon Foundation, 219
annual general meeting (AGM), 15
annualized return, 251–253
anticipation stock, of inventory, 183
Appendices, IPS, 369
Apple, 334–335
arbitrage, 236
arbitrage pricing theory (APT), 353
arithmetic return, 246
Armitage, Seth, 105

artificial intelligence (AI), 456, 460–462. 
see also  machine learning
asset(s). see also  investment 
characteristics of assets
physical, 472
quick, 160
risk-free, 291–294
and capital allocation line, 291–292
and capital market line, 319–321
combining risky assets with, 315–318
and homogeneity of expectations 
assumption, 317–318
two-fund separation theorem, 
292–293
utility theory and selection of, 
273–276
risk of two-asset portfolio, 258–259
risky
combining risk-free assets with, 
315–318
covariance and correlation of risks, 
277–279
efficient frontier of, 291
importance of correlation of risks in 
portfolio, 282
portfolio return, 276
portfolio risk, 276–282
risk and return relationship, 279–281
273–276
tradable, 319
variance of return for single, 256
asset allocation. see also  strategic asset 
allocation (SAA)
in portfolio management, 223
tactical, 393–394
asset-based loans, 192
asset beta, 95–98
asset class(es)

adding to investment opportunity set, 
289
correlation matrix, 386–387
correlation of risk among, 285
defining, 384
diversification with, 286nominal returns, 260–262
real returns, 261–262
risk and return of, 260, 263
robo-advisory services to manage, 
467–468
in strategic asset allocation, 385–387
asset risk premium, 216
assignments of accounts receivable, 192
assumptions
CAPM, 335–337, 348n.6
heterogeneous beliefs, 347, 350–351
homogeneity of expectations, 317–318, 
336–337, 352
infinite divisibility, 337
AstraZeneca PLC, 246
audit committee, 23
audit function, 17
audit systems, 22
Australia
equity risk premiums, 90
robo-advisory services in, 466
Australian Financial Services license, 466
Australian Securities and Investment 
Commission, 466
Austria, 19
authorities, investment policy, 172
automated advice, 457
Automated Clearing House (ACH), 
177–178
automated trading, 456
average accounting rate of return (AAR), 
57–58
average inventory period, 161
A.W. Jones & Co., 235
B

B
backtesting simulations, 469
Baidu, 244
balanced funds, 229–230, 232–233
Bancel, Franck, 108
bank certificates of deposit (CDs), 168
banker’s acceptances (BAs), 168, 190
bank runs, 429n.24
bankruptcy, business risk and, 145–147
bankruptcy risk, 29
banks
credit from, 189–190
portfolio management for, 220
risk management for, 410
bank sweep services, 168
Barings Bank, 428
BAs. see banker’s acceptances
Belgium, 90
beliefs, investors’ , 336–337, 347,  
350–351
benchmark rate, 174
best-in-class, 37
beta, 328–335
asset, 95–98
calculation and interpretation, 
331–332
and CAPM, 332–333, 352

I-2 Index
beta ( Continued )
estimating, 94–100
with CAPM, 332–333
inferring asset betas, 98
pure-play method, 97, 98
and expected return, 333–335
levering and unlevering, 95
return-generating models, 328–329
risk budgeting with, 422
as risk metric, 436
and security characteristic line, 346
bid–ask spread, 266
Big Data, 457–460
challenges of, 460
defined, 457
extracting information from, 463–465
in risk analysis, 468–469
sources of, 458–460
Bill & Melinda Gates Foundation, 219
bill-to-bill terms, 177
bitcoin, 471
blockchains, 470–471
Blume, Marshall, 94n.22
board, risk governance, 413, 420
board member–shareholder 
relationships, 8–9, 12–13
board of directors, 21–25
committees, 22–25
governance committee, 23
investment committee, 24
nomination committee, 23
remuneration (compensation) 
committee, 23
risk committee, 24
composition of, 21–22, 32
employee representation on, 19
functions and responsibilities, 22
manager relations with, 13
staggered boards, 21–22
stakeholder management mechanisms, 
17

17
as stakeholders, 9–10
bond equivalent yield, 170
bond ETFs, 234
bond mutual funds, 229–232
bonds
correlation of T-bills/stocks with, 284, 
285
defined, 259
government, 386
historical risk and return, 259–260
investment grade, 386
municipal, 379
nominal returns of, 262
real returns of, 261–262
surety, 443
US Treasury, 88, 90, 386
bond yield plus risk premium approach, 
93
borrowers, size and short-term strategy 
of, 191
borrowing
costs of, 186, 193–194
short-term, 167, 191–192
borrowing rates, effects on leveraged 
portfolios, 324–326
bottom-up portfolio analysis, 223
BP plc, 38Brazil, 24
breakeven points
and leverage, 143–144
operating, 143–145
breaking the buck, 231
break point, 102, 103
broad-based equity ETFs, 234
brokerage commissions, 266
Brounen, Dirk, 108
Bruce, Roger, 209
Bruner, Robert F., 89n.12
budgeting, risk, 421–423
Bühner, Thomas, 105
business processes, as Big Data sources, 
458–460
business risk
components of, 128
for creditors and owners, 145–147
defined, 95

financial risk, 136–140
and leverage, 128–136
operating risk, 130–136
sales risk, 128–130
buy-and-hold strategies, 246n.2
buyout funds, 237
buy-side firms, 225
C
CAC 40 Index, 318
Cadbury Report, 7
Canada
ACH system, 178
common law system, 27
say on pay, 18
cannibalization, 51
capital
cost of ( see cost of capital)
human, 419n.12
proportions of, 81–82
capital allocation line. see also  capital 
market line
defined, 273, 314
of optimal portfolio, 294–295
and optimal risky portfolio, 291–292
and portfolio selection, 273–276
for risk-free assets in portfolios of risky 
assets, 316
SML vs., 337–339
capital asset pricing model (CAPM), 
335–354
applications, 340–351
capital budgeting, 340–341
estimate of expected return, 340–341
portfolio construction, 348–351
portfolio performance evaluation, 
341–346
security characteristic line, 346–347
security selection, 347–348
assumptions of, 335–337
and beta/expected return, 333–335
cost of common equity, 88–92, 
107–108

107–108
extensions, 353–354
limitations, 351–352
and portfolio construction, 348–351
security market line, 337–340
and expected return, 338–339
portfolio beta, 339–340capital budget, planning of, 48
capital budgeting, 47–75
CAPM for, 340–341
and cost of capital, 82–84
importance of, 47–48
investment decision criteria, 52–68
average accounting rate of return, 
57–58
internal rate of return, 53–54, 60–66
net present value, 52–53, 58–63
payback period, 54–57
popularity and use of capital 
budgeting methods, 66–68
profitability index, 58
popularity and use of, 66–68
practice problems, 70–72
principles, 50–52
process, 48–49
solutions to problems, 73–75
capital gains taxes, 254
capital market expectations, 385
capital market line (CML), 318–326
defined, 319–321
and definition of market, 319
of leveraged portfolios, 322–326
with different lending/borrowing 
rates, 324–326
with equal lending/borrowing rates, 
323
passive and active portfolios, 318
risk and return on, 321–322

and single-index model of beta, 329, 330
capital market theory, 314–326
capital market line, 318–326
portfolio of risk-free and risky assets, 
314–318
combining risk-free asset with risky 
assets, 315–318
homogeneity of expectations 
capital rationing, 52
capital structure
marginal cost of capital structure, 
102–105
target, 80
CAPM. see capital asset pricing model
captive finance subsidiaries, 175
capture (data processing method), 463
carbon assets, 39
Carhart, Mark, 329
carrying costs, 184
cash
minimum balances, 165
monitoring uses and levels of, 166–167
cash before delivery (CBD), 177
cash collections systems, 177–180
cash concentration, 179
cash conversion cycle, 163
cash dividends, in returns, 245
cash flows, 164–167
in capital budgeting, 50–51
conventional, 51
discounted cash flow techniques, 67n.5
free cash flow to equity, 84n.7
free cash flow to the firm, 84n.6
incremental, 51
IRR vs. NPV and patterns in, 60–61

Index  I-3
monitoring cash uses and levels, 
166–167
nonconventional, 51
short-term, 165–166
cash forecasting systems, 166
identifying typical cash flows, 
165–166
and minimum cash balances, 165
typical, 165–166
cash inflows, in forecasts, 166
cash management, 164–167
cash on delivery (COD), 177
cash outflows, in forecasts, 166
cash position, 164–167
Cathay Pacific Airways, 210–213
CBD. see cash before delivery
C/C++ (programming language), 465
CDs. see certificates of deposit
Central Bank of Brazil, 24
central banks, 438
centralization, of financial organization, 
186
CEO duality, 21
CEOs. see chief executive officers
certificates of deposit (CDs), 168
CFA Institute, 369
CFOs. see chief financial officers
Chapter 7 bankruptcy, 146n.8, 147
Chapter 11 bankruptcy, 146–147
charitable foundations, endowments for, 
218–220
charities, strategic asset allocation for, 
395–397
chief executive officers (CEOs), 21
chief financial officers (CFOs), 107–108
chief risk officers (CROs), 419
China
two-tier boards, 10

China
China Investment Corporation, 221
Citibank Inc., 90
Citigroup, Inc., 93
civil law system, 27
clearing, post-trade, 472–473
clients
gathering information from, 381–384
individual investors as, 216
institutional investors as, 216–222
Climate Bond Initiative, 38
climate change, 38
closed-end funds, 228
CML. see capital market line
COD. see cash on delivery
Code of Hammurabi, 441
codes of ethics (generally), 20
collateral, 19
collateralized loans, 189, 191
Columbia University, 218
Comcast, 13
commercial paper (CP), 169, 190
commissions, brokerage, 266
commitment fees, 193n.10
committed lines of credit, 190
Committee on the Financial Aspects of 
Corporate Governance, 7
commodities, correlation with other 
asset classes, 386
common equity, cost of. see cost of 
common equitycommon law system, 27
common shares, 31–32
communication
analysis of, 466
in risk management framework, 412
co-movement patterns, 213–215
Companies Act 2006 (United Kingdom), 
14
company(-ies)
comparable, 95

14
as risk drivers, 434
company stakeholders, 8–14
relationships, 11–14
controlling shareholder–minority 
shareholder relationships, 12–13
manager–board relationships, 13
principal–agent relationship, 11
shareholder–manager/director 
relationships, 11–12
shareholder vs. creditor interests, 13
various conflicts, 13
stakeholder groups, 8–11
board of directors, 9–10
creditors, 9
customers, 10
employees, 9
governments, 10
managers, 9
regulators, 10
shareholders, 8–9
suppliers, 10
company value, cost of capital and, 78
comparable company, 95
compensation
and company performance, 32–33
policy development, 18
remuneration vs., 9n.3
say on pay, 18–19
compensation committee, 23, 24
compensation plans, 33
compensation policies, 29
complacency, passive investment 
strategies and, 171
compliance, 473
“comply or explain” codes, 34
component cost of capital, 78
conditional value at risk (CVaR), 437
conflicts of interest, 18
Conroy, Robert M., 89n.12
consensus mechanism, 470, 471
contingent claims, 444

contractual infrastructure, 14
contribution margin, 131
control, governance practices and, 30
controlling shareholders, 9
control systems
board’s role in, 22
weak, 28
conventional cash flow, 51
convertible arbitrage, 236
core–satellite approach, 397–398
Corning, 209–210
corporate bond mutual funds, 231
corporate exhaust, 459
corporate governance, 5–36
about, 6–8
analyst considerations, 31–36
composition of investors, 33–34economic ownership and voting 
long-term risk management, 35
remuneration and company 
boards of directors, 21–25
composition of, 21–22
defined, 6
factors affecting, 25–28
market factors, 25–26
non-market factors, 27–28

non-profit organizations, 10–11
risks and benefits, 28–31
benefits of effective governance, 29–31
risks of poor governance, 28–29
stakeholder management, 14–20
about, 14
defined, 14
mechanisms, 15–20
corporate governance committee, 23
corporate governance industry, 28
corporate governance reports, 20
corporate transparency, 17
correlation(s)
of asset classes, 285, 386–387
defined, 277
and historical risk, 284
and investment opportunity set, 288–289
and portfolio risk, 277–279, 282
and risk diversification, 284
of risk-free asset in portfolio of risky 
assets, 315
risk from changing, 427n.21
correlation coefficient, 277
COSCO Pacific, 210–213
cost of capital, 50, 77–121
about, 78–79
for capital budgeting and security 
valuation, 82–84
and company value, 78
cost of common equity, 88–93
bond yield plus risk premium 
approach, 93
CAPM approach, 88–92

dividend discount model approach, 
92–93
and equity risk premium, 89–92
cost of debt, 84–86
debt-rating approach, 85
estimating, 86
yield-to-maturity approach, 84–85
cost of preferred equity
best estimate, 87–88
calculating, 87

I-4 Index
cost of capital ( Continued )
cost of preferred stock, 86–88
and country risk, 100–101
defined, 78
estimating, 93–108
with beta and project beta, 94–100
with weighted average cost of capital, 
98–100
flotation costs, 105–107
in investment decision-making by 
CFOs, 107–108
marginal cost of capital schedule, 
102–105
practice problems, 111–117
solutions to problems, 118–121
and taxes, 79–80
weights for, 80–82
92–93
after-tax, 85
for capital budgeting, 50
company’s, 93n.19
defined, 84
and governance, 30
and taxes, 79
costs
carrying, 184
financing, 50
fixed
and breakeven points, 145
and degree of operating leverage, 
133–135
and degree of total leverage, 142–143
and leverage, 125–128
flotation, 105–107
inventory, 184
opportunity, 50, 51

ordering, 184
policy, 184
stock-out, 184
sunk, 51
transaction, 336, 348n.6, 425–426
variable, 126–128, 133–135
cost structure, leverage and, 126–128
counterparty risk, 425, 431
country risk, cost of capital and, 100–101
covariance
and correlation of risks in portfolio, 
277–279
of return, 257
and strategic asset allocation, 390
covenants, 9, 19
C P.  see commercial paper
credit
and accounts receivable management, 
175
as drag on liquidity, 158for short-term financing, 189–191
trade, 185, 186
credit accounts, 176–177
credit default swaps, 438n.32
credit events, 438
credit insurance, 176
credit limits, 159
credit lines
restrictions on, 159
for short-term financing, 189–191
creditors
contractual agreements with, 19
legal protections for, 27
shareholder interests vs., 13
as stakeholders, 9
creditors, business risk for,  
145–147
credit rating agencies, 30
credit ratings, 101, 438
credit risk, 30, 171, 425, 438. see also  
default risk

credit scoring model, 177
credit-worthiness, 159, 177, 191
CROs. see chief risk officers
cross-shareholdings, 33–34
cryptocurrencies, 472
cryptography, 470
culture, risk, 416
cumulative voting, 16
curation (data processing method),  
463
currency risk, managing, 409–410
current ratio, 160
customers
contractual agreements with, 20
receipts of, 177–180
shareholder conflicts with, 13
as stakeholders, 10
supplier conflicts with, 13
CVaR. see conditional value at risk
CVS Corporation, 95
D
Damodaran, Aswath, 101n.31
data
alternative, 457, 460
overfitting of, 461
semi-structured, 458
structured, 458
traditional, 457
unstructured, 458
databases, 465, 470
data processing methods, 463
data science, 463–465
data visualization, 463–465
datasets
analysis of large, 456
in machine learning, 461
Daves, Phillip R., 94n.21
David and Lucile Packard Foundation, 
219
days in receivables, 160, 181
day’s sales outstanding, 160
DB pension plans. see defined benefit 

DC pension plans. see defined 
contribution pension plansdealers, risk shifting to, 445
debt
cost of ( see cost of debt)
fixed- vs. floating-rate, 86
leveraging role of, 139–140
nonrated, 86
with optionlike features, 86
debt incurrence test, 102
debt-rating approach, for cost of debt, 
85
debt-to-equity ratio, 81–82
decision making, ineffective, 29
decisions
capital budgeting, investment decision 
criteria for, 52–68
57–58
internal rate of return, 53–54
net present value, 52–53
CFOs, investment decision-making by, 
107–108
risk management, 407–408
decomposition of total risk, 330
dedicated short bias strategies, 236
deep learning, 462
Deepwater Horizon oil spill, 38
default risk. see also  credit risk
attributes and safety measures, 171
defined, 425
governance and, 29, 30
defined benefit (DB) pension plans, 217

defined contribution (DC) pension 
plans, 216
degree of financial leverage (DFL)
defined, 137
and degree of total leverage,  
142–143
degree of operating leverage (DOL)
calculating, 135
defined, 130
and financial risk, 140–142
and operating risk, 130–135
degree of total leverage (DTL), 
141–143
Dell Corporation, 184n.8
delta, 436
Denmark, 90
derivatives
beta for, 436
risk shifting with, 443–445
DFL. see degree of financial leverage
digital wealth managers, 468
Dimson, Elroy, 89–90
direct debit programs, 178
directors. see board members
disbursement float, 186
discounted payback period, 56–57
discounted receivables, 190
discounted securities, yields of,  
169–170
discount interest, 169
discounts, trade, 187–188

Index  I-5
distributed ledger technology (DLT), 
469–473
about, 469–471
applications of, 472–473
post-trade clearing and settlement, 
472–473
tokenization, 472
financial record keeping with, 457
permissioned and permissionless 
networks, 471
distributional characteristics of assets, 
264–266
kurtosis, 265–266
skewness, 264–265
diversification
and employee stock options, 208–210, 
286, 381
and investing in portfolios vs. single 
equities, 208–210
and portfolio risk, 278
of portfolio risk, 282–287
as risk modification method, 441
diversification ratio, 212
dividend discount model approach
for cost of common equity, 92–93
for cost of equity, 91
in decision-making by CFOs’ , 107
dividend income, taxes on, 254
DLT. see distributed ledger technology
“The Doctrine of No Surprises, ” 410
documentary credit accounts, 176
Dodd–Frank Act (2011), 18
DOL. see degree of operating leverage
Dow Jones 30 Index, 332
Dow Jones Industrial Average, 284
downside risk, 213–215
drag on liquidity, 158–159

DTL. see degree of total leverage
dual-class share structure
and controlling–minority shareholder 
relationships, 12–13
and voting control, 31–32
duration, 436
duty of care, 22
duty of loyalty, 22
E
e-commerce, 186–187
economic activity, risk and, 407
economic order quantity–reorder point 
(EOQ-ROP) approach, 183
EDI. see electronic data interchange
efficient frontier, 288–300
indifference curve, 294–295
investment opportunity set, 288–289
investor preferences and optimal 
portfolio, 299–300
Markowitz, 291, 319–320
minimum-variance portfolios, 289–291
portfolio selection example, 294–299
for risk-free assets, 291–294
and strategic asset allocation, 390–391
EFT. see electronic funds transfer
Ehrhardt, Michael C., 94n.21
elasticity, 130
electronic data interchange (EDI), 
186–187electronic funds transfer (EFT),  
177–180
emerging markets, 236
employee(s), 9
employee benefit plans, 23
employee representatives, 21
employee rights, 19–20

employee stock options, diversification 
and, 208–210, 286, 381
employee stock ownership plans 
(ESOPs), 19
employment contracts, 19
endowments, portfolio management for, 
218–220
energy sector
ESG factors in investment analysis, 39
thematic investing, 37
Enron Corporation, 28, 208–209, 432
enterprise risk management
defined, 411
process for, 413–415
risk governance in, 417–419
risk tolerance in, 420
enterprise risk management system, 22
environmental, social, governance (ESG) 
considerations, 36–40
about, 6
as catalysts for growth, 38–39
governance ( see corporate governance)
implementation methods, 37–38, 40
in investment analysis, 39–40
in investment policy statements, 
380–381
market overview, 39
terminology, 36–37
environmental projects, capital 
budgeting for, 49
EOQ-ROP approach. see economic 
order quantity–reorder point 
approach
equities
correlation of, 386–387
investing in portfolios vs., 207–208
and diversification, 208–210
and downside risk, 213–215

and modern portfolio theory, 
215–216
and portfolio composition, 212–213
and risk–return tradeoff, 210–212
equity market neutral strategies, 236
equity risk premium (ERP), 89–92
Erb, Claude, 101n.32
ESG considerations. see environmental, 
social, governance considerations
ESG integration/incorporation, 37
ESG investing, 37
ESOPs. see employee stock ownership 
plans
estimation
of beta, 94–100
inferring asset beta, 98
market model, 332–333
of cost of capital, 93–108
and decision-making by CFOs, 
107–108
and flotation costs, 105–107and marginal cost of capital 
structure, 102–105
98–100
of cost of debt, 86
of cost of equity, 88–93
of cost of preferred equity, 87–88
of expected returns, 340–341
of value by analysts, 48
of weighted average cost of capital, 
98–100
estimation period, beta, 94
ETFs. see exchange traded funds
ethics. see codes of ethics

Eurodollar rate, 190
Eurodollar time deposits, 168
Europe
correlation of equities, 386–387
Giro system, 178
hybrid/balanced funds, 232–233
money market funds, 230–231
mutual fund assets, 230
rights offerings, 105
European Union
employee rights, 19
sell-out rights, 16
European Works Councils, 19
Evaluation and Review, IPS, 369
evaluation datasets, 461
event-driven strategies, 236
ex ante  models, 352
Excel VBA (programming language), 
465
exchange traded funds (ETFs),  
233–235
exclusionary screening, 37
execution step (portfolio management), 
223–225
asset allocation, 223
portfolio construction, 223–225
security analysis, 223
executive (management) board, 10
executive (internal) directors, 9, 21
expansion projects, capital budgeting 
for, 49
expectations
capital market, 385
assumption, 317–318, 336–337, 
352
expected inflation rate, 259
expected return(s)
and beta, 333–335
CAPM estimation of, 340–341
and historical mean return, 259–260

and SML, 338–339
expected risk premium, 259
“expert system, ” as artificial intelligence, 
460
ex post  models, 352
exposure, risk, 409–410
external auditors, 17
external (non-executive) directors,  
10, 21
externality, 51
extreme value theory, 437
Ezzell, John R., 83n.3, 106n.37

I-6 Index
F
Facebook, 13, 32
factoring, 190, 192
Fama, Eugene, 89n.11, 89n.12, 329
F&C Stewardship Growth Fund, 
380–381
federal agency securities, 168
Federal Reserve, 438
feedback
in portfolio management, 225–226
performance measurement and 
reporting, 226
portfolio monitoring and rebalancing, 
225
in risk management framework, 415
Fidelity, 341–342
Financial Conduct Authority (FCA), 
368, 466
financial crisis (2008), 265–266, 429
financial leverage, 136–140
degree of, 137–138, 142–143
leveraging role of debt, 139–140
financial record keeping, 457
Financial Reporting Council, 7
financial risks, 95
defined, 424
drivers of, 434–435
and leverage, 136–140
non-financial vs., 432–433
types of, 424–426
financing
short-term, 189–194
borrowing approaches, 191–192
costs of borrowing for, 193–194
sources of, 189–191
financing costs, 50
Finland, 10
fintech, in investment management, 
455–477
about, 455–456

455–477
applications of, 465–469
natural language processing, 465–466
risk analysis, 468–469
robo-advisory services, 466–468
text analytics, 465
artificial intelligence, 460–461
defining, 456–457
distributed ledger technology, 469–473
machine learning, 460–462
practice problems, 475–476
solutions to problems, 477
first-order risk, 436n.28
Fisher, Irving, 82n.2Fitch Ratings, 438
fixed costs
133–135
fixed-income arbitrage, 236
fixed-rate debt, 86
fixed rate perpetual preferred stock, 
86–87
flexibility, of short-term borrowing 
strategy, 191
float, 179
float factor, 179
floating-rate debt, 86

float, 179
Ford Foundation, 219
forecasting, of short-term cash flows, 
165–166
foreign countries, diversification of 
investment in, 286
foreign exchange risk, 171
forward commitments, 444
fossil fuels, 37
foundations, portfolio management for, 
218–220
401(k) plans, 208–210
four-factor models for beta, 329, 353–354
France
corporate governance systems, 14
frequency of capital budgeting, 67
free cash flow to equity (FCFE), 84n.7
free cash flow to the firm (FCFF), 84n.6
French, Kenneth, 89n.11, 89n.12, 329
frictionless markets, 336
Frontier Airlines, 438n.30
FTSE 100 Index, 370, 375
fully automated digital wealth managers, 
468
fundamental factor models, 329
G
gamma, 436
Gascon, Henri (case study), 373–374, 
376, 382–384
Gascon, Jacques (case study), 374–375
general meetings, 15–16
geometric mean return, 246–247
Germany
cumulative voting rules, 16

employee representation on boards, 19
flotation costs, 105
Giro system, 177–178
Gitman, Lawrence, 107n.39
GlaxoSmithKline Plc, 18, 340–341
global bond mutual funds, 231
global ETFs, 234
global financial crisis of late 2000s
corporate governance and, 6
media’s effect on regulation following, 27global macro strategies, 236
global minimum-variance portfolios, 290
Global Reporting Initiative (GRI), 39
Global Sustainable Investing Alliance 
(GSIA), 39
gold, correlation with other asset classes, 
386
Google, 13, 244
Gordon, Myron J., 92n.18
Gordon growth model, 92
governance
corporate ( see corporate governance)
risk, 417–424
for enterprises, 417–419
establishing risk tolerance level, 
419–421
example, 423–424
with risk budgeting, 421–423
governance codes, 34
government(s)
governmental infrastructure, 14

government bond mutual funds, 231
government bonds, 386
Government of Singapore Investment 
Corporation, 221
government policies, as risk drivers, 434
governments, as Big Data sources, 458
Graham, John, 107
the “Greeks, ” 436
green bonds, 38
green finance, 38
GRI. see Global Reporting Initiative
gross return, 253–254
growth rate, sustainable, 92–93
Gulf Cooperation Council, 24
Gulf of Mexico oil spill (2010), 38
H
hackers, 428
Hamada, Robert S., 95n.24
Hang Seng Index, 213–215
Harvard University, 218
Harvey, Campbell R., 100n.28, 101n.32, 
107
health risk, 430
hedge funds, 26, 235–236
hedges, risk budgeting with, 423
Herstatt risk, 426n.19
heterogeneous beliefs assumption, 347, 
350–351
high-frequency trading (HFT), 469
high-yield bond mutual funds, 231
Hirschleifer, John, 82n.2
historical equity risk premium approach, 
89–92
historical mean return, 259–260
historical returns, 259–264
estimating cost of equity with, 89–92
historical mean return and expected

historical mean return and expected 
return, 259–260
nominal and real returns of asset 
classes in other countries, 
262–263
nominal returns of major US asset 
classes, 260–261

Index  I-7
real returns of major US asset classes, 
261–262
risk–return tradeoff for, 263–264
historical risk
risk of major asset classes, 263
risk–return tradeoff, 263–264
HKSE. see Hong Kong Stock Exchange
holding period return, 245
holding periods, CAPM assumptions 
about, 336
Home Depot, 438
homogeneity of expectations assumption, 
317–318, 336–337, 352
Hong Kong Monetary Authority 
Investment Portfolio, 221
Hong Kong Stock Exchange (HKSE)
HSBC Holdings on, 317–318
volatility of returns, 210–213
Hostess, 438n.30
hostile takeovers, 26
HSBC Holdings, 317–318
human capital, 419n.12
human rights, 38, 40
Hutchison Whampoa, 210–213
hybrid ETFs, 234
hybrid funds, 229–230, 232–233
I
Ibbotson, Roger G., 94n.23
IBM, 394
ICOs. see initial coin offerings
image recognition algorithms, 462
impact investing, 38
incentive plans, 18
income needs, in portfolio management, 
222
incremental cash flow, 51
indenture, 19
independent directors, 21
independent projects, 51
index funds
actively managed funds vs., 232
diversification with, 286

ETFs vs., 233, 235
India
one-tier boards, 10
pension fund investment restrictions, 
380
indifference curves
of optimal investor portfolio, 294–295
in portfolio selection, 274–276
and risk aversion, 269–271
and strategic asset allocation, 391
individual investors
and enterprise risk management, 
418–419
operational risks for, 430
portfolio management for, 216
risk drivers for, 435
risk interactions for, 431–432
risk management as concern of, 408
risk management process for, 415
risk tolerance of, 420n.14
individually managed accounts, 235
individuals, as Big Data sources, 459, 460
industry(-ies)
diversification according to, 381
as risk drivers, 434infinite divisibility assumption, 337
inflation, expected rate of, 259
inflation-protected bond mutual funds, 
231
informationally efficient markets, 318
information asymmetry, 12
information ratio, 350
infrastructure, risk, 412
initial coin offerings (ICOs), 472
installment credit accounts, 176
institutional investors

portfolio management for, 216–222
banks, 220
defined-benefit pension plans, 217
endowments and foundations, 
218–220
insurance companies, 220
investment companies, 221
sovereign wealth funds, 221
relative risk objectives of, 370
insurance
credit, 176
risk transfer with, 441–443
for risky portfolios, 287
insurance companies, 220, 440
interest, discount, 169
interest rate, risk-free, 93n.19, 259
interest rate risk, 171
internal (executive) directors, 9, 21
internal rate of return (IRR)
for capital budgeting, 53–54
multiple IRR problem, 64–66
no IRR problem, 64–66
defined, 248
ranking conflicts of NPV and IRR, 
60–63
due to cash flow patterns, 60–61
due to project scale, 62–63
international ETFs, 234
Internet of Things (IoT), 459
Introduction, IPS, 369
inventory
anticipation stock, 183
as drag on liquidity, 158
number of days of, 161, 185
precautionary stocks, 182
purchasing–inventory–payables 
process, 186–187
safety stock, 183
inventory blanket liens, 192

inventory costs, 184
inventory management, 182–185
and accounts payable management, 
186
approaches, 183–184
evaluating, 184–185
financial impact of inventory methods, 
185
and inventory costs, 184
inventory turnover, 160, 184–185
investment characteristics of assets, 
244–267
distributional characteristics,  
264–266
market characteristics, 266–267
return characteristics, 244–259
covariance of return, 257
historical returns, 259–264types, 245
variance of returns, 257
risk characteristics, 258–259
investment companies, portfolio 
management for, 221
Investment Company Act (1940), 235
Investment Company Institute,  
226–227
Investment Constraints, IPS, 369
investment decision criteria for capital 
budgeting, 52–68
57–58
popularity and use of capital budgeting 
methods, 66–68
investment decision-making, by CFOs,

investment decision-making, by CFOs, 
107–108
investment grade bonds, 386
Investment Guidelines, IPS, 369
investment ideas, in capital budgeting 
process, 48
investment instruments, for short-term 
funds management, 168–171. see 
also specific types
investment management, fintech in, 
455–477
natural language processing,  
465–466
extracting information from,  
463–465
distributed ledger technology,  
469–473
investment managers, selection of,  
397
Investment Objectives, IPS, 369
investment opportunity schedule (IOS), 
82

82
investment policies
components, 172–173
evaluating, 173–174
short-term funds management in, 
171–174

I-8 Index
investment policy statements (IPSs), 
368–381
components of, 369
defined, 222
and investor constraints, 376–381
legal and regulatory factors,  
379–380
liquidity, 376–378
tax concerns, 379
time horizon, 378–379
unique circumstances, 380–381
in planning step of portfolio 
management, 222–223
and portfolio construction, 389–392
return objectives, 375–376
risk objectives, 370–375
investment risks, short-term funds 
management and, 170–171
investment strategy, in portfolio 
construction, 393–397
investor questionnaires, 467
investors. see also  individual investors
beliefs of, 336–337, 347, 350–351
capital market expectations of, 385
CAPM assumptions about, 336
composition of, 33–34
constraints on
379–380
and portfolio planning, 376–381
objectives of, 243–244
preferences of, 299–300
willingness and ability to take risk, 
371–373
IOS. see investment opportunity 
schedule
IoT. see Internet of Things

schedule
IPSs. see investment policy statements
Ireland, 90
IRR. see internal rate of return
Italy, 27, 90
J
J. Paul Getty Trust, 219
Japan
employee involvement with decision 
making, 19
380
Java (programming language), 465
Jensen, Michael C., 94n.20
Jensen’s alpha
defined, 343–344
and security selection, 347
JIT method. see just-in-time method
John D. and Catherine T. MacArthur 
Foundation, 219
Jong, Abe de, 108
just-in-time (JIT) method, 183–184K
Kaplan, Paul D., 94n.23
Kaserer, Christoph, 105
Koedijk, Kees, 108
Kohl’s, 162–163
Kunkel, Robert A., 94n.21
Kuwait Investment Authority, 221
L
labor laws, 19
labor unions, 19
laddering strategies, 172
law, governance and, 20
LBOs. see leveraged buyouts
leases, 86
Lee, Inmoo, 105
Lee, Rafaelina M., 100n.30
Leeson, Nick, 428

legal environment, 27
legal factors, in IPSs, 379–380
legal infrastructure, 14
legal risk, 29, 426–427
Lehman Brothers, 429, 438
lending portfolios, 322
lending rates, effects on leveraged 
leverage, 125–154
about, 126–128
breakeven points, 143–145
business risk, 128–136
components of business risk, 128
defined, 125
financial, 136–140
degree of financial leverage, 137–138
fixed costs as, 125
measuring, 438
practice problems, 149–152
solutions to problems, 153–154
total, 140–143
leveraged buyouts (LBOs), 237
leveraged portfolios
capital market line for, 322–326
with different lending and borrowing 
with equal lending and borrowing 
rates, 323
leveraged positions, 255, 323
leveraged returns, 255
Li, Wei, 89n.12
Libor. see London Interbank Offered 
Rate
Li & Fung, 210–213
Lilly Endowment, 219

Rate
limitations, investment policy, 172
lines of credit
Lintner, John, 216, 335
liquidation, 146, 147
liquidity, 156–164
defined, 156–157
drags and pulls on, 158–159
as investor constraints, 376–378liquidity management, 157–159
as market characteristic, 266–267
measuring, 159–164, 438
and portfolio management, 222
primary sources, 157
secondary sources, 157–158
liquidity management, 157–159
liquidity ratios, 159–160
liquidity risk
as financial risk, 425–426
interactions of market and solvency 
risk with, 431
safety measures for, 171
solvency risk vs., 429n.23
Lleras, Miguel Palacios, 89n.12
Lloyd’s of London, 442–443
load funds, 228–229
loans
asset-based, 192
collateralized, 189, 191
Lochhead, Scott, 105
lockbox systems, 178
London Interbank Offered Rate (Libor)
as benchmark for returns, 375
defined, 190
marginal cost of capital structure, 104
London Stock Exchange
board composition rules, 24

and Committee on the Financial 
Aspects of Corporate Governance, 
7
long hedge fund strategies, 236
Long-Term Capital Management, 431
loss(es)
scenario, 422
stock-out, 182
low liquidity positions, 159
Luxembourg, 19
M
M2, 342–343
machine learning (ML), 460–462
defined, 461
in risk analysis, 469
types of, 461–462
macroeconomic factor models, 328–329
macroeconomic risk drivers, 434
managed accounts, 235
risk governance by, 419
in risk management framework, 
413–414
management (executive) board, 10
managers
digital wealth, 468
relations with board, 13
shareholder relationships, 11–12
use of fintech by, 455
manufacturing resource planning (MRP) 
systems, 183–184
marginal cost of capital (MCC), 82–83
marginal cost of capital (MCC) schedule, 
102–105
Mariscal, Jorge O., 100n.30
market characteristics of assets, 266–267
market index, for beta, 94

Index  I-9
market model, 94n.20, 330–333
market portfolio, in CAPM, 352
market price of risk, 273
market risk, 171, 425, 431
markets
algorithmic trading and fragmentation 
of, 469
as Big Data sources, 458
defined, 319
informationally efficient, 318
Markets in Financial Instruments 
Directive (MiFID), 368
Markowitz, Harry, 215, 335
Markowitz efficient frontier, 291, 
319–320
Marsh, Paul, 89–90
Massachusetts Institute of Technology, 
218
Massachusetts Mutual Life Insurance 
Company, 224–225
Massey Energy, 35
matching strategies, 171–172, 192
matrix pricing, 85
MCC. see marginal cost of capital
MCC schedule. see marginal cost of 
capital schedule
mean return, 246
media, governance and, 27
Mercurio, V., 107n.39
Metropolitan Life Insurance Company, 
225
Mian, Shehzad L., 175n.5
MiFID. see Markets in Financial 
Instruments Directive
Miles, James A., 83n.3
Miller, Merton, 95n.24
“mind maps, ” 464
minimum cash balances, 165
minimum-variance frontier, 290

and efficient frontier of risky assets, 
291
global, 290
minority (non-controlling) shareholders, 
9, 12, 16
mismatching strategies, 171–172
Mittoo, Usha, 108
ML. see machine learning
model risk, 427
modern portfolio theory (MPT), 
215–216, 335, 435
Modigliani, Franco, 95n.24, 342
Modigliani, Leah, 342
money market funds, 169, 230–231
money market yield, 170
money-weighted return, 248–249
monitoring
in capital budgeting process, 48–49
in portfolio management, 225
monthly billing terms, 177
Moody’s Analytics, 438
mortality risk, 430
Mossin, Jan, 335
MPT. see modern portfolio theory
MRP systems. see manufacturing 
resource planning systemsMSCI EAFE Index
correlation with other indexes, 386
MSCI Emerging Markets, 258–259, 386
MSCI Europe, 386
MSCI US Index, 386
MSCI World Index, 386
multi-factor model, 328
multiple-class share structure, 12–13
multiple IRR problem, for capital 
projects, 64–66

municipal bonds, 379
mutual funds, 226–233
about, 226–230
hedge funds vs., 235–236
short-term investment, 169
SMAs vs., 235
types, 230–233
bond mutual funds, 231–232
stock mutual funds, 232
mutually exclusive projects, 51
N
NASDAQ, 284
NASDAQ 100 Index, 332
national tax-free bond mutual funds, 
231
National Welfare Fund, 221
natural language processing (NLP), 
465–466
NBC, 443n.36
negative correlation, 277
negative screening, 37
net asset value
mutual fund, 226–227
Netherlands
fact finding requirements, 381
net operating cycle, 163–164
net present value (NPV), 58–63
in capital-budgeting decisions, 83
defined, 52–53
and IRR, 53–54
NPV profile, 58–60
ranking conflicts between IRR and, 
60–63
and stock prices, 67–68
net return, 253–254
networks
neural, 461, 462

networks
permissioned and permissionless, 471
neural networks, 461, 462
new products, capital budgeting for, 49
New York Stock Exchange (NYSE)
correlations of stocks, 284
trading volume, 336
Nikkei 300 Index, 318
Nikkei 500 Index, 213–215
N L P.  see natural language processing
no IRR problem, for capital projects, 
64–66no-load funds, 228
nominal rate, for securities, 169
nominal returns
of asset classes in other countries, 
262–263
of asset classes in United States, 
260–261
defined, 254
nonbank finance companies, 190
non-controlling (minority) shareholders, 
9
nonconventional cash flow, 51
non-executive (external) directors,  
9–10, 21
non-financial risks
financial vs., 432–433
types of, 426–430
nonmarket securities, weight of, 350
nonrated debt, cost of, 86
nonsystematic risk, 326–328
normal distribution, 264
norms-based screening, 37
Northern Telecom, 209–210

Northwestern University, 218
Norwegian Government Pension  
Fund-Global, 221
NoSQL (database), 465
NPV. see net present value
number of days of inventory, 161, 185
number of days of payables, 161, 188
number of days of receivables, 160, 181
NYSE. see New York Stock Exchange
O
of investors, 243–244
return, 375–376
risk, 370–375
of strategic asset allocation, 388–389
OECD. see Organisation for Economic 
Co-operation and Development
O’Halloran, Elizabeth, 89n.12
one-tier board structure, 9–10, 21
open book credit accounts, 176
open distributed ledger networks, 471
open-end funds, 228
operating breakeven points, 143–145
operating cycle, 163
operating income, 140
operating leverage. see degree of 
operating leverage
operating risk
defined, 95, 128
and leverage, 130–136
operational efficiency, 30
operational risk, 428–430, 438–439
opportunity costs, 50, 51
optimal portfolio, 243–364
331–332

331–332
estimation, 332–333
return-generating models,  
328–329

I-10  Index
optimal portfolio ( Continued )
and capital asset pricing model, 
335–354
assumptions, 335–337
and capital market theory, 314–326
risk-free and risky assets, portfolio of, 
314–318
and efficient frontier, 288–300
minimum-variance portfolios, 
289–291
risk-free assets, 291–294
and investment characteristics of 
assets, 244–267
distributional characteristics, 
264–266
as investor objective, 243–244
for investor with heterogeneous beliefs, 
350–351
optimal risky portfolio, 313–314
and portfolio risk, 276–287
diversification of risk, 282–287
portfolio with many risky assets, 
281–282
portfolio with two risky assets, 
276–281
practice problems, 302–308, 356–361

276–281
pricing of risk, 326–328
and risk aversion, 267–276
concepts, 267–268
indifference curves, 269–271
utility theory, 268–276
solutions to problems, 309–312, 362–364
optimal risky portfolio
and capital market line, 320
and homogeneity of expectations, 
317–318
portfolio selection for, 313–314
optionlike features, debt with, 86
options, 444–445
ordering costs, 184
ordinary terms, 176
Organisation for Economic 
Co-operation and Development 
(OECD), 7, 38, 216–217
organizational infrastructure, 14
overdraft lines of credit, 189
overfitting, of data, 461
overinvestment, in inventory, 182–183
Owens Corning Corporation, 146–147, 
209–210
owners, business risk for, 145–147
ownership, voting rights and, 31–32
P
P2P basis. see peer-to-peer basis, of 
record keeping
passive portfolios, 318passive strategies
borrowing, 191
employed by robo-advisors, 467
short-term investing, 171
payback period
capital budgeting, 54–56
discounted, 56–57
drawbacks of, 55–56
payments, as pull on liquidity, 158

peer-to-peer (P2P) basis, of record 
keeping, 457
pension funds
enterprise risk management for, 418
investment restrictions for, 379–380
defined benefit, 217
defined contribution, 216
Pensions Act (1995), 368
Pensions Regulator, 369
performance evaluation, 342. see also  
portfolio performance evaluation
performance measurement, in portfolio 
management, 226
performance reporting, in portfolio 
periodicity, of beta return interval, 94
permissioned networks, 471
permissionless networks, 471
per unit contribution margin, 131
Peterson, James D., 94n.23
pet projects, 49
physical assets, 472
PI. see profitability index
planning step (portfolio management), 
222–223
point of sale (POS) systems, 178
poison pills, 26
policy costs, 184
policy portfolios, risk objectives for, 370
pooled investments, 226–237
exchange traded funds, 233–235
hedge funds, 235–236
types of, 230–233
separately managed accounts, 235

venture capital funds, 237
population standard deviation, 257
Porter, R. Burr, 106n.37
portfolio beta, SML and, 339–340
portfolio construction, 384–398
about, 384–385
and CAPM, 348–351
implementing investment strategy, 
393–397
organizing principles for, 397–398
and portfolio management, 223–225
strategic asset allocation, 385–393
for European charity, 395–397
objective of, 388–389
for private investor, 392–393
specifying asset classes for, 386–387
portfolio management, 207–241
investing in portfolios vs. single 
equities, 207–208
diversification, 208–210
downside risk, 213–215and modern portfolio theory, 
215–216
risk–return tradeoff, 210–212
investment clients, 216–222
individual investors, 216
institutional investors, 216–222

practice problems, 239–240
risk budgeting for, 421–422
solutions to problems, 241
steps in, 222–226
execution, 223–225
feedback, 225–226
planning, 222–223
portfolio managers, risk management 
by, 408
341–346
example, 344–346
Jensen’s alpha, 343–344, 346
Sharpe ratio, 342
Treynor ratio, 342
portfolio planning, 368–384
case studies, 373–376, 382–384
gathering client information, 381–384
investment policy statements, 368–381
components, 369
investor constraints, 376–381
legal and regulatory factors, 379–380
unique circumstances on, 380–381
portfolio returns
defined, 253
for portfolios of risky assets, 276, 
315–316
portfolio risk, 276–287
diversification, 282–287
avenues for diversification, 285–287
correlation and risk diversification, 
284
historical correlation among asset 
classes, 285

284
historical risk and correlation, 284
for portfolios of risky assets
with many risky assets, 281–282
with one risk-free asset, 315–316
with two risky assets, 276–281
scenario analysis for, 469
portfolios
composition of, 212–213
as investment approach, 207–208
215–216

Index  I-11
portfolio selection
and capital allocation line, 273–276
comprehensive example, 294–299
for optimal risky portfolio, 313–314
and risk aversion, 273–276
with utility theory, 273–276
positive correlation, 277
positive screening, 37
POS systems. see point of sale systems
post-auditing, 48–49
472–473
precautionary stocks, of inventory, 182
preferred stock
cost of, 86–88
fixed rate perpetual, 86–87
premiums, of asset classes, 262. see also  
risk premiums
pre-tax nominal return, 254
PRI. see Principles of Responsible 
Investment
priced risk, 89
price impact, in cost of trading, 266
price takers, 337
pricing. see also  capital asset pricing 
model (CAPM)
arbitrage pricing theory, 353
matrix, 85
risk, 326–328
primary sources of liquidity, 157
Princeton University, 218
Principles of Corporate Governance,  7, 22
Principles of Responsible Investment 
(PRI) initiative, 39
private investors, strategic asset 
allocation for, 392–393
probability, 435

Procedures, IPS, 369
profitability, degree of operating leverage 
and, 133–134
profitability index (PI), 58
programming languages, 464–465
project beta. see beta
project sequencing, 51–52
proposals, in capital budgeting process, 48
proxy, for market portfolio, 352
proxy contests, 26
proxy voting, 16, 28
pull on liquidity, 158–159
purchasing–inventory–payables process, 
186–187
pure-play method, for beta, 95–98
purpose, investment policy, 172
Python (programming language), 464
Q
Qtel, 12
quality, investment policy, 173
quick assets, 160
quick ratio, 160
R
R (programming language), 464
rate of return
average accounting, 57–58
internal ( see internal rate of return 
(IRR))
required, 50, 91rationing, capital, 52
real estate, correlation with other asset 
classes, 386
real returns
262–263
261–262
defined, 254–255
real risk-free interest rate, 259
rebalancing, in portfolio management, 225
rebalancing policy, 395

receipts, customers’ , 177–180
discounted, 190
number of days of, 160, 181
record keeping, 457
regression analysis, 332–333
regular lines of credit, 189, 190
regulations, 20
regulators
and remuneration policies, 18
regulatory compliance, 473
regulatory factors, in IPSs, 379–380
regulatory projects, capital budgeting 
for, 49
regulatory risk, 29, 427
related-party transactions
and poor governance, 29
relative risk objectives, 370
remuneration. see compensation
reorganization, 146–147
replacement projects, capital budgeting 
for, 49
reporting, 17
reports
analyzed with machine learning, 466
in portfolio management, 226
on short-term investment portfolio, 174
repurchase agreements, 168
reputational risk, 29
required rate of return, 50, 91
responsible investing (RI), 36–37
restrictions, investment policy, 172
return(s), 244–259

annualized, 251–253
arithmetic, 246
and beta, 331–332, 339–340
on capital market line, 321–322
CAPM’s prediction of, 352
covariance of, 257
expected
geometric mean, 246–247
gross, 253–254
historical, 263
return, 259–260nominal and real returns of asset 
262–263
261–262
historical mean, 259–260
holding period, 245
leveraged, 255
mean, 246
money-weighted, 248–249
net, 253–254
nominal
262–263
260–261
pre-tax/after-tax, 254
portfolio
315–316
real, 254–255
262–263
of asset classes in United States,

262–263
261–262
risk and, 279–281 ( see also  risk–return 
tradeoff)
risk-free, 319–321
for risky assets, 276
uncorrelated, 277
variance of, 257
for portfolio of assets, 257, 281–282
for portfolio of risky assets, 315
for single asset, 256
and standard deviation, 257
return-generating models for beta, 
328–329, 351. see also  capital 
asset pricing model (CAPM)
decomposition of total risk for, 330
market model, 330–331
single-index models, 330
three- and four-factor, 329
return interval, beta, 94
return objectives, on IPSs, 375–376
reverse mortgage, 244n.1
revolving credit accounts, 176
revolving credit agreements, 189–191
rho, 436
RI. see responsible investing
rights, shareholder. see shareholder 
rights
risk(s). see also  portfolio risk
acceptance of, 441
accounting, 427
business

counterparty, 425, 431

I-12  Index
risk(s) ( Continued )
country, 100–101
credit, 171, 425, 438
currency, 409–410
default, 171, 425
defined, 409
downside, 213–215
and economic activity, 407
financial, 95
first- vs. second-order, 436n.28
foreign exchange, 171
health, 430
Herstatt, 426n.19
historical, 263–264
identification of, 424–433
financial risks, 424–426, 432–433
and interactions between risks, 
430–432
non-financial risks, 424, 426–430, 
432–433
in risk management framework, 411
infrastructure, 412
interactions between, 430–432
interest rate, 171
investment, 170–171
investors’ willingness/ability to take 
risk, 371–373
legal, 426–427
liquidity, 425–426
of major asset classes, 263
market, 171, 425, 431
market price of, 273
measurement of, 411–412, 435–439, 
446–447
model, 427
mortality, 430

446–447
model, 427
non-financial, 424, 426–430, 432–433
nonsystematic, 326–328
operating, 95, 128, 130–136
operational, 428–430, 438–439
prevention and avoidance of, 439–440
priced, 89
pricing of, 326–328
regulatory, 427
relationship of return and, 279–281
sales, 95, 128–130
settlement, 426
solvency, 429, 431
systematic, 326–328
and calculation of beta, 331–332
drivers of, 435
in Jensen’s alpha, 343
for single-index model of beta, 331
and strategic asset allocation, 384
in Treynor ratio, 342
tail, 427–428
tax, 427
total, 330, 342
tracking, 370n.2
of two-asset portfolio, 258–259unsystematic, 436n.27
value at risk, 370n.1
conditional, 437
and kurtosis, 265
as risk metric, 436–438
“wrong-way, ” 431
risk attitude, clients’ , 371
risk averse (term), 268
risk aversion, 267–276
in CAPM assumptions, 336
and indifference curves, 269–271
and optimal portfolio, 299–300
and utility theory, 268–276
computation of utility, 272

portfolio selection with utility theory, 
273–276
risk aversion coefficient, 269
risk budgeting, 393, 394, 421–423
risk culture, 416
risk drivers, 409n.1, 434–435
risk exposure, 409–410
capital allocation line and optimal risky 
portfolio, 291–292
292–293
273–276
risk-free rate of interest, 93n.19, 259
risk-free return, capital market line and, 
319–321
risk governance, 417–424
establishing risk tolerance level,  
419–421
risk infrastructure, 412
risk management, 407–454
and corporate governance, 35
in decision process, 407–408
defined, 410
and drivers of risk, 434–435
enterprise

identification of risks, 424–433
430–432
432–433
long-term, 35
metrics for, 435–439, 446–447
in portfolio construction, 224
by portfolio managers, 408
practice problems, 450–452
in real time, with fintech, 468–469risk governance, 417–424
419–421
risk management process, 409–417
benefits from, 416
for enterprises, 413–415
framework for, 411–417
good vs. bad, 410–411
for individuals, 415
risk exposure in, 409–410
risk modification methods, 439–447
acceptance of risk, 441
example, 446–447
prevention and avoidance of risk, 
439–440
selecting, 445–446
shifting of risk, 443–445
transfer of risk, 441–443
solutions to problems, 453–454
risk management framework, 411–417
risk mitigation, 412
risk modification, 439–447

439–440
risk monitoring, 412
risk neutral (term), 268
risk objectives, on IPSs, 370–375
risk position, 409n.1
asset, 216
bond yield plus, 93
defined, 263
equity, 89–92
expected, 259
historical equity risk premium 
approach, 89–92
for real returns, 254
and adding assets to portfolios, 287
and investing in portfolios vs. equities, 
210–212
for strategic asset allocation, 387
risk seeking (term), 267–268
risk shifting, 443–445
risk tolerance, 419–421
defined, 268
in enterprise risk management, 417
on investment policy statements, 
371–373
in portfolio management, 222
and shareholder–manager 
relationships, 12
risk transfer, 441–443
risky assets
combining risk-free assets with, 315–318
277–279
importance of correlation of risks in

portfolio return for, 276

Index  I-13
portfolio risk with, 276–282
relationship of risk and return, 279–281
utility theory and selection of, 273–276
risky portfolios
insurance for, 287
317–318
selection for, 313–314
Rite Aid Corporation, 95
Ritter, Jay, 105
Robert Wood Johnson Foundation, 219
robo-advisory services, 455, 457, 466–468
rogue traders, 428
Ross, Stephen, 353
Russia, 379
S
SAA. see strategic asset allocation
SAFE Investment Company, 221
safety projects, capital budgeting for, 49
safety stock, of inventory, 183
sales risk, 95, 128–130
SAMA Foreign Holdings, 221
sample standard deviation, 257
Sampo, 377–378
Sarbanes–Oxley Act of 2002 (SOX), 7
SASB. see Sustainability Accounting 
scale, project, 62–63
scenario analysis, 437, 469
scenario loss, 422
schedules
accounts receivable aging, 180–181
investment opportunity, 82
marginal cost of capital, 102–105
Scholz, Peter, 467
SCL. see security characteristic line

search (data processing method), 463
secondary sources of liquidity, 157–158
second-order risk, 436n.28
sector ETFs, 234
Securities Act (1933), 235–236
security analysis, in portfolio 
management, 223
security characteristic line (SCL), 
346–347
security market line (SML), 337–340
portfolio beta, 339–340
and security selection, 347–348
security selection
and CAPM, 347–348
defined, 394
security valuation, cost of capital for, 
82–84
self-insurance, 441
self-investment limits, 379–380
sell-side firms, 225
semi-structured data, 458
sensors, as Big Data sources, 459, 460
separately managed accounts (SMAs), 235
settlement, post-trade, 472–473
settlement risk, 426
Shanghai Stock Exchange, 319shareholder(s)
conflicts with governments or 
regulators, 13
controlling shareholders vs. minority 
shareholders, 12–13
creditor interests vs., 13
customer conflicts with, 13

manager/director relationships, 11–12
shareholder activism, 25–26, 34
shareholder engagement, 25
shareholder rights, 34
shareholder rights plan (poison pill), 26
shareholder theory, 7
Shari’a, 380
Sharpe, William, 216, 335
Sharpe ratio, 287, 342
short hedge fund strategies, 236
short selling, 336n.4
short-term borrowing, 167
short-term cash flows, 165–166
identifying typical cash flows, 165–166
short-term financing, 189–194
short-term funds management, 167–174
evaluating, 174
investment instruments, 168–171
strategies for, 171–174
short-term investment portfolio reports, 
174
short-term investments, 168–171
examples, 168–169
investment risks, 170–171
managing cash positions with, 167
yields of, 169–170
SI. see sustainable investing
Siegel, Jeremy, 90n.14
Singapore, 16
single-factor models of beta, limitations 
of, 352

of, 352
single-index models for beta, 330. see 
also capital asset pricing model 
(CAPM)
calculation and interpretation of beta 
with, 331–332
defined, 329
single-period models of beta, limitations 
of, 352
small-capitalization stocks, beta 
adjustments for, 94
“smart contracts, ” 470
SMAs. see separately managed accounts
Smith, Clifford W., 175n.5
SML. see security market line
smoothing techniques, for beta, 94
socially responsible investing (SRI), 37, 
380–381
social media, 27
solvency ratios, 438
solvency risk, 429, 431
South Africa, 18, 90
sovereign wealth funds (SWFs), 221
sovereign yield spread, 100SOX. see Sarbanes–Oxley Act of 2002
S&P 500 Index
as benchmark, 375
correlations of stocks, 284, 332
diversification with stocks, 348–349
as market index, 318
as market proxy, 319–321
reported returns, 245
return and risk of two-asset portfolio, 
258–259
returns for Enron vs., 208–209

258–259
tail risk with, 427
Spain, 16, 90
Spartan 500 Index fund, 341–342
SQL (database), 465
SQLite (database), 465
SRI. see socially responsible investing
staggered boards, 21–22, 26
stakeholder(s), 8–14
relationships, 11–14, 25–28
stakeholder management, 5–36, 14–20
about, 14

board of directors, 17
contractual agreements with 
creditors, 19
customers/suppliers, 20
employee laws/contracts, 19–20
laws and regulations, 20
related-party transaction policies, 18
remuneration policies, 18
reporting and transparency, 17

I-14  Index
stakeholder theory, 7
standard deviation
and correlation, 277
for portfolio of two assets, 277
of risk-free asset, 320
as risk metric, 435–436
and variance of returns, 257
Standard & Poor’s, 438
Stanford University, 218
Statement of Duties and Responsibilities, 
IPS, 369
Statement of Purpose, IPS, 369
statistical factor models, 329
Staunton, Mike, 89–90
Steiner, Fabian, 105
stock(s)
correlation of T-bills/bonds with, 285
employee stock options, 208–210, 286, 
381
fixed rate perpetual preferred, 86–87
historical risk and correlation, 285
nominal returns, 259–262
preferred, 86–88
risk and return, 259–260
skewness of stock returns, 264–265
stock funds, 229
stock-out costs, 184
stock-out losses, 182
stock price, net present value and, 67–68
storage (data processing method), 463
straight voting, 12
stranded assets, 39
strategic analysis, 412
strategic asset allocation (SAA), 385–393

specifying asset classes for, 385–387
stress testing, 437, 468
stretching payables, 187
structured data, 458
subsidiary, captive finance, 175
Summer Olympics (1980), 443n.36
sunk costs, 51
supervised learning, 461–462
supervisory board, 10
suppliers
surety bonds, 443
survey approach, for cost of equity, 92
Sustainability Accounting Standards 
Board (SASB), 39
sustainable growth rate, 92–93
sustainable investing (SI), 36–37
swaps, credit default, 438n.32
Sweden, 90
SWFs. see sovereign wealth funds
Switzerland, 90, 105, 379
syndicates, 442–443
systematic risk, 326–328
in Jensen’s alpha, 343for single-index model of beta, 331
T
T. Rowe Price Corporate Income Fund, 
231–232
tactical asset allocation, 393–394
“tag clouds, ” 464
tail risk, 427–428
takeover(s), 12

takeover defenses
takeover market, 26
Target, 162–163, 184
target balance, 167
target capital structure, 80
tax-advantaged securities, 169
taxes
capital gains, 254
and cost of capital, 79–80
on dividend income, 254
and IPSs, 379
tax risk, 427
T-bills. see US Treasury bills
Temasek Holdings, 221
tender offers, 26
terrorism, as operational risk, 429
Tertilt, Michael, 467
Texas A&M University System, 218
three-dimensional (3D) graphics, 463
three-factor models for beta, 329
time horizon
for cash forecasting, 166
for portfolio management, 222
and portfolio planning, 378–379
and risk tolerance, 371
top-down portfolio analysis, 223, 397
TOPIX Index, 89, 371
total leverage, 140–143
total risk
decomposition of, 330
in Sharpe ratio, 342
tracking error, 370n.2
tracking risk, 370n.2
tradable assets, 319
trade credit, 185, 186

traders, rogue, 428
trading
algorithmic, 469
automated, 456
cost of, 266, 287
high-frequency, 469
traditional data, 457
training, in machine learning, 461
training datasets, 461
transaction costs, 336, 348n.6, 425–426
transactions motive, 182
transfer (data processing method), 463
transfer, risk, 441–443
transparency. see corporate transparency
Treasury bills, 259Treynor, Jack, 216, 335
trust receipt agreements, 192
Turkey, 16
turnover
accounts receivable, 160
inventory, 160, 184–185
two-asset portfolio, risk of, 258–259
two-fund separation theorem, 292–293
two-tier board structure, 10
typical cash flows, identifying, 165–166
U
uncommitted lines of credit, 189, 190
uncorrelated returns, 277
underinvestment, in inventory, 183
underlying, risk budgeting based on, 422
unions, 19
United Kingdom

IPS requirement, 368
United Nations, 39
UN Global Compact, 37
bank sources of credit, 189
bond mutual funds, 231n.15
capital budgeting, 67
cash underwritten offers, 105
equity risk premium, 89–90
ETFs, 233
four-factor model use, 354
mutual funds, 230–231
nominal returns of major asset classes, 
260–261
379
portfolio management by banks, 220, 
221
real returns of major asset classes, 
261–262
risk diversification by insurance 
companies, 442
risk of asset classes, 263
taxes and cost of capital, 79
US Bankruptcy Code, 146
US Federal Reserve, 231

reporting requirements, 235
robo-advisory services regulated by, 466
and stakeholder relationships, 28

Index  I-15
US Territories, ACH system, 178
US Treasury bills (T-bills)
as benchmark, 171
correlation of stocks/bonds with, 285
nominal returns, 260–261
as proxy of risk-free return, 319–321
risk–return tradeoff, 261, 263
short-term investment, 168
in short-term portfolio report, 174
yield, 169–170
US Treasury bonds
correlation with other asset classes, 
386
in cost of equity, 88, 90
universal owners, 38–39
university endowments, 218
University of Michigan, 218
University of Texas System, 218
University of Virginia, 224
unlimited funds, 52
unstructured data, 458
unsupervised learning, 462
unsystematic risk, 436n.27
utility, 269, 389–390
computation of, 272
and risk seeking, 267
utility maximization, 336
utility theory
portfolio selection with, 273–276
and risk aversion, 268–276
V
validation datasets, 461
valuation principles, in capital 
budgeting, 48
value, company, 78
value at risk (VaR), 370n.1

value-based investing, 37
values-based investing, 37
Vanguard Group, 232
VaR. see value at risk
variable costs
133–135
and leverage, 126–128
variance
of returns, 257
for portfolio of risky assets, 315for single asset, 256
for single-index model of beta, 330
variety, of collected data, 457–458
vega, 436
velocity, of collected data, 457, 458
vendors, number, size, location of, 186
Viskanta, Tadas, 101n.32
volatility, portfolio management and, 
210–212
Volkswagen, emissions scandal, 38
volume, of collected data, 457, 458
voting, 16
voting rights
in dual-class share structure, 31–32
shareholder, 31–32
W
WACC. see weighted average cost of 
capital
Walgreens, 95
Wal-Mart Stores, Inc.
inventory management, 184
liquidity management, 161–163
and market model, 330–331
operating leverage, 135–136
wage/hour discrimination suit, 38
warehouse receipt agreements, 192

Wataniya, 12
weather, risk associated with, 428
Webvan.com, 147
weighing
for cost of capital, 80–82
of nonmarket securities in portfolio, 350
weighted average cost of capital 
(WACC)
in capital budgeting decisions, 82–83
computing, 79
defined, 79
estimations, 98–100
and raising of additional capital, 
102–105
risk factors in, 93
Wellcome Trust, 220
William and Flora Hewlett Foundation, 
219
willingness to take risk, investors’ , 
371–373
W.K. Kellogg Foundation, 219
working capital management, 155–201
about, 155–156
accounts payable management, 185–188
trade discounts, 187–188accounts receivable management, 
175–181
forecasting short-term, 165–166
166–167
defined, 155
financial impact of inventory 
methods, 185

measuring, 159–164
practice problems, 196–198
short-term funds management, 
167–174
solutions to problems, 199–201
wrap accounts, 235
“wrong-way” risk, 431
Y
Yahoo! Finance, 245
Yale University, 218–220, 224
yields
bond equivalent, 170
defined, 169–170
of discounted securities, 169–170
money market, 170
on short-term investments,  
169–170
sovereign yield spread, 100
yield-to-maturity (YTM) approach, 
84–85
Yue Yuen Industrial, 210–213
Z
Zhao, Quanshui, 105

Derivatives 
STUDY SESSION 
Study Session 18 Derivatives
TOPIC LEVEL LEARNING OUTCOME
The candidate should be able to demonstrate a working knowledge of the analysis of 
derivatives, including forwards, futures, options, and swaps. 
Derivatives—financial instruments whose prices are derived from the value of 
some underlying asset—have become increasingly important for managing financial 
risk, exploiting investment opportunities, and creating synthetic asset class exposure. 
As in other security markets, arbitrage and market efficiency play a critical role in 
establishing prices for these securities.

Derivatives
This study session builds the conceptual framework for understanding the basic 
derivatives and derivative markets. Essential features and valuation concepts for 
forward commitments such as forwards, futures, and swaps and contingent claims 
such as options are introduced.
Reading 56 Derivative Markets and Instruments  
by Don M. Chance, PhD, CFA 
Reading 57 Basics of Derivative Pricing and Valuation  
by Don M. Chance, PhD, CFADErIvATI vES 
18

Derivative Markets and Instruments
by Don M. Chance, PhD, CFA
Don M. Chance, PhD, CFA, is at Louisiana State University (USA).
a. define a derivative and distinguish between exchange-  traded and 
over-  the- counter derivatives;
b. contrast forward commitments with contingent claims;
c. define forward contracts, futures contracts, options (calls and 
puts), swaps, and credit derivatives and compare their basic 
characteristics;
d. describe purposes of, and controversies related to, derivative 
markets;
e. explain arbitrage and the role it plays in determining prices and 
promoting market efficiency.
Equity, fixed-  income, currency, and commodity markets are facilities for trading the 
basic assets of an economy. Equity and fixed-  income securities are claims on the 
assets of a company. Currencies are the monetary units issued by a government or

central bank. Commodities are natural resources, such as oil or gold. These underlying 
assets are said to trade in cash markets  or spot markets  and their prices are some -
times referred to as cash prices  or spot prices , though we usually just refer to them 
as stock prices, bond prices, exchange rates, and commodity prices. These markets 
exist around the world and receive much attention in the financial and mainstream 
media. Hence, they are relatively familiar not only to financial experts but also to the 
general population.1rEADING
56
© 2013 CFA Institute. All rights reserved.

Reading 56 ■ Derivative Markets and Instruments 6
Somewhat less familiar are the markets for derivatives , which are financial 
instruments that derive their values from the performance of these basic assets. This 
reading is an overview of derivatives. Subsequent readings will explore many aspects 
of derivatives and their uses in depth. Among the questions that this first reading will 
address are the following:
■■What are the defining characteristics of derivatives?
■■What purposes do derivatives serve for financial market participants?
■■What is the distinction between a forward commitment and a contingent claim?
■■What are forward and futures contracts? In what ways are they alike and in 
what ways are they different?
■■What are swaps?
■■What are call and put options and how do they differ from forwards, futures, 
and swaps?
■■What are credit derivatives and what are the various types of credit derivatives?
■■What are the benefits of derivatives?

■■What are some criticisms of derivatives and to what extent are they well 
founded?
■■What is arbitrage and what role does it play in a well-  functioning financial 
market?
This reading is organized as follows. Section 2 explores the definition and uses of 
derivatives and establishes some basic terminology. Section 3 describes derivatives 
markets. Section 4 categorizes and explains types of derivatives. Sections 5 and 6 
discuss the benefits and criticisms of derivatives, respectively. Section 7 introduces 
the basic principles of derivative pricing and the concept of arbitrage. Section 8 pro -
vides a summary.
DERIVATIVES: DEFINITIONS AND USES
The most common definition of a derivative reads approximately as follows:
A derivative is a financial instrument that derives its performance from the 
performance of an underlying asset.
This definition, despite being so widely quoted, can nonetheless be a bit troublesome.

For example, it can also describe mutual funds and exchange-  traded funds, which would 
never be viewed as derivatives even though they derive their values from the values 
of the underlying securities they hold. Perhaps the distinction that best characterizes 
derivatives is that they usually transform  the performance of the underlying asset 
before paying it out in the derivatives transaction. In contrast, with the exception of 
expense deductions, mutual funds and exchange-  traded funds simply pass through the 
returns of their underlying securities. This transformation of performance is typically 
understood or implicit in references to derivatives but rarely makes its way into the 
formal definition. In keeping with customary industry practice, this characteristic will 
be retained as an implied, albeit critical, factor distinguishing derivatives from mutual 
funds and exchange-  traded funds and some other straight pass-  through instruments.

Also, note that the idea that derivatives take their performance  from an underlying 
asset encompasses the fact that derivatives take their value and certain other char -
acteristics from the underlying asset. Derivatives strategies perform in ways that are 
derived from the underlying and the specific features of derivatives.2

Derivatives: Definitions and Uses 7
Derivatives are similar to insurance in that both allow for the transfer of risk 
from one party to another. As everyone knows, insurance is a financial contract that 
provides protection against loss. The party bearing the risk purchases an insurance 
policy, which transfers the risk to the other party, the insurer, for a specified period 
of time. The risk itself does not change, but the party bearing it does. Derivatives 
allow for this same type of transfer of risk. One type of derivative in particular, the 
put option, when combined with a position exposed to the risk, functions almost 
exactly like insurance, but all derivatives can be used to protect against loss. Of course, 
an insurance contract must specify the underlying risk, such as property, health, or 
life. Likewise, so do derivatives. As noted earlier, derivatives are associated with an 
underlying asset. As such, the so-  called “underlying asset” is often simply referred

to as the underlying , whose value is the source of risk.1 In fact, the underlying need 
not even be an asset itself. Although common derivatives underlyings are equities, 
fixed-  income securities, currencies, and commodities, other derivatives underlyings 
include interest rates, credit, energy, weather, and even other derivatives, all of which 
are not generally thought of as assets. Thus, like insurance, derivatives pay off on the 
basis of a source of risk, which is often, but not always, the value of an underlying asset. 
And like insurance, derivatives have a definite life span and expire on a specified date.
Derivatives are created in the form of legal contracts. They involve two parties—the 
buyer and the seller (sometimes known as the writer)—each of whom agrees to do 
something for the other, either now or later. The buyer, who purchases the derivative, 
is referred to as the long  or the holder because he owns (holds) the derivative and

holds a long position. The seller is referred to as the short  because he holds a short 
position.2
A derivative contract always defines the rights and obligations of each party. These 
contracts are intended to be, and almost always are, recognized by the legal system 
as commercial contracts that each party expects to be upheld and supported in the 
legal system. Nonetheless, disputes sometimes arise, and lawyers, judges, and juries 
may be required to step in and resolve the matter.
There are two general classes of derivatives. Some provide the ability to lock in a 
price at which one might buy or sell the underlying. Because they force the two parties 
to transact in the future at a previously agreed-  on price, these instruments are called 
forward commitments . The various types of forward commitments are called forward 
contracts, futures contracts, and swaps. Another class of derivatives provides the right

but not the obligation  to buy or sell the underlying at a pre-  determined price. Because 
the choice of buying or selling versus doing nothing depends on a particular random 
outcome, these derivatives are called contingent claims . The primary contingent 
claim is called an option . The types of derivatives will be covered in more detail later 
in this reading and in considerably more depth later in the curriculum.
The existence of derivatives begs the obvious question of what purpose they serve. 
If one can participate in the success of a company by holding its equity, what reason 
can possibly explain why another instrument is required that takes its value from the 
performance of the equity? Although equity and other fundamental markets exist 
and usually perform reasonably well without derivative markets, it is possible that 
derivative markets can improve  the performance of the markets for the underlyings. 
As you will see later in this reading, that is indeed true in practice.

1 Unfortunately, English financial language often evolves without regard to the rules of proper usage. 
Underlying  is typically an adjective and, therefore, a modifier, but the financial world has turned it into a noun.
2 In the financial world, the long always benefits from an increase in the value of the instrument he owns, 
and the short  always benefits from a decrease in the value of the instrument he has sold. Think of the long 
as having possession of something and the short as having incurred an obligation to deliver that something.

Reading 56 ■ Derivative Markets and Instruments 8
Derivative markets create beneficial opportunities that do not exist in their absence. 
Derivatives can be used to create strategies that cannot be implemented with the 
underlyings alone. For example, derivatives make it easier to go short, thereby ben -
efiting from a decline in the value of the underlying. In addition, derivatives, in and 
of themselves, are characterized by a relatively high degree of leverage, meaning that 
participants in derivatives transactions usually have to invest only a small amount of 
their own capital relative to the value of the underlying. As such, small movements 
in the underlying can lead to fairly large movements in the amount of money made 
or lost on the derivative. Derivatives generally trade at lower transaction costs than 
comparable spot market transactions, are often more liquid than their underlyings, 
and offer a simple, effective, and low-  cost way to transfer risk. For example, a share -

holder of a company can reduce or even completely eliminate the market exposure 
by trading a derivative on the equity. Holders of fixed-  income securities can use 
derivatives to reduce or completely eliminate interest rate risk, allowing them to 
focus on the credit risk. Alternatively, holders of fixed-  income securities can reduce 
or eliminate the credit risk, focusing more on the interest rate risk. Derivatives permit 
such adjustments easily and quickly. These features of derivatives are covered in more 
detail later in this reading.
The types of performance transformations facilitated by derivatives allow market 
participants to practice more effective risk management. Indeed, the entire field of 
derivatives, which at one time was focused mostly on the instruments themselves, 
is now more concerned with the uses of the instruments. Just as a carpenter uses a 
hammer, nails, screws, a screwdriver, and a saw to build something useful or beautiful,

a financial expert uses derivatives to manage risk. And just as it is critically important 
that a carpenter understand how to use these tools, an investment practitioner must 
understand how to properly use derivatives. In the case of the carpenter, the result is 
building something useful; in the case of the financial expert, the result is managing 
financial risk. Thus, like tools, derivatives serve a valuable purpose but like tools, they 
must be used carefully.
The practice of risk management has taken a prominent role in financial mar -
kets. Indeed, whenever companies announce large losses from trading, lending, or 
operations, stories abound about how poorly these companies managed risk. Such 
stories are great attention grabbers and a real boon for the media, but they often miss 
the point that risk management does not guarantee that large losses will not occur. 
Rather, risk management  is the process by which an organization or individual defines

the level of risk it wishes to take, measures the level of risk it is taking, and adjusts 
the latter to equal the former . Risk management never offers a guarantee that large 
losses will not occur, and it does not eliminate the possibility of total failure. To do so 
would typically require that the amount of risk taken be so small that the organization 
would be effectively constrained from pursuing its primary objectives. Risk taking is 
inherent in all forms of economic activity and life in general. The possibility of failure 
is never eliminated.
EXAMPLE 1   
Characteristics of Derivatives
1 Which of the following is the best example of a derivative?
A A global equity mutual fund
B A non-  callable government bond
C A contract to purchase Apple Computer at a fixed price
2 Which of the following is not a characteristic of a derivative?

The Structure of Derivative Markets 9
A An underlying
B A low degree of leverage
C Two parties—a buyer and a seller
3 Which of the following statements about derivatives is not true?
A They are created in the spot market.
B They are used in the practice of risk management.
C They take their values from the value of something else.
C is correct. Mutual funds and government bonds are not derivatives. A gov -
ernment bond is a fundamental asset on which derivatives might be created, 
but it is not a derivative itself. A mutual fund can technically meet the definition 
of a derivative, but as noted in the reading, derivatives transform the value of a 
payoff of an underlying asset. Mutual funds merely pass those payoffs through 
to their holders.
B is correct. All derivatives have an underlying and must have a buyer and a 
seller. More importantly, derivatives have high degrees of leverage, not low 
degrees of leverage.

A is correct. Derivatives are used to practice risk management and they take 
(derive) their values from the value of something else, the underlying. They are 
not created in the spot market, which is where the underlying trades.
Note also that risk management is a dynamic and ongoing process, reflecting the 
fact that the risk assumed can be difficult to measure and is constantly changing. 
As noted, derivatives are tools, indeed the tools that make it easier to manage risk. 
Although one can trade stocks and bonds (the underlyings) to adjust the level of risk, 
it is almost always more effective to trade derivatives.
Risk management is addressed more directly elsewhere in the CFA curriculum, 
but the study of derivatives necessarily entails the concept of risk management. In 
an explanation of derivatives, the focus is usually on the instruments and it is easy to 
forget the overriding objective of managing risk. Unfortunately, that would be like a

carpenter obsessed with his hammer and nails, forgetting that he is building a piece of 
furniture. It is important to always try to keep an eye on the objective of managing risk.
THE STRUCTURE OF DERIVATIVE MARKETS
Having an understanding of equity, fixed-  income, and currency markets is extremely 
beneficial—indeed, quite necessary—in understanding derivatives. One could hardly 
consider the wisdom of using derivatives on a share of stock if one did not understand 
the equity markets reasonably well. As you likely know, equities trade on organized 
exchanges as well as in over-  the- counter (OTC) markets. These exchange-  traded 
equity markets—such as the Deutsche Börse, the Tokyo Stock Exchange, and the 
New York Stock Exchange and its Eurex affiliate—are formal organizational structures 
that bring buyers and sellers together through market makers, or dealers, to facilitate 
transactions. Exchanges have formal rule structures and are required to comply with 
all securities laws.3

Reading 56 ■ Derivative Markets and Instruments 10
OTC securities markets operate in much the same manner, with similar rules, 
regulations, and organizational structures. At one time, the major difference between 
OTC and exchange markets for securities was that the latter brought buyers and sell -
ers together in a physical location, whereas the former facilitated trading strictly in 
an electronic manner. Today, these distinctions are blurred because many organized 
securities exchanges have gone completely to electronic systems. Moreover, OTC 
securities markets can be formally organized structures, such as NASDAQ, or can 
merely refer to informal networks of parties who buy and sell with each other, such 
as the corporate and government bond markets in the United States.
The derivatives world also comprises organized exchanges and OTC markets. 
Although the derivatives world is also moving toward less distinction between these

markets, there are clear differences that are important to understand.
3.1 Exchange-  Traded Derivatives Markets
Derivative instruments are created and traded either on an exchange or on the OTC 
market. Exchange-  traded derivatives are standardized, whereas OTC derivatives are 
customized. To standardize a derivative contract means that its terms and conditions 
are precisely specified by the exchange and there is very limited ability to alter those 
terms. For example, an exchange might offer trading in certain types of derivatives 
that expire only on the third Friday of March, June, September, and December. If a 
party wanted the derivative to expire on any other day, it would not be able to trade 
such a derivative on that exchange, nor would it be able to persuade the exchange to 
create it, at least not in the short run. If a party wanted a derivative on a particular 
entity, such as a specific stock, that party could trade it on that exchange only if the

exchange had specified that such a derivative could trade. Even the magnitudes of 
the contracts are specified. If a party wanted a derivative to cover €150,000 and the 
exchange specified that contracts could trade only in increments of €100,000, the 
party could do nothing about it if it wanted to trade that derivative on that exchange.
This standardization of contract terms facilitates the creation of a more liquid 
market for derivatives. If all market participants know that derivatives on the euro 
trade in 100,000-  unit lots and that they all expire only on certain days, the market 
functions more effectively than it would if there were derivatives with many differ -
ent unit sizes and expiration days competing in the same market at the same time. 
This standardization makes it easier to provide liquidity. Through designated market 
makers, derivatives exchanges guarantee that derivatives can be bought and sold.3

The cornerstones of the exchange-  traded derivatives market are the market makers 
(or dealers) and the speculators, both of whom typically own memberships on the 
exchange.4 The market makers stand ready to buy at one price and sell at a higher 
price. With standardization of terms and an active market, market makers are often 
able to buy and sell almost simultaneously at different prices, locking in small, short-  
term profits—a process commonly known as scalping. In some cases, however, they 
are unable to do so, thereby forcing them to either hold exposed positions or find 
other parties with whom they can trade and thus lay off (get rid of) the risk. This is 
3 It is important to understand that merely being able to buy and sell a derivative, or even a security, does 
not mean that liquidity is high and that the cost of liquidity is low. Derivatives exchanges guarantee that a 
derivative can be bought and sold, but they do not guarantee the price. The ask price (the price at which

the market maker will sell) and the bid price (the price at which the market maker will buy) can be far 
apart, which they will be in a market with low liquidity. Hence, such a market can have liquidity, loosely 
defined, but the cost of liquidity can be quite high. The factors that can lead to low liquidity for derivatives 
are similar to those for securities: little trading interest and a high level of uncertainty.
4 Exchanges are owned by their members , whose memberships convey the right to trade. In addition, 
some exchanges are themselves publicly traded corporations whose members are shareholders, and there 
are also non-  member shareholders.

The Structure of Derivative Markets 11
when speculators come in. Although speculators are market participants who are 
willing to take risks, it is important to understand that being a speculator does not 
mean the reckless assumption of risk. Although speculators will take large losses at 
times, good speculators manage those risks by watching their exposures, absorbing 
market information, and observing the flow of orders in such a manner that they are 
able to survive and profit. Often, speculators will hedge their risks when they become 
uncomfortable.
Standardization also facilitates the creation of a clearing and settlement opera -
tion. Clearing  refers to the process by which the exchange verifies the execution of a 
transaction and records the participants’ identities. Settlement  refers to the related 
process in which the exchange transfers money from one participant to the other 
or from a participant to the exchange or vice versa. This flow of money is a critical

element of derivatives trading. Clearly, there would be no confidence in markets in 
which money is not efficiently collected and disbursed. Derivatives exchanges have 
done an excellent job of clearing and settlement, especially in comparison to securities 
exchanges. Derivatives exchanges clear and settle all contracts overnight, whereas 
most securities exchanges require two business days.
The clearing and settlement process of derivative transactions also provides a credit 
guarantee. If two parties engage in a derivative contract on an exchange, one party will 
ultimately make money and the other will lose money. Derivatives exchanges use their 
clearinghouses to provide a guarantee to the winning party that if the loser does not 
pay, the clearinghouse will pay the winning party. The clearinghouse is able to provide 
this credit guarantee by requiring a cash deposit, usually called the margin bond  or 
performance bond , from the participants to the contract. Derivatives clearinghouses

manage these deposits, occasionally requiring additional deposits, so effectively that 
they have never failed to pay in the nearly 100 years they have existed. We will say 
more about this process later and illustrate how it works.
Exchange markets are said to have transparency , which means that full information 
on all transactions is disclosed to exchanges and regulatory bodies. All transactions 
are centrally reported within the exchanges and their clearinghouses, and specific laws 
require that these markets be overseen by national regulators. Although this would 
seem a strong feature of exchange markets, there is a definite cost. Transparency 
means a loss of privacy: National regulators can see what transactions have been 
done. Standardization means a loss of flexibility: A participant can do only the trans -
actions that are permitted on the exchange. Regulation means a loss of both privacy 
and flexibility. It is not that transparency or regulation is good and the other is bad.

It is simply a trade-  off.
Derivatives exchanges exist in virtually every developed (and some emerging 
market) countries around the world. Some exchanges specialize in derivatives and 
others are integrated with securities exchanges.
Although there have been attempts to create somewhat non-  standardized deriva -
tives for trading on an exchange, such attempts have not been particularly successful. 
Standardization is a critical element by which derivatives exchanges are able to pro -
vide their services. We will look at this point again when discussing the alternative 
to standardization: customized OTC derivatives.
3.2 Over-  the-  Counter Derivatives Markets
The OTC derivatives markets comprise an informal network of market participants 
that are willing to create and trade virtually any type of derivative that can legally exist. 
The backbone of these markets is the set of dealers, which are typically banks. Most

of these banks are members of a group called the International Swaps and Derivatives 
Association (ISDA), a worldwide organization of financial institutions that engage in 
derivative transactions, primarily as dealers. As such, these markets are sometimes

Reading 56 ■ Derivative Markets and Instruments 12
called dealer markets . Acting as principals, these dealers informally agree to buy and 
sell various derivatives. It is informal  because the dealers are not obligated to do so. 
Their participation is based on a desire to profit, which they do by purchasing at one 
price and selling at a higher price. Although it might seem that a dealer who can “buy 
low, sell high” could make money easily, the process in practice is not that simple. 
Because OTC instruments are not standardized, a dealer cannot expect to buy a 
derivative at one price and simultaneously sell it to a different party who happens to 
want to buy the same derivative at the same time and at a higher price.
To manage the risk they assume by buying and selling customized derivatives, OTC 
derivatives dealers typically hedge their risks by engaging in alternative but similar 
transactions that pass the risk on to other parties. For example, if a company comes to

a dealer to buy a derivative on the euro, the company would effectively be transferring 
the risk of the euro to the dealer. The dealer would then attempt to lay off (get rid 
of) that risk by engaging in an alternative but similar transaction that would transfer 
the risk to another party. This hedge might involve another derivative on the euro or 
it might simply be a transaction in the euro itself. Of course, that begs the question 
of why the company could not have laid off the risk itself and avoided the dealer. 
Indeed, some can and do, but laying off risk is not simple. Unable to find identical 
offsetting transactions, dealers usually have to find similar  transactions with which 
they can lay off the risk. Hedging one derivative with a different kind of derivative 
on the same underlying is a similar but not identical transaction. It takes specialized 
knowledge and complex models to be able to do such transactions effectively, and

dealers are more capable of doing so than are ordinary companies. Thus, one might 
think of a dealer as a middleman, a sort of financial wholesaler using its specialized 
knowledge and resources to facilitate the transfer of risk. In the same manner that one 
could theoretically purchase a consumer product from a manufacturer, a network of 
specialized middlemen and retailers is often a more effective method.
Because of the customization of OTC derivatives, there is a tendency to think 
that the OTC market is less liquid than the exchange market. That is not necessarily 
true. Many OTC instruments can easily be created and then essentially offset by 
doing the exact opposite transaction, often with the same party. For example, sup -
pose Corporation A buys an OTC derivative from Dealer B. Before the expiration 
date, Corporation A wants to terminate the position. It can return to Dealer B and 
ask to sell a derivative with identical terms. Market conditions will have changed, of

course, and the value of the derivative will not be the same, but the transaction can 
be conducted quite easily with either Corporation A or Dealer B netting a gain at the 
expense of the other. Alternatively, Corporation A could do this transaction with a 
different dealer, the result of which would remove exposure to the underlying risk but 
would leave two transactions open and some risk that one party would default to the 
other. In contrast to this type of OTC liquidity, some exchange-  traded derivatives have 
very little trading interest and thus relatively low liquidity. Liquidity is always driven 
by trading interest, which can be strong or weak in both types of markets.
OTC derivative markets operate at a lower degree of regulation and oversight than 
do exchange-  traded derivative markets. In fact, until around 2010, it could largely 
be said that the OTC market was essentially unregulated. OTC transactions could

be executed with only the minimal oversight provided through laws that regulated 
the parties themselves, not the specific instruments. Following the financial crisis 
that began in 2007, new regulations began to blur the distinction between OTC 
and exchange-  listed markets. In both the United States (the Wall Street Reform 
and Consumer Protection Act of 2010, commonly known as the Dodd–Frank Act) 
and Europe (the Regulation of the European Parliament and of the Council on OTC 
Derivatives, Central Counterparties, and Trade Repositories), regulations are changing 
the characteristics of OTC markets.

The Structure of Derivative Markets 13
When the full implementation of these new laws takes place, a number of OTC 
transactions will have to be cleared through central clearing agencies, information on 
most OTC transactions will need to be reported to regulators, and entities that operate 
in the OTC market will be more closely monitored. There are, however, quite a few 
exemptions that cover a significant percentage of derivative transactions. Clearly, the 
degree of OTC regulation, although increasing in recent years, is still lighter than that 
of exchange-  listed market regulation. Many transactions in OTC markets will retain 
a degree of privacy with lower transparency, and most importantly, the OTC markets 
will remain considerably more flexible than the exchange-  listed markets.
EXAMPLE 2   
Exchange-  Traded versus Over-  the-  Counter Derivatives
1 Which of the following characteristics is not associated with exchange-  
traded derivatives?
A Margin or performance bonds are required.

B The exchange guarantees all payments in the event of default.
C All terms except the price are customized to the parties’ individual 
needs.
2 Which of the following characteristics is associated with over-  the- counter 
derivatives?
A Trading occurs in a central location.
B They are more regulated than exchange-  listed derivatives.
C They are less transparent than exchange-  listed derivatives.
3 Market makers earn a profit in both exchange and over-  the- counter deriv -
atives markets by:
A charging a commission on each trade.
B a combination of commissions and markups.
C buying at one price, selling at a higher price, and hedging any risk.
4 Which of the following statements most  accurately describes exchange-  
traded derivatives relative to over-  the- counter derivatives? Exchange-  
traded derivatives are more likely to have:
A greater credit risk.
B standardized contract terms.
C greater risk management uses.

C is correct. Exchange-  traded contracts are standardized, meaning that the 
exchange determines the terms of the contract except the price. The exchange 
guarantees against default and requires margins or performance bonds.
C is correct. OTC derivatives have a lower degree of transparency than exchange-  
listed derivatives. Trading does not occur in a central location but, rather, is quite 
dispersed. Although new national securities laws are tightening the regulation 
of OTC derivatives, the degree of regulation is less than that of exchange-  listed 
derivatives.

Reading 56 ■ Derivative Markets and Instruments 14
C is correct. Market makers buy at one price (the bid), sell at a higher price (the 
ask), and hedge whatever risk they otherwise assume. Market makers do not 
charge a commission. Hence, A and B are both incorrect.
B is correct. Standardization of contract terms is a characteristic of exchange-  
traded derivatives. A is incorrect because credit risk is well-  controlled in exchange 
markets. C is incorrect because the risk management uses are not limited by 
being traded over the counter.
TYPES OF DERIVATIVES
As previously stated, derivatives fall into two general classifications: forward com -
mitments and contingent claims. The factor that distinguishes forward commitments 
from contingent claims is that the former obligate  the parties to engage in a trans -
action at a future date on terms agreed upon in advance, whereas the latter provide

one party the right but not the obligation  to engage in a future transaction on terms 
agreed upon in advance.
4.1 Forward Commitments
Forward commitments are contracts entered into at one point in time that require 
both parties to engage in a transaction at a later point in time (the expiration) on 
terms agreed upon at the start. The parties establish the identity and quantity of 
the underlying, the manner in which the contract will be executed or settled when 
it expires, and the fixed price at which the underlying will be exchanged. This fixed 
price is called the forward price .
As a hypothetical example of a forward contract, suppose that today Markus and 
Johannes enter into an agreement that Markus will sell his BMW to Johannes for a 
price of €30,000. The transaction will take place on a specified date, say, 180 days from 
today. At that time, Markus will deliver the vehicle to Johannes’s home and Johannes

will give Markus a bank-  certified check for €30,000. There will be no recourse, so if 
the vehicle has problems later, Johannes cannot go back to Markus for compensation. 
It should be clear that both Markus and Johannes must do their due diligence and 
carefully consider the reliability of each other. The car could have serious quality 
issues and Johannes could have financial problems and be unable to pay the €30,000. 
Obviously, the transaction is essentially unregulated. Either party could renege on his 
obligation, in response to which the other party could go to court, provided a formal 
contract exists and is carefully written. Note finally that one of the two parties is likely 
to end up gaining and the other losing, depending on the secondary market price of 
this type of vehicle at expiration of the contract.
This example is quite simple but illustrates the essential elements of a forward 
contract. In the financial world, such contracts are very carefully written, with legal

provisions that guard against fraud and require extensive credit checks. Now let us 
take a deeper look at the characteristics of forward contracts.
4.1.1  Forward Contracts
The following is the formal definition of a forward contract:4

Types of Derivatives 15
A forward contract is an over-  the- counter derivative contract in which two 
parties agree that one party, the buyer, will purchase an underlying asset 
from the other party, the seller, at a later date at a fixed price they agree on 
when the contract is signed.
In addition to agreeing on the price at which the underlying asset will be sold at 
a later date, the two parties also agree on several other matters, such as the specific 
identity of the underlying, the number of units of the underlying that will be delivered, 
and where the future delivery will occur. These are important points but relatively 
minor in this discussion, so they can be left out of the definition to keep it uncluttered.
As noted earlier, a forward contract is a commitment. Each party agrees that it 
will fulfill its responsibility at the designated future date. Failure to do so constitutes 
a default and the non-  defaulting party can institute legal proceedings to enforce per -

formance. It is important to recognize that although either party could default to the 
other, only one party at a time can default. The party owing the greater amount could 
default to the other, but the party owing the lesser amount cannot default because 
its claim on the other party is greater. The amount owed is always based on the net 
owed by one party to the other.
To gain a better understanding of forward contracts, it is necessary to examine 
their payoffs. As noted, forward contracts—and indeed all derivatives—take (derive) 
their payoffs from the performance of the underlying asset. To illustrate the payoff of 
a forward contract, start with the assumption that we are at time t = 0 and that the 
forward contract expires at a later date, time t = T.5 The spot price of the underlying 
asset at time 0 is S0 and at time T is ST. Of course, when we initiate the contract at 
time 0, we do not know what ST will ultimately be. Remember that the two parties,

the buyer and the seller, are going long and short, respectively.
At time t = 0, the long and the short agree that the short will deliver the asset to 
the long at time T for a price of F0(T). The notation F0(T) denotes that this value is 
established at time 0 and applies to a contract expiring at time T. F0(T) is the forward 
price. Later, you will learn how the forward price is determined. It turns out that it is 
quite easy to do, but we do not need to know right now.6
So, let us assume that the buyer enters into the forward contract with the seller 
for a price of F0(T), with delivery of one unit of the underlying asset to occur at time 
T. Now, let us roll forward to time T, when the price of the underlying is ST. The long 
is obligated to pay F0(T), for which he receives an asset worth ST. If ST > F0(T), it is 
clear that the transaction has worked out well for the long. He paid F0(T) and receives 
something of greater value. Thus, the contract effectively pays off ST ‒ F0(T) to the

long, which is the value of the contract at expiration. The short has the mirror image 
of the long. He is required to deliver the asset worth ST and accept a smaller amount, 
F0(T). The contract has a payoff for him of F0(T) ‒ ST, which is negative. Even if the 
asset’s value, ST, is less than the forward price, F0(T), the payoffs are still ST ‒ F0(T) 
for the long and F0(T) ‒ ST for the short. We can consolidate these results by writing 
the short’s payoff as the negative of the long’s, ‒[ ST ‒ F0(T)], which serves as a useful 
reminder that the long and the short are engaged in a zero-  sum game, which is a 
type of competition in which one participant’s gains are the other’s losses. Although 
both lose a modest amount in the sense of both having some costs to engage in the 
5 Such notations as t = 0 and t = T are commonly used in explaining derivatives. To indicate that t = 0 
simply means that we initiate a contract at an imaginary time designated like a counter starting at zero.

To indicate that the contract expires at t = T simply means that at some future time, designated as T, the 
contract expires. Time T could be a certain number of days from now or a fraction of a year later or T 
years later. We will be more specific in later readings that involve calculations. For now, just assume that 
t = 0 and t = T are two dates—the initiation and the expiration—of the contract.
6 This point is covered more fully elsewhere in the readings on derivatives, but we will see it briefly later 
in this reading.

Reading 56 ■ Derivative Markets and Instruments 16
transaction, these costs are relatively small and worth ignoring for our purposes at this 
time. In addition, it is worthwhile to note how derivatives transform the performance 
of the underlying. The gain from owning the underlying would be ST ‒ S0, whereas the 
gain from owning the forward contract would be ST ‒ F0(T). Both figures are driven 
by ST, the price of the underlying at expiration, but they are not the same.
Exhibit 1 illustrates the payoffs from both buying and selling a forward contract.
Exhibit 1   Payoffs from a Forward Contract
A. Payoff from Buying = S T – F0(T)
Payoff
0
ST
B. Payof f from Selling = –[S T – F0(T)]
Payoff
0
ST
The long hopes the price of the underlying will rise above the forward price, F0(T), 
whereas the short hopes the price of the underlying will fall below the forward price. 
Except in the extremely rare event that the underlying price at T equals the forward 
price, there will ultimately be a winner and a loser.

An important element of forward contracts is that no money changes hands 
between parties when the contract is initiated. Unlike in the purchase and sale of an 
asset, there is no value exchanged at the start. The buyer does not pay the seller some 
money and obtain something. In fact, forward contracts have zero value at the start. 
They are neither assets nor liabilities. As you will learn in later readings, their values 
will deviate from zero later as prices move. Forward contracts will almost always have 
non-  zero values at expiration.

Types of Derivatives 17
As noted previously, the primary purpose of derivatives is for risk management. 
Although the uses of forward contracts are covered in depth later in the curriculum, 
there are a few things to note here about the purposes of forward contracts. It should 
be apparent that locking in the future buying or selling price of an underlying asset 
can be extremely attractive for some parties. For example, an airline anticipating the 
purchase of jet fuel at a later date can enter into a forward contract to buy the fuel at 
a price agreed upon when the contract is initiated. In so doing, the airline has hedged 
its cost of fuel. Thus, forward contracts can be structured to create a perfect hedge, 
providing an assurance that the underlying asset can be bought or sold at a price 
known when the contract is initiated. Likewise, speculators, who ultimately assume 
the risk laid off by hedgers, can make bets on the direction of the underlying asset

without having to invest the money to purchase the asset itself.
Finally, forward contracts need not specifically settle by delivery of the underlying 
asset. They can settle by an exchange of cash. These contracts—called non-  deliverable 
forwards  (NDFs), cash-  settled forwards , or contracts for differences —have the same 
economic effect as do their delivery-  based counterparts. For example, for a physical 
delivery contract, if the long pays F0(T) and receives an asset worth ST, the contract 
is worth ST – F0(T) to the long at expiration. A non-  deliverable forward contract 
would have the short simply pay cash to the long in the amount of ST – F0(T). The 
long would not take possession of the underlying asset, but if he wanted the asset, 
he could purchase it in the market for its current price of ST. Because he received a 
cash settlement in the amount of ST – F0(T), in buying the asset the long would have

to pay out only ST – [ST – F0(T)], which equals F0(T). Thus, the long could acquire 
the asset, effectively paying F0(T), exactly as the contract promised. Transaction costs 
do make cash settlement different from physical delivery, but this point is relatively 
minor and can be disregarded for our purposes here.
As previously mentioned, forward contracts are OTC contracts. There is no for -
mal forward contract exchange. Nonetheless, there are exchange-  traded variants of 
forward contracts, which are called futures contracts or just futures.
4.1.2  Futures
Futures contracts are specialized versions of forward contracts that have been stan -
dardized and that trade on a futures exchange. By standardizing these contracts and 
creating an organized market with rules, regulations, and a central clearing facility, 
the futures markets offer an element of liquidity and protection against loss by default.
Formally, a futures contract is defined as follows:

A futures contract is a standardized derivative contract created and traded 
on a futures exchange in which two parties agree that one party, the buyer, 
will purchase an underlying asset from the other party, the seller, at a later 
date and at a price agreed on by the two parties when the contract is initi -
ated and in which there is a daily settling of gains and losses and a credit 
guarantee by the futures exchange through its clearinghouse.
First, let us review what standardization means. Recall that in forward contracts, 
the parties customize the contract by specifying the underlying asset, the time to 
expiration, the delivery and settlement conditions, and the quantity of the underly -
ing, all according to whatever terms they agree on. These contracts are not traded 
on an exchange. As noted, the regulation of OTC derivatives markets is increasing, 
but these contracts are not subject to the traditionally high degree of regulation that

applies to securities and futures markets. Futures contracts first require the existence 
of a futures exchange, a legally recognized entity that provides a market for trading 
these contracts. Futures exchanges are highly regulated at the national level in all 
countries. These exchanges specify that only certain contracts are authorized for 
trading. These contracts have specific underlying assets, times to expiration, delivery

Reading 56 ■ Derivative Markets and Instruments 18
and settlement conditions, and quantities. The exchange offers a facility in the form 
of a physical location and/or an electronic system as well as liquidity provided by 
authorized market makers.
Probably the most important distinctive characteristic of futures contracts is the 
daily settlement of gains and losses and the associated credit guarantee provided by the 
exchange through its clearinghouse. When a party buys a futures contract, it commits 
to purchase the underlying asset at a later date and at a price agreed upon when the 
contract is initiated. The counterparty (the seller) makes the opposite commitment, an 
agreement to sell the underlying asset at a later date and at a price agreed upon when 
the contract is initiated. The agreed-  upon price is called the futures price . Identical 
contracts trade on an ongoing basis at different prices, reflecting the passage of time

and the arrival of new information to the market. Thus, as the futures price changes, 
the parties make and lose money. Rising (falling) prices, of course, benefit (hurt) the 
long and hurt (benefit) the short. At the end of each day, the clearinghouse engages 
in a practice called mark to market , also known as the daily settlement . The clear -
inghouse determines an average of the final futures trades of the day and designates 
that price as the settlement price . All contracts are then said to be marked to the 
settlement price . For example, if the long purchases the contract during the day at a 
futures price of £120 and the settlement price at the end of the day is £122, the long’s 
account would be marked for a gain of £2. In other words, the long has made a profit 
of £2 and that amount is credited to his account, with the money coming from the 
account of the short, who has lost £2. Naturally, if the futures price decreases, the

long loses money and is charged with that loss, and the money is transferred to the 
account of the short.7
The account is specifically referred to as a margin  account. Of course, in equity 
markets, margin accounts are commonly used, but there are significant differences 
between futures margin accounts and equity margin accounts. Equity margin accounts 
involve the extension of credit. An investor deposits part of the cost of the stock 
and borrows the remainder at a rate of interest. With futures margin accounts, both 
parties deposit a required minimum sum of money, but the remainder of the price 
is not borrowed. This required margin is typically less than 10% of the futures price, 
which is considerably less than in equity margin trading. In the example above, let 
us assume that the required margin is £10, which is referred to as the initial margin . 
Both the long and the short put that amount into their respective margin accounts.

This money is deposited there to support the trade, not as a form of equity, with the 
remaining amount borrowed. There is no formal loan created as in equity markets. 
A futures margin is more of a performance bond or good faith deposit, terms that 
were previously mentioned. It is simply an amount of money put into an account that 
covers possible future losses.
Associated with each initial margin is another figure called the maintenance 
margin . The maintenance margin is the amount of money that each participant must 
maintain in the account after the trade is initiated, and it is always significantly lower 
than the initial margin. Let us assume that the maintenance margin in this example is 
£6. If the buyer’s account is marked to market with a credit of £2, his margin balance 
moves to £12, while the seller’s account is charged £2 and his balance moves to £8. 
The clearinghouse then compares each participant’s balance with the maintenance

margin. At this point, both participants more than meet the maintenance margin.
7 The actual amount of money charged and credited depends on the contract size and the number of 
contracts. A price of £120 might actually refer to a contract that has a standard size of £100,000. Thus, 
£120 might actually mean 120% of the standard size, or £120,000. In addition, the parties are likely to hold 
more than one contract. Hence, the gain of £2 referred to in the text might really mean £2,000 (122% minus 
120% times the £100,000 standard size) times the number of contracts held by the party.

Types of Derivatives 19
Let us say, however, that the price continues to move in the long’s favor and, 
therefore, against the short. A few days later, assume that the short’s balance falls to 
£4, which is below the maintenance margin requirement of £6. The short will then 
get a margin call , which is a request to deposit additional funds. The amount that 
the short has to deposit, however, is not the £2 that would bring his balance up to 
the maintenance margin. Instead, the short must deposit enough funds to bring the 
balance up to the initial margin. So, the short must come up with £6. The purpose 
of this rule is to get the party’s position significantly above the minimum level and 
provide some breathing room. If the balance were brought up only to the mainte -
nance level, there would likely be another margin call soon. A party can choose not 
to deposit additional funds, in which case the party would be required to close out

the contract as soon as possible and would be responsible for any additional losses 
until the position is closed.
As with forward contracts, neither party pays any money to the other when the 
contract is initiated. Value accrues as the futures price changes, but at the end of each 
day, the mark-  to- market process settles the gains and losses, effectively resetting the 
value for each party to zero.
The clearinghouse moves money between the participants, crediting gains to the 
winners and charging losses to the losers. By doing this on a daily basis, the gains and 
losses are typically quite small, and the margin balances help ensure that the clearing -
house will collect from the party losing money. As an extra precaution, in fast-  moving 
markets, the clearinghouse can make margin calls during the day, not just at the end 
of the day. Yet there still remains the possibility that a party could default. A large loss

could occur quickly and consume the entire margin balance, with additional money 
owed.8 If the losing party cannot pay, the clearinghouse provides a guarantee that it 
will make up the loss, which it does by maintaining an insurance fund. If that fund 
were depleted, the clearinghouse could levy a tax on the other market participants, 
though that has never happened.
Some futures contracts contain a provision limiting price changes. These rules, 
called price limits , establish a band relative to the previous day’s settlement price, within 
which all trades must occur. If market participants wish to trade at a price above the 
upper band, trading stops, which is called limit up , until two parties agree on a trade 
at a price lower than the upper limit. Likewise, if market participants wish to trade 
at a price below the lower band, which is called limit down , no trade can take place 
until two parties agree to trade at a price above the lower limit. When the market hits

these limits and trading stops, it is called locked limit . Typically, the exchange rules 
provide for an expansion of the limits the next day. These price limits, which may be 
somewhat objectionable to proponents of free markets, are important in helping the 
clearinghouse manage its credit exposure. Just because two parties wish to trade a 
futures contract at a price beyond the limits does not mean they should be allowed to 
do so. The clearinghouse is a third participant in the contract, guaranteeing to each 
party that it ensures against the other party defaulting. Therefore, the clearinghouse 
has a vested interest in the price and considerable exposure. Sharply moving prices 
make it more difficult for the clearinghouse to collect from the parties losing money.
Most participants in futures markets buy and sell contracts, collecting their 
profits and incurring their losses, with no ultimate intent to make or take delivery of

the underlying asset. For example, the long may ultimately sell her position before 
expiration. When a party re-  enters the market at a later date but before expiration and 
8 For example, let us go back to when the short had a balance of £4, which is £2 below the maintenance 
margin and £6 below the initial margin. The short will get a margin call, but suppose he elects not to deposit 
additional funds and requests that his position be terminated. In a fast-  moving market, the price might 
increase more than £4 before his broker can close his position. The remaining balance of £4 would then 
be depleted, and the short would be responsible for any additional losses.

Reading 56 ■ Derivative Markets and Instruments 20
engages in the opposite transaction—a long selling her previously opened contract 
or a short buying her previously opened contract—the transaction is referred to as 
an offset. The clearinghouse marks the contract to the current price relative to the 
previous settlement price and closes out the participant’s position.
At any given time, the number of outstanding contracts is called the open interest . 
Each contract counted in the open interest has a long and a corresponding short. The 
open interest figure changes daily as some parties open up new positions, while other 
parties offset their old positions. It is theoretically possible that all longs and shorts 
offset their positions before expiration, leaving no open interest when the contract 
expires, but in practice there is nearly always some open interest at expiration, at 
which time there is a final delivery or settlement.

When discussing forward contracts, we noted that a contract could be written such 
that the parties engage in physical delivery or cash settlement at expiration. In the 
futures markets, the exchange specifies whether physical delivery or cash settlement 
applies. In physical delivery contracts, the short is required to deliver the underlying 
asset at a designated location and the long is required to pay for it. Delivery replaces 
the mark-  to- market process on the final day. It also ensures an important principle that 
you will use later: The futures price converges to the spot price at expiration . Because 
the short delivers the actual asset and the long pays the current spot price for it, the 
futures price at expiration has to be the spot price at that time. Alternatively, a futures 
contract initiated right at the instant of expiration is effectively a spot transaction and, 
therefore, the futures price at expiration must equal the spot price. Following this logic,

in cash settlement contracts, there is a final mark to market, with the futures price 
formally set to the spot price, thereby ensuring automatic convergence.
In discussing forward contracts, we described the process by which they pay off as 
the spot price at expiration minus the forward price, ST – F0(T), the former determined 
at expiration and the latter agreed upon when the contract is initiated. Futures contracts 
basically pay off the same way, but there is a slight difference. Let us say the contract 
is initiated on Day 0 and expires on Day T. The intervening days are designated Days 
1, 2, …, T. The initial futures price is designated f0(T) and the daily settlement prices 
on Days 1, 2, …, T are designated f1(T), f2(T), …, fT(T). There are, of course, futures 
prices within each trading day, but let us focus only on the settlement prices for now. 
For simplicity, let us assume that the long buys at the settlement price on Day 0 and

holds the position all the way to expiration. Through the mark-  to- market process, the 
cash flows to the account of the long will be
f1(T) – f0(T) on Day 1
f2(T) – f1(T) on Day 2
f3(T) – f2(T) on Day 3
…
fT(T) – fT–1(T) on Day T
These add up to
fT(T) – f0(T) on Day T.
And because of the convergence of the final futures price to the spot price,
fT(T) – f0(T) = ST – f0(T),
which is the same as with forward contracts.9 Note, however, that the timing of these 
profits is different from that of forwards. Forward contracts realize the full amount, 
ST – f0(T), at expiration, whereas futures contracts realize this amount in parts on a 
9 Because of this equivalence, we will not specifically illustrate the profit graphs of futures contracts. You 
can generally treat them the same as those of forwards, which were shown in Exhibit 1.

Types of Derivatives 21
day-  to- day basis. Naturally, the time value of money principle says that these are not 
equivalent amounts of money. But the differences tend to be small, particularly in 
low-  interest-  rate environments, some of these amounts are gains and some are losses, 
and most futures contracts have maturities of less than a year.
But the near equivalence of the profits from a futures and a forward contract dis -
guises an important distinction between these types of contracts. In a forward contact, 
with the entire payoff made at expiration, a loss by one party can be large enough to 
trigger a default. Hence, forward contracts are subject to default and require careful 
consideration of the credit quality of the counterparties. Because futures contracts 
settle gains and collect losses daily, the amounts that could be lost upon default are 
much smaller and naturally give the clearinghouse much greater flexibility to manage 
the credit risk it assumes.

Unlike forward markets, futures markets are highly regulated at the national level. 
National regulators are required to approve new futures exchanges and even new 
contracts proposed by existing exchanges as well as changes in margin requirements, 
price limits, and any significant changes in trading procedures. Violations of futures 
regulations can be subject to governmental prosecution. In addition, futures markets 
are far more transparent than forward markets. Futures prices, volume, and open 
interest are widely reported and easily obtained. Futures prices of nearby expiring 
contracts are often used as proxies for spot prices, particularly in decentralized spot 
markets, such as gold, which trades in spot markets all over the world.
In spite of the advantages of futures markets over forward markets, forward mar -
kets also have advantages over futures markets. Transparency is not always a good

thing. Forward markets offer more privacy and fewer regulatory encumbrances. In 
addition, forward markets offer more flexibility. With the ability to tailor contracts to 
the specific needs of participants, forward contracts can be written exactly the way 
the parties want. In contrast, the standardization of futures contracts makes it more 
difficult for participants to get exactly what they want, even though they may get close 
substitutes. Yet, futures markets offer a valuable credit guarantee.
Like forward markets, futures markets can be used for hedging or speculation. For 
example, a jewelry manufacturer can buy gold futures, thereby hedging the price it 
will have to pay for one of its key inputs. Although it is more difficult to construct a 
futures strategy that hedges perfectly than to construct a forward strategy that does so, 
futures offer the benefit of the credit guarantee. It is not possible to argue that futures

are better than forwards or vice versa. Market participants always trade off advantages 
against disadvantages. Some participants prefer futures, and some prefer forwards. 
Some prefer one over the other for certain risks and the other for other risks. Some 
might use one for a particular risk at a point in time and a different instrument for 
the same risk at another point in time. The choice is a matter of taste and constraints.
The third and final type of forward commitment we will cover is swaps. They go a 
step further in committing the parties to buy and sell something at a later date: They 
obligate the parties to a sequence of multiple purchases and sales.
4.1.3  Swaps
The concept of a swap is that two parties exchange (swap) a series of cash flows. One 
set of cash flows is variable or floating and will be determined by the movement of an 
underlying asset or rate. The other set of cash flows can be variable and determined

by a different underlying asset or rate, or it can be fixed. Formally, a swap is defined 

Reading 56 ■ Derivative Markets and Instruments 22
A swap is an over-  the- counter derivative contract in which two parties agree 
to exchange a series of cash flows whereby one party pays a variable series 
that will be determined by an underlying asset or rate and the other party 
pays either (1) a variable series determined by a different underlying asset 
or rate or (2) a fixed series.
As with forward contracts, swap contracts also contain other terms—such as the 
identity of the underlying, the relevant payment dates, and the payment procedure—
that are negotiated between the parties and written into the contract. A swap is a bit 
more like a forward contract than a futures contract in that it is an OTC contract, so 
it is privately negotiated and subject to default. Nonetheless, the similarities between 
futures and forwards apply to futures and swaps and, indeed, combinations of futures 
contracts expiring at different dates are often compared to swaps.

As with forward contracts, either party can default but only one party can default 
at a particular time. The money owed is always based on the net owed by one party to 
the other. Hence, the party owing the lesser amount cannot default to the party owing 
the greater amount. Only the latter can default, and the amount it owes is the net of 
what it owes and what is owed to it, which is also true with forwards.
Swaps are relatively young financial instruments, having been created only in the 
early 1980s. Thus, it may be somewhat surprising to learn that the swap is the most 
widely used derivative, a likely result of its simplicity and embracement by the cor -
porate world. The most common swap is the fixed-  for-  floating interest rate swap . 
In fact, this type of swap is so common that it is often called a “plain vanilla swap” 
or just a “vanilla swap, ” owing to the notion that vanilla ice cream is considered plain 
(albeit tasty).

Let us examine a scenario in which the vanilla interest rate swap is frequently 
used. Suppose a corporation borrows from a bank at a floating rate. It would prefer 
a fixed rate, which would enable it to better anticipate its cash flow needs in making 
its interest payments.10 The corporation can effectively convert its floating-  rate loan 
to a fixed-  rate loan by adding a swap, as shown in Exhibit 2.
Exhibit 2   Using an Interest Rate Swap to Convert a Floating-  Rate Loan to a 
Fixed-  Rate Loan
Corporation Borrowing at
Floating RateSwap Dealer
Bank Lender(fixed swap payments)(floating swap payments)
(floating inter est payments)
10 Banks prefer to make floating-  rate loans because their own funding is typically short term and at floating 
rates. Thus, their borrowing rates reset frequently, giving them a strong incentive to pass that risk on to 
their customers through floating-  rate loans.

Types of Derivatives 23
The interest payments on the loan are tied to a specific floating rate. For a dollar-  
based loan, that rate has typically been US dollar Libor.11 The payments would be based 
on the rate from the Libor market on a specified reset date times the loan balance 
times a factor reflecting the number of days in the current interest calculation period. 
The actual payment is made at a later date. Thus, for a loan balance of, say, $10 million 
with monthly payments, the rate might be based on Libor on the first business day of 
the month, with interest payable on the first business day of the next month, which 
is the next reset date, and calculated as $10 million times the rate times 30/360. The 
30/360 convention, an implicit assumption of 30 days in a month, is common but 
only one of many interest calculation conventions used in the financial world. Often, 
“30” is replaced by the exact number of days since the last interest payment. The use

of a 360-  day year is a common assumption in the financial world, which originated 
in the pre-  calculator days when an interest rate could be multiplied by a number like 
30/360, 60/360, 90/360, etc., more easily than if 365 were used.
Whatever the terms of the loan are, the terms of the swap are typically set to 
match those of the loan. Thus, a Libor-  based loan with monthly payments based on 
the 30/360 convention would be matched with a swap with monthly payments based 
on Libor and the 30/360 convention and the same reset and payment dates. Although 
the loan has an actual balance (the amount owed by borrower to creditor), the swap 
does not have such a balance owed by one party to the other. Thus, it has no principal, 
but it does have a balance of sorts, called the notional principal , which ordinarily 
matches the loan balance. A loan with only one principal payment, the final one, will 
be matched with a swap with a fixed notional principal. An amortizing loan, which

has a declining principal balance, will be matched with a swap with a pre-  specified 
declining notional principal that matches the loan balance.
As with futures and forwards, no money changes hands at the start; thus, the value 
of a swap when initiated must be zero. The fixed rate on the swap is determined by 
a process that forces the value to zero, a procedure that will be covered later in the 
curriculum. As market conditions change, the value of a swap will deviate from zero, 
being positive to one party and negative to the other.
As with forward contracts, swaps are subject to default, but because the notional 
amount of a swap is not typically exchanged, the credit risk of a swap is much less 
than that of a loan.12 The only money passing from one party to the other is the net 
difference between the fixed and floating interest payments. In fact, the parties do 
not even pay each other. Only one party pays the other, as determined by the net of

the greater amount owed minus the lesser amount. This does not mean that swaps 
are not subject to a potentially large amount of credit risk. At a given point in time, 
one party could default, effectively owing the value of all remaining payments, which 
could substantially exceed the value that the non-  defaulting party owes to the default -
ing party. Thus, there is indeed credit risk in a swap. This risk must be managed by 
careful analysis before the transaction and by the potential use of such risk-  mitigating 
measures as collateral.
11 Recall that US dollar Libor (London Interbank Offered Rate) is the estimated rate on a dollar-  based loan 
made by one London bank to another. Such a loan takes the form of a time deposit known as a Eurodollar 
because it represents a dollar deposited in a European bank account. In fact, Libor is the same as the so-  
called Eurodollar rate. The banks involved can be British banks or British branches of non-  British banks.

The banks estimate their borrowing rates, and a single average rate is assembled and reported each day. 
That rate is then commonly used to set the rate on many derivative contracts.
12 It is possible that the notional principal will be exchanged in a currency swap, whereby each party 
makes a series of payments to the other in different currencies. Whether the notional principal is exchanged 
depends on the purpose of the swap. This point will be covered later in the curriculum. At this time, you 
should see that it would be fruitless to exchange notional principals in an interest rate swap because that 
would mean each party would give the other the same amount of money when the transaction is initiated 
and re-  exchange the same amount of money when the contract terminates.

Reading 56 ■ Derivative Markets and Instruments 24
There are also interest rate swaps in which one party pays on the basis of one interest 
rate and the other party pays on the basis of a different interest rate. For example, one 
party might make payments at Libor, whereas the other might make payments on the 
basis of the U. S. Treasury bill rate. The difference between Libor and the T-  bill rate, 
often called the TED spread (T-  bills versus Eurodollar), is a measure of the credit risk 
premium of London banks, which have historically borrowed short term at Libor, 
versus that of the U. S. government, which borrows short term at the T-  bill rate. This 
transaction is called a basis swap. There are also swaps in which the floating rate is 
set as an average rate over the period, in accordance with the convention for many 
loans. Some swaps, called overnight indexed swaps, are tied to a Fed funds–type rate,

reflecting the rate at which banks borrow overnight. As we will cover later, there are 
many other different types of swaps that are used for a variety of purposes. The plain 
vanilla swap is merely the simplest and most widely used.
Because swaps, forwards, and futures are forward commitments, they can all 
accomplish the same thing. One could create a series of forwards or futures expiring 
at a set of dates that would serve the same purpose as a swap. Although swaps are 
better suited for risks that involve multiple payments, at its most fundamental level, a 
swap is more or less just a series of forwards and, acknowledging the slight differences 
discussed above, more or less just a series of futures.
EXAMPLE 3   
Forward Contracts, Futures Contracts, and Swaps
1 Which of the following characterizes forward contracts and swaps but not 
futures?
A They are customized.
B They are subject to daily price limits.
C Their payoffs are received on a daily basis.

2 Which of the following distinguishes forwards from swaps?
A Forwards are OTC instruments, whereas swaps are exchange traded.
B Forwards are regulated as futures, whereas swaps are regulated as 
C Swaps have multiple payments, whereas forwards have only a single 
payment.
3 Which of the following occurs in the daily settlement of futures contracts?
A Initial margin deposits are refunded to the two parties.
B Gains and losses are reported to other market participants.
C Losses are charged to one party and gains credited to the other.
A is correct. Forwards and swaps are OTC contracts and, therefore, are cus -
tomized. Futures are exchange traded and, therefore, are standardized. Some 
futures contracts are subject to daily price limits and their payoffs are received 
daily, but these characteristics are not true for forwards and swaps.
C is correct. Forwards and swaps are OTC instruments and both are regulated

as such. Neither is regulated as a futures contract or a security. A swap is a 
series of multiple payments at scheduled dates, whereas a forward has only one 
payment, made at its expiration date.

Types of Derivatives 25
C is correct. Losses and gains are collected and distributed to the respective 
parties. There is no specific reporting of these gains and losses to anyone else. 
Initial margin deposits are not refunded and, in fact, additional deposits may 
be required.
This material completes our introduction to forward commitments. All forward 
commitments are firm contracts. The parties are required to fulfill the obligations they 
agreed to. The benefit of this rigidity is that neither party pays anything to the other 
when the contract is initiated. If one party needs some flexibility, however, it can get it 
by agreeing to pay the other party some money when the contract is initiated. When 
the contract expires, the party who paid at the start has some flexibility in deciding 
whether to buy the underlying asset at the fixed price. Thus, that party did not actually 
agree to do anything. It had a choice. This is the nature of contingent claims.
4.2 Contingent Claims

A contingent claim  is a derivative in which the outcome or payoff is dependent on 
the outcome or payoff of an underlying asset. Although this characteristic is also 
associated with forward commitments, a contingent claim has come to be associated 
with a right , but not an obligation , to make a final payment contingent on the perfor -
mance of the underlying. Given that the holder of the contingent claim has a choice, 
the term contingent claim  has become synonymous with the term option . The holder 
has a choice of whether or not to exercise the option. This choice creates a payoff that 
transforms the underlying payoff in a more pronounced manner than does a forward, 
futures, or swap. Those instruments provide linear payoffs: As the underlying goes up 
(down), the derivative gains (loses). The further up (down) the underlying goes, the 
more the derivative gains (loses). Options are different in that they limit losses in one

direction. In addition, options can pay off as the underlying goes down. Hence, they 
transform the payoffs of the underlying into something quite different.
4.2.1  Options
We might say that an option, as a contingent claim, grants the right but not the 
obligation to buy an asset at a later date and at a price agreed on when the option is 
initiated. But there are so many variations of options that we cannot settle on this 
statement as a good formal definition. For one thing, options can also grant the right 
to sell instead of the right to buy. Moreover, they can grant the right to buy or sell 
earlier than at expiration. So, let us see whether we can combine these points into an 
all- encompassing definition of an option.
An option is a derivative contract in which one party, the buyer, pays a 
sum of money to the other party, the seller or writer, and receives the right 
to either buy or sell an underlying asset at a fixed price either on a specific

expiration date or at any time prior to the expiration date.
Unfortunately, even that definition does not cover every unique aspect of options. 
For example, options can be created in the OTC market and customized to the terms of 
each party, or they can be created and traded on options exchanges and standardized. 
As with forward contracts and swaps, customized options are subject to default, are 
less regulated, and are less transparent than exchange-  traded derivatives. Exchange-  
traded options are protected against default by the clearinghouse of the options 
exchange and are relatively transparent and regulated at the national level. As noted 
in the definition above, options can be terminated early or at their expirations. When

Reading 56 ■ Derivative Markets and Instruments 26
an option is terminated, either early or at expiration, the holder of the option chooses 
whether to exercise it. If he exercises it, he either buys or sells the underlying asset, 
but he does not have both rights. The right to buy is one type of option, referred to as 
a call or call option , whereas the right to sell is another type of option, referred to as 
a put or put option . With one very unusual and advanced exception that we do not 
cover, an option is either a call or a put, and that point is made clear in the contract.
An option is also designated as exercisable early (before expiration) or only at 
expiration. Options that can be exercised early are referred to as American-  style . 
Options that can be exercised only at expiration are referred to as European-  style . It 
is extremely important that you do not associate these terms with where these options 
are traded . Both types of options trade on all continents.13

As with forwards and futures, an option can be exercised by physical delivery or 
cash settlement, as written in the contract. For a call option with physical delivery, 
upon exercise the underlying asset is delivered to the call buyer, who pays the call 
seller the exercise price. For a put option with physical delivery, upon exercise the 
put buyer delivers the underlying asset to the put seller and receives the strike price. 
For a cash settlement option, exercise results in the seller paying the buyer the cash 
equivalent value as if the asset were delivered and paid for.
The fixed price at which the underlying asset can be purchased is called the exer -
cise price  (also called the “strike price, ” the “strike, ” or the “striking price”). This price 
is somewhat analogous to the forward price because it represents the price at which 
the underlying will be purchased or sold if the option is exercised. The forward price,

however, is set in the pricing of the contract such that the contract value at the start 
is zero. The strike price of the option is chosen by the participants. The actual price 
or value of the option is an altogether different concept.
As noted, the buyer pays the writer a sum of money called the option premium , 
or just the “premium. ” It represents a fair price of the option, and in a well-  functioning 
market, it would be the value of the option. Consistent with everything we know about 
finance, it is the present value of the cash flows that are expected to be received by the 
holder of the option during the life of the option. At this point, we will not get into 
how this price is determined, but you will learn that later. For now, there are some 
fundamental concepts you need to understand, which form a basis for understanding 
how options are priced and why anyone would use an option.
Because the option buyer (the long) does not have to exercise the option, beyond

the initial payment of the premium, there is no obligation of the long to the short. 
Thus, only the short can default, which would occur if the long exercises the option 
and the short fails to do what it is supposed to do. Thus, in contrast to forwards and 
swaps, in which either party could default to the other, default in options is possible 
only from the short to the long.
Ruling out the possibility of default for now, let us examine what happens when 
an option expires. Using the same notation used previously, let ST be the price of the 
underlying at the expiration date, T, and X be the exercise price of the option. Remember 
that a call option allows the holder, or long, to pay X and receive the underlying. It 
should be obvious that the long would exercise the option at expiration if ST is greater 
than X, meaning that the underlying value is greater than what he would pay to obtain 
the underlying. Otherwise, he would simply let the option expire. Thus, on the expi -

ration date, the option is described as having a payoff of Max (0,ST – X). Because the 
holder of the option would be entitled to exercise it and claim this amount, it also 
represents the value of the option at expiration. Let us denote that value as cT. Thus,
13 If you dig deeper into the world of options, you will find Asian options and Bermuda options. Geography 
is a common source of names for options as well as foods and in no way implies that the option or the food 
is available only in that geographical location.

Types of Derivatives 27
cT = Max (0,ST – X) (payoff to the call buyer),
which is read as “take the maximum of either zero or ST – X. ” Thus, if the underlying 
value exceeds the exercise price ( ST > X), then the option value is positive and equal 
to ST – X. The call option is then said to be in the money . If the underlying value is 
less than the exercise price ( ST < X), then ST – X is negative; zero is greater than a 
negative number, so the option value would be zero. When the underlying value is less 
than the exercise price, the call option is said to be out of the money . When ST = X, 
the call option is said to be at the money , although at the money is, for all practical 
purposes, out of the money because the value is still zero.
This payoff amount is also the value of the option at expiration. It represents value 
because it is what the option is worth at that point. If the holder of the option sells it

to someone else an instant before expiration, it should sell for that amount because 
the new owner would exercise it and capture that amount. To the seller, the value of 
the option at that point is ‒ Max (0,ST – X), which is negative to the seller if the option 
is in the money and zero otherwise.
Using the payoff value and the price paid for the option, we can determine the 
profit from the strategy, which is denoted with the Greek symbol Π. Let us say the 
buyer paid c0 for the option at time 0. Then the profit is
Π = Max (0,ST – X) – c0 (profit to the call buyer),
To the seller, who received the premium at the start, the payoff is
–cT = –Max (0,ST – X) (payoff to the call seller),
The profit is
Π = – Max (0,ST – X) + c0 (profit to the call seller),
Exhibit 3 illustrates the payoffs and profits to the call buyer and seller as graphical 
representations of these equations, with the payoff or value at expiration indicated by

the dark line and the profit indicated by the light line. Note in Panel A that the buyer 
has no upper limit on the profit and has a fixed downside loss limit equal to the pre -
mium paid for the option. Such a condition, with limited loss and unlimited gain, is a 
temptation to many unsuspecting investors, but keep in mind that the graph does not 
indicate the frequency with which gains and losses will occur. Panel B is the mirror 
image of Panel A and shows that the seller has unlimited losses and limited gains. One 
might suspect that selling a call is, therefore, the worst investment strategy possible. 
Indeed, it is a risky strategy, but at this point these are only simple strategies. Other 
strategies can be added to mitigate the seller’s risk to a substantial degree.

Reading 56 ■ Derivative Markets and Instruments 28
Exhibit 3   Payoff and Profit from a Call Option
A. Payoff and Profit from Buying
B. Payoff and Profit from Selling
Payoff and Profit
Profit
0c0
Payoff
STPayoff and Profit
Profit0
–c0Payoff
ST X
Now let us consider put options. Recall that a put option allows its holder to sell 
the underlying asset at the exercise price. Thus, the holder should exercise the put at 
expiration if the underlying asset is worth less than the exercise price ( ST < X). In that 
case, the put is said to be in the money. If the underlying asset is worth the same as 
the exercise price ( ST = X), meaning the put is at the money, or more than the exer -
cise price ( ST > X), meaning the put is out of the money, the option holder would not 
exercise it and it would expire with zero value. Thus, the payoff to the put holder is
pT = Max (0,X – ST) (payoff to the put buyer),
If the put buyer paid p0 for the put at time 0, the profit is

Π = Max (0,X – ST) – p0 (profit to the put buyer),
And for the seller, the payoff is
–pT = –Max (0,X – ST) (payoff to the put seller),
And the profit is
Π = – Max (0,X – ST) + p0 (profit to the put seller),

Types of Derivatives 29
Exhibit 4 illustrates the payoffs and profits to the buyer and seller of a put.
Exhibit 4   Payoff and Profit from a Put Option
Payoff and ProfitPayoff and Profit
Profit0
–p0Payoff
ST X
Profit
0p0
Payoff
ST X
The put buyer has a limited loss, and although the gain is limited by the fact that 
the underlying value cannot go below zero, the put buyer does gain more the lower 
the value of the underlying. In this manner, we see how a put option is like insurance. 
Bad outcomes for the underlying trigger a payoff for both the insurance policy and 
the put, whereas good outcomes result only in loss of the premium. The put seller, 
like the insurer, has a limited gain and a loss that is larger the lower the value of the 
underlying. As with call options, these graphs must be considered carefully because 
they do not indicate the frequency with which gains and losses will occur. At this

point, it should be apparent that buying a call option is consistent with a bullish point 
of view and buying a put option is consistent with a bearish point of view. Moreover, 
in contrast to forward commitments, which have payoffs that are linearly related to 
the payoffs of the underlying (note the straight lines in Exhibit 1), contingent claims 
have payoffs that are non-  linear in relation to the underlying. There is linearity over 
a range—say, from 0 to X or from X upward or downward—but over the entire range 
of values for the underlying, the payoffs of contingent claims cannot be depicted with 
a single straight line.

Reading 56 ■ Derivative Markets and Instruments 30
We have seen only a snapshot of the payoff and profit graphs that can be created 
with options. Calls can be combined with puts, the underlying asset, and other calls 
or puts with different expirations and exercise prices to create a diverse set of payoff  
and profit graphs, some of which are covered later in the curriculum.
Before leaving options, let us again contrast the differences between options and 
forward commitments. With forward commitments, the parties agree to trade an 
underlying asset at a later date and at a price agreed upon when the contract is ini -
tiated. Neither party pays any cash to the other at the start. With options, the buyer 
pays cash to the seller at the start and receives the right, but not the obligation, to 
buy (if a call) or sell (if a put) the underlying asset at expiration at a price agreed upon 
(the exercise price) when the contract is initiated. In contrast to forwards, futures,

and swaps, options do have value at the start: the premium paid by buyer to seller. 
That premium pays for the right , eliminating the obligation , to trade the underlying 
at a later date, as would be the case with a forward commitment.
Although there are numerous variations of options, most have the same essential 
features described here. There is, however, a distinctive family of contingent claims 
that emerged in the early 1990s and became widely used and, in some cases, heavily 
criticized. These instruments are known as credit derivatives.
4.2.2  Credit Derivatives
Credit risk is surely one of the oldest risks known to mankind. Human beings have 
been lending things to each other for thousands of years, and even the most primitive 
human beings must have recognized the risk of lending some of their possessions to 
their comrades. Until the last 20 years or so, however, the management of credit risk 
was restricted to simply doing the best analysis possible before making a loan, moni -

toring the financial condition of the borrower during the loan, limiting the exposure 
to a given party, and requiring collateral. Some modest forms of insurance against 
credit risk have existed for a number of years, but insurance can be a slow and cum -
bersome way of protecting against credit loss. Insurance is typically highly regulated, 
and insurance laws are usually very consumer oriented. Thus, credit insurance as a 
financial product has met with only modest success.
In the early 1990s, however, the development of the swaps market led to the 
creation of derivatives that would hedge credit risk. These instruments came to be 
known as credit derivatives , and they avoided many of the regulatory constraints of 
the traditional insurance industry. Here is a formal definition:
A credit derivative is a class of derivative contracts between two parties, 
a credit protection buyer and a credit protection seller, in which the latter

provides protection to the former against a specific credit loss.
One of the first credit derivatives was a total return swap , in which the underlying 
is typically a bond or loan, in contrast to, say, a stock or stock index. The credit protec -
tion buyer offers to pay the credit protection seller the total return on the underlying 
bond. This total return consists of all interest and principal paid by the borrower plus 
any changes in the bond’s market value. In return, the credit protection seller typically 
pays the credit protection buyer either a fixed or a floating rate of interest. Thus, if 
the bond defaults, the credit protection seller must continue to make its promised 
payments, while receiving a very small return or virtually no return from the credit 
protection buyer. If the bond incurs a loss, as it surely will if it defaults, the credit 
protection seller effectively pays the credit protection buyer.

Another type of credit derivative is the credit spread option , in which the under -
lying is the credit (yield) spread on a bond, which is the difference between the bond’s 
yield and the yield on a benchmark default-  free bond. As you will learn in the fixed-  
income material, the credit spread is a reflection of investors’ perception of credit risk. 
Because a credit spread option requires a credit spread as the underlying, this type of

Types of Derivatives 31
derivative works only with a traded bond that has a quoted price. The credit protection 
buyer selects the strike spread it desires and pays the option premium to the credit 
protection seller. At expiration, the parties determine whether the option is in the 
money by comparing the bond’s yield spread with the strike chosen, and if it is, the 
credit protection seller pays the credit protection buyer the established payoff. Thus, 
this instrument is essentially a call option in which the underlying is the credit spread.
A third type of credit derivative is the credit-  linked note (CLN) . With this deriv -
ative, the credit protection buyer holds a bond or loan that is subject to default risk 
(the underlying reference security) and issues its own security (the credit-  linked note) 
with the condition that if the bond or loan it holds defaults, the principal payoff on 
the credit-  linked note is reduced accordingly. Thus, the buyer of the credit-  linked note

effectively insures the credit risk of the underlying reference security.
These three types of credit derivatives have had limited success compared with 
the fourth type of credit derivative, the credit default swap (CDS) . The credit default 
swap, in particular, has achieved much success by capturing many of the essential 
features of insurance while avoiding the high degree of consumer regulations that are 
typically associated with traditional insurance products.
In a CDS, one party—the credit protection buyer, who is seeking credit protection 
against a third party—makes a series of regularly scheduled payments to the other 
party, the credit protection seller. The seller makes no payments until a credit event 
occurs. A declaration of bankruptcy is clearly a credit event, but there are other types 
of credit events, such as a failure to make a scheduled payment or an involuntary 
restructuring. The CDS contract specifies what constitutes a credit event, and the

industry has a procedure for declaring credit events, though that does not guarantee 
the parties will not end up in court arguing over whether something was or was not 
a credit event.
Formally, a credit default swap is defined as follows:
A credit default swap is a derivative contract between two parties, a credit 
protection buyer and a credit protection seller, in which the buyer makes a 
series of cash payments to the seller and receives a promise of compensation 
for credit losses resulting from the default of a third party.
A CDS is conceptually a form of insurance. Sellers of CDSs, oftentimes banks or 
insurance companies, collect periodic payments and are required to pay out if a loss 
occurs from the default of a third party. These payouts could take the form of resti -
tution of the defaulted amount or the party holding the defaulting asset could turn 
it over to the CDS seller and receive a fixed amount. The most common approach

is for the payout to be determined by an auction to estimate the market value of the 
defaulting debt. Thus, CDSs effectively provide coverage against a loss in return for 
the protection buyer paying a premium to the protection seller, thereby taking the 
form of insurance against credit loss. Although insurance contracts have certain legal 
characteristics that are not found in credit default swaps, the two instruments serve 
similar purposes and operate in virtually the same way: payments made by one party 
in return for a promise to cover losses incurred by the other.
Exhibit 5 illustrates the typical use of a CDS by a lender. The lender is exposed 
to the risk of non-  payment of principal and interest. The lender lays off this risk by 
purchasing a CDS from a CDS seller. The lender—now the CDS buyer—promises 
to make a series of periodic payments to the CDS seller, who then stands ready to 
compensate the CDS buyer for credit losses.

Reading 56 ■ Derivative Markets and Instruments 32
Exhibit 5   Using a Credit Default Swap to Hedge the Credit Risk of a Loan
Lender (CDS buyer) CDS Seller
Borrower(interest and
principal payments)(periodic payments)(compensation for credit losses)
Clearly, the CDS seller is betting on the borrower’s not defaulting or—more gen -
erally, as insurance companies operate—that the total payouts it is responsible for 
are less than the total payments collected. Of course, most insurance companies are 
able to do this by having reliable actuarial statistics, diversifying their risk, and selling 
some of the risk to other insurance companies. Actuarial statistics are typically quite 
solid. Average claims for life, health, and casualty insurance are well documented, and 
insurers can normally set premiums to cover losses and operate at a reasonable profit. 
Although insurance companies try to manage some of their risks at the micro level

(e.g., charging smokers more for life and health insurance), most of their risk man -
agement is at the macro level, wherein they attempt to make sure their risks are not 
concentrated. Thus, they avoid selling too much homeowners insurance to individuals 
in tornado-  prone areas. If they have such an exposure, they can use the reinsurance 
market to sell some of the risk to other companies that are not overexposed to that 
risk. Insurance companies attempt to diversify their risks and rely on the principle of 
uncorrelated risks, which plays such an important role in portfolio management. A 
well-  diversified insurance company, like a well-  diversified portfolio, should be able to 
earn a return commensurate with its assumed risk in the long run.
Credit default swaps should operate the same way. Sellers of CDSs should recognize 
when their credit risk is too concentrated. When that happens, they become buyers of

CDSs from other parties or find other ways to lay off the risk. Unfortunately, during 
the financial crisis that began in 2007, many sellers of CDSs failed to recognize the 
high correlations among borrowers whose debt they had guaranteed. One well-  known 
CDS seller, AIG, is a large and highly successful traditional insurance company that 
got into the business of selling CDSs. Many of these CDSs insured against mortgages. 
With the growth of the subprime mortgage market, many of these CDS-  insured 
mortgages had a substantial amount of credit risk and were often poorly documented. 
AIG and many other CDS sellers were thus highly exposed to systemic credit con -
tagion, a situation in which defaults in one area of an economy ripple into another, 
accompanied by bank weaknesses and failures, rapidly falling equity markets, rising 
credit risk premiums, and a general loss of confidence in the financial system and the

economy. These presumably well-  diversified risks guaranteed by CDS sellers, operating 
as though they were insurance companies, ultimately proved to be poorly diversified. 
Systemic financial risks can spread more rapidly than fire, health, and casualty risks. 
Virtually no other risks, except those originating from wars or epidemics, spread in 
the manner of systemic financial risks.
Thus, to understand and appreciate the importance of the CDS market, it is neces -
sary to recognize how that market can fail. The ability to separate and trade risks is a 
valuable one. Banks can continue to make loans to their customers, thereby satisfying

Types of Derivatives 33
the customers’ needs, while laying off the risk elsewhere. In short, parties not wanting 
to bear certain risks can sell them to parties wanting to assume certain risks. If all 
parties do their jobs correctly, the markets and the economy work more efficiently. If, 
as in the case of certain CDS sellers, not everyone does a good job of managing risk, 
there can be serious repercussions. In the case of AIG and some other companies, 
taxpayer bailouts were the ultimate price paid to keep these large institutions afloat 
so that they could continue to provide their other critical services to consumers. 
The rules proposed in the new OTC derivatives market regulations—which call for 
greater regulation and transparency of OTC derivatives and, in particular, CDSs—have 
important implications for the future of this market and these instruments.
EXAMPLE 4   
Options and Credit Derivatives
1 An option provides which of the following?

A Either the right to buy or the right to sell an underlying
B The right to buy and sell, with the choice made at expiration
C The obligation to buy or sell, which can be converted into the right to 
buy or sell
2 Which of the following is not a characteristic of a call option on a stock?
A A guarantee that the stock will increase
B A specified date on which the right to buy expires
C A fixed price at which the call holder can buy the stock
3 A credit derivative is which of the following?
A A derivative in which the premium is obtained on credit
B A derivative in which the payoff is borrowed by the seller
C A derivative in which the seller provides protection to the buyer 
against credit loss from a third party
A is correct. An option is strictly the right to buy (a call) or the right to sell (a 
put). It does not provide both choices or the right to convert an obligation into 
a right.

a right.
A is correct. A call option on a stock provides no guarantee of any change in the 
stock price. It has an expiration date, and it provides for a fixed price at which 
the holder can exercise the option, thereby purchasing the stock.
C is correct. Credit derivatives provide a guarantee against loss caused by a 
third party’s default. They do not involve borrowing the premium or the payoff.
4.2.3  Asset-  Backed Securities
Although these instruments are covered in more detail in the fixed-  income material, 
we would be remiss if we failed to include them with derivatives. But we will give 
them only light coverage here.

Reading 56 ■ Derivative Markets and Instruments 34
As discussed earlier, derivatives take (derive) their value from the value of the 
underlying, as do mutual funds and exchange-  traded funds (ETFs). A mutual fund or 
an ETF holding bonds is virtually identical to the investor holding the bonds directly. 
Asset-  backed securities (ABSs) take this concept a step further by altering the payment 
streams. ABSs typically divide the payments into slices, called tranches, in which the 
priority of claims has been changed from equivalent to preferential. For example, in 
a bond mutual fund or an ETF, all investors in the fund have equal claims, and so the 
rate of return earned by each investor is exactly the same. If a portfolio of the same 
bonds were assembled into an ABS, some investors in the ABS would have claims 
that would supersede those of other investors. The differential nature of these claims 
becomes relevant when either prepayments or defaults occur.

Prepayments mostly affect only mortgages. When a portfolio of mortgages is 
assembled into an ABS, the resulting instrument is called a collateralized mortgage 
obligation  (CMO). Commonly but not always, the credit risk has been reduced or 
eliminated, perhaps by a CDS, as discussed earlier. When homeowners pay off their 
mortgages early due to refinancing at lower rates, the holders of the mortgages suf -
fer losses. They expected to receive a stream of returns that is now terminated. The 
funds that were previously earning a particular rate will now have to be invested to 
earn a lower rate. These losses are the mirror images of the gains homeowners make 
when they proudly proclaim that they refinanced their mortgages and substantially 
lowered their payments.
CMOs partition the claims against these mortgages into different tranches, which 
are typically called A, B, and C. Class C tranches bear the first wave of prepayments

until that tranche has been completely repaid its full principal investment. At that 
point, the Class B tranche holders bear the next prepayments until they have been fully 
repaid. The Class A tranche holders then bear the next wave of prepayments.14 Thus, 
the risk faced by the various tranche holders is different from that of a mutual fund 
or ETF, which would pass the returns directly through such that investors would all 
receive the same rates of return. Therefore, the expected returns of CMO tranches vary 
and are commensurate with the prepayment risk they assume. Some CMOs are also 
characterized by credit risk, perhaps a substantial amount, from subprime mortgages.
When bonds or loans are assembled into ABSs, they are typically called collater -
alized bond obligations  (CBOs) or collateralized loan obligations  (CLOs). These 
instruments (known collectively as collateralized debt obligations , or CDOs) do not

traditionally have much prepayment risk but they do have credit risk and oftentimes 
a great deal of it. The CDO structure allocates this risk to tranches that are called 
senior, mezzanine, or junior tranches (the last sometimes called equity tranches). 
When defaults occur, the junior tranches bear the risk first, followed by the mezzanine 
tranches, and then the senior tranches. The expected returns of the tranches vary 
according to the perceived credit risk, with the senior tranches having the highest 
credit quality and the junior the lowest. Thus, the senior tranches have the lowest 
expected returns and the junior tranches have the highest.
An asset-  backed security is formally defined as follows:
An asset-  backed security is a derivative contract in which a portfolio of debt 
instruments is assembled and claims are issued on the portfolio in the form 
of tranches, which have different priorities of claims on the payments made

by the debt securities such that prepayments or credit losses are allocated to 
the most-  junior tranches first and the most-  senior tranches last.
14 The reference to only three tranches is just a general statement. There are many more types of tranches. 
Our discussion of the three classes is for illustrative purposes only and serves to emphasize that there are 
high-  priority claims, low-  priority claims, and other claims somewhere in the middle.

Types of Derivatives 35
ABSs seem to have only an indirect and subtle resemblance to options, but they are 
indeed options. They promise to make a series of returns that are typically steady. These 
returns can be lowered if prepayments or defaults occur. Thus, they are contingent 
on prepayments and defaults. Take a look again at Exhibit 4, Panel B (the profit and 
payoff of a short put option). If all goes well, there is a fixed return. If something goes 
badly, the return can be lowered, and the worse the outcome, the lower the return. 
Thus, holders of ABSs have effectively written put options.
This completes the discussion of contingent claims. Having now covered forward 
commitments and contingent claims, the final category of derivative instruments is 
more or less just a catch-  all category in case something was missed.
4.3 Hybrids
The instruments just covered encompass all the fundamental instruments that exist in

the derivatives world. Yet, the derivatives world is truly much larger than implied by 
what has been covered here. We have not covered and will touch only lightly on the 
many hybrid instruments that combine derivatives, fixed-  income securities, curren -
cies, equities, and commodities. For example, options can be combined with bonds to 
form either callable bonds or convertible bonds. Swaps can be combined with options 
to form swap payments that have upper and lower limits. Options can be combined 
with futures to obtain options on futures. Options can be created with swaps as the 
underlying to form swaptions. Some of these instruments will be covered later. For 
now, you should just recognize that the possibilities are almost endless.
We will not address these hybrids directly, but some are covered elsewhere in the 
curriculum. The purpose of discussing them here is for you to realize that derivatives

create possibilities not otherwise available in their absence. This point will lead to a 
better understanding of why derivatives exist, a topic we will get to very shortly.
EXAMPLE 5   
Forward Commitments versus Contingent Claims
1 Which of the following is not a forward commitment?
A An agreement to take out a loan at a future date at a specific rate
B An offer of employment that must be accepted or rejected in two 
weeks
C An agreement to lease a piece of machinery for one year with a series 
of fixed monthly payments
2 Which of the following statements is true about contingent claims?
A Either party can default to the other.
B The payoffs are linearly related to the performance of the underlying.
C The most the long can lose is the amount paid for the contingent 
claim.
B is correct. Both A and C are commitments to engage in transactions at future 
dates. In fact, C is like a swap because the party agrees to make a series of future

payments and in return receives temporary use of an asset whose value could 
vary. B is a contingent claim. The party receiving the employment offer can 
accept it or reject it if there is a better alternative.

Reading 56 ■ Derivative Markets and Instruments 36
C is correct. The maximum loss to the long is the premium. The payoffs of 
contingent claims are not linearly related to the underlying, and only one party, 
the short, can default.
4.4 Derivatives Underlyings
Before discussing the purposes and benefits of derivatives, we need to clarify some 
points that have been implied so far. We have alluded to certain underlying assets, 
this section will briefly discuss the underlyings more directly.
4.4.1  Equities
Equities are one of the most popular categories of underlyings on which derivatives are 
created. There are two types of equities on which derivatives exist: individual stocks 
and stock indexes. Derivatives on individual stocks are primarily options. Forwards, 
futures, and swaps on individual stocks are not widely used. Index derivatives in the 
form of options, forwards, futures, and swaps are very popular. Index swaps, more

often called equity swaps, are quite popular and permit investors to pay the return on 
one stock index and receive the return on another index or a fixed rate. They can be 
very useful in asset allocation strategies by allowing an equity manager to increase or 
reduce exposure to an equity market or sector without trading the individual securities.
In addition, options on stocks are frequently used by companies as compensation 
and incentives for their executives and employees. These options are granted to pro -
vide incentives to work toward driving the stock price up and can result in companies 
paying lower cash compensation.15 Some companies also issue warrants, which are 
options sold to the public that allow the holders to exercise them and buy shares 
directly from the companies.16
4.4.2  Fixed-  Income Instruments and Interest Rates
Options, forwards, futures, and swaps on bonds are widely used. The problem with

creating derivatives on bonds, however, is that there are almost always many issues 
of bonds. A single issuer, whether it is a government or a private borrower, often has 
more than one bond issue outstanding. For futures contracts, with their standardiza -
tion requirements, this problem is particularly challenging. What does it mean to say 
that a futures contract is on a German bund, a US Treasury note, or a UK gilt? The 
most common solution to this problem is to allow multiple issues to be delivered on 
a single futures contract. This feature adds some interesting twists to the pricing and 
trading strategies of these instruments.
Until now, we have referred to the underlying as an asset . Yet, one of the largest 
derivative underlyings is not an asset. It is simply an interest rate. An interest rate is 
not an asset. One cannot hold an interest rate or place it on a balance sheet as an asset. 
Although one can hold an instrument that pays an interest rate, the rate itself is not

15 Unfortunately, the industry has created some confusion with the terminology of these instruments. They 
are often referred to as stock options , and yet ordinary publicly traded options not granted to employees 
are sometimes referred to as stock options. The latter are also sometimes called equity options , whereas 
employee-  granted options are almost never referred to as equity options. If the terms executive stock 
options  and employee stock options  were always used, there would be no problem. You should be aware of 
and careful about this confusion.
16 A warrant is a type of option, similar to the employee stock option, written by the company on its own 
stock, in contrast to exchange-  traded and OTC options, in which the company is not a party to the option 
contract. Also note that, unfortunately, the financial world uses the term warrant  to refer to a number of 
other option-  like instruments. Like a lot of words that have multiple meanings, one must understand the

Types of Derivatives 37
an asset. But there are derivatives in which the rate, not the instrument that pays the 
rate, is the underlying. In fact, we have already covered one of these derivatives: The 
plain vanilla interest rate swap in which Libor is the underlying.17 Instead of a swap, 
an interest rate derivative could be an option. For example, a call option on 90-  day 
Libor with a strike of 5% would pay off if at expiration Libor exceeds 5%. If Libor is 
below 5%, the option simply expires unexercised.
Interest rate derivatives are the most widely used derivatives. With that in mind, 
we will be careful in using the expression underlying asset  and will use the more 
generic underlying .
4.4.3  Currencies
Currency risk is a major factor in global financial markets, and the currency deriv -
atives market is extremely large. Options, forwards, futures, and swaps are widely 
used. Currency derivatives can be complex, sometimes combining elements of other

underlyings. For example, a currency swap involves two parties making a series of 
interest rate payments to each other in different currencies. Because interest rates 
and currencies are both subject to change, a currency swap has two sources of risk. 
Although this instrument may sound extremely complicated, it merely reflects the 
fact that companies operating across borders are subject to both interest rate risk and 
currency risk and currency swaps are commonly used to manage those risks.
4.4.4  Commodities
Commodities are resources, such as food, oil, and metals, that humans use to sustain 
life and support economic activity. Because of the economic principle of comparative 
advantage, countries often specialize in the production of certain resources. Thus, the 
commodities market is extremely large and subject to an almost unimaginable array 
of risks. One need only observe how the price of oil moves up as tension builds in

the Middle East or how the price of orange juice rises on a forecast of cold weather 
in Florida.
Commodity derivatives are widely used to speculate in and manage the risk asso -
ciated with commodity price movements. The primary commodity derivatives are 
futures, but forwards, swaps, and options are also used. The reason that futures are 
in the lead in the world of commodities is simply history. The first futures markets 
were futures on commodities. The first futures exchange, the Chicago Board of Trade, 
was created in 1848, and until the creation of currency futures in 1972, there were no 
futures on any underlying except commodities.
There has been a tendency to think of the commodities world as somewhat sep -
arate from the financial world. Commodity traders and financial traders were quite 
different groups. Since the creation of financial futures, however, commodity and 
financial traders have become relatively homogeneous. Moreover, commodities are

increasingly viewed as an important asset class that should be included in investment 
strategies because of their ability to help diversify portfolios.
4.4.5  Credit
As we previously discussed, credit is another underlying and quite obviously not an 
asset. Credit default swaps (CDSs) and collateralized debt obligations (CDOs) were 
discussed extensively in an earlier section. These instruments have clearly established 
that credit is a distinct underlying that has widespread interest from a trading and risk 
management perspective. In addition, to the credit of a single entity, credit derivatives 
17 As you will see later, there are also futures in which the underlying is an interest rate (Eurodollar futures) 
and forwards in which the underlying is an interest rate (forward rate agreements, or FRAs).

Reading 56 ■ Derivative Markets and Instruments 38
are created on multiple entities. CDOs themselves are credit derivatives on portfolios 
of credit risks. In recent years, indexes of CDOs have been created, and instruments 
based on the payoffs of these CDO indexes are widely traded.
4.4.6  Other
This category is included here to capture some of the really unusual underlyings. One 
in particular is weather. Although weather is hardly an asset, it is certainly a major 
force in how some entities perform. For example, a ski resort needs snow, farmers 
need an adequate but not excessive amount of rain, and public utilities experience 
strains on their capacity during temperature extremes. Derivatives exist in which the 
payoffs are measured as snowfall, rainfall, and temperature. Although these deriva -
tives have not been widely used—because of some complexities in pricing, among 
other things—they continue to exist and may still have a future. In addition, there are

derivatives on electricity, which is also not an asset. It cannot be held in the traditional 
sense because it is created and consumed almost instantaneously. Another unusual 
type of derivative is based on disasters in the form of insurance claims.
Financial institutions will continue to create derivatives on all types of risks and 
exposures. Most of these derivatives will fail because of little trading interest, but a 
few will succeed. If that speaks badly of derivatives, it must be remembered that most 
small businesses fail, most creative ideas fail, and most people who try to become 
professional entertainers or athletes fail. It is the sign of a healthy and competitive 
system that only the very best survive.
THE SIZE OF THE DERIVATIVES MARKET
In case anyone thinks that the derivatives market is not large enough to justify studying, 
we should consider how big the market is. Unfortunately, gauging the size of the deriv -

atives market is not a simple task. OTC derivatives contracts are private transactions. No 
reporting agency gathers data, and market size is not measured in traditional volume-  
based metrics, such as shares traded in the stock market. Complicating things further is 
the fact that derivatives underlyings include equities, fixed-  income securities, interest 
rates, currencies, commodities, and a variety of other underlyings. All these underlyings 
have their own units of measurement. Hence, measuring how “big” the underlying 
derivatives markets are is like trying to measure how much fruit consumers purchase; 
the proverbial mixing of apples, oranges, bananas, and all other fruits.
The exchange-  listed derivatives market reports its size in terms of volume, meaning 
the number of contracts traded. Exchange-  listed volume, however, is an inconsistent 
number. For example, US Treasury bond futures contracts trade in units covering $100,000

face value. Eurodollar futures contracts trade in units covering $1,000,000 face value. 
Crude oil trades in 1,000-  barrel (42 gallons each) units. Yet, one traded contract of each 
gets equal weighting in volume totals.
The March–April issue of the magazine Futures Industry  (available to subscribers) 
reports the annual volume of the entire global futures and options industry. For 2011, 
that volume was more than 25 billion contracts.
OTC volume is even more difficult to measure. There is no count of the number of 
contracts that trade. In fact, volume  is an almost meaningless concept in OTC markets 
because any notion of volume requires a standardized size. If a customer goes to a swaps 
dealer and enters into a swap to hedge a $50 million loan, there is no measure of how 
much volume that transaction generated. The $50  million swap’s notional principal, 
however, does provide a measure to some extent. Forwards, swaps, and OTC options all

have notional principals, so they can be measured in that manner. Another measure of 
the size of the derivatives market is the market value of these contracts. As noted, for -
wards and swaps start with zero market value, but their market value changes as market 
conditions change. Options do not start with zero market value and almost always have 
a positive market value until expiration, when some options expire out of the money.

The Purposes and Benefits of Derivatives 39
The OTC industry has taken both of these concepts—notional principal and market 
value—as measures of the size of the market. Notional principal is probably a more 
accurate measure. The amount of a contract’s notional principal is unambiguous: It is 
written into the contract and the two parties cannot disagree over it. Yet, notional prin -
cipal terribly overstates the amount of money actually at risk. For example, a $50 million 
notional principal swap will have nowhere near $50 million at risk. The payments on such 
a swap are merely the net of two opposite series of interest payments on $50 million. 
The market value of such a swap is the present value of one stream of payments minus 
the present value of the other. This market value figure will always be well below the 
notional principal. Thus, market value seems like a better measure except that, unlike 
notional principal, it is not unambiguous. Market value requires measurement, and two

parties can disagree on the market value of the same transaction.
Notional principal and market value estimates for the global OTC derivatives market are 
collected semi-  annually by the Bank for International Settlements of Basel, Switzerland, 
and published on its website (http://www.bis.org/statistics/derstats.htm). At the end 
of 2011, notional principal was more than $600  trillion and market value was about 
$27 trillion. A figure of $600 trillion is an almost unfathomable number and, as noted, 
is a misleading measure of the amount of money at risk.18 The market value figure of 
$27 trillion is a much more realistic measure, but as noted, it is less accurate, relying on 
estimates provided by banks.
Hence, the exchange-  listed and OTC markets use different measures and each of those 
measures is subject to severe limitations. About all we can truly say for sure about the 
derivatives market is, “It is big.”
THE PURPOSES AND BENEFITS OF DERIVATIVES

Economic historians know that derivatives markets have existed since at least the 
Middle Ages. It is unclear whether derivatives originated in the Asian rice markets 
or possibly in medieval trade fairs in Europe. We do know that the origin of modern 
futures markets is the creation of the Chicago Board of Trade in 1848. To understand 
why derivatives markets exist, it is useful to take a brief look at why the Chicago Board 
of Trade was formed.
In the middle of the 19th century, midwestern America was rapidly becoming the 
center of agricultural production in the United States. At the same time, Chicago was 
evolving into a major American city, a hub of transportation and commerce. Grain 
markets in Chicago were the central location to which midwestern farmers brought 
their wheat, corn, and soybeans to sell. Unfortunately, most of these products arrived 
at approximately the same time of the year, September through November. The stor -

age facilities in Chicago were strained beyond capacity. As a result, prices would fall 
tremendously and some farmers reportedly found it more economical to dump their 
grains in the Chicago River rather than transport them back to the farm. At other 
times of the year, prices would rise steeply. A group of businessmen saw this situation 
as unnecessary volatility and a waste of valuable produce. To deal with this problem, 
they created the Chicago Board of Trade and a financial instrument called the “to-  
arrive” contract. A farmer could sell a to-  arrive contract at any time during the year. 
This contract fixed the price of the farmer’s grain on the basis of delivery in Chicago 
at a specified later date. Grain is highly storable, so farmers can hold on to the grain 
and deliver it at almost any later time. This plan substantially reduced seasonal market 
volatility and made the markets work much better for all parties.5

18 To put it in perspective, it would take 19 million years for a clock to tick off 600 trillion seconds!

Reading 56 ■ Derivative Markets and Instruments 40
The traders in Chicago began to trade these contracts, speculating on movements 
in grain prices. Soon, it became apparent that an important and fascinating market 
had developed. Widespread hedging and speculative interest resulted in substantial 
market growth, and about 80 years later, a clearinghouse and a performance guaran -
tee were added, thus completing the evolution of the to-  arrive contract into today’s 
modern futures contract.
Many commodities and all financial assets that underlie derivatives contracts are 
not seasonally produced. Hence, this initial motivation for futures markets is only 
a minor advantage of derivatives markets today. But there are many reasons why 
derivative markets serve an important and useful purpose in contemporary finance.
5.1 Risk Allocation, Transfer, and Management
Until the advent of derivatives markets, risk management was quite cumbersome.

Setting the actual level of risk to the desired level of risk required engaging in trans -
actions in the underlyings. Such transactions typically had high transaction costs and 
were disruptive of portfolios. In many cases, it is quite difficult to fine-  tune the level 
of risk to the desired level. From the perspective of a risk taker, it was quite costly to 
buy risk because a large amount of capital would be required.
Derivatives solve these problems in a very effective way: They allow trading the 
risk without trading the instrument itself. For example, consider a stockholder who 
wants to reduce exposure to a stock. In the pre-  derivatives era, the only way to do so 
was to sell the stock. Now, the stockholder can sell futures, forwards, calls, or swaps, 
or buy put options, all while retaining the stock. For a company founder, these types 
of strategies can be particularly useful because the founder can retain ownership and

probably board membership. Many other excellent examples of the use of derivatives 
to transfer risk are covered elsewhere in the curriculum. The objective at this point 
is to establish that derivatives provide an effective method of transferring risk from 
parties who do not want the risk to parties who do. In this sense, risk allocation is 
improved within markets and, indeed, the entire global economy.
The overall purpose of derivatives is to obtain more effective risk management 
within companies and the entire economy. Although some argue that derivatives do 
not serve this purpose very well (we will discuss this point in Section 6), for now you 
should understand that derivatives can improve the allocation of risk and facilitate 
more effective risk management for both companies and economies.
5.2 Information Discovery
One of the advantages of futures markets has been described as price discovery . A 
futures price has been characterized by some experts as a revelation of some infor -

mation about the future. Thus, a futures price is sometimes thought of as predictive. 
This statement is not strictly correct because futures prices are not really forecasts 
of future spot prices. They provide only a little more information than do spot 
prices, but they do so in a very efficient manner. The markets for some underlyings 
are highly decentralized and not very efficient. For example, what is gold worth? It 
trades in markets around the world, but probably the best place to look is at the gold 
futures contract expiring soonest. What is the value of the S&P 500 Index when the 
US markets are not open? As it turns out, US futures markets open before the US 
stock market opens. The S&P 500 futures price is frequently viewed as an indication 
of where the stock market will open.

The Purposes and Benefits of Derivatives 41
Derivative markets can, however, convey information not impounded in spot 
markets. By virtue of the fact that derivative markets require less capital, information 
can flow into the derivative markets before it gets into the spot market. The difference 
may well be only a matter of minutes or possibly seconds, but it can provide the edge 
to astute traders.
Finally, we should note that futures markets convey another simple piece of infor -
mation: What price would one accept to avoid uncertainty? If you hold a stock worth 
$40 and could hedge the next 12 months’ uncertainty, what locked-  in price should 
you expect to earn? As it turns out, it should be the price that guarantees the risk-  free 
rate minus whatever dividends would be paid on the stock. Derivatives—specifically, 
futures, forwards, and swaps—reveal the price that the holder of an asset could take 
and avoid the risk.

What we have said until now applies to futures, forwards, and swaps. What about 
options? As you will learn later, given the underlying and the type of option (call or 
put), an option price reflects two characteristics of the option (exercise price and time 
to expiration), three characteristics of the underlying (price, volatility, and cash flows it 
might pay), and one general macroeconomic factor (risk-  free rate). Only one of these 
factors, volatility, is not relatively easy to identify. But with the available models to price 
the option, we can infer what volatility people are using from the actual market prices 
at which they execute trades. That volatility, called implied volatility , measures the 
expected risk of the underlying. It reflects the volatility that investors use to determine 
the market price of the option. Knowing the expected risk of the underlying asset is 
an extremely useful piece of information. In fact, for options on broad-  based market

indexes, such as the S&P 500, the implied volatility is a good measure of the general 
level of uncertainty in the market. Some experts have even called it a measure of fear. 
Thus, options provide information about what investors think of the uncertainty in 
the market, if not their fear of it.19
In addition, options allow the creation of trading strategies that cannot be done 
by using the underlying. As the exhibits on options explained, these strategies provide 
asymmetrical performance: limited movement in one direction and movement in the 
other direction that changes with movements in the underlying.
5.3 Operational Advantages
We noted earlier that derivatives have lower transaction costs than the underlying. The 
transaction costs of derivatives can be high relative to the value of the derivatives, but 
these costs are typically low relative to the value of the underlying. Thus, an investor 
who wants to take a position in, say, an equity market index would likely find it less

costly to use the futures to get a given degree of exposure than to invest directly in 
the index to get that same exposure.
Derivative markets also typically have greater liquidity than the underlying spot 
markets, a result of the smaller amount of capital required to trade derivatives than to 
get the equivalent exposure directly in the underlying. Futures margin requirements 
and option premiums are quite low relative to the cost of the underlying.
One other extremely valuable operational advantage of derivative markets is the 
ease with which one can go short. With derivatives, it is nearly as easy to take a short 
position as to take a long position, whereas for the underlying asset, it is almost always 
much more difficult to go short than to go long. In fact, for many commodities, short 
selling is nearly impossible.
19 The Chicago Board Options Exchange publishes a measure of the implied volatility of the S&P 500 Index

option, which is called the VIX (volatility index). The VIX is widely followed and is cited as a measure of 
investor uncertainty and sometimes fear.

Reading 56 ■ Derivative Markets and Instruments 42
5.4 Market Efficiency
In the study of portfolio management, you learn that an efficient market is one in 
which no single investor can consistently earn returns in the long run in excess of 
those commensurate with the risk assumed. Of course, endless debates occur over 
whether equity markets are efficient. No need to resurrect that issue here, but let us 
proceed with the assumption that equity markets—and, in fact, most free and com -
petitive financial markets—are reasonably efficient. This assumption does not mean 
that abnormal returns can never be earned, and indeed prices do get out of line with 
fundamental values. But competition, the relatively free flow of information, and ease 
of trading tend to bring prices back in line with fundamental values. Derivatives can 
make this process work even more rapidly.
When prices deviate from fundamental values, derivative markets offer less costly

ways to exploit the mispricing. As noted earlier, less capital is required, transaction 
costs are lower, and short selling is easier. We also noted that as a result of these 
features, it is possible, indeed likely, that fundamental value will be reflected in the 
derivatives markets before it is restored in the underlying market. Although this time 
difference could be only a matter of minutes, for a trader seeking abnormal returns, 
a few minutes can be a valuable opportunity.
All these advantages of derivatives markets make the financial markets in general 
function more effectively. Investors are far more willing to trade if they can more 
easily manage their risk, trade at lower cost and with less capital, and go short more 
easily. This increased willingness to trade increases the number of market participants, 
which makes the market more liquid. A very liquid market may not automatically be 
an efficient market, but it certainly has a better chance of being one.

Even if one does not accept the concept that financial markets are efficient, it is 
difficult to say that markets are not more effective and competitive with derivatives. 
Yet, many blame derivatives for problems in the market. Let us take a look at these 
arguments.
CRITICISMS AND MISUSES OF DERIVATIVES
The history of financial markets is filled with extreme ups and downs, which are often 
called bubbles and crashes. Bubbles occur when prices rise for a long time and appear 
to exceed fundamental values. Crashes occur when prices fall rapidly. Although bubbles, 
if they truly exist, are troublesome, crashes are even more so because nearly everyone 
loses substantial wealth in a crash. A crash is then typically followed by a government 
study commissioned to find the causes of the crash. In the last 30 years, almost all 
such studies have implicated derivatives as having some role in causing the crash. Of 
course, because derivatives are widely used and involve a high degree of leverage, it is

a given that they would be seen in a crash. It is unclear whether derivatives are the real 
culprit or just the proverbial smoking gun used by someone to do something wrong.
The two principal arguments against derivatives are that they are such speculative 
devices that they effectively permit legalized gambling and that they destabilize the 
financial system. Let us look at these points more closely.
6.1 Speculation and Gambling
As noted earlier, derivatives are frequently used to manage risk. In many contexts, this 
use involves hedging or laying off risk. Naturally, for hedging to work, there must be 
speculators. Someone must accept the risk. Derivatives markets are unquestionably 
attractive to speculators. All the benefits of derivatives draw speculators in large 6

Criticisms and Misuses of Derivatives 43
numbers, and indeed they should. The more speculators that participate in the market, 
the cheaper it is for hedgers to lay off risk. These speculators take the form of hedge 
funds and other professional traders who willingly accept risk that others need to 
shed. In recent years, the rapid growth of these types of investors has been alarming 
to some but almost surely has been beneficial for all investors.
Unfortunately, the general image of speculators is not a good one. Speculators are 
often thought to be short-  term traders who attempt to exploit temporary inefficiencies, 
caring little about long-  term fundamental values. The profits from short-  term trading 
are almost always taxed more heavily than the profits from long-  term trading, clearly 
targeting and in some sense punishing speculators. Speculators are thought to engage 
in price manipulation and to trade at extreme prices.20 All of this type of trading is

viewed more or less as just a form of legalized gambling.
In most countries, gambling is a heavily regulated industry. In the United States, 
only certain states permit private industry to offer gambling. Many states operate 
gambling only through the public sector in the form of state-  run lotteries. Many peo -
ple view derivatives trading as merely a form of legalized and uncontrolled gambling.
Yet, there are notable differences between gambling and speculation. Gambling 
typically benefits only a limited number of participants and does not generally help 
society as a whole. But derivatives trading brings extensive benefits to financial markets, 
as explained earlier, and thus does benefit society as a whole. In short, the benefits of 
derivatives are broad, whereas the benefits of gambling are narrow.
Nonetheless, the argument that derivatives are a form of legalized gambling will 
continue to be made. Speculation and gambling are certainly both forms of financial

risk taking, so these arguments are not completely off base. But insurance companies 
speculate on loss claims, mutual funds that invest in stocks speculate on the perfor -
mance of companies, and entrepreneurs go up against tremendous odds to speculate 
on their own ability to create successful businesses. These so-  called speculators are 
rarely criticized for engaging in a form of legalized gambling, and indeed entrepreneurs 
are praised as the backbone of the economy. Really, all investment is speculative. So, 
why is speculation viewed as such a bad thing by so many? The answer is unclear.
6.2 Destabilization and Systemic Risk
The arguments against speculation through derivatives often go a step further, claiming 
that it is not merely speculation or gambling per se but rather that it has destabilizing 
consequences. Opponents of derivatives claim that the very benefits of derivatives 
(low cost, low capital requirements, ease of going short) result in an excessive amount

of speculative trading that brings instability to the market. They argue that specula -
tors use large amounts of leverage, thereby subjecting themselves and their creditors 
to substantial risk if markets do not move in their hoped-  for direction. Defaults by 
speculators can then lead to defaults by their creditors, their creditors’ creditors, and 
so on. These effects can, therefore, be systemic and reflect an epidemic contagion 
whereby instability can spread throughout markets and an economy, if not the entire 
world. Given that governments often end up bailing out some banks and insurance 
companies, society has expressed concern that the risk managed with derivatives 
must be controlled.
This argument is not without merit. Such effects occurred in the Long-  Term 
Capital Management fiasco of 1998 and again in the financial crisis of 2008, in which 
derivatives, particularly credit default swaps, were widely used by many of the problem

20 Politicians and regulators have been especially critical of energy market speculators. Politicians, in 
particular, almost always blame rising oil prices on speculators, although credit is conspicuously absent 
for falling oil prices.

Reading 56 ■ Derivative Markets and Instruments 44
entities. Responses to such events typically take the course of calling for more rules 
and regulations restricting the use of derivatives, requiring more collateral and credit 
mitigation measures, backing up banks with more capital, and encouraging, if not 
requiring, OTC derivatives to be centrally cleared like exchange-  traded derivatives.
In response, however, we should note that financial crises—including the South 
Sea and Mississippi bubbles and the stock market crash of 1929, as well as a handful 
of economic calamities of the 19th and 20th centuries—have existed since the dawn 
of capitalism. Some of these events preceded the era of modern derivatives markets, 
and others were completely unrelated to the use of derivatives. Some organizations, 
such as Orange County, California, in 1994–1995, have proved that derivatives are not 
required to take on excessive leverage and nearly bring the entity to ruin. Proponents

of derivatives argue that derivatives are but one of many mechanisms through which 
excessive risk can be taken. Derivatives may seem dangerous, and they can be if 
misused, but there are many ways to take on leverage that look far less harmful but 
can be just as risky.
Another criticism of derivatives is simply their complexity. Many derivatives 
are extremely complex and require a high-  level understanding of mathematics. The 
financial industry employs many mathematicians, physicists, and computer scien -
tists. This single fact has made many distrust derivatives and the people who work 
on them. It is unclear why this reason has tarnished the reputation of the derivatives 
industry. Scientists work on complex problems in medicine and engineering without 
public distrust. One explanation probably lies in the fact that scientists create models 
of markets by using scientific principles that often fail. To a physicist modeling the

movements of celestial bodies, the science is reliable and the physicist is unlikely to 
misapply the science. The same science applied to financial markets is far less reliable. 
Financial markets are driven by the actions of people who are not as consistent as the 
movements of celestial bodies. When financial models fail to work as they should, 
the scientists are often blamed for either building models that are too complex and 
unable to accurately capture financial reality or misusing those models, such as using 
poor estimates of inputs. And derivatives, being so widely used and heavily leveraged, 
are frequently in the center of it all.
EXAMPLE 6   
Purposes and Controversies of Derivative Markets
1 Which of the following is not an advantage of derivative markets?
A They are less volatile than spot markets.
B They facilitate the allocation of risk in the market.
C They incur lower transaction costs than spot markets.
2 Which of the following pieces of information is not conveyed by at least

one type of derivative?
A The volatility of the underlying
B The most widely used strategy of the underlying
C The price at which uncertainty in the underlying can be eliminated
3 Which of the following responds to the criticism that derivatives can be 
destabilizing to the underlying market?
A Market crashes and panics have occurred since long before derivatives 
existed.

Elementary Principles of Derivative Pricing 45
B Derivatives are sufficiently regulated that they cannot destabilize the 
spot market.
C The transaction costs of derivatives are high enough to keep their use 
at a minimum level.
A is correct. Derivative markets are not by nature more or less volatile than 
spot markets. They facilitate risk allocation by making it easier and less costly 
to transfer risk, and their transaction costs are lower than those of spot markets.
B is correct. Options do convey the volatility of the underlying, and futures, 
forwards, and swaps convey the price at which uncertainty in the underlying 
can be eliminated. Derivatives do not convey any information about the use of 
the underlying in strategies.
A is correct. Derivatives regulation is not more and is arguably less than spot 
market regulation, and the transaction costs of derivatives are not a deterrent

to their use; in fact, derivatives are widely used. Market crashes and panics have 
a very long history, much longer than that of derivatives.
An important element of understanding and using derivatives is having a healthy 
respect for their power. Every day, we use chemicals, electricity, and fire without 
thinking about their dangers. We consume water and drive automobiles, both of which 
are statistically quite dangerous. Perhaps these risks are underappreciated, but it is 
more likely the case that most adults learn how to safely use chemicals, electricity, 
fire, water, and automobiles. Of course, there are exceptions, many of which are fool -
ish, and foolishness is no stranger to the derivatives industry. The lesson here is that 
derivatives can make our financial lives better, but like chemicals, electricity, and all 
the rest, we need to know how to use them safely, which is why they are an important 
part of the CFA curriculum.

Later in the curriculum, you will learn a great deal about how derivatives are 
priced. At this point, we introduce the pricing of derivatives. This material not only 
paves the way for a deeper understanding of derivatives but also complements earlier 
material by helping you understand how derivatives work.
ELEMENTARY PRINCIPLES OF DERIVATIVE PRICING
Pricing and valuation are fundamental elements of the CFA Program. The study of 
fixed-  income and equity securities, as well as their application in portfolio manage -
ment, is solidly grounded on the principle of valuation. In valuation, the question is 
simple: What is something worth? Without an answer to that question, one can hardly 
proceed to use that something  wisely.
Determining what a derivative is worth is similar to determining what an asset is 
worth. As you learn in the fixed-  income and equity readings, value is the present value

of future cash flows, with discounting done at a rate that reflects both the opportunity 
cost of money and the risk. Derivatives valuation applies that same principle but in 
a somewhat different way.7

Reading 56 ■ Derivative Markets and Instruments 46
Think of a derivative as attached  to an underlying. We know that the derivative 
derives  its value from the value of the underlying. If the underlying’s value changes, so 
should the value of the derivative. The underlying takes its value from the discounted 
present value of the expected future cash flows it offers, with discounting done at a rate 
reflecting the investor’s risk tolerance. But if the value of the underlying is embedded 
in the value of the derivative, it would be double counting to discount the derivative’s 
expected future cash flows at a risky discount rate. That effect has already been incor -
porated into the value of the underlying, which goes into the value of the derivative.
Derivatives usually take their values from the underlying by constructing a hypo -
thetical combination of the derivatives and the underlyings that eliminates risk. This

combination is typically called a hedge portfolio . With the risk eliminated, it follows 
that the hedge portfolio should earn the risk-  free rate. A derivative’s value is the price 
of the derivative that forces the hedge portfolio to earn the risk-  free rate.
This principle of derivative valuation relies completely on the ability of an investor 
to hold or store the underlying asset. Let us take a look at what that means.
7.1 Storage
As noted previously, the first derivatives were agricultural commodities. Most of 
these commodities can be stored (i.e., held) for a period of time. Some extreme cases, 
such as oil and gold, which are storable for millions of years, are excellent examples 
of fully storable commodities. Grains, such as wheat and corn, can be stored for long 
but not infinite periods of time. Some commodities, such as bananas, are storable 
for relatively short periods of time. In the CFA Program, we are more interested in

financial assets. Equities and currencies have perpetual storability, whereas bonds are 
storable until they mature.
Storage incurs costs. Commodity storage costs can be quite expensive. Imagine 
storing 1,000 kilograms of gold or a million barrels of oil. Financial assets, however, 
have relatively low storage costs. Some assets pay returns during storage. Stocks pay 
dividends and bonds pay interest. The net of payments offered minus storage costs 
plays a role in the valuation of derivatives.
An example earlier in this reading illustrates this point. Suppose an investor 
holds a dividend-  paying stock and wants to eliminate the uncertainty of its selling 
price over a future period of time. Suppose further that the investor enters into a 
forward contract that commits him to deliver the stock at a later date, for which he 
will receive a fixed price. With uncertainty eliminated, the investor should earn the

risk-  free rate, but in fact, he does not. He earns more because while holding the stock, 
he collects dividends. Therefore, he should earn the risk-  free rate minus  the dividend 
yield, a concept known as the cost of carry, which will be covered in great detail in 
later readings. The cost of carry plus the dividends he earns effectively means that 
he makes the risk-  free rate. Now, no one is claiming that this is a good way to earn 
the risk-  free rate. There are many better ways to do that, but this strategy could be 
executed. There is one and only one forward price that guarantees that this strategy 
earns a return of the risk-  free rate minus the dividend yield, or the risk-  free rate after 
accounting for the dividends collected. If the forward price at which contracts are 
created does not equal this price, investors can take advantage of this discrepancy by 
engaging in arbitrage, which is discussed in the next section.

Forwards, futures, swaps, and options are all priced in this manner. Hence, they rely 
critically on the ability to store or hold the asset. Some underlyings are not storable. 
We previously mentioned electricity. It is produced and consumed almost instanta -
neously. Weather is also not storable. Fresh fish have very limited storability. Although 
this absence of storability may not be the reason, derivative markets in these types of 
underlyings have not been particularly successful, whereas those in underlyings that 
are more easily storable have often been successful.

Elementary Principles of Derivative Pricing 47
The opposite of storability is the ability to go short—that is, to borrow the underly -
ing, sell it, and buy it back later. We discussed earlier that short selling of some assets 
can be difficult. It is not easy to borrow oil or soybeans. There are ways around this 
constraint, but derivatives valuation is generally much easier when the underlying can 
be shorted. This point is discussed in more depth later in the curriculum.
7.2 Arbitrage
What we have been describing is the foundation of the principle of arbitrage . In 
well-  functioning markets with low transaction costs and a free flow of information, 
the same asset cannot sell for more than one price. If it did, someone would buy it in 
the cheaper market and sell it in the more expensive market, earning a riskless profit. 
The combined actions of all parties doing this would push up the lower price and 
push down the higher price until they converged. For this reason, arbitrage is often

referred to as the law of one price . Of course, for arbitrage to be feasible, the ability 
to purchase and sell short the asset is important.
Obviously, this rule does not apply to all markets. The same consumer good 
can easily sell for different prices, which is one reason why people spend so much 
time shopping on the internet. The costs associated with purchasing the good in the 
cheaper market and selling it in the more expensive market can make the arbitrage 
not worthwhile. The absence of information on the very fact that different prices exist 
would also prevent the arbitrage from occurring. Although the internet and various 
price-  comparing websites reduce these frictions and encourage all sellers to offer 
competitive prices, consumer goods are never likely to be arbitragable.21
Financial markets, of course, are a different matter. Information on securities prices 
around the world is quite accessible and relatively inexpensive. Most financial markets

are fairly competitive because dealers, speculators, and brokers attempt to execute 
trades at the best prices. Arbitrage is considered a dependable rule in the financial 
markets. Nonetheless, there are people who purport to make a living as arbitrageurs. 
How could they exist? To figure that out, first consider some examples of arbitrage.
The simplest case of an arbitrage might be for the same stock to sell at different 
prices in two markets. If the stock were selling at $52 in one market and $50 in 
another, an arbitrageur would buy the stock at $50 in the one market and sell it at 
$52 in the other. This trade would net an immediate $2 profit at no risk and would 
not require the commitment of any of the investor’s capital. This outcome would be 
a strong motivation for all arbitrageurs, and their combined actions would force the 
lower price up and the higher price down until the prices converged.
But what would be the final price? It is entirely possible that $50 is the true fun -

damental value and $52 is too high. Or $52 could be the true fundamental value and 
$50 is too low. Or the true fundamental value could lie somewhere between the two. 
Arbitrage does not tell us the true fundamental value. It is not an absolute  valuation 
methodology, such as the discounted cash flow equity valuation model. It is a relative  
valuation methodology. It tells us the correct price of one asset or derivative relative  
to another asset or derivative.
Now, consider another situation, illustrated in Exhibit 6. Observe that we have one 
stock, AXE Electronics, that today is worth $50 and one period later will be worth 
either $75 or $40. We will denote these prices as AXE = $50, AXE+ = $75, and AXE– 
= $40. Another stock, BYF Technology, is today worth $38 and one period later will 
21 If the same consumer good sells for different prices in markets with a relatively free flow of information

(e.g., via price-  comparing websites), it still may not be possible to truly arbitrage. Buying the good at a lower 
price and selling it at a higher price but less than the price of the most expensive seller may not be practical, 
but the most expensive seller may be driven out of business. When everyone knows what everyone else is 
charging, the same effect of arbitrage can still occur.

Reading 56 ■ Derivative Markets and Instruments 48
be worth $60 or $32. Thus, BYF = $38, BYF+ = $60, and BYF– = $32. Assume that 
the risk-  free borrowing and lending rate is 4%. Also assume no dividends are paid on 
either stock during the period covered by this example.
Exhibit 6   Arbitrage Opportunity with Stock AXE, Stock BYF, and a Risk-  Free 
Bond
AXE = $50
BYF = $38AXE+ = $75
BYF+ = $60
AXE– = $40
BYF– = $32
Note : The risk-  free rate is 4%.
The opportunity exists to make a profit at no risk without committing any of our 
funds, as demonstrated in Exhibit 7. Suppose we borrow 100 shares of stock AXE, 
which is selling for $50, and sell them short, thereby receiving $5,000. We take $4,750 
and purchase 125 shares of stock BYF (125 × $38 = $4,750). We invest the remaining 
$250 in risk-  free bonds at 4%. This transaction will not require us to use any funds 
of our own: The short sale will be sufficient to fund the investment in BYF and leave 
money to invest in risk-  free bonds.

Exhibit 7   Execution of Arbitrage Transaction with Stock AXE, Stock BYF, and 
a Risk-  Free Bond
(AXE = $50, BYF = $38)
Sell short 100 shar es of
AXE for $5,000
Buy 125 shar es of BYF for
$4,750
Invest $250 in risk-fr ee
bonds at 4%
Net investment: $0(AXE+ = $75, BYF+ = $60)
Sell 125 shares of
BYF for $7,500
Buy back 100 shares of AXE for
$7,500 to cover short position
Bonds ar e worth $250(1.04) = $260
Total value = $260
(AXE– = $40, BYF– = $32)
BYF for $4,000
$4,000 to cover short position

Elementary Principles of Derivative Pricing 49
If the top outcome in Exhibit 7 occurs, we sell the 125 shares of BYF for 125 × 
$60 = $7,500. This amount is sufficient to buy back the 100 shares of AXE, which 
is selling for $75. But we will also have the bonds, which are worth $250 × 1.04 = 
$260. If the bottom outcome occurs, we sell the 125 shares of BYF for 125 × $32 = 
$4,000—enough money to buy back the 100 shares of AXE, which is selling for $40. 
Again, we will have the risk-  free bonds, worth $260. Regardless of the outcome, we 
end up with $260.
Recall that we invested no money of our own and end up with a sure $260. It 
should be apparent that this transaction is extremely attractive, so everyone would 
do it. The combined actions of multiple investors would drive down the price of AXE 
and/or drive up the price of BYF until an equilibrium is reached, at which point this 
transaction would no longer be profitable. As noted earlier, we cannot be sure of

the correct fundamental price, but let us assume that BYF’s price remains constant. 
Then AXE would fall to $47.50. Alternatively, if we assume that AXE’s price remains 
constant, then the price of BYF would rise to $40. These values are obtained by noting 
that the prices for both outcomes occur according to the ratio 1.25 ($75/$60 = 1.25; 
$40/$32 = 1.25). Thus, their initial prices should be consistent with that ratio. If BYF is 
$38, AXE should be $38 × 1.25 = $47.50. If AXE is $50, BYF should be $40.00 because 
$40.00 × 1.25 = $50. Of course, the two prices could settle in between. Arbitrage is 
only a relative pricing method. It prices the two stocks in relation to each other but 
does not price either on the basis of its own fundamentals.
Of course, this example is extremely simplified. Clearly, a stock price can change 
to more than two other prices. Also, if a given stock is at one price, another stock

may be at any other price. We have created a simple case here to illustrate a point. 
But as you will learn later in the curriculum, when derivatives are involved, the sim -
plification here is relatively safe. As we know, the price of a derivative is determined 
by the price of the underlying. Hence, when the underlying is at one particular price, 
the derivative’s price will be determined by that price. The two assets need not be two 
stocks; one can be a stock and the other can be a derivative on the stock.
To see that point, consider another type of arbitrage opportunity that involves a 
forward contract. Recall from the previous example that at the start, AXE sells for $50. 
Suppose we borrow $50 at 4% interest by issuing a risk-  free bond, use the money to 
buy one share of stock AXE, and simultaneously enter into a forward contract to sell 
this share at a price of $54 one period later. The stock will then move to either $75 or

$40 in the next period. The forward contract requires that we deliver the stock and 
accept $54 for it. And of course, we will owe $50 × 1.04 = $52 on the loan.
Now consider the two outcomes. Regardless of the outcome, the end result is the 
same. The forward contract fixes the delivery price of the stock at $54:
AXE goes to $75
Deliver stock to settle forward contract + $54
Pay back loan – $52
Net + $2
AXE goes to $40
Net + $2

Reading 56 ■ Derivative Markets and Instruments 50
In either case, we made $2, free and clear. In fact, we can even accommodate the 
possibility of more than two future prices for AXE and we will always make $2.22 The 
key point is that we faced no risk and did not have to invest any of our own money, 
but ended up with $2, which is clearly a good trade. The $2 is an arbitrage profit. But 
where did it originate?
It turns out that the forward price, $54, was an inappropriate price given current 
market conditions. In fact, it was just an arbitrary price made up to illustrate the 
point. To eliminate the opportunity to earn the $2 profit, the forward price should 
be $52, which is equal, not coincidentally, to the amount owed on the loan. It is also 
no coincidence that $52 is the price of the asset increased by the rate of interest. We 
will cover this point later in the curriculum, but for now consider that you have just 
seen your first derivative pricing model.23

Of course, many market participants would do this transaction as long as it gener -
ated an arbitrage profit. These forces of arbitrage would either push the forward price 
down or the stock price up, or both, until an equilibrium is reached that eliminates 
the opportunity to profit at no risk with no commitment of one’s own funds.
To summarize, the forces of arbitrage in financial markets assure us that the same 
asset cannot sell for different prices, nor can two equivalent combinations of assets that 
produce the same results sell for different prices. Realistically, some arbitrage oppor -
tunities can exist on a temporary basis, but they will be quickly exploited, bringing 
relative prices back in line with each other. Other apparent arbitrage opportunities 
will be too small to warrant exploiting.
Not to be naive, however, we must acknowledge that there is a large industry of

people who call themselves arbitrageurs. So, how can such an industry exist if there 
are no opportunities for riskless profit? One explanation is that most of the arbitrage 
transactions are more complex than the simple examples used here. Many involve 
estimating information, which can result in differing opinions. Arbitrage involving 
options, for example, usually requires an estimate of a stock’s volatility. Different 
participants have different opinions about the volatility. It is quite possible that the 
two counterparties trading with each other believe that each is arbitraging against 
the other.24
But more importantly, the absence of arbitrage opportunities is upheld, ironically, 
only if participants believe that arbitrage opportunities do exist. If traders believe that 
no opportunities exist to earn arbitrage profits, then traders will not follow market 
prices and compare those prices with what they ought to be. Thus, eliminating arbitrage

opportunities requires that participants be alert in watching for arbitrage opportuni -
ties. In other words, strange as it may sound, disbelief and skepticism concerning the 
absence of arbitrage opportunities are required for the no-  arbitrage rule to be upheld.
Markets in which arbitrage opportunities are either nonexistent or quickly elimi -
nated are relatively efficient markets. Recall that efficient markets are those in which 
it is not possible to consistently earn returns in excess of those that would be fair 
compensation for the risk assumed. Although abnormal returns can be earned in a 
variety of ways, arbitrage profits are definitely examples of abnormal returns. Thus, 
they are the most egregious violations of the principle of market efficiency.
22 A good study suggestion is to try this example with any future stock price. You should get the same 
result, a $2 risk-  free profit.
23 This illustration is the quick look at forward pricing alluded to in Section 3.1.1.

24 In reality, many of the transactions that arbitrageurs do are not really arbitrage. They are quite specula -
tive. For example, many people call themselves arbitrageurs because they buy companies that are potential 
takeover targets and sell the companies they think will be the buyers. This transaction is not arbitrage by 
any stretch of the definition. Some transactions are called “risk arbitrage, ” but this term is an oxymoron. 
As an investment professional, you should simply be prepared for such misuses of words, which simply 
reflect the flexibility of language.

Elementary Principles of Derivative Pricing 51
Throughout the derivatives component of the CFA curriculum, we will use the 
principle of arbitrage as a dominant theme and assume that arbitrage opportunities 
cannot exist for any significant length of time nor can any one investor consistently 
capture them. Thus, prices must conform to models that assume no arbitrage. But we 
do not want to take the absence of arbitrage opportunities so seriously that we give 
up and believe that arbitrage opportunities never exist. Otherwise, they will arise and 
someone else will take them. Consider the rule of arbitrage a law that will be broken 
from time to time but one that holds far more often than not and one that should be 
understood and respected.
EXAMPLE 7   
Arbitrage
1 Which of the following is a result of arbitrage?
A The law of one price
B The law of similar prices
C The law of limited profitability
2 When an arbitrage opportunity exists, what happens in the market?

A The combined actions of all arbitrageurs force the prices to converge.
B The combined actions of arbitrageurs result in a locked-  limit situation.
C The combined actions of all arbitrageurs result in sustained profits to 
all.
3 Which of the following accurately defines arbitrage?
A An opportunity to make a profit at no risk
B An opportunity to make a profit at no risk and with the investment of 
no capital
C An opportunity to earn a return in excess of the return appropriate for 
the risk assumed
4 Which of the following ways best describes how arbitrage contributes to 
market efficiency?
A Arbitrage penalizes those who trade too rapidly.
B Arbitrage equalizes the risks taken by all market participants.
C Arbitrage improves the rate at which prices converge to their relative 
A is correct. Arbitrage forces equivalent assets to have a single price. There is 
nothing called the law of similar prices or the law of limited profitability.

A is correct. Prices converge because of the heavy demand for the cheaper asset 
and the heavy supply of the more expensive asset. Profits are not sustained, and, 
in fact, they are eradicated as prices converge. Locked-  limit is a condition in the 
futures market and has nothing to do with arbitrage.
B is correct. An opportunity to profit at no risk could merely describe the pur -
chase of a risk-  free asset. An opportunity to earn a return in excess of the return 
appropriate for the risk assumed is a concept studied in portfolio management

Reading 56 ■ Derivative Markets and Instruments 52
and is often referred to as an abnormal return. It is certainly desirable but is 
hardly an arbitrage because it requires the assumption of risk and the invest -
ment of capital. Arbitrage is risk free and requires no capital because selling the 
overpriced asset produces the funds to buy the underpriced asset.
C is correct. Arbitrage imposes no penalties on rapid trading; in fact, it tends 
to reward those who trade rapidly to take advantage of arbitrage opportunities. 
Arbitrage has no effect of equalizing risk among market participants. Arbitrage 
does result in an acceleration of price convergence to fair values relative to 
instruments with equivalent payoffs.
SUMMARY
This first reading on derivatives introduces you to the basic characteristics of deriv -
atives, including the following points:
■■A derivative is a financial instrument that derives its performance from the 

■■The underlying asset, called the underlying, trades in the cash or spot markets 
and its price is called the cash or spot price.
■■Derivatives consist of two general classes: forward commitments and contin -
gent claims.
■■Derivatives can be created as standardized instruments on derivatives 
exchanges or as customized instruments in the over-  the- counter market.
■■Exchange-  traded derivatives are standardized, highly regulated, and transparent 
transactions that are guaranteed against default through the clearinghouse of 
the derivatives exchange.
■■Over-  the- counter derivatives are customized, flexible, and more private and less 
regulated than exchange-  traded derivatives, but are subject to a greater risk of 
default.
■■A forward contract is an over-  the- counter derivative contract in which two par -
ties agree that one party, the buyer, will purchase an underlying asset from the

other party, the seller, at a later date and at a fixed price they agree upon when 
the contract is signed.
■■A futures contract is similar to a forward contract but is a standardized deriva -
tive contract created and traded on a futures exchange. In the contract, two par -
ties agree that one party, the buyer, will purchase an underlying asset from the 
other party, the seller, at a later date and at a price agreed on by the two parties 
when the contract is initiated. In addition, there is a daily settling of gains and 
losses and a credit guarantee by the futures exchange through its clearinghouse.
■■A swap is an over-  the- counter derivative contract in which two parties agree to 
exchange a series of cash flows whereby one party pays a variable series that will 
be determined by an underlying asset or rate and the other party pays either 
a variable series determined by a different underlying asset or rate or a fixed 
series.

Summary 53
■■An option is a derivative contract in which one party, the buyer, pays a sum of 
money to the other party, the seller or writer, and receives the right to either 
buy or sell an underlying asset at a fixed price either on a specific expiration 
date or at any time prior to the expiration date.
■■A call is an option that provides the right to buy the underlying.
■■A put is an option that provides the right to sell the underlying.
■■Credit derivatives are a class of derivative contracts between two parties, the 
credit protection buyer and the credit protection seller, in which the latter pro -
vides protection to the former against a specific credit loss.
■■A credit default swap is the most widely used credit derivative. It is a derivative 
contract between two parties, a credit protection buyer and a credit protection 
seller, in which the buyer makes a series of payments to the seller and receives 
a promise of compensation for credit losses resulting from the default of a third

party.
■■An asset-  backed security is a derivative contract in which a portfolio of debt 
instruments is assembled and claims are issued on the portfolio in the form of 
tranches, which have different priorities of claims on the payments made by the 
debt securities such that prepayments or credit losses are allocated to the most-  
junior tranches first and the most-  senior tranches last.
■■Derivatives can be combined with other derivatives or underlying assets to form 
hybrids.
■■Derivatives are issued on equities, fixed-  income securities, interest rates, 
currencies, commodities, credit, and a variety of such diverse underlyings as 
weather, electricity, and disaster claims.
■■Derivatives facilitate the transfer of risk, enable the creation of strategies and 
payoffs not otherwise possible with spot assets, provide information about 
the spot market, offer lower transaction costs, reduce the amount of capital 
required, are easier than the underlyings to go short, and improve the efficiency

of spot markets.
■■Derivatives are sometimes criticized for being a form of legalized gambling and 
for leading to destabilizing speculation, although these points can generally be 
refuted.
■■Derivatives are typically priced by forming a hedge involving the underlying 
asset and a derivative such that the combination must pay the risk-  free rate and 
do so for only one derivative price.
■■Derivatives pricing relies heavily on the principle of storage, meaning the ability 
to hold or store the underlying asset. Storage can incur costs but can also gen -
erate cash, such as dividends and interest.
■■Arbitrage is the condition that two equivalent assets or derivatives or combina -
tions of assets and derivatives sell for different prices, leading to an opportunity 
to buy at the low price and sell at the high price, thereby earning a risk-  free 
profit without committing any capital.
■■The combined actions of arbitrageurs bring about a convergence of prices.

Hence, arbitrage leads to the law of one price: Transactions that produce equiv -
alent results must sell for equivalent prices.

Reading 56 ■ Derivative Markets and Instruments 54
1 A derivative is  best  described as a financial instrument that derives its perfor -
mance by:
A passing through the returns of the underlying.
B replicating the performance of the underlying.
C transforming the performance of the underlying.
2 Compared with exchange-  traded derivatives, over-  the- counter derivatives 
would most likely  be described as:
A standardized.
B less transparent.
C more transparent.
3 Exchange-  traded derivatives are:
A largely unregulated.
B traded through an informal network.
C guaranteed by a clearinghouse against default.
4 Which of the following derivatives is classified as a contingent claim?
A Futures contracts
B Interest rate swaps
C Credit default swaps
5 In contrast to contingent claims, forward commitments provide the:
A right to buy or sell the underlying asset in the future.
B obligation to buy or sell the underlying asset in the future.

C promise to provide credit protection in the event of default.
6 Which of the following derivatives provide payoffs that are non-  linearly related 
to the payoffs of the underlying?
A Options
B Forwards
C Interest-  rate swaps
7 An interest rate swap is a derivative contract in which:
A two parties agree to exchange a series of cash flows.
B the credit seller provides protection to the credit buyer.
C the buyer has the right to purchase the underlying from the seller.
8 Forward commitments subject to default are:
A forwards and futures.
B futures and interest rate swaps.
C interest rate swaps and forwards.
9 Which of the following derivatives is  least likely  to have a value of zero at initia -
tion of the contract?
A Futures
B Options
C Forwards

Practice Problems 55
10 A credit derivative is a derivative contract in which the:
A clearinghouse provides a credit guarantee to both the buyer and the seller.
B seller provides protection to the buyer against the credit risk of a third party.
C the buyer and seller provide a performance bond at initiation of the 
contract.
11 Compared with the underlying spot market, derivative markets are more likely  
to have:
A greater liquidity.
B higher transaction costs.
C higher capital requirements.
12 Which of the following characteristics is least likely  to be a benefit associated 
with using derivatives?
A More effective management of risk
B Payoffs similar to those associated with the underlying
C Greater opportunities to go short compared with the spot market
13 Which of the following is most likely  to be a destabilizing consequence of spec -
ulation using derivatives?
A Increased defaults by speculators and creditors
B Market price swings resulting from arbitrage activities

C The creation of trading strategies that result in asymmetric performance
14 The law of one price is best described as:
A the true fundamental value of an asset.
B earning a risk-  free profit without committing any capital.
C two assets that will produce the same cash flows in the future must sell for 
equivalent prices.
15 Arbitrage opportunities exist when:
A two identical assets or derivatives sell for different prices.
B combinations of the underlying asset and a derivative earn the risk-  free rate.
C arbitrageurs simultaneously buy takeover targets and sell takeover acquirers.

Reading 56 ■ Derivative Markets and Instruments 56
SOLUTIONS
1 C is correct. A derivative is a financial instrument that transforms the perfor -
mance of the underlying. The transformation of performance function of deriv -
atives is what distinguishes it from mutual funds and exchange traded funds 
that pass through the returns of the underlying.
 A is incorrect because derivatives, in contrast to mutual funds and exchange 
traded funds, do not simply pass through the returns of the underlying at 
payout. B is incorrect because a derivative transforms rather than replicates the 
performance of the underlying.
2 B is correct. Over-  the counter-  derivatives markets are customized and mostly 
unregulated. As a result, over-  the- counter markets are less transparent in com -
parison with the high degree of transparency and standardization associated 
with exchange-  traded derivative markets.
 A is incorrect because exchange-  traded derivatives are standardized, whereas

over-  the counter derivatives are customized. C is incorrect because exchange-  
traded derivatives are characterized by a high degree of transparency because 
all transactions are disclosed to exchanges and regulatory agencies, whereas 
over-  the- counter derivatives are relatively opaque.
3 C is correct. Exchanged-  traded derivatives are guaranteed by a clearinghouse 
against default.
 A is incorrect because traded derivatives are characterized by a relatively high 
degree of regulation. B is incorrect because the terms of exchange-  traded deriv -
atives terms are specified by the exchange.
4 C is correct. A credit default swap (CDS) is a derivative in which the credit 
protection seller provides protection to the credit protection buyer against the 
credit risk of a separate party. CDS are classified as a contingent claim.
 A is incorrect because futures contracts are classified as forward commit -
ments. B is incorrect because interest rate swaps are classified as forward 
commitments.

5 B is correct. Forward commitments represent an obligation to buy or sell the 
underlying asset at an agreed upon price at a future date.
 A is incorrect because the right to buy or sell the underlying asset is a charac -
teristic of contingent claims, not forward commitments. C is incorrect because 
a credit default swap provides a promise to provide credit protection to the 
credit protection buyer in the event of a credit event such as a default or credit 
downgrade and is classified as a contingent claim.
6 A is correct. Options are classified as a contingent claim which provides payoffs 
that are non-  linearly related to the performance of the underlying.
 B is incorrect because forwards are classified as a forward commitment, which 
provides payoffs that are linearly related to the performance of the underlying. 
C is incorrect because interest-  rate swaps are classified as a forward commit -
ment, which provides payoffs that are linearly related to the performance of the

7 A is correct. An interest rate swap is defined as a derivative in which two par -
ties agree to exchange a series of cash flows: One set of cash flows is variable, 
and the other set can be variable or fixed.

Solutions 57
 B is incorrect because a credit derivative is a derivative contract in which the 
credit protection seller provides protection to the credit protection buyer. C is 
incorrect because a call option gives the buyer the right to purchase the under -
lying from the seller.
8 C is correct. Interest rate swaps and forwards are over-  the- counter contracts 
that are privately negotiated and are both subject to default. Futures contracts 
are traded on an exchange, which provides a credit guarantee and protection 
 A is incorrect because futures are exchange-  traded contracts which provide 
daily settlement of gains and losses and a credit guarantee by the exchange 
through its clearinghouse. B is incorrect because futures are exchange-  traded 
contracts which provide daily settlement of gains and losses and a credit guar -
antee by the exchange through its clearinghouse.
9 B is correct. The buyer of the option pays the option premium to the seller of

the option at the initiation of the contract. The option premium represents the 
value of the option, whereas futures and forwards have a value of zero at the 
initiation of the contract.
 A is incorrect because no money changes hands between parties at the initi -
ation of the futures contract, thus the value of the futures contract is zero at 
initiation. C is incorrect because no money changes hands between parties at 
the initiation of the forward contract, thus the value of the forward contract is 
zero at initiation.
10 B is correct. A credit derivative is a derivative contract in which the credit 
credit risk of a third party.
 A is incorrect because the clearinghouse provides a credit guarantee to both the 
buyer and the seller of a futures contract, whereas a credit derivative is between 
two parties, in which the credit protection seller provides a credit guarantee to

the credit protection buyer. C is incorrect because futures contracts require that 
both the buyer and the seller of the futures contract provide a cash deposit for 
a portion of the futures transaction into a margin account, often referred to as a 
performance bond or good faith deposit.
11 A is correct. Derivative markets typically have greater liquidity than the under -
lying spot market as a result of the lower capital required to trade derivatives 
compared with the underlying. Derivatives also have lower transaction costs 
and lower capital requirements than the underlying.
 B is incorrect because transaction costs for derivatives are lower than the 
underlying spot market. C is incorrect because derivatives markets have lower 
capital requirements than the underlying spot market.
12 B is correct. One of the benefits of derivative markets is that derivatives create 
trading strategies not otherwise possible in the underlying spot market, thus

providing opportunities for more effective risk management than simply repli -
cating the payoff of the underlying.
 A is incorrect because effective risk management is one of the primary pur -
poses associated with derivative markets. C is incorrect because one of the 
operational advantages associated with derivatives is that it is easier to go short 
compared to the underlying spot market.
13 A is correct. The benefits of derivatives, such as low transaction costs, low 
capital requirements, use of leverage, and the ease in which participants can go 
short, also can result in excessive speculative trading. These activities can lead 
to defaults on the part of speculators and creditors.

Reading 56 ■ Derivative Markets and Instruments 58
 B is incorrect because arbitrage activities tend to bring about a convergence of 
prices to intrinsic value. C is incorrect because asymmetric performance is not 
itself destabilizing.
14 C is correct. The law of one price occurs when market participants engage in 
arbitrage activities so that identical assets sell for the same price in different 
markets.
 A is incorrect because the law of one price refers to identical assets. B is incor -
rect because it refer to arbitrage not the law of one price.
15 A is correct. Arbitrage opportunities exist when the same asset or two equiv -
alent combinations of assets that produce the same results sell for different 
prices. When this situation occurs, market participants would buy the asset in 
the cheaper market and simultaneously sell it in the more expensive market, 
thus earning a riskless arbitrage profit without committing any capital.

B is incorrect because it is not the definition of an arbitrage opportunity. C is 
incorrect because it is not the definition of an arbitrage opportunity.

Basics of Derivative Pricing and Valuation
a. explain how the concepts of arbitrage, replication, and risk 
neutrality are used in pricing derivatives;
b. distinguish between value and price of forward and futures 
contracts;
c. explain how the value and price of a forward contract are 
determined at expiration, during the life of the contract, and at 
initiation;
d. describe monetary and nonmonetary benefits and costs 
associated with holding the underlying asset and explain how they 
affect the value and price of a forward contract;
e. define a forward rate agreement and describe its uses;
f. explain why forward and futures prices differ;
g. explain how swap contracts are similar to but different from a 
series of forward contracts;
h. distinguish between the value and price of swaps;
i. explain how the value of a European option is determined at

expiration;
j. explain the exercise value, time value, and moneyness of an 
option;
k. identify the factors that determine the value of an option and 
explain how each factor affects the value of an option;
l. explain put–call parity for European options;
m. explain put–call–forward parity for European options;
n. explain how the value of an option is determined using a one-  
period binomial model;
o. explain under which circumstances the values of European and 
American options differ.rEADING
57
© 2014 CFA Institute. All rights reserved.

Reading 57 ■ Basics of Derivative Pricing and Valuation 60
It is important to understand how prices of derivatives are determined. Whether one 
is on the buy side or the sell side, a solid understanding of pricing financial products 
is critical to effective investment decision making. After all, one can hardly determine 
what to offer or bid for a financial product, or any product for that matter, if one has 
no idea how its characteristics combine to create value.
Understanding the pricing of financial assets is important. Discounted cash flow 
methods and models, such as the capital asset pricing model and its variations, are 
useful for determining the prices of financial assets. The unique characteristics of 
derivatives, however, pose some complexities not associated with assets, such as equi -
ties and fixed-  income instruments. Somewhat surprisingly, however, derivatives also 
have some simplifying characteristics. For example, as we will see in this reading, in

well-  functioning derivatives markets the need to determine risk premiums is obviated 
by the ability to construct a risk-  free hedge. Correspondingly, the need to determine 
an investor’s risk aversion is irrelevant for derivative pricing, although it is certainly 
relevant for pricing the underlying.
The purpose of this reading is to establish the foundations of derivative pricing 
on a basic conceptual level. The following topics are covered:
■■How does the pricing of the underlying asset affect the pricing of derivatives?
■■How are derivatives priced using the principle of arbitrage?
■■How are the prices and values of forward contracts determined?
■■How are futures contracts priced differently from forward contracts?
■■How are the prices and values of swaps determined?
■■How are the prices and values of European options determined?
■■How does American option pricing differ from European option pricing?
This reading is organized as follows. Section 2 explores two related topics, the

pricing of the underlying assets on which derivatives are created and the principle 
of arbitrage. Section 3 describes the pricing and valuation of forwards, futures, and 
swaps. Section 4 introduces the pricing and valuation of options. Section 5 provides 
a summary.
FUNDAMENTAL CONCEPTS OF DERIVATIVE PRICING
In this section, we will briefly review the concepts associated with derivatives, the types 
of derivatives, and the pricing principles of the underlying assets. We will also look at 
arbitrage, a critical concept that links derivative pricing to the price of the underlying.
2.1 Basic Derivative Concepts
The definition of a derivative is as follows:
A derivative is created as a contract between two parties, the buyer and the seller. 
Derivatives trade in markets around the world, which include organized exchanges,

where highly standardized and regulated versions exist, and over-  the- counter markets, 1
2

Fundamental Concepts of Derivative Pricing 61
where customized and more lightly regulated versions trade. The basic characteristics 
of derivatives that influence pricing are not particularly related to where the derivatives 
trade, but are critically dependent on the types of derivatives.
The two principal types of derivatives are forward commitments and contingent 
claims. A forward commitment is an obligation to engage in a transaction in the 
spot market at a future date at terms agreed upon today.1 By entering into a forward 
commitment, a party locks in the terms of a transaction that he or she will conduct 
later. The word “commitment” is critical here. A forward contract is a firm obligation.
There are three types of forward commitments: forward contracts, futures con -
tracts, and swap contracts. These contracts can be referred to more simply as forwards, 
futures, and swaps.
A forward contract  is an over-  the- counter derivative contract in which two

from the other party, the seller, at a later date at a fixed price they agree 
upon when the contract is signed.
A futures contract  is a standardized derivative contract created and traded 
date at a price agreed upon by the two parties when the contract is initi -
A swap contract  is an over-  the- counter derivative contract in which two 
parties agree to exchange a series of cash flows whereby one party pays a 
variable series that will be determined by an underlying asset or rate and 
the other party pays either 1) a variable series determined by a different 
underlying asset or rate or 2) a fixed series.

As these definitions illustrate, forwards and futures are similar. They both establish 
the terms of a spot transaction that will occur at a later date. Forwards are custom -
ized, less transparent, less regulated, and subject to higher counterparty default risk. 
Futures are standardized, more transparent, more regulated, and generally immune 
to counterparty default. A swap is equivalent to a series of forward contracts, a point 
that will be illustrated later.
A contingent claim is a derivative in which the outcome or payoff is determined 
by the outcome or payoff of an underlying asset, conditional on some event occurring. 
Contingent claims include options, credit derivatives, and asset-  backed securities. 
Because credit derivatives and asset-  backed securities are highly specialized, this 
reading will focus only on options.
Recall the definition of an option:
An option  is a derivative contract in which one party, the buyer, pays a

to either buy or sell an underlying asset at a fixed price either on a specific 
Options can be either customized over-  the- counter contracts or standardized and 
traded on exchanges.
1 Remember that the term “spot market” refers to the market in which the underlying trades. A transaction 
in the spot market involves a buyer paying for an asset and receiving it right away or at least within a few 
days, given the normal time required to settle a financial transaction.

Reading 57 ■ Basics of Derivative Pricing and Valuation 62
Because derivatives take their prices from the price of the underlying, it is import -
ant to first understand how the underlying is priced. We will approach the underlying 
from a slightly different angle, one that emphasizes the often-  subtle costs of holding 
the underlying, which turn out to play a major role in derivative pricing.
2.2 Pricing the Underlying
The four main types of underlying on which derivatives are based are equities, fixed-  
income securities/interest rates, currencies, and commodities. Equities, fixed-  income 
securities (but not interest rates), currencies, and commodities are all assets. An 
interest rate is not an asset, but it can be structured as the underlying of a derivative.2
Consider a generic underlying asset. This asset is something of value that you can 
own. Some assets are financial assets, such as equities, bonds, and currencies, and

some are real assets, such as commodities (e.g., gold, oil, and agricultural products) 
and certain physical objects (e.g., houses, automobiles, and computers).
The price of a financial asset is often determined using a present value of future 
cash flows approach. The value of the financial asset is the expected future price plus 
any interim payments such as dividends or coupon interest discounted at a rate appro -
priate for the risk assumed. Such a definition presumes a period of time over which 
an investor anticipates holding an asset, known as the holding period. The investor 
forecasts the price expected to prevail at the end of the holding period as well as any 
cash flows that are expected to be earned over the holding period. He then takes 
that predicted future price and expected cash flows and finds their current value by 
discounting them to the present. Thereby, the investor arrives at a fundamental value

for the asset and will compare that value with its current market price. Based on any 
differential relative to the cost of trading and his confidence in his valuation model, 
he will make a decision about whether to trade.
2.2.1  The Formation of Expectations
Let us first assume that the underlying does not pay interest or dividends, nor does 
it have any other cash flows attributable to holding the asset. Exhibit 1 illustrates the 
basic idea behind the valuation process. Using a probability distribution, the investor 
forecasts the future over a holding period spanning time 0 to time T. The center of 
the distribution is the expected price of the asset at time T, which we denote as E(ST), 
and represents the investor’s prediction of the spot price at T. The investor knows 
there is risk, so this prediction is imperfect—hence the reason for the probability 
distribution. Nonetheless, at time 0 the investor makes her best prediction of the spot

price at time T, which becomes the foundation for determining what she perceives 
to be the value of the asset.3
2 This is a good example of why it is best not to use the term “underlying asset ” when speaking of derivatives. 
Not all derivatives have underlying assets, but all have underlyings, some of which are not assets. Some 
other examples of non-  asset underlyings used in derivatives are weather, insurance claims, and shipping 
rates. There are also some derivatives in which the underlying is another derivative.
3 The distribution shown here is symmetrical and relatively similar to a normal distribution, but this 
characterization is for illustrative purposes only. We are making no assumptions about symmetry or 
normality at this point.

Fundamental Concepts of Derivative Pricing 63
Exhibit 1   The Formation of Expectations for an Asset
E(ST)
T 0
2.2.2  The Required Rate of Return on the Underlying Asset
To determine the value of the asset, this prediction must be converted into its price or 
present value. The specific procedure is to discount this expected future price, but that 
is the easy part. Determining the rate at which to discount the expected future price 
is the hard part. We use the symbol k to denote this currently unknown discount rate, 
which is often referred to as the required rate of return and sometimes the expected 
rate of return or just the expected return. At a minimum, that rate will include the 
risk-  free rate of interest, which we denote as r. This rate represents the opportunity 
cost, or so-  called time value of money, and reflects the price of giving up your money 
today in return for receiving more money later.
2.2.3  The Risk Aversion of the Investor

At this point, we must briefly discuss an important characteristic of investors: their 
degree of risk aversion. We can generally characterize three potential types of investors 
by how they feel about risk: risk averse, risk neutral, or risk seeking.
Risk-  neutral investors are willing to engage in risky investments for which they 
expect to earn only the risk-  free rate. Thus, they do not expect to earn a premium 
for bearing risk. For risk-  averse investors, however, risk is undesirable, so they do not 
consider the risk-  free rate an adequate return to compensate them for the risk. Thus, 
risk-  averse investors require a risk premium, which is an increase in the expected 
return that is sufficient to justify the acceptance of risk. All things being equal, an 
investment with a higher risk premium will have a lower price. It is very important 
to understand, however, that risk premiums are not automatically earned. They are

merely expectations. Actual outcomes can differ. Clearly stocks that decline in value 
did not earn risk premiums, even though someone obviously bought them with the 
expectation that they would. Nonetheless, risk premiums must exist in the long run 
or risk-  averse investors would not accept the risk.
The third type of investor is one we must mention but do not treat as realistic. Risk 
seekers are those who prefer risk over certainty and will pay more to invest when there 
is risk, implying a negative risk premium. We almost always assume that investors 
prefer certainty over uncertainty, so we generally treat a risk-  seeking investor as just 
a theoretical possibility and not a practical reality.4
4 People who gamble in casinos or play lotteries appear to be risk-  seekers, given the advantage of the 
casino or the lottery organizer, but they are merely earning utility from the game itself, not necessarily 
from the expected financial outcome.

Reading 57 ■ Basics of Derivative Pricing and Valuation 64
We will assume that investors are risk averse. To justify taking risk, risk-  averse 
investors require a risk premium. We will use the Greek symbol λ (lambda) to denote 
the risk premium.5
2.2.4  The Pricing of Risky Assets
Exhibit 2 illustrates the process by which an investor obtains the current price, S0, by 
discounting the expected future price of an asset with no interim cash flows, E(ST), 
by r (the risk-  free rate) plus λ (the risk premium) over the period from 0 to T.
Exhibit 2   Discounting the Expected Future Price to Obtain the Current Price
E(ST)E(ST)
(1 + r + λ)T
TS0 =
0
2.2.5  Other Benefits and Costs of Holding an Asset
Many assets generate benefits and some incur costs to their owners. Some of these 
costs are monetary and others are nonmonetary. The dividends paid by companies 
and coupon interest paid by borrowers on their bonds represent obvious benefits to

the holders of these securities. With currencies representing investments that earn the 
risk-  free rate in a foreign country, they too generate benefits in the form of interest. 
Barring default, interest payments on bonds and currencies are relatively certain, 
so we will treat them as such. Dividend payments are not certain, but dividends do 
tend to be fairly predictable. As such, we will make an assumption common to most 
derivative models that dividends are certain.6
There is substantial evidence that some commodities generate a benefit that is 
somewhat opaque and difficult to measure. This benefit is called the convenience 
yield . It represents a nonmonetary advantage of holding the asset. For most financial 
assets, convenience yields are either nonexistent or extremely limited. Financial assets 
do not possess beauty that might make a person enjoy owning them just to look at 
them. Convenience yields are primarily associated with commodities and generally

exist as a result of difficulty in either shorting the commodity or unusually tight sup -
plies. For example, if a commodity cannot be sold short without great difficulty or 
cost, the holder of the commodity has an advantage if market conditions suggest that 
the commodity should be sold. Also, if a commodity is in short supply, the holders of 
the commodity can sometimes extract a price premium that is believed by some to 
be higher than what would be justified in well-  functioning markets. The spot price 
of the commodity could even be above the market’s expectation of its future price, a 
condition that would seem to imply a negative expected return. This scenario raises 
the question of why anyone would want to hold the commodity if its expected return 
is negative. The convenience yield provides a possible explanation that attributes an 
5 Although the risk-  free rate is invariant with a country’s economy, the risk premium varies with the

amount of risk taken. Thus, while the risk-  free rate is the same when applied to every investment, the risk 
premium is not the same for every investment.
6 Some derivative models incorporate uncertain dividends and interest, but those are beyond the scope 
of this introductory reading.

Fundamental Concepts of Derivative Pricing 65
implied but non-  financial expected return to the advantage of holding a commodity 
in short supply. The holder of the commodity has the ability to sell it when market 
conditions suggest that selling is advisable and short selling is difficult.
One cost incurred in owning commodities is the cost of storage. One could hardly 
own gold, oil, or wheat without incurring some costs in storing these assets. There 
are also costs incurred in protecting and insuring some commodities against theft or 
destruction. Depending on the commodity, these costs can be quite significant. For 
financial assets, however, the storage costs are so low that we can safely ignore them.
Finally, there is the opportunity cost of the money invested. If a person buys an 
asset, he forgoes interest on his money. The effect on this interest is reflected by com -
pounding the price paid for the asset to a future value at the risk-  free rate of interest.

Thus, an investor who buys a stock that costs £50 in a market in which the risk-  free 
rate is 4% will effectively have paid £50 × 1.04 = £52 a year later. Of course, the stock 
could be worth any value at that time, and any gain or loss should be determined in 
comparison to the effective price paid of £52.
As we described earlier, we determine the current price of an asset by discounting 
the expected future price by the sum of the risk-  free rate ( r) plus the risk premium 
(λ). When we introduce costs and benefits of holding the asset, we have to make an 
adjustment. With the exception of this opportunity cost of money, we will incorporate 
the effect of these costs and benefits by determining their value at the end of the holding 
period. Under the assumption that these costs and benefits are certain, we can then 
discount them at the risk-  free rate to obtain their present value. There is a logic to

doing it this way (i.e., finding their future value and discounting back to the present, 
as opposed to finding their present value directly). By finding their future value, we 
are effectively saying that the costs and benefits adjust the expected payoff at the end 
of the holding period. But because they are certain, we can discount their effects at 
the risk-  free rate. So we have effectively just found their present value. The net effect 
is that the costs reduce the current price and the benefits increase the current price. 
We use the symbol θ (theta) to denote the present value of the costs and γ (gamma) 
as the present value of any benefits.
The net of the costs and benefits is often referred to by the term carry , or some -
times cost of carry . The holding, storing, or “carrying” of an asset is said to incur a 
net cost that is essentially what it takes to “carry” an asset. Exhibit 3 illustrates the 
effect in which the carry adjusts the price of an asset in the valuation process.

Exhibit 3   Pricing an Asset That Incurs Costs and Generates Benefits
(1 + r  + λ)T
TS0 = – θ + γ
0

Reading 57 ■ Basics of Derivative Pricing and Valuation 66
EXAMPLE 1   
Pricing the Spot Asset
1 Which of the following factors does not affect the spot price of an asset 
that has no interim costs or benefits?
A The time value of money
B The risk aversion of investors
C The price recently paid by other investors
2 Which of the following does not represent a benefit of holding an asset?
A The convenience yield
B An optimistic expected outlook for the asset
C Dividends if the asset is a stock or interest if the asset is a bond
C is correct. The price recently paid by other investors is past information and 
does not affect the spot price. The time value of money and the risk aversion of 
investors determine the discount rate. Only current information is relevant as 
investors look ahead, not back.
B is correct. An optimistic forecast for the asset is not a benefit of holding the 
asset, but it does appear in the valuation of the asset as a high expected price

at the horizon date. Convenience yields and dividends and interest are benefits 
of holding the asset.
To recap, although the various underlyings differ with respect to the specifics 
of pricing, all of them are based on expectations, risk, and the costs and benefits of 
holding a specific underlying. Understanding how assets are priced in the spot mar -
ket is critical to understanding how derivatives are priced. To understand derivative 
pricing, it is necessary to establish a linkage between the derivative market and the 
spot market. That linkage occurs through arbitrage.
2.3 The Principle of Arbitrage
Arbitrage is a type of transaction undertaken when two assets or portfolios produce 
identical results but sell for different prices. If a trader buys the asset or portfolio at 
the cheaper price and sells it at the more expensive price, she will generate a net inflow 
of funds at the start. Because the two assets or portfolios produce identical results,

a long position in one and a short position in the other means that at the end of the 
holding period, the payoffs offset. Hence, no money is gained or lost at the end of 
the holding period, so there is no risk. The net effect is that the arbitrageur receives 
money at the start and never has to pay out any money later. Such a situation amounts 
to free money, like walking down the street, finding money on the ground, and never 
having to give it up. Exhibit 4 illustrates this process for assets A and B, which have 
no dividends or other benefits or costs and pay off identically but sell for different 
prices, with S0A < S0B.

Fundamental Concepts of Derivative Pricing 67
Exhibit 4   Executing an Arbitrage
T 0S0A < S0B:
Buy A at S0A
Sell B at S0B
Cash flow = S0B – S0A( > 0)STA = STB:
Sell A for STA
Buy B for STB
Cash flow = STA – STB(= 0)Given:  Assets A and B produce the same values at time 
T but at time 0, A is selling for less than B.
2.3.1  The (In)Frequency of Arbitrage Opportunities
When arbitrage opportunities exist, traders exploit them very quickly. The combined 
actions of many traders engaging in the same transaction of buying the low-  priced 
asset or portfolio and selling the high-  priced asset or portfolio results in increased 
demand and an increasing price for the former and decreased demand and a decreas -
ing price for the latter. This market activity will continue until the prices converge. 
Assets that produce identical results can thus have only one true market price. This 
rule is called the “law of one price. ” With virtually all market participants alert for the

possibility of earning such profits at no risk, it should not be surprising that arbitrage 
opportunities are rare.
In practice, prices need not converge precisely, or even all that quickly, because the 
transaction cost of exploiting an opportunity could exceed the benefit. For example, 
say you are walking down the sidewalk of the Champs-  Élysées in Paris and notice a €1 
coin on the sidewalk. You have a bad back, and it would take some effort to bend over. 
The transaction cost of exploiting this opportunity without any risk could exceed the 
benefit of the money. Some arbitrage opportunities represent such small discrepancies 
that they are not worth exploiting because of transaction costs.
Significant arbitrage opportunities, however, will be exploited. A significant oppor -
tunity arises from a price differential large enough to overcome the transaction costs. 
Any such price differential will continue to be exploited until the opportunity disap -

pears. Thus, if you find a €10 note on the Champs-  Élysées sidewalk, there is a good 
chance you will find it worth picking up (even with your bad back), and even if you 
do not pick it up, it will probably not be there for long. With enough people alert for 
such opportunities, only a few will arise, and the ones that do will be quickly exploited 
and disappear. In this manner, arbitrage makes markets work much more efficiently.
2.3.2  Arbitrage and Derivatives
It may be difficult to conceive of many investments that would produce identical 
payoffs. Even similar companies such as McDonalds and Burger King, which are in 
the same line of business, do not perform identically. Their performance may be cor -
related, but each has its own unique characteristics. For equity securities and with no 
derivatives involved, about the only such situation that could exist in reality is a stock 
that trades simultaneously in two different markets, such as Royal Dutch Shell, which

trades in Amsterdam and London but is a single company. Clearly there can be only 
one price. If those two markets operate in different currencies, the currency-  adjusted 
prices should be the same. Bonds issued by the same borrower are also potentially 
arbitrageable. All bonds of an issuer will be priced off of the term structure of interest 
rates. Because of this common factor, bonds of different maturities can be arbitraged 
against each other. But in general, two securities are unlikely to perform identically.

Reading 57 ■ Basics of Derivative Pricing and Valuation 68
The picture changes, however, if we introduce derivatives. For most derivatives, 
the payoffs come (derive) directly from the value of the underlying at the expiration 
of the derivative. Although no one can predict with certainty the value of the under -
lying at expiration, as soon as that value is determined, the value of the derivative at 
expiration becomes certain. So, while the performance of McDonalds’ stock may have 
a strong correlation to the performance of Burger King’s stock, neither completely 
determines the other. But derivatives on McDonalds’ stock and derivatives on Burger 
King’s stock are completely determined by their respective stocks. All of the uncer -
tainty in a derivative comes from the uncertainty in the underlying. As a result, the 
price of the derivative is tied to the price of the underlying. That being the case, the 
derivative can be used to hedge the underlying, or vice versa.

Exhibit 5 illustrates this point. When a long position in the underlying is com -
bined with a short position in the derivative to produce a perfect hedge, all of the 
risk is eliminated and the position should earn the risk-  free rate. If not, arbitrageurs 
begin to trade. If the position generates a return in excess of the risk-  free rate, the 
arbitrageurs see an opportunity because the hedged position of the underlying (long 
asset and short derivative) earns more than the risk-  free rate and a risk-  free loan 
undertaken as a borrower incurs a cost equal to the risk-  free rate. Therefore, imple -
menting the hedged position and borrowing at the risk-  free rate earns a return in 
excess of the risk-  free rate, incurs a cost of the risk-  free rate, and has no risk. As a 
result, an investor can earn excess return at no risk without committing any capital. 
Arbitrageurs will execute this transaction in large volumes, continuing to exploit the

pricing discrepancy until market forces push prices back in line such that both risk-  
free transactions earn the risk-  free rate.
Exhibit 5   Hedging the Underlying with a Derivative (or Vice Versa)
T 0 Long position in underlying
+ Short position in derivative Underlying payof f
– Derivative payoff
= Risk-free return
Out of this process, one and only one price can exist for the derivative. Otherwise, 
there will be an arbitrage opportunity. We typically take the underlying price as given 
and infer the unique derivative price that prohibits any arbitrage opportunities. Most 
derivatives pricing models are established on this foundation. We simply assume that 
no arbitrage opportunities can exist and infer the derivative price that guarantees 
there are no arbitrage opportunities.
2.3.3  Arbitrage and Replication
Because a long asset and a short derivative on the asset can be combined to produce 
a position equivalent to a risk-  free bond, it follows that the long asset and a short

risk-  free asset (meaning to borrow at the risk-  free rate) can be combined to produce 
a long derivative. Alternatively, a short derivative and the short risk-  free asset can be 
combined to produce a short asset position. Exhibit 6 shows this process, referred to 
as replication . Replication is the creation of an asset or portfolio from another asset, 
portfolio, and/or derivative.

Fundamental Concepts of Derivative Pricing 69
Exhibit 6   Arbitrage, Replication, and Derivatives
Long asset +Short derivative =Long risk-  free 
asset (lending)
Long 
Asset+Short risk-  free 
asset (borrowing)=–Long 
derivative
Short 
derivative+Short risk-  free 
asset (borrowing)=−Short asset
If all assets are correctly priced to prohibit arbitrage, however, the ability to rep -
licate seems useless. Why would one replicate an asset or derivative if there is no 
cost advantage? Buying a government security to earn the risk-  free rate is easier than 
buying the asset and selling a derivative to produce a risk-  free position. At this point, 
that is certainly a reasonable question. As we progress through this material, however, 
we will relax the assumption that everything is always correctly priced and we will 
admit the possibility of occasional arbitrage opportunities. For example, it may be 
more profitable to hedge a portfolio with a derivative to produce a risk-  free rate than

to invest in the risk-  free asset. In addition, we might find that replication can have 
lower transaction costs. For example, a derivative on a stock index combined with the 
risk-  free asset [Long derivative (Stock index futures) + Long risk-  free asset (Lending) 
= Long asset (Stock index)] can potentially replicate an index fund at lower transaction 
costs than buying all the securities in the index. Replication is the essence of arbitrage. 
The ability to replicate something with something else can be valuable to investors, 
either through pricing differentials, however temporary, or lower transaction costs.
2.3.4  Risk Aversion, Risk Neutrality, and Arbitrage-  Free Pricing
Most investors are risk averse. They do not accept risk without the expectation of a 
return commensurate with that risk. Thus, they require risk premiums to justify the 
risk. One might think that this point implies a method for pricing derivatives based

on the application of a risk premium to the expected payoff of the derivative and its 
risk. As we will describe later, this methodology is not appropriate in the pricing of 
As previously described, a derivative can be combined with an asset to produce a 
risk-  free position. This fact does not mean that one should  create such a combination. 
It merely means that one can do so. The derivative price is the price that guarantees 
the risk-  free combination of the derivative and the underlying produces a risk-  free 
return. The derivative price can then be inferred from the characteristics of the under -
lying, the characteristics of the derivative, and the risk-  free rate. The investor’s risk 
aversion is not a factor in determining the derivative price. Because the risk aversion 
of the investor is not relevant to pricing the derivative, one can just as easily obtain 
the derivative price by assuming that the investor is risk neutral. That means that the

expected payoff of the derivative can be discounted at the risk-  free rate rather than 
the risk-  free rate plus a risk premium. Virtually all derivative pricing models ultimately 
take this form: discounting the expected payoff of the derivative at the risk-  free rate.
The entire process of pricing derivatives is not exactly as we have described it at 
this point. There is an intermediate step, which entails altering the probabilities of the 
outcomes from the true probabilities to something called risk-  neutral probabilities. We 
will illustrate this process later in this reading. The important point to understand is

Reading 57 ■ Basics of Derivative Pricing and Valuation 70
that while the risk aversion of investors is relevant to pricing assets, it is not relevant 
to pricing derivatives. As such, derivatives pricing is sometimes called risk-  neutral 
pricing . Risk-  neutral pricing uses the fact that arbitrage opportunities guarantee that 
a risk-  free portfolio consisting of the underlying and the derivative must earn the risk-  
free rate. There is only one derivative price that meets that condition. Any mispricing 
of the derivative will lead to arbitrage transactions that drive the derivative price back 
to where it should be, the price that eliminates arbitrage opportunities.
The overall process of pricing derivatives by arbitrage and risk neutrality is called 
arbitrage-  free pricing . We are effectively determining the price of a derivative by 
assuming that the market is free of arbitrage opportunities. This notion is also some -

times called the principle of no arbitrage . If there are no arbitrage opportunities, 
combinations of assets and/or derivatives that produce the same results must sell 
for the same price. The correct derivative price assures us that the market is free of 
arbitrage opportunities.
2.3.5  Limits to Arbitrage
As we previously described, there may be reasons to not pick up a coin lying on the 
ground. Likewise, some small arbitrage profits are never exploited. A bond selling 
for €1,000 might offer an arbitrage profit by trading a derivative on the bond and a 
risk-  free asset at a total cost of €999, but the profit of €1 might be exceeded by the 
transaction costs. Such small differentials can easily remain essentially trapped within 
the bounds of transaction costs. In addition, arbitrage can require capital. Not everyone 
can borrow virtually unlimited amounts of money at what amounts to a risk-  free rate. 
Moreover, some transactions can require additional capital to maintain positions. The

corresponding gains from an offsetting position might not be liquid. Hence, on paper 
the position is hedged, but in practice, one position has a cash outflow while the other 
generates gains on paper that are realized only later. Borrowing against those future 
gains is not always easy.
Moreover, some apparent arbitrage transactions are not completely risk free. As 
you will learn later, option pricing requires knowledge of the volatility of the under -
lying asset, which is information that is not easy to obtain and subject to different 
opinions. Executing an arbitrage can entail risk if one lacks accurate information on 
the model inputs.
Some arbitrage positions require short-  selling assets that can be difficult to short. 
Some securities are held only by investors who are unwilling to lend the securities 
and who, by policy, are not arbitrageurs themselves. Some commodities, in particular, 
can be difficult and costly to sell short. Hence, the arbitrage might exist in only one

direction, which keeps the price from becoming seemingly too high or seemingly 
too low but permitting it to move virtually without limit in the opposite direction.
Arbitrage positions rely on the ultimate realization by other investors of the 
existence of the mispricing. For some investors, bearing these costs and risks until 
other investors drive the price back to its appropriate level can be nearly impossible.
The arbitrage principle is the essence of derivative pricing models. Yet, clearly 
there are limits to the ability of all investors to execute arbitrage transactions. In 
studying derivative pricing, it is important to accept the no-  arbitrage rule as a par -
adigm, meaning a framework for analysis and understanding. Although no market 
experts think that arbitrage opportunities never occur, it is a common belief that 
finding and exploiting them is a challenging and highly competitive process that will

not yield frequent success. But it is important that market participants stay alert for 
and exploit whatever arbitrage opportunities arise. In response, the market functions 
more efficiently.

Fundamental Concepts of Derivative Pricing 71
EXAMPLE 2   
Arbitrage
1 Which of the following best describes an arbitrage opportunity? It is an 
opportunity to:
A earn a risk premium in the short run.
B buy an asset at less than its fundamental value.
C make a profit at no risk with no capital invested.
2 What most likely  happens when an arbitrage opportunity exists?
A Investors trade quickly and prices adjust to eliminate the opportunity.
B Risk premiums increase to compensate traders for the additional risk.
C Markets cease operations to eliminate the possibility of profit at no 
risk.
3 Which of the following best describes how derivatives are priced?
A A hedge portfolio is used that eliminates arbitrage opportunities.
B The payoff of the underlying is adjusted downward by the derivative 
value.
C The expected future payoff of the derivative is discounted at the risk-  
free rate plus a risk premium.
4 An investor who requires no premium to compensate for the assumption

of risk is said to be which of the following?
A Risk seeking
B Risk averse
C Risk neutral
5 Which of the following is a limit to arbitrage?
A Clearinghouses restrict the transactions that can be arbitraged.
B Pricing models do not show whether to buy or sell the derivative.
C It may not always be possible to raise sufficient capital to engage in 
arbitrage.
C is correct because it is the only answer that is based on the notion of when 
an arbitrage opportunity exists: when two identical assets or portfolios sell 
for different prices. A risk premium earned in the short run can easily have 
occurred through luck. Buying an asset at less than fair value might not even 
produce a profit.
A is correct. The combined actions of traders push prices back in line to a level at 
which no arbitrage opportunities exist. Markets certainly do not shut down, and 
risk premiums do not adjust and, in fact, have no relevance to arbitrage profits.

A is correct. A hedge portfolio is formed that eliminates arbitrage opportunities 
and implies a unique price for the derivative. The other answers are incorrect 
because the underlying payoff is not adjusted by the derivative value and the 
discount rate of the derivative does not include a risk premium.

Reading 57 ■ Basics of Derivative Pricing and Valuation 72
C is correct. Risk-  seeking investors give away a risk premium because they enjoy 
taking risk. Risk-  averse investors expect a risk premium to compensate for the 
risk. Risk-  neutral investors neither give nor receive a risk premium because they 
have no feelings about risk.
C is correct. It may not always be possible to raise sufficient capital to engage in 
arbitrage. Clearinghouses do not restrict arbitrage. Pricing models show what 
the price of the derivative should be.
Thus, comparison with the market price will indicate if the derivative is 
overpriced and should be sold or if it is underpriced and should be purchased.
2.4 The Concept of Pricing vs. Valuation
In equity markets, analysis is undertaken with the objective of determining the value, 
sometimes called the fundamental value, of a stock. When a stock trades in the market

for a price that differs from its fundamental value, investors will often buy or sell the 
stock based on the perceived mispricing. The fundamental value of a stock is typically 
determined by analyzing the company’s financial statements, projecting its earnings 
and dividends, determining a discount rate based on the risk, and finding the present 
value of the future dividends. These steps make up the essence of dividend discount 
models. Other approaches include comparing the book value of a company to its market 
value, thereby using book value as a proxy for fundamental value, or by application 
of a price/earnings ratio to projected next-  period earnings, or by discounting free 
cash flow. Each of these approaches purports to estimate the company’s fundamental 
value, leading to the notion that a company is worth something that may or may not 
correspond to its price in the market.
In derivative markets, the notion of valuation as a representation of fundamental

value is still a valid concept, but the terminology can be somewhat different and can 
lead to some confusion. Options are not a problem in this regard. They can be analyzed 
to determine their fundamental value, and the market price can be compared with the 
fundamental value. Any difference can then presumably be exploited via arbitrage. 
The combined actions of numerous investors should ultimately lead to the market 
price converging to its fundamental value, subject to the above limits to arbitrage.
The world of forwards, futures, and swaps, however, uses different terminology 
with respect to price and value. These contracts do not require the outlay of cash at 
the start the way an option, stock, or bond does. Forwards, futures, and swaps start off 
with values of zero. Then as the underlying moves, their values become either positive 
or negative. The forward, futures, or swap price is a concept that represents the fixed

price or rate at which the underlying will be purchased at a later date. It is not an 
amount to be paid at the start. This fixed price or rate is embedded into the contract 
while the value will fluctuate as market conditions change. But more importantly, the 
value and price are not at all comparable with each other.
Consider a simple example. Suppose you own a stock priced at $102. You have 
a short forward contract to sell the stock at a price of $100 one year from now. The 
risk-  free rate is 4%. Your position is riskless because you know that one year from now, 
you will sell the stock for $100. Thus, you know you will get $100 one year from now, 
which has a present value of $100/(1.04) = $96.15. Notice the discounting at the risk-  
free rate, which is appropriate because the position is riskless. Your overall position is 
that you own an asset worth $102 and are short a contract worth something, and the

two positions combine to have a value of $96.15. Therefore, the forward contract must 
have a value of $96.15 − $102 = −$5.85. Your forward contract is thus worth −$5.85. To

Pricing and Valuation of Forward Commitments 73
the party on the opposite side, it is worth +$5.85.7 The price of the forward contract 
is still $100, which was set when you created the contract at an earlier date. As you 
can see, the $100 forward price is not comparable to the $5.85 value of the contract.
Although the forward price is fixed, any new forward contract calling for delivery 
of the same asset at the same time will have a different price. We will cover that point 
in more detail later. For now, it is important to see that your contract has a price of 
$100 but a value of −$5.85, which are two entirely different orders of magnitude. This 
information does not imply that the forward contract is mispriced. The value is the 
amount of wealth represented by owning the forward contract. The price is one of 
the terms the parties agreed on when they created the contract.8 This idea applies in 
the same manner for futures and swaps.
PRICING AND VALUATION OF FORWARD 
COMMITMENTS

In this section, we will go into pricing forward commitments in a little more detail. 
Let us start by establishing that today, at time 0, we create a forward commitment that 
expires at time T. The value of the underlying today is S0. At expiration the underlying 
value is ST, which is not known at the initiation of the contract.
3.1 Pricing and Valuation of Forward Contracts
Previously, we noted that price and value are entirely different concepts for forward 
commitments. We gave an example of a forward contract with a price of $100 but a 
value of −$5.85 to the seller and +$5.85 to the buyer. In the next subsection, we will 
delve more deeply into understanding these concepts of pricing and valuation for 
forward contracts.
3.1.1  Pricing and Valuation of Forward Contracts at Expiration
Recall that a forward contract specifies that one party agrees to buy the underlying

from the other at the expiration date at a price agreed on at the start of the contract. 
Suppose that you enter into a contract with another party in which you will buy a 
used car from that party in one year at a price of $10,000. Then $10,000 is the forward 
price. One year later, when the contract expires, you are committed to paying $10,000 
and accepting delivery of the car. Let us say that at that time, you check the used car 
market and find that an identical car is worth $10,800. How much is your forward 
contract worth to you at that time? It obligates you to pay $10,000 for a car that you 
would otherwise have to pay $10,800. Thus, the contract benefits you by $800, so its 
value is $800. If you were on the opposite side of the transaction, its value would be 
−$800. If the market price of the car were below $10,000, the contract would have 
negative value to you and the mirror image positive value to the seller.3

7 This concept of the value of the forward contract as it evolves toward expiration is sometimes referred 
to as its mark-  to- market value. The same notion is applicable to swaps. In futures, of course, contracts are 
automatically marked to market by the clearinghouse, and gains and losses are converted into actual cash 
flows from one party to the other.
8 The forward price is more like the exercise price of the option. It is the price the two parties agree will 
be paid at a future date for the underlying. Of course, the option has the feature that the holder need not 
ever pay that price, which is the case if the holder chooses not to exercise the option.

Reading 57 ■ Basics of Derivative Pricing and Valuation 74
This example leads us to our first important derivative pricing result. The forward 
price, established at the initiation date of contract is F0(T). Let us denote the value at 
expiration of the forward contract as VT(T). This value is formally stated as
VT(T) = ST – F0(T)  
In words,
The value of a forward contract at expiration is the spot price of the under -
lying minus the forward price agreed to in the contract.
In the financial world, we generally define value as the value to the long position, so 
the above definition is generally correct but would be adjusted if we look at the trans -
action from the point of view of the short party. In that case, we would multiply the 
value to the long party by −1 to calculate the value to the short party. Alternatively, 
the value to the short party is the forward price minus the spot price at expiration.
If a forward contract could be initiated right at the instant of expiration, the

forward price would clearly be the spot price. Such a contract would essentially be a 
spot transaction.
3.1.2  Pricing and Valuation at Initiation Date
In Exhibit 7, we see the nature of the problem of pricing a forward contract. We are 
situated at time 0, facing an uncertain future. At the horizon date, time T, the under -
lying price will be ST. Of course, at time 0 we do not know what ST will turn out to 
be. Yet at time 0, we need to establish the forward price, F0(T), which is the price we 
agree to pay at time T to purchase the asset.
Exhibit 7   The Time Horizon of Forward Contracts
T 0Agree to pay 
F0(T) at time T
to buy the assetPay F0(T) and
receive the
asset worth ST
When a forward contract is initiated, neither party pays anything to the other. It is a 
valueless contract, neither an asset nor a liability. Therefore, its value at initiation is zero:
V0(T) = 0  
The forward price that the parties agree to at the initiation date of the contract is

a special price that results in the contract having zero value and prohibiting arbitrage. 
This is our first important result:
Because neither the long nor the short pays anything to the other at the 
initiation date of a forward contract, the value of a forward contract when 
initiated is zero.
If this statement were not true and one party paid a sum of money to the other, 
the party receiving the money could find another party and engage in the opposite 
transaction, with no money paid to the other on this second contract. The two trans -
actions would completely offset, thereby eliminating the risk. Yet, the first party would 
have captured some cash from the second and consequently earned an arbitrage 
profit because his position is completely hedged. He would walk away with money (1)
(2)

Pricing and Valuation of Forward Commitments 75
and never have to worry about paying it back. The forward price is the price the two 
parties agree on that generates a value of zero at the initiation date. Finding that price 
is actually quite easy.
Consider a very simple asset price at S0 today that pays no dividends or interest, 
nor does it yield any nonfinancial benefits or incur any carrying costs. As described 
earlier, we can peer into the future, but at best we can make only a forecast of the 
price of this asset at our horizon date of time T. That forecast was previously referred 
to as the expected spot price at expiration, E(ST). On the surface, it might seem that 
pricing a forward contract would somehow involve a discounting of the expected 
spot price. As we said earlier, however, that is not how derivatives are priced—they 
are priced using arbitrage.
Suppose we hold the asset and enter into a forward contract to sell the asset at the

price F0(T). It should be easy to see that we have constructed a risk-  free position. We 
know that the asset, currently worth S0, will be sold later at F0(T) and that this price 
should guarantee a risk-  free return. Thus, we should find the following relationship,
FT
SrT 0
01()=+()
We can easily solve for the forward price to obtain
F0(T) = S0(1 + r)T  
Or, in words,
The forward price is the spot price compounded at the risk-  free rate over 
the life of the contract.
There is a nice logic to this relationship. While the spot price is what someone 
would have to pay today to buy the asset, a forward contract locks in the purchase 
price at the horizon date. When that date arrives, the investor will own the asset. 
Instead of buying the asset today, suppose the investor uses the forward contract to 
guarantee that she will own the asset at the horizon date. By using the forward con -
tract, the investor will not have committed the money, S0, that would have forgone

interest at the rate r for the period 0 to T. Notice how the risk premium on the asset 
does not directly appear in the pricing relationship. It does appear implicitly, because 
it determines the spot price paid to buy the asset. Knowing the spot price, however, 
eliminates the necessity of determining the risk premium. The derivatives market can 
simply let the spot market derive the risk premium.
As a simple example, let us say the underlying price, S0, is £50, the risk-  free rate, r, 
is 3%, and the contract expires in three months, meaning that T = 3/12 = 0.25. Then 
the forward price is £50(1.03)0.25 = £50.37. Thus, the two parties would agree that 
the buyer will pay £50.37 to the seller in three months, and the seller will deliver the 
underlying to the buyer at expiration.
Now suppose the asset generates cash payments and/or benefits and incurs stor -
age costs. As we discussed, the net cost of carry consists of the benefits, denoted as

γ (dividends or interest plus convenience yield), minus the costs, denoted as θ, both 
of which are in present value form. To put these concepts in future value form, we 
simply compound them at the risk-  free rate, (γ − θ)(1 + r)T. Because this is their value 
at the expiration date of the contract, we can add them to F0(T) in Equation 3, thereby 
restating that equation as
110
0+() =()+−() +()rFT r
STTγθ(3)
(4)

Reading 57 ■ Basics of Derivative Pricing and Valuation 76
The numerator is how much money we end up with at T. Rearranging, we obtain 
the forward price as
FT Sr
FT Sr rT
TT00
001
11()=− + () +()
()=+() −−() +()γθ
γθor
We see that the forward price determined using Equation 4 is reduced by the future 
value of any benefits and increased by the future value of any costs. In other words,
The forward price of an asset with benefits and/or costs is the spot price 
compounded at the risk-  free rate over the life of the contract minus the 
future value of those benefits and costs.
Again, the logic is straightforward. To acquire a position in the asset at time T, 
an investor could buy the asset today and hold it until time T. Alternatively, he could 
enter into a forward contract, committing him to buying the asset at T at the price 
F0(T). He would end up at T holding the asset, but the spot transaction would yield 
benefits and incur costs, whereas the forward transaction would forgo the benefits

but avoid the costs.
Assume the benefits exceed the costs. Then the forward transaction would return 
less than the spot transaction. The formula adjusts the forward price downward by the 
expression –(γ – θ)(1 + r)T to reflect this net loss over the spot transaction. In other 
words, acquiring the asset in the forward market would be cheaper because it forgoes 
benefits that exceed the costs. That does not mean the forward strategy is better. It 
costs less but also produces less. Alternatively, if the costs exceeded the benefits, the 
forward price would be higher because the forward contract avoids the costs at the 
expense of the lesser benefits.
Returning to our simple example, suppose the present value of the benefits is γ = £3 
and the present value of the costs is θ = £4. The forward price would be £50(1.03)0.25 – 
(£3 − £4)(1.03)0.25 = £51.38. The forward price, which was £50.37 without these costs 
and benefits, is now higher because the carrying costs exceed the benefits.

The value of the contract when initiated is zero provided the forward price con -
forms to the appropriate pricing formula. To keep the analysis as simple as possible, 
consider the case in which the asset yields no benefits and incurs no costs. Going 
long the forward contract or going long the asset produces the same position at T: 
ownership of the asset. Nonetheless, the strategies are not equivalent. Going long the 
forward contract enables the investor to avoid having to pay the price of the asset, S0, 
so she would collect interest on the money. Thus, the forward strategy would have a 
value of S0, reflecting the investment of that much cash invested in risk-  free bonds, 
plus the value of the forward contract. The spot strategy would have a value of S0, 
reflecting the investment in the asset. These two strategies must have equal values. 
Hence, the value of the forward contract must be zero.
Although a forward contract has zero value at the start, it will not have zero value

during its life. We now take a look at what happens during the life of the contract.
3.1.3  Pricing and Valuation during the Life of the Contract
We previously worked an example in which a forward contract established with a price 
of $100 later has a value of −$5.85 to the seller and +$5.85 to the buyer. Generally we 
would say the value is $5.85. We explained that with the spot price at $102, a party 
that is long the asset and short the forward contract would guarantee the sale of the 
asset priced at $102 at a price of $100 in one year. The present value of $100 in one 
year at 4% is $96.15. Thus, the party guarantees that his $102 asset will be effectively 
sold at a present value of $96.15, for a present value loss of $5.85.
In general, we can say that(5)

Pricing and Valuation of Forward Commitments 77
The value of a forward contract is the spot price of the underlying asset 
minus the present value of the forward price.
Again, the logic is simple. A forward contract provides a type of synthetic posi -
tion in the asset, for which we promise to pay the forward price at expiration. Thus, 
the value of the forward contract is the value of the asset minus the present value of 
the forward price. Let us write out this relationship using Vt(T) as the value of the 
forward contract at time t, which is some point in time after the contract is initiated 
and before it expires:
Vt(T) = St – F0(T)(1 + r)–(T–t)  
Note that we are working with the spot price at t, but the forward price was fixed 
when the contract was initiated.9
Now, recall the problem we worked in which the underlying had a price of £50 
and the contract was initiated with a three-  month life at a price of £50.37. Move one

month later, so that the remaining time is two months: T – t = 2/12 = 0.167. Let the 
underlying price be £52. The value of the contract would be £52 − £50.37(1.03)−0.167 
= £1.88.
If the asset has a cost of carry, we must make only a small adjustment:
Vt(T) = St – (γ – θ)(1 + r)t – F0(T)(1 + r)–(T–t)  
Note how we adjust the formula by the net of benefits minus costs. The forward 
contract forgoes the benefits and avoids the costs of holding the asset. Consequently, 
we adjust the value downward to reflect the forgone benefits and upward to reflect 
the avoided costs. Remember that the costs (θ) and benefits (γ) are expressed on a 
present value basis as of time 0. We need their value at time t. We could compound 
them from 0 to T and then discount them back to t by the period T – t, but a shorter 
route is to simply compound them from 0 to t. In the problem we previously worked, 
in which we priced the forward contract when the asset has costs and benefits, the

benefits (γ) were £3 and the costs (θ) were £4, giving us a forward price of £51.38. 
We have now moved one month ahead, so t = 1/12  = 0.0833 and T – t = 2/12  = 
0.167. Hence the value of the forward contract would be £52 – (£3 − £4)(1.03)0.0833 
– £51.38(1.03)−0.167 = £1.88. In this case, the effect of the compounding of the net 
of costs and benefits (£1) over one month has no appreciable effect on the value, but 
that result is not a general rule. 
It is important to note that although we say that Equation 7 holds during the life of 
the contract at some arbitrary time t, it also holds at the initiation date and at expira -
tion. For the initiation date, we simply change t to 0 in Equation 7. Then we substitute 
Equation 5 for F0(T) in Equation 7, obtaining V0(T) = 0, confirming that the value of 
a forward contract at initiation is zero. At expiration, we let t = T in Equation 7 and 
obtain the spot price minus the forward price, as presented in Equation 1.10

3.1.4  A Word about Forward Contracts on Interest Rates
Forward contracts in which the underlying is an interest rate are called forward rate 
agreements , or FRAs. These instruments differ slightly from most other forward 
contracts in that the underlying is not an asset. Changes in interest rates, such as the 
value of an asset, are unpredictable. Moreover, virtually every company and organi -
zation is affected by the uncertainty of interest rates. Hence, FRAs are very useful 
devices for many companies. FRAs are forward contracts that allow participants to (6)
(7)
9 An alternative approach to valuing a forward contract during its life is to determine the price of a new 
forward contract that would offset the old one. The discounted difference between the new forward price 
and the original forward price will lead to the same value.
10 You might be wondering whether the cost and benefit terms disappear when t = T. With the costs and

benefits defined as those incurred over the period t to T, at expiration their value is zero by definition.

Reading 57 ■ Basics of Derivative Pricing and Valuation 78
make a known interest payment at a later date and receive in return an unknown 
interest payment. In that way, a participant whose business will involve borrowing at a 
future date can hedge against an increase in interest rates by buying an FRA (the long 
side) and locking in a fixed payment and receiving a random payment that offsets the 
unknown interest payment it will make on its loan. Note that the FRA seller (the short 
side) is hedging against a decrease in interest rates. Also, consider that the FRA seller 
could be a lender wishing to lock in a fixed rate on a loan it will make at a future date.
Even though FRAs do not involve an underlying asset, they can still be combined 
with an underlying asset to produce a hedged position, thereby leading to fairly 
straightforward pricing and valuation equations. The math is a little more complex 
than the math for forwards on assets, but the basic ideas are the same.

FRAs are often based on Libor, the London Interbank Offered Rate, which rep -
resents the rate on a Eurodollar time deposit, a loan in dollars from one London 
bank to another.11 As an example, assume we are interested in going long a 30-  day 
FRA with a fixed rate (the FRA rate) in which the underlying is 90-  day Libor. A long 
position means that in 30 days, we will make a known interest payment and receive an 
interest payment corresponding to the discounted difference between 90-  day Libor on 
that day and the FRA rate. We can either enter into a 30-  day FRA on 90-  day Libor or 
create a synthetic FRA. To do the latter, we would go long a 120-  day Eurodollar time 
deposit and short a 30-  day Eurodollar time deposit. Exhibit 8 shows the structure of 
this strategy. We omit some of the details here, such as how much face value we should 
take on the two Eurodollar transactions as well as the size of the FRA. Those technical

issues are covered in more advanced material. At this time, we focus on the fact that 
going long over the 120-  day period and short over the 30-  day period leaves an investor 
with no exposure over the 30-  day period and then converts to a position that starts 
30 days from now and matures 90 days later. This synthetic position corresponds to 
a 30-  day FRA on 90-  day Libor. Exhibit 8 illustrates this point.12
Exhibit 8   Real FRA and Synthetic FRA (30-  Day FRA on 90-  Day Libor)
120= Synthetic long 30-day
FRA on 90-day LiborShort
30-day
EurodollarSynthetic
FRA
03 0120Long 120-day Eurodollar
03 0Real
FRA120 03 0= Underlying (90-day Libor)Long
30-day
FRA on 
90-day
LiborFRA expiration and settlement
11 Other rates such as Euribor (Euro Interbank Offered Rate) and Tibor (Tokyo Interbank Offered Rate) 
are also used.
12 The real FRA we show appears to imply that an investor enters into a Eurodollar transaction in 30

days that matures 90 days later. This is not technically true. The investor does, however, engage in a cash 
settlement in 30 days that has the same value and economic form as such a transaction. Specifically, set -
tlement at expiration of the FRA is an amount equal to the discounted difference between the underlying 
90- day Libor rate on that day and the FRA rate multiplied by a notional principal amount. These details 
are covered in the Level II and Level III CFA Program curriculum.

Pricing and Valuation of Forward Commitments 79
FRAs, and indeed all forward contracts relating to bonds and interest rates, are 
closely tied to the term structure of interest rates, a concept covered in virtually all 
treatments of fixed-  income securities. Buying a 120-  day zero-  coupon bond and selling 
a 30-  day zero-  coupon bond produces a forward position in a 90-  day zero-  coupon bond 
that begins in 30 days. From that forward position, one can infer the forward rate. It 
would then be seen that the FRA rate is the forward rate, even though the derivative 
itself is not a forward contract on a bond.
EXAMPLE 3   
Forward Contract Pricing and Valuation
1 Which of the following best describes the difference between the price of 
a forward contract and its value?
A The forward price is fixed at the start, and the value starts at zero and 
then changes.
B The price determines the profit to the buyer, and the value determines 
the profit to the seller.

C The forward contract value is a benchmark against which the price 
is compared for the purposes of determining whether a trade is 
advisable.
2 Which of the following best describes the value of the forward contract at 
expiration? The value is the price of the underlying:
A minus the forward price.
B divided by the forward price.
C minus the compounded forward price.
3 Which of the following factors does not affect the forward price?
A The costs of holding the underlying
B Dividends or interest paid by the underlying
C Whether the investor is risk averse, risk seeking, or risk neutral
4 Which of the following best describes the forward rate of an FRA?
A The spot rate implied by the term structure
B The forward rate implied by the term structure
C The rate on a zero-  coupon bond of maturity equal to that of the for -
ward contract
A is correct. The forward price is fixed at the start, whereas the value starts

at zero and then changes. Both price and value are relevant in determining 
the profit for both parties. The forward contract value is not a benchmark for 
comparison with the price.
A is correct because the holder of the contract gains the difference between 
the price of the underlying and the forward price. That value can, of course, be 
negative, which will occur if the holder is forced to buy the underlying at a price 
higher than the market price.

Reading 57 ■ Basics of Derivative Pricing and Valuation 80
C is correct. The costs of holding the underlying, known as carrying costs, and 
the dividends and interest paid by the underlying are extremely relevant to the 
forward price. How the investor feels about risk is irrelevant, because the forward 
price is determined by arbitrage.
B is correct. FRAs are based on Libor, and they represent forward rates, not spot 
rates. Spot rates are needed to determine forward rates, but they are not equal 
to forward rates. The rate on a zero-  coupon bond of maturity equal to that of 
the forward contract describes a spot rate.
As noted, we are not covering the details of derivative pricing but rather are focus -
ing on the intuition. At this point, we have covered the intuition of pricing forward 
contracts. We now move to futures contracts.
3.2 Pricing and Valuation of Futures Contracts
Futures contracts differ from forward contracts in that they have standard terms,

are traded on a futures exchange, and are more heavily regulated, whereas forward 
contracts are typically private, customized transactions. Perhaps the most import -
ant distinction is that they are marked to market on a daily basis, meaning that the 
accumulated gains and losses from the previous day’s trading session are deducted 
from the accounts of those holding losing positions and transferred to the accounts 
of those holding winning positions. This daily settling of gains and losses enables the 
futures exchange to guarantee that a party that earns a profit from a futures trans -
action will not have to worry about collecting the money. Thus, futures exchanges 
provide a credit guarantee, which is facilitated through the use of a clearinghouse. 
The clearinghouse collects and disburses cash flows from the parties on a daily basis, 
thereby settling obligations quickly before they accumulate to much larger amounts.

There is no absolute assurance that a clearinghouse will not fail, but none has ever 
done so since the first one was created in the 1920s.
The pattern of cash flows in a futures contract is quite similar to that in a forward 
contract. Suppose you enter into a forward contract two days before expiration in 
which you agree to buy an asset at €100, the forward price. Two days later, the asset is 
selling for €103, and the contract expires. You therefore pay €100 and receive an asset 
worth €103, for a gain of €3. If the contract were cash settled, instead of involving 
physical delivery, you would receive €3 in cash, which you could use to defer a portion 
of the cost of the asset. The net effect is that you are buying the asset for €103, paying 
€100 plus the €3 profit on the forward contract.
Had you chosen a futures contract, the futures price at expiration would still con -
verge to the spot price of €103. But now it would matter what the futures settlement

price was on the next to last day. Let us assume that price was €99. That means on the 
next to last day, your account would be marked to market for a loss of €1, the price of 
€100 having fallen to €99. That is, you would be charged €1, with the money passed on 
to the opposite party. But then on the last day, your position would be marked from 
€99 to €103, a gain of €4. Your net would be €1 lost on the first day and €4 gained on 
the second for a total of €3. In both situations you gain €3, but with the forward con -
tract, you gain it all at expiration, whereas with the futures contract, you gain it over 
two days. With this two-  day example, the interest on the interim cash flow would be 
virtually irrelevant, but over longer periods and with sufficiently high interest rates, 
the difference in the amount of money you end up with could be noticeable.

Pricing and Valuation of Forward Commitments 81
The value of a futures contract is the accumulated gain or loss on a futures contract 
since its previous day’s settlement. When that value is paid out in the daily settlement, 
the futures price is effectively reset to the settlement price and the value goes to zero. 
The different patterns of cash flows for forwards and futures can lead to differences 
in the pricing of forwards versus futures. But there are some conditions under which 
the pricing is the same. It turns out that if interest rates were constant, forwards and 
futures would have the same prices. The differential will vary with the volatility of 
interest rates. In addition, if futures prices and interest rates are uncorrelated, for -
wards and futures prices will be the same. If futures prices are positively correlated 
with interest rates, futures contracts are more desirable to holders of long positions

than are forwards. The reason is because rising prices lead to futures profits that are 
reinvested in periods of rising interest rates, and falling prices leads to losses that 
occur in periods of falling interest rates. It is far better to receive cash flows in the 
interim than all at expiration under such conditions. This condition makes futures 
more attractive than forwards, and therefore their prices will be higher than forward 
prices. A negative correlation between futures prices and interest rates leads to the 
opposite interpretation, with forwards being more desirable than futures to the long 
position. The more desirable contract will tend to have the higher price.
The practical realities, however, are that the derivatives industry makes virtually no 
distinction between futures and forward prices.13 Thus, we will make no distinction 
between futures and forward pricing, except possibly in noting some subtle issues 
that may arise from time to time.
EXAMPLE 4

EXAMPLE 4   
Futures Pricing and Valuation
1 Which of the following best describes how futures contract payoffs differ 
from forward contract payoffs?
A Forward contract payoffs are larger.
B They are equal, ignoring the time value of money.
C Futures contract payoffs are larger if the underlying is a commodity.
2 Which of the following conditions will not make futures and forward 
prices equivalent?
A Interest rates are constant.
B Futures prices are uncorrelated with interest rates.
C The volatility of the forward price is different from the volatility of the 
futures price.
3 With respect to the value of a futures contract, which of the following 
statements is most  accurate? The value is the:
A futures price minus the spot price.
B present value of the expected payoff at expiration.
C accumulated gain since the previous settlement, which resets to zero 
upon settlement.

13 At the time of this writing, many forwards (and swaps) are being processed through clearinghouses, a 
response to changes brought about by key legislation in several countries that was adopted following the 
financial crises of 2008. These OTC instruments are thus being effectively marked to market in a similar 
manner to the futures contracts described here. The full extent of this evolution of OTC trading through 
clearinghouses is not yet clear.

Reading 57 ■ Basics of Derivative Pricing and Valuation 82
B is correct. Forward payoffs occur all at expiration, whereas futures payoffs occur 
on a day-  to- day basis but would equal forward payoffs ignoring interest. Payoffs 
could differ, so forward payoffs are not always larger. The type of underlying is 
not relevant to the point of which payoff is larger.
C is correct. Constant interest rates or the condition that futures prices are 
uncorrelated with interest rates will make forward and futures prices equivalent. 
The volatility of forward and futures prices has no relationship to any difference.
C is correct. Value accumulates from the previous settlement and goes to zero 
when distributed.
3.3 Pricing and Valuation of Swap Contracts
Recall the structure of a forward contract, as depicted in Exhibit 7. The investor is at 
time 0 and needs to determine the price, F0(T), that she will agree to pay at time T to

purchase the asset. This price is set such that there is no value to the contract at that 
time. Value can arise later as prices change, but when initiated, the contract has zero 
value. Neither party pays anything to the other at the start.
Now consider a swap starting at time 0 and ending at time T. We will let this swap 
be the type that involves a fixed payment exchanged for a floating payment. The contract 
specifies that the two parties will make a series of n payments at times that we will 
designate as 1, 2, …, n, with the last payment occurring at time T. On each of these 
payment dates, the owner of the swap makes a payment of FS0(n, T) and receives a 
payment based on the value of the underlying at the time of each respective payment, 
S1, S2, …, Sn. So from the point of view of the buyer, the sequence of cash flows from 
the swap is S1 – FS0(n, T), S2 – FS0(n, T), …, Sn – FS0(n, T). The notation FS0(n, T)

denotes the fixed payment established at time 0 for a swap consisting of n payments 
with the last payment at time T. We denote the time to each payment as t1, t2, …, tn, 
where tn = T. This structure is shown in Exhibit 9.
Exhibit 9   Structure of Cash Flows in a Swap
tn = T 0Agree to make n
payments of  
FS0(n,T) at times t1, 
t2, …, tn and receive 
S1, S2, …, Sn
Sn – FS0(n,T) S2 – FS0(n,T) S1 – FS0(n,T)
t1 t2
Comparing Exhibit 7 with Exhibit 9 reveals some similarities. A swap is in some 
sense a series of forward contracts, specifically a set of contracts expiring at various 
times in which one party agrees to make a fixed payment and receive a variable pay -
ment. Now consider Exhibit 10, which breaks down a swap into a series of implicit 
forward contracts, with the expiration of each forward contract corresponding to a 
swap payment date.

Pricing and Valuation of Forward Commitments 83
Exhibit 10   A Swap as a Series of Forward Contracts
payments of  FS0(n,T) at
times t1, t2, …, tn and
receive S1, S2, …, Sn Sn – FS0(n,T) S2 – FS0(n,T) S1 – FS0(n,T)
t1 t2
Agree to pay F0(n)
at time tn and
receive Sn Sn – F0(tn)
tn 0Agree to pay F0(2)
at time t2 and
receive S2 S2 – F0(t2)
t2 0S
w
a
p
+
+...F
o
r
w
a
r
d
sAgree to pay F0(1)
at time t1 and
receive S1 S1 – F0(t1)
t1 0
Recall from the material on forward contracts that the forward price is determined 
by the spot price and the net cost of carry (Equation  5), the latter being partially 
determined by the length of time of the contract. It should be obvious that a forward 
contract expiring at time t1 will not have the same price, F0(t1), as a forward contract 
expiring at time t2, F0(t2), and likewise for all of the implicit remaining forward con -
tracts expiring up through time tn. The cost of carrying an asset over different time

periods will vary by the length of the time periods. In other words, the prices of the 
implicit forward contracts imbedded in a swap will not be equal:
F0(t1) ≠ F0(t2) ≠ … ≠ F0(tn)  
But for a swap, all the fixed payments are equal. So, how can we equate a swap 
to a series of forward contracts? It turns out that we can, and in doing so, we recall a 
valuable point about forward pricing.
Recall that the forward price is the price that produces a zero value of the contract 
at the start. Zero value is essential if there is no exchange of cash flows from one party 
to the other. And although no exchange of cash flows is customary, it is not mandatory. 
The parties could agree on any forward price at the start. If the zero-  value forward 
price were $30 and the parties agreed on a price of $28, it should be apparent that 
the buyer would be getting a great price. The seller, being rational, would require that 
the buyer compensate him at the start. The seller should be getting $30 at expiration

and instead will get $28. So the buyer should compensate the seller to the amount of 
the present value of $2 at expiration. If the parties agree on a price greater than $30, 
similar compensation would have to be paid from seller to buyer.
A forward transaction that starts with a nonzero value is called an off-  market 
forward. There is generally no prohibition on the use of off-  market forward contracts, 
so two parties can engage in a series of forward contracts at whatever fixed price they 
so desire. Assume they agree on the price FS0(T). That is, each forward contract will 
be created at the fixed price that corresponds to the fixed price of a swap of the same

Reading 57 ■ Basics of Derivative Pricing and Valuation 84
maturity with payments made at the same dates as the series of forward contracts. 
That means that some of the forward contracts would have positive values and some 
would have negative values, but their combined values would equal zero.
Now, it sounds like that price would be hard to find, but it is not. We would not, 
however, go about finding it by taking random guesses. Doing so would take seem -
ingly forever. Along the way, we would notice that some of these implicit forward 
contracts would have positive values and some would have negative values. If the 
positives outweighed the negatives, then the overall swap value would be positive, 
which is too high. Likewise, we might plug in a number that would produce an overall 
negative value, with the implicit forward contract values tending to be predominantly 
negative, which is too low.
Not surprisingly, we can find that price easily by appealing to the principle of

arbitrage. We said that the principle of arbitrage will guide us all the way through  
derivative pricing. We will omit the details, but here is the general idea.
Suppose we buy an asset that pays the amounts S1, S2, …, Sn at times t1, t2, …, tn. 
These are unknown amounts. A simple example would be a floating-  rate bond for 
which the S values represent the coupons that are unknown at the start but ultimately 
are determined by the evolution of interest rates. Then suppose we finance the pur -
chase of that asset by borrowing money that we promise to repay with equal fixed 
payments of FS0(T). That strategy replicates the swap. As you have already learned, 
replication is the key to pricing.
Valuation of the swap during its life again appeals to replication and the principle 
of no arbitrage. We will find a way to reproduce the remaining payments on the swap 
with other transactions. The value of that strategy is the value of the swap.

To obtain the fixed rate on the swap or to value it later during its life, we will need 
information from the market for the underlying. As we previously noted, there are 
derivatives on bonds and interest rates, equities, currencies, and commodities. It is 
not possible to provide a general and simple statement of how to price swaps that 
covers all of these cases, but that topic is covered in advanced material.
EXAMPLE 5   
Swap Pricing and Valuation
1 A swap is equivalent to a series of:
A forward contracts, each created at the swap price.
B long forward contracts, matched with short futures contracts.
C forward contracts, each created at their appropriate forward prices.
2 If the present value of the payments in a forward contract or swap is not 
zero, which of the following is most likely to be true?
A The contract cannot legally be created.
B The contract must be replicated by another contract with zero value.
C The party whose stream of payments to be received is greater has to

pay the other party the present value difference.
A is correct. Each implicit forward contract is said to be off-  market, because it 
is created at the swap price, not the appropriate forward price, which would be 
the price created in the forward market.

Pricing and Valuation of Options 85
C is correct. The party whose stream of payments to be received is greater has 
to pay the other party the present value difference. Such a contract can legally 
be created, but the party receiving the greater present value must compensate 
the other party with a cash payment at the start. Replication is never required.
PRICING AND VALUATION OF OPTIONS
Unlike a forward, futures, or swap contract, an option is clearly an asset to the holder 
and a liability to the seller. The buyer of an option pays a sum of money, called the 
premium, and receives the right to buy (a call) or sell (a put) the underlying. The seller 
receives the premium and undertakes a potential obligation because the buyer has the 
right, but not the obligation, to exercise the option. Options are, therefore, contingent 
claims. Pricing the option is the same as assigning its value. Some confusion from

that terminology may still arise, in that an option could trade in the market for an 
amount that differs from its value.
As mentioned, there are two general types of options. Calls represent the right 
to buy, and puts represent the right to sell. There are also two important exercise 
characteristics of options. American options allow exercise at any time up to the 
expiration, while European options allow exercise only at expiration. It is important to 
understand that the terms “ American” and “European” have no relationship to where 
the options are traded. Because the right to exercise can be a complex feature of an 
option, European options are easier to understand, and we will focus on them first.
We will use the same notation used with forwards. We start by assuming that 
today is time 0, and the option expires at time T. The underlying is an asset currently 
priced at S0, and at time T, its price is ST. Of course, we do not know ST until we get

to the expiration. The option has an exercise or strike price of X. The symbols we use 
For calls,
 c0 = value (price) of European call today
 cT = value (price) of European call at expiration
 C0 = value (price) of American call today
 CT = value (price) of American call at expiration
For puts,
 p0 = value (price) of European put today
 pT = value (price) of European put at expiration
 P0 = value (price) of American put today
 PT = value (price) of American put at expiration
4.1 European Option Pricing
Recall that in studying forward contracts earlier in this reading, the first thing we 
learned is how a forward contract pays off at expiration. Then we backed up and 
determined how forward contracts are priced and valued prior to expiration. We 
follow that same approach for options.4

Reading 57 ■ Basics of Derivative Pricing and Valuation 86
4.1.1  Value of a European Option at Expiration
Recall that a European call option allows the holder to buy the underlying at expira -
tion by paying the exercise price. Therefore, exercise is justified only if the value of 
the underlying exceeds the exercise price. Otherwise, the holder would simply let the 
call expire. So if the call is worth exercising ( ST > X), the holder pays X and receives 
an asset worth ST. Thus, the option is worth ST – X. If the call is not worth exercising 
(ST ≤ X), the option simply expires and is worth nothing at expiration.14 Thus, the 
value of the option at expiration is the greater of either zero or the underlying price 
at expiration minus the exercise price, which is typically written as
cT = Max(0, ST – X)  
This formula is also sometimes referred to as the exercise value  or intrinsic value . 
In this reading, we will use the term exercise value.

Taking a simple example, if the exercise price is €40 and the underlying price 
is at expiration €43, the call is worth cT = Max(€0,€43 − €40) = Max(€0,€3) = €3. If 
the underlying price at expiration is €39, the call is worth cT = Max(0,€39 − €40) = 
Max(€0,−€1) = €0.
For puts, the holder has the right to sell the underlying at X. If the underlying is 
worth less than X at expiration ( X > ST), the put will be exercised and worth X – ST 
because it allowed the holder to avoid the loss in value of the asset of that amount. If 
the underlying is equal to or worth more than the exercise price at expiration ( ST ≥ 
X), the put will simply expire with no value. So, the put is worth the greater of either 
zero or the exercise price minus the price of the underlying at expiration.
pT = Max(0, X – ST)  
As discussed above, this formula is referred to as the exercise value or intrinsic value, 
and as noted, we will use the term exercise value.

Using the same example as with the call, if the underlying is €43 at expiration, the 
put is worth pT = Max(€0,€40 – €43) = Max(0,−€3) = €0. If the underlying is €39 at 
expiration, the put is worth pT = Max(€0,€40 − €39) = Max(€0,€1) = €1.
Thus, the holder of an option looks out into the future and sees these relationships 
as the payoff possibilities. That does not mean the holder knows what ST will be, but 
the holder knows that all of the uncertainty of the option payoff is determined by the 
behavior of the underlying.
The results of this section can be restated as follows:
The value of a European call at expiration is the exercise value, which is 
the greater of zero or the value of the underlying minus the exercise price.
The value of a European put at expiration is the exercise value, which is 
the greater of zero or the exercise price minus the value of the underlying.

To understand option pricing, we have to work our way forward in a gradual man -
ner. The next valuable steps involve using our intuition to identify some characteristics 
that will influence the value of the option. We might not be able to quantify their 
effects just yet, but we can rationalize why these factors affect the value of an option.(8)
(9)
14 In all the remaining material, we identify conditions at expiration, such as ST > X and ST ≤ X. Here we 
merged the equality case ( ST = X) with the less-  than case (<). We could have done it the other way around 
(ST < X and ST ≥ X), which would have had no effect on our interpretations or any calculations of option 
value. For convenience, in some situations we will use one specification and in some the other.

Pricing and Valuation of Options 87
4.1.2  Effect of the Value of the Underlying
The value of the underlying is obviously a critical element in determining the value 
of an option. It is the uncertainty of the underlying that provides the motivation for 
using options. It is easy to rationalize the direction of the effect of the underlying.
A call option can be viewed as a mean of acquiring the underlying, whereas a 
put option can be viewed as a means of selling the underlying. Thus, a call option is 
logically worth more if the underlying is worth more, and a put option is logically 
worth more if the underlying is worth less.
The value of the underlying also forms one of the boundaries for calls. The value 
of a call option cannot exceed the value of the underlying. After all, a call option is 
only a means of acquiring the underlying. It can never give the holder more benefit 
than the underlying. Hence, the value of the underlying forms an upper boundary on

what a call is worth. The underlying does not provide an upper or lower boundary 
for puts. That role is played by the exercise price, as we will see in the next section.
To recap what we learned here,
The value of a European call option is directly related to the value of the 
The value of a European put option is inversely related to the value of the 
4.1.3  Effect of the Exercise Price
The exercise price is a critical factor in determining the value of an option. The exer -
cise price is the hurdle beyond which the underlying must go to justify exercise. For 
a call, the underlying must rise above the exercise price, and for a put, the underlying 
must fall below the exercise price, to justify exercise. When the underlying is beyond 
the exercise price in the appropriate direction (higher for a call, lower for a put), the 
option is said to be in the money . When the underlying is precisely at the exercise

price, the option is said to be at the money . When the underlying has not reached 
the exercise price (currently lower for a call, higher for a put), the option is said to be 
out of the money . This characterization of whether the option is in-, at-, or out-  of- 
the- money is referred to as the option’s moneyness .
For a call option, a lower exercise price has two benefits. One is that there are more 
values of the underlying at expiration that are above the exercise price, meaning that 
there are more outcomes in which the call expires in-  the- money. The other benefit 
is that assuming the call expires in-  the- money, for any value of the underlying, the 
option value is greater the lower the exercise price. In other words, at expiration the 
underlying value ST will be above the exercise price far more often, the lower is X. 
And if ST is indeed higher than X, the payoff of ST – X is greater, the lower is X.

For puts, the effect is just the opposite. To expire in-  the- money, the value of the 
underlying must fall below the exercise price. The higher the exercise price, the better 
chance the underlying has of getting below it. Likewise, if the value of the underlying 
does fall below the exercise price, the higher the exercise price, the greater the payoff. 
So, if X is higher, ST will be below it more often, and if ST is less than X, the payoff of 
X – ST is greater, the higher is X for whatever value of ST occurs.
The exercise price also helps form an upper bound for the value of a European put. 
If you were holding a European put, the best outcome you could hope for is a zero 
value of the underlying. For equities, that would mean complete failure and dissolution

Reading 57 ■ Basics of Derivative Pricing and Valuation 88
of the company with shareholders receiving no final payment.15 In that case, the put 
would pay X – ST, but with ST at zero, the put would pay X. If the underlying value 
goes to zero during the life of the European put, however, the holder cannot collect 
that payoff until expiration. Nonetheless, the holder would have a risk-  free claim on a 
payoff of X at expiration. Thus, the most the put would be worth is the present value 
of X, meaning X discounted from expiration to the current day at the risk-  free rate.16 
Although the holder cannot collect the payoff by exercising the option, he could sell 
it for the present value of X.
To recap these results,
The value of a European call option is inversely related to the exercise price.
The value of a European put option is directly related to the exercise price.
4.1.4  Effect of Time to Expiration
Logic suggests that longer-  term options should be worth more than shorter-  term

options. That statement is usually true but not always. A call option unquestionably 
benefits from additional time. For example, the right to buy an asset for $50 is worth 
a lot more if that right is available for two years instead of one. The additional time 
provides further opportunity for the underlying to rise above the exercise price. 
Although that means there is also additional time for the underlying to fall below 
the exercise price, it hardly matters to the holder of the call because the loss on the 
downside is limited to the premium paid.
For a European put option, the additional time still provides more opportunity 
for the underlying price to fall below the exercise price, but with the additional risk 
of it rising above the exercise price mitigated by the limited loss of the premium if 
the put expires out-  of- the- money. Thus, it sounds as if puts benefit from longer time, 
but that is not necessarily true. There is a subtle penalty for this additional time. Put

option holders are awaiting the sale of the underlying, for which they will receive the 
exercise price. The longer they have to wait, the lower the present value of the payoff. 
For some puts, this negative effect can dwarf the positive effect. This situation occurs 
with a put the longer the time to expiration, the higher the risk-  free rate of interest, 
and the deeper it is in-  the- money. The positive effect of time, however, is somewhat 
more dominant.
Note that we did not mention this effect for calls. For calls, the holder is waiting 
to pay out money at expiration. More time lowers the value of this possible outlay. 
Hence, a longer time period helps call option buyers in this regard.
The value of a European call option is directly related to the time to expiration.
15 You might think this point means that people who buy puts are hoping the company goes bankrupt,

a seemingly morbid motivation. Yet, put buyers are often people who own the stock and buy the put for 
protection. This motivation is no different from owning a house and buying fire insurance. You do not 
want the house to burn down. If your sole motivation in buying the insurance were to make a profit on 
the insurance, you would want the house to burn down. This moral hazard problem illustrates why it is 
difficult, if not impossible, to buy insurance on a house you do not own. Likewise, executives are prohibited 
from owning puts on their companies’ stock. Individual investors can own puts on stocks they do not own, 
because they cannot drive the stock price down.
16 For the put holder to truly have a risk-  free claim on X at expiration, given zero value of the underlying 
today, the underlying value must go to zero and have no possibility of any recovery. If there is any possi -
bility of recovery, the underlying value would not go to zero, as is often observed when a legal filing for

bankruptcy is undertaken. Many equities do recover. If there were some chance of recovery but the equity 
value was zero, demand for the stock would be infinite, which would push the price up.

Pricing and Valuation of Options 89
The value of a European put option can be either directly or inversely related 
to the time to expiration. The direct effect is more common, but the inverse 
effect can prevail with a put the longer the time to expiration, the higher the 
risk-  free rate, and the deeper it is in-  the- money.
4.1.5  Effect of the Risk-  Free Rate of Interest
We have already alluded to the effect of the risk-  free rate. For call options, a longer time 
to expiration means that the present value of the outlay of the exercise price is lower. 
In other words, with a longer time to expiration, the call option holder continues to 
earn interest on the money that could be expended later in paying the exercise price 
upon exercise of the option. If the option is ultimately never exercised, this factor is 
irrelevant, but it remains at best a benefit and at worst has no effect. For puts, the 
opposite argument prevails. A longer time to expiration with a higher interest rate

lowers the present value of the receipt of the exercise price upon exercise. Thus, the 
value today of what the put holder might receive at expiration is lower. If the put is 
ultimately never exercised, the risk-  free rate has no effect. Thus, at best, a higher risk-  
free rate has no effect on the value of a put. At worst, it decreases the value of the put.
These results are summarized as follows:
The value of a European call is directly related to the risk-  free interest rate.
The value of a European put is inversely related to the risk-  free interest rate.
4.1.6  Effect of Volatility of the Underlying
In studying the pricing of equities, we are conditioned to believe that volatility has a 
negative effect. After all, investors like return and dislike risk. Volatility is certainly an 
element of risk. Therefore, volatility is bad for investors, right? Well, partially right.
First, not all volatility is bad for investors. Unsystematic volatility should be

irrelevant. Investors can hold diversified portfolios. Systematic volatility is clearly 
undesirable, but do not think that this means that volatility should be completely 
avoided where possible. If volatility were universally undesirable, no one would take 
risks. Clearly risks have to be taken to provide opportunity for reward.
With options, volatility of the underlying is, however, universally desirable. The 
greater the volatility of the underlying, the more an option is worth. This seemingly 
counterintuitive result is easy to understand with a little explanation.
First, let us make sure we know what volatility really means. In studying asset 
returns, we typically represent volatility with the standard deviation of the return, 
which measures the variation from the average return. The S&P 500 Index has an 
approximate long-  run volatility of around 20%. Under the assumption of a normal 
distribution, a standard deviation of 20% implies that about 68% of the time, the returns

will be within plus or minus one standard deviation of the average. About 95% of the 
time, they will be within plus or minus two standard deviations of the average. About 
99% of the time, they will be within plus or minus three standard deviations of the 
average. When the distribution is non-  normal, different interpretations apply, and 
in some extreme cases, the standard deviation can be nearly impossible to interpret.
Standard deviation is not the only notion of volatility, however, and it is not even 
needed at this point. You can proceed fairly safely with a measure as simple as the 
highest possible value minus the lowest, known as the range. The only requirement 
we need right now is that the concept of volatility reflects dispersion—how high and 
how low the underlying can go.

Reading 57 ■ Basics of Derivative Pricing and Valuation 90
So, regardless of how we measure volatility, the following conditions will hold:
1 A call option will have a higher payoff the higher the underlying is at expiration.
2 A call option will have a zero payoff if it expires with the underlying below the 
exercise price.
If we could impose greater volatility on the underlying, we should be able to see that 
in Condition 1, the payoff has a better chance of being greater because the underlying 
has a greater possibility of large positive returns. In Condition 2, however, the zero 
payoff is unaffected if we impose greater volatility. Expiring more out-  of- the- money 
is not worse than expiring less out-  of- the- money, but expiring more in-  the- money is 
better than expiring less-  in- the- money.17
For puts, we have
1 A put option will have a higher payoff the lower the underlying is at expiration.
2 A put option will have a zero payoff if it expires with the underlying above the

If we could impose greater volatility, we would find that it would have a beneficial 
effect in (1) because a larger positive payoff would have a greater chance of occurring. 
In (2), the zero payoff is unaffected. The greater of the option expiring more out-  of- 
the- money is irrelevant. Expiring more out-  of- the- money is not worse than expiring 
less out-  of- the- money.
Thus, we summarize our results in this section as
The value of a European call is directly related to the volatility of the 
The value of a European put is directly related to the volatility of the 
The combined effects of time and volatility give rise to the concept of the time 
value of an option. The time value  of an option is the difference between the market 
price of the option and its intrinsic value. It represents the market valuation of the 
potential for higher exercise value relative to the potential for lower exercise value

given the volatility of the underlying. Time value of an option is not to be confused 
with the time value of money, which is the notion of money later being worth less 
than money today as a result of the combined effects of time and interest. Time 
value results in an option price being greater with volatility and time but declining as 
expiration approaches. At expiration, no time value remains and the option is worth 
only its exercise value. As such, an option price is said to decay over time, a process 
characterized as time value decay , which is covered in more advanced material.
4.1.7  Effect of Payments on the Underlying and the Cost of Carry
We previously discussed how payments on the underlying and carrying costs enter 
into the determination of forward prices. They also affect option prices. Payments 
on the underlying refer to dividends on stocks and interest on bonds. In addition, 
some commodities offer a convenience yield benefit. Carrying costs include the actual

physical costs of maintaining and/or storing an asset.
Let us first consider the effect of benefits. Payments of dividends and interest 
reduce the value of the underlying. Stocks and bonds fall in value as dividends and 
interest are paid. These benefits to holders of these securities do not flow to holders 
of options. For call option holders, this reduction is a negative factor. The price of 
17 Think of an option expiring out-  of- the- money as like it being dead. (Indeed, the option is dead.) Being 
“more dead” is not worse than being “less dead. ”

Pricing and Valuation of Options 91
the underlying is hurt by such payments, and call holders do not get to collect these 
payments. For put holders, the effect is the opposite. When the value of the underlying 
is reduced, put holders are helped.
Carrying costs have the opposite effect. They raise the effective cost of holding or 
shorting the asset. Holding call options enables an investor to participate in movements 
of the underlying without incurring these costs. Holding put options makes it more 
expensive to participate in movements in the underlying than by short selling because 
short sellers benefit from carrying costs, which are borne by owners of the asset.
To summarize the results from this section,
A European call option is worth less the more benefits that are paid by the 
underlying and worth more the more costs that are incurred in holding the 
A European put option is worth more the more benefits that are paid by

the underlying and worth less the more costs that are incurred in holding 
the underlying.
4.1.8  Lowest Prices of Calls and Puts
What we have learned so far forms a framework for understanding how European 
options are priced. Let us now go a step further and establish a minimum price for 
these options.
First, we need to look at a call option as similar to the purchase of the underlying 
with a portion of the purchase price financed by borrowing. If the underlying is a stock, 
this transaction is usually called a margin transaction. Assume that the underlying is 
worth S0. Also assume that you borrow cash in the amount of the present value of X, 
promising to pay X back T periods later at an interest rate of r. Thus, X/(1 + r)T is the 
amount borrowed, and X is the amount to be paid back. Now move forward to time 
T and observe the price of the underlying, ST. Upon paying back the loan, the overall 
strategy will be worth ST – X, which can be positive or negative.

Next, consider an alternative strategy of buying a call option expiring at T with 
an exercise price of X, the same value as the face value of the loan. We know that the 
option payoffs will be ST – X if it expires in-  the- money ( ST > X) and zero if not ( ST 
≤ X). Exhibit 11 compares these two strategies.18
Exhibit 11   Call Option vs. Leveraged (Margin) Transaction
Outcome at T
Call Expires  
Out-  of- the-  Money  
(ST ≤ X)Call Expires  
In- the-  Money  
(ST > X)
Call 0 ST – X
Leveraged transaction
  Asset ST ST
18 Note in Exhibit 11, and in others to come, that the inequality ≤ is referred to as out-  of- the- money. The 
case of equality is technically referred to as at-  the- money but the verbiage is simplified if we continue to 
call it out-  of- the- money. It is certainly not in-  the- money and at-  the- money is arguably the same as out-  of- 
the- money. Regardless of one’s preference, the equality case can be attached to either of the two outcomes

Reading 57 ■ Basics of Derivative Pricing and Valuation 92
(ST > X)
  Loan –X –X
  Total ST – X ST – X
When the call expires in-  the- money, both transactions produce identical payoffs. 
When the call expires out-  of- the- money, the call value is zero, but the leveraged 
transaction is almost surely a loss. Its value ST – X is negative or zero at best (if ST is 
exactly equal to X).
If two strategies are found to produce equivalent results in some outcomes but one 
produces a better result in all other outcomes, then one strategy dominates the former. 
Here we see that the call strategy dominates the leveraged strategy. Any strategy that 
dominates the other can never have a lower value at any time. Why would anyone 
pay more for one strategy than for another if the former will never produce a better 
result than the latter? Thus, the value of the call strategy, c0, has to be worth at least

the value of the leveraged transaction, S0 (the value of the asset), minus X/(1 + r)T 
(the value of the loan). Hence, c0 ≥ S0 − X/(1 + r)T.
The inequality means that this statement provides the lowest price of the call, but 
there is one more thing we need to do. It can easily be true that X/(1 + r)T > S0. In that 
case, we are saying that the lowest value is a negative number, but that statement is 
meaningless. A call can never be worth less than zero, because its holder cannot be 
forced to exercise it. Thus, we tend to express this relationship as
cS XrT
00 01 ≥− +()

Max,
which represents the greater of the value of zero or the underlying price minus the 
present value of the exercise price. This value becomes the lower limit of the call price.
Now consider an analogous result for puts. Suppose we want to profit from a 
declining price of the underlying. One way to do this is to sell the underlying short.

Suppose we do that and invest cash equal to the present value of X into risk-  free bonds 
that pay X at time T. At time T, given a price of the underlying of ST, the short sale 
pays off – ST, a reflection of the payment of ST to cover the short sale. The bonds pay 
X. Hence, the total payoff is X – ST.
Now, compare that result with the purchase of a put expiring at T with exercise 
price of X. If the put expires in–the-  money ( ST < X), it is worth X – ST. If it expires 
out- of- the- money ( ST ≥ X), it is worth zero. Exhibit 12 illustrates the comparison of 
the put with the short sale and bond strategy. We see that for the in-  the- money case, 
the put and short sale and bond strategies match each other. For the out-  of- the- money 
case, however, the put performs better because the short sale and bond strategy pays 
X – ST. With ST ≥ X, this payment amount is negative. With the put dominating the 
short sale and bond strategy, the put value cannot be less than the value of the short

sale and bond strategy, meaning p0 ≥ X/(1 + r)T − S0. But as with calls, the right-  hand 
side can be negative, and it hardly helps us to say that a put must sell for more than a 
negative number. A put can never be worth less than zero, because its owner cannot 
be forced to exercise it. Thus, the overall result is expressed succinctly as
pX rST
00 01 ≥+ () −

Max,(10)
(11)Exhibit 11   (Continued)

Pricing and Valuation of Options 93
Exhibit 12   Put vs. Short Sale and Bond Purchase
Put Expires  
(ST < X)Put Expires  
(ST ≥ X)
Put X – ST 0
Short sale and bond purchase
  Short sale –ST –ST
  Bond X X
  Total X – ST X – ST
Let us look at some basic examples. Assume the exercise price is €60, the risk-  free 
rate is 4%, and the expiration is nine months, so T = 9/12 = 0.75. Consider two cases:
Underlying: S0 = €70
Minimum call price = Max[0,€70 – €60/(1.04)0.75] = Max(0,€11.74) = €11.74
Minimum put price = Max[0,€60/(1.04)0.75 − €70] = Max(0,−€11.74) = €0.00
Underlying: S0 = €50
Minimum call price = Max[0,€50 – €60/(1.04)0.75] = Max(0,−€8.26) = €0.00
Minimum put price = Max[0,€60/(1.04)0.75 − €50] = Max(0,€8.26) = €8.26
To recap, in this section we have established lower limits for call and put option 
values. Formally restating these results in words,
The lowest value of a European call is the greater of zero or the value of the

underlying minus the present value of the exercise price.
The lowest value of a European put is the greater of zero or the present value 
of the exercise price minus the value of the underlying.
EXAMPLE 6   
Basic Principles of European Option Pricing
1 Which of the following factors does not affect the value of a European 
option?
C The percentage of the investor’s assets invested in the option
2 Which of the following statements imply that a European call on a stock is 
worth more?
A Less time to expiration
B A higher stock price relative to the exercise price
C Larger dividends paid by the stock during the life of the option
3 Why might a European put be worth less the longer the time to 
expiration?

Reading 57 ■ Basics of Derivative Pricing and Valuation 94
A The cost of waiting to receive the exercise price is higher.
B The risk of the underlying is lower over a longer period of time.
C The longer time to expiration means that the put is more likely to 
expire out-  of- the- money.
4 The loss in value of an option as it moves closer to expiration is called 
what?
A Time value decay
B Volatility diminution
C Time value of money
5 How does the minimum value of a call or put option differ from its exer -
cise value?
A The exercise price is adjusted for the time value of money.
B The minimum value reflects the volatility of the underlying.
C The underlying price is adjusted for the time value of money.
C is correct. The investor’s exposure to the option is not relevant to the price one 
should pay to buy or ask to sell the option. Volatility and dividends or interest 
paid by the underlying are highly relevant to the value of the option.

B is correct. The higher the stock price and the lower the exercise price, the 
more valuable is the call. Less time to expiration and larger dividends reduce 
the value of the call.
A is correct. Although the longer time benefits the holder of the option, it also 
has a cost in that exercise of a longer-  term put comes much later. Therefore, the 
receipt of the exercise price is delayed. Longer time to expiration does not lower 
the risk of the underlying. The longer time also does not increase the likelihood 
of the option expiring out-  of- the- money.
A is correct. An option has time value that decays as the expiration approaches. 
There is no such concept as volatility diminution. Time value of money relates 
only to the value of money at one point in time versus another.
A is correct. The minimum value formula is the greater of zero or the differ -
ence between the underlying price and the present value of the exercise price,

whereas the exercise value is the maximum of zero and the appropriate difference 
between the underlying price and the exercise price. Volatility does not affect 
the minimum price. It does not make sense to adjust the underlying price for 
the time value of money for the simple reason that it is already adjusted for the 
time value of money.
4.1.9  Put–Call Parity
One of the first concepts that a trader learns in options is the parity relationship 
between puts and calls. Even though the word “parity” means “equivalence, ” puts and 
calls are not equivalent. There is, however, a relationship between the call price and 
the price of its corresponding put, which we refer to as put–call parity.

Pricing and Valuation of Options 95
Suppose Investor A owns an asset that has a current price of S0. Assume the asset 
makes no cash payments and has no carrying costs. The end of the holding period is 
time T, at which point the asset will be worth ST. Fearing the possibility that ST will 
decline, Investor A buys a put option with an exercise price of X, which can be used 
to sell the asset for X at time T. This put option has a premium of p0. Combined with 
the value of the asset, the investor’s current position is worth S0 + p0, which is the 
investor’s money at risk. This strategy of holding the asset and a put is sometimes 
called a protective put .
At expiration, the value of the asset is ST. The value of the put will be either zero 
or X – ST. If the asset increases in value such that ST ≥ X, then the overall position is 
worth ST. The asset has performed well, and the investor will let the put expire. If the

asset value declines to the point at which ST < X, the asset is worth ST, and the put 
is worth X – ST, for a total of X. In other words, the investor would exercise the put, 
selling the asset for X, which exceeds the asset’s current value of ST.
This strategy seems like a reasonable and possibly quite attractive investment. 
Investor A receives the benefit of unlimited upside potential, with the downside per -
formance truncated at X. Exhibit 13 shows the performance of the protective put. The 
graph on the left illustrates the underlying asset and the put. The graph on the right 
shows their combined effects.
Exhibit 13   Protective Put (Asset Plus Long Put)
Value
Underlying Asset
0X
XSTLong PutValue
 + Long Put
0X
XST
Consider Investor B, an options trader. At time 0, this investor buys a call option 
on this asset with an exercise price of X that expires at T and a risk-  free zero-  coupon 
bond with a face value of X that matures at T. The call costs c0, and the bond costs the

present value of X, which is X/(1 + r)T. Thus, Investor B has invested funds of c0 + X/
(1 + r)T. This strategy is sometimes known as a fiduciary call . If the underlying price 
exceeds the exercise price at expiration, the call will be worth ST – X, and the bond 
will mature and pay a value of X. These values combine to equal ST. If the underlying 
price does not exceed the exercise price at expiration, the call expires worthless and 
the bond is worth X for a combined value of X.
Exhibit  14 shows the performance of the fiduciary call. The graph on the left 
shows the call and bond, and the graph on the right shows the combined effects of 
the two strategies.

Reading 57 ■ Basics of Derivative Pricing and Valuation 96
Exhibit 14   Fiduciary Call (Long Call Plus Risk-  Free Bond)
Value
Risk-Free Bond
0X
XSTLong
CallValue
Long Call + 
0X
XST
Comparing Exhibit 13 with Exhibit 14 shows that a protective put and a fiduciary 
call produce the same result. Exhibit 15 shows this result more directly by identifying 
the payoffs in the various outcomes. Recall that Investor A committed funds of S0 + 
p0, while Investor B committed funds of c0 + X/(1 + r)T. If both investors receive the 
same payoffs at time T regardless of the asset price at T, the amounts they invest at 
time 0 have to be the same. Thus, we require
Sp cX rT
00 0 1 += ++ ()
This relationship is known as put–call parity .
Exhibit 15   Protective Put vs. Fiduciary Call
(ST < X)Call Expires  
(ST ≥ X)
Protective put
  Asset ST ST
  Long put X – ST 0
  Total X ST
Fiduciary call
  Long call 0 ST – X
  Risk-  free bond X X
  Total X ST

Risk-  free bond X X
  Total X ST
For a simple example, assume call and put options with an exercise price of ¥100,000 
in which the underlying is at ¥90,000 at time 0. The risk-  free rate is 2% and the options 
expire in two months, so T = 2/12 = 0.167. To completely fill in the puzzle, we would 
need to know the put or call price, from which we could obtain the other. For now, 
let us write this relationship as
pc Xr ST
00 0 1 −= +() −(12)

Pricing and Valuation of Options 97
The right side would be ¥100,000/(1.02)0.167 − ¥90,000 = ¥9,670. Thus, the put price 
should exceed the call price by ¥9,670. Thus, if the call were priced at ¥5,000, the put 
price would be ¥14,670. If we knew the put price, we could obtain the call price. Put–call 
parity does not tell us which price is correct, and it requires knowledge of one price 
to get the other. Alternatively, it can tell us the difference in the put and call prices.
Put–call parity must hold, at least within transaction costs, or arbitrage opportu -
nities would arise. For example, suppose Investor C observes market prices and finds 
that the left- hand side of put–call parity, S0 + p0, is less than the right-  hand side, c0 + 
X/(1 + r)T. Thus, the put and the stock cost less than the call and the bond. Knowing 
that there should be equality (parity), Investor C executes an arbitrage transaction,

selling the overpriced transactions (the call and the bond) and buying the underpriced 
transactions (the asset and the put).19 By selling the higher priced side and buying 
the lower priced side, Investor C will take in more money than she will pay out, a net 
inflow of c0 + X/(1 + r)T – (S0 + p0). At expiration, the long put and long asset will 
offset the short call and bond, as shown in Exhibit 16.
Exhibit 16   Put–Call Parity Arbitrage
Transaction Cash Flow at Time 0Put Expires  
(ST ≥ X)
Buy asset –S0 ST ST
Buy put –p0 X – ST 0
Sell call +c0 0 –(ST – X)
Borrow +X/(1 + r)T–X –X
Total –S0 – p0 + c0 +  
X/(1 + r)T > 00 0
In simple terms, if ST < X, the short call expires out-  of- the- money and the put 
is exercised to sell the asset for X. This cash, X, is then used to pay off the loan. The 
net effect is that no money flows in or out at T. If ST ≥ X, the put expires out-  of- the

money, and the short call is exercised, meaning that Investor C must sell the asset 
for X. This cash, X, is then used to pay off the loan. Again, no money flows in or out. 
The net effect is a perfect hedge in which no money is paid out or received at T. But 
there was money taken in at time 0. Taking in money today and never having to pay 
it out is an arbitrage profit. Arbitrage opportunities like this, however, will be noticed 
by many investors who will engage in the same transactions. Prices will adjust until 
parity is restored, whereby S0 + p0 = c0 + X/(1 + r)T.
19 Selling the bond is equivalent to borrowing, meaning to issue a loan.

Reading 57 ■ Basics of Derivative Pricing and Valuation 98
Put–call parity provides tremendous insights into option pricing. Recall that we 
proved that going long the asset and long a put is equivalent to going long a call and long 
a risk-  free bond. We can rearrange the put–call parity equation in the following ways:
Sp cX r
pc SX r
cp SX r
Sc pT
T
T00 0
00 0
00 0
00 01
1
1+= ++()
⇒
=− ++()
=+ −+()
=− +XXr
Xr Sp cT
T1
100 0+()
+() =+ −
By using the symbols and the signs in these versions of put–call parity, we can see 
several important interpretations. In the equations below, plus signs mean long and 
minus signs mean short:
pc SX rT
00 0 1 =− ++() ⇒= long put l ong ca ll, short asset, l ong bon d d
long cal ll ong put, l ong asset, short b cp SX rT
00 0 1 =+ −+() ⇒= o ond
long asse tl ong ca ll, short put, long Sc pX rT
00 0 1 =− ++() ⇒=   bond
long bond l ong asset, l ong put, sho Xr Sp cT100 0 +() =+ −⇒ = rrt cal l
You should be able to convince yourself of any of these points by constructing a table

similar to Exhibit 15.20
4.1.10  Put–Call–Forward Parity
Recall that we demonstrated that one could create a risk-  free position by going long 
the asset and selling a forward contract.21 It follows that one can synthetically create a 
position in the asset by going long a forward contract and long a risk-  free bond. Recall 
our put–call parity discussion and assume that Investor A creates his protective put 
in a slightly different manner. Instead of buying the asset, he buys a forward contract 
and a risk-  free bond in which the face value is the forward price. Exhibit 17 shows that 
this strategy is a synthetic protective put. Because we showed that the fiduciary call 
is equivalent to the protective put, a fiduciary call has to be equivalent to a protective 
put with a forward contract. Exhibit 18 demonstrates this point.
Exhibit 17   Protective Put with Forward Contract vs. Protective Put with 
Asset
Put Expires In-  the-  Money  
(ST < X)Put Expires Out-  of- the-  Money

(ST < X)Put Expires Out-  of- the-  Money  
(ST ≥ X)
Protective put with asset
Asset ST ST
Long put X – ST 0
Total X ST
20 As a further exercise, you might change the signs of each term in the above and provide the appropriate 
interpretations.
21 You might wish to review Exhibit 6.

Pricing and Valuation of Options 99
(ST ≥ X)
Protective put with forward contract
Risk-  free bond F0(T) F0(T)
Forward contract ST – F0(T) ST – F0(T)
Total X ST
Exhibit 18   Protective Put with Forward Contract vs. Fiduciary Call
Put Expires In-  the-  Money 
(ST < X)Call Expires In-  the-  Money 
(ST ≥ X)
Protective Put with Forward Contract
Total X ST
Fiduciary Call
Call 0 ST – X
Total X ST
It follows that the cost of the fiduciary call must equal the cost of the synthetic pro -
tective put, giving us what is referred to as put–call–forward parity ,
FT rp cX rTT
00 0 11 () +() += ++ ()
Returning to our put–call parity example, a forward contract on ¥90,000 expir -
ing in two months with a 2% interest rate would have a price of ¥90,000(1.02)0.167 = 
¥90,298. Rearranging Equation 13, we have

pc XF TrT
00 0 1 −= − () +()
The right-  hand side is (¥100,000 − ¥90,298)/(1.02)0.167 = ¥9,670, which is the same 
answer we obtained using the underlying asset rather than the forward contract. 
Naturally these two models give us the same answer. They are both based on the 
assumption that no arbitrage is possible within the spot, forward, and options markets.
So far we have learned only how to price options in relation to other options, 
such as a call versus a put or a call or a put versus a forward. We need a way to price 
options versus their underlying.(13)Exhibit 17   (Continued)

Reading 57 ■ Basics of Derivative Pricing and Valuation 100
EXAMPLE 7   
Put–Call Parity
1 Which of the following statements best describes put–call parity?
A The put price always equals the call price.
B The put price equals the call price if the volatility is known.
C The put price plus the underlying price equals the call price plus the 
present value of the exercise price.
2 From put–call parity, which of the following transactions is risk-  free?
A Long asset, long put, short call
B Long call, long put, short asset
C Long asset, long call, short bond
C is correct. The put and underlying make up a protective put, while the call 
and present value of the exercise price make up a fiduciary call. The put price 
equals the call price for certain combinations of interest rates, times to expira -
tion, and option moneyness, but these are special cases. Volatility has no effect 
on put–call parity.

A is correct. The combination of a long asset, long put, and short call is risk free 
because its payoffs produce a known cash flow of the value of the exercise price. 
The other two combinations do not produce risk-  free positions. You should 
work through the payoffs of these three combinations in the form of Exhibit 12.
4.2 Binomial Valuation of Options
Because the option payoff is determined by the underlying, if we know the outcome 
of the underlying, we know the payoff of the option. That means that the price of the 
underlying is the only element of uncertainty. Moreover, the uncertainty is not so much 
the value of the underlying at expiration as it is whether the underlying is above or 
below the exercise price. If the underlying is above the exercise price at expiration, the 
payoff is ST – X for calls and zero for puts. If the underlying is below the exercise price

at expiration, the payoff is zero for calls and X − ST for puts. In other words, the payoff 
of the option is straightforward and known, as soon as we know whether the option 
expires in- or out-  of- the- money. Note that for forwards, futures, and swaps, there is 
no such added complexity. The payoff formula is the same regardless of whether the 
underlying is above or below the hurdle.
As a result of this characteristic of options, derivation of an option pricing model 
requires the specification of a model of a random process that describes movements 
in the underlying. Given the entirely different nature of the payoffs above and below 
the exercise price, it might seem difficult to derive the option price, even if we could 
model movements in the underlying. Fortunately, the process is less difficult than it 
first appears.
At this level of treatment, we will start with a very simple model that allows only 
two possible movements in the underlying—one going up and one going down from

where it is now. This model with two possible outcomes is called the binomial model . 
Start with the underlying at S0, and let it go up to  S1+ or down to  S1−. We cannot 
arbitrarily set these values at just anything. We will be required to know the values

Pricing and Valuation of Options 101
of S1+ and  S1−. That does not mean we know which outcome will occur. It means that 
we know only what the possibilities are. In doing so, we effectively know the volatility. 
Assume the probability of the move to  S1+ is q and the probability of the move to  S1− 
is 1 – q. We specify the returns implied by these moves as up and down factors, u and 
d, where
uS
SdS
S==+−
1
01
0,
Now, consider a European call option that expires at time 1 and has an exercise 
price of X. Let the call prices be c0 today and  c1+ and  c1− at expiration. Exhibit 19 
illustrates the model. Our objective is to determine the price of the option today, 
meaning to determine a formula for c0. Knowing what we know about arbitrage and 
the pricing of forward contracts, it would seem we could construct a risk-  free portfolio 
involving this option.
Exhibit 19   The Binomial Option Pricing Model
S0
C0()
()10
11 1 Max0,SS uX
cS XS X+
++ +=>
=− =−
()
()10
11 0, 0SS dX
cM ax SX−
−−=<
=− =

++ +=>
=− =−
()
()10
11 0, 0SS dX
cM ax SX−
−−=<
=− =
Because call options and the underlying move together, one possibility is that 
buying the underlying and selling a call could create a hedge. Indeed it does, but one 
unit of each is not the appropriate balance. Let us sell one call and hold h units of the 
underlying. The value h is unknown at the moment, but we will be able to determine 
its value. The value today of a combination of h units of the underlying and one short 
call is
V0 = hS0 – c0
Think of V0 as the amount of money invested. Depending on which of the two 
paths is taken by the underlying, the value of this portfolio at time 1 will be
Vh Sc
Vh Sc11 1
11 1++ +
−− −=−
=−or(14)
(15)

Reading 57 ■ Basics of Derivative Pricing and Valuation 102
If the portfolio were hedged, then  V1+ would equal  V1−. We can set  V1+ and  V1− equal 
to each other and solve for the value of h that assures us that the portfolio is hedged:
VV
hS ch Sc
hcc
SS11
11 11
11
11+−
++ −−
+−
+−=
⇒− =−
⇒=−
−
The values on the right-  hand side are known, so we can easily calculate h. Thus, we 
can derive the number of units of the underlying that will perfectly hedge one unit 
of the short call.
We know that a perfectly hedged investment should earn the risk-  free rate, r. Thus, 
the following statement must be true:
VV Vr11 01+−=+()  (or )
We can substitute the value of  V1+ or V1− from Equation 15 into the above equation. 
Then we do a little algebra, which is not important to this discussion, and obtain the 
formula for the option price,
ccc
r
rd
ud011 1
1
1=+−()
+
=+−
−+−ππ
πwher e
Equation 17 shows that the value of the call today is a weighted average of the

next two possible call prices at expiration, where the weights, π and 1 – π, are given 
by the second formula in Equation 17.
This formula sheds a great deal of light on option pricing. Notice the following:
■■The volatility of the underlying, which is reflected in the difference between  S1+ 
and S1− and affects  c1+ and  c1−, is an important factor in determining the value 
of the option.
■■The probabilities of the up and down moves, q and 1 – q, do not appear in the 
formula.22
■■The values π and 1 – π are similar to probabilities and are often called synthetic 
or pseudo probabilities. They produce a weighted average of the next two possi -
ble call values, a type of expected future value.
■■The formula takes the form of an expected future value, the numerator, dis -
counted at the risk-  free rate.
On the first point, if volatility increases, the difference between  S1+ and  S1− 
increases, which widens the range between  c1+ and  c1−, leading to a higher option

value. The upper payoff,  c1+, will be larger and the lower payoff,  c1−, will still be zero.23 
On the second point, the actual probabilities of the up and down moves do not matter. 
This result is because of our ability to construct a hedge and the rule of arbitrage. On 
the third point, the irrelevance of the actual probabilities is replaced by the relevance 
of a set of synthetic or pseudo probabilities, π and 1 – π, which are called risk-  neutral (16)
(17)
22 We introduced them earlier to help make this point, but ultimately they serve no purpose.
23 Although the lower payoff is zero in this example, that will not always be the case.

Pricing and Valuation of Options 103
probabilities . On the fourth point, these risk-  neutral probabilities are used to find a 
synthetic expected value, which is then discounted at the risk-  free rate. Thus, the 
option is valued as though investors are risk neutral. As we discussed extensively 
earlier, that is not the same as assuming that investors are risk neutral.
If the option does not trade at the specified formula, Equation 17, investors can 
engage in arbitrage transactions. If the option is trading too high relative to the formula, 
investors can sell the call, buy h shares of the underlying, and earn a return in excess 
of the risk-  free rate, while funding the transaction by borrowing at the risk-  free rate. 
The combined actions of arbitrageurs will result in downward pressure on the option 
price until it converges to the model price. If the option price is too low, buying the 
call, selling short h units of the asset, and investing the proceeds in risk-  free bonds

will generate risk-  free cash that will earn more than the risk-  free rate. The combined 
actions of arbitrageurs doing this will pressure the call price to rise until it reaches 
the price given by the model.
We will omit the details, but the hedge portfolio can also be constructed with 
puts.24 Changing the c’s to p’s leads to the binomial put option pricing formula,
ppp
r011 1
1=+−()
++−ππ
with the risk-  neutral probability π determined by the same formula as for calls, as 
shown in Equation 17.
Let us construct a simple example. Let S0 be £40 and the risk-  free rate be 5%. The 
up and down factors are u = 1.20 and d = 0.75. Thus, the next two possible prices of 
the asset are  S1+ = £40(1.20) = £48 and  S1− = £40(0.75) = £30. Consider a call and a 
put that have exercise prices of £38. Then the next two possible values of the call and 
put are
c
c
p1
1
10483 81 0
0303 80
0384+
−
+=− ()
=− () =
=−Max
Max
Max,
,
,££ =£
££ £
££ 880
0383 081() =
=− () =−£
££ £ p Max,
Next we compute the risk-  neutral probability,

π=+−
−=10 05 075
1200 750 667..
...
The values of the call and put are
c
p0
00 667 10 10 667 0
105635
0 667 01 0 667=() +−()=
=() +−.£ .£
.£.
.£ .and
(()=£
.£.8
105254
The binomial model, as we see it here, is extremely simple. In reality, of course, 
there are more than two possible next-  period prices for the underlying. As it turns 
out, we can extend the number of periods and subdivide an option’s life into an 
increasing number of smaller time periods. In that case, we can obtain a more accurate 
and realistic model for option pricing, one that is widely used in practice. Given our 
objective in this reading of understanding the basic ideas behind derivative pricing, 
the one-  period model is sufficient for the time being.(18)
24 A long position in h units of the underlying would be hedged with one long put. The formula for h is 
the same as the one given here for calls, with call prices in the numerator instead of put prices.

Reading 57 ■ Basics of Derivative Pricing and Valuation 104
EXAMPLE 8   
Binomial Valuation of Options
1 Which of the following terms directly represents the volatility of the 
underlying in the binomial model?
A The standard deviation of the underlying
B The difference between the up and down factors
C The ratio of the underlying value to the exercise price.
2 Which of the following is not a factor in pricing a call option in the bino -
mial model?
A The risk-  free rate
B The exercise price
C The probability that the underlying will go up
3 Which of the following best describes the binomial option pricing 
formula?
A The expected payoff is discounted at the risk-  free rate plus a risk 
premium.
B The spot price is compounded at the risk-  free rate minus the volatility 
premium.
C The expected payoff based on risk-  neutral probabilities is discounted 
at the risk-  free rate.
B is correct. The up and down factors express how high and how low the under -

lying can go. Standard deviation does not appear directly in the binomial model, 
although it is implicit. The ratio of the underlying value to the exercise price 
expresses the moneyness of the option.
C is correct. The actual probabilities of the up and down moves are irrelevant to 
pricing options. The risk-  free and exercise price are, of course, highly relevant.
C is correct. Risk-  neutral probabilities are used, and discounting is at the risk-  
free rate. There is no risk premium incorporated into option pricing because 
of the use of arbitrage.
We have now seen how to obtain the price of a European option. Let us now 
consider what happens if the options are American, meaning they have the right to 
be exercised early.
4.3 American Option Pricing
First, we will use upper case letters for American call and put prices: C0 and P0. 
Second, we know that American options possess every characteristic of European

options and one additional trait: They can be exercised at any time prior to expiration.

Pricing and Valuation of Options 105
Early exercise cannot be required, so the right to exercise early cannot have negative 
value. Thus, American options cannot sell for less than European options. Thus, we 
can state the following:
Cc
Pp00
00≥
≥
Given the price of the underlying at S0, the early-  exercise feature means that we 
can exercise the option at any time. So, we can claim the value Max(0, S0 – X) for 
calls and Max(0, X – S0) for puts. These values establish new minimum prices for 
American calls and puts,
CS X
PX S00
000
0=− ()
=− ()Max
Max,
,
For call options, we previously learned that a European call has a minimum value 
given by Equation 10, which is restated here:
cS XrT

Max,
Comparing Max(0, S0 – X) (the minimum for American calls) with Max[0, S0 – X/
(1 + r)T] (the minimum for European calls) reveals that the latter is either the same or 
higher. There are some circumstances in which both minima are zero, some in which

the American minimum is zero and the European minimum is positive, and some in 
which both are positive, in which case S0 – X/(1 + r)T is unquestionably more than 
S0 – X. Given that an American call price cannot be less than a European call price, 
we have to reestablish the American call minimum as Max[0, S0 – X/(1 + r)T].
For put options, we previously learned that a European put has a minimum value 
given by Equation 11, which is restated here:
pX rST

Max,
Comparing Max(0, X – S0) (the minimum for American puts) with Max[0, X/(1 + 
r)T – S0] (the minimum for European puts) reveals that the former is never less. In 
some circumstances, they are both zero. In some, X – S0 is positive and X/(1 + r)T – 
S0 is negative, and in some cases both are positive but X – S0 is unquestionably more 
than X/(1 + r)T – S0. Thus, the American put minimum value is the exercise value, 
which is Max(0, X – S0).
So, now we have new minimum prices for American calls and puts:
CS Xr
PX ST
00
0001

CS Xr
PX ST
00
0001
0≥− +()


≥− ()Max
Max,
,
Thus, in the market these options will trade for at least these values.
Let us return to the previous examples for the minimum values. The exercise 
price is €60, the risk-  free rate is 4%, and the expiration is T = 0.75. Consider the two 
cases below:
■■The minimum European call price was previously calculated as €11.74. The 
exercise value of the American call is Max(0,€70 − €60) = €10. The American 
call has to sell for at least as much as the European call, so the minimum price 
of the American call is €11.74.
■■The minimum European put price was €0.00. This is also the exercise value of 
the American put [Max(0,€60 − €70) = €0.00], so the minimum price of the 
American put is still €0.00(19)
(20)
(21)

Reading 57 ■ Basics of Derivative Pricing and Valuation 106
■■The minimum European call price was previously calculated as €0.00. The exer -
cise value of the American call is Max(0,€50 − €60) = €0.00, so €0.00 is still the 
minimum price of the American call.
■■The minimum European put price was previously calculated as €8.26. The 
exercise value of the American put is Max(0,€60 − €50) = €10. So, €10 is the 
minimum price of the American put.
The call result leads us to a somewhat surprising conclusion. With the exception 
of what happens at expiration when American and European calls are effectively the 
same and both worth the exercise value, an American call is always worth more in 
the market than exercised. That means that an American call will never be exercised 
early. This result is probably not intuitive.
Consider a deep in-  the- money call. One might think that if the holder expected

the underlying to not increase any further, exercise might be justified. Yet, we said the 
call would sell for more in the market than its exercise value. What is the rationale? 
If the investor thinks the underlying will not go up any further and thus expects no 
further gains from the option, why would she prefer the underlying? Would the investor 
be happier holding the underlying, which she believes is not expected to increase? 
Moreover, she would tie up more funds exercising to acquire the underlying than if 
she just held on to the option or, better yet, sold it to another investor.
So far, however, we have left out a possible factor that can affect early exercise. 
Suppose the underlying is a stock and pays dividends. When a stock goes ex-  dividend, 
its price instantaneously falls. Although we will omit the details, an investor holding 
a call option may find it worthwhile to exercise the call just before the stock goes

ex- dividend. The capture of the dividend, thereby avoiding the ex-  dividend drop in 
the price of the underlying, can make early exercise worthwhile. If the underlying is 
a bond, coupon interest can also motivate early exercise. But if there are significant 
carrying costs, the motivation for early exercise is weakened. Storage costs lend a 
preference for owning the option over owning the underlying.
Because the minimum value of an American put exceeds the minimum value of 
the European put, there is a much stronger motivation for early exercise. Suppose 
you owned an American put on a stock that is completely bankrupt, with a zero stock 
price and no possibility of recovery. You can either wait until expiration and capture 
its exercise value of Max(0, X – ST) = Max(0, X – 0) = Max(0, X) = X, or you can capture 
that value by exercising now. Obviously now is better. As it turns out, however, the 
underlying does not need to go all the way to zero. There is a critical point at which

a put is so deep in-  the- money that early exercise is justified. This rationale works 
differently for a call. A deep in-  the- money put has a limit to its ultimate value. It can 
get no deeper than when the underlying goes to zero. For a call, there is no limit to 
its moneyness because the underlying has no upper limit to its price.
Although dividends and coupon interest encourage early exercise for calls, they 
discourage early exercise for puts. The loss from the decline in the price of the under -
lying that is avoided by exercising a call just before the decline works to the benefit of 
a put holder. Therefore, if a put holder were considering exercising early, he would be 
better off waiting until right after the dividend or interest were paid. Carrying costs 
on the underlying, which discourage exercise for calls, encourage exercise for puts.
At this point, we cannot determine the critical prices at which American options

are best exercised early. We require more knowledge and experience with option 
pricing models, which is covered in more advanced material.

Summary 107
EXAMPLE 9   
American Option Pricing
1 With respect to American calls, which of the following statements is most  
accurate?
A American calls should be exercised early if the underlying has reached 
its expected maximum price.
B American calls should be exercised early if the underlying has a lower 
expected return than the risk-  free rate.
C American calls should be exercised early only if there is a dividend or 
other cash payment on the underlying.
2 The effect of dividends on a stock on early exercise of a put is to:
A make early exercise less likely.
B have no effect on early exercise.
C make early exercise more likely.
C is correct. Cash payments on the underlying are the only reason to exercise 
American calls early. Interest rates, the expected return on the underlying, and 
any notion of a maximum price is irrelevant. But note that a dividend does not 
mean that early exercise should automatically be conducted. A dividend is only

a necessary condition to justify early exercise for calls.
A is correct. Dividends drive down the stock price when the dividend is paid. 
Thus, all else being equal, a stock paying dividends has a built-  in force that drives 
down the stock price. This characteristic discourages early exercise, because 
stock price declines are beneficial to holders of puts.
SUMMARY
This reading on derivative pricing provides a foundation for understanding how 
derivatives are valued and traded. Key points include the following:
■■The price of the underlying asset is equal to the expected future price dis -
counted at the risk-  free rate, plus a risk premium, plus the present value of any 
benefits, minus the present value of any costs associated with holding the asset.
■■An arbitrage opportunity occurs when two identical assets or combinations of 
assets sell at different prices, leading to the possibility of buying the cheaper

asset and selling the more expensive asset to produce a risk-  free return without 
investing any capital.
■■In well-  functioning markets, arbitrage opportunities are quickly exploited, and 
the resulting increased buying of underpriced assets and increased selling of 
overpriced assets returns prices to equivalence.

Reading 57 ■ Basics of Derivative Pricing and Valuation 108
■■Derivatives are priced by creating a risk-  free combination of the underlying and 
a derivative, leading to a unique derivative price that eliminates any possibility 
of arbitrage.
■■Derivative pricing through arbitrage precludes any need for determining risk 
premiums or the risk aversion of the party trading the option and is referred to 
as risk-  neutral pricing.
■■The value of a forward contract at expiration is the value of the asset minus the 
forward price.
■■The value of a forward contract prior to expiration is the value of the asset 
■■The forward price, established when the contract is initiated, is the price agreed 
to by the two parties that produces a zero value at the start.
■■Costs incurred and benefits received by holding the underlying affect the for -
ward price by raising and lowering it, respectively.

■■Futures prices can differ from forward prices because of the effect of interest 
rates on the interim cash flows from the daily settlement.
■■Swaps can be priced as an implicit series of off-  market forward contracts, 
whereby each contract is priced the same, resulting in some contracts being 
positively valued and some negatively valued but with their combined value 
equaling zero.
■■At expiration, a European call or put is worth its exercise value, which for calls 
is the greater of zero or the underlying price minus the exercise price and for 
puts is the greater of zero and the exercise price minus the underlying price.
■■European calls and puts are affected by the value of the underlying, the exercise 
price, the risk-  free rate, the time to expiration, the volatility of the underlying, 
and any costs incurred or benefits received while holding the underlying.
■■Option values experience time value decay, which is the loss in value due to the

passage of time and the approach of expiration, plus the moneyness and the 
volatility.
■■The minimum value of a European call is the maximum of zero and the under -
lying price minus the present value of the exercise price.
■■The minimum value of a European put is the maximum of zero and the present 
value of the exercise price minus the price of the underlying.
■■European put and call prices are related through put–call parity, which specifies 
that the put price plus the price of the underlying equals the call price plus the 
■■European put and call prices are related through put–call–forward parity, which 
shows that the put price plus the value of a risk-  free bond with face value equal 
to the forward price equals the call price plus the value of a risk-  free bond with 
face value equal to the exercise price.
■■The values of European options can be obtained using the binomial model,

which specifies two possible prices of the asset one period later and enables the 
construction of a risk-  free hedge consisting of the option and the underlying.
■■American call prices can differ from European call prices only if there are cash 
flows on the underlying, such as dividends or interest; these cash flows are the 
only reason for early exercise of a call.
■■American put prices can differ from European put prices, because the right to 
exercise early always has value for a put, which is because of a lower limit on 
the value of the underlying.

Practice Problems 109
1 An arbitrage opportunity is least likely  to be exploited when:
A one position is illiquid.
B the price differential between assets is large.
C the investor can execute a transaction in large volumes.
2 An arbitrageur will most likely  execute a trade when:
A transaction costs are low.
B costs of short-  selling are high.
C prices are consistent with the law of one price.
3 An arbitrage transaction generates a net inflow of funds:
A throughout the holding period.
B at the end of the holding period.
C at the start of the holding period.
4 The price of a forward contract:
A is the amount paid at initiation.
B is the amount paid at expiration.
C fluctuates over the term of the contract.
5 Assume an asset pays no dividends or interest, and also assume that the asset 
does not yield any non-  financial benefits or incur any carrying cost. At initia -
tion, the price of a forward contract on that asset is:
A lower than the value of the contract.

B equal to the value of the contract.
C greater than the value of the contract.
6 With respect to a forward contract, as market conditions change:
A only the price fluctuates.
B only the value fluctuates.
C both the price and the value fluctuate.
7 The value of a forward contract at expiration is:
A positive to the long party if the spot price is higher than the forward price.
B negative to the short party if the forward price is higher than the spot price.
C positive to the short party if the spot price is higher than the forward price.
8 At the initiation of a forward contract on an asset that neither receives benefits 
nor incurs carrying costs during the term of the contract, the forward price is 
equal to the:
A spot price.
B future value of the spot price.
C present value of the spot price.
9 Stocks BWQ and ZER are each currently priced at $100 per share. Over the 
next year, stock BWQ is expected to generate significant benefits whereas stock

ZER is not expected to generate any benefits. There are no carrying costs asso -
ciated with holding either stock over the next year. Compared with ZER, the 
one-  year forward price of BWQ is most likely :

Reading 57 ■ Basics of Derivative Pricing and Valuation 110
A lower.
B the same.
C higher.
10 If the net cost of carry of an asset is positive, then the price of a forward con -
tract on that asset is most likely :
A lower than if the net cost of carry was zero.
B the same as if the net cost of carry was zero.
C higher than if the net cost of carry was zero.
11 If the present value of storage costs exceeds the present value of its convenience 
yield, then the commodity’s forward price is most likely :
A less than the spot price compounded at the risk-  free rate.
B the same as the spot price compounded at the risk-  free rate.
C higher than the spot price compounded at the risk-  free rate.
12 Which of the following factors most likely  explains why the spot price of a com -
modity in short supply can be greater than its forward price?
A Opportunity cost
B Lack of dividends
C Convenience yield
13 When interest rates are constant, futures prices are most likely :
A less than forward prices.

B equal to forward prices.
C greater than forward prices.
14 In contrast to a forward contract, a futures contract:
A trades over-  the- counter.
B is initiated at a zero value.
C is marked-  to- market daily.
15 To the holder of a long position, it is more desirable to own a forward contract 
than a futures contract when interest rates and futures prices are:
A negatively correlated.
B uncorrelated.
C positively correlated.
16 The value of a swap typically:
A is non-  zero at initiation.
B is obtained through replication.
C does not fluctuate over the life of the contract.
17 The price of a swap typically:
A is zero at initiation.
B fluctuates over the life of the contract.
C is obtained through a process of replication.
18 The value of a swap is equal to the present value of the:
A fixed payments from the swap.
B net cash flow payments from the swap.
C underlying at the end of the contract.

19 A European call option and a European put option are written on the same 
underlying, and both options have the same expiration date and exercise price. 
At expiration, it is possible that both options will have:
A negative values.
B the same value.
C positive values.
20 At expiration, a European put option will be valuable if the exercise price is:
A less than the underlying price.
B equal to the underlying price.
C greater than the underlying price.
21 The value of a European call option at expiration is the greater of zero or the:
A value of the underlying.
B value of the underlying minus the exercise price.
C exercise price minus the value of the underlying.
22 For a European call option with two months until expiration, if the spot price is 
below the exercise price, the call option will most likely  have:
A zero time value.
B positive time value.
C positive exercise value.
23 When the price of the underlying is below the exercise price, a put option is:
A in- the- money.

B at- the- money.
C out- of- the- money.
24 If the risk-  free rate increases, the value of an in-  the- money European put option 
will most likely :
A decrease.
B remain the same.
C increase.
25 The value of a European call option is inversely related to the:
A exercise price.
B time to expiration.
C volatility of the underlying.
26 The table below shows three European call options on the same underlying:
Time to Expiration Exercise Price
Option 1 3 months $100
Option 2 6 months $100
Option 3 6 months $105
 The option with the highest value is most likely :
A Option 1.
B Option 2.
C Option 3.
27 The value of a European put option can be either directly or inversely related to 
the:

Reading 57 ■ Basics of Derivative Pricing and Valuation 112
28 Prior to expiration, the lowest value of a European put option is the greater of 
zero or the:
A exercise price minus the value of the underlying.
B present value of the exercise price minus the value of the underlying.
C value of the underlying minus the present value of the exercise price.
29 A European put option on a dividend-  paying stock is most likely  to increase if 
there is an increase in:
A carrying costs.
B the risk-  free rate.
C dividend payments.
30 Based on put-  call parity, a trader who combines a long asset, a long put, and a 
short call will create a synthetic:
A long bond.
B fiduciary call.
C protective put.
31 Which of the following transactions is the equivalent of a synthetic long call 
position?
B Long asset, long put, short bond
C Short asset, long call, long bond

32 Which of the following is least likely  to be required by the binomial option pric -
ing model?
A Spot price
B Two possible prices one period later
C Actual probabilities of the up and down moves
33 An at-  the- money American call option on a stock that pays no dividends has 
three months remaining until expiration. The market value of the option will 
most likely  be:
A less than its exercise value.
B equal to its exercise value.
C greater than its exercise value.
34 At expiration, American call options are worth:
A less than European call options.
B the same as European call options.
C more than European call options.
35 Which of the following circumstances will most likely  affect the value of an 
American call option relative to a European call option?
A Dividends are declared
B Expiration date occurs
C The risk-  free rate changes
36 Combining a protective put with a forward contract generates equivalent out -
comes at expiration to those of a:
A fiduciary call.

B long call combined with a short asset.
C forward contract combined with a risk-  free bond.

Reading 57 ■ Basics of Derivative Pricing and Valuation 114
SOLUTIONS
1 A is correct. An illiquid position is a limit to arbitrage because it may be diffi -
cult to realize gains of an illiquid offsetting position. A significant opportunity 
arises from a sufficiently large price differential or a small price differential that 
can be employed on a very large scale.
2 A is correct. Some arbitrage opportunities represent such small price discrepan -
cies that they are only worth exploiting if the transaction costs are low. An arbi -
trage opportunity may require short-  selling assets at costs that eliminate any 
profit potential. If the law of one price holds, there is no arbitrage opportunity.
3 C is correct. Arbitrage is a type of transaction undertaken when two assets or 
portfolios produce identical results but sell for different prices. A trader buys 
the asset or portfolio with the lower price and sells the asset or portfolio with

the higher price, generating a net inflow of funds at the start of the holding 
period. Because the two assets or portfolios produce identical results, a long 
position in one and short position in the other means that at the end of the 
holding period, the payoffs offset. Therefore, there is no money gained or lost at 
the end of the holding period, so there is no risk.
4 B is correct. The forward price is agreed upon at the start of the contract and is 
the fixed price at which the underlying will be purchased (or sold) at expiration. 
Payment is made at expiration. The value of the forward contract may change 
over time, but the forward price does not change.
5 C is correct. The price of a forward contract is a contractually fixed price, 
established at initiation, at which the underlying will be purchased (or sold) at 
expiration. The value of a forward contract at initiation is zero; therefore, the 
forward price is greater than the value of the forward contract at initiation.

6 B is correct. The value of the forward contract, unlike its price, will adjust as 
market conditions change. The forward price is fixed at initiation.
7 A is correct. When a forward contract expires, if the spot price is higher than 
the forward price, the long party profits from paying the lower forward price 
for the underlying. Therefore, the forward contract has a positive value to the 
long party and a negative value to the short party. However, if the forward price 
is higher than the spot price, the short party profits from receiving the higher 
forward price (the contract value is positive to the short party and negative to 
the long party).
8 B is correct. At initiation, the forward price is the future value of the spot price 
(spot price compounded at the risk-  free rate over the life of the contract). If the 
forward price were set to the spot price or the present value of the spot price, 
it would be possible for one side to earn an arbitrage profit by selling the asset

and investing the proceeds until contract expiration.
9 A is correct. The forward price of each stock is found by compounding the spot 
price by the risk-  free rate for the period and then subtracting the future value of 
any benefits and adding the future value of any costs. In the absence of any ben -
efits or costs, the one-  year forward prices of BWQ and ZER should be equal. 
After subtracting the benefits related to BWQ, the one-  year forward price of 
BWQ is lower than the one-  year forward price of ZER.
10 A is correct. An asset’s forward price is increased by the future value of any 
costs and decreased by the future value of any benefits: F0(T) = S0(1 + r)T – (γ 
– θ)(1 + r)T. If the net cost of carry (benefits less costs) is positive, the forward 
price is lower than if the net cost of carry was zero.

Solutions 115
11 C is correct. When a commodity’s storage costs exceed its convenience yield 
benefits, the net cost of carry (benefits less costs) is negative. Subtracting this 
negative amount from the spot price compounded at the risk-  free rate results in 
an addition to the compounded spot price. The result is a commodity forward 
price which is higher than the spot price compounded. The commodity’s for -
ward price is less than the spot price compounded when the convenience yield 
benefits exceed the storage costs and the commodity’s forward price is the same 
as the spot price compounded when the costs equal the benefits.
12 C is correct. The convenience yield is a benefit of holding the asset and gener -
ally exists when a commodity is in short supply. The future value of the con -
venience yield is subtracted from the compounded spot price and reduces the 
commodity’s forward price relative to it spot price. The opportunity cost is the

risk-  free rate. In the absence of carry costs, the forward price is the spot price 
compounded at the risk-  free rate and will exceed the spot price. Dividends are 
benefits that reduce the forward price but the lack of dividends has no effect on 
the spot price relative to the forward price of a commodity in short supply.
13 B is correct. When interest rates are constant, forwards and futures will likely 
have the same prices. The price differential will vary with the volatility of 
interest rates. In addition, if futures prices and interest rates are uncorrelated, 
forward and futures prices will be the same. If futures prices are positively 
correlated with interest rates, futures contracts are more desirable to holders 
of long positions than are forwards. This is because rising prices lead to future 
profits that are reinvested in periods of rising interest rates, and falling prices 
lead to losses that occur in periods of falling interest rates. If futures prices are

negatively correlated with interest rates, futures contracts are less desirable to 
holders of long positions than are forwards. The more desirable contract will 
tend to have the higher price.
14 C is correct. Futures contracts are marked-  to- market on a daily basis. The 
accumulated gains and losses from the previous day’s trading session are 
deducted from the accounts of those holding losing positions and transferred to 
the accounts of those holding winning positions. Futures contracts trade on an 
exchange, forward contracts are over-  the- counter transactions. Typically both 
forward and futures contracts are initiated at a zero value.
15 A is correct. If futures prices and interest rates are negatively correlated, for -
wards are more desirable to holders of long positions than are futures. This is 
because rising prices lead to futures profits that are reinvested in periods of fall -
ing interest rates. It is better to receive all of the cash at expiration under such

conditions. If futures prices and interest rates are uncorrelated, forward and 
futures prices will be the same. If futures prices are positively correlated with 
interest rates, futures contracts are more desirable to holders of long positions 
than are forwards.
16 B is correct. Valuation of the swap during its life appeals to replication and 
the principle of arbitrage. Valuation consists of reproducing the remaining 
payments on the swap with other transactions. The value of that replication 
strategy is the value of the swap. The swap price is typically set such that the 
swap contract has a value of zero at initiation. The value of a swap contract will 
change during the life of the contract as the value of the underlying changes in 
value.
17 C is correct. Replication is the key to pricing a swap. The swap price is deter -
mined at initiation by replication. The value (not the price) of the swap is typi -
cally zero at initiation and the fixed swap price is typically determined such that

Reading 57 ■ Basics of Derivative Pricing and Valuation 116
18 B is correct. The principal of replication articulates that the valuation of a swap 
is the present value of all the net cash flow payments from the swap, not simply 
the present value of the fixed payments of the swap or the present value of the 
underlying at the end of the contract.
19 B is correct. If the underlying has a value equal to the exercise price at expira -
tion, both options will have zero value since they both have the same exercise 
price. For example, if the exercise price is $25 and at expiration the underlying 
price is $25, both the call option and the put option will have a value of zero. 
The value of an option cannot fall below zero. The holder of an option is not 
obligated to exercise the option; therefore, the options each have a minimum 
value of zero. If the call has a positive value, the put, by definition, must have a 
zero value and vice versa. Both cannot have a positive value.

20 C is correct. A European put option will be valuable at expiration if the exer -
cise price is greater than the underlying price. The holder can put (deliver) the 
underlying and receive the exercise price which is higher than the spot price. 
A European put option would be worthless if the exercise price was equal to or 
less than the underlying price.
21 B is correct. The value of a European call option at expiration is the greater of 
zero or the value of the underlying minus the exercise price.
22 B is correct. A European call option with two months until expiration will typi -
cally have positive time value, where time value reflects the value of the uncer -
tainty that arises from the volatility in the underlying. The call option has a zero 
exercise value if the spot price is below the exercise price. The exercise value 
of a European call option is Max(0, St – X ), where St is the current spot price at 
time t and X is the exercise price.

23 A is correct. When the price of the underlying is below the exercise price for a 
put, the option is said to be in-  the- money. If the price of the underlying is the 
same as the exercise price, the put is at-  the- money and if it is above the exercise 
price, the put is out-  of- the- money.
24 A is correct. An in-  the- money European put option decreases in value with an 
increase in the risk-  free rate. A higher risk-  free rate reduces the present value of 
any proceeds received on exercise.
25 A is correct. The value of a European call option is inversely related to the exer -
cise price. A lower exercise price means there are more potential outcomes at 
which the call expires in-  the- money. The option value will be greater the lower 
the exercise price. For a higher exercise price, the opposite is true. Both the 
time to expiration and the volatility of the underlying are directly (positively) 
related to the value of a European call option.

26 B is correct. The value of a European call option is inversely related to the exer -
cise price and directly related to the time to expiration. Option 1 and Option 2 
have the same exercise price; however, Option 2 has a longer time to expiration. 
Consequently, Option 2 would likely have a higher value than Option 1. Option 
2 and Option 3 have the same time to expiration; however, Option 2 has a lower 
exercise price. Thus, Option 2 would likely have a higher value than Option 3.
27 B is correct. The value of a European put option can be either directly or 
indirectly related to time to expiration. The direct effect is more common, but 
the inverse effect can prevail the longer the time to expiration, the higher the 
risk-  free rate, and the deeper in-  the- money is the put. The value of a European 
put option is directly related to the exercise price and the volatility of the 

Solutions 117
28 B is correct. Prior to expiration, the lowest value of a European put is the 
greater of zero or the present value of the exercise price minus the value of the 
29 C is correct. Payments, such as dividends, reduce the value of the underlying 
which increases the value of a European put option. Carrying costs reduce the 
value of a European put option. An increase in the risk-  free interest rate may 
decrease the value of a European put option.
30 A is correct. A long bond can be synthetically created by combining a long 
asset, a long put, and a short call. A fiduciary call is created by combining a long 
call with a risk free bond. A protective put is created by combining a long asset 
with a long put.
31 B is correct. According to put−call parity, a synthetic call can be constructed by 
combining a long asset, long put, and short bond positions.
32 C is correct. The actual probabilities of the up and down moves in the under -

lying do not appear in the binomial option pricing model, only the pseudo or 
“risk-  neutral” probabilities. Both the spot price of the underlying and two possi -
ble prices one period later are required by the binomial option pricing model.
33 C is correct. Prior to expiration, an American call option will typically have 
a value in the market that is greater than its exercise value. Although the 
American option is at-  the- money and therefore has an exercise value of zero, 
the time value of the call option would likely lead to the option having a positive 
market value.
34 B is correct. At expiration, the values of American and European call options 
are effectively the same; both are worth the greater of zero and the exercise 
value.
35 A is correct. When a dividend is declared, an American call option will have 
a higher value than a European call option because an American call option 
holder can exercise early to capture the value of the dividend. At expiration,

both types of call options are worth the greater of zero and the exercise value. A 
change in the risk-  free rate does not affect the relative values of American and 
European call options.
36 A is correct. Put−call forward parity demonstrates that the outcome of a pro -
tective put with a forward contract (long put, long risk-  free bond, long forward 
contract) equals the outcome of a fiduciary call (long call, long risk-  free bond). 
The outcome of a protective put with a forward contract is also equal to the 
outcome of a protective put with asset (long put, long asset).

Alternative Investments
Study Session 19 Alternative Investments
The candidate should be able to demonstrate a working knowledge of alternative 
investments, including hedge funds, private equity, real estate, commodities, and 
infrastructure. The candidate should be able to describe key attributes and consider -
ations in adding these investments to a portfolio.
Investors often turn to alternative investments for potential diversification benefits 
and higher returns. As a result, alternative investments now represent meaningful 
allocations in many institutional and private wealth portfolios. Although the category 
of “alternative investments” is not always clearly or precisely defined, alternative 
investments often have a number of characteristics in common. These include lower 
levels of liquidity, transparency, and disclosure vs. traditional asset classes (equity, 
fixed income), more complex legal structures, and performance-  based compensation

This study session provides an overview of the more widely used alternative invest -
ments, including hedge funds, private equity, real estate, commodities, and infrastruc -
ture investment. Each is examined with emphasis on their distinguishing character -
istics, considerations for valuation, and potential benefits and risks. Similarities and 
differences with traditional investments (stocks, bonds) are also considered.
Reading 58 Introduction to Alternative Investments  
by Terri Duhon, George Spentzos, CFA, FSIP , and 
Scott D. Stewart, CFAALTE rNATI vE INvESTMENTS
19

Introduction to Alternative Investments
by Terri Duhon, George Spentzos, CFA, FSIP , and Scott D. Stewart, CFA
Terri Duhon is at Said Business School, Oxford University, CHAPS Co, and Morgan 
Stanley International (United Kingdom). George Spentzos, CFA, FSIP (United Kingdom). 
Scott D. Stewart, CFA, is at Cornell University (USA).
a. compare alternative investments with traditional investments; 
b. describe categories of alternative investments;
c. describe potential benefits of alternative investments in the 
context of portfolio management;
d. describe hedge funds, private equity, real estate, commodities, 
infrastructure, and other alternative investments, including, as 
applicable, strategies, sub-  categories, potential benefits and risks, 
fee structures, and due diligence;
e. describe, calculate, and interpret management and incentive fees 
and net-  of- fees returns to hedge funds;

f. describe issues in valuing and calculating returns on hedge funds, 
private equity, real estate, commodities, and infrastructure;
g. describe risk management of alternative investments.
Assets under management in vehicles classified as alternative investments have grown 
rapidly since the mid-  1990s. This growth has largely occurred because of interest in 
these investments by institutions, such as endowment and pension funds, as well as 
high-  net- worth individuals seeking diversification and return opportunities. Alternative 
investments are perceived to behave differently from traditional investments. Investors 
may seek either absolute return or relative return.1rEADING
58
CFA Institute acknowledges the research assistance of John W. Stewart, CFA, on the data analysis in this 
reading.

Reading 58 ■ Introduction to Alternative Investments 124
Some investors hope alternative investments will provide positive returns through -
out the economic cycle; this goal is an absolute return objective. Alternative investments 
are not free of risk, however, and their returns may be negative and/or correlated with 
other investments, including traditional investments, especially in periods of finan -
cial crisis. Some investors in alternative investments have a relative return objective. 
A relative return objective, which is often the objective of portfolios of traditional 
investment, seeks to achieve a return relative to an equity or fixed-  income benchmark.
This reading is organized as follows. Section 2 describes alternative investments’ 
basic characteristics and categories; general strategies of alternative investment 
portfolio managers; the role of alternative investments in a diversified portfolio; and

investment structures used to provide access to alternative investments. Sections 3 
through 7 describe features of hedge funds, private equity, real estate, commodities, 
and infrastructure, respectively, along with issues in calculating returns to and valuation 
of each.1 Section 8 briefly describes other alternative investments. Section 9 provides 
an overview of risk management, including due diligence, of alternative investments. 
A summary and practice problems conclude the reading.
ALTERNATIVE INVESTMENTS
Alternative investments fall outside of the definition of long-  only, publicly traded 
investments in stocks, bonds, and cash (often referred to as traditional investments). 
In other words, they are alternatives to long-  only positions in stocks, bonds, and 
cash. The terms “traditional” and “alternatives” should not be construed to imply 
that alternatives are necessarily uncommon and/or relatively recent additions to the

investment universe. Alternative investments include investments in assets such as 
real estate and commodities, which are arguably two of the oldest investment classes.
Alternative investments also include non-  traditional approaches to investing within 
special vehicles, such as private equity funds, hedge funds, and some exchange-  traded 
funds (ETFs). These funds may give the manager flexibility to use derivatives and 
leverage, make investments in illiquid assets, and take short positions. The assets in 
which these vehicles invest can include traditional assets (stocks, bonds, and cash) as 
well as other assets. Management of alternative investments is typically active. Passive 
versions of commodities and real estate investments are available, but hedge funds, 
private equity, and infrastructure investments are almost always actively managed. 
Alternative investments, particularly investments through special vehicles, are often

characterized by high fees, concentrated portfolios, high use of leverage, and restric -
tions on fund redemptions.
Several other characteristics are common to many, but not all, alternative invest -
ments. An alternative investment might not be expected to have all the following 
characteristics but will typically be expected to have some of them:
■■Illiquidity of underlying investments
■■Narrow manager specialization
■■Low correlation of returns with those of traditional investments
■■Less regulation and less transparency than traditional investments
■■Limited and potentially problematic historical risk and return data
■■Unique legal and tax considerations2
1 CFA Institute acknowledges the contributions of Michael Underhill of Capital Innovations, LLC, to the 
section on infrastructure.

Alternative Investments 125
Although assets under management (AUM) in alternative investments have grown 
rapidly, they remain smaller than either fixed-  income or equity investable assets, as 
illustrated in Exhibit 1.
Exhibit 1   Global Assets Under Management, December 2014
Fixed Income
39%
Equities
36%Alternatives
25%
Private
Equity
4%Hedge
Funds
3%Commodity
Funds
0.2%Institutionally
Owned Real Estate
3%Commercial
Real Estate
15%
Sources:  Based on data from Boston Consulting Group and DTZ Research.
Institutions and high-  net- worth individuals have been at the forefront of those 
investing in alternative investments with the expectation of diversifying their portfo -
lios and enhancing their risk–return profiles. Their hopes that alternative investments 
will behave differently from traditional investments and will provide positive absolute 
returns throughout the economic cycle may not be realistic. Alternative investments

are not free of risk, and their returns may be correlated with those of other risky 
investments, especially in periods of financial crisis. During a long historical period, 
the average correlation of returns from alternative investments with those of traditional 
investments may be low, but in any particular period, the correlation can differ from 
the average. During periods of economic crisis, such as late 2008, correlations among 
risky assets can increase dramatically.
Investors must be careful in evaluating the historical record of alternative invest -
ments because reported return data can be problematic. Further, reported returns and 
standard deviations are averages and may not be representative of sub-  periods within 
the reported period or future periods. Many investments, such as direct real estate and 
private equity, are often valued using estimated (appraised) values rather than actual 
market prices for the subject investments. As a result, the volatility of their returns,

as well as the correlation of their returns with the returns of traditional asset classes, 
will tend to be underestimated. Private equity market returns may be estimated using 
the technique proposed by Woodward and Hall (2004) to address data problems with 
historical published indexes, which reflect underlying investments held at cost.2 The 
record of alternative investment universes, such as hedge fund indexes, may be subject 
to a variety of biases, including survivorship and backfill biases.3 Thus, the indexes 
2 This technique involves statistical estimation of quarterly market returns using published fund index 
and securities market index returns.
3 Survivorship bias relates to the inclusion of only “live” investment funds. The returns of funds that have 
been liquidated are excluded. Backfill bias results from including previous return data for funds that enter 
the index. Both biases may result in returns that are artificially high, because survivorship bias most likely

results in the index excluding poorly performing funds and backfill bias most likely results in the index 
including high-  performing funds. Using fund-  of- funds returns (instead of individual funds), as in Exhibit 2, 
reduces the influence of these biases.

Reading 58 ■ Introduction to Alternative Investments 126
may be inherently biased upward. Commodity indexes can be weighted heavily in one 
particular sector, such as oil and gas. Different weightings and constituents in index 
construction can significantly affect the indexes and their results and comparability.
Exhibit 2 shows the historical returns to various investment classes, as well as the 
standard deviations of the returns, based on selected indexes. The indexes were selected 
for their breadth and data quality but may not be fully representative of returns to 
the investment class, and there may be issues with the data. For example, the return 
to the S&P Global REIT (Real Estate Investment Trust) Index may not be represen -
tative of returns to equity investment in real estate through private markets (direct 
ownership of real estate). Private equity and venture capital monthly market-  based 
returns are unavailable, so the returns in Exhibit 2 are modeled using the technique

proposed by Woodward and Hall (2004). Hedge fund returns are based on managed 
funds valuations, not underlying securities prices. The average annual returns and 
standard deviations are shown for three periods: the 25-  year period of Q1 1990 to 
Q4 2014, the period Q4 2007 to Q4 2009, and the most recent 5-  year period of Q1 
2010 to Q4 2014.
Exhibit 2   Alternative Investments Historical Returns and Volatilities
Q1 1990–Q4 2014 Q4 2007–Q4 2009 Q1 2010–Q4 2014
Index Mean St. Dev. Mean St. Dev. Mean St. Dev.
Global stocks 6.9% 16.5% –10.8% 24.2% 10.7% 15.9%
Global bonds 6.3 5.8 6.7 9.0 2.6 4.8
Hedge funds 7.2 6.0 –4.9 8.0 3.4 4.1
Commodities 2.2 21.8 –15.9 32.1 –5.0 18.1
Real estate 10.4 18.1 –17.6 33.8 15.4 17.7
Private equity 15.4 20.3 –10.0 27.8 20.7 19.4
Venture capital 15.0 47.2 –9.5 29.9 33.6 35.3
One-  month Libor 3.42 0.70 1.9 0.5 0.2 0.0
Note : Mean and standard deviation are based on annualized US dollar returns.

Sources:  Global stocks = MSCI All Country World Index (ACWI); Global bonds = Bloomberg Barclays Global Aggregate Index; Hedge 
funds = Hedge Fund Research, Inc. (HFRI) Fund of Funds Composite Index; Commodities = S&P GSCI Commodity Index; Real estate = 
S&P Global REIT Index; Private equity = modeled using Cambridge Associates and S&P Midcap indexes; Venture capital = modeled using 
Cambridge Associates and NASDAQ indexes.
During the 25-  year period, the mean returns to hedge funds, real estate, private 
equity, and venture capital exceeded the mean returns to global stocks and bonds. The 
average standard deviation of all but hedge funds also exceeded the average standard 
deviation of global stocks and bonds. Hedge funds appear to have had a higher aver -
age return and lower standard deviation than global stocks for the 25-  year period, 
but this result may be caused, at least partially, by hedge fund indexes’ reporting

biases. Commodities had the lowest mean return for the 25-  year period and higher 
standard deviation than all but venture capital. The higher mean returns of alterna -
tive investments, except for commodities, compared with stocks and bonds, may be 
because of active managers’ exploitation of less efficiently priced assets, illiquidity 
premiums, and/or account leverage. The higher mean returns may also be the result 
of tax advantages. For example, REITs may not be subject to taxes at the fund level if 
they meet certain conditions.
In a poorly performing economy, the use of leverage and investment in illiquid 
assets may be reasonably expected to lead to poor results. Leveraged investments 
are more sensitive to market conditions than similar unleveraged investments, and

Alternative Investments 127
illiquid assets may be difficult to sell and are exposed to high transaction costs during 
market downturns. From Q4 2007 through Q4 2009, a period categorized as a time of 
financial crisis, the mean returns to alternative investments, other than hedge funds, 
were similar to or even lower than those to global stocks, and the standard deviations 
exceeded those of global stocks. Alternative investments did not provide the desired 
protection during the Q4 2007–Q4 2009 period. It is the long-  term return potential, 
however, that attracts many investors, and real estate, private equity, and venture capital 
performed very well from Q1 2010 through Q4 2014, the five-  year period following 
the financial crisis. During this period, real estate, private equity, and venture capital 
had average annual returns exceeding the average annual return of global stocks. Also 
during this period, hedge funds and commodities average annual returns were less

than the average annual return of global stocks.
The 2015 annual report for the Yale University Endowment provides one investor’s 
reasoning behind the attractiveness of investing in alternatives:
“The heavy [73%] allocation to nontraditional asset classes stems from 
their return potential and diversifying power. Today’s actual and target 
portfolios have significantly higher expected returns than the 1985 portfolio 
with similar volatility. Alternative assets, by their very nature, tend to be 
less efficiently priced than traditional marketable securities, providing an 
opportunity to exploit market inefficiencies through active management. 
The Endowment’s long time horizon is well suited to exploit illiquid, less 
efficient markets such as venture capital, leveraged buyouts, oil and gas, 
timber, and real estate. ”4
The links between this quote and the expected characteristics of alternative invest -
ments are clear: diversifying power (low correlations among returns), higher expected

returns (positive absolute return), and illiquid and potentially less efficient markets. 
These links also highlight the importance of having the ability and willingness to take 
a long-  term perspective. Allocating a portion of an endowment portfolio to alternative 
investments is not unique to Yale. INSEAD, as of August 2015, had allocated 38% of its 
endowment to alternative investments including real estate, hedge funds, and private 
equity and debt. The remaining 62% was invested in traditional financial assets such 
as global stocks and bonds.5 These examples are not to imply that every university 
endowment fund invests in alternative investments, but many do.
High-  net- worth investors have also embraced alternative investments. According 
to the Spectrem Group’s 2014 study of American investors, 42% of investors with 
more than $25 million in assets have invested in hedge funds and 69% of investors 
with more than $125 million have invested in hedge funds. The authors noted that

wealthy investors were choosing alternatives for higher returns and improved diver -
sification.6 The increasing interest in alternative investments by both institutional 
investors and high-  net- worth individuals has resulted in significant growth in each 
category of alternative investments since the beginning of 2000. The following exam -
ples illustrate growth in the categories of private equity, real estate, and commodities 
in the period up to 2015.
■■Global private capital fundraising was approximately $589 billion in 2014, com -
pared with $238 billion in 2000.7
4 http://static1.squarespace.com/static/55db7b87e4b0dca22fba2438/t/578e41ff -
e58c629352d7560a/1468940803516/Yale_Endowment_15.pdf
5 https://www.insead.edu/sites/default/files/assets/dept/give/docs/INSEAD-  Endowment-  Report-  2014-  2015.
pdf
6 http://spectrem.com/Content_Press/december-  3-2014-  press-  release.aspx.
7 Preqin Global Private Equity & Venture Capital Report, 2016.

Reading 58 ■ Introduction to Alternative Investments 128
■■Global REITs grew to $1.8 trillion in market value by September 2015. In 1990, 
the market capitalization of global REITs was less than $10 billion.8
■■The number of new commodity trading advisers (CTAs) averaged 169 annually 
for the five years ending 2013, compared with 37 for the five years ending 2004.9
The enthusiasm for alternative investments was tested during 2008, when assets 
under management in alternative investment declined as losses were incurred and 
investors withdrew funds. However, alternative investments continue to represent a 
significant proportion of the portfolios of pension funds, endowments, foundations, 
and high-  net- worth individuals. By 2012, a resurgence of interest in alternative invest -
ments occurred. The alternative investments available vary in characteristics and 
performance, and suitability for an investor has to be carefully considered.
EXAMPLE 1   
Characteristics of Alternative Investments

Compared with traditional investments, alternative investments are most likely  
to be characterized by high:
A leverage.
C regulation.
Solution:
A is correct. Alternative investments are likely to use more leverage than tra -
ditional investments. Alternative investments are likely to be more illiquid and 
subject to less regulation compared with traditional investments.
2.1 Categories of Alternative Investments
Considering the variety of characteristics common to many alternative investments, it 
is not surprising that no consensus exists on a definitive list of these investments. There 
is even considerable debate as to what represents a category versus a sub-  category of 
alternative investments. For instance, some listings define distressed securities as a 
separate category, whereas others consider distressed securities as a sub-  category of 
the hedge funds and/or private equity categories, or even a subset of high-  yield bond

investing. Similarly, managed futures are sometimes defined as a separate category 
and sometimes as a sub-  category of hedge funds and/or commodities. The following 
list offers one approach to define broad categories of alternative investments. Each 
category is described in detail later in this reading.
■■Hedge funds.  Hedge funds are private investment vehicles that manage port -
folios of securities and derivative positions using a variety of strategies. They 
may use long and short positions, may be highly leveraged, and aim to deliver 
investment performance that is independent of broad market performance.
■■Private equity funds.  Private equity funds generally invest in companies 
(either start-  up or established) that are not listed on a public exchange, or they 
invest in public companies with the intent to take them private. The majority of 
8 https://www.cohenandsteers.com/insights/education/about-  reits and Ernst & Young, Global Real Estate 
Investment Trust Report , 2007.

9 Overview of CTA Fund Industry, Preqin, 2013.

Alternative Investments 129
private equity activity involves leveraged buyouts of established profitable and 
cash-  generative companies with solid customer bases, proven products, and 
high-  quality management. Venture capital , which typically involves investing 
in or providing financing to start-  up or young companies with high growth 
potential, is a small portion of the private equity market.
■■Real estate.  Real estate investments may be in buildings and/or land, including 
timberland and farmland, either directly or indirectly. The growing popular -
ity of securitizations broadened the definition of real estate investing. It now 
includes private commercial real estate equity (e.g., ownership of an office 
building), private commercial real estate debt (e.g., directly issued loans or 
mortgages on commercial property), public real estate equity (e.g., REITs), and 
public real estate debt (e.g., mortgage-  backed securities) investments.

■■Commodities.  Commodities investments may be in physical commodity 
products such as grains, metals, and crude oil, either through owning cash 
instruments, using derivative products, or investing in businesses engaged 
in the production of physical commodities. The main vehicles investors use 
to gain exposure to commodities are commodity futures contracts and funds 
benchmarked to commodity indexes. Commodity indexes are typically based on 
various underlying commodity futures.
■■Infrastructure.  Infrastructure assets are capital-  intensive, long-  lived, real 
assets, such as roads, dams, and schools, which are intended for public use 
and provide essential services. Infrastructure assets may be financed, owned, 
and operated by governments, but increasingly the private sector is investing 
in infrastructure assets. Investors may gain exposure to these assets directly or 
indirectly. Indirect investment vehicles include shares of companies, ETFs, pri -

vate equity funds, listed funds, and unlisted funds that invest in infrastructure.
■■Other.  Other alternative investments may include tangible assets (such as fine 
wine, art, antique furniture and automobiles, stamps, coins, and other collect -
ibles) and intangible assets (such as patents).
2.2 Returns to Alternative Investments
Portfolio managers invest in one of two basic ways to achieve returns: passively or 
actively. Passive managers assume that markets are efficient and focus on beta driv -
ers of return. Beta, a measure of sensitivity relative to a particular market index, is 
a measure of systematic risk.10 Some portfolios of REITs and commodity and infra -
structure ETFs may be passively managed to provide beta exposure to a category of 
alternative investments.
Active managers, whether in alternative or traditional investments, assume that 
inefficiencies exist that may be exploited to earn positive return after adjusting for

beta risk. Alternative investments are generally actively managed. Actively managed 
alternative investment strategies reflect several characteristics that differentiate them 
from long-  only passive investments in traditional assets. Active investment strategies 
(these are not mutually exclusive) can be categorized as follows:
■■Absolute return.  Absolute return strategies seek to generate returns that are 
independent of market returns; theoretically, betas of funds using absolute 
return strategies should be close to zero.11 As a result, with an absolute return 
10 Systematic risk should not be confused with the term “systemic risk, ” which is used in the credit markets 
to mean highly correlated default risk.
11 In practice, most funds have some market exposure.

Reading 58 ■ Introduction to Alternative Investments 130
strategy, there is typically no market index specified to beat. Instead, the formal 
performance objective tends to be stated relative to either a cash rate such as 
Libor, a return exceeding the inflation rate (a real return target), or an absolute, 
nominal return target such as 10%.
■■Market segmentation.  Market segmentation exists when capital can -
not migrate effortlessly from lower expected return areas to higher ones. 
Segmentation typically results from institutional, contractual, or regulatory 
restrictions on traditional asset managers or from differences across investors 
in investment objectives or liabilities. Segmentation brought on by investment 
constraints includes portfolios managed relative to published market indexes, 
limitations on the use of derivatives, and restrictions on the proportion of low-  
quality or non-  domestic securities. Portfolios may also be subject to environ -

mental, social, and governance constraints and mandates. Restrictions on some 
portfolios may provide an opportunity for managers with more flexibility to 
move into higher-  returning segments more quickly than managers with more-  
restricted or more-  conservative portfolios.
■■Concentrated portfolios.  This strategy entails concentrating assets among 
fewer securities, strategies, and/or managers, which results in less diversifica -
tion but may enable an investor to achieve higher returns if these concentrated 
positions outperform the market.
In addition to diversification benefits in a portfolio context, some of the attraction 
of alternative investments seems to be based on expected returns. When considering 
expected returns, however, investors must also factor in the risks associated with 
those returns. Risks can be considered both on a stand-  alone basis and within the 
context of a portfolio. As mentioned earlier, risks for alternative investments include

low liquidity, limited redemption availability and transparency, and the challenge of 
manager diversification.
Returns may be measured relative to stand-  alone risk using risk ratios and explor -
ing return distributions. A commonly reported risk ratio is the Sharpe ratio, which 
equals an investment’s return, net of a risk-  free rate, divided by its return standard 
deviation. The Sharpe ratio is a common measure among the investment community 
because it is easily calculated using historical results. The Sharpe ratio has short -
comings, however. It equally penalizes upside and downside volatility, fails to capture 
non-  symmetric distributions, and may not fully reflect tails in return distributions. 
The return distributions to alternative investments are typically non-  symmetric and 
skewed, making the Sharpe ratio a less than ideal measure. Other risk measures, such 
as those that emphasize downside risk, are also frequently considered.12 A popular

downside measure is the Sortino ratio, which uses a similar numerator to the Sharpe 
ratio: mean realized return less target return. If the target return is specified as the 
risk-  free rate of return, the Sortino ratio’s numerator is the same as the Sharpe ratio’s. 
The Sortino ratio replaces, in the denominator, the standard deviation of returns with 
a downside deviation that is the standard deviation of the returns that are below the 
target return.
Sharpe and Sortino ratios for traditional and alternative investments, based on the 
same information used in Exhibit 2, are shown in Panel A of Exhibit 3. In calculating 
the Sortino ratio, the target return was assumed to be 0%. It should again be noted 
that the reported or available historical return data used may be unreliable and/or 
not representative of the return data for the investment class.
12 The Sharpe ratio is discussed in greater detail in the reading “Statistical Concepts and Market Returns. ”

Several other risk measures are used in practice and are discussed throughout the CFA Progrmam curriculum.

Alternative Investments 131
Other downside risk measures, such as the chance of losing a certain amount of 
money in a given period, are also used in practice. Panel B of Exhibit 3 includes some 
other measures indicative of downside risk: the frequencies of monthly returns less 
than –1%, –5%, and –10% from 1990 through 2014, and in the right-  hand column, 
the worst return reported in a month.
Exhibit 3   
Sharpe Ratios, Sortino Ratios, and Downside Risk 
Measures, Based on 1990–2014 Returns
Panel A  Sharpe and Sortino Ratios (using annualized 
returns)
Index Sharpe Ratio Sortino Ratio
Global stocks 0.21 0.43
Global bonds 0.49 1.09
Hedge funds 0.63 0.74
Commodities –0.06 0.12
Real estate 0.38 0.79
Private equity 0.59 1.19
Venture capital 0.25 0.63
Panel B  Downside Frequencies
Frequency of Monthly Return  
Less Than…Worst 
Monthly 
Return Index –1% –5% –10%
Global stocks 32.0% 9.3% 1.7% –19.8%
Global bonds 14.7 0.0 0.0 –3.8
Hedge funds 12.3 1.0 0.0 –7.5
Commodities 37.7 17.0 5.3 –28.2

Real estate 27.7 7.0 2.3 –30.5
Private equity 29.3 8.7 2.0 –22.3
Venture capital 36.0 23.7 13.7 –40.5
Sharpe ratios (using Libor as a proxy for the risk-  free rate) indicate that based on 
reported data, during the 25-  year period from 1990 through 2014, hedge funds offered 
the best risk–return trade-  off and commodities the worst. The Sortino ratio, however, 
using a target return of 0%, indicates that private equity and global bonds offered 
superior risk–return trade-  offs during this period. Global fixed-  income investments 
displayed the most attractive downside risk profile (see Panel B), in part as a result of

Reading 58 ■ Introduction to Alternative Investments 132
the bond bull market during this 25-  year period. Venture capital displayed the least 
attractive downside risk profile, but its higher reported return (see Exhibit 2) results in 
higher Sharpe and Sortino ratios than global stocks and commodities during the period.
The Sharpe ratio and downside risk measures do not take into account the poten -
tially low level of correlation of alternative investments with traditional investments. 
A less-  than-  perfect correlation between investments reduces the standard deviation 
of a diversified portfolio below the weighted average of the standard deviations of the 
investments. Risk in the portfolio context is discussed in the next section.
2.3 Portfolio Context: Integration of Alternative Investments 
with Traditional Investments
A key motivation cited for investing in alternative investments is their diversifying

potential: Investors perceive an opportunity to improve the risk–return relationship 
within the portfolio context. Given the historical return, volatility, and correlation 
profiles of alternative investments, combining a portfolio of alternative investments 
with a portfolio of traditional investments potentially improves the overall portfolio’s 
risk–return profile. The correlation between some categories of alternative investments 
and traditional investments has historically, over long periods, been low or at least less 
than perfect, providing diversification opportunities. The historically higher returns 
by many categories of alternative investments compared with traditional investments 
result in potentially higher returns to a portfolio containing alternative investments, 
and the less-  than-  perfect correlation with traditional investments results in portfolio 
risk (standard deviation) being less than a weighting of the standard deviations. In

identifying the appropriate allocation to alternative investments, however, an invest -
ment manager is likely to consider more than mean return and average standard devi -
ation of returns. When considering potential portfolio combinations, the manager’s 
analysis may include historical downside frequencies and worst return in a month for 
potential portfolio combinations.
The purported diversification benefits and improved risk–return contributions 
of alternative investments to portfolios explain why institutional investors such as 
pension funds may allocate a portion of their portfolios to alternative investments. 
There are challenges, however, including obtaining reliable measures of risk and 
return, identifying the appropriate allocation, and selecting portfolio managers. It is 
important to note that expected diversification benefits from alternative investments 
are not always realized, including sometimes when they are most needed. Correlations

between risky investments increase during periods of market stress and can approach 
1.0 during financial crises.
2.4 Investment Structures
A common structure for many alternative investments, such as hedge funds and pri -
vate equity funds, is a partnership in which the fund manager is the general partner  
(GP) and investors are limited partners  (LPs). Limited partnerships are restricted to 
investors who are expected to understand and to be able to assume the risks associated 
with the investments. Fund investments, because they are not offered to the general 
public, may be unregulated or less regulated than offerings to the general public.13 
The GP runs the business and theoretically bears unlimited liability for anything that 
might go wrong. Because most individuals are unwilling to bear unlimited liability, 
13 In the United States, the US Securities Act of 1933 regulates the process by which investment securities

are offered. Most alternative investment funds are structured as “private placements, ” which are defined 
within Regulation D of the Securities Act and sometimes called “Reg D Offerings. ”

Hedge Funds 133
the GP is usually a limited liability corporation. Limited partners own a fractional 
interest in the partnership based on their investment and as agreed to by the partners. 
An LP’s fractional interest is often referred to as his share of the partnership. These 
partnerships are frequently located in tax-  efficient locations, which benefit both the 
GP and the LPs. Funds set up as private investment partnerships typically have a limit 
on the number of LPs.14
Funds are generally structured with a management fee  based on assets under 
management (sometimes called the base fee) plus an incentive fee  (or performance 
fee) based on realized profits. Sometimes, the fee structure specifies that the incentive 
fee is earned only after the fund achieves a specified return known as a hurdle rate. 
Fee calculations also take into account high-  water marks , which reflect the highest 
cumulative return used to calculate an incentive fee. It is the highest value, net of fees,

that the fund has reached. The use of high-  water marks protects clients from paying 
twice for the same performance. Many alternative investment funds, including hedge 
funds, use this basic partnership and fee structure. Fee structures are discussed in 
more detail later in the reading.
HEDGE FUNDS
In 1949, Alfred Winslow Jones, a sociologist investigating fundamental and technical 
research to forecast the stock market for Fortune  magazine, set up an investment fund 
with himself as GP . The fund followed three key tenets: (1) Always maintain short 
positions, (2) always use leverage, and (3) charge only an incentive fee of 20% of profits 
with no fixed fees. Jones called his portfolio a “hedged” fund (eventually shortened to 
“hedge fund”) because he had short positions to offset his long positions in the stock 
market. Theoretically, the overall portfolio was hedged against major market moves.
Although Jones’ original three tenets still have some relevance to the hedge fund

industry, not all hedge funds maintain short positions and/or use leverage, and most 
hedge funds have some non-  incentive fees. A contemporary hedge fund may have 
the following characteristics:
■■It is an aggressively managed portfolio of investments across asset classes and 
regions that is leveraged, takes long and short positions, and/or uses derivatives.
■■It has a goal of generating high returns, either in an absolute sense or over a 
specified market benchmark, and it has few, if any, investment restrictions.
■■It is set up as a private investment partnership open to a limited number of 
investors willing and able to make a large initial investment.
■■It imposes restrictions on redemptions . Investors may be required to keep 
their money in the hedge fund for a minimum period (referred to as a lockup 
period ) before they are allowed to make withdrawals or redeem shares. 
Investors may be required to give notice of their intent to redeem; the notice

period  is typically 30 to 90 days in length. Also, investors may be charged a fee 
to redeem shares.3
14 Because of the inherent risk involved in alternative investments, investment is typically restricted to a 
specified number of investors meeting certain criteria. The number and criteria can be specified by regu -
lation or set by the fund. In the United States, the number depends on whether funds target “ Accredited 
Investors ” or “ Qualified Purchasers ” (as defined by the Investment Company Act of 1940, Sections 3(c) 
1 and 7, respectively). A fund can have no more than 100 Accredited Investors (individuals with at least 
$1 million and institutions with at least $5 million in investable assets) or no more than 500 Qualified 
Purchasers (individuals with at least $5 million and institutions with at least $25 million in investable assets).

Reading 58 ■ Introduction to Alternative Investments 134
Investors’ willingness to invest in hedge funds, despite the restrictions on redemp -
tions, is largely because of the reported returns of some hedge funds and their 
perceived low correlation with traditional investments. The positive performance of 
many funds in the early 2000s, when other investments had declined, supported the 
diversification potential of hedge funds in a portfolio. The growth of interest in hedge 
funds as investments led to the emergence of funds of hedge funds.
Funds of hedge funds  are funds that hold a portfolio of hedge funds. They make 
hedge funds accessible to smaller investors while allowing those investors to be 
diversified to some extent among hedge funds. Also, funds of hedge funds (commonly 
shortened to “ funds of funds ”) are assumed to have some expertise in conducting due 
diligence on hedge funds and may be able to negotiate better redemption terms than

individual investors can. Funds of hedge funds invest in numerous hedge funds and 
may diversify across fund strategies, investment regions, and management styles. The 
distinction between a single hedge fund and a fund of hedge funds is not necessarily 
clear-  cut because many hedge funds invest in other hedge funds.
Hedge fund managers are less restricted than traditional investment managers 
and thus may have the flexibility to invest anywhere they see opportunity. Most 
hedge funds do have a broadly stated strategy but are allowed some deviation from 
that strategy. Hedge funds are often given the flexibility to invest a percentage of the 
AUM, generally less than 20%, how and when they see fit. A hedge fund can also be 
structured as part of one “asset management” business that is “contracted” to manage 
several different funds (e.g., SuperStar Asset Management might manage SuperStar 
Credit Fund, SuperStar Commodities Fund, and SuperStar Multi-  Strategy Fund).

The growing popularity of hedge funds is illustrated by AUM and net asset flows 
for the period of 1990 through 2015. Hedge Fund Research, Inc. (HFRI) reports that 
AUM grew from approximately $39 billion in 1990 to $491 billion in 2000 and to 
$2.9 trillion in 2015.15
Exhibit 4 compares the returns and a variety of risk and performance measures of 
the HFRI Fund of Funds Composite Index, the MSCI ACWI Index, and the Bloomberg 
Barclays Global Aggregate Index. The HFRI Fund of Funds Index is an equally weighted 
performance index of funds of hedge funds included in the HFR database. Hedge 
fund indexes suffer from issues related to self-  reporting, but the Fund of Funds index 
reflects the actual performance of portfolios of hedge funds. This index may show 
a lower reported return because of the added layer of fees,16 but it may represent 
average hedge fund performance more realistically than HFRI’s composite index of 
individual funds.

As shown in Exhibit 4, over the 25-  year period, hedge funds had higher returns 
than stocks and bonds and an almost identical standard deviation as bonds. As a result, 
the Sharpe ratio for hedge funds appeared to dominate these and other investments 
(see Exhibit 3) in both return and risk. Note that the returns and volatilities (standard 
deviations) represent an average and are not representative of any single year. Hedge 
funds do not appear as attractive as bonds if returns are adjusted for downside devia -
tion, as reflected in the Sortino measures in Exhibit 4. The “worst drawdown” reflecting 
the period of largest cumulative negative returns for hedge funds and global equities 
was during the period that began in 2007 (when each peaked) and ended in 2009.
15 That is, January 2016.
16 A fund of funds has an extra layer of fees. Each hedge fund in which a fund of funds invests is structured

to receive a management fee plus a performance fee, and the fund of funds itself may also be structured 
to receive a management fee plus a performance fee.

Hedge Funds 135
Exhibit 4   Risk–Return Characteristics of Hedge Funds and Other 
Investments, 1990–2014
FoF Hedge Global Stocks Global Bonds
Annualized return 7.2% 6.9% 6.3%
Annualized volatility 6.0% 16.5% 5.8%
Sharpe ratio 0.63 0.21 0.49
Sortino ratio 0.74 0.43 1.09
Percentage of positive months 69.3% 61.3% 62.7%
Best month 6.8% 11.9% 6.2%
Worst month –7.5% –19.8% –3.8%
Worst drawdown –22.2% –54.6% –10.1%
Sources:  Fund-  of- funds (FoF) hedge data are from HFRI Fund of Funds Composite Index; global 
stocks data are from MSCI ACWI; global bonds data are from Bloomberg Barclays Global 
Aggregate Index.
3.1 Hedge Fund Strategies
Hedge funds are typically classified by strategy, although categorizations vary. Many 
classifying organizations focus on the most common strategies, but others have clas -
sification systems based on different criteria such as the underlying assets in which 
the funds are invested. Also, classifications change over time as new strategies, often

based on new products and opportunities in the market, are introduced. Classifying 
hedge funds is important so that investors can review aggregate performance data, 
select strategies to build a portfolio of funds, and select or construct appropriate 
performance benchmarks. In 2015, HFRI identified four broad categories of strat -
egies: event-  driven, relative value, macro, and equity hedge.17 Exhibit 5 shows the 
approximate percentage of hedge fund AUM by strategy, according to HFRI, for 1990, 
2010, and 2015. Based on percentage of hedge fund AUM by strategy, event-  driven 
and relative value strategies have grown in popularity during the last 25 years, while 
macro and equity hedge funds have declined.
Exhibit 5   Percentage of AUM by Strategy
Event Driven Relative Value Macro Equity HedgeA. 1990
10
14
3937B. 2010
26
24 2030C. 2015
26 28
27 19
17 The Chartered Alternative Investment Analyst (CAIA) Association classifies hedge funds into four

broad categories: corporate restructuring, convergence trading, opportunistic, and market directional. These 
categories approximately coincide with event driven, relative value, macro, and equity hedge, respectively.

Reading 58 ■ Introduction to Alternative Investments 136
3.1.1  Event-  Driven Strategies
Event-  driven strategies seek to profit from short-  term events, typically involving 
potential changes in corporate structure such as an acquisition or restructuring, that 
are expected to affect individual companies. This strategy is considered “bottom up” 
(company-  level analysis followed by aggregation and analysis of a larger group, such 
as an industry) as opposed to “top down” (global macro analysis followed by sectoral/
regional analysis followed by company analysis). Investments may include long and 
short positions in common and preferred stocks, as well as debt securities and options. 
Further subdivisions of this category by HFRI include the following:
■■Merger arbitrage.  Generally, these strategies involve going long (buying) the 
stock of the company being acquired and going short (selling) the stock of the 
acquiring company when the merger or acquisition is announced. The manager

may expect to profit from the deal spread, which reflects the uncertainty of the 
deal closing, or may expect the acquirer to ultimately overpay for the acquisi -
tion and perhaps suffer from an increased debt load. The primary risk in this 
strategy is that the announced merger or acquisition does not occur, and the 
hedge fund has not closed its positions on a timely basis.
■■Distressed/restructuring.  These strategies focus on the securities of compa -
nies either in bankruptcy or perceived to be near to bankruptcy. Hedge funds 
attempt to profit from distressed securities in a variety of ways. The hedge fund 
may simply purchase fixed-  income securities trading at a significant discount 
to par. This transaction takes place in anticipation of the company restructuring 
and the fund earning a profit from the subsequent sale of the securities. The 
hedge fund may also use a more complicated approach, for example, buying

senior debt and shorting junior debt or buying preferred stock and shorting 
common stock. These transactions take place in expectation of a profit as the 
spread between the securities widens. The fund may also short sell the compa -
ny’s stock, but this transaction involves considerable risk given the potential for 
loss if the company’s prospects improve.
■■Activist.  The term “activist” is short for “activist shareholder. ” These strategies 
focus on the purchase of sufficient equity in order to influence a company’s 
policies or direction. For example, the activist hedge fund may advocate for 
divestitures, restructuring, capital distributions to shareholders, and/or changes 
in management and company strategy. These hedge funds are distinct from 
private equity because they operate in the public equity market.
■■Special situations.  These strategies focus on opportunities in the equity of 
companies that are currently engaged in restructuring activities other than

mergers, acquisitions, or bankruptcy. These activities include security issuance 
or repurchase, special capital distributions, and asset sales/spin-  offs.
3.1.2  Relative Value Strategies
Relative value funds seek to profit from a pricing discrepancy (an unusual short-  term 
relationship) between related securities. The expectation is that the pricing discrepancy 
will be resolved in time. This strategy typically involves buying and selling related 
securities. Examples of relative value strategies include the following:
■■Fixed-  income convertible arbitrage.  These market-  neutral (a zero-  beta 
portfolio, at least in theory) investment strategies seek to exploit a perceived 
mispricing between a convertible bond and its component parts (the underlying 
bond and the embedded stock option). The strategy typically involves buying 
convertible debt securities and simultaneously selling the same issuer’s common 
stock.

Hedge Funds 137
■■Fixed-  income asset backed.  These strategies focus on the relative value 
between a variety of asset-  backed securities (ABS) and mortgage-  backed securi -
ties (MBS) and seek to take advantage of mispricing across different ABS.
■■Fixed-  income general.  These strategies focus on the relative value within the 
fixed-  income markets. Strategies may incorporate trades between two corporate 
issuers, between corporate and government issuers, between different parts of 
the same issuer’s capital structure, or between different parts of an issuer’s yield 
curve. Currency dynamics and government yield curve considerations may also 
come into play when managing these fixed-  income instruments.
■■Volatility.  These strategies typically use options to go long or short market vol -
atility either in a specific asset class or across asset classes. Option prices reflect 
implied volatility, and an increase in market volatility leads to an increase in 
option prices.

■■Multi-  strategy.  These strategies trade relative value within and across asset 
classes or instruments. Rather than focusing on one type of trade (e.g., convert -
ible arbitrage), a single basis for trade (e.g., volatility), or a particular asset class 
(e.g., fixed income), this strategy instead looks for investment opportunities 
wherever they might exist.
3.1.3  Macro Strategies
Macro hedge funds emphasize a top-  down approach to identify economic trends 
evolving across the world. Trades are made based on expected movements in eco -
nomic variables. Generally, these funds trade opportunistically in the fixed-  income, 
equity, currency, and commodity markets. Macro hedge funds use long and/or short 
positions to potentially profit from a view on overall market direction as influenced 
by major economic trends and/or events.
3.1.4  Equity Hedge Strategies
Equity hedge strategies can be thought of as the original hedge fund category. They

are focused on public equity markets and take long and short positions in equity 
and equity derivative securities. Some hedge funds, called equity-  only funds, invest 
exclusively in common equity securities. Equity hedge strategies are not focused on 
equity trades categorized as consistent with event-  driven or macro strategies. Equity 
hedge strategies use a bottom-  up as opposed to top-  down approach. Other investors, 
not structured as hedge funds, may use some similar strategies. Examples of equity 
hedge strategies include the following:
■■Market neutral.  These strategies use quantitative (technical) and/or funda -
mental analysis to identify under- and over-  valued equity securities. The hedge 
fund takes long positions in securities it has identified as undervalued and short 
positions in securities it has identified as overvalued. The hedge fund tries to 
maintain a net position that is neutral with respect to market risk. Ideally, the

portfolio should have a beta of approximately zero. The intent is to profit from 
individual securities movements while hedging against market risk.
■■Fundamental growth.  These strategies use fundamental analysis to identify 
companies expected to exhibit high growth and capital appreciation. The hedge 
fund takes long positions in identified companies.
■■Fundamental value.  These strategies use fundamental analysis to identify com -
panies that are undervalued. The hedge fund takes long positions in identified 

Reading 58 ■ Introduction to Alternative Investments 138
■■Quantitative directional.  These strategies use technical analysis to iden -
tify companies that are under- and overvalued and to ascertain relationships 
between securities. The hedge fund takes long positions in securities identified 
as undervalued and short positions in securities identified as overvalued. The 
hedge fund typically varies levels of net long or short exposure depending on 
the anticipated market direction and stage in the market cycle. Similar long–
short approaches exist that are based on fundamental analysis.
■■Short bias.  These strategies use quantitative (technical) and/or fundamental 
analysis to identify overvalued equity securities. The hedge fund takes short 
positions in securities identified as overvalued. The fund typically varies its net 
short exposure based on market expectations, going fully short in declining 
markets.

markets.
■■Sector specific.  These strategies exploit expertise in a particular sector and use 
quantitative (technical) and fundamental analysis to identify opportunities in 
the sector.
Many hedge funds start as a focused operation, specializing in one strategy or asset 
class and, if successful, may diversify over time to become multi-  strategy funds. Large, 
multi-  strategy funds are an alternative to funds of hedge funds. Although funds of 
hedge funds may offer advantages (for example, access by smaller investors, diversified 
hedge fund portfolio, better redemption terms, and/or due diligence expertise) that 
multi-  strategy funds lack, a primary difference between a multi-  strategy hedge fund 
and a fund of hedge funds is the extra layer of fees associated with a fund of funds. 
Each hedge fund in which a fund of hedge funds invests is structured to receive a 
management fee plus an incentive fee, and the fund of hedge funds itself is also struc -

tured to receive a management fee and may receive an incentive fee.
3.2 Hedge Funds and Diversification Benefits
Given the broad range of strategies across hedge funds, general statements about hedge 
fund performance are not necessarily meaningful. Further, there is a general lack of 
performance persistence; hedge fund strategies that generate the highest returns in 
some years can be the ones to perform the most poorly in subsequent years.
The general premise of hedge funds is that they can make money (in other words, 
earn absolute returns) regardless of the stock market’s direction. Their flexibility and the 
fact that they typically are not restricted to long-  only positions gives them the oppor -
tunity to respond to market fluctuations. In addition, hedge funds have traditionally 
been thought of as “arbitrage” players, meaning that they seek to earn returns while 
hedging against risks. Of course, in efficient markets, it is hard to find true arbitrage

opportunities. In fact, one of the benefits some hedge funds provide to the financial 
marketplace is that they help make markets more efficient by providing liquidity with 
contrarian views and speeding up price responses to new information. As the hedge 
fund market has grown, many traditional hedge fund strategies have become increas -
ingly crowded, forcing funds to take on more risk to generate competitive returns.
Less-  than-  perfect correlation with the stock market may provide diversification 
benefits. The claim is sometimes made by hedge funds that their performance is 
uncorrelated, not just less than perfectly correlated, with stock market performance, 
but overall this claim is unsubstantiated. Looking at Exhibit 6, the claims of lack of 
correlation with the stock market appear to be supported from 2000 through 2001 but 
not in 2008 or from 2010 through 2014. During financial crisis periods, the correlation 
between hedge fund and stock market performances may increase.

Hedge Funds 139
Exhibit 6   Returns for Hedge Funds, Global Stocks, and Bonds, 2000–2014
Global Equity Global Bonds FoF HedgeAnnual Return (%)
20
10
0
–10
–20
–30
–40
–50
2000–2001 2008 2010–2014
3.3 Hedge Fund Fees and Other Considerations
Hedge fund assets under management grew to $2.9 trillion by the end of 2015 but 
remain a small percentage of the asset management business overall. Hedge funds, 
however, earn a significantly higher percentage of fees. For example, according to one 
estimate for 2013, hedge funds managed less than 3% of total managed funds (hedge 
funds plus mutual funds) but earned more than 30% of managed fund revenue (fees).18 
Fund revenue depends on fee structure and fund performance.
3.3.1  Fees and Returns
It is important to consider a hedge fund’s fee structure prior to making an investment. 
This fee structure accounts for the disproportionately high revenues earned relative 
to mutual funds and affects the returns to investors. A common fee structure in the

hedge fund market was once “2 and 20, ” which reflects a 2% management fee and a 
20% incentive fee; both fees are paid by LP investors. The average industry fee is now 
closer to a 1.6% management fee and 17.75% incentive fee.19 Additionally, funds of 
hedge funds may charge investors a 1% management fee and a 10% incentive fee. 
The incentive fee may be calculated on profits net of management fees or on profits 
before management fees (in other words, the incentive fee is calculated independent 
of management fees).
Sometimes, the fee structure specifies that the incentive fee is earned only after the 
fund achieves a specified return known as a hurdle rate. The hurdle rate is frequently 
set based on a risk-  free rate proxy (e.g., Libor or a specified Treasury bill rate) plus a 
premium but may be set as an absolute, nominal, or real return target. The incentive 
fee can be based on returns in excess of the hurdle rate (hard hurdle rate) or on the 
entire return (soft hurdle rate).

18 Estimate prepared by Citigroup Inc. and reported by Bloomberg (29 January 2015).
19 Fees on new funds have declined through the years. HFRI reported in March 2016 that management 
fees for new funds averaged 1.6% and incentive fees averaged 17.75% in 2015. In 2007, it reported that new 
fund incentive fees averaged 18.5%.

Reading 58 ■ Introduction to Alternative Investments 140
The fee structure may specify that before an incentive fee is paid, following a 
year in which the fund’s value has declined, the fund’s value must return to a pre -
vious high-  water mark. Note that the high-  water mark is typically the highest value 
reported by the fund; the amount reported is net of fees. High-  water marks reflect 
the highest cumulative return used to calculate an incentive fee. In other words, the 
hedge fund must recover its past losses and return to its high-  water mark before any 
additional incentive fee is earned. Clients are not charged an incentive fee if the latest 
cumulative return does not exceed the prior high-  water mark. This use of a high-  water 
mark protects clients from paying twice for the same performance. Although poorly 
performing hedge funds may not receive an incentive fee, the management fee is 
earned irrespective of returns.

Although “2 and 20” and “1 and 10” represent commonly quoted fee structures 
for hedge funds and funds of hedge funds, respectively, many fee structure variations 
exist in the marketplace. Hedge funds charge different rates, and different classes of 
investors may have different fee structures within the same fund. Hedge funds may 
be willing to negotiate terms, including fees and notice and lockup periods, with 
potential investors. A fee structure may differ from 2 and 20 based on the promised 
length of the investment. In other words, the longer investors agree to keep their 
money in the hedge fund, the lower the fees. A fee structure may also vary from 2 
and 20 based on supply and demand as well as historical performance. Sometimes, 
rebates or reductions in fees are given to investors or to the placement agent who 
introduced another investor to the hedge fund.
The following example demonstrates fee structures and their effect on the resulting

returns to investors.
EXAMPLE 2   
Fee and Return Calculations
AWJ Capital is a hedge fund with $100 million of initial investment capital. It 
charges a 2% management fee based on year-  end AUM and a 20% incentive fee. 
In its first year, AWJ Capital has a 30% return. Assume management fees are 
calculated using end-  of- period valuation.
1 What are the fees earned by AWJ if the incentive and management fees 
are calculated independently? What is an investor’s effective return given 
this fee structure?
2 What are the fees earned by AWJ assuming that the incentive fee is cal -
culated based on return net of the management fee? What is an investor’s 
net return given this fee structure?
3 If the fee structure specifies a hurdle rate of 5% and the incentive fee is 
based on returns in excess of the hurdle rate, what are the fees earned by 
AWJ assuming the performance fee is calculated net of the management 
fee? What is an investor’s net return given this fee structure?

In the second year, the fund value declines to $110 million.
4 The fee structure is as specified for Question 1 but also includes the use 
of a high-  water mark (computed net of fees). What are the fees earned by 
AWJ in the second year? What is an investor’s net return for the second 
year given this fee structure?

Hedge Funds 141
In the third year, the fund value increases to $128 million.
5 The fee structure is as specified in Questions 1 and 4. What are the fees 
earned by AWJ in the third year? What is an investor’s net return for the 
third year given this fee structure?
6 What are the arithmetic and geometric mean annual returns for the three-  
year period based on the fee structure specified in Questions 1, 4, and 5? 
What is the capital gain to the investor for the three-  year period? What 
are the total fees paid to AWJ for the three-  year period?
AWJ fees
$130 million × 2% = $2.6 million management fee
($130 – $100) million × 20% = $6 million incentive fee
Total fees to AWJ Capital = $8.6 million
Investor return: ($130 – $100 – $8.6) million/$100 million = 21.40%
($130 – $100 – $2.6) million × 20% = $5.48 million incentive fee
Total fees to AWJ Capital = $8.08 million

Investor return: ($130 – $100 – $8.08) million/$100 million = 21.92%
($130 – $100 – $5 – $2.6) million × 20% = $4.48 million incentive fee
Total fees to AWJ Capital = $7.08 million
Investor return: ($130 – $100 – $7.08) million/$100 million = 22.92%
$110 million × 2% = $2.2 million management fee
No incentive fee because the fund has declined in value.
Total fees to AWJ Capital = $2.2 million
Investor return: ($110 – $2.2 – $121.4) million/$121.4 million = −11.20%
The beginning capital position in the second year for the investors is ($130 − $8.6) 
million = $121.4 million. The ending capital position at the end of the second 
year is ($110 − $2.2) million = $107.8 million.
$128 million × 2% = $2.56 million management fee
($128 – $121.4) million × 20% = $1.32 million incentive fee. 
The $121.4 million represents the high-  water mark established at the end of 
Year 1.

Year 1.
Total fees to AWJ Capital = $3.88 million
Investor return: ($128 – $3.88 – $107.8) million/$107.8 million = 15.14%

Reading 58 ■ Introduction to Alternative Investments 142
The ending capital position at the end of Year 3 is $124.12  million. This 
amount is the new high-  water mark.
Arithmetic mean annual return = (21.4% – 11.20% + 15.14%)/3 = 8.45%
Geometric mean annual return = [Cube root of (124.12/100)] – 1 = 7.47%
Capital gain to the investor = ($124.12 – $100) million = $24.12 million
Total fees = ($8.6 + $2.2 + $3.88) million = $14.68 million
As the example illustrates, the return to an LP investor in a fund differs significantly 
from the return to the fund. Hedge fund indexes generally report performance net of 
fees. If fee structures vary, however, the net-  of- fees returns may vary among investors 
and from that included in the index. The multilayered fee structure of funds of hedge 
funds has the effect of further diluting returns to the investor, but this disadvantage is 
balanced with several attractive features. Funds of hedge funds may provide a diversi -

fied portfolio of hedge funds, may provide access to hedge funds that may otherwise 
be closed to direct investments, and may offer expertise in and conduct due diligence 
in selecting the individual hedge funds. Fund-  of- funds money is considered “fast” 
money by hedge fund managers because fund-  of- funds managers tend to be the first 
to redeem their money when hedge funds start to perform poorly,20 and they may 
also have negotiated redemption terms that are more favorable (for example, a shorter 
lockup period and/or notice period).
EXAMPLE 3   
Comparison of Returns—Investment Directly into a 
Hedge Fund or through a Fund of Hedge Funds
An investor is contemplating investing €100 million in either the ABC Hedge 
Fund (ABC HF) or the XYZ Fund of Funds (XYZ FOF). XYZ FOF has a “1 and 
10” fee structure and invests 10% of its AUM in ABC HF. ABC HF has a standard 
“2 and 20” fee structure with no hurdle rate. Management fees are calculated

on an annual basis on AUM at the beginning of the year. Management fees and 
incentive fees are calculated independently. ABC HF has a 20% return for the 
year before management and incentive fees.
1 Calculate the return to the investor from investing directly in ABC HF.
2 Calculate the return to the investor from investing in XYZ FOF. Assume 
that the other investments in the XYZ FOF portfolio generate the same 
return before management fees as ABC HF and have the same fee struc -
ture as ABC HF.
3 Why would the investor choose to invest in an FOF instead of an HF given 
the effect of the “double fee” demonstrated in the answers to Questions 1 
and 2?
20 Anecdotal evidence suggests that many funds of funds that cater to high-  net- worth investors move 
money faster than funds of funds that serve institutional clients.

Hedge Funds 143
ABC HF has a profit before fees on a €100 million investment of €20 million (= 
100 million × 20%). The management fee is €2 million (= €100 million × 2%), and 
the incentive fee is €4 million (= 20 million × 20%). The return to the investor 
is 14% (= [20 – 2 – 4]/100).
XYZ FOF earns a 14% return or €14 million profit after fees on €100 million 
invested with hedge funds. XYZ FOF charges the investor a management fee 
of €1  million (= €100  million × 1%) and an incentive fee of €1.4  million (= 
€14 million × 10%). The return to the investor is 11.6% (= [14 – 1 – 1.4]/100).
This scenario assumed that returns were the same for all underlying hedge funds. 
In practice, this result will not likely be the case, and XYZ FOF may provide due 
diligence expertise and potentially valuable diversification.
The hedge fund business is attractive to portfolio managers because fees can

generate significant revenue if the fund performs well and AUM are large. Many new 
hedge funds launched throughout the late 1990s and early 2000s. Not all hedge funds 
remain in business long, however. One study suggests that more than a quarter of 
all hedge funds fail within the first three years because of performance problems.21 
This outcome is one of the reasons survivorship bias is such a problem in hedge fund 
indexes. Because of the survivorship and backfill biases, hedge fund indexes may not 
reflect actual average hedge fund performance but rather reflect only the performance 
of hedge funds that are performing well.
3.3.2  Other Considerations
Hedge funds may use leverage to seek higher returns on their investments. Leverage 
has the effect of magnifying gains or losses because the hedge fund can take a large 
position relative to the capital committed. Hedge funds may leverage their portfolios 
by borrowing capital and/or using derivatives.

For example, if a hedge fund expects the price of Nestlé SA to increase, it can take 
a number of actions to benefit from the expected price increase. The fund can buy a 
thousand shares of Nestlé, buy 10 futures contracts on Nestlé on the NYSE Euronext, 
buy calls on 1,000 shares of Nestlé, or sell puts on a thousand shares of Nestlé to profit 
from the expected price increase. The profit or loss from holding the futures will be 
similar to the profit or loss from holding the shares, but the capital requirement for 
the investment in the futures is far lower. If the hedge fund had bought calls on 1,000 
shares of Nestlé, the fund would have paid a relatively small premium and potentially 
experienced a significant profit if Nestlé had increased in price. The maximum loss 
to the fund would have been the premium paid. If the hedge fund had sold puts on 
1,000 shares of Nestlé expecting the price to rise and the puts to not be exercised, the

fund would have a maximum profit equal to the relatively small premium received. 
If Nestlé had declined in price, however the potential loss would be extremely large.
Investors, including hedge funds, are required to put up some collateral when using 
derivatives if they are going to be exposed to potential losses on their positions. This 
collateral requirement helps to protect against default on the position and helps to 
protect the counterparty (or clearinghouse) on the derivative. The amount of collateral 
21 Brooks and Kat (2002).

Reading 58 ■ Introduction to Alternative Investments 144
depends on the investment’s riskiness as well as the creditworthiness of the hedge 
fund or other investor. Collateral is not invested in a fund’s strategy and may be a 
drag on performance.
The borrowing of capital also leverages a portfolio. It often takes the form of buying 
on margin. By borrowing, a hedge fund can invest a larger amount than was invested 
in the fund. Hedge funds normally trade through prime brokers , which provide 
services including custody, administration, lending, short borrowing, and trading. A 
hedge fund will normally negotiate its margin requirements with its prime broker(s). 
The prime broker effectively lends the hedge fund money to make investments, and 
the hedge fund puts money or other collateral into a margin account with the prime 
broker. The margin account represents the hedge fund’s equity in the position. The 
margin requirement depends on the investment’s riskiness and the creditworthiness

of the hedge fund.
The smaller the margin requirement, the more leverage is available to the hedge 
fund. Leverage is a large part of the reason that hedge funds make either larger-  than-  
normal returns or significant losses; the leverage magnifies both gains and losses. If 
the margin account or the hedge fund’s equity in a position declines below a certain 
level, the lender initiates a margin call and requests the hedge fund put up more 
collateral. Margin calls can have the effect of magnifying losses because in order to 
meet a margin call, the hedge fund may liquidate (close) the losing position. This 
liquidation can lead to further losses if the order size is sufficiently large to move the 
security’s market price.
Another factor that can magnify losses for hedge funds is investor redemptions. 
Redemptions  frequently occur when a hedge fund is performing poorly. In the 
hedge fund industry, a drawdown  is a reduction in net asset value (NAV).22 When

drawdowns occur, investors may decide to exit the fund or redeem at least a portion 
of their shares. Redemptions may require the hedge fund manager to liquidate some 
positions and incur transaction costs. As already stated, the liquidation of a position 
may further magnify the losses on the position. Redemption fees may serve to dis -
courage redemption and to help the hedge fund managers recover transaction costs. 
Notice periods may allow the hedge fund manager to liquidate a position in an orderly 
fashion without magnifying the losses. Lockup periods give the hedge fund manager 
time to implement and potentially realize a strategy’s expected results. If the hedge 
fund experiences a drawdown shortly after the fund launch, the lockup period will 
force investors to stay in the fund rather than withdraw. A hedge fund’s ability to 
demand a long lockup period and still raise a significant amount of money depends

a great deal on the reputation of either the firm or the hedge fund manager. Funds of 
hedge funds may offer more redemption flexibility than afforded by direct investment 
in hedge funds because of special redemption arrangements with the underlying 
hedge fund managers, maintenance of a cash fund, or access to temporary financing.
Although hedge funds are not subject to extensive regulation globally, there have 
been calls for more oversight. In the United States, hedge funds larger than $100 mil -
lion are registered with the SEC (Securities and Exchange Commission). Additional 
regulation has been established in recent years. Under the Alternative Investment 
Fund Managers Directive (AIFMD), hedge funds that operate or market themselves 
in the European Union must be authorized. The AIFMD was implemented in the 
European Union (EU) in 2013, and in the United States, regular submission of the 
risk disclosure form “Form PF” to the Financial Stability Oversight Council has been

required since 2012. Regulation may not require hedge funds to be transparent to 
outsiders or proactive in communicating their strategies and reporting their returns.
22 NAV per share is the value of the fund’s total assets minus liabilities, divided by the number of shares 

Hedge Funds 145
Offshore jurisdictions (for example, the Cayman Islands) are often the locale for 
registering hedge funds, whether managed in the United States, Europe, or Asia. 
Some hedge funds choose to register domestically, however. The choice to register 
in, for example, the United States or the United Kingdom may result from the added 
credibility of registering with the SEC or the Financial Services Authority, respectively. 
Sometimes, onshore hedge funds set up complementary offshore funds to attract 
additional capital.
EXAMPLE 4   
Effect of Redemption
A European credit hedge fund has a very short notice period of a week because 
the fund’s managers believe that it invests in highly liquid asset classes and is 
market neutral. The fund has a small number of holdings that represent a signif -
icant portion of the outstanding issue of each holding. The fund’s lockup period 
has expired. Unfortunately, in one particular month, because of the downgrades

of two large holdings, the hedge fund has a drawdown (decline in NAV) of more 
than 5%. The declines in value of the two holdings result in margin calls from 
their prime broker, and the drawdown results in requests to redeem 50% of total 
partnership interests. The combined requests are most likely  to:
A force the hedge fund to liquidate or unwind 50% of its positions in an 
orderly fashion throughout the week.
B have little effect on the prices received when liquidating the positions 
because it has a week before the partnership interests are redeemed.
C result in a forced liquidation, which will further drive down prices and 
result in a bigger drawdown, so that the remaining investors will redeem 
their partnership interests leading to fund liquidation and closure.
Solution:
C is correct. One week may not be enough time to unwind the fund’s positions in 
an orderly fashion so that the unwinding does not further drive down prices. A

downgrading is not likely to have a temporary effect, so even if other non-  losing 
positions are liquidated to meet the redemption requests, it is unlikely that the 
two large holdings will return to previous or higher values. Also, the hedge fund 
may have a week to satisfy the requests for redemptions, but the margin call 
must be met immediately. Thus, it is most likely that a forced liquidation will 
drive down prices, resulting in further drawdowns and redemption requests so 
that ultimately the fund will liquidate and cease to exist.
3.4 Hedge Fund Valuation Issues
Valuations are important for calculating performance and meeting redemptions. The 
frequency with which and how hedge funds are valued varies among funds. Hedge 
funds are generally valued on a daily, weekly, monthly, and/or quarterly basis. The 
valuation may use market or estimated values of underlying positions. When market 
prices or quotes are used for valuation, funds may differ in which price or quote they

use (for example, bid price, ask price, average quote, or median quote). A common 
practice is to use the average quote ([Bid + Ask]/2). A more conservative and theoret -
ically accurate approach is to use bid prices for longs and ask prices for shorts; these 
are the prices at which the positions could be closed.

Reading 58 ■ Introduction to Alternative Investments 146
The underlying positions may be in highly illiquid or non-  traded investments, 
and therefore, it is necessary to estimate values because there are no reliable mar -
ket values. Estimated values may be computed using statistical models. Any model 
should be independently tested, benchmarked, and calibrated to industry-  accepted 
standards to ensure a consistency of approach. Because of the potential for conflicts 
of interests affecting estimates of value, hedge funds should develop procedures for 
in- house valuations, communicate these procedures to clients, and adhere to them.
Liquidity is an important issue for valuation, but becomes particularly so for strat -
egies involving convertible bonds, collateralized debt obligations, distressed debt, and 
emerging market fixed-  income securities, which may be relatively illiquid. If a quoted 
market price is available, the use of liquidity discounts or “haircuts” is actually incon -

sistent with valuation guidance under most generally accepted accounting standards. 
Many practitioners, however, believe that liquidity discounts are necessary to reflect 
fair value. This assumption has resulted in some funds having two NAVs—trading 
and reporting. The trading NAV incorporates liquidity discounts, based on the size of 
the position held relative to the total amount outstanding in the issue and its trading 
volume. The reporting NAV is based on quoted market prices.
EXAMPLE 5   
Hedge Fund Valuation
A hedge fund with a market-  neutral strategy restricts its investment universe to 
domestic publicly traded equity securities that are actively traded. In calculating 
net asset value, the fund is most likely to use which of the following to value 
underlying positions?
A Average quotes
B Average quotes adjusted for liquidity
C Bid price for shorts and ask price for longs
Solution:
A is correct. The fund is most likely to use average quotes. The securities are

actively traded, so no liquidity adjustment is required. If the fund uses bid–ask 
prices, it will use ask prices for shorts and bid prices for longs; these are the 
prices at which the positions are closed.
3.5 Due Diligence for Investing in Hedge Funds
When investing in hedge funds, investors must consider many issues. A basic question 
is whether one wants to rely on the expertise of a manager of a fund of hedge funds 
to invest in a portfolio of hedge funds or whether one has the expertise to undertake 
the hedge fund investment selection process. Funds of hedge funds potentially offer 
the benefits of providing a diversified portfolio of hedge funds, supplying expertise in 
conducting due diligence, and negotiating favorable redemption terms. These potential 
benefits come at the cost of an additional layer of fees. Also, although a fund of hedge 
funds may provide expertise in due diligence, the investor should still conduct due 
diligence when choosing a fund of hedge funds.

Investors in hedge funds should consider many factors in their decision-  making 
process. This section highlights some of the key due diligence points to consider but 
does not provide an exhaustive list of factors. Key factors to consider include investment

Hedge Funds 147
strategy, investment process, competitive advantage, track record, size and longevity, 
management style, key person risk, reputation, investor relations, plans for growth, 
and risk management systems.
Investment strategy and process are challenging to fully assess because hedge funds 
may limit disclosure in order to maintain their competitive advantage and to not give 
away information that is considered proprietary. It should be possible, however, to 
identify in which markets the hedge fund invests, the general investment strategy (for 
example, long–short, relative arbitrage, and so on) and the basic process to implement 
this strategy, and the benchmark against which the fund gauges its performance.
Track record is a commonly viewed consideration because it should be readily 
available and is often assumed to be an indicator of future performance and risk 
(perhaps incorrectly, based on studies of performance persistence).23 Investors should

determine how the returns are calculated (e.g., based on estimates of value or market 
prices) and reported (e.g., before or after fees) and how the returns and risks compare 
with some benchmark. The investor should inquire about the fee structure because 
this information will affect, as demonstrated earlier, the return to the investor.
Size and longevity are also common items for review.24 The older a fund, the more 
likely it has not caused significant losses to its investors (otherwise, it is likely to have 
experienced redemptions, been unable to raise further capital, and been liquidated). 
As a result, older funds are likely to have experienced growth in AUM through both 
capital appreciation and additional investments (capital injections). Many investors 
require hedge funds to have a minimum track record of two years before they will 
invest. This requirement makes it particularly difficult for start-  up funds to raise

money because their managers need capital to invest before they can build a track 
record. In many cases, start-  up funds receive money from seed investors who want a 
share of the business for their investment.
A hedge fund’s size is an important consideration for investors because many 
investors set a minimum size on their investments and restrict the percentage of a 
fund’s overall AUM that their investment can represent. For example, if an investor’s 
minimum investment size is $10 million and the investor’s maximum percentage of a 
fund is 10%, the minimum hedge fund size the investor can consider is $100 million 
(= $10 million/0.1).
The hedge fund due diligence process also focuses on many qualitative factors, 
including management style, key person risk, reputation, investor relations, and plans 
for growth. A thorough due diligence process will also include a review of management 
procedures, including leverage, brokerage, and diversification policies. The use of

leverage and counterparty risk can significantly affect a fund’s risk and performance. In 
addition to gathering information about the fund’s prime broker and custody arrange -
ments for securities, the investor should identify the auditor of the hedge fund and 
ensure that the auditor is independent and known for conducting competent audits.
Risk management of systems is an important consideration for reviewing a hedge 
fund. Relevant risk management questions to ask are varied and related to the type of 
securities in which the fund invests. Ultimately, the answers should provide comfort 
to investors that the fund performs risk management in a rigorous fashion. In many 
cases, particularly with smaller funds or those that invest in more unusual or illiquid 
assets, the answers to these questions may indicate either that the systems and processes 
are simplistic or that the answers themselves are very complex. Commonly, hedge

fund managers believe that their strategies, systems, and processes are proprietary, 
23 For a discussion on the record of institutional investors’ record at selecting managers, see Stewart, 
Heisler, Knittel, and Neumann (2009).
24 For a discussion of quantitative factors investors use to select investment managers, see Heisler, Knittel, 
Neumann, and Stewart (2007).

Reading 58 ■ Introduction to Alternative Investments 148
and they are unwilling to provide too much information to potential investors. This 
reluctance can make due diligence very challenging. Regulation of hedge funds is likely 
to increase in the future, which may help with the due diligence process.
EXAMPLE 6   
Due Diligence
HF A and HF B invest in the same asset class using a similar investment strat -
egy. A potential investor has gathered the following data from the hedge funds:
Characteristic HF A HF B
Annualized returns 15% 10%
Sharpe ratio 1.3 1.6
Size (US$ millions) 200 500
Fees 1.5 and 15 2 and 20
Track record 2 years 5 years
Based on the above information, the investor is most likely  to:
A invest in HF B because of its higher Sharpe ratio.
B question how the annualized returns are calculated.
C invest in HF A because of its higher returns and lower fees.
Solution:
B is correct. It is important to know how returns are calculated and if they are

comparable before making any decision. If the returns are both reported net of 
fees, the higher fees on HF B may account for most of the difference in returns.
PRIVATE EQUITY
Private equity generally means investing in privately owned companies or in public 
companies with the intent to take them private. There are different stages and types 
of private equity investing. The focus of private equity firms, which may manage 
many private equity funds, may change through time as business conditions and the 
availability of financing change. A possible categorization of private equity identifies 
leveraged buyouts, venture capital, development capital, and distressed investing as 
primary private equity strategies.
Leveraged buyouts  (LBOs) or highly leveraged transactions refer to private 
equity firms establishing buyout funds (or LBO funds) that acquire public companies 
or established private companies with a significant percentage of the purchase price

financed through debt. The target company’s assets typically serve as collateral for the 
debt, and the target company’s cash flows are expected to be sufficient to service the 
debt. The debt becomes part of the target company’s capital structure if the buyout 
goes through. After the buyout, the target company becomes or remains a privately 
owned company.
Venture capital  entails investing in or providing financing to private companies 
with high growth potential. Typically, these are start-  up or young companies, but 
venture capital can be provided at a variety of stages. In contrast, development 4

Private Equity 149
capital  generally refers to minority equity investments in more-  mature companies 
that are looking for capital to expand or restructure operations, enter new markets, 
or finance major acquisitions.
Distressed investing  typically entails buying the debt of mature companies 
in financial difficulties. These companies may be in bankruptcy proceedings, have 
defaulted on debt, or seem likely to default on debt. Some investors attempt to identify 
companies with a temporary cash flow problem but a good business plan that will 
help the company survive and, in the end, flourish. These investors buy the company’s 
debt in expectation of both the company and its debt increasing in value. Turnaround 
investors buy debt and plan to be more active in the management and direction of the 
company. They seek distressed companies to restructure and revive.
The level of activity in private equity has grown over time, but it is cyclical. The

cyclicality is shown visually in Exhibit 7, which displays committed capital raised by 
funds between 2004 and 2015. Note that detailed information on private equity activity 
is not always readily available.
Exhibit 7   Private Equity Funds Raised, 2004–2015
$ (billions)
500
450
400
350
300
250
200
150
100
50
0
04 15 14 13 12 11 10 09 08 07 06 05
Source:  PitchBook, PE Activity, 2014 and 2015.
4.1 Private Equity Structure and Fees
Like hedge funds, private equity funds are typically structured as partnerships in which 
outside investors are Limited Partners (LPs) and the private equity firm, which may 
manage a number of funds, is the General Partner (GP). Most private equity firms 
charge both a management fee and an incentive fee on a fund basis. The management 
fees generally range from 1% to 3% of committed capital . Committed capital is the 
amount that the LPs have agreed to provide to the private equity fund. Private equity

funds raise committed capital and draw down on those commitments over three to 
five years when they have a specific investment to make. Until the committed capital 
is fully drawn down and invested, the management fee is based on committed capital, 
not invested capital. The committed capital basis for management fees is an important 
distinction from hedge funds, whose management fees are based on AUM. After the

Reading 58 ■ Introduction to Alternative Investments 150
committed capital is fully invested, the fees are paid only on the funds remaining in 
the investment vehicle; as investments are exited, capital is paid back to the investors, 
and investors no longer pay fees on that portion of their investment.
For most private equity funds, the GP does not earn an incentive fee until the 
LPs have received back their initial investment. The GP typically receives 20% of the 
total profit, net of any hard hurdle rate, of the private equity fund as an incentive or 
profit sharing fee.25 The LPs receive 80% of the total profit of the equity fund plus the 
return of their initial investment. If distributions are made based on profits earned 
over time rather than at exit from investments of the fund, the distributions may 
result in receipts by the GP of more than 20% of the total profit. Most private equity 
partnership agreements include policies that protect the LPs from this contingency.

These policies include prohibiting distributions of incentive fees to the GP until the 
LPs have received back their invested capital, setting up an escrow account for a 
portion of the incentive fees, and incorporating a clawback  provision that requires 
the GP to return any funds distributed as incentive fees until the LPs have received 
back their initial investment and 80% of the total profit.
In addition to both management and incentive (profit-  sharing) fees, LBO firms 
may generate income from sources other than the fund’s management fees and profit 
sharing. These income sources include a fee paid to the firm for arranging the buyout 
of a company, compensation if an intended acquisition falls through, and a fee for 
arranging for divestitures of assets after the buyout is complete. Private equity firms 
may also charge consulting fees directly to underlying companies.
4.2 Private Equity Strategies
There are many private equity strategies. A common categorization, as indicated

earlier, identifies leveraged buyouts, venture capital, development capital, and dis -
tressed investing as the primary strategies. LBOs and venture capital are the dominant 
strategies, however.
4.2.1  Leveraged Buyouts
LBOs are sometimes referred to as “going private” transactions because, after the acqui -
sition of a publicly traded company, the target company’s equity is generally no longer 
publicly traded. When the target company is an established private company, it is not 
a “going private” transaction. The LBO may also be of a specific type. In management 
buyouts  (MBOs), the current management team is involved in the acquisition, and in 
management buy-  ins (MBIs), the current management team is being replaced and 
the acquiring team will be involved in managing the company. LBO managers seek to 
add value—from improving company operations and growing revenue and ultimately 
increasing profits and cash flows. The sources of growth in earnings before interest,

taxes, depreciation, and amortization (EBITDA), in order of contribution to growth, 
include organic revenue growth, cost reduction/restructuring, acquisition, and other, 
according to the Private Equity Growth Capital Council. The potential returns in this 
category, however, result to a large extent from the use of leverage. If debt financing 
is unavailable or costly, LBOs are less likely to occur.
4.2.1.1  LBO Financing  Debt is central to the structure and feasibility of buyouts in 
private equity. Target companies are rarely purchased using only the equity of the buyout 
company. To potentially increase equity returns and increase the number of transac -
tions a particular fund can make, private equity firms use debt to finance a significant 
proportion of each deal (in other words, they use leverage). For example, in a buyout 
25 The incentive fee may also be calculated on a deal-  by- deal basis.

Private Equity 151
deal, a private equity firm may invest equity representing 30% of the purchase price 
and raise the rest of the purchase price in the debt markets. It may use a combination 
of bank loans, often called leveraged loans because of the amount of the company’s 
capital structure they represent, and high-  yield bonds.
To protect investors, leveraged loans often carry covenants that may require or 
restrict certain actions. For instance, the covenants may require the company to main -
tain specified financial ratios within certain limits, submit information so that the bank 
can monitor performance, or operate within certain parameters. The covenants may 
restrict the company from further borrowing (in other words, no additional bonds can 
be issued and no additional funds can be borrowed from banks or other sources), or 
they may impose limits on paying dividends or making operating decisions. Similarly,

bond terms may include covenants intended to protect the bondholders. One of the 
key differences between leveraged loans and high-  yield bonds, however, is that lever -
aged loans are generally senior secured debt whereas the bonds are unsecured in the 
case of bankruptcy. Even given covenants on the bonds, the bonds issued to finance 
an LBO are usually high-  yield bonds that receive low quality ratings and must offer 
high coupons to attract investors because of the amount of leverage used.
A typical LBO capital structure includes equity, bank debt (leveraged loans), 
and high-  yield bonds. Leveraged loans often provide a larger amount of capital than 
either equity or high-  yield bonds. As an alternative to high-  yield bonds, mezzanine 
financing  may also be used.26 Mezzanine financing refers to debt or preferred shares 
with a relationship to common equity resulting from a feature such as attached war -

rants or conversion options. Being subordinate to both senior and high yield debt, 
mezzanine financing typically pays a higher coupon rate. In addition to interest or 
dividends, this type of financing offers a potential return based on increases in the 
value of common equity.
The variety of available financing choices provides flexibility for a target company 
to match its repayment schedules with expected inflows, and it also permits higher 
levels of leverage compared with traditional bank debt. The optimal capital structure 
takes into account a variety of factors, including the company’s projected cash flows, 
investor willingness to purchase different types of debt and accept different levels 
of leverage, the availability of equity, and the required rates of return for equity and 
different types of debt considering leverage. The optimal capital structure will be 
different for every deal.
4.2.1.2  Characteristics of Attractive Target Companies for LBOs  Private equity firms

invest in companies across many sectors, although an individual firm may specialize in 
a certain sector or sectors. Whatever the targeted sector(s), private equity firms look for 
several characteristics, any one of which may make a company particularly attractive 
as an LBO target. The characteristics include the following:
■■Undervalued/depressed stock price.  The private equity firm perceives the 
company’s intrinsic value to exceed its market price. Private equity firms are 
therefore willing to pay a premium to the market price to secure shareholder 
approval. Firms try to buy assets or companies cheaply, and they may focus on 
companies that are out of favor in the public markets and have stock prices that 
reflect this perception.
■■Willing management and shareholders.  Existing management is looking for a 
deal. Management may have identified opportunities but does not have access 
to the resources to make substantial investments in new processes, personnel,

equipment, and so on to drive long-  term growth. Current shareholders may 
26 This type of loan is referred to as mezzanine financing  because of its location on the balance sheet and 
is a type  of financing.

Reading 58 ■ Introduction to Alternative Investments 152
have insufficient access to capital and welcome a private equity partner. Family 
business owners may want to cash out. Private equity firms can provide man -
agement and owners with the time and capital to expand a company or turn it 
around.
■■Inefficient companies.  Private equity firms seek to generate attractive returns 
on equity by creating value in the companies they buy. They achieve this goal by 
identifying companies that are inefficiently managed and that have the potential 
to perform well if managed better.
■■Strong and sustainable cash flow.  Companies that generate strong cash flow 
are attractive because in an LBO transaction, the target company will be taking 
on a significant portion of debt. Cash flow is necessary to make interest pay -
ments on the increased debt load.
■■Low leverage.  Private equity firms focus on target companies that currently

have no significant debt on their balance sheets. This characteristic makes it 
easier to use debt to finance a large portion of the purchase price.
■■Assets.  Private equity managers like companies that have a significant amount 
of unencumbered physical assets. These physical assets can be used as security, 
and secured debt is cheaper than unsecured debt.
4.2.2  Venture Capital
Venture capital (VC) is often categorized by the stage at which the company of inter -
est (the portfolio company) receives it. The company in which a private equity firm 
is investing is often called the portfolio company  because it will become part of the 
fund’s portfolio. The VC stages range from inception of an idea for a company to 
the point when the company is about to make an IPO (initial public offering) or be 
acquired—most typically, by a strategic buyer. The investment return required varies 
based on the company’s stage of development. Investors in early-  stage companies

will demand higher expected returns relative to later-  stage investors, because the 
earlier the stage of development, the higher the risk. The ultimate returns realized 
depend on the portfolio company’s success in transitioning from a startup to a going 
and growing concern.
Venture capitalists, like all private equity managers, are not passive investors. They 
are actively involved with the companies in which they invest. The VC fund typically 
receives an equity interest in the company in which it is investing. The VC fund may 
also provide some debt financing.
1 Formative-  stage financing occurs when the company is still in the process of 
being formed and encompasses several financing steps, described as follows:
a Angel investing is capital provided at the idea stage. Funds may be used to 
transform the idea into a business plan and to assess market potential. The 
amount of financing at this stage is typically small and provided by individu -

als (often friends and family) rather than by VC funds.
b Seed-  stage financing or seed capital generally supports product develop -
ment and/or marketing efforts, including market research. This point is 
generally the first stage at which VC funds invest.
c Early-  stage financing (early-  stage VC) is provided to companies mov -
ing toward operation but before commercial production and sales have 
occurred. Early-  stage financing may be provided to initiate commercial 
production and sales.

Private Equity 153
2 Later-  stage financing (expansion VC) is provided after commercial produc -
tion and sales have begun but before any IPO. Funds may be used for initial 
expansion of a company already producing and selling a product or for major 
expansion, such as physical plant expansion, product improvement, or a major 
marketing campaign.
3 Mezzanine-  stage financing27 (mezzanine venture capital) is provided to prepare 
a company to go public. It represents the bridge financing needed to fund a 
private firm until it can complete an IPO.
Formative-  stage financing generally is done via ordinary or convertible preferred 
share sales to the investor(s) (VC fund), and management retains control of the 
company. Later-  stage financing generally involves management selling control of the 
company to the VC investor; financing is provided through equity and debt (the fund 
may also use convertible bonds or convertible preferred shares). The debt financing is

not intended for income generation to the VC fund; rather, it is for the recovery and 
control of assets in a bankruptcy situation. Simply put, debt financing provides more 
protection to the VC fund than equity.
To make an investment, a venture capitalist needs to be convinced that the port -
folio company’s management team is competent and has a solid business plan with 
strong prospects for growth and development. Because these investments are not in 
mature businesses with years of operational and financial performance history, the 
complexity involved with VC involves accurately estimating company valuation based 
on future prospects. This estimation is more of an unknown than in LBO investing, 
which targets mature, underperforming public companies. As the portfolio company 
matures and moves into later-  stage financing, the level of certainty around valuation 
increases, but less so than with an LBO investment.
4.2.3  Other Private Equity Strategies

There are several other specialties for private equity firms. These specialties include 
development capital, also called minority equity investing, which earns profits from 
funding business growth or restructuring. Many times, minority equity investing is 
initiated and sought by management, which is interested in realizing earnings from 
selling a portion of its shares before the company can go public. Although this scenario 
occurs most commonly with private companies, publicly quoted companies some -
times seek private equity capital in opportunities called PIPEs (private investment in 
public equities).
Distressed investing by a private equity firm typically involves purchasing the 
debt of troubled companies (companies that are bankrupt, in default, or likely to 
default). The distressed debt often trades at prices significantly less than its face value. 
If the company can be turned around, the debt may recover its value. The return on

investment is a function of the ability of the turnaround investor to restructure the 
company either operationally or financially. Distressed debt investors may be involved 
in the turnaround and may assume an active role in the company’s management and 
direction or in its reorganization. Some distressed investors are passive investors who 
simply try to identify companies that they expect to increase in value; debt holders 
will benefit from the increase before equity holders. Distressed debt investors are 
sometimes referred to as vulture investors.
Other private equity strategies may involve providing specific financing (for exam -
ple, mezzanine funds) or investing in companies in specific industries. As the financial 
environment changes and evolves, additional strategies may emerge.
27 The term “mezzanine-  stage financing” is used because this financing is provided at the stage between 
being a private and public company. The focus is on when  the financing occurs.

Reading 58 ■ Introduction to Alternative Investments 154
4.2.4  Exit Strategies
The ultimate goal for private equity is to improve new or underperforming businesses 
and exit them at higher valuations. Private equity firms buy and hold companies for an 
average of five years. The time to exit, however, can range from less than 6 months to 
more than 10 years. Before deciding on an exit strategy, private equity managers take 
into account the dynamics of the industry in which the portfolio company competes, 
overall economic cycles, interest rates, and company performance.
Below are common exit strategies pursued by private equity portfolio managers:
■■Trade sale.  This strategy refers to the sale of a company to a strategic buyer 
such as a competitor. A trade sale can be conducted through an auction pro -
cess or by private negotiation. Benefits of a trade sale include (a) an immediate 
cash exit for the private equity fund; (b) potential for high valuation of the asset

because strategic buyers may be willing and able to pay more than other poten -
tial buyers as a result of anticipated synergies; (c) fast and simple execution; 
(d) lower transaction costs than an IPO; and (e) lower levels of disclosure and 
higher confidentiality than an IPO because the private equity firm is generally 
dealing with only one other party. Disadvantages of trade sales include (a) possi -
ble opposition by management; (b) lower attractiveness to employees of the 
portfolio company than an IPO; (c) a limited number of potential trade buyers; 
and (d) a possible lower price than in an IPO.
■■IPO.  This approach involves the portfolio company selling its shares, including 
some or all of those held by the private equity firm, to public investors through 
an IPO. Advantages for an IPO exit include (a) potential for the highest price; 
(b) management approval, because management will be retained; (c) public -

ity for the private equity firm; and (d) potential ability to retain future upside 
potential, because the private equity firm may choose to remain a large share -
holder. Disadvantages for an IPO exit include (a) high transaction costs paid 
to investment banks and lawyers; (b) long lead times; (c) risk of stock market 
volatility; (d) high disclosure requirements; (e) potential lock-  up period, which 
requires the private equity firm to retain an equity position for a specified 
period after the IPO; and (f) the fact that an IPO is usually appropriate only for 
larger companies with attractive growth profiles.
■■Recapitalization.  A recapitalization is not a true exit strategy, because the 
private equity firm typically maintains control; however, it does allow the 
private equity investor to extract money from the company. Recapitalization is 
a very popular strategy when interest rates are low, as the private equity firm

re- leverages or introduces leverage to the company and pays itself a dividend. A 
recapitalization is often a prelude to a later exit.
■■Secondary sales.  This approach represents a sale to another private equity firm 
or other group of investors.
■■Write-  off/liquidation.  A write-  off occurs when a transaction has not gone well, 
and the private equity firm is updating its value of the investment or liquidating 
the portfolio company to move on to other projects.
The foregoing exit strategies may be pursued individually, combined together, or 
used for a partial exit strategy. For example, it is not unusual to see a private equity 
fund sell a portion of a portfolio company to a competitor via a trade sale and then 
complete a secondary sale to another private equity firm for the remaining portion. 
Company shares may also be distributed to fund investors, although such a move is 
unusual.

Private Equity 155
4.3 Private Equity: Diversification Benefits, Performance, and 
Risk
Private equity funds may provide higher return opportunities relative to traditional 
investments through their ability to invest in private companies, their influence 
on portfolio companies’ management and operations, and/or their use of leverage. 
Investments in private equity funds can add diversity to a portfolio composed of 
publicly traded stocks and bonds because they may have less-  than-  perfect correlation 
with those investments.
Exhibit 8 shows the mean annual returns for the Cambridge Associates US Private 
Equity Index, the NASDAQ and S&P 500 indexes, and the Cambridge Associates 
mPME (Modified Public Market Equivalent) S&P 500 Index for a variety of periods 
ending 31 December 2014. Public market equivalent (PME) index returns use inter -
nal rate of return (IRR) calculations to simulate investment of private equity cash

flows in a market index, such as the S&P 500. The technique involves recording the 
timing of cash flows for the fund and computing period returns, assuming the flows 
are invested in a market index instead of the fund. Based on the returns shown in 
Exhibit 8, US private equity funds, based on the Cambridge Associates’ estimates, on 
average outperformed stocks based on the NASDAQ and S&P 500 indexes only in the 
10- and 20-  year periods ending 31 December 2014. The returns to US private equity 
underperformed these indexes’ returns for the 1- and 3--year periods and were similar 
for the 5-  year period ending 31 December 2014. The mPME index returns were more 
similar to the S&P 500 index returns than returns on private equity.
Exhibit 8   Comparison of Annual Returns with US Private Equity, US Stocks, 
and a PME Index
1 Y ear 3 Y ears 5 Y ears 10 Y ears 20 Y ears
US private equitya11.3 15.6 15.8 12.9 13.5
NASDAQ 13.4 22.1 15.9 8.1 9.6
S&P 500 13.7 20.4 15.5 7.7 9.9

mPME S&P 500b13.6 20.5 15.5 8.7 8.7
a Private equity returns are net of expenses; US Stocks and PME Index are gross.
b Cambridge Associates mPME.
Source:  US Private Equity Index and selected benchmark statistics, 31 December 2014, 
Cambridge Associates.
Published private equity indexes may be an unreliable measure of performance, 
however, because of challenges in measuring the historical performance of private 
equity investing. As with hedge funds, private equity return indexes rely on self-  
reporting and are subject to survivorship, backfill, and other biases. These character -
istics typically lead to overstatement of published returns. Moreover, prior to 2009, 
in the absence of a liquidity event, private equity firms did not necessarily mark their 
investments to market. This failure to mark to market leads to understatement of 
measures of volatility and correlations with other investments. Thus, data adjustments

are required to more reliably measure the benefits of private equity investing.
Exhibit 9 lists annualized standard deviations of published quarterly and annual 
returns of private equity investments from 1990 through 2014. The volatility calculated 
using published quarterly returns reflects few liquidity events and results in much 
lower volatility estimates than using annual returns. Note that the difference between 
the two measures (quarterly and annual) using MSCI World is insignificant because 
the stocks in the index are marked to market regularly. In July 2009, private equity

Reading 58 ■ Introduction to Alternative Investments 156
firms began reporting investments at their estimated fair values; these estimates are 
frequently based on market multiples. This change in valuation methodology is reflected 
in the new International Private Equity and Venture Capital Valuation Guidelines.28
Exhibit 9   Annualized Standard Deviations of Returns to 
Private Equity Investments, 1990–2014
Quarterly Annual
Venture capital* 22.3 54.5
Private equity* 12.8 21.1
MSCI World 17.1 18.4
* Cambridge Associates, LLC, January 1990–December 2014
According to the historical standard deviations of annual returns shown in Exhibit 9, 
private equity investments, including venture capital, are riskier than investing in 
common stocks. Investors should require a higher return from accepting a higher 
risk, including illiquidity and leverage risks.
Even given its higher risk, private equity, including venture capital investing,

may provide benefits to a diversified portfolio. If investors believe they can identify 
skillful private equity fund managers (managers who can identify attractive portfo -
lio companies and invest in them at reasonable valuations, as well as improve their 
operations and profitability), investors may benefit from superior returns (returns in 
excess of those expected given the additional leverage, market, and liquidity risks). 
Kaplan and Schoar (2005) find significant differences in the returns to the top quartile 
of funds compared with the bottom quartile of funds; the cash flow IRR was 22% a 
year for the top quartile compared with 3% a year for the bottom quartile from 1980 
through 2001. Further, Kaplan and Schoar find evidence of performance persistence. 
Identifying top-  performing funds appears to be critical.29
4.4 Portfolio Company Valuation
In order to identify and invest in attractive portfolio companies, private equity profes -

sionals must be able to value those companies. Three common approaches are used 
in the private equity industry to value a company: market or comparable, discounted 
cash flow (DCF), and asset based. Which approaches are favored depend in part on 
the portfolio company’s industry, and it is common for funds to use more than one 
approach to arrive at a value.
A market or comparables approach values a company or its equity using multiples 
of different measures. For example, an earnings before interest, taxes, depreciation, 
and amortization (EBITDA) multiple is commonly used in valuing large, mature pri -
vate companies that are capital intensive and leveraged. For other types of companies, 
multiples of measures based on net income or revenue may be more appropriate. The 
EBITDA multiple may be determined by looking at the market value of equity plus 
debt (enterprise value) of a similar publicly traded company or the price recently paid

28 Interestingly, based on the calculations of author Scott Stewart, data since July 2009 are inconsistent 
with improvements in marking to market.
29 See the CFA Research Foundation’s 2013 monograph Manager Selection  for information on selecting 
skillful alternative investment managers.

Private Equity 157
for a comparable business, divided by EBITDA. Net income and revenue multiples 
may be based on the multiples from transactions in comparable companies but are 
frequently based on heuristics.30
EXAMPLE 7   
Portfolio Company Valuation
A private equity fund is considering purchasing a radio broadcaster that had 
an EBITDA of $200 million. In the past year, three radio broadcasting compa -
nies were sold for 8 × EBITDA, 10 × EBITDA, and 9 × EBITDA. Based on this 
information, the maximum value the private equity fund is most likely to assign 
to the broadcaster is:
A $1,600 million.
B $1,800 million.
C $2,000 million.
Solution:
C is correct. The maximum value the private equity fund is most likely to assign 
is that using the highest multiple (10 × $200 million = $2,000 million). The min -
imum value the seller may be willing to accept is that using the lowest multiple. 
In negotiations, growth prospects, risk, size, current market conditions, and so 
on will be considered.

A discounted cash flow (DCF) approach values a company or its equity as the 
present value of the relevant expected future cash flows. Future free cash flow projec -
tions may be discounted to compute a present value for the portfolio company or its 
equity. Free cash flow to the firm discounted at the weighted average cost of capital 
may be used to estimate the company’s value. Free cash flow to equity discounted 
at the cost of equity may be used to estimate the value of the company’s equity. One 
simple approach takes a measure such as income or cash flow and divides it by a capi -
talization rate to arrive at a value estimate. This approach is conceptually different but 
practically similar to using an income or cash-  based multiple. If the value estimated 
using a DCF approach is higher than the investment’s current price, the opportunity 
may be an attractive one.
An asset-  based approach values a company using the values of its underlying assets

less the value of any related liabilities. In effect, this approach arrives at the value of the 
company to the equity holders. The approach assumes that a company’s value equals 
the sum of the values of the company’s assets minus its liabilities. The valuations can 
be arrived at using market (fair) values or other values such as liquidation values. Fair 
values assume an orderly transaction, whereas liquidation values assume a distressed 
transaction. The liquidation value is an estimate of how much money could be raised 
if a company’s assets were sold in a liquidation scenario. Liquidation value is the net 
amount that will be realized if the business is terminated, the assets are sold, and the 
liabilities are satisfied. In a weak economic environment, liquidation values will most 
likely be far lower than the immediately previous fair values because there will tend 
to be many assets for sale and fewer potential buyers.

30 Heuristics are mental shortcuts based on experience and knowledge that simplify decision making. 
They are sometimes called “rules of thumb. ”

Reading 58 ■ Introduction to Alternative Investments 158
4.5 Private Equity: Investment Considerations and Due 
Diligence
Current and anticipated economic conditions, including interest rate and capital avail -
ability expectations, are critical factors to consider when evaluating an investment in 
private equity. Refinancing risk must also be evaluated. If refinancing becomes unavail -
able, a lack of financing can result in default. The extent to which there is undrawn but 
committed capital can also affect the private equity sector and the returns to investors.
Investing in private equity firms requires patience. Investors who are comfortable 
with long-  term commitment of funds and illiquidity are best suited to considering 
private equity investing. Private equity typically requires a long-  term commitment by 
an LP because of the long time lag between investments in and exits from portfolio 
companies. Once a commitment has been made and an investor becomes an LP , the

investor has very limited liquidity choices. Because many investors are averse to illi -
quidity, there should be a liquidity risk premium for private equity investors.
Assuming these characteristics are acceptable, the investor must consider the choice 
of GP . In this regard, many of the due diligence questions for hedge fund selection 
are relevant for private equity. Some of the important issues to investigate are the 
GP’s experience and knowledge—financial and operating, the valuation methodology 
used, the alignment of the GP’s incentives with the LPs’ interests, the plan to draw on 
committed capital, and the planned exit strategies.
REAL ESTATE
Real estate investing is often thought of as direct or indirect ownership (equity investing) 
in real estate property such as land and buildings. Real estate investing, however, also 
includes lending (debt investing) against real estate property—for example, provid -

ing a mortgage loan or purchasing mortgage-  backed securities (MBS). The property 
generally serves as collateral for the lending.
Key reasons for investing in real estate include the following:
■■Potential for competitive long-  term total returns driven by both income genera -
tion and capital appreciation.
■■Prospect that multiple-  year leases with fixed rents for some property types may 
lessen cash flow effects from economic shocks.
■■Likelihood that less-  than-  perfect correlation with other asset classes may pro -
vide diversification benefits.
■■Potential to provide an inflation hedge if rents can be adjusted quickly for 
inflation.
Real estate property ownership is represented by a title and may reflect access to 
air rights, mineral rights, and surface rights in addition to the rights of use of buildings 
and land. Titles can be purchased, leased, sold, mortgaged, or transferred together 
or separately, in whole or in part. Real estate investments may also be in the form of

partnerships, equity, or debt. Much real estate is residential, but if it is owned with 
the intention to let, lease, or rent it in order to generate income, it is classified as 
commercial (i.e., income-  producing) real estate. In addition to residential real estate 
classified as commercial, commercial real estate includes other types of real estate 
properties such as office and retail properties. Some real estate properties may be 
farmed, provide forest products, or have natural resources that can be obtained by 
extraction to generate income. The resulting products, such as wheat, timber, gold, 
and oil, are considered commodities. As a result, some investors include timberland 5

Real Estate 159
and farmland in their commodities portfolio rather than in their real estate portfolio. 
Other investors simply treat farmland and timberland as a separate category from 
both real estate and commodities.
Institutional ownership of commercial property totaled close to $2.5 trillion as of 
2014, as shown in Exhibit 10, up from $2.1 trillion in 2008.
Exhibit 10   Institutionally Owned Global Real Estate 
Property AUM, 2014 (US$ millions)
Europe 922,064
North America 1,244,464
Australasia 102,672
Asia 136,896
Latin America 23,808
Other 50,096
Total 2,480,000
Source:  Based on data from Property Funds Research.
Real estate property exhibits unique features compared with other investment 
asset classes. The basic indivisibility, unique characteristics (i.e., no two properties 
are identical), and fixed location of real estate property have implications for inves -
tors. For example, the size of investment may have to be large and may be relatively

illiquid. Also, real estate property typically requires operational management. Real 
estate may be subject to government regulations affecting what can be done to modify 
the existing land or property, to whom and how ownership can be transferred, and to 
other restrictions on ownership. Local or regional markets and real estate property 
values can be independent of countrywide or global price movements, because local 
factors may override wider market trends. Cross-  border investment in real estate is 
increasingly common and requires knowledge of country, regional, and local markets.
5.1 Forms of Real Estate Investment
Real estate investing may take a variety of forms. Real estate investments may be clas -
sified along two dimensions: debt or equity based, and in private or public markets. 
Equity investments in real estate that occur in the private markets are often referred 
to as direct investments in real estate. The money to finance real estate property

purchases comes from many sources. A well-  known form of debt financing of real 
estate purchases is mortgages. Private investors—institutional and individual, real 
estate corporations, and REITs—may provide the equity financing for the purchase.
REITs sell shares to raise funds to make property purchases. REIT shares are 
typically publicly traded and represent an indirect investment in real estate property. 
Similarly, mortgages may be packaged and securitized into asset-  backed securitized 
debt obligations (i.e., MBS) that represent rights to receive cash flows from portfolios 
of mortgage loans. Exhibit 11 shows some examples of the basic forms of real estate 

Reading 58 ■ Introduction to Alternative Investments 160
Exhibit 11   Basic Forms of Real Estate Investments and Examples
Debt Equity
Private ■■Mortgages
■■Construction lending■■Direct ownership of real estate. 
Ownership can be through, sole 
ownership, joint ventures, real 
estate limited partnerships, or 
other commingled funds.
Public ■■MBS (residential and 
commercial)
■■Collateralized mortgage 
obligations■■Shares in real estate 
corporations
■■Shares of REITs
Within the basic forms, there can be many variations.
■■Direct ownership can be free and clear, whereby the title to the property is 
transferred to the owner unencumbered by any financing lien, such as from a 
mortgage. Initial purchase costs associated with direct ownership may include 
legal expenses, survey costs, engineering/environmental studies, and valuation 
(appraisal) fees. Of course, ongoing maintenance and refurbishment charges 
are also incurred. The property must be managed, which has related costs. The

owner may manage the property or may employ a local managing agent.
■■Leveraged ownership occurs when the property title is obtained through an 
equity purchase combined with mortgage financing. In addition to the initial 
purchase costs, there are mortgage arrangement fees. A mortgage is secured 
by the property, and in the event of a breach of lending terms, the creditor can 
petition for the title. Any appreciation (depreciation) of the property’s value 
plus the net operating income in excess of the debt servicing costs provides 
investors with a leveraged gain (loss) on their equity.
■■Financing provided to leveraged owners is frequently in the form of stand-  alone 
mortgage loans. These loans represent passive investments in which the lender 
expects to receive a predefined stream of payments throughout the finite life 
of the mortgage. The loan may become a form of property ownership if the 
borrower defaults. Investments may be in the form of “whole” loans based on

specific properties (typically, direct investment through private markets) or 
through participation in a pool of mortgage loans (typically, indirect investment 
in real estate through publicly traded securities such as MBS).
■■Real estate equity investors may use different types of pooled vehicles arranged 
by an intermediary. These vehicles include the following:
■●Real estate limited partnerships offer exposure to real estate projects 
while preserving limited liability (to the amount of the initial investment) 
and leaving management and liability to GPs who specialize in real estate 
■●REITs issue shares that are typically publicly traded. REITs invest in various 
types of real estate and provide retail investors with access to a diversified 
real estate property portfolio and professional management. REITs are 
required to distribute most of their taxable income to their shareholders.
■■Securitization of residential and commercial mortgages provides retail and

institutional investors with access to a diversified portfolio of mortgages and 
allows the original lenders to alter their portfolio of investments. Mortgages are 
combined into pools and then into slices (called tranches) by investment banks.

Real Estate 161
The tranches, each having different payment characteristics, are then sold to 
investors. These securities are generally not considered alternative investments 
but are held as part of the fixed-  income (or credit) portfolio.
REITs and partnerships have fees for managing the assets embedded in their val -
uations. Fee structures for investment funds can be similar to those in private equity, 
with investment management fees based on committed capital or invested capital. 
These fees typically range from 1% to 2% of capital per annum. Funds also charge 
performance-  based fees, similar to a private equity fund.
5.2 Real Estate Investment Categories
The majority of real estate property may be classified as either commercial or resi -
dential. In this reading, residential properties are defined narrowly to include only 
owner-  occupied, single residences (often referred to as single-  family residential

property). Residential properties owned with the intention to let, lease, or rent them 
are classified as commercial. Commercial properties also include office, retail, indus -
trial and warehouse, and hospitality (e.g., hotel and motel) properties. Commercial 
properties may also have mixed uses. Commercial properties generate returns from 
income (e.g., rent) and capital appreciation. Several factors will affect opportunities 
for capital appreciation, including development strategies, market conditions, and 
property-  specific features.
5.2.1  Residential Property
For many individuals and families, real estate investment takes the form of direct equity 
investment (i.e., ownership) in a residence with the intent to occupy.31 In other words, 
a home is purchased. Given the price of homes, most purchasers cannot provide the 
entire financing (i.e., pay cash) and must borrow funds to make the purchase. Any 
appreciation (depreciation) in the value of the home increases (decreases) the owner’s

equity in the home.
Financial institutions are the main providers (originators) of debt financing (typ -
ically, through mortgages) for home ownership. The originators of single-  family res -
idential mortgages are making a direct, debt investment in the home. Before offering 
a mortgage, the due diligence process should include the following:
■■ensuring that the borrower is making an appropriate equity investment in the 
home (in other words, paying an adequate proportion of the purchase price),
■■conducting a credit review of the borrower,
■■establishing that the borrower has sufficient cash flows to make the required 
payments on the mortgage and to maintain the home,
■■appraising (estimating the value of) the home, and
■■ensuring that adequate and appropriate insurance is in place on the home and, 
in some cases, on the borrower.
Home loans may be held on the originator’s balance sheet or securitized and 
offered to the financial markets. Securitization provides indirect, debt investment

opportunities in residential property via securitized debt products, such as residential 
mortgage-  backed securities (RMBS), to other investors.
31 Residential properties (single- or multi-  family) are considered commercial property if they are main -
tained as rental properties.

Reading 58 ■ Introduction to Alternative Investments 162
5.2.2  Commercial Real Estate
Commercial property has traditionally been considered an appropriate direct invest -
ment—equity and debt—for institutional funds or high-  net- worth individuals with long 
time horizons and limited liquidity needs. This perception of appropriateness for only 
certain types of investors was primarily because of the complexity of the investments, 
the large investments required, and the relative illiquidity of the investments. Direct, 
equity investing (i.e., ownership) is further complicated because commercial property 
requires active and experienced, professional management. The success of the equity 
investment is a function of a variety of factors, including how well the property is 
managed, general economic and specific real estate market conditions, and the extent 
and terms of any debt financing.
In order to provide direct debt financing, the lender (investor) will conduct finan -

cial analyses to establish the borrower’s creditworthiness, to ensure that the property 
will generate cash flows sufficient to service the debt, to estimate the value of the 
property, and to evaluate economic conditions. The estimate of the property value 
is critical because the loan-  to- value ratio is a critical factor in the lending decision. 
The borrower’s equity in the property is an indicator of commitment to the success 
of the project and provides a cushion to the lender because the property is generally 
used as collateral for the loan.
Indirect investment vehicles provide individual investors with the opportunity to 
invest in real estate. For example, shares of REITs provide indirect, equity investment 
opportunities in real estate, and commercial mortgage-  backed securities (CMBS) 
provide indirect, debt investment opportunities in real estate.
5.2.3  REIT Investing
REITs are listed on stock exchanges in more than 35 countries, and their combined

market capitalization exceeded $1.1 trillion in 2016.32 The risk and return character -
istics of REITs depend on the type of investment they make. Mortgage REITs, which 
invest primarily in mortgages, are similar to fixed-  income investments. Equity REITs, 
which invest primarily in commercial or residential properties and use leverage, are 
similar to direct equity investments in leveraged real estate.
Gross income from rents represents a relatively predictable income stream and, 
after servicing the debt, is a source of return to equity REITs. Although the regula -
tions with respect to REITs vary among countries, in general, equity REITs have an 
obligation to distribute the majority of their income to shareholders to retain their 
regulatory tax-  advantaged status. Often, at least 90% of revenue (including rent and 
realized capital gains), net of expenses, must be distributed in the form of dividends.
The business strategy for equity REITs is simple: Maximize property occupancy

rates and rents in order to maximize income and dividends. Equity REITs, like other 
public companies, must report earnings per share based on net income as defined by 
generally accepted accounting principles (GAAP).
5.2.4  Mortgage-  Backed Securities (MBS)
The MBS structure is based on the securitization model of buying a pool of assets 
and assigning the income and principal returns into individual security tranches, as 
illustrated in Exhibit 12 for commercial mortgage-  backed securities (CMBS). On the 
right-  hand side of the exhibit, the ranking of losses indicates the priority of claims 
against the real estate property. MBS may be issued privately or publicly. These secu -
rities are often included in broad fixed-  income indexes and in indexes that are used 
to indicate the performance of real estate investments.
32 National Association of Real Estate Investment Trusts, July 2016.

Real Estate 163
Exhibit 12   CMBS Security Structure
Collection of Assets
Pool of
PropertiesReal
Estate
AssetCombination of Funding
Pool of
LoansDebt
70%–75%
Property
Owners’ Equity
25%–30%Assorted Securities
Commercial Mortgage-
Backed SecuritiesInvestment-
Grade CMBS
60%–70%
BB Rated
B Rated
UnratedHigh-Yield
CMBS
5%–10%Last
Loss
First
LossProperty
25%–30%
5.2.5  Timberland and Farmland
Timberland offers an income stream based on the sale of timber products as a compo -
nent of total return and has historically provided a return that is not highly correlated 
with other asset classes. Timberland functions as both a factory and a warehouse. 
Timber can be grown and easily stored by not harvesting. This feature offers the 
flexibility of harvesting more trees when timber prices are up and delaying harvests 
when prices are down. Timberland has three primary return drivers: biological growth, 
commodity price changes, and land price changes.

Farmland is often perceived to provide a hedge against inflation. Its returns include 
an income component related to harvest quantities and agricultural commodity 
prices. Farmland consists of two main property types: row crops that are planted and 
harvested annually (i.e., more than one planting and harvesting can occur in a year 
depending on the crop and the climate) and permanent crops that grow on trees or 
vines. Unlike with timberland, farm products must be harvested when ripe, so there is 
little flexibility in harvesting. Farmland may also be used as pastureland for livestock. 
Similar to timberland, farmland has three primary return drivers: harvest quantities, 
commodity prices, and land price changes.
5.3 Real Estate Performance and Diversification Benefits
A variety of indexes globally are intended to measure returns to real estate. These 
indexes vary, however, in the selection and valuation of components and longevity.

A real estate index can generally be categorized as an appraisal index, a repeat sales 
(transaction-  based) index, or a REIT index. Appraisal indexes use estimates of value 
(appraisals) as inputs. These appraisals, conducted by experts, rely on comparable sales 
and cash flow analysis techniques. Even though the appraisals are done by experts, 
they are still subjective. The appraisals are done periodically, often annually, but some 
appraised values included in an index may be from more than one year earlier. This 
factor, and the way appraisals are conducted, may result in indexes that understate 
Repeat sales indexes are constructed using repeat sales of properties. The changes 
in property prices with repeat sales are measured and used to construct the index. 
These indexes suffer from a sample selection bias because the properties that sell 
in each period vary and may not be representative of the larger market. Also, the

Reading 58 ■ Introduction to Alternative Investments 164
properties that transact are not a random sample and may be biased toward those 
that have increased or decreased in value depending on current economic conditions. 
The higher the number of sales, the more reliable and relevant the index.
REIT indexes use the prices of publicly traded shares of REITs to construct the 
indexes. The more frequently the shares trade, the more reliable the index. The index 
is not necessarily representative of the properties of interest to the investor, however.
Investors will find a variety of indexes to choose from and may find one that seems 
representative of the market of interest to them. Investors should be aware, however, 
of how the index is constructed and the inherent limitations resulting from the con -
struction method. Investors should also be aware that the apparent low volatility and 
low correlation of real estate with other asset classes may result from limitations in

the real estate index construction.
Exhibit 13 provides a comparison of returns on US real estate based on different 
indexes. The National Council of Real Estate Investment Fiduciaries (NCREIF) con -
structs a variety of appraisal-  based indexes. The National Association of Real Estate 
Investment Trusts (NAREIT), together with the FTSE Group and European Public 
Real Estate Association, constructs a variety of indexes based on the prices of shares 
of REITs and listed real estate companies. The NAREIT returns based on publicly 
traded US REIT share prices are clearly more volatile—displaying a higher standard 
deviation and a lower worst-  calendar-  year return—than the NCREIF returns based 
on appraisals. The NCREIF Farmland index shows the least reported volatility. The 
lowest annualized return shown is that of commercial property based on appraisals 
(NCREIF Property index).
Exhibit 13   Historical Returns of US Real Estate Indexes, 1991–2014
NCREIF Data NAREIT

Property* Timber Farmland All REITs
Annualized return 7.8% 10.5% 11.9% 11.9%
Annualized standard 
deviation8.6% 9.2% 6.9% 18.9%
Worst calendar year –16.9% –5.2% 2.0% –37.3%
* Commercial real estate property
Exhibit 14 displays global and regional REIT returns. The table shows some dis -
parity among regional returns and supports the importance of knowledge of country, 
local, and regional markets. A cursory examination, however, indicates a significant 
degree of correlation among the regional returns. In fact, correlations between the 
regional and global returns all exceed 0.9.
Exhibit 14   Historical Returns of Global REITs
Global Americas Asia-  Pacific Europe Middle East/Africa
3 Years 15.1% 13.8% 15.3% 18.2% 19.1%
5 Years 11.5% 15.5% 7.6% 9.6%
10 Years 6.7% 7.8% 6.6% 4.1%

Real Estate 165
15 Years 9.9% 12.4% 7.4% 9.8%
Standard deviation (15-  year) 23.4% 21.6% 28.1% 30.0%
Note : Data are as of 31 December 2014.
Source:  Based on data from FTSE NAREIT.
From 1990 through 2014, the monthly return correlations of global REITs (S&P 
Global REIT Index) and global stocks (MSCI ACWI) and global REITs and global 
bonds (Bloomberg Barclays Global Aggregate Index) were 0.62 and 0.35, respectively. 
Correlations of global real estate and equity returns are relatively high, and correlation 
of global real estate and bond returns are lower. The returns from investing in REITs 
and investing in equities are more highly correlated with each other than with bonds 
because both are affected similarly by the business cycle.
5.4 Real Estate Valuation
Until a property is actually sold, real estate values can only be estimated. This estima -
tion process is often referred to as appraising the property. A variety of approaches

are used to value real estate property. Common techniques for appraising real estate 
property include comparable sales, income, and cost approaches.
■■Comparable sales approach.  This approach involves determining an approx -
imate value based on recent sales of similar properties. Adjustments are made 
for differences in key characteristics of the property being appraised and the 
sold properties identified as similar. Key characteristics include condition, age, 
location, and size. Adjustments are also made for price changes in the relevant 
real estate market between dates of sales.
■■Income approach.  Direct capitalization and discounted cash flow approaches 
are two income-  based approaches to appraising an income-  producing property.
■●The direct capitalization approach estimates the value of an income-  
producing property based on the level and quality of its net operating 
income (NOI). Similar to EBITDA, NOI represents the income to the prop -

erty after deducting operating expenses, including property taxes, insurance, 
maintenance, utilities, and repairs but before depreciation, financing costs, 
and income taxes. NOI is a proxy for property-  level operating cash flow. The 
expected annual NOI is divided by a capitalization rate (cap rate) to estimate 
the property’s value. A cap rate is a discount rate less a growth rate. The 
reciprocal of the cap rate is a multiple that can be applied to NOI. The cap 
rate is estimated for a given property based on relevant information, includ -
ing cap rates on sales of comparable properties, general business conditions, 
property quality, and assessment of management. The analysis might include 
assessing the strength of tenants, the level of landlord involvement, the 
extent and adequacy of repairs and improvements, the vacancy rate, man -
agement and operating costs, and expected inflation of costs and rent.Exhibit 14   (Continued)

Reading 58 ■ Introduction to Alternative Investments 166
■●The discounted cash flow approach discounts future projected cash flows 
to arrive at a present value for the property. Typically, the analysis involves 
projections of annual operating cash flows for a finite number of periods 
and a resale or reversion value at the end of that total period. The projected 
resale value is often estimated using a direct capitalization approach.
■■Cost approach.  This approach evaluates the property’s replacement cost by 
estimating the market value of the land and the costs of rebuilding using cur -
rent construction costs and standards. Costs include building materials, labor 
to build, tenant improvements, and various “soft” costs, including architectural, 
engineering, and construction supervision costs; legal, insurance, and bro -
kerage fees; and environmental assessment costs. The cost of rebuilding is the 
replacement cost of the building(s) in new condition and is adjusted to take into

account the location and condition of the existing building(s).
A combination and reconciliation of the values from the different approaches is typ -
ically performed to increase confidence in the appraisal.
5.4.1  REIT Valuations
REITs are composed of a portfolio of real estate properties or mortgages, and as a 
result, a REIT security’s valuation depends on the entire pool’s characteristics. There 
are two basic approaches to estimating a REIT’s intrinsic value: income based and asset 
based. The value estimates can be compared with the REIT’s observed market price.
Income-  based approaches for REITs are typically similar to the direct capitalization 
approach. A measure of income, which is a cash flow proxy, is capitalized into a value 
indication by using a cap rate (an alternative calculation could multiply the income 
measure by the reciprocal of the cap rate). Two common measures used are funds from 
operations (FFO) and adjusted funds from operations (AFFO). FFO, in its most basic

form, equals net income plus depreciation charges on real estate property less gains 
from sales of real estate property plus losses on sales of real estate property. These 
adjustments to net income effectively exclude depreciation and the gains and losses 
from sales of real estate property from the FFO. Depreciation is excluded because 
it represents a non-  cash charge and is often unrelated to changes in the value of the 
property. Gains and losses from sales are excluded because these are assumed to be 
non-  recurring. AFFO adjusts the FFO for recurring capital expenditures. It is similar 
to a free cash flow measure.
The cap rate and its reciprocal multiple are estimated based on a variety of factors, 
including market cap rates and current market and economic conditions, expecta -
tions for growth in the relevant measure, risks associated with the REIT’s underlying 
properties, the financial leverage of the REIT, and multiples of recent transactions.

Asset-  based approaches calculate a REIT’s NAV. Generally, a REIT’s NAV is calcu -
lated as the estimated market value, based on appraisals, of a REIT’s total assets minus 
the value of its total liabilities. REIT shares frequently trade at prices that differ from 
NAV per share. Both premiums and discounts to the NAV are observed in the market.
5.5 Real Estate Investment Risks
Real estate investments, like any investment, may fail to perform in accordance with 
expectations. Property values are subject to variability based on national and global 
economic conditions, local real estate conditions, and interest rate levels. Other risks 
inherent to real estate investment include the ability of fund management to select, 
finance, and manage real properties, as well as changes in government regulations. 
Management of the underlying properties includes handling rentals or leasing of the 
property, controlling expenses, directing maintenance and improvements, and ulti -

mately disposing of the property. Expenses may increase because of circumstances

Commodities 167
beyond management’s control. Returns to both debt and equity investors in real estate 
depend to a large extent on the ability of the owners or their agents to successfully 
operate the underlying properties.
Investments in distressed properties and property development are subject to 
greater risks than investments in properties with stable operations and/or in sound 
financial condition. Property development is subject to special risks, including reg -
ulatory issues, construction delays, and cost overruns. Regulatory issues include the 
failure to receive zoning, occupancy and other approvals and permits, as well as the 
effect of environmental regulation. Economic conditions can also change during the 
development and disposition period, which can be very lengthy. Adverse effects of 
regulatory issues and changes in economic condition include increasing construction 
time or the time until a property is fully leased out, increasing construction costs, and

decreasing the level of rents relative to initial expectations. Acquisitions and devel -
opments may be financed with lines of credit or other forms of temporary financing 
rather than long-  term debt financing . There is a risk that long-  term financing with 
acceptable terms might not be available when desired. Financing problems with one 
property may cause further activity by the same owner to be curtailed.
It is important to recognize that many equity investment real estate funds pursue 
leverage to potentially increase returns to their investors. Leverage magnifies the 
effect of gains and losses, because of operations and changes in property value, on 
the equity investors. Leverage increases the risk to debt investors as well as to equity 
investors. Leverage increases the risk that the real estate fund will have insufficient 
funds to make expected interest payments and that the debt investor will receive less

than the entire principal. As the loan-  to- value ratio increases, the latter risk increases.
COMMODITIES
Commodities are physical products. Returns on commodity investments are based 
on changes in price rather than on an income stream such as interest, dividends, or 
rent. In fact, holding commodities (i.e., the physical products) incurs costs for trans -
portation and storage. Thus, most commodity investors do not trade actual physical 
commodities but rather trade commodity derivatives. The underlying for a commodity 
derivative may be a single commodity or an index of commodities.
Trading in physical commodities is primarily limited to a smaller group of enti -
ties that are part of the physical supply chain. Some investors that are not part of the 
supply chain may invest in physical commodities, but the commodities are typically 
those that are non-  perishable, of high value relative to weight and volume, and easily

stored at relatively low cost. Most investors invest in commodities using commodity 
derivatives. Because the prices of commodity derivatives are, to a significant extent, a 
function of the underlying commodity prices, however, it is important to understand 
the physical supply chain and general supply–demand dynamics for a commodity. 
The supply chain consists of entities that actually produce the commodities, users of 
the commodities, and participants in between. These entities may trade commodity 
derivatives for hedging purposes. Other investors, sometimes referred to as speculators, 
trade commodity derivatives in search of profit based largely on changes or expected 
changes in the price of the underlying commodities. Non-  hedging investors include 
retail and institutional investors, hedge funds, proprietary desks within financial 
institutions, and trading desks operating within the physical supply chain.

Commodities include precious and base (i.e., industrial) metals, energy products, 
and agricultural products. Exhibit 15 shows some examples of each type. The relative 
importance, amount, and price of individual commodities evolve with society’s prefer -
ences and needs. The increasing industrialization of China, India, and other emerging 6

Reading 58 ■ Introduction to Alternative Investments 168
markets has driven strong global demand for commodities. Developing markets need 
increasing amounts of oil, steel, and other materials to support manufacturing, infra -
structure development, and consumption demands of their populations. Emerging 
technologies, such as advanced cell phones and electric vehicles, may create demand 
for new materials to meet manufacturing needs. Thus, commodities of interest evolve 
over time.
Exhibit 15   Examples of Commodities
Sector Sample Commodities
Energy Oil, natural gas, electricity, coal
Base metals Copper, aluminum, zinc, lead, tin, nickel
Precious metals Gold, silver, platinum
Agriculture Grains, livestock, coffee
Other Carbon credits, freight, forest products
Commodities may be further classified based on a variety of factors, including 
physical location and grade or quality. For example, there are many grades and locations

of oil. Similarly, there are many grades and locations of wheat. Commodity derivative 
contracts specify terms such as quantity, quality, maturity date, and delivery location.
Commodity derivatives may be attractive to investors not only for the potential 
profits but also because of the perceptions that commodities are effective hedges 
against inflation (i.e., commodity prices historically have been positively correlated 
with inflation) and that commodities are effective for portfolio diversification (i.e., 
commodity returns have historically low correlations with returns of other investments 
in the same portfolio). Institutional investors, particularly endowments, foundations, 
and increasingly corporate and public pension funds as well as sovereign wealth funds 
are allocating more of their portfolios to investments in commodities and commodity 
derivatives. There were $326 billion in commodity investments under management 
in 2015, compared with less than $20 billion in 2001.33

6.1 Commodity Derivatives and Indexes
The majority of commodities investing is implemented through derivatives, and com -
modity index futures are a popular derivative.34 Commodity derivatives include futures, 
forwards, options, and swaps. These contracts may trade on exchanges (exchange-  
traded products, or ETPs) or over the counter (OTC). They are described as follows:
■■Futures and forward contracts are obligations to buy or sell a specific amount 
of a given commodity at a fixed price, location, and date in the future. Futures 
contracts are ETPs, marked to market daily, and generally are not settled with 
delivery or receipt of the physical commodity. Forward contracts trade OTC, 
and the expectation is that delivery and receipt of the physical commodity will 
occur. Counterparty risk is higher for forward contracts.
33 Managed futures strategies; Source: BarclayHedge, http://www.barclayhedge.com/research/indices/
cta/Money_Under_Management.html

34 Stoll and Whaley (2009) report commodities indexing totaling $174 billion as of July 2009.

Commodities 169
■■Option contracts for commodities give their holders the right, but not the obli -
gation, to buy or sell a specific amount of a given commodity at a specified price 
and delivery location on or before a specified date in the future. Options can be 
ETPs or OTC traded.
■■Swap contracts are agreements to exchange streams of cash flows between two 
parties based on future commodity or commodity index prices. One party typ -
ically makes fixed payments in exchange for payments that depend on a speci -
fied commodity or commodity index price.
Commodity indexes typically use the price of futures contracts on the commodities 
included in them rather than the prices of the commodities themselves. As a result, 
the performance of a commodity index can differ widely from the performance of the 
underlying commodities. Commodity indexes also vary in the commodities included 
in them and the weighting methods used. Thus, they vary in their exposures to specific

commodities or commodity sectors.
6.2 Other Commodity Investment Vehicles
Commodity exposure can be achieved through other means than direct investment in 
commodities or commodity derivatives. Although commodity exposure is most com -
monly accessed via commodity derivatives, either directly or through an investment 
manager, alternative means are becoming increasingly popular. Alternative means of 
achieving commodity exposure include the following:
■■Exchange-  traded funds may be suitable for investors who can buy only equity 
shares or seek the simplicity of trading them. ETFs may invest in commodities 
or futures of commodities (often, specializing in a particular sector) seeking 
to track the performance of the commodities. For example, the SPDR Gold 
Shares ETF attempts to track the price of gold. It owned more than $50 billion 
in gold bullion as of November 2010 and more than $38 billion in gold bullion 
as of October 2016. There are also commodity index-  linked ETFs. ETFs may

use leverage. Similar to mutual funds or unit trusts, ETFs charge fees that are 
included in their expense ratios, although the ETF expense ratios are generally 
lower than those of most mutual funds.
■■Common stock of companies exposed to a particular commodity—such as 
Royal Dutch Shell, which is exposed to oil—may be purchased. Investors may 
consider owning shares in a few commodity-  exposed companies in order to 
have a small exposure to commodities. It is unclear, however, whether the 
performance of these stocks closely tracks the performance of the underlying 
commodity(ies).
■■Managed futures funds are actively managed investment funds. Professional 
money managers invest in the futures market (and forward market sometimes) 
on behalf of the funds. These funds historically focused on commodity futures, 
but today they may invest in other futures contracts as well. Managed futures 
funds may concentrate on specific commodity sectors or may be broadly

diversified. They are similar to hedge funds in that each fund has a GP , and fees 
typically follow a 2-  and-  20 structure. The funds may operate similarly to mutual 
funds with shares that are available to the general public, or they may operate 
like hedge funds and restrict sales to high-  net- worth and institutional investors. 
The former may appeal to retail investors because of the professional manage -
ment, low minimum investment, and relatively high liquidity.

Reading 58 ■ Introduction to Alternative Investments 170
■■Individual managed accounts are managed by chosen professional money man -
agers with expertise in commodities and futures on behalf of high-  net- worth 
individuals or institutional investors.
■■Funds exist that specialize in specific commodity sectors. For example, private 
energy partnerships, similar to private equity funds, are a popular way for insti -
tutions to gain exposure to the energy sector. Management fees can range from 
1% to 3% of committed capital with a lockup period of 10 years and extensions 
of 1- and 2-  year periods. Publicly available energy mutual funds and unit trusts 
typically focus on the oil and gas sector. They may focus on upstream (drilling), 
midstream (refineries), or downstream (chemicals). Management fees for these 
funds are in line with those of other public equity managers and range from 
0.4% to 1%.
6.3 Commodity Performance and Diversification Benefits

The arguments for investing in commodities include the potential for returns, portfolio 
diversification, and inflation protection. Investors may invest in commodities if they 
believe prices will increase in the short or intermediate terms. If commodity prices 
determine inflation index levels, then over time, on average, commodities should yield 
a zero real return. Commodity futures contracts may offer liquidity or other premiums, 
creating the opportunity for a real return different from zero.
The portfolio diversification argument is based on the observation that commod -
ities historically have behaved differently from stocks and bonds during the business 
cycle. Exhibit 16 shows the correlation between selected commodities, global equity, 
and global bond indexes. In the 25-  year period from 1990 through 2014, commodities 
exhibited a low correlation with traditional assets; the correlations of commodities with

global stocks and global bonds were 0.247 and 0.183, respectively. The correlations of 
stocks, bonds, and commodities are expected to be positive because each of the assets 
has some exposure to the global business cycle. Note that the selected commodity 
index (the S&P GSCI [Goldman Sachs Commodity Index]) is heavily weighted toward 
the energy sector and that each commodity may exhibit unique behavior.
Exhibit 16   Monthly Commodities Return Correlations, 1990–2014
Global StocksGlobal 
Bonds CommoditiesOne-  Month 
Libor US CPI
Global stocks 1.000 0.307 0.247 –0.054 –0.029
Global bonds 1.000 0.183 0.049 –0.038
Commodities 1.000 0.060 0.315
One-  month Libor 1.000 0.166
Sources:  Global stocks = MSCI ACWI; global bonds = Bloomberg Barclays Global Aggregate Index; commodities = S&P GSCI.
The argument for commodities as a hedge against inflation is related to the fact that 
some commodity prices affect inflation calculations. Commodities, especially energy

and food, affect consumers’ cost of living. The positive correlation of 0.315 between 
monthly commodity price changes and monthly changes in the US CPI supports this 
assertion. The monthly return correlations between the US CPI and global stocks and 
global bonds are close to zero. The volatility of commodity prices, especially energy 
and food, is much higher than that of reported consumer inflation. Consumer infla -
tion is computed from many products used by consumers, including housing, that

Commodities 171
change more slowly than commodity prices. Commodity investments, especially when 
combined with leverage, exhibit high volatility and have led to many well-  publicized 
losses among commodity players. Exhibit 17 provides a sample of these losses.
Exhibit 17   Large Commodity Investor Losses
Affected Company Loss
Bank of Montreal (2007) Wrong-  way bets on natural gas led to a pre-  tax loss of 
C$680 million (US$663 million)
Amaranth Advisors LLC 
(2006)Bad bets on natural gas triggered US$6.6 billion of 
losses
China Aviation Oil 
(Singapore) Corp. (2004)Loss of US$550 million on speculative oil futures 
trades, forcing debt restructuring
Source:  “The 20 Biggest Trading Disasters, ” Telegraph , January 2008.
6.4 Commodity Prices and Investments
Commodity spot prices are a function of supply and demand, costs of production 
and storage, value to users, and global economic conditions. Non-  hedging investors

with positions in physical commodities may be accumulating or divesting a particular 
commodity. Supplies of commodities are determined by production and inventory 
levels as well as the actions of non-  hedging investors. Demand for commodities is 
determined by the needs of end users and the actions of non-  hedging investors.
Commodity supplies cannot be altered quickly by producers because extended 
lead times may exist and affect production levels. For example, agricultural output 
may be altered by planting more crops and changing farming techniques, but at least 
one growing cycle is required before the actual output occurs. And for agricultural 
products, at least one factor that is outside of the producer’s control—the weather—will 
significantly affect output. Increased oil and mining production may require a number 
of years. Weather can also have a significant effect on oil production in parts of the

world. For commodities, suppliers’ inability to quickly respond to changes in demand 
levels may result in supply levels that are too low in times of economic growth and 
too high in times of economic slowing. In addition, despite advancing technology, 
the cost of new supply may grow over time. For example, the cost of new energy and 
mineral exploration tends to exceed that of past finds because easy discoveries tend 
to be exploited first. If production costs are high, producers are unlikely to produce 
more than what is needed to meet anticipated demand and are unlikely to maintain 
more than modest levels of inventory.
Overall demand levels are influenced by global manufacturing dynamics and eco -
nomic growth. Manufacturing needs can change in a period of months as orders and 
inventories vary. Investors seek to anticipate these changes by monitoring economic 
events, including government policy, inventory levels, and growth forecasts. When

demand levels and investors’ orders to buy and sell during a given period change 
quickly, the resulting mismatch of supply and demand may lead to price volatility.
6.4.1  Pricing of Commodity Futures Contracts
It is important to understand futures contracts and the sources of return for each 
commodity futures contract because commodity investments often involve the use of 
futures contracts. These contracts trade on exchanges. The buyer (i.e., the long side) of 
a futures contract is obligated to take delivery of the commodity or its cash equivalent 
based on the spot price at expiration and will pay a settlement price. The settlement

Reading 58 ■ Introduction to Alternative Investments 172
price is an amount specified in the contract or the previous mark-  to- market price if 
the contract has been marked to market. In other words, the long side is obligated 
to buy the commodity at the settlement price. The long side of a futures contract 
increases in value when the underlying commodity increases in value. The seller of a 
futures contract (i.e., the short side) is obligated to deliver the commodity or its cash 
equivalent based on the spot price at expiration and will receive the settlement price.
Futures positions are often closed over the life of the contract by taking the oppo -
site position to that originally entered into. In other words, the long side will sell an 
identical futures contract, and the short side will buy an identical futures contract. 
If a contract is outstanding at expiration, it is typically not settled by delivery and

receipt of the physical commodity but rather is settled by cash equal to the difference 
between the cash equivalent and settlement price. If a contract is physically settled, 
specific rules apply that define the characteristics of acceptable delivery, such as the 
quality of the commodity and the delivery location.
Parties to a futures contract are required to make an initial margin payment on 
the contract; each party has a separate margin account. Futures contracts and margin 
accounts are typically marked to market daily. On a daily basis, the futures exchange 
calculates price changes in the contract and the values of the margin accounts given 
the new price. If the value in a margin account declines sufficiently, the investor will 
receive a margin call and will be required to make an additional payment into the 
margin account. If the investor is unable or unwilling to do so, the investor’s position 
will be closed.

Given the characteristics of a commodity, the price of a futures contract (futures 
price) may be approximated by the following formula:35
Futures price ≈ Spot price (1 + r) + Storage costs – Convenience yield
where r is the period’s short-  term risk-  free interest rate. Arbitrage opportunities exist 
if the futures price differs from the spot price compounded at the risk-  free rate. For 
example, if a commodity’s spot price is 100, the risk-  free rate is 5%, and the one-  year 
futures price is 107 as opposed to 105, an arbitrageur can buy the commodity for 100 
and sell a futures contract for 107. Assuming no storage costs, when the commodity 
is delivered for 107, the arbitrageur earns 2 points in excess of that earned investing 
in the risk-  free asset. Commodities typically incur a storage cost, however. The buyer 
of a futures contract, in effect, gains access to the commodity in the future without

buying it now and incurring storage costs. The futures price includes an amount for 
storage costs of the underlying commodity during the life of the contract. The storage 
and interest costs together are sometimes referred to as “the cost of carry” or “the 
carry. ” Finally, the buyer of the futures contract has no immediate access to the com -
modity but will receive it in the future. The buyer has given up the convenience of 
having physical possession of the commodity and having it immediately available for 
use. The futures price is adjusted for the loss of convenience; the convenience yield is 
subtracted to arrive at the futures price. The value of convenience may vary over time 
and across users. For example, the convenience yield to having heating oil in January 
in Canada is higher than the convenience yield to having heating oil in Canada in July 
or to having heating oil in Australia in January.
Futures prices may be higher or lower than spot prices depending on the con -

venience yield. When futures prices are higher than the spot price, the commodity 
forward curve is upward sloping, and the prices are referred to as being in contango. 
Contango  occurs when there is little or no convenience yield. When futures prices 
35 Futures pricing is discussed in greater detail in Level II of the CFA Program curriculum.

Infrastructure 173
are lower than the spot price, the commodity forward curve is downward sloping, 
and the prices are referred to as being in backwardation. Backwardation  occurs when 
the convenience yield is high.
There are three sources of return for each commodity futures contract: the roll 
yield, the collateral yield, and the change in spot prices for the underlying commodity.
Roll Yield  The term “roll yield” refers to the difference between a commodity’s spot 
price and the price specified by its futures contract (or the difference between two futures 
contracts with different expiration dates). The formula shows that, with a convenience 
yield high enough to position the futures price below the spot price, the price of the 
futures contract generally rolls up to the spot price as the expiry date of the futures 
contract approaches. This price convergence earns the bearer of the futures contract a

positive roll yield. This explanation is called the theory of storage . An alternative theory, 
called the hedging pressure hypothesis , suggests the difference between the spot and 
futures price is determined by user preferences and risk premiums.
Collateral Yield  The collateral yield component of commodity index returns is the 
interest earned on the collateral (plus invested cash up to the value of the underlying 
asset) posted as a good-  faith deposit for the futures contracts. In measuring this return 
component, index managers typically assume that futures contracts are fully collateral -
ized and that the collateral is invested in risk-  free assets. Thus, the returns on a passive 
investment in commodity futures are expected to equal the return on the collateral 
plus a risk premium (i.e., the hedging pressure hypothesis) or the convenience yield 
net of storage costs (i.e., the theory of storage).
Change in Spot Prices  The primary determinant of spot (or current) prices is the

relationship between current supply and demand, as discussed earlier.
INFRASTRUCTURE
The assets underlying infrastructure investments are real, capital intensive, long-  lived 
assets, which are intended for public use and provide essential services. Most infra -
structure assets are financed, owned, and operated by governments, but increasingly, 
infrastructure assets are being financed privately. The use of public–private partner -
ships (PPPs) is increasing. By the end of 2014, unlisted funds had invested more than 
$200 billion in infrastructure projects, up from $6 billion in 2004.36
The intent of infrastructure investor(s) may be to lease the assets back to the gov -
ernment, to sell newly constructed assets to the government, or to hold and operate 
the assets. From an investment perspective, if the assets are being held and operated, 
the relatively inelastic demand for the assets and services is advantageous; regulation

and the high costs of the assets create high barriers to entry, which give the provider 
of the services a strong competitive position. Investors expect these assets to generate 
stable cash flows, which adjust for economic growth and inflation. Investors may also 
expect capital appreciation depending on the type of investment.
Investing in infrastructure may enable investors to add a steady income stream, to 
further diversify their portfolio by adding an asset class with low correlation to other 
investments, and to gain some protection against inflation. Infrastructure investments, 
which are in long-  lived assets, may also better match the longer-  term liability structure 
of some investors, such as pension funds and life insurance companies. Allocations to 7
36 Preqin Performance Analyst, 2015.

Reading 58 ■ Introduction to Alternative Investments 174
infrastructure investments have increased because of interest by investors (demand 
side) and desire by governments to finance infrastructure assets and to privatize the 
provision of services and the underlying assets (supply side).
7.1 Categories of Infrastructure Investments
Infrastructure investments are frequently categorized based on underlying assets. The 
broadest categorization is into economic and social infrastructure assets. Economic 
infrastructure assets are necessary to support economic activity and include assets 
such as transportation and utility assets. Transportation assets include assets such as 
roads, bridges, tunnels, airports, ports, and railway lines. Utility assets include assets 
to transmit, store, and distribute gas, water, and electricity; generate power; treat 
waste; and broadcast and transmit information. The latter assets may be categorized

separately as communication assets. Social infrastructure assets are directed toward 
human activities and include assets such as educational, healthcare, and correctional 
facilities.
Infrastructure investments may also be categorized by the underlying asset’s 
stage of development. Investing in existing infrastructure assets may be referred to 
as brownfield investment. The assets may be currently owned by a government that 
wants to privatize the asset, to lease out the asset, or to sell and lease back the asset. 
Typically, some financial and operating history is available on the asset. Investing 
in infrastructure assets that are to be constructed may be referred to as greenfield 
investment. The intent may be to hold and operate the assets or to lease or sell the 
assets to the government after construction.
Infrastructure investments may also be categorized by the geographical location 
of the underlying assets. Infrastructure investments are available globally. Risks and

expected returns may differ based on the underlying asset’s category, stage of devel -
opment, and geographical location. The form of investment also affects risks and 
7.2 Forms of Infrastructure Investments
Infrastructure investments, similar to real estate investments, may take a variety of 
forms. The investment form potentially affects the investment’s liquidity as well as 
the cash flows and income streams to the investor. An investor may invest directly in 
the underlying assets, but most investors invest indirectly. Investing directly in infra -
structure provides control over the asset and the opportunity to capture the asset’s full 
value. But it entails a large investment, resulting in concentration and liquidity risks, 
and the assets must be managed and operated . Indirect investment vehicles include 
shares of companies, ETFs, listed funds, private equity funds, and unlisted mutual funds

that invest in infrastructure. Investors concerned about liquidity may choose to invest 
through publicly traded infrastructure securities and/or master limited partnerships.
Publicly traded infrastructure securities provide the benefit of not only liquidity but 
also reasonable fees, transparent governance, market prices, and the ability to diversify 
across underlying assets. An investor should be aware, however, that publicly traded 
infrastructure securities represent a small segment of the infrastructure investment 
universe and tend to be clustered in categories of assets. Master limited partnerships 
(MLPs) trade on exchanges and are pass-  through entities similar to REITs. Similar to 
REITs, regulations may vary across countries, and income is allocated to the investors 
for taxation. MLPs generally distribute most free cash flow to their investors. Typically, 
the GP manages the partnership, receives a fee, and holds a small partnership interest.

Other Alternative Investments 175
7.3 Risks and Returns Overview
The lowest-  risk infrastructure investments have more-  stable cash flows and higher 
dividend payout ratios but also typically have fewer growth opportunities and lower 
expected returns compared with higher-  risk infrastructure investments. For example, 
an investment in an MLP with a brownfield investment in an asset that is being leased 
back to a government, such as a school, or in an asset with a history of steady cash 
flows, such as some toll roads, represents a low-  risk infrastructure investment. An 
investment in a private equity fund with a greenfield investment is a riskier investment.
Risks include revenues being different than expected, leverage creating financing 
risk, operational risk, and construction risk. An inherent risk for many infrastructure 
investments is regulatory risk. Because essential services are often being provided,

governments typically regulate many aspects of infrastructure investments, including 
the sale of the underlying assets, operations of the assets including service quality, 
and prices/profit margins. Global infrastructure investing introduces additional risks, 
such as currency, political, and profit repatriation risks.
Preqin maintains a return series of private funds investing in infrastructure deals. 
Standard and Poor’s, FTSE, and other firms publish indexes of publicly traded infra -
structure companies. For the five years ending December 2014, the Preqin index37 
returned 10.1% per annum, the S&P and FTSE infrastructure indexes returned on 
average 10.4%, and the MSCI global equity index (ACWI) returned 9.7%.
OTHER ALTERNATIVE INVESTMENTS
Numerous other investments do not fit within the definition of traditional investments 
(i.e., long-  only investments in stocks, bonds, and cash) and may be considered alter -

native investments. Many of these other investments are categorized as collectibles.
Collectibles are tangible assets such as antiques and fine art, fine wine, rare stamps 
and coins, jewelry and watches, and sports memorabilia. Collectibles do not provide 
current income, but they can potentially provide long-  term capital appreciation, 
diversify a portfolio, and be a source of enjoyment while held. There is no guarantee, 
however, that an investor will realize any of these benefits. Collectibles can fluctuate 
dramatically in value and be highly illiquid, with potential difficulty in realizing gains. 
Transactions can occur in a number of ways and settings, including through profes -
sional auctioneers; in local flea markets, online auctions, garage sales, and antique 
stores; or directly with personal collectors. Investors must have a degree of expertise; 
otherwise, one may be vulnerable to fads, fakes, and fraud. Also, some collectibles must

be stored in appropriate conditions to preserve their condition and avoid declines in 
value because of the asset’s deterioration. Wine should be cellared, art should be kept 
in a humidity- and temperature-  controlled environment, and coins and stamps must 
be handled with care to preserve their values. Although some collectibles (e.g., some 
great wines; fine art; and rare stamps, coins, and trading cards) have experienced great 
appreciation, this result is by no means the norm.
A number of indexes provide information about returns to these investments. 
None of these indexes is necessarily reliable or representative of performance for a 
collectibles asset class as a whole. For instance, the Stanley Gibbons GB250 Stamp 
Index measures the performance, using retail and auction prices, of 250 rare stamps 
traded in Great Britain. This index has increased from £3,253,500 at the end of 2005 8
37 Note that these returns are based on fund IRR calculations.

Reading 58 ■ Introduction to Alternative Investments 176
to £8,471,750 at the end of 2014.38 This increase equals a 10% annual return during 
the 10-  year period. This return, however, does not represent the return to the overall 
population of traded stamps.
The popularity of art as an investment has led to the creation of a number of art 
price indexes. For example, Artprice provides statistics, econometric data, and indexes 
to help measure returns on artworks. Another company that develops indexes, Art 
Market Research, does not restrict itself to art but has more than 500 indexes in three 
broad categories: Painting; Antiques, Collectibles, Etc.; and Other Markets. These 
indexes range from very broad (e.g., Painting [General] and Antiques [General]) to 
more specific (e.g., Chinese Ceramics [General] and Ancient Coins [General]) to very 
specific (e.g., Wrist-  Watches Patek Philippe, Continental Flint-  Lock Pistols 1700–1800,

and in wine, Château Lafite 1961). Subscribers are even able to specify parameters 
and create their own indexes. Christie’s first published an index of wine auction prices 
(listed by château) in 1972.
Collectors have no doubt been trading sports memorabilia since sporting events 
began taking place. One can only imagine the market for a piece of equipment or a 
keepsake of a martial artist in ancient China, an Olympian in ancient Greece, or a 
gladiator in ancient Rome. Trading cards—sports and other—have been swapped 
and sold in the United States since the early 1900s and are increasing in popularity 
elsewhere.39 As is the case with any collectible, considerable expertise and perhaps a 
little luck are required to invest successfully in sports memorabilia.
RISK MANAGEMENT OVERVIEW
Alternative investments pose unusual challenges for investors seeking to manage risk. 
They are often characterized by asymmetric risk and return profiles, limited portfolio

transparency, and illiquidity. Investors in alternatives may be exposed to a variety of 
risks, including operational risk, financial risk, counterparty risk, and liquidity risk. 
The returns to some types of alternatives, such as private equity, may rely to a great 
extent on manager skill rather than on general asset class performance. For these 
reasons, traditional risk and return measures (such as mean return, standard deviation 
of returns, and beta) may not provide an adequate picture of alternative investments’ 
characteristics. Moreover, these measures may be unreliable or not representative of 
specific investments.
9.1 Investment and Risk Management Process
Investment risk management is not solely the responsibility of either the investor or 
the manager of an investment portfolio. The investor, possibly in consultation with 
others, decides on an allocation to alternative investments. The investor then needs to

decide the vehicles and managers of the investments as well as the amounts that will 
be allocated to each alternative investment class and manager. Risk has to be taken 
into account and due diligence conducted in making these decisions. The investment 
portfolio manager makes investment decisions consistent with the portfolio’s estab -
lished investment policies, taking risk into account. Investor due diligence should be 
used to ensure the portfolio manager effectively manages portfolio risk. Pension con -
sultants, wealth managers, and individual investors all recognize that risk management 
processes can differ substantially between different alternative investment categories.9
38 http://www.stanleygibbons.com/investment/gb250-  stamp-  index/.
39 The most valuable baseball card in history, T206 Honus Wagner, was sold in 2007 for $2.35 million.

Risk Management Overview 177
9.1.1  Risk Management Issues
Risks vary across alternative investments. The risks associated with investing in private 
markets (e.g., private equity funds and real estate ownership) differ from the risks 
associated with investing in publicly traded markets (e.g., commodity futures and 
REITs). Private equity and direct real estate ownership may involve selecting companies 
or properties, managing them, and then selling them years later. Private equity and 
hedge funds may have long lockup periods. As a result, investors’ funds may be tied 
up for years. Intermediate valuations are challenging. As a result, any malfeasance 
or mismanagement may go undetected for years, so investor due diligence is critical. 
The illiquid nature of alternative investments also means that poor manager selection 
can create a lingering drag on the portfolio. Limited partnership vehicles may limit 
the visibility of underlying holdings and liquidity to investor assets.

Portfolios of publicly traded securities are more liquid and have prices that are 
more timely and observable than those of privately held assets. For investors who seek 
liquidity, publicly traded securities such as shares of REITs, ETFs, and publicly traded 
private equity firms may serve as the means for investing in alternatives.
9.1.2  Risk Issues for Implementation
For allocation purposes, the investor should recognize that historical returns and the 
standard deviation of those returns using indexes may not be representative of the 
returns and volatility of alternative investments. Further, those investments’ reported 
correlations with other investments may vary from the actual correlations. As is always 
the case, even if these are relevant and representative measures of historical perfor -
mance, past performance is not necessarily representative of future performance. The 
performance of alternative investments can be highly correlated with the business

cycle, especially commodities and real estate investments, and may be susceptible to 
bubbles (i.e., much higher prices than justified by fundamentals). Investors should 
consider valuation before making allocation changes.
When selecting managers or funds, the investor should recognize that returns 
and risks may differ significantly among individual managers or funds and the overall 
investment class. Large institutional investors deal with this challenge by diversifying 
across managers or funds, but this approach may not be practical for smaller investors. 
As a result, these smaller investors may invest in (publicly traded) or with (private) a 
few large, diversified funds.
Alternative investment portfolio managers need to be mindful of several risks. In the 
case of illiquid investments, most notably in private equity or venture capital, there is a 
real possibility of 100% loss of equity on individual investments. As a result, portfolios

should be diversified sufficiently to reduce the possibility of this outcome happening 
to all investments. Investors commonly require managers to follow diversification 
concentration guidelines to limit these risks. At the same time, the manager should 
avoid diluting the opportunity for making substantial returns by arbitrarily identifying 
a target number of investments and, in the process, selecting inferior investments. 
Managers should consider and manage the risk associated with the use of leverage.
Performance fee structures, although high, may encourage alignment of interests 
between investors and managers. Established portfolio managers, however, may seek 
to attract large amounts of capital and to profit from the management fees based on 
AUM or committed capital without seeking superior performance. Performance fees 
may also encourage hedge fund managers who experience a large loss to liquidate 
their funds instead of working them back to par.

Reading 58 ■ Introduction to Alternative Investments 178
9.1.3  Due Diligence Issues Regarding Risk
Due diligence of alternative investment managers necessitates special procedures, 
over and above the process required for a manager of a portfolio of publicly traded 
securities. Historical performance measures may be unreliable or not representative 
as a result of intermediate valuation estimates and narrow portfolio diversification. 
With limited transparency and long horizons of many alternative investments, the 
honesty of the company’s staff needs to be carefully reviewed.
Hedge funds will have trading desks much like long-  only investment firms, but 
private equity and real estate companies usually make investment decisions via an 
investment committee of partners. The investment committee may or may not include 
external non-  executive directors or subject matter experts. The committee votes on 
the rationale, analysis, and suitability of every investment and requires a majority in

favor before investor funds are committed. This committee may also oversee and vote 
on investments’ exit strategies, including timing and realization price.
Independent valuation of illiquid underlying assets should be performed regularly. 
Often, this analysis is done in conjunction with a portfolio review explaining the per -
formance of every transaction in detail, its status, and future strategy for the portfolio. 
Limits on security type, leverage, sector, geography, and individual positions should 
be well defined in the offering memorandum, and the positions should be carefully 
monitored by the manager and regularly reported to clients.
Hedge fund risk is often monitored by a chief risk officer, who should be separated 
from the investment process. As part of the risk management process, a hedge fund 
needs to establish and maintain limits on leverage, sector, and individual positions. 
Investments in commodities may be subject to counterparty risks as well as leverage

risks. The exposure to counterparty risk and leverage risk should be regularly monitored 
and reported. Policies limiting leverage, positions, and sectors as well as counterparty 
exposures may be adopted.
One issue for investors is that hedge and commodity funds may seek to keep their 
positions and strategies private. This lack of transparency makes it difficult for the 
investor to effectively manage diversification across funds and to conduct adequate 
due diligence.
9.2 Risk–Return Measures
The Sharpe ratio is a risk–return measure frequently reported because of its ease 
of calculation and understandability. The Sharpe ratio may not be the appropriate 
risk–return measure for some alternative investments because measures of return and 
standard deviation may be irrelevant or unreliable given the assets’ illiquid nature. The 
illiquid nature of these assets means that estimates, rather than observable transaction

prices, may be used for valuation purposes. As a result, returns may be smoothed 
and/or overstated and the volatility of returns understated. Also, the use of standard 
deviation to measure risk ignores the diversification effect for a broad portfolio of 
managers and alternative investments.
Many alternative investments do not exhibit close-  to- normal distributions of 
returns, which is a crucial assumption for standard deviation’s validity as a com -
prehensive risk measure. Alternative investment returns tend to be leptokurtic, 
or negatively skewed (in other words, they have fat tails characterized by positive 
average returns and long-  tails downside characterized by potential extreme losses). 
For this reason, a measure of downside risk, ideally non-  normal, would be useful. 
Downside risk measures focus on the left side of the return distribution curve where 
losses occur. For example, value at risk (VaR) is a measure of the minimum amount

of loss expected for a given period at a given level of probability. In other words, this 
measure answers a question such as, “What is the minimum amount expected to be

Risk Management Overview 179
lost in a year with a 5% probability?” This measure, however, if it is calculated using 
standard deviation, will underestimate the VaR for a negatively skewed distribution. 
Shortfall or safety-  first risk measures the probability that the portfolio value will fall 
below some minimum acceptable level over a given period. In other words, this mea -
sure answers a question such as, “What is the probability of losing 20% of principal 
in any given year?” Shortfall risk also uses standard deviation as the measure of risk. 
The Sortino ratio, another risk–return measure, uses downside deviation rather than 
standard deviation as a measure of risk. Assuming normal probability distributions 
when calculating these measures will lead to underestimating downside risk for a 
negatively skewed distribution.
Understanding and evaluating “tail events”—low-  probability, high-  severity instances

of stress—is an important yet extraordinarily difficult aspect of the risk management 
process. Stress testing/scenario analysis is often used as a complement to VaR to 
develop a better understanding of a portfolio’s potential loss under both normal and 
stressed market conditions. Stress testing involves estimating losses under extremely 
unfavorable conditions.
9.3 Due Diligence Overview
Manager selection is a critical factor in portfolio performance. A manager should have 
a verifiable track record and display a high level of expertise and experience with the 
asset type. The asset management team should be assigned an appropriate workload 
and provided sufficient resources. Moreover, it should be rewarded with an effective 
compensation package to ensure alignment of interest, continuity, motivation, and 
thoughtful oversight of assets.
Fraud, although infrequent, is always a possibility. The investor should be skeptical

of unusually good and overly consistent reported performance. Third-  party custody 
of assets and independent verification of results can help reduce the chance of an 
investor being defrauded. Diversification across managers is also wise.
For an investor considering a new investment, a proper due diligence process 
should be carried out to ensure that the targeted investment is in compliance with 
its prospectus and that it will meet her investment strategy, risk and return objec -
tives, and restrictions. Existing investors should monitor results and fund holdings 
to determine whether a fund has performed in line with expectations and continues 
to comply with its prospectus.
Exhibit  18 lists key items that should be considered in a typical due diligence 
process.

Reading 58 ■ Introduction to Alternative Investments 180
Exhibit 18   A Typical Due Diligence Process
Organization ■■Experience and quality of management team, compensation, and staffing
■■Analysis of prior and current funds
■■Track record/alignment of interests
■■Reputation and quality of third-  party service providers (e.g., lawyers, auditors, prime 
brokers)
Portfolio management ■■Investment process
■■Target markets/asset types/strategies
■■Sourcing of investments
■■Role of operating partners
■■Underwriting
■■Environmental and engineering review process
■■Integration of asset management/acquisitions/dispositions
■■Disposition process, including its initiation and execution
Operations and controls ■■Reporting and accounting methodology
■■Audited financial statements and other internal controls
■■Valuations—frequency and approach(es)
■■Insurance and contingency plans
Risk management ■■Fund policies and limits
■■Risk management policy
■■Portfolio risk and key risk factors

■■Leverage and currency—risks/constraints/hedging
Legal review ■■Fund structure
■■Registrations
■■Existing/prior litigation
Fund terms ■■Fees (management and performance) and expenses
■■Contractual terms
■■Investment period and fund term and extensions
■■Carried interest
■■Distributions
■■Conflicts
■■Limited partners’ rights
■■“Key person” and/or other termination procedures
Alternative investing may add value to an investor’s portfolio. To be effective, how -
ever, alternative investing requires thoughtful implementation, including consideration 
of the amount to allocate to alternative investments and of diversification among 
alternative investments. Valuation issues, manager selection, and risk management 
should also be considered.

Summary 181
SUMMARY
This reading has provided an overview of the characteristics, potential benefits, and 
risks of alternative investments. It also described features of some categories of alter -
native investments. Including alternative investments in an investor’s portfolio may 
result in benefits, such as diversification benefits. These benefits do not come without 
associated risks, however. It is important that investors understand these risks before 
including alternative investments in their portfolios. Some key points of the reading 
are summarized as follows:
■■Alternative investments are alternatives to long-  only positions in stocks, bonds, 
and cash. Alternative investments include investments in assets such as real 
estate and commodities as well as investments in special vehicles such as pri -
vate equity and hedge funds.
■■Alternative investment strategies are typically active, return-  seeking strategies.

■■Characteristics common to many alternative investments, compared with tradi -
tional investments, include lower liquidity, less regulation, lower transparency, 
higher fees, and limited and potentially problematic historical risk and return 
data.
■■Alternative investments often have unusual legal and tax considerations and 
may be highly leveraged.
■■Alternative investments are attractive to investors because of the potential for 
diversification (reduced risk) and/or higher returns when added to a portfolio of 
traditional investments.
■■The risks associated with alternative investments must be factored into the 
investment decision-  making process.
■■Many alternative investments are valued for performance-  reporting purposes, 
including reporting to index providers, using estimated values rather than 
actual market prices. As a result, the volatility of returns and correlation of 
returns with the returns to traditional investments will tend to be underesti -

mated. It is important to identify and understand how alternative investments 
are valued.
■■Indexes for alternative investments may be subject to a variety of biases, includ -
ing survivorship and backfill biases.
■■Many alternative investments, such as hedge and private equity funds, use a 
partnership structure with a general partner that manages the business and 
limited partners (investors) who own fractional interests in the partnership.
■■The general partner typically receives a management fee based on assets under 
management or committed capital (the former is common to hedge funds and 
the latter is common to private equity funds) and an incentive fee based on 
realized profits.
■■Hurdle rates, high-  water marks, lockup and notice periods, and clawback provi -
sions may also be specified in a partnership agreement.
■■The fee structure affects the returns to investors (limited partners) in alternative 
investments such as hedge and private equity funds.

■■Hedge funds are typically classified by strategy. One such classification includes 
four broad categories of strategies: event-  driven, relative value, macro, and 
equity hedge.

Reading 58 ■ Introduction to Alternative Investments 182
■■Primary private equity fund strategies include leveraged buyouts, venture 
capital, development capital, and distressed investing. Leveraged buyouts and 
venture capital are the dominant strategies.
■■Real estate investing includes direct and indirect ownership of real estate prop -
erty and lending against real estate properties.
■■Real estate property has some unique features, including basic indivisibility, 
heterogeneity (no two properties are identical), and fixed location.
■■The required amount to directly invest in real estate may be large, and the 
investment may be relatively illiquid. Different investment forms, such as REITs 
and mortgage securitizations, partially address these issues.
■■Commodity investments may involve investing in actual physical commodities 
or in producers of commodities, but more typically, these investments are made 
using commodity derivatives.

■■Returns to commodity investing are based on changes in price and do not 
include an income stream such as dividends, interest, or rent.
■■Infrastructure assets are capital intensive, long-  lived, real assets that are 
intended for public use and provide essential services. Investors expect these 
assets to generate stable cash flows, which adjust for economic growth and 
inflation, and they may also expect capital appreciation.
■■Category, stage of development, and geographic location of underlying assets 
and the form of infrastructure investment affect risks and expected returns of 
infrastructure investments.
■■Managing risks associated with alternative investments can be challenging 
because these investments are often characterized by asymmetric risk and 
return profiles, limited portfolio transparency, and illiquidity.
■■Traditional risk and return measures (such as mean return, standard deviation

of returns, and beta) may provide an inadequate picture of alternative invest -
ments’ risk and return characteristics. Moreover, these measures may be unreli -
able or not representative of specific investments.
■■Operational, financial, counterparty, and liquidity risks may be key consider -
ations for those investing in alternative investments.
■■It is critical to perform due diligence to assess whether (a) the manager can 
effectively pursue the proposed investment strategy; (b) the appropriate organi -
zational structure and policies for managing investments, operations, risk, and 
compliance are in place; and (c) the fund terms appear reasonable.
■■The inclusion of alternative investments in a portfolio, including the amounts to 
allocate, should be considered in the context of an investor’s risk–return objec -
tives, constraints, and preferences.

References 183
Brooks, C., and H. Kat. 2002. “The Statistical Properties of Hedge 
Fund Index Returns and Their Implications for Investors. ” 
Journal of Alternative Investments , vol. 5, no. 2: 26–44. 
Heisler, J., C. Knittel, J. Neumann, and S. Stewart. 2007. “Why 
Do Institutional Plan Sponsors Hire and Fire Their Investment 
Managers?” Journal of Business and Economic Studies , vol. 13, 
no. 1: 88–118.
Kaplan, Steven N., and Antoinette Schoar. 2005. “Private Equity 
Performance, Returns, Persistence, and Capital Flows. ” Journal 
of Finance , vol. 60, no. 4: 1791–1823 .Stewart, S., J. Heisler, C. Knittel, and J. Neumann. 2009. “ Absence 
of Value: An Analysis of Investment Allocation Decisions by 
Institutional Plan Sponsors. ” Financial Analysts Journal , vol. 
65, no. 6: 34–51 .
Stoll, Hans R., and Robert E. Whaley. 2009. “Commodity Index 
Investing and Commodity Futures Prices. ” Working paper, 
Vanderbilt University.
Woodward, Susan, and Robert Hall. 2004. “Benchmarking the

Returns to Venture. ” National Bureau of Economic Research. 
January 2004.

Reading 58 ■ Introduction to Alternative Investments 184
1 Which of the following is least likely  to be considered an alternative 
investment?
A Real estate
B Commodities
C Long-  only equity funds
2 Private equity funds are most likely  to use:
A merger arbitrage strategies.
B leveraged buyouts.
C market-  neutral strategies.
3 An investor is seeking an investment that can take long and short positions, 
may use multi-  strategies, and historically exhibits low correlation with a tra -
ditional investment portfolio. The investor’s goals will be best satisfied with an 
investment in:
A real estate.
B a hedge fund.
C a private equity fund.
4 Relative to traditional investments, alternative investments are least likely  to be 
characterized by:
A high levels of transparency.
B limited historical return data.
C significant restrictions on redemptions.
5 Alternative investment funds are typically managed:
A actively.
B to generate positive beta return.
C assuming that markets are efficient.

6 Compared with traditional investments, alternative investments are more likely  
to have:
A greater use of leverage.
B long-  only positions in liquid assets.
C more transparent and reliable risk and return data.
7 An investor is most likely to consider adding alternative investments to a tradi -
tional investment portfolio because:
A of their historically higher returns.
B of their historically lower standard deviation of returns.
C their inclusion is expected to reduce the portfolio’s Sharpe ratio.
8 The potential benefits of allocating a portion of a portfolio to alternative invest -
A ease of manager selection. 
B improvement in portfolio risk–return.
C accessible and reliable measures of risk and return.
9 An investor may prefer a single hedge fund to a fund of funds if he seeks:

Practice Problems 185
A due diligence expertise.
B better redemption terms.
C a less complex fee structure.
10 Hedge funds are similar to private equity funds in that both:
A are typically structured as partnerships.
B assess management fees based on assets under management.
C do not earn an incentive fee until the initial investment is repaid.
11 An investor seeks a current income stream as a component of total return, 
and desires an investment that historically has low correlation with other asset 
classes. The investment most likely  to achieve the investor’s goals is:
A timberland.
B collectibles.
C commodities.
12 Both event-  driven and macro hedge fund strategies use:
A long–short positions. 
B a top-  down approach.
C long-  term market cycles. 
13 Hedge fund losses are most likely  to be magnified by a:
A margin call.
B lockup period.
C redemption notice period.
14 The first stage of financing at which a venture capital fund most likely  invests is 
the:
A seed stage.
B mezzanine stage.

the:
C angel investing stage.
15 What is the most significant drawback of a repeat sales index to measure 
returns to real estate? 
A Sample selection bias 
B Understatement of volatility
C Reliance on subjective appraisals
16 Compared with direct investment in infrastructure, publicly traded infrastruc -
ture securities are characterized by:
A higher concentration risk.
B more-  transparent governance.
C greater control over the infrastructure assets.
17 An equity hedge fund following a fundamental growth strategy uses fundamen -
tal analysis to identify companies that are most likely  to:
A be undervalued. 
B be either undervalued or overvalued.
C experience high growth and capital appreciation.
18 Which of the following is most likely to be available when conducting hedge 
fund due diligence?
A The benchmark used by the fund
B Information on systems risk management

Reading 58 ■ Introduction to Alternative Investments 186
C Details of investment strategies and processes
19 A private equity fund desiring to realize an immediate and complete cash exit 
from a portfolio company is most likely  to pursue a(n):
A IPO. 
B trade sale.
C recapitalization.
20 As the loan-  to- value ratio increases for a real estate investment, risk most likely  
increases for:
A debt investors only.
B equity investors only.
C both debt and equity investors.
21 Which of the following forms of infrastructure investments is the most liquid?
A An unlisted infrastructure mutual fund
B A direct investment in a greenfield project 
C An exchange-  traded master limited partnership (MLP)
22 An investor chooses to invest in a brownfield rather than a greenfield infra -
structure project. The investor is most likely  motivated by:
A growth opportunities.
B predictable cash flows.
C higher expected returns.
23 The privatization of an existing hospital is best described as:
A a greenfield investment.

B a brownfield investment.
C an economic infrastructure investment.
24 A hedge fund invests primarily in distressed debt. Quoted market prices are 
available for the underlying holdings but they trade infrequently. Which of the 
following will the hedge fund most likely  use in calculating net asset value for 
trading purposes?
C Bid prices for short positions and ask prices for long positions
25 Angel investing capital is typically provided in which stage of financing?
A Later-  stage.
B Formative-  stage.
C Mezzanine-  stage.
26 If a commodity’s forward curve is in contango, the component of a commodi -
ties futures return most likely  to reflect this is:
A spot prices.
B the roll yield.
C the collateral yield.
27 United Capital is a hedge fund with $250 million of initial capital. United 
charges a 2% management fee based on assets under management at year end,

and a 20% incentive fee based on returns in excess of an 8% hurdle rate. In its 
first year, United appreciates 16%. Assume management fees are calculated 
using end-  of- period valuation. The investor’s net return assuming the perfor -
mance fee is calculated net of the management fee is closest  to:

Practice Problems 187
A 11.58%.
B 12.54%.
C 12.80%.
28 Capricorn Fund of Funds invests GBP 100 million in each of Alpha Hedge 
Fund and ABC Hedge Fund. Capricorn FOF has a “1 and 10” fee structure. 
Management fees and incentive fees are calculated independently at the end 
of each year. After one year, net of their respective management and incen -
tive fees, the investment in Alpha is valued at GBP80 million and the invest -
ment in ABC is valued at GBP140 million. The annual return to an investor in 
Capricorn, net of fees assessed at the fund of funds level, is closest  to:
A 7.9%.
B 8.0%.
C 8.1%.
29 The following information applies to Rotunda Advisors, a hedge fund:
■●$288 million in assets under management (AUM) as of prior year-  end
■●2% management fee (based on year-  end AUM)
■●20% incentive fee calculated:
 ■net of management fee
 ■using a 5% soft hurdle rate 
 ■using a high-  water mark (high-  water mark is $357 million)
■●Current year fund return is 25%

 The total fee earned by Rotunda in the current year is closest  to:
A $7.20 million.
B $20.16 million.
C $21.60 million.
30 A hedge fund has the following fee structure:
Annual management fee based on year-  end AUM 2%
Incentive fee 20%
Hurdle rate before incentive fee collection starts 4%
Current high-  water mark $610 million
 The fund has a value of $583.1 million at the beginning of the year. After one 
year, it has a value of $642 million before fees. The net return to an investor for 
this year is closest  to: 
A 6.72%.
B 6.80%.
C 7.64%.
31 Ash Lawn Partners, a fund of hedge funds, has the following fee structure: 
■●2/20 underlying fund fees with incentive fees calculated independently
■●Ash Lawn fees are calculated net of all underlying fund fees
■●1% management fee (based on year-  end market value)
■●10% incentive fee calculated net of management fee 
■●The fund and all underlying funds have no hurdle rate or high-  water mark 
fee conditions

Reading 58 ■ Introduction to Alternative Investments 188
 In the latest year, Ash Lawn’s fund value increased from $100 million to 
$133 million before deduction of management and incentive fees of the fund or 
underlying funds. Based on the information provided, the total fee earned by all 
funds in the aggregate is closest  to:
A $11.85 million.
B $12.75 million.
C $12.87 million.
32 Risks in infrastructure investing are most likely  greatest when the project 
involves:
A construction of infrastructure assets.
B investment in existing infrastructure assets.
C investing in assets that will be leased back to a government.
33 An investor in a private equity fund is concerned that the general partner can 
receive incentive fees in excess of the agreed-  on incentive fees by making distri -
butions over time based on profits earned rather than making distributions only 
at exit from investments of the fund. Which of the following is most likey to

protect the investor from the general partner receiving excess fees?
A A high hurdle rate
B A clawback provision
C A lower capital commitment
34 Until the committed capital is fully drawn down and invested, the management 
fee for a private equity fund is based on:
A invested capital. 
B committed capital. 
C assets under management. 
35 A private equity fund is estimating the value of a privately held company that 
is financed with both debt and equity, is generating positive revenues, and has 
negative EBITDA. The private equity fund is most likely able to estimate the 
company’s equity value using: 
A net income multiples.
B market value of its assets.
C expected free cash flow to equity and cost of equity.
36 An analyst wanting to assess the downside risk of an alternative investment is 
least likely  to use the investment’s:
A Sortino ratio.
B value at risk (VaR).
C standard deviation of returns.
37 An effective risk management process used by alternative investment funds 
most likely includes:

most likely includes: 
A in- house valuations.
B internal custody of assets.
C segregation of risk and investment process duties.

Solutions 189
SOLUTIONS
1 C is correct. Long-  only equity funds are typically considered traditional invest -
ments and real estate and commodities are typically classified as alternative 
2 B is correct. The majority of private equity activity involves leveraged buyouts. 
Merger arbitrage and market neutral are strategies used by hedge funds. 
3 B is correct. Hedge funds may use a variety of strategies (event-  driven, relative 
value, macro and equity hedge), generally have a low correlation with tradi -
tional investments, and may take long and short positions.
4 A is correct. Alternative investments are characterized as typically having low 
levels of transparency.
5 A is correct. There are many approaches to managing alternative investment 
funds but typically these funds are actively managed.
6 A is correct. Investing in alternative investments is often pursued through such 
special vehicles as hedge funds and private equity funds, which have flexibility

to use leverage. Alternative investments include investments in such assets as 
real estate, which is an illiquid asset, and investments in such special vehicles 
as private equity and hedge funds, which may make investments in illiquid 
assets and take short positions. Obtaining information on strategies used and 
identifying reliable measures of risk and return are challenges of investing in 
alternatives. 
7 A is correct. The historically higher returns to most categories of alternative 
investments compared with traditional investments result in potentially higher 
returns to a portfolio containing alternative investments. The less than per -
fect correlation with traditional investments results in portfolio risk (standard 
deviation) being less than the weighted average of the standard deviations of the 
investments. This has potential to increase the Sharpe ratio in spite of the his -
torically higher standard deviation of returns of most categories of alternative 

8 B is correct. Adding alternative investments to a portfolio may provide diver -
sification benefits because of these investments’ less than perfect correlation 
with other assets in the portfolio. As a result, allocating a portion of one’s funds 
to alternatives could potentially result in an improved risk–return relationship. 
Challenges to allocating a portion of a portfolio to alternative investments 
include obtaining reliable measures of risk and return as well as selecting port -
folio managers for the alternative investments.
9 C is correct. Hedge funds of funds have multi-  layered fee structures, while the 
fee structure for a single hedge fund is less complex. Funds of funds presum -
ably have some expertise in conducting due diligence on hedge funds and may 
be able to negotiate more favorable redemption terms than could an individual 
investor in a single hedge fund.
10 A is correct. Private equity funds and hedge funds are typically structured

as partnerships where investors are limited partners (LP) and the fund is the 
general partner (GP). The management fee for private equity funds is based on 
committed capital whereas for hedge funds the management fees are based on 
assets under management. For most private equity funds, the general partner 
does not earn an incentive fee until the limited partners have received their 
initial investment back.

Reading 58 ■ Introduction to Alternative Investments 190
11 A is correct. Timberland offers an income stream based on the sale of timber 
products as a component of total return and has historically generated returns 
not highly correlated with other asset classes.
12 A is correct. Long–short positions are used by both types of hedge funds to 
potentially profit from anticipated market or security moves. Event-  driven 
strategies use a bottom-  up approach and seek to profit from short-  term events 
typically involving a corporate action, such as an acquisition or a restructuring. 
Macro strategies seek to profit from expected movements in evolving economic 
variables. 
13 A is correct. Margin calls can magnify losses. To meet the margin call, the 
hedge fund manager may be forced to liquidate a losing position in a security, 
which, depending on the position size, could exert further price pressure on the 
security, resulting in further losses. Restrictions on redemptions, such as lockup

and notice periods, may allow the manager to close positions in a more orderly 
manner and minimize forced-  sale liquidations of losing positions. 
14 A is correct. The seed stage supports market research and product development 
and is generally the first stage at which venture capital funds invest. The seed 
stage follows the angel investing stage. In the angel investing stage, funds are 
typically provided by individuals (often friends or family), rather than a venture 
capital fund, to assess an idea’s potential and to transform the idea into a plan. 
Mezzanine-  stage financing is provided by venture capital funds to prepare the 
portfolio company for its IPO. 
15 A is correct. A repeat sales index uses the changes in price of repeat-  sale prop -
erties to construct the index. Sample selection bias is a significant drawback 
because the properties that sell in each period vary and may not be representa -
tive of the overall market the index is meant to cover. The properties that trans -

act are not a random sample and may be biased toward properties that changed 
in value. Understated volatility and reliance on subjective appraisals by experts 
are drawbacks of an appraisal index.
16 B is correct. Publicly traded infrastructure securities, which include shares 
of companies, exchange-  traded funds, and listed funds that invest in infra -
structure, provide the benefits of transparent governance, liquidity, reasonable 
fees, market prices, and the ability to diversify across underlying assets. Direct 
investment in infrastructure involves a large capital investment in any single 
project, resulting in high concentration risks. Direct investment in infrastruc -
ture provides control over the assets and the opportunity to capture the assets’ 
full value. 
17 C is correct. Fundamental growth strategies take long positions in companies 
identified, using fundamental analysis, to have high growth and capital appreci -

ation. Fundamental value strategies use fundamental analysis to identify under -
valued companies. Market-  neutral strategies use quantitative and/or fundamen -
tal analysis to identify under- and overvalued companies.
18 A is correct. It should be possible to identify the benchmark against which the 
fund gauges its performance in the hedge fund due diligence process. It should 
also be possible to establish the range of markets in which the fund invests 
as well as the fund’s general strategy. Hedge funds consider their strategies, 
systems, and processes to be proprietary and are unwilling to provide too much 
information to potential investors. 
19 B is correct. Private equity funds can realize an immediate cash exit in a trade 
sale. Using this strategy, the portfolio company is typically sold to a strategic 
buyer.

Solutions 191
20 C is correct. The higher the loan-  to- value ratio, the higher leverage is for a real 
estate investment, which increases the risk to both debt and equity investors. 
21 C is correct. A publicly traded infrastructure security, such as an exchange-  
traded MLP , provides the benefit of liquidity. 
22 B is correct. A brownfield investment is an investment in an existing infrastruc -
ture asset, which is more likely to have a history of steady cash flows compared 
with that of a greenfield investment. Growth opportunities and returns are 
expected to be lower for brownfield investments, which are less risky than 
greenfield investments.
23 B is correct. Investing in an existing infrastructure asset with the intent to 
privatize, lease, or sell and lease back the asset is referred to as a brownfield 
investment. An economic infrastructure asset supports economic activity and 
includes such assets as transportation and utility assets. Hospitals are social

infrastructure assets, which are focused on human activities. 
24 B is correct. Many practitioners believe that liquidity discounts are necessary to 
reflect fair value. This has resulted in some funds having two NAVs - for trading 
and reporting. The fund may use average quotes for reporting purposes but 
apply liquidity discounts for trading purposes.
25 B is correct. Formative-  stage financing occurs when the company is still in the 
process of being formed and encompasses several financing steps. Angel invest -
ing capital is typically raised in this early stage of financing.
26 B is correct. Roll yield refers to the difference between the spot price of a com -
modity and the price specified by its futures contract (or the difference between 
two futures contracts with different expiration dates). When futures prices are 
higher than the spot price, the commodity forward curve is upward sloping, and 
the prices are referred to as being in contango. Contango occurs when there is

little or no convenience yield.
27 B is correct. The net investor return is 12.54%, calculated as:
End of year capital = $250 million × 1.16 = $290 million
Management fee = $290 million × 2% = $5.8 million
Hurdle amount = 8% of $250 million = $20 million;
Incentive fee = ($290 − $250 − $20 − $5.8) million × 20% = $2.84 million
Total fees to United Capital = ($5.8 + $2.84) million = $8.64 million
Investor net return: ($290 − $250 − $8.64) / $250 = 12.54%
28 A is correct because the net investor return is 7.9%, calculated as:
 First, note that “1 and 10” refers to a 1% management fee, and a 10% incentive 
fee.
End of year capital = GBP140 million + GBP80 million = GBP220 million
Management fee = GBP220 million × 1% = GBP2.2 million
Incentive fee = (GBP220 − GBP200) million × 10% = GBP2 million
Total fees to Capricorn = (GBP2.2 + GBP2) million = GBP4.2 million
Investor net return: (GBP220 − GBP200 − GBP4.2) / GBP200 = 7.9%
29 A is correct. Rotunda earns a management fee of $7.20 million but does not

earn an incentive fee because the year-  end fund value net of management fee 
does not exceed the high-  water mark of $357 million.

Reading 58 ■ Introduction to Alternative Investments 192
 Rotunda fees:
End-  of- year AUM = Prior year-  end AUM × (1 + Fund return) = $288 mil -
lion × 1.25 = $360 million
$360 million × 2% = $7.20 million management fee
$360 million – $7.2 million = $352.8 million AUM net of management fee
 The year-  end AUM net of fees does not exceed the $357 million high-  water 
mark. Therefore, no incentive fee is earned.
30 C is correct. The management fee for the year is 
$642 × 0.02 = $12.84 million. 
 Because the ending value exceeds the high-  water mark, the hedge fund can 
collect an incentive fee. The incentive fee is
{$642 – [$610 × (1 + 0.04)]} × 0.20 = $1.52 million.
 The net return to the investor for the year is
[($642 – $12.84 – $1.52)/$583.1] – 1 ≈ 0.07638 ≈ 7.64%.
31 B is correct. Total fees paid to all funds (underlying funds and Ash Lawn) are 
$12.75 million, consisting of underlying fund fees of $9.26 million and Ash 
Lawn fees of $3.49 million, calculated as follows:
 Underlying fund fees:

Underlying fund fees:
Management fee = $133 million × 0.02 = $2.66 million. 
Incentive fee = ($133 – $100) million × 0.20 = $6.60 million. 
Total underlying fund fees ($2.66 + $6.60) million = $9.26 million. 
 Ash Lawn fees:
AUM at end of year, net of underlying fund fees = $133 million – $9.26 mil -
lion = $123.74 million.
Ash Lawn management fee = $123.74 million × 0.01 = $1.24 million 
(rounded).
AUM net of underlying fund fees and Ash Lawn management fee = ($123.74 
– $1.24) million = $122.50 million (rounded).
Ash Lawn incentive fee = ($122.50 – $100) million × 0.10 = $2.25 million 
Total Ash Lawn fees = ($1.24 + $2.25) million = $3.49 million (rounded). 
 Total fees of underlying funds and Ash Lawn:
($9.26 + $3.49) million = $12.75 million (rounded). 
32 A is correct. Infrastructure projects involving construction have more risk than 
investments in existing assets with a demonstrated cash flow or investments in

assets that are expected to generate regular cash flows because the assets will be 
leased back to a government.
33 B is correct. A clawback provision requires the general partner in a private 
equity fund to return any funds distributed (to the general partner) as incen -
tive fees until the limited partners have received back their initial investments 
and the contracted portion of the total profits. A high hurdle rate will result in

Solutions 193
distributions occurring only after the fund achieves a specified return. A high 
hurdle rate decreases the likelihood of, but does not prevent, excess distribu -
tions. Management fees, not incentive fees, are based on committed capital.
34 B is correct. Until the committed capital is fully drawn down and invested, the 
management fee for a private equity fund is based on committed capital, not 
invested capital. 
35 C is correct. The private equity fund can estimate the company’s value by dis -
counting the expected free cash flow to equity using the cost of equity, which is 
a discounted cash flow approach. A negative EBITDA number implies nega -
tive net income, which makes net income multiples, a comparable approach, 
inapplicable for valuation. In order to use an asset-  based approach, the private 
equity fund needs the market value of its liabilities, not just the market value of 
its assets. 
36 C is correct. Downside risk measures focus on the left side of the return distri -

bution curve where losses occur. The standard deviation of returns assumes that 
returns are normally distributed. Many alternative investments do not exhibit 
close-  to- normal distribution of returns, which is a crucial assumption for the 
validity of a standard deviation as a comprehensive risk measure. Assuming 
normal probability distributions when calculating these measures will lead to an 
underestimation of downside risk for a negatively skewed distribution. Both the 
Sortino ratio and the value-  at- risk measure are both measures of downside risk.
37 C is correct. Investment risk should be monitored by a chief risk officer who is 
separated from the investment process. Risk factors monitored include leverage, 
sector, and individual position limits as well as counterparty risks. Independent 
(as opposed to in-  house) valuation of underlying positions should be performed 
and reviewed on a regular basis. Third-  party custody of assets can help reduce 
the chance of fraud.

Index I-1
A
absolute return, for alternative 
investments, 129–130
Accredited Investors, 133n.14
active management, 124, 129
activist strategy, hedge fund, 136
adjusted funds from operations (AFFO), 
166
Africa, 164–165
agriculture, 167, 168
AIG, 32, 33
Alternative Investment Fund Managers 
Directive (AIFMD), 144
alternative investments, 123–193
categories of, 128–129
collectibles, 175–176
commodities, 167–173
derivatives and indexes, 168–169
investment vehicles, 169–170
performance and diversification 
benefits, 170–171
prices of, 171–173
common characteristics, 124–128
defined, 123–124
hedge funds, 133–148
about, 133–135
diversification benefits, 138–139
due diligence, 146–148
fees and returns, 139–143
investment strategies for,  
135–138
and redemptions, 144–145
valuation issues, 145–146
historical records of, 126
infrastructure investments,  
173–175
portfolio diversification with, 132
practice problems, 184–188
private equity, 148–158
diversification benefits, 155–156
due diligence, 158

investment strategies, 150–154
portfolio company valuation, 
156–157
structure and fees, 149–150
real estate, 158–167
forms of investment, 159–161
investment categories, 161–163
benefits, 163–165
risks with, 166–167
valuation, 165–166
returns from, 129–132
risk management, 176–180
due diligence with, 178–180
process, 177
risk–return measures, 178–179
solutions to problems, 189–193
structures for, 132–133
and traditional investments, 132
Amaranth Advisors LLC, 171American options (American-style 
options)
defined, 26, 85
pricing, 104–107
Americas, 164–165
appraisal indexes (real estate), 163
arbitrage
commodities, 172
defined, 47
in derivatives pricing, 47–52, 66–72
executing, 67
with forward contracts, 49–50
frequency of arbitrage opportunities, 67
and hedge funds, 136
limits to, 70
and put–call parity, 97
and relative valuation, 47–49
and replication, 68–69
risk, 50n.24
with stocks and risk-free bonds, 47–49
arbitrage-free pricing, 70
Art Market Research, 176
Artpiece, 176

Asia, 159. see also  specific countries and 
regions
Asia-Pacific, 164–165
ask price, 10n.3, 145
asset-backed securities, 33–35
asset-based valuation approach
for private equity, 157
for REITs, 166
assets under management (AUM)
alternative investments, 123–124
global, 125
growth of, 134–135
hedge funds, 134–135
institutionally owned real estate, 159
by strategy, 135
at the money, 27, 87
AUM. see assets under management
Australasia, 159
average quote, for hedge fund valuation, 
145
B
backfill bias, 125n.3
backwardation, 173
Bank for International Settlements (BIS), 39
Bank of Montreal, 171
base metals, as commodities, 167, 168
basis swaps, 24
beta, 129
biases, 125–126, 143
bid prices, 10n.3, 145
binomial valuation of options, 100–104
BIS. see Bank for International 
Settlements
Bloomberg Barclays Global Aggregate 
Index, 134, 165
bonds
arbitrage with, 47–49, 67
convertible, 146downside frequencies of, 131
margin, 11
performance of, 11, 134–135
puts vs. short sales and, 93

returns, 126, 139, 170
risk-free, 47–49
Sharpe and Sortino ratios, 131
volatility, 126
bottom up strategies, 136, 137
brokers, 144
brownfield investments, 174
bubbles, 42
buyers, derivatives, 7
C
CAIA Association. see Chartered 
Alternative Investment Analyst 
Association
call options (calls)
American, 105–107
European ( see European call options)
fiduciary, 95–96, 99
margin transactions vs., 91–92
payoff from, 26–28
profits from, 27–28
Cambridge Associates Modified Public 
Market Equivalent (mPME), 155
capital
committed, 149–150
development, 148–149
and private equity valuation, 158
capitalization rate (cap rate), 165, 166
carry, 65
cash flows
DCF valuation approach, 157, 166
free cash flow to equity, 157
in swaps, 82
cash markets, 5
cash prices. see spot prices
cash-settled forwards. see nondeliverable 
forwards (NDFs)
cash settlement
of futures, 20
of options, 26
CBOT. see Chicago Board of Trade
CDSs. see credit default swaps
Chartered Alternative Investment Analyst

Chartered Alternative Investment Analyst 
(CAIA) Association, 135n.17
Chicago, Illinois, 39
Chicago Board of Trade (CBOT), 37, 
39–40
China, 167–168
China Aviation Oil Corp., 171
Christie’s, 176
clawback, private equity, 150
clearing (term), 11
clearinghouse
daily settlement by, 18, 19
in exchange-traded derivatives 
market, 11
CLNs. see credit-linked notes

I-2 Index
CMBS. see commercial mortgage-backed 
CMOs. see collateralized mortgage 
collateral
for hedge funds, 143–144
real estate as, 158
collateralized bond obligations, 34
collateralized debt obligations
defined, 34
underlying for, 37–38
valuation of, 146
collateralized loan obligations, 34
collateralized mortgage obligations 
(CMOs), 34
collateral yield, 173
commercial mortgage-backed securities 
(CMBS), 162–163
commercial real estate investments
direct and indirect investing in, 162
global assets under management, 125
institutionally owned, 159
committed capital, for private equity, 
149–150
benefits and costs of holding, 64–65
defined, 129
downside frequencies, 131
growth in, 127
returns on, 126, 131, 167, 170
risk–return tradeoffs for, 132

as underlying, 5, 37
commodity exchange traded funds, 129
commodity futures, 37
pricing of, 171–173
risk management with, 177
commodity indexes, 126, 168–169
commodity trading advisers (CTAs), 128
common stock, for commodities 
investing, 169
communication assets, 174
comparable sales approach to real estate 
valuation, 165
complexity, of derivatives, 44
concentrated portfolio strategies, 130
consumer goods, arbitrage opportunity 
with, 47
contango, 172–173
contingent claims, 25–35. see also  
options
credit derivatives, 30–33
defined, 7, 61
forward commitments vs., 35–36
options, 25–30, 33
contracts for differences. see 
nondeliverable forwards (NDFs)
convenience yield. see roll yield
convertible bonds, 146
cost approach to real estate valuation, 166cost of carry
and price of European options, 90–91
and price of forward contracts, 77
and storage, 46
for underlying assets, 65
cost of equity, in private equity 
valuation, 156–157
costs

costs
of holding assets, 64–66
opportunity, 63, 65
rebuilding, 166
“soft, ” 166
transaction, 41, 70
counterparties, futures, 18
covenants, with leveraged loans, 151
crashes, 42
credit, as underlying, 37–38
credit default swaps (CDSs), 31–33, 37
credit-linked notes (CLNs), 31
credit risk, 30, 32
credit spread options, 30–31
crop types (farmland investments), 163
cross-border real estate investments, 159
CTAs. see commodity trading advisers
currencies, as underlying, 5, 37. see also  
specific currencies
currency swaps, 23n.12, 37
D
daily settlement, 18, 19
D CF. see discounted cash flow valuation 
approach
dealer market. see over-the-counter 
(OTC) derivatives market
dealers, in OTC derivatives market, 12
debt, distressed, 146
debt financing, for real estate, 161, 162. 
see also  mortgages
default
in forward contracts, 15
in swaps, 23
delivery
demand, for commodities, 171
derivatives, 5–58
benefits of, 41–42
characteristics of, 8–9

contingent claims, 25–35
criticisms of, 42–45
defined, 6, 60–62
forward commitments, 14–25
contingent claims vs., 35–36
forward contracts, 14–17, 24, 73–80
futures contracts, 17–21, 24, 80–82
pricing, 73–85
swaps, 21–25, 82–85
hedging with, 67–68
hybrid, 35
markets for, 9–14, 38–39
practice problems, 54–55
pricing, 45–52, 59–117
about, 60
arbitrage and, 47–52, 66–72definition of derivatives, 60–62
forward commitments, 73–85
options, 85–100, 104–107
practice problems, 109–113
pricing underlying assets, 62–66
solutions to problems, 114–117
storage in, 46–47
valuation vs. pricing, 72–73
purposes of, 39–41, 44–45
solutions to problems, 56–58
types of, 14–39
underlyings for, 36–39
uses of, 7–9
valuation of, 45–52
pricing vs. valuation, 72–73
derivatives market, 9–14
exchange-traded, 10–11, 13–14

over-the-counter, 11–14
size of, 38–39
destabilization, economic, 43–44
Deutsche Börse, 9
development capital, 148–149
direct capitalization approach to real 
estate valuation, 165
direct investment, in infrastructure 
assets, 174
direct ownership, of real estate, 160, 161
disclosure, by hedge funds, 147
discounted cash flow (DCF) valuation 
approach
for real estate, 166
distressed debt, valuation of, 146
distressed investing (private equity), 149, 
153
distressed property investments, 167
distressed/restructuring strategy, for 
hedge funds, 136
with alternative investments, 125, 127, 
132
with commodities, 170–171
with hedge funds, 138–139
with private equity, 155–156
with real estate, 158, 163–165
Dodd–Frank Act. see Wall Street Reform 
and Consumer Protection Act 
(2010)
downside risk
measures of, 178–179
and returns, 131
and Sharpe ratios, 130–131
drawdown, hedge funds, 144–145
due diligence
for hedge fund investing, 146–148

for private equity investments, 158
and risk management for alternative 
investments, 178–180
E
early exercise, of American options, 
104–106
(EBITDA)
for leveraged buyouts, 150
for private equity, 156–157

Index  I-3
economic destabilization, 43–44
economic infrastructure assets, 174
efficient markets, 42, 50, 138
emerging markets, fixed-income 
securities for, 146
endowments, 127
energy
as commodity, 167, 168
speculators on, 43n.20
energy mutual funds, 170
energy unit trusts, 170
equities. see also  stock
returns on hedge funds vs., 139
as underlying, 5, 36
equity
minority equity investing, 153
in residential properties, 161
equity hedge strategies, 135, 137–138
equity markets
efficiency of, 42
OTC derivatives market vs., 9–10
equity-only funds, 137
equity options, 36n.15
equity real estate investment trusts, 162
equity swaps, 36
equity tranches, 34
estimates, of alternative investment 
values, 125
ETFs. see exchange-traded funds
Eurex, 9
Euro Interbank Offered Rate (Euribor), 
78n.11
Europe, 159, 164–165. see also  specific 
European call options
and American call options, 105
binomial option pricing with, 101–103

exercise price of, 87, 88
at expiration, 86
minimum prices for, 91–93
payments on underlying and carrying 
costs for, 91
and risk-free rate of interest, 89
time to expiration for, 88
and value of underlying, 87
volatility of underlying for, 90
European options (European-style options)
pricing, 85–100
and exercise price, 87–88
minimum prices of calls and puts, 
91–93
and payments on underlying/cost of 
carry, 90–91
put–call–forward parity, 98–99
put–call parity, 94–98, 100
and time to expiration, 88–89
and volatility of underlying, 89–90
European Public Real Estate Association, 
164
European put options
and American put options, 105
binomial option pricing with, 103exercise price of, 87–88
time to expiration for, 88, 89

European Union (EU), 144
event-driven strategies, with hedge 
funds, 135–136
exchange-traded derivatives market, 
10–11
OTC vs., 13–14
size of, 38
exchange-traded funds (ETFs)
as alternative investments, 124
and beta exposure, 129
for commodities investing, 169
derivatives vs., 6
exchange-traded options, 25
exercise price, of options, 26, 87–88
exercise value, of European options, 86
exit strategies, for private equity 
investments, 154
expansion venture capital, 153
expiration
of forward contracts, 73–74
of options, 26–30, 86
time to, 88–89
F
fair value, 157
farmland, investing in, 158–159, 163
“fast” money, 142
fees
fund, 133
for hedge funds, 133, 134n.16, 139–143
incentive
for fund investments, 133
hedge funds, 139–140
private equity, 150
hedge funds, 139–140, 143
private equity, 149–150
net-of-fees returns, 142
1 and 10 fee structure, 139
performance, 133, 177
with private equity investments, 
149–150

149–150
for REITs and real estate partnerships, 
161
2 and 20 fee structure, 139, 140
FFO. see funds from operations
fiduciary calls, 95–96, 99
financial crisis (2008), 43–44
financing
of leveraged buyouts, 150–151
of real estate investments, 161, 162 ( see 
also mortgages)
venture capital, 152–153
fixed-for-floating interest rate swaps, 
22–23
fixed income asset backed strategies, for 
hedge funds, 137
fixed income convertible arbitrage 
strategy, for hedge funds, 136fixed income general strategies, for 
fixed-income investments. see also  
bonds
as assets under management, 125
as underlying, 5, 36–37
formative-stage financing (venture 
capital), 152
Fortune  magazine, 133
forward commitments, 14–25, 73–85
options vs., 30
pricing of, 73–85
valuation of, 73–85
forward price, 14, 26
forward rate agreements (FRAs), 77–79

forwards (forward contracts), 14–17
arbitrage with, 49–50
for commodities, 168
defined, 14–15, 61
futures vs., 21, 24, 80–81
on interest rates, 77–79
off-market, 83–84
pricing and valuation of, 73–80
put–call parity for, 98–99
swaps and, 24, 82–83
time horizon of, 74
FRAs. see forward rate agreements
FTSE Group, 164
FTSE infrastructure index, 175
fundamental growth strategies, for 
fundamental value strategies, for hedge 
funds, 137
funds
for commodities investing, 169, 170
structure of, 132–133
funds from operations (FFO), 166
funds of funds
benefits of, 146
defined, 134
fee structures for, 139–140, 142
multi-strategy hedge funds vs., 138
performance of, 134–135
returns on, 139, 142, 143
futures (futures contracts), 17–21
commodities, 37, 168, 171–173
defined, 17, 61
forwards vs., 21, 24
price discovery with, 40–41
pricing and valuation of, 80–82
swaps vs., 24
futures markets, regulation of, 21
futures price, 18, 40–41
G

G
gambling, speculation vs., 43
GB 250 Stamp Index, 175–176
generally accepted accounting principles 
(GAAP), 162
general partners (GPs)
funds as, 132
in private equity investments, 149, 150, 
158

I-4 Index
Global S&P REIT index, 126
growth strategies, for hedge funds, 138
H
“haircuts, ” 146
hard hurdle rate, 139
hedge fund indexes, 125, 143
Hedge Fund Research, Inc. (HFRI), 134, 
135
hedge funds, 133–149
classifying, 135
defined, 128
due diligence, 146–148, 178
fees, 139–143
historical returns and volatility, 126
investment strategies for, 135–138
equity hedge strategies, 137–138
event-driven strategies, 136
macro strategies, 137
relative value strategies, 136–137
registration of, 144
returns, 131, 139–143
risks of, 132, 178
hedge portfolios, 46
hedging
with credit default swaps, 32
with derivatives, 67–68
with forward contracts, 17
with futures, 21
inflation hedges, 158, 170–171
in OTC derivatives market, 12
hedging pressure hypothesis, 173

heuristics, 157n.30
HFRI. see Hedge Fund Research, Inc.
HFRI Fund of Funds Index, 134
high net worth investors
alternative investments of, 125, 
127–128
commercial property investment by, 
162
high water marks
hedge funds, 140
historical returns
of alternative investments, 125
of commodities, 170
of investment classes, 126
of private equity investments, 
155–156
of real estate investments, 164–165
Honus Wagner baseball card, 176n.39
hurdle rate, hedge fund, 139
hybrid derivatives, 35
I
illiquid asset investments
due diligence with, 178
and historical returns, 126–127
risk issues with, 177
valuation of, 146implied volatility, 41
incentive fees
for hedge funds, 139–140
for private equity, 150
income, net operating, 165
income approach to real estate valuation, 
165–166
indexes
for collectibles investments, 175–176
commodity, 168–169
bias in, 126
hedge fund, 125, 143
of real estate returns, 163–165
index swaps, 36
India, 167–168

indirect investment
in commercial real estate, 162
in infrastructure assets, 174
individual managed accounts, of 
commodities, 170
inflation hedges
commodities as, 170–171
information discovery, 40–41
infrastructure assets, 129, 173–174
infrastructure exchange traded funds, 
129
infrastructure investments, 173–175
assets for, 129
categories of, 174
forms of, 174
risks and returns with, 175
initial margin requirement, 18
initial public offerings (IPOs), 154
initiation date, forward contracts at, 
74–76
INSEAD, 127
alternative investments of, 125
commercial property investment by, 162
insurance
and credit default swaps, 31, 32
and derivatives, 7
intangible assets, as alternative 
investments, 129
interest, open, 20
interest rates
forwards on, 77–79
risk-free, 89
term structure of, 79
as underlying, 36–37
interest rate swaps, 22–23
International Private Equity and Venture 
Capital Valuation Guidelines, 156

International Swaps and Derivatives 
Association (ISDA), 11
in the money, 27, 87
intrinsic value, of European options, 86
Investment Company Act (1940), 133n.14
investment strategies
for hedge funds, 135–138
for private equity, 150–154
investors
high net worth
127–128
162institutional
162
risk aversion of, 63–64, 69–70
vulture, 153
IPOs. see initial public offerings
ISDA. see International Swaps and 
Derivatives Association
J
Jones, Alfred Winslow, 133
junior tranche, 34
L
later-stage financing (venture capital), 
153
Latin America, 159
law of one price, 47, 67
leases, multiple-year, 158
leverage
and derivatives, 44
and hedge funds, 143–144
in real estate investing, 167
risk associated with, 177
leveraged buyouts (LBOs), 150–152
defined, 148
financing of, 150–151
target companies for, 151–152

leveraged loans, covenants with, 151
leveraged ownership, of real estate,  
160
leveraged transactions, call options vs., 
91–92
Rate
life of contract, pricing/valuation over, 
76–77
limit down, 19
limited partners (LPs)
investors as, 132
in private equity, 149, 150, 158
in real estate, 160
limit up, 19
liquidation, private equity, 154, 157
liquidation value, of private equity, 157
liquidity
of alternative investments, 177
of derivatives, 41
of exchange-traded derivatives market, 
10
of OTC derivatives market, 12
and valuation, 146
loans
leveraged, 150–151
stand-alone mortgage, 160–161
loan-to-value ratio, for commercial real 
estate, 162
locked limit, 19
lockup period, hedge fund, 133, 144
asset returns vs., 170
defined, 23n.11
in forward rate agreements, 78
swaps based on, 23
and TED spread, 24
as underlying, 37

Index  I-5
long (term), 7
Long-Term Capital Management, 43
losses, on commodities, 171
LPs. see limited partners
M
macro strategies, with hedge funds, 135, 
137
maintenance margin requirement, 18
managed futures funds, 169
management buy-ins (MBIs), 150
management buyouts (MBOs), 150
management fees
for hedge funds, 139–140, 143
for private equity investments, 
149–150
margin
for futures, 18–19
for hedge funds, 144
margin bond, 11
margin calls, 19, 144
margin transactions, 91–92
market efficiency, 42, 50, 138
market makers, 10–11
market neutral strategies, for hedge 
funds, 137
market or comparables valuation 
approach, for private equity, 
156–157
markets
cash, 5
derivatives, 9–14, 38–39
efficient, 42, 50, 138
equity, 9–10, 42
spot, 5
market segmentation, 130
market value, 38–39, 157
marking to market, for futures, 18, 80
mark-to-market value, 73n.7
master limited partnerships (MLPs), 
174, 175
MBIs. see management buy-ins
MBOs. see management buyouts
MBSs. see mortgage-backed securities

members, exchange, 10n.4
merger arbitrage strategy, for hedge 
funds, 136
mezzanine financing, for leveraged 
buyouts, 151
mezzanine-stage financing (mezzanine 
venture capital), 153
mezzanine tranche, 34
Middle East, 164–165
minimum prices
of American options, 105–106
of European options, 91–93
MLPs. see master limited partnerships
moneyness, 87
mortgage-backed securities (MBSs), 
162–163
mortgage real estate investment trusts, 
162
mortgages, 160–161
for residential property, 161
securitization of, 160–163
MSCI ACWI Index, 134, 165, 175
MSCI World Index, 155, 156
multiple-year leases, 158multi-strategy strategies, for hedge 
funds, 137
mutual funds, derivatives vs., 6
N
NAREIT. see National Association of 
Real Estate Investment Trusts
NASDAQ 100 Index (NASDAQ), 10, 155
National Association of Real Estate 
Investment Trusts (NAREIT), 164
National Council of Real Estate 
Investment Fiduciaries (NCREIF), 
164
NAV. see net asset value

164
NCREIF. see National Council of Real 
Estate Investment Fiduciaries
NCREIF Farmland index, 164
NCREIF Property index, 164
NDFs. see nondeliverable forwards
Nestlé SA, 143
net asset value (NAV)
and drawdown, 144
of REITs, 166
trading vs. reporting, 146
net-of-fees returns, hedge fund, 142
net operating income (NOI), 165
New York Stock Exchange, 9
no arbitrage, principle of, 70
NOI. see net operating income
nondeliverable forwards (NDFs), 17
non-traded investments, valuation of, 146
North America, 159. see also  United 
States
notes, credit-linked, 31
notice period, hedge fund, 133
notional principal
in currency swaps, 23n.12
defined, 23
as measure of OTC market, 39
NYSE Euronext, 143
O
off-market forwards, 83–84
offsetting transactions, with futures, 20
one price, law of, 47, 67
open interest, 20
opportunity costs, 63, 65
option premium (option price), 26
options (options contracts), 25–30, 33. see 
also specific types, e.g.:  call options

binomial valuation of, 100–104
commodity, 169
defined, 7, 25, 61
forward commitments vs., 30
implied volatility with, 41
pricing, 85–100, 104–107
American options, 104–107
European options, 85–100
on stocks, 36
Orange County, California, 44
OTC derivatives market. see over-the-
counter derivatives market
out of the money, 27, 87
overnight indexed swaps, 24
over-the-counter (OTC) derivatives 
market, 11–14
equities market vs., 9–10
exchange-traded vs., 13–14
size of, 38–39owner’s equity, in residential properties, 
161
ownership, of real estate, 160
P
passive management, 129
payments, on underlying assets, 90–91
payoffs
from call options, 26–28
with contingent claims, 25
from forward contracts, 15–16
with futures, 20–21
from put options, 28–30
performance bond, 11
performance fees
and risk, 177
permanent crops, 163
physical delivery. see delivery
plain vanilla swaps, 22–23, 37
pooled real estate vehicles, 160
portfolio company
defined, 152

valuation of, 156–157
portfolios, hedge, 46
PPPs. see public–private partnerships
precious metals, 167, 168
premium, risk, 63
prepayment, 34
Preqin index, 175
present value of future cash flows 
approach, 62
price discovery, 40–41
price limits, futures, 19
prices
ask, 10n.3, 145
bid, 10n.3, 145
exercise, 26
forward, 14, 26
futures, 18, 40–41
option, 26
settlement, 18
spot, 5, 40–41, 171, 173
pricing
derivatives, 45–52, 59–117
about, 60
and arbitrage, 47–52, 66–72
definition of derivatives, 60–62
forward contracts, 73–80
futures, 80–82, 171–173
of risky assets, 64
swap contracts, 82–85
of underlying assets, 62–66
benefits and costs of holding assets, 
64–66
forming price expectations, 62–63

64–66
pricing of risky assets, 64
required rate of return on assets, 63
risk aversion of investors, 63–64

I-6 Index
prime brokers, 144
principle of no arbitrage, 70
private energy partnerships, 170
exit strategies, 154
leveraged buyouts, 150–152
minority and distressed, 153
portfolio company valuation, 156–157
returns for, 125, 155–156
private equity funds
defined, 128–129
returns in, 155–156
private placements, 132n.13
probabilities, risk-neutral, 102–103
profits
with calls, 27–28
with puts, 28–29
property development investments, 167
protective puts
fiduciary calls vs., 96, 99
with forward contracts, 98–99
publicly traded infrastructure securities, 
174
public–private partnerships (PPPs),  
173

put options (puts)
European ( see European put options)
and insurance, 7
payoffs from, 28–30
profits from, 28–29
protective, 95, 96, 98–99
Q
Qualified Purchasers, 133n.14
quantitative directional strategies, for 
hedge funds, 138
R
rate of return, on underlying, 63
commercial, 125, 158–159, 162
growth in, 128
institutionally owned, 125, 159
risks with, 166–167Sharpe and Sortino ratios, 131
real estate investment trusts (REITs)
equity, 162
function of, 159
mortgage, 162
returns on, 164–165
shares of, 160
tax advantages for, 126
valuation of, 166
real estate limited partnerships, 160
rebuilding cost, 166
recapitalization, private equity, 154

redemptions, hedge fund, 133, 144–145
refinancing risk, 158
Reg D Offerings, 132n.13
regulation
of futures, 21
of OTC derivatives market, 12–13
Regulation D, 132n.13
Regulation of the European 
Parliament and of the Council 
on OTC Derivatives, Central 
Counterparties, and Trade 
Repositories, 12–13
regulatory risk, 175
REIT indexes, 163, 164
REITs. see real estate investment trusts
relative value strategies, with hedge 
funds, 135–137
repeat sales indexes (real estate), 
163–164
replication, 68–69
reporting NAV, 146
residential mortgage-backed securities 
(RMBS), 161
residential property investments, 158, 
161
return(s). see also  specific types of 
absolute, 129–130
net-of-fees, 142
total, 158
risk(s)
with alternative investments, 125, 
130–131, 178–179
with arbitrage transactions, 70
credit, 30, 32
downside, 130–131, 178–179
with infrastructure investments, 175
measures of, 130–131
with real estate investments, 166–167
refinancing, 158
regulatory, 175
safety-first, 179

shortfall, 179
systematic, 129
systemic, 32, 43–44
transfer of, 8, 40
value at risk, 178–179
risk allocation, 40
risk arbitrage, 50n.24
risk aversion, 63–64, 69
risk-free bonds, arbitrage with,  
47–49
risk-free rate of interest, 89risk management
with alternative investments, 176–180
due diligence, 178–180
with derivatives, 8, 9, 40
systems, 147–148
risk-neutral investors, 63
risk-neutral pricing, 70
risk-neutral probabilities, 102–103
risk premium, 63
risk–return tradeoff
for traditional and alternative 
investments, 130–132
risk-seeking investors, 63
risky assets, pricing, 64
RMBS. see residential mortgage-backed 
roll yield (convenience yield), 64–65, 173
row crops, 163
Royal Dutch Shell, 169
“rules of thumb, ” 157n.30
S
safety-first risk, 179
scenario analysis, 179
secondary sales, of private equity, 154

sector specific strategies, for hedge 
funds, 138
Securities Act (1933), 132n.13
securitization, of mortgages, 160–163
sellers, derivatives, 7
senior tranche, 34
settlement
cash, 20, 26
daily, 18, 19
defined, 11
settlement price, 18
Sharpe ratios
and downside risks, 130–132
as risk–return measure, 178
short (term), 7
short bias strategies, for hedge funds, 
138
shortfall risk, 179
short positions, 41, 47
short selling
and limits to arbitrage, 70
using puts vs., 93
social infrastructure assets, 174
“soft” costs, 166
soft hurdle rate, 139
Sortino ratios, 130–132, 179
implied volatility and, 41
returns for, 155
volatility of, 89
SPDR Gold Shares ETF, 169
special situations strategies, for hedge 
funds, 136
Spectrem Group, 127
speculation, 21, 42–43
speculators
in commodities market, 167
in energy markets, 43n.20

Index  I-7
in exchange-traded derivatives market, 
10–11
forward contracts for, 17
gambling by, 43
S&P Global REIT Index, 165
S&P GSCI (Goldman Sachs Commodity 
Index), 170
S&P infrastructure index, 175
spot assets, pricing, 66
spot markets, 5
spot prices, 5
for commodities, 171, 173
and futures price, 40–41
spread, 24
stand-alone mortgage loans, 160–161
and volatility, 89
standardization
of exchange-traded derivatives, 11
of futures contracts, 17–18
Stanley Gibbons, 175
stock
arbitrage with, 47–49, 67, 68
returns on, 126, 139, 170
volatility of, 126
stock options, 36n.15
storage
in derivatives pricing, 46–47
and holding of assets, 65
theory of, 173
stress testing, 179
strike price. see exercise price
supply, of commodities, 171
survivorship bias, 125n.3, 143
swaps (swap contracts), 21–25
currency, 23n.12, 37
defined, 21–22, 61
equity, 36
index, 36
interest rate, 22–23

equity, 36
index, 36
plain vanilla, 22–23, 37
pricing and valuation of, 82–85
total return, 30
systematic risk, 129
systemic risk, 32, 43–44
T
T206 Honus Wagner baseball card, 
176n.39
tail events, 179
tangible assets, 129, 175–176
target companies, for leveraged buyouts, 
151–152
taxes, on REITs, 126
T-bills. see US Treasury billsTED spread, 24
term structure of interest rates, 79
theory of storage, 173
Tibor. see Tokyo Interbank Offered Rate
timberland, investing in, 158–159, 163
time horizon, for forward contracts, 74
time to expiration, option pricing and, 
88–89
time value decay, 90
time value of money, 63
time value of options, 90
titles, real estate, 158
to-arrive contracts, 39–40
Tokyo Interbank Offered Rate (Tibor), 
78n.11
Tokyo Stock Exchange, 9
top down strategies, 136, 137
total return, on real estate, 158
total return swaps, 30
track record, of hedge funds, 147
trade sales, private equity, 154
trading NAV, 146
traditional investments, 124
integration of alternative investments 
with, 132

with, 132
Sharpe ratios for, 131
tranches, 34, 160–161
transaction costs, derivative, 41, 70
transactions-based indexes (real estate), 
163–164
transparency
11
of futures market, 21
transportation assets, 174
U
underlying (underlying assets), 5
defined, 7
and derivatives valuation, 46–47
hedging of, 67–68
payments on, 90–91
performance of, 6
pricing, 62–66
in pricing of European options, 87, 
89–91
for puts, 95
storage of, 46–47
types of, 36–39
value of, 87
volatility of, 89–90
United Kingdom, hedge fund 
registration, 145
alternative investors, 133n.14
hedge fund registration, 144, 145
returns on real estate, 164–165
US Consumer Price Index (US CPI),  
170US Securities and Exchange Commission 
(SEC), 144, 145
US Treasury bills (T-bills), 24
university endowment funds, 127
US CPI. see US Consumer Price Index
utility assets, 174
V
valuation
binomial, 100–104

of derivatives, 45–52, 73–85
and arbitrage, 47–52
options, 100–104
and storage, 46–47
of hedge funds, 145–146
of non-traded investments, 146
of portfolio company for private equity 
investment, 156–157
of real estate, 162, 165–166
value at risk (VaR), 178–179
value strategies, for hedge funds, 137
vanilla swaps, 22–23, 37
venture capital (VC), 152–153
defined, 129, 148
downside frequencies, 131, 132
expansion, 153
mezzanine, 153
returns, 126, 155–156
volatility
and arbitrage, 50
implied, 41
of underlying, 89–90
volatility strategies, for hedge funds,  
137
vulture investors, 153
W
Wagner, Honus, 176n.39
Wall Street Reform and Consumer 
Protection Act (2010), 12–13
warrants, 36
weather, derivatives on, 38
write-offs, private equity, 154
writer, derivatives, 7
Y
Yale University, 127
yields
collateral, 173

Y
yields
roll (convenience), 64–65, 173
Z
zero-sum game, 15

Economics
Study Session 4 Economics (1)
Study Session 5 Economics (2)
The candidate should be able to demonstrate knowledge of microeconomic and 
macroeconomic principles.
The next study sessions introduce fundamental microeconomic and macroeconomic 
concepts relevant to financial analysis and investment management. Microeconomic 
factors such as a firm’s competitive (or non-  competitive) environment and its pricing 
strategy may be critical inputs for cash flow forecasting and bottom up security selec -
tion approaches. Economic output, global trade flows, monetary and fiscal policies, 
and the business cycle are key considerations for conducting top own investment 
analysis and economic forecasting.
Candidates should be familiar with the material covered in the following prerequisite 
economics readings available in Candidate Resources on the CFA Institute website:
■■Demand and Supply Analysis: Introduction
■■Demand and Supply Analysis: Consumer Demand

■■Demand and Supply Analysis: The Firm

Economics (1)
This study session begins by introducing fundamental concepts of demand and 
supply analysis for individual consumers and firms. Also covered are the various 
market structures (perfect competition, oligopoly, monopoly) in which firms operate. 
Key macroeconomic concepts and principles then follow, including aggregate output 
and income measurement, aggregate demand and supply analysis, and analysis of 
economic growth factors. The study session concludes with coverage of the business 
cycle and its effect on economic activity. 
Reading 14  Topics in Demand and Supply Analysis  
by Richard V. Eastin, PhD, and Gary L. Arbogast, PhD, CFA
Reading 15 The Firm and Market Structures  
by Richard Fritz, PhD, and Michele Gambera, PhD, CFA 
Reading 16 Aggregate Output, Prices, and Economic Growth  
by Paul R. Kutasovic, PhD, CFA, and Richard Fritz, PhD
Reading 17 Understanding Business Cycles  
by Michele Gambera, PhD, CFA, Milton Ezrati, and Bolong Cao, 
PhD, CFAECONO mICS

4
© 2018 CFA Institute . All rights reserved.

Topics in Demand and Supply Analysis
by Richard V . Eastin, PhD, and Gary L. Arbogast, PhD, CFA
Richard V. Eastin, PhD, is at the University of Southern California (USA). Gary L. 
Arbogast, PhD, CFA (USA).
a. calculate and interpret price, income, and cross-  price elasticities 
of demand and describe factors that affect each measure;
b. compare substitution and income effects;
c. distinguish between normal goods and inferior goods;
d. describe the phenomenon of diminishing marginal returns;
e. determine and interpret breakeven and shutdown points of 
production;
f. describe how economies of scale and diseconomies of scale affect 
costs.
In a general sense, economics  is the study of production, distribution, and consumption 
and can be divided into two broad areas of study: macroeconomics and microeco -
nomics. Macroeconomics  deals with aggregate economic quantities, such as national

output and national income, and is rooted in microeconomics , which deals with 
markets and decision making of individual economic units, including consumers and 
businesses. Microeconomics is a logical starting point for the study of economics.
Microeconomics classifies private economic units into two groups: consumers 
(or households) and firms. These two groups give rise, respectively, to the theory of 
the consumer and the theory of the firm as two branches of study. The theory of the 
consumer  deals with consumption (the demand for goods and services) by utility-  
maximizing individuals (i.e., individuals who make decisions that maximize the sat -
isfaction received from present and future consumption). The theory of the firm  deals 
with the supply of goods and services by profit-  maximizing firms.1READING
14
© 2016 CFA Institute. All rights reserved.

Reading 14 ■ Topics in Demand and Supply Analysis 6
It is expected that candidates will be familiar with the basic concepts of demand and 
supply. This material is covered in detail in the recommended prerequisite readings. In 
this reading, we will explore how buyers and sellers interact to determine transaction 
prices and quantities. The reading is organized as follows: Section 2 discusses the 
consumer or demand side of the market model, and Section 3 discusses the supply 
side of the consumer goods market, paying particular attention to the firm’s costs. 
Section 4 provides a summary of key points in the reading.
DEMAND ANALYSIS: THE CONSUMER
The fundamental model of the private-  enterprise economy is the demand and supply 
model of the market. In this section, we examine three important topics concerning 
the demand side of the model: (1) elasticities, (2) substitution and income effects, 
and (3) normal and inferior goods. The candidate is assumed to have a basic under -

standing of the demand and supply model and to understand how a market discovers 
the equilibrium price at which the quantity willingly demanded by consumers at that 
price is just equal to the quantity willingly supplied by firms. Here, we explore more 
deeply some of the concepts underlying the demand side of the model.
2.1 Demand Concepts
The quantity of a good that consumers are willing to buy depends on a number of 
different variables. Perhaps the most important of those variables is the item’s own 
price. In general, economists believe that as the price of a good rises, buyers will 
choose to buy less of it, and as its price falls, they buy more. This opinion is so nearly 
universal that it has come to be called the law of demand .
Although a good’s own price is important in determining consumers’ willingness 
to purchase it, other variables also influence that decision. Consumers’ incomes, their 
tastes and preferences, and the prices of other goods that serve as substitutes or com -

plements are just a few of the other variables that influence consumers’ demand for a 
product or service. Economists attempt to capture all these influences in a relationship 
called the demand function . (A function is a relationship that assigns a unique value 
to a dependent variable for any given set of values of a group of independent variables.)
Equation  1 is an example of a demand function. In Equation  1, we are saying, 
“The quantity demanded of good X depends on (is a function of) the price of good 
X, consumers’ income, and the price of good Y”:
Qf PI Pxd
xy =(),,
where
 Qxd = the quantity demanded of some good X (such as per household demand 
for gasoline in liters per month)
 Px = the price per unit of good X (such as € per liter)
 I = consumers’ income (as in €1,000s per household annually)
 Py = the price of another good, Y. (There can be many other goods, not just 
one, and they can be complements or substitutes.)2
(1)

Demand Analysis: The Consumer 7
Often, economists use simple linear equations to approximate real-  world demand 
and supply functions in relevant ranges. Equation 2 illustrates a hypothetical example 
of our function for gasoline demand:
Qxd= 84.5 – 6.39 Px + 0.25 I – 2Py
where the quantity of gasoline demanded  Qxd()  is a function of the price of a liter of 
gasoline ( Px), consumers’ income in €1,000s ( I), and the average price of an automobile 
in €1,000s ( Py).
The signs of the coefficients on gasoline price (negative) and consumers’ income 
(positive) reflect the relationship between those variables and the quantity of gasoline 
consumed. The negative sign on average automobile price indicates that if automo -
biles go up in price, fewer will likely be purchased and driven; hence, less gasoline 
will be consumed. (As discussed later, such a relationship would indicate that gaso -
line and automobiles have a negative cross-  price elasticity of demand and are thus 
complements.)

To continue our example, suppose that the price of gasoline ( Px) is €1.48 per liter, 
per household income ( I) is €50,000, and the price of the average automobile ( Py) is 
€20,000. In this case, this function would predict that the per-  household monthly 
demand for gasoline would be 47.54 liters, calculated as follows:
Qxd= 84.5 – 6.39(1.48) + 0.25(50) – 2(20) = 47.54
recalling that income and automobile prices are measured in thousands. Note that the 
sign on the “own-  price” variable ( Px) is negative; thus, as the price of gasoline rises, per 
household consumption would decrease by 6.39 liters per month for every €1 increase 
in gas price. Own price  is used by economists to underscore that the reference is to 
the price of a good itself and not the price of some other good.
In our example, there are three independent variables in the demand function 
and one dependent variable. If any one of the independent variables changes, so

does the quantity demanded. It is often desirable to concentrate on the relationship 
between the dependent variable and just one of the independent variables at a time. 
To accomplish this goal, we can hold the other independent variables constant and 
rewrite the equation.
For example, to concentrate on the relationship between the quantity demanded of 
the good and its own price, Px, we hold constant the values of income and the price of 
good Y. In our example, those values are 50 and 20, respectively. The equation would 
then be rewritten as
Qxd= 84.5 – 6.39 Px + 0.25(50) – 2(20) = 57 – 6.39 Px
The quantity of gasoline demanded is a function of the price of gasoline (6.39 
per liter), per household income (€50,000), and the average price of an automobile 
(€20,000). Notice that income and the price of automobiles are not ignored; they are 
simply held constant, and they are “collected” in the new constant term, 57 [84.5 +

(0.25)(50) – (2)(20)]. Notice also that we can solve for Px in terms of  Qxd by rearranging 
Equation 3, which gives us Equation 4:
PQxxd=−8920 156 ..   (2)
(3)
(4)

Reading 14 ■ Topics in Demand and Supply Analysis 8
Equation 4 gives the price of gasoline as a function of the quantity of gasoline 
consumed per month and is referred to as the inverse demand function . Qx in 
Equation 4 must be restricted to be less than or equal to 57 so that price is not neg -
ative. The graph of the inverse demand function is called the demand curve  and is 
shown in Exhibit 1.1
Exhibit 1   Household Demand Curve for Gasoline
Px (€ per liter)
8.92
2.48
1.48
57
41.1547.54Qx (liters per month)
The demand curve represents the highest quantity willingly purchased at each 
price as well as the highest price willingly paid for each quantity. In this example, 
this household would be willing to purchase 47.54 liters of gasoline per month at a 
price of €1.48 per liter. If price were to rise to €2.48 per liter, the household would be 
willing to purchase only 41.15 liters per month.
This demand curve is drawn with price on the vertical axis and quantity on the

horizontal axis. It can be correctly interpreted as specifying either  the highest quantity 
a household would buy at a given price or the highest price it would be willing to pay 
for a given quantity. In our example, at a price of €1.48 per liter, households would 
each be willing to buy 47.54 liters per month. Alternatively, the highest price they 
would be willing to pay for 47.54 liters per month is €1.48 per liter. If the price were 
to rise by €1, households would reduce the quantity they each bought by 6.39 units, 
to 41.15 liters. The slope of the demand curve is measured as the change in price, P, 
divided by the change in quantity, Q (∆P/∆Q, where ∆ stands for “the change in”). In 
this case, the slope of the demand curve is 1/–6.39, or –0.156.
The general model of demand and supply can be highly useful in understanding 
directional changes in prices and quantities that result from shifts in one curve or the

other. Often, though, we need to measure how sensitive quantity demanded or sup -
plied is to changes in the independent variables that affect them. This is the concept 
of elasticity of demand  and elasticity of supply . Fundamentally, all elasticities are 
calculated in the same way: They are ratios of percentage changes. Let us begin with 
the sensitivity of quantity demanded to changes in the own price.
1 Following usual practice, we show linear demand curves intersecting the quantity axis at a price of 
zero. Real-  world demand functions may be non-  linear in some or all parts of their domain. Thus, linear 
demand functions in practical cases are approximations of the true demand function that are useful for a 
relevant range of values.

Demand Analysis: The Consumer 9
2.2 Own-  Price Elasticity of Demand
In Equation 1, we expressed the quantity demanded of some good as a function of 
several variables, one of which was the price of the good itself (the good’s “own-  price”).
In Equation 3, we introduced a hypothetical household demand function for gas -
oline, assuming that the household’s income and the price of another good (automo -
biles) were held constant. That function was given by the simple linear expression  Qxd 
= 57 – 6.39 Px. Using this expression, if we were asked how sensitive the quantity of 
gasoline demanded is to changes in price, we might say that whenever price changes 
by one unit, quantity changes by 6.39 units in the opposite direction; for example, if 
price were to rise by €1, quantity demanded would fall by 6.39 liters per month. The 
coefficient on the price variable (–6.39) could be the measure of sensitivity we are 
seeking.

seeking.
There is a drawback associated with that measure, however. It is dependent on 
the units in which we measured Q and P. When we want to describe the sensitivity of 
demand, we need to recall the specific units in which Q and P were measured—liters 
per month and euros per liter—in our example. This relationship cannot readily be 
extrapolated to other units of measure—for example, gallons and dollars. Economists, 
therefore, prefer to use a gauge of sensitivity that does not depend on units of mea -
sure. That metric is called elasticity . Elasticity is a general measure of how sensitive 
one variable is to any other variable, and it is expressed as the ratio of percentage 
changes in each variable: %∆ y/%∆x. In the case of own-  price elasticity of demand , 
that measure is illustrated in Equation 5:
EQ
Ppd xd
xx=%
%∆
∆
This equation expresses the sensitivity of the quantity demanded to a change in 
price.  Epd
x is the good’s own-  price elasticity and is equal to the percentage change in

quantity demanded divided by the percentage change in price. This measure is inde -
pendent of the units in which quantity and price are measured. If quantity demanded 
falls by 8% when price rises by 10%, then the elasticity of demand is simply –0.8. It 
does not matter whether we are measuring quantity in gallons per week or liters per 
day, and it does not matter whether we measure price in dollars per gallon or euros 
per liter; 10% is 10%, and 8% is 8%. So the ratio of the first to the second is still –0.8.
We can expand Equation  5 algebraically by noting that the percentage change 
in any variable x is simply the change in x (∆x) divided by the level of x. So, we can 
rewrite Equation 5, using a few simple steps, as
EQ
PQ
Q
P
PQ
PP
Qpd xd
xxd
xd
x
xxd
xx
xd x== =



%
%∆
∆∆
∆∆
∆
To get a better idea of price elasticity, it might be helpful to illustrate using our 
hypothetical demand function:  Qxd = 57 − 6.39 Px. When the relationship between two 
variables is linear,  ∆∆QPxd

x  is equal to the slope coefficient on Px in the demand 
function. Thus, in our example, the elasticity of demand is –6.39 multiplied by the 
ratio of price to quantity. We need to choose a price at which to calculate the elasticity 
coefficient. Using our hypothetical original price of €1.48, we can find the quantity 
associated with that particular price by inserting 1.48 into the demand function as 
given in Equation 3:
Q = 57 − (6.39)(1.48) = 47.54  (5)
(6)

Reading 14 ■ Topics in Demand and Supply Analysis 10
and we find that Q = 47.54 liters per month.
The result of our calculation is that at a price of 1.48, the elasticity of our market 
demand function is −6.39(1.48/47.54) = −0.2. How do we interpret that value? It 
means, simply, that when price equals 1.48, a 1% rise in price would result in a fall in 
quantity demanded of 0.2%.
In our example, when the price is €1.48 per liter, demand is not very sensitive to 
changes in price because a 1% rise in price would reduce quantity demanded by only 
0.2%. In this case, we would say that demand is inelastic . To be precise, when the 
magnitude (ignoring algebraic sign) of the own-  price elasticity coefficient has a value 
of less than one, demand is said to be inelastic. When that magnitude is greater than 
one, demand is said to be elastic . And when the elasticity coefficient is equal to neg -
ative one, demand is said to be unit elastic , or unitary elastic. Note that if the law of

demand holds, own-  price elasticity of demand will always be negative because a rise 
in price will be associated with a fall in quantity demanded, but it can be either elastic 
(very sensitive to a change in price) or inelastic (insensitive to a change in price). In 
our hypothetical example, suppose the price of gasoline was very high, say, €5 per 
liter. In this case, the elasticity coefficient would be −1.28:
Q = 57 − (6.39)(5) = 25.05
and
−6.39 (5/25.05) = −1.28
Because the magnitude of the elasticity coefficient is greater than one, we know 
that demand is elastic at that price.2 In other words, at lower prices (€1.48 per liter), 
a slight change in the price of gasoline does not have much effect on the quantity 
demanded, but when gasoline is expensive (€5 per liter), consumer demand for gas is 
highly affected by changes in price.
By examining Equation 6 more closely, we can see that for a linear demand curve

the elasticity depends on where on the curve we calculate it. The first term, ∆ Q/∆P, 
which is the inverse of the slope of the demand curve, remains constant along the 
entire demand curve. But the second term, P/Q, changes depending on where we are 
on the demand curve. At very low prices, P/Q is very small, so demand is inelastic. But 
at very high prices, Q is low and P is high, so the ratio P/Q is very high and demand 
is elastic. Exhibit 2 illustrates a characteristic of all negatively sloped linear demand 
curves. Above the midpoint of the curve, demand is elastic; below the midpoint, 
demand is inelastic; and at the midpoint, demand is unit elastic.
2 If interested, evidence on price elasticities of demand for gasoline can be found in Molly Espey, “Explaining 
the Variation in Elasticity Estimates of Gasoline Demand in the United States: A Meta-  analysis, ” Energy 
Journal , vol. 17, no. 3 (1996): 49–60. The robust estimates were about –0.26 for short-  run elasticity—less

Demand Analysis: The Consumer 11
Exhibit 2   The Elasticity of a Linear Demand Curve
P
QElastic Demand above Midpoint 
Inelastic Demand Below Midpoint Unit-Elastic Demand at Midpoint 
Note:  For all negatively sloped, linear demand curves, 
elasticity varies depending on where it is calculated. 
2.2.1  Extremes of Price Elasticity
There are two special cases in which linear demand curves have the same elasticity at 
all points: vertical demand curves and horizontal demand curves. Consider a vertical 
demand curve, as in Panel A of Exhibit 3, and a horizontal demand curve, as in Panel 
B. In the first case, the quantity demanded is the same, regardless of price. There is 
no demand curve that is perfectly vertical at all possible prices, but it is reasonable 
to assume that, over some range of prices, the same quantity would be purchased 
at a slightly higher price or a slightly lower price. Thus, in that price range, quantity

demanded is not at all sensitive to price, and we would say that demand is perfectly 
inelastic  in that range.
Exhibit 3   The Extremes of Price Elasticity
P
QP
Q
Note: A vertical demand 
has zero elasticity and is 
called perfectly inelastic. Note:  A horizontal demand 
has infinite elasticity and is 
called perfectly elastic. Panel A Panel B
In the second case, the demand curve is horizontal at some given price. It implies 
that even a minute price increase will reduce demand to zero, but at that given price, 
the consumer would buy some large, unknown amount. This situation is a reasonable 
description of the demand curve facing an individual seller in a perfectly competitive 
market, such as the wheat market. At the current market price of wheat, an individual 
farmer could sell all she has. If, however, she held out for a price above market price, 
it is reasonable to believe that she would not be able to sell any at all; other farmers’

Reading 14 ■ Topics in Demand and Supply Analysis 12
wheat is a perfect substitute for hers, so no one would be willing to buy any of hers at 
a higher price. In this case, we would say that the demand curve facing a seller under 
conditions of perfect competition is perfectly elastic .
2.2.2  Predicting Demand Elasticity
Own-  price elasticity of demand is a measure of how sensitive the quantity demanded 
is to changes in the price of a good or service, but what characteristics of a good or 
its market might be informative in determining whether demand is highly elastic? 
Perhaps the most important characteristic is whether there are close substitutes for 
the good in question. If there are close substitutes for the good, then if its price rises 
even slightly, a consumer would tend to purchase much less of this good and switch to 
the less costly substitute. If there are no substitutes, however, then it is likely that the

demand is much less elastic. Consider a consumer’s demand for some broadly defined 
product, such as bread. There really are no close substitutes for the entire category of 
bread, which includes all types from French bread to pita bread to tortillas and so on. 
So, if the price of all bread were to rise, perhaps a consumer would purchase a little 
less of it each week, but probably not a significantly smaller amount. Now, consider 
that the consumer’s demand is for a particular baker’s specialty bread instead of the 
category “bread” as a whole. Surely, there are close substitutes for Baker Bob’s Whole 
Wheat Bread with Sesame Seeds than for bread in general. We would expect, then, 
that the demand for Baker Bob’s special loaf is much more elastic than for the entire 
category of bread.
In addition to the degree of substitutability, other characteristics tend to be generally 
predictive of a good’s elasticity of demand. These include the portion of the typical

budget that is spent on the good, the amount of time that is allowed to respond to the 
change in price, the extent to which the good is seen as necessary or optional, and so 
on. In general, if consumers tend to spend a very small portion of their budget on a 
good, their demand tends to be less elastic than if they spend a very large part of their 
income. Most people spend only a little on toothpaste each month, for example, so 
it really does not matter whether the price rises 10%. They would probably still buy 
about the same amount. If the price of housing were to rise significantly, however, 
most households would try to find a way to reduce the quantity they buy, at least in 
the long run.
This example leads to another characteristic regarding price elasticity. For most 
goods and services, the long-  run demand is much more elastic than the short-  run 
demand. For example, if the price of gasoline rises, we probably would not be able to

respond quickly to reduce the quantity we consume. In the short run, we tend to be 
locked into modes of transportation, housing and employment location, and so on. 
With a longer adjustment period, however, we can adjust the quantity consumed in 
response to the change in price by adopting a new mode of transportation or reducing 
the distance of our commute. Hence, for most goods, long-  run elasticity of demand 
is greater than short-  run elasticity. Durable goods, however, tend to behave in the 
opposite way. If the price of washing machines were to fall, people might react quickly 
because they have an old machine that they know will need to be replaced fairly soon 
anyway. So when price falls, they might decide to go ahead and make a purchase. If 
the price of washing machines were to stay low forever, however, it is unlikely that a 
typical consumer would buy more machines over a lifetime.
Knowing whether the good or service is seen to be discretionary or non-  discretionary

helps to understand its sensitivity to a price change. Faced with the same percentage 
increase in prices, consumers are much more likely to give up their Friday night 
restaurant meal (discretionary) than they are to cut back significantly on staples in 
their pantry (non-  discretionary). The more a good is seen as being necessary, the less 
elastic its demand is likely to be.

Demand Analysis: The Consumer 13
In summary, own-  price elasticity of demand is likely to be greater (i.e., more 
sensitive) for items that have many close substitutes, occupy a large portion of the 
total budget, are seen to be optional instead of necessary, or have longer adjustment 
times. Obviously, not all these characteristics operate in the same direction for all 
goods, so elasticity is likely to be a complex result of these and other characteristics. 
In the end, the actual elasticity of demand for a particular good turns out to be an 
empirical fact that can be learned only from careful observation and, often, sophis -
ticated statistical analysis.
2.2.3  Elasticity and Total Expenditure
Because of the law of demand, an increase in price is associated with a decrease in 
the number of units demanded of some good or service. But what can we say about 
the total expenditure on that good? That is, what happens to price times quantity

when price falls? Recall that elasticity is defined as the ratio of the percentage change 
in quantity demanded to the percentage change in price. So if demand is elastic, a 
decrease in price is associated with a larger percentage rise in quantity demanded. 
Although each unit of the good has a lower price, a sufficiently greater number of 
units are purchased so that total expenditure (price times quantity) would rise as price 
falls when demand is elastic.
If demand is inelastic, however, a given percentage decrease in price is associated 
with a smaller percentage rise in quantity demanded. Consequently, when demand 
is inelastic, a fall in price brings about a fall in total expenditure.
In summary, when demand is elastic, price and total expenditure move in opposite  
directions. When demand is inelastic, price and total expenditure move in the same  
direction. This relationship is easy to identify in the case of a linear demand curve.

Recall that above the midpoint, demand is elastic, and below the midpoint, demand 
is inelastic. In the upper section of Exhibit 4, total expenditure ( P × Q) is measured 
as the area of a rectangle whose base is Q and height is P. Notice that as price falls, 
the areas of the inscribed rectangles (each outlined with their own dotted or dashed 
line) at first grow in size, become largest at the midpoint of the demand curve, and 
thereafter become smaller as price continues to fall and total expenditure declines 
toward zero. In the lower section of Exhibit 4, total expenditure is shown for each 
quantity purchased.

Reading 14 ■ Topics in Demand and Supply Analysis 14
Exhibit 4   Elasticity and Total Expenditure
P
QIn the elastic range, a fall 
in price accompanies a 
rise in total expenditure 
In the inelastic range, a fall 
in price accompanies a fall 
in total expenditure 
Note:  Figure depicts the relationship among changes in price, 
changes in quantity, and changes in total expenditure. 
Maximum total expenditure occurs at the unit-elastic point 
on a linear demand curve (the cross-hatched rectangle). QTotal Expenditure
The relationships just described hold for any demand curve, so it does not matter 
whether we are dealing with the demand curve of an individual consumer, the demand 
curve of the market, or the demand curve facing any given seller. For a market, the 
total expenditure by buyers becomes the total revenue to sellers in that market. It 
follows, then, that if market demand is elastic, a fall in price will result in an increase

in total revenue to sellers as a whole, and if demand is inelastic, a fall in price will 
result in a decrease in total revenue to sellers. If the demand faced by any given seller 
were inelastic at the current price, that seller could increase revenue by increasing its 
price. But because demand is negatively sloped, the increase in price would decrease 
total units sold, which would almost certainly decrease total production cost. If raising 
price both increases revenue and decreases cost, such a move would always be profit 
enhancing. Faced with inelastic demand, a one-  product seller would always be inclined 
to raise the price until the point at which demand becomes elastic.
2.3 Income Elasticity of Demand
Elasticity is a measure of how sensitive one variable is to change in the value of 
another variable. Up to this point, we have focused on price elasticity, but the quantity 
demanded of a good is also a function of consumer income.

Income elasticity of demand is defined as the percentage change in quantity 
demanded  %∆Qxd()  divided by the percentage change in income (%∆ I), holding all 
other things constant, as shown in Equation 7:
EQ
IId xd
=%
%∆
∆(7)

Demand Analysis: The Consumer 15
The structure of this expression is identical to the structure of own-  price elasticity 
given in Equation 5. (All elasticity measures that we will examine have the same gen -
eral structure; the only thing that changes is the independent variable of interest.) For 
example, if the income elasticity of demand for some good has a value of 0.8, we would 
interpret that to mean that whenever income rises by 1%, the quantity demanded at 
each price would rise by 0.8%.
Although own-  price elasticity of demand will almost always be negative, income  
elasticity of demand can be negative, positive, or zero. Positive income elasticity 
means that as income rises, quantity demanded also rises. Negative income elasticity 
of demand means that when people experience a rise in income, they buy less of these 
goods, and when their income falls, they buy more of the same good.
Goods with positive income elasticity are called “normal” goods. Goods with

negative income elasticity are called “inferior” goods. Typical examples of inferior 
goods are rice, potatoes, or less expensive cuts of meat. We will discuss the concepts 
of normal and inferior goods in a later section.
In our discussion of the demand curve, we held all other things constant, including 
consumer income, to plot the relationship between price and quantity demanded. If 
income were to change, the entire demand curve would shift one way or the other. 
For normal goods, a rise in income would shift the entire demand curve upward and 
to the right. For inferior goods, however, a rise in income would result in a downward 
and leftward shift in the entire demand curve.
2.4 Cross-  Price Elasticity of Demand
We previously discussed a good’s own-  price elasticity. However, the price of another 
good might also have an impact on the demand for that good or service, and we should 
be able to define an elasticity with respect to the other price ( Py) as well. That elasticity

is called the cross-  price elasticity of demand  and takes on the same structure as 
own-  price elasticity and income elasticity of demand, as represented in Equation 8:
EQ
Ppd xd
yy=%
%∆
∆
Note how similar this equation is to the equation for own-  price elasticity. The only 
difference is that the subscript on P is now y, where y indicates some other good. This 
cross-  price elasticity of demand measures how sensitive the demand for good X is to 
changes in the price of some other good, Y, holding all other things constant. For some 
pairs of goods, X and Y, when the price of Y rises, more of good X is demanded; the 
cross-  price elasticity of demand is positive. Those goods are referred to as substitutes . 
In economics, if the cross-  price elasticity of two goods is positive, they are substitutes, 
irrespective of whether someone would consider them “similar. ”
This concept is intuitive if you think about two goods that are seen to be close

substitutes, perhaps like two brands of beer. When the price of one of your favorite 
brands of beer rises, you would probably buy less of that brand and more of a cheaper 
brand, so the cross-  price elasticity of demand would be positive. For substitute goods, 
an increase in the price of one good would shift the demand curve for the other good 
upward and to the right.
Alternatively, two goods whose cross-  price elasticity of demand is negative are 
said to be complements . Typically, these goods tend to be consumed together as a 
pair, such as gasoline and automobiles or houses and furniture. When automobile 
prices fall, we might expect the quantity of autos demanded to rise, and thus we might 
expect to see a rise in the demand for gasoline.(8)

Reading 14 ■ Topics in Demand and Supply Analysis 16
Whether two goods are substitutes or complements might not be immediately 
intuitive. For example, grocery stores often put things like coffee on sale in the hope 
that customers will come in for coffee and end up doing their weekly shopping there 
as well. In that case, coffee and, say, cabbage could very well empirically turn out to 
be complements even though we would not think that the price of coffee has any 
relation to sales of cabbage. Regardless of whether someone would see two goods as 
related in some fashion, if the cross-  price elasticity of two goods is negative, they are 
complements.
Although a conceptual understanding of demand elasticities is helpful in sorting out 
the qualitative and directional effects among variables, using an empirically estimated 
demand function can yield insights into the behavior of a market. For illustration, let 
us return to our hypothetical individual demand function for gasoline in Equation 2,

duplicated here for convenience:
The quantity demanded of a given good  Qxd()  is a function of its own price ( Px), con -
sumer income ( I), and the price of another good ( Py).
To derive the market demand function, the individual consumers’ demand func -
tions are simply added together. If there were 1,000 individuals who represented a 
market and they all had identical demand functions, the market demand function 
would be the individual consumer’s demand function multiplied by the number of 
consumers. Using the individual demand function given by Equation 2, the market 
demand function would be as shown in Equation 9:
Qxd= 84,500 – 6,390 Px + 250 I – 2,000 Py  
Earlier, when we calculated own-  price elasticity of demand, we needed to choose 
a price at which to calculate the elasticity coefficient. Similarly, we need to choose 
actual values for the independent variables— Px, I, and Py—and insert these values into

the “estimated” market demand function to find the quantity demanded. Choosing 
€1.48 for Px, €50 (in thousands) for I, and €20 (in thousands) for Py, we find that the 
quantity of gasoline demanded is 47,543 liters per month. We now have everything 
we need to calculate own-  price, income, and cross-  price elasticities of demand for 
our market. Those elasticities are expressed in Equations 10, 11, and 12. Each of those 
expressions has a term denoting the change in quantity divided by the change in each 
respective variable: own price, ∆ Qx/∆Px; income, ∆ Qx/∆I, and cross price, ∆ Qx/∆Py.
As we stated in the discussion of own-  price elasticity, when the relationship 
between two variables is linear, the change in quantity  ∆Qxd()  divided by the change 
in own price (∆ Px), income (∆ I), or cross price (∆ Py) is equal to the slope coefficient 
on that other variable. The elasticities are calculated by inserting the slope coefficients 
from Equation 9 into the elasticity formulas.

Own-  price elasticity:
EQ
PP
Qpd xd
xx
xd x=



=−()
 ∆
∆6 390148
47 542 8,.
,.  =−020 .
Income elasticity:
EQ
II
QId xd
xd=



=()

=∆
∆25050
47 542 8026,..(9)
(10)
(11)

Demand Analysis: The Consumer 17
Cross-  price elasticity:
EQ
PP
Qpd xd
yy
xd y=



=−()

=∆
∆200020
47 542 8,.− −084 .
In our example, at a price of €1.48, the own-  price elasticity of demand is –0.20; a 
1% increase in the price of gasoline leads to a decrease in quantity demanded of about 
0.20% (Equation 10). Because the absolute value of the own-  price elasticity is less than 
one, we characterize demand as being inelastic  at that price; for example, an increase 
in price would result in an increase in total expenditure on gasoline by consumers in 
that market. The income elasticity of demand is 0.26 (Equation 11): A 1% increase in 
income would result in an increase of 0.26% in the quantity demanded of gasoline. 
Because that elasticity is positive (but small), we would characterize gasoline as a 
normal good. The cross-  price elasticity of demand between gasoline and automobiles 
is −0.84 (Equation 12): If the price of automobiles rose by 1%, the demand for gasoline

would fall by 0.84%. We would, therefore, characterize gasoline and automobiles as 
complements because the cross-  price elasticity is negative. The magnitude is quite 
small, however, so we would conclude that the complementary relationship is weak.
EXAMPLE 1   
Calculating Elasticities from a Given Demand Function
An individual consumer’s monthly demand for downloadable e-  books is given 
by the equation  Qebd = 2 – 0.4 Peb + 0.0005 I + 0.15 Phb, where  Qebd equals the 
number of e-  books demanded each month, I equals the household monthly 
income, Peb equals the price of e-  books, and Phb equals the price of hardbound 
books. Assume that the price of e-  books is €10.68, household income is €2,300, 
and the price of hardbound books is €21.40.
1 Determine the value of own-  price elasticity of demand for e-  books.
2 Determine the income elasticity of demand for e-  books.
3 Determine the cross-  price elasticity of demand for e-  books with respect 
to the price of hardbound books.

The own-  price elasticity of demand is given by  ∆∆QP PQebd
eb eb ebd() () . Notice 
from the demand function that  ∆∆QPebd
eb  = −0.4. Inserting the given variable 
values into the demand function yields  Qebd = 2 − (0.4)(10.68) + (.0005)(2300) + 
(0.15)(21.4) = 2.088. So at a price of €10.68, the own-  price elasticity of demand 
equals (–0.4)(10.68/2.088) = −2.046, which is elastic because in absolute value 
the elasticity coefficient is greater than 1.
Recall that income elasticity of demand is given by  ∆∆QI IQebd
ebd() () . Notice 
from the demand function that  ∆∆QIebd
  = 0.0005. Inserting the values for I 
and Qebd yields income elasticity of (0.0005)(2,300/2.088) = 0.551, which is pos -
itive, so e-  books are a normal good.(12)

Reading 14 ■ Topics in Demand and Supply Analysis 18
Recall that cross-  price elasticity of demand is given by (∆ Qeb/∆Phb)(Phb/Qeb), 
and notice from the demand function that ∆ Qeb/∆Phb = 0.15. Inserting the values 
for Phb and Qeb yields a cross-  price elasticity of demand for e-  books of (0.15)
(21.40/2.088) = 1.537, which is positive, implying that e-  books and hardbound 
books are substitutes.
2.5 Substitution and Income Effects
The law of demand states that if nothing changes other than the price of a particular 
good or service itself, a decrease in that good’s price will tend to result in a greater 
quantity of that good being purchased. Simply stated, it is the assumption that a 
demand curve has negative slope; that is, where price per unit is measured on the 
vertical axis and quantity demanded per time period is measured on the horizontal 
axis, the demand curve is falling from left to right, as shown in Exhibit 5.

Exhibit 5   A Negatively Sloped Demand Curve—The Law of Demand
Px
QxDemand Curve for Good X
There are two reasons why a consumer would be expected to purchase more of 
a good when its price falls and less of a good when its price rises. These two reasons 
are known as the substitution effect and the income effect of a change in price. We 
address these two effects separately and then examine the combination of the two.
When the price of something—say, gasoline—falls, that good becomes relatively 
less costly compared with other goods or services a consumer might purchase. For 
example, gasoline is used in driving to work, so when its price falls, it is relatively 
cheaper to drive to work than to take public transportation. Hence, the consumer is 
likely to substitute a little more driving to work for a little less public transportation. 
When the price of beef falls, it becomes relatively cheaper than chicken. The typical

consumer is, therefore, likely to purchase a little more beef and a little less chicken.
On its own, the substitution effect suggests that when the price of something 
falls, consumers tend to purchase more of that good. But another influence is often 
at work as well—the income effect. Consider a consumer spending all of her “money 
income” on a given combination of goods and services. (Her money income is simply 
the quantity of dollars or euros, or other relevant currency, that is available to her 
to spend in any given time period.) Now suppose the price of something she was 
regularly purchasing falls while her money income and the prices of all other goods 
remain unchanged. Economists refer to this as an increase in purchasing power or 
real income . For most goods and services, consumers tend to buy more of them when 
their income rises. So when the price of a good—say, beef—falls, most consumers 
would tend to buy more beef because of the increase in their real income. Although

Demand Analysis: The Consumer 19
the consumer’s money income (the number on her paycheck) is assumed not to have 
changed, her real income has risen because she can now buy more beef—and other 
goods, too—as a result of the fall in the price of that one good. So, quite apart from 
the substitution effect of a fall in a good’s price, the income effect tends to cause 
consumers to purchase more of that good as well.
Substitution and income effects work the other way, too. If the price of beef were 
to rise, the substitution effect would cause the consumer to buy less of it and substi -
tute more chicken for the now relatively more expensive beef. Additionally, the rise 
in the price of beef results in a decrease in the consumer’s real income because now 
she can buy less goods with the same amount of money income. If beef is a good 
that consumers tend to buy more of when their income rises and less of when their

income falls, then the rise in beef price would have an income effect that causes the 
consumer to buy less of it.
2.6 Normal and Inferior Goods
Economists classify goods on various dimensions, one of which relates to how con -
sumers’ purchases of a good respond to changes in consumer income. Earlier, when 
discussing income elasticity of demand, we introduced the concept of normal goods 
and inferior goods. For most goods and services, an increase in income would cause 
consumers to buy more; these are called normal goods . But that does not hold true 
for all goods: There are goods that consumers buy less of when their income rises and 
goods that they buy more of when their incomes fall. These are called inferior goods . 
This section will distinguish between normal goods and inferior goods.
We previously discussed income and substitution effects of a change in price. If 
a good is normal, a decrease in price will result in the consumer buying more of that

good. Both the substitution effect and the income effect are at play here:
■■A decrease in price tends to cause consumers to buy more of this good in place 
of other goods—the substitution effect.
■■The increase in real income resulting from the decline in this good’s price 
causes people to buy even more of this good when its price falls—the income 
effect.
So, we can say that for normal goods (restaurant meals, for example, as most people 
tend to eat out more often when their incomes rise), the substitution and the income 
effects reinforce one another to cause the demand curve to be negatively sloped.
For inferior goods (cheaper cuts of meat or generic beverages, for example, which 
most people buy less of as their incomes rise), an increase in income causes consumers 
to buy less, not more, and if their incomes fall, they buy more, not less. “Inferior” does 
not imply anything at all about the quality of the good; it is simply used to refer to a

good for which an increase in income causes some people to buy less of it.
The same good could be normal for some consumers while it is inferior for others. 
Consider a very low-  income segment of the population. For those consumers, an 
increase in their income might very well result in their buying more fast-  food meals. 
They might take some of that added income and enjoy eating out at a fast-  food restau -
rant a little more often. Now consider a high-  income group. If their income rises, 
they might be much less inclined to eat at fast-  food restaurants and instead do their 
dining out at a fashionable French bistro, for example. So, fast-  food meals might be 
a normal good for some people and an inferior good for others.
Let us now consider the substitution and income effects of a change in the price of 
normal and inferior goods. The substitution effect says that if the price of a good falls, 
the consumer will substitute more of this good in the consumption bundle and buy

less of some other good. The substitution effect is true for both normal and inferior 
goods. Next, we provide an example.

Reading 14 ■ Topics in Demand and Supply Analysis 20
We begin with a hypothetical consumer with a certain money income (R$200,000). 
Given the prices for all goods, he makes a decision to buy a given amount of Good 
X, coffee. If the price of coffee falls, the consumer is better off than when the price 
was higher. We can assume that this consumer would have been willing to pay some 
amount of money each month to be able to buy coffee at the lower price. We now 
have two states of the world: In State 1, he spends his income on all the various goods, 
including his desired quantity of coffee at the original price. In State 2, he is able to 
buy coffee at the new lower price, but because he has paid a portion of his income to 
buy coffee at the lower price, he now has less money income to spend on all goods 
combined. If we adjusted the amount of money he would have to pay to lock in the 
lower price of coffee until he is just indifferent between the two states of the world,

we would have exactly offset the “good” thing of the lower price with the “bad” thing 
of less income. This removes the income effect of the price decrease and allows us to 
isolate the pure substitution effect. We find that in State 2, he would buy more coffee 
than in State 1. The pure substitution effect is always in the direction of buying more 
at the lower relative price.
Continuing our example, assume that we give back to the consumer the amount 
of money he is willing to pay for the privilege of buying coffee at the lower price. 
Clearly, he is better off because now he can buy coffee at the lower price without 
having to pay for the privilege. We want to know whether, with this higher money 
income, he will now buy more or less coffee at the lower price. The answer depends 
on whether coffee is a normal or an inferior good for this consumer. Recall that for 
normal goods, an increase in income causes consumers to buy more, but for inferior

goods, an increase in income causes consumers to buy less.
In conclusion, the substitution effect of a change in the price of a good will always 
be in the direction of buying more at a lower price or less at a higher price. The income 
effect of that same price change, however, depends on whether the good is normal or 
inferior. If the good is normal, the income effect reinforces the substitution effect, both 
leading to a negatively sloped demand curve. But if the good is inferior, the income 
effect and the substitution effect work in opposite directions; the income effect tends 
to mitigate the substitution effect.
Exhibit 6 summarizes the substitution and income effects for normal and inferior 
goods.
Exhibit 6   The Substitution and Income Effects of a Price Decrease on 
Normal and Inferior Goods
Substitution Effect Income Effect
Normal good Buy more because the good 
is relatively cheaper than its 
substitutes.Buy more because the increase 
in purchasing power raises the

in purchasing power raises the 
total consumption level.
Inferior good Buy more because the good 
substitutes.Buy less because the increase 
in real income prompts the con -
sumer to buy less of the inferior 
good in favor of its preferred 
substitutes.

Demand Analysis: The Consumer 21
 
Exceptions to the Law of Demand
In virtually every case in the real world, the law of demand holds: A decrease in price 
results in an increase in quantity demanded, resulting in a negatively sloped demand 
curve. In a few unusual cases, however, we may find a positively sloped demand curve—a 
decrease (increase) in price may result in a decrease (increase) in the quantity demanded. 
These unusual cases are called Giffen goods and Veblen goods.
In theory, it is possible for the income effect to be so strong and so negative as to 
overpower the substitution effect. In such a case, more of a good would be consumed 
as the price rises and less would be consumed as the price falls. These goods are called 
Giffen goods , named for Robert Giffen based on his observations of the purchasing 
habits of the Victorian era poor. For many decades, no one really believed that a Giffen 
good actually existed anywhere other than in textbooks. But in recent years, studies have

documented a few rare cases. One study was conducted in a poor rural community where 
individuals spend a very large portion of their incomes on rice. For these individuals, rice 
was an inferior good. Under the law of demand, the quantity of rice purchased would 
rise with the decline in price, but the rise in quantity would be partially offset by the 
income effect (a decrease in the amount of rice purchased as a result of rising incomes). 
What the experimenters discovered, however, was that for a certain subset of consumers, 
the quantity of rice purchased declined in absolute terms—the income effect actually 
overwhelmed the substitution effect. For consumers living at subsistence levels—incomes 
just barely sufficient to enable them to meet their caloric intake needs—a decline in the 
price of the staple enabled them to shift more of their consumption from rice to the 
alternate sources of calories in their diet (e.g., meat).

With some goods, the item’s price tag itself might drive the consumer’s preferences 
for it. Thorstein Veblen posited just such a circumstance in his concept of conspicuous 
consumption. According to this way of thinking, a consumer might derive utility out of 
being known by others to consume a so-  called high-  status good, such as a luxury auto -
mobile or a very expensive piece of jewelry. Importantly, it is the high price itself that 
partly imparts value to such a good. These are called Veblen goods , and they derive 
their value from the consumption of them as symbols of the purchaser’s high status in 
society; they are certainly not inferior goods. It is argued that by increasing the price of 
a Veblen good, the consumer would be more inclined to purchase it, not less.
EXAMPLE 2   
Income and Substitution Effects of a Decrease in Price
Monica has a monthly entertainment budget that she spends on (a) movies and 
(b) an assortment of other entertainment items. When the price of each movie

is $8, she spends a quarter of her budget on six movies a month and the rest of 
her budget on other entertainment. Monica was offered an opportunity to join 
a movie club at her local theater that allows her to purchase movies at half the 
regular price, and she can choose each month whether to join the movie club 
or not. There is a membership fee she must pay for each month she belongs to 
the club. Monica is exactly indifferent between (a) not buying the membership 
and, therefore, paying $8 for movies and (b) buying the membership and paying 
$4 per movie. So, she flips a coin each month to determine whether to join the

Reading 14 ■ Topics in Demand and Supply Analysis 22
club that month. In months that she does join the club, she sees eight movies. 
For her birthday, a friend gave her a one-  month club membership as a gift, and 
that month she saw 12 movies.
1 If there were no club and the price of movies were to simply fall from $8 
to $4, how many more movies would Monica buy each month?
2 Determine how much Monica is willing to pay each month for the privi -
lege of buying movies at half price. (What is the value of X that makes her 
indifferent between joining the club and not joining it?)
3 Of the increased number of movies Monica would purchase if the price 
were to fall from $8 to $4, determine how much of the increase would be 
attributable to the substitution effect and how much to the income effect 
of that price decrease.
4 For Monica, are movies a normal, inferior, or Giffen good?
Six movies. When her friend gave her a club membership, she bought 12 movies

instead of her usual 6. With the gift of the club membership, Monica could buy 
movies at a price of $4 without paying for that privilege. This is the same as if 
the price of each movie fell from $8 to $4.
Note that Monica is indifferent between two states of the world: State A, in 
which she has all of her entertainment budget to spend on movies and other 
entertainment but must pay full price of $8 per movie, and State B, in which 
she has to pay some dollar amount X for the privilege of buying movies at half 
price. So, X is the maximum she would pay for a membership fee. She buys 
eight movies in months when she joins the club. Without a club membership, 
those movies would cost her $64 (8 movies × $8). With a club membership, the 
movies would cost her $32 (8 movies × $4). So the most she is willing to pay for 
a club membership is $32. (Note that one might be tempted to say she would be 
willing to pay only $24 for the membership because she was buying six movies

at $8, spending $48, whereas if she were able to buy six movies at only $4 per 
movie, she would have to spend only $24. But because of the substitution effect, 
she would now be willing to buy more movies than before, so her benefit from 
the half-  price privilege is worth more than $24.)
When Monica pays the club membership herself, she buys eight movies, two 
more than usual. Because Monica is equally well off whether she joins the club 
for a monthly fee and thereby pays half price or whether she does not join the 
club and pays full price, we can say that the income effect of the price decrease 
has been removed by charging her the monthly fee. So the increase from six 
movies to eight is the result of the substitution effect. When Monica’s friend 
gave her the gift of a club membership, allowing her to pay half price without 
paying for the privilege, Monica bought 12 movies, 6 more than usual and 4 
more than she would have had she paid the membership fee. The increase from

Supply Analysis: The Firm 23
When the price fell from $8 to $4, Monica bought more movies, so clearly movies 
are not a Giffen good for her. Additionally, because the substitution effect and 
the income effect are in the same direction of buying more movies, they are a 
normal good for Monica. The substitution effect caused her to buy two more 
movies, and the income effect caused her to buy an additional four movies.
SUPPLY ANALYSIS: THE FIRM
To fully comprehend the supply side of a consumer goods market, an analyst must 
understand the firm’s costs. (As a reminder, this reading builds on the basics of the 
market model as covered in the recommended prerequisite reading material.)
The firm’s marginal cost is the foundation of the firm’s ability and willingness to 
offer a given quantity for sale, and its costs depend on both the productivity of its 
inputs and their prices. In this section, we will describe the firm’s cost curves—total,

average, and marginal costs in both the short run and in the long run—paying special 
attention to what economists call the law of diminishing marginal returns . We will 
then use this information to explore the conditions under which a firm would find it 
beneficial to continue operation, even if its economic profits are negative, and at what 
levels of production its shutdown and breakeven points occur. Long-  run costs will be 
examined in the context of economies and diseconomies of scale.
3.1 Marginal Returns and Productivity
There is an economic phenomenon known as increasing marginal returns , in which 
marginal product —the productivity of each additional unit of a resource—increases 
as additional units of that input are employed.
Initially, a firm can experience increasing returns from adding labor to the pro -
duction process because of the concepts of specialization and division of labor. At 
first, by having too few workers relative to total physical capital, the understaffing

situation requires employees to multi-  task and share duties. As more workers are 
added, employees can specialize, become more adept at their individual functions, 
and realize an increase in marginal productivity. But after a certain output level, the 
law of diminishing marginal returns becomes evident.
When more and more workers are added to a fixed capital base, the marginal return 
of the labor factor eventually decreases because the fixed input restricts the output 
potential of additional workers. As an illustration, consider automobile production. 
When an auto manufacturing plant is operating at full capacity, adding additional labor 
will not increase production because the physical plant is already 100% employed. 
More labor hours will merely add to costs without adding to output. Assuming all 
workers are of equal quality and motivation, the decline in marginal product occurs 
in the short run, where all other resources (typically, plant size, physical capital, and

technology) are fixed.
Marginal returns are directly related to input productivity , a measure of the 
output per unit of input.
3.1.1  Productivity: The Relationship between Production and Cost
The cost of producing anything depends on the amount of inputs , or factors of pro -
duction  (these terms are synonymous), and the input prices. Examples of factors of 
production are employee hours, machine hours, raw materials, and so on. For simplicity, 3

Reading 14 ■ Topics in Demand and Supply Analysis 24
economists typically concentrate on only two inputs, labor and capital, although obvi -
ously there can be many inputs to a particular production process. The labor input is 
simply employee time, and it is measured as labor hours per time period, such as per 
week or per month. We denote labor hours as L. If a firm is using two laborers per 
week and each laborer works 35 hours per week, then L equals 70 labor hours per 
week. We denote hours of capital as K. If the firm is using three machines and each 
one is used for 12 hours per week, then K equals 36 machine hours per week. That 
is, the capital input is measured as machine hours used per time period. In this way, 
capital and labor are stated in similar terms. They represent flows of services—labor 
hours and machine hours—that are used to produce a flow of output per time period.
Accordingly, the respective input prices would be the wage rate per labor hour (we

use w to denote wage rate) and the rental rate per machine hour (we use r to denote 
the rental rate per machine hour). It is helpful to think of a firm as renting the services 
of labor and of machines. Although the firm might own its own machines, it could 
in theory rent its machines out to another user, so it is forgoing the rate it could earn 
elsewhere when it is using its machines internally instead of renting them out. So, a 
firm is not using its own machines “for free. ” It is incurring the opportunity cost  of 
not being able to rent those machines to another user.
The total cost  of production (TC) is the number of hours of labor multiplied by the 
wage rate plus the number of machine hours multiplied by the rental rate of machines:
TC = ( w)(L) + ( r)(K)
This formula illustrates that the total cost is just the cost of all the firm’s inputs. It 
is not a cost function, however, which is a relationship between the cost of production

and the flow of output. The cost function C = f( Q), where ( Q) denotes the flow of 
output in units of production per time period, relates the production cost per time 
period to the number of units of output produced per time period.
Two things could cause the cost of producing any given level of output to fall: 
Either the price of one or both inputs could fall or the inputs themselves could become 
more productive and less of them would be needed (e.g., a worker is more productive 
when fewer hours of labor are needed to produce the same output). The reverse is 
true also: A rise in cost could result from either a rise in input prices or a fall in input 
productivity, or both.
Why is productivity important? Cost-  minimization and profit-  maximization 
behavior dictate that the firm strives to maximize productivity—for example, produce 
the most output per unit of input or produce any given level of output with the least

amount of inputs. A firm that lags behind the industry in productivity is at a compet -
itive disadvantage and is likely to face decreases in future earnings and shareholders’ 
wealth. An increase in productivity lowers production costs, which leads to greater 
profitability and investment value. These productivity benefits can be fully or partially 
distributed to other stakeholders of the business, such as to consumers in the form of 
lower prices and to employees in the form of enhanced compensation. Transferring 
some or all of the productivity rewards to non-  equity holders creates synergies that 
benefit shareholders over time.
The benefits from increased productivity are as follows:
■■lower business costs, which translate into increased profitability;
■■an increase in the market value of equity and shareholders’ wealth resulting 
from an increase in profit; and
■■an increase in worker rewards, which motivates further productivity increases 
from labor.

Undoubtedly, increases in productivity reinforce and strengthen the competitive 
position of the firm over the long run. A fundamental analysis of a company should 
examine the firm’s commitment to productivity enhancements and the degree to which

Supply Analysis: The Firm 25
productivity is integrated into the competitive nature of the industry or market. In 
some cases, productivity is not only an important promoter of growth in firm value 
over the long term but is also the key factor for economic survival. A business that 
lags the market in terms of productivity often finds itself less competitive, while at 
the same time confronting profit erosion and deterioration in shareholders’ wealth. 
Typical productivity measures for a firm are based on the concepts of total product, 
average product, and marginal product of labor.
3.1.2  Total, Average, and Marginal Product of Labor
When measuring a firm’s operating efficiency, it is easier and more practical to use 
a single resource factor as the input variable rather than a bundle of the different 
resources that the firm uses in producing units of output. As discussed in the pre -
vious section, labor is typically the input that is the most identifiable and calculable

for measuring productivity. However, any input that is not difficult to quantify can 
be used. As an example, a business that manually assembles widgets has 50 workers, 
one production facility, and an assortment of equipment and hand tools. The firm 
would like to assess its productivity when using these three input factors to produce 
widgets. In this example, it is most appropriate to use labor as the input factor for 
determining productivity because the firm uses only one (fixed) plant building and a 
variety of other physical capital.
We will use labor as the input variable to illustrate the concepts of total product, 
average product, and marginal product. Exhibit 7 provides a summary of these three 
concepts.
Exhibit 7   Definitions and Calculations for Total, Marginal, and Average Product of Labor
Term Calculation
Total product Sum of the output from all inputs during a time period; usually illustrated as the total output 
(Q) using labor quantity ( L)

Average product Total product divided by the quantity of a given input; measured as total product divided by 
the number of worker hours used at that output level ( Q/L)
Marginal product The amount of additional output resulting from using one more unit of input assuming 
other inputs are fixed; measured by taking the difference in total product and dividing by the 
change in the quantity of labor (∆ Q/∆L)
Total product ( Q) is defined as the aggregate sum of production for a firm during 
a time period. As a measure of productivity, total product provides superficial infor -
mation about how effective and efficient a firm is in terms of producing output. For 
instance, three firms—Company A, Company B, and Company C—that make up an 
entire industry have total output levels of 100,000 units, 180,000 units, and 200,000 
units, respectively. Obviously, Company C dominates the market with a 41.7% share,

followed by Company B’s 37.5% share and Company A’s 20.8% portion of the market. 
However, this information says little about how efficient each firm is in generating its 
total output level. Total product only provides insight into a firm’s production volume 
relative to the industry; it does not show how efficient a firm is in producing its output.
Average product  of labor (APL) measures the productivity of an input (in this 
case, labor) on average and is calculated by dividing total product by the total num -
ber of units for the given input that is used to generate that output. Average product 
is usually measured on the basis of the labor input. It is a representative or overall 
measure of labor’s productivity: Some workers are more productive than average, and 
others are less productive than average.

Reading 14 ■ Topics in Demand and Supply Analysis 26
Exhibit 8 compares the productivity of the three firms introduced earlier. Company 
A employs 100 worker hours and produces 100,000 widgets per hour. Company B 
employs 200 worker hours and produces 180,000 widgets per hour. Company C 
employs 250 worker hours and produces 200,000 widgets per hour.
Exhibit 8   Comparing Productivity
Output  
(Q)Number of Worker 
Hours ( L)Average Product of 
Labor (APL)
Company A 100,000 100 1,000
Company B 180,000 200 900
Company C 200,000 250 800
Using this metric, it is apparent that Company A, with APL equal to 1,000, is the 
most efficient firm, despite having the lowest market share. Company C has the largest 
market share, but it is the least efficient of the three, with APL equal to 800. Assuming 
that Company A can maintain its productivity advantage over the long run, it will 
be positioned to generate the greatest return on investment through lower costs and

higher profit outcomes relative to the other firms in the market.
Marginal product of labor (MPL), also known as marginal return , measures the 
productivity of each additional unit of input and is calculated by observing the dif -
ference in total product when adding another unit of input (assuming other resource 
quantities are held constant). It is a gauge of the productivity of the individual addi -
tional worker hour rather than an average across all workers.
Exhibit 9 provides a numerical illustration for total, average, and marginal prod -
ucts of labor.
Exhibit 9   Total, Average, and Marginal Product of Labor
Labor  
(L)Total Product  
(QL)Average Product  
(APL)Marginal Product  
(MPL)
0 0 — —
1 100 100 100
2 210 105 110
3 300 100 90
4 360 90 60
5 400 80 40
6 420 70 20
7 350 50 –70
Total product increases as the firm adds each additional hour of labor—until the 
seventh labor hour, at which point total production declines by 70 units. Obviously,

the firm would want to avoid negative worker productivity.
At an employment level of five labor hours, APL is 80 units (400/5) and MPL is 
40 units [(400 – 360)/(5 – 4)]. The average productivity for all five labor hours is 80 
units, but the productivity of the fifth labor hour is only 40 units.

Supply Analysis: The Firm 27
EXAMPLE 3   
Calculation and Interpretation of Total, Average, and 
Marginal Product
Exhibit 10 illustrates the production relationship between the number of machine 
hours and total product.
1 Interpret the results for total, average, and marginal product.
2 Indicate at what point increasing marginal returns change to diminishing 
marginal returns.
Exhibit 10   
Machine 
Hours ( K)Total Product 
(QK)Average Product 
(APK)Marginal Product 
(MPK)
0 0 — —
1 1,000 1,000 1,000
2 2,500 1,250 1,500
3 4,500 1,500 2,000
4 6,400 1,600 1,900
5 7,400 1,480 1,000
6 7,500 1,250 100
7 7,000 1,000 –500
Total product increases up to six machine hours, where it tops out at 7,500. 
Because total product declines from Hour 6 to Hour 7, the marginal product 
for Machine Hour 7 is negative 500 units. Average product peaks at 1,600 units 
with four machine hours. Average product increases at a steady pace with the 
addition of Machine Hours 2 and 3. The addition of Machine Hour 4 continues

to increase average product but at a decreasing rate. Beyond four machine hours, 
average product decreases—at an increasing rate. Marginal product peaks with 
Machine Hour 3 and decreases thereafter.
The marginal product, MPK, of Machine Hour 3 is 2,000. The marginal product 
of each additional machine hour beyond Machine Hour 3 declines. Diminishing 
marginal returns are evident beyond Machine Hour 3.
A firm has a choice of using total product, average product, marginal product, 
or some combination of the three to measure productivity. Because total product is 
simply an indication of a firm’s output volume and potential market share, average 
product and marginal product are better gauges of a firm’s productivity. Both can 
reveal competitive advantage through production efficiency. However, individual 
worker productivity is not easily measurable when workers perform tasks collectively. 
In this case, average product is the preferred measure of productivity performance.

Reading 14 ■ Topics in Demand and Supply Analysis 28
Referring to the total product column in Exhibit 9, output is more than twice as 
great (210 widgets) when two hours of labor are used as opposed to only one hour (100 
widgets.) In this range of production, there is an increase in return when employee 
hours are added to the production process. This is the phenomenon of increasing 
3.2 Breakeven and Shutdown Analysis
Two important considerations of any firm are its level of profitability and whether to 
continue to operate in the current environment. Economists define profit differently 
than do accountants. Economic profit  is defined as the difference between total revenue 
(TR) and total economic costs . Accounting profit  is the difference between TR and 
total accounting cost . TR is the same from both an accounting standpoint and an 
economic standpoint; it is derived by multiplying the selling price per unit of output

by the number of units: TR = ( P)(Q). The difference between the two measures of 
profit, therefore, lies in an understanding of economic cost (also called “opportunity 
cost, ” which is defined in detail in the next section).
3.2.1  Economic Cost vs. Accounting Cost
The opportunity cost of any particular decision, such as to produce a given level of 
output, can be determined by measuring the benefit forgone by not implementing 
the next best alternative. Suppose that a firm is currently operating with hired labor 
and its own plant and equipment to produce output at some level. The firm must 
continuously decide either to keep the level of output the same or to change it. The 
decision to maintain the same output requires that the firm hire the same amount of 
labor input and use the same level of its capital inputs as before. The labor expense 
is both an economic cost and an accounting cost because the money spent on labor

hours could have been used for something else (opportunity cost), and it is also a 
current expense for the firm (accounting cost.)
Accountants typically attempt to recognize the cost of plant and equipment in the 
form of accounting depreciation, which is a means of distributing the historical cost 
of the fixed capital among the units of production for financial reporting purposes. 
The money spent in the past on the firm’s plant and equipment is what economists 
call a “sunk cost. ” Because sunk costs cannot be altered, they cannot affect an optimal 
decision, which is forward looking. Sunk costs are therefore ignored, and the key 
management question is, Going forward, what are the opportunity costs and benefits 
of maintaining a given level of output?
Here is where economic depreciation comes into play. To understand the oppor -
tunity costs of using our plant and equipment—already bought and paid for—for one

more period of time to produce output, we have to ask the question, What else could 
be done with that fixed capital if it were not used to produce our output? The answer 
might be that because there is no external market for our machines and buildings, we 
are forgoing nothing by using it to produce output. Or it might be that there is a mar -
ket where we could rent out or sell our capital equipment elsewhere instead of using 
it to produce output. That rental rate is the economic depreciation associated with 
using our own equipment to produce output instead of renting or selling it elsewhere.
Economic depreciation is forward looking. It asks, What am I giving up if I use my 
resources to produce output in the coming period? Accounting depreciation is back -
ward looking. It asks, How should I distribute the historical cost—that I have already 
paid—across units of output that I intend to produce this period? Both concepts are

useful—one for making managerial decisions about output and the other as a way 
spreading historical costs for reporting or tax purposes—but there is not necessarily 
a direct relationship between the two.

Supply Analysis: The Firm 29
3.2.2  Marginal Revenue, Marginal Cost, and Profit Maximization
It is assumed that any for-  profit firm’s management is tasked with achieving the goal 
of shareholder wealth maximization. Put most simply, that translates into the goal 
of economic profit maximization. Hereafter, when the word profit  is used, it will be 
economic profit that we have in mind. Because profit is defined as TR minus TC, 
anything that increases revenue more than cost or decreases cost more than revenue 
will increase profit. Before we address profit maximization, we must introduce two 
important concepts: marginal revenue and marginal cost.
Marginal revenue  (MR) is the additional revenue the firm realizes from the decision 
to increase output by one unit per time period. That is, MR = ΔTR/Δ Q. If the firm is 
operating in what economists call a perfectly competitive market, it is one of many 
sellers of identical products in an environment characterized by low or non-  existent

barriers to entry. Under perfect competition, the firm has no pricing power because 
there are many perfect substitutes for the product it sells. If it were to attempt to raise 
the price even by a very small amount, it would lose all of its sales to competitors. On 
the other hand, it can sell essentially any amount of product it wants without lowering 
the price below the market price.
Take the wheat market as an example of a perfectly competitive market. A seller 
of wheat would have no control over the market price of wheat; thus, because TR = 
(P)(Q), MR for this firm is simply price per unit of output. This firm is said to face a 
perfectly horizontal (zero-  sloped), or infinitely elastic, demand curve for its product. 
For example, if the firm is selling 1,000 bushels of wheat per week at a price of £3 per 
bushel, TR is £3,000. If the firm were to increase its output by one unit, then TR would 
rise by exactly £3 because the firm would not have to lower its price to sell that added

unit. So, for sellers in a market with perfect competition, MR = P.
In contrast, if a firm sells a product that is differentiated from other firms’ products 
and that has a large market share, the firm is said to be operating in an environment of 
imperfect competition. In the extreme case of imperfect competition, there might be 
only one firm selling a product with no close substitutes. That firm holds a monopoly, 
and it is subject to the market demand curve for its product. Whether a monopoly 
or simply operating under imperfect competition, the firm faces a negatively sloped 
demand curve and must lower its price to sell another unit. Thus, MR will be lower 
than price.
To illustrate this concept, we will decompose MR. Recall from earlier in the 
reading that
TR = ( P)(Q)
and
MR = ΔTR/Δ Q
Change in total revenue (ΔTR), the numerator of the ratio, can be written as ( P)
(ΔQ) + ( Q)(ΔP).
There are two competing forces affecting revenue: (1) Additional units are sold at

the new price, and (2) all units must now be sold at the lower price. The firm is selling 
more units, but it is selling all units at a lower price than before.
To find MR, we divide the change in TR by the change in quantity:
MR =()()+()()=+() PQ
QQP
QPQP
Q∆
∆∆
∆∆
∆
In other words, MR is equal to price but with an “adjustment” equal to ( Q)(ΔP/ΔQ).
Taking this one step further, recall that earlier we said (Δ P/ΔQ) is the slope of the 
demand curve. From our expression just given, MR = P + Q(ΔP/ΔQ); so, MR is equal 
to price with an adjustment equal to quantity times the slope of the demand curve.

Reading 14 ■ Topics in Demand and Supply Analysis 30
A perfectly competitive firm faces a demand curve with a slope of zero. Substituting 
0 for Δ P/ΔQ into the expression given, it becomes clear that MR is equal to price 
for the perfectly competitive firm—it need not lower its price to sell an additional 
unit. For a firm in an imperfectly competitive market, however, the demand curve is 
negatively sloped (Δ P/ΔQ < 0). Substituting this negative number into the expression 
for MR, P + Q(ΔP/ΔQ), it becomes clear that MR for an imperfectly competitive firm 
is less than price.
Marginal cost  (MC) is the increase to total cost resulting from the firm’s decision 
to increase output by one additional unit per time period: MC = ΔTC/Δ Q. Economists 
distinguish between short-  run marginal cost (SMC) and long-  run marginal cost (LMC). 
Labor is variable over the short run, but the quantity of capital cannot be changed in

the short run because there is a lead time required to build or buy new plant equip -
ment and put it in place. In the long run, all inputs are variable.
SMC is essentially the additional cost of the variable input, labor, that must be 
incurred to increase the level of output by one unit. LMC is the additional cost of all 
inputs necessary to increase the level of output, allowing the firm the flexibility of 
changing both labor and capital inputs in a way that maximizes efficiency.
Understanding MC is aided by recalling that cost is directly  related to input 
prices and inversely  related to productivity. For example, if the wage rate were to rise, 
cost would also rise. If labor were to become more productive, cost would fall. This 
relationship can be captured in an expression that relates SMC to wage rate ( w) and 
MPL: SMC = w/MPL.
This relationship between cost and productivity also holds with average variable

cost. Variable costs  are all costs that fluctuate with the level of production and sales. 
Average variable cost  (AVC) is the ratio of total variable cost to total output: AVC = 
TVC/ Q. Again, if labor’s wage rises, AVC also rises; but if labor were to become more 
productive, AVC falls. This relationship is captured by the expression AVC = w/APL.
Earlier, we noted that over some range of low output, the firm might benefit from 
increasing marginal productivity of its labor input as workers begin to specialize. As 
the MPL increases, SMCs decline. Eventually, as more and more labor is added to a 
fixed amount of capital, the MPL must fall, causing SMCs to rise.
We began this section by stating that the goal of management is to maximize 
profit. We now address the conditions necessary for reaching that goal. Consider a 
firm currently producing 1,000 widgets each week and whose management is con -
templating increasing that output incrementally. Would that additional unit increase

profit? Clearly, profit would be increased (or losses reduced) if the additional revenue 
from that next unit were greater than the additional cost. So, a profit-  seeking firm 
should increase Q if MR > MC. Conversely, if the additional unit added more to cost 
than to revenue, the firm should reduce output because it would save more in cost 
than it would lose in revenue. Only if the additional cost were exactly equal to the 
additional revenue would the firm be maximizing its profit.
There is another condition (called a second-  order condition) necessary for profit 
maximization: At the level of output at which MR = MC, MC cannot be falling. This 
condition is fairly intuitive. If MC is falling with additional output, MPL would be 
rising. (Recall that SMC = w/MPL) If one additional hour of labor input causes MC 
to fall, the firm would want to add that hour and continue adding labor until SMC 
becomes positively sloped. We can sum up the profit-  maximization decision for an

operating firm as follows: Produce the level of output such that (1) MR = MC and 
(2) MC is not falling.

Supply Analysis: The Firm 31
3.2.3  Understanding the Interaction between Total, Variable, Fixed, and Marginal 
Cost and Output
Exhibit 11 shows the graphical relationships between total cost, total fixed cost, and 
total variable cost. TC is the summation of all costs, where costs are classified on the 
basis of whether they are fixed or variable. Total fixed cost  (TFC) is the summation 
of all expenses that do not change as the level of production varies. Total variable 
cost  (TVC) is the summation of all variable expenses; TVC rises with increased pro -
duction and falls with decreased production. At zero production, TC is equal to TFC 
because TVC at this output level is zero. The curve for TC always lies parallel to and 
above the TVC curve by the amount of TFC.
Exhibit 11   Total Cost, Total Variable Cost, and Total Fixed Cost
Cost
Q0 Quantity of OutputTFCTCTVC
Exhibit 12 shows the relationships between the average total cost  (ATC), average

variable cost (AVC), average fixed cost  (AFC), and marginal cost (MC) curves in 
the short run. As output quantity increases, AFC declines because TFCs are spread 
over a larger number of units. Both ATC and AVC take on a bowl-  shaped pattern in 
which each curve initially declines, reaches a minimum average cost output level, and 
then increases after that point. The MC curve intersects both the ATC and the AVC 
at their minimum points—points S and T. When MC is less than AVC, AVC will be 
decreasing. When MC is greater than AVC, AVC will be increasing.

Reading 14 ■ Topics in Demand and Supply Analysis 32
Exhibit 12   Average Total Cost, Average Variable Cost, Average Fixed Cost, 
and Marginal Cost
Cost per Unit
AVCMC
A
A = B
AFC BXT
S
RX = Y
YATC
Q1 QAVCQATC Q2 Q0Quantity of Outpu t
S, the lowest point on the AVC curve, is where MC equals AVC. Beyond quantity QAV C, MC is 
greater than AVC; thus, the AVC curve begins to rise. Note that it occurs at a quantity lower than 
the minimum point on the ATC curve.
T, the lowest point on the ATC curve, is where MC equals ATC. Beyond quantity QATC, MC is 
greater than ATC; thus, the ATC curve is rising.
A, the difference between ATC and AVC at output quantity Q1, is the amount of AFC.
R indicates the lowest point on the MC curve. Beyond this point of production, fixed input con -
straints reduce the productivity of labor.
X indicates the difference between ATC and AVC at quantity Q2. It is less than A because AFC ( Y) 
falls with output.

Exhibit 13 shows an example of how total, average, and marginal costs are derived. 
TC is calculated by summing TFC and TVC. MC is derived by observing the change 
in TC as the quantity variable changes. There is a relationship that always holds for 
average and marginal costs: If MC is less than average cost, average cost must fall, and 
if MC is greater than average cost, average cost must rise. For example, in Exhibit 13, 
AVC begins to increase as output rises from 2 to 3 units because MC (50) is greater 
than AVC (41.7). Also from Exhibit 13, ATC declines up to 3 units because MC is 
less than ATC. After 3 units, ATC increases because the MC of Unit 4 (85) exceeds 
the ATC of all prior units (75). Initially, the MC curve declines because of increasing 
marginal returns to labor, but at some point, it begins to increase because of the law 
of diminishing marginal returns.
Exhibit 13   Total, Average, Marginal, Fixed, and Variable Costs
Quantity ( Q) TFCaAFC TVC AVC TC ATC MC

0 100 — 0 — 100 — —
1 100 100.0 50 50.0 150 150.0 50
2 100 50.0 75 37.5 175 87.5 25
3 100 33.3 125 41.7 225 75.0 50
4 100 25.0 210 52.5 310 77.5 85
5 100 20.0 300 60.0 400 80.0 90
6 100 16.7 450 75.0 550 91.7 150
7 100 14.3 650 92.9 750 107.1 200
8 100 12.5 900 112.5 1,000 125.0 250

Supply Analysis: The Firm 33
9 100 11.1 1,200 133.3 1,300 144.4 300
10 100 10.0 1,550 155.0 1,650 165.0 350
a Includes all opportunity costs.
As stated earlier, TC increases as the firm expands output and decreases when 
production is cut. TC increases at a decreasing rate up to a certain output level. 
Thereafter, the rate of increase accelerates as the firm gets closer to full utilization of 
capacity. The rate of change in TC mirrors the rate of change in TVC. In Exhibit 13, 
TC at 5 units is 400—of which 300 is variable cost and 100 is fixed cost. At 10 units, 
TC is 1,650—of which 1,550 is variable cost and 100 is fixed cost.
Fixed costs typically are incurred whether the firm produces anything or not. Fixed 
costs may stay the same over a given range of production but can change to another 
constant level when production moves outside of that range. The latter is referred

to as a quasi-  fixed cost , although it remains categorized as part of TFC. Examples 
of fixed costs are debt service, real estate lease agreements, and rental contracts. 
Normal profit  is also considered to be a fixed cost because it is a return required by 
investors on their equity capital regardless of output level. Quasi-  fixed cost examples 
would be certain utilities and administrative salaries that could be lower or avoided 
altogether when output is zero but would rise to higher constant levels over different 
production ranges.
Other fixed costs evolve primarily from investments in such fixed assets as real 
estate, production facilities, and equipment. These fixed costs cannot be arbitrarily 
cut when production declines. When a firm downsizes, the last expense to be cut is 
usually fixed cost.
TVC has a direct relationship with quantity. When quantity increases, TVC 
increases; when quantity decreases, TVC declines. At zero production, TVC is always

zero. Variable cost examples are payments for labor, raw materials, and supplies. The 
change in TVC declines up to a certain output point and then increases as production 
approaches capacity limits. In Exhibit 13, TVC increases with an increase in quantity. 
However, the change from 1 to 2 units is 25 (75 – 50), and the change from 9 to 10 
units is 350.
Exhibit 14 illustrates the relationships between MC, ATC, AVC, and AFC for the 
data presented in Exhibit 13.Exhibit 13   (Continued)

Reading 14 ■ Topics in Demand and Supply Analysis 34
Exhibit 14   Average Total Cost, Average Variable Cost, Average Fixed Cost, 
and Marginal Cost for Exhibit 13 Data
Cost
MC
ATC
AVC
AFC
050100150200250300350
11 0 2345 78 9 6
Output Quantity
Dividing TFC by quantity yields AFC. AFC decreases throughout the production 
span, reflecting the spreading of a constant cost over more and more production 
units. At high production volumes, AFC may be so low that it is a small proportion 
of ATC. In Exhibit 13, AFC declines from 100 at 1 unit to 20 at 5 units, and then to 
10 at an output level of 10 units.
In Exhibit 13, AVC at 5 units is 60 (300/5). Over an initial range of production, 
AVC declines and then reaches a minimum point. Thereafter, AVC increases as the 
firm uses more of its production capacity. This higher cost results primarily from 
production constraints imposed by the fixed assets at higher volume levels. The

lowest AVC quantity does not correspond to the least-  cost quantity for ATC because 
AFC is still declining. In Exhibit 13, AVC is minimized at 2 units, whereas ATC is 
minimized at 3 units.
ATC is calculated by dividing TC by quantity (or by summing AFC and AVC). In 
Exhibit 13, at 3 units, ATC is 75 (TC of 225/3 units of production or AFC of 33.3 + 
AVC of 41.7). This is the least average cost point of production and the minimum 
point on the ATC curve. Although cost-  minimizing behavior on the part of the firm 
would dictate operating at the minimum point on its ATC curve, the profit-  maximizing 
quantity may not correspond to this minimum ATC point. Profit per unit, but not 
necessarily total profit, is maximized at this point.
EXAMPLE 4   
Calculation and Interpretation of Total, Average, Marginal, 
Fixed, and Variable Costs
The first three columns of Exhibit 15 display data on quantity, TFC, and TVC, 
which are used to calculate TC, AFC, AVC, ATC, and MC. Examine the results

for total, average, marginal, fixed, and variable costs. Identify the quantity levels 
at which the ATC, AVC, and MC values reach their minimum points. Explain 
the relationship between TFC and TC at a quantity of zero output.

Supply Analysis: The Firm 35
Exhibit 15   
Q TFCaTVC AFC AVC TC ATC MC
0 5,000 0 — — 5,000 — —
1 5,000 2,000 5,000.0 2,000 7,000 7,000.0 2,000
2 5,000 3,800 2,500.0 1,900 8,800 4,400.0 1,800
3 5,000 5,400 1,666.7 1,800 10,400 3,466.7 1,600
4 5,000 8,000 1,250.0 2,000 13,000 3,250.0 2,600
5 5,000 11,000 1,000.0 2,200 16,000 3,200.0 3,000
6 5,000 15,000 833.3 2,500 20,000 3,333.3 4,000
7 5,000 21,000 714.3 3,000 26,000 3,714.3 6,000
8 5,000 28,800 625.0 3,600 33,800 4,225.0 7,800
9 5,000 38,700 555.6 4,300 43,700 4,855.6 9,900
10 5,000 51,000 500.0 5,100 56,000 5,600.0 12,300
a Includes all opportunity costs
Solution:
TFC remains unchanged at 5,000 throughout the entire production range, 
whereas AFC continuously declines from 5,000 at 1 unit to 500 at 10 units. 
Both AVC and MC initially decline and then reach their lowest level at 3 units, 
with costs of 1,800 and 1,600, respectively. Beyond 3 units, both AVC and MC 
increase, indicating that the cost of production rises with greater output. The

least-  cost point for ATC is 3,200 at 5 units. At zero output, TC is 5,000, which 
equals the amount of TFC (at zero output, the firm will need no variable inputs, 
but it is committed to its fixed plant and equipment in the short run).
3.2.4  Revenue under Conditions of Perfect and Imperfect Competition
Recall from our earlier discussion of profit-  maximizing conditions that a firm can 
generally be classified as operating in either a perfectly competitive or an imperfectly 
competitive environment. The difference between the two manifests itself in the 
slope of the demand curve facing the firm. If the environment of the firm is perfectly 
competitive, it must take the market price of its output as given, so it faces a perfectly 
elastic, horizontal demand curve. In this case, as we saw previously, the firm’s MR 
and the price of its product are identical. Additionally, the firm’s average revenue  
(AR), or revenue per unit, is also equal to price per unit. However, a firm that faces

a negatively sloped demand curve must lower its price to sell an additional unit, so 
its MR is less than price ( P).
These characteristics of MR are also applicable to the TR functions. Under con -
ditions of perfect competition, TR (as always) is equal to price times quantity: TR = 
(P)(Q). But under conditions of perfect competition, price is dictated by the market; 
the firm has no control over price. As the firm sells one more unit, its TR rises by the 
exact amount of price per unit.
Under conditions of imperfect competition, price is a variable under the firm’s 
control, and therefore price is a function of quantity: P = f( Q), and TR = f( Q) × Q. 
For simplicity, suppose the firm is monopolistic and faces the market demand curve, 
which we will assume is linear and negatively sloped. Because the monopolist is the 
only seller, its TR is identical to the total expenditure of all buyers in the market. 
Earlier, we noted what happens as price is reduced and quantity sold increases in this

Reading 14 ■ Topics in Demand and Supply Analysis 36
environment: At first, a decrease in price increases total expenditure by buyers and 
TR to the firm because the decrease in price is outweighed by the increase in units 
sold. But as price continues to fall, the decrease in price overshadows the increase in 
quantity, and total expenditure (revenue) falls. We can now depict the demand and 
TR functions for firms under conditions of perfect and imperfect competition, as 
shown in Exhibit 16.
Exhibit 16   Demand and Total Revenue Functions for Firms under 
Conditions of Perfect and Imperfect Competition
A. Perfectly Competitive Firm
P
QDemand Curve: P = MR
TR
QTR CurveB. Imperfectly Competitive Firm
P
QDemand Curve
TR
QTR
CurveMR
Curve
Panel A of Exhibit 16 depicts the demand curve (upper graph) and total revenue 
curve (lower graph) for the firm under conditions of perfect competition. Notice that 
the vertical axis in the upper graph is price per unit (e.g., £/bushel), whereas TR is

measured on the vertical axis in the lower graph (e.g., £/week.) The same is true for 
the respective axes in Panel B, which depicts the demand and total revenue curves for 
the monopolist. The TR curve for the firm under conditions of perfect competition 
is linear, with a slope equal to price per unit. The TR curve for the monopolist first 
rises (in the range where MR is positive and demand is elastic) and then falls (in the 
range where MR is negative and demand is inelastic) with output.
3.2.5  Profit-  Maximization, Breakeven, and Shutdown Points of Production
We can now combine the firm’s short-  run TC curves with its TR curves to represent 
profit maximization in the cases of perfect competition and imperfect competition. 
Exhibit 17 shows both the AR and average cost curves in one graph for the firm under 
conditions of perfect competition.

Supply Analysis: The Firm 37
Exhibit 17   Demand and Average and Marginal Cost Curves for the Firm 
under Conditions of Perfect Competition
ATC
AVCSMC
Demand CurveP
P = MR
Q
Q* Q′
The firm is maximizing profit by producing Q*, where price is equal to SMC and 
SMC is rising. (Note that there is another output level, Q′, where P = SMC, but at that 
point, SMC is still falling, so this cannot be a profit-  maximizing solution.) If market 
price were to rise, the firm’s demand and MR curve would simply shift upward, and 
the firm would reach a new profit-  maximizing output level to the right of Q*. If, on 
the other hand, market price were to fall, the firm’s demand and MR curve would 
shift downward, resulting in a new and lower level of profit-  maximizing output. As 
depicted, this firm is currently earning a positive economic profit because market 
price exceeds ATC at output level Q*. This profit is possible in the short run, but in

the long run, competitors would enter the market to capture some of those profits 
and would drive the market price down to a level equal to each firm’s ATC.
Exhibit 18 depicts the cost and revenue curves for the monopolist that is facing a 
negatively sloped market demand curve. The MR and demand curves are not identical 
for this firm. But the profit-  maximizing rule is still the same: Find the level of Q that 
equates SMC to MR—in this case, Q*. Once that level of output is determined, the 
optimal price to charge is given by the firm’s demand curve at P*. This monopolist is 
earning positive economic profit because its price exceeds its ATC. The barriers to 
entry that give this firm its monopolistic power mean that outside competitors would 
be unable to compete away this firm’s profits.
Exhibit 18   Demand and Average and Marginal Cost Curves for the 
Monopolistic Firm
ATC
AVC
MR CurveSMC
Demand Curve P = ARP
P*
Q
Q*

Reading 14 ■ Topics in Demand and Supply Analysis 38
3.2.6  Breakeven Analysis
A firm is said to break even if its TR is equal to its TC. It can also be said that a firm 
breaks even if its price (AR) is exactly equal to its ATC, which is true under conditions 
of perfect and imperfect competition. Of course, the goal of management is not just 
to break even but to maximize profit. However, perhaps the best the firm can do is 
cover all of its economic costs. Economic costs are the sum of total accounting costs 
and implicit opportunity costs. A firm whose revenue is equal to its economic costs 
is covering the opportunity cost of all of its factors of production, including capital. 
Economists would say that such a firm is earning normal profit, but not positive eco -
nomic profit. It is earning a rate of return on capital just equal to the rate of return 
that an investor could expect to earn in an equivalently risky alternative investment

(opportunity cost). Firms that are operating in a very competitive environment with 
no barriers to entry from other competitors can expect, in the long run, to be unable 
to earn a positive economic profit; the excess rate of return would attract entrants who 
would produce more output and ultimately drive the market price down to the level 
at which each firm is at best just earning a normal profit. This situation, of course, 
does not imply that the firm is earning zero accounting profit.
Exhibit 19 depicts the condition for both a firm under conditions of perfect com -
petition (Panel A) and a monopolist (Panel B) in which the best each firm can do is 
to break even. Note that at the level of output at which SMC is equal to MR, price is 
just equal to ATC. Hence, economic profit is zero, and the firms are breaking even.

Supply Analysis: The Firm 39
Exhibit 19   Examples of Firms under Perfect Competition and Monopolistic 
Firms That Can, at Best, Break Even
ATC
AVCSMC
Q
Q*A. Perfect Competition
P = AR = MR
ATC
AVC
SMC
Demand Curve
P = AR
MR CurveP
P*
Q
Q*B. Monopolist
3.2.7  The Shutdown Decision
In the long run, if a firm cannot earn at least a zero economic profit, it will not operate 
because it is not covering the opportunity cost of all of its factors of production, labor, 
and capital. In the short run, however, a firm might find it advantageous to continue 
to operate even if it is not earning at least a zero economic profit. The discussion that 
follows addresses the decision to continue to operate and earn negative profit or shut 
down operations.
Recall that typically some or all of a firm’s fixed costs are incurred regardless of 
whether the firm operates. The firm might have a lease on its building that it cannot

avoid paying until the lease expires. In that case, the lease payment is a sunk cost: It 
cannot be avoided, no matter what the firm does. Sunk costs must be ignored in the 
decision to continue to operate in the short run. As long as the firm’s revenues cover 
at least its variable cost, the firm is better off continuing to operate. If price is greater 
than AVC, the firm is not only covering all of its variable cost but also a portion of 
fixed cost.

Reading 14 ■ Topics in Demand and Supply Analysis 40
For example, suppose a firm is producing 100 widgets and selling them at a price 
of €4 each. Obviously, its TR is €400 per time period. Suppose, also, that at that level 
of output, its ATC is €7, made up of AVC of €3.75 plus AFC of €3.25 per period. This 
firm is said to be earning negative economic profit (also referred to as economic loss , 
a condition in which revenues fall short of total opportunity cost) of €300 because its 
TC is €700 and its TR is only €400. Should this firm shut down immediately? If the 
fixed cost is unavoidable, then the firm is obligated to pay it whether it operates or 
not. The TFC is €325 (€3.25 per unit on 100 units). If it shuts down and earns zero 
revenue, then its variable cost would be zero but its losses would still equal the €325 
of unavoidable fixed cost. If, however, it continued to operate, it could earn revenue

of €400 that would cover its variable cost of €375 and contribute €25 toward the fixed 
costs. In other words, this firm would lose less by continuing to operate (€300) than 
by shutting down (€325).
In the long run, unless market price increases, this firm would exit the industry. 
But in the short run, it will continue to operate at a loss. Exhibit 20 depicts a firm 
under conditions of perfect competition facing three alternative market price ranges 
for its output. At any price above P1, the firm can earn a positive profit and clearly 
should continue to operate. At a price below P2, the minimum AVC, the firm could 
not even cover its variable cost and should shut down. At prices between P2 and P1, 
the firm should continue to operate in the short run because it is able to cover all of 
its variable cost and contribute something toward unavoidable fixed costs. Economists 
refer to the minimum AVC point as the shutdown point  and the minimum ATC 
point as the breakeven point .

Exhibit 20   A Firm under Conditions of Perfect Competition Will Choose to 
Shut Down If Market Price Is Less Than Minimum AVC
ATC
AVCSMC
Shutdown PointBreakeven Poin tP
QP1
P2
EXAMPLE 5   
Breakeven Analysis and Profit Maximization When the 
Firm Faces a Negatively Sloped Demand Curve under 
Imperfect Competition
Revenue and cost information for a future period is presented in Exhibit  21 
for WR International, a newly formed corporation that engages in the manu -
facturing of low-  cost, pre-  fabricated dwelling units for urban housing markets

Supply Analysis: The Firm 41
in emerging economies. (Note that quantity increments are in blocks of 10 for 
a 250 change in price.) The firm has few competitors in a market setting of 
imperfect competition.
1 How many units must WR International sell to initially break even?
2 Where is the region of profitability?
3 At what point will the firm maximize profit? At what points are there 
economic losses?
Exhibit 21   
Quantity  
(Q)Price  
(P)Total Revenue  
(TR)Total Cost  
(TC)aProfit
0 10,000 0 100,000 –100,000
10 9,750 97,500 170,000 –72,500
20 9,500 190,000 240,000 –50,000
30 9,250 277,500 300,000 –22,500
40 9,000 360,000 360,000 0
50 8,750 437,500 420,000 17,500
60 8,500 510,000 480,000 30,000
70 8,250 577,500 550,000 27,500
80 8,000 640,000 640,000 0
90 7,750 697,500 710,000 –12,500
100 7,500 750,000 800,000 –50,000
WR International will initially break even at 40 units of production, where TR 
and TC equal 360,000.

The region of profitability will range from greater than 40 units to less than 80 
units. Any production quantity of less than 40 units and any quantity greater 
than 80 units will result in an economic loss.
Maximum profit of 30,000 will occur at 60 units. Lower profit will occur at any 
output level that is higher or lower than 60 units. From 0 units to less than 40 
units and for quantities greater than 80 units, economic losses occur.
Given the relationships between TR, TVC, and TFC, Exhibit 22 summarizes the 
decisions to operate, shut down production, or exit the market in both the short run 
and the long run. The firm must cover its variable cost to remain in business in the 
short run; if TR cannot cover TVC, the firm shuts down production to minimize 
loss. The loss would be equal to the amount of fixed cost. If TVC exceeds TR in the 
long run, the firm will exit the market to avoid the loss associated with fixed cost at

zero production. By exiting the market, the firm’s investors do not suffer the erosion

Reading 14 ■ Topics in Demand and Supply Analysis 42
of their equity capital from economic losses. When TR is enough to cover TVC but 
not all of TFC, the firm can continue to produce in the short run but will be unable 
to maintain financial solvency in the long run.
Exhibit 22   Short Run and Long Run Decisions to Operate or Not
Revenue–Cost Relationship Short-  Run Decision Long-  Term Decision
TR = TC Stay in market Stay in market
TR = TVC but < TC Stay in market Exit market
TR < TVC Shut down production Exit market
EXAMPLE 6   
Shutdown Analysis
For the most recent financial reporting period, a business domiciled in Ecuador 
(which recognizes the US dollar as an official currency) has revenue of $2 million 
and TC of $2.5 million, which are or can be broken down into TFC of $1 million 
and TVC of $1.5 million. The net loss on the firm’s income statement is reported 
as $500,000 (ignoring tax implications). In prior periods, the firm had reported 
profits on its operations.

1 What decision should the firm make regarding operations over the short 
term?
2 What decision should the firm make regarding operations over the long 
term?
3 Assume the same business scenario except that revenue is now $1.3 mil -
lion, which creates a net loss of $1.2 million. What decision should the 
firm make regarding operations in this case?
In the short run, the firm is able to cover all of its TVC but only half of its 
$1 million in TFC. If the business ceases to operate, its loss would be $1 million, 
the amount of TFC, whereas the net loss by operating would be minimized at 
$500,000. The firm should attempt to operate by negotiating special arrangements 
with creditors to buy time to return operations back to profitability.
If the revenue shortfall is expected to persist over time, the firm should cease 
operations, liquidate assets, and pay debts to the extent possible. Any resid -

ual for shareholders would decrease the longer the firm is allowed to operate 
unprofitably.
The firm would minimize loss at $1 million of TFC by shutting down. If the 
firm decided to continue to do business, the loss would increase to $1.2 mil -
lion. Shareholders would save $200,000 in equity value by pursuing this option. 
Unquestionably, the business would have a rather short life expectancy if this 
loss situation were to continue.

Supply Analysis: The Firm 43
When evaluating profitability, particularly of start-  up firms and businesses using 
turnaround strategies, analysts should consider highlighting breakeven and shutdown 
points in their financial research. Identifying the unit sales levels at which the firm 
enters or leaves the production range for profitability and at which the firm can no 
longer function as a viable business entity provides invaluable insight for investment 
3.3 Understanding Economies and Diseconomies of Scale
Rational behavior dictates that the firm select an operating size or scale that maxi -
mizes profit over any time frame. The time frame that defines the short run and long 
run for any firm is based on the ability of the firm to adjust the quantities of the fixed 
resources it uses. The short run is the time period during which at least one of the 
factors of production, such as technology, physical capital, and plant size, is fixed.

The long run is defined as the time period during which all factors of production are 
variable. Additionally, in the long run, firms can enter or exit the market based on 
decisions regarding profitability. The long run is often referred to as the “planning 
horizon” in which the firm can choose the short-  run position or optimal operating 
size that maximizes profit over time. The firm is always operating in the short run 
but planning in the long run.
The time required for long-  run adjustments varies by industry. For example, the 
long run for a small business using very little technology and physical capital may be 
less than a year, whereas for a capital-  intensive firm, the long run may be more than a 
decade. Given enough time, however, all production factors are variable, which allows 
the firm to choose an operating size or plant capacity based on different technologies 
and physical capital. In this regard, costs and profits will differ between the short run 
and the long run.

3.3.1  Short- and Long-  Run Cost Curves
Recall that when we addressed the short-  run cost curves of the firm, we assumed 
that the capital input was held constant. That meant that the only way to vary output 
in the short run is to change the level of the variable input—in our case, labor. If the 
capital input—namely, plant and equipment—were to change, however, we would 
have an entirely new set of short-  run cost curves, one for each level of capital input.
The short-  run total cost includes all the inputs—labor and capital—the firm is 
using to produce output. For reasons discussed earlier, the typical short-  run total cost 
(STC) curve might rise with output, first at a decreasing rate because of specialization 
economies and then at an increasing rate, reflecting the law of diminishing marginal 
returns to labor. Total fixed cost (the quantity of capital input multiplied by the rental

rate on capital) determines the vertical intercept of the STC curve. At higher levels 
of fixed input, TFC is greater but the production capacity of the firm is also greater. 
Exhibit 23 shows three different STC curves for the same technology but using three 
distinct levels of capital input—Points 1, 2, and 3 on the vertical axis.

Reading 14 ■ Topics in Demand and Supply Analysis 44
Exhibit 23   Short-  Run Total Cost Curves for Various Plant Sizes
$/Time Period STC1STC2STC3
Use Largest Plant
Use
Medium
PlantUse Smallest
Plant
3
2
1
Q
Qa Qb
Plant Size 1 is the smallest and, of course, has the lowest fixed cost; hence, its STC1 
curve has the lowest vertical intercept. But note that STC1 begins to rise more steeply 
with output, reflecting the lower plant capacity. Plant Size 3 is the largest of the three 
and reflects that size with both a higher fixed cost and a lower slope at any level of 
output. If a firm decided to produce an output between zero and Qa, it would plan 
on building Plant Size 1 because for any output level in that range, its cost is less than 
it would be for Plant Size 2 or 3. Accordingly, if the firm were planning to produce 
output greater than Qb, it would choose Plant Size 3 because its cost for any of those 
levels of output would be lower than for Plant Size 1 or 2. And of course, Plant Size 2

would be chosen for output levels between Qa and Qb. The long-  run total cost curve 
is derived from the lowest level of STC for each level of output because in the long 
run, the firm is free to choose which plant size it will operate. This curve is called an 
“envelope curve. ” In essence, this curve envelopes—encompasses—all possible com -
binations of technology, plant size, and physical capital.
For each STC curve, there is also a corresponding short-  run average total cost  
(SATC) curve and a corresponding long-  run average total cost  (LRAC) curve, the 
envelope curve of all possible short-  run average total cost curves. The shape of the 
LRAC curve reflects an important concept called economies of scale  and disecon -
omies of scale .
3.3.2  Defining Economies of Scale and Diseconomies of Scale
When a firm increases all of its inputs in order to increase its level of output (obviously, 
a long-  run concept), it is said to scale up  its production. Scaling down  is the reverse—

decreasing all of its inputs in order to produce less in the long run. Economies of scale 
occur if, as the firm increases its output, cost per unit of production falls. Graphically, 
this definition translates into a LRAC curve with a negative slope. Exhibit 24 depicts 
several SATC curves, one for each plant size, and the LRAC curve representing 
economies of scale.

Supply Analysis: The Firm 45
Exhibit 24   Short-  run Average Total Cost Curves for Various Plant Sizes and 
Their Envelope Curve, LRAC: Economies of Scale
$/Unit
Units/Time Perio dSATC1
SATC2SATC3SATC4
LRAC
Diseconomies of scale occur if cost per unit rises as output increases. Graphically, 
diseconomies of scale translate into an LRAC curve with a positive slope. Exhibit 25 
depicts several SATC curves, one for each plant size, and their envelope curve, the 
LRAC curve, representing diseconomies of scale.
Exhibit 25   Short-  run Average Total Cost Curves for Various Plant Sizes and 
Their Envelope Curve, LRAC: Diseconomies of Scale
$/Unit
Units/Time Perio dSATC1SATC2SATC3SATC4LRAC
As the firm grows in size, economies of scale and a lower ATC can result from 
the following factors:
■■Increasing returns to scale , which is when a production process allows for 
increases in output that are proportionately larger than the increase in inputs.

■■Having a division of labor and management in a large firm with numerous 
workers, which allows each worker to specialize in one task rather than perform 
many duties, as in the case of a small business (as such, workers in a large firm 
become more proficient at their jobs).
■■Being able to afford more expensive, yet more efficient equipment and to adapt 
the latest in technology that increases productivity.
■■Effectively reducing waste and lowering costs through marketable byproducts, 
less energy consumption, and enhanced quality control.
■■Making better use of market information and knowledge for more effective 
managerial decision making.
■■Obtaining discounted prices on resources when buying in larger quantities.

Reading 14 ■ Topics in Demand and Supply Analysis 46
A classic example of a business that realizes economies of scale through greater 
physical capital investment is an electric utility. By expanding output capacity to 
accommodate a larger customer base, the utility company’s per-  unit cost will decline. 
Economies of scale help explain why electric utilities have naturally evolved from 
localized entities to regional and multi-  region enterprises. Wal-  Mart is an example of 
a business that uses bulk purchasing power to obtain deep discounts from suppliers 
to keep costs and prices low. Wal-  Mart also uses the latest technology to monitor 
point-  of- sale transactions to gather timely market information to respond to changes 
in customer buying behavior, which leads to economies of scale through lower dis -
tribution and inventory costs.
The factors that can lead to diseconomies of scale, inefficiencies, and rising costs 
when a firm increases in size include the following:

■■Decreasing returns to scale , which is when a production process leads to 
increases in output that are proportionately smaller than the increase in inputs.
■■Being so large that it cannot be properly managed.
■■Overlapping and duplication of business functions and product lines.
■■Higher resource prices because of supply constraints when buying inputs in 
large quantities.
Before its restructuring, General Motors (GM) was an example of a business 
that had realized diseconomies of scale by becoming too large. Scale diseconomies 
occurred through product overlap and duplication (i.e., similar or identical automobile 
models), and the fixed cost for these models was not spread over a large volume of 
output. (Recently, the company has decided to discontinue various low-  volume product 
models that overlapped with other models.) GM had numerous manufacturing plants 
throughout the world and sold vehicles in more than a hundred countries. Given this

geographical dispersion in production and sales, the company had communication 
and management coordination problems, which resulted in higher costs. Also, GM 
had significantly higher labor costs than its competitors. As the largest producer in 
the market, it had been a target of labor unions for higher compensation and benefits 
packages relative to other firms.
Economies and diseconomies of scale can occur at the same time; the impact on 
long-  run average total cost (LRAC) depends on which dominates. If economies of 
scale dominate, LRAC decreases with increases in output. The reverse holds true when 
diseconomies of scale prevail. There may be a range of output over which LRAC falls 
(economies of scale) and then a range over which LRAC might be constant, followed 
by a range over which diseconomies of scale prevail, as depicted in Exhibit 26.
The minimum point on the LRAC curve is referred to as the minimum efficient

scale . The minimum efficient scale is the optimal firm size under perfect competition 
over the long run. Theoretically, perfect competition forces the firm to operate at the 
minimum point on the LRAC curve because the market price will be established at 
this level over the long run. If the firm is not operating at this least-  cost point, its 
long-  term viability will be threatened.

Supply Analysis: The Firm 47
Exhibit 26   LRAC Can Exhibit Economies and Diseconomies of Scale
$/Unit
Units/Time PeriodSATC1SATC2SATC3 SATC4SATC5SATC6
LRAC
EXAMPLE 7   
Long-  Run Average Total Cost Curve
Exhibit  27 displays the long-  run average total cost curve (LRACUS) and the 
short-  run average total cost curves for three hypothetical US-  based automobile 
manufacturers—Starr Vehicles (Starr), Rocket Sports Cars (Rocket), and General 
Auto (GenAuto). The LRAC curve for foreign-  owned automobile companies that 
compete in the US auto market (LRACforeign ) is also indicated in the graph. (The 
market structure implicit in the exhibit is imperfect competition.)
To what extent are the cost relationships depicted in Exhibit 27 useful for an 
economic and financial analysis of the three US-  based auto firms?
Exhibit 27   
Cost Per Unit
Q0 Quantity of Outpu tStarr
RocketGenAutoLRACus
LRACforeign
Solution:
First, it is observable that the foreign auto companies have a lower LRAC com -

pared with that of the US automobile manufacturers. This competitive position 
places the US firms at a cost—and possibly, pricing—disadvantage in the market, 
with the potential to lose market share to the lower-  cost foreign competitors. 
Second, only Rocket operates at the minimum point of the LRACUS, whereas 
GenAuto is situated in the region of diseconomies of scale and Starr is positioned 
in the economies of scale portion of the curve. To become more efficient and 
competitive, GenAuto needs to downsize and restructure, which means moving

Reading 14 ■ Topics in Demand and Supply Analysis 48
down the LRACUS curve to a smaller, yet lower-  cost production volume. In 
Contrast, Starr has to grow in size to become more efficient and competitive 
by lowering per-  unit costs.
From a long-  term investment prospective and given its cost advantage, Rocket 
has the potential to create more investment value relative to GenAuto and Starr. 
Over the long run, if GenAuto and Starr can lower their ATC, they will become 
more attractive to investors. But if any of the three US auto companies cannot 
match the cost competitiveness of the foreign firms, they may be driven from 
the market. In the long run, the lower-  cost foreign automakers pose a severe 
competitive challenge to the survival of the US manufacturers and their ability 
to maintain and grow shareholders’ wealth.
SUMMARY
This reading addressed several important concepts that extend the basic market model

of demand and supply to assist the analyst in assessing a firm’s breakeven and shut -
down points of production. Demand concepts covered include own-  price elasticity 
of demand, cross-  price elasticity of demand, and income elasticity of demand. Supply 
concepts covered include total, average, and marginal product of labor; total, variable, 
and marginal cost of labor; and total and marginal revenue. These concepts are used 
to calculate the breakeven and shutdown points of production.
■■Elasticity of demand is a measure of how sensitive quantity demanded is to 
changes in various variables.
■■Own-  price elasticity of demand is the ratio of percentage change in quantity 
demanded to percentage change in a good or service’s own price.
■■If own-  price elasticity of demand is greater than one in absolute terms, demand 
is elastic and a decline in price will result in higher total expenditure on that 
good.
■■If own-  price elasticity of demand is less than one in absolute terms, demand is

inelastic and a decline in price will result in a lower total expenditure on that 
good.
■■If own-  price elasticity of demand is equal to negative one, demand is unit, or 
unitary, elastic and total expenditure on that good is independent of price.
■■Own-  price elasticity of demand will almost always be negative.
■■Income elasticity of demand is the ratio of the percentage change in quantity 
demanded to the percentage change in consumer income.
■■Demand is negatively sloped because of either the substitution effect or the 
income effect.
■■The substitution effect is the phenomenon in which, as a good’s price falls, more 
of this good is substituted for other, more expensive goods.
■■The income effect is the phenomenon in which, as a good’s price falls, real 
income rises and, if this good is normal, more of it will be purchased.
■■If the good is inferior, the income effect will partially or fully offset the substitu -
tion effect.

■■There are two exceptions to the law of demand: Giffen goods and Veblen goods.

Summary 49
■■Giffen goods are highly inferior and make up a large portion of the consumer 
budget. As price falls, the substitution effect tends to cause more of the good to 
be consumed, but the highly negative income effect overwhelms the substitu -
tion effect. Demand curves for Giffen goods are positively sloped.
■■Veblen goods are highly valued high-  priced “status” goods; consumers may tend 
to buy more of a good if its price rises.
■■If income elasticity of demand is positive, the good is a normal good. If income 
elasticity of demand is negative, the good is an inferior good.
■■Cross-  price elasticity of demand is the ratio of the percentage change in quan -
tity demanded of one good to the percentage change in the price of a related 
good.
■■If cross-  price elasticity between two goods is positive, they are substitutes, and 
if cross-  price elasticity between two goods is negative, they are complements.
■■The law of demand states that a decrease in price will cause an increase in

quantity demanded.
■■Total product of labor is a short-  run concept that is the total quantity that 
is able to be produced for each level of labor input, holding all other inputs 
constant.
■■Average product of labor (APL) is the total product of labor divided by number 
of labor hours.
■■Marginal product of labor (MPL) is the change in total product divided by the 
change in labor hours. MPL might rise as more labor is added to a fixed amount 
of capital.
■■The law of diminishing returns dictates that additional output must fall as more 
and more labor is added to a fixed amount of capital.
■■Production costs increase as input prices rise and fall as inputs become more 
productive.
■■Short-  run total cost (STC) is the total expenditure on fixed capital plus the total 
expenditure on labor.
■■Short-  run marginal cost (SMC) equals the ratio of wage to marginal product of 
labor (MPL).
■■Average variable cost (AVC) is the ratio of wage to average product of labor 
(APL).

(APL).
■■Average total cost (ATC) is total cost (TC) divided by the number of units 
produced.
■■Revenue is price times quantity sold.
■■Marginal revenue (MR) is the ratio of change in revenue to change in output.
■■Firms under conditions of perfect competition have no pricing power and, 
therefore, face a perfectly horizontal demand curve at the market price. For 
firms under conditions of perfect competition, price is identical to marginal 
revenue (MR).
■■Firms under conditions of imperfect competition face a negatively sloped 
demand curve and have pricing power. For firms under conditions of imperfect 
competition, marginal revenue (MR) is less than price.
■■Economic profit equals total revenue (TR) minus total economic cost, whereas 
accounting profit equals TR minus total accounting cost.
■■Economic cost takes into account the total opportunity cost of all factors of 
■■Opportunity cost is the next best alternative forgone in making a decision.

Reading 14 ■ Topics in Demand and Supply Analysis 50
■■Maximum economic profit requires that (1) marginal revenue (MR) equals mar -
ginal cost (MC) and (2) MC not be falling with output.
■■The breakeven point occurs when total revenue (TR) equals total cost (TC), 
otherwise stated as the output quantity at which average total cost (ATC) equals 
price.
■■Shutdown occurs when a firm is better off not operating than continuing to 
operate.
■■If all fixed costs are sunk costs, then shutdown occurs when the market price 
falls below minimum average variable cost. After shutdown, the firm incurs 
only fixed costs and loses less money than it would operating at a price that 
does not cover variable costs.
■■In the short run, it may be rational for a firm to continue to operate while earn -
ing negative economic profit if some unavoidable fixed costs are covered.
■■Economies of scale is defined as decreasing long-  run cost per unit as output

increases. Diseconomies of scale is defined as increasing long-  run cost per unit 
as output increases.
■■Long-  run average total cost is the cost of production per unit of output under 
conditions in which all inputs are variable.
■■Specialization efficiencies and bargaining power in input price can lead to econ -
omies of scale.
■■Bureaucratic and communication breakdowns and bottlenecks that raise input 
prices can lead to diseconomies of scale.
■■The minimum point on the long-  run average total cost curve defines the mini -
mum efficient scale for the firm.

Practice Problems 51
1 If the price elasticity coefficient of the demand curve for paper clips is equal to 
–1, demand is:
A elastic.
B inelastic.
C unit elastic.
2 The demand for membership at a local health club is determined by the follow -
ing equation:
QPhmd
hm =−400 5
 where  Qhmd is the number of health club members and Phm is the price of 
membership. If the price of health club membership is $35, the price elasticity 
of demand is closest  to:
A –0.778.
B –0.500.
C –0.438.
3 Price elasticity of demand for a good will most likely  be greater if:
A there are no substitutes for the good. 
B consumers consider the good as discretionary.
C consumers spend a small portion of their budget on the good.
4 If the income elasticity of demand for a product is –0.6, a:
A 1% increase in income will result in a 0.6% increase in demand.
B 1% increase in income will result in a 0.6% decrease in demand.
C 0.6% increase in income will result in a 1% decrease in demand.

5 An individual’s demand for onions is given by the following equation:
QP IPod
ot =− +− 30 05 0 009 016 .. .
 where  Qod is the number of onions demanded, Po is the price per pound of 
onions, I is the household income, and Pt is the price per pound of tomatoes.
 If the price of onions is $1.25, household income is $2,500, and the price of 
tomatoes is $3.75, the cross-  price elasticity of demand for onions with respect 
to the price of tomatoes is closest  to:
A –1.0597.
B –0.0242.
C –0.0081.
6 Movement along the demand curve for good X occurs due to a change in:
A income.
B the price of good X.
C the price of a substitute for good X.

Reading 14 ■ Topics in Demand and Supply Analysis 52
7 A wireless phone manufacturer introduced a next-  generation phone that 
received a high level of positive publicity. Despite running several high-  speed 
production assembly lines, the manufacturer is still falling short in meeting 
demand for the phone nine months after introduction. Which of the following 
statements is the most  plausible explanation for the demand/supply imbalance?
A The phone price is low relative to the equilibrium price.
B Competitors introduced next-  generation phones at a similar price.
C Consumer incomes grew faster than the manufacturer anticipated.
8–11
The market demand function for four-  year private universities is given by the equation
Qprd= 84 – 3.1 Ppr + 0.8 I + 0.9 Ppu
where  Qprd is the number of applicants to private universities per year in thousands, 
Ppr is the average price of private universities (in thousands of USD), I is the household

monthly income (in thousands of USD), and Ppu is the average price of public 
(government-  supported) universities (in thousands of USD). Assume that Ppr is equal 
to 38, I is equal to 100, and Ppu is equal to 18.
8 The price elasticity of demand for private universities is closest  to:
A –3.1.
B –1.9.
C 0.6.
9 The income elasticity of demand for private universities is closest  to:
A 0.5.
B 0.8.
C 1.3.
10 The cross-  price elasticity of demand for private universities with respect to the 
price of public universities is closest  to:
A 0.3.
B 3.1.
C 3.9.
11 If the cross-  price elasticity between two goods is negative, the two goods are 
classified as:
A normal.
B substitutes.
C complements.
12 In the case of a normal good with a decrease in own price, which of the follow -
ing statements is most likely  true?
A Both the substitution and income effects lead to an increase in the quantity 
purchased.

Practice Problems 53
B The substitution effect leads to an increase in the quantity purchased, while 
the income effect has no impact.
C The substitution effect leads to an increase in the quantity purchased, while 
the income effect leads to a decrease.
13 For a Giffen good, the:
A demand curve is positively sloped.
B substitution effect overwhelms the income effect.
C income and substitution effects are in the same direction.
14 Normal profit is best described as:
A zero economic profit.
B total revenue minus all explicit costs.
C the sum of accounting profit plus economic profit.
15 A company plans to hire additional factory employees. In the short run, mar -
ginal returns are most likely to decrease if:
A the factory is operating at full capacity.
B the factory is experiencing a labor shortage.
C workers are required to multitask and share duties. 
16 The production relationship between the number of machine hours and total 
product for a company is presented below.

Machine Hours Total Product Average Product
1 3 3.00
2 8 4.00
3 14 4.67
4 19 4.75
5 21 4.20
 Diminishing marginal returns first occur beyond machine hour:
A 3.
B 4.
C 5. 
17 The marketing director for a Swiss specialty equipment manufacturer estimates 
the firm can sell 200 units and earn total revenue of CHF500,000. However, if 
250 units are sold, revenue will total CHF600,000. The marginal revenue per 
unit associated with marketing 250 units instead of 200 units is closest  to:
A CHF 2,000.
B CHF 2,400.
C CHF 2,500.
18 An agricultural firm operating in a perfectly competitive market supplies wheat 
to manufacturers of consumer food products and animal feeds. If the firm were 
able to expand its production and unit sales by 10% the most likely  result would 
be:
A a 10% increase in total revenue.
B a 10% increase in average revenue.
C an increase in total revenue of less than 10%.

Reading 14 ■ Topics in Demand and Supply Analysis 54
19 An operator of a ski resort is considering offering price reductions on weekday 
ski passes. At the normal price of €50 per day, 300 customers are expected to 
buy passes each weekday. At a discounted price of €40 per day 450 customers 
are expected to buy passes each weekday. The marginal revenue per customer 
earned from offering the discounted price is closest  to:
A €20.
B €40.
C €50.
20 The marginal revenue per unit sold for a firm doing business under conditions 
of perfect competition will most likely  be:
A equal to average revenue.
B less than average revenue.
C greater than average revenue.
21–23
A firm’s director of operations gathers the following information about the firm’s cost 
structure at different levels of output:
Exhibit 1   
Quantity  
(Q)   Total Fixed Cost  
   (TFC )Total Variable Cost  
(TVC )
0 200 0
1 200 100
2 200 150
3 200 200
4 200 240
5 200 320

1 200 100
2 200 150
3 200 200
4 200 240
5 200 320
21 Refer to the data in Exhibit 1. When quantity produced is equal to 4 units, the 
average fixed cost ( AFC ) is closest  to:
A 50.
B 60.
C 110.
22 Refer to the data in Exhibit 1. When the firm increases production from 4 to 5 
units, the marginal cost ( MC) is closest  to:
A 40.
B 64.
C 80.
23 Refer to the data in Exhibit 1. The level of unit production resulting in the low -
est average total cost ( ATC ) is closest  to:
A 3.

B 4.
C 5.
24 The short-  term breakeven point of production for a firm operating under per -
fect competition will most likely  occur when:
A price is equal to average total cost.
B marginal revenue is equal to marginal cost.
C marginal revenue is equal to average variable costs.
25 The short-  term shutdown point of production for a firm operating under per -
26 Under conditions of perfect competition, a company will break even when mar -
ket price is equal to the minimum point of the:
A average total cost curve.
B average variable cost curve.
C short-  run marginal cost curve. 
27 A company will shut down production in the short run if total revenue is less 
than total:
A fixed costs.
B variable costs.

28 A company has total variable costs of $4 million and fixed costs of $3 million. 
Based on this information, the company will stay in the market in the long term 
if total revenue is at least:
A $3.0 million.
B $4.5 million.
C $7.0 million. 
29 When total revenue is greater than total variable costs but less than total costs, 
in the short term a firm will most likely :
A exit the market.
B stay in the market.
C shut down production.
30 A profit maximum is least likely  to occur when:
A average total cost is minimized.
B marginal revenue equals marginal cost.
C the difference between total revenue and total cost is maximized.
31 A firm that increases its quantity produced without any change in per-  unit cost 
is experiencing:
A economies of scale.
B diseconomies of scale.
C constant returns to scale.
32 A company is experiencing economies of scale when:

Reading 14 ■ Topics in Demand and Supply Analysis 56
A cost per unit increases as output increases.
B it is operating at a point on the LRAC curve where the slope is negative. 
C It is operating beyond the minimum point on the long-  run average total cost 
curve.
33 Diseconomies of scale most likely  result from:
A specialization in the labor force.
B overlap of business functions and product lines.
C discounted prices on resources when buying in larger quantities.
34 A firm is operating beyond minimum efficient scale in a perfectly competitive 
industry. To maintain long-  term viability the most likely  course of action for the 
firm is to:
A operate at the current level of production.
B increase its level of production to gain economies of scale.
C decrease its level of production to the minimum point on the long-  run aver -
age total cost curve.
35 Under conditions of perfect competition, in the long run firms will most likely  
earn:
A normal profits.
B positive economic profits.

earn:
C negative economic profits.
The following information relates to Questions 36 
and 37
The manager of a small manufacturing firm gathers the following information about 
the firm’s labor utilization and production:
Exhibit 2   
Labor ( L) Total Product ( TP)
0 0
1 150
2 320
3 510
4 660
5 800
36 Refer to the data in Exhibit 2. The number of workers resulting in the highest 
level of average product of labor is closest  to:
A 3.
B 4.
C 5.

Practice Problems 57
37 Refer to the data in Exhibit 2. The marginal product of labor demonstrates 
increasing returns for the firm if the number of workers is closest  to but not 
more than:
A 2.
B 3.
C 4.

Reading 14 ■ Topics in Demand and Supply Analysis 58
SOLUTIONS
1 C is correct. When the price elasticity of demand coefficient is –1, demand is 
said to be unit elastic, or unitary elastic. 
2 A is correct. Inserting the price of $35 into the demand function, quantity 
demanded is calculated as
Qhmd=− () = 400 535 225
 At a price of $35 per health club membership, the elasticity of demand is
 Price elasticity of demand =  ∆∆QP PQhmd
hm hm hmd() ×()  
 Price elasticity of demand =  –5 × (35/225) = –0.778
3 B is correct. Price elasticity of demand is likely to be greater for items that are 
seen as optional or discretionary. 
4 B is correct. Income elasticity is a measure of how sensitive quantity demanded 
is to a change in income. If the income elasticity of demand for the product is 
–0.6, whenever income increases by 1%, the quantity demanded of the product 
at each price decreases by 0.6%. Consequently, as income rises, consumers will 
purchase less of the product.

purchase less of the product. 
5 B is correct. The cross-  price elasticity of demand measures the responsiveness 
of the demand for onions in response to a change in the price of tomatoes. 
From the demand function equation:
 Qod = 3 – 0.05 Po + 0.009 I – 0.16 Pt
 Qod = 3 – 0.05(1.25) + 0.009(2,500) – 0.16(3.75) = 24.8375
 At a price of onions of $1.25 and a price of tomatoes of $3.75, the cross-  price 
elasticity of demand is calculated as follows:
 Cross-  price elasticity of demand =  ∆∆QP PQod
tt od() ×()  
 Cross-  price elasticity of demand =  –0.16 × (3.75/24.8375) = –0.0242
6 B is correct. The demand curve shows quantity demanded as a function of own 
price only.
7 A is correct. The situation described is one of excess demand because, in order 
for markets to clear at the given level of quantity supplied, the company would 
need to raise prices.
8 B is correct. From the demand function:
 Solve for  Qprd:
 ∆∆QPprd
pr  = –3.1 (the coefficient in front of own price)

 Qprd = 84 – 3.1 Ppr + 0.8 I +0.9 Ppu
  = 84 – 3.1(38) + 0.8(100) + 0.9(18)
  = 62.4

Solutions 59
 At Ppr = 38, 
 price elasticity of demand =  ∆∆QP PQprd
pr pr prd() ()  
  = (–3.1)(38/62.4)
  = –1.9
9 C is correct. From the demand function:
 ∆∆QIprd
  = 0.8 (coefficient in front of the income variable)
 Qprd = 84 – 3.1 Ppr + 0.8 I + 0.9 Ppu
  = 62.4
 At I = 100,
 the income elasticity of demand =  ∆∆QI IQprd
prd() ()  
  = (0.8)(100/62.4)
  = 1.3
10 A is correct. From the demand function:
 ∆∆QPprd
pu  = 0.9 (the coefficient in front of Ppu)
  = 62.4
 At P = 38, and Ppu = 18,
 the cross-  price elasticity of demand =  ∆∆QP PQprd
pu pu prd() ()  
  = (0.9)(18/62.4)
  = 0.3
11 C is correct. With complements, consumption goes up or down together. With 
a negative cross-  price elasticity, as the price of one good goes up, the demand 
for both falls.
12 A is correct. In the case of normal goods, the income and substitution effects

are reinforcing, leading to an increase in the amount purchased after a drop in 
price.
13 A is correct. The income effect overwhelms the substitution effect such that an 
increase in the price of the good results in greater demand for the good, result -
ing in a positively sloped demand curve.
14 A is correct. Normal profit is the level of accounting profit such that implicit 
opportunity costs are just covered; thus, it is equal to a level of accounting 
profit such that economic profit is zero.
15 A is correct. The law of diminishing returns occurs in the short run when addi -
tional output falls as more and more labor is added to a fixed amount of capital. 
When a factory is operating at full capacity, adding additional employees will

Reading 14 ■ Topics in Demand and Supply Analysis 60
not increase production because the physical plant is already 100% employed. 
More labor hours will add to costs without adding to output, thus resulting in 
diminishing marginal returns. 
16 A is correct. Diminishing marginal returns occur when the marginal product of 
a resource decreases as additional units of that input are employed. Marginal 
product, which is the additional output resulting from using one more unit of 
input, is presented below.
Machine Hours Total Product Average Product Marginal Product
1 3 3.00 3
2 8 4.00 5
3 14 4.67 6
4 19 4.75 5
5 21 4.20 2
 The marginal product of the third machine hour is 6 and declines thereafter. 
Consequently, diminishing marginal returns are first evident beyond three 
machine hours. 
17 A is correct. Marginal revenue per unit is defined as the change in total revenue 
divided by the change in quantity sold. MR = ∆TR ÷ ∆ Q. In this case, change

in total revenue equals CHF100,000, and change in total units sold equals 50. 
CHF100,000 ÷ 50 = CHF2,000.
18 A is correct. In a perfectly competitive market, an increase in supply by a single 
firm will not affect price. Therefore, an increase in units sold by the firm will be 
matched proportionately by an increase in revenue.
19 A is correct. Marginal revenue per unit is defined as the change in total rev -
enues divided by the change in quantity sold. MR = ∆TR ÷ ∆ Q. In this case, 
change in total revenue per day equals €3,000 [(450 × €40) – (300 × €50)], and 
change in units sold equals 150 (450 – 300). €3,000 ÷ 150 = €20.
20 A is correct. Under perfect competition, a firm is a price taker at any quantity 
supplied to the market, and AR = MR = Price.
21 A is correct. Average fixed cost is equal to total fixed cost divided by quantity 
produced: AFC = TFC/ Q = 200/4 = 50.
22 C is correct. Marginal cost is equal to the change in total cost divided by the

change in quantity produced. MC = ∆TC/∆ Q = 80/1 = 80.
23 C is correct. Average total cost is equal to total cost divided by quantity pro -
duced. At 5 units produced the average total cost is 104. ATC = TC/ Q = 520/5 = 
104.
24 A is correct. Under perfect competition, price equals marginal revenue. A firm 
breaks even when marginal revenue equals average total cost.
25 C is correct. The firm should shut down production when marginal revenue is 
less than average variable cost.
26 A is correct. A company is said to break even if its total revenue is equal to its 
total cost. Under conditions of perfect competition, a company will break even 
when market price is equal to the minimum point of the average total cost 
curve. 
27 B is correct. A company will shut down production in the short run when total 
revenue is below total variable costs.

Solutions 61
28 C is correct. A company will stay in the market in the long term if total revenue 
is equal to or greater than total cost. Because total costs are $7 million ($4 mil -
lion variable costs and $3 million fixed costs), the company will stay in the 
market in the long term if total revenue equals at least $7 million. 
29 B is correct. When total revenue is enough to cover variable costs but not total 
fixed costs in full, the firm can survive in the short run but would be unable to 
maintain financial solvency in the long run.
30 A is correct. The quantity at which average total cost is minimized does not 
necessarily correspond to a profit maximum.
31 C is correct. Output increases in the same proportion as input increases occur 
at constant returns to scale.
32 B is correct. Economies of scale occur if, as the firm increases output, cost per 
unit of production falls. Graphically, this definition translates into a long-  run 
average cost curve (LRAC) with a negative slope.

average cost curve (LRAC) with a negative slope. 
33 B is correct. As the firm increases output, diseconomies of scale and higher 
average total costs can result when there is overlap and duplication of business 
functions and product lines. 
34 C is correct. The firm operating at greater than long-  run efficient scale is sub -
ject to diseconomies of scale. It should plan to decrease its level of production.
35 A is correct. Competition should drive prices down to long-  run marginal cost, 
resulting in only normal profits being earned.
36 A is correct. Three workers produce the highest average product equal to 170. 
AP = 510/3 = 170.
37 B is correct. Marginal product is equal to the change in total product divided 
by the change in labor. The increase in MP from 2 to 3 workers is 190: MP = 
∆TP/∆ L = (510 – 320)/(3 – 2) = 190/1 = 190.

The Firm and Market Structures
by Richard Fritz, PhD, and Michele Gambera, PhD, CFA
Richard Fritz, PhD, is at the School of Economics at Georgia Institute of Technology (USA). 
Michele Gambera, PhD, CFA, is at UBS Asset Management (Americas), Inc. (USA).
a. describe characteristics of perfect competition, monopolistic 
competition, oligopoly, and pure monopoly;
b. explain relationships between price, marginal revenue, marginal 
cost, economic profit, and the elasticity of demand under each 
market structure;
c. describe a firm’s supply function under each market structure;
d. describe and determine the optimal price and output for firms 
under each market structure;
e. explain factors affecting long-  run equilibrium under each market 
structure;
f. describe pricing strategy under each market structure; 
g. describe the use and limitations of concentration measures in 
identifying market structure;

h. identify the type of market structure within which a firm 
operates. 
The purpose of this reading is to build an understanding of the importance of market 
structure. As different market structures result in different sets of choices facing a 
firm’s decision makers, an understanding of market structure is a powerful tool in 
analyzing issues such as a firm’s pricing of its products and, more broadly, its potential 
to increase profitability. In the long run, a firm’s profitability will be determined by 
the forces associated with the market structure within which it operates. In a highly 
competitive market, long-  run profits will be driven down by the forces of competi -
tion. In less competitive markets, large profits are possible even in the long run; in 1READING
15

Reading 15 ■ The Firm and Market Structures 64
the short run, any outcome is possible. Therefore, understanding the forces behind 
the market structure will aid the financial analyst in determining firms’ short- and 
long-  term prospects.
Section 2 introduces the analysis of market structures. The section addresses ques -
tions such as: What determines the degree of competition associated with each market 
structure? Given the degree of competition associated with each market structure, 
what decisions are left to the management team developing corporate strategy? How 
does a chosen pricing and output strategy evolve into specific decisions that affect 
the profitability of the firm? The answers to these questions are related to the forces 
of the market structure within which the firm operates.
Sections 3, 4, 5, and 6 analyze demand, supply, optimal price and output, and fac -
tors affecting long-  run equilibrium for perfect competition, monopolistic competition,

oligopoly, and pure monopoly, respectively.
Section 7 reviews techniques for identifying the various forms of market struc -
ture. For example, there are accepted measures of market concentration that are used 
by regulators of financial institutions to judge whether or not a planned merger or 
acquisition will harm the competitive nature of regional banking markets. Financial 
analysts should be able to identify the type of market structure a firm is operating 
within. Each different structure implies a different long-  run sustainability of profits. 
ANALYSIS OF MARKET STRUCTURES
Traditionally, economists classify a market into one of four structures: perfect com -
petition, monopolistic competition, oligopoly, and monopoly. Section 2.1 explains 
that four-  way classification in more detail. Section 2.2 completes the introduction by 
providing and explaining the major points to evaluate in determining the structure

to which a market belongs.
2.1 Economists’ Four Types of Structure
Economists define a market as a group of buyers and sellers that are aware of each 
other and are able to agree on a price for the exchange of goods and services. While 
the internet has extended a number of markets worldwide, certain markets are limited 
by geographic boundaries. For example, the internet search engine Google operates 
in a worldwide market. In contrast, the market for premixed cement is limited to the 
area within which a truck can deliver the mushy mix from the plant to a construction 
site before the compound becomes useless. Thomas L. Friedman’s international best 
seller The World Is Flat1 challenges the concept of the geographic limitations of the 
market. If the service being provided by the seller can be digitized, its market expands 
worldwide. For example, a technician can scan your injury in a clinic in Switzerland.

That radiographic image can be digitized and sent to a radiologist in India to be read. 
As a customer (i.e., patient), you may never know that part of the medical service 
provided to you was the result of a worldwide market.
Some markets are highly concentrated, with the majority of total sales coming from 
a small number of firms. For example, in the market for small consumer batteries, 
three firms controlled 87 percent of the US market (Duracell 43 percent, Energizer 
33 percent, and Rayovac 11 percent) as of 2005. Other markets are very fragmented, 
such as automobile repairs, where small independent shops often dominate and large 2
1 Friedman (2006).

Analysis of Market Structures 65
chains may or may not exist. New products can lead to market concentration: It is 
estimated that the Apple iPod had a world market share of over 70 percent among 
MP3 players in 2009.
THE IMPORTANCE OF MARKET STRUCTURE 
Consider the evolution of television broadcasting. As the market environment for tele -
vision broadcasting evolved, the market structure changed, resulting in a new set of 
challenges and choices. In the early days, there was only one choice: the “free” analog 
channels that were broadcast over the airwaves. In most countries, there was only one 
channel, owned and run by the government. In the United States, some of the more 
populated markets were able to receive more channels because local channels were 
set up to cover a market with more potential viewers. By the 1970s, new technologies 
made it possible to broadcast by way of cable connectivity and the choices offered to

consumers began to expand rapidly. Cable television challenged the “free” broadcast 
channels by offering more choice and a better-  quality picture. The innovation was 
expensive for consumers and profitable for the cable companies. By the 1990s, a new 
alternative began to challenge the existing broadcast and cable systems: satellite tele -
vision. Satellite providers offered a further expanded set of choices, albeit at a higher 
price than the free broadcast and cable alternatives. In the early 2000s, satellite television 
providers lowered their pricing to compete directly with the cable providers. Today, cable 
program providers, satellite television providers, and terrestrial digital broadcasters that 
offer premium and pay-  per-  view channels compete for customers who are increasingly 
finding content on the internet.
This is a simple illustration of the importance of market structure. As the market 
for television broadcasting became increasingly competitive, managers had to make

decisions regarding product packaging, pricing, advertising, and marketing in order to 
survive in the changing environment.
Market structure can be broken down into four distinct categories: perfect com -
petition, monopolistic competition, oligopoly, and monopoly.
We start with the most competitive environment, perfect competition . Unlike 
some economic concepts, perfect competition is not merely an ideal based on assump -
tions. Perfect competition is a reality—for example, in several commodities markets, 
where sellers and buyers have a strictly homogeneous product and no single producer 
is large enough to influence market prices. Perfect competition’s characteristics are 
well recognized and its long-  run outcome unavoidable. Profits under the conditions of 
perfect competition are driven to the required rate of return paid by the entrepreneur 
to borrow capital from investors (so-  called normal profit or rental cost of capital). This

does not mean that all perfectly competitive industries are doomed to extinction by 
a lack of profits. On the contrary, millions of businesses that do very well are living 
under the pressures of perfect competition.
Monopolistic competition  is also highly competitive; however, it is considered 
a form of imperfect competition. Two economists, Edward H. Chamberlin (US) and 
Joan Robinson (UK), identified this hybrid market and came up with the term because 
there are strong elements of competition in this market structure and also some 
monopoly-  like conditions. The competitive characteristic is a notably large number of 
firms, while the monopoly aspect is the result of product differentiation. That is, if the 
seller can convince consumers that its product is uniquely different from other, similar 
products, then the seller can exercise some degree of pricing power over the market. 
A good example is the brand loyalty associated with soft drinks such as Coca-  Cola.

Many of Coca-  Cola’s customers believe that their beverages are truly different from and 
better than all other soft drinks. The same is true for fashion creations and cosmetics.

Reading 15 ■ The Firm and Market Structures 66
The oligopoly  market structure is based on a relatively small number of firms 
supplying the market. The small number of firms in the market means that each firm 
must consider what retaliatory strategies the other firms will pursue when prices and 
production levels change. Consider the pricing behavior of commercial airline com -
panies. Pricing strategies and route scheduling are based on the expected reaction of 
the other carriers in similar markets. For any given route—say, from Paris, France, to 
Chennai, India—only a few carriers are in competition. If one of the carriers changes 
its pricing package, others will likely retaliate. Understanding the market structure of 
oligopoly markets can help in identifying a logical pattern of strategic price changes 
for the competing firms.
Finally, the least competitive market structure is monopoly . In pure monopoly

markets, there are no other good substitutes for the given product or service. There is 
a single seller, which, if allowed to operate without constraint, exercises considerable 
power over pricing and output decisions. In most market-  based economies around the 
globe, pure monopolies are regulated by a governmental authority. The most common 
example of a regulated monopoly is the local electrical power provider. In most cases, 
the monopoly power provider is allowed to earn a normal return on its investment 
and prices are set by the regulatory authority to allow that return.
2.2 Factors That Determine Market Structure
Five factors determine market structure:
1 The number and relative size of firms supplying the product;
2 The degree of product differentiation;
3 The power of the seller over pricing decisions;
4 The relative strength of the barriers to market entry and exit; and
5 The degree of non-  price competition.

The number and relative size of firms in a market influence market structure. If 
there are many firms, the degree of competition increases. With fewer firms supplying 
a good or service, consumers are limited in their market choices. One extreme case is 
the monopoly market structure, with only one firm supplying a unique good or service. 
Another extreme is perfect competition, with many firms supplying a similar product. 
Finally, an example of relative size is the automobile industry, in which a small number 
of large international producers (e.g., Ford and Toyota) are the leaders in the global 
market, and a number of small companies either have market power because they are 
niche players (e.g., Ferrari) or have little market power because of their narrow range 
of models or limited geographical presence (e.g., Škoda).
In the case of monopolistic competition, there are many firms providing products

to the market, as with perfect competition. However, one firm’s product is differenti -
ated in some way that makes it appear better than similar products from other firms. 
If a firm is successful in differentiating its product, the differentiation will provide 
pricing leverage. The more dissimilar the product appears, the more the market will 
resemble the monopoly market structure. A firm can differentiate its product through 
aggressive advertising campaigns; frequent styling changes; the linking of its product 
with other, complementary products; or a host of other methods.
When the market dictates the price based on aggregate supply and demand con -
ditions, the individual firm has no control over pricing. The typical hog farmer in 
Nebraska and the milk producer in Bavaria are price takers . That is, they must accept 
whatever price the market dictates. This is the case under the market structure of 
perfect competition. In the case of monopolistic competition, the success of product

differentiation determines the degree with which the firm can influence price. In the 
case of oligopoly, there are so few firms in the market that price control becomes

Analysis of Market Structures 67
possible. However, the small number of firms in an oligopoly market invites complex 
pricing strategies. Collusion, price leadership by dominant firms, and other pricing 
strategies can result.
The degree to which one market structure can evolve into another and the dif -
ference between potential short-  run outcomes and long-  run equilibrium conditions 
depend on the strength of the barriers to entry and the possibility that firms fail to 
recoup their original costs or lose money for an extended period of time and are 
therefore forced to exit the market. Barriers to entry can result from very large cap -
ital investment requirements, as in the case of petroleum refining. Barriers may also 
result from patents, as in the case of some electronic products and drug formulas. 
Another entry consideration is the possibility of high exit costs. For example, plants 
that are specific to a special line of products, such as aluminum smelting plants, are

non-  redeployable, and exit costs would be high without a liquid market for the firm’s 
assets. High exit costs deter entry and are therefore also considered barriers to entry. 
In the case of farming, the barriers to entry are low. Production of corn, soybeans, 
wheat, tomatoes, and other produce is an easy process to replicate; therefore, those 
are highly competitive markets.
Non-  price competition dominates those market structures where product differen -
tiation is critical. Therefore, monopolistic competition relies on competitive strategies 
that may not include pricing changes. An example of non-  price competition is product 
differentiation through marketing. In other circumstances, non-  price competition may 
occur because the few firms in the market feel dependent on each other. Each firm 
fears retaliatory price changes that would reduce total revenue for all of the firms in 
the market. Because oligopoly industries have so few firms, each firm feels dependent

on the pricing strategies of the others. Therefore, non-  price competition becomes a 
dominant strategy.
Exhibit 1   Characteristics of Market Structure
Market StructureNumber of 
SellersDegree of 
Product 
DifferentiationBarriers to 
EntryPricing Power 
of FirmNon-  price 
Competition
Perfect competition Many Homogeneous/ 
StandardizedVery Low None None
Monopolistic competition Many Differentiated Low Some Advertising 
and Product 
Differentiation
Oligopoly Few Homogeneous/ 
StandardizedHigh Some or 
ConsiderableAdvertising 
Monopoly One Unique Product Very High Considerable Advertising
From the perspective of the owners of the firm, the most desirable market struc -
ture is that with the most control over price, because this control can lead to large 
profits. Monopoly and oligopoly markets offer the greatest potential control over price; 
monopolistic competition offers less control. Firms operating under perfectly compet -

itive market conditions have no control over price. From the consumers’ perspective, 
the most desirable market structure is that with the greatest degree of competition, 
because prices are generally lower. Thus, consumers would prefer as many goods and 
services as possible to be offered in competitive markets.

Reading 15 ■ The Firm and Market Structures 68
As often happens in economics, there is a trade-  off. While perfect competition 
gives the largest quantity of a good at the lowest price, other market forms may spur 
more innovation. Specifically, there may be high costs in researching a new product, 
and firms will incur such costs only if they expect to earn an attractive return on 
their research investment. This is the case often made for medical innovations, for 
example—the cost of clinical trials and experiments to create new medicines would 
bankrupt perfectly competitive firms but may be acceptable in an oligopoly market 
structure. Therefore, consumers can benefit from less-  than-  perfectly-  competitive 
markets.
PORTER’S FIVE FORCES AND MARKET STRUCTURE 
A financial analyst aiming to establish market conditions and consequent profitability of 
incumbent firms should start with the questions framed by Exhibit 1: How many sellers

are there? Is the product differentiated? and so on. moreover, in the case of monopolies 
and quasi monopolies, the analyst should evaluate the legislative and regulatory frame -
work: Can the company set prices freely, or are there governmental controls? Finally, the 
analyst should consider the threat of competition from potential entrants.
This analysis is often summarized by students of corporate strategy as “Porter’s five 
forces,” named after Harvard Business School professor michael E. Porter. His book, 
Competitive Strategy , presented a systematic analysis of the practice of market strategy. 
Porter (2008) identified the five forces as:
■■ Threat of entry;
■■ Power of suppliers;
■■ Power of buyers (customers);
■■ Threat of substitutes; and
■■ Rivalry among existing competitors.
It is easy to note the parallels between four of these five forces and the columns in 
Exhibit 1. The only “orphan” is the power of suppliers, which is not at the core of the

theoretical economic analysis of competition, but which has substantial weight in the 
practical analysis of competition and profitability.
Some stock analysts (e.g., Dorsey 2004) use the term “economic moat” to suggest 
that there are factors protecting the profitability of a firm that are similar to the moats 
(ditches full of water) that used to protect some medieval castles. A deep moat means 
that there is little or no threat of entry by invaders, i.e. competitors. It also means that 
customers are locked in because of high switching costs.
PERFECT COMPETITION
Perfect competition is characterized by the five conditions presented in Exhibit 1, above:
1 There are a large number of potential buyers and sellers.
2 The products offered by the sellers are virtually identical.
3 There are few or easily surmountable barriers to entry and exit.
4 Sellers have no market-  pricing power.
5 Non-  price competition is absent.

While few markets achieve the distinction of being perfectly competitive, it is useful 
to establish the outcome associated with this market structure as a benchmark against 
which other market structures can be compared. The most typical example of perfect 
competition is found in certain aspects of the agriculture industry, such as the large 3

Perfect Competition 69
number of farmers growing corn for animal feed. Corn is a primary source of food for 
pork, beef, and poultry production. A bushel of corn from Farmer Brown is virtually 
identical to a bushel of corn from Farmer Lopez. If a hog farmer needs corn to feed 
his hogs, it does not matter whether the corn comes from Farmer Brown or Farmer 
Lopez. Furthermore, the aggregate corn market is well defined, with active futures and 
spot markets. Information about the corn market is easy and inexpensive to access, 
and there is no way to differentiate the product, such as by advertising. Agribusiness 
is capital intensive, but where arable land is relatively abundant and water is available, 
the barriers to entry (e.g., capital and expertise) for corn production are relatively low.
3.1 Demand Analysis in Perfectly Competitive Markets
The price of a homogeneous product sold in a competitive market is determined by the

demand and supply in that market. Economists usually represent demand and supply 
in a market through demand and supply curves in a two-  axis plane, where quantity 
and price are shown on the x-axis and y-axis, respectively. Economists believe that 
demand functions have negative slopes, as shown in Exhibit 2. That is, at high prices, 
less is demanded. For normal goods and services, as the price declines, the quantity 
demanded increases. This concept is based on two effects: the income effect and the 
substitution effect. The income effect results from the increased purchasing power 
the consumer has when prices fall. With lower prices, the consumer can afford to 
purchase more of the product. The substitution effect comes from the increasing 
attractiveness of the lower-  priced product. If soybean prices are unchanged and corn 
prices decrease, hog farmers will substitute corn for soybeans as feed for their animals.
Exhibit 2   Market Demand in Perfect Competition 
QuantityDemandPrice

Assume the demand for this product can be specified as
QD = 50 – 2 P
where QD is the quantity of demand and P is the product’s price. This demand function 
can be rearranged in terms of price:
P = 25 – 0.5 QD
In this form, total revenue (TR) is equal to price times quantity, or P × QD. Thus,
TR== − PQ QQDD D 25 052.

Reading 15 ■ The Firm and Market Structures 70
Average revenue (AR) can be found by dividing TR by QD. Therefore,
AR TR== − () =− QQ QQ QDD DD D 25 05 25 052..
Note that the AR function is identical to the market demand function. The assumption 
here is that the relationship between price and quantity demanded is linear. Clearly, 
that may not be the case in the real market. Another simplifying assumption made 
is that the price of the product is the only determinant of demand. Again, that is not 
likely in the real market. For example, economic theory suggests that consumer income 
is another important factor in determining demand. The prices of related goods and 
services, such as substitutes and complements, are also considered factors affecting 
demand for a particular product.
Marginal revenue (MR) is the change in total revenue per extra increment sold 
when the quantity sold changes by a small increment, ∆ QD. Substituting ( QD +∆QD)

into the total revenue (TR) equation, marginal revenue can be expressed as:
MRTR==+ () −+ + ()

−−∆
∆∆∆ ∆
QQQ QQ QQ QQ
DDD DD DD DD 25 05 22 50 522..2 2
225 0525 05
=−−=− −∆
∆∆ ∆
∆∆Q
QQ QQ
QQQD
DD DD
DDD..
For example, suppose QD = 5 and ∆ QD = 1, then total revenue increases from 112.50 
[= 25(5) – 0.5 (52)] to 132 [= 25(6) – 0.5(62)], and marginal revenue is 19.5 = (132 – 
112.5)/1. Note that marginal revenue is equal to (25 – QD – 0.5∆ QD). Now suppose 
that ∆ QD is much smaller, for example ∆ QD = 0.1. In this case, total revenue increases 
to 114.495 [= 25(5.1) – 0.5(5.12)], and marginal revenue is 1.995/0.1  = 19.95. It is 
straightforward to confirm that as ∆ QD gets smaller marginal revenue gets closer to 
20 = 25 – QD. So, for very small changes in the quantity sold we can write marginal 
revenue as2
MR = 25 – QD
Although we have introduced the concept of marginal revenue in the context of 
the demand curve for the market as a whole, its usefulness derives from its role in

the output and pricing decisions of individual firms. As we will see, marginal revenue 
and an analogous concept, marginal cost, are critical in determining firms’ profit-  
maximizing strategies.
3.1.1  Elasticity of Demand
Consumers respond differently to changes in the price of different kinds of products 
and services. The quantity demanded for some products is very price sensitive, while 
for other products, price changes result in little change in the quantity demanded. 
Economists refer to the relationship between changes in price and changes in the 
quantity demanded as the price elasticity of demand. Therefore, the demand for the 
former group of products—those that are very price sensitive—is said to have high 
price elasticity, whereas the demand for the latter group is said to have low price elas -
ticity. Understanding the sensitivity of demand changes to changes in price is critical 
to understanding market structures.

Price elasticity of demand  measures the percentage change in the quantity 
demanded given a percentage change in the price of a given product. Because the 
relationship of demand to price is negative, the price elasticity of demand would be 
negative. Many economists, however, present the price elasticity as an absolute value, 
2 Readers who are familiar with calculus will recognize this as the derivative of total revenue with respect 
to the quantity sold.

Perfect Competition 71
so that price elasticity has a positive sign. We will follow that convention.  Higher price 
elasticity indicates that consumers are very responsive to changes in price. Lower val -
ues for price elasticity imply that consumers are not very responsive to price changes. 
Price elasticity can be measured with the following relationship:
εP = –(% change in QD) ÷ (% change in P)
where εP is price elasticity of demand, QD is the quantity demanded, and P is the 
product’s price.
Price elasticity of demand falls into three categories. When demand is very 
responsive to price change, it is identified as elastic . When demand is not responsive 
to price change, it is identified as inelastic . When the percentage change in quantity 
demanded is exactly the same as the percentage change in price, the demand is called 
unitary elastic .
εP > 1 Demand is elastic
εP = 1 Demand is unitary elastic
εP < 1 Demand is inelastic

Price elasticity of demand depends on several factors. Price elasticity will be higher 
if there are many close substitutes for the product . If a product has many good alter -
natives, consumers will be more sensitive to price changes. For example, carbonated 
beverages (“soft drinks”) have many close substitutes. It takes strong brand loyalty 
to keep customer demand high in the soft drink market when one brand’s price is 
strategically lowered; the price elasticity of demand for Coca-  Cola has been estimated 
to be 3.8. For products with numerous close substitutes, demand is highly elastic. For 
products with few close substitutes, demand is lower in price elasticity and would be 
considered price inelastic. The demand for first-  class airline tickets is often seen as 
inelastic because only very wealthy people are expected to buy them; the demand for 
economy-  class tickets is elastic because the typical consumer for this product is more

budget-  conscious. Consumers do not consider economy-  class airline tickets a close 
substitute for first-  class accommodations, particularly on long flights.
The airline ticket example introduces another determinant of price elasticity of 
demand. The greater the share of the consumer’s budget spent on the item, the higher the 
price elasticity of demand . Expensive items, such as durable goods (e.g., refrigerators 
and televisions), tend to have higher elasticity measures, while less expensive items, 
such as potatoes and salt, have lower elasticity values. Consumers will not change 
their normal salt consumption if the price of salt decreases by 10 percent. Instead, 
they will buy their next package of salt when they run out, with very little regard to 
the price change.
The airline ticket also makes a good example for the final factor determining price 
elasticity. Price elasticity of demand also depends on the length of time within which

the demand schedule is being considered . Holiday airline travel is highly price elastic. 
Consumers shop vigorously for vacation flights because they have time to plan their 
holiday. Business airline travelers typically have less flexibility in determining their 
schedules. If your business requires a face-  to- face meeting with a client, then the price 
of the ticket is somewhat irrelevant. If gasoline prices increase, there is very little you 
can do in the short run but pay the higher price. However, evidence of commuter 
choices indicates that many use alternative transportation methods after the gasoline 
price spikes. In the long run, higher gasoline prices will lead consumers to change 
their modes of transportation, trading in less efficient vehicles for automobiles with 
higher gas mileage or public transit options where available.
There are two extreme cases of price elasticity of demand. One extreme is the

horizontal demand schedule . This term implies that at a given price, the response 
in the quantity demanded is infinite. This is the demand schedule faced by a perfectly 
competitive firm, because it is a price taker , as in the case of a corn farmer. If the corn

Reading 15 ■ The Firm and Market Structures 72
farmer tried to charge a higher price than the market price, nobody would buy her 
product. On the other hand, the farmer has no incentive to sell at a lower price because 
she can sell all she can produce at the market price. In a perfectly competitive market 
the quantity supplied by an individual firm has a negligible effect on the market price. 
In the case of perfect price elasticity , the measure is εP = ∞.
The other extreme is the vertical demand schedule . The vertical demand schedule 
implies that some fixed quantity is demanded, regardless of price. An example of such 
demand is the diabetic consumer with the need for a certain amount of insulin. If the 
price of insulin goes up, the patient will not consume less of it. The amount desired is 
set by the patient’s medical condition. The measure for perfect price inelasticity  is εP = 0.
The nature of the elasticity calculation and consumer behavior in the marketplace

imply that for virtually any product (excluding cases of perfect elasticity and perfect 
inelasticity), demand is more elastic at higher prices and less elastic (more inelastic) 
at lower prices. For example, at current low prices, the demand for table salt is very 
inelastic. However, if table salt increased in price to hundreds of dollars per ounce, 
consumers would become more responsive to its price changes. Exhibit  3 reports 
several empirical estimates of price elasticity of demand.
Exhibit 3   Empirical Price Elasticities3
Commodity (Good/Service)Price Elasticity of 
Market Demand
Alcoholic beverages consumed at home
  Beer 0.84
  Wine 0.55
  Liquor 0.50
Coffee
  Regular 0.16
  Instant 0.36
Credit charges on bank cards 2.44
Furniture 3.04
Glassware/china 1.20
International air transportation United States/Europe 1.20
Shoes 0.73
Soybean meal 1.65
Tomatoes 2.22
3.1.2  Other Factors Affecting Demand
There are two other important forces that influence shifts in consumer demand. One

influential factor is consumer income and the other is the price of a related product. 
For normal goods, as consumer income increases, the demand increases. The degree to 
which consumers respond to higher incomes by increasing their demand for goods and 
services is referred to as income elasticity of demand. Income elasticity of demand  
3 Various sources, as noted in McGuigan, Moyer, and Harris (2008), p. 95. These are the elasticities with 
respect to the product’s own price; by convention, they are shown here as positive numbers.

Perfect Competition 73
measures the responsiveness of demand to changes in income. The calculation is 
similar to that of price elasticity, with the percentage change in income replacing the 
percentage change in price. Note the new calculation below:
εY = (% change in QD) ÷ (% change in Y)
where εY is income elasticity of demand, QD is the quantity demanded, and Y is con -
sumer income. For normal goods, the measure εY will be a positive value. That is, as 
consumers’ income rises, more of the product is demanded. For products that are 
considered luxury items, the measure of income elasticity will be greater than one. 
There are other goods and services that are considered inferior products. For inferior 
products, as consumer income rises, less of the product is demanded. Inferior prod -
ucts will have negative values for income elasticity. For example, a person on a small 
income may watch television shows, but if this person had more income, she would

prefer going to live concerts and theater performances; in this example, television 
shows would be the inferior good.
As a technical issue, the difference between price elasticity of demand and income 
elasticity of demand is that the demand adjustment for price elasticity represents 
a movement along the demand schedule  because the demand schedule represents 
combinations of price and quantity. The demand adjustment for income elasticity 
represents a shift in the demand curve  because with a higher income one can afford 
to purchase more of the good at any price. For a normal good, an increase in income 
would shift the demand schedule out to the right, away from the origin of the graph, 
and a decrease in income would shift the demand curve to the left, toward the origin.
The final factor influencing demand for a product is the change in price of a related 
product, such as a strong substitute or a complementary product. If a close competitor

in the beverage market lowers its price, consumers will substitute that product for your 
product. Thus, your product’s demand curve will shift to the left, toward the origin 
of the graph. Cross-  price elasticity of demand  is the responsiveness of the demand 
for product A that is associated with the change in price of product B:
εX = (% change in QDA) ÷ (% change in PB)
where εX is cross-  price elasticity of demand, QDA is the quantity demanded of product 
A, and PB is the price of product B.
When the cross-  price elasticity of demand between two products is positive , the 
two products are considered to be substitutes . For example, you may expect to have 
positive cross-  price elasticity between honey and sugar. If the measure of cross-  price 
elasticity is negative , the two products are referred to as complements  of each other. 
For example, if the price of DVDs goes up, you would expect consumers to buy fewer

DVD players. In this case, the cross-  price elasticity of demand would have a negative 
value.
Reviewing cross-  price elasticity values provides a simple test for the degree of 
competition in the market. The more numerous and the closer the substitutes for a 
product, the lower the pricing power of firms selling in that market; the fewer the 
substitutes for a product, the greater the pricing power. One interesting application was 
a US Supreme Court case involving the production and sale of cellophane by DuPont.4 
The court noted that the relevant product market for DuPont’s cellophane was the 
broader flexible packaging materials market. The Supreme Court found the cross-  price 
elasticity of demand between cellophane and other flexible packaging materials to be 
sufficiently high and exonerated DuPont from a charge of monopolizing the market.
Because price elasticity of demand relates changes in price to changes in the

quantity demanded, there must be a logical relationship between marginal revenue 
and price elasticity. Recall that marginal revenue equals the change in total revenue 
4 US v. DuPont , 351 US 377 (1956), as noted in McGuigan, Moyer, and Harris (2008).

Reading 15 ■ The Firm and Market Structures 74
given a change in output or sales. An increase in total revenue results from a decrease 
in price that results in an increase in sales. In order for the increase in the quantity 
demanded to be sufficient to offset the decline in price, the percentage change in 
quantity demanded must be greater than the percentage decrease in price. The rela -
tionship between TR and price elasticity is as follows:
ε
εP
PPP >↑
=1 Dem and is el astic TR andT R
1 Dem and is unita r→↓ ↓→ ↑
yy elastic  no change in TR
1 Dem and is inelasticP
PP→
<< ↑ 0ε→ →↓ → TR andT R ↑↓ P
Total revenue is maximized when marginal revenue is zero. The logic is that as 
long as marginal revenue is positive (i.e., each additional unit sold contributes to 
additional total revenue), total revenue will continue to increase. Only when marginal 
revenue becomes negative will total revenue begin to decline. Therefore, the percentage

decrease in price is greater than the percentage increase in quantity demanded. The 
relationship between MR and price elasticity can be expressed as
MR = P[1 – (1/εP)]
An understanding of price elasticity of demand is an important strategic tool. It 
would be very useful to know in advance what would happen to your firm’s total rev -
enue if you increased the product’s price. If you are operating in the inelastic portion 
of the demand curve, increasing the price of the product will increase total revenue. 
On the other hand, if you are operating in the elastic portion of the product’s demand 
curve, increasing the price will decrease total revenue.
Decision makers can also use the relationship between marginal revenue and price 
elasticity of demand in other ways. For example, suppose you are a farmer considering 
planting soybeans or some other feed crop, such as corn. From Exhibit 3, we know 
that soybean meal’s price elasticity of demand has been estimated to be 1.65. We also

know that the current (August 2010) soybean meal price is $330.14 per metric ton. 
Therefore, by solving the equation above, we find that the expected marginal revenue 
per metric ton of soybean meal is $130.05. Soybeans may prove to be a profitable 
crop for the farmer. However, just a few years earlier, in August of 2006, the price of 
a metric ton of soybean meal was $175.91. Given the crop’s price elasticity of demand, 
the estimated marginal revenue per metric ton was then $69.30. The lower price 
translates into lower marginal revenue and might induce the farmer to plant a more 
profitable feed crop instead.
How do business decision makers decide what level of output to bring to the 
market? To answer that question, the firm must understand its cost of resources, 
its production relations, and its supply function. Once the supply function is well 
defined and understood, it is combined with the demand analysis to determine the 
profit-  maximizing levels of output.

3.1.3  Consumer Surplus: Value Minus Expenditure
To this point, we have discussed the fundamentals of supply and demand curves and 
explained a simple model of how a market can be expected to arrive at an equilibrium 
combination of price and quantity. While it is certainly necessary for the analyst to 
understand the basic workings of the market model, it is also crucial to have a sense 
of why we might care about the nature of the equilibrium. In this section we review 
the concept of consumer surplus , which is helpful in understanding and evaluating 
business pricing strategies. Consumer surplus is defined as the difference between 
the value that a consumer places on the units purchased and the amount of money 
that was required to pay for them. It is a measure of the value gained by the buyer 
from the transaction.

Perfect Competition 75
To get an intuitive feel for the concept of consumer surplus, consider the last 
thing you purchased. Whatever it was, think of how much you actually paid for it. 
Now contrast that price with the maximum amount you would have been willing to 
pay rather than go without the item altogether. If those two numbers are different, 
we say you received some consumer surplus from your purchase. You got a “bargain” 
because you would have been willing to pay more than you had to pay.
Earlier, we referred to the law of demand, which says that as price falls, consumers 
are willing to buy more of the good. This observation translates into a negatively sloped 
demand curve. Alternatively, we could say that the highest price that consumers are 
willing to pay for an additional unit declines as they consume more and more of a 
good. In this way, we can interpret their willingness to pay  as a measure of how much

they value  each additional unit of the good. This is a very important point: In order to 
purchase a unit of some good, consumers must give up something else they value. So 
the price they are willing to pay for an additional unit of a good is a measure of how 
much they value that unit, in terms of the other goods they must sacrifice to consume it.
If demand curves are negatively sloped, it must be because the value of each addi -
tional unit of the good falls as more of the good is consumed. We shall explore this 
concept further below, but for now, it is enough to recognize that the demand curve 
can therefore be considered a marginal value curve , because it shows the highest 
price consumers would be willing to pay for each additional unit. In effect, the demand 
curve is the willingness of consumers to pay for each additional unit.
This interpretation of the demand curve allows us to measure the total value of

consuming any given quantity of a good: It is the sum of all the marginal values of each 
unit consumed, up to and including the last unit. Graphically, this measure translates 
into the area under the consumer’s demand curve, up to and including the last unit 
consumed, as shown in Exhibit 4, where the consumer is choosing to buy Q1 units of 
the good at a price of P1. The marginal value of the Q1th unit is clearly P1, because that 
is the highest price the consumer is willing to pay for that unit. Importantly, however, 
the marginal value of each unit up to  the Q1th is greater than P1.
Exhibit 4   Consumer Surplus 
Price
QuantityP1
Q1Demand Curve (also the
marginal value curve) Consumer Surplus (the 
area of the shaded triangle) 
Note:  Consumer surplus is the area beneath 
the demand curve and above the price paid. 
Because the consumer would have been willing to pay more for each of those 
units than she actually paid ( P1), we can say she received more value than the cost to

her of buying them. This extra value is the buyer’s consumer surplus. The total value  
of quantity Q1 to the buyer is the area of the vertically crosshatched trapezoid in 
Exhibit 4. The total expenditure  is only the area of the rectangle with height P1 and 
base Q1 (bottom section). The total consumer surplus received from buying Q1 units

Reading 15 ■ The Firm and Market Structures 76
at a level price of P1 per unit is the difference between the area under the demand 
curve and the area of the rectangle P1 × Q1. The resulting area is shown as the lightly 
shaded triangle (upper section).
EXAMPLE 1   
Consumer Surplus
A market demand function is given by the equation QD = 180 – 2 P. Find the 
value of consumer surplus if price is equal to 65.
Solution: 
First, input 65 into the demand function to find the quantity demanded at that 
price: QD = 180 – 2(65) = 50. Then, to make drawing the demand curve easier, 
invert the demand function by solving for P in terms of QD: P = 90 – 0.5 QD. 
Note that the price intercept is 90 and the quantity intercept is 180. Draw the 
demand curve:
6590
50QuantityPrice
D
180
Find the area of the triangle above the price of 65 and below the demand curve, 
up to quantity 50: Area = ½ (Base)(Height) = ½ (50)(25) = 625.
3.2 Supply Analysis in Perfectly Competitive Markets

Consider two corn farmers, Mr. Brown and Ms. Lopez. They both have land available 
to them to grow corn and can sell at one price, say 3 currency units per kilogram. They 
will try to produce as much corn as is profitable at that price. If the price is driven up 
to 5 currency units per kilogram by new consumers entering the market—say, ethanol 
producers—Mr. Brown and Ms. Lopez will try to produce more corn. To increase their 
output levels, they may have to use less productive land, increase irrigation, use more 
fertilizer, or all three. Their production costs will likely increase. They will both still 
try to produce as much corn as possible in order to profit at the new, higher price of 
5 currency units per kilogram. Exhibit 5 illustrates this example. Note that the supply 
functions for the individual firms have positive slopes. Thus, as prices increase, the 
firms supply greater quantities of the product.

Perfect Competition 77
Exhibit 5   Firm and Market Supply in Perfect Competition 
Panel B. Lopez
P
Q 4 5Panel C. Industry 
P
Q 25 35Panel A. Brown
P
5
3
Q 5 7Others
Notice that the market supply curve is the sum of the supply curves of the indi -
vidual firms—Brown, Lopez, and others—that make up the market. Assume that the 
supply function for the market can be expressed as a linear relationship, as follows:
QS = 10 + 5 P, or P = –2 + 0.2 QS,
where QS is the quantity supplied and P is the price of the product.
Before we analyze the optimal supply level for the firm, we need to point out that 
economic costs and profits differ from accounting costs and profits in a significant 
way. Economic costs  include all the remuneration needed to keep the productive 
resource in its current employment or to acquire the resource for productive use.
In order to evaluate the remuneration needed to keep the resource in its current 
use and attract new resources for productive use, economists refer to the resource’s

opportunity cost . Opportunity cost is measured by determining the resource’s next 
best opportunity. If a corn farmer could be employed in an alternative position in the 
labor market with an income of 50,000, then the opportunity cost of the farmer’s labor 
is 50,000. Similarly, the farmer’s land and capital could be leased to another farmer or 
sold and reinvested in another type of business. The return foregone by not doing so 
is an opportunity cost. In economic terms, total cost includes the full normal market 
return on all the resources utilized in the business. Economic profit  is the difference 
between TR and total cost (TC). Economic profit differs from accounting profit because 
accounting profit does not include opportunity cost. Accounting profit includes only 
explicit payments to outside providers of resources (e.g. workers, vendors, lenders) 
and depreciation based on the historic cost of physical capital.
3.3 Optimal Price and Output in Perfectly Competitive Markets

Carrying forward our examples from Sections 3.1 and 3.2, we can now combine the 
market supply and demand functions to solve for the equilibrium price and quantity, 
where Q* represents the equilibrium level of both supply and demand.
PQ QP
QQ
Q
QDS
DS=− =− +=
−= −+
=
=25 05 20 2
25 05 20 2
27 07
38 57..
..
.
.*
*
According to the market demand curve, the equilibrium price is
P = 25 – 0.5 Q* = 25 – 0.5(38.57) = 25 – 19.29 = 5.71.

Reading 15 ■ The Firm and Market Structures 78
With many firms in the market and total output in the market of almost 39 units of 
the product, the effective market price would be 5.71. This result becomes the demand 
function for each perfectly competitive firm. Even if a few individual producers could 
expand production, there would not be a noticeable change in the market equilibrium 
price. In fact, if any one firm could change the equilibrium market price, the market 
would not be in perfect competition. Therefore, the demand curve that each per -
fectly competitive firm faces is a horizontal line at the equilibrium price, as shown in 
Exhibit 6, even though the demand curve for the whole market is downward sloping.
Exhibit 6   Individual Firm’s Demand in Perfect Competition 
Quantity Firm’s Demand Price 
5.71
EXAMPLE 2   
Demand Curves in Perfect Competition
Is it possible that the demand schedule faced by Firm A is horizontal while the

demand schedule faced by the market as a whole is downward sloping?
A No, because Firm A can change its output based on demand changes.
B No, because a horizontal demand curve means that elasticity is infinite.
C Yes, because consumers can go to another firm if Firm A charges a higher 
price, and Firm A can sell all it produces at the market price.
Solution: 
C is correct. Firm A cannot charge a higher price and has no incentive to sell 
at a price below the market price.
To analyze the firm’s revenue position, recall that average revenue is equivalent to 
the firm’s demand function. Therefore, the horizontal line that represents the firm’s 
demand curve is the firm’s AR schedule.
Marginal revenue is the incremental increase in total revenue associated with each 
additional unit sold. For every extra unit the firm sells, it receives 5.71. Thus, the firm’s 
MR schedule is also the horizontal line at 5.71. TR is calculated by multiplying AR by

Perfect Competition 79
the quantity of products sold. Total revenue is the area under the AR line at the point 
where the firm produces the output. In the case of perfect competition, the following 
conditions hold for the individual firm:
Price = Average revenue = Marginal revenue
The next step is to develop the firm’s cost functions. The firm knows that it can sell 
the entire product it produces at the market’s equilibrium price. How much should 
it produce? That decision is determined by analysis of the firm’s costs and revenues. 
A corn farmer uses three primary resources: land, labor, and capital. In economics, 
capital is any man-  made aid to production. For the corn farmer, his or her capital 
includes the irrigation system, tractors, harvesters, trucks, grain bins, fertilizer, and 
so forth. The labor includes the farmer, perhaps members of the farmer’s family, and 
hired labor. In the initial stages of production, only the farmer and the farmer’s family

are cultivating the land, with a significant investment in capital. They have a tractor, 
fertilizer, irrigation equipment, grain bins, seed, and a harvester. The investment in 
land and capital is relatively high compared with the labor input. In this production 
phase, the average cost of producing a bushel of corn is high. As they begin to expand 
by adding labor to the collection of expensive land and capital, the average cost of 
producing corn begins to decline—for example, because one tractor can be used more 
intensively to plow a larger amount of land. When the combination of land, labor, 
and capital approaches an efficient range, the average cost of producing a bushel of 
corn declines.
Given a certain level of technology, there is a limit to the increase in productivity. 
Eventually something begins to cause declining marginal productivity. That is, each 
additional unit of input produces a progressively smaller increase in output. This

force is called the law of diminishing returns . This “law” helps define the shape of 
the firm’s cost functions. Average cost and marginal cost will be U-  shaped. Over the 
initial stages of output, average and marginal costs will decline. At some level of out -
put, the law of diminishing returns will overtake the efficiencies in production and 
average and marginal costs will increase.
Average cost (AC) is Total cost (TC) divided by Output ( Q). Therefore,
AC = TC/ Q
Note that we have defined average cost (AC) in terms of total costs. Many authors 
refer to this as “average total cost” to distinguish it from a related concept, “average 
variable cost, ” which omits fixed costs. In the remainder of this reading, average cost 
should be understood to mean average total cost .
Marginal cost (MC) is the change in TC associated with an incremental change 
in output:
MC = ∆TC/∆ Q
By definition, fixed costs do not vary with output, so marginal cost reflects only changes

in variable costs.5 MC declines initially because processes can be made more efficient 
and specialization makes workers more proficient at their tasks. However, at some 
higher level of output, MC begins to increase (e.g., must pay workers a higher wage 
to have them work overtime and, in agriculture, less fertile land must be brought into 
production). MC and AC will be equal at the level of output where AC is minimized. 
This is a mathematical necessity and intuitive. If you employ the least expensive labor 
in the initial phase of production, average and marginal cost will decline. Eventually, 
additional labor will be more costly. For example, if the labor market is at or near full 
employment, in order to attract additional workers, you must pay higher wages than 
5 Readers who are familiar with calculus will recognize that MC is simply the derivative of total cost with 
respect to quantity produced.

Reading 15 ■ The Firm and Market Structures 80
they are currently earning elsewhere. Thus, the additional (marginal) labor is more 
costly, and the higher cost increases the overall average as soon as MC exceeds AC. 
Exhibit 7 illustrates the relationship between AC and MC.
Exhibit 7   Individual Firm’s Short-  Run Cost Schedules 
AC: Average
Total Cost  MC: Short-Run
Marginal Cost Cost per Unit
of Output  
Quantity (firm) 
Now combine the revenue and cost functions from Exhibits 6 and 7. In short-  run 
equilibrium, the perfectly competitive firm can earn an economic profit (or an eco -
nomic loss). In this example, the equilibrium price, 5.71, is higher than the minimum 
AC. The firm will always maximize profit at an output level where MR = MC. Recall 
that in perfect competition, the horizontal demand curve is the marginal revenue 
and average revenue schedules. By setting output at point A in Exhibit 8, where MR 
= MC, the firm will maximize profits. Total revenue is equal to P × Q—in this case,

5.71 times QC. Total cost is equal to QC times the average cost of producing QC, at 
point B in Exhibit 8. The difference between the two areas is economic profit.

Perfect Competition 81
Exhibit 8   Perfectly Competitive Firm’s Short-  Run Equilibrium 
of Output  
Quantity Firm’s Demand
 = AR = MR  AC1 at QC5.71
QCA
B
3.4 Factors Affecting Long-  Run Equilibrium in Perfectly 
Competitive Markets
In the long run, economic profit will attract other entrepreneurs to the market, result -
ing in the production of more output. The aggregate supply will increase, shifting the 
industry supply ( S1) curve to the right, away from the origin of the graph. For a given 
demand curve, this increase in supply at each price level will lower the equilibrium 
price, as shown in Exhibit 9.
Exhibit 9   Perfectly Competitive Market with Increased Supply 
Panel C. Industry 
P
Q 3945Panel A. Brown
P
$5.71
$4.50
Q 8 10SI
SI′
OthersPanel B. Lopez
P
QS2
6 7S2′S1
S1′
In the long run, the perfectly competitive firm will operate at the point where 
marginal cost equals the minimum of average cost, because at that point, entry is no

longer profitable: In equilibrium, price equals not only marginal cost (firm equilib -
rium) but also minimum average cost, so that total revenues equal total costs. This

Reading 15 ■ The Firm and Market Structures 82
result implies that the perfectly competitive firm operates with zero economic profit. 
That is, the firm receives its normal profit (rental cost of capital), which is included 
in its economic costs. Recall that economic profits occur when total revenue exceeds 
total cost (and therefore differ from accounting profits). With low entry cost and 
homogeneous products to sell, the perfectly competitive firm earns zero economic 
profit in the long run.
Exhibit 10 illustrates the long-  run equilibrium position of the perfectly competitive 
firm. Note that total revenue equals price ($4.50) times quantity ( QE) and total cost 
equals average cost ($4.50) times quantity ( QE).
Exhibit 10   Perfectly Competitive Firm’s Long-  Run Equilibrium 
Average
Total Cost  Long-Run
Marginal Cost Dollars per Unit
of Output (price)  
 = AR = MR  $4.50
QE
The long-  run marginal cost schedule is the perfectly competitive firm’s supply curve.

The firm’s demand curve is dictated by the aggregate market’s equilibrium price. The 
basic rule of profit maximization is that MR = MC, as is the case in long-  run equi -
librium. The firm’s demand schedule is the same as the firm’s marginal revenue and 
average revenue. Given its cost of operation, the only decision the perfectly competitive 
firm faces is how much to produce. The answer is the level of output that maximizes 
its return, and that level is where MR = MC. The demand curve is perfectly elastic. 
Of course, the firm constantly tries to find ways to lower its cost in the long run.

Monopolistic Competition 83
SCHUMPETER ON INNOVATION AND PERFECT 
COMPETITION 
The Austrian-  American economist Joseph A. Schumpeter6 pointed out that technical 
change in economics can happen in two main ways:
1 Innovation of process: a new, more efficient way to produce an existing good or 
service.
2 Innovation of product: a new product altogether or an innovation upon an exist -
ing product.
Innovation of process is related to production methods. For example, instead of 
mixing cement by hand, since the invention of the electric engine it has been possible 
to use electric mixers. A more recent innovation has been to use the internet to provide 
technical support to personal computer users: A technician can remotely log on to the 
customer’s PC and fix problems instead of providing instructions over the phone. The 
result is likely the same, but the process is more efficient.
Innovation of product is related to the product itself. mP3 players, smart phones,

robot surgery, and GPS vehicle monitoring have existed only for a few years. They are 
new products and services. While portable music players existed before the mP3 player, 
no similar service existed before GPS monitoring of personal vehicles and freight trucks 
was invented.
How does the reality of continuous innovation of product and process, which is a 
characteristic of modern economies, fit into the ideal model of perfect competition, 
where the product is made by a huge number of tiny, anonymous suppliers? This seems 
a contradiction because the tiny suppliers cannot all be able to invent new products—
and indeed, the markets for portable music players and smart phones do not look like 
perfect competition.
Schumpeter suggested that perfect competition is more of a long-  run type of market. 
In the short run, a company develops a new process or product and is the only one to take 
advantage of the innovation. This company likely will have high profits and will outpace

any competitors. A second stage is what Schumpeter called the swarming (as when a 
group of bees leaves a hive to follow a queen): In this case, some entrepreneurs notice 
the innovation and follow the innovator through imitation. Some of them will fail, while 
others will succeed and possibly be more successful than the initial innovator. The third 
stage occurs when the new technology is no longer new because everyone has imitated 
it. At this point, no economic profits are realized, because the new process or product 
is no longer a competitive advantage, in the sense that everyone has it—which is when 
perfect competition prevails and we have long-  run equilibrium until a new innovation 
of process or product is introduced.
MONOPOLISTIC COMPETITION
Early in the 20th century, economists began to realize that most markets did not oper -
ate under the conditions of perfect competition.7 Many market structures exhibited

characteristics of strong competitive forces; however, other distinct non-  competitive 
factors played important roles in the market. As the name implies, monopolistic com -
petition is a hybrid market. The most distinctive factor in monopolistic competition is 
product differentiation . Recall the characteristics from Exhibit 1:
1 There are a large number of potential buyers and sellers.4
6 See part 2 of Schumpeter (1942) for the famous “creative destruction” process.
7 Chamberlin (1933).

Reading 15 ■ The Firm and Market Structures 84
2 The products offered by each seller are close substitutes for the products offered 
by other firms, and each firm tries to make its product look different.
3 Entry into and exit from the market are possible with fairly low costs.
4 Firms have some pricing power.
5 Suppliers differentiate their products through advertising and other non-  price 
While the market is made up of many firms that compose the product group, 
each producer attempts to distinguish its product from that of the others. Product 
differentiation is accomplished in a variety of ways. For example, consider the wide 
variety of communication devices available today. Decades ago, when each commu -
nication market was controlled by a regulated single seller (the telephone company), 
all telephones were alike. In the deregulated market of today, the variety of physical 
styles and colors is extensive. All versions accomplish many of the same tasks.

The communication device manufacturers and providers differentiate their prod -
ucts with different colors, styles, networks, bundled applications, conditional con -
tracts, functionality, and more. Advertising is usually the avenue pursued to convince 
consumers there is a difference between the goods in the product group. Successful 
advertising and trademark branding result in customer loyalty. A good example is 
the brand loyalty associated with Harley-  Davidson motorcycles. Harley-  Davidson’s 
customers believe that their motorcycles are truly different from and better than all 
other motorcycles. The same kind of brand loyalty exists for many fashion creations 
and cosmetics.
The extent to which the producer is successful in product differentiation deter -
mines pricing power in the market. Very successful differentiation results in a market 
structure that resembles the single-  seller market (monopoly). However, because there

are relatively low entry and exit costs, competition will, in the long run, drive prices 
and revenues down toward an equilibrium similar to perfect competition. Thus, 
the hybrid market displays characteristics found in both perfectly competitive and 
monopoly markets.
4.1 Demand Analysis in Monopolistically Competitive Markets
Because each good sold in the product group is somewhat different from the others, 
the demand curve for each firm in the monopolistic competition market structure is 
downward sloping to the right. Price and the quantity demanded are negatively related. 
Lowering the price will increase the quantity demanded, and raising the price will 
decrease the quantity demanded. There will be ranges of prices within which demand 
is elastic and (lower) prices at which demand is inelastic. Exhibit 11 illustrates the 
demand, marginal revenue, and cost structures facing a monopolistically competitive 
firm in the short run.

Monopolistic Competition 85
Exhibit 11   Short-  Run Equilibrium in Monopolistic Competition 
Marginal Cost Price
Quantity MC = MR  
D MR  P1
C1
Q1
In the short run, the profit-  maximizing choice is the level of output where MR = 
MC. Because the product is somewhat different from that of the competitors, the firm 
can charge the price determined by the demand curve. Therefore, in Exhibit 11, Q1 
is the ideal level of output and P1 is the price consumers are willing to pay to acquire 
that quantity. Total revenue is the area of the rectangle P1 × Q1.
4.2 Supply Analysis in Monopolistically Competitive Markets
In perfect competition, the firm’s supply schedule is represented by the marginal 
cost schedule. In monopolistic competition, there is no well-  defined supply function. 
The information used to determine the appropriate level of output is based on the 
intersection of MC and MR. However, the price that will be charged is based on the

market demand schedule. The firm’s supply curve should measure the quantity the 
firm is willing to supply at various prices. That information is not represented by 
either marginal cost or average cost.
4.3 Optimal Price and Output in Monopolistically Competitive 
Markets
As seen in Section 4.1, in the short run, the profit-  maximizing choice is the level 
of output where MR = MC and total revenue is the area of the rectangle P1 × Q1 in 
Exhibit 11.
The average cost of producing Q1 units of the product is C1, and the total cost is 
the area of the rectangle C1 × Q1. The difference between TR and TC is economic 
profit. The profit relationship is described as
π = TR – TC
where π is total profit, TR is total revenue, and TC is total cost.
THE BENEFITS OF IMPERFECT COMPETITION
Is monopolistic competition indeed imperfect—that is, is it a bad thing? At first, one would 
say that it is an inefficient market structure because prices are higher and the quantity

supplied is less than in perfect competition. At the same time, in the real world, we see

Reading 15 ■ The Firm and Market Structures 86
more markets characterized by monopolistic competition than markets meeting the strict 
conditions of perfect competition. If monopolistic competition were that inefficient, one 
wonders, why would it be so common?
A part of the explanation goes back to Schumpeter. Firms try to differentiate their 
products to meet the needs of customers. Differentiation provides a profit incentive 
to innovate, experiment with new products and services, and potentially improve the 
standard of living.
moreover, because each customer has tastes and preferences that are a bit different, 
slight variations of each good or service are likely to capture the niche of the market 
that prefers them. An example is the market for candy, where one can find chocolate, 
liquorice, mint, fruit, and many other flavors.
A further reason why monopolistic competition may be good is that people like variety.

Traditional economic theories of international trade suggested that countries should buy 
products from other countries that they cannot produce domestically. Therefore, Norway 
should buy bananas from a tropical country and sell crude oil in exchange. But this is 
not the only kind of exchange that happens in reality: For example, Germany imports 
Honda, Subaru, and Toyota cars from Japan and sells Volkswagen, Porsche, mercedes, 
and B mW cars to Japan. In theory, this should not occur because each of the countries 
produces good cars domestically and does not need to import them. The truth, however 
(see, for example, Krugman 1989), is that consumers in both countries enjoy variety. 
Some Japanese drivers prefer to be at the steering wheel of a B mW; others like Hondas, 
and the same happens in Germany. Variety and product differentiation, therefore, are 
not necessarily bad things.
4.4 Factors Affecting Long-  Run Equilibrium in Monopolistically 

Because TC includes all costs associated with production, including opportunity cost, 
economic profit is a signal to the market, and that signal will attract more competition. 
Just as with the perfectly competitive market structure, with relatively low entry costs, 
more firms will enter the market and lure some customers away from the firm making 
an economic profit. The loss of customers to new entrant firms will drive down the 
demand for all firms producing similar products. In the long run for the monopo -
listically competitive firm, economic profit will fall to zero. Exhibit 12 illustrates the 
condition of long-  run equilibrium for monopolistic competition.
Exhibit 12   Long-  Run Equilibrium in Monopolistic Competition 
AC: Long-Run
Average Cost  MC: Long-Run
Quantity MR  C1 = P1
Q1 Q2

Oligopoly 87
In long-  run equilibrium, output is still optimal at the level where MR = MC, which 
is Q1 in Exhibit 12. Again, the price consumers are willing to pay for any amount of 
the product is determined from the demand curve. That price is P1 for the quantity 
Q1 in Exhibit 12, and total revenue is the area of the rectangle P1 × Q1. Notice that 
unlike long-  run equilibrium in perfect competition, in the market of monopolistic 
competition, the equilibrium position is at a higher level of average cost than the 
level of output that minimizes average cost. Average cost does not reach its minimum 
until output level Q2 is achieved. Total cost in this long-  run equilibrium position is 
the area of the rectangle C1 × Q1. Economic profit is total revenue minus total cost. 
In Exhibit 12, economic profit is zero because total revenue equals total cost: P1 × 
Q1 = C1 × Q1.
In the hybrid market of monopolistic competition, zero economic profit in long-  run

equilibrium resembles perfect competition. However, the long-  run level of output, Q1, 
is less than Q2, which corresponds to the minimum average cost of production and 
would be the long run level of output in a perfectly competitive market. In addition, 
the economic cost in monopolistic competition includes some cost associated with 
product differentiation, such as advertising. In perfect competition, there are no costs 
associated with advertising or marketing because all products are homogeneous. Prices 
are lower, but consumers may have little variety.
OLIGOPOLY
An oligopoly market structure is characterized by only a few firms doing business 
in a relevant market. The products must all be similar and, to a great extent, be 
substitutes for one another. In some oligopoly markets, the goods or services may 
be differentiated by marketing and strong brand recognition, as in the markets for 
breakfast cereals and for bottled or canned beverages. Other examples of oligopoly

markets are made up of homogeneous products with little or no attempt at product 
differentiation, such as petroleum and cement. The most distinctive characteristic of 
oligopoly markets is the small number of firms that dominate the market . There are so 
few firms in the relevant market that their pricing decisions are interdependent . That 
is, each firm’s pricing decision is based on the expected retaliation by the other firms. 
Recall from Exhibit 1 the characteristics of oligopoly markets:
1 There are a small number of potential sellers.
2 The products offered by each seller are close substitutes for the products 
offered by other firms and may be differentiated by brand or homogeneous and 
unbranded.
3 Entry into the market is difficult, with fairly high costs and significant barriers 
to competition.
4 Firms typically have substantial pricing power.
5 Products are often highly differentiated through marketing, features, and other 
non-  price strategies.

Because there are so few firms, each firm can have some degree of pricing power, 
which can result in substantial profits. Another by-  product of the oligopoly market 
structure is the attractiveness of price collusion. Even without price collusion, a 
dominant firm may easily become the price maker in the market. Oligopoly markets 
without collusion typically have the most sophisticated pricing strategies. Examples 
of non-  colluding oligopolies include the US tobacco market and the Thai beer market. 5

Reading 15 ■ The Firm and Market Structures 88
In 2004, four firms controlled 99 percent of the US tobacco industry.8 Brands owned 
by Singha Co. and by ThaiBev controlled over 90 percent of the Thai beer market in 
2009. (This situation is expected to change soon, as the Association of Southeast Asian 
Nations trade agreement will open the doors to competition from other ASEAN pro -
ducers.) Perhaps the most well-  known oligopoly market with collusion is the OPEC 
cartel, which seeks to control prices in the petroleum market by fostering agreements 
among oil-  producing countries.
5.1 Demand Analysis and Pricing Strategies in Oligopoly 
Markets
Oligopoly markets’ demand curves depend on the degree of pricing interdependence. 
In a market where collusion is present, the aggregate market demand curve is divided 
up by the individual production participants. Under non-  colluding market conditions, 
each firm faces an individual demand curve. Furthermore, non-  colluding oligopoly

market demand characteristics depend on the pricing strategies adopted by the par -
ticipating firms. There are three basic pricing strategies: pricing interdependence, the 
Cournot assumption, and the Nash equilibrium.
The first pricing strategy is to assume pricing interdependence among the firms in 
the oligopoly. A good example of this situation is any market where there are “price 
wars, ” such as the commercial airline industry. For example, flying out of the Atlanta, 
Georgia, hub, Delta Air Lines and AirTran Airways jointly serve several cities. AirTran 
is a low-  cost carrier and typically offers lower fares to destinations out of Atlanta. 
Delta tends to match the lower fares for those cities also served by AirTran when the 
departure and arrival times are similar to its own. However, when Delta offers service 
to the same cities at different time slots, Delta’s ticket prices are higher.
The most common pricing strategy assumption in these price war markets is that

competitors will match a price reduction and ignore a price increase. The logic is 
that by lowering its price to match a competitor’s price reduction, the firm will not 
experience a reduction in customer demand. Conversely, by not matching the price 
increase, the firm stands to attract customers away from the firm that raised its prices. 
The oligopolist’s demand relationship must represent the potential increase in market 
share when rivals’ price increases are not matched and no significant change in market 
share when rivals’ price decreases are matched.
Given a prevailing price, the price elasticity of demand will be much greater if the 
price is increased and less if the price is decreased. The firm’s customers are more 
responsive to price increases because its rivals have lower prices. Alternatively, the 
firm’s customers are less responsive to price decreases because its rivals will match 
its price change.

This implies that the oligopolistic firm faces two different demand structures, one 
associated with price increases and another relating to price reductions. Each demand 
function will have its own marginal revenue structure as well. Consider the demand and 
marginal revenue functions in Exhibit 13(A). The functions DP↑ and MRP↑ represent 
the demand and marginal revenue schedules associated with higher prices, while the 
functions DP↓ and MRP↓ represent the lower prices’ demand and marginal revenue 
schedules. The two demand schedules intersect at the prevailing price (i.e., the price 
where price increase and price decrease are both equal to zero).
8 These examples are based on “Industry Surveys, ” Net Advantage Database, Standard & Poor’s; and 
Market Share Reports, Gale Research, annual issues, as noted in McGuigan, Moyer, and Harris (2016).

Oligopoly 89
Exhibit 13(A)   Kinked Demand Curve in Oligopoly Market 
DP↑ 
MRP↑ MCPrice
Quantity MRP↓ DP↓P
Q
This oligopolistic pricing strategy results in a kinked demand curve, with the two 
segments representing the different competitor reactions to price changes. The kink 
in the demand curve also yields a discontinuous marginal revenue structure, with one 
part associated with the price increase segment of demand and the other relating to 
the price decrease segment. Therefore, the firm’s overall demand equals the relevant 
portion of DP↑ and the relevant portion of DP↓. Exhibit 13(B) represents the firm’s new 
demand and marginal revenue schedules. The firm’s demand schedule in Exhibit 13(B) 
is segment DP↑ and DP↓, where overall demand D = DP↑ + DP↓.
Exhibit 13(B)   Kinked Demand Curve in Oligopoly Market 
MC3
MC2
MC1Price
Quantity MRP↓MR
DP↓DP↑Kinked at
Prevailing Price
P
Q
Notice in Exhibit 13(B) that a wide variety of cost structures are consistent with

the prevailing price. If the firm has relatively low marginal costs, MC1, the profit-  
maximizing pricing rule established earlier, MR = MC, still holds for the oligopoly firm. 
Marginal cost can rise to MC2 and MC3 before the firm’s profitability is challenged. If 
the marginal cost curve MC2 passes through the gap in marginal revenue, the most 
profitable price and output combination remains unchanged at the prevailing price 
and original level of output.

Reading 15 ■ The Firm and Market Structures 90
Criticism of the kinked demand curve analysis focuses on its inability to determine 
what the prevailing price is from the outset. The kinked demand curve analysis does 
help explain why stable prices have been observed in oligopoly markets and is therefore 
a useful tool for analyzing such markets. However, because it cannot determine the 
original prevailing price, it is considered an incomplete pricing analysis.
The second pricing strategy was first developed by French economist Augustin 
Cournot in 1838. In the Cournot assumption , each firm determines its profit-  
maximizing production level by assuming that the other firms’ output will not change. 
This assumption simplifies pricing strategy because there is no need to guess what 
the other firm will do to retaliate. It also provides a useful approach to analyzing real-  
world behavior in oligopoly markets. Take the most basic oligopoly market situation,

a two-  firm duopoly market.9 In equilibrium, neither firm has an incentive to change 
output, given the other firm’s production level. Each firm attempts to maximize its 
own profits under the assumption that the other firm will continue producing the same 
level of output in the future. The Cournot strategy assumes that this pattern continues 
until each firm reaches its long-  run equilibrium position. In long-  run equilibrium, 
output and price are stable: There is no change in price or output that will increase 
profits for either firm.
Consider this example of a duopoly market. Assume that the aggregate market 
demand has been estimated to be
QD = 450 – P
The supply function is represented by constant marginal cost MC = 30.
The Cournot strategy’s solution can be found by setting QD = q1 + q2, where q1 
and q2 represent the output levels of the two firms. Each firm seeks to maximize 
profit, and each firm believes the other firm will not change output as it changes its

own output (Cournot’s assumption). The firm will maximize profit where MR = MC. 
Rearranging the aggregate demand function in terms of price, we get:
P = 450 – QD = 450 – q1 – q2, and MC = 30
Total revenue for each of the two firms is found by multiplying price and quantity:
TR  45  45  and
TR  45 11 12 11 12
22== −− () =− −
== −Pq qq qq qq q
Pq q00
012,
112 22 21  45 − () =− − qq qq qq 022
Marginal revenue is defined as the change in total revenue, given a change in sales 
(q1 or q2).10 For the profit-  maximizing output, set MR = MC, or
450 – 2 q1 – q2 = 30 
and
450 – q1 – 2q2 = 30
Find the simultaneous equilibrium for the two firms by solving the two equations 
with two unknowns:
450 – 2 q1 – q2 = 450 – q1 – 2q2
9 The smallest possible oligopoly market is a duopoly, which is made up of only two sellers.
10 The marginal revenue formulas can be obtained using the technique introduced in Section 3.1. For the

market demand function, total revenue is P × Q = 450 Q – Q2 and our technique yields MR = ΔTR/Δ Q = 
450 – 2 Q. For the individual firms in the Cournot duopoly, MR1 = ∆TR1/∆q1 = 450 – 2 q1 – q2, and MR2 
= ∆TR2/∆q2 = 450 – q1 – 2q2. Each of these marginal revenue formulas is, of course, the derivative of the 
relevant total revenue formula with respect to the relevant quantity.

Oligopoly 91
Because q2 = q1 under Cournot’s assumption, insert this solution into the demand 
function and solve as
450 – 2 q1 – q1 = 450 – 3 q1 = 30
Therefore, q1 = 140, q2 = 140, and Q = 280.
The price is P = 450 – 280 = 170.
In the Cournot strategic pricing solution, the market equilibrium price will be 
170 and the aggregate output will be 280 units. This result, known as the Cournot 
equilibrium, differs from the perfectly competitive market equilibrium because the 
perfectly competitive price will be lower and the perfectly competitive output will be 
higher. In general, non-  competitive markets have higher prices and lower levels of 
output in equilibrium when compared with perfect competition. In competition, the 
equilibrium is reached where price equals marginal cost.
PC = MRC = MC, so 450 – Q = 30 
where PC is the competitive firm’s equilibrium price.
Q = 420, and PC = 30.
Exhibit 14 describes the oligopoly, competitive, and monopoly market equilibrium

positions, where PM is the monopoly optimum price, PC is the competitive price, and 
PCournot  is the oligopoly price under the Cournot assumption.
Exhibit 14   Cournot Equilibrium in Duopoly Market 
DemandPrice
Quantity PM
PCournot
PC
210 280 420240
170
30
In the later discussion regarding monopoly market structure, equilibrium will be 
established where MR = MC. That solution is also shown in Exhibit 14. The monop -
oly firm’s demand schedule is the aggregate market demand schedule. Therefore, the 
solution is
MR = MC
From Footnote 10, MR = 450 – 2 Q; therefore,
450 – 2 Q = 30   and    Q = 210
From the aggregate demand function, solve for price:
PM = 450 – 210 = 240
Note that the Cournot solution falls between the competitive equilibrium and the 
monopoly solution.

Reading 15 ■ The Firm and Market Structures 92
It can be shown that as the number of firms increases from two to three, from 
three to four, and so on, the output and price equilibrium positions move toward the 
competitive equilibrium solution. This result has historically been the theoretical basis 
for the antitrust policies established in the United States.
The third pricing strategy is attributed to one of the 1994 Nobel Prize winners, John 
Nash, who first developed the general concepts. In the previous analysis, the concept 
of market equilibrium occurs when firms are achieving their optimum remuneration 
under the circumstances they face. In this optimum environment, the firm has no 
motive to change price or output level. Existing firms are earning a normal return 
(zero economic profit), leaving no motive for entry to or exit from the market. All 
firms in the market are producing at the output level where price equals the average 
cost of production.

In game theory  (the set of tools that decision makers use to consider responses by 
rival decision makers), the Nash equilibrium  is present when two or more participants 
in a non-  cooperative game have no incentive to deviate from their respective equilib -
rium strategies after they have considered and anticipated their opponent’s rational 
choices or strategies. In the context of oligopoly markets, the Nash equilibrium is an 
equilibrium defined by the characteristic that none of the oligopolists can increase 
its profits by unilaterally changing its pricing strategy. The assumption is made that 
each participating firm does the best it can, given the reactions of its rivals. Each 
firm anticipates that the other firms will react to any change made by competitors by 
doing the best they can under the altered circumstances. The firms in the oligopoly 
market have interdependent actions. The actions are non-  cooperative, with each firm

making decisions that maximize its own profits. The firms do not collude in an effort 
to maximize joint profits. The equilibrium is reached when all firms are doing the 
best they can, given the actions of their rivals.
Exhibit 15 illustrates the duopoly result from the Nash equilibrium. Assume there 
are two firms in the market, ArcCo and BatCo. ArcCo and BatCo can charge high 
prices or low prices for the product. The market outcomes are shown in Exhibit 15.
Exhibit 15   Nash Equilibrium in Duopoly Market 
ArcCo – Low Price
50
7080
0
BatCo – Low Price BatCo – High PriceArcCo – Low Price
ArcCo – High Price
300
350500
300
BatCo – Low Price BatCo – High PriceArcCo – High Price
For example, the top left solution indicates that when both ArcCo and BatCo offer 
the product at low prices, ArcCo earns a profit of 50 and BatCo earns 70. The top right 
solution shows that if ArcCo offers the product at a low price, BatCo earns zero profits.

The solution with the maximum joint profits is the lower right equilibrium, where 
both firms charge high prices for the product. Joint profits are 800 in this solution.

Oligopoly 93
However, the Nash equilibrium requires that each firm behaves in its own best 
interest. BatCo can improve its position by offering the product at low prices when 
ArcCo is charging high prices. In the lower left solution, BatCo maximizes its profits 
at 350. While ArcCo can earn 500 in its best solution, it can do so only if BatCo also 
agrees to charge high prices. This option is clearly not in BatCo’s best interest because 
it can increase its return from 300 to 350 by charging lower prices.
This scenario brings up the possibility of collusion. If ArcCo agrees to share at 
least 51 of its 500 when both companies are charging high prices, BatCo should also 
be willing to charge high prices. While, in general, such collusion is unlawful in most 
countries, it remains a tempting alternative. Clearly, conditions in oligopolistic indus -
tries encourage collusion, with a small number of competitors and interdependent

pricing behavior. Collusion is motivated by several factors: increased profits, reduced 
cash flow uncertainty, and improved opportunities to construct barriers to entry.
When collusive agreements are made openly and formally, the firms involved 
are called a cartel . In some cases, collusion is successful; other times, the forces of 
competition overpower collusive behavior. There are six major factors that affect the 
chances of successful collusion.11
1 The number and size distribution of sellers.  Successful collusion is more likely 
if the number of firms is small or if one firm is dominant. Collusion becomes 
more difficult as the number of firms increases or if the few firms have similar 
market shares. When the firms have similar market shares, the competitive 
forces tend to overshadow the benefits of collusion.
2 The similarity of the products.  When the products are homogeneous, collusion 
is more successful. The more differentiated the products, the less likely it is that

collusion will succeed.
3 Cost structure.  The more similar the firms’ cost structures, the more likely it is 
that collusion will succeed.
4 Order size and frequency.  Successful collusion is more likely when orders are 
frequent, received on a regular basis, and relatively small. Frequent small 
orders, received regularly, diminish the opportunities and rewards for cheating 
on the collusive agreement.
5 The strength and severity of retaliation.  Oligopolists will be less likely to break 
the collusive agreement if the threat of retaliation by the other firms in the mar -
ket is severe.
6 The degree of external competition.  The main reason to enter into the formal 
collusion is to increase overall profitability of the market, and rising profits 
attract competition. For example, the average extraction cost of a barrel of 
crude oil from the Persian Gulf is $3, while the average cost from the Alaskan 
fields is $30. It is more likely that crude oil producers in the Persian Gulf will

successfully collude because of the similarity in their cost structures. If OPEC 
had held crude oil prices down below $30 per barrel, there would not have 
been a viable economic argument to explore oil fields in Alaska. Extracting 
petroleum from Canadian oil sands becomes economically attractive only at 
prices above $50 per barrel. OPEC’s successful cartel raised crude oil prices to 
the point where outside sources became economically possible and in doing so 
increased the competition the cartel faces.
There are other possible oligopoly strategies that are associated with decision 
making based on game theory. The Cournot equilibrium and the Nash equilibrium are 
examples of specific strategic games. A strategic game is any interdependent behavioral 
11 McGuigan, Moyer, and Harris (2016).

Reading 15 ■ The Firm and Market Structures 94
choice employed by individuals or groups that share a common goal (e.g., military 
units, sports teams, or business decision makers). Another prominent decision-  making 
strategy in oligopolistic markets is the first-  mover advantage in the Stackelberg model , 
named after the economist who first conceptualized the strategy.12 The important 
difference between the Cournot model and the Stackelberg model is that Cournot 
assumes that in a duopoly market, decision making is simultaneous, while Stackelberg 
assumes that decisions are made sequentially. In the Stackelberg model, the leader 
firm chooses its output first and then the follower firm chooses after observing the 
leader’s output. It can be shown that the leader firm has a distinct advantage, being 
a first mover.13 In the Stackelberg game, the leader can aggressively overproduce to 
force the follower to scale back its production or even punish or eliminate the weaker

opponent. This approach is sometimes referred to as a “top dog” strategy.14 The leader 
earns more than in Cournot’s simultaneous game, while the follower earns less. Many 
other strategic games are possible in oligopoly markets. The important conclusion is 
that the optimal strategy of the firm depends on what its adversary does. The price 
and marginal revenue the firm receives for its product depend on both its decisions 
and its adversary’s decisions.
5.2 Supply Analysis in Oligopoly Markets
As in monopolistic competition, the oligopolist does not have a well-  defined supply 
function. That is, there is no way to determine the oligopolist’s optimal levels of output 
and price independent of demand conditions and competitor’s strategies. However, 
the oligopolist still has a cost function that determines the optimal level of supply. 
Therefore, the profit-  maximizing rule established earlier is still valid: The level of

output that maximizes profit is where MR = MC. The price to charge is determined 
by what price consumers are willing to pay for that quantity of the product. Therefore, 
the equilibrium price comes from the demand curve, while the output level comes 
from the relationship between marginal revenue and marginal cost.
Consider an oligopoly market in which one of the firms is dominant and thus able 
to be the price leader. Dominant firms generally have 40 percent or greater market 
share. When one firm dominates an oligopoly market, it does so because it has greater 
capacity, has a lower cost structure, was first to market, or has greater customer loyalty 
than other firms in the market.
Assuming there is no collusion, the dominant firm becomes the price maker, and 
therefore its actions are similar to monopoly behavior in its segment of the market. 
The other firms in the market follow the pricing patterns of the dominant firm.

Why wouldn’t the price followers attempt to gain market share by undercutting the 
dominant firm’s price? The most common explanation is that the dominant firm’s 
supremacy often stems from a lower cost of production. Usually, the price followers 
would rather charge a price that is even higher than the dominant firm’s price choice. 
If they attempt to undercut the dominant firm, the followers risk a price war with a 
lower-  cost producer that can threaten their survival. Some believe that one explanation 
for the price leadership position of the dominant firm is simply convenience. Only 
one firm has to make the pricing decisions, and the others can simply follow its lead.
12 Von Stackelberg (1952). See also Kelly (2011) for a comparison between the Cournot and Stackelberg 
equilibriums.
13 Nicholson and Snyder (2016).
14 Fudenberg and Tirole (1984).

Oligopoly 95
Exhibit 16 establishes the dominant firm’s pricing decision. The dominant firm’s 
demand schedule, DL, is a substantial share of the total market demand, DT. The low-  
cost position of the dominant firm is represented by its marginal cost, MCL. The sum 
of the marginal costs of the price followers is established as ΣMCF and represents a 
higher cost of production than that of the price leader.
Exhibit 16   Dominant Oligopolist’s Price Leadership 
ΣMCF Price
Quantity MRL  DLDTMCL  PL
QL QT
There is an important reason why the total demand curve and the leader demand 
curve are not parallel in Exhibit 16: Remember that the leader is the low-  cost producer. 
Therefore, as price decreases, fewer of the smaller suppliers will be able to profitably 
remain in the market, and several will exit because they do not want to sell below cost. 
Therefore, the leader will have a larger market share as P decreases, which implies

that QL increases at a low price, exactly as shown by a steeper DT in the diagram.
The price leader identifies its profit-  maximizing output where MRL = MCL, at 
output QL. This is the quantity it wants to supply; however, the price it will charge is 
determined by its segment of the total demand function, DL. At price PL, the dominant 
firm will supply quantity QL of total demand, DT. The price followers will supply the 
difference to the market, ( QT – QL) = QF. Therefore, neither the dominant firm nor 
the follower firms have a single functional relationship that determines the quantity 
supplied at various prices.
5.3 Optimal Price and Output in Oligopoly Markets
From the discussion above, it is clear that there is no single optimum price and output 
analysis that fits all oligopoly market situations. The interdependence among the few 
firms that make up the oligopoly market provides a complex set of pricing alternatives,

depending on the circumstances in each market. In the case of the kinked demand 
curve, the optimum price is the prevailing price at the kink in the demand function. 
However, as previously noted, the kinked demand curve analysis does not provide 
insight into what established the prevailing price in the first place.
Perhaps the case of the dominant firm, with the other firms following the price 
leader, is the most obvious. In that case, the optimal price is determined at the output 
level where MR = MC. The profit-  maximizing price is then determined by the output 
position of the segment of the demand function faced by the dominant firm. The price

Reading 15 ■ The Firm and Market Structures 96
followers have little incentive to change the leader’s price. In the case of the Cournot 
assumption, each firm assumes that the other firms will not alter their output following 
the dominant firm’s selection of its price and output level.
Therefore, again, the optimum price is determined by the output level where MR 
= MC. In the case of the Nash equilibrium, each firm will react to the circumstances 
it faces, maximizing its own profit. These adjustments continue until there are stable 
prices and levels of output. Because of the interdependence, there is no certainty as 
to the individual firm’s price and output level.
5.4 Factors Affecting Long-  Run Equilibrium in Oligopoly 
Markets
Long-  run economic profits are possible for firms operating in oligopoly markets. 
However, history has shown that, over time, the market share of the dominant firm 
declines. Profits attract entry by other firms into the oligopoly market. Over time,

the marginal costs of the entrant firms decrease because they adopt more efficient 
production techniques, the dominant firm’s demand and marginal revenue shrink, 
and the profitability of the dominant firm declines. In the early 1900s, J.P . Morgan, 
Elbert Gary, Andrew Carnegie, and Charles M. Schwab created the United States 
Steel Corporation (US Steel). When it was first formed in 1901, US Steel controlled 
66 percent of the market. By 1920, US Steel’s market share had declined to 46 percent, 
and by 1925 its market share was 42 percent.
In the long run, optimal pricing strategy must include the reactions of rival firms. 
History has proven that pricing wars should be avoided because any gains in market 
share are temporary. Decreasing prices to drive competitors away lowers total rev -
enue to all participants in the oligopoly market. Innovation may be a way—though 
sometimes an uneconomical one—to maintain market leadership.
OLIGOPOLIES: APPEARANCE VERSUS BEHAVIOR

When is an oligopoly not an oligopoly? There are two extreme cases of this situation. A 
normal oligopoly has a few firms producing a differentiated good, and this differentiation 
gives them pricing power.
At one end of the spectrum, we have the oligopoly with a credible threat of entry. In 
practice, if the oligopolists are producing a good or service that can be easily replicated, 
has limited economies of scale, and is not protected by brand recognition or patents, 
they will not be able to charge high prices. The easier it is for a new supplier to enter 
the market, the lower the margins. In practice, this oligopoly will behave very much like 
a perfectly competitive market.
At the opposite end of the spectrum, we have the case of the cartel. Here, the oligopo -
lists collude and act as if they were a single firm. In practice, a very effective cartel enacts 
a cooperative strategy. As shown in Section 5.1, instead of going to a Nash equilibrium,

the cartel participants go to the more lucrative (for them) cooperative equilibrium.
A cartel may be explicit (that is, based on a contract) or implicit (based on signals). 
An example of signals in a duopoly would be that one of the firms reduces its prices and 
the other does not. Because the firm not cutting prices refuses to start a price war, the 
firm that cut prices may interpret this signal as a “suggestion” to raise prices to a higher 
level than before, so that profits may increase for both.

Monopoly 97
MONOPOLY
Monopoly market structure is at the opposite end of the spectrum from perfect com -
petition. For various reasons, there are significant barriers to entry such that a single 
firm produces a highly specialized product and faces no threat of competition. There 
are no good substitutes for the product in the relevant market, and the market demand 
function is the same as the individual firm’s demand schedule. The distinguishing 
characteristics of monopoly are that a single firm represents the market and significant 
barriers to entry exist . Exhibit 1 identified the characteristics of monopoly markets:
1 There is a single seller of a highly differentiated product.
2 The product offered by the seller has no close substitute.
3 Entry into the market is very difficult, with high costs and significant barriers to 
competition.
4 The firm has considerable pricing power.
5 The product is differentiated through non-  price strategies such as advertising.

Monopoly markets are unusual. With a single seller dominating the market, power 
over price decisions is significant. For a single seller to achieve this power, there must 
be factors that allow the monopoly to exist. One obvious source of monopoly power 
would be a patent or copyright that prevents other firms from entering the market. 
Patent and copyright laws exist to reward intellectual capital and investment in research 
and development. In so doing, they provide significant barriers to entry.
Another possible source of market power is control over critical resources used 
for production. One example is De Beers Consolidated Mines Limited. De Beers 
owned or controlled all diamond mining operations in South Africa and established 
pricing agreements with other important diamond producers. In doing so, De Beers 
was able to control the prices for cut diamonds for decades. Technically, De Beers was 
a near-  monopoly dominant firm rather than a pure monopoly, although its pricing

procedure for cut diamonds resembled monopoly behavior.
Perhaps the most common form of monopolistic market power occurs as the 
result of government-  controlled authorization. In most urban areas, a single source 
of water and sewer services is offered. In some cases, these services are offered by a 
government-  controlled entity. In other cases, private companies provide the services 
under government regulation. Such “natural” monopolies require a large initial invest -
ment that benefits from economies of scale; therefore, government may authorize a 
single seller to provide a certain service because having multiple sellers would be too 
costly. For example, electricity in most markets is provided by a single seller. Economies 
of scale result when significant capital investment benefits from declining long-  run 
average costs. In the case of electricity, a large gas-  fueled power plant producing 
electricity for a large area is substantially more efficient than having a small diesel

generator for every building. That is, the average cost of generating and delivering a 
kilowatt of electricity will be substantially lower with the single power station, but 
the initial fixed cost of building the power station and the lines delivering electricity 
to each home, factory, and office will be very high.
In the case of natural monopolies, limiting the market to a single seller is considered 
beneficial to society. One water and sewer system is deemed better for the community 
than dozens of competitors because building multiple infrastructures for running water 
and sewer service would be particularly expensive and complicated. One electrical 
power grid supplying electricity for a community can make large capital investments 
in generating plants and lower the long-  run average cost, while multiple power grids 
would lead to a potentially dangerous maze of wires. Clearly, not all monopolies are

in a position to make significant economic profits. Regulators, such as public utility 6

Reading 15 ■ The Firm and Market Structures 98
commissions in the United States, attempt to determine what a normal return for the 
monopoly owners’ investment should be, and they set prices accordingly. Nevertheless, 
monopolists attempt to maximize profits.
Not all monopolies originate from “natural” barriers. For some monopolists, barriers 
to entry do not derive from increasing returns to scale. We mentioned that marketing 
and brand loyalty are sources of product differentiation in monopolistic competition. 
In some highly successful cases, strong brand loyalty can become a formidable bar -
rier to entry. For example, if the Swiss watchmaker Rolex is unusually successful in 
establishing brand loyalty, so that its customers think there is no close substitute for 
its product, then the company will have monopoly-  like pricing power over its market.
The final potential source of market power is the increasing returns associated with

network effects. Network effects result from synergies related to increasing market 
penetration. By achieving a critical level of adoption, Microsoft was able to extend 
its market power through the network effect—for example, because most computer 
users know how to use Microsoft Word. Therefore, for firms, Word is cheaper to adopt 
than other programs because almost every new hire will be proficient in using the 
software and will need no further training. At some level of market share, a network-  
based product or service (think of Facebook or eBay) reaches a point where each 
additional share point increases the probability that another user will adopt.15 These 
network effects increase the value to other potential adopters. In Microsoft’s case, 
the network effects crowded out other potential competitors, including Netscape’s 
internet browser, that might have led to applications bypassing Windows. Eventually,

Microsoft’s operating system’s market share reached 92 percent of the global market. 
Similar situations occur in financial markets: If a publicly listed share or a derivative 
contract is more frequently traded on a certain exchange, market participants wishing 
to sell or buy the security will go to the more liquid exchange because they expect to 
find a better price and faster execution there.
6.1 Demand Analysis in Monopoly Markets
The monopolist’s demand schedule is the aggregate demand for the product in the 
relevant market. Because of the income effect and the substitution effect, demand is 
negatively related to price, as usual. The slope of the demand curve is negative and 
therefore downward sloping. The general form of the demand relationship is
QD = a – bP      or, rewritten,       P = a/b – (1/ b)QD
Therefore, total revenue = TR=× =() −() PQ abQb QDD12
Marginal revenue is the change in revenue given a change in the quantity demanded.

Because an increase in quantity requires a lower price, the marginal revenue sched -
ule is steeper than the demand schedule. If the demand schedule is linear, then the 
marginal revenue curve is twice as steep as the demand schedule.16
MR = ∆TR/∆ Q = (a/b) – (2/ b)QD
The demand and marginal revenue relationship is expressed in Exhibit 17.
15 When a network-  based device reaches a 30 percent share, the next 50 percentage points are cheaper 
to promote, according to McGuigan, Moyer, and Harris (2016).
16 Marginal revenue can be found using the technique shown in Section 3.1 or, for readers who are familiar 
with calculus, by taking the derivative of the total revenue function: MR = ∆TR/∆ Q = (a/b) – (2/ b)QD.

Monopoly 99
Exhibit 17   Monopolist’s Demand and Marginal Revenue 
Price
Quantity MR  D
Suppose a company operating on a remote island is the single seller of natural gas. 
Demand for its product can be expressed as
 QD = 400 – 0.5 P, which can be rearranged as
 P = 800 – 2 QD
Total revenue is  PQ QQDD ×= =−TR 800 22, and marginal revenue is MR = 800 
– 4QD.17
In Exhibit 17, the demand curve’s intercept is 800 and the slope is –2. The marginal 
revenue curve in Exhibit 17 has an intercept of 800 and a slope of –4.
Average revenue is TR/ QD; therefore, AR = 800 – 2 QD, which is the same as the 
demand function. In the monopoly market model, average revenue is the same as the 
market demand schedule.
6.2 Supply Analysis in Monopoly Markets
A monopolist’s supply analysis is based on the firm’s cost structure. As in the market 
structures of monopolistic competition and oligopoly, the monopolist does not have a 
well-  defined supply function that determines the optimal output level and the price to

charge. The optimal output is the profit-  maximizing output level. The profit-  maximizing 
level of output occurs where marginal revenue equals marginal cost, MR = MC.
Assume the natural gas company has determined that its total cost can be expressed 
as
TC = 20,000 + 50 Q + 3Q2
Marginal cost is ∆TC/∆ Q = MC = 50 + 6 Q.18
Supply and demand can be combined to determine the profit-  maximizing level of 
output. Exhibit 18 combines the monopolist’s demand and cost functions.
17 MR = ΔTR/Δ Q = 800 – 4 Q; see footnote 16.
18 The marginal cost equation can be found in this case by applying the technique used to find the marginal 
revenue equation in Section 3.1, or by taking the derivative of the total cost function.

Reading 15 ■ The Firm and Market Structures 100
Exhibit 18   Monopolist’s Demand, Marginal Revenue, and Cost Structures 
Price and Cost
PE
ACE
Quantity QDEMR  MC AC
D
In Exhibit 18, the demand and marginal revenue functions are clearly defined by 
the aggregate market. However, the monopolist does not have a supply curve. The 
quantity that maximizes profit is determined by the intersection of MC and MR, QDE.
The price consumers are willing to pay for this level of output is PE, as determined 
by the demand curve, PE.
The profit-  maximizing level of output is MR = MC: 800 – 4 QD = 50 + 6 QD; there -
fore, QD = 75 when profit is maximized.
Total profit equals total revenue minus total cost: 
π= −− ++ () =− +− 800 22 0 000 50 32 0 000 750 522 2QQ QQ QQDD DD D ,,
Profit is represented by the difference between the area of the rectangle QDE × PE, 
representing total revenue, and the area of the rectangle QDE × ACE, representing 
total cost.
MONOPOLISTS AND THEIR INCENTIVES

In theoretical models, which usually take product quality and technology as given, 
monopolists can choose to vary either price or quantity. In real life, they also have the 
ability to vary their product.
A monopolist can choose to limit quality if producing a higher-  quality product is 
costly and higher quality does not increase profits accordingly. For example, the quality 
of domestically produced cars in most developed countries improved dramatically once 
foreign imports became more available. Before the opening of borders to foreign imports, 
the single incumbent that dominated the market (for example, Fiat in Italy) or the small 
group of incumbents acting as a collusive oligopoly (such as the Detroit “Big Three” in 
the United States) were the effective monopolists of their domestic automobile markets. 
Rust corrosion, limited reliability, and poor gas mileage were common.19

Similarly, regulated utilities may have limited incentives to innovate. Several studies, 
including Gómez-  Ibáñez (2003), have found that state-  owned and other monopoly 
telephone utilities tended to provide very poor service before competition was intro -
duced. Poor service may not be limited to poor connection quality but may also include 
extensive delays in adding new users and limited introduction of new services, such as 
caller ID or automatic answering services.
19 For more on this topic, see Banker, Khosla, and Sinha (1998).

Monopoly 101
Intuitively, a monopolist will not spend resources on quality control, research and 
development, or even customer relations unless there is a threat of entry of a new com -
petitor or unless there is a clear link between such expenses and a profit increase. In 
contrast, in competitive markets, including oligopoly, innovation and quality are often 
ways to differentiate the product and increase profits.
6.3 Optimal Price and Output in Monopoly Markets
Continuing the natural gas example from above, the total profit function can be 
solved using the quadratic formula.20 Another method to solve the profit function is 
to evaluate ∆π/∆ QD and set it equal to zero. This identifies the point at which profit 
is unaffected by changes in output.21 Of course, this will give the same result as we 
found by equating marginal revenue with marginal cost. The monopoly will maximize 
profits when Q* = 75 units of output and the price is set from the demand curve at 650.

P* = 800 – 2(75) = 650 per unit
To find total maximum profits, substitute these values into the profit function above:
π= −+ −= −+ () −() = 20 000 750 52 0 000 750 75 5758 12522,, , QQDD
Note that the price and output combination that maximizes profit occurs in the 
elastic portion of the demand curve in Exhibit 18. This must be so because marginal 
revenue and marginal cost will always intersect where marginal revenue is positive. 
This fact implies that quantity demanded responds more than proportionately to prices 
changes, i.e. demand is elastic, at the point at which MC = MR. As noted earlier, the 
relationship between marginal revenue and price elasticity, EP, is:
MR = P[1 – 1/ EP]
In monopoly, MR = MC; therefore,
P[1 – 1/ EP] = MC
The firm can use this relationship to determine the profit-  maximizing price if the 
firm knows its cost structure and the price elasticity of demand, EP. For example, 
assume the firm knows that its marginal cost is constant at 75 and recent market anal -

ysis indicates that price elasticity is estimated to be 1.5. The optimal price is solved as
P[1 – 1/1.5] = 75 and
P = 225
Exhibit 18 indicated that the monopolist wants to produce at QE and charge the 
price of PE. Suppose this is a natural monopoly that is operating as a government 
franchise under regulation. Natural monopolies are usually found where production 
is based on significant economies of scale and declining cost structure in the market. 
Examples include electric power generation, natural gas distribution, and the water 
and sewer industries. These are often called public utilities. Exhibit 19 illustrates such 
a market in long-  run equilibrium.
20 The quadratic formula, where aQ2 + bQ + c = 0, is  Qb ba ca =− ±−() {}242 .
21 Maximum profit occurs where ∆π/∆ QD = 0 = 750 – 10 QD. Therefore, profits are maximized at QD = 75.

Reading 15 ■ The Firm and Market Structures 102
Exhibit 19   Natural Monopoly in a Regulated Pricing Environment 
PM
PR
PC
Quantity QM QR QCMR  LRAC
LRMC
D
In Exhibit 19, three possible pricing and output solutions are presented. The first 
is what the monopolist would do without regulation: The monopolist would seek to 
maximize profits by producing QM units of the product, where long-  run marginal cost 
equals marginal revenue, LRMC = MR. To maximize profits, the monopolist would 
raise the price to the level the demand curve will accept, PM.
In perfect competition, the price and output equilibrium occurs where price is 
equal to the marginal cost of producing the incremental unit of the product. In a 
competitive market, the quantity produced would be higher, QC, and the price lower, 
PC. For this regulated monopoly, the competitive solution would be unfair because 
at output QC, the price PC would not cover the average cost of production. One pos -

sibility is to subsidize the difference between the long-  run average cost, LRAC, and 
the competitive price, PC, for each unit sold.
Another solution is for the regulator to set the price at the point where long-  run 
average cost equals average revenue. Recall that the demand curve represents the 
average revenue the firm receives at each output level. The government regulator 
will attempt to determine the monopolistic firm’s long-  run average cost and set the 
output and price so that the firm receives a fair return on the owners’ invested capi -
tal. The regulatory solution is output level QR, with the price set at PR. Therefore, the 
regulatory solution is found between the unregulated monopoly equilibrium and the 
competitive equilibrium.
6.4 Price Discrimination and Consumer Surplus
Monopolists can be more or less effective in taking advantage of their market structure. 
At one extreme, we have a monopolist that charges prices and supplies quantities that

are the same as they would be in perfect competition; this scenario may be a result 
of regulation or threat of entry (if the monopolist charged more, another company 
could come in and price the former monopolist out of the market). At the opposite 
extreme, hated by all consumers and economists, is the monopolist that extracts the 
entire consumer surplus. This scenario is called first-  degree price discrimination , 
where a monopolist is able to charge each customer the highest price the customer 
is willing to pay. This is called price discrimination because the monopolist charges a 
different price to each client. How can this be? For example, if the monopolist knows 
the exact demand schedule of the customer, then the monopolist is able to capture 
the entire consumer surplus. In practice, the monopolist is able to measure how 
often the product is used and charges the customer the highest price the consumer is

Monopoly 103
willing to pay for that unit of good. Another possibility is that public price disclosure 
is non-  existent, so that no customer knows what the other customers are paying. 
Interestingly, not every consumer is worse off in this case, because some consumers 
may be charged a price that is below that of perfect competition, as long as the mar -
ginal revenue exceeds the marginal cost.
In second-  degree price discrimination  the monopolist offers a menu of quantity-  
based pricing options designed to induce customers to self-  select based on how 
highly they value the product. Such mechanisms include volume discounts, volume 
surcharges, coupons, product bundling, and restrictions on use. In practice, producers 
can use not just the quantity but also the quality (e.g., “professional grade”) to charge 
more to customers that value the product highly.
Third-  degree price discrimination  happens when customers are segregated by

demographic or other traits. For example, some econometric software is licensed 
this way: A student version can handle only small datasets and is sold for a low price; 
a professional version can handle very large datasets and is sold at a much higher 
price because corporations need to compute the estimates for their business and are 
therefore willing to pay more for a license. Another example is that airlines know that 
passengers who want to fly somewhere and come back the same day are most likely 
business people; therefore, one-  day roundtrip tickets are generally more expensive 
than tickets with a return flight at a later date or over a weekend.
Price discrimination has many practical applications when the seller has pricing 
power. The best way to understand how this concept works is to think of consumer 
surplus: As seen in this reading, a consumer may be willing to pay more for the first 
unit of a good, but to buy a second unit she will want to pay a lower price, thus get -

ting a better deal on the first unit. In practice, sellers can sometimes use income and 
substitution effects to their advantage. Think of something you often buy, perhaps 
lunch at your favorite café. How much would you be willing to pay for a “lunch club 
membership card” that would allow you to purchase lunches at, say, half price? If the 
café could extract from you the maximum amount each month that you would be 
willing to pay for the half-  price option, then it would successfully have removed the 
income effect from you in the form of a monthly fixed fee. Notice that a downward-  
sloping demand curve implies that you would end up buying more lunches each month 
than before you purchased the discount card, even though you would be no better or 
worse off than before. This is a way that sellers are sometimes able to extract consumer 
surplus by means of creative pricing schemes. It’s a common practice among big-  box

retailers, sports clubs, and other users of what is called “two-  part tariff pricing, ” as 
in the example below.
EXAMPLE 3   
Price Discrimination
Nicole’s monthly demand for visits to her health club is given by the following 
equation: QD = 20 – 4 P, where QD is visits per month and P is euros per visit. 
The health club’s marginal cost is fixed at €2 per visit.
1 Draw Nicole’s demand curve for health club visits per month.
2 If the club charged a price per visit equal to its marginal cost, how many 
visits would Nicole make per month?
3 How much consumer surplus would Nicole enjoy at that price?
4 How much could the club charge Nicole each month for a membership 
fee?

Reading 15 ■ The Firm and Market Structures 104
QD = 20 – 4 P, so when P = 0, QD = 20. Inverting, P = 5 – 0.25 QD, so when Q 
= 0, P = 5.
QD = 20 – 4(2) = 12. Nicole would make 12 visits per month at a price of €2 
per visit.
Nicole’s consumer surplus can be measured as the area under her demand curve 
and above the price she pays for a total of 12 visits, or (0.5)(12)(3) = 18. Nicole 
would enjoy a consumer surplus of €18 per month.
The club could extract all of Nicole’s consumer surplus by charging her a monthly 
membership fee of €18 plus a per-  visit price of €2. This pricing method is called 
a two-  part tariff because it assesses one price per unit of the item purchased plus 
a per-  month fee (sometimes called an “entry fee”) equal to the buyer’s consumer 
surplus evaluated at the per-  unit price.
6.5 Factors Affecting Long-  Run Equilibrium in Monopoly 
Markets

Markets
The unregulated monopoly market structure can produce economic profits in the 
long run. In the long run, all factors of production are variable, while in the short run, 
some factors of production are fixed. Generally, the short-  run factor that is fixed is 
the capital investment, such as the factory, machinery, production technology, avail -
able arable land, and so forth. The long-  run solution allows for all inputs, including 
technology, to change. In order to maintain a monopoly market position in the long 
run, the firm must be protected by substantial and ongoing barriers to entry. If the 
monopoly position is the result of a patent, then new patents must be continuously 
added to prevent the entry of other firms into the market.
For regulated monopolies, such as natural monopolies, there are a variety of long-  
run solutions. One solution is to set the price equal to marginal cost, P = MC. However,

that price will not likely be high enough to cover the average cost of production, as 
Exhibit 19 illustrated. The answer is to provide a subsidy sufficient to compensate 
the firm. The national rail system in the United States, Amtrak, is an example of a 
regulated monopoly operating with a government subsidy.
National ownership of the monopoly is another solution. Nationalization of the 
natural monopoly has been a popular solution in Europe and other parts of the world. 
The United States has generally avoided this potential solution. One problem with 
this arrangement is that once a price is established, consumers are unwilling to accept 
price increases, even as factor costs increase. Politically, raising prices on products 
from government-  owned enterprises is highly unpopular.
Establishing a governmental entity that regulates an authorized monopoly is another 
popular solution. Exhibit 19 illustrated the appropriate decision rule. The regulator sets

price equal to long-  run average cost, PR = LRAC. This solution assures that investors 
will receive a normal return for the risk they are taking in the market. Given that no 
other competitors are allowed, the risk is lower than in a highly competitive market 
environment. The challenge facing the regulator is determining the authentic risk-  
related return and the monopolist’s realistic long-  run average cost.

Identification of Market Structure 105
The final solution is to franchise the monopolistic firm through a bidding war. 
Again, the public goal is to select the winning firm based on price equaling long-  run 
average cost. Retail outlets at rail stations and airports and concession outlets at sta -
diums are examples of government franchises. The long-  run success of the monopoly 
franchise depends on its ability to meet the goal of pricing its products at the level 
of its long-  run average cost.
EXAMPLE 4   
Monopolies and Efficiency
Are monopolies always  inefficient?
A No, because if they charge more than average cost they are nationalized.
B Yes, because they charge all consumers more than perfectly competitive 
markets would.
C No, because economies of scale and regulation (or threat of entry) may 
give a better outcome for buyers than perfect competition.
Solution: 
C is correct. Economies of scale and regulation may make monopolies more 
efficient than perfect competition.

IDENTIFICATION OF MARKET STRUCTURE
Monopoly markets and other situations where companies have pricing power can be 
inefficient because producers constrain output to cause an increase in prices. Therefore, 
there will be less of the good being consumed and it will be sold at a higher price, 
which is generally inefficient for the market as a whole. This is why competition law 
regulates the degree of market competition in several industries of different countries.
Market power in the real world is not always as clear as it is in textbook examples. 
Governments and regulators often have the difficult task of measuring market power 
and establishing whether a firm has a dominant position that may resemble a monop -
oly. For example, in the 1990s, US regulators prosecuted agricultural corporation 
Archer Daniels Midland for conspiring with Japanese competitors to fix the price of

lysine, an amino acid used as an animal feed additive. The antitrust action resulted in 
a settlement that involved over US$100 million in fines paid by the cartel members. 
Another example occurred in the 1970s, when US antitrust authorities broke up the 
local telephone monopoly, leaving AT&T the long-  distance business (and opening that 
business to competitors), and required AT&T to divest itself of the local telephone 
companies it owned. This antitrust decision brought competition, innovation, and 
lower prices to the US telephone market.
European regulators (specifically, the European Commission) have affected the 
mergers and monopoly positions of European corporations (as in the case of the 
companies Roche, Rhone-  Poulenc, and BASF, which were at the center of a vitamin 
price-  fixing case) as well as non-  European companies (such as Intel) that do business 
in Europe. Moreover, the merger between the US company General Electric and the

European company Honeywell was denied by the European Commission on grounds 
of excessive market concentration.7

Reading 15 ■ The Firm and Market Structures 106
Quantifying excessive market concentration is difficult. Sometimes, regulators 
need to measure whether something that has not yet occurred might generate exces -
sive market power. For example, a merger between two companies might allow the 
combined company to be a monopolist or quasi monopolist in a certain market.
A financial analyst hearing news about a possible merger should always consider 
the impact of competition law (sometimes called antitrust law)—that is, whether a 
proposed merger may be blocked by regulators in the interest of preserving a com -
petitive market.
7.1 Econometric Approaches
How should one measure market power? The theoretical answer is to estimate the 
elasticity of demand and supply in a market. If demand is very elastic, the market 
must be very close to perfect competition. If demand is rigid (inelastic), companies 
may  have market power. This is the approach taken in the cellophane case mentioned 
in Section 3.1.2.

From the econometric point of view, this estimation requires some attention. 
The problem is that observed price and quantity are the equilibrium values of price 
and quantity and do not represent the value of either supply or demand. Technically, 
this is called the problem of endogeneity, in the sense that the equilibrium price and 
quantity are jointly determined by the interaction of demand and supply. Therefore, 
to have an appropriate estimation of demand and supply, we will need to use a model 
with two equations, namely, an equation of demanded quantity (as a function of price, 
income of the buyers, and other variables) and an equation of supplied quantity (as 
a function of price, production costs, and other variables). The estimated parameters 
will then allow us to compute elasticity.
Regression analysis is useful in computing elasticity but requires a large number 
of observations. Therefore, one may use a time-  series approach and, for example,

look at 20 years of quarterly sales data for a market. However, the market structure 
may have changed radically over those 20 years, and the estimated elasticity may not 
apply to the current situation. Moreover, the supply curve may change as a result of 
a merger among large competitors, and the estimation based on past data may not 
be informative regarding the future state of the market post merger.
An alternative approach is a cross-  sectional regression analysis. Instead of look -
ing at total sales and average prices in a market over time (the time-  series approach 
mentioned above), we can look at sales from different companies in the market 
during the same year, or even at single transactions from many buyers and compa -
nies. Clearly, this approach requires substantial data-  gathering effort, and therefore, 
this estimation method can be complicated. Moreover, different specifications of the 
explanatory variables (for example, using total GDP rather than median household

income or per-  capita GDP to represent income) may sometimes lead to dramatically 
different estimates.
7.2 Simpler Measures
Trying to avoid the above drawbacks, analysts often use simpler measures to estimate 
elasticity. The simplest measure is the concentration ratio, which is the sum of the 
market shares of the largest N firms. To compute this ratio, one would, for example, 
add the sales values of the largest 10 firms and divide this figure by total market sales. 
This number is always between zero (perfect competition) and 100 percent (monopoly).
The main advantage of the concentration ratio is that it is simple to compute, as 
shown above. The disadvantage is that it does not directly quantify market power. 
In other words, is a high concentration ratio a clear signal of monopoly power? The 
analysis of entry in Section 2 explains clearly that this is not the case: A company may

Identification of Market Structure 107
be the only incumbent in a market, but if the barriers to entry are low, the simple 
presence of a potential  entrant may be sufficient to convince the incumbent to behave 
like a firm in perfect competition. For example, a sugar wholesaler may be the only 
one in a country, but the knowledge that other large wholesalers in the food industry 
might easily add imported sugar to their range of products should convince the sugar 
wholesaler to price its product as if it were in perfect competition.
Another disadvantage of the concentration ratio is that it tends to be unaffected 
by mergers among the top market incumbents. For example, if the largest and second-  
largest incumbents merge, the pricing power of the combined entity is likely to be 
larger than that of the two pre-  existing companies. But the concentration ratio may 
not change much.
CALCULATING THE CONCENTRATION RATIO

Suppose there are eight producers of a certain good in a market. The largest producer 
has 35 percent of the market, the second largest has 25 percent, the third has 20 per -
cent, the fourth has 10  percent, and the remaining four have 2.5  percent each. If we 
computed the concentration ratio of the top three producers, it would be 35  + 25  + 
20 = 80 percent, while the concentration ratio of the top four producers would be 35 + 
25 + 20 + 10 = 90 percent.
If the two largest companies merged, the new concentration ratio for the top three 
producers would be 60 (the sum of the market shares of the merged companies) + 
20 + 10 = 90 percent, and the concentration ratio for the four top producers would be 
92.5  percent. Therefore, this merger affects the concentration ratio very mildly, even 
though it creates a substantial entity that controls 60 percent of the market.
For example, the effect of consolidation in the US retail gasoline market has resulted

in increasing degrees of concentration. In 1992, the top four companies in the US retail 
gasoline market shared 33 percent of the market. By 2001, the top four companies con -
trolled 78 percent of the market (Exxon mobil 24 percent, Shell 20 percent, BP/Amoco/
Arco 18 percent, and Chevron/Texaco 16 percent).
To avoid the known issues with concentration ratios, economists O.C. Herfindahl 
and A.O. Hirschman suggested an index where the market shares of the top N com -
panies are first squared and then added. If one firm controls the whole market (a 
monopoly), the Herfindahl–Hirschman index (HHI) equals 1. If there are M firms in 
the industry with equal market shares, then the HHI equals (1/ M). This provides a 
useful gauge for interpreting an HHI. For example, an HHI of 0.20 would be analogous 
to having the market shared equally by 5 firms.
The HHI for the top three companies in the example in the box above would be

0.352 + 0.252 + 0.202 = 0.225 before the merger, while after the merger, it would be 
0.602 + 0.202 + 0.102 = 0.410, which is substantially higher than the initial 0.225. 
This is why the HHI is widely used by competition regulators. However, just like the 
concentration ratio, the HHI does not take the possibility of entry into account, nor 
does it consider the elasticity of demand. As a consequence, the HHI has limited use 
for a financial analyst trying to estimate the potential profitability of a company or 
group of companies.

Reading 15 ■ The Firm and Market Structures 108
EXAMPLE 5   
The Herfindahl–Hirschman Index
Suppose a market has 10 suppliers, each of them with 10 percent of the market. 
What are the concentration ratio and the HHI of the top four firms?
A Concentration ratio 4 percent and HHI 40
B Concentration ratio 40 percent and HHI 0.4
C Concentration ratio 40 percent and HHI 0.04
Solution: 
C is correct. The concentration ratio for the top four firms is 10 + 10 + 10 + 
10 = 40 percent, and the HHI is 0.102 × 4 = 0.01 × 4 = 0.04.
SUMMARY
In this reading, we have surveyed how economists classify market structures. We 
have analyzed the distinctions between the different structures that are important 
for understanding demand and supply relations, optimal price and output, and the 
factors affecting long-  run profitability. We also provided guidelines for identifying 
market structure in practice. Among our conclusions are the following:

■■Economic market structures can be grouped into four categories: perfect com -
■■The categories differ because of the following characteristics: The number of 
producers is many in perfect and monopolistic competition, few in oligopoly, 
and one in monopoly. The degree of product differentiation, the pricing power 
of the producer, the barriers to entry of new producers, and the level of non-  
price competition (e.g., advertising) are all low in perfect competition, mod -
erate in monopolistic competition, high in oligopoly, and generally highest in 
monopoly.
■■A financial analyst must understand the characteristics of market structures in 
order to better forecast a firm’s future profit stream.
■■The optimal marginal revenue equals marginal cost. However, only in perfect 
competition does the marginal revenue equal price. In the remaining structures, 
price generally exceeds marginal revenue because a firm can sell more units

only by reducing the per unit price.
■■The quantity sold is highest in perfect competition. The price in perfect com -
petition is usually lowest, but this depends on factors such as demand elasticity 
and increasing returns to scale (which may reduce the producer’s marginal 
cost). Monopolists, oligopolists, and producers in monopolistic competition 
attempt to differentiate their products so that they can charge higher prices.
■■Typically, monopolists sell a smaller quantity at a higher price. Investors may 
benefit from being shareholders of monopolistic firms that have large margins 
and substantial positive cash flows.
■■Competitive firms do not earn economic profit. There will be a market com -
pensation for the rental of capital and of management services, but the lack of 
pricing power implies that there will be no extra margins.

References 109
Banker, R.D., I. Khosla, and K.K. Sinha. 1998. “Quality and 
Competition. ” Management Science , vol. 44, no. 9:1179–1192. 
Chamberlin, Edward H. 1933. The Theory of Monopolistic 
Competition . Cambridge, MA: Harvard University Press.
Dorsey, Pat. 2004. The Five Rules for Successful Stock Investing: 
Morningstar’s Guide to Building Wealth and Winning in the 
Market . Hoboken, NJ: John Wiley & Sons.
Friedman, Thomas L. 2006. The World Is Flat: A Brief History of 
the Twenty-  first Century . New York: Farrar, Straus and Giroux.
Fudenberg, Drew, and Jean Tirole. 1984. “The Fat Cat Effect, the 
Puppy Dog Ploy and the Lean and Hungry Look. ” American 
Economic Review , vol. 74, no. 2:361–366.
Gómez-  Ibáñez, José A. 2006. Regulating Infrastructure: 
Monopoly, Contracts, and Discretion . Cambridge, MA: 
Harvard University Press.
Kelly, Anthony. 2011. Decision Making Using Game Theory: 
An Introduction for Managers . Cambridge, UK: Cambridge

University Press.Krugman, Paul R. 1989. “Industrial Organization and 
International Trade. ” In Handbook of Industrial Organization , 
vol. 2. Edited by Richard Schmalensee and Robert Willig. 
Amsterdam: Elsevier B.V.
McCloskey, Donald. 1985. The Applied Theory of Price . 2nd ed. 
New York: Macmillan.
McGuigan, James R., R. Charles Moyer, and Frederick H. Harris. 
2016. Managerial Economics: Applications, Strategy and 
Tactics . 14th ed. Mason, OH: Thomson South-Western.
Porter, Michael E. 2008. “The Five Competitive Forces that Shape 
Strategy. ” Harvard Business Review , vol. 86, no. 1:78–93.
Nicholson, Walter, and Christopher M. Snyder. 2016. 
Microeconomic Theory: Basic Principles and Extensions . 12th 
ed. Mason, OH: Thomson South-Western.
Schumpeter, Joseph A. 1942. Capitalism, Socialism and 
Democracy . New York: HarperCollins.
von Stackelberg, Heinrich. 1952. The Theory of the Market

Economy . New York: Oxford University Press.■■While in the short run firms in any market structure can have economic profits, 
the more competitive a market is and the lower the barriers to entry, the faster 
the extra profits will fade. In the long run, new entrants shrink margins and 
push the least efficient firms out of the market.
■■Oligopoly is characterized by the importance of strategic behavior. Firms can 
change the price, quantity, quality, and advertisement of the product to gain 
an advantage over their competitors. Several types of equilibrium (e.g., Nash, 
Cournot, kinked demand curve) may occur that affect the likelihood of each 
of the incumbents (and potential entrants in the long run) having economic 
profits. Price wars may be started to force weaker competitors to abandon the 
market.
■■Measuring market power is complicated. Ideally, econometric estimates of the 
elasticity of demand and supply should be computed. However, because of the

lack of reliable data and the fact that elasticity changes over time (so that past 
data may not apply to the current situation), regulators and economists often 
use simpler measures. The concentration ratio is simple, but the HHI, with little 
more computation required, often produces a better figure for decision making.

Reading 15 ■ The Firm and Market Structures 110
1 A market structure characterized by many sellers with each having some pric -
ing power and product differentiation is best described as:
A oligopoly.
B perfect competition.
C monopolistic competition.
2 A market structure with relatively few sellers of a homogeneous or standardized 
product is best described as:
B monopoly.
C perfect competition.
3 Market competitors are least likely  to use advertising as a tool of differentiation 
in an industry structure identified as:
A monopoly.
4 Upsilon Natural Gas, Inc. is a monopoly enjoying very high barriers to entry. 
Its marginal cost is $40 and its average cost is $70. A recent market study has 
determined the price elasticity of demand is 1.5. The company will most likely  
set its price at:
A $40.
B $70.
C $120.
5 The demand schedule in a perfectly competitive market is given by P = 93 –

1.5Q (for Q ≤ 62) and the long-  run cost structure of each company is:
Total cost: 256 + 2 Q + 4Q2
Average cost: 256/ Q + 2 + 4 Q
Marginal cost: 2 + 8 Q
 New companies will enter the market at any price greater than:
A 8.
B 66.
C 81.
6 Companies most likely  have a well-  defined supply function when the market 
structure is:
7 Aquarius, Inc. is the dominant company and the price leader in its market. One 
of the other companies in the market attempts to gain market share by under -
cutting the price set by Aquarius. The market share of Aquarius will most likely :

C stay the same.
8 SigmaSoft and ThetaTech are the dominant makers of computer system soft -
ware. The market has two components: a large mass-  market component in 
which demand is price sensitive, and a smaller performance-  oriented com -
ponent in which demand is much less price sensitive. SigmaSoft’s product is 
considered to be technically superior. Each company can choose one of two 
strategies:
■●Open architecture (Open):  Mass market focus allowing other software vend -
ers to develop products for its platform.
■●Proprietary (Prop):  Allow only its own software applications to run on its 
platform.
 Depending upon the strategy each company selects, their profits would be:
SigmaSoft – Ope n
400600
ThetaTech – Ope nSigmaSoft – P rop
650700
ThetaTech – Ope n
800
300
ThetaTech – P ropSigmaSoft – P rop
600
400
ThetaTech – P rop
 The Nash equilibrium for these companies is:
A proprietary for SigmaSoft and proprietary for ThetaTech.

B open architecture for SigmaSoft and proprietary for ThetaTech.
C proprietary for SigmaSoft and open architecture for ThetaTech.
9 A company doing business in a monopolistically competitive market will most 
likely  maximize profits when its output quantity is set such that:
A average cost is minimized.
B marginal revenue equals average cost.
C marginal revenue equals marginal cost.
10 Oligopolistic pricing strategy most likely  results in a demand curve that is:
A kinked.
B vertical.
C horizontal.
11 Collusion is less likely  in a market when:
A the product is homogeneous.
B companies have similar market shares.
C the cost structures of companies are similar.
12 If companies earn economic profits in a perfectly competitive market, over the 
long run the supply curve will most likely :
A shift to the left.
B shift to the right.
C remain unchanged.

Reading 15 ■ The Firm and Market Structures 112
13 Over time, the market share of the dominant company in an oligopolistic mar -
ket will most likely :
14 A government entity that regulates an authorized monopoly will most likely  
base regulated prices on:
A marginal cost.
B long run average cost.
C first degree price discrimination.
15 An analyst gathers the following market share data for an industry:
Company Sales  
(in millions of €)
ABC 300
Brown 250
Coral 200
Delta 150
Erie 100
All others 50
 The industry’s four-  company concentration ratio is closest  to:
A 71%.
B 86%.
C 95%.
16 An analyst gathered the following market share data for an industry comprised 
of five companies:
Company Market Share (%)
Zeta 35
Yusef 25
Xenon 20
Waters 10
Vlastos 10
 The industry’s three-  firm Herfindahl–Hirschmann Index is closest  to:
A 0.185.
B 0.225.
C 0.235.
17 One disadvantage of the Herfindahl–Hirschmann Index is that the index:
A is difficult to compute.

B fails to reflect low barriers to entry.
C fails to reflect the effect of mergers in the industry.
18 In an industry comprised of three companies, which are small-  scale manu -
facturers of an easily replicable product unprotected by brand recognition or 
patents, the most  representative model of company behavior is:

19 Deep River Manufacturing is one of many companies in an industry that make 
a food product. Deep River units are identical up to the point they are labeled. 
Deep River produces its labeled brand, which sells for $2.20 per unit, and 
“house brands” for seven different grocery chains which sell for $2.00 per unit. 
Each grocery chain sells both the Deep River brand and its house brand. The 
best characterization of Deep River’s market is:

Reading 15 ■ The Firm and Market Structures 114
SOLUTIONS
1 C is correct. Monopolistic competition is characterized by many sellers, differ -
entiated products, and some pricing power.
2 A is correct. Few sellers of a homogeneous or standardized product character -
izes an oligopoly.
3 B is correct. The product produced in a perfectly competitive market cannot be 
differentiated by advertising or any other means.
4 C is correct. Profits are maximized when MR = MC. For a monopoly, MR = P[1 
– 1/Ep]. Setting this equal to MC and solving for P:
 $40 =  P[1 – (1/1.5)] = P × 0.333
 P = $120
5 B is correct. The long-  run competitive equilibrium occurs where MC = AC = P 
for each company. Equating MC and AC implies 2 + 8 Q = 256/ Q + 2 + 4 Q.
 Solving for Q gives Q = 8. Equating MC with price gives P = 2 + 8 Q = 66. Any 
price above 66 yields an economic profit because P = MC > AC, so new compa -
nies will enter the market.
6 B is correct. A company in a perfectly competitive market must accept whatever

price the market dictates. The marginal cost schedule of a company in a per -
fectly competitive market determines its supply function.
7 A is correct. As prices decrease, smaller companies will leave the market 
rather than sell below cost. The market share of Aquarius, the price leader, will 
increase.
8 C is correct. In the Nash model, each company considers the other’s reaction 
in selecting its strategy. In equilibrium, neither company has an incentive to 
change its strategy. ThetaTech is better off with open architecture regardless of 
what SigmaSoft decides. Given this choice, SigmaSoft is better off with a pro -
prietary platform. Neither company will change its decision unilaterally.
9 C is correct. The profit maximizing choice is the level of output where marginal 
revenue equals marginal cost.
10 A is correct. The oligopolist faces two different demand structures, one for 
price increases and another for price decreases. Competitors will lower prices

to match a price reduction, but will not match a price increase. The result is a 
kinked demand curve.
11 B is correct. When companies have similar market shares, competitive forces 
tend to outweigh the benefits of collusion.
12 B is correct. The economic profit will attract new entrants to the market and 
encourage existing companies to expand capacity.
13 B is correct. The dominant company’s market share tends to decrease as profits 
attract entry by other companies.
14 B is correct. This allows the investors to receive a normal return for the risk 
they are taking in the market.
15 B is correct. The top four companies in the industry comprise 86 percent of 
industry sales: (300 + 250 + 200 + 150)/(300 + 250 + 200 + 150 + 100 + 50) = 
900/1050 = 86%.
16 B is correct. The three-  firm Herfindahl–Hirschmann Index is 0.352 + 0.252 + 
0.202 = 0.225.

17 B is correct. The Herfindahl–Hirschmann Index does not reflect low barriers to 
entry that may restrict the market power of companies currently in the market.
18 B is correct. The credible threat of entry holds down prices and multiple incum -
bents are offering undifferentiated products.
19 C is correct. There are many competitors in the market, but some product dif -
ferentiation exists, as the price differential between Deep River’s brand and the 
house brands indicates.

Aggregate Output, Prices, 
and Economic Growth
by Paul R. Kutasovic, PhD, CFA, and Richard Fritz, PhD
Paul R. Kutasovic, PhD, CFA, is at New York Institute of Technology (USA). Richard Fritz, 
PhD, is at the School of Economics at Georgia Institute of Technology (USA).
a. calculate and explain gross domestic product (GDP) using 
expenditure and income approaches;
b. compare the sum-  of- value-  added and value-  of- final-  output 
methods of calculating GDP; 
c. compare nominal and real GDP and calculate and interpret the 
GDP deflator; 
d. compare GDP , national income, personal income, and personal 
disposable income; 
e. explain the fundamental relationship among saving, investment, 
the fiscal balance, and the trade balance; 
f. explain the IS and LM curves and how they combine to generate 
the aggregate demand curve; 
g. explain the aggregate supply curve in the short run and long run;

h. explain causes of movements along and shifts in aggregate 
demand and supply curves;
i. describe how fluctuations in aggregate demand and aggregate 
supply cause short-  run changes in the economy and the business 
cycle;
j. distinguish between the following types of macroeconomic 
equilibria: long-  run full employment, short-  run recessionary gap, 
short-  run inflationary gap, and short-  run stagflation;
k. explain how a short-  run macroeconomic equilibrium may occur 
at a level above or below full employment; 
l. analyze the effect of combined changes in aggregate supply and 
demand on the economy; 
(continued)READING
16

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 118
m. describe sources, measurement, and sustainability of economic 
growth;
n. describe the production function approach to analyzing the 
sources of economic growth;
o. distinguish between input growth and growth of total factor 
productivity as components of economic growth.
In the field of economics, microeconomics  is the study of the economic activity and 
behavior of individual economic units, such as a household, a company, or a market 
for a particular good or service, and macroeconomics  is the study of the aggregate 
activities of households, companies, and markets. Macroeconomics focuses on national 
aggregates, such as total investment , the amount spent by all businesses on plant 
and equipment; total consumption , the amount spent by all households on goods 
and services; the rate of change in the general level of prices; and the overall level of

interest rates.
Macroeconomic analysis examines a nation’s aggregate output and income, its 
competitive and comparative advantages, the productivity of its labor force, its price 
level and inflation rate, and the actions of its national government and central bank. 
The objective of macroeconomic analysis is to address such fundamental questions as:
■■What is an economy’s aggregate output, and how is aggregate income 
measured?
■■What factors determine the level of aggregate output/income for an economy?
■■What are the levels of aggregate demand and aggregate supply of goods and 
services within the country?
■■Is the level of output increasing or decreasing, and at what rate?
■■Is the general price level stable, rising, or falling?
■■Is unemployment rising or falling?
■■Are households spending or saving more?
■■Are workers able to produce more output for a given level of inputs?
■■Are businesses investing in and expanding their productive capacity?
■■Are exports (imports) rising or falling?

From an investment perspective, investors must be able to evaluate a country’s 
current economic environment and to forecast its future economic environment in 
order to identify asset classes and securities that will benefit from economic trends 
occurring within that country. Macroeconomic variables—such as the level of infla -
tion, unemployment, consumption, government spending, and investment—affect 
the overall level of activity within a country. They also have different impacts on the 
growth and profitability of industries within a country, the companies within those 
industries, and the returns of the securities issued by those companies.
This reading is organized as follows: Section 2 describes gross domestic product 
and related measures of domestic output and income. Section 3 discusses short-  run 
and long-  run aggregate demand and supply curves, the causes of shifts and movements 1

Aggregate Output and Income 119
along those curves, and factors that affect equilibrium levels of output, prices, and 
interest rates. Section 4 discusses sources, sustainability, and measures of economic 
growth. A summary and practice problems complete the reading.
AGGREGATE OUTPUT AND INCOME
The aggregate output  of an economy is the value of all the goods and services pro -
duced in a specified period of time. The aggregate income  of an economy is the value 
of all the payments earned by the suppliers of factors used in the production of goods 
and services. Because the value of the output produced must accrue to the factors of 
production, aggregate output and aggregate income within an economy must be equal.
There are four broad forms of payments (i.e., income): compensation of employees, 
rent, interest, and profits. Compensation of employees includes wages and benefits 
(primarily employer contributions to private pension plans and health insurance)

that individuals receive in exchange for providing labor. Rent  is payment for the use 
of property. Interest  is payment for lending funds. Profit  is the return that owners 
of a company receive for the use of their capital and the assumption of financial risk 
when making their investments. Although businesses are the direct owners of much of 
the property and physical capital in the economy, by virtue of owning the businesses, 
households are the ultimate owners of these assets and hence the ultimate recipients 
of the profits. In reality, of course, a portion of profits are usually retained within 
businesses to help finance maintenance and expansion of capacity. Similarly, because 
the government is viewed as operating on a non-  profit basis, any revenue it receives 
from ownership of companies and/or property may be viewed as being passed back 
to households in the form of lower taxes. Therefore, for simplicity, it is standard in

macroeconomics to attribute all income to the household sector unless the analysis 
depends on a more precise accounting.
Aggregate expenditure , the total amount spent on the goods and services produced 
in the (domestic) economy during the period, must also be equal to aggregate output 
and aggregate income. However, some of this expenditure may come from foreigners 
in the form of net exports.1 Thus, aggregate output, aggregate income, and aggregate 
expenditure all refer to different ways of decomposing the same quantity.
Exhibit 1 illustrates the flow of inputs, output, income, and expenditures in a very 
simple economy. Households supply the factors of production (labor and capital) to 
businesses in exchange for wages and profit (aggregate income) totaling £100. These 
flows are shown by the top two arrows. Companies use the inputs to produce goods 
and services (aggregate output) which they sell to households (aggregate expenditure)

for £100. The output and expenditure flows are shown by the bottom two arrows. 
Aggregate output, income, and expenditure are all equal to £100.
In this simplified example, households spend all of their income on domestically 
produced goods and services. They do not buy foreign goods, save for the future, or 
pay taxes. Similarly, businesses do not sell to foreigners or the government and do 
not invest to increase their productive capacity. These important components of the 
economy will be added in Section 2.2. But first we need to discuss how output and 
income are measured.2
1 Note that “aggregate expenditure” as defined here does not equal the amount spent by domestic  resi -
dents on goods and services because it includes exports (purchases of domestic products by foreigners) 
and excludes imports (purchases of foreign products by domestic residents). Thus, spending by domestic 
residents does not necessarily equal domestic income/output. Indeed, within any given period, it usually

does not. This will be explained in more detail in Section 2.2.3.

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 120
Exhibit 1   Output, Income, and Expenditure in a Simple Economy: The 
Circular Flow
HouseholdsBusiness
Firms  
Goods and Services Labor and Capital 
Consumption Expenditure £100 Income £100 (= Wages + Profits) 
2.1 Gross Domestic Product
Gross domestic product  (GDP) measures
■■the market value of all final goods and services produced within the economy in 
a given period of time (output definition) or, equivalently,
■■the aggregate income earned by all households, all companies, and the govern -
ment within the economy in a given period of time (income definition).
Intuitively, GDP measures the flow of output and income in the economy.2 GDP 
represents the broadest measure of the value of economic activity occurring within 
a country during a given period of time.
Therefore, GDP can be determined in two different manners. In the income 
approach, GDP is calculated as the total amount earned by households and companies

in the economy. In the expenditure approach, GDP is calculated as the total amount 
spent on the goods and services produced within the economy during a given period. 
For the economy as a whole, total income must equal total expenditures, so the two 
approaches yield the same result.
Many developed countries use a standardized methodology for measuring GDP . This 
methodology is described in the official handbook of the Organisation for Economic 
Co- Operation and Development (Paris: OECD Publishing). The OECD reports the 
national accounts for many developed nations. In the United States, the National 
Income and Product Accounts (also called NIPA, or national accounts, for short) is 
the official US government accounting of all the income and expenditure flows in the 
US economy. The national accounts are the responsibility of the US Department of 
2 Some textbooks and countries measure flows of income and output by using gross national product (GNP)

rather than GDP . The difference is subtle but can be important in some contexts. GDP includes production 
within national borders regardless of whether the factors of production (labor, capital, and property) are 
owned domestically or by foreigners. In contrast, GNP measures output produced by domestically owned 
factors of production regardless of whether the production occurs domestically or overseas.

Aggregate Output and Income 121
Commerce and are published in its Survey of Current Business . In Canada, similar 
data are available from Statistics Canada, whereas in China, the National Bureau of 
Statistics of China provides GDP data.
To ensure that GDP is measured consistently over time and across countries, the 
following three broad criteria are used:
■■All goods and services included in the calculation of GDP must be produced 
during the measurement period . Therefore, items produced in previous peri -
ods—such as houses, cars, machinery, or equipment—are excluded. In addition, 
transfer payments from the government sector to individuals, such as unem -
ployment compensation or welfare benefits, are excluded. Capital gains that 
accrue to individuals when their assets appreciate in value are also excluded.
■■The only goods and services included in the calculation of GDP are those whose 
value can be determined by being sold in the market . This enables the price of

goods or services to be objectively determined. For example, a liter of extra 
virgin olive oil is more valuable than a liter of spring water because the market 
price of extra virgin olive oil is higher than the market price of spring water. The 
value of labor used in activities that are not sold on the market, such as com -
muting, gardening, etc., is also excluded from GDP . By-  products of production 
processes are also excluded if they have no explicit market value, such as air 
pollution, water pollution, and acid rain.
■■Only the market value of final goods and services is included in GDP . Final 
goods and services are those that are not resold. Intermediate goods  are goods 
that are resold or used to produce another good.3 The value of intermediate 
goods is excluded from GDP because additional value is added during the pro -
duction process, and all the value added during the entire production process

is reflected in the final sale price of the finished good. An alternative approach 
to measuring GDP is summing all the value added during the production and 
distribution processes. The most direct approach, however, is to sum the market 
value of all the final goods and services produced within the economy in a given 
time period.
Two distinct, but closely related, measurement methods can be used to calculate 
GDP based on expenditures: value of final output and sum of value added. These 
two methods are illustrated in Exhibit 2. In this example, a farmer sells wheat to a 
miller. The miller grinds the wheat into flour and sells it to a baker who makes bread 
and sells it to a retailer. Finally, the bread is sold to retail customers. The wheat and 
flour are both intermediate goods in this example because they are used as inputs to 
produce another good. Thus, they are not counted (directly) in GDP . For the purposes

of GDP , the value of the final product is €1.00, which includes the value added by the 
bread retailer as a distributor of the bread. If, in contrast, the baker sold directly to 
the public, the value counted in GDP would be the price at which the baker sold the 
bread, €0.78. The left column of the exhibit shows the total revenue received at each 
stage of the process, whereas the right column shows the value added at each stage. 
Note that the market value of the final product (€1.00) is equal to the sum of the value 
added at each of the stages. Thus, the contribution to GDP can be measured as either 
the final sale price or the sum of the value added at each stage.
3 “Final goods” should not be confused with so-  called final sales, and “intermediate goods” should not 
be confused with inventories. GDP includes both final sales to customers and increases in companies’ 
inventories. If sales exceed current production, then GDP is less than final sales by the amount of goods

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 122
Exhibit 2   Value of Final Product Equals Income Created
Receipts at Each  
Stage (€)Value Added  
(= Income Created)  
at Each Stage (€)
Receipts of farmer from miller 0.15 0.15 Value added by farmer
Receipts of miller from baker 0.46 0.31 Value added by miller
Receipts of baker from retailer 0.78 0.32 Value added by baker
Receipts of retailer from final customer 1.00 0.22 Value added by retailer
1.00 1.00
Value of final output Total value added =  
Total income created
EXAMPLE 1   
Contribution of Automobile Production to GDP
Exhibit 3 provides simplified information on the cost of producing an automobile 
in the United States at various stages of the production process. The example 
assumes the automobile is produced and sold domestically and assumes no 
imported material is used. Calculate the contribution of automobile production 
to GDP using the value-  added method, and show that it is equivalent to the

expenditure method. What impact would the use of imported steel or plastics 
have on GDP?
Exhibit 3   Cost of Producing Automobiles
Stage of ProductionSales Value 
($)
1 Production of basic materials
   Steel 1,000
   Plastics 3,000
   Semiconductors 1,000
2 Assembly of automobile (manufacturer price) 15,000
3 Wholesale price for automobile dealer 16,000
4 Retail price 18,000
Solution:
GDP includes only the value of final goods and ignores intermediate goods in 
order to avoid double counting. Thus, the final sale price of $18,000 and not the 
total sales value of $54,000 (summing sales at all the levels of production) would 
be included in GDP . Alternatively, we can avoid double counting by calculating 
and summing the value added at each stage. At each stage of production, the 
difference between what a company pays for its inputs and what it receives for 
the product is its contribution to GDP . The value added for each stage of pro -
duction is computed as follows:

Aggregate Output and Income 123
Stage of Production Sales Value ($)Value 
Added ($)
   Steel 1,000 1,000
   Plastics 3,000 3,000
   Semiconductors 1,000 1,000
   Total Inputs 5,000 (sum of 3 inputs)
2 Assembly of car (manufacturer price) 15,000 10,000 = (15,000 – 5,000)
3 Wholesale price for car dealer 16,000 1,000 = (16,000 – 15,000)
4 Retail price 18,000 2,000 = (18,000 – 16,000)
Total expenditures 18,000
Total value added 18,000
Thus, the sum of the value added by each stage of production is equal to 
$18,000, which is equal to the final selling price of the automobile. If some of 
the inputs (steel, plastics, or semiconductors) are imported, the value added 
would be reduced by the amount paid for the imports.
2.1.1  Goods and Services Included at Imputed Values
As a general rule, only the value of goods and services whose value can be determined 
by being sold in the market  are included in the measurement of GDP . Owner-  occupied

housing and government services, however, are two examples of services that are not 
sold in the marketplace but are still included in the measurement of GDP .
When a household (individual) rents a place to live, he or she is buying housing 
services. The household pays the owner of the property rent in exchange for shelter. 
The income that a property owner receives is included in the calculation of GDP . 
However, when a household purchases a home, it is implicitly paying itself in exchange 
for the shelter. As a result, the government must estimate (impute) a value for this 
owner-  occupied rent, which is then added to GDP .
The value of government services provided by police officers, firemen, judges, and 
other government officials is a key factor that affects the level of economic activity. 
However, valuing these services is difficult because they are not sold in a market like 
other services; individual customers cannot decide how much to consume or how

much they are willing to pay. Therefore, these services are simply included in GDP at 
their cost (e.g., wages paid) with no value added attributed to the production process.
For simplicity and global comparability, the number of goods and services with 
imputed values that are included in the measurement of GDP are limited. In general, 
non-  market activity is excluded from GDP . Thus, activities performed for one’s own 
benefit, such as cooking, cleaning, and home repair, are excluded. Activities in the 
so- called underground economy are also excluded. The underground economy reflects 
economic activity that people hide from the government either because it is illegal or 
because they are attempting to evade taxation. Undocumented laborers who are paid 
“off the books” are one example. The illegal drug trade is another.4 Similarly, barter 
transactions, such as neighbors exchanging services with each other (for example,

helping your neighbor repair her fence in exchange for her plowing your garden), are 
excluded from GDP .
4 Member states of the European Union are expected to measure and include illegal activities for statis -
tical and comparative purposes. Guidelines for what activities to include and how to measure them have 
been established; member states were required to comply with the guidelines effective September 2014.

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 124
Exhibit 4 shows the estimated size of the underground economy in various countries 
as a percentage of nominal GDP . The estimates range from 8 percent in the United 
States to 60 percent in Peru. Based on these estimates, the US national income accounts 
fail to account for roughly 7.4 percent (= 8/108) of economic activity, whereas in Peru, 
the national accounts miss roughly 37.5 percent (= 60/160) of the economy. For most 
of the countries shown, the national accounts miss 12–20 percent of the economy.
Exhibit 4   Underground Economy as a Percentage of Nominal GDP (2006) 
CountryUnderground Economy as a  
Percentage of Nominal GDP (%)
Peru 60.0
Mexico 32.1
South Korea 27.5
Costa Rica 26.8
Greece 26.0
India 24.4
Italy 23.1
Spain 20.2
Sweden 16.3
Germany 15.4
Canada 14.1
China 14.0
France 13.2
Japan 8.9
United States 8.0
Source:  Friedrich Schneider and Andreas Buehm, Linz University, 2009.

It should be clear from these estimates of the underground economy that the 
reliability of official GDP data varies considerably across countries. Failure to capture 
a significant portion of activity is one problem. Poor data collection practices and 
unreliable statistical methods within the official accounts are also potential problems.
2.1.2  Nominal and Real GDP
In order to evaluate an economy’s health, it is often useful to remove the effect of 
changes in the general price level on GDP because higher (lower) income driven solely 
by changes in the price level is not indicative of a higher (lower) level of economic 
activity. To accomplish this, economists use real GDP , which indicates what would 
have been the total expenditures on the output of goods and services if prices were 
unchanged. Per capita real GDP  (real GDP divided by the size of the population) has 
often been used as a measure of the average standard of living in a country.

Suppose we are interested in measuring the GDP of an economy. For the sake 
of simplicity, suppose that the economy consists of a single automobile maker and 
that in 2009, 300,000 vehicles are produced with an average market price of €18,750. 
GDP in 2009 would be €5,625,000,000. Economists define the value of goods and 
services measured at current prices as nominal GDP . Suppose that in 2010, 300,000 
vehicles are again produced but that the average market price for a vehicle increases 
by 7 percent to €20,062.50. GDP in 2010 would be €6,018,750,000. Even though no

Aggregate Output and Income 125
more cars were produced in 2010 than in 2009, it appears that the economy grew by 
(€6,018,750,000/€5,625,000,000) – 1 = 7% between 2009 and 2010, although it actually 
did not grow at all.
Nominal and real GDP can be expressed as
Nominal GDPt = Pt × Qt
where
 Pt = Prices in year t
 Qt = Quantity produced in year t
Real GDPt = PB × Qt
where
 PB = Prices in the base year
Taking the base year to be 2009 and putting in the 2009 and 2010 numbers gives:
Nominal GDP2009 = (€18,750 × 300,000) = €5,625,000,000
Real GDP2009 = (€18,750 × 300,000) = €5,625,000,000
Nominal GDP2010 = (€20,062.50 × 300,000) = €6,018,750,000
Real GDP2010 = (€18,750 × 300,000) = €5,625,000,000
In this example, real GDP did not change between 2009 and 2010 because the total 
output remained the same: 300,000 vehicles. The difference between nominal GDP 
in 2010 and real GDP in 2010 was the 7 percent inflation rate.
Now suppose that the auto manufacturer produced 3 percent more vehicles in

2010 than in 2009 (i.e., production in 2010 was 309,000 vehicles). Real GDP would 
increase by 3 percent from 2009 to 2010. With a 7 percent increase in prices, nominal 
GDP for 2010 would now be
 Nominal GDP2010 = (1.03 × 300,000) × (1.07 × €18,750)
  = (309,000 × €20,062.50)
  = €6,199,312,500
The implicit price deflator for GDP , or simply the GDP deflator , is defined as
GDP deflatorValue of current y ear output at current y ear =pprices
Value of current y ear output at base y ear prices10×0 0
Thus, in the example the GDP deflator for 2010 is [(309,000 × €20,062.50)/ (309,000 × 
€18,750)](100) = (1.07)(100) = 107. The GDP deflator broadly measures the aggregate 
changes in prices across the overall economy, and hence changes in the deflator provide 
a useful gauge of inflation within the economy.
Real GDP is equal to nominal GDP divided by the GDP deflator scaled by 100:
Real GDP = [Nominal GDP/(GDP deflator/100)]

This relation gives the GDP deflator its name. That is, the measure of GDP in terms 
of current prices, nominal GDP , is adjusted for inflation by dividing it by the deflator. 
The expression also shows that the GDP deflator is the ratio of nominal GDP to real 
GDP scaled by 100:
GDP deflator = (Nominal GDP/Real GDP) × 100
Thus, real GDP for 2010 would be
 Real GDP2010 = [Nominal GDP/(GDP deflator/100)]
  = [€6,199,312,500/(107/100)]
  = €5,793,750,000

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 126
Note that €5,793,750,000 represents 3 percent real growth over 2009 GDP and 
3 percent higher real GDP for 2010 than under the assumption of no growth in unit 
car sales in 2010.
What would be the increase in nominal  GDP for 2010 compared with 2009 with 
the 3 percent greater automobile production and 7 percent inflation?
(Nominal GDP2010/Nominal GDP2009) – 1  
= (€6,199,312,500/€5,625,000,000) – 1  
= 0.102
So, nominal GDP would increase by 10.2 percent, which equals [(1.07 × 1.03) – 1] 
or approximately 7% + 3% = 10%. Which number is more informative about growth 
in economic activity, 3  percent real growth or 10.2  percent nominal growth? The 
real growth rate is more informative because it exactly captures increases in output. 
Nominal growth, by blending price changes with output changes, is less directly 
informative about output changes. In summary, real economic growth is measured

by the percentage change in real GDP . When measuring real economic activity or 
when comparing one nation’s economy to another, real GDP and real GDP growth 
should be used because they more closely reflect the quantity of output available for 
consumption and investment.
EXAMPLE 2   
Calculating the GDP Deflator
John Lambert is an equity analyst with Equitytrust, a Canadian investment 
management firm that primarily invests in Canadian stocks and bonds. The 
investment policy committee for the firm is concerned about the possibility 
of inflation. The implicit GDP deflator is an important measure of the overall 
price level in the economy, and changes in the deflator provide an important 
gauge of inflation within the economy. GDP data have been released by Statistics 
Canada and are shown in Exhibit 5. Lambert is asked by the committee to use 
the GDP data to calculate the implicit GDP price deflator from 2005 to 2009 
and the inflation rate for 2009.
Exhibit 5   Real and Nominal GDP for Canada

Seasonally adjusted at annual rates (SAAR)
2005 2006 2007 2008 2009
GDP at market prices (million C$) 1,373,845 1,450,405 1,529,589 1,599,608 1,527,258
Real GDP (million 2002 C$) 1,247,807 1,283,033 1,311,260 1,318,054 1,285,604
Solution:
The implicit GDP price deflator measures inflation across all sectors of the econ -
omy, including the consumer, business, government, exports, and imports. It is 
calculated as the ratio of nominal to real GDP and reported as an index number 
with the base year deflator equal to 100. The implicit GDP price deflator for the 
Canadian economy for 2009 is calculated as (1,527,258/1,285,604) × 100 = 118.8. 
The results for the other years are shown in the following table:

Aggregate Output and Income 127
Implicit GDP price deflator 110.1 113.0 116.6 121.4 118.8
The inflation rate is calculated as a percentage change in the index. For 2009, 
the annual inflation rate is equal to [(118.8/121.4) – 1] or –2.1 percent. This 
shows that Canada actually experienced deflation in 2009 even though prices 
are still above their level in 2007.
2.2 The Components of GDP
Having defined GDP and discussed how it is measured, we can now consider the major 
components of GDP , the flows among the four major sectors of the economy—the 
household sector, the business sector, the government sector, and the foreign or external 
sector (comprising transactions with the “rest of the world”)—and the markets through 
which they interact. An expression for GDP , based on the expenditure approach, is

GDP = C + I + G + (X – M)  
where
 C = Consumer spending on final goods and services
 I = Gross private domestic investment, which includes business investment in 
capital goods (e.g., plant and equipment) and changes in inventory ( inven -
tory investment )
 G = Government spending on final goods and services
 X = Exports
 M = Imports
Exhibit 6 shows the flow of expenditures, income, and financing among the four 
sectors of the economy and the three principal markets. In the exhibit, solid arrows 
point in the direction of expenditure on final goods and services. For simplicity, cor -
responding flows of output are not shown separately. The flow of factors of production 
is also shown with a solid arrow. Financial flows, including income and net taxes, are 
shown with dashed arrows pointing to the recipient of funds.(1)

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 128
Exhibit 6   Output, Income, and Expenditure Flows
Goods MarketHouseholds
Net Taxes (T)
Government
Spending (G)Consumption (C)
Net Exports 
(X–M)Investment (I)C + I + G + (X–M)Income
Labor, Capital,
Land
Government Borrowing Net Foreign Borrowing/LendingFactor Market
Financial 
MarketsGovernment
Household Savings (S)
Business Financing: Debt and EquityFirms
Rest of the
World
2.2.1  The Household and Business Sectors
The very top portion of Exhibit 6 shows the services of labor, land, and capital flowing 
through the factor market  to business firms and the flow of income back from firms 
to households. Households spend part of their income on consumption ( C) and save 
(S) part of their income for future consumption. Current consumption expenditure 
flows through the goods market  to the business sector. Household saving flows into 
the financial markets  where it provides funding for businesses that need to borrow or

raise equity capital. Firms borrow or raise equity primarily to finance investment ( I) 
in inventory, property, plant, and equipment. Investment ( I) is shown flowing from 
firms through the goods market and back to firms because the business sector both 
demands and produces the goods needed to build productive capacity ( capital goods ).
In most developed economies, like Italy and the United States, expenditures on 
capital goods represent a significant portion of GDP . Investments (expenditures) on 
capital goods accounted for approximately 21.1 percent of Italy’s GDP in 2007, while 
in the United States investments accounted for approximately 18.4 percent of GDP . 
In some developing countries, notably China (40.0 percent) and India (33.8 percent), 
investment spending accounts for a substantially larger share of the economy.5 As we 
will examine in greater detail later, investment spending is an important determinant

of an economy’s long-  term growth rate. At the same time, investment spending is the 
most volatile component of the economy, and changes in capital spending, especially 
spending on inventories, are one of the main factors causing short-  run economic 
fluctuations.
5 See Exhibit  27 later in this reading for investment details for other countries. OECD.Stat Extracts: 
Country Statistical Profiles 2009 (stats.oecd.org) and Economic Report of the President  (Washington, DC: 
US Government Printing Office, 2010): Table B-  12, page 345.

Aggregate Output and Income 129
2.2.2  The Government Sector
The government sector collects taxes from households and businesses. For simplicity, 
only the taxes collected from the household sector are shown in Exhibit 6. In turn, 
the government sector purchases goods and services ( G) from the business sector. For 
example, the government sector hires construction companies to build roads, schools, 
and other infrastructure goods. Government expenditure ( G) also reflects spending 
on the military, police and fire protection, the postal service, and other government 
services. Provision of these services makes the government a major source of employ -
ment in most countries. To keep Exhibit 6 simple, however, government employment 
and the corresponding income are not explicitly shown.
Governments also make transfer payments to households. In general, these are 
designed to address social objectives such as maintaining minimum living standards,

providing health care, and assisting the unemployed with retraining and temporary 
support. In Exhibit 6, transfer payments are subtracted from taxes and reflected in 
net taxes ( T).
Transfer payments are not included in government expenditures on goods and 
services ( G) because they represent a monetary transfer by the government of tax 
revenue back to individuals with no corresponding receipt of goods or services. The 
household spending facilitated by the transfer payments is, of course, included in 
consumption ( C) and, hence, GDP . It is worth noting that transfers do not always take 
the form of direct payments to beneficiaries. Instead, the government may pay for or 
even directly provide goods or services to individuals. For example, universal health 
care programs often work in this way.
If, as is usually the case, government expenditure ( G) exceeds net taxes ( T), then 
the government has a fiscal deficit  and must borrow in the financial markets. Thus,

the government may compete with businesses in the financial markets for the funds 
generated by household saving. The only other potential source of funds in an economy 
is capital flows from the rest of the world. These will be discussed in the next section.
In 2007, the ratio of general government spending (which includes central govern -
ment as well as state, provincial, and local government) to GDP in Italy was 44.8 percent 
while in the United States it was 31.2 percent. In countries where the government 
provides more services, such as universal health care in Italy, the government’s con -
tribution to GDP is greater. France’s government sector represents 46.3 percent of 
GDP . In other countries, the public sector makes up a smaller share. For example, in 
Costa Rica, which has no standing army or navy, government spending is 16.1 percent 
of GDP . Exhibit 7 shows data on tax revenues, general government spending, and 
transfer payments as a share of nominal GDP .

Exhibit 7   General Government Spending and Taxes as a Percentage of GDP (2007)
General Government Tax 
Revenues as a Percentage of GDPGeneral Government Spending  
as a Percentage of GDP
Country TotalGoods and Services  
and Debt Service Transfer Payments
Canada 33.3% 31.9% 17.1% 14.8%
Mexico 20.5 22.6 Not available Not available
United States 28.3 31.2 19.5 11.7
Japan 28.1 30.5 14.9 15.6
South Korea 28.7 24.0 15.7 8.3
France 43.6 46.3 20.2 26.1
Germany 36.2 36.0 13.7 22.3

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 130
Greece 31.3 36.7 19.8 16.9
Italy 43.3 44.8 21.5 23.3
Spain 37.2 35.3 16.6 18.7
Sweden 48.2 44.5 17.7 26.8
Costa Rica 14.0 16.1 Not available Not available
Sources:  OECD Stat Extracts: Country Statistical Profiles 2009 (stats.oecd.org) and Revenue Statistics 1965–2008: 2009 Edition  (OECD).
2.2.3  The External Sector
Trade and capital flows involving the rest of the world are shown in the bottom right 
quadrant of Exhibit 6. Net exports ( X – M) reflects the difference between the value 
of goods and services sold to foreigners—exports ( X)—and the portion of domestic 
consumption ( C), investment ( I), and government expenditure ( G) that represents 
purchases of goods and services from the rest of the world—imports ( M).

A balance of trade deficit  means that the domestic economy is spending more on 
foreign goods and services than foreign economies are spending on domestic goods 
and services. It also means that the country is spending more than it produces because 
domestic saving is not sufficient to finance domestic investment plus the government’s 
fiscal balance. A trade deficit must be funded by borrowing from the rest of the world 
through the financial markets. The rest of the world is able to provide this financing 
because, by definition, it must be running a corresponding trade surplus and spending 
less than it produces.
It bears emphasizing that trade and capital flows between an economy and the 
rest of the world must balance. One area’s deficit is another’s surplus, and vice versa. 
This is an accounting identity that must hold. In effect, having allowed a country to 
run a trade deficit, foreigners must, in aggregate, finance it. However, the financing 
terms may or may not be attractive.

Exhibit 8 reports trade balances for the United States with selected countries. Note 
that Canada was the largest trading partner, both in terms of exports and imports, 
in 2008. China was a close second in selling goods to US markets, but China was not 
an important consumer of US goods. Hence, the US trade deficit with China was the 
largest by far. Overall, in 2008 the US balance of trade deficit was $231,115 million.
Exhibit 8   US International Trade in Goods—Selected Countries, 2008 
(millions of US dollars) 
Exports Imports Balance
Total, all countries 1,276,994 2,117,245 –840,251
Europe 321,151 440,802 –119,651
  Euro area 198,538 277,728 –79,190
   France 28,603 44,036 –15,433
   Germany 54,209 97,597 –43,388
   Italy 15,330 36,140 –20,810Exhibit 7   (Continued)

Aggregate Output and Income 131
Canada 261,872 342,920 –81,048
Mexico 151,147 219,808 –68,661
China 69,552 337,963 –268,411
India 17,623 25,739 –8,116
Japan 64,457 139,587 –75,130
Source:  Economic Report of the President  (Washington, DC: US Government Printing Office, 
2010): Table B-  105, page 451.
2.3 GDP , National Income, Personal Income, and Personal 
Disposable Income
This section examines the calculation of GDP and other income measures in detail 
by means of an analysis of data from Statistics Canada.
Exhibit 9 provides data on the level of Canadian GDP and its components mea -
sured at market prices (nominal GDP), leaving certain quantities to be determined.
Exhibit 9   GDP Release for the Canadian Economy  
(millions of C$ at market prices, seasonally adjusted at annual rates)
Expenditure based:
  Consumer spending 758,966 801,742 851,603 890,351 898,728
  Government spending 259,857 277,608 293,608 314,329 333,942

Government gross fixed investment 37,067 41,151 45,321 50,955 59,078
  Business gross fixed investment 255,596 283,382 301,885 313,574 269,394
  Exports 519,435 524,075 534,718 563,948 438,553
  Deduct: Imports 468,270 487,674 505,055 539,012 464,722
  Change in inventories* 10,614 9,362 8,266 5,472 –8,180
  Statistical discrepancy 580 759 –757 –9 465
GDP at Market Prices 1,373,845 1,450,405 1,529,589 1,599,608 TBD
Income based:
  Wages, salaries, and supplementary labor 
income695,093 743,392 784,885 818,613 819,066
  Corporate profits before tax** 185,855 194,024 203,392 210,756 149,438
  Government business enterprise profits 
before taxes15,293 14,805 15,493 16,355 12,975
  Interest income 61,421 66,404 71,589 83,998 63,947
  Unincorporated business net income, 
including rent85,234 86,750 90,411 94,559 99,879
  Taxes less subsidies on factors of 
production61,982 64,536 67,900 71,094 70,604
  Taxes less subsidies on products 93,302 96,052 98,816 94,840 93,030
(continued)Exhibit 8   (Continued)

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 132
National Income 1,198,180 1,265,963 1,332,486 1,390,215 TBD
  Statistical discrepancy –581 –759 757 10 –466
  Capital consumption allowance 176,246 185,201 196,346 209,383 218,785
  Undistributed corporate profits 91,926 96,793 90,829 110,431 56,969
  Corporate income taxes 51,631 47,504 54,867 53,176 34,319
  Transfer payments: government to 
consumer136,247 145,754 154,609 163,979 174,390
Personal Income 1,035,586 1,106,832 1,174,683 1,224,653 TBD
Personal Disposable Income 794,269 853,190 901,634 949,484 965,628
  Interest paid to business 14,029 16,978 19,063 19,558 18,115
  Consumer transfers to foreigners 4,395 4,483 5,533 5,117 4,737
Personal saving 16,878 29,987 25,435 34,458 TBD
* Includes change in government inventory.
** Includes inventory valuation adjustment.
Source:  Statistics Canada.

The exhibit shows the two approaches to measuring GDP: 1) expenditures on final 
output measured as the sum of sales to the final users and 2) the sum of the factor 
incomes generated in the production of final output. In theory, the two approaches 
should provide the same estimate of GDP . As shown in the exhibit, however, in practice 
they differ because of the use of different data sources. The difference is accounted 
for by a statistical discrepancy . Market analysts more closely follow the expenditure 
approach because the expenditure data are more timely and reliable than data for the 
income components.6
Using the expenditure approach, Statistics Canada measures Canadian GDP as 
follows:
GDP   Consum er spending on goods and services  
 Business g=
+ rross fixed inv estment 
 Change in inv entories  
 Gov ernmen+
+ t t spending on goods and ser vices 
 Gov ernment gross fixe d +   investment 
 Exports Imports  
 Statistical  discrepanc y+−
+Exhibit 9   (Continued)

6 As shown in Exhibit 9, Statistics Canada divides the total statistical discrepancy roughly equally (with 
opposite signs) between the income- and expenditure-  based measures of GDP . In the US national accounts, 
the statistical discrepancy appears only in the income-  based breakdown of GDP because the expenditures 
data are believed to be more accurate than the income data.

Aggregate Output and Income 133
Note that the Canadian national income accounts classify a portion of government 
expenditures as gross fixed investment. Not all countries make this distinction. The 
United States, for example, does not. Also note that the change in business invento -
ries must be included in expenditures. Otherwise, goods produced but not yet sold 
would be left out of GDP .
The income-  based approach calculates GDP as the sum of factor incomes and 
essentially measures the cost of producing final output. However, two of the costs 
entering into the gross value of output are not really earned by a factor of production. 
These items, depreciation and indirect taxes, are discussed below. GDP is estimated 
in the income approach as follows:7
 GDP = National income + Capital consumption allowance + Statistical 
discrepancy
where national income  is the income received by all factors of production used in 
the generation of final output:
National income   Compensation of employ ees

National income   Compensation of employ ees 
 Corporate an=
+ d d gov ernment enterprise profits before taxes  
 Interest i + n ncom e 
 Unincorporated business net inco me proprietor' s i + n ncom e 
 Rent 
 Indirect business taxes less subsidie s()
+
+
Compensation of employees includes wages and supplements to wages, which 
are primarily payments for pensions and health insurance. Corporate profits before 
taxes include three items: 1) dividends paid to households, 2) undistributed corporate 
profits (retained earnings) that remain in the business sector, and 3) corporate taxes 
paid to government. Interest income is the interest paid by businesses to households, 
government, and foreigners to compensate them for the loan of a financial asset. 
Unincorporated net income, including rent, is the earnings that flow to unincor -
porated proprietors and farm operators for running their own business. “Indirect 
business taxes less subsidies” reflects taxes and subsidies included in the final price

of the good or service. It is the (net) portion of national income that is directly paid 
to the government. In the Canadian accounts, these are measured in two ways: 1) 
“taxes less subsidies on products, ” which includes sales taxes, fuel taxes, and import 
duties, and 2) “taxes less subsidies on factors of production, ” which is mainly property 
taxes and payroll taxes.
The capital consumption allowance  (CCA) is a measure of the wear and tear 
(depreciation) of the capital stock that occurs in the production of goods and services. 
This measure acknowledges the fact that some income/output must be allocated to 
replacement of the existing capital stock as it wears out. Loosely speaking, one may 
think of Profit + CCA as the total amount earned by capital, with the CCA being the 
amount that must be earned and reinvested just to maintain the existing productivity 
of the capital.
Along with the GDP report, Statistics Canada and other government statistical

agencies provide information on personal income and saving. Personal income  is a 
broad measure of household income and measures the ability of consumers to make 
purchases. As such, it is one of the key determinants of consumption spending. Personal 
7 Construction of the national income accounts varies across countries. In the United States, for example, 
national income is defined to include income received by US-  owned factors of production even if the 
income is generated outside the United States. To compute US GDP , the national income data must be 
adjusted for net foreign factor income. No adjustment is required in the Canadian data since the data are 
measured on a geographic basis equivalent to GDP .

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 134
income includes all income received by households, whether earned or unearned. 
It differs from national income in that some of the income earned by the factors of 
production (indirect business taxes, corporate income taxes, retained earnings) is 
not received by households and instead goes to the government or business sectors. 
Similarly, households receive some income from governments (transfer payments, such 
as social insurance payments, unemployment compensation, and disability payments) 
that is not earned. Thus, the following adjustments are made to national income in 
order to derive personal income:
Personal income National income  
Indirect business taxes =
−
−CCorpor ate income taxes  
Undistributed corporate profits −
+TTransfer pa yments
Personal disposable income  (PDI) is equal to personal income less personal taxes. It 
measures the amount of after-  tax income that households have to spend on goods and

services or to save. Thus, it is the most relevant, and most closely watched, measure 
of income for household spending and saving decisions.
Finally, household saving is equal to PDI less three items: consumption expenditures, 
interest paid by consumers to business, and personal transfer payments to foreigners. 
The corresponding measure of saving for the business sector equals undistributed 
corporate profits plus the capital consumption allowance.
EXAMPLE 3   
Canadian GDP Release and Other Measures of Production 
and Income
The investment policy committee at Equitytrust asks John Lambert to review the 
Canadian GDP data shown in Exhibit 9 and data from the Department of Finance 
Canada that show that the combined federal–provincial government deficit for 
2009 was 84,249 (million C$), with the federal deficit at 55,590 (million C$).
1 Calculate 2009 GDP using the expenditure approach, and indicate how 
the expenditures are represented in Exhibit 6.

2 Calculate 2009 GDP using the income approach.
3 Calculate personal income for 2009.
4 Using the Canadian data for 2009, calculate the level of household saving 
(S), the saving rate, and net taxes ( T) paid by the household sector. Given 
that the combined government budget deficit was 84,249 (million C$) in 
2009, calculate tax revenues for the Canadian economy.
5 Calculate the impact of foreign trade on the Canadian economy in 2009 
and Canada’s net foreign borrowing/lending in 2009.
6 Calculate the net amount of borrowing/lending by the business sector in 
2009.
(All numbers in millions)
In the expenditure approach, nominal GDP is calculated as the sum of spending 
by the major sectors in the economy:

Aggregate Output and Income 135
GDP = Consumer spending on goods and services + Business gross fixed 
investment + Government spending on goods and services + 
Government gross fixed investment + Exports – Imports + Change in 
inventories + Statistical discrepancy 
Substituting the numbers from Exhibit 9,
 GDP = 898,728 + 269,394 + 333,942 + 59,078 + 438,553 – 464,722 – 
8,180 + 465
  = C$1,527,258
In Exhibit 6, these expenditures are represented by the arrows pointing to the 
goods market and by the arrow pointing back to firms labeled as C + I + G + 
(X – M).
On the income side, nominal GDP is equal to national income plus the capital 
consumption allowance plus a statistical discrepancy. National income is defined 
as the sum of income received by the factors of production and is given by
National income = Compensation of employees + Corporate and govern -
ment enterprise profits before taxes + Interest income + 
Unincorporated business net income (proprietor’s income)

+ Rent + Inventory valuation adjustment + Indirect busi -
ness taxes - Subsidies
Substituting in the numbers from Exhibit 9, we get C$1,308,939, where indirect 
business taxes are equal to 70,604 + 93,030 = C$163,634. Using this result,
GDP = 1,308,939 + 218,785 – 466 = C$1,527,258
Personal income is calculated as
Personal income = National income – Indirect business taxes – Corporate 
income taxes – Undistributed corporate profits + Transfer 
payments 
Substituting in the numbers from Exhibit 9,
 Personal income = 1,308,939 – (70,604 + 93,030) – 34,319 – 56,969 + 
174,390
  = C$1,228,407
Household saving is equal to personal disposable income less three items: 
consumption expenditures, interest paid by consumers to business, and per -
sonal transfer payments to foreigners. Consumption ( C) is given in Exhibit 9 as 
C$898,728. Substituting the numbers, saving ( S) = 965,628 – 898,728 – 18,115 
– 4,737 = C$44,048.
The Canadian saving rate for 2009 = (44,048/965,628) = 4.6%

Net taxes paid by the household sector consists of two components: 1) taxes 
paid by households to the government minus 2) government transfer payments 
to households. From Exhibit 9, government transfer payments to households

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 136
for 2009 were C$174,390. The tax outlay for households in 2009 is the differ -
ence between personal income and personal disposable income. Therefore, tax 
payments by households to government equal
1,228,407 – 965,628 = C$262,779
Thus, net taxes going to government ( T) from the household sector is C$88,389. 
However, personal taxes do not cover all sources of receipts for government. 
Government receipts also come from such sources as corporate income taxes, 
indirect taxes on businesses and consumers, and contributions for social insur -
ance. The total tax receipts for all levels of government can be estimated from 
the deficit information. From Exhibit 9, government spending for 2009 totaled 
(333,942 + 59,078) = C$393,020. Therefore, total tax revenue from all sources 
is equal to 393,020 minus 84,249 or C$308,771.
Solution to 5: 
The international sector had a large impact on the Canadian economy in 2009.

Exports declined sharply—by 22.2 percent—going from C$563,948 in 2008 to 
C$438,553 in 2009. Imports declined from C$539,012 in 2008 to C$464,722 in 
2009, a 13.8 percent decrease. As a result, the Canadian economy moved from 
a trade surplus of C$24,936 in 2008 to a deficit of C$26,169 in 2009. This huge 
swing in the trade balance had a very significant negative impact on the Canadian 
economy and subtracted from GDP growth.
Canada funded the large trade deficit in 2009 by borrowing C$26,169 from 
the rest of the world through the financial markets. As discussed in Section 
2.2.3, trade and capital flows between an economy and the rest of the world 
must balance. A trade deficit must be funded by a capital inflow.
Solution to 6: 
Borrowing by the business sector depends on the level of saving in the sector 
(i.e., internally generated funds) and the level of business investment in both 
fixed assets and inventories (i.e., the amount that must be financed). For 2009,

gross saving in the business sector is equal to undistributed corporate profits 
(56,969) plus the capital consumption allowance (218,785). Thus, business sav -
ing is C$275,754. Because this number exceeds business fixed and inventory 
investment of C$261,214 (269,394 – 8,180), the business sector was a net lender 
of funds totaling C$14,540.
AGGREGATE DEMAND, AGGREGATE SUPPLY , AND 
EQUILIBRIUM
In this section, we will build a model of aggregate demand and aggregate supply and 
use it to discuss how aggregate output and the level of prices are determined in the 
economy. Aggregate demand  (AD) represents the quantity of goods and services 
that households, businesses, government, and foreign customers want to buy at any 
given level of prices. Aggregate supply  (AS) represents the quantity of goods and 
services producers are willing to supply at any given level of prices. It also reflects the 
amount of labor and capital that households are willing to offer into the marketplace

Aggregate Demand, Aggregate Supply, and Equilibrium 137
3.1 Aggregate Demand
As we will see, the aggregate demand curve looks like the ordinary demand curves 
that we encounter in microeconomics: quantity demanded increases as the price level 
declines. But our intuitive understanding of that relationship—lower price allows 
us to buy more of a good with a given level of income —does not apply here because 
income is not fixed. Instead, aggregate income/expenditure is to be determined within 
the model along with the price level. Thus, we will need to explain the relationship 
between price and quantity demanded somewhat differently.
The aggregate demand curve represents the combinations of aggregate income 
and the price level at which two conditions are satisfied. First, aggregate expenditure 
equals aggregate income. As indicated in our discussion of GDP accounting, this must 
always be true after the fact. The new aspect here is the requirement that planned

expenditure equal actual  (or realized) income. To understand the distinction, consider 
business inventories. If businesses end up with more inventory than they planned, then 
the difference represents unplanned (or unintended) business investment and actual 
output in the economy exceeded planned  expenditure by that amount. Second, the 
available real money supply is willingly held by households and businesses.
The first condition—equality of planned expenditures and actual income/out -
put—gives rise to what is called the IS curve . The second condition—equilibrium in 
the money market—is embodied in what is called the LM curve . When we put them 
together, we get the aggregate demand curve.
3.1.1  Balancing Aggregate Income and Expenditure: The IS Curve
Total expenditure on domestically produced output comes from four sources: house -
hold consumption ( C), investments ( I), government spending ( G), and net exports 
(X – M). This can be expressed as
Expenditure = C + I + G + (X – M)

Personal disposable income is equal to GDP ( Y) plus transfer payments ( F) minus 
retained earnings and depreciation (= business saving, SB) minus direct and indirect 
taxes ( R). Households allocate disposable income between consumption of goods and 
services ( C) and household saving ( SH). Therefore,
Y + F – SB – R = C + SH
Rearranging this equation, we get
Y = C + S + T
where T = (R – F) denotes net taxes and S = (SB + SH) denotes total private sector saving.
Because total expenditures must be identical to aggregate income ( Y), we have 
the following relationship:
C + S + T = C + I + G + (X – M)
By rearranging this equation, we get the following fundamental relationship among 
domestic saving, investment, the fiscal balance, and the trade balance:
S = I + (G – T) + ( X – M)  
This equation shows that domestic private saving is used or absorbed in one of three 
ways: investment spending ( I), financing government deficits ( G – T), and building

up financial claims against overseas economies [positive trade balance, ( X – M) > 0]. 
If there is a trade deficit [( X – M) < 0], then domestic private saving is being supple -
mented by inflows of foreign saving and overseas economies are building up financial 
claims against the domestic economy.(2)

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 138
By rearranging the identity, we can examine the implications of government 
deficits and surpluses:
G – T = (S – I) – ( X – M)
A fiscal deficit [( G – T) > 0] implies that the private sector must save more than it 
invests [( S – I) > 0] or the country must run a trade deficit [( X – M) < 0] with corre -
sponding inflow of foreign saving, or both.
EXAMPLE 4   
Foreign Capital Inflows Help Finance Government Deficits
The budgetary situation changed dramatically in Canada during 2009. As noted 
in Example  3, the Department of Finance Canada reported that in 2009 the 
combined federal–provincial government had a deficit of 84,249 (million C$). 
Thus, the government sector operated at a deficit that needed to be financed. 
How was this deficit financed?
Solution: 
Using the formula G – T = (S – I) – ( X – M) shows that a budget deficit is 
financed through either higher domestic saving ( S), lower business investment

(I), or borrowing from foreigners ( X – M). Private saving is given by
 Private saving = Household saving + Undistributed corporate profits + 
Capital consumption allowance
Household saving for 2009 is given in the solution to part 4 of Example 3. Using 
that figure and the 2009 values for undistributed corporate profits and capital 
consumption allowance from Exhibit 9, we get
Private saving = 44,048 + 56,969 + 218,785 = C$319,802
Comparing this number to the level of private investment in 2009 shows that 
private sector saving exceeded investment spending by C$58,588 [319,802 – 
(269,394 – 8,180)]. Thus, domestic private saving financed over 69.5 percent of 
the deficit (58,588/84,249).
To finance the rest of the government deficit, foreign imports ( M) would 
have to exceed exports ( X) by C$25,661. From Exhibit 9, the actual trade deficit 
(amount of foreign borrowing) was C$26,169, slightly greater than the amount 
required. This difference is largely due to the statistical discrepancy caused

by different data sources being used for expenditure-  based and income-  based 
estimates of GDP .
Equation 2 is the key relationship that must hold in order for aggregate income 
and aggregate expenditure to be equal. Up to this point, we have treated it as simply 
an accounting identity. We now need to think of it as the outcome of explicit deci -
sions on the part of households, businesses, government, and foreigners. When we 
do so, we are faced with the question of what underlies these decisions and how the 
requisite balance is established.
Economists have found that the dominant determinant of consumption spending 
is disposable income ( Y – SB – T). This can be expressed formally by indicating that 
consumption is a function C(·) of disposable income,
C = C(Y – SB – T)

Aggregate Demand, Aggregate Supply, and Equilibrium 139
or, dropping the technically correct but practically insignificant adjustment for retained 
earnings and depreciation ( SB), a function of GDP minus net taxes,
C = C(Y – T)
When households receive an additional unit of income, some proportion of this 
additional income is spent and the remainder is saved. The marginal propensity to 
consume  (MPC) represents the proportion of an additional unit of disposable income 
that is consumed or spent. Because the amount that is not spent is saved, the marginal 
propensity to save  (MPS) is MPS = 1 – MPC.
According to the consumption function, either an increase in real income or a 
decrease in taxes will increase aggregate consumption. Somewhat more sophisticated 
models of consumption recognize that consumption depends not only on current 
disposable income but also on wealth. Except for the very rich, individuals tend to

spend a higher fraction of their current income as their wealth increases because with 
higher current wealth, there is less need to save to provide for future consumption.
Exhibit 10 shows household consumption expenditures as a percentage of GDP 
for selected countries.
Exhibit 10   Household Final Consumption Expenditures as 
a Percentage of GDP , 20078
United States 70.1
Mexico 65.4
Italy 58.7
France 56.7
Germany 56.6
Canada 56.5
Japan 56.3
These figures reflect the average propensity to consume  (APC)—that is, the ratio 
C/Y—rather than a measure of how the next unit of income would be divided between 
spending and saving, the MPC. However, they are reasonable proxies for the MPC 
in each country. Comparing Germany’s 56.6 percent APC with Mexico’s 65.4 per -
cent, the implication is that the Mexican economy is more sensitive to changes in 
disposable household income than the German economy. All other things being 
equal, macroeconomic policies that increase disposable household income, such as

lowering government taxes, would have a larger impact on the economies of Mexico 
(65.4 percent) and the United States (70.1 percent) than similar policies would have 
in Germany (56.6 percent) or France (56.7 percent).
Companies are the primary source of investment spending ( I). They make invest -
ment decisions in order to expand their stock of physical capital, such as building 
new factories or adding new equipment to existing facilities. A definition of physical 
capital is any manmade aid to production . Companies also buy investment goods, such 
as manufacturing plants and equipment to replace existing facilities and equipment 
that wear out. Total investment, including replacement of worn-  out capital, is called 
gross investment , as opposed to net investment , which reflects only the addition of new 
8 OECD.Stat Extracts: Country Statistical Profiles 2009 (stats.oecd.org).

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 140
capacity. GDP includes gross investment; hence the name gross  domestic product. 
Total investment spending in such developed countries as Italy, Germany, the United 
Kingdom, and the United States ranged between 18 and 22 percent of GDP in 2007.9
Investment decisions depend primarily on two factors: the level of interest rates 
and aggregate output/income. The level of interest rates reflects the cost of financing 
investment. The level of aggregate output serves as a proxy for the expected profitability 
of new investments. When an economy is underutilizing its resources, interest rates 
are typically very low and yet investment spending often remains dormant because 
the expected return on new investments is also low. Conversely, when output is high 
and companies have little spare capacity, the expected return on new investments is 
high. Thus, investment decisions may be modeled as a decreasing function I(·,·) of the

real interest rate  (nominal interest rate minus the expected rate of inflation) and an 
increasing function of the level of aggregate output. Formally,
I = I(r, Y)
where I is investment spending, r is the real interest rate, and Y is, as usual, aggregate 
income. This investment function leaves out some important drivers of investment 
decisions, such as the availability of new and better technology. Nonetheless, it reflects 
the two most important considerations: the cost of funding (represented by the real 
interest rate) and the expected profitability of the new capital (proxied by the level 
of aggregate output).
Many government spending decisions are insensitive to the current level of 
economic activity, the level of interest rates, the currency exchange rate, and other 
economic factors. Thus, economists often treat the level of government spending on 
goods and services ( G) as an exogenous  policy variable determined outside the mac -

roeconomic model. In essence, this means that the adjustments required to maintain 
the balance among aggregate spending, income, and output must occur primarily 
within the private sector.
Tax policy may also be viewed as an exogenous policy tool. However, the actual 
amount of net taxes ( T) collected is closely tied to the level of economic activity. Most 
countries impose income taxes or value-  added taxes (VAT) or both that increase with 
the level of income or expenditure. Similarly, at least some transfer payments to the 
household sector are usually based on economic need and are hence inversely related 
to aggregate income. Each of these factors makes net taxes ( T) rise and fall with aggre -
gate income, Y. The government’s fiscal balance can be represented as
GT tY −= −()G
where  G is the exogenous level of government expenditure and t(Y) indicates that net 
taxes are an (increasing) function of aggregate income, Y. The fiscal balance decreases

(smaller deficit or larger surplus) as aggregate income ( Y) increases and increases as 
income declines. This effect is called an automatic stabilizer  because it tends to mit -
igate changes in aggregate output.
Net exports ( X – M) are primarily a function of income in the domestic country 
and in the rest of the world and the relative prices of domestic and foreign goods and 
services. As domestic income rises, some of the additional demand that is induced will 
be for imported goods. Thus, net exports will decline. An increase in income in the rest 
of the world will lead to an increase in demand for the domestic country’s products 
and hence an increase net exports. A decrease in the relative price of domestically 
produced goods and services, perhaps because of a depreciation of the currency, will 
shift demand toward these products and hence increase net exports.
9 OECD.Stat Extracts: Country Statistical Profiles 2009 (stats.oecd.org) and Economic Report of the

President , (Washington, DC: US Government Printing Office, 2010): Table B-  2, page 330. See Exhibit 27 
in this reading for investment details on other countries.

Aggregate Demand, Aggregate Supply, and Equilibrium 141
We are now in a position to describe how aggregate expenditure and income are 
brought into balance. Slightly rearranging Equation 2, equality of expenditure and 
income implies
S – I = (G – T) + ( X – M)
Based on the discussion above, we know that both the government’s fiscal balance 
and the trade balance decrease as income rises because of net taxes and imports, 
respectively. Hence, the right-  hand side of this equation declines with income. This 
is shown by the downward-  sloping line in Exhibit 11. Assuming the direct effect of 
higher income on saving is larger than the impact on investment, the left-  hand side 
of the equation increases as income rises. This is shown by the solid upward-  sloping 
line in Exhibit 11. Note that this line is drawn for a given level of the real interest rate, 
r0. The intersection of these curves shows the level of income at which expenditure

and income balance. At higher levels of income, the saving–investment differential 
(S – I) exceeds the combined fiscal and trade balances, implying “excess saving” or 
insufficient expenditure. At lower levels of income, the saving–investment differential 
is smaller than the combined fiscal and trade balances, implying planned expenditure 
exceeds output (= income).
Exhibit 11   Balancing Aggregate Income and Expenditure
Income, YS–I (r = r0)
S–I (r = r1 < r0)
(G–T) + (X–M)Real Interest Rate, r
The dashed, upward-  sloping line in the exhibit reflects a lower real interest rate, 
r1 < r0. This line lies to the right of the solid line because for any value of the saving–
investment differential ( S – I), the higher level of investment induced by a lower real 
interest rate requires a higher level of income to induce higher saving. With a lower 
real interest rate, the curves intersect at a higher level of income. Thus, we see that

equilibrating income and expenditure entails an inverse relationship between income 
and the real interest rate . Economists refer to this relationship as the IS curve  because 
investment ( I) and saving ( S) are the primary components that adjust to maintain 
the balance between aggregate expenditure and income. The IS curve is illustrated in 
Exhibit 12 in the next section.

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 142
EXAMPLE 5   
The IS Curve
The following equations are given for a hypothetical economy:
C=2,000 + 0.7( Y – T) Consumption function
I=400 + 0.2 Y – 30 r Investment function
G=1,500 Government spending
(X – M)=1,000 – 0.1 Y Net export function
T=–200 + 0.3 Y Tax function 
1 Based on these equations, determine the combinations of aggregate 
income ( Y) and the real interest rate ( r) that are consistent with equating 
income and expenditure. That is, find the equation that describes the IS 
curve.
2 Given a real interest rate of 4 percent, find the level of GDP , consumption 
spending, investment spending, net exports, and tax receipts.
3 Suppose the government increased expenditure from 1,500 to 2,000. Find 
the new IS curve. Does the increase in government spending result in an 
equal increase in equilibrium income for any given level of the real inter -
est rate? Why or why not?

4 Given a real interest rate of 4 percent, determine how the increased gov -
ernment spending is funded.
5 Suppose that the output/income level calculated in Question 2 is the most 
that can be produced with the economy’s resources. If the economy is 
operating at that level when the government increases expenditure from 
1,500 to 2,000, what must happen to maintain the balance between expen -
diture and income?
Starting with the basic GDP identity Y = C + I + G + (X – M) and substituting 
for each expenditure component using the equations above gives
Y = 2,000 + 0.7( Y – T) + 400 + 0.2 Y – 30 r + 1,500 + 1,000 – 0.1 Y
Substituting in the tax equation and solving for Y, we get
 Y = 2,000 + 0.7( Y + 200 – 0.3 Y) + 400 + 0.2 Y – 30 r + 1,500 + 1,000 – 0.1 Y
  = 5,040 + 0.59 Y – 30 r
 Y = 12,292.7 – 73.2 r
The final equation is the IS curve. It summarizes combinations of income and 
the real interest rate at which income and expenditure are equal. Equivalently,

it reflects equilibrium in the goods market.
If the real interest rate is 4 percent, then GDP and the components of GDP are
 Y = 12,292.7 – 73.2(4) = 11,999.9
 T = –200 + 0.3(11,999.9) = 3,399.9
 C = 2,000 + 0.7(11,999.9 – 3,399.9) = 8,020
 I = 400 + 0.2(11,999.9) – 30(4) = 2,680.0
 (X – M) = 1,000 – 0.10(11,999.9) = –200.0

Aggregate Demand, Aggregate Supply, and Equilibrium 143
Following the steps above but with G = 2,000, the IS curve is
Y = 13,512.2 – 73.2 r 
At any given level of the interest rate, aggregate income increases by 1,219.5 = 
(13,512.2 – 12,292.7). This is 2.44 (= 1,219.5/500) times the increase in govern -
ment spending. The increase in government spending has a “multiplier” effect on 
equilibrium income because as income rises, both consumption and investment 
spending also rise, leading to an even greater increase in income, which leads 
to even more spending, etc. However, some of the increased private spending 
goes for imports, and higher income also induces higher taxes and saving. The 
condition for equality of income and expenditure can be written as
G = (S – I) + T + (M – X)
So the increase in government spending must be balanced by some combination 
of 1) an increase in saving relative to investment, 2) an increase in taxes, and 3)

a rise in imports relative to exports. Given the interest rate, each of these will be 
induced by an increase in aggregate income. Because saving ( S) equals Y – C – T,
∆∆ ∆∆ ∆∆ ∆∆
∆∆
∆SY CT YY TT
YT=−−=− −()−
=− () +− ()
=07
10 70 71
03.
..
. 
YYT YY
YY−=− ()
=− () =03 03 0303
0310 30 21.. ..
.. .∆∆ ∆
∆∆ 
Using this result along with the investment, tax, and trade balance functions gives
∆∆ ∆∆ ∆
∆∆ ∆GY YY Y
YG G=−() ++ =
=() =0210 20 30 10 41
10 41 244.. .. .
/. . So, ..
Note that an extra unit of income increases saving by 0.21 but also increases 
investment spending by 0.20. So, in this hypothetical economy, the saving–invest -
ment differential ( S – I) is very insensitive to the level of aggregate income. All 
else the same, this implies that relatively large changes in income are required to 
restore the expenditure/income balance whenever there is a change in spending 
behavior.
Using the results above,
Change in fiscal  balance =− =− () 
= (∆∆ ∆ GT G10 3244
0 268 500..
. ) )=
=−() =− ()

0 268 500..
. ) )=
=−() =− ()
=−134
2440 1
0 244 50Change in trade ba lance ∆∆XM G ..
.0 0 122
2440 21 020
0 0244 5() =−
−() =−() =− ()
= (Change in SI SI G ∆∆ .. .
. ) )=12
So, the increase in government spending (500) is ultimately financed by a large 
increase in taxes (500 – 134 = 366), a very small increase in private sector excess 
saving (12), and an increase in capital flows from abroad (122).
If the economy is operating at maximum output, then an increase in government 
expenditure must “crowd out” an equal amount of private expenditure in order 
to keep total expenditure equal to output/income. In this simple model, this 
implies that the real interest rate must rise enough that investment spending

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 144
falls by the amount of the increase in government spending. Using the new IS 
curve equation from Question 3 and the original level of income from Question 
2, we need the interest rate such that
Y = 13,512.2 – 73.2 r = 11,999.9 => r = 20.66%
So the real interest rate would soar from 4 percent to 20.66 percent to choke 
off investment spending.
3.1.2  Equilibrium in the Money Market: The LM Curve
The IS curve tells us what level of income is consistent with a given level of the real 
interest rate but does not address the appropriate level of interest rates, nor does it 
depend on the price level. In order to determine the interest rate and introduce a con -
nection between output and the price level, we must consider supply and demand in 
the financial markets. To keep the model as simple as possible, we will deal explicitly 
with demand and supply for only one financial asset: money. All other assets (e.g.,

stocks and bonds) are implicitly treated as a composite alternative to holding money. 
In some of the subsequent discussion, however, we will note differential impacts on 
equity and fixed-  income securities.
The quantity theory of money  equation provides a straightforward connection 
among the nominal money supply ( M), the price level ( P), and real income/expen -
diture ( Y):
MV = PY
In this equation, V is the velocity of money , the average rate at which money circu -
lates through the economy to facilitate expenditure. This equation essentially defines 
V. The equation begins to have economic content only when we make assumptions 
about how velocity is related to such economic variables as the interest rate. In the 
simplest case, if velocity is assumed to be constant, then the quantity theory of money 
equation implies that the money supply determines the nominal value of output ( PY). 
Therefore, an increase in the money supply will increase the nominal value of output.

However, this equation alone cannot tell us how that increase would be split between 
price and quantity.
The quantity theory equation can be rewritten in terms of the supply and demand 
for real money balances:
M/P = (M/P)D = kY
where k = 1/ V reflects how much money people want to hold for every currency unit 
of real income. The demand for real money balances is typically assumed to depend 
inversely on the interest rate because a higher interest rate encourages investors to 
shift their assets out of money (bank deposits) into higher-  yielding securities. Although 
the quantity theory of money suggests that the demand for real money balances is 
proportional to real income, this need not be the case. The important point is that 
money demand increases with income. Thus, demand for real money balances is an 
increasing function M(·,·) of real income and a decreasing function of the interest 
rate. Equilibrium in the money market requires
M/P = M(r,Y)

Holding the real money supply ( M/P) constant, this equation implies a positive 
relationship between real income ( Y) and the real interest rate ( r). Given the real 
money supply, an increase in real income must be accompanied by an increase in 
the interest rate in order to keep the demand for real money balances equal to the 
supply. This relationship, which economists refer to as the LM curve , is shown by the 
upward-  sloping curve in Exhibit 12.

Aggregate Demand, Aggregate Supply, and Equilibrium 145
Exhibit 12   The IS and LM Curves
Income, YReal Interest Rate, r
LM [M/P = (M/P)0]
LM [M/P > (M/P)0]
IS
The intersection of the IS and LM curves determines the combination of real 
income and the real interest rate that is consistent with both the equality of income 
and (planned) expenditure (the IS curve) and equilibrium in the money market (the 
LM curve). In Exhibit 12, the dashed LM curve reflects a higher real money supply 
than the solid LM curve. With a higher real money supply, the intersection of the IS 
and LM curves occurs at a higher level of real income and a lower level of the real 
3.1.3  The Aggregate Demand Curve
If the nominal money supply ( M) is held constant, then a higher or lower real money 
supply ( M/P) arises because of changes in the price level. If the price level declines, 
the real money supply increases and, as shown in Exhibit 12, real income increases

while the real interest rate declines. Conversely, an increase in the price level leads 
to a decline in real income and an increase in the real interest rate. This inverse rela -
tionship between the price level and real income is illustrated in Exhibit 13. This is 
the aggregate demand curve  (AD curve).

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 146
Exhibit 13   The Aggregate Demand Curve 
Income, Output, Y Y2 Y1Price Level
AD1P1P2B
A
As shown in Exhibit  13, an increase in the price level from P1 to P2 reduces 
income from Y1 to Y2. Our development of the AD curve emphasized only one 
channel through which prices affect the quantity of output demanded (i.e., planned 
real expenditure)—the interest rate. There are, however, other mechanisms. Higher 
prices erode the purchasing power of retirees and others whose income is fixed in 
nominal terms. Similarly, higher prices reduce the real value of nominal assets (e.g., 
stocks and bonds) and may reduce consumption relative to current income as people 
seek to rebuild the real purchasing power of their wealth. Higher domestic prices also 
make domestically produced goods more expensive relative to imports (assuming a 
constant currency exchange rate). In each case, lower prices have the opposite effect,

increasing aggregate expenditure and income.
It should be clear that many interesting and important aspects of the economy 
are subsumed into the AD curve: saving, investment, trade and capital flows, interest 
rates, asset prices, fiscal and monetary policy, and more. All of these disappear behind 
a deceptively simple relationship between price and output/income.
Before moving on to consider aggregate supply, let’s look more closely at the 
interaction of interest rates and income implicit in movements along the AD curve. 
For simplicity, we assume there are no changes in the fiscal or trade balances so that 
maintaining the balance between aggregate expenditure and aggregate income requires 
that changes in investment spending equal changes in private saving. As the price level 
increases, the real money supply ( M/P) declines. To induce a corresponding decline 
in money demand, the interest rate must rise so that other assets are more attrac -

tive and income must fall to reduce the transactional need for money balances. The 
higher interest rate induces companies to reduce investment spending. The decline in 
income reduces household saving. The slope of the AD curve depends on the relative 
sensitivities of investment, saving, and money demand to income and the interest rate . 
The AD curve will be flatter if
■■investment expenditure is highly sensitive to the interest rate;
■■saving is insensitive to income;
■■money demand is insensitive to interest rates; and
■■money demand is insensitive to income.

Aggregate Demand, Aggregate Supply, and Equilibrium 147
The first two conditions directly imply that income will have to move more to 
induce a large enough change in saving to match the change in investment spending. 
All else equal, each of the last two conditions implies that a larger change in the 
interest rate is required to bring money demand in line with money supply. This, in 
turn, implies a larger change in investment spending and a correspondingly larger 
change in saving and income.
EXAMPLE 6   
Aggregate Demand
The money demand and supply equations for our hypothetical economy are
MP Yr
MP Pd =− +− ()
=300 05 30
5 200.
, real money  demand
real mone y suupply ()
1 Find the equation for the LM curve.
2 Using the IS curve from Question 1 of Example 5, find the equation of the 
AD curve.
3 Find the levels of GDP and the interest rate if P = 1.
4 What will happen to GDP and the interest rate if the price level rises to 
1.1 or falls to 0.9?

5 Suppose investment spending were more sensitive to the interest rate so 
that the IS becomes ( Y = 12,292.7 – 150 r). What happens to the slope of 
the AD curve? What does this imply about the effectiveness of monetary 
policy?
Setting the real money supply equal to real money demand and rearranging, 
we get the LM equation:
Y = 600 + 2( M/P) + 60 r
Or with M = 5,200,
Y = 600 + 10,400/ P + 60 r (LM equation) 
From Question 1 of Example 5, the IS equation is Y = 12,292.7 – 73.2 r. We now 
have two equations and two unknowns. The easiest way to solve this problem 
is to multiply the LM curve by 1.22 (= 73.2/60.0) and then add the equations:
122 732 2447 32
12 292 77 32.. .
,. .YM Pr
Yr=+ () + ()
=−LM equatio n
IS equuatio n ()
Adding the two equations and solving for Y,
YM P
PM=+ () ()
=+5 867 01 099
5 867 05 715 3,. .
,. ,.AD curve
with   = 5,20 00 ()
If P = 1, the AD curve gives GDP as Y = 5,867.0 + 5,715.3 = 11,582.3. From the

money demand and supply equation, the equilibrium interest rate is
5,200/1 = –300 + 0.5(11,582.3) – 30 r = > r = 9.7%

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 148
If the price level increases to 1.1, GDP declines to Y = 5,867.0 + 5,715.3/1.1 = 
11,062.7. If the price level falls to 0.9, GDP increases to Y = 5,867.0 + 5,715.3/0.9 = 
12,217.3. To find the interest rate in each case, we plug these values for Y into 
the IS curve.
If
If  
 PY rr
PY== =− => =
==11 11 062 71 2 292 77 32 16 8
09 12.: ,. ,. .. %
.: ,2217 31 2 292 77 32 10 ., .. .% =− => =  rr
Thus, we have the following relationship among the price level, GDP , and the 
interest rate:
Price Level GDP Interest Rate
0.9 12,217.3 1.0
1.0 11,582.3 9.7
1.1 11,062.7 16.8
The inverse relationship between GDP and the price level is the AD curve. The 
inverse relationship between GDP and the interest rate reflects the IS curve.
If the interest rate parameter in the IS curve is 150 instead of 73.2, we can 
multiply the LM equation by 2.5 (= 150/60) instead of 1.22 (= 73.2/60) to get 
the system of equations:

25 15 51 5L M equatio n
12 292 71 5I S equati.,
,.YM Pr
Yr=+ () + ()
=−00 0
0o on ()
Adding these equations and solving for Y gives
YM P
PM=+ () ()
=+394771 429 new AD curve
39477w ith ,. .
,. ,.0
07 428 6 = = () 52,00
Comparing the new AD curve to the original AD curve indicates that output ( Y) 
is now more sensitive to the price level. That is, the AD curve is flatter. Monetary 
policy is now more effective because, at any given price level, an increase in M 
has a greater impact on Y. This can be understood as follows: As the real money 
supply increases, the interest rate must fall and/or expenditure must increase in 
order to induce households to hold the increased money supply. With investment 
spending now more sensitive to the interest rate, income will have to rise by 
more in order to increase saving by a corresponding amount.
3.2 Aggregate Supply
Aggregate demand only tells us the relationship between the price level and the amount

of output demanded at those prices. To understand what price and output level will 
prevail in the economy, we need to add aggregate supply, the amount of output pro -
ducers are willing to provide at various prices. The aggregate supply curve  (AS curve) 
represents the level of domestic output that companies will produce at each price 
level. Unlike the demand side, we must distinguish between the short- and long-  run 
AS curves, which differ with respect to how wages and other input prices respond to 
changes in final output prices. “Long run” and “short run” are relative terms and are 
necessarily imprecise with respect to calendar time. The “long run” is long enough that 
wages, prices, and expectations can adjust but not long enough that physical capital is 
a variable input. Capital and the available technology to use that capital remain fixed. 
This condition implies a period of at least a few years and perhaps a decade. The truly

Aggregate Demand, Aggregate Supply, and Equilibrium 149
long run in which even the capital stock is variable may be thought of as covering 
multiple decades. Consideration of the very long run is postponed to our discussion 
of economic growth in Section 4.
In the very short run, perhaps a few months or quarters, companies will increase 
or decrease output to some degree without changing price. This is shown in Exhibit 14 
by the horizontal line labeled VSRAS. If demand is somewhat stronger than expected, 
companies earn higher profit by increasing output as long as they can cover their 
variable costs. So they will run their plant and equipment more intensively, demand 
more effort from their salaried employees, and increase the hours of employees who 
are paid on the basis of hours worked. If demand is somewhat weaker than projected, 
companies can run their plants less intensively, cut labor hours, and utilize staff to

perform maintenance and carry out efficiency-  enhancing projects that are often 
postponed during busier periods.
Exhibit 14   Aggregate Supply Curve
Output, Y Y1 Y2Price Level, P
P2
P1SRAS
VSRASLRAS
Over somewhat longer periods, the AS curve is upward sloping because more 
costs become variable. This is represented by the short-  run aggregate supply (SRAS) 
curve in Exhibit 14. In most businesses, wages are adjusted once a year, but for com -
panies with union contracts, several years may pass before the contracts expire. The 
prices for raw materials and other inputs may also be established under long-  term 
contracts. Hence, wages and other input costs are relatively inflexible in the short 
run and do not fully adjust to changes in output prices. As the price level rises, most 
companies enjoy higher profit margins and hence expand production. In Exhibit 14, 
when prices move from P1 to P2, the quantity of aggregate output supplied increases

from Y1 to Y2. Conversely, a reduction in the price level squeezes profit margins and 
causes companies to reduce production.
Over time, however, wages and other input prices tend to “catch up” with the prices 
of final goods and services. In other words, wages and prices that are inflexible or 
slow to adjust in the short run adjust to changes in the price level over the long run. 
Thus, over the long run, when the aggregate price level changes, wages and other input 
prices change proportionately so that the higher aggregate price level has no impact on

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 150
aggregate supply. This is illustrated by the vertical long-  run aggregate supply (LRAS) 
curve in Exhibit 14. As prices move from P1 to P2, the quantity of output supplied 
remains at Q1 in the long run. The only change that occurs is that prices shift to a 
higher level (from P1 to P2).
The position of the LRAS curve is determined by the potential output of the 
economy. The amount of output produced depends on the fixed amount of capital 
and labor and the available technology. This classical model of aggregate supply can 
be expressed as
YK LY =() = F,
where  K is the fixed amount of capital and  L is the available labor supply. The stock 
of capital is assumed to incorporate the existing technological base.10 The available 
labor supply is also held constant, and workers are assumed to have a given set of 
skills. The long-  run equilibrium level of output, Y1 in Exhibit 14, is referred to as the

full employment , or natural , level of output. At this level of output, the economy’s 
resources are deemed to be fully employed and (labor) unemployment is at its natural 
rate. This concept of a natural rate of unemployment assumes the macroeconomy is 
currently operating at an efficient and unconstrained level of production. Companies 
have enough spare capacity to avoid bottlenecks, and there is a modest, stable pool 
of unemployed workers (job seekers equal job vacancies) looking for and transitioning 
into new jobs.
3.3 Shifts in Aggregate Demand and Supply
In the next two sections, the aggregate demand (AD) and aggregate supply (AS) models 
are used to address three critical macroeconomic questions:
1 What causes an economy to expand or contract?
2 What causes inflation and changes in the level of unemployment?
3 What determines an economy’s rate of sustainable growth, and how can it be 
measured?
Before addressing these questions, we need to distinguish between 1) the long-

run growth rate of real GDP and 2) short-  run fluctuations in real GDP around this 
long-  run trend.
The business cycle is a direct result of short-  term fluctuations of real GDP . It 
consists of periods of economic expansion and contraction. In an expansion, real 
GDP is increasing, the unemployment rate is declining, and capacity utilization is 
rising. In a contraction, real GDP is decreasing, the unemployment rate is rising, 
and capacity utilization is declining. Shifts in the AD and AS curves determine the 
short-  run changes in the economy associated with the business cycle. In addition, the 
AD–AS model provides a framework for estimating the sustainable growth rate of an 
economy, which is addressed in Section 4.
From an asset allocation perspective, it is important to determine the current 
phase of the business cycle as well as how fast the economy is growing relative to its 
sustainable growth rate. The expected rate of return on equities and fixed-  income

securities, for example, depends on estimates of the growth rate of GDP and inflation. 
For equities, GDP growth is the primary determinant of aggregate corporate profits. 
For fixed-  income securities, the expected rate of inflation determines the spread 
10 Note that investment, I, reflects replacement of worn-  out capital plus the change in capital, ∆ K. Over 
short periods of time, net investment is assumed to have a negligible effect on aggregate supply. The 
cumulative effect of investment on economic growth is discussed in Section 4.

Aggregate Demand, Aggregate Supply, and Equilibrium 151
between real and nominal rates of return. In order to use the AD and AS model to 
analyze the economy and to make investment decisions, we need to first understand 
what factors cause the curves to shift.
3.3.1  Shifts in Aggregate Demand
In addition to price, factors that influence the level of spending by households, com -
panies, governments, and foreigners (i.e., the aggregate level of expenditures) will 
cause the AD curve to shift. A shift to the right represents an increase in aggregate 
demand at any price level. Exhibit 15 shows this as a shift from AD1 to AD2. A shift 
to the left represents a decrease in aggregate demand at any price level. This is indi -
cated by a move from AD1 to AD3. Key factors that directly or indirectly influence 
the level of aggregate expenditures and cause the aggregate demand curve to shift 
include changes in
■■household wealth;
■■consumer and business expectations;
■■capacity utilization;

■■monetary policy;
■■the exchange rate;
■■growth in global economy; and
■■fiscal policy (government spending and taxes).
Exhibit 15   Shifts in the Aggregate Demand Curve
Income, Output, YPrice Level
AD2AD1 AD3
Household Wealth  Household wealth includes the value of both financial assets (e.g., 
cash, savings accounts, investment securities, and pensions) and real assets (e.g., real 
estate). The primary reason households save a portion of their current income is to 
accumulate wealth for consumption in the future. The proportion of disposable income 
that households save depends partly on the value of the financial and real assets that 
they have already accumulated. If these assets increase in value, households will tend 
to save less and spend a greater proportion of their income because they will still be 
able to meet their wealth accumulation goals. As a result, an increase in household 
wealth increases consumer spending and shifts the aggregate demand curve to the

right. In contrast, a decline in wealth will reduce consumer spending and shift the AD 
curve to the left. This is often referred to as the wealth effect  and is one explanation 
for how changes in equity prices affect economic activity. Higher equity prices increase

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 152
household wealth, which increases consumer spending and reduces the amount saved 
out of current income. Economic studies estimate that an increase or decrease in wealth 
in developed countries increases or decreases annual consumer spending by 3–7 percent 
of the change in wealth.11 A smaller but still statistically significant wealth effect has 
been found in a number of emerging markets (developing countries).12
Exhibit 16   Housing Prices and the Saving Rate in the United Kingdom
Y earHousing Prices  
(first quarter of each year)  
(Index 2000 Q1 = 100) Saving Rate (%)
2000 100 4.7
2002 122.7 5.8
2004 180.5 3.7
2006 206.3 2.9
2007 225.9 2.1
2008 220.5 1.2
2009 192.7 7.0
Source:  Office of National Statistics, United Kingdom.
EXAMPLE 7   
The Wealth Effect on Saving and Consumption
The importance of the wealth effect on consumption, and its relationship to 
housing prices, was evident in the recession that began in late 2007. During this

period, global GDP declined by the steepest amount in the post–World War II 
period. A major factor associated with the economic downturn was the sharp 
fall in housing prices, especially in countries that experienced a housing boom 
earlier in the decade, such as the United States, the United Kingdom, Spain, 
and Ireland. In each of these countries, consumers reduced spending sharply 
and raised the level of saving in response to the decline in wealth. Do the data 
in Exhibit 16 provide support for the wealth effect?
Solution: 
Housing prices in the United Kingdom rose by nearly 126  percent [(225.9 – 
100)/100] between 2000 and 2007. As predicted, the saving rate declined (with 
a lag), going from an average of 5.3  percent of income in 2000 and 2002 to 
1.2 percent in 2008. Then, as housing prices fell by 14.7 percent between 2007 
and 2009, the saving rate rose dramatically from 1.2 percent in 2008 to 7 per -
cent in 2009. Of course, the decline in housing prices was not the only factor

contributing to the increase in the saving rate. Stock prices also declined in this 
period, further reducing wealth in the United Kingdom, and the recession raised 
uncertainty over future jobs and income.
11 See, for example, Case, Quigley, and Shiller (2005).
12 See Funke (2004).

Aggregate Demand, Aggregate Supply, and Equilibrium 153
Consumer and Business Expectations  Psychology has an important impact on 
consumer and business spending. When consumers are confident about their future 
income and the stability/safety of their jobs, they tend to spend a higher portion of their 
disposable income. This shifts the AD curve to the right. Consumer spending declines 
and the AD curve shifts to the left when consumers become less confident. Similarly, 
when businesses are optimistic about their future growth and profitability, they spend 
(invest) more on capital projects, which also shifts the AD curve to the right.
Capacity Utilization  Capacity utilization is a measure of how fully an economy’s 
production capacity is being used. Companies with excess capacity have little incen -
tive to invest in new property, plant, and equipment. In contrast, when companies are 
operating at or near full capacity, they will need to increase investment spending in

order to expand production. Data from the OECD and the US Federal Reserve indicate 
that when aggregate capacity utilization reaches 82 to 85 percent, production blockages 
arise, prompting companies to increase their level of investment spending. This shifts 
the AD curve to the right.
Fiscal Policy  Fiscal policy  is the use of taxes and government spending to affect the 
level of aggregate expenditures.13 An increase in government spending, one of the 
direct components of AD, shifts the AD curve to the right, whereas a decrease in gov -
ernment spending shifts the AD curve to the left. Taxes affect GDP indirectly through 
their effect on consumer spending and business investment. Lower taxes will increase 
the proportion of personal income and corporate pre-  tax profits that consumers and 
businesses have available to spend and will shift the AD curve to the right. In contrast, 
higher taxes will shift the AD curve to the left.

Monetary Policy  Money  is generally defined as currency in circulation plus deposits 
at commercial banks. Monetary policy  refers to action taken by a nation’s central 
bank to affect aggregate output and prices through changes in bank reserves, reserve 
requirements, or its target interest rate.
Most countries have fractional reserve banking systems in which each bank 
must hold reserves (vault cash plus deposits at the central bank) at least equal to the 
required reserve ratio times its customer deposits. Banks with excess reserves can 
lend them to banks that need reserves to meet their reserve requirements. The central 
bank can increase the money supply by 1) buying securities from banks, 2) lowering 
the required reserve ratio, and/or 3) reducing its target for the interest rate at which 
banks borrow and lend reserves among themselves. In each case, the opposite action 
would decrease the money supply.

When the central bank buys securities from banks in an open-  market operation, 
it pays for them with a corresponding increase in bank reserves. This increases the 
amount of deposits banks can accept from their customers—that is, the money supply. 
Similarly, cutting the required reserve ratio increases the level of deposits (i.e., money) 
consistent with a given level of reserves in the system. If the central bank chooses to 
target an interbank lending rate, as the Federal Reserve targets the federal funds rate 
in the United States, then it must add or drain reserves via open-  market operations 
to maintain the target interest rate. If it raises (lowers) its target interest rate, it will 
have to drain (add) reserves in order to make reserves more (less) expensive in the 
interbank market. Thus, open-  market operations and interest rate targeting are very 
closely related. The main distinction is whether the central bank chooses to target a

13 Government spending and taxes may be adjusted for other purposes too. In macroeconomics, however, 
the term “fiscal policy” is usually reserved for actions intended to affect the overall level of expenditure.

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 154
level of reserves and let the market determine the interest rate or chooses to target 
the interest rate and let the market (banks) determine the level of reserves they desire 
to hold at that rate.
An increase in the money supply shifts the AD curve to the right so that each price 
level corresponds to a higher level of income and expenditure.14 There are various 
channels through which the additional expenditures may be induced. For example, 
the interest rate reduction required to induce investors to hold the additional money 
balances will encourage companies to investment more and households to borrow to 
purchase durable goods, such as cars. In addition, banks may facilitate greater expen -
diture by raising credit limits and loosening credit standards. Conversely, a reduction 
in the money supply shifts the AD curve to the left.
Exhibit 17 illustrates the short-  run and long-  run effect of expansionary monetary

policy. Suppose the central bank expands the money supply in an attempt to stimulate 
demand when the economy is already in long-  run equilibrium. The expansionary policy 
will shift the AD curve to the right, from AD1 to AD2. In the very short run, output 
will expand from Y1 to Y2 without an increase in the price level. After operating at 
higher-  than-  normal production rates for a few months or quarters, companies will 
begin to push for price increases and input prices will begin to rise as well. The aggre -
gate supply curve will steepen, and prices will increase to P3 while output declines 
to Y3. As input prices become more flexible, the AS curve will steepen until, in the 
long run, it is vertical and output has returned to the long-  run natural level, Y1, with 
prices rising to P4. Thus, expanding the money supply increases output in the short 
run, but in the long run it affects only the price level.
Exhibit 17   Short-  Run and Long-  Run Effect of Monetary Expansion

Output, Y Y1 Y2 Y3Price Level, P
P4SRAS
VSRAS
AD2
AD1LRAS
P3
P1
14 An unusual but important special case known as a liquidity trap  occurs if a) banks are willing to hold 
virtually unlimited excess reserves rather than expand their balance sheets by taking deposits and making 
loans and/or b) demand for money balances by households and companies is insensitive to the level of 
income. In a liquidity trap, monetary policy will be ineffective and the AD curve will not shift despite the 
central bank’s efforts. Some have argued that this was a reasonable description of the US situation in 2010.

Aggregate Demand, Aggregate Supply, and Equilibrium 155
Exchange Rate  An exchange rate is the price of one currency relative to another. 
Changes in the exchange rate affect the price of exports and imports and thus aggre -
gate demand. For example, a lower euro relative to other currencies makes European 
exports cheaper in world markets and foreign products sold in Europe (European 
imports) more expensive. Therefore, a lower euro should cause European exports to 
increase and imports to decline, causing the AD curve to shift to the right. Conversely, 
a stronger euro reduces exports and raises imports, and the AD curve shifts to the left.
Growth in the Global Economy  International trade is what links countries together 
and creates a global economy. Faster economic growth in foreign markets encourages 
foreigners to buy more products from domestic producers and increases exports. 
For example, rapid GDP growth in ASEAN member countries has increased their

demand for foreign products. Japan has benefited from this rapid growth because it 
has exported more products to them. In terms of the AD and AS model, the AD curve 
for Japan has shifted to the right because of increased demand for Japanese products in 
ASEAN countries, resulting in higher exports. A decline in the growth rates of ASEAN 
members’ economies would have a negative effect on the Japanese economy because 
exports would be lower. This would cause the Japanese AD curve to shift to the left.
What happens to interest rates when the AD curve shifts? In the case of an 
increase in the money supply, the interest rate declines at each price level because 
the increase in income ( Y) increases saving and rates must decline to induce a corre -
sponding increase in investment spending ( I). In each of the other cases considered 
above, a rightward shift in the AD curve will increase the interest rate at each price

level. With the real money supply held constant, the interest rate must rise as income 
increases. The increase in the interest rate reduces the demand for money at each 
level of expenditure/income and, therefore, allows expenditure/income to increase 
without an increase in the money supply. In terms of the quantity theory of money 
equation, this corresponds to a higher velocity of money, V.
The main factors that shift the AD curve are summarized in Exhibit 18. In each 
case, the impact of the factor is considered in isolation. In practice, however, various 
factors may be at work simultaneously and there may be interaction among them. 
This is especially true with regard to expectational factors—consumer and business 
confidence—which are likely to be influenced by other developments.
Exhibit 18   Impact of Factors Shifting Aggregate Demand
An Increase in the Following Factors: Shifts the AD Curve: Reason: 
Stock prices Rightward: Increase in AD Higher consumption

Housing prices Rightward: Increase in AD Higher consumption
Consumer confidence Rightward: Increase in AD Higher consumption
Business confidence Rightward: Increase in AD Higher investment
Capacity utilization Rightward: Increase in AD Higher investment
Government spending Rightward: Increase in AD Government spending a component of 
AD
Taxes Leftward: Decrease in AD Lower consumption and investment
Bank reserves Rightward: Increase in AD Lower interest rate, higher investment 
and possibly higher consumption
Exchange rate (foreign currency per unit 
domestic currency)Leftward: Decrease in AD Lower exports and higher imports
Global growth Rightward: Increase in AD Higher exports

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 156
EXAMPLE 8   
Shifts in Aggregate Demand
Francois Ubert is a portfolio manager with EuroWorld, a French investment 
management firm. Ubert is considering increasing his clients’ portfolio expo -
sure to Brazilian equities. Before doing so, he asks you to prepare a report on 
the following recent economic events in Brazil and to summarize the impact of 
each event on the Brazilian economy and on Brazilian equity and fixed-  income 
1 The Brazilian central bank reduced bank reserves, resulting in a lower 
money supply.
2 The capacity utilization rate in Brazil is currently estimated to be 86.4 per -
cent, a 2.7 percent increase from the previous year.
3 Corporate profits reported by Brazilian companies increased by 30 per -
cent over last year’s levels, and corporations have revised their forecasts of 
future profitability upward.
4 The government recently announced that it plans to start construction on

a number of hydroelectric projects to reduce Brazil’s reliance on imported 
oil.
5 Forecasts by private sector economists project that the European econ -
omy will enter a recession in the next year.
This monetary policy action is designed to reduce consumption and business 
investment spending. The reduction in real money balances will increase interest 
rates and discourage lending within the banking system. Higher interest rates 
and tighter credit will reduce both investment and consumption expenditures 
and shift the AD curve to the left. The prices of fixed-  income securities will fall 
because of the rise in interest rates. The reduction in aggregate output should 
lower corporate profits, and it is likely that equity prices will also fall.
Capacity utilization is a key factor determining the level of investment spending. 
A current utilization rate of over 86 percent and an increase from the previous

year indicate a growing lack of spare capacity in the Brazilian economy. As a 
result, businesses will probably increase their level of capital spending. This 
will increase AD and shift the AD curve to the right. Higher economic activity 
(income/output) will cause upward pressure on interest rates and may have a neg -
ative impact on fixed-  income securities. Higher income/output should increase 
corporate profits and is likely to have a positive impact on equity securities.
Expected corporate profits are an important determinant of the level of invest -
ment spending. The large increase in expected profits will raise the level of 
investment spending and increase aggregate demand. This will shift the AD 
curve to the right. The increase in corporate profits and the resulting increase 
in economic output should have a positive impact on equities. The increase in 
output will put upward pressure on interest rates and downward pressure on 
the prices of fixed-  income securities.

Aggregate Demand, Aggregate Supply, and Equilibrium 157
Fiscal policy uses government spending to influence the level and growth rate 
of economic activity. The announcement indicates an increase in government 
spending, which is a direct component of AD. Therefore, higher spending on 
the projects will increase AD and shift the AD curve to the right. The increase 
in output and expenditure should be positive for equities. But it will be nega -
tive for existing fixed-  income investments because higher interest rates will be 
required to induce investors to buy and hold the government debt issued to 
fund the new projects.
A recession in Europe will decrease the demand for Brazilian exports by European 
households and businesses and shift the AD curve to the left. The resulting 
decline in income and downward pressure on prices will be positive for fixed-  
income securities but negative for equities.
3.3.2  Shifts in Short-  Run Aggregate Supply

Factors that change the cost of production or expected profit margins will cause the 
SRAS curve to shift. These factors include changes in
■■nominal wages;
■■input prices, including the price of natural resources;
■■expectations about future output prices and the overall price level;
■■business taxes and subsidies; and
■■the exchange rate.
In addition, factors that shift the long-  run AS curve (see Section 3.3.3) will also 
shift the SRAS curve by a corresponding amount because the SRAS and LRAS reflect 
the same underlying resources and technology. As the economy’s resources and tech -
nology change, the full employment (or natural) level of output changes, and both the 
LRAS and SRAS shift accordingly.
Change in Nominal Wages  Changes in nominal wages shift the short-  run AS curve 
because wages are often the largest component of a company’s costs. An increase in 
nominal wages raises production costs, resulting in a decrease in AS and a leftward

shift in the SRAS curve. Lower wages shift the AS curve to the right. It is important to 
note that changes in nominal wages have no impact on the LRAS curve.
A better way to measure the impact of labor costs on the AS curve is to measure 
the change in unit labor cost. We define the change in unit labor cost as
 % Change in unit labor cost = % Change in nominal wages 
– % Change in productivity
EXAMPLE 9   
Unit Labor Cost and Short-  Run Aggregate Supply
Suppose Finnish workers are paid €20 an hour and are able to produce 100 cell 
phones in an hour. The labor cost per cell phone is €0.20 (€20 divided by 100 
units). If the wages per hour for Finnish workers rise by 10 percent from €20 
to €22 and they are able to raise their productivity by 10 percent, what is the 
impact on unit labor cost and the short-  run aggregate supply curve?

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 158
Solution: 
The workers can now produce 110 cell phones per hour, and unit labor cost 
will not change (22/110 = 0.20). In this case, the SRAS curve will remain in its 
original position. If wages had increased by 20 percent instead of 10 percent, 
then unit labor cost would have increased and the SRAS would shift to the left. 
Conversely, if the wage increase were only 5 percent, then unit labor cost would 
have decreased and the SRAS would shift to the right.
Change in Input Prices  The price of raw materials is an important component of cost 
for many businesses. Lower input prices reduce the cost of production, which, in turn, 
makes companies willing to produce more at any output price. This is reflected in a 
rightward shift of the SRAS curve. Conversely, higher input prices increase production 
costs, which, in turn, causes companies to reduce production at any output price. This

shifts the SRAS curve to the left. During the 1970s, high oil prices caused the SRAS 
curve in most countries to shift to the left. In contrast, in the mid-  1980s, declining oil 
prices lowered the cost of production and shifted the SRAS curve in most countries 
to the right. Oil prices currently have a smaller impact on the global economy than 
in the 1970s and 1980s because most countries have reduced their reliance on oil and 
improved their energy efficiency so that they now use less energy per unit of GDP .
Change in Expectations about Future Prices  The impact of expected future prices on 
current output decisions is not as straightforward as it might seem. First, each company 
is primarily concerned about the price of its own output rather than the general price 
level. The latter may be more reflective of its costs. If it expects its own output price to 
rise (fall) relative to the general price level, then it may increase (decrease) production

in response to the perceived change in its profit margin. As more and more companies 
become optimistic (pessimistic) about their ability to raise the relative price of their 
product, the SRAS will shift to the right (left). In the aggregate, of course, companies 
can neither raise nor lower their prices relative to the general price level. Hence, shifts 
in the SRAS driven by such price expectations are likely to be modest and temporary. 
Second, considering future prices introduces a temporal aspect into decision making. 
If the future price level is expected to be higher, companies may decide to produce 
more today in order to expand inventory available for future sale. But they will only do 
so if the cost of carrying inventory (financing, storage, and spoilage) is less than they 
expect to save on production costs by producing more today and less in the future. 
Conversely, they may cut current production and sell out of existing inventory if they

expect future prices (and costs) to be lower.
The upshot is that expectations of higher (lower) future prices are likely to shift 
the SRAS curve to the right (left), but the impact may be modest and/or temporary.
Change in Business Taxes and Subsidies  Higher business taxes increase production 
costs per unit and shift the short-  run AS curve to the left. Business subsidies are a 
payment from the government to the producer. Subsidies for businesses lower their 
production costs and shift the SRAS curve to the right.
Change in the Exchange Rate  Many countries import raw materials, including energy 
and intermediate goods. As a result, changes in the exchange rate can affect the cost 
of production and, therefore, aggregate supply. A higher Yen relative to the Euro will 
lower the cost of raw materials and intermediate goods imported to Japan from Europe. 
This, in turn, will lower the production costs of Japanese producers and shift the AS

curve in Japan to the right. A lower Yen will have the opposite effect.

Aggregate Demand, Aggregate Supply, and Equilibrium 159
3.3.3  Shifts in Long-  Run Aggregate Supply
As discussed above, the position of the LRAS curve is determined by the potential 
output of the economy. Potential GDP  measures the productive capacity of the econ -
omy and is the level of real GDP that can be produced at full employment. Potential 
GDP is not a static concept but can increase each year at a steady rate as the econ -
omy’s resource capacity grows. Therefore, any factor increasing the resource base of 
an economy causes the LRAS curve to shift as shown in Exhibit 19.
Exhibit 19   Shift in Long-  Run Aggregate Supply (LRAS) Curve
LRAS1 LRAS2
These factors include changes in
■■supply of labor and quality of labor forces (human capital);
■■supply of natural resources;
■■supply of physical capital; and
■■productivity and technology.
Supply of Labor  The larger the supply of labor, the more output the economy can

produce. The labor supply depends on growth in the population, the labor force par -
ticipation rate (the percentage of the population working or looking for work), and 
net immigration. The determinants of the labor supply are discussed in more detail in 
Section 4. Increases in the labor supply shift the LRAS curve to the right. Decreases 
shift the curve to the left.
Supply of Natural Resources  Natural resources are essential inputs to the production 
process and include everything from available land to oil to water. Increased availability 
of natural resources shifts the LRAS curve to the right.
Supply of Physical Capital  Investment in new property, plant, equipment, and soft -
ware is an essential ingredient for growth. An increase in the stock of physical capital 
will increase the capacity of the economy to produce goods and services. Simply put, 
if workers are provided with more and better equipment to use, they should be able to

produce more output than they could with the older equipment. Thus, strong growth 
in business investment, which increases the supply of physical capital, shifts the LRAS 
curve to the right.
Supply of Human Capital  Another way to raise the productive capacity of a country 
is to increase human capital—the quality of the labor force—through training, skills 
development, and education. Improvement in the quality of the labor force shifts the 
LRAS curve to the right.

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 160
Labor Productivity and Technology  Another important factor affecting the produc -
tive capacity of an economy is how efficient labor is in transforming inputs into final 
goods and services. Productivity  measures the efficiency of labor and is the amount 
of output produced by workers in a given period of time—for example, output per 
hour worked. An increase in productivity decreases labor cost, improves profitability, 
and results in higher output. Two of the main drivers of labor productivity—physical 
capital per worker and the quality of the workforce—have been discussed above. The 
third key determinant of productivity is technology. Advances in technology shift the 
EXAMPLE 10   
Unit Labor Cost and Long-  Run Aggregate Supply
Finnish workers are paid €20 per hour and are able to produce 100 cell phones 
in an hour. If workers develop a new technique for assembly and are able to

produce 200 cell phones per hour, what is the impact on the long-  run aggregate 
supply curve?
Solution: 
Labor cost per unit will decline to €0.10 (20/200 = €0.10 per cell phone). As a 
result, profit per unit will rise and companies will have an incentive to increase 
production. Thus, the LRAS curve shifts to the right.
The factors shifting the AS curve are summarized in Exhibit 20. Rightward shifts 
in the SRAS or LRAS curves are defined as an increase in supply. Leftward shifts in 
the SRAS or LRAS curves represent a decrease in supply.
Exhibit 20   Impact of Factors Shifting Aggregate Supply
An Increase in Shifts SRAS Shifts LRAS Reason
Supply of labor Rightward Rightward Increases resource base
Supply of natural resources Rightward Rightward Increases resource base
Supply of human capital Rightward Rightward Increases resource base
Supply of physical capital Rightward Rightward Increases resource base
Productivity and technology Rightward Rightward Improves efficiency of inputs

Nominal wages Leftward No impact Increases labor cost
Input prices (e.g., energy) Leftward No impact Increases cost of production
Expectation of future prices Rightward No impact Anticipation of higher costs and/or perception of 
improved pricing power
Business taxes Leftward No impact Increases cost of production
Subsidy Rightward No impact Lowers cost of production
Exchange rate Rightward No impact Lowers cost of production
As with our summary of factors that shift the AD curve, Exhibit 20 considers each 
of the factors affecting aggregate supply in isolation. In practice, various factors will be 
at work simultaneously, and there may be interaction among them. This is especially 
important with respect to interaction between factors listed as affecting only SRAS 
and those that also impact LRAS.

Aggregate Demand, Aggregate Supply, and Equilibrium 161
For example, consider an increase in the cost of natural resource inputs (e.g., 
energy). This shifts the SRAS curve to the left, but according to Exhibit 20, it has no 
effect on LRAS. This presumes that there has not been a permanent change in the 
relative prices of the factors of production. If there has been a permanent change, 
companies will be forced to conserve on the now more expensive input and will not 
be able to produce as efficiently. The LRAS curve would, therefore, shift to the left, 
just as it would if the available supply of natural resources had declined relative to the 
supply of other inputs. Indeed, that is the most likely cause of a permanent change 
in relative input prices.
EXAMPLE 11   
Shifts in Aggregate Supply
John Donovan is a portfolio manager for a global mutual fund. Currently, his 
fund has 10 percent of its assets invested in Chinese equities. He is considering

increasing the fund’s allocation to the Chinese equity market. His decision will be 
based on an analysis of the following economic developments and their impact 
on the Chinese economy and equity market. What is the impact on SRAS and 
LRAS from the following factors?
1 Global oil prices, currently near their longer-  run trend at $75 a barrel, 
have increased from $35 a barrel over the last three years because of 
strong demand from China and India.
2 The number of students studying engineering has dramatically increased 
at Chinese universities over the last decade.
3 Wages for China’s workers are rising, leading some multinational compa -
nies to consider shifting their investments to Vietnam or India.
4 Recent data show that business investment as a share of GDP is over 
40 percent in China.
5 The People’s Bank of China is likely to permit the yuan to appreciate by 
10 percent over the next year.
Higher energy prices cause a decrease in short-  run AS and shift the SRAS curve

to the left. Because oil prices are back to their longer-  run trend, the leftward 
shift in SRAS essentially reverses a previous shift that occurred when oil prices 
fell to $35, and it is likely that there will be no impact on the LRAS curve. Lower 
output and profit are likely to have a negative effect on Chinese equity prices.
More students studying engineering indicates an improvement in the quality of 
the labor force—an increase in human capital. As a result, AS increases and the 
AS curve shifts to the right. Both short-  run and long-  run curves are affected. 
Higher output and profits may be expected to have a positive effect on Chinese 
equity prices.
The increase in wages increases labor costs for businesses, causes short-  run 
aggregate supply to decline, and shifts the SRAS curve to the left. Lower output 
and profit should have a negative effect on Chinese equity prices.

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 162
The high level of business investment indicates that the capital stock in China is 
growing at a fast rate. This means that workers have more capital to use, which 
increases their productivity. Thus, AS increases and the AS curve shifts to the 
right. Both short-  run AS and long-  run AS are affected. Higher output should 
have a positive effect on Chinese equity prices.
The probable appreciation of the yuan means that the cost of imported raw 
materials, such as iron ore, coal, and oil, will be lower for Chinese companies. 
As a result, short-  run AS increases and the SRAS curve shifts to the right. The 
LRAS curve may also shift to the right if the appreciation of the yuan is perma -
nent and global commodity prices do not fully adjust. Higher output and profit 
should have a positive effect on Chinese equity prices.15
 
The implications of the above factors for equity investment in China are

ambiguous. If the long-  run effects dominate, however, then the net impact should 
be positive. The positive factors—the high level of investment and the growing 
pool of engineering students—have a lasting impact on output and profit. The 
negative factors—higher wages and oil prices—should be temporary because 
wages will realign with the price level and the increase in oil prices appears to 
offset a previous temporary decline. The reduction in raw material prices due 
to the stronger currency is positive for output, profit, and equities in the short 
run and perhaps in the long run as well.
3.4 Equilibrium GDP and Prices
Now that we have discussed the components of the AD and AS model, we can com -
bine them to determine the real level of GDP and the price level. Equilibrium occurs 
where the AD and AS curves intersect. At this point, the quantity of aggregate output 
demanded (or the level of aggregate expenditures) is equal to the quantity of aggre -

gate output supplied. In Exhibit 21, equilibrium price and GDP occur at P1 and Y1. If 
the price level is above P1, then the quantity of output supplied exceeds the amount 
demanded. This situation would result in unsold inventories and would require a 
reduction in production and in prices. If the price level is below P1, then the quantity 
of aggregate output demanded exceeds the quantity of aggregate output supplied. This 
situation would result in a shortage of goods that would put upward pressure on prices.
It is important to understand that short-  run macroeconomic equilibrium may 
occur at a level above or below full employment. We consider four possible types of 
macroeconomic equilibrium:
1 Long-  run full employment
2 Short-  run recessionary gap
3 Short-  run inflationary gap
4 Short-  run stagflation
15 The alert reader may have noted that the stronger yuan will also reduce export demand and shift the

AD curve to the left. The combined impact of the AD and AS shifts on output, profit, and equity prices 
is ambiguous.

Aggregate Demand, Aggregate Supply, and Equilibrium 163
From an investment perspective, the performance of asset classes and financial 
markets will differ in each of the above cases as the economy makes the adjustment 
toward the macroeconomic equilibrium. We look at these differences later in the 
reading.
3.4.1  Long-  Run Equilibrium
Exhibit 21 shows the long-  run full employment equilibrium for an economy. In this 
case, equilibrium occurs where the AD curve intersects the SRAS curve at a point on 
the LRAS curve. Because equilibrium occurs at a point on the LRAS curve, the econ -
omy is at potential real GDP . Both labor and capital are fully employed, and everyone 
who wants a job has one. In the long run, equilibrium GDP is equal to potential GDP .
Exhibit 21   Long-  Run Macroeconomic Equilibrium
AD
Y1P1Price
Level 
Income, Output, YSRASLRAS
In practice, the level of potential GDP is difficult to measure with precision. Because

of fluctuations arising from shifts in the AD and SRAS curves, the economy rarely 
operates at potential GDP . Thus, potential GDP is not observable from the data on 
actual GDP . In addition, potential GDP is determined by factors that are themselves 
difficult to measure (see Section 4.2). Thus, “bottom-  up” estimates of the level  of 
potential output are also quite imprecise. However, as will be discussed in Section 4, 
economists have confidence that the long-  run growth rate  of potential GDP can be 
estimated well enough to provide meaningful guidance for analysts and policymakers. 
Hence, in the short run, economists generally focus on factors that cause actual GDP 
to grow faster or slower than their estimate of the long-  run growth rate of potential 
output. In addition, they focus on measures that indicate, albeit imprecisely, the extent 
to which the economy is operating above or below its productive capacity, such as 
unemployment and capacity utilization.
3.4.2  Recessionary Gap

Cyclical fluctuations in real GDP and prices are caused by shifts in both the AD and 
SRAS curves. A decline in AD or a leftward shift in the AD curve results in lower 
GDP and lower prices. Such declines in AD lead to economic contractions, and if 
such declines drive demand below the economy’s potential GDP , the economy goes 
into a recession. In Exhibit 22, when aggregate demand falls, the equilibrium shifts 
from Point A to Point B. Real GDP contracts from Y1 to Y2, and the aggregate price 
level falls from P1 to P2. Because of the decline in demand, companies reduce their

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 164
workforce and the unemployment rate rises. The economy is in recession,16 and the 
recessionary gap is measured as the difference between Y2 and Y1 or the amount by 
which equilibrium output is below potential GDP . Thus, a recessionary gap occurs 
when the AD curve intersects the short-  run AS curve at a short-  run equilibrium 
level of GDP below potential GDP . Most importantly, in contrast to full employment, 
equilibrium GDP is below potential GDP .
Exhibit 22   Recessionary Gap
AD1
Y1P1Price 
Level 
Income, Output, YShort-run ASLong-run AS
AD2 Y2P2A
B
Any of the factors discussed in Section 3.3.1 could cause the shift in the AD 
curve. Tightening of monetary policy, higher taxes, more pessimistic consumers and 
businesses, and lower equity and housing prices all reduce AD and are all possible 
causes of a recession.
The question is, How does the economy return to full employment? There is consid -

erable debate among economists about the answer to this question. Some economists 
argue that an automatic, self-  correcting mechanism will push the economy back to 
its potential, without the need for government action. The idea is that because of the 
decline in prices and higher unemployment, workers will be willing to accept lower 
nominal wages. Workers will do this because each currency unit of wages now buys 
more goods and services because of their lower price. As a result, lower wages and 
input prices will cause the SRAS curve to shift to the right (see Exhibit 20) and push 
the economy back to full employment and potential GDP .
The problem is that this price mechanism can take several years to work. As an 
alternative, government can use the tools of fiscal and monetary policy to shift the 
AD curve to the right (from Point B to Point A in Exhibit 22) and move the economy 
back to full employment. On the fiscal side, policymakers can reduce taxes or increase

government spending. On the monetary side, the central bank can lower interest 
rates or increase the money supply. The problem, however, is that variable lags in 
the effectiveness of these policy measures imply that policy adjustments may end up 
reinforcing rather than counteracting underlying shifts in the economy.
Investment Implications of a Decrease in AD  Aggregate demand and aggregate supply 
are theoretical measures that are very hard to measure directly. Most governments, 
however, publish statistics that provide an indication of the direction that aggregate 
16 A recession  is defined as a period during which real GDP decreases (i.e., “negative growth”) for at least 
two successive quarters or a period of significant decline in total output, income, employment, and sales 
usually lasting from six months to a year.

Aggregate Demand, Aggregate Supply, and Equilibrium 165
demand and supply are moving over time. For example, statistics on consumer senti -
ment, factory orders for durable and nondurable goods, the value of unfilled orders, the 
number of new housing starts, the number of hours worked, and changes in inventories 
provide an indication of the direction of aggregate demand. If these statistics suggest 
that a recession is caused by a decline in AD, the following conditions are likely to occur:
■■Corporate profits will decline.
■■Commodity prices will decline.
■■Interest rates will decline.
■■Demand for credit will decline.
This suggests the following investment strategy:
■■Reduce investments in cyclical companies17 because their earnings are likely to 
decline the most in an economic slowdown.
■■Reduce investments in commodities and/or commodity-  oriented companies 
because the decline in commodity prices will slow revenue growth and reduce 

■■Increase investments in defensive companies18 because they are likely to 
experience only modest earnings declines in an economic slowdown.
■■Increase investments in investment-  grade or government-  issued fixed-  income 
securities. The prices of these securities should increase as interest rates 
decline.
■■Increase investments in long-  maturity fixed-  income securities because their 
prices will be more responsive to the decline in interest rates than the prices of 
shorter-  maturity securities.
■■Reduce investments in speculative equity securities and in fixed-  income securi -
ties with low credit quality ratings.
As with most investment strategies, this strategy will be most successful if it is 
implemented before other market participants recognize the opportunities and asset 
prices adjust.
EXAMPLE 12   
Using AD and AS: The Recession of 2007–2009
Many Asian economies were more adversely affected than the United States by

the global recession that began in late 2007. In the first quarter of 2009, real GDP 
fell at an annualized rate of 16 percent in Japan and 11 percent in Singapore, 
compared with a 6 percent annualized decline in the United States. Using the 
data on exports as a share of GDP shown in Exhibit 23, explain how the following 
economic factors contributed to the recession in the Asian economies:
1 Collapse of house prices and home construction in the United States.
2 Oil prices rising from around $30 a barrel in 2004 to nearly $150 a barrel 
in 2008. ( Note : Most Asian economies rely on imports for almost all 
of their oil and energy needs. In contrast, the United States has a large 
domestic energy industry and imports about one-  half of its oil.)
17 Cyclical companies are companies with sales and profits that regularly expand and contract with the 
business cycle or state of economy (for example, automobile and chemical companies).

18 Defensive companies are companies with sales and profits that have little sensitivity to the business 
cycle or state of the economy (for example, food and pharmaceutical companies).

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 166
3 The dramatic reduction in credit availability following the collapse or near 
collapse of major financial institutions in 2008.
Exhibit 23   Exports as a Share of GDP , 2007
EconomyExports as a  
Percentage of GDPPercentage of Exports  
Going to United States
Singapore 186 11.2
Hong Kong 166 11.5
Taiwan 62 11.6
South Korea 53 10.9
Germany 47 7.1
China 37 26.4
Mexico 28 80.2
Kenya 27 8.2
Japan 17 20.1
India 14 17.0
United States 12 —
Ethiopia 11 6.7
Sources:  World Bank: World Development Indicators and OECD Stat Extracts.
The collapse in housing prices caused housing construction spending, a com -
ponent of business investment, to decline in the United States. The decline 
in housing prices also caused a sharp fall in household wealth. As a result, 
consumption spending in the United States declined because of the wealth 
effect. The decline in both consumption and housing construction shifted the

AD curve for the United States to the left, resulting in a US recession. The link 
to the Asian economies was through global trade because exports represented 
such a large share of the Asian economies’ GDP (Exhibit  23). In turn, these 
economies exported a significant amount of goods and services to the United 
States. Thus, the recession in the United States and especially the decline in US 
consumption spending caused a sharp fall in exports among Asian economies. 
This lowered their AD and caused the AD curve to shift to the left, resulting in 
a recessionary gap in these economies.
The rise in oil prices increased input cost and shifted the short-  run AS curve 
to the left. Because the eastern Asian economies are heavily dependent on 
imported oil, their economies were more adversely affected than the economy 
of the United States.
The decline in housing prices caused financial institutions in the United States

to suffer large losses on housing-  related loans and securities. Several large lend -
ers collapsed, and the US Treasury and the Federal Reserve had to intervene to 
prevent a wave of bankruptcies among large financial institutions. As a result of 
the crisis, it became difficult for households and businesses to obtain credit to 
finance their spending. This caused AD to fall and increased the severity of the

Aggregate Demand, Aggregate Supply, and Equilibrium 167
recession in the United States, resulting in a significant decline in US imports 
and thus exports from the Asian economies. In addition, the financial crisis 
made it more difficult to get trade finance, further reducing exports from Asia.
In summary, global investors need to be aware of the growing linkages among 
economies and the extent that one economy’s growth depends on demand from 
within as well as from outside of that economy. Data on exports as a percentage 
of an economy’s GDP provide an indication of this dependence. Although Japan 
is often viewed as an export-  driven economy, Exhibit 23 shows that exports are 
only 17 percent of its GDP . Similarly, the economy of India depends largely on 
domestic spending for growth because exports account for only 14 percent of 
GDP .
3.4.3  Inflationary Gap
Increases in AD lead to economic expansions as real GDP and employment increase.

If the expansion drives the economy beyond its production capacity, however, infla -
tion19 will occur. As summarized in Exhibit 18, higher government spending, lower 
taxes, a more optimistic outlook among consumers and businesses, a weaker domestic 
currency, rising equity and housing prices, and an increase in the money supply would 
each stimulate aggregate demand and shift the AD curve to the right. If aggregate 
supply does not increase to match the increase in AD, a rise in the overall level of 
prices will result.
In Exhibit 24, an increase in AD will shift the equilibrium level of GDP from Point 
A to Point B. Real output increases from Y1 to Y2, and the aggregate price level rises 
from P1 to P2. As a result of the increase in aggregate demand, companies increase 
their production and hire more workers. The unemployment rate declines. Once an 
economy reaches its potential GDP , however, companies must pay higher wages and

other input prices to further increase production. The economy now faces an inflation -
ary gap, measured by the difference between Y2 and Y1 in Exhibit 24. An inflationary 
gap occurs when the economy’s short-  run level of equilibrium GDP is above potential 
GDP, resulting in upward pressure on prices.
Exhibit 24   Inflationary Gap
AD1
Y1P1Price
Level 
Y2 Income, Output, YSRAS1
P2LRAS
AD2P3
Y3ABCSRAS2
19 The inflation rate is defined as the increase in the general price level from one period to the next.

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 168
GDP cannot remain at Y2 for long because the economy is over-  utilizing its resourc -
es—i.e., extra shifts of workers are hired and plant and equipment are operating at 
their maximum capacity. Eventually, workers become tired and plant and equipment 
wear out. The increase in the general price level and input prices will set in motion 
the process of returning the economy back to potential GDP . Higher wages and input 
prices shift the SRAS curve to the left (from SRAS1 to SRAS2), moving the economy 
to Point C in Exhibit 24. Again, this self-  correcting mechanism may work slowly.
A nation’s government and/or its central bank can attempt to use the tools of fiscal 
and monetary policy to control inflation by shifting the AD curve to the left (AD2 to 
AD1 in Exhibit 24) so that the return to full employment occurs without the price 
increase. From a fiscal perspective, policymakers can raise taxes or cut government

spending. From a monetary perspective, the central bank can reduce bank reserves, 
resulting in a decrease in the growth of the money supply and higher interest rates.
Investment Implications of an Increase in AD Resulting in an Inflationary Gap  If 
economic statistics (consumer sentiment, factory orders for durable and nondurable 
goods, etc.) suggest that there is an expansion caused by an increase in AD, the following 
conditions are likely to occur:
■■Corporate profits will rise.
■■Commodity prices will increase.
■■Interest rates will rise.
■■Inflationary pressures will build.
■■Increase investment in cyclical companies because they are expected to have 
the largest increase in earnings.
■■Reduce investments in defensive companies because they are expected to have 
only a modest increase in earnings.
■■Increase investments in commodities and commodity-  oriented equities because 
they will benefit from higher production and output.

■■Reduce investments in fixed-  income securities, especially longer-  maturity secu -
rities, because they will decline in price as interest rates rise. Raise exposure to 
speculative fixed-  income securities (junk bonds) because default risks decrease 
in an economic expansion.
3.4.4  Stagflation: Both High Inflation and High Unemployment
Structural fluctuations in real GDP are caused by fluctuations in SRAS. Declines in 
aggregate supply bring about stagflation —high unemployment and increased infla -
tion. Increases in aggregate supply conversely give rise to high economic growth and 
low inflation.
Exhibit 25 shows the case of a decline in aggregate supply, perhaps caused by an 
unexpected increase in basic material and oil prices. The equilibrium level of GDP 
shifts from Point A to B. The economy experiences a recession as GDP falls from Y1 
to Y2, but the price level, instead of falling, rises from P1 to P2. Over time, the reduc -

tion in output and employment should put downward pressure on wages and input 
prices and shift the SRAS curve back to the right, re-  establishing full employment 
equilibrium at Point A. However, this mechanism may be painfully slow. Policymakers 
may use fiscal and monetary policy to shift the AD curve to the right, as previously 
discussed, but at the cost of a permanently higher price level at Point C.

Aggregate Demand, Aggregate Supply, and Equilibrium 169
Exhibit 25   Stagflation
AD
Y1P2Price 
Level 
Income, Output, YSRAS1SRAS2LRAS
Y2P1 AC
B
The global economy experienced stagflation in the mid-  1970s and early 1980s. 
Both unemployment and inflation soared. The problem was caused by a sharp decline 
in aggregate supply fueled by higher input prices, especially the price of oil. In 1973, 
the price of oil quadrupled. A steep global recession began in late 1973 and lasted 
through early 1975. The recession was unusual because prices rose rather than 
declined as would be expected in a typical demand-  caused downturn. In 1979–1980, 
the price of oil doubled. Higher energy prices shifted the SRAS curve to the left, as 
shown in Exhibit 25, leading to a global recession in 1980–1982. In the United States, 
the contraction in output was reinforced by the Federal Reserve’s decision to tighten 
monetary policy to fight the supply-  induced inflation.

Investment Implications of Shift in AS  Labor and raw material costs, including energy 
prices, determine the direction of shifts in short-  run aggregate supply: Higher costs 
for labor, raw materials, and energy lead to a decrease in aggregate supply, resulting in 
lower economic growth and higher prices. Conversely, lower labor costs, raw material 
prices, and energy prices lead to an increase in aggregate supply, resulting in higher 
economic growth and a lower aggregate price level. Productivity is also an important 
factor. Higher rates of productivity growth shift the AS to the right, resulting in higher 
output and lower unit input prices. Lower rates of productivity growth do the opposite 
and shift the AS curve to the left.
From an investment perspective, a decline in AS (leftward shift of the SRAS curve) 
suggests
■■reducing investment in fixed income because rising output prices (i.e., inflation) 
put upward pressure on nominal interest rates;

■■reducing investment in most equity securities because profit margins are 
squeezed and output declines; and
■■increasing investment in commodities or commodity-  based companies because 
prices and profits are likely to rise.
On the other hand, an increase in AS (rightward shift of the SRAS curve) due to higher 
productivity growth or lower labor, raw material, and energy costs is favorable for 
most asset classes other than commodities.

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 170
3.4.5  Conclusions on AD and AS
The business cycle and the resulting fluctuations in real GDP are caused by shifts 
in the AD and AS curves. The impact of these shifts can be summarized as follows:
■■An increase in AD raises real GDP , lowers the unemployment rate, and 
increases the aggregate level of prices.
■■A decrease in AD lowers real GDP , increases the unemployment rate, and 
decreases the aggregate level of prices.
■■An increase in AS raises real GDP , lowers the unemployment rate, and lowers 
the aggregate level of prices.
■■A decrease in AS lowers real GDP , raises the unemployment rate, and raises the 
aggregate level of prices.
If both curves shift, the effect is a combination of the above individual effects. We 
can look at four possible cases:
1 Both AD and AS increase.  If both AD and AS increase, real GDP will increase 
but the impact on inflation is not clear unless we know the magnitude of the

changes because an increase in AD will increase the price level, whereas an 
increase in AS will decrease the price level. If AD increases more than AS, the 
price level will increase. If AS increases more than AD, however, the price level 
will decline.
2 Both AD and AS decrease.  If both AD and AS decrease, real GDP and employ -
ment will decline, but the impact on the price level is not clear unless we know 
the magnitude of the changes because a decrease in AD decreases the price 
level, whereas a decrease in AS increases the price level. If AD decreases more 
than AS, the price level will fall. If AS decreases more than AD, the price level 
will rise.
3 AD increases and AS decreases.  If AD increases and AS declines, the price level 
will rise, but the effect on real GDP is not clear unless we know the magni -
tude of the changes because an increase in AD increases real GDP , whereas 
a decrease in AS decreases real GDP . If AD increases more than AS declines,

GDP will rise. If AS decreases more than AD increases, real GDP will fall.
4 AD decreases and AS increases.  If AD decreases and AS increases, the price 
level will decline but the impact on real GDP is not clear unless we know the 
magnitudes of the changes because a decrease in AD decreases real GDP , 
whereas an increase in AS increases real GDP . If AD decreases more than AS 
increases, real GDP will fall. If AS increases more than AD declines, real GDP 
will rise.
Exhibit 26 summarizes these four cases.
Exhibit 26   Effect of Combined Changes in AS and AD
Change in AS Change in ADEffect on  
Real GDPEffect on Aggregate  
Price Level
Increase Increase Increase Indeterminate
Decrease Decrease Decrease Indeterminate
Increase Decrease Indeterminate Decrease
Decrease Increase Indeterminate Increase

Aggregate Demand, Aggregate Supply, and Equilibrium 171
Whether the growth of the economy is demand- or supply-  driven has an impact 
on asset prices. Demand-  driven expansions are normally associated with rising 
interest rates and inflation, whereas contractions are associated with lower inflation 
and interest rates. Supply-  driven expansions are associated with lower inflation and 
interest rates, whereas supply-  driven contractions are associated with rising inflation 
and interest rates.
EXAMPLE 13   
Investment Strategy Based on AD and AS Curves
An analyst is evaluating the possibility of investing in China, Italy, Mexico, or 
Brazil. What are the equity and fixed-  income investment opportunities in these 
countries based on the following events?
1 The Chinese government announced a spending plan of $1.2 trillion or 
13 percent of GDP . In addition, the central bank of China eased monetary 
policy, resulting in a surge of lending.

2 The Italian government announced a decline in labor productivity, and it 
expects this trend to continue into the future.
3 In response to rising inflationary pressure, the Mexican central bank tight -
ened monetary policy, and the government announced tax increases and 
spending cuts to balance the budget.
4 A major discovery of oil off the coast of Brazil lowered oil prices, while 
the Brazilian government announced a major increase in spending on 
public infrastructure to stimulate the economy.
Stimulative fiscal and monetary policies should result in a demand-  driven expan -
sion. Investors should reduce investments in fixed-  income securities and defen -
sive companies and invest in cyclical companies and commodities. As a result, 
the prospects for growth-  oriented equity investments look favorable in China.
A decline in labor productivity will result in a decline in AS; i.e., the AS curve

will shift to the left. This is typically a poor investment environment. Investors 
should reduce investments in both fixed-  income and equity securities and invest 
in commodities. Entry into Italian stocks and bonds does not look attractive.
The policy measures put in place by the Mexican government and central bank 
will cause a drop in AD and likely result in a recession. Investors should increase 
their investments in fixed-  income securities because interest rates will most likely 
decline as the recession deepens. This is a poor environment for equity securities.
This is a situation where both the AD and AS curves will shift. The increase in 
spending on public infrastructure will shift the AD curve to the right, resulting 
in higher aggregate expenditures and prices. Lower oil prices will shift the AS 
curve to the right, resulting in higher GDP but lower prices. Thus, GDP will

clearly increase, but the impact on prices and inflation is indeterminate. As a 
result, investors should increase their investment in equity securities; however, 
the impact on fixed-  income securities is unclear.

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 172
EXAMPLE 14   
Using AD and AS to Explain Japan’s Economic Problem
Japan has experienced sluggish growth in real GDP for nearly two decades fol -
lowing the bursting of an asset and investment bubble in the late 1980s. At the 
same time, Japan has experienced deflation (declining prices) over this period. 
The reasons for this protracted period of stagnation continue to be debated 
among economists. Failure to recognize a change in the Japanese growth rate 
has hurt many investors, especially those taking a long-  term perspective. From 
their peak in 1989, Japanese equity prices, as measured by the Nikkei index, 
fell by over 60 percent before bottoming out in mid-  1992. Since that time, the 
market has been essentially flat despite considerable volatility.
The performance of the Japanese economy can be explained using the AD 
and AS model. The protracted slowdown of growth in Japan beginning in the

early 1990s can be linked to the effect of the collapse of the equity and com -
mercial real estate markets in the late 1980s and to excessive investment in 
capital goods (new factories and equipment) in the 1980s. These problems were 
compounded by persistent weakness in the banking sector, a profound lack of 
confidence among businesses and consumers, and negative demographics with 
slow growth in the working age population.
The sum of these developments caused a decline in both the AD and AS 
curves. Aggregate demand declined, causing the AD curve to shift to the left 
for the following reasons:
■■The wealth effect due to the decline in equity and real estate prices sharply 
reduced consumption spending. Asset prices have yet to recover from the 
fall.
■■Excessive investment in capital goods caused a sharp decline in business 
investment.
■■Lack of confidence among businesses and consumers.
■■Problems in the banking sector made monetary policy ineffective because

banks were unable to lend, which negatively affected both consumer and 
business spending.
AS declined for the following reasons:
■■Marked slowing in private investment spending reduced the capital stock. 
This also reduced potential GDP .
■■Slow population growth limited the growth in the labor supply. This also 
reduced potential GDP .
■■Higher energy prices slowed growth because of Japan’s heavy dependence 
on imported energy.
As would be expected, the declines in both AD and AS resulted in slow GDP 
growth. The fact that prices fell indicates that the AD curve shifted more than 
the AS curve.

Economic Growth and Sustainability 173
ECONOMIC GROWTH AND SUSTAINABILITY
We now shift focus from the short-  run cyclical movement of the economy to its long-  
term growth rate. Economic growth is calculated as the annual percentage change in 
real GDP or the annual change in real per capita GDP:
■■Growth in real GDP measures how rapidly the total economy is expanding.
■■Per capita GDP , defined as real GDP divided by population, determines the 
standard of living in each country and the ability of the average person to buy 
goods and services.
Economic growth is important because rapid growth in per capita real GDP can 
transform a poor nation into a wealthy one. Even small differences in the growth 
rate of per capita GDP , if sustained over time, have a large impact on an economy’s 
standard of living. One should think of the growth rate of GDP as the equivalent of a 
rate of return on a portfolio. Small differences in return compounded over many years

make a big difference. Nevertheless, there is a limit to how fast an economy can grow. 
Faster growth is not always better for an economy because there are costs associated 
with excess growth, such as higher inflation, potential environmental damage, and 
the lower consumption and higher savings needed to finance the growth.
This raises the issue of sustainable growth, which requires an understanding of the 
concept of potential GDP . Recall that potential GDP measures the productive capacity 
of the economy and is the level of real GDP that an economy could produce if capital 
and labor are fully employed. In order to grow over time, an economy must add to 
its productive capacity. Thus, the sustainable rate of economic growth  is measured 
by the rate of increase in the economy’s productive capacity or potential GDP . It is 
important to note that economists cannot directly measure potential output. Instead, 
they estimate it using a variety of techniques discussed later in this reading.

For global investors, estimating the sustainable rate of economic growth for an econ -
omy is important for both asset allocation and security selection decisions. Investors 
need to understand how the rate of economic growth differs among countries and 
whether these growth rates are sustainable. When examining the GDP data, global 
investors need to address a number of questions, including the following:
1 What are the underlying determinants or sources of growth for the country?
2 Are these sources of growth likely to remain stable or change over time?
3 How can we measure and forecast sustainable growth for different countries?
4.1 The Production Function and Potential GDP
The neoclassical or Solow growth model is the framework used to determine the 
underlying sources of growth for an economy. The model shows that the economy’s 
productive capacity and potential GDP increase for two reasons:
1 accumulation of such inputs as capital, labor, and raw materials used in produc -
tion, and

tion, and
2 discovery and application of new technologies that make the inputs in the 
production process more productive—that is, able to produce more goods and 
services for the same amount of input.4

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 174
The model is based on a production function  that provides the quantitative link 
between the level of output that the economy can produce and the inputs used in the 
production process, given the state of technology. A two-  factor production function 
with labor and capital as the inputs is expressed mathematically as
Y = AF(L,K)
where Y denotes the level of aggregate output in the economy, L is the quantity of 
labor or number of workers in the economy, K is the capital stock or the equipment 
and structures used to produce goods and services, and A represents technological 
knowledge or total factor productivity  (TFP). TFP is a scale factor that reflects the 
portion of growth that is not accounted for by the capital and labor inputs. The main 
factor influencing TFP is technological change. Like potential GDP , TFP is not directly 
observed in the economy and must be estimated.

The production function shows that output in the economy depends on inputs 
and the level of technology. The economy’s capacity to produce goods grows when 
these inputs increase and/or technology advances. The more technologically advanced 
an economy is, the more output it is able to produce from a given amount of inputs.
Two assumptions about the production function provide a link to microeconomics. 
First, we assume that the production function has constant returns to scale. This means 
that if all the inputs in the production process are increased by the same percentage, 
then output will rise by that percentage. Thus, doubling all inputs would double out -
put. Second, we assume that the production function exhibits diminishing marginal 
productivity  with respect to any individual input. This property plays an important 
role in assessing the contribution of labor and capital to economic growth. Marginal

productivity looks at the extra output that is produced from a one-  unit increase in 
an input if the other inputs are unchanged. It applies to any input as long as the other 
inputs are held constant. For example, if we have a factory of a fixed size and we add 
more workers to the factory, the marginal productivity of labor measures how much 
additional output each additional worker will produce.
Diminishing marginal productivity means that at some point the extra output 
obtained from each additional unit of the input will decline. In the above example, if 
we hire more workers at the existing factory (fixed capital input in this case), output 
will rise by a smaller and smaller amount with each additional worker. Traditionally, 
economists focused on the labor input and how the productivity of labor would 
decline given a fixed amount of land. The traditional growth theory, where labor is 
the only (variable) input, was developed by Thomas Malthus in his 1798 publication,

Essay on the Principle of Population . Malthus argued that as the population and labor 
force grew, the additional output produced by an additional worker would decline 
essentially to zero and there would be no long-  term economic growth. This gloomy 
forecast caused others to label economics the “dismal science. ”
The dire prediction implied by declining marginal productivity of labor never 
materialized, and economists changed the focus of the analysis away from labor to 
capital. In this case, if we add more and more capital to a fixed number of workers, 
the amount of additional output contributed by each additional amount of capital

Economic Growth and Sustainability 175
will fall. Thus, if capital grows faster than labor, capital will become less productive, 
resulting in slower and slower growth. Diminishing marginal productivity of capital 
has two major implications for potential GDP:
1 Long-  term sustainable growth cannot rely solely on capital deepening 
investment  that increases the stock of capital relative to labor. More gener -
ally, increasing the supply of some input(s) relative to other inputs will lead to 
diminishing returns and cannot be the basis for sustainable growth.
2 Given the relative scarcity and hence high productivity of capital in develop -
ing countries, the growth rates of developing countries should exceed those of 
developed countries. As a result, there should be a convergence  of incomes 
between developed and developing countries over time.
Because of diminishing returns to capital, the only way to sustain growth in

potential GDP per capita is through technological change or growth in total factor 
productivity. This results in an upward shift in the production function: The economy 
produces more goods and services using the same level of labor and capital inputs. In 
terms of the formal production function shown above, this is reflected by an increase 
in the technology parameter, A.
Using the production function, Robert Solow developed a model that explained the 
contribution of labor, capital, and technology (total factor productivity) to economic 
growth. The growth accounting equation shows that the rate of growth of potential 
output equals growth in technology plus the weighted average growth rate of labor 
and capital.
 Growth in potential GDP = Growth in technology + WL (Growth in labor) + 
WC (Growth in capital)
where WL and WC are the relative shares of capital and labor in national income. The 
capital share is the sum of corporate profits, net interest income, net rental income,

and depreciation divided by GDP . The labor share is employee compensation divided 
by GDP . For the United States, WL and WC are roughly 0.7 and 0.3, respectively.
The growth accounting equation highlights a key point: The contribution of labor 
and capital to long-  term growth depends on their respective shares of national income. 
For the United States, because labor’s share is higher, an increase in the growth rate 
of labor will have a significantly larger impact (roughly double) on potential GDP 
growth than will an equivalent increase in the growth rate of capital.
The growth accounting equation can be further modified to explain growth in per 
capita GDP . Because it measures the standard of living and purchasing power of the 
average person in an economy, per capita GDP is more relevant than the absolute 
level of GDP in comparing economic performance among countries. Transforming the 
growth accounting equation into per capita terms results in the following equation:

Growth in per capita potential GDP = Growth in technology + 
WC (Growth in capital-  to- labor ratio)
The capital-  to- labor ratio measures the amount of capital available per worker 
and is weighted by the share of capital in national income. Because capital’s share 
in national income in the US economy is 0.3, a 1 percent increase in the amount of 
capital available for each worker increases per capita output by only 0.3 percent. The 
equation shows that improvements in technology are more important than capital in 
raising an economy’s standard of living.

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 176
4.2 Sources of Economic Growth
The growth accounting equation focuses on the main determinants of growth—capital, 
labor and technology—and omits a number of other sources of growth to simplify the 
analysis. For many countries, however, natural resource and human capital inputs play 
an important role in explaining economic growth. Therefore, there are five important 
sources of growth for an economy:
■■Labor supply;
■■Human capital;
■■Physical capital;
■■Technology; and
■■Natural resources.
These sources of growth determine the capacity of the economy to supply goods and 
services.
Labor Supply  Growth in the number of people available for work (quantity of work -
force) is an important source of economic growth and partially accounts for the superior 
growth performance, among the advanced economies, of the US economy versus the 
European and Japanese economies. Most developing countries, such as China, India,

and Mexico, have a large potential labor supply. We can measure the potential size 
of the labor input as the total number of hours available for work, which is given by
Total hours worked = Labor force × Average hours worked per worker
The labor force  is defined as the portion of the working age population (over the 
age of 16) that is employed or available for work but not working (unemployed). The 
contribution of labor to overall output is also affected by changes in the average hours 
worked per worker. Average hours worked is highly sensitive to the business cycle. 
However, the long-  term trend has been toward a shorter workweek in the advanced 
countries. This development is the result of legislation, collective bargaining agree -
ments, and the growth of part-  time and temporary work.
Human Capital  In addition to the quantity of labor, the quality of the labor force is 
important. Human capital is the accumulated knowledge and skill that workers acquire

from education, training, and life experience. It measures the quality of the workforce. 
In general, better-  educated and skilled workers will be more productive and more 
adaptable to changes in technology.
An economy’s human capital is increased through investment in education and 
on- the- job training. Like physical capital, investment in education is costly. Studies 
show that there is a significant return on education. That is, people with more educa -
tion earn higher wages. Moreover, education may also have a spillover or externality 
impact: Increasing the educational level of one person not only raises the output 
of that person but also the output of those around him or her. The spillover effect 
operates through the link between education and advances in technology. Education 
not only improves the quality of the labor force but also encourages growth through 
innovation. Investment in health is also a major contributor to human capital, espe -
cially in developing countries.

Physical Capital Stock  The physical capital stock  (accumulated amount of build -
ings, machinery, and equipment used to produce goods and services) increases from 
year to year as long as net investment (gross investment less depreciation of capital) 
is positive. Thus, countries with a higher rate of investment should have a growing 
physical capital stock and a higher rate of GDP growth. Exhibit 27 shows the level of

Economic Growth and Sustainability 177
business investment as a share of GDP . The exhibit shows significant variation across 
countries, with the investment share in the United States being low in comparison to 
other developed countries.
As is evident in Exhibit 27, the correlation between economic growth and invest -
ment is high. Economies that devote a large share of GDP to investment, such as China, 
India, and South Korea, have high growth rates. The fastest-  growing economies in 
Europe over the last decade, Ireland and Spain, have the highest investment-  to- GDP 
ratios. Economies that devote a smaller share of GDP to investment, such as Brazil 
and Mexico, have slower growth rates. The data show why the Chinese economy has 
expanded at such a rapid rate, achieving an annual GDP growth rate of over 10 percent 
over the last two decades. Investment spending in China on new factories, equipment, 
and infrastructure as a percentage of GDP is the highest in the world.

Exhibit 27   Business Investment as a Percentage of GDP
Developed economies 1994 2000 2005 2007Average Annual  
Real GDP Growth,  
1991–2009 (%)
  United States 17.2 19.9 19.2 18.4 2.2
  Japan 28.5 25.2 23.3 23.2 1.1
  Germany 22.6 21.5 17.4 18.7 1.4
  France 18.4 19.5 20.0 21.5 1.5
  Italy 18.5 20.3 20.7 21.1 1.0
  United Kingdom 16.1 17.1 16.9 17.8 2.2
  Canada 18.8 19.2 21.3 22.6 2.1
  Ireland 16.1 23.1 26.6 26.3 5.1
  Spain 20.7 25.8 29.4 31.0 2.6
  Australia 23.9 22.0 27.0 27.7 3.2
  South Korea 36.4 31.1 29.3 28.8 4.9
  New Zealand 20.9 20.4 24.1 22.9 2.7
Developing economies 1994 2000 2005 2007Average Annual  
  Brazil 18.5 16.8 15.9 17.5 2.8
  China 34.5 34.3 41.0 40.0 10.2
  India NA 22.9 30.4 33.8 6.4
  Indonesia 24.8 19.9 23.6 24.9 4.6
  Mexico 19.4 21.4 20.1 20.8 2.4
  Turke y 22.9 20.4 21.0 21.5 3.4
Source:  OECD StatLink.
Technology  The most important factor affecting economic growth is technology,

especially in developed countries such as the United States. Technology  refers to the 
process a company uses to transform inputs into outputs. Technological advances are 
discoveries that make it possible to produce more or higher-  quality goods and services

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 178
with the same resources or inputs. At the same time, technological progress results in 
the creation of new goods and services. Finally, technological progress improves how 
efficiently businesses are organized and managed.
Technological advances are very important because they allow an economy to 
overcome the limits imposed by diminishing marginal returns. Thus, an economy 
will face limits to growth if it relies exclusively on expanding the inputs or factors of 
Because most technological change is embodied in new machinery, equipment, 
and software, physical capital must be replaced, and perhaps expanded, in order to 
take advantage of changes in technology. One of the key drivers of growth in devel -
oped countries over the last decade has been the information technology (IT) sector. 
Growth in the IT sector has been driven by technological innovation that has caused

the price of key technologies, such as semiconductors, to fall dramatically. The steep 
declines in prices have encouraged investment in IT at the expense of other assets. 
The sector has grown very fast and has made a significant contribution to economic 
growth, employment, and exports.
Countries can innovate through expenditures, both public and private, on research 
and development (R&D). Thus, expenditures on R&D and the number of patents issued, 
although not directly measuring innovation, provide some useful insight into innovative 
performance. Countries can also acquire new technology through imitation or copying 
the technology developed elsewhere. The embodiment of technology in capital goods 
can also enable relatively poor countries to jump ahead of the technology leaders.
Total factor productivity (TFP) is the component of productivity that proxies tech -
nological progress and organizational innovation. TFP is the amount by which output

would rise because of improvements in the production process. It is calculated as a 
residual, the difference between the growth rate of potential output and the weighted 
average growth rate of capital and labor. Specifically,
 TFP growth = Growth in potential GDP – [ WL (Growth in labor) + 
WC (Growth in capital)]
Natural Resources  Raw materials are an essential input to growth and include every -
thing from available land to oil to water. Historically, consumption of raw materials 
has increased as economies have grown. There are two categories of natural resources:
1 Renewable resources  are those that can be replenished, such as a forest. For 
example, if a tree is cut, a seedling can be planted and a new forest harvested in 
the future.
2 Non-  renewable resources  are finite resources that are depleted once they are 
consumed. Oil and coal are examples.
Natural resources account for some of the differences in growth among countries.

Today, such countries as Brazil and Australia, as well as those in the Middle East, have 
relatively high per capita incomes because of their resource base. Countries in the 
Middle East have large pools of oil. Brazil has an abundance of land suitable for large-  
scale agricultural production, making it a major exporter of coffee, soybeans, and beef.
Even though natural resources are important, they are not necessary for a country 
to achieve a high level of income provided it can acquire the requisite inputs through 
trade. Countries in eastern Asia, such as Japan and South Korea, have experienced 
rapid economic growth but own few natural resources.

Economic Growth and Sustainability 179
4.3 Measures of Sustainable Growth
Measuring how fast an economy can grow is an important exercise. Economists 
project potential GDP into the future to forecast the sustainable growth path for the 
economy. An economy’s potential GDP is an unobserved concept that is approximated 
using a number of alternative methods. It is important to note that estimates of the 
economy’s potential growth can change as new data become available. Being able to 
understand such a change is critical for financial analysts because equity returns are 
highly dependent on the sustainable rate of economic growth.
We discussed in the previous section that the growth rate of potential GDP depends 
on the rate of technological progress as well as the growth rate of
■■the labor force;
■■physical and human capital; and
■■natural resources.
How can we summarize all of these forces driving economic growth and develop

a method to measure/estimate the growth rate of potential GDP? One way is to use 
the growth accounting equation discussed in Section 4.1.
The problem with this approach is that there are no observed data on potential 
GDP or on total factor productivity and both must be estimated. In addition, data on 
the capital stock and the labor and capital shares of national income are not available 
for many countries, especially the developing countries.
As an alternative, we can focus on the productivity of the labor force, where we 
generally have more reliable data. Labor productivity  is defined as the quantity of 
goods and services (real GDP) that a worker can produce in one hour of work. Our 
standard of living improves if we produce more goods and services for each hour of 
work. Labor productivity is calculated as real GDP for a given year divided by the

total number of hours worked in that year, counting all workers. We use total hours, 
rather than the number of workers, to adjust for the fact that not everyone works the 
same number of hours.
Labor productivity = Real GDP/Aggregate hours
Therefore, we need to understand the forces that make labor more productive. 
Productivity is determined by the factors that we examined in the preceding section: 
education and skill of workers (human capital), investments in physical capital, and 
improvements in technology. An increase in any of these factors will increase the 
productivity of the labor force. The factors determining labor productivity can be 
derived from the production functions under the assumption of constant returns to 
scale, where a doubling of inputs causes output to double as well. Dividing the pro -
duction function by 1/ L, we get the following:
Y/L= AF(1,K/L)
where Y/L is output per worker, which is a measure of labor productivity. The equa -

tion states that labor productivity depends on physical capital per worker ( K/L) and 
technology ( A). Recall that “ A” can also be interpreted as total factor productivity. 
As this equation indicates, labor productivity and total factor productivity are related 
but distinct concepts. TFP is a scale factor that does not depend on the mix of inputs. 
Changes in TFP are measured as a residual, capturing growth that cannot be attributed 
to specific inputs. On the other hand, as shown in this equation, labor productiv -
ity—output per worker—  depends on both the general level of productivity (reflected

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 180
in TFP) and the mix of inputs. Increases in either TFP or the capital-  to- labor ratio 
boost labor productivity. Because both output and labor input can be observed, labor 
productivity can be measured directly.
Labor productivity is a key concept for measuring the health and prosperity of an 
economy and its sustainable rate of growth. An analyst examining the growth pros -
pects for an economy needs to focus on the labor productivity data for that country. 
Labor productivity largely explains the differences in the living standards and the 
long-  term sustainable growth rates among countries. The distinction between the 
level and growth rate of productivity is important to understand. Exhibit 28 provides 
such a comparison for selected countries.
Exhibit 28   Labor Productivity: Level vs. Growth Rate in Select Countries
Level of Labor Productivity  
(2008 GDP per hour worked)Labor Productivity Average Annual

Growth Rate, 2001–2008 
United States $55.3 2.0%
Ireland 54.7 2.4
France 53.2 1.3
Germany 50.5 1.5
Sweden 45.9 2.0
United Kingdom 44.9 2.1
Canada 43.2 0.9
Spain 42.5 0.9
Italy 41.1 0.0
Japan 38.3 1.9
Greece 32.1 2.2
South Korea 25.3 4.7
Turke y 23.8 NA
Mexico 18.6 0.5
Source:  OECD Stat Extracts.
Level of Labor Productivity  The higher the level of labor productivity, the more goods 
and services the economy can produce with the same number of workers. The level of 
labor productivity depends on the accumulated stock of human and physical capital 
and is much higher in the developed countries. For example, China has a population 
of over 1.4 billion people, compared with over 325 million people in the United States. 
Because of its much larger population, China has significantly more workers than the 
United States. The US economy as measured by real GDP is much larger, however. As 
shown in Exhibit 28, the United States has the highest level of productivity in the world,

producing over $55 of GDP per hour worked. Similarly, workers in France, Germany, 
and Ireland have high levels of productivity. In comparison, Mexican workers produce 
only $18.6 worth of GDP per hour worked. Thus, US workers are nearly three times 
more productive than Mexican workers.
Growth Rate of Labor Productivity  The growth rate of labor productivity is the per -
centage increase in productivity over a year. It is among the economic statistics that 
economists and financial analysts watch most closely. In contrast to the level of pro -
ductivity, the growth rate of productivity is typically higher in the developing countries 
where human and physical capital is scarce but growing rapidly.

Economic Growth and Sustainability 181
If productivity growth is rapid, it means the same number of workers can produce 
more and more goods and services. In this case, companies can afford to pay higher 
wages and still make a profit. Thus, high rates of productivity growth will translate 
into rising profits and higher stock prices.
In contrast, persistently low productivity growth suggests the economy is in bad 
shape. Without productivity gains, businesses have to either cut wages or boost prices 
in order to increase profit margins. Low rates of productivity growth should be asso -
ciated with slow growth in profits and flat or declining stock prices.
EXAMPLE 15   
Prospects for Equity Returns in Mexico
John Todd, CFA, manages a global mutual fund with nearly 30 percent of its 
assets invested in Europe. Because of the low population growth rate, he is 
concerned about the long-  term outlook for the European economies. With

potentially slower economic growth in Europe, the environment for equities 
may be less attractive. Therefore, he is considering reallocating some of the 
assets from Europe to Mexico. Based on the data in Exhibits 27 and 28, do you 
think that investment opportunities are favorable in Mexico? According to the 
OECD, the Mexican population increased by 0.8  percent in 2008, compared 
with a 0.3 percent increase in the European Union (27 countries).
Solution: 
Other than the higher population growth rate, the potential sources of growth 
for Mexico are not favorable. The level of business investment (Exhibit 27) in 
Mexico is quite low, especially in comparison to China, and even below that of 
many of the advanced economies in Europe, such as Spain and Italy. The level 
of labor productivity in Mexico is well below that in most European countries. 
This is not surprising given that the amount of capital per worker in Mexico is

much lower than that in Europe. What is surprising and of concern is the rate of 
labor productivity growth in Mexico. Labor productivity in Mexico is growing 
at a 0.5 percent annual rate, well below that of Germany, France, and the United 
Kingdom. This means that the rightward shift in the AS curve is greater for the 
European countries than for Mexico, despite the more favorable demographic 
trend in Mexico. In addition, it implies that there is more potential for expanding 
profit margins in Europe than in Mexico. Thus, the analysis of potential growth 
does not suggest a favorable outlook for equity returns in Mexico. In the absence 
of more favorable considerations—e.g., compelling equity valuations—John Todd 
should decide not to reallocate assets from Europe to Mexico.
Measuring Sustainable Growth  Labor productivity data can be used to estimate the 
rate of sustainable growth of the economy. A useful way to describe potential GDP is

as a combination of aggregate hours worked and the productivity of those workers:
Potential GDP = Aggregate hours worked × Labor productivity
Transforming the above equation into growth rates, we get the following:
 Potential growth rate = Long-  term growth rate of labor force + 
Long-  term labor productivity growth rate

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 182
Thus, potential growth is a combination of the long-  term growth rate of the labor 
force and the long-  term growth rate of labor productivity. Therefore, if the labor force 
is growing at 1 percent per year and productivity per worker is rising at 2 percent 
per year, then potential GDP (adjusted for inflation) is rising at 3 percent per year.
EXAMPLE 16   
Estimating the Rate of Growth in Potential GDP
Exhibit 29 provides data on sources of growth for Canada, Germany, Japan, and 
the United States. Estimate the growth rates of the labor force, labor productiv -
ity, and potential GDP for each country by averaging the growth rates for these 
variables for the last two decades.
Exhibit 29   Sources of Growth: Average Annual Growth Rate
1971–1980 1981–1990 1991–2000 2001–2008
Canada
Labor force 2.1% 1.8% 1.1% 1.5%
Productivity 1.8 1.0 1.8 0.9
GDP 4.0 2.8 2.9 2.4
Germany
Labor force –0.9% 0.0% –0.4% –0.4%
Productivity 3.7 2.3 2.5 1.5

GDP 2.9 2.3 2.1 1.0
Japan
Labor force 0.3% 0.5% –0.9% –0.7%
Productivity 4.2 3.4 2.2 2.1
GDP 4.5 3.9 1.2 1.4
Labor force 1.6% 1.8% 1.5% 0.3%
Productivity 1.6 1.4 1.8 2.0
GDP 3.2 3.2 3.3 2.2
Solution: 
Potential GDP is calculated as the sum of the trend growth rate in the labor 
force and the trend growth rate in labor productivity. The growth in the labor 
force can differ from the population growth rate because of changes in the labor 
force participation rate and changes in hours worked per person. Estimating 
based on the average for the last two decades gives

Economic Growth and Sustainability 183
Projected Growth  
in Labor ForceProjected Growth  
in Labor ProductivityProjected Growth  
in Potential GDP
Canada 1.3% 1.3% 2.6%
Germany –0.4 2.0 1.6
Japan –0.8 2.1 1.3
United 
States0.9 1.9 2.8
The most striking result is the difference in labor force growth in Germany and 
Japan in contrast to that in the United States and Canada. Most of the differ -
ence between the growth rates in potential GDP among these countries can be 
explained by the demographic factor. The results suggest that Japan’s sluggish 
growth over the last two decades is likely to continue. The weak productivity 
growth in Canada is of concern and is indicative of a low rate of innovation 
among Canadian companies.
EXAMPLE 17   
Prospects for Fixed-  Income Investments
As a fixed-  income analyst for a large Canadian bank, you have just received 
the latest GDP forecast from the OECD for Canada, Germany, Japan, and the 
United States. The forecast is given below:
Exhibit 30   OECD GDP Forecast

Projected Average Annual  
GDP Growth (2010–2012)
Canada 4.0%
Germany 1.5
Japan 0.5
United States 3.8
To evaluate the future prospects for fixed-  income investments, analysts must 
estimate the future rate of inflation and assess the possibility of changes in mon -
etary policy by the central bank. An important indicator for both of these factors 
is the degree of slack in the economy. One way to measure the degree of slack in 
the economy is to compare the growth rates of actual GDP and potential GDP .
Based on the estimates of potential GDP from the previous example and the 
information in Exhibit 30, evaluate the prospects for fixed-  income investments 
in each of the countries.

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 184
Solution: 
In comparing the OECD forecast for GDP growth with the estimated growth 
rate in potential GDP , there are two cases to consider:
1 If actual GDP is growing at a faster rate than potential GDP , it signals 
growing inflationary pressures and an increased likelihood that the central 
bank will raise interest rates.
2 If actual GDP is growing at a slower rate than potential GDP , it signals 
growing resource slack, less inflationary pressures, and an increased likeli -
hood that the central bank will reduce rates or leave them unchanged.
Exhibit 31 provides a comparison of actual and potential GDP for the above 
Exhibit 31   Actual vs. Potential GDP
GDP Growth (2010–2012) Potential GDP Growth
Canada 4.0% 2.6%
Germany 1.5 1.6
Japan 0.5 1.3
United States 3.8 2.8
The data suggest that inflationary pressure will grow in the United States and

Canada and that both the Federal Reserve and the Bank of Canada will eventually 
raise interest rates. Thus, the environment for bond investing is not favorable in 
the United States and Canada, because bond prices are likely to decline.
With Germany growing at its potential rate of GDP growth, the rate of 
inflation should neither rise nor fall. Monetary policy is set by the European 
Central Bank (ECB), but data on the German economy play a big role in the 
ECB’s decision. Based on the above data, no change in ECB policy is likely. For 
bond investors, little change in bond prices is likely in Germany, so investors 
need to focus on the interest (coupon) income received from the bond.
Finally, growing resource slack in Japan will put downward pressure on 
inflation and may force the Bank of Japan to keep rates low. Bond prices should 
rise in this environment.
SUMMARY
This reading introduces important macroeconomic concepts and principles for mac -

roeconomic forecasting and related investment decision making. Macroeconomics 
examines the economy as a whole by focusing on a country’s aggregate output of final 
goods and services, total income, aggregate expenditures, and the general price level. 
The first step in macroeconomic analysis is to measure the size of an economy. Gross 
domestic product enables us to assign a monetary value to an economy’s level of output 
or aggregate expenditures. The interaction of aggregate demand and aggregate sup -
ply determines the level of GDP as well as the general price level. The business cycle

Summary 185
reflects shifts in aggregate demand and short-  run aggregate supply. The long-  term 
sustainable growth rate of the economy depends on growth in the supply and quality 
of inputs (labor, capital, and natural resources) and advances in technology. From 
an investment perspective, macroeconomic analysis and forecasting are important 
because business profits, asset valuations, interest rates, and inflation rates depend on 
the business cycle in the short to intermediate term and on the drivers of sustainable 
economic growth in the long term. In addition, it is important to understand fiscal 
and monetary policies’ economic impact on and implications for inflation, household 
consumption and saving, capital investment, and exports.
■■GDP is the market value of all final goods and services produced within a coun -
try in a given time period.
■■GDP can be valued by looking at either the total amount spent on goods and

services produced in the economy or the income generated in producing those 
■■GDP counts only final purchases of newly produced goods and services during 
the current time period. Transfer payments and capital gains are excluded from 
GDP .
■■With the exception of owner-  occupied housing and government services, which 
are estimated at imputed values, GDP includes only goods and services that are 
valued by being sold in the market.
■■Intermediate goods are excluded from GDP in order to avoid double counting.
■■GDP can be measured either from the value of final output or by summing the 
value added at each stage of the production and distribution process. The sum 
of the value added by each stage is equal to the final selling price of the good.
■■Nominal GDP is the value of production using the prices of the current year. 
Real GDP measures production using the constant prices of a base year. The 
GDP deflator equals the ratio of nominal GDP to real GDP .

■■Households earn income in exchange for providing—directly or indirectly 
through ownership of businesses—the factors of production (labor, capital, 
natural resources including land). From this income, they consume, save, and 
pay net taxes.
■■Businesses produce most of the economy’s output/income and invest to main -
tain and expand productive capacity. Companies retain some earnings but pay 
out most of their revenue as income to the household sector and as taxes to the 
government.
■■The government sector collects taxes from households and businesses and pur -
chases goods and services from the private business sector.
■■Foreign trade consists of exports and imports. The difference between the two 
is net exports. If net exports are positive (negative), then the country spends 
less (more) than it earns. Net exports are balanced by accumulation of either 
claims on the rest of the world (net exports > 0) or obligations to the rest of the 
world (net exports < 0).

■■Capital markets provide a link between saving and investment in the economy.
■■From the expenditure side, GDP includes personal consumption ( C), gross 
private domestic investment ( I), government spending ( G), and net exports ( X 
– M).
■■The major categories of expenditure are often broken down into subcategories. 
Gross private domestic investment includes both investment in fixed assets 
(plant and equipment) and the change in inventories. In some countries, gov -
ernment investment spending is separated from other government spending.

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 186
■■National income is the income received by all factors of production used in the 
generation of final output. It equals GDP minus the capital consumption allow -
ance (depreciation) and a statistical discrepancy.
■■Personal income reflects pre-  tax income received by households. It equals 
national income plus transfers minus undistributed corporate profits, corporate 
income taxes, and indirect business taxes.
■■Personal disposable income equals personal income minus personal taxes.
■■Private saving must equal investment plus the fiscal and trade deficits. That is, S 
= I + (G – T) + ( X – M).
■■Consumption spending is a function of disposable income. The marginal pro -
pensity to consume represents the fraction of an additional unit of disposable 
income that is spent.
■■Investment spending depends on the average interest rate and the level of 
aggregate income. Government purchases and tax policy are often considered

to be exogenous variables determined outside the macroeconomic model. 
Actual taxes collected depend on income and are, therefore, endogenous—that 
is, determined within the model.
■■The IS curve reflects combinations of GDP and the real interest rate such that 
aggregate income/output equals planned expenditures. The LM curve reflects 
combinations of GDP and the interest rate such that demand and supply of real 
money balances are equal.
■■Combining the IS and LM relationships yields the aggregate demand curve.
■■Aggregate demand and aggregate supply determine the level of real GDP and 
the price level.
■■The aggregate demand curve is the relationship between real output (GDP) 
demanded and the price level, holding underlying factors constant. Movements 
along the aggregate demand curve reflect the impact of price on demand.
■■The aggregate demand curve is downward sloping because a rise in the price 
level reduces wealth, raises real interest rates, and raises the price of domes -

tically produced goods versus foreign goods. The aggregate demand curve is 
drawn assuming a constant money supply.
■■The aggregate demand curve will shift if there is a change in a factor, other than 
price, that affects aggregate demand. These factors include household wealth, 
consumer and business expectations, capacity utilization, monetary policy, 
fiscal policy, exchange rates, and foreign GDP .
■■The aggregate supply curve is the relationship between the quantity of real GDP 
supplied and the price level, keeping all other factors constant. Movements 
along the supply curve reflect the impact of price on supply.
■■The short-  run aggregate supply curve is upward sloping because higher prices 
result in higher profits and induce businesses to produce more and laborers to 
work more. In the short run, some prices are sticky, implying that some prices 
do not adjust to changes in demand.
■■In the long run, all prices are assumed to be flexible. The long-  run aggregate

supply curve is vertical because input costs adjust to changes in output prices, 
leaving the optimal level of output unchanged. The position of the curve is 
determined by the economy’s level of potential GDP .

Summary 187
■■The level of potential output, also called the full employment or natural level of 
output, is unobservable and difficult to measure precisely. This concept rep -
resents an efficient and unconstrained level of production at which companies 
have enough spare capacity to avoid bottlenecks and there is a balance between 
the pool of unemployed workers and the pool of job openings.
■■The long-  run aggregate supply curve will shift because of changes in labor sup -
ply, supply of physical and human capital, and productivity/technology.
■■The short-  run supply curve will shift because of changes in potential GDP , 
nominal wages, input prices, expectations about future prices, business taxes 
and subsidies, and the exchange rate.
■■The business cycle and short-  term fluctuations in GDP are caused by shifts in 
aggregate demand and aggregate supply.
■■When the level of GDP in the economy is below potential GDP , such a reces -

sionary situation exerts downward pressure on the aggregate price level.
■■When the level of GDP is above potential GDP , such an overheated situation 
puts upward pressure on the aggregate price level.
■■Stagflation, a combination of high inflation and weak economic growth, is 
caused by a decline in short-  run aggregate supply.
■■The sustainable rate of economic growth is measured by the rate of increase in 
the economy’s productive capacity or potential GDP .
■■Growth in real GDP measures how rapidly the total economy is expanding. Per 
capita GDP , defined as real GDP divided by population, reflects the standard 
of living in a country. Real GDP growth rates and levels of per capita GDP vary 
widely among countries.
■■The sources of economic growth include the supply of labor, the supply of phys -
ical and human capital, raw materials, and technological knowledge.
■■Output can be described in terms of a production function. For example, Y

= AF(L,K) where L is the quantity of labor, K is the capital stock, and A rep-
resents technological knowledge or total factor productivity. The function F(·) is 
assumed to exhibit constant returns to scale but diminishing marginal produc -
tivity for each input individually.
■■Total factor productivity is a scale factor that reflects the portion of output 
growth that is not accounted for by changes in the capital and labor inputs. TFP 
is mainly a reflection of technological change.
■■Based on a two-  factor production function, Potential GDP growth = Growth in 
TFP + WL (Growth in labor) + WC (Growth in capital), where WL and WC (= 1 
– WL) are the shares of labor and capital in GDP .
■■Diminishing marginal productivity implies that
■●Increasing the supply of some input(s) relative to other inputs will lead to 
diminishing returns and cannot be the basis for sustainable growth. In par -
ticular, long-  term sustainable growth cannot rely solely on capital deepen -

ing, that is, increasing the stock of capital relative to labor.
■●Given the relative scarcity and hence high productivity of capital in develop -
ing countries, the growth rate of developing countries should exceed that of 
developed countries.
■■The labor supply is determined by population growth, the labor force partici -
pation rate, and net immigration. The capital stock in a country increases with 
investment. Correlation between long-  run economic growth and the rate of 
investment is high.

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 188
Case, K., J. Quigley, and R. Shiller. 2005. “Comparing Wealth 
Effects: The Stock Market versus the Housing Market. ” 
Advances in Macroeconomics , vol. 5, no. 1.Funke, N. 2004. “Is There a Stock Market Wealth Effect in 
Emerging Markets?” International Monetary Fund  (March).■■In addition to labor, capital, and technology, human capital—essentially, the 
quality of the labor force—and natural resources are important determinants of 
output and growth.
■■Technological advances are discoveries that make it possible to produce 
more and/or higher-  quality goods and services with the same resources or 
inputs. Technology is the main factor affecting economic growth in developed 
■■The sustainable rate of growth in an economy is determined by the growth rate 
of the labor supply plus the growth rate of labor productivity.

Practice Problems 189
1 Which of the following statements is the most  appropriate description of gross 
domestic product (GDP)? 
A The total income earned by all households, firms, and the government 
whose value can be verified.
B The total amount spent on all final goods and services produced within the 
economy over a given time period.
C The total market value of resalable and final goods and services produced 
within the economy over a given time period.
2 The component least likely  to be included in a measurement of gross domestic 
product (GDP) is:
A the value of owner occupied rent.
B the annual salary of a local police officer.
C environmental damage caused by production.
3 Which of the following conditions is least likely  to increase a country’s GDP?
A An increase in net exports.
B Increased investment in capital goods.
C Increased government transfer payments.
4 Which of the following would be included in Canadian GDP for a given year? 
The market value of:

A wine grown in Canada by US citizens.
B electronics made in Japan and sold in Canada.
C movies produced outside Canada by Canadian film makers.
5 Suppose a painting is produced and sold in 2010 for £5,000. The expenses 
involved in producing the painting amounted to £2,000. According to the sum-  
of- value-  added method of calculating GDP , the value added by the final step of 
creating the painting was:
A £2,000.
B £3,000.
C £5,000.
6 A GDP deflator less than 1 indicates that an economy has experienced:
A inflation.
B deflation.
C stagflation.
7 The most  accurate description of nominal GDP is:
A a measure of total expenditures at current prices.
B the value of goods and services at constant prices.
C a measure to compare one nation's economy to another.
8 From the beginning to the ending years of a decade, the annual value of final 
goods and services for country X increased from €100 billion to €300 billion.

Over that time period, the GDP deflator increased from 111 to 200. Over the 
decade, real GDP for country X increased by approximately:
A 50%.

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 190
B 67%.
C 200%.
9 If the GDP deflator values for 2008 and 2010 were 190 and 212.8, respectively, 
which of the following best describes the annual growth rate of the overall price 
level?
A 5.8%.
B 6%.
C 12%.
10 The numerator of the GDP price deflator reflects:
A the value of base year output at current prices.
B the value of current year output at current prices.
C the value of current year output at base year prices.
11 Consider the following data for 2010 for a hypothetical country:
Account name Amount ($ trillions)
Consumption 15.0
Capital consumption allowance 1.5
Government spending 3.8
Imports 1.7
Gross private domestic investment 4.0
Exports 1.5
 Based only on the data given, the gross domestic product and national income 
are respectively closest  to:
A 21.1 and 20.6.
B 22.6 and 21.1.
C 22.8 and 20.8.
12 In calculating personal income for a given year, which of the following would 
not be subtracted from national income?

A Indirect business taxes.
B Undistributed corporate profits.
C Unincorporated business net income.
13 Equality between aggregate expenditure and aggregate output implies that the 
government’s fiscal deficit must equal:
A Private saving – Investment – Net exports.
B Private saving – Investment + Net exports.
C Investment – Private saving + Net exports.
14 Because of a sharp decline in real estate values, the household sector has 
increased the fraction of disposable income that it saves. If output and invest -
ment spending remain unchanged, which of the following is most likely ?
A A decrease in the government deficit.
B A decrease in net exports and increased capital inflow.
C An increase in net exports and increased capital outflow.
15 Which curve represents combinations of income and the real interest rate at 
which planned expenditure equals income?
A The IS curve.

Practice Problems 191
B The LM curve.
C The aggregate demand curve.
16 An increase in government spending would shift the:
A IS curve and the LM curve.
B IS curve and the aggregate demand curve.
C LM curve and the aggregate demand curve.
17 An increase in the nominal money supply would shift the:
18 An increase in the price level would shift the:
A IS curve.
B LM curve.
C aggregate demand curve.
19 As the price level declines along the aggregate demand curve, the interest rate is 
most likely  to:
A decline.
B increase.
20 The full employment, or natural, level of output is best described as:
A the maximum level obtainable with existing resources.
B the level at which all available workers have jobs consistent with their skills.
C a level with a modest, stable pool of unemployed workers transitioning to 
new jobs.

new jobs.
21 Which of the following best describes the aggregate supply curve in the short-  
run (e.g., 1 to 2 years)? The short run aggregate supply curve is:
A flat because output is more flexible than prices in the short run.
B vertical because wages and other input prices fully adjust to the price level.
C upward sloping because input prices do not fully adjust to the price level in 
the short run.
22 If wages were automatically adjusted for changes in the price level, the short-  
run aggregate supply curve would most likely  be:
A flatter.
B steeper.
C unchanged.
23 The least likely  cause of a decrease in aggregate demand is:
A higher taxes.
B a weak domestic currency.
C a fall in capacity utilization.
24 Which of the following is most likely  to cause the long-  run aggregate supply 
curve to shift to the left?
A Higher nominal wages.
B A decline in productivity.
C A increase in corporate taxes.
25 Increased household wealth will most likely  cause an increase in:

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 192
A household saving.
B investment expenditures.
C consumption expenditures.
26 The most likely  outcome when both aggregate supply and aggregate demand 
increase is:
A a rise in inflation.
B higher employment.
C an increase in nominal GDP .
27 Which of the following is least likely  to be caused by a shift in aggregate 
demand?
A Stagflation.
B A recessionary gap.
C An inflationary gap.
28 Following a sharp increase in the price of energy, the overall price level is most 
likely  to rise in the short run:
A and remain elevated indefinitely unless the central bank tightens.
B but be unchanged in the long run unless the money supply is increased.
C and continue to rise until all prices have increased by the same proportion.
29 Among developed economies, which of the following sources of economic 
growth is most likely  to explain superior growth performance?
A Technology.
B Capital stock.
C Labor supply.

30 Which of the following can be measured directly?
A Potential GDP .
B Labor productivity.
C Total factor productivity.
31 The sustainable growth rate is best estimated as:
A the weighted average of capital and labor growth rates.
B growth in the labor force plus growth of labor productivity.
C growth in total factor productivity plus growth in the capital-  to- labor ratio.
32 In the neoclassical or Solow growth model, an increase in total factor produc -
tivity reflects an increase in:
A returns to scale.
B output for given inputs.
C the sustainable growth rate.

Practice Problems 193
33–34
An economic forecasting firm has estimated the following equation from historical 
data based on the neoclassical growth model:
 Potential output growth = 1.5 + 0.72 × Growth of labor + 0.28 × 
Growth of capital
33 The intercept (1.5) in this equation is best interpreted as:
A the long-  run sustainable growth rate.
B the growth rate of total factor productivity.
C above trend historical growth that is unlikely to be sustained.
34 The coefficient on the growth rate of labor (0.72) in this equation is best inter -
preted as:
A the labor force participation rate.
B the marginal productivity of labor.
C the share of income earned by labor.
35 Convergence of incomes over time between emerging market countries and 
developed countries is most likely  due to:
A total factor productivity.
B diminishing marginal productivity of capital.
C the exhaustion of non-  renewable resources.

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 194
SOLUTIONS
1 B is correct. GDP is the total amount spent on all final goods and services pro -
duced within the economy over a specific period of time.
2 C is correct. By-  products of production processes that have no explicit market 
value are not included in GDP .
3 C is correct. Government transfer payments, such as unemployment compensa -
tion or welfare benefits, are excluded from GDP .
4 A is correct. Canadian GDP is the total market value of all final goods and ser -
vices produced in a given time period within Canada. The wine was produced 
in Canada and counts towards Canadian GDP .
5 B is correct. This is the value added by the artist: £5,000 – £2,000 = £3,000.
6 B is correct. The GDP Deflator = Nominal GDP/Real GDP . To get a ratio 
less than 1, real GDP exceeds nominal GDP , which indicates that prices have 
decreased and, accordingly, deflation has occurred.

7 A is correct. Nominal GDP is defined as the value of goods and services mea -
sured at current prices. Expenditure is used synonymously with the value of 
goods and services since aggregate expenditures must equal aggregate output of 
8 B is correct. Real GDP in the first year was €100 billion/1.11 = €90 and in the 
last year it was €300 billion/2.00 = €150. Thus, (€150 – €90)/€90 = 0.67 or 67%.
9 A is correct: (212.8/190)1/2 – 1 = 0.0583 or 5.8%.
10 B is correct. 
Value of current y ear output at base y ear prices×100 0
11 B is correct. GDP = Consumption + Gross private domestic investment + 
Government Spending + Exports – Imports = 15 + 4 + 3.8 + 1.5 – 1.7 = 22.6. 
National income = GDP – CCA = 22.6 – 1.5 = 21.1
12 C is correct. Unincorporated business net income is also known as proprietor’s 
income and is included in personal income.

13 A is correct. The fundamental relationship among saving, investment, the fiscal 
balance, and the trade balance is S = I + (G – T) + ( X – M). This form of the 
relationship shows that private saving must fund investment expenditures, the 
government fiscal balance, and net exports (= net capital outflows). Rearranging 
gives G – T = (S – I) – ( X – M). The government’s fiscal deficit ( G – T) must 
be equal to the private sector’s saving/investment balance ( S – I) minus net 
exports.
14 C is correct. The fundamental relationship among saving, investment, the fiscal 
balance, and the trade balance is S = I + (G – T) + ( X – M). Given the levels of 
output and investment spending, an increase in saving (reduction in consump -
tion) must be offset by either an increase in the fiscal deficit or an increase in 
net exports. Increasing the fiscal deficit is not one of the choices, so an increase

in net exports and corresponding increase in net capital outflows (increased 
lending to foreigners and/or increased purchases of assets from foreigners) is 
the correct response.
15 A is correct. The IS curve represents combinations of income and the real inter -
est rate at which planned expenditure equals income.

Solutions 195
16 B is correct. The IS curve represents combinations of income and the real inter -
est rate at which planned expenditure equals income. Equivalently, it represents 
combinations such that
S(Y) = I(r) + ( G – T) + ( X – M)
 where S(Y) indicates that planned saving is a (increasing) function of income 
and I(r) indicates that planned investment is a (decreasing) function of the real 
interest rate. To maintain this relationship, an increase in government spend -
ing ( G) requires an increase in saving at any given level of the interest rate ( r). 
This implies an increase in income ( Y) at each interest rate level—a rightward 
shift of the IS curve. Unless the LM curve is vertical, the IS and LM curves will 
intersect at a higher level of aggregate expenditure/income. Since the LM curve 
embodies a constant price level, this implies an increase in aggregate expendi -
ture at each price level—a rightward shift of the Aggregate Demand curve.

17 C is correct. The LM curve represents combinations of income and the interest 
rate at which the demand for real money balances equals the supply. For a given 
price level, an increase in the nominal money supply is also an increase in the 
real money supply. To increase the demand for real money balances, either the 
interest must decline or income must increase. Therefore, at each level of the 
interest rate, income (= expenditure) must increase—a rightward shift of the 
LM curve. Since the IS curve is downward sloping (higher income requires a 
lower interest rate), a rightward shift in the LM curve means that the IS and 
LM curves will intersect at a higher level of aggregate expenditure/income. This 
implies a higher level of aggregate expenditure at each price level—a rightward 
shift of the Aggregate Demand curve.
18 B is correct. The LM curve represents combinations of income and the interest 
rate at which the demand for real money balances equals the supply. For a given

nominal money supply, an increase in the price level implies a decrease in the 
real money supply. To decrease the demand for real money balances, either the 
interest must increase or income must decrease. Therefore, at each level of the 
interest rate, income (= expenditure) must decrease—a leftward shift of the LM 
curve.
19 A is correct. A decrease in the price level increases the real money supply and 
shifts the LM curve to the right. Since the IS curve is downward sloping, the 
IS and LM curves will intersect at a higher level of income and a lower interest 
rate.
20 C is correct. At the full employment, or natural, level of output the economy 
is operating at an efficient and unconstrained level of production. Companies 
have enough spare capacity to avoid bottlenecks, and there is a modest, stable 
pool of unemployed workers (job seekers equal job vacancies) looking for and 
transitioning into new jobs.
21 C is correct. Due to long-  term contracts and other rigidities, wages and other

input costs do not fully adjust to changes in the price level in the short-  run. 
Given input prices, firms respond to output price changes by expanding or con -
tracting output to maximize profit. Hence, the SRAS is upward sloping.
22 B is correct. The slope of the short-  run aggregate supply curve reflects the 
extent to which wages and other input costs adjust to the overall price level. 
Automatic adjustment of wages would mitigate the impact of price changes 
on profitability. Hence, firms would not adjust output as much in response to 
changing output prices—the SRAS curve would be steeper.

Reading 16 ■ Aggregate Output, Prices, and Economic Growth 196
23 B is correct. A weak domestic currency will result in an increase in aggregate 
demand at each price level—a rightward shift in the AD curve. A weaker cur -
rency will cause a country’s exports to be cheaper in global markets. Conversely, 
imports will be more expensive for domestic buyers. Hence, the net exports 
component of aggregate demand will increase.
24 B is correct. Productivity measures the efficiency of labor and is the amount of 
output produced by workers in a given period of time. A decline in productivity 
implies decreased efficiency. A decline in productivity increases labor costs, 
decreases profitability and results in lower output at each output price level—a 
leftward shift in both the short-  run and long-  run aggregate supply curves.
25 C is correct. The wealth effect explains the impact of increases or decreases in 
household wealth on economic activity. Household wealth includes financial

and real assets. As asset values increase, consumers save less and spend more 
out of current income since they will still be able to meet their wealth accumu -
lation goals. Therefore, an increase in household wealth results in a rightward 
shift in the aggregate demand curve.
26 B is correct. Higher aggregate demand (AD) and higher aggregate supply (AS) 
raise real GDP and lower unemployment, meaning employment levels increase.
27 A is correct. Stagflation occurs when output is declining and prices are rising. 
This is most likely due to a decline in aggregate supply—a leftward shift of the 
SRAS curve. Depending on the source of the shift, the LRAS may shift too.
28 B is correct. An increase in energy prices will shift the short-  run aggregate sup -
ply curve (SRAS) to the left, reducing output and increasing prices. If there is 
no change in the aggregate demand curve, in particular if the central bank does 
not expand the money supply, slack in the economy will put downward pressure

on in input prices, shifting the SRAS back to its original position. In the long 
run, the price level will be unchanged.
29 A is correct. Technology is the most important factor affecting economic 
growth for developed countries. Technological advances are very important 
because they allow an economy to overcome the limits imposed by diminishing 
30 B is correct. Labor productivity can be directly measured as output/hour.
31 B is correct. Output growth is equal to the growth rate of the labor force plus 
the growth rate of labor productivity, i.e. output per worker. Unlike total factor 
productivity, output per worker is observable, so this is the most practical way 
to approach estimation of sustainable growth.
32 B is correct. Total factor productivity (TFP) is a scale factor primarily reflecting 
technology. An increase in TFP means that output increases for any level of 
factor inputs.
33 B is correct. The estimated equation is the standard Solow growth accounting

equation. The intercept is the growth rate of total factor productivity.
34 C is correct. In the standard Solow growth accounting equation, the coefficient 
on each factor’s growth rate is its share of income.
35 B is correct. Diminishing marginal productivity of capital means that as a 
country accumulates more capital per worker the incremental boost to output 
declines. Thus, all else the same, economies grow more slowly as they become 
more capital intensive. Given the relative scarcity and hence high marginal pro -
ductivity of capital in developing countries, they tend to grow more rapidly than 
developed countries. This leads to convergence in income levels over time.

Understanding Business Cycles
by Michele Gambera, PhD, CFA, Milton Ezrati, and Bolong Cao, PhD, CFA
Michele Gambera, PhD, CFA, is at UBS Asset Management (Americas), Inc. (USA). Milton 
Ezrati (USA). Bolong Cao, PhD, CFA, is at Ohio University (USA).
a. describe the business cycle and its phases;
b. describe how resource use, housing sector activity, and external 
trade sector activity vary as an economy moves through the 
business cycle;
c. describe theories of the business cycle;
d. describe types of unemployment and compare measures of 
unemployment;
e. explain inflation, hyperinflation, disinflation, and deflation;
f. explain the construction of indexes used to measure inflation;
g. compare inflation measures, including their uses and limitations;
h. distinguish between cost-  push and demand-  pull inflation; 
i. interpret a set of economic indicators and describe their uses and 
limitations.

Agricultural societies experience good harvest times and bad ones. Weather is a main 
factor that influences crop production, but other factors, such as plant and animal 
diseases, also influence the harvest. Modern diversified economies are less influenced 
by weather and diseases but, as with crops, there are fluctuations in economic output, 
with good times and bad times. 1READING
17

Reading 17 ■ Understanding Business Cycles 198
This reading addresses changes in economic activity and factors that affect it. 
Some of the factors that influence short-  term economic movements—such as changes 
in population, technology, and capital—are the same as those that affect long-  term 
sustainable economic growth. Other factors, such as money supply and inflation, are 
more specific to short-  term economic fluctuations.
This reading is organized as follows. Section 2 describes the business cycle and 
its phases. The typical behaviors of businesses and households in different phases 
and transitions between phases are described. Section 3 provides an introduction 
to business cycle theory, in particular how different economic schools of thought 
interpret the business cycle and their recommendations with respect to it. Section 4 
introduces basic concepts concerning unemployment and inflation, two measures of

short-  term economic activity that are important to economic policymakers. Section 
5 discusses variables that demonstrate predictable relationships with the economy, 
focusing on variables whose movements have value in predicting the future course of 
the economy. A summary and practice problems conclude the reading.
OVERVIEW OF THE BUSINESS CYCLE
Burns and Mitchell (1946) define the business cycle as follows:
Business cycles are a type of fluctuation found in the aggregate economic 
activity of nations that organize their work mainly in business enterprises: 
a cycle consists of expansions occurring at about the same time in many 
economic activities, followed by similarly general recessions, contractions, 
and revivals which merge into the expansion phase of the next cycle; this 
sequence of events is recurrent but not periodic; in duration, business 
cycles vary from more than one year to 10 or 12 years.
This long definition is rich with important insights. First, business cycles are typ -

ical of economies that rely mainly on business enterprises—therefore, not agrarian 
societies or centrally planned economies. Second, a cycle has an expected sequence 
of phases, alternating between expansion and contraction. Third, such phases occur 
at about the same time throughout the economy—that is, not just in agriculture or 
not just in tourism but in almost all sectors. Fourth, cycles are recurrent (i.e., they 
happen again and again over time) but not periodic (i.e., they do not all have the exact 
same intensity and/or duration). Finally, cycles typically last between 1 and 12 years.
Although Burns and Mitchell’s definition may appear obvious in part, it indeed 
remains helpful even more than 60 years after it was written. Although “rules of thumb” 
are often referred to when talking about market activity (e.g., shares always rally in 
January and big crashes occur in October), reality is much more complex. As Burns and

Mitchell remind us, history never repeats itself in quite the same way, but it certainly 
offers patterns that can be used when analyzing the present and forecasting the future.
2.1 Phases of the Business Cycle
A typical business cycle consists of four phases: trough, expansion, peak, contraction. 
The period of expansion  occurs after the trough  (lowest point) of a business cycle 
and before its peak  (highest point). The peak and trough represent turning points in 
the cycle. Contraction  is the period after the peak and before the trough.1 During the 
expansion phase, aggregate economic activity is increasing ( aggregate  is used because 2
1 For more information, see www.nber.org/cycles/recessions.html.

Overview of the Business Cycle 199
some individual economic sectors may not be growing). The contraction—often called 
a recession , but may be called a depression  when exceptionally severe—is a period 
in which aggregate economic activity is declining (although some individual sectors 
may be growing). Business cycles can be thought of as fluctuations around the trend 
growth of an economy. 
Exhibit 1 Panel A shows a stylized representation of the business cycle. Panel B 
provides a description of some important characteristics of each phase. The description 
distinguishes between early and late stages of the expansion phase. The early stage 
is closer to the trough and the late stage is closer to the peak. Exhibit 1 Panel B also 
describes how several important economic variables evolve through the course of a 
business cycle.
Exhibit 1   
Panel A: Representation of a Business Cycle
Level of National Economic Activity
TimePeak
Peak
TroughExpansion ContractionGrowth           Trend

Reading 17 ■ Understanding Business Cycles 200
Panel B: Characteristics
Early Expansion 
(Recovery) Late Expansion Peak Contraction (Recession)
Economic 
Activity ■■Gross domestic prod -
uct (GDP), industrial 
production, and other 
measures of economic 
activity stabilize 
and then begin to 
increase.■■Activity measures 
show an accelerat -
ing rate of growth.■■Activity measures 
show decelerating 
rate of growth.■■Activity measures show 
outright declines.
Employment ■■Layoffs slow but new 
hiring does not yet 
occur and the unem -
ployment rate remains 
high. Business turns 
to overtime and 
temporary employees 
to meet rising product 
demands.■■Business begins full 
time rehiring as 
overtime hours rise. 
The unemployment 
rate falls.■■Business slows its 
rate of hiring. The 
unemployment 
rate continues 
to fall but at a 
decreasing rate.■■Business first cuts hours 
and freezes hiring, fol -
lowed by outright layoffs. 
The unemployment rate 
rises.
Consumer 
and Business 
Spending■■Upturn in spending 
often most pro -

nounced in housing, 
durable consumer 
items, and orders 
for light producer 
equipment.■■Upturn in spend -
ing becomes more 
broad-  based. 
Business begins to 
order heavy equip -
ment and engage in 
construction.■■Capital spending 
expands rapidly, 
but the growth 
rate of spending 
starts to slow 
down.■■Decreased spending most 
evident in industrial 
production, housing, 
consumer durable items, 
and orders for new busi -
ness equipment. 
Inflation ■■Inflation remains 
moderate and may 
continue to fall.■■Inflation picks up 
modestly.■■Inflation further 
accelerates.■■Inflation decelerates but 
with a lag.
The behavior of businesses and households frequently incorporates leads and lags, 
relative to what are established as turning points in a business cycle. For example, at 
the beginning of the expansion phase, companies may want to fully use their existing 
workforce and wait to hire new employees until they are sure that the economy is indeed

growing. However, gradually all economic variables are going to revert toward their 
normal range of values (e.g., GDP growth will be a positive number). As the economy 
returns to normal, any countercyclical economic policies adopted by a central bank 
(the monetary authority in most modern economies) are gradually phased out. For 
example, if the central bank reduced interest rates to stimulate the economy during 
a recession, it may start increasing rates toward their historical norms.
During a recession, investors place relatively high values on such safer assets as 
government securities and shares of companies with steady (or growing) positive cash 
flows, such as utilities and producers of staple goods. Such preferences reflect the fact 
that the marginal utility of a safe income stream increases in periods when employ -
ment is insecure or declining. When asset markets expect the end of a recession and 
the beginning of an expansion phase, risky assets will be repriced upward. When an

expansion is expected, the markets will start incorporating higher profit expectations 
into the prices of corporate bonds and stocks, particularly those of such cyclical 
companies as producers of discretionary goods, for example automobiles. Typically, Exhibit 1   (Continued)

Overview of the Business Cycle 201
equity markets will hit a trough about three to six months before the economy bottoms 
and well before the economic indicators turn up. Indeed, the equity stock market is 
classified as a leading indicator of the economy.
When an economy’s expansion is well established, a later part of an expansion called 
a boom  often follows. The boom is an expansionary phase, which is characterized by 
economic growth “testing the limits” of the economy. For example, companies may 
expand so much that they have difficulty finding qualified workers, and will compete 
with other prospective employers by raising wages. The resulting rise in labor costs 
may lead to a reduction of profits. Another example is that companies may begin 
to believe that the economy will continue expanding for the foreseeable future and 
decide to borrow money to expand their production capacity. The government and/or

central bank may step in if it is concerned about the economy overheating. Consider 
the following situation. The central bank is concerned that excessive salary growth 
may lead to inflation. For example, companies will try to pass on higher production 
costs to their customers or excessive borrowing may cause investors to have cash flow 
problems. At the height of the boom phase, the economy is said to be overheating 
(just like the engine of a car that has been pushed to an excessive level).
During the boom, the riskiest assets will often have substantial price increases. Safe 
assets, such as government bonds that were more highly prized during the recession, 
may have lower prices and thus higher yields. In addition, investors may fear higher 
inflation, which also contributes to higher nominal yields.
The end of the expansion, or boom, is characterized by the peak of the business 
cycle, which is also the beginning of the contraction (also known as downturn). Here,

either because of restrictive economic policies established to tame an overheated 
economy or because of some other shock, such as energy prices or a credit crisis, 
the economy stumbles and starts slowing down. Unemployment increases and GDP 
growth decreases during this part of the business cycle.
EXAMPLE 1   
When Do Recessions Begin and End? 
A simple and commonly referred to rule is: A recession has started when a country 
or region experiences two consecutive quarters of negative real GDP growth. 
Real GDP growth is a measure of the “real” or “inflation-  adjusted” growth of 
the overall economy. This rule can be misleading because it does not indicate 
a recession if real GDP growth is negative in one quarter, slightly positive the 
next quarter, and again negative in the next quarter. Many analysts question this 
result. This issue is why, in some countries, there are statistical and economic 
committees that apply the principles stated by Burns and Mitchell to several

macroeconomic variables (and not just real GDP growth) as a basis to identify 
business cycle peaks and troughs. The National Bureau of Economic Research 
(NBER) is the well-  known organization that dates business cycles in the United 
States. Interestingly, the economists and statisticians on NBER’s Business Cycle 
Dating Committee analyze numerous time series of data focusing on employ -
ment, industrial production, and sales. Because the data are available with a 
delay (preliminary data releases can be revised even one year after the period 
they refer to), it also means that the Committee’s determinations may take place 
well after the business cycle turning points have occurred. As we will see later in 
the reading, there are practical indicators that may help economists understand 
in advance if a cyclical turning point is about to happen.
1 Which of the following rules is most  likely  to be used to determine 
whether the economy is in a recession?

Reading 17 ■ Understanding Business Cycles 202
A The central bank has run out of foreign reserves.
B Real GDP has two consecutive quarters of negative growth.
C Economic activity experiences a significant decline in two business 
sectors.
2 Suppose you are interested in forecasting earnings growth for a company 
active in a country where no official business cycle dating committee 
(such as the NBER) exists. The variables you are most likely  to consider to 
identify peaks and troughs of a country’s business cycle are:
A inflation, interest rates, and unemployment.
B stock market values and money supply.
C unemployment, GDP growth, industrial production, and inflation.
B is correct. GDP is a measure of economic activity for the whole economy. 
Changes in foreign reserves or a limited number of sectors may not have a 
material impact on the whole economy.
C is correct. Unemployment, GDP growth, industrial production, and inflation

are measures of economic activity. The discount rate, the monetary base, and 
stock market indexes are not direct measures of economic activities. The first 
two are determined by monetary policy, which react to economic activities, 
whereas the stock market indexes tend to be forward looking or leading indi -
cators of the economy.
Investors, who are often optimists in the expansion phase, tend to be overly pes -
simistic at the bottom of the business cycle. It is worth noting that in many business 
cycles, the duration of economic contractions have been shorter than the duration 
of expansions.
Many economic variables and sectors of the economy have distinctive cyclical 
patterns. Knowledge of these patterns can offer insight into likely cyclical directions 
overall or can be particularly applicable to an investment strategy that requires more 
specific rather than general cyclical insights for investment success. The following

sections provide overviews of how the use of resources (the factors of production) 
typically evolves through the business cycle and how the sectors of real estate and 
external trade characteristically behave.
2.2 Resource Use through the Business Cycle
This section provides a broad overview of how the use of resources needed to produce 
goods and services typically evolves during a business cycle.
There are significant links between fluctuations in inventory, employment, and 
investment in physical capital with economic fluctuations. When a downturn starts, 
aggregate demand decreases, and as a result, inventories may start to accumulate. 
Companies may slow production and have equipment that is being used at less than 
full capacity. Subsequently, companies are likely to stop ordering new inventories and 
new production equipment.
Companies do not necessarily reduce their workforces immediately; instead, they 
reduce costs by other means, such as eliminating overtime. If it is just a temporary

economic slowdown, retaining workers that are not being fully utilized may be a 
better alternative than firing workers and replacing them later. Finding and training

Overview of the Business Cycle 203
new workers is costly and it may be more cost efficient to keep workers on the payroll, 
even if they are not fully utilized, while waiting out a short period of slow business. 
Second, some economists suggest that there is an implicit bond of loyalty between a 
company and its workers, and thus workers will be more productive if they know that 
the company is not disposing of them at the first sign of economic trouble.
If the downturn becomes more severe, companies will start reducing costs more 
aggressively, cutting all non-  essential costs. This step often means terminating con -
sultants, workers beyond the strict minimum, standing supply orders, advertising 
campaigns, and so on. Capacity utilization will be low, and few companies will invest 
in new equipment and structures. Companies will try to liquidate their inventories 
of unsold products. In addition, banks will be reluctant to lend because bankruptcy

risks are perceived to be higher. As a result, the economy enters what seems to be a 
downward spiral.
The gap between the recession output (GDPR) and the potential output (GDPP), 
the level of real GDP that could be achieved if all resources were fully utilized, is an 
indicator of slack resources (unemployment for labor and idleness for physical cap -
ital). Decreases in aggregate demand are likely to depress wages or wage growth as 
well as prices of inputs and capital goods. After a while, all of these input prices will 
be relatively very low. In addition, the monetary authority may cut interest rates to 
try to revive the economy.
As the prices and interest rates decrease, consumers and companies may begin 
to purchase more and aggregate demand may begin to rise. Companies may increase 
production as a result of increased demand and low levels of inventory of finished 
products. Also, because interest rates have fallen, some companies and households

may decide to start investing in structures, housing, and durable goods (equipment for 
companies, appliances for households). This stage is the turning point of the business 
cycle; aggregate demand starts to increase and economic activity increases.
When economic activity increases, companies are unlikely to immediately start the 
costly process of selecting and hiring new workers. They may wait for the expansion 
to give clear signs of life. However, if enough new investment triggers an increase 
in aggregate demand, companies will start replenishing their inventories of finished 
products. This replenishment will increase the demand for intermediate products, 
which will further increase aggregate demand. This stage is often called inventory 
rebuilding or restocking in the financial press and may be followed by additional 
increases in capital expenditures. Demand for all factors of production—land, labor, 
materials, and physical capital—increases.

As aggregate demand continues to grow, a boom phase of the cycle begins. In a 
boom phase, the economy may experience shortages and the demand for factors of 
production may exceed supply. It is possible that the excess demand is triggered by 
overly optimistic expectations of demand for products, which means that the supply of 
physical capital and production capacity may exceed the demand for products in the 
future. Past examples of excessive supply attributable to overinvestment include fiber 
optic infrastructure during the 1990s technology boom and residential overbuilding in 
many countries during the 2000s housing bubble. This overinvestment, which results 
in unused productive capacity, are possible triggers for the next recession.
2.2.1  Fluctuation in Capital Spending
This section describes how capital spending—spending on tangible goods, such as 
property, plant, and equipment—typically fluctuates with the business cycle. Because

business profits and cash flows are sensitive to changes in economic activity, capital 
spending is also sensitive to changes in economic activity. Shifts in capital spending 
tend to affect the overall economic cycle in three stages or phases.

Reading 17 ■ Understanding Business Cycles 204
In the early stage of a contraction, the downturn in spending on equipment usually 
occurs abruptly as demand for companies’ products starts to decrease. Businesses, 
seeing a decline in sales and expecting a drop in profits and free cash flow, will halt 
new ordering and may even cancel existing orders because there is no perceived need 
to expand production capacity. The initial cuts typically occur in orders for technology 
and light equipment because there are shorter lead times from order to delivery and 
managers may simply not place any additional orders. It often takes longer to cancel 
or halt construction activity or the installation of larger, more complex pieces of 
equipment, and cutbacks in these areas unfold with a longer lag. Typically, the initial 
cutbacks at this stage exaggerate the economy’s contraction. Then later, as the general 
cyclical downturn matures, cutbacks in spending on structures and heavy equipment

further intensify the contraction.
In the early stages of an expansion, when the economy begins its recovery, sales 
are still at such low levels that a business is likely to have excess productive capacity 
and has little need to expand it. But although capacity utilization remains low, capital 
spending may begin to increase. There are two primary reasons underlying the increase 
in capital spending. One, growth in earnings and free cash flow attributable to the 
economic improvement gives businesses the financial ability to increase spending. 
Two, the upturn in sales may convince managers to reinstate some orders that had 
been canceled. Typically, the orders initially reinstated are for equipment with a high 
rate of obsolescence, such as software, systems, and technological hardware. This type 
of equipment is likely to enhance efficiency more than expand capacity; enhancing 
efficiency may be the initial focus of new orders. An increase in new orders for equip -

ment to enhance efficiency often provides the first signal of recovery. Because orders 
precede actual shipments and possibly payments, an emphasized and widely watched 
indicator of the future direction of capital spending is orders for capital equipment.
In the later stage of expansion, productive capacity may begin to limit ability 
to respond to demand. Orders and sales at this stage focus on capacity expansion 
and increasingly are for heavy and complex equipment, warehouses, and factories. 
Spending on new capacity may begin before capacity seems to need additions. This 
seeming disconnect occurs because there can be a long lag between order and delivery 
or completion of heavy and complex equipment, warehouses, factories, and so on. 
Also, because economies are always changing their needs, physical capital that counts 
as capacity in the statistics may be less relevant to current production needs even 
though the underlying assets remain fully serviceable. The composition of the econ -

omy’s capacity may not be optimal for the current economic structure, necessitating 
spending for new capital. A company, for instance, that needs more transportation 
equipment cannot substitute with a surplus of forklifts, although they are counted in 
overall capacity. Similarly, a company that needs warehouse space in the suburbs of 
Mumbai benefits little from its surplus warehouse space in Goa. The increase in capital 
spending to increase capacity may occur surprisingly soon after capacity utilization 
picks up. New orders intended to increase capacity may be an early indicator of the 
late stage of the expansion phase.
EXAMPLE 2   
Capital Spending
1 The most likely reason that US analysts often follow new orders for capital 
goods excluding defense and aircraft is because:
A the military is part of the public sector.
B aircraft and defense equipment orders are often the same so there is 
double counting.

Overview of the Business Cycle 205
C armed forces and airlines tend to place infrequent and large orders, 
which create a false signal for the index.
2 Orders for equipment decline before construction orders in a recession 
because:
A businesses are uncertain about cyclical directions.
B they are easier to cancel than large construction contracts.
C business values light equipment less than structures and heavy 
machinery.
C is correct. Business cycle indicators need to represent the activities in the 
whole economy and thus should not be influenced by some particular sectors 
that may have uncorrelated fluctuations.
B is correct. Because it usually takes much longer time to plan and complete 
large construction projects than for equipment orders, construction projects 
may be less influenced by business cycles.
Note : New orders statistics include orders that will be delivered over several years. For example, it

is common for airlines to order 40 airplanes to be delivered over five years. Therefore, analysts use 
“core” orders that exclude defense and aircrafts for a better understanding of the economy’s trend.
2.2.2  Fluctuation in Inventory Levels
Inventory accumulation and cutbacks by businesses can occur with such speed and 
frequency that they have a much greater effect on economic growth than justified by 
their relatively small aggregate size relative to the economy as a whole. A key indi -
cator in this area is the inventory–sales ratio that measures the inventories available 
for sale to the level of sales. The interaction of this gauge with the cycle develops in 
three distinct stages.
Toward the peak of the economic cycle, as sales fall or slow, businesses may lag in 
cutting back on new production and inventories increase. The lower sales combined 
with higher inventories result in an increase in inventory–sales ratios. This apparent

increase in inventories may hide signs of a weakening economy. Practitioners (invest -
ment analysts and others) look for measures that focus on what are commonly called 
“final sales, ” which exclude the effects of inventory changes. To adjust and sell off these 
unwanted inventories, a business may cut production below even the reduced sales 
levels. This cut in production causes subsequent indicators in the overall economy to 
look weaker than they otherwise might have been. Although final sales offer a reality 
check, the production cutbacks involved in reducing inventory levels may lead to order 
cancellations and layoffs by producers that may subsequently cut final sales further 
and deepen cyclical corrections.
With businesses producing at rates below the sales volumes necessary to dispose 
of unwanted inventories, inventory–sales ratios begin to fall back toward normal. 
When these indicators return to acceptable levels and businesses no longer have any

need to further reduce inventories, they will raise production levels. The increase in 
production results in a seemingly improved economic situation, even if sales remain 
depressed. Again, final sales may provide a more realistic picture of the underlying 
economic situation. At this phase in the cycle, the seemingly minor increase in pro -
duction levels can actually mark the beginning of the cyclical turn because layoffs 
may slow or stop and demand for other inputs may also increase.

Reading 17 ■ Understanding Business Cycles 206
As sales begin their cyclical upturn, a business may initially fail to keep production 
on pace with sales, which causes it to lose inventory to the initial sales increase. The 
subsequent fall in inventory–sales ratios, when it occurs in the face of rising sales, 
quickly prompts a surge in production not only to catch up with sales but also to 
replenish depleted inventories. However, sometimes during short or severe recessions, 
when businesses have not had time to adjust or reduce inventories to acceptable levels, 
companies may initially consider increased production unnecessary. As a result, the 
lag between increased sales and production may be longer than in other cycles. But 
whether the production upturn occurs with a short or a long lag, it typically marks a 
turn in hiring patterns and for a time can markedly exaggerate the cyclical strength.
EXAMPLE 3   
Inventory Fluctuation

EXAMPLE 3   
1 Although a small part of the overall economy, changes in inventories can 
influence economic growth measures significantly because they:
A reflect general business sentiment.
B tend to move forcefully up or down.
C determine the availability of goods for sale.
2 Inventories tend to rise when:
A inventory–sales ratios are low.
B inventory–sales ratios are high.
C economic activity begins to rebound.
3 Inventories will often fall early in a recovery because:
A businesses need profit.
B sales outstrip production.
C businesses ramp up production because of increased economic 
activity.
B is correct. As stated in the reading, inventory level fluctuates dramatically 
over the business cycle.
A is correct. When the economy starts to recover, sales of inventories can out -
pace production, which results in low inventory–sales ratios. Companies then 
need to accumulate more inventories to restore the ratio to normal level. C is

incorrect because, in the early stages of a recovery, inventories are likely to fall 
as sales increase faster than production.
B is correct. The companies are slow to increase production in early recovery 
phase because they first want to confirm the recession is over. Increasing output 
also takes time after the downsizing during the recession.
2.2.3  Consumer Behavior
Households represent the largest single sector of almost every developed economy 
(for example, it is 70% of the US economy). As a result, patterns of household con -
sumption determine overall economic direction more than any other sector. Patterns

Overview of the Business Cycle 207
of household consumption are important to practitioners for a variety of reasons. For 
example, equity analysts covering consumer product companies would have a high 
interest in the sector.
Two primary measures of household consumption are retail sales and a broad-  
based indicator of consumer spending that also includes purchases outside purely 
retail establishments, such as utilities, household services, and so on. Often these 
measures are presented in nominal terms and deflated to indicate directions of real 
or unit purchases and growth. Some additional measures make finer distinctions, 
such as tracking spending, both real and nominal, of a specific group(s) of consumer 
products. The three major divisions are (1) durable goods, such as autos, appliances, 
and furniture; (2) non-  durable goods, such as food, medicine, cosmetics, and clothing; 
and (3) services, such as medical treatment, entertainment, communications, and

personal services. Because durable purchases usually replace items with longer useful 
lives, during economic downturns households can postpone such purchases more 
readily than spending on either services or non-  durable goods. Comparing trends in 
durable purchases with those in the other categories can give practitioners a notion 
of the economy’s progress through the cycle; a weakness in durables spending may be 
an early indication of general economic weakness, and an increase in such spending 
may signal a more general cyclical recovery.
Beyond direct observations of consumer spending and its mix, practitioners can 
also gauge future directions by analyzing measures of consumer confidence or senti -
ment to ascertain how aggressive consumers may be in their spending. Usually, such 
information is in the form of surveys intended to provide practitioners with a general 
guide to trends. But in practice, they frequently do not reflect actual consumer behavior

because survey respondents may answer what they imagine are the preferences of the 
typical consumer, indicating behavior contrary to their own.
Growth in income is typically a better indicator of consumption prospects, and 
household income figures are widely available in most countries. Especially relevant 
is after-  tax income or what is frequently called disposable income. Some analysts 
chart consumer spending based on a concept termed permanent income. Permanent 
income excludes temporary income and unsustainable losses and gains and tries to 
capture the income flow on which households believe they can rely. The basic level 
of consumption reflects this notion of permanent income. However, spending on 
durables tends to rise and fall with disposable income, regardless of the source, not 
just permanent income.
But consumer spending patterns frequently diverge from trends in income, no 
matter how income is measured. An analysis of the saving rates can assist practitioners

in this regard. Cross-  border comparisons of saving rates are difficult because saving 
rates are calculated in different ways in different countries and sometimes in different 
ways within the same country. But because all measures of saving rates aim in one way 
or another to measure the percentage of income households set aside from spending, 
changes in saving rates can capture consumers’ intent to reduce spending out of cur -
rent income. The saving rate may also reflect future income uncertainties perceived 
by consumers (precautionary savings). Therefore, a higher saving rate may indicate 
consumers’ ability to spend despite possible lower income in the future. A rise in the 
saving rate, usually measured as a percentage of income, may indicate caution among 
households and signal economic weakening. At the same time, the greater the stock 
of savings in the household sector and the wider the gap between ongoing income

and spending, the greater the capacity for households to increase their spending. So, 
although unusually high savings may at first say something negative about the cyclical 
outlook, they point longer-  term to the potential for recovery.

Reading 17 ■ Understanding Business Cycles 208
EXAMPLE 4   
Consumer Behavior
1 Durable goods have the most pronounced cyclical behavior because:
A they have a longer useful life.
B their purchase cannot be delayed.
C they are needed more than non-  durable goods or services.
2 Permanent income provides a better guide to:
A saving rates.
B spending on services.
C spending on durable goods.
A is correct. Durable goods are usually big ticket items, the life span of which can 
be extended with repairs and without incurring the high replacement costs. So, 
consumers tend to delay replacement when economic outlook is not favorable.
B is correct. Households adjust consumption of discretionary goods and services 
based on the perceived permanent income level rather than temporary earning 
fluctuations. Saving rates and durable goods consumption are more related to 
the short-  term uncertainties caused by recessions.
2.3 Housing Sector Behavior

Although generally a much smaller part of the overall economy than consumer spend -
ing, housing activity experiences dramatic swings that it often counts more in overall 
economic movements than the sector’s relatively small size might suggest. Almost 
every major economy offers statistics on new and existing home sales, residential 
construction activity, and sometimes, importantly, the inventory of unsold homes on 
the market. Statistics are also potentially available for the average or median price of 
homes, sometimes recorded by type of housing unit and sometimes as the price per 
square foot or square meter. Whatever the specific statistics, the relationships in this 
area typically follow fairly regular cyclical patterns.
Because many home buyers finance their purchase with a mortgage, the sector 
is especially sensitive to interest rates. Home buying and consequently construction

activity expand in response to lower mortgage rates and contract in response to higher 
mortgage rates.
Beyond such interest rate effects, housing also follows its own internal cycle. When 
housing prices are low relative to average incomes, and especially when mortgage 
rates are also low, the cost of owning a house falls and demand for housing increases. 
Often indicators of the cost of owning a house are available to compare household 
incomes with the cost of supporting an average house, both its price and the expense 
of a typical mortgage. Commonly, housing prices and mortgage rates rise dispropor -
tionately as expansionary cycles mature, bringing on an increase in relative housing 
costs, even as household incomes rise. The resulting slowdown of house sales can 
lead to a cyclical downturn first in buying and then, as the inventory of unsold houses 
builds, in actual construction activity.
These links, clear as they are, are far from mechanical. If housing prices have

risen rapidly in the recent past, for instance, many people will buy to gain exposure 
to the expected price gains, even as the purchase in other respects becomes harder

Overview of the Business Cycle 209
to rationalize. Such behavior can extend the cycle upward and may result in a more 
severe correction. This result occurs because “late buying” activity invites overbuild -
ing. The large inventory of unsold homes eventually puts downward pressure on real 
estate prices, catching late buyers, who have stretched their resources. This pattern 
occurred in many countries during the 2008–2009 global financial crisis.
Behind such cyclical considerations, housing, more than most economic sectors, 
responds to demographics, in particular the pace of family or household formation 
in an economy. Not every economy has data on family formation, but almost all offer 
information on the growth of particular age groups or cohorts in their respective 
populations. A focus on those cohorts, typically 25- to 40-  year-  olds, when household 
formation commonly occurs, usually can substitute for direct measures of net family

formation. Adjusted for older people who are vacating existing homes, such calcu -
lations serve as an indicator of underlying, longer-  term, secular housing demand. 
Although such measures have little to do with business cycles, they do offer a gauge, 
along with affordability, of how quickly the housing market can correct excess and 
return to growth. In China, for instance, where the government estimated a need for 
about 400  million more urban housing units over the following 25 years, housing 
demand may quickly reverse cyclical weakness more so than in such economies as 
Italy or Japan where net new family formation is relatively slight.
EXAMPLE 5   
Housing Sector Behavior
1 Housing is more sensitive than other sectors of the economy to:
A interest rates.
B permanent income.
C government spending.
2 Apart from questions of affordability, house buying is most likely  affected 
by:
A the rate of family formation.
B expectation of housing price increases.

C both the rate of family formation and expectation of housing price 
increases.
A is correct. Because real estate purchases are usually financed with mortgage 
loans, interest rate changes directly influence the monthly payment amounts.
C is correct. Family formation constitutes the actual need for housing, whereas 
buying on the expectation of housing price increases reflects the fact that real 
estate has investment value.
2.4 External Trade Sector Behavior
The external trade sector varies tremendously in size and importance from one econ -
omy to another. In such places as Singapore, where almost all inputs are imported 
and the bulk of the economy’s output finds its way to the export market, trade (the 
sum of both exports and imports) easily exceeds its GDP . In other places, such as the 
United States, external trade assumes a much smaller part of GDP . Since the 1970s,

Reading 17 ■ Understanding Business Cycles 210
the relative size of external trade has grown in almost every country in the world. With 
the rise in external trade, the business cycles of the large economies in the world can 
be more easily transmitted to other economies.
Typically, imports rise, all else equal, with the pace of domestic GDP growth, as 
needs and wants or generally rising demand also increase purchases of goods and 
services from abroad. Thus, imports respond to the domestic cycle. Exports are more 
dependent on cycles in the rest of the world. If these external cycles are strong, all else 
equal, exports will grow even if the domestic economy should experience a decline in 
growth. To understand the impact of exports, financial analysts need to understand 
the strength of the major trading partners of the economy under consideration. Most 
practitioners look at the net difference between exports and imports (they use the

balance of payments, which calculates trade’s contribution to the economy as exports 
less imports). The net effect of trade may offset cyclical weakness and, depending on 
the importance of exports to the economy, could erase it altogether. For these reasons, 
such differences can mean the pattern of external trade balances is entirely different 
from the rest of the domestic economic cycle.
Currency also has an independent effect that can move trade in directions strikingly 
different from the domestic economic cycle. When a nation’s currency appreciates (the 
currency gains in strength relative to other currencies), foreign goods seem cheaper 
than domestic goods to the domestic population, prompting, all else equal, a relative 
rise in imports. At the same time, such currency appreciation makes that nation’s 
exports more expensive in global markets and may reduce exports. Of course, currency 
depreciation has the opposite effect. Although currency moves may be volatile and

on occasion extreme, they only have a significant effect on trade and the balance of 
payments when they cumulate in a single direction for some time. Moves from one 
month or quarter to the next, however great, have a minimal effect until they persist. 
Thus cumulative currency movements that take place over a period of years will have 
an impact on trade flows that will persist even if the currency subsequently moves in 
the opposite direction for a temporary period.
Financial analysts need to consider a wide range of variables, both in the domestic 
economy and abroad, to assess relative GDP growth rates and then factor in currency 
considerations to ascertain whether they reinforce other cyclical forces or counteract 
them. Generally, GDP growth differentials in global economic growth rates between 
countries have the most immediate and straightforward effects; domestic changes in 
economic activity raise or reduce imports and foreign economic activity changes raise

or reduce exports. Currency moves have a more complex and, despite the interim 
short-  term currency moves, a more gradual effect.
EXAMPLE 6   
External Trade
1 Imports generally respond to:
A the level of exports.
B domestic industrial policy.
C domestic GDP growth rate.
2 Exports generally respond to the:
A level of unionization.
B global GDP growth rates.
C domestic GDP growth rates.

Theories of the Business Cycle 211
C is correct. As a part of aggregate demand, imports reflect the domestic needs 
for foreign goods, which vary together with domestic economic growth.
B is correct. Exports reflect the foreign demands on domestic output, which 
depend on the conditions of global economy.
THEORIES OF THE BUSINESS CYCLE
Business cycles have been recognized since the early days of economic theory, and 
considerable effort has gone into identifying different cycles and explaining them. 
Until the 1930s, however, the general view was that they were a natural feature of the 
economy and the pain of recessions is temporary. But the depth and severity of the 
1930s downturn (known as the Great Depression) created a crisis in economic theory.
After the Great Depression (which began in 1929), the debate between various 
economic schools of thought (Neoclassical, Austrian, and Keynesian) spurred changes

in the way the business cycle was described and explained. Similarly, after the reces -
sions triggered by the oil shocks of 1973 and 1979, the old paradigm was taken apart 
and new developments in economics and quantitative methods led to an improved 
understanding of short-  term economic dynamics. In this section, we will review and 
summarize some of the main theories.
3.1 Neoclassical and Austrian Schools
Neoclassical analysis relies on the concept of general equilibrium—that is, all markets 
will reach equilibrium because of the “invisible hand, or free market, ” and the price 
will be found for every good at which supply equals demand. All resources are used 
efficiently based on the principle of marginal cost equaling marginal revenue, and no 
involuntary unemployment of labor or capital takes place. In theory, if a shock of any 
origin shifts either the aggregate demand or aggregate supply curve, the economy will

quickly readjust and reach its equilibrium via lower interest rates and lower wages. In 
practice, because the neoclassical school provides that the invisible hand will reallocate 
capital and labor so that they will be used to produce whatever consumers want, it 
does not allow for “fluctuations found in the aggregate economic activity. ” 
Neoclassical economists rely on Say’s law : All that is produced will be sold 
because supply creates its own demand. French economist J.B. Say pointed out that 
if something is produced, the capital and labor used for that production will have to 
be compensated. This compensation of the factors (interest for capital and wages for 
labor) creates purchasing power in the sense that the workers receive a paycheck and 
thus can buy goods and services they need. Widespread declines in demand would 
be strictly temporary.
The Neoclassical school does not have a theory of the business cycle, and the

closest it gets to it is Schumpeter’s creative destruction theory, which shows cycles 
within industries as a result of technological progress but no economy-  wide fluctua -
tions.2 Schumpeter formulated a theory of innovations, which explained cycles limited 3
2 Joseph Alois Schumpeter was born in Austria and studied with members of the Austrian school, such 
as Menger and Hayek, but he was more Neoclassical than Austrian in the economic sense. He taught in 
the United States for many years.

Reading 17 ■ Understanding Business Cycles 212
to individual industries: When an inventor comes up with a new product (e.g., the 
digital music player in recent decades) or a new, better way to produce an existing 
good or service (e.g., radio frequency identification tracking of inventories), then the 
entrepreneur that introduces the new discovery will likely have bigger profits and may 
drive the existing producers out of business. Therefore, innovations can generate crises 
that affect only the industry affected by the new invention. Neoclassical economics 
recognizes that business cycles exist but treats them as temporary disequilibria.
In the neoclassical school, a massive crisis, such as the Great Depression of the 
1930s with widespread unemployment of more than 20% throughout the industri -
alized world, is impossible. Yet, it happened. The crisis started in the United States 
and successively affected many other countries. The 1929 crisis touched many sectors

at the same time and in a dramatic fashion. Because the neoclassical theory denied 
the possibility of a prolonged depression, it could not be used to explain how to fight 
such a depression. The main adjustment mechanism proposed by the neoclassical 
school—cuts in wages—was difficult to achieve and, as we shall see, was questioned 
by the Keynesian school.
The Austrian school, including F. von Hayek and L. von Mises, shared some views of 
the neoclassical school, but focused more on two topics that were largely unimportant 
in the neoclassical framework: the roles of money and government. Money was not 
necessary in the neoclassical model, because the exchange of goods and services could 
occur in the form of barter and still reach general equilibrium. Money was seen just 
as a way to simplify exchange. Similarly, the role of government in the neoclassical 
model was quite limited because the economy could take care of itself and little else

was needed of the government besides upholding the law and securing the borders.
The Austrian school has a theory of what causes the business cycle: It is misguided 
government intervention. Von Hayek argued that fluctuations are caused by govern -
ments that try to increase GDP and employment (thus perhaps increasing voters’ 
consensus) by adopting expansionary monetary policies. Governments lower the 
market interest rate below its natural value (aggregate demand shifts right) and thus 
lead companies to overinvest (an inflationary gap). Once companies realize that they 
have accumulated too much equipment and too many structures, they will suddenly 
stop investing, which depresses aggregate demand (aggregate demand shifts left dra -
matically) and causes a crisis throughout the economy. To reach the new equilibrium, 
all prices including wages must decrease.
As a result of manipulating interest rates the economy exhibits fluctuations that

would not have happened otherwise. Therefore, Austrian economists advocate limited 
government intervention in the economy, lest the government causes a boom-  and-  bust 
cycle. The best thing to do in the recession phase is to allow the necessary market 
adjustment to take place as quickly as possible.
3.2 Keynesian and Monetarist Schools
The Keynesian and Monetarist schools of economic thought have been among the 
most influential. Their prescriptions concerning the business cycle are discussed in 
the following sections.
3.2.1  Keynesian School
As previously mentioned, if a recession occurs, the Neoclassical and Austrian schools 
argue in general that no government intervention is needed. Unemployment and 
excess supply of goods will be solved by allowing market prices to decrease (including 
wages) until all markets clear: Supply equals demand and factors of production are 
fully employed.

Theories of the Business Cycle 213
British economist John Maynard Keynes3 disagreed with both Neoclassical and 
Austrian views. He observed that a generalized price and wage reduction (solely brought 
about through market forces), necessary to bring markets back to equilibrium during 
a recession, would be hard to attain. For example, workers may not want to see their 
nominal compensation decrease because nobody likes a pay cut.
But Keynes thought that even if workers agreed to accept lower salaries, this sit -
uation might exacerbate the crisis by reducing aggregate demand rather than solving 
it because lower wage expectations would shift aggregate demand left. For example, 
if wages fell, workers would need to cut back on their spending. This response would 
cause a further contraction in the demand for all sorts of goods and services, start -
ing from the more expensive items, such as durable goods, and move in a “domino

effect” through the economy (the downward spiral of the aggregate demand curve 
continuously shifting left, as mentioned earlier).
Furthermore, Keynes believed there could be circumstances in which lower inter -
est rates would not reignite growth because business confidence or “animal spirit” 
was too low. As a consequence, Keynes advocated government intervention in the 
form of fiscal policy. While he accepted the possibility that markets would reach the 
equilibrium envisioned by Neoclassical and Austrian economists over the long run, 
he famously quipped that “in the long run, we are all dead;” that is, the human suf -
fering is excessive while waiting for all shocks to be absorbed and for the economy 
to return to equilibrium.
When crises occur, the government should intervene to keep capital and labor 
employed by deliberately running a larger fiscal deficit. This intervention would limit 
the damages of major recessions. Although this concept continues to be a highly

politically charged debate, many economists agree that government expenditure can 
limit the negative effect of major economic crises in the short term. The practical 
criticisms that are often expressed about Keynesian fiscal policy are:
1 Fiscal deficits mean higher government debt that needs to be serviced and 
repaid eventually. There is a danger that government finances could move out of 
control.
2 Keynesian cyclical policies are focused on the short term. In the long run, the 
economy may come back and the presence of the expansionary policy may 
cause it to “overheat”—that is, to have unsustainably fast economic growth, 
which causes inflation and other problems. This result is because of the typical 
lags involved in expansionary policy taking effect on the economy.
3 Fiscal policy takes time to implement. Quite often, by the time stimulatory 
fiscal policy kicks in, the economy is already recovering. (Monetary policy 
determines the available quantities of money and loans in an economy.)

Keynes’ writings did not advocate a continuous presence of the government in 
the economy, nor did he suggest using economic policy to “fine tune” the business 
cycle. He only advocated decisive action in case of a serious economic crisis, such as 
the Great Depression.
3 John Maynard Keynes’ name is often mentioned in full, with first and middle name, to avoid confusion 
with his father, John Neville Keynes, who was also an economist.

Reading 17 ■ Understanding Business Cycles 214
 
The Perspective of Hyman Minsky
A different view of business cycles came from Hyman minsky. His view had something 
in common with the Austrian school and something in common with Keynes. minsky 
believed that excesses in financial markets exacerbate economic fluctuations. For exam -
ple, a rapid growth of credit, often given to risky ventures in the late expansion phase 
of the cycle, will be followed by a “credit crunch” during the down-  swing phase. minsky 
traced excesses to a type of complacency in which people underestimate the risk of 
events that have not occurred in a while. Therefore, if the economy has been in a long 
expansion, people may think that the market works very well and that the expansion 
will last forever—that is, extrapolating past experiences. In this sense, minsky could be 
seen as a precursor of behavioral finance, which is the branch of finance that studies

how cognition biases, such as overconfidence and short memory, induce investors to 
be overconfident and make suboptimal choices.
The term Minsky moment  has been coined for a point in business cycle when, after 
individuals become overextended in borrowing to finance speculative investments, 
people start realizing that something is likely to go wrong and a panic ensues leading 
to asset sell-  offs. The subprime crisis that affected many industrialized countries starting 
in 2008 has been represented as a “ minsky moment”4 because it came after years in 
which risk premiums (e.g., the differentials, or spreads, between very risky bonds and 
very safe bonds) were at historically low levels. Typically, low risk premiums suggest 
that no adverse events are expected—in other words, investors believe that because 
the economy and the markets have been enjoying a protracted expansion, there is no 
reason to worry about the future. As a consequence, many market observers suggest

that business cycles are being tamed. This kind of view of the world leads people to 
underestimate risk, for example, by not doing the appropriate diligent research before 
granting a loan or before purchasing a security—in a word, complacency.
The “ minsky moment” has been compared with a cartoon in which a cartoon character 
walks over a cliff without realizing that it is doing so. When he looks down and sees that 
he is walking on thin air, he panics and falls to the bottom of the canyon—just like the 
world economy in 2008.
A warning in 2005 by Alan Greenspan, then chairman of the US Federal Reserve,5 was 
not taken seriously by market participants. Greenspan said that historically, extended 
periods of low risk premiums always ended badly. This warning was to a large extent in 
line with minsky’s view: People tend to extrapolate the recent past, and if little volatility 
has occurred recently, they may think that low volatility will persist indefinitely.

Some market analysts, after the crisis, pointed out that not even Greenspan knew how 
accurate his remark would turn out to be. As explained by Reinhart and Rogoff (2009) and 
Siegel (2009), when rates were very low, investors tried to get extra yield by investing in 
complex and potentially more risky assets, such as securitized subprime mortgages and 
collateralized debt obligations whose credit-  worthiness was much lower than expected.
As soon as the economy started having difficulties, the value of many risky securities 
dropped dramatically, placing investors globally into a state of panic and causing a 
dramatic fall in aggregate demand. The crisis is another example of why thinking that a 
new era has started and the things learned from analyzing the past no longer apply is 
generally a very costly mistake.
4 Paul McCulley (for example, see McCulley 2009) originated this expression.
5 Alan Greenspan, Chairman of the US Federal Reserve at the time, remarked in 2005: “Thus, this vast

increase in the market value of asset claims is in part the indirect result of investors accepting lower 
compensation for risk. Such an increase in market value is too often viewed by market participants as 
structural and permanent. To some extent, those higher values may be reflecting the increased flexibility 
and resilience of our economy. But what they perceive as newly abundant liquidity can readily disappear. 
Any onset of increased investor caution elevates risk premiums and, as a consequence, lowers asset values 
and promotes the liquidation of the debt that supported higher asset prices. This is the reason that history 
has not dealt kindly with the aftermath of protracted periods of low risk premiums” (Greenspan 2005).

Theories of the Business Cycle 215
3.2.2  Monetarist School
The Monetarist school, generally identified with Milton Friedman, objected to 
Keynesian intervention for four main reasons:
1 The Keynesian model does not recognize the supreme importance of the money 
supply. If the money supply grows too fast, there will be an unsustainable boom, 
and if it grows too slowly, there will be a recession. Friedman focused mainly on 
broad measures of money, such as M2.
2 The Keynesian model lacks a complete representation of utility-  maximizing 
agents and is thus not logically sound.
3 Keynes’ short-  term view failed to consider the long-  term costs of government 
intervention (e.g., growing government debt and high cost of interest on this 
debt).
4 The timing of governments’ economic policy responses was uncertain, and the 
stimulative effects of a fiscal expansion may take effect after the crisis was over, 
and thus cause more harm than good.6

Therefore, Monetarists advocate a focus on maintaining steady growth of the money 
supply, and otherwise a very limited role for government in the economy. Fiscal and 
monetary policy should be clear and consistent over time, so all economic agents can 
forecast government actions. In this way, the uncertainty of economic fluctuations 
would not be increased by any uncertainty about the timing and magnitude of eco -
nomic policies and their lagged effects.
According to the Monetarist school, business cycles may occur both because of 
exogenous shocks and because of government intervention. It is better to let aggregate 
demand and supply find their own equilibrium than to risk causing further economic 
fluctuations. However, a key part of monetarist thought is that the money supply needs 
to continue to grow at a moderate rate. If it falls, as occurred in the 1930s, the eco -

nomic downturn could be severe, whereas if money grows too fast, inflation will follow.
3.3 The New Classical School
Starting in the 1970s, economists such as Robert Lucas started questioning the foun -
dations of the models used to explain business cycles. Among other things, Lucas 
agreed with Friedman (1968) and pointed out that the macroeconomic models should 
try to represent the actions of economic agents with a utility function and a budget 
constraint, just like the models used in microeconomics. This approach has come 
to be known as new classical macroeconomics —an approach to macroeconomics 
that seeks the macroeconomic conclusions of individuals maximizing utility on the 
basis of rational expectations and companies maximizing profits. The assumption is 
made that all agents are roughly alike, and thus solving the problem of one agent is 
the same as solving that of millions of similar agents (or the per capita income and 
consumption of the average agent).

The New Classical models are dynamic in the sense of describing fluctuations 
over many periods and present general equilibrium in the sense of determining all 
prices rather than one price. The models by Edward C. Prescott and Finn E. Kydland, 
who are among the pioneers of this approach, have an economic agent that has to 
6 Markets may react differently to changes in interest rates and other tools of monetary policy. There is a 
long chain of events from the time when interest rates are cut, to when banks change the rates they charge 
clients, to when a company sees that rates are lower and thus decides to invest in new equipment, to when 
the equipment is finally purchased. Therefore, by the time these events all happen, the economy may be 
in expansion and the new investment may lead the economy to overheating.

Reading 17 ■ Understanding Business Cycles 216
face external shocks (e.g., as a result of changes in technology, tastes, or world prices) 
and thus optimizes its choices to reach the highest utility. If all agents act in similar 
fashion, the markets will gradually adjust toward equilibrium.
3.3.1  Models without Money: Real Business Cycle Theory
New Classical economists comment that some policy recommendations made in 
the past were rather illogical: for example, if everybody knows that in a recession 
the government will give out low rate loans to corporations that want to invest in 
new equipment and structures, why would any reasonable company invest outside 
recessions unless absolutely required to? Obviously, if most companies thought that, 
they would stop investing, thus causing a recession that otherwise would not have 
occurred. Essentially, the government’s anti-  cyclical policy could cause a recession.
Because, just like the neoclassical models, the initial New Classical models did

not include money, they were called real business cycle models (often abbreviated as 
RBC). Cycles have real causes, such as the aforementioned changes in technology, 
whereas monetary variables, such as inflation, are assumed to have no effect on GDP 
and unemployment.7
RBC models of the business cycle conclude that expansions and contractions rep -
resent efficient operation of the economy in response to external real shocks. Because 
the level of economic activity at any time is consistent with maximizing expected 
utility, the policy recommendation of RBC theory is for government not to intervene 
in the economy with discretionary fiscal and monetary policy.
Critics of RBC models often focus on the labor market. Because RBC models 
rely on efficient markets, it follows that unemployment can only be short term: apart 
from frictional unemployment,8 if markets are efficient, a person who does not have 
a job can only be a person who does not want to work. If a person is unemployed, in

the context of efficient markets, he just needs to lower his wage rate until he finds an 
employer who hires him. This assumption is logical because if markets are perfectly 
flexible, all markets must find equilibrium and full employment.
Therefore, as suggested particularly by the earliest RBC models, a person is unem -
ployed because he or she is asking for wages that are too high, or in other words, this 
person’s utility function is maximized by having more leisure (e.g., free time to visit 
museums, watch games on TV, and enjoy time with friends) and less consumption 
(which could be increased by giving up some leisure and finding a job). However, the 
observation that during a recession many people are eagerly searching for jobs and are 
unable to find employment despite dropping their asking wages substantially suggests 
that this theory is unrealistic.
Although many find this explanation unconvincing, RBC theorists argue that,

undeniably, markets would clear if people were rational and avoided unrealistic 
expectations of earnings or simply enjoyed their leisure accompanied by optimally 
meager consumption.
An interesting feature of RBC models is that they give aggregate supply a more 
prominent role than many other theories. For example, supply has a limited impor -
tance in the Keynesian theory, probably because Keynes was more concerned with 
7 See Plosser (1989) and Romer (2011) for an introduction to RBC models. Basically, RBC models assume 
that economic agents are fully rational and that markets function with no imperfection or friction. As a 
consequence, any changes in monetary aggregates or other monetary policies will promptly cause changes 
in price levels and other variables without affecting real GDP or employment.
8 Frictional unemployment arises not because of the lack of general job opportunities but from the fact

that both employers and potential employees need some time to find a good match between the job vacancy 
and the candidate’s interests, skills and location preference, and so on. The frictionally unemployed can 
be those people who quit their previous jobs voluntarily but have yet to find or start a new job and new 
entrants to the labor force, such as recent college graduates, or re-  entrants, such as formerly discouraged 
workers who have started looking for but have yet to find a job.

Theories of the Business Cycle 217
the Great Depression, which was largely a crisis of aggregate demand. RBC models 
show that supply shocks, such as advances in technology or changes in the relative 
prices of inputs, cause the aggregate supply (AS) to shift left. A new technology can 
change potential GDP , for example, thus moving long-  run AS to the right. Adjustment 
will be needed because not all companies can adopt the new technology at once, and 
therefore short-  run AS will not jump to the new equilibrium immediately. Similarly, 
an increase of energy prices shifts short-  run AS to the left (higher prices and lower 
GDP). In the long run companies and households can learn to use less of the expensive 
energy inputs (substitution effect), and therefore long-  run AS will shift right (higher 
GDP) if the economy learns to produce more goods with less energy.
3.3.2  Models with Money
Inflation is often seen as a cause of business cycles, because when monetary policy ends

up being too expansionary, the economy grows at an unsustainable pace—creating an 
inflationary gap. The result is that, for example, suppliers cannot keep up with demand. 
In this environment, prices will tend to grow faster than normal—that is, inflation.
As a consequence, the central bank will often intervene to limit inflation by “tight -
ening” monetary policy, which generally means increasing interest rates, so that the 
cost of borrowing will be higher and demand for goods and services will slow down (a 
leftward shift in aggregate demand caused by the higher cost of money). This response 
will decrease equilibrium GDP and can result in a recession.
Given that inflation appears to trigger policy responses from central banks, it is an 
important part of modern business cycles. Therefore, it can be helpful to use models 
that include money to explain economic growth. As mentioned earlier, RBC models 
assume that transactions could occur with barter, and thus do not explicitly include

money. More recent dynamic general equilibrium models (for example, Christiano, 
Eichenbaum, and Evans 2005) include money and inflation.
Monetary policy can be incorporated into dynamic general equilibrium models 
with money. In one type of model, the economy receives shocks from changes in 
technology and consumer preferences (like in the RBC case), but can also receive 
shocks from monetary policy, which sometimes can tame the business cycle and at 
other times may exacerbate it.
Another group of dynamic general equilibrium models are the Neo-  Keynesians  or 
New Keynesians .9 Like the New Classical school, the Neo-  Keynesian school attempts 
to place macroeconomics on sound microeconomic foundations. In contrast to the 
New Classical school the Neo-  Keynesian school assumes slow-  to- adjust (“sticky”) 
prices and wages. The Neo-  Keynesian models show that markets do not reach equi -
librium immediately and seamlessly, but even small imperfections may cause markets

to be in disequilibrium for a long time. As a consequence, government intervention 
as advocated in the 1930s by Keynes may be useful to eliminate unemployment and 
bring markets toward equilibrium.
The typical example of these imperfections, which also appeared in Keynes’ work, 
is that workers do not want their wages to decrease to help the market reach a new 
equilibrium (i.e., wages are often downwardly sticky).10 Another possibility that some 
economists suggested in the 1980s is called the “menu costs” explanation: It is costly 
for companies to continuously adjust prices to make markets clear, just like it would 
9 For an introduction to Neo-  Keynesian models, see Romer (2011) and Mankiw (1989).
10 As mentioned earlier, Keynes thought that even if workers agreed to accept lower wages, this might 
exacerbate the crisis rather than solving it because lower wage expectations would shift AD left.

Reading 17 ■ Understanding Business Cycles 218
be costly for a restaurant to print new menus daily with updated prices.11 Another 
explanation is that every time an economic shock hits a company, the company will 
need some time to reorganize its production.
EXAMPLE 7   
Real Business Cycle Models
1 The main difference between New Classical (RBC) and Neo-  Keynesian 
models is that the New Classical models:
A are monetarist.
B use utility-  maximizing agents, whereas Neo-  Keynesian does not.
C assume that prices adjust quickly to changes in supply and demand, 
whereas Neo-  Keynesians assume that prices adjust slowly.
2 Basic RBC models focus on the choices of a typical individual, who can 
choose between consuming more (thus giving up leisure) and enjoying 
leisure more (thus giving up consumption). What causes persistent unem -
ployment in this model?
A Contractionary monetary policy causes a shock to real variables.
B The economy returns to equilibrium promptly, thus persistent unem -

ployment does not exist.
C The utility function: If the individual prefers leisure much more than 
consumption, she will forego consumption and instead choose unem -
ployment to enjoy more leisure when the market salary is low.
C is correct. A key feature of Neo-  Keynesian macroeconomics is the stickiness 
of prices. In contrast, New Classical views assume flexible price adjustments 
that ensure market clearing. 
C is correct. Shocks in the standard New Classical model can only have a tem -
porary effect, thus A is not the right answer. Unemployment can still exist when 
the labor market is cleared, so a rational explanation is provided in C.
In recent years, a consensus concerning business cycles has gradually started 
building in macroeconomics. It is too early to say that economists agree on all causes 
of and remedies for business fluctuations, but at least an analytical framework has 
emerged, which encompasses both New Classical and Neo-  Keynesian approaches.

Woodford (2009), among others, shows that new research seems to be leading to a 
unified approach.
The debate about business cycles often receives a politically partisan treatment in 
the press because some people are generally against government intervention in the 
economy (for example, because it may lead to large deficits) and others are in favor 
11 Clearly, both this example and the “menu costs” name were initially envisioned before personal computers 
and laser printers became affordable and widely used. Still, one can imagine the cost for a store owner to 
replace the price tags on every item in the store on a daily basis, and also how this would confuse shoppers.

Unemployment and Inflation 219
(for example, because it may alleviate the effects of a large economic shock). It is 
important to base investment decisions on analysis and not on politics; the financial 
analyst must try as much as possible to set personal biases aside.
However, there is little doubt that central banks try to manage the business cycle 
by raising interest rates when the economy is growing rapidly and inflation accelerates 
and cutting rates when the economy is weak. In the 2008–2009 downturn, when offi -
cial interest rates approached zero, central bankers extended their actions to include 
“quantitative easing” to try to lower interest rates further out on the yield curve to 
stimulate the economy.
EXAMPLE 8   
Analyzing Government Expenditure
Simple criteria for the financial analyst wondering whether a government’s 
expenditure is excessive (i.e., unsustainably high and/or of an inappropriate 
composition) include the following:12

1 Does the government always have a deficit no matter the cyclical phase, or 
does it have surpluses during economic booms?
2 Does the government have a deficit because of a defined series of neces -
sary investments that will improve the productivity of the country, or is it 
spending much of its money on questionable uses?
3 Is the growth rate of debt (government budget deficit as a percentage 
of GDP) higher than GDP growth? If so, the debt level will not likely be 
sustainable.
When government expenditures are excessive, inflation often follows. After 
that, a recession may occur because the central bank takes necessary measures 
to slow down an overheated economy. That is, if government purchases increase 
aggregate demand too much, thus causing inflation (expansionary fiscal policy), 
the central bank will intervene to stop prices from increasing too quickly (tight -
ening or contractionary monetary policy).
UNEMPLOYMENT AND INFLATION

Many governments and central banks have economic policy objectives related to 
limiting the rate at which citizens are unemployed and containing price inflation (i.e., 
preserving the purchasing power of a domestic currency). The relationships of these 
variables to the business cycle are discussed in the following sections. In general, 
unemployment is at its highest just as the recovery starts and is at its lowest at the 
peak of the economy.
4.1 Unemployment
A typical cause of business cycle downturns is a tight labor market—that is, one with 
low unemployment. An overheated economy leads to inflation when unemployment 
is very low. Workers ask for higher wages because they expect prices of goods and 
services to keep going up, and at the same time they have market power against 4
12 For a more formal and data-  rich approach, see Reinhart and Rogoff (2009).

Reading 17 ■ Understanding Business Cycles 220
employers because there are few available workers to be hired. This upward pressure 
on wages coupled with the impact of wage escalator clauses (automatic increases in 
wages as the consumer price index grows) triggers a price–wage inflationary spiral. 
This issue was a particular problem in industrialized countries in the 1960s and 1970s 
and remains an issue today.
A key aspect in this process is inflation expectations. Because inflation expecta -
tions are high, the request for higher wages is stronger, which induces employers to 
increase prices in advance to keep their profit margins stable. This avalanche process 
grows with time. Central banks act, sometimes drastically, to slow down the economy 
and reset inflationary expectations throughout the economy at a low level, so that if 
everyone expects low inflation, the inflationary spiral itself will stop. These actions

may trigger a deep recession. Therefore, whenever a financial analyst sees signs of 
a price–wage spiral in the making, a reasonable response would be to consider the 
effect of both high inflation and sharp tightening of monetary policy.
This example shows that measures of labor market conditions are important in 
assessing whether an economy is at risk of cyclical downturn.
The following are the definitions of a few terms that are used to summarize the 
state of the labor market:
■■Employed : The number of people with a job. This figure normally does not 
include people working in the informal sector (e.g., unlicensed cab drivers, 
illegal workers, etc.).
■■Labor force : The number of people who either have a job or are actively looking 
for a job. This number excludes retirees, children, stay-  at- home parents, full-  
time students, and other categories of people who are neither employed nor 
actively seeking employment.

■■Unemployed : People who are actively seeking employment but are currently 
without a job. Some special subcategories include:
■●Long-  term unemployed : People who have been out of work for a long time 
(more than three to four months in many countries) but are still looking for 
a job.
■●Frictionally unemployed : People who are not working at the time of filling 
out the statistical survey because they are taking time to search for a job 
that matches their skills, interests, and other preferences better than what 
is currently available, or people who have left one job and are about to start 
another job. The frictionally unemployed includes people who have vol -
untarily left their previous positions in order to change their jobs, in other 
words, they are “between jobs, ” and those new entrants or re-  entrants into 
the labor force who have not yet found work. Frictional unemployment is 
short-  term and transitory in nature

■■Unemployment rate : The ratio of unemployed to labor force.
■■Activity ratio  (or participation ratio): The ratio of labor force to total popula -
tion of working age (i.e., those between 16 and 64 years of age).
■■Underemployed : A person who has a job but has the qualifications to work at 
a significantly higher-  paying job. For example, a lawyer who is out of work and 
takes a job in a bookstore could call herself underemployed. This lawyer would 
count as employed for the computation of the unemployment rate (she does 
have a job, even if it may not be her highest paying job). Although the unem -
ployment rate statistic is criticized for not taking the issue of underemployment 
into account, it may be difficult to classify whether a person is truly underem -
ployed—for example, the lawyer may find legal work too stressful and prefers 
working at the bookstore. However, data for part-  time working is sometimes a 
good proxy.

Unemployment and Inflation 221
■■Discouraged worker : A person who has stopped looking for a job. Perhaps 
because of a weak economy, the discouraged worker has given up seeking 
employment. Discouraged workers are statistically outside the labor force (sim -
ilar to children and retirees), which means they are not counted in the official 
unemployment rate. During prolonged recessions, the unemployment rate may 
actually decrease because many discouraged workers stop seeking work. It is 
important to observe the participation rate together with the unemployment 
rate to understand if unemployment is decreasing because of an improved 
economy or because of an increase in discouraged workers. Discouraged 
workers and underemployed people may be considered examples of “hidden 
unemployment. ”
■■Voluntarily unemployed : person voluntarily outside the labor force, such as a 
jobless worker refusing an available vacancy for which the wage is lower than 
their threshold or those who retired early.

4.1.1  The Unemployment Rate
The unemployment rate is certainly the most quoted measure of unemployment; it 
attempts to measure those people who have no work but would work if they could 
find it, generally stated as a percentage of the overall labor force. In the United States, 
the indicator emerges from a monthly survey of households by the US Bureau of 
Labor Statistics, which asks how many household members have jobs and how many 
of working age do not have jobs but are seeking work. Other statistical bureaus rely 
on other sources for the calculation, using claims for unemployment assistance, for 
instance, or their equivalent. Some statistical bureaus measure the labor force simply 
as those of working age, regardless of whether they are ready or willing to work. These 
differences can make precise international comparisons problematic. One solution 
is to use the International Labour Organization (ILO) statistics that try to estimate

on a consistent basis. As indicated earlier, some statistical agencies add perspective 
with other measures; for example, what proportion of those who have ceased work are 
discouraged, underemployed, or have opted out of the labor force for other reasons 
or are working part-  time.
Although these various unemployment measures provide insight to the state of the 
economy, they are inaccurate in pointing to cyclical directions for two primary reasons, 
both of which make unemployment a lagging economic indicator of the business cycle.
One reason is that the unemployment rate tends to point to a past economic 
condition—that is, it lags the cycle—because the labor force expands and declines in 
response to the economic environment. Compounding the inaccuracy, when times get 
hard, discouraged workers cease searching for work, reducing the number typically 
counted as unemployed and making the jobs market look stronger than it really is.

Conversely, when the jobs market picks up, these people return to the search, and 
because they seldom find work immediately, they at least initially raise the calculation 
of those unemployed, giving the false impression of the lack of recovery in the jobs 
market, when, in fact, it is the improvement that brought these people back into the 
labor force in the first place. Sometimes this cyclical flow of new jobs seekers is so 
great that the unemployment rate actually rises even as the economic recovery gains 
momentum. Those agencies that measure the labor force in terms of the working-  age 
population avoid this bias, because this measure (working-  age population) is unaffected 
by economic conditions in the labor market. But this approach introduces biases of 
its own, such as counting as unemployed those people who have severe disabilities 
and could never seek work.
The second reason the unemployment indicator tends to lag the cycle comes from

the typical reluctance of businesses to lay off people. The reluctance may stem from 
a desire to retain good workers for the long run, or just reflect constraints written

Reading 17 ■ Understanding Business Cycles 222
into labor contracts that make layoffs expensive. The reluctance makes the various 
measures of unemployment rise more slowly as the economy slides into recession 
than they otherwise might. Then as the recovery develops, a business waits to hire 
until it has fully employed the workers it has kept on the payroll during the recession; 
this delay causes decreases in the unemployment rate to lag in the cyclical recovery, 
sometimes for a long time.
4.1.2  Overall Payroll Employment and Productivity Indicators
To get a better picture of the employment cycle, practitioners often rely on more 
straightforward measures of payroll growth. By measuring the size of payrolls, practi -
tioners sidestep such issues as the ebb and flow of discouraged workers. These statistics, 
however, do have biases of their own. It is hard, for instance, to count employment in 
smaller businesses, which may be significant drivers of employment growth. Still, there

is a clear indication of economic trouble when payrolls shrink and a clear indication 
of recovery when they rise.
The examination of other measures can also assist in understanding the employ -
ment situation and its use in determining cyclical directions. Two additional measures 
are hours worked, especially overtime, and the use of temporary workers. A business 
does not want to make mistakes with full-  time staff, either hiring or firing. Thus, at 
the first signs of economic weakness, managers cut back hours, especially overtime. 
Such movements can simply reflect minor month-  to- month production shifts, but 
if followed by cutbacks in part-  time and temporary staff, the picture gives a strong 
signal of economic weakness, especially if confirmed by other independent indicators. 
Similarly, on the cyclical upswing, a business turns first to increases in overtime and 
hours. If a business then increases temporary staffing, it gives a good signal of eco -

nomic recovery long before any movement in rehiring fulltime staff again, especially 
if confirmed by independent cyclical indicators.
Productivity measures also offer insight into this cyclical process. Because produc -
tivity is usually measured by dividing output by hours worked, a business’s tendency 
to keep workers on the payroll even as output falls usually prompts a reduction in 
measured productivity. If measures are available promptly enough, this sign of cyclical 
weakness might precede even the change in hours. This drop in productivity precedes 
any change in full-  time payrolls. Productivity also responds promptly when business 
conditions improve and the business first begins to utilize its underemployed workers, 
which occurs earlier than any upturn in full-  time payrolls.
On a more fundamental level, productivity can also pick up in response to techno -
logical breakthroughs or improved training techniques. As already mentioned, such

changes affect potential GDP . If strong enough, they can negatively affect employment 
trends, keeping them slower than they would be otherwise by relieving the need for 
additional staff to increase production. But these influences usually unfold over decades 
and mean little to cyclical considerations, which, at most, unfold over years. What is 
more, there are few statistical indicators to gauge the onset of technological change, 
confining analysts to the use of anecdotal evidence or occasional longitudinal studies.
EXAMPLE 9   
Analyzing Unemployment
1 At the peak of the business cycle, if the unemployment rate is low, the 
majority of the unemployed are most likely :
A discouraged workers.
B long-  term unemployed.

Unemployment and Inflation 223
C frictionally unemployed.
2 As an economy starts to recover from a trough in the business cycle, the 
unemployment rate is most likely  to:
A continue to rise with a decline in the number of discouraged workers.
B start to decline with an increase in the number of discouraged 
workers.
C continue to rise with an increase in the number of discouraged 
workers.
3 An analyst observes that the unemployment rate is high and rising, 
whereas productivity and hours worked have declined. The analyst is most 
likely  to conclude that the labor market is signaling the:
A end of a recession.
B deepening of a recession.
C peak of the business cycle.
C is correct. At the peak of a business cycle, the labor market is usually tight 
and people become unemployed largely because they are either “between jobs” 
or they have entered or reentered the labor force but have not yet found work. 

A is correct. As the economy starts to recover, discouraged workers return to 
the labor force and start looking for jobs, which increases both the number of 
unemployed and the size of the labor force. The unemployment rate rises because 
the rise in the unemployed population is proportionately larger than the increase 
in the size of the labor force. B and C are incorrect because an increase in the 
number of discouraged workers typically occurs when the economy is contracting. 
B is correct. High and rising unemployment, declining hours worked, and falling 
productivity are all signs of a weak economy getting weaker. When the econ -
omy first slows down, businesses cut back employees’ hours. As the recession 
deepens, they then lay off employees, leading to a higher unemployment rate. 
Yet, because workforce turnover is costly for businesses, the scale of the layoff 
can be less than the decline in output, resulting in a decline in productivity. A

is incorrect because toward the end of a recession, businesses are hesitant to 
increase hiring and instead use more overtime, increasing both productivity 
and the hours worked. C is incorrect because at the peak of a business cycle, 
the unemployment rate is usually low and the level of hours worked is high. 
4.2 Inflation
The overall price level changes at varying rates during different phases of a business 
cycle. Thus, when studying business cycles, it is important to understand this phe -
nomenon. In general, the inflation rate is pro-  cyclical (that is it goes up and down 
with  the cycle), but with a lag of a year or more.
Inflation  refers to a sustained rise in the overall level of prices in an economy. 
Economists use various price indexes to measure the overall price level, also called the 
aggregate price level. The inflation rate  is the percentage change in a price index—
that is, the speed of overall price level movements. Investors follow the inflation rate

closely, not only because it can help to infer the state of the economy but also because 
an unexpected change may result in a change in monetary policy, which can in turn

Reading 17 ■ Understanding Business Cycles 224
have a large and immediate impact on asset prices. In developing countries, very 
high inflation rates can lead to social unrest or even shifts of political power, which 
constitutes political risk for investments in those economies.
Central banks, the monetary authority in most economies, monitor the domestic 
inflation rates closely when conducting monetary policy. Monetary policy determines 
interest rates and the available quantities of money and loans in an economy. A high 
inflation rate combined with fast economic growth and low unemployment usually 
indicates the economy is overheating, which may trigger some policy movements to 
cool it down. However, if a high inflation rate is combined with a high level of unem -
ployment and a slowdown of the economy—an economic state known as stagflation  
(for stagnation plus inflation)—the economy will typically be left to correct itself

because no short-  term economic policy is thought to be effective.
4.2.1  Deflation, Hyperinflation, and Disinflation
There are various terms related to the levels and changes of the inflation rate.
■■Deflation : A sustained decrease in aggregate price level, which corresponds to a 
negative inflation rate—that is, an inflation rate of less than 0%.
■■Hyperinflation : An extremely fast increase in aggregate price level, which cor -
responds to an extremely high inflation rate—for example, 500% to 1000% per 
year.
■■Disinflation : A decline in the inflation rate, such as from around 15% to 20% 
to 5% or 6%. Disinflation is very different from deflation because even after a 
period of disinflation, the inflation rate remains positive and the aggregate price 
level keeps rising (although at a slower speed).
Inflation means that the same amount of money can purchase less real goods 
or services in the future. So, the value of money or the purchasing power of money

decreases in an inflationary environment. When deflation occurs, the value of money 
actually increases. Because most debt contracts are written in fixed monetary amounts, 
the liability of a borrower also rises in real terms during deflation. As the price level 
falls, the revenue of a typical company also falls during a recession. Facing increasing 
real debt, a company that is short of cash usually cuts its spending, investment, and 
workforce sharply. Less spending and high unemployment then further exacerbate 
the economic contraction. To avoid getting too close to deflation, the consensus on 
the preferred inflation rate is around 2% per year for developed economies. Deflation 
occurred in the United States during the Great Depression and briefly during the 
recession following the global financial crisis of 2008–2009. Since the late 1990s, Japan 
has experienced several episodes of deflation.
Hyperinflation usually occurs when large scale government spending is not backed

by real tax revenue and the monetary authority accommodates government spending 
by increasing the money supply. Hyperinflation may also be caused by the shortage 
of supply created during or after a war, economic regime transition, or prolonged 
economic distress of an economy caused by political instability. During hyperinflation, 
people are eager to change their cash into real goods because prices are rising very 
fast. As a result, money changes hands at extremely high frequency. The government 
also has to print more money to support its increased spending. As more cash chases 
a limited supply of goods and services, the rate of price increases accelerates. After 
World War I, a famous case of hyperinflation occurred in Germany from 1923 to 1924. 
During the peak of this episode, prices doubled every 3.7 days. After World War II, 
Hungary experienced a severe hyperinflation during which prices doubled every 15.6

hours at its peak in 1946. In 1993, the inflation rate in Ukraine peaked at 10,155% 
per year. In January 1994, the monthly  inflation rate peaked at 313 million percent in 
Yugoslavia. The most recent hyperinflation in Zimbabwe reached a peak of monthly

Unemployment and Inflation 225
inflation at 79.6 billion percent in the middle of November 2008. Because the basic 
cause for hyperinflation is too much money in circulation, regaining control of the 
money supply is the key to ending hyperinflation.
Exhibit 2 shows recent episodes of disinflation in selected countries around the 
world. The first episode happened during the early 1980s. Because of the two oil 
crises in the 1970s, many countries around the world were experiencing high levels 
of inflation. In Exhibit  2, the annual inflation rates in most counties around 1980 
ranged between 10% and 20%. Even though this level is still far from hyperinflation, it 
generated social pressure against inflationary monetary policy. At the cost of a severe 
recession early in the 1980s, these countries brought inflation rates down to around 
5% on average by 1985. In the first years of the 1990s, inflationary experience varied

widely in world markets as some countries entered recessions, such as the United 
States and the United Kingdom, and others boomed. However, from the beginning 
to the end of the decade, there was a broad-  based decline in inflation rates; in some 
countries annual inflation rates were below 2% by the end of the decade. In many 
countries, the decline in inflation was attributed to high productivity growth rates.
Exhibit 2   Two Episodes of Disinflation around the World Annual Inflation Rates
First Episode Second Episode
Y ear 1979 1980 1983 1984 1985 1990 1991 1998 1999
Country
Australia 9.1 10.2 10.1 3.9 6.7 7.3 3.2 0.9 1.5
Canada 9.1 10.1 5.9 4.3 4.0 4.8 5.6 1.0 1.7
Finland 7.5 11.6 8.4 7.1 5.2 6.1 4.3 1.4 1.2
France 10.6 13.6 9.5 7.7 5.8 3.2 3.2 0.6 0.5
Germany 4.0 5.4 3.3 2.4 2.1 2.7 4.0 1.0 0.6
Italy 14.8 21.1 14.6 10.8 9.2 6.5 6.3 2.0 1.7
Japan 3.7 7.8 1.9 2.3 2.0 3.1 3.3 0.7 –0.3
South Korea 18.3 28.7 3.4 2.3 2.5 8.6 9.3 7.5 0.8
Spain 15.7 15.6 12.2 11.3 8.8 6.7 5.9 1.8 2.3

Sweden 7.2 13.7 8.9 8.0 7.4 10.4 9.4 –0.3 0.5
United Kingdom 13.4 18.0 4.6 5.0 6.1 7.0 7.5 1.6 1.3
United States 11.3 13.5 3.2 4.3 3.5 5.4 4.2 1.6 2.2
Average 10.4 14.1 7.2 5.8 5.3 6.0 5.5 1.6 1.2
G–7 Countries 9.6 12.5 4.6 4.6 3.9 4.8 4.4 1.3 1.4
Source:  The Organisation for Economic Co-  Operation and Development (OECD).
4.2.2  Measuring Inflation: The Construction of Price Indexes
Because the inflation rate is measured as the percentage change of a price index, it is 
important to understand how a price index is constructed so that the inflation rate 
derived from that index can be accurately interpreted. A price index  represents the 
average prices of a basket of goods and services, and various methods can be used 
to average the different prices. Exhibit 3 shows a simple example of the change of a 
consumption basket over time.

Reading 17 ■ Understanding Business Cycles 226
Exhibit 3   Consumption Basket and Prices over Two Months
Time January 2010 February 2010
Goods Quantity Price Quantity Price
Rice 50 kg ¥3/kg 70 kg ¥4/kg
Gasoline 70 liters ¥4.4/liter 60 liters ¥4.5/liter
For January 2010, the total value of the consumption basket is:
Value of rice + Value of gasoline = (50 × 3) + (70 × 4.4) = ¥458
A price index uses the relative weight of a good in a basket to weight the price in the 
index. Therefore, the same consumption basket in February 2010 is worth:
Value of rice + Value of gasoline = (50 × 4) + (70 × 4.5) = ¥515
The price index in the base period is usually set to 100. So, if the price index in 
January 2010 is 100, then the price index in February 2010 is
Price index in February 2010 = 515
458100 112 45×= ¥. and
Inflation rate = 112 45
10010 1245 12 45... % −= =
A price index created by holding the composition of the consumption basket con -

stant is called a Laspeyres index . Most price indexes around the world are Laspeyres 
indexes because the survey data on the consumption basket is only available with a 
lag. In many countries, the basket is updated every five years. Because most price 
indexes are created to measure the cost of living, simply using a fixed basket of goods 
and services has three serious biases:
■■Substitution bias: As the price of one good or service rises, people may sub -
stitute it with other goods or services that have a lower price. This substitu -
tion will result in an upward bias in the measured inflation rate based on a 
Laspeyres index.
■■Quality bias: As the quality of the same product improves over time, it satisfies 
people’s needs and wants better. One such example is the quality of cars. Over 
the years, the prices of cars have been rising but the safety and reliability of cars 
have also been enhanced. If not adjusted for quality, the measured inflation rate 
will experience another upward bias.

■■New product bias: New products are frequently introduced and a fixed basket 
of goods and services will not include them. In general, this situation again 
creates an upward bias in the inflation rate.
It is relatively easy to resolve the quality bias and new product bias. Many countries 
adjust for the quality of the products in a basket, a practice called hedonic pricing. 
New products can be introduced into the basket over time. The substitution bias 
can be somewhat resolved by using chained price index formula. One such example 
is the Fisher index , which is the geometric mean of the Laspeyres index and the

Unemployment and Inflation 227
Paasche index . The latter is an index formula using the current composition of the 
basket. Using the consumption basket for February 2010 in Exhibit 3, the value of 
the Paasche index is
Paasche I ndex02 201070 46 04 5
70 36 04 4100 ==×() +×()
×() +×()×
=IP.
.
5 550
474100 116 03×= .
The value of the Fisher index is
Fisher Index02/2010  = IIPL×= ×= 116 03 112 45 114 23.. .
where IL is the Laspeyres index.
4.2.3  Price Indexes and Their Usage
Most countries use a consumer price index (CPI) specific to the domestic economy to 
track inflation. Exhibit 4 shows the different weights for various categories of goods 
and services in the consumer price indexes of different countries.
Exhibit 4   The Consumption Basket of Different Consumer Price Indexes
Country Japan China India GermanyUnited 
States United States
Name of Index CPI CPI CPI(UNME) HICP PCE CPI-  U
Yeara2005 2005 1984/85 2008 2009 2007/08
Category (%):
  Food and Beverage 25.9 34 47.1 16.7 7.8 14.8

Food and Beverage 25.9 34 47.1 16.7 7.8 14.8
  Housing and Utility 27.2 13 21.9 23.1 18.8 37.4
  Furniture 3.4 6 2.0 6.1 2.5 4.6
  Apparel 4.6 9 7.0 5.3 3.2 3.7
  Medical Care 4.5 10 2.5 4.4 16.2 6.5
  Transportation and 
Communication 13.9 10 5.2 17.6 9.1 20.1
  Education and Recreation 14.6 14 6.8 13.3 7.0b9.5
  Others 5.9 4 7.5 13.5 35.4 3.5
a The base year of the weights where it is appropriate.
b Recreation only.
Source:  Government websites and authors’ calculation.
As shown in Exhibit  4, in different countries the consumer price indexes have 
different names and different weights on various categories of goods and services. 
For example, food weights are higher in the CPI for China and India, but less for the 
developed countries; a greater proportion of income of the average consumer goes 
to food in the developing countries of China and India than in the developed coun -
tries shown in Exhibit 4. The scope of the index is also different among countries.

For China, Japan, and Germany, the surveys used to collect data for CPI cover both 
urban and rural areas. The CPI for the United States covers only urban areas using a 
household survey, which is why it is called the CPI-  U. On the other hand, the personal 
consumption expenditures  (PCE) price index covers all personal consumption in 
the United States using business surveys.

Reading 17 ■ Understanding Business Cycles 228
The producer price index  (PPI) is another important inflation measure. The PPI 
reflects the price changes experienced by domestic producers in a country. Because 
price increases may eventually pass through to consumers, the PPI can influence the 
future CPI. The items in the PPI include fuels, farm products (such as grains and meat), 
machinery and equipment, chemical products (such as drugs and paints), transporta -
tion equipment, metals, pulp and paper, and so on. These products are usually further 
grouped by stage-  of- processing categories: crude materials, intermediate materials, 
and finished goods. Similar to the CPI, scope and weights vary among countries. The 
differences in the weights can be much more dramatic for the PPI than for the CPI 
because different countries may specialize in different industries. In some countries, 
the PPI is called the wholesale price index  (WPI).

As an important inflation indicator, many economic activities are indexed to a 
certain price index. For example, the United States’ Treasury Inflation-  Protected 
Securities  (TIPS) adjusts the bond’s principal according to the US CPI-  U index. The 
terms of labor contracts and commercial real estate leases may adjust periodically 
according to the CPI. Recurring payments in business contracts can be linked to the 
PPI or its sub-  indexes for a particular category of products.
Central banks usually use a consumer price index to monitor inflation. For example, 
the European Central Bank (the ECB), the central bank for the European Union (EU) 
focuses on the Harmonised Index of Consumer Prices (HICP). Each member country 
in the EU first reports their own individual HICP and then Eurostat, the statistical 
office for the EU, aggregates the country level HICPs with country weights. But there 
are exceptions. The Reserve Bank of India follows the inflation in India using a WPI.

Because food items only represent about 27% in the India WPI (much lower than the 
70% in the India rural CPI), the rural CPIs can rise faster than the WPI when there is 
high food price inflation. Besides the weight differences, the wholesale prices in the 
WPI also understate market prices because they do not take into account retail margins 
(markups). The choice of inflation indicator may also change over time. The central 
bank of the United States, known as the Federal Reserve Board (the Fed) once focused 
on the CPI-  U produced by the Bureau of Labor Statistics under the US Department 
of Labor. Because the CPI-  U is a Laspeyres index and it has the previously discussed 
upward biases, the Fed switched in 2000 to the PCE index, a Fisher index produced by 
the Bureau of Economic Analysis under the US Department of Commerce. The PCE 
index also has the advantage that it covers the complete range of consumer spending 
rather than just a basket.
 
Headline and Core Inflation

Headline inflation  refers to the inflation rate calculated based on the price index that 
includes all goods and services in an economy. Core inflation  usually refers to the 
inflation rate calculated based on a price index of goods and services except food and 
energy. Policymakers often choose to focus on the core inflation rate when reading the 
trend in the economy and making economic policies. The reason is that policymakers 
are trying to avoid overreaction to short-  term fluctuations in food and energy prices that 
may not have a significant impact on future headline inflation.
The ultimate goal for policymakers is to control headline inflation, which reflects 
the actual cost of living. The fluctuations in the prices of food and energy are often 
the result of short-  term changes in supply and demand. These changes in the prices of 
energy, particularly oil, are internationally determined and not necessarily reflective of

the domestic business cycle. These imbalances may not persist, or even if some changes 
are permanent, the economy may be able to absorb them over time. These possibilities

Unemployment and Inflation 229
make headline inflation a noisy predictor. The core inflation rate may be a better signal 
of the trend in domestically driven inflation. To the extent that some trends in the head -
line inflation rate are permanent, policymakers need to pay attention to these as well.
Besides tracking inflation, financial analysts also use the price index to deflate GDP 
(i.e., to eliminate the price effect in nominal GDP data so as to identify trends in real 
economic growth). Many countries publish a particular price index, called the GDP 
deflator, for that purpose. Sub-  indexes are also commonly available and may prove 
more valuable to an analyst with an interest in a particular industry or company.
 
Sub-  Indexes and Relative Prices
As mentioned previously, a sub-  index refers to the price index for a particular category 
of goods or services. Relative price  is the price of a specific good or service in compar -

ison with those of other goods and services. Good examples for relative prices include 
the prices for food and energy. The movements in a sub-  index or a relative price may 
be difficult to detect in the headline inflation rate. Because macroeconomic policy 
decision-  makers rely heavily on the headline inflation rate, they may not be aware of 
price movements at the sub-  index level. These prices movements, however, can be 
very useful for analyzing the prospects of an industry or a company. For example, if the 
producer price index for the machinery used by an industry rises quickly, the allowable 
capital depreciation permitted by the existing tax code may not generate sufficient tax 
benefits for the companies in that industry to meet future replacement expenses. The 
future profitability of the industry may decline for this reason. The decline in prices for 
flat screen televisions provides an example of relative price movements. The price drop

for these TVs may help to lower inflation pressure but can hurt manufacturers’ profits.
EXAMPLE 10   
Inflation
1 Which one of the following statements regarding the movements of over -
all price levels is most  accurate?
A Disinflation means that the overall price level declines.
B Deflation occurs when the inflation rate turns negative.
C When the price of chicken rises, the inflation rate will increase.
2 Deflation can exacerbate a recession because firms may reduce their 
investments and hiring when:
A the slower pace of inflation lowers aggregate demand.
B their revenues decline but their debt burden rises in real terms.
C prices of their products continue to fall because of intense 
3 Which one of the following economic phenomena related to inflation 
cannot be determined by using observations of the inflation rate alone?
A Deflation
B Stagflation
C Hyperinflation

Reading 17 ■ Understanding Business Cycles 230
4 If a price index is calculated based on a fixed basket of goods, in an infla -
tionary environment the inflation rate calculated based on this index over 
time will:
A overstate the actual cost of living.
B understate the actual cost of living.
C track the actual cost of living quite closely.
5 To adjust nominal economic growth for general price level changes in a 
country, an analyst would prefer to use:
A the CPI.
B the GDP deflator.
C the Personal Consumption Expenditures (PCE) index.
6 To estimate the trends in sales and production costs of a given industry, 
an analyst would prefer to collect data on:
A the sub-  index of the wholesale price index (WPI) for that industry.
B the sub-  indexes of both the CPI and WPI that are relevant to the 
industry.
C the sub-  indexes of the CPI relevant to the output and inputs of that 
industry.
7 Compared with core inflation, headline inflation:
A has an upward bias.

B is more subject to short-  term market conditions.
C can more accurately predict future inflation.
B is correct. When the inflation rate falls below zero—that is, the overall price 
level declines—the economy is experiencing deflation. A is incorrect because 
disinflation indicates that the overall price level is rising but at a slower pace. 
C is incorrect because inflation measures are designed to reflect changes in the 
overall price level. Consumption baskets in modern economies usually contain 
a large number of goods and services, thus the price of a particular product 
usually cannot significantly influence the overall price level.
B is correct. As the prices of the output of firms fall, the firms receive lower 
revenues. Because the nominal amount of debt that firms carry is usually fixed, 
lower general price levels leads to higher debt balances in real terms. These

two forces push firms closer to default, so they may scale back spending on 
investments and labor, which, in turn, further lowers the aggregate demand 
and pushes the general price level even lower. In macroeconomic analysis, it 
is usually the changes in aggregate demand that influence inflation instead of 
the reverse causality. Furthermore, neither inflation fluctuations nor aggregate 
demand shifts explain the potential damaging effect of deflation. Price decline 
attributable to the competitive environment is a microeconomic phenomenon 
that is not sufficient to explain the macroeconomic impact of deflation.
B is correct. A high inflation rate alone does not indicate stagflation, which 
happens if high unemployment occurs together with high inflation.

Unemployment and Inflation 231
A is correct. Upward biases, such as the substitution bias or quality bias, will 
overstate the actual cost of living.
B is correct. The GDP deflator reflects the prices of the goods and services 
produced domestically. Both the CPI and PCE indexes are constructed using 
consumption baskets, and the components of a consumption basket can be very 
different from the components of output of that same country.
B is correct. A sub-  index of the CPI reflects the market price changes of the 
products of an industry, whereas a sub-  index of the WPI reflects the price 
changes of the inputs of an industry. The different composition of outputs and 
inputs of an industry need to be appropriately accounted for when selecting a 
price series. Furthermore, the WPI may not take the markups set by the industry 
into account.
Solution to 7: 
B is correct. Headline inflation is heavily influenced by food and energy price

fluctuations, which are affected by short-  term supply and demand changes in 
these markets. These market conditions may not persist. It is also possible for 
an economy to absorb the price changes so that they will not have long-  lasting 
impact on the headline inflation rate. This means headline inflation contains a 
great deal of noise and is not a reliable predictor of future inflation trends. The 
biases in various inflation measures are inherent in the index construction meth -
odology and are not related to the price movements of the goods and services.
4.2.4  Explaining Inflation
Economists describe two types of inflation: cost-  push , in which rising costs, usu -
ally wages, compel businesses to raise prices generally; and demand-  pull, in which 
increasing demand raise prices generally, which then are reflected in a business’s costs 
as workers demand wage hikes to catch up with the rising cost of living. Whatever

the sequence by which prices and costs rise in an economy, the fundamental cause is 
the same: excessive demands—either for raw materials, finished goods, or labor—that 
outstrip the economy’s ability to respond. The initial signs appear in the areas with 
the greatest constraints: the labor market, the commodity market, or in some area of 
final output. Even before examining particular cost and price measures, practitioners, 
when considering inflation, look to indicators that might reveal when the economy 
faces such constraints.
4.2.4.1  Cost-  Push Inflation  In the area of cost-  push inflation, analysts may look at 
commodity prices because commodities are an input to production. But because wages 
are the single biggest cost to businesses, practitioners focus most particularly on wage-  
push inflation, which is tied to the labor market. Because the object is to gauge demand 
for labor relative to capacity, the unemployment rate is key, as well as measures of the

number of workers available to meet the economy’s expanding needs. Obviously, the 
higher the unemployment rate, the lower the likelihood that shortages will develop in 
labor markets, whereas the lower the unemployment rate, the greater likelihood that 
shortages will drive up wages. Because the unemployment rate generally only counts 
people who are looking for work, some practitioners argue that it fails to account for 
the economy’s full labor potential, and they state that a tight labor market will bring 
people out in search of work and ease any potential wage strains. To account for this

Reading 17 ■ Understanding Business Cycles 232
issue and to modify the unemployment rate indicator, these practitioners also look at 
the participation rate of people in the labor force, arguing that it gives a fuller and more 
accurate picture of potential than the unemployment rate.
Analysis in this area recognizes that not all labor is alike. Structural factors related 
to training deficiencies, cultural patterns in all or some of the population, inefficiencies 
in the labor market, and the like can mean that the economy will effectively face labor 
shortages long before the unemployment rate reaches very low figures. This effective 
unemployment rate, below which pressure emerges in labor markets, is frequently 
referred to as the non-  accelerating inflation rate of unemployment  (NAIRU) or, 
drawing on the work of the Nobel Prize winner Milton Friedman, the natural rate of 
unemployment  (NARU). Of course, these rates vary from one economy to another

and over time in a single economy. It is this rate rather than full employment that 
determines when an economy will experience bottlenecks in the labor market and 
wage-  push inflationary pressures.
Take, for example, the technology sector. It has grown so rapidly in some econ -
omies that training in the labor force cannot keep up with demand. This sector can, 
as a consequence, face shortages of trained workers and attendant wage pressures 
even though the economy as a whole seems to have considerable slack in the overall 
labor market. Until training (supply) catches up with demand, that economy may 
experience wage and inflation pressure at rates of unemployment that in other places 
and circumstances might suggest ample slack in the labor market and much less 
wage-  push pressure.
Assessments of wage-  push inflation also consider direct observations of wage 
trends that, when they accelerate, might force businesses to raise prices (initiating

the wage-  price spiral mentioned earlier in this reading). Statistical agencies provide 
a wide array of wage-  cost indicators, such as hourly wage gauges, weekly earnings, 
and overall labor costs, including the outlays for benefits. Some of these indicators 
include the effects of special overtime pay or bonuses, others do not. And although 
these measures give an idea of the cost to businesses and hence the kind of wage-  push 
inflationary pressure, a complete picture only emerges when practitioners examine 
such trends alongside productivity measures.
Productivity, or output per hour, is an essential part of wage-  push inflation anal -
ysis because the output available from each worker determines the number of units 
over which businesses can spread the cost of worker compensation. The greater each 
worker’s output is per hour, the lower price businesses need to charge for each unit 
of output to cover hourly labor costs. And by extension, the faster output per hour

grows, the faster labor compensation can expand without putting undue pressure 
on businesses’ costs per unit of output. The equation for this unit labor cost  (ULC) 
indicator, as it is called, is as follows:
ULC = W/O,
where
 ULC = unit labor costs
 O = output per hour per worker
 W = total labor compensation per hour per worker
Many factors can affect labor productivity across time and between economies. 
The cyclical swings have already been described, as have the effects of technology 
and training. The pace of development also tends to increase worker productivity 
because the more sophisticated equipment, systems, and technologies workers have 
at their disposal, the higher their output per hour. Whatever causes the productivity 
growth, if it fails to keep up with worker compensation, unit costs to a business rise 
and, as a business tries to protect its profit margins, prices generally come under 
increasing upward pressure. Generally this situation occurs because heavy demand

Unemployment and Inflation 233
for labor relative to available labor resources has pushed up compensation faster than 
productivity. Practitioners use a variety of indicators to identify cost- or wage-  push 
inflationary pressure.
EXAMPLE 11   
Unemployment Too High
Which of the following is not a problem with the NARU and NAIRU?
A They only work in monetarist models.
B They may change over time given changes in technology and economic 
C They do not account for bottlenecks in segments of the labor market (e.g., 
college graduates).
Solution: 
A is correct. The NARU and NAIRU are the unemployment rates at which the 
inflation rate will not rise because of a shortage of labor. This concept does not 
tie to a particular school of macroeconomic models.
4.2.4.2  Demand-  Pull Inflation  The search for indicators from the demand-  pull side of 
the inflation question brings practitioners back to the relationship between actual and

potential real GDP and industrial capacity utilization. The higher the rate of capacity 
utilization or the closer actual GDP is to potential, the more likely an economy will 
suffer shortages, bottlenecks, a general inability to satisfy demand, and hence, price 
increases. The more an economy operates below its potential or the lower the rate of 
capacity utilization, the less such supply pressure will exist and the greater likelihood 
of a slowdown in inflation, or outright deflation. In addition to these macro indicators, 
practitioners will also look for signs of inflationary pressure in commodity prices, in 
part because they are a cost to business, but more as a general sign of excess demand. 
For an individual economy, observations of commodity prices could be misleading 
because commodities trade in a global market and accordingly reflect global economic 
conditions more than those in an individual economy.

Taking a different perspective, Monetarists contend that inflation is fundamentally 
a monetary phenomenon. A surplus of money, they argue, will inflate the money price 
of everything in the economy. Stated in terms of straightforward supply and demand 
relationships, a surplus of money would bring down its value just as a surplus in any 
market would bring down the price of the product in excess. Because the price of 
money is stated in terms of the products it can buy, its declining value would have an 
expression in higher prices generally, that is, in inflation. This Monetarist argument, 
as it is called, finds a more simple expression in the old saying that inflation results 
when too much money chases too few goods. Although it seems distant from other 
explanations of inflation, in practice, it is not that distinct. The excess of money creates 
the inflation by increasing liquidity, which ultimately causes a rapid rise in demand. In

this sense, the Monetarist argument is a special case under the more general heading 
of demand-  pull concepts of inflation. The practical distinction between the monetarist 
and other approaches is in identifying the initial cause of the demand excess.
Practitioners can track this effect by examining various money supply indica -
tors, usually provided by the central bank. To detect an inflationary potential or the 
opposite, they note accelerations or decelerations in money growth from past trends. 
Obviously, accelerations, in the absence of a special explanation, signal the potential 
for inflationary pressure. In applying this approach, practitioners also compare money

Reading 17 ■ Understanding Business Cycles 234
growth with the growth of the nominal economy, represented by nominal GDP . If 
money growth outpaces the growth of the nominal economy, there is an inflationary 
potential, especially if money growth has also accelerated from its trend. There is a 
disinflationary or deflationary potential if money growth trails the economy’s rate of 
expansion, especially if it has also decelerated from its trend.
 
Inflation (I)
Some practitioners view the likelihood of inflationary pressure from the vantage point 
of the ratio of nominal GDP to money supply, commonly called the “velocity of money.” 
If this ratio remains stable around a constant or a historical trend, they see reason to 
look for relative price stability. If velocity falls, it could suggest a surplus of money that 
might have inflationary potential, but much depends on why it has declined. If velocity 
has fallen because a cyclical correction has brought down the GDP numerator relative

to the money denominator, then practitioners view prospects as more likely to lead to 
a cyclical upswing to reestablish the former relationship than inflationary pressure. If 
velocity has fallen, however, because of an increase in the money denominator, then 
inflationary pressure becomes more likely. If velocity rises, financial analysts might be 
concerned about a shortage of money in the economy and disinflation or deflation.
The 2008–2009 global recession and financial crisis offers an extreme example of these 
velocity ambiguities. As the global economy slipped into recession, which held back the 
GDP numerator in velocity measures, central banks, most notably the Federal Reserve in 
the United States, tried to help financial institutions cope by injecting huge amounts of 
money into their respective financial systems, raising the velocity denominator. Velocity 
measures plummeted accordingly. The expectation is that subsequent GDP growth as

economies and financial markets heal will bring velocity back to a more normal level and 
trend. That said, the fear is that the monetary surge will, over the very long run, lead to 
inflation. For policy makers, this situation has created a very difficult policy choice. On the 
one side, they need to sustain the supply of money to help their respective economies 
cope with the after effects of the financial crisis. On the other side, they need ultimately 
to withdraw any monetary excess to preclude potential inflationary pressures.
4.2.5  Inflation Expectations
Beyond demand-  pull, monetary, and cost-  push inflation considerations, practitioners 
also need to account for the effect of inflation expectations. Once inflation becomes 
embedded in an economy, businesses, workers, consumers, and economic actors of 
every kind begin to expect it and build those expectations into their actions. This 
reaction, in turn, creates an inflationary momentum of its own. Such expectations

give inflation something of a self-  sustaining character and cause it to persist in an 
economy even after its initial cause has disappeared. High inflation rates persisted 
in the 1970s and early 1980s in Europe and the United States on the basis of expec -
tations even after these economies had sunk into recession. The resulting slow or 
negative economic growth combined with high unemployment and rising inflation 
was termed “stagflation. ”
Measuring inflation expectations is not easy. Some practitioners gauge expectations 
by relying on past inflation trends and on the assumption that market participants 
largely extrapolate their past experiences. In some markets, surveys of inflation expec -
tations are available, although these are often biased by the way the questions are asked. 
Another indicator of inflation expectations becomes available when governments 
issue bonds, such as Treasury Inflation-  Protected Securities (TIPS), that adjust in

various ways to compensate holders for inflation. By comparing the interest available

Unemployment and Inflation 235
on these bonds with other government bonds that do not offer such inflation-  linked 
adjustments, practitioners can gauge the general level of inflation expectations among 
market participants and factor it into their own inflation forecasts and strategies.
For example, if today’s yield on the 10-  year nominal bond of a certain country 
is 3.5% and the yield on the 10-  year inflation-  protected bond of the same country is 
1.5%, we infer that the market is pricing in a 3.5% – 1.5% = 2% average annual inflation 
over the next 10 years. However, this calculation needs to be treated with caution 
because the market for inflation-  linked bonds is relatively small and thus yields can be 
influenced by other factors, such as the very strong demand from US pension funds 
seeking to match their liabilities.
EXAMPLE 12   
Inflation (II)
1 To examine whether there is inflationary pressure caused by rising costs, 
an analyst will most likely  gather data on:

A the growth rates of money supply and nominal GDP .
B the unemployment rate, the NAIRU, and productivity growth.
C commodity prices, past inflation trends, and expected inflation 
surveys.
2 The most recent macroeconomic data for an economy is given in the fol -
lowing table:
Variable Value
Hourly wage growth rate 3.4%
Unit labor cost growth rate –0.25%
Nominal GDP growth rate 3.4%
Money supply growth rate 6.7%
Implied inflation rate from government issued inflation-  
linked securities2.2%
 Based on the information in the table, an analyst will conclude that cur -
rent inflation pressure in this economy is most likely  caused by:
A rising wages.
B rising inflation expectations.
C bottlenecks in increasing supply to satisfy demand.
3 Cost-  push inflation most likely  occurs when:
A unemployment rates are low.
B unemployment rates are high.
C unemployment is either high or low.
4 Unit labor costs measure:
A hourly wage rates.
B total labor compensation per hour.

C a combination of hourly wages and output.
5 Demand-  pull inflation:
A is a discredited concept.
B depends on the movements in commodity prices.

Reading 17 ■ Understanding Business Cycles 236
C reflects the state of economic activity relative to potential.
6 Monetarists believe inflation:
A reflects the growth of money.
B is driven by the level of interest rates.
C is largely a cost-  push phenomenon.
7 The inflationary potential of a particular inflation rate depends on the 
economy’s NAIRU or NARU, which, in turn, depends in part on:
A the intensity of past cyclical swings.
B the bargaining power of trade unions.
C the skill set of the labor force relative to the economy’s industrial mix.
8 Which of the following is not a problem with the NARU and NAIRU?
A They are not observable directly.
B They work only in monetarist models.
C They change over time given changes in technology and economic 
B is correct. Comparing the current unemployment rate with the NAIRU 
and productivity growth with the wage growth can help an analyst determine 
whether inflation may be rising because of higher costs (cost-  push inflation).

Comparing the monetary growth with nominal GDP growth is helpful to 
determine whether high demand is creating inflationary pressure (demand-  pull 
inflation). Commodity price increases could be an indicator of either cost-  push 
or demand-  pull inflation but may contain limited information in some situations. 
Past inflation trends and surveys on inflation expectations can help to gauge 
expected inflation rates; inflation expectations can be a driver of inflation even 
in the absence of the original underlying cause.
C is correct. The table shows that growth in the money supply has outpaced 
nominal GDP growth, which can result in too much money chasing too few goods. 
In other words, inflation pressure results from demand beyond the economy’s 
current capacity to produce. Although the wage rate is rising, the negative unit 
labor cost growth rate indicates an increase in productivity. Thus, it is unlikely

the economy will experience cost-  push inflation. The implied inflation rate is 
very modest, which is unlikely to lead to a rising inflation rate.
A is correct. When unemployment is below the NAIRU, there is a shortage of 
labor that pushes up labor cost.
C is correct. Unit labor costs reflect the labor cost in each unit of output.
C is correct. When the economy is operating above its potential capacity allowed 
by the resources available, inflation will start to rise.
A is correct. Monetarists emphasize the role of money growth in determining 
the inflation rate, especially in the long run. As Milton Friedman famously put 
it: “Inflation is always and everywhere a monetary phenomenon. ”

Economic Indicators 237
C is correct. If the skill set of a large part of the labor force cannot satisfy the hir -
ing need from the employers, the NAIRU of such an economy can be quite high.
Solution to 8: 
B is correct. The NAIRU or NARU reflects the potential of an economy and thus 
cannot be directly observed from the economic data. They also change over time 
depending on technological progress and social factors.
ECONOMIC INDICATORS
As used in business cycle contexts, an economic indicator  is a variable that provides 
information on the state of the overall economy. Economic indicators are often classified 
according to whether they lag, lead, or coincide with changes in an economy’s growth. 
Leading economic indicators  have turning points that usually precede those of the 
overall economy. They are believed to have value for predicting the economy’s future 
state, usually near-  term. Coincident economic indicators  have turning points that

are usually close to those of the overall economy. They are believed to have value for 
identifying the economy’s present state. Lagging economic indicators  have turning 
points that take place later than those of the overall economy. They are believed to 
have value in identifying the economy’s past condition.
To get as clear of a picture as possible, practitioners frequently consider several 
related indicators simultaneously. What follows is a review of these indicators and 
how practitioners use them.
5.1 Popular Economic Indicators
A very useful approach for practitioners is to take an aggregate perspective on leading, 
lagging, and coincident indicators. These aggregate measures typically are a composite 
of economic indicators known respectively to lead the cycle, run coincident with it, 
or lag it at cyclical turns. For obvious reasons, the leading indicators in particular 
help with anticipating cyclical turns up or down and allow strategists and others to

position themselves and their companies in a secure and timely way to benefit from 
movements in the economic cycle.
The exact indicators combined into these composites vary from one economy to 
the other. Even within an economy, they can have a remarkably diverse and eclectic 
character. In the United States, for instance, the composite leading indicator known 
as the Index of Leading Economic Indicators  (LEI) has 10 component parts that run 
the gamut from orders for capital goods, to changes in consumer expectations, to 
swings in stock prices. Such composite indicators in other countries include equally 
eclectic combinations.
Similar statistics are available for numerous economies. The Conference Board, a 
US industry research organization, computes leading, lagging, and coincident indica -
tors for the United States and nine other countries plus the Euro area (Eurozone). For 
about 30 countries and several aggregates, such as the EU and G–7, the Organisation

for Economic Co-  Operation and Development (OECD) calculates CLI (Composite 
Leading Indicators) indexes, which gauge the state of the business cycle in the econ -
omy. One of the interesting features of CLI indexes is that they are consistent across 
countries, and therefore, can be compared more easily to see how each region is faring. 
The Economic Cycle Research Institute (ECRI), a private company, also computes 
leading indicator indexes for about 20 countries on a weekly basis.5

Reading 17 ■ Understanding Business Cycles 238
Although specifics for leading, coincident, and lagging indicators vary from one 
economy to another, they have much in common. In each case, they bring together 
various economic and financial measures that have displayed a consistently leading, 
coincident, or lagging relationship to that economy’s general cycle. However, as reported 
by the Conference Board, the timing record of the various composite indexes for the 
United States has varied over the last 50 years. The coincident index closely matches the 
NBER peak and trough dates, with 8 of the last 13 turning points corresponding to the 
beginning or end of a recession. The leading indicator index displays more variability, 
leading cyclical contractions by 8 to 20 months and expansions by 1 to 10 months.13
Exhibit 5 presents the 10 leading, 4 coincident, and 7 lagging indicators tracked 
for the United States by the Conference Board. In addition to naming the indicators, it

also offers a general description of why each measure fits in each of the three groups.
Exhibit 5   Leading, Coincident, and Lagging Indicators—United States
Indicator and Description Reason
Leading
1 Average weekly hours, manufacturing Because businesses will cut overtime before laying off workers 
in a downturn and increase it before rehiring in a cyclical 
upturn, these measures move up and down before the general 
economy.
2 Average weekly initial claims for unemployment 
insuranceThis measure offers a very sensitive test of initial layoffs and 
rehiring.
3 Manufacturers’ new orders for consumer goods and 
materialsBecause businesses cannot wait too long to meet demands for 
consumer goods or materials without ordering, these gauges 
tend to lead at upturns and downturns. Indirectly, they cap -
ture changes in business sentiment as well, which also often 
leads the cycle.
4 ISM new order indexa This index is a diffusion index that reflects the month-  to-

month change in new orders for final sales. The weakening of 
demand, which can lead to a recession, is usually first reflected 
in the decline of new orders.
5 Manufacturers’ new orders for non-  defense capital 
goods excluding aircraftIn addition to offering a first signal of movement, up or down, 
in an important economic sector, movement in this area also 
indirectly captures business expectations.
6 Building permits for new private housing units Because most localities require permits before new building 
can begin, this gauge foretells new construction activity.
7 S&P 500 Index Because stock prices anticipate economic turning points, both 
up and down, their movements offer a useful early signal on 
economic cycles.
8 Leading Credit Index This index aggregates the information from six leading 
financial indicators, which reflect the strength of the financial 
system to endure stress. A vulnerable financial system can 
amplify and propagate the effects of negative shocks, resulting

in a widespread recession for the whole economy.
13 See pages 14 and 15 in Business Cycle Indicators Handbook  (The Conference Board 2001).

Economic Indicators 239
Leading
9 Interest rate spread between 10-  year treasury yields 
and overnight borrowing rates (federal funds rate)Because long-  term yields express market expectations about 
the direction of short-  term interest rates, and rates ultimately 
follow the economic cycle up and down, a wider spread, by 
anticipating short rate increases, also anticipates an economic 
upswing. Conversely, a narrower spread, by anticipating short 
rate decreases, also anticipates an economic downturn.
10 Average Consumer Expectations for Business and 
Economic ConditionsIf consumers are optimistic about future business and eco -
nomic conditions, they tend to increase spending. Because 
consumption is about two-  thirds of the US economy, its future 
movements offers early insight into the direction ahead for the 
whole economy.
Coincident
1 Employees on non-  agricultural payrolls Once recession or recovery is clear, businesses adjust their 
fulltime payrolls.

2 Aggregate real personal income (less transfer 
payments)By measuring the income flow from non-  corporate profits and 
wages, this measure captures the current state of the economy.
3 Industrial Production Index Measures industrial output, thus capturing the behavior of the 
most volatile part of the economy. The service sector tends to 
be more stable.
4 Manufacturing and trade sales In the same way as aggregate personal income and the indus -
trial production index, this aggregate offers a measure of the 
current state of business activity.
Lagging
1 Average Duration of Unemployment Because businesses wait until downturns look genuine to 
lay off, and wait until recoveries look secure to rehire, this 
measure is important because it lags the cycle on both the way 
down and the way up.
2 Inventory–sales ratio Because inventories accumulate as sales initially decline and 
then, once a business adjusts its ordering, become depleted as

sales pick up, this ratio tends to lag the cycle.
3 Change in unit labor costs Because businesses are slow to fire workers, these costs tend 
to rise into the early stages of recession as the existing labor 
force is used less intensely. Late in the recovery when the 
labor market gets tight, upward pressure on wages can also 
raise such costs. In both cases, there is a clear lag at cyclical 
turns.
4 Average bank prime lending rate Because this is a bank administered rate, it tends to lag other 
rates that move either before cyclical turns or with them.
5 Commercial and industrial loans outstanding Because these loans frequently support inventory building, 
they lag the cycle for much the same reason that the inven -
tory–sales ratio does.

Reading 17 ■ Understanding Business Cycles 240
Lagging
6 Ratio of consumer installment debt to income Because consumers only borrow heavily when confident, this 
measure lags the cyclical upturn, but debt also overstays cycli -
cal downturns because households have trouble adjusting to 
income losses, causing it to lag in the downturn.
7 Change in consumer price index for services Inflation generally adjusts to the cycle late, especially the more 
stable services area.
a A diffusion index usually measures the percentage of components in a series that are rising in the same period. It indicates how widespread 
a particular movement in the trend is among the individual components.
Let us consider a few examples that show the use of these statistics in identifying 
a business cycle phase. An increase in the reported ratio of consumer installment 
debt to income lags (occurs after) cyclical upturns; so the increase, by itself, would

be evidence that an upturn has been underway. That could confirm the implication 
of positive changes in coincident indicators that an expansion is in place. As a lead -
ing economic indicator, a positive change in the S&P 500 Index is supposed to lead 
(come before) an increase in aggregate economic activity. An increase in the S&P 500 
would be positive for future economic growth, all else equal. However, if the S&P 
500 showed an increase but the aggregate index did not, we would likely not draw a 
positive conclusion. For a final example, if we observed that the LEI moved up a small 
amount on two consecutive observations, we might conclude that a modest economic 
expansion is expected.
The component indicators for other countries, though different in specifics, are 
similar in most respects. The Eurozone, for instance, composes its leading index from 
eight components:
1 Economic sentiment index
2 Residential building permits
3 Capital goods orders
4 The Euro Stoxx Equity Index
5 M2 money supply

6 An interest rate spread
7 Eurozone Manufacturing Purchasing Managers Index
8 Eurozone Service Sector Future Business Activity Expectations Index
The parallels between many of these components and those used in the United 
States are clear, but Europe has a services component in its business activity mea -
sures that the United States lacks, whereas Europe forgoes many of the overtime and 
employment gauges that the United States includes.
Japan’s leading index contains 10 components:
1 New orders for machinery and construction equipment
2 Real operating profits
3 Overtime worked
4 Dwelling units started
5 Six- month growth rate in labor productivity
6 Business failures
7 Business confidence (Tankan Survey)Exhibit 5   (Continued)

Economic Indicators 241
8 Stock prices
9 Real M2 money supply
10 Interest rate spread
Again many are similar, but Japan includes labor market indicators more like the 
United States than Europe and adds a measure of business failures not included in 
the other two.
Similarities and differences along these lines appear in indicators for the United 
Kingdom, Australia, South Africa, specific European economies, and other countries. 
The general tone is, however, similar to the detail provided here for the United States.
 
Building Permits as a Leading Economic Indicator
Exhibit 6 shows an example of a leading economic indicator in Germany, the granted 
building permits along with its relationship to the growth of Germany’s GDP. In Exhibit 6, 
the growth rate of building permits usually peaks one quarter ahead of the GDP growth 
rate, with the exception for the first half of 2008 and 2010. Before 2006, the growth 
rate of building permits usually bottomed out earlier than the GDP growth rate by four

quarters. But after 2006, the troughs of the two series almost coincide. The uncertainty 
of the relationships between an indicator and business cycles is very common. Some 
indicators may be good predictors for economic expansions but poor predictors for 
recessions. This uncertainty is why economists and statisticians often combine different 
indicators and try to find common factors among them when building indicator indexes.
Exhibit 6   The Growth Rates of Germany GDP and Number of Building 
Permits
2
1
0
–1
–2
–3
1Q03 1Q05 1Q07 1Q09 1Q10 1Q04 1Q06 1Q08
GDP Growth Number of Building Permits
Note : The quarter-  to- quarter growth rates are normalized by using the standard deviations 
of the two series, respectively.
Source:  Federal Statistical Office of Germany.

Reading 17 ■ Understanding Business Cycles 242
 
Diffusion Index of Economic Indicators
In the United States, the Conference Board also compiles a monthly diffusion index of the 
leading, lagging, and coincident indicators. The diffusion index  reflects the proportion 
of the index’s components that are moving in a pattern consistent with the overall index. 
Analysts often rely on these diffusion indexes to provide a measure of the breadth of 
the change in a composite index.
For example, the Conference Board tracks the growth of each of the 10 constituents 
of its leading indicator measure, assigning a value of 1.0 to each indicator that rises by 
more than 0.05% during the monthly measurement period, a value of 0.5 for each com -
ponent indicator that changes by less than 0.05%, and a value of 0 for each component 
indicator that falls by more than 0.05%. These assigned values, which of course differ in 
other indexes in other countries, are then summed and divided by 10 (the number of

components). Then to make the overall measure resemble the more familiar indexes, 
the Board multiplies the result by 100.
A simple numerical example will help explain. Say, for ease of exposition, the indicator 
has only four component parts: stock prices, money growth, orders, and consumer con -
fidence. In one month, stock prices rise 2.0%, money growth rises 1.0%, orders are flat, 
and consumer confidence falls by 0.6%. Using the Conference Board’s assigned values, 
these would contribute respectively: 1.0 + 1.0 + 0.5 + 0 to create a numerator of 2.5. 
When divided by four (the number of components) and multiplied by 100, it generates 
an indicator of 62.5 for that month.
Assume that the following month stock prices fall 0.8%, money grows by 0.5%, orders 
pick up 0.5%, and consumer confidence grows 3.5%. Applying the appropriate values, 
the components would add to 0 + 1.0 + 1.0 + 1.0 = 3.0. Divided by the number of com -

ponents and multiplied by 100, this yields an index value of 75. The 20.0% increase in 
the index value means more components of the composite index are rising. Given this 
result, an analyst can be more confident that the higher composite index value actually 
represents broader movements in the economy. In general, a diffusion index does not 
reflect outliers in any component (like a straight arithmetic mean would do) but instead 
tries to capture the overall change common to all components.
5.2 Other Variables Used as Economic Indicators
In addition to this array of measures, public agencies and trade associations provide 
aggregate cyclical measures. These may include surveys of industrialists, bankers, 
labor associations, and households on the state of their finances, level of activity, and 
their confidence in the future. In the United States, for instance, the Federal Reserve 
polls its 12 branches for a qualitative report on business activity and expectations in

their respective regions. It summarizes those findings in what it calls the “Beige Book” 
released every 6 weeks. Also in the United States, the Institute of Supply Management 
(ISM) polls its members to build indexes of manufacturing orders, output, employment, 
pricing, and comparable gauges for services. Over the last decade, so-  called “purchasing 
managers” indexes along the lines of the ISM have been introduced in a wide range of 
countries, including Europe and China. Japan’s industrial organization polls its mem -
bers in a similar way and releases the findings in what is called the “Tankan Report. ” 
These diverse sources multiply within and across economies. Practitioners can use 
these sources to assess whether they confirm or contradict other more broad-  based 
cyclical indicators, giving pause to, or greater confidence in, those earlier conclusions.
Using a statistical technique called “principal components analysis, ” the Federal

Reserve Bank of Chicago computes the Chicago Fed National Activity Index (CFNAI). 
The CFNAI is computed using 85 monthly macroeconomic series. These series cover 
industrial production, personal income, capital utilization, employment by sectors, 
housing starts, retail sales, and so on. Principal components analysis “extracts” the

Economic Indicators 243
underlying trend that is common to most of these variables, thus distilling the essence 
of the US business cycle. Similarly, the Bank of Italy in conjunction with the Centre 
for Economic Policy Research (CEPR) produces the Euro–Coin statistic, which is also 
based on principal component analysis. There are more than one hundred macroeco -
nomic series included in Euro–Coin. The Euro–Coin also includes data derived from 
surveys, interest rates, and other financial variables. Both CFNAI and Euro–Coin are 
freely available online.
EXAMPLE 13   
Economic Indicators
1 Leading, lagging, and coincident indicators are:
A the same worldwide.
B based on historical cyclical observations.
C based on Keynesian and/or Monetarist theory.
2 A diffusion index:
A measures growth.
B reflects the consensus change in economic indicators.
C is roughly analogous to the indexes used to measure industrial 
3 In the morning business news, a financial analyst, Kevin Durbin, learned

that average hourly earnings had increased last month. The most appro -
priate action for Durbin is to:
A call his clients to inform them of a good trading opportunity today.
B examine other leading indicators to see any confirmation of a possible 
turning point for the economy.
C use the news in his research report as a confirmation for his belief that 
the economy has recovered from a recession.
4 The following table shows the trends in various economic indicators in the 
two most recent quarters:
Economic Indicator Trend
Interest rate spread between long-  term government 
bonds and overnight borrowing rateNarrowing
New orders for capital goods Declining
Residential building permits Declining
Employees on non-  agricultural payrolls Turned from rising to 
falling
Manufacturing and trade sales Stable
Average duration of unemployment Small decline
Change in unit labor costs Rising
 Given the information, this economy is most likely  experiencing a:
A continuing recession.
B peak in the business cycle.

C strong recovery out of a trough.
5 The indicator indexes created by various organizations or research 
agencies:

Reading 17 ■ Understanding Business Cycles 244
A include only leading indicators to compute their value.
B are highly reliable signals on the phase of business cycles.
C evolve over time in terms of composition and computation formula.
6 Which one of the following trends in various economic indicators is most  
consistent with a recovery from a recession? 
A A declining inventory-  to- sales ratio and stable industrial production 
index.
B A rising broad stock market index and unit labor costs turning from 
increasing to decreasing.
C A decrease in average weekly initial claims for unemployment insur -
ance and an increase in aggregate real personal income.
B is correct. The recognition of economic indicators is based on empirical 
observations for an economy.
B is correct. The diffusion indexes are constructed to reflect the common trends 
embedded in the movements of all the indicators included in such an index.

B is correct. Financial analysts need to synthesize the information from various 
indicators in order to gather a reliable reading of the economic trends.
B is correct. The first three indicators are leading indicators and all of them are 
indicating an impending recession, which means the economy has reached the 
peak in this cycle. Non-  agricultural payrolls and manufacturing and trade sales 
are coincident indicators. The trends in these two variables further indicate that 
the economy may begin to decline. The trends in the last two indicators—both 
lagging indicators—indicate that the economy may either continue to grow or 
it may be close to a peak. Aggregating the signals given by all three groups of 
economic indicators, it appears the economy may be near the peak of a business 
cycle.
C is correct. The indicator indexes are constantly updated for their composition 
and methodology based on the accumulation of empirical knowledge, and they

can certainly include more than just leading indicators.
C is correct. The improving leading indicator, average weekly initial claims for 
unemployment insurance, and the improving coincident indicator, aggregate 
real personal income, are most consistent with an economic recovery. Even 
though a declining inventory-  to- sales ratio, a lagging indicator, is consistent 
with an early recovery, the coincident indicator, the stable industrial production 
index, does not support that conclusion. Although a rising stock market index 
can signal economic expansion, the lagging indicator, the unit labor costs, has 
peaked, which is more consistent with a recession.

Summary 245
SUMMARY
This reading has summarized business cycle analysis. Among the points made are 
■■Business cycles are a fundamental feature of market economies but their ampli -
tude and length varies considerably.
■■Business cycles have four phases: trough, expansion, peak, and contraction.
■■Keynesian theories focus on fluctuations of aggregate demand (AD). If AD 
shifts left, Keynesians advocate government intervention to restore full employ -
ment and avoid a deflationary spiral. Monetarists argue that the timing of 
government policies is uncertain and it is generally better to let the economy 
find its new equilibrium unassisted, but ensure that the money supply is kept 
growing at an even pace.
■■New Classical and Real Business Cycle (RBC) theories also consider fluctuations 
of aggregate supply (AS). If AS shifts left because of an input price increase or 
right because of a price decrease or technical progress, the economy will grad -

ually converge to its new equilibrium. Government intervention is generally not 
necessary because it may exacerbate the fluctuation or delay the convergence to 
equilibrium. New Keynesians argue that frictions in the economy may prevent 
convergence and government policies may be needed.
■■The demand for factors of production may change in the short run as a result 
of changes in all components of GDP: consumption (e.g., households worry 
about the future, save more, and thus shift AD left), investment (e.g., companies 
expect customers to increase demand and buy new equipment, thus shifting 
AD right; another example is that companies introduce new technologies, thus 
shifting long-  term AS right), government (e.g., fiscal and monetary policies shift 
AD), and net exports (e.g., faster growth in other countries generates higher 
demand for the home country’s products, thus shifting AD, or higher prices of 
imported inputs shift AS left). Any shifts in AD and AS will affect the demand

for the factors of production (capital and labor) that are used to produce the 
new level of GDP .
■■Unemployment has different subcategories. Frictional (people that are not 
working because they are in between jobs); structural (people that are unem -
ployed because they do not have the skills required by the openings or reside 
far away from the jobs); discouraged workers are unemployed people who have 
given up looking for jobs because they do not believe they can find one (they 
are considered outside the labor force in unemployment statistics); and volun -
tarily unemployed are people who do not wish to work, for example because 
they are in school, retired early, or very rich (they are also considered outside 
the labor force in unemployment statistics).
■■There are different types of inflation. Hyperinflation indicates a high (e.g., 100% 
annual) and increasing rate of inflation; deflation indicates a negative inflation

rate (prices decrease); imported inflation is associated with increasing cost of 
inputs that come from abroad; demand inflation is caused by constraints in 
production that prevent companies from making as many goods as the mar -
ket demands (it is sometimes called wartime inflation because in times of war, 
goods tend to be rationed).

Reading 17 ■ Understanding Business Cycles 246
Burns, Wesley Clair, and Arthur F. Mitchell. 1946. Measuring 
Business Cycles . National Bureau of Economic Research.
Christiano, Lawrence J., Martin Eichenbaum, and Charles L. 
Evans. 2005. “Nominal Rigidities and the Dynamic Effects of a 
Shock to Monetary Policy. ” Journal of Political Economy , vol. 
113, no. 1 (February): 1–45. 
Friedman, Milton. 1968. “The Role of Monetary Policy. ” American 
Economic Review , vol. 58, no. 1 (March):1–17.
Greenspan, Alan. 2005. “Remarks on Central Banking. ” Speech 
given at the annual Kansas City Fed symposium in Jackson 
Hole, WY. Available online at http://www.federalreserve.gov/
boarddocs/speeches/2005/20050826/default.htm.
Mankiw, N. Gregory. 1989. “Real Business Cycles: A New 
Keynesian Perspective. ” Journal of Economic Perspectives , vol. 
3, no. 3:79–90. 
McCulley, Paul. 2009. “The Shadow Banking System and Hyman 
Minsky’s Economic Journey. ” In Insights into the Global

Financial Crisis . Edited by Laurence B. Siegel. Charlottesville, 
VA: Research Foundation of CFA Institute.Plosser, Charles I. 1989. “Understanding Real Business Cycles. ” 
Journal of Economic Perspectives , vol. 3, no. 3:51–77. 
Reinhart, Carmen, and Kenneth Rogoff. 2009. This Time Is 
Different: Eight Centuries of Financial Folly . Princeton, NJ: 
Princeton University Press.
Romer, David. 2011. Advanced Macroeconomics , 4th edition. 
Columbus, OH: McGraw-Hill Education.
Siegel, Lawrence Bed. . 2009. Insights into the Global Financial 
Crisis . Charlottesville, VA: Research Foundation of CFA 
Institute.
The Conference Board. 2001. Business Cycle Indicators 
Handbook . New York: The Conference Board (June).
Woodford, Michael. 2009. “Convergence in Macroeconomics: 
Elements of the New Synthesis. ” American Economic Journal: 
Macroeconomics , vol. 1, no. 1 (January): 267–279.■■Economic indicators are statistics on macroeconomic variables that help in

understanding which stage of the business cycle an economy is at. Of particu -
lar importance are the leading indicators, which suggest where the economy is 
likely to be in the near future. No economic indicator is perfect, and many of 
these statistics are subject to periodic revisions.
■■Price levels are affected by real factors and monetary factors. Real factors 
include aggregate supply (an increase in supply leads to lower prices) and 
aggregate demand (an increase in demand leads to higher prices). Monetary 
factors include the supply of money (more money circulating, if the economy 
is in equilibrium, will lead to higher prices) and the velocity of money (higher 
velocity, if the economy is in equilibrium, will lead to higher prices).
■■Inflation is measured by many indexes. Consumer price indexes reflect the 
prices of a basket of goods and services that is typically purchased by a normal 
household. Producer price indexes measure the cost of a basket of raw mate -

rials, intermediate inputs, and finished products. GDP deflators measure the 
price of the basket of goods and services produced within an economy in a 
given year. Core indexes exclude volatile items, such as agricultural products 
and energy, whose prices tend to vary more than other goods.

Practice Problems 247
1 The characteristic business cycle patterns of trough, expansion, peak, and con -
traction are:
A periodic.
B recurrent.
C of similar duration.
2 During the contraction phase of a business cycle, it is most likely  that:
A inflation indicators are stable.
B aggregate economic activity is decreasing.
C investor preference for government securities declines.
3 An economic peak is most  closely associated with:
A accelerating inflation.
B stable unemployment.
C declining capital spending.
4 Based on typical labor utilization patterns across the business cycle, productiv -
ity (output per hours worked) is most likely  to be highest:
A at the peak of a boom.
B into a maturing expansion
C at the bottom of a recession.
5 As the expansion phase of the business cycle advances from early stage to late 
stage, businesses most likely  experience a decrease in: 
A labor costs.
B capital investment.
C availability of qualified workers.

C availability of qualified workers. 
6 An analyst writes in an economic report that the current phase of the business 
cycle is characterized by accelerating inflationary pressures and borrowing by 
companies. The analyst is most likely  referring to the:
A peak of the business cycle.
B contraction phase of the business cycle.
C early expansion phase of the business cycle.
7 In a recession, companies are most likely  to adjust their stock of physical capital 
by:
A selling it at fire sale prices.
B not maintaining equipment.
C quickly canceling orders for new construction equipment.
8 The inventory/sales ratio is most likely  to be rising:
A as a contraction unfolds.
B partially into a recovery.
C near the top of an economic cycle.
9 The Austrian economic school attributes the primary cause of the business 
cycle to:
A misguided government intervention.

Reading 17 ■ Understanding Business Cycles 248
B the creative destruction of technological progress.
C sticky price and wage expectations that exaggerate trends.
10 A decrease in a country’s total imports is most likely  caused by: 
A an increase in the pace of domestic GDP growth. 
B a cyclical downturn in the economies of primary trading partners.
C persistent currency depreciation relative to primary trading partners.
11 Monetarists favor a limited role for the government because they argue:
A government policy responses may lag.
B firms take time to adjust to systemic shocks to the economy.
C resource use is efficient with marginal revenue and cost equal.
12 The discouraged worker category is defined to include people who:
A are overqualified for their job.
B could look for a job but choose not to.
C currently look for work without finding it.
13 According to the Austrian school, the most appropriate government response to 
an economic recession is to:
A allow the market to adjust naturally.

A allow the market to adjust naturally. 
B maintain steady growth in the money supply.
C decrease the market rate of interest below its natural value.
14 A national government responds to a severe recession by funding numerous 
infrastructure projects using deficit spending. Which school of economic 
thought is most  consistent with such action.
A Keynesian
B Monetarist 
C Neoclassical
15 According to Real Business Cycle models, an economic contraction is most 
likely  caused by: 
A sticky wages.
B rising energy prices.
C a contraction in the money supply.
16 The unemployment rate is considered a lagging indicator because:
A new job types must be defined to count their workers.
B multi-  worker households change jobs at a slower pace.
C businesses are slow to hire and fire due to related costs.
17 The category of persons who would be most likely  to be harmed by an increase 
in the rate of inflation is:
A homeowners with fixed 30-  year mortgages.
B retirees relying on a fixed annuity payment.

C workers employed under contracts with escalator clauses.
18 A decrease in both the labor force participation ratio and the unemployment 
rate is most likely  caused by:
A an increase in discouraged workers.
B an increase in underemployed workers. 
C a decrease in voluntarily unemployed persons.

Practice Problems 249
19 The term that describes when inflation declines but nonetheless remains at a 
positive level is:
A deflation.
B stagflation.
C disinflation.
20 During an economic recovery, a lagging unemployment rate is most likely  
attributable to:
A businesses quickly rehiring workers.
B new job seekers entering the labor force.
C underemployed workers transitioning to higher-  paying jobs.
21 The treasury manager of a large company has recently left his position to accept 
a promotion with a competitor six months from now. A statistical employment 
survey conducted now should categorize the status of the former treasury man -
ager as:
A underemployed.
B voluntarily unemployed.
22 Deflation is most likely  to be associated with:
A a shortage of government revenue.
B substantial macroeconomic contraction.
C explicit monetary policy to combat inflation.
23 The least likely  consequence of a period of hyperinflation is the:
A reduced velocity of money.

B increased supply of money.
C possibility of social unrest.
24–25
Exhibit 1   Consumption Baskets and Prices Over Two Months
Date November 2010 December 2010
Goods Quantity Price Quantity Price 
Sugar 70 kg € 0.90 / kg 120 kg € 1.00 / kg
Cotton 60 kg € 0.60 / kg 50 kg € 0.80 / kg
24 Assuming the base period for 2010 consumption is November and the initial 
price index is set at 100, then the inflation rate after calculating the December 
price index as a Laspeyres index is closest  to: 
A 19.2%.
B 36.4%.
C 61.6%.

Reading 17 ■ Understanding Business Cycles 250
25 For the December consumption basket in Exhibit 1, the value of the Paasche 
index is closest  to:
A 116.
B 148.
C 160.
26 A central bank will most likely  allow the economy to self-  correct in periods of: 
A high inflation, fast economic growth, and low unemployment.
B low inflation, slow economic growth, and high unemployment.
C high inflation, slow economic growth, and high unemployment.
27 Disinflation is best described as a: 
A decline in price levels.
B negative inflation rate.
C decline in the inflation rate. 
28 The characteristic of national consumer price indexes which is most  typically 
shared across major economies worldwide is:
A the geographic areas covered in their surveys.
B the weights they place on covered goods and services.
C their use in the determination of macroeconomic policy.
29 Of the following statements regarding the Producer Price Index (PPI), which is 
the least likely ? The PPI:
A can influence the future CPI.

B category weights can vary more widely than analogous CPI terms.
C is used more frequently than CPI as a benchmark for adjusting labor con -
tract payments.
30 The following presents selected commodity price data for July–August 2015: 
July 2015 August 2015
Milk 18 €1.00/L 17 €1.00/L
Orange juice 6 €2.00/L 4 €2.50/L
 Given the consumption basket and prices presented, which type of price index 
will result in the highest calculated inflation rate over a two-  month time period?
A One that uses a current consumption basket
B One that uses a constant consumption basket
C One reflecting substitutions made by consumers over time
31 The inflation rate most likely  relied on to determine public economic policy is:
A core inflation.
B headline inflation.
C index of food and energy prices.
32 What is the most  important effect of labor productivity in a cost-  push inflation 
scenario?

scenario?
A Rising productivity indicates a strong economy and a bias towards inflation.

Practice Problems 251
B The productivity level determines the economy’s status relative to its “natu -
ral rate of unemployment. ”
C As productivity growth proportionately exceeds wage increases, product 
price increases are less likely.
33 Which of the following statements is the best description of the characteristics 
of economic indicators?
A Leading indicators are important because they track the entire economy.
B Lagging indicators in measuring past conditions do not require revisions.
C A combination of leading and coincident indicators can offer effective 
forecasts.
34 A product is part of a price index based on a fixed consumption basket. If, over 
time, the product’s quality improves while its price stays constant, the measured 
inflation rate is most likely :
A unaffected. 
B biased upward.
C biased downward.
35 A price index of goods and services that excludes food and energy is most likely  
used to calculate: 
C headline inflation.

C headline inflation. 
36 When the spread between 10-  year US Treasury yields and the federal funds 
rate narrows and at the same time the prime rate stays unchanged, this mix of 
indicators most likely  forecasts future economic:
A growth.
B decline.
C stability.
37 Which of the following economic developments is most likely  to cause cost-  
push inflation? 
A Industrial capacity utilization rises to a very high level. 
B Labor productivity increases faster than hourly labor costs.
C A shortage of trained workers emerges throughout the economy.
38 An economist expects the following:
■●The decline in the unemployment rate will result in higher revenues for 
home retailers. 
■●A tighter labor market will put upward pressure on wages, compelling home 
retailers to raise prices. 
 Which type of inflation best corresponds to the economist’s expectations?
A Stagflation
B Cost-  push inflation
C Demand-  pull inflation

39 If relative to prior values of their respective indicators, the inventory–sales ratio 
has risen, unit labor cost is stable, and real personal income has decreased, it is 
most likely  that a peak in the business cycle:
A has occurred.
B is just about to occur.

Reading 17 ■ Understanding Business Cycles 252
C will occur sometime into the future.
40 Current economic statistics indicating little change in services inflation, rising 
residential building permits, and increasing average duration of unemployment 
are best interpreted as:
A conflicting evidence about the direction of economy. 
B evidence that a cyclical upturn is expected to occur in the future.
C evidence that a cyclical downturn is expected to occur in the future.
41 When aggregate real personal income, industrial output, and the S&P 500 Index 
all increase in a given period, it is most accurate  to conclude that a cyclical 
upturn is:
A occurring.
B about to end.
C about to begin.
42 Which of the following is most likely  to increase after an increase in aggregate 
real personal income? 
A Equity prices
B Building permits for new private housing units
C The ratio of consumer installment debt to income
43 Which of the following indicators is most  appropriate in predicting a turning

point in the economy? 
A The Industrial Production Index
B The average bank prime lending rate
C Average weekly hours, manufacturing

Solutions 253
SOLUTIONS
1 B is correct. The stages of the business cycle occur repeatedly over time.
2 B is correct. The net trend during contraction is negative.
3 A is correct. Inflation is rising at peaks.
4 C is correct. At the end of a recession, firms will run “lean production” to gen -
erate maximum output with the fewest number of workers.
5 C is correct. When an economy’s expansion is well established, businesses often 
have difficulty finding qualified workers. 
6 A is correct. Accelerating inflation and rapidly expanding capital expenditures 
typically characterize the peak of the business cycle. During such times, many 
businesses finance their capital expenditures with debt to expand their produc -
tion capacity.
7 B is correct. Physical capital adjustments to downturns come through aging of 
equipment plus lack of maintenance.
8 C is correct. Near the top of a cycle, sales begin to slow before production is 
cut, leading to an increase in inventories relative to sales.

9 A is correct. Austrian economists see monetary policy mistakes as leading to 
booms and busts.
10 C is correct. When a nation’s currency depreciates, domestic goods seem 
cheaper than foreign goods, placing downward pressure on demand for 
imports. When the depreciation persists for some time, the country’s total 
imports are likely to decrease. 
11 A is correct. Monetarists caution policy effects can occur long after the need 
for which they were implemented is no longer an issue.
12 B is correct. Discouraged workers are defined as persons who have stopped 
looking for work and are outside the labor force.
13 A is correct. Austrian economists advocate limited government intervention in 
the economy. They advise that the best thing to do in a recession is to allow the 
necessary market adjustment to take place. 
14 A is correct. Keynesian economics is based on government intervention in the 
form of fiscal policy. The national government responds to the recession by

using deficit spending to fund infrastructure projects. 
15 B is correct. Real Business Cycle models conclude that expansions and contrac -
tions of the economy are responses to external shocks, such as supply shocks 
arising from advances in technology or changes in the relative prices of inputs 
(e.g., energy prices). An increase in energy prices shifts short-  run aggregate sup -
ply to the left, resulting in higher prices and lower GDP . 
16 C is correct. This effect makes unemployment rise more slowly as recessions 
start and fall more slowly as recoveries begin.
17 B is correct. With inflation, a fixed amount of money buys fewer goods and 
services, thus reducing purchasing power.
18 A is correct. Discouraged workers have given up seeking employment and are 
statistically outside the labor force. Therefore, an increase in discouraged work -
ers will decrease the labor force and thus the labor participation ratio, which

is the ratio of labor force to total working age population. Additionally, an 
increase in discouraged workers will decrease the unemployment rate because 
discouraged workers are not counted in the official unemployment rate.

Reading 17 ■ Understanding Business Cycles 254
19 C is correct. Disinflation is known as a reduction of inflation from a higher to 
lower, but still above zero, level.
20 B is correct. In an economic recovery, new job seekers return to the labor force, 
and because they seldom find work immediately, their return may initially raise 
the unemployment rate. 
21 C is correct. Frictionally unemployed people are not working at the time of the 
employment survey but have recently left one job and are about to start another 
job. The frictionally unemployed have a job waiting for them and are not 100% 
unemployed, it is just that they have not started the new job yet. Although the 
treasury manager has left his current employment, he has accepted a new posi -
tion at another firm starting in six months.
22 B is correct. Deflation is connected to a vicious cycle of reduced spending and 
higher unemployment.
23 A is correct. In hyperinflation, consumers accelerate their spending to beat

prices increases and money circulates more rapidly.
24 A is correct. The Laspeyres index is calculated with these inputs:
■●November consumption bundle: 70 × 0.9 + 60 × 0.6 = 99
■●December consumption bundle: 70 × 1 + 60 × 0.8 = 118
■●December price index: (118/99) × 100 = 119.19
■●Inflation rate: (119.19/100) – 1 = 0.1919 = 19.19%
25 A is correct. The Paasche index uses the current product mix of consumption 
combined with the variation of prices. So for December, its value is
(120 × 1 + 50 × 0.8)/(120 × 0.9 + 50 × 0.6) = (160/138) × 100 = 115.9
26 C is correct. This scenario is often referred to as stagflation. Here, the econ -
omy is likely to be left to self-  correct because no short-  term economic policy is 
thought to be effective. 
27 C is correct. Disinflation is a decline in the inflation rate—for example, from 7% 
to 4%. 
28 C is correct. Central banks typically use consumer price indexes to monitor 
inflation and evaluate their monetary policies.

29 C is correct. The CPI is typically used for this purpose, while the PPI is more 
closely connected to business contracts.
30 B is correct. The inflation rate calculated by using a constant consumption bas -
ket (the Laspeyres index) is 10%, derived as follows:
 July 2015 consumption basket =  (18 × €1) + (6 × €2) = €30
 August 2015 consumption basket =  (18 × €1) + (6 × €2.5) = €33
 Value of the Laspeyres index ( IL) = (€33/€30) × 100 = €110
 Inflation rate =  (110/100) – 1 = 0.10 = 10% 
 The inflation rate calculated using a current consumption basket (the Paasche 
index) is 8%, derived as follows: 
 July 2015 consumption basket =  (17 × €1) + (4 × €2) = €25
 August 2015 consumption basket =  (17 × €1) + (4 × €2.5) = €27
 Value of the Paasche index ( IP) = (€27/€25) × 100 = €108
 Inflation rate =  (108/100) – 1 = 0.08 = 8%

Solutions 255
 The inflation rate calculated by “chaining” the monthly prices of consumption 
baskets as they change over time (the Fisher index) is derived as follows:
 Value of the Fisher index =  IIPL−  
 Value of the Fisher Index =  ¬¬110 108×  = €108.99 
 Inflation rate =  (108.99/100) – 1 = 0.0899 = 8.99%
31 A is correct. Core inflation is less volatile since it excludes food and energy 
prices and therefore will not be as likely to lead to policy overreactions when 
serving as a target.
32 C is correct. For productivity, or output per hour, the faster that it can grow, the 
further that wages can rise without putting pressure on business costs per unit 
of output.
33 C is correct. While no single indicator is definitive, a mix of them—which can 
be affected by various economic determinants—can offer the strongest signal of 
34 B is correct. As the quality of a product improves, it satisfies people’s needs

and wants better. The measured inflation rate is skewed higher than otherwise 
unless an adjustment is made for the increase in the quality of the good. Even 
if the good’s price had increased over time, the improvements in quality would 
still bias the measured inflation rate upward. 
35 A is correct. A price index of goods and services that excludes food and energy 
is used to calculate core inflation. Policymakers often use core inflation when 
reading the trend in the economy and making economic policies. The reason 
is because policymakers are trying to avoid overreaction to short-  term fluctua -
tions in prices as a result of short-  term changes in supply and demand.
36 B is correct. The narrowing spread of this leading indicator foretells a drop in 
short-  term rates and a fall in economic activity. The prime rate is a lagging indi -
cator and typically moves after the economy turns.
37 C is correct. Cost-  push inflation occurs when rising costs compel businesses to

raise prices generally. A shortage of trained workers leads to wage pressures, 
and even if such shortages impact only certain sectors of the economy, the 
economy overall may experience inflationary pressure.
38 B is correct. Cost-  push inflation refers to the situation in which rising costs, 
usually wages, compel businesses to raise prices.
39 A is correct. Both inventory–sales and unit labor costs are lagging indicators 
that decline somewhat after a peak. Real personal income is a coincident indica -
tor that by its decline shows a slowdown in business activity.
40 B is correct. Rising building permits—a leading indicator—indicates that 
an upturn is expected to occur or continue. Increasing average duration of 
unemployment—a lagging indicator—indicates that a downturn has occurred, 
whereas the lack of any change in services inflation—also a lagging indicator—is 
neither negative nor positive for the direction of the economy. Taken together,

these statistics indicate that a cyclical upturn may be expected to occur. 
41 A is correct. Aggregate real personal income and industrial output are coin -
cident indicators, whereas the S&P 500 is a leading indicator. An increase in 
aggregate personal income and industrial output signals that an expansion is 
occurring, whereas an increase in the S&P 500 signals that an expansion will 
occur or is expected to continue. Taken together, these statistics indicate that a 
cyclical upturn is occurring.

Reading 17 ■ Understanding Business Cycles 256
42 C is correct. Aggregate real personal income is a coincident indicator of the 
business cycle and the ratio of consumer installment debt to income is a lagging 
indicator. Increases in the ratio of consumer installment debt follows increases 
in average aggregate income during the typical business cycle. 
43 C is correct. Leading economic indicators have turning points that usually 
precede those of the overall economy. Average weekly hours, manufacturing is 
a leading economic indicator. The Industrial Production Index is a coincident 
economic indicator, and the average bank prime lending rate is a lagging eco -
nomic indicator.

Economics (2)
This study session begins with monetary and fiscal policy, including their use by 
central banks and governments. Economics in a global context is then introduced. 
Next follows a discussion on the flows of goods and services and physical and finan -
cial capital that occur across national borders. Highlighted in the discussion are the 
relationships between different types of flows and the benefits of trade to trade part -
ners. Finally, given that operations and investments in global markets involve foreign 
exchange (currency) risk, the session concludes with an overview of currency market 
fundamentals. 
Reading 18 Monetary and Fiscal Policy  
by Andrew Clare, PhD, and Stephen Thomas, PhD
Reading 19 International Trade and Capital Flows  
by Usha Nair-  Reichert, PhD, and Daniel Robert Witschi, 
PhD, CFA
Reading 20 Currency Exchange Rates  
by William A. Barker, PhD, CFA, Paul D. McNelis, and 
Jerry NickelsburgECONO mICS
5

5

Monetary and Fiscal Policy
by Andrew Clare, PhD, and Stephen Thomas, PhD
Andrew Clare, PhD, and Stephen Thomas, PhD, are at Cass Business School (United 
Kingdom).
a. compare monetary and fiscal policy;
b. describe functions and definitions of money;
c. explain the money creation process;
d. describe theories of the demand for and supply of money; 
e. describe the Fisher effect;
f. describe roles and objectives of central banks;
g. contrast the costs of expected and unexpected inflation; 
h. describe tools used to implement monetary policy;
i. describe the monetary transmission mechanism;
j. describe qualities of effective central banks;
k. explain the relationships between monetary policy and economic 
growth, inflation, interest, and exchange rates;
l. contrast the use of inflation, interest rate, and exchange rate 
targeting by central banks;
m. determine whether a monetary policy is expansionary or 
contractionary;

n. describe limitations of monetary policy;
o. describe roles and objectives of fiscal policy;
p. describe tools of fiscal policy, including their advantages and 
disadvantages;
q. describe the arguments about whether the size of a national debt 
relative to GDP matters;
18

Reading 18 ■ Monetary and Fiscal Policy 260
r. explain the implementation of fiscal policy and difficulties of 
implementation;
s. determine whether a fiscal policy is expansionary or 
t. explain the interaction of monetary and fiscal policy.
The economic decisions of households can have a significant impact on an economy. 
For example, a decision on the part of households to consume more and to save less 
can lead to an increase in employment, investment, and ultimately profits. Equally, the 
investment decisions made by corporations can have an important impact on the real 
economy and on corporate profits. But individual corporations can rarely affect large 
economies on their own; the decisions of a single household concerning consumption 
will have a negligible impact on the wider economy.
By contrast, the decisions made by governments can have an enormous impact

on even the largest and most developed of economies for two main reasons. First, the 
public sectors of most developed economies normally employ a significant propor -
tion of the population, and they are usually responsible for a significant proportion 
of spending in an economy. Second, governments are also the largest borrowers in 
world debt markets. Exhibit 1 gives some idea of the scale of government borrowing 
and spending.
Exhibit 1   
Panel A. Central Government Debt to GDP , 2009
Total Central Government Debt as % of GDP
225
200
175
150
125
100
75
50
25
0
Japan US Italy Belgium Greece UK Hungary Austria France Portugal1

Introduction 261
Panel B. Public Sector Spending to GDP , 2009
Government Consumption as % of GDP
30
25
20
15
510
0
Japan US Italy Belgium Greece UK Hungary Austria France Portugal
Note : All data are for 2009.
Source : Thomson Financial.
Government policy is ultimately expressed through its borrowing and spending 
activities. In this reading, we identify and discuss two types of government policy that 
can affect the macroeconomy and financial markets: monetary policy and fiscal policy.
Monetary policy  refers to central bank activities that are directed toward influ -
encing the quantity of money and credit in an economy.1 By contrast, fiscal policy  
refers to the government’s decisions about taxation and spending. Both monetary 
and fiscal policies are used to regulate economic activity over time. They can be used 
to accelerate growth when an economy starts to slow or to moderate growth and 
activity when an economy starts to overheat. In addition, fiscal policy can be used to

redistribute income and wealth.
The overarching goal of both monetary and fiscal policy is normally the creation of 
an economic environment where growth is stable and positive and inflation is stable 
and low. Crucially, the aim is therefore to steer the underlying economy so that it does 
not experience economic booms that may be followed by extended periods of low or 
negative growth and high levels of unemployment. In such a stable economic environ -
ment, householders can feel secure in their consumption and saving decisions, while 
corporations can concentrate on their investment decisions, on making their regular 
coupon payments to their bond holders and on making profits for their shareholders.
The challenges to achieving this overarching goal are many. Not only are economies 
frequently buffeted by shocks (such as oil price jumps), but some economists believe 
that natural cycles in the economy also exist. Moreover, there are plenty of examples

from history where government policies—either monetary, fiscal, or both—have 
exacerbated an economic expansion that eventually led to damaging consequences 
for the real economy, for financial markets, and for investors.Exhibit 1   (Continued)  
1 Central banks can implement monetary policy almost completely independent of government interference 
and influence at one end of the scale, or simply as the agent of the government at the other end of the scale.

Reading 18 ■ Monetary and Fiscal Policy 262
The balance of the reading is organized as follows. Section 2 provides an intro -
duction to monetary policy and related topics. Section 3 presents fiscal policy. The 
interactions between monetary policy and fiscal policy are the subject of Section 4. 
MONETARY POLICY
As stated above, monetary policy refers to government or central bank activities that 
are directed toward influencing the quantity of money and credit in an economy. 
Before we can begin to understand how monetary policy is implemented, we must 
examine the functions and role of money . We can then explore the special role that 
central banks  play in today’s economies.
EXAMPLE 1   
1 Which of the following statements best describes monetary policy? 
Monetary policy:
A involves the setting of medium-  term targets for broad money 
aggregates.
B involves the manipulation by a central bank of the government’s bud -

get deficit.
C seeks to influence the macro economy by influencing the quantity of 
money and credit in the economy.
2 Which of the following statements best describes fiscal policy? Fiscal 
policy:
A is used by governments to redistribute wealth and incomes.
B is the attempt by governments to balance their budgets from one year 
to the next.
C involves the use of government spending and taxation to influence 
economy activity.
C is correct. Choice A is incorrect because, although the setting of targets for 
monetary aggregates is a possible tool of monetary policy, monetary policy itself 
is concerned with influencing the overall, or macro, economy.
C is correct. Note that governments may wish to use fiscal policy to redistribute 
incomes and balance their budgets, but the overriding goal of fiscal policy is 
usually to influence a broader range of economic activity.
2.1 Money
To understand the nature, role, and development of money in modern economies,

it is useful to think about a world without money—where to purchase any good or 
service, an individual would have to “pay” with another good or service. An economy 
where such economic agents as households, corporations, and even governments pay 2

Monetary Policy 263
for goods and services in this way is known as a barter economy . There are many 
drawbacks to such an economy. First, the exchange of goods for other goods (or ser -
vices) would require both economic agents in the transaction to want what the other 
is selling. This means that there has to be a double coincidence of wants . It might 
also be impossible to undertake transactions where the goods are indivisible—that 
is, where one agent wishes to buy a certain amount of another’s goods, but that agent 
only has one indivisible unit of another good that is worth more than the good that 
the agent is trying to buy. Another problem occurs if economic agents do not wish to 
exchange all of their goods on other goods and services. This may not be a problem, 
however, when the goods they have to sell can be stored safely so that they retain their 
value for the future. But if these goods are perishable, they will not be able to store

value for their owner. Finally, in a barter economy, there are many measures of value: 
the price of oranges in terms of pears; of pears in terms of bread; of bread in terms 
of milk; or of milk in terms of oranges. A barter economy has no common measure 
of value that would make multiple transactions simple.
2.1.1  The Functions of Money
The most generic definition of money is that it is any generally accepted medium of 
exchange. A medium of exchange  is any asset that can be used to purchase goods 
and services or to repay debts. Money can thus eliminate the debilitating double 
coincidence of the “wants” problem that exists in a barter economy. When this 
medium of exchange exists, a farmer wishing to sell wheat for wine does not need to 
identify a wine producer in search of wheat. Instead, he can sell wheat to those who 
want wheat in exchange for money. The farmer can then exchange this money for 
wine with a wine producer, who in turn can exchange that money for the goods or

services that she wants.
However, for money to act as this liberating medium of exchange, it must possess 
certain qualities. It must:
 i. be readily acceptable,
 ii. have a known value,
 iii. be easily divisible,
 iv. have a high value relative to its weight, and
 v. be difficult to counterfeit.
Qualities (i) and (ii) are closely related; the medium of exchange will only be 
acceptable if it has a known value. If the medium of exchange has quality (iii), then 
it can be used to purchase items of relatively little value and of relatively large value 
with equal ease. Having a high value relative to its weight is a practical convenience, 
meaning that people can carry around sufficient wealth for their transaction needs. 
Finally, if the medium of exchange can be counterfeited easily, then it would soon 
cease to have a value and would not be readily acceptable as a means of effecting 
transactions; in other words, it would not satisfy qualities (i) and (ii).

Given the qualities that money needs to have, it is clear why precious metals 
(particularly gold and silver) often fulfilled the role of medium of exchange in early 
societies, and as recently as the early part of the twentieth century. Precious metals 
were acceptable as a medium of exchange because they had a known value, were easily 
divisible, had a high value relative to their weight, and could not be easily counterfeited.
Thus, precious metals were capable of acting as a medium of exchange. But they 
also fulfilled two other useful functions that are essential for the characteristics of 
money. In a barter economy, it is difficult to store wealth from one year to the next 
when one’s produce is perishable, or indeed, if it requires large warehouses in which 
to store it. Because precious metals like gold had a high value relative to their bulk and 
were not perishable, they could act as a store of wealth . However, their ability to act

Reading 18 ■ Monetary and Fiscal Policy 264
as a store of wealth not only depended on the fact that they did not perish physically 
over time, but also on the belief that others would always value precious metals. The 
value from year to year of precious metals depended on people’s continued demand 
for them in ornaments, jewellery, and so on. For example, people were willing to use 
gold as a store of wealth because they believed that it would remain highly valued. 
However, if gold became less valuable to people relative to other goods and services 
year after year it would not be able to fulfill its role as a store of value , and as such 
might also lose its status as a medium of exchange.
Another important characteristic of money is that it can be used as a universal 
unit of account. As such, it can create a single unitary measure of value  for all 
goods and services. In an economy where gold and silver are the accepted medium

of exchange, all prices, debts, and wealth can be recorded in terms of their gold or 
silver coin exchange value. Money, in its role as a unit of account, drastically reduces 
the number of prices in an economy compared to barter, which requires that prices 
be established for a good in terms of all other goods for which it might be exchanged.
In summary, money fulfills three important functions, it:
■■acts as a medium of exchange;
■■provides individuals with a way of storing wealth; and
■■provides society with a convenient measure of value and unit of account.
2.1.2  Paper Money and the Money Creation Process
Although precious metals like gold and silver fulfilled the required functions of 
money relatively well for many years, and although carrying gold coins around was 
easier than carrying around one’s physical produce, it was not necessarily a safe way 
to conduct business.
A crucial development in the history of money was the promissory note . The

process began when individuals began leaving their excess gold with goldsmiths, 
who would look after it for them. In turn the goldsmiths would give the depositors 
a receipt, stating how much gold they had deposited. Eventually these receipts were 
traded directly for goods and services, rather than there being a physical transfer of 
gold from the goods buyer to the goods seller. Of course, both the buyer and seller 
had to trust the goldsmith because the goldsmith had all the gold and the goldsmith’s 
customers had only pieces of paper. These depository receipts represented a promise to 
pay a certain amount of gold on demand. This paper money therefore became a proxy 
for the precious metals on which they were based, that is, they were directly related to 
a physical commodity. Many of these early goldsmiths evolved into banks, taking in 
excess wealth and in turn issuing promissory notes that could be used in commerce.

In taking in other people’s gold and issuing depository receipts and later prom -
issory notes, it became clear to the goldsmiths and early banks that not all the gold 
that they held in their vaults would be withdrawn at any one time. Individuals were 
willing to buy and sell goods and services with the promissory notes, but the majority 
of the gold that backed the notes just sat in the vaults—although its ownership would 
change with the flow of commerce over time. A certain proportion of the gold that 
was not being withdrawn and used directly for commerce could therefore be lent to 
others at a rate of interest. By doing this, the early banks created money.
The process of money creation  is a crucial concept for understanding the role 
that money plays in an economy. Its potency depends on the amount of money that 
banks keep in reserve to meet the withdrawals of its customers. This practice of lending 
customers’ money to others on the assumption that not all customers will want all of

their money back at any one time is known as fractional reserve banking .

Monetary Policy 265
We can illustrate how it works through a simple example. Suppose that the 
bankers in an economy come to the view that they need to retain only 10 percent of 
any money deposited with them. This is known as the reserve requirement .2 Now 
consider what happens when a customer deposits €100 in the First Bank of Nations. 
This deposit changes the balance sheet of First Bank of Nations, as shown in Exhibit 2, 
and it represents a liability to the bank because it is effectively loaned to the bank by 
the customer. By lending 90 percent of this deposit to another customer the bank has 
two types of assets: (1) the bank’s reserves of €10, and (2) the loan equivalent to €90. 
Notice that the balance sheet still balances; €100 worth of assets and €100 worth of 
liabilities are on the balance sheet.
Now suppose that the recipient of the loan of €90 uses this money to purchase some 
goods of this value and the seller of the goods deposits this €90 in another bank, the

Second Bank of Nations. The Second Bank of Nations goes through the same process; 
it retains €9 in reserve and loans 90 percent of the deposit (€81) to another customer. 
This customer in turn spends €81 on some goods or services. The recipient of this 
money deposits it at the Third Bank of Nations, and so on. This example shows how 
money is created when a bank makes a loan.
Exhibit 2   Money Creation via Fractional Reserve Banking
First Bank of Nations
Assets Liabilities
Reserves €10 Deposits €100
Loans €90
Second Bank of Nations
Reserves €9 Deposits €90
Loans €81
Third Bank of Nations
Reserves €8.1 Deposits €81
Loans €72.9
This process continues until there is no more money left to be deposited and 
loaned out. The total amount of money ‘created’ from this one deposit of €100 can 
be calculated as:
New deposit/Reserve requirement = €100/0.10 = €1,000
It is the sum of all the deposits now in the banking system. You should also note

that the original deposit of €100, via the practice of reserve banking, was the catalyst 
for €1,000 worth of economic transactions. That is not to say that economic growth 
would be zero without this process, but instead that it can be an important component 
in economic activity.(1)
2 This is an example of a voluntary  reserve requirement because it is self-  imposed.

Reading 18 ■ Monetary and Fiscal Policy 266
The amount of money that the banking system creates through the practice of 
fractional reserve banking is a function of 1 divided by the reserve requirement, a 
quantity known as the money multiplier .3 In the case just examined, the money 
multiplier is 1/0.10 = 10. Equation 1 implies that the smaller the reserve requirement, 
the greater the money multiplier effect.
In our simplistic example, we assumed that the banks themselves set their own 
reserve requirements. However, in some economies, the central bank sets the reserve 
requirement, which is a potential means of affecting money growth. In any case, a pru -
dent bank would be wise to have sufficient reserves such that the withdrawal demands 
of their depositors can be met in stressful economic and credit market conditions.
Later, when we discuss central banks and central bank policy, we will see how central 
banks can use the mechanism just described to affect the money supply. Specifically,

the central bank could, by purchasing €100 in government securities credited to the 
bank account of the seller, seek to initiate an increase in the money supply. The central 
bank may also lend reserves directly to banks, creating excess reserves (relative to 
any imposed or self-  imposed reserve requirement) that can support new loans and 
money expansion.
EXAMPLE 2   
Money and Money Creation
1 To fulfill its role as a medium of exchange, money should:
A be a conservative investment.
B have a low value relative to its weight.
C be easily divisible and a good store of value.
2 If the reserve requirement for banks in an economy is 5 percent, how 
much money could be created with the deposit of an additional £100 into 
a deposit account?
A £500
B £1,900
C £2,000
3 Which of the following functions does money normally fulfill for a soci -
ety? It:
A acts as a medium of exchange only.
B provides economic agents with a means of storing wealth only.

C provides society with a unit of account, acts as a medium of exchange, 
and acts as a store of wealth.
C is correct. Money needs to have a known value and be easily divisible. It 
should also be readily acceptable, difficult to counterfeit, and have a high value 
relative to its weight.
3 This quantity, known as the simple money multiplier, represents a maximum expansion. To the extent 
that banks hold excess reserves or that money loaned out is not re-  deposited, the money expansion would 
be less. More complex multipliers incorporating such factors are developed in more advanced texts.

Monetary Policy 267
C is correct. To calculate the increase in money from an additional deposit in the 
banking system, use the following expression: new deposit/reserve requirement.
C is correct. Money needs to be able to fulfill the functions of acting as a unit 
of account, a medium of exchange, and a means of storing wealth.
2.1.3  Definitions of Money
The process of money creation raises a fundamental issue: What is money? In an 
economy with money but without promissory notes and fractional reserve banking, 
money is relatively easy to define: Money is the total amount of gold and silver coins 
in circulation, or their equivalent. The money creation process above, however, indi -
cates that a broader definition of money might encompass all the notes and coins in 
circulation plus all bank deposits.
More generally, we might define money as any medium that can be used to purchase 
goods and services. Notes and coins can be used to fulfill this purpose, and yet such

currency is not the only means of purchasing goods and services. Personal cheques 
can be written based on a bank chequing account, while debit cards can be used for 
the same purpose. But what about time deposits or savings accounts? Nowadays 
transfers can be made relatively easily from a savings account to a current account; 
therefore, these savings accounts might also be considered as part of the stock of 
money. Credit cards are also used to pay for goods and services; however, there is an 
important difference between credit card payments and those made by cheques and 
debit cards. Unlike a cheque or debit card payment, a credit card payment involves 
a deferred payment. Basically, the greater the complexity of any financial system, the 
harder it is to define money.
The monetary authorities in most modern economies produce a range of measures 
of money (see Exhibit 3). But generally speaking, the money stock consists of notes

and coins in circulation, plus the deposits in banks and other financial institutions 
that can be readily used to make purchases of goods and services in the economy. In 
this regard, economists often speak of the rate of growth of narrow money  and/or 
broad money . By narrow money, they generally mean the notes and coins in circula -
tion in an economy, plus other very highly liquid deposits. Broad money encompasses 
narrow money but also includes the entire range of liquid assets that can be used to 
Because financial systems, practice, and institutions vary from economy to econ -
omy, so do definitions of money; thus, it is difficult to make international comparisons. 
Still, most central banks produce both a narrow and broad measure of money, plus 
some intermediate ones too. Exhibit 3 shows the money definitions in four economies.
Exhibit 3   Definitions of Money
Money Measures in the United States

The US Federal Reserve produces two measures of money. The first is M1, which 
comprises notes and coins in circulation, travelers’ cheques of non-  bank issuers, 
demand deposits at commercial banks, plus other deposits on which cheques 
can be written. M2 is the broadest measure of money currently produced by 
the Federal Reserve and includes M1, plus savings and money market deposits, 
time deposit accounts of less than $100,000, plus other balances in retail money 
market and mutual funds.

Reading 18 ■ Monetary and Fiscal Policy 268
Money Measures in the Eurozone
The European Central Bank (ECB) produces three measures of euro area money 
supply. The narrowest is M1. M1 comprises notes and coins in circulation, plus all 
overnight deposits. M2 is a broader definition of euro area money that includes 
M1, plus deposits redeemable with notice up to three months and deposits with 
maturity up to two years. Finally, the euro area’s broadest definition of money is 
M3, which includes M2, plus repurchase agreements, money market fund units, 
and debt securities with up to two years maturity.
Money Measures in Japan
The Bank of Japan calculates three measures of money. M1 is the narrowest 
measure and consists of cash currency in circulation. M2 incorporates M1 but 
also includes certificates of deposit (CDs). The broadest measure, M3, incor -
porates M2, plus deposits held at post offices, plus other savings and deposits

with financial institutions. There is also a “broad measure of liquidity” that 
encompasses M3 as well as a range of other liquid assets, such as government 
bonds and commercial paper.
Money Measures in the United Kingdom
The United Kingdom produces a set of four measures of the money stock. M0 
is the narrowest measure and comprises notes and coins held outside the Bank 
of England, plus Bankers’ deposits at the Bank of England. M2 includes M0, 
plus (effectively) all retail bank deposits. M4 includes M2, plus wholesale bank 
and building society deposits and also certificates of deposit. Finally, the Bank 
of England produces another measure called M3H , which is a measure created 
to be comparable with money definitions in the EU (see above). M3H includes 
M4, plus UK residents’ and corporations’ foreign currency deposits in banks 
and building societies.
2.1.4  The Quantity Theory of Money
The previous section of this reading shows that there are many definitions of money.

In this section, we explore the important relationship between money and the price 
level. This relationship is best expressed in the quantity theory of money , which 
asserts that total spending (in money terms) is proportional to the quantity of money. 
The theory can be explained in terms of Equation 2, known as the quantity equation 
of exchange :
M × V = P × Y
where M is the quantity of money, V is the velocity of circulation of money (the aver -
age number of times in a given period that a unit of currency changes hands), P is the 
average price level, and Y is real output. The expression is really just an accounting 
identity. Effectively, it says that over a given period, the amount of money used to 
purchase all goods and services in an economy, M × V, is equal to monetary value of 
this output, P × Y. If the velocity of money is approximately constant—which is an 
assumption of quantity theory—then spending P × Y is approximately proportional

to M. The quantity equation can also be used to explain a consequence of money 
neutrality . If money neutrality holds, then an increase in the money supply, M, will (2)Exhibit 3   (Continued)

Monetary Policy 269
not affect Y, real output, or the speed with which money changed hands, V, because 
if real output is unaffected, there would be no need for money to change hands more 
rapidly.4 However, it will cause the aggregate price level, P, to rise.
The simple quantity theory gave rise to the equally simple idea that the price level, 
or at least the rate of inflation, could be controlled by manipulating the rate of growth 
of the money supply. Economists who believe this are referred to as monetarists . They 
argue that there is a causal relationship running from money growth to inflation. In 
the past, some governments have tried to apply this logic in their efforts to control 
inflation, most notably and unsuccessfully the United Kingdom’s government in 1979 
(see Example 5). However, it is possible that causality runs the other way—that is, from 
real activity to the money supply. This means that the quantity of money in circulation

is determined by the level of economic activity, rather than vice versa.
2.1.5  The Demand for Money
The amount of wealth that the citizens of an economy choose to hold in the form of 
money—as opposed to bonds or equities—is known as the demand for money. There 
are three basic motives for holding money:
■■transactions-  related;
■■precautionary; and
■■speculative.
Money balances that are held to finance transactions are referred to as transactions 
money balances . The size of the transactions balances will tend to increase with the 
average value of transactions in an economy. Generally speaking, as gross domestic 
product (GDP) grows over time, transactions balances will also tend to grow; however, 
the ratio of transactions balances to GDP remains fairly stable over time.
As the name suggests, precautionary money balances  are held to provide a buf -
fer against unforeseen events that might require money. These balances will tend to

be larger for individuals or organizations that enter into a high level of transactions 
over time. In other words, a precautionary buffer of $100 for a company that regularly 
enters into transactions worth millions of dollars might be considered rather small. 
When we extend this logic to the overall economy, we can see that these precaution -
ary balances will also tend to rise with the volume and value of transactions in the 
economy, and therefore, GDP as well.
Finally, the speculative demand for money  (sometimes called the portfolio 
demand for money ) relates to the demand to hold speculative money balances based 
on the potential opportunities or risks that are inherent in other financial instruments 
(e.g., bonds). Speculative money balances  consist of monies held in anticipation that 
other assets will decline in value. But in choosing to hold speculative money balances 
rather than bonds, investors give up the return that could be earned from the bond or

other financial assets. Therefore, the speculative demand for money will tend to fall as 
the returns available on other financial assets rises. However, it will tend to rise as the 
perceived risk in other financial instruments rises. In equilibrium, individuals will tend 
to increase their holdings of money relative to riskier assets until the marginal benefit 
of having a lower risk portfolio of wealth is equal to the marginal cost of giving up a 
unit of expected return on these riskier assets. In aggregate then, speculative balances 
will tend to be inversely related to the expected return on other financial assets and 
directly related to the perceived risk of other financial assets.
4 Note that the full version of the quantity theory of money uses the symbol T rather than Y to indicate 
transactions because money is used not just for buying goods and services but also for financial transactions. 
We will return to this point in the discussion of quantitative easing.

Reading 18 ■ Monetary and Fiscal Policy 270
EXAMPLE 3   
Money
1 The transactions demand for money refers to the demand to hold money:
A as a buffer against unforeseen events.
B to use in the purchase of goods and services.
C based on the opportunity or risks available on other financial 
instruments.
2 The speculative demand for money will tend to:
A fall as the perceived risk on other assets rises.
B rise as the expected returns on other assets fall.
C be inversely related to the transactions demand for money.
3 What is the difference between narrow and broad money? Broad money:
A is limited to those liquid assets most commonly used to make 
purchases.
B can be used to purchase a wider range of goods and services than nar -
row money.
C encompasses narrow money and refers to the stock of the entire range 
of liquid assets that can be used to make purchases.
B is correct. The transactions demand for money refers to the amount of money

that economic agents wish to hold to pay for goods and services.
B is correct. If the expected return on other assets falls, then the opportunity 
cost of holding money also falls and can, in turn, lead to an increase in the 
speculative demand for money.
C is correct. This is the definition of broad money. Broad money encompasses 
narrow money.
2.1.6  The Supply and Demand for Money
We have now discussed definitions of money, its relationship with the aggregate price 
level, and the demand for it. We now discuss the interaction between the supply of 
and demand for money.
As with most other markets, the supply of money and the demand to hold it will 
interact to produce an equilibrium price for money. In this market, the price of money 
is the nominal interest rate that could be earned by lending it to others. Exhibit 4 
shows the supply and demand curves for money. The vertical scale represents the rate

of interest; the horizontal scale plots the quantity of nominal money in the economy. 
The supply curve (MS) is vertical because we assume that there is a fixed nominal 
amount of money circulating at any one time. The demand curve (MD) is downward 
sloping because as interest rates rise, the speculative demand for money falls. The 
supply and demand for money are both satisfied at an equilibrium interest rate of I0. 
I0 is the rate of interest at which no excess money balances exist.

Monetary Policy 271
Exhibit 4   The Supply and Demand for Money
M1MS
MD
M2 M0
Quantity of MoneyI1
I0
I2Nominal Rate of Interest
To see why I0 is the equilibrium rate of interest where there are no excess money 
balances, consider the following. If the interest rate on bonds were I1 instead of I0, 
there would be excess supply of money ( M0 – M1). Economic agents would seek to 
buy bonds with their excess money balances, which would force the price of bonds up 
and the interest rate back down to I0. Similarly, if bonds offered a rate of interest, I2, 
there would be an excess demand for money ( M2 –M0). Corporations and individuals 
would seek to sell bonds so that individuals could increase their money holdings, 
but in doing so, the price of bonds would fall and the interest rate offered on them 
would rise until it reached I0. Interest rates effectively adjust to bring the market into 
equilibrium (“clear the market”). In this simple example, we have also assumed that

the supply of money and bonds is fixed as economic agents readjust their holdings. In 
practice, this may not be true, but the dynamics of the adjustment process described 
here essentially still hold.
Exhibit 4 also reemphasises the relationship between the supply of money and 
the aggregate price level, which we first encountered when discussing the quantity 
theory of money. Suppose that the central bank increases the supply of money from 
M0 to M2, so that the vertical supply curve shifts to the right. Because the increase 
in the supply of money makes it more plentiful and hence less valuable, its price (the 
interest rate) falls as the price level rises.
This all sounds very simple, but in practice the effects of an increase in the money 
supply are more complex. The initial increase in the money supply will create excess 
supply of cash. People and companies could get rid of the excess by loaning the money

Reading 18 ■ Monetary and Fiscal Policy 272
to others by buying bonds, as implied above, but they might also deposit it in a bank or 
simply use it to buy goods and services. But an economy’s capacity to produce goods 
and services depends on the availability of real things: notably, natural resources, 
capital, and labour—that is, factors of production supplied either directly or indirectly 
by households. Increasing the money supply does not change the availability of these 
real things. Thus, some economists believe that the long-  run impact of an exogenous 
increase in the supply of money is an increase in the aggregate price level.
This phenomenon—whereby an increase in the money supply is thought in the 
long run simply to lead to an increase in the price level while leaving real variables 
like output and employment unaffected—is known as money neutrality . To see 
why in the long run money should have a neutral effect on real things, consider the 
following simple example.

Suppose the government declared today that 1kg would henceforth be referred 
to as 2kg and that 1.5kg would be referred to as 3kg. In other words, suppose that 
they halved the “value” of a kilogram. Would anything real have changed? A 1kg bag 
of sugar would not have changed physically, although it would be relabelled as a 2kg 
bag of sugar. However, there might be some short-  run effects; confused people might 
buy too little sugar, and some people might go on crash diets! But ultimately people 
would adjust. In the long run, the change wouldn’t matter. There is a clear parallel here 
with the theory of money neutrality. Doubling the prices of everything—halving the 
value of a currency—does not change anything real. This is because, like kilograms, 
money is a unit of account. However, halving the value of a currency could affect real 
things in the short run.
There are two points worth making with regard to money neutrality. First, although

the simple kilogram analogy above does suggest that money should not affect real 
things in the long run, as the British economist Keynes said: “ In the long run we are all 
dead !” In practice, it is very difficult for economists to be sure that money neutrality 
holds in the long run. And second, we must assume that monetary authorities do 
believe that the money supply can affect real things in the short run. If they did not, 
then there would be almost no point to monetary policy.
2.1.7  The Fisher Effect
The Fisher effect  is directly related to the concept of money neutrality. Named after 
the economist Irving Fisher, the Fisher effect states that the real rate of interest in an 
economy is stable over time so that changes in nominal interest rates are the result of 
changes in expected inflation. Thus, the nominal interest rate ( Rnom) in an economy 
is the sum of the required real rate of interest ( Rreal) and the expected rate of inflation 
(πe) over any given time horizon:

Rnom = Rreal + πe
According to money neutrality, over the long term the money supply and/or the 
growth rate in money should not affect Rreal but will affect inflation and inflation 
The Fisher effect also demonstrates that embedded in every nominal interest rate 
is an expectation of future inflation. Suppose that 12-  month US government T-  bills 
offered a yield equal to 4 percent over the year. Suppose also that T-  bill investors 
wished to earn a real rate of interest of 2 percent and expected inflation to be 2 percent 
over the next year. In this case, the return of 4 percent would be sufficient to deliver 
the investors’ desired real return of 2  percent (so long as inflation did not exceed 
2  percent). Now suppose that investors changed their view about future inflation 
and instead expected it to equal 3 percent over the next 12 months. To compensate

them for the higher expected inflation, the T-  bill rate would have to rise to 5 percent, 
thereby preserving the required 2 percent real return.(3)

Monetary Policy 273
There is one caveat to this example. Investors can never be sure about future values 
of such economic variables as inflation and real growth. To compensate them for this 
uncertainty, they require a risk premium . The greater the uncertainty, the greater the 
required risk premium. So all nominal interest rates are actually comprised of three 
components:
■■a required real return;
■■a component compensating investors for expected inflation; and
■■a risk premium to compensate them for uncertainty.
EXAMPLE 4   
Interest Rates and the Supply of Money
1 According to the quantity equation of exchange, an increase in the money 
supply can lead to an:
A increase in the aggregate price level, regardless of changes in the 
velocity of circulation of money.
B increase in the aggregate price level as long as the velocity of circu -
lation of money rises sufficiently to offset the increase in the money 
supply.
C increase in the aggregate price level as long as the velocity of circu -

lation of money does not fall sufficiently to offset the increase in the 
money supply and real output is unchanged.
2 The nominal interest rate comprises a real rate of interest:
A plus a risk premium only.
B plus a premium for expected inflation only.
C compensation for both expected inflation and risk.
3 An expansion in the money supply would most likely :
A lead to a decline in nominal interest rates.
B lead to an increase in nominal interest rates.
C reduce the equilibrium amount of money that economic agents would 
wish to hold.
C is correct. If the velocity of circulation of money does not change with an 
increase in the money supply and real output is fixed, then the aggregate price 
level should increase. If the velocity of circulation of money falls sufficiently, or 
if real output rises sufficiently, then the increase in money may have no impact 
on prices.
C is correct. Investors demand a real rate of interest and compensation for

expected inflation and a risk premium to compensate them for uncertainty.
A is correct. Increasing the supply of money, all other things being equal, will 
reduce its “price, ” that is, the interest rate on money balances.

Reading 18 ■ Monetary and Fiscal Policy 274
EXAMPLE 5   
Mrs. Thatcher’s Monetary Experiment
The Background
Over the 1970s, the United Kingdom had one of the worst inflation records of 
any developed economy. Retail price inflation averaged 12.6 percent over that 
decade and peaked at 26.9  percent in August  1975. Over this period, then-  
Prime Minister Margaret Thatcher and her advisers had become convinced 
that inflation could not be controlled by the income and price policies used in 
the United Kingdom in the past. Instead, they believed that inflation could be 
tamed by controlling the rate of growth of the money supply. Mrs. Thatcher’s 
first administration took power in May 1979 with the intention of pursuing a 
monetarist agenda—that is, a macroeconomic policy that would be underpinned 
by targets for money supply growth.
The Medium-  Term Financial Strategy
Targets for monetary growth were set for a definition of the money supply

known as Sterling M3 (£M3), which was to be kept in the range of 7–11 percent 
for the period 1980–1981 and then gradually reduced to within 4–8 percent by 
1983–1984. This set of targets was known as the Medium Term Financial Strategy 
(MTFS). The idea was simple: Control the rate of growth of the money supply, 
and the rate of growth of prices (i.e., inflation) would remain under control too. 
The instrument of control was the Bank of England’s policy interest rate that 
would be set to achieve the desired rate of growth of the money supply. This 
was a macroeconomic policy built, however imperfectly, on an interpretation 
of the quantity theory of money.
The theory was simple, but the practice proved to be less so. Over the first 
two and a half years of the MTFS, £M3 overshot its target by 100 percent. The 
inability of the monetary authorities to control the rate of growth of the broad 
money supply was largely caused by Thatcher’s abolition of exchange controls

in 1979. By abolishing these controls, there was a significant increase in foreign 
exchange business that came into the British banking system, which changed 
the velocity of money and therefore meant that the relationship between broad 
money and nominal incomes had changed fundamentally.5
Despite the inability to control the money supply, in 1983 the Thatcher 
administration reasserted its confidence in the policy and published a further 
set of monetary targets for several years ahead. However, the persistent failure 
to meet these targets, too, eventually led to the abandonment of any type of 
monetary targeting by the summer of 1985.
The experience of the UK monetary authorities over this period emphasizes 
how unstable the relationship between money and the policy interest rate could 
be along with the relationship between money and aggregate demand—partic -
ularly in an economy that is experiencing rapid financial innovation, as the UK

economy was following the abolition of exchange controls and the introduction 
of greater competition within the banking industry.
Today the Bank of England is responsible for the operation and implemen -
tation of monetary policy in the United Kingdom. The trends in money supply 
are watched very carefully, but they are not the subject of targets, per se.
5 See Goodhart (1989) for a discussion.

Monetary Policy 275
2.2 The Roles of Central Banks
Central banks play a number of key roles in modern economies. Generally, a central 
bank is the monopoly supplier of the currency, the banker to the government and the 
bankers’ bank, the lender of last resort, the regulator and supervisor of the payments 
system, the conductor of monetary policy, and the supervisor of the banking system. 
Let us examine these roles in turn.
In its earliest form, money could be exchanged for a pre-  specified precious com -
modity, usually gold, and promissory notes were issued by many private banks. Today, 
however, state-  owned institutions—usually central banks—are designated in law as 
being the monopoly suppliers of a currency. Initially, these monopolists supplied money 
that could be converted into a pre-  specified amount of gold; they adhered to a gold 
standard . For example, up until 1931, bank notes issued by Britain’s central bank, the

Bank of England, could be redeemed at the bank for a pre-  specified amount of gold. 
But Britain, like most other major economies, abandoned this convertibility principle 
in the first half of the twentieth century. Money in all major economies today is not 
convertible by law into anything else, but it is, in law, legal tender . This means that 
it must be accepted when offered in exchange for goods and services. Money that is 
not convertible into any other commodity is known as fiat money . Fiat money derives 
its value via government decree and because people accept it for payment of goods 
and services and for debt repayment.
As long as fiat money is acceptable to everyone as a medium of exchange, and it 
holds its value over time, then it will also be able to serve as a unit of account. However, 
once an economy has moved to a system of fiat money, the role of the supplier of that 
money becomes even more crucial because they could, for example, expand the supply

of this money indefinitely should they wish to do so. Central banks therefore play a 
crucial role in modern economies as the suppliers and guardians of the value of their 
fiat currencies and as institutions charged with the role of maintaining confidence in 
their currencies. As the monopoly suppliers of an economy’s currency, central banks 
are at the centre of economic life. As such, they assume other roles in addition to 
being the suppliers and guardians of the value of their currencies.
Most central banks act as the banker to the government and to other banks. They 
also act as a lender of last resort  to banks. Because the central bank effectively has 
the capacity to print money, it is in the position to be able to supply the funds to banks 
that are facing a damaging shortage. The facts that economic agents know that the 
central bank stands ready to provide the liquidity required by any of the banks under

its jurisdiction and that they trust government bank deposit insurance help to prevent 
bank runs in the first place. However, the recent financial crisis has shown that this 
knowledge is not always sufficient to deter a bank run.
EXAMPLE 6   
The Northern Rock Bank Run
In the latter part of the summer of 2007, the fall in US house prices and the related 
implosion of the US sub-  prime mortgage market became the catalyst for a global 
liquidity crisis. Banks began to hoard cash and refused to lend to other banks 
at anything other than extremely punitive interest rates through the interbank 
market. This caused severe difficulties for a UK mortgage bank, Northern Rock. 
Northern Rock’s mortgage book had expanded rapidly in the preceding years 
as it borrowed aggressively from the money markets. It is now clear that this 
expansion was at the expense of loan quality. The then UK regulatory authority,

Reading 18 ■ Monetary and Fiscal Policy 276
the Financial Services Authority (FSA),6 later reported in 2008 that Northern 
Rock’s lending practices did not pay due regard to either the credit quality of the 
mortgagees or the values of the properties on which the mortgages were secured. 
Being at the worst end of banking practice, and relying heavily on international 
capital markets for its funding, Northern Rock was therefore very susceptible 
to a global reduction in liquidity. As the liquidity crisis took hold, Northern 
Rock found that it could not replace its maturing money market borrowings. 
On 12 September 2007, in desperate need of liquidity, Northern Rock’s board 
approached the UK central bank to ask for the necessary funds.
However, the news of Northern Rock’s perilous liquidity position became 
known by the public and, more pertinently, by Northern Rock’s retail deposi -
tors. On 14 September, having heard the news, queues began to form outside

Northern Rock branches as depositors tried to withdraw their savings. On that 
day, it was estimated that Northern Rock depositors withdrew around £1bn, 
representing 5 percent of Northern Rock’s deposits. Further panic ensued as 
investors in “internet only” Northern Rock accounts could not withdraw their 
money because of the collapse of Northern Rock’s website. A further £1bn was 
withdrawn over the next two days.
Northern Rock’s share price dropped rapidly, as did the share prices of 
other similar UK banks. The crisis therefore threatened to engulf more than 
one bank. To prevent contagion, the Chancellor of the Exchequer announced 
on 17 September that the UK government would guarantee all Northern Rock 
deposits. This announcement was enough to stabilize the situation, and given 
that lending to Northern Rock was now just like lending to the government, 
deposits actually started to rise again.
Eventually Northern Rock was nationalized by the UK government, with

the hope that at some time in the future it could be privatized once its balance 
sheet had been repaired.
Central banks are also often charged by the government to supervise the bank -
ing system, or at least to supervise those banks that they license to accept deposits. 
However, in some countries, this role is undertaken by a separate authority. In other 
countries, the central bank can be jointly responsible with another body for the 
supervision of its banks.
Exhibit 5 lists the banking supervisors in the G-  10 countries; central banks are 
underlined. As the exhibit shows, most but not all bank systems have a single super -
visor, which is not necessarily a central bank. A few countries, such as Germany and 
the United States, have more than one supervisor.
Exhibit 5   Banking Supervision in the G10
Country Institution(s)
Belgium Banking and Finance Commission
Canada Office of the Superintendent of Financial Institutions
France Commission Bancaire

Germany Federal Banking Supervisory Office; Deutsche Bundesbank
Italy Bank of Italy
6 In 2013, the Financial Services Authority was replaced by two new regulatory authorities, the Financial 
Conduct Authority (FCA) and the Prudential Regulation Authority (PRA).

Monetary Policy 277
Japan Financial Services Agency
Netherlands Bank of Netherlands
Sweden Swedish Financial Supervisory Authority
Switzerland Federal Commission
United Kingdom Bank of England
United States Office of the Comptroller of the Currency; Federal Reserve ; 
Federal Deposit Insurance Corporation
The United Kingdom is an interesting case study in this regard. Until May 1997, 
the Bank of England had statutory responsibility for banking supervision in the United 
Kingdom. In May 1997, banking supervision was removed from the Bank of England 
and assigned to a new agency, the Financial Services Authority (FSA). However, the 
removal of responsibility for banking supervision from the central bank was seen by 
some as being a contributory factor in the run on the mortgage bank Northern Rock, 
and generally as a contributory factor in the recent banking crisis. Because of this 
perceived weakness in the separation of the central bank from banking supervision,

the Bank of England regained responsibility for banking supervision and regulation 
in 2013. 
Perhaps the least appreciated role of a central bank is its role in the payments 
system . Central banks are usually asked to oversee, regulate, and set standards for a 
country’s payments system. Every day millions of financial transactions take place in 
a modern economy. For the system to work properly, procedures must be robust and 
standardized. The central bank will usually oversee the payments system and will also 
be responsible for the successful introduction of any new processes. Given the inter -
national nature of finance, the central bank will also be responsible for coordinating 
payments systems internationally with other central banks.
Most central banks will also be responsible for managing their country’s foreign 
currency reserves  and also its gold reserves. With regard to the latter, even though 
countries abandoned the gold standard in the early part of the twentieth century, the

world’s central bankers still hold large quantities of gold. As such, if central banks 
were to decide to sell significant proportions of their gold reserves, it could potentially 
depress gold prices.
Finally, central banks are usually responsible for the operation of a country’s 
monetary policy . This is arguably the highest profile role that these important orga -
nizations assume. Recall that monetary policy refers to central bank activities that are 
directed toward influencing the quantity of money and credit in an economy. As the 
monopoly supplier of a country’s currency, central banks are in the ideal position to 
implement and/or determine monetary policy.
To summarise, central banks assume a range of roles and responsibilities. They 
do not all assume responsibility for the supervision of the banks, but all of the other 
roles listed below are normally assumed by the central bank:
■■Monopoly supplier of the currency;
■■Banker to the government and the bankers’ bank;

■■Lender of last resort;
■■Regulator and supervisor of the payments system;Exhibit 5   (Continued)

Reading 18 ■ Monetary and Fiscal Policy 278
■■Conductor of monetary policy; and
■■Supervisor of the banking system.
2.3 The Objectives of Monetary Policy
Central banks fulfill a variety of important roles, but for what overarching purpose? 
A brief perusal of the websites of the world’s central banks will reveal a wide range 
of explanations of their objectives. Their objectives are clearly related to their roles, 
and so there is frequent mention of objectives related to the stability of the financial 
system and to the payments systems. Some central banks are charged with doing all 
they can to maintain full employment and output. But some also have related but less 
tangible roles, like “maintaining confidence in the financial system, ” or even to “promote 
understanding of the financial sector. ” But there is one overarching objective that most 
seem to acknowledge explicitly, and that is the objective of maintaining price stability .

So although central banks usually have to perform many roles, most specify an 
overarching objective. Exhibit 6 lists what we might call the primary objective(s) of a 
number of central banks, from both developed and developing economies.
Exhibit 6   The Objectives of Central Banks
The Central Bank of Brazil
Its “institutional mission” is to “ensure the stability of the currency’s purchasing 
power and a solid and efficient financial system. ”
The European Central Bank
“[T]o maintain price stability is the primary objective of the Euro system and of 
the single monetary policy for which it is responsible. This is laid down in the 
Treaty on the Functioning of the European Union, Article 127 (1). ”
“Without prejudice to the objective of price stability” , the euro system will also 
“support the general economic policies in the Community with a view to con -
tributing to the achievement of the objectives of the Community. ” These include

a “high level of employment” and “sustainable and non-  inflationary growth. ”
The US Federal Reserve
“The Federal Reserve sets the nation’s monetary policy to promote the objectives 
of maximum employment, stable prices, and moderate long-  term interest rates. ”
The Reserve Bank of Australia
“It is the duty of the Reserve Bank Board, within the limits of its powers, to 
ensure that the monetary and banking policy of the Bank is directed to the 
greatest advantage of the people of Australia and that the powers of the Bank 
... are exercised in such a manner as, in the opinion of the Reserve Bank Board, 
will best contribute to:
a the stability of the currency of Australia;
b the maintenance of full employment in Australia; and
c the economic prosperity and welfare of the people of Australia. ”

Monetary Policy 279
The Bank of Korea
“The primary purpose of the Bank, as prescribed by the Bank of Korea Act of 
1962, is the pursuit of price stability. ”
Source:  Central bank websites found at http://www.bis.org/cbanks.htm.
EXAMPLE 7   
Central Banks
1 A central bank is normally not the:
A lender of last resort.
B banker to the government and banks.
C body that sets tax rates on interest on savings.
2 Which of the following best describes the overarching, long-  run objective 
of most central banks?
A Price stability
B Fast economic growth
C Current account surplus
C is correct. A central bank is normally the lender of last resort and the banker 
to the banks and government, but the determination of all tax rates is normally 
the preserve of the government and is a fiscal policy issue.
A is correct. Central banks normally have a variety of objectives, but the over -
riding one is nearly always price stability.

As we have already discussed, one of the essential features of a monetary system 
is that the medium of exchange should have a relatively stable value from one period 
to the next. Arguably then, the overarching goal of most central banks in maintaining 
price stability is the associated goal of controlling inflation. But before we explore the 
tools central banks use to control inflation, we should first consider the potential costs 
of inflation. In other words, we should ask why it is that central bankers believe that 
it is so important to control a nominal variable.
2.3.1  The Costs of Inflation
Huge efforts have been put into controlling inflation since the major economies 
experienced such high levels of inflation in the 1970s. From the early 1970s then, 
inflation has been seen as a very bad thing. But why? What are the costs of inflation? 
The debate around the “costs” of inflation really centers on the distinction between

expected inflation  and unexpected inflation . Expected inflation is clearly the level 
of inflation that economic agents expect in the future. Unexpected inflation can be 
defined as the level of inflation that we experience that is either below or above that 
which we expected; it is the component of inflation that is a surprise.Exhibit 6   (Continued)

Reading 18 ■ Monetary and Fiscal Policy 280
At a micro level, high inflation means that businesses constantly have to change 
the advertised prices of their goods and services. These are known as menu costs . 
There also exists what economists refer to as “shoe leather” costs of inflation. In times 
of high inflation, people would naturally tend to hold less cash and would therefore 
wear out their shoe leather (or more likely the engines of their cars) in making frequent 
trips to the bank to withdraw cash. But these are relatively old arguments, used to 
demonstrate that inflation is bad. In a modern economy, with the internet and with 
transactions becoming increasingly cashless, these costs associated with inflation will 
be lower today than they may have been in the past.
To demonstrate the potentially more significant costs of inflation, consider the 
following. Imagine a world where inflation is high but where all prices (including

asset prices) in an economy are perfectly indexed to inflation, and that technology 
has eliminated the issues surrounding the menu and shoe leather costs of inflation. 
In such a world, would economic agents care about inflation? Probably not. If the 
average price of goods and services rose by 10 percent, people’s salaries (and all other 
prices) would rise by the same amount, which would therefore make economic agents 
indifferent to the rise in prices.
In practice, however, all prices, wages, salaries, rents, and so forth are not indexed, 
in which case economic agents would certainly need to think about inflation more 
carefully. But what if inflation in this world where prices are no longer perfectly 
indexed is high, but perfectly predictable? In this alternative, imaginary world, eco -
nomic agents would have to think about inflation, but not too hard as long as they 
were capable of calculating the impact of the known inflation rate on all future prices.

So, if everyone knew that inflation was going to be 10 percent over the next year, 
then everyone could bargain for a 10 percent increase in their salaries to accommo -
date this, and companies could plan to put up the prices of their goods and services 
by 10 percent. Actually, in this world, an expectation of 10 percent inflation would 
become a self-  fulfilling prophecy.
However, economic agents would worry about inflation in a world where all prices 
were not indexed and, crucially, where inflation was high and unpredictable. In fact 
this is a crude description the inflationary backdrop in many developed economies 
over the 1970s and 1980s, including the United States, France, the United Kingdom, 
Italy, and Canada.
Arguably it is unexpected inflation  that is most costly. Inflation that is fully antic -
ipated can be factored into wage negotiations and priced into business and financial 
contracts. But when inflation turns out to be higher than is anticipated, then borrowers

benefit at the expense of lenders because the real value of their borrowing declines. 
Conversely, when inflation is lower than is anticipated, lenders benefit at the expense 
of borrowers because the real value of the payment on debts rises. Furthermore, if 
inflation is very uncertain or very volatile, then lenders will ask for a premium to 
compensate them for this uncertainty. As a result, the costs of borrowing will be 
higher than would otherwise have been the case. Higher borrowing costs could in 
turn reduce economic activity, for example, by discouraging investment.
It is also possible that inflation uncertainty  can exacerbate the economic cycle. 
Inflation uncertainty is the degree to which economic agents view future rates of 
inflation as hard to forecast. Take for example the case of an imaginary television 
manufacturer. Suppose one day that the manufacturer looks out at the market for 
televisions and sees that the market price of televisions has risen by 10 percent. Armed

with this information, the manufacturer assumes that there has been an increase in 
demand for televisions or maybe a reduction in supply. So to take advantage of the 
new, higher prices, the manufacturer extends the factory, employs more workers, and 
begins to produce more televisions.

Monetary Policy 281
Having now increased the output of the factory, the manufacturer then attempts 
to sell the extra televisions that the factory has produced. But to its horror, the man -
ufacturer finds out that there is no extra demand for televisions. Instead, the 10 per -
cent rise in television prices was caused by a generalized 10 percent increase in all 
consumer prices across the economy. The manufacturer realizes that it has surplus 
stock, surplus factory capacity, and too many workers. So, it cuts back on production, 
lays off some of the workforce, and realizes that it won’t need to invest in new plant 
or machinery for a long time.
This example emphasizes the potentially destabilizing impact of unexpected 
inflation. It demonstrates how unanticipated inflation can reduce the information 
content of market prices for economic agents. If we scale this example up, it should 
not be too difficult to imagine how unanticipated increases or decreases in the general

price level could help to exacerbate—and in some extreme cases cause—economic 
Over the last two to three decades the consensus among economists has been 
that unanticipated and high levels of inflation can have an impact on real things like 
employment, investment and profits, and therefore that controlling inflation should 
be one of the main goals of macroeconomic policy. In summary:
Expected inflation  can give rise to:
■■menu costs and
■■shoe leather costs.
Unanticipated (unexpected) inflation  can in addition:
■■lead to inequitable transfers of wealth between borrowers and lenders (includ -
ing losses to savings);
■■give rise to risk premia in borrowing rates and the prices of other assets; and
■■reduce the information content of market prices.
2.3.2  Monetary Policy Tools7
Central banks have three primary tools available to them: open market operations, 
the refinancing rate, and reserve requirements.

2.3.2.1  Open Market Operations  One of the most direct ways for a central bank to 
increase or reduce the amount of money in circulation is via open market operations . 
Open market operations involve the purchase and sale of government bonds from and 
to commercial banks and/or designated market makers. For example, when the central 
bank buys government bonds from commercial banks, this increases the reserves of 
private sector banks on the asset side of their balance sheets. If banks then use these 
surplus reserves by increasing lending to corporations and households, then via the 
money multiplier process explained in Section 2.1.2, broad money growth expands. 
Similarly, the central bank can sell government bonds to commercial banks. By doing 
this, the reserves of commercial banks decline, reducing their capacity to make loans 
(i.e., create credit) to households and corporations and thus causing broad money

growth to decline through the money multiplier mechanism. In using open market 
operations, the central bank may target a desired level of commercial bank reserves 
or a desired interest rate for these reserves.
7 Monetary policy tools and operations often vary considerably from economy to economy. We have tried 
to describe the generics of the process here. For a more-  detailed review of monetary operations across the 
world, see Gray and Talbot (2006).

Reading 18 ■ Monetary and Fiscal Policy 282
2.3.2.2  The Central Bank’s Policy Rate  The most obvious expression of a central 
bank’s intentions and views comes via the interest rate it sets. The name of the official 
interest rate  (or official policy rate  or just policy rate ) varies from central bank to 
central bank, but its purpose is to influence short- and long-  term interest rates and 
ultimately real economic activity.
The interest rate that a central bank sets and that it announces publicly is nor -
mally the rate at which it is willing to lend money to the commercial banks (although 
practices do vary from country to country). This policy rate can be achieved by using 
short-  term collateralized lending rates, known as repo rates. For example, if the central 
bank wishes to increase the supply of money, it might buy bonds (usually government 
bonds) from the banks, with an agreement to sell them back at some time in the future.

This transaction is known as a repurchase agreement . Normally, the maturity of repo 
agreements ranges from overnight to two weeks. In effect, this represents a secured 
loan to the banks, and the lender (in this case the central bank) earns the repo rate.
Suppose that a central bank announces an increase in its official interest rate. 
Commercial banks would normally increase their base rates  at the same time. A 
commercial bank’s base rate is the reference rate on which it bases lending rates to 
all other customers. For example, large corporate clients might pay the base rate plus 
1 percent on their borrowing from a bank, while the same bank might lend money to 
a small corporate client at the base rate plus 3 percent. But why would commercial 
banks immediately increase their base or reference rates just because the central bank’s 
refinancing rate had increased?
The answer is that commercial banks would not want to have lent at a rate of interest

that would be lower than they might be charged by the central bank. Effectively, the 
central bank can force commercial banks to borrow from it at this rate because it can 
conduct open market operations that create a shortage of money, forcing the banks to 
sell bonds to it with a pre-  agreed repurchase price (i.e., do a repurchase agreement). 
The repo rate would be such that the central bank earned the official refinancing rate 
on the transactions.
The name of each central bank’s official refinancing rate varies. The Bank of 
England’s refinancing rate is the two-  week repo rate . In other words, the Bank of 
England fixes the rate at which it is willing to lend two-  week money to the banking 
sector. The ECB’s official policy rate is known as the refinancing rate  and defines the 
rate at which it is willing to lend short-  term money to the euro area banking sector.
The corresponding rate in the United States is the discount rate, which is the

rate for member banks borrowing directly from the Federal Reserve System. But the 
most important interest rate used in US monetary policy is the federal funds rate . 
The federal funds rate (or fed funds rate ) is the interbank lending rate on overnight 
borrowings of reserves. The Federal Open Market Committee (FOMC) seeks to 
move this rate to a target level by reducing or adding reserves to the banking system 
by means of open market operations. The level of the rate is reviewed by the FOMC 
at its meetings held every six weeks (although the target can be changed between 
meetings, if necessary).
Through the setting of a policy rate, a central bank can manipulate the amount 
of money in the money markets. Generally speaking, the higher the policy rate, the 
higher the potential penalty that banks will have to pay to the central bank if they 
run short of liquidity, the greater will be their willingness to reduce lending, and the 
more likely that broad money growth will shrink.

2.3.2.3  Reserve Requirements  The third primary way in which central banks can 
limit or increase the supply of money in an economy is via their reserve requirements . 
We have already seen that the money creation process is more powerful the lower 
the percentage reserve requirement of banks. So, a central bank could restrict money 
creation by raising the reserve requirements of banks. However, this policy tool is not

Monetary Policy 283
used much nowadays in developed economies. Indeed, some central banks, such as the 
Bank of England, do not even set minimum reserve requirements for the banks under 
their jurisdiction anymore. Changing reserve requirements frequently is disruptive 
for banks. For example, if a central bank increased the reserve requirements, a bank 
that was short on reserves might have to cease its lending activities until it had built 
up the necessary reserves, because deposits would be unlikely to rise quickly enough 
for the bank to build its reserves in this way. However, reserve requirements are still 
actively used in many developing countries to control lending—for example in China 
and in India—and they remain a potential policy tool for those central banks that do 
not currently use it.
To summarize, central banks can manipulate the money supply in one of three ways:
■■open market operations;
■■its official policy rate and associated actions in the repo market; and

■■manipulation of official reserve requirements.
2.3.3  The Transmission Mechanism
The overarching goal of a central bank is to maintain price stability. We demonstrated 
above how a central bank can manipulate the money supply and growth of the money 
supply. We also indicated how policy rates set and targeted by the central banks are 
usually very short term in nature; often they target overnight interest rates. However, 
most businesses and individuals in the real economy borrow and lend over much 
longer time frames than this. It may not be obvious, then, how changing short-  term 
interest rates can influence the real economy, particularly if money neutrality holds in 
the long run. The fact that central bankers believe that they can affect real economic 
variables, in particular economic growth, by influencing broad money growth suggests 
that they believe that money is not neutral—at least not in the short run.

Exhibit 7 presents a stylized representation of the monetary transmission mecha -
nism . This is the process whereby a central bank’s interest rate gets transmitted through 
the economy and ultimately affects the rate of increase of prices—that is, inflation.
Exhibit 7   A Stylized Representation of the Monetary Transmission Mechanism
Market Rates
Asset Prices Total Demand
Import
PricesDomestic
Inflationary
Pressure
InflationDomestic Demand
Net External Demand
Expectations/
Confidence
Exchange RateOfficial
Rate
Source:  Bank of England.
The implementation of the policy may begin to work through the economy via four 
interrelated channels. Those channels include bank lending rates, asset prices, agents’

Reading 18 ■ Monetary and Fiscal Policy 284
expectations, and exchange rates. First, as described above, the base rates of commercial 
banks and interbank rates should rise in response to the increase in the official rate. 
Banks would, in turn, increase the cost of borrowing for individuals and companies 
over both short- and long-  term horizons. Businesses and consumers would then tend 
to borrow less as interest rates rise. An increase in short-  term interest rates could 
also cause the price of such assets as bonds or the value of capital projects to fall as 
the discount rate for future cash flows rises.
Market participants would then come to the view that higher interest rates will 
lead to slower economic growth, reduced profits, and reduced borrowing to finance 
asset purchases. Exporters’ profits might decline if the rise in interest rates causes the 
country’s exchange rate to appreciate, because this would make domestic exports more

expensive to overseas buyers and dampen demand to purchase them. The fall in asset 
prices as well as an increase in prices would reduce household financial wealth and 
therefore lead to a reduction in consumption growth. Expectations regarding interest 
rates can play a significant role in the economy. Often companies and individuals will 
make investment and purchasing decisions based on their interest rate expectations, 
extrapolated from recent events. If the central bank’s interest rate move is widely 
expected to be followed by other interest rate increases, investors and companies will 
act accordingly. Consumption, borrowing, and asset prices may all decline as a result 
of the revision in expectations.
There is a whole range of interconnected ways in which a rise in the central bank’s 
policy rate can reduce real domestic demand and net external demand (that is, the 
difference between export and import consumption). Weaker total demand would

tend to put downward pressure on the rate of domestic inflation—as would a stronger 
currency, which would reduce the prices of imports. Taken together, these might begin 
to put downward pressure on the overall measure of inflation.
To summarize, the central bank’s policy rate works through the economy via any 
one, and often all, of the following interconnected channels:
■■Short-  term interest rates;
■■Changes in the values of key asset prices;
■■The exchange rate; and
■■The expectations of economic agents.
EXAMPLE 8   
Central Bank Tools
1 Which of the following variables are most likely  to be affected by a change 
in a central bank’s policy rate?
A Asset prices only
B Expectations about future interest rates only
C Both asset prices and expectations about future interest rates
2 Which of the following does a central bank seek to influence directly via 
the setting of its official interest rate?
A Inflation expectations
B Import prices
C Domestic inflation

Monetary Policy 285
C is correct. The price of equities, for example, might be affected by the expec -
tation of future policy interest rate changes. In other words, a rate change may 
be taken as a signal of the future stance of monetary policy—contractionary or 
expansionary.
A is correct. By setting its official interest rate, a central bank could expect to 
have a direct influence on inflation expectations—as well as on other market 
interest rates, asset prices, and the exchange rate (where this is freely floating). 
If it can influence these factors, it might ultimately hope to influence import 
prices (via changes in the exchange rate) and also domestically generated infla -
tion (via its impact on domestic and/or external demand). The problem is that 
the workings of the transmission mechanism—from the official interest rate to 
inflation—are complex and can change over time.
2.3.4  Inflation Targeting

Over the 1990s, a consensus began to build among both central bankers and politicians 
that the best way to control inflation and thereby maintain price stability was to target 
a certain level of inflation and to ensure that this target was met by monitoring a wide 
range of monetary, financial, and real economic variables. Nowadays, inflation-  targeting 
frameworks are the cornerstone of monetary policy and macroeconomic policy in 
many economies. Exhibit 8 shows the growth in the number of inflation-  targeting 
monetary policy regimes over time.
The inflation-  targeting framework that is now commonly practiced was pioneered 
in New Zealand. In 1988, the New Zealand Minister of Finance, Roger Douglas, 
announced that economic policy would focus on bringing inflation down from the 
prevailing level of around 6.0 percent to a target range of 0 to 2 percent. This goal was 
given legal status by the Reserve Bank of New Zealand Act 1989. As part of the Act,

the Reserve Bank of New Zealand (RBNZ) was given the role of pursuing this target. 
The bank was given operational independence ; it was free to set interest rates in 
the way that it thought would best meet the inflation target. Although the RBNZ had 
independent control of monetary policy, it was still accountable to the government 
and was charged with communicating its decisions in a clear and transparent way. 
As Exhibit 8 shows, the New Zealand model was widely copied.
Exhibit 8   The Progressive Adoption of Inflation Targeting by Central Banks
1989 New Zealand
1990 Chile Canada
1991 Israel United Kingdom
1992 Sweden Finland Australia
1995 Spain
1998 Czech Republic South Korea Poland
1999 Mexico Brazil Colombia ECB
2000 South Africa Thailand
2001 Iceland Norway Hungary Peru Philippines
2005 Guatemala Indonesia Romania
2006 Turke y Serbia
2007 Ghana
Note : Spain and Finland later joined the EMU.

Reading 18 ■ Monetary and Fiscal Policy 286
Sources:  For 2001 and earlier, Truman (2003). For 2002 to 2007, Roger (2010).
Although these inflation-  targeting regimes vary a little from economy to economy, 
their success is thought to depend on three key concepts: central bank independence, 
credibility, and transparency.
Central Bank Independence8  In most cases, the central bank that is charged with 
targeting inflation has a degree of independence from its government. This indepen -
dence is thought to be important. It is conceivable that politicians could announce an 
inflation target and direct the central bank to set interest rates accordingly. Indeed, 
this was the process adopted in the United Kingdom between 1994 and 1997. But 
politicians have a constant eye on re-  election and might be tempted, for example, to 
keep rates “too low” in the lead up to an election in the hope that this might help their

re- election prospects. As a consequence, this might lead to higher inflation. Thus, it 
is now widely believed that monetary policy decisions should rest in the hands of an 
organization that is remote from the electoral process. The central bank is the natural 
candidate to be the monopoly supplier of a currency.
However, there are degrees of independence. For example, the head of the central 
bank is nearly always chosen by government officials. The Chairman of the US Federal 
Reserve’s Board of Governors is appointed by the President of the United States of 
America; the Head of the ECB is chosen by the committee of Euro area finance min -
isters; while the Governor of the Bank of England is chosen by the Chancellor of the 
Exchequer. So, in practice, separating control from political influence completely is 
probably an impossible (although a desirable) goal.
There are further degrees of independence. Some central banks are both oper -

ationally and target independent . This means that they not only decide the level 
of interest rates, but they also determine the definition of inflation that they target, 
the rate of inflation that they target, and the horizon over which the target is to be 
achieved. The ECB has independence of this kind. By contrast, other central banks—
including those in New Zealand, Sweden, and the United Kingdom—are tasked to hit 
a definition and level of inflation determined by the government. These central banks 
are therefore only operationally independent.
Credibility  The independence of the central bank and public confidence in it are key 
in the design of an inflation-  targeting regime.
To illustrate the role of credibility, suppose that instead of the central bank, the 
government assumes the role of targeting inflation but the government is heavily 
indebted. Given that higher inflation reduces the real value of debt, the government

would have an incentive to avoid reaching the inflation target or to set a high inflation 
target such that price stability and confidence in the currency could be endangered. 
As a result, few would believe the government was really intent on controlling infla -
tion; thus, the government would lack credibility. Many governments have very large 
levels of debt, especially since the 2008–2009 global financial crisis. In such a situa -
tion, economic agents might expect a high level of inflation, regardless of the actual, 
stated target. The target might have little credibility if the organization’s likelihood 
of sticking to it is in doubt.Exhibit 8   (Continued)
8 For information about the degree of independence of any central bank, the roles that it assumes in an 
economy, and the framework in which it operates, analysts should go to a central bank’s website. A list of 
central bank websites can be found at http://www.bis.org/cbanks.htm.

Monetary Policy 287
If a respected central bank assumes the inflation-  targeting role and if economic 
agents believe that the central bank will hit its target, the belief itself could become 
self-  fulfilling. If everyone believes that the central bank will hit an inflation target of 
2 percent next year, this expectation might be built into wage claims and other nominal 
contracts that would make it hit the 2 percent target. It is for this reason that central 
bankers pay a great deal of attention to inflation expectations. If these expectations 
were to rise rapidly, perhaps following a rapid increase in oil prices, unchecked expec -
tations could get embedded into wage claims and eventually cause inflation to rise.
Transparency  One way of establishing credibility is for a central bank to be transparent 
in its decision making. Many, if not all, independent inflation-  targeting central banks 
produce a quarterly assessment of their economies. These Inflation Reports , as they

are usually known, give central banks’ views on the range of indicators that they watch 
when they come to their (usually) monthly interest rate decision. They will consider 
and outline their views on the following subjects, usually in this order:
■■Broad money aggregates and credit conditions;
■■Conditions in financial markets;
■■Developments in the real economy (e.g., the labour market); and
■■Evolution of prices.
Consideration of all of these important components of an economy is then usually 
followed by a forecast of growth and inflation over a medium-  term horizon, usually 
two years.
By explaining their views on the economy and by being transparent in decision 
making, the independent, inflation-  targeting central banks seek to gain reputation and 
credibility, making it easier to influence inflation expectations and hence ultimately 
easier to meet the inflation target.
The Target  Whether the target is set by the central bank or by the government for

the central bank to hit, the level of the target and the horizon over which the target is 
to be hit is a crucial consideration in all inflation-  targeting frameworks.
Exhibit 9   A Range of Inflation Targets
Country/Region
Australia Australian Federal Reserve’s target is inflation between 2.0% 
and 3.0%.
Canada Bank of Canada’s target is CPI inflation within 1.0% and 3.0%.
Euro-  area ECB’s target is CPI inflation below a ceiling of 2%.
South Korea Bank of Korea’s target for 2010–2012 is CPI inflation within 
±1.0 percentage of 3.0%.
New Zealand Reserve Bank of New Zealand’s target is inflation between 1.0% 
and 3.0%.
Sweden Riksbank’s target is CPI inflation within ±1.0 percentage point 
of 2.0%.
United Kingdom Bank of England’s target is CPI inflation within ±1.0 percent -
age point of 2.0%.
Source:  Central bank websites (http://www.bis.org/cbanks.htm).

Reading 18 ■ Monetary and Fiscal Policy 288
Exhibit 9 shows that many central banks in developed economies target an infla -
tion rate of 2  percent based on a consumer price index. Given that the operation 
of monetary policy is both art and science, the banks are normally allowed a range 
around the central target of +1 percent or –1 percent. For example, with a 2 percent 
target, they would be tasked to keep inflation between 1 percent and 3 percent. But 
why target 2 percent and not 0 percent?
The answer is that aiming to hit 0  percent could result in negative inflation, 
known as deflation . One of the limitations of monetary policy that we discuss below 
is its ability or inability to deal with periods of deflation. If deflation is something to 
be avoided, why not target 10 percent? The answer to this question is that levels of 
inflation that high would not be consistent with price stability; such a high inflation

rate would further tend to be associated with high inflation volatility and uncertainty. 
Central bankers seem to agree that 2 percent is far enough away from the risks of 
deflation and low enough not to lead to destabilizing inflation shocks.
Finally, we should keep in mind that the headline inflation rate that is announced 
in most economies every month, and which is the central bank’s target, is a mea -
sure of how much a basket of goods and services has risen over the previous twelve 
months. It is history. Furthermore, interest rate changes made today will take some 
time to have their full effect on the real economy as they make their way through the 
monetary transmission mechanism. It is for these two reasons that inflation targeters 
do not target current inflation but instead usually focus on inflation two years ahead.
Although inflation-  targeting mandates may vary from country to country, they have

common elements: the specification of an explicit inflation target, with permissible 
bounds, and a requirement that the central bank should be transparent in its objectives 
and policy actions. This is all usually laid out in legislation that imposes statutory 
obligations on the central bank. As mentioned earlier, New Zealand pioneered the 
inflation-  targeting approach to monetary policy that has since been copied widely. 
Below is New Zealand’s Policy Targets Agreement, which specifies the inflation-  
targeting mandate of its central bank, the Reserve Bank of New Zealand.
Exhibit 10   New Zealand’s Policy Targets Agreement
“This agreement between the Minister of Finance and the Governor of the Reserve 
Bank of New Zealand (the Bank) is made under section 9 of the Reserve Bank of 
New Zealand Act 1989 (the Act). The Minister and the Governor agree as follows:
1 Price stability
a Under Section 8 of the Act the Reserve Bank is required to conduct

monetary policy with the goal of maintaining a stable general level of 
prices.
b The Government’s economic objective is to promote a growing, open 
and competitive economy as the best means of delivering permanently 
higher incomes and living standards for New Zealanders. Price stabil -
ity plays an important part in supporting this objective.
2 Policy target
a In pursuing the objective of a stable general level of prices, the Bank 
shall monitor prices as measured by a range of price indexes. The price 
stability target will be defined in terms of the All Groups Consumers 
Price Index (CPI), as published by Statistics New Zealand.
b For the purpose of this agreement, the policy target shall be to keep 
future CPI inflation outcomes between 1 per cent and 3 per cent on 
average over the medium term.
3 Inflation variations around target

Monetary Policy 289
a For a variety of reasons, the actual annual rate of CPI inflation will 
vary around the medium-  term trend of inflation, which is the focus 
of the policy target. Amongst these reasons, there is a range of events 
whose impact would normally be temporary. Such events include, for 
example, shifts in the aggregate price level as a result of exceptional 
movements in the prices of commodities traded in world markets, 
changes in indirect taxes,9 significant government policy changes that 
directly affect prices, or a natural disaster affecting a major part of the 
economy.
b When disturbances of the kind described in clause 3(a) arise, the Bank 
will respond consistent with meeting its medium-  term target.
4 Communication, implementation and accountability
a On occasions when the annual rate of inflation is outside the medium-  
term target range, or when such occasions are projected, the Bank 
shall explain in Policy Statements made under section 15 of the Act

why such outcomes have occurred, or are projected to occur, and what 
measures it has taken, or proposes to take, to ensure that inflation 
outcomes remain consistent with the medium-  term target.
b In pursuing its price stability objective, the Bank shall implement 
monetary policy in a sustainable, consistent and transparent manner 
and shall seek to avoid unnecessary instability in output, interest rates 
and the exchange rate.
c The Bank shall be fully accountable for its judgments and actions in 
implementing monetary policy. ”
Source:  http://www.rbnz.govt.nz/.
To summarize, an inflation-  targeting framework normally has the following set 
of features:
■■An independent and credible central bank;
■■A commitment to transparency;
■■A decision-  making framework that considers a wide range of economic and 
financial market indicators; and
■■A clear, symmetric and forward-  looking medium-  term inflation target, suffi -

ciently above 0 percent to avoid the risk of deflation but low enough to ensure a 
significant degree of price stability.
Indeed, independence, credibility, and transparency are arguably the crucial ingre -
dients for an effective central bank, whether they target inflation or not.
The Main Exceptions to the Inflation-  Targeting Rule  Although the practice of inflation 
targeting is widespread, there are two prominent central banks that have not adopted 
a formal inflation target along the lines of the New Zealand model: the Bank of Japan 
and the US Federal Reserve System.Exhibit 10   (Continued)
9 “Indirect taxes” refer to such taxes as sales taxes and value-  added taxes that are levied on goods and 
services rather than directly on individuals and companies.

Reading 18 ■ Monetary and Fiscal Policy 290
The Bank of Japan
Japan’s central bank, the Bank of Japan (BoJ), does not target an explicit mea -
sure of inflation. Japan’s government and its monetary authorities have been 
trying to combat deflation for much of the last two decades. However, despite 
their efforts—including the outright printing of money—inflation has remained 
very weak. Inflation targeting is seen very much as a way of combating and con -
trolling inflation; as such, it would seem to have no place in an economy that 
suffers from persistent deflation.
Some economists have argued, however, that an inflation target is exactly 
what the Japanese economy needs. By announcing that positive inflation of 
say 3 percent is desired by the central bank, this might become a self-  fulfilling 
prophecy if Japanese consumers and companies factor this target into nominal 
wage and price contracts. But for economic agents to believe that the target will

be achieved, they have to believe that the central bank is capable of achieving 
it. Given that the BoJ has failed to engineer persistent, positive inflation, it is 
debatable how much credibility Japanese households and corporations would 
afford such an inflation-  targeting policy.
The US Federal Reserve System
It is perhaps rather ironic that the world’s most influential central bank, the 
US Federal Reserve, which controls the supply of the world’s de facto reserve 
currency, the US dollar, does not have an explicit inflation target. However, it 
is felt that the single-  minded pursuit of inflation might not be compatible with 
the Fed’s statutory goal as laid out in the Federal Reserve Act, which charges the 
Fed’s board to:
“promote effectively the goals of maximum employment, stable prices, and 
moderate long-  term interest rates. ”
In other words, it has been argued that inflation targeting might compromise 
the goal of “maximum employment. ” In practice, however, the Fed has indicated

that it sees core inflation measured by the personal consumption expenditure 
(PCE) deflator of about, or just below, 2 percent as being compatible with 
“stable prices. ” Financial markets therefore watch this US inflation gauge very 
carefully in order to try and anticipate the rate actions of the Fed.
Monetary Policy in Developing Countries  Developing economies often face significant 
impediments to the successful operation of any monetary policy—that is, the achieve -
ment of price stability. These include:
■■the absence of a sufficiently liquid government bond market and developed 
interbank market through which monetary policy can be conducted;
■■a rapidly changing economy, making it difficult to understand what the neutral 
rate might be and what the equilibrium relationship between monetary aggre -
gates and the real economy might be;
■■rapid financial innovation that frequently changes the definition of the money 
supply;

supply;
■■a poor track record in controlling inflation in the past, making monetary policy 
intentions less credible; and
■■an unwillingness of governments to grant genuine independence to the central 
bank.

Monetary Policy 291
Taken together, any or all of these impediments might call into question the effective -
ness of any developing economy’s monetary policy framework, making any related 
monetary policy goals difficult to achieve.
EXAMPLE 9   
Central Bank Effectiveness
1 The reason some inflation-  targeting banks may target low inflation 
and not 0 percent inflation is best described by which of the following 
A Some inflation is viewed as being good for an economy.
B Targeting zero percent inflation runs a higher risk of a deflationary 
outcome.
C It is very difficult to eliminate all inflation from a modern economy.
2 The degree of credibility that a central bank is afforded by economic 
agents is important because:
A they are the lender of last resort.
B their targets can become self-  fulfilling prophecies.
C they are the monopolistic suppliers of the currency.
B is correct. Inflation targeting is art, not science. Sometimes inflation will be

above target and sometimes below. Were central banks to target zero percent, then 
inflation would almost certainly be negative on some occasions. If a deflationary 
mindset then sets in among economic agents, it might be difficult for the central 
bank to respond to this because they cannot cut interest rates much below zero.
B is correct. If a central bank operates within an inflation-  targeting regime and 
if economic agents believe that it will achieve its target, this expectation will 
become embedded into wage negotiations, for example, and become a self-  
fulfilling prophecy. Also, banks need to be confident that the central bank will 
lend them money when all other sources are closed to them; otherwise, they 
might curtail their lending drastically, leading to a commensurate reduction in 
money and economic activity.
2.3.5  Exchange Rate Targeting
Many developing economies choose to operate monetary policy by targeting their

currency’s exchange rate, rather than an explicit level of domestic inflation. Such 
targeting involves setting a fixed level or band of values for the exchange rate against a 
major currency, with the central bank supporting the target by buying and selling the 
national currency in foreign exchange markets. There are recent examples of developed 
economies using such an approach. In the 1980s, following the failure of its policy of 
trying to control UK inflation by setting medium-  term goals for money supply growth 
(see Example 5), the UK government decided to operate monetary policy such that 
the sterling’s exchange rate equalled a pre-  determined value in terms of German 
deutschemarks. The basic idea is that by tying a domestic economy’s currency to that 
of an economy with a good track record on inflation, the domestic economy would 
effectively “import” the inflation experience of the low inflation economy.

Reading 18 ■ Monetary and Fiscal Policy 292
Suppose that a developing country wished to maintain the value of its currency 
against the US dollar. The government and/or central bank would announce the cur -
rency exchange rate that they wished to target. To simplify matters, let us assume that 
the domestic inflation rates are very similar in both countries and that the monetary 
authorities of the developing economy have set an exchange rate target that is consis -
tent with relative price levels in the two economies. Under these (admittedly unlikely) 
circumstances, in the absence of shocks, there would be no reason for the exchange 
rate to deviate significantly from this target level. So as long as domestic inflation 
closely mirrors US inflation, the exchange rate should remain close to its target (or 
within a target band). It is in this sense that a successful exchange rate policy imports 
the inflation of the foreign economy.

Now suppose that economic activity in the developing economy starts to rise 
rapidly and that domestic inflation in the developing economy rises above the level 
in the United States. With a freely floating exchange rate regime, the currency of the 
developing economy would start to fall against the dollar. To arrest this fall, and to 
protect the exchange rate target, the developing economy’s monetary authority sells 
foreign currency reserves and buys its own currency. This has the effect of reducing 
the domestic money supply and increasing short-  term interest rates. The developing 
economy experiences a monetary policy tightening which, if expected to bring down 
inflation, will cause its exchange rate to rise against the dollar.
By contrast, in a scenario in which inflation in the developing country fell relative 
to the United States, the central bank would need to sell the domestic currency to

support the target, tending to increase the domestic money supply and reduce the 
rate of interest.
In practice, the interventions of the developing economy central bank will simply 
stabilize the value of its currency, with many frequent adjustments. But this simplis -
tic example should demonstrate one very important fact: When the central bank or 
monetary authority chooses to target an exchange rate, interest rates and conditions 
in the domestic economy must adapt to accommodate this target and domestic interest 
rates and money supply can become more volatile.
The monetary authority’s commitment to and ability to support the exchange rate 
target must be credible for exchange rate targeting to be successful. If that is not the 
case, then speculators may trade against the monetary authority. Speculative attacks 
forced sterling out of the European Exchange Rate Mechanism in 1992. The fixed 
exchange rate regime was abandoned and the United Kingdom allowed its currency to

float freely. Eventually, the UK government adopted a formal inflation target in 1997. 
Similarly, in the Asian financial crisis of 1997–1998, Thailand’s central bank tried to 
defend the Thai baht against speculative attacks for much of the first half of 1997 but 
then revealed at the beginning of July that it had no reserves left. The subsequent 
devaluation triggered a debt crisis for banks and companies that had borrowed in 
foreign currency, and contagion spread throughout Asia.
Despite these risks, many currencies are pegged to other currencies, most notably 
the US dollar. Exhibit 11 shows a list of some of the currencies that were pegged to 
(fixed against) the US dollar at the end of 2009. Other currencies operate under a 
“managed exchange rate policy, ” where they are allowed to fluctuate within a range 
that is maintained by a monetary authority via market intervention.
Exhibit 11   Select Currencies Pegged to the US Dollar, as of December 2009

■■The Netherlands Antilles ■■Hong Kong SAR
■■Jordan ■■Lebanon
■■Barbados ■■Saudi Arabia
■■Maldives ■■Oman

Monetary Policy 293
■■Belize ■■Qatar
■■The Bahamas
EXAMPLE 10   
Exchange Rate Targeting
1 When the central bank chooses to target a specific value for its exchange 
rate:
A it must also target domestic inflation.
B it must also set targets for broad money growth.
C conditions in the domestic economy must adapt to accommodate this 
target.
2 With regard to monetary policy, what is the hoped for benefit of adopting 
an exchange rate target?
A Freedom to pursue redistributive fiscal policy
B Freedom to set interest rates according to domestic conditions
C To “import” the inflation experience of the economy whose currency is 
being targeted
3 Which of the following is least  likely to be an impediment to the success -
ful implementation of monetary policy in developing economies?
A Fiscal deficits
B Rapid financial innovation
C Absence of a liquid government bond market
C is correct. The adoption of an exchange rate target requires that the central

bank set interest rates to achieve this target. If the target comes under pressure, 
domestic interest rates may have to rise, regardless of domestic conditions. It 
may have a “target” level of inflation in mind as well as “targets” for broad money 
growth, but as long as it targets the exchange rate, domestic inflation and broad 
money trends must simply be allowed to evolve.
C is correct. Note that interest rates have to be set to achieve this target and 
are therefore subordinate to the exchange rate target and partially dependent 
on economic conditions in the foreign economy.
A is correct. Note that the absence of a liquid government bond market through 
which a central bank can enact open market operations and/or repo transactions 
will inhibit the implementation of monetary policy—as would rapid financial 
innovation because such innovation can change the relationship between money Exhibit 11   (Continued)

Reading 18 ■ Monetary and Fiscal Policy 294
and economic activity. Fiscal deficits, on the other hand, are not normally an 
impediment to the implementation of monetary policy, although they could be 
if they were perceived to be unsustainable.
2.4 Contractionary and Expansionary Monetary Policies and 
the Neutral Rate
Most central banks will adjust liquidity conditions by adjusting their official policy 
rate.10 When they believe that economic activity is likely to lead to an increase in 
inflation, they might increase interest rates, thereby reducing liquidity. In these cases, 
market analysts describe such actions as contractionary  because the policy is designed 
to cause the rate of growth of the money supply and the real economy to contract 
(see Exhibit 7 for the possible transmission mechanism here). Conversely, when the 
economy is slowing and inflation and monetary trends are weakening, central banks 
may increase liquidity by cutting their target rate. In these circumstances, monetary

policy is said to be expansionary .
Thus, when policy rates are high, monetary policy may be described as contrac -
tionary; when low, they may be described as expansionary. But what are they “high” 
and “low” in comparison to?
The neutral rate of interest  is often taken as the point of comparison. One way 
of characterizing the neutral rate is to say that it is that rate of interest that neither 
spurs on nor slows down the underlying economy. As such, when policy rates are 
above the neutral rate, monetary policy is contractionary; when they are below the 
neutral rate, monetary policy is expansionary. The neutral rate should correspond to 
the average policy rate over a business cycle.
However, economists’ views of the neutral rate for any given economy might differ, 
and therefore, their view of whether monetary policy is contractionary, neutral, or 
expansionary might differ too. What economists do agree on is that the neutral policy 
rate for any economy comprises two components:

■■Real trend rate of growth of the underlying economy, and
■■Long-  run expected inflation.
The real trend rate of growth of an economy is also difficult to discern, but it 
corresponds to that rate of economic growth that is achievable in the long run that 
gives rise to stable inflation. If we are thinking about an economy with a credible 
inflation-  targeting regime, where the inflation target is say 2 percent per year and 
where an analyst believes that the economy can grow sustainably over the long term 
at a rate of 2.5 percent per year, then they might also estimate the neutral rate to be:
Neutral rate = Trend growth + Inflation target = 2.5% + 2% = 4.5%
The analyst would therefore describe the central bank’s monetary policy as being 
contractionary when its policy rate is above 4.5 percent and expansionary when it is 
below this level.
In practice, central banks often indicate what they believe to be the neutral rate

of interest for their economy too. But determining this “neutral rate” is more art than 
science. For example, many analysts have recently revised down their estimates of 
trend growth for many western countries following the collapse of the credit bubble, 
because in many cases, the governments and private individuals of these economies 
are now being forced to reduce consumption levels and pay down their debts.(4)
10 Although, if they have reduced their policy rate to 0 percent, to increase liquidity further they have to 
resort to less-  conventional monetary policy measures.

Monetary Policy 295
What’s the Source of the Shock to the Inflation Rate?
An important aspect of monetary policy for those charged with its conduct is the 
determination of the source of any shock to the inflation rate. Suppose that the mon -
etary authority sees that inflation is rising beyond its target, or simply in a way that 
threatens price stability. If this rise was caused by an increase in the confidence of 
consumers and business leaders, which in turn has led to increases in consumption 
and investment growth rates, then we could think of it as being a demand shock . In 
this instance, it might be appropriate to tighten monetary policy in order to bring the 
inflationary pressures generated by these domestic demand pressures under control.
However, suppose instead that the rise in inflation was caused by a rise in the price 
of oil (for the sake of argument). In this case, the economy is facing a supply shock ,

and raising interest rates might make a bad situation worse. Consumers are already 
facing an increase in the cost of fuel prices that might cause profits and consumption 
to fall and eventually unemployment to rise. Putting up interest rates in this instance 
might simply exacerbate the oil price-  induced downturn, which might ultimately 
cause inflation to fall sharply.
It is important, then, for the monetary authority to try to identify the source of the 
shock before engineering a contractionary or expansionary monetary policy phase.
2.5 Limitations of Monetary Policy
The limitations of monetary policy include problems in the transmission mechanism 
and the relative ineffectiveness of interest rate adjustment as a policy tool in defla -
tionary environments.
2.5.1  Problems in the Monetary Transmission Mechanism
In Exhibit 7, we presented a stylized representation of the monetary policy transmission 
mechanism, including the channels of bank lending rates, asset prices, expectations,

and exchange rates. The implication of the diagram is that there are channels through 
which the actions of the central bank or monetary authority are transmitted to both 
the nominal and real economy. However, there may be some occasions when the will 
of the monetary authority is not transmitted seamlessly through the economy.
Suppose that a central bank raises interest rates because it is concerned about the 
strength of underlying inflationary pressures. Long-  term interest rates are influenced 
by the path of expected short-  term interest rates, so the outcome of the rate hike 
will depend on market expectations. Suppose that bond market participants think 
that short-  term rates are already too high, that the monetary authorities are risking 
a recession, and that the central bank will likely undershoot its inflation target. This 
fall in inflation expectations could cause long-  term interest rates to fall. That would

make long-  term borrowing cheaper for companies and households, which could in 
turn stimulate economic activity rather than cause it to contract.
Arguably, the more credible the monetary authority, the more stable the long end 
of the yield curve; moreover, the monetary authority will be more confident that its 
“policy message” will be transmitted throughout the economy. A term recently used 
in the marketplace is bond market vigilantes . These “vigilantes” are bond market 
participants who might reduce their demand for long-  term bonds, thus pushing up 
their yields, if they believe that the monetary authority is losing its grip on infla -
tion. That yield increase could act as a brake on any loose monetary policy stance. 
Conversely, the vigilantes may push long-  term rates down by increasing their demand 
for long-  dated government bonds if they expect that tight monetary policy is likely 
to cause a sharp slowdown in the economy, thereby loosening monetary conditions

Reading 18 ■ Monetary and Fiscal Policy 296
A credible monetary policy framework and authority will tend not to require the 
vigilantes to do the work for it.
In very extreme instances, there may be occasions where the demand for money 
becomes infinitely elastic—that is, where the demand curve is horizontal and individ -
uals are willing to hold additional money balances without any change in the interest 
rate—so that further injections of money into the economy will not serve to further 
lower interest rates or affect real activity. This is known as a liquidity trap . In this 
extreme circumstance, monetary policy can become completely ineffective. The eco -
nomic conditions for a liquidity trap are associated with the phenomenon of deflation .
2.5.2  Interest Rate Adjustment in a Deflationary Environment and Quantitative Easing 
as a Response
Deflation is a pervasive and persistent fall in a general price index and is more difficult

for conventional monetary policy to deal with than inflation. This is because cutting 
nominal interest rates much below zero to stimulate the economy is difficult.11 It is 
at this point that the economic conditions for a liquidity trap arise.
Deflation raises the real value of debt, while the persistent fall in prices can 
encourage consumers to put off consumption today, leading to a fall in demand that 
leads to further deflationary pressure. Thus a deflationary “trap” can develop, which 
is characterized by weak consumption growth, falling prices, and increases in real 
debt levels. Japan eventually found itself in such a position following the collapse of 
its property bubble in the early 1990s.
If conventional monetary policy—the adjustment of short-  term interest rates—is 
no longer capable of stimulating the economy once the zero or even negative nominal 
interest rate bound has been reached, is monetary policy useless?

In the aftermath of the collapse of the high-  tech bubble in November 2002, Federal 
Reserve Governor (now Chairman) Ben Bernanke gave a speech entitled “Deflation: 
Making Sure ‘It’ Doesn’t Happen Here. ” In this speech, Bernanke stated that inflation 
was always and everywhere a monetary phenomenon, and he expressed great confi -
dence that by expanding the money supply by various means (including dropping it 
out of a helicopter on the population below), the Federal Reserve as the monopoly 
supplier of money could always engineer positive inflation in the US economy. He said:
I am confident that the Fed would take whatever means necessary to prevent 
significant deflation in the United States and, moreover, that the US central 
bank, in cooperation with other parts of the government as needed, has 
sufficient policy instruments to ensure that any deflation that might occur 
would be both mild and brief.
Following the collapse of the credit bubble in 2008, a number of governments

along with their central banks cut rates to (near) zero, including those in the United 
States and the United Kingdom. However, there was concern that the underlying 
economies might not respond to this drastic monetary medicine, mainly because the 
related banking crisis had caused banks to reduce their lending drastically. In order to 
kick start the process, both the Federal Reserve and the Bank of England effectively 
printed money and pumped it in to their respective economies. This “unconventional” 
approach to monetary policy, known as quantitative easing  (QE), is operationally 
similar to open market purchase operations but conducted on a much larger scale.
The additional reserves created by central banks in a policy of quantitative eas -
ing can be used to buy any assets. The Bank of England chose to buy gilts  (bonds 
issued by the UK government), where the focus was on gilts with three to five years

11 Interest rates were cut to below zero in several European countries in 2014 and subsequently in Japan 
in 2016.

Monetary Policy 297
maturity. The idea was that this additional reserve would kick-  start lending, causing 
broad money growth to expand, which would eventually lead to an increase in real 
economic activity. But there is no guarantee that banks will respond in this way. In 
a difficult economic climate, it may be better to hold excess reserves rather than to 
lend to households and businesses that may default.
In the United States, the formal plan for QE mainly involved the purchase of 
mortgage bonds issued or guaranteed by Freddie Mac and Fannie Mae. Part of the 
intention was to push down mortgage rates to support the US housing market, as 
well as to increase the growth rate of broad money. Before implementing this formal 
program, the Federal Reserve intervened in several other markets that were failing 
for lack of liquidity, including interbank markets and the commercial paper market. 
These interventions had a similar effect on the Federal Reserve’s balance sheet and

the money supply as the later QE program.
This first round of QE by the Federal Reserve was then followed by a further 
round of QE, known as QE2. In November 2010, the Federal Reserve judged that the 
US economy had not responded sufficiently to the first round of QE (QE1). The Fed 
announced that it would create $600 billion and use this money to purchase long-  dated 
US Treasuries in equal tranches over the following eight months. The purpose of QE2 
was to ensure that long bond yields remained low in order to encourage businesses 
and households to borrow for investment and consumption purposes, respectively.
As long as they have the appropriate authority from the government, central banks 
can purchase any assets in a quantitative easing program. But the risks involved in 
purchasing assets with credit risk should be clear. In the end, the central bank is just 
a special bank. If it accumulates bad assets that then turn out to create losses, it could

face a fatal loss of confidence in its main product: fiat money.
2.5.3  Limitations of Monetary Policy: Summary
The ultimate problem for monetary authorities as they try to manipulate the supply of 
money in order to influence the real economy is that they cannot control the amount 
of money that households and corporations put in banks on deposit, nor can they 
easily control the willingness of banks to create money by expanding credit. Taken 
together, this also means that they cannot always control the money supply. Therefore, 
there are definite limits to the power of monetary policy.
EXAMPLE 11   
The Limits of Monetary Policy: The Case of Japan
Between the 1950s and 1980s, Japan’s economy achieved faster real growth than 
any other G7 economy. But the terrific success of the economy sowed the seeds 
of the problems that were to follow. The very high real growth rates achieved by 
Japan over four decades became built in to asset prices, particularly equity and

commercial property prices. Toward the end of the 1980s, asset prices rose to 
even higher levels when the Bank of Japan followed a very easy monetary policy 
as it tried to prevent the Japanese yen from appreciating too much against the 
US dollar. However, when interest rates went up in 1989–1990 and the econ -
omy slowed, investors eventually came to believe that the growth assumptions 
that were built in to asset prices and other aspects of the Japanese economy 
were unrealistic. This realization caused Japanese asset prices to collapse. For 
example, the Nikkei 225 stock market index reached 38,915 in 1989; by the end 
of March 2003, it had fallen by 80 percent to 7,972. The collapse in asset prices 
caused wealth to decline dramatically. Consumer confidence understandably

Reading 18 ■ Monetary and Fiscal Policy 298
fell sharply too, and consumption growth slowed. Corporate spending also fell, 
while bank lending contracted sharply in the weak economic climate. Although 
many of these phenomena are apparent in all recessions, the situation was made 
worse when deflation set in. In an environment when prices are falling, con -
sumers may put off discretionary spending today until tomorrow; by doing this, 
however, they exacerbate the deflationary environment. Deflation also raises the 
real value of debts; as deflation takes hold, borrowers find the real value of their 
debts rising and may try to increase their savings accordingly. Once again, such 
actions exacerbate the recessionary conditions.
The Monetary Policy Response
Faced with such a downturn, the conventional monetary policy response is to 
cut interest rates to try to stimulate real economic activity. The Japanese central 
bank, the Bank of Japan, cut rates from 8 percent in 1990 to 1 percent by 1996.

By February 2001, the Japanese policy rate was cut to zero where it stayed. 
Once rates are at or near zero, there are two broad approaches suggested by 
theory, though the two are usually complementary. First, the central bank can try 
to convince markets that interest rates will remain low for a long time, even after 
the economy and inflation pick up. This will tend to lower interest rates along 
the yield curve. Second, the central bank can try to increase the money supply 
by purchasing assets from the private sector, so-  called quantitative easing. The 
Bank of Japan (BoJ) did both in 2001. It embarked on a program of quantitative 
easing supplemented by an explicit promise not to raise short-  term interest rates 
until deflation had given way to inflation.
Quantitative easing simply involves the printing of money by the central 
bank. In practice, this involved the BoJ using open market operations to add 
reserves to the banking system through the direct purchase of government

securities in the open market.
The reserve levels became the new target. The BoJ’s monetary policy com -
mittee determined the level of reserves and the quantity of bond purchases that 
should be undertaken, rather than voting on the policy rate.
The success of this policy is difficult to judge. As the chart below shows, 
although deflation turned to inflation for a while, it returned to deflation in 
2008–2009 when the Japanese economy suffered a sharp recession along with 
much of the rest of the world. At that time, having reversed its QE policy during 
2004–2008 by reducing its bond holdings, the Bank of Japan began to buy again.
Economists debate the point, but arguably, the Bank of Japan needed to 
implement a much larger program of QE to eliminate deflation. Japan’s pro -
gram amounted to a cumulative 7–8 percent of GDP spread over three years, 
whereas the United States and United Kingdom implemented programs totaling

12 percent and 14 percent, respectively, in about one year between 2009 and 
2010. The Japanese experience suggests that there may be limits to the power 
of monetary policy.

Monetary Policy 299
Exhibit 12   Inflation and Deflation in Japan
0Inflation (% year over year)
5
4
3
2
1
–1
–2
–3
90 10 94 00 06 92 98 04 96 02 08
Source:  Thomson Financial.
EXAMPLE 12   
Evaluating Monetary Policy
1 If an economy’s trend GDP growth rate is 3 percent and its central bank 
has a 2 percent inflation target, which policy rate is most consistent  with 
an expansionary monetary policy?
A 4 percent
B 5 percent
C 6 percent
2 An increase in a central bank’s policy rate might be expected to reduce 
inflationary pressures by:
A reducing consumer demand.
B reducing the foreign exchange value of the currency.
C driving up asset prices leading to an increase in personal sector 
wealth.
3 Which of the following statements best describes a fundamental limitation 
of monetary policy? Monetary policy is limited because central bankers:
A cannot control the inflation rate perfectly.
B are appointed by politicians and are therefore never truly independent.

C cannot control the amount of money that economic agents put in 
banks, nor the willingness of banks to make loans.

Reading 18 ■ Monetary and Fiscal Policy 300
A is correct. The neutral rate of interest, which in this example is 5 percent, 
is considered to be that rate of interest that neither spurs on nor slows down 
the underlying economy. As such, when policy rates are above the neutral rate, 
monetary policy is contractionary; when they are below the neutral rate, mon -
etary policy is expansionary. It comprises two components: the real trend rate 
of growth of the underlying economy (in this example, 3 percent) and long-  run 
expected inflation (in this example, 2 percent).
A is correct. If an increase in the central bank’s policy rate is successfully trans -
mitted via the money markets to other parts of the financial sector, consumer 
demand might decline as the rate of interest on mortgages and other credit 
rises. This decline in consumer demand should, all other things being equal and 
amongst other affects, lead to a reduction in upward pressure on consumer prices.

C is correct. Central bankers do not control the decisions of individuals and 
banks that can influence the money creation process.
FISCAL POLICY
The second set of tools used for influencing economic activity consists of the tools 
associated with fiscal policy. These involve the use of government spending and 
changing tax revenue to affect a number of aspects of the economy:
■■Overall level of aggregate demand in an economy and hence the level of eco -
nomic activity.
■■Distribution of income and wealth among different segments of the population.
■■Allocation of resources between different sectors and economic agents.
Often, a discussion of fiscal policy focuses on the impact of changes in the differ -
ence between government spending and revenue on the aggregate economy, rather 
than on the actual levels of spending and revenue themselves.
3.1 Roles and Objectives of Fiscal Policy
A primary aim for fiscal policy is to help manage the economy through its influence

on aggregate national output, that is, real GDP .
3.1.1  Fiscal Policy and Aggregate Demand
Aggregate demand is the amount companies and households plan to spend. We can 
consider a number of ways that fiscal policy can influence aggregate demand. For 
example, an expansionary  policy could take one or more of the following forms:
■■Cuts in personal income tax raise disposable income with the objective of 
boosting aggregate demand.
■■Cuts in sales (indirect) taxes to lower prices which raises real incomes with the 
objective of raising consumer demand.
■■Cuts in corporation (company) taxes to boost business profits, which may raise 
capital spending.3

Fiscal Policy 301
■■Cuts in tax rates on personal savings to raise disposable income for those with 
savings, with the objective of raising consumer demand.
■■New public spending on social goods and infrastructure, such as hospitals 
and schools, boosting personal incomes with the objective of raising aggregate 
demand.
We must stress, however, that the reliability and magnitude of these relationships 
will vary over time and from country to country. For example, in a recession with 
rising unemployment, it is not always the case that cuts in income taxes will raise 
consumer spending because consumers may wish to raise their precautionary (rainy 
day) saving in anticipation of further deterioration in the economy. Indeed, in very 
general terms economists are often divided into two camps regarding the workings 
of fiscal policy: Keynesians  believe that fiscal policy can have powerful effects on 
aggregate demand, output, and employment when there is substantial spare capacity

in an economy. Monetarists  believe that fiscal changes only have a temporary effect 
on aggregate demand and that monetary policy is a more effective tool for restraining 
or boosting inflationary pressures. Monetarists tend not to advocate using monetary 
policy for countercyclical adjustment of aggregate demand. This intellectual division 
will naturally be reflected in economists’ divergent views on the efficacy of the large 
fiscal expansions observed in many countries following the credit crisis of 2008, along 
with differing views on the possible impact of quantitative easing.
3.1.2  Government Receipts and Expenditure in Major Economies
In Exhibit 13, we present the total government revenues as a percentage of GDP for 
some major economies. This is the share of a country’s output that is gathered by the 
government through taxes and such related items as fees, charges, fines, and capital 
transfers. It is often considered as a summary measure of the extent to which a gov -

ernment is involved both directly and indirectly in the economic activity of a country.
Taxes are formally defined as compulsory, unrequited payments to the general 
government (they are unrequited in the sense that benefits provided by a govern -
ment to taxpayers are usually not related to payments). Exhibit 13 contains taxes on 
incomes and profits, social security contributions, indirect taxes on goods and services, 
employment taxes, and taxes on the ownership and transfer of property.
Exhibit 13   General Government Revenues as Percent of GDP
1995 2000 2005 2006 2007 2008
Australia 34.5 36.1 36.5 36.4 36.0 35.3
Germany 45.1 46.4 43.6 43.7 43.8 43.8
Japan 31.2 31.4 31.7 34.5 33.5 34.4
United Kingdom 38.2 40.3 40.8 41.4 41.4 42.2
United States 33.8 35.4 33.0 33.8 34.0 32.3
OECD 37.9 39.0 37.7 38.6 38.6 37.9
Source:  Organisation for Economic Co-  Operation and Development (OECD).
Taxes on income and profits have been fairly constant for the Organisation for

Economic Co-  Operation and Development (OECD) countries overall at around 
12.5–13 percent of GDP since the mid-  1990s, while taxes on goods and services have 
been steady at about 11 percent of GDP for that period. Variations between countries 
can be substantial; taxes on goods and services are around 5 percent of GDP for the 
United States and Japan but over 16 percent for Denmark.

Reading 18 ■ Monetary and Fiscal Policy 302
Exhibit 14 shows the percentage of GDP represented by government expenditure 
in a variety of major economies over time. Generally, these have been fairly constant 
since 1995, though Germany had a particularly high number at the start of the period 
because of reunification costs.
Exhibit 14   General Government Expenditures as Percent of GDP
Australia 38.2 35.2 34.8 34.5 34.2 34.3
Germany 54.8 45.1 46.9 45.3 43.6 43.8
Japan 36.0 39.0 38.4 36.2 36.0 37.1
United Kingdom 44.1 36.6 44.0 44.1 44.2 47.5
United States 37.1 33.9 36.2 36.0 36.8 38.8
OECD 42.7 38.7 40.5 39.9 39.9 41.4
Source:  OECD.
Clearly, the possibility that fiscal policy can influence output means that it may 
be an important tool for economic stabilization . In a recession, governments can 
raise spending ( expansionary fiscal policy ) in an attempt to raise employment and 
output. In boom times—when an economy has full employment and wages and prices

are rising too fast—then government spending may be reduced and taxes raised 
(contractionary fiscal policy ).
Hence, a key concept is the budget surplus/deficit , which is the difference between 
government revenue and expenditure for a fixed period of time, such as a fiscal or 
calendar year. Government revenue includes tax revenues net of transfer payments; 
government spending includes interest payments on the government debt. Analysts 
often focus on changes in the budget surplus or deficit from year to year as indica -
tors of whether the fiscal policy is getting tighter or looser. An increase in a budget 
surplus would be associated with contractionary fiscal policy, while a rise in a deficit 
is an expansionary fiscal policy. Of course, over the course of a business cycle the 
budget surplus will vary automatically in a countercyclical way. For example, as an 
economy slows and unemployment rises, government spending on social insurance

and unemployment benefits will also rise and add to aggregate demand. This is known 
as an automatic stabilizer . Similarly, if boom conditions ensue and employment and 
incomes are high, then progressive income and profit taxes are rising and also act as 
automatic stabilizers increasing budget surplus or reducing budget deficit. The great 
advantage of automatic stabilizers is that they are indeed automatic, not requiring the 
identification of shocks to which policymakers must consider a response. By reducing 
the responsiveness of the economy to shocks, these automatic stabilizers reduce output 
fluctuations. Automatic stabilizers should be distinguished from discretionary fiscal 
policies, such as changes in government spending or tax rates, which are actively used 
to stabilize aggregate demand. If government spending and revenues are equal, then 
the budget is balanced .

Fiscal Policy 303
Exhibit 15   General Government Net Borrowing or Lending as Percent of 
GDP
Australia –3.7 0.9 1.7 1.9 1.8 1.0
Germany –9.7 1.3 –3.3 –1.6 0.2 0.0
Japan –4.7 –7.6 –6.7 –1.6 –2.5 –2.7
United Kingdom –5.8 3.7 –3.3 –2.7 –2.7 –5.3
United States –3.3 1.5 –3.3 –2.2 –2.8 –6.5
OECD –4.8 0.2 –2.7 –1.3 –1.3 –1.3
EXAMPLE 13   
Sources and Uses of Government Cash Flows: The Case of 
the United Kingdom
The precise components of revenue and expenditure will of course vary over time 
and between countries. But, as an example of the breakdown of expenditure and 
revenue, in Exhibits 16 and 17 we have presented the budget projections of the 
United Kingdom for 2010/2011. The budget projected that total spending would 
come to £697bn, while total revenue would only be £548bn. The government was 
therefore forecasting a budget shortfall of £149bn for the fiscal year, meaning 
that it had an associated need to borrow £149bn from the private sector in the

United Kingdom or the private and public sectors of other economies.

Reading 18 ■ Monetary and Fiscal Policy 304
Exhibit 16   Where Does the Money Go? The United Kingdom, 2010–
2011
Social protection:
28.0% 
Personal social
services: 4.6% 
Health: 17.5%
Transport: 3.0%Education: 12.8%Defense: 5.7% Industry, agriculture,
and employment: 3.0% Housing and
environment: 3.9% Public order and
safety: 5.0% Debt interest: 
6.3% Other: 10.2%Total Spending: £697 billion
Note : “Other” includes recreation, culture, religion, public sector pensions, and general 
public services.
Source:  HM Treasury, United Kingdom.
Exhibit 17   Where Does the Money Come From? The United Kingdom, 
2010–2011
Income tax: 27.3%
National Insurance
(labor) tax: 18.0% 
Excise duties (taxes on 
alcohol, tobacco): 8.4% Corporation tax: 7.8% Value Added Tax
(VAT): 14.8% Business property 
tax: 4.6% Municipal (local
government) tax: 4.6% Other: 14.5%Total Government Receipts: £548 billion
Note : “Other Receipts” includes capital taxes, stamp duties on share and property transactions,

Fiscal Policy 305
3.1.3  Deficits and the National Debt
Government deficits are the difference between government revenues and expendi -
tures over a period of calendar time, usually a year. Government (or national) debt 
is the accumulation over time of these deficits. Government deficits are financed 
by borrowing from the private sector, often via private pension and insurance fund 
portfolio investments. We saw above that governments are more likely to have deficits 
than surpluses over long periods of time. As a result, there may exist a large stock 
of outstanding government debt owned by the private sector. This will vary as the 
business cycle ebbs and flows. Exhibit 18 shows the time path of the ratio of public 
debt to GDP for the United Kingdom over several hundred years. It can be clearly 
seen that the major cause of fluctuations in that ratio through history has been the 
financing of wars, in particular the Napoleonic Wars of 1799–1815 and the First and

Second World Wars of 1914–1918 and 1939–1945.
Exhibit 18   UK National Debt as Percent of GDP (1692–2010) 
Debt as Percent of GDP
300
250
200
150
100
50
0
1692 1792 1942 1992 1742 1892 1842
Source:  http://ukpublicspending.co.uk.
With the onset of the credit crisis of 2008, governments actively sought to stimulate 
their economies through increased expenditures without raising taxes and revenues. 
This led to increased borrowing, shown in Exhibits 15 and 19, which has become a 
concern in the financial markets in 2010 for such countries as Greece. Indeed, between 
2008 and 2009, central government debt rose from $1.2 trillion to $1.6 trillion in the 
United Kingdom and from $5.8 trillion to $7.5 trillion for the United States.12
12 www.oecd.org.

Reading 18 ■ Monetary and Fiscal Policy 306
Exhibit 19   General Government Gross Financial Liabilities as Percent of 
GDP
Australia 42.5 25.4 16.9 16.2 15.3 14.3
Germany 55.7 60.4 71.1 69.2 65.3 68.8
Japan 86.2 135.4 175.3 172.1 167.1 172.1
United Kingdom 51.6 45.1 46.1 45.9 46.9 56.8
United States 70.6 54.4 61.3 60.8 61.8 70.0
OECD 69.9 68.3 75.9 74.6 73.1 78.4
Source:  www.oecd.org.
Ultimately, if the ratio of debt to GDP rises beyond a certain unknown point, then 
the solvency of the country comes into question. An additional indicator for potential 
insolvency is the ratio of interest rate payments to GDP , which is shown for some 
major economies in Exhibit 20. These represent payments required of governments 
to service their debts as a percentage of national output and as such reflect both the 
size of debts and the interest charged on them. Such ratios could rise rapidly with

the growing debt ratios of 2009 and 2010, particularly if the interest rates on the debt 
were to rise from the historically low levels.
Exhibit 20   General Government Net Debt Interest Payments as Percent of 
GDP
Australia 3.5 1.7 1.0 0.8 0.6 0.5
Germany 2.9 2.7 2.4 2.4 2.4 2.3
Japan 1.3 1.5 0.8 0.6 0.6 0.9
United Kingdom 3.1 2.4 1.8 1.8 1.8 1.9
United States 3.5 2.5 1.8 1.8 1.9 1.8
OECD 3.6 2.5 1.8 1.7 1.7 1.6
Governments’ spending was far in excess of revenues following the credit crisis of 
2007–2010 as governments tried to stimulate their economies; this level of spending 
raised concerns in some quarters about the scale of governmental debt accumulation. 
Exhibit 19 shows that gross government financial liabilities relative to GDP for the 
OECD countries overall rose from 73.1 percent in 2007 to 78.4 percent in 2008. In 
Japan, where fiscal spending has been used to stimulate the economy from the early

1990s, the ratio has risen from 86.2 percent in 1995 to 172.1 percent in 2008. If an 
economy grows in real terms, so do the real tax revenues and hence the ability to 
service a growing real debt at constant tax rate levels. However, if the real growth in 
the economy is lower than the real interest rate on the debt, then the debt ratio will 
worsen even though the economy is growing because the debt burden (i.e., the real 
interest rate times the debt) grows faster than the economy. Hence, an important 
issue for governments and their creditors is whether their additional spending leads 
to sufficiently higher tax revenues to pay the interest on the debt used to finance the 
extra spending.

Fiscal Policy 307
However, within a national economy, the real value of the outstanding debt will 
fall if the overall price level rises (i.e., inflation, and hence a rise in nominal GDP even 
if real GDP is static) and thus the ratio of debt to GDP may not be rising. But if the 
general price level falls (i.e., deflation), then the ratio may stay elevated for longer. 
If net interest payments rise rapidly and investors lose confidence in a government’s 
ability to honour its debts, then financing costs may escalate even more quickly and 
make the situation unstable.
Should we be concerned about the size of a national debt (relative to GDP)? There 
are strong arguments both for and against:
The arguments against being concerned about national debt (relative to GDP) 
■●The scale of the problem may be overstated because the debt is owed inter -
nally to fellow citizens. This is certainly the case in Japan, where 93 percent

is owned by Japanese residents. In the United States and United Kingdom, 
the figures are 63 percent and 69 percent, respectively. South Korea and 
Canada have only 7 percent and 5 percent non-  resident ownership of gov -
ernment debt, respectively. But Italy has 49 percent.13
■●A proportion of the money borrowed may have been used for capital invest -
ment projects or enhancing human capital (e.g., training, education); these 
should lead to raised future output and tax revenues.
■●Large fiscal deficits require tax changes which may actually reduce distor -
tions caused by existing tax structures.
■●Deficits may have no net impact because the private sector may act to offset 
fiscal deficits by increasing saving in anticipation of future increased taxes. 
This argument is known as “Ricardian equivalence” and is discussed in more 
detail later.
■●If there is unemployment in an economy, then the debt is not diverting 
activity away from productive uses (and indeed the debt could be associated

with an increase in employment).
The arguments in favour of being concerned are:
■●High levels of debt to GDP may lead to higher tax rates in the search for 
higher tax revenues. This may lead to disincentives to economic activity as 
the higher marginal tax rates reduce labour effort and entrepreneurial activ -
ity, leading to lower growth in the long run.
■●If markets lose confidence in a government, then the central bank may have 
to print money to finance a government deficit. This may lead ultimately 
to high inflation, as evidenced by the economic history of Germany in the 
1920s and more recently in Zimbabwe.
■●Government borrowing may divert private sector investment from taking 
place (an effect known as crowding out ); if there is a limited amount of sav -
ings to be spent on investment, then larger government demands will lead 
to higher interest rates and lower private sector investing.
An important distinction to make is between long- and short-  run effects. Over

short periods of time (say, a few years), crowding out may have little effect. If it lasts 
for a longer time, however, then capital accumulation in an economy may be damaged. 
Similarly, tax distortions may not be too serious over the short-  term but will have a 
more substantial impact over many years.
13 These data come from the Bank for International Settlements (BIS), IMF, and central bank websites. 
All figures are as of 2008.

Reading 18 ■ Monetary and Fiscal Policy 308
EXAMPLE 14   
Types of Fiscal Policies
1 Which of the following is not associated with an expansionary fiscal 
policy?
A A rise in capital gains taxes
B Cuts in personal income taxes
C New capital spending by the government on road building
2 Fiscal expansions will most likely  have the most impact on aggregate out -
put when the economy is in which of the following states?
A Full employment
B Near full employment
C Considerable unemployment
3 Which one of the following is most likely  a reason to not use fiscal deficits 
as an expansionary tool?
A They may crowd out private investment.
B They may facilitate tax changes to reduce distortions in an economy.
C They may stimulate employment when there is substantial unemploy -
ment in an economy.
A is correct. A rise in capital gains taxes reduces income available for spending 
and hence reduces aggregate demand, other things being equal. Cutting income

tax raises disposable income, while new road building raises employment and 
incomes; in both cases, aggregate demand rises and hence policy is expansionary.
C is correct. When an economy is close to full employment a fiscal expansion 
raising aggregate demand can have little impact on output because there are 
few spare unused resources (e.g., labour or idle factories); instead, there will be 
upward pressure on prices (i.e., inflation).
A is correct. A frequent argument against raises in fiscal deficits is that the 
additional borrowing to fund the deficit in financial markets will displace private 
sector borrowing for investment (i.e., “crowd it out”).
3.2 Fiscal Policy Tools and the Macroeconomy
We now look at the nature of the fiscal tools available to a government. Government 
spending can take a variety of forms:
■■Transfer payments  are welfare payments made through the social security

system and, depending on the country, comprise payments for state pensions, 
housing benefits, tax credits and income support for poorer families, child 
benefits, unemployment benefits, and job search allowances. Transfer payments 
exist to provide a basic minimum level of income for low-  income households, 
and they also provide a means by which a government can change the overall 
income distribution in a society. Note that these payments are not included

Fiscal Policy 309
in the definition of GDP because they do not reflect a reward to a factor of 
production for economic activity. Also, they are not considered to be part of 
general government spending on goods and services.
■■Current government spending  involves spending on goods and services that 
are provided on a regular, recurring basis—including health, education, and 
defense. Clearly, such spending will have a big impact on a country’s skill level 
and overall labour productivity.
■■Capital expenditure  includes infrastructure spending on roads, hospitals, pris -
ons, and schools. This investment spending will add to a nation’s capital stock 
and affect productive potential for an economy.
Government spending can be justified on both economic and social grounds:
■■To provide such services as defense that benefit all citizens equally.
■■For infrastructure capital spending (e.g., roads) to help a country’s economic 
growth.

growth.
■■To guarantee a minimum level of income for poorer people and hence redistrib -
ute income and wealth (e.g., welfare and related benefits).
■■To influence a government’s economic objectives of low inflation and high 
employment and growth (e.g., management of aggregate demand).
■■To subsidize the development of innovative and high-  risk new products or mar -
kets (e.g., alternative energy sources).
Government revenues can take several forms:
■■Direct taxes  are levied on income, wealth, and corporate profits and include 
capital gains taxes, national insurance (or labour) taxes, and corporate taxes. 
They may also include a local income or property tax for both individuals and 
businesses. Inheritance tax on a deceased’s estate will have both revenue-  raising 
and wealth-  redistribution aspects.
■■Indirect taxes  are taxes on spending on a variety of goods and services in an 
economy—such as the excise duties on fuel, alcohol, and tobacco as well as

sales (or value-  added tax)—and often exclude health and education products on 
social grounds. In addition, taxes on gambling may also be considered to have 
a social aspect in deterring such activity, while fuel duties will have an environ -
mental purpose in making fuel consumption and hence travel more expensive.
Taxes can be justified both in terms of raising revenues to finance expenditures and 
in terms of income and wealth redistribution policies. Economists typically consider 
four desirable attributes of a tax policy:
■■Simplicity : This refers to ease of compliance by the taxpayer and enforcement 
by the revenue authorities. The final liability should be certain and not easily 
manipulated.
■■Efficiency : Taxation should interfere as little as possible in the choices individ -
uals make in the market place. Taxes affect behaviour and should, in general, 
discourage work and investment as little as possible. A major philosophical

issue among economists is whether tax policy should deliberately deviate from 
efficiency to promote “good” economic activities, such as savings, and dis -
courage harmful ones, such as tobacco consumption. Although most would 
accept a limited role in guiding consumer choices, some will question how well 
equipped policymakers are to decide on such objectives and whether there will 
be unwanted ancillary effects, such as giving tax breaks for saving among peo -
ple who already save and whose behaviour does not change.

Reading 18 ■ Monetary and Fiscal Policy 310
■■Fairness : This refers to the fact that people in similar situations should pay the 
same taxes (“horizontal equity”) and that richer people should pay more taxes 
(“vertical equity”). Of course, the concept of fairness is really subjective. Still, 
most would agree that income tax rates should be progressive—that is, that 
households and corporations should pay proportionately more as their incomes 
rise. However, some people advocate “flat” tax rates, whereby all should pay the 
same proportion of taxable income.
■■Revenue sufficiency : Although revenue sufficiency may seem obvious as a 
criterion for tax policy, there may be a conflict with fairness and efficiency. 
For example, one may believe that increasing income tax rates to reduce fiscal 
deficits reduces labour effort and that tax rate increases are thus an inefficient 
policy tool.
EXAMPLE 15   
Some Issues with Tax Policy

EXAMPLE 15   
1 Incentives . Some economists believe that income taxes reduce the incen -
tive to work, save, and invest and that the overall tax burden has become 
excessive. These ideas are often associated with supply-  side economics 
and the US economist Arthur Laffer. A variety of income tax cuts and 
simplifications have taken place in the United States since 1981, and 
although there is substantial controversy, some claim that work effort did 
rise (although tax cuts had little impact on savings). Similarly, some found 
that business investment did rise, while others claimed it was independent 
of such cuts.
2 Fairness . How do we judge the fairness of the tax system? One way is to 
calibrate the tax burden falling on different groups of people ranked by 
their income and to assess how changes in taxes affect these groups. Of 
course, this imposes huge data demands on investigators and must be

considered incomplete. In the United States, it has been found that the 
federal system is indeed highly progressive. Many countries use such 
methods to analyze the impact of tax changes on different income groups 
when they announce their annual fiscal policy plans.
3 Tax reform . There is continuous debate on reforming tax policy. Should 
there be a flat-  rate tax on labour income? Should all investment be imme -
diately deducted for corporate taxes? Should more revenue be sourced 
from consumption taxes? Should taxes be indexed to inflation? Should 
dividends be taxed when profits have already been subject to tax? Should 
estates be taxed at all? Many of these issues are raised in the context of 
their impact on economic growth.
EXAMPLE 16   
Fiscal Tools
1 Which of the following is not a tool of fiscal policy?
A A rise in social transfer payments
B The purchase of new equipment for the armed forces

Fiscal Policy 311
C An increase in deposit requirements for the buying of houses
2 Which of the following is not an indirect tax?
A Excise duty
B Value-  added Tax
C Employment taxes
3 Which of the following statements is most  accurate?
A Direct taxes are useful for discouraging alcohol consumption.
B Because indirect taxes cannot be changed quickly, they are of no use 
in fiscal policy.
C Government capital spending decisions are slow to plan, implement, 
and execute and hence are of little use for short-  term economic 
stabilization.
C is correct. Rises in deposit requirements for house purchases are intended to 
reduce the demand for credit for house purchases and hence would be consid -
ered a tool of monetary policy. This is a policy used actively in several countries, 
and is under consideration by regulators in other countries to constrain house 
price inflation.
C is correct. Both excise duty and VAT are applied to prices, whereas taxes on

employment apply to labour income and hence are not indirect taxes.
C is correct. Capital spending is much slower to implement than changes in 
indirect taxes; and indirect taxes affect alcohol consumption more directly than 
direct taxes.
3.2.1  The Advantages and Disadvantages of Using the Different Tools of Fiscal Policy
The different tools used to expedite fiscal policy as a means to try to put or keep an 
economy on a path of positive, stable growth with low inflation have both advantages 
and disadvantages:
Advantages: 
■■Indirect taxes can be adjusted almost immediately after they are announced 
and can influence spending behaviour instantly and generate revenue for the 
government at little or no cost to the government.
■■Social policies, such as discouraging alcohol or tobacco use, can be adjusted 
almost instantly by raising such taxes.

Reading 18 ■ Monetary and Fiscal Policy 312
Disadvantages: 
■■Direct taxes are more difficult to change without considerable notice, often 
many months, because payroll computer systems will have to be adjusted 
(although the announcement itself may well have a powerful effect on spend -
ing behaviour more immediately). The same may be said for welfare and other 
social transfers.
■■Capital spending plans take longer to formulate and implement, typically over 
a period of years. For example, building a road or hospital requires detailed 
planning, legal permissions, and implementation. This is often a valid criticism 
of an active fiscal policy and was widely heard during the US fiscal stimulus in 
2009–2010. On the other hand, such policies add to the productive potential of 
an economy, unlike a change in personal or indirect taxes. Of course, the slower 
the impact of a fiscal change, the more likely other exogenous changes will

already be influencing the economy before the fiscal change kicks in.
The above-  mentioned tools may also have expectational effects at least as powerful 
as the direct effects. The announcement of future income tax rises a year ahead could 
potentially lead to reduced consumption immediately. Such delayed tax rises were a 
feature of UK fiscal policy of 2009–2010; however, the evidence is anecdotal because 
spending behaviour changed little until the delayed tax changes actually came into force.
We may also consider the relative potency of the different fiscal tools. Direct 
government spending has a far bigger impact on aggregate spending and output than 
income tax cuts or transfer increases; however, if the latter are directed at the poorest 
in society (basically, those who spend all their income), then this will give a relatively 
strong boost. Further discussion and examples of these comparisons are given in 
section 4 below on the interaction between monetary and fiscal policy.

3.2.2  Modeling the Impact of Taxes and Government Spending: The Fiscal Multiplier
The conventional macroeconomic model has government spending, G, adding directly 
to aggregate demand, AD, and reducing it via taxes, T; these comprise both indirect 
taxes on expenditures and direct taxes on factor incomes. Further government spending 
is increased via the payment of transfer benefits, B, such as social security payments. 
Hence, the net impact of the government sector on aggregate demand is:
G – T + B = Budget surplus OR deficit
Net taxes ( NT; taxes less transfers) reduce disposable income ( YD) available to indi -
viduals relative to national income or output ( Y) as follows:
YD = Y – NT = (1 – t) Y
where t is the net tax rate . Net taxes are often assumed to be proportional to national 
income, Y, and hence total tax revenue from net taxes is tY. If t = 20% or 0.2, then for 
every $1 rise in national income, net tax revenue will rise by 20 cents and household

disposable income will rise by 80 cents.
The fiscal multiplier  is important in macroeconomics because it tells us how much 
output changes as exogenous changes occur in government spending or taxation. The 
recipients of the increase in government spending will typically save a proportion 1 – c 
of each additional dollar of disposable income, where c is the marginal propensity 
to consume  (MPC) this additional income. Ignoring income taxes, we can see that 
$c will, in turn, be spent by these recipients on more goods and services. The recip -
ients of this $ c will themselves spend a proportion c of this additional income (i.e., 
$c × c, or c-squared). This process continues with income and spending growing at 
a constant rate of c as it passes from hand to hand through the economy. This is the 
familiar geometric progression with constant factor c, where 0 < c < 1. The sum of 
this geometric series is 1/(1 – c).(5)
(6)

Fiscal Policy 313
We define s as the marginal propensity to save  (MPS), the amount saved out of 
an additional dollar of disposable income. Because c + s = 1, hence s =1 – c.
Exhibit 21   Disposable Income, Saving, and the MPC
Income Income tax Disposable income Consumption Saving
$100 $20 $80 $72 $8
In Exhibit 21, the MPC out of disposable income is 90% or 0.9 (72/80).The MPS 
is therefore 1 – 0.9 or 0.1
For every dollar of new (additional) spending, total incomes and spending rises 
by $1/(1 – c). And because 0 < c < 1, this must be > 1; this is the multiplier. If c = 0.9 
(or individuals spend 90 percent of additions to income), then the multiplier = 1/
(1 – 0.9) = 10.
A formal definition of the multiplier would be the ratio of the change in equilib -
rium output to the change in autonomous spending that caused the change. This is 
a monetary measure, but because prices are assumed to be constant in this analysis,

real and monetary amounts are identical. Given that fiscal policy is about changes 
in government spending, G, net taxes, NT, and tax rates, t, we can see that the mul -
tiplier is an important tool for calibrating the possible impact of policy changes on 
output. How can we introduce tax changes into the multiplier concept? We do this by 
introducing the idea of disposable income, YD, defined as income less income taxes 
net of transfers, Y – NT.
Households  spend a proportion c of disposable income, YD, that is, cYD or c(Y 
– NT) or c(1 – t)Y. The marginal propensity to consume  in the presence of taxes 
is then c(1 – t). If the government increases spending, say on road building, by an 
amount, G, then disposable income rises by (1 – t)G and consumer spending by c(1 – t)
G. Provided there are unused sources of capital and labour in the economy, this leads 
to a rise in aggregate demand and output; the recipients of this extra consumption

spending will have (1 – t)c(1 – t)G extra disposable income available and will spend c 
of it. This cumulative extra spending and income will continue to spread through the 
economy at a decreasing rate as 0 < c(1 – t) < 1. The overall final impact on aggregate 
demand and output will effectively be the sum of this decreasing geometric series with 
common ratio c(1 – t), and this sums to 1/[1 – c(1 – t)]. This is known as the fiscal 
multiplier  and is very relevant to studies of fiscal policy as changes in G or tax rates 
will affect output in an economy through the value of the multiplier.
For example, if the tax rate is 20 percent, or 0.2, and the marginal propensity to 
spend is 90 percent, or 0.9, then the fiscal multiplier will be: 1/[1 – 0.9(1 – 0.2)] or 
1/0.28 = 3.57. In other words, if the government raises G by $1 billion, total incomes 
and spending rise by $3.57 billion.
Discretionary fiscal policy (see below) will involve changes in these variables with 
a view to influencing Y.

3.2.3  The Balanced Budget Multiplier
If a government increases G by the same amount as it raises taxes, the aggregate 
output actually rises. Why is this?
It is because the marginal propensity to spend out of disposable income is less 
than 1, and hence for every dollar less in YD, spending only falls $ c. Hence, aggre -
gate spending falls less than the tax rise by a factor of c. A balanced budget leads to 
a rise in output, which in turn leads to further rises in output and incomes via the 
multiplier effect.

Reading 18 ■ Monetary and Fiscal Policy 314
Suppose an economy has an equilibrium output or income level of $1,000 con -
sisting of $900 of consumption and $100 of investment spending, which is fixed and 
not related to income. If government spending is set at $200, financed by a tax rate of 
20 percent (giving tax revenue of $200), what will happen to output? First, additional 
government spending of $200 will raise output by that amount; but will taxes of $200 
reduce output by a similar amount? Not if the MPC is less than 1; suppose it is 0.9, and 
hence spending will only fall by 90 percent of $200, or $180. The initial impact of the 
balanced fiscal package on aggregate demand will be to raise it by $200–$180 = $20. 
This additional output will, in turn, lead to further increases in income and output 
through the multiplier effect.
Even though the above policy involved a combination of government spending and

tax increases that initially left the government’s budget deficit/surplus unchanged, the 
induced rise in output will lead to further tax revenue increases and a further change 
in the budget position. Could the government adjust the initial change in spending to 
offset exactly the eventual total change in tax revenues? The answer is “yes, ” and we 
can ask what will be the effect on output of this genuinely balanced budget change? 
This balanced budget multiplier always takes the value unity.
EXAMPLE 17   
Government Debt, Deficits, and Ricardo
The total stock of government debt is the outstanding stock of IOUs issued by 
a government and not yet repaid. They are issued when the government has 
insufficient tax revenues to meet expenditures and has to borrow from the 
public. The size of the outstanding debt equals the cumulative quantity of net 
borrowing it has done, and the fiscal or budget deficit is added in the current

period to the outstanding stock of debt. If the outstanding stock of debt falls, 
we have a negative deficit or a surplus.
If a government reduces taxation by $10 billion one year and replaces that 
revenue with borrowing of $10 billion from the public, will it have any real impact 
on the economy? The important issue here is how people perceive that action: 
Do they recognize what will happen over time as interest and bond principal 
have to be repaid out of future taxes? If so, they may think of the bond finance 
as equivalent to delayed taxation finance; thus, the reduction in current taxation 
will have no impact on spending because individuals save more in anticipation 
of higher future taxes to repay the bond. This is called Ricardian equivalence  
after the economist David Ricardo. If people do not correctly anticipate all the 
future taxes required to repay the additional government debt, then they feel 
wealthier when the debt is issued and may increase their spending, adding to

aggregate demand.
Whether Ricardian equivalence holds in practice is ultimately an empirical 
issue and is difficult to calibrate conclusively given the number of things that 
are changing at any time in a modern economy.
3.3 Fiscal Policy Implementation: Active and Discretionary 
Fiscal Policy
In the following, we discuss major issues in fiscal policy implementation.

Fiscal Policy 315
3.3.1  Deficits and the Fiscal Stance
An important question is the extent to which the budget is a useful measure of the 
government’s fiscal stance. Does the size of the deficit actually indicate whether fiscal 
policy is expansionary  or contractionary ? Clearly, such a question is important 
for economic policymakers insofar as the deficit can change for reasons unrelated 
to actual fiscal policy changes. For example, the automatic stabilizers  mentioned 
earlier will lead to changes in the budget deficit unrelated to fiscal policy changes; a 
recession will cause tax revenues to fall and the budget deficit to rise. An observer 
may conclude that fiscal policy has been loosened and is expansionary and that no 
further government action is required.
To this end, economists often look at the structural (or cyclically adjusted) bud -
get deficit  as an indicator of the fiscal stance. This is defined as the deficit that would

exist if the economy was at full employment (or full potential output ). Hence, if we 
consider a period of relatively high unemployment, such as 2009–2010 with around 
9–10 percent of the workforce out of work in the United States and Europe, then the 
budget deficits in those countries would be expected to be reduced substantially if the 
economies returned to full employment. At this level, tax revenues would be higher 
and social transfers lower. Recent data for major countries are given in Exhibit 22, 
where negative numbers refer to deficits and positive numbers are surpluses.
Exhibit 22   General Government Net Cyclically Adjusted Borrowing or 
Lending as Percent of GDP
Australia –3.1 0.1 1.1 1.4 1.3 0.1
Germany –9.5 –1.8 –2.3 –1.5 –0.4 –0.5
Japan –4.6 –7.1 –6.5 –1.8 –3.0 –2.3
United Kingdom –5.6 0.9 –3.7 –3.3 –3.5 –5.1
United States –2.9 0.7 –3.6 –2.6 –3.2 –6.1
OECD –4.6 –1.1 –3.1 –1.9 –2.1 –3.7

A further reason why actual government deficits may not be a good measure of 
fiscal stance is the distinction between real and nominal interest rates and the role 
of inflation adjustment when applied to budget deficits. Although national economic 
statistics treat the cash interest payments on debt as government expenditure it 
makes more sense to consider only the inflation-  adjusted (or real) interest payments 
because the real value of the outstanding debt is being eroded by inflation. Automatic 
stabilizers—such as income tax, VAT, and social benefits—are important because as 
output and employment fall and reduce tax revenues, so net tax revenues also fall as 
unemployment benefits rise. This acts as a fiscal stimulus and serves to reduce the 
size of the multiplier, dampening the output response of whatever caused the fall in 
output in the first place. By their very nature, automatic stabilizers do not require pol -

icy changes; no policymaker has to decide that an economic shock has occurred and 
how to respond. Hence, the responsiveness of the economy to shocks is automatically 
reduced, as are movements in employment and output.

Reading 18 ■ Monetary and Fiscal Policy 316
In addition to these automatic adjustments, governments also use discretionary 
fiscal adjustments to influence aggregate demand. These will involve tax changes 
and/or spending cuts or increases usually with the aim of stabilizing the economy. A 
natural question is why fiscal policy cannot stabilize aggregate demand completely, 
hence ensuring full employment at all times.
3.3.2  Difficulties in Executing Fiscal Policy
Fiscal policy cannot stabilize aggregate demand completely because the difficulties in 
executing fiscal policy cannot be completely overcome.
First, the policymaker does not have complete information on how the economy 
functions. It may take several months for policymakers to realize that an economy is 
slowing, because data appear with a considerable time lag and even then are subject 
to substantial revision. This is often called the recognition lag  and has been likened

to the problem of driving with the rear view mirror. Then, when policy changes are 
finally decided on, they may take many months to implement. This is the action lag . 
If a government decides to raise spending on capital projects to increase employment 
and incomes, for example, these may take many months to plan and put into action. 
Finally, the result of these actions on the economy will take additional time to become 
evident; this is the impact lag . These types of policy lags also occur in the case of 
discretionary monetary policy.
A second aspect of time in this process is the uncertainty of where the economy 
is heading independently of these policy changes. For example, a stimulus may occur 
simultaneously with a surprise rise in investment spending or in the demand for a coun -
try’s exports just as discretionary government spending starts to rise. Macroeconomic 
forecasting models do not generally have a good track record for accuracy and hence

cannot be relied on to aid the policy-  making process in this context. In addition, when 
discretionary fiscal adjustments are announced (or are already underway), private 
sector behaviour may well change leading to rises in consumption or investment, both 
of which will reinforce the effects of a rise in government expenditure. Again, this will 
make it difficult to calibrate the required fiscal adjustment to secure full employment.
There are wider macroeconomic issues also involved here.
■■If the government is concerned with both unemployment and inflation in an 
economy, then raising aggregate demand toward the full employment level may 
also lead to a tightening labour market and rising wages and prices. The policy -
maker may be reluctant to further fine tune fiscal policy in an uncertain world 
because it might induce inflation.
■■If the budget deficit is already large relative to GDP and further fiscal stimulus

is required, then the necessary increase in the deficit may be considered unac -
ceptable by the financial markets when government funding is raised, leading 
to higher interest rates on government debt and political pressure to tackle the 
deficit.
■■Of course, all this presupposes that we know the level of full employment, 
which is difficult to measure accurately. Fiscal expansion raises demand, but 
what if we are already at full employment, which will be changing as produc -
tive capacity changes and workers’ willingness to work at various wage levels 
changes?
■■If unused resources reflect a low supply of labour or other factors rather than a 
shortage of demand, then discretionary fiscal policy will not add to demand and 
will be ineffective, raising the risk of inflationary pressures in the economy.
■■The issue of crowding out may occur: If the government borrows from a limited 
pool of savings, the competition for funds with the private sector may crowd

out private firms with subsequent less investing and economic growth. In

Fiscal Policy 317
addition, the cost of borrowing may rise, leading to the cancellation of poten -
tially profitable opportunities. This concept is the subject of continuing empiri -
cal debate and investigation.
EXAMPLE 18   
Evaluating Fiscal Policy
1 Which of the following statements is least  accurate?
A The economic data available to policymakers have a considerable time 
lag.
B Economic models always offer an unambiguous guide to the future 
path of the economy.
C Surprise changes in exogenous economic variables make it difficult to 
use fiscal policy as a stabilization tool.
2 Which of the following statements is least  accurate?
A Discretionary fiscal changes are aimed at stabilizing an economy.
B In the context of implementing fiscal policy, the recognition lag is 
often referred to as “driving in the rear view mirror. ”
C Automatic fiscal stabilizers include new plans for additional road 
building by the government.
3 Which of the following statements regarding a fiscal stimulus is most

accurate?
A Accommodative monetary policy reduces the impact of a fiscal 
stimulus.
B Different statistical models will predict different impacts for a fiscal 
stimulus.
C It is always possible to predict precisely the impact of a fiscal stimulus 
on employment.
4 Which of the following statements is most  accurate?
A An increase in the budget deficit is always expansionary.
B An increase in government spending is always expansionary.
C The structural deficit is always larger than the deficit below full 
employment.
5 Crowding out refers to a:
A fall in interest rates that reduces private investment.
B rise in private investment that reduces private consumption.
C rise in government borrowing that reduces the ability of the private 
sector to access investment funds.
6 A contractionary fiscal policy will always involve which of the following?
A A balanced budget
B A reduction in government spending
C A fall in the budget deficit or rise in the surplus

7 Which one of the following statements is most  accurate?
A Ricardian equivalence refers to individuals having no idea of future tax 

Reading 18 ■ Monetary and Fiscal Policy 318
B If there is high unemployment in an economy, then easy monetary and 
fiscal policies should lead to an expansion in aggregate demand.
C Governments do not allow political pressures to influence fiscal poli -
cies but do allow voters to affect monetary policies.
B is correct. Economic forecasts from models will always have an element of 
uncertainty attached to them and thus are not unambiguous or precise in their 
prescriptions. Once a fiscal policy decision has been made and implemented, 
unforeseen changes in other variables may affect the economy in ways that 
would lead to changes in the fiscal policy if we had perfect foresight. Note that 
it is true that official economic data may be available with substantial time lags, 
making fiscal judgements more difficult.
C is correct. New plans for road building are discretionary and not automatic.

B is correct. Different models embrace differing views on how the economy 
works, including differing views on the impact of fiscal stimuli.
A is correct. Note that increases in government spending may be accompanied 
by even bigger rises in tax receipts and hence may not be expansionary.
C is correct. A fall in interest rates is likely to lead to a rise in investment. 
Crowding out refers to government borrowing that reduces the ability of the 
private sector to invest.
C is correct. Note that a reduction in government spending could be accompa -
nied by an even bigger fall in taxation, making it be expansionary.
B is correct. Note that governments often allow pressure groups to affect fiscal 
policy and that Ricardian equivalence involves individuals correctly anticipating 
future taxes, so A and C are not correct choices.
THE RELATIONSHIP BETWEEN MONETARY AND 

Both monetary and fiscal policies can be used to try and influence the macroeconomy. 
But the impact of monetary policy on aggregate demand may differ depending on the 
fiscal policy stance. Conversely, the impact of fiscal policy might vary under various 
alternative monetary policy conditions. Clearly, policymakers need to understand this 
interaction. For example, they need to consider the impact of changes to the budget 
when monetary policy is accommodative as opposed to when it is restrictive: Can we 
expect the same impact on aggregate demand in both situations?4

The Relationship between Monetary and Fiscal Policy 319
Although both fiscal and monetary policy can alter aggregate demand, they do 
so through differing channels with differing impact on the composition of aggregate 
demand. The two policies are not interchangeable. Consider the following cases in 
which the assumption is made that wages and prices are rigid :
■■Easy fiscal policy/tight monetary policy : If taxes are cut or government spending 
rises, the expansionary fiscal policy will lead to a rise in aggregate output. If this 
is accompanied by a reduction in money supply to offset the fiscal expansion, 
then interest rates will rise and have a negative effect on private sector demand. 
We have higher output and higher interest rates, and government spending will 
be a larger proportion of overall national income.
■■Tight fiscal policy/easy monetary policy : If a fiscal contraction is accompanied 
by expansionary monetary policy and low interest rates, then the private sector

will be stimulated and will rise as a share of GDP , while the public sector will 
shrink.
■■Easy monetary policy/easy fiscal policy : If both fiscal and monetary policy 
are easy, then the joint impact will be highly expansionary—leading to a rise 
in aggregate demand, lower interest rates (at least if the monetary impact is 
larger), and growing private and public sectors.
■■Tight monetary policy/tight fiscal policy : Interest rates rise (at least if the mone -
tary impact on interest rates is larger) and reduce private demand. At the same 
time, higher taxes and falling government spending lead to a drop in aggregate 
demand from both public and private sectors.
4.1 Factors Influencing the Mix of Fiscal and Monetary Policy
Although governments are concerned about stabilizing the level of aggregate demand 
at close to the full employment level, they are also concerned with the growth of 
potential output. To this end, encouraging private investment will be important. It

may best be achieved by accommodative monetary policy with low interest rates and 
a tight fiscal policy to ensure free resources for a growing private sector.
At other times, the lack of a good quality, trained workforce—or perhaps a modern 
capital infrastructure—will be seen as an impediment to growth; thus, an expansion 
in government spending in these areas may be seen as a high priority. If taxes are not 
raised to pay for this, then the fiscal stance will be expansionary. If a loose monetary 
policy is chosen to accompany this expansionary spending, then it is possible  that 
inflation may be induced. Of course, it is an open question as to whether policymakers 
can judge the appropriate levels of interest rates or fiscal spending levels.
Clearly, the mix of policies will be heavily influenced by the political context. A 
weak government may raise spending to accommodate the demands of competing 
vested interests (e.g., subsidies to particular sectors, such as agriculture in the EC), and

thus a restrictive monetary policy may be needed to hold back the possibly inflationary 
growth in aggregate demand through raised interest rates and less credit availability.
Both fiscal and monetary policies suffer from lack of precise knowledge of where 
the economy is today, because data appear initially subject to revision and with a 
time lag. However, fiscal policy suffers from two further issues with regard to its use 
in the short run.
As we saw earlier, it is difficult to implement quickly because spending on capital 
projects takes time to plan, procure, and put into practice. In addition, it is politically 
easier to loosen fiscal policy than to tighten it; in many cases, automatic stabilizers 
are the source of fiscal tightening, because tax rates are not changing and political

Reading 18 ■ Monetary and Fiscal Policy 320
opposition is muted. Similarly, the independence of many central banks means that 
decisions on raising interest rates are outside the hands of politicians and thus can 
be taken more easily.
The interaction between monetary and fiscal policies was also implicitly evident 
in our discussion of Ricardian equivalence because if tax cuts have no impact on 
private spending as individuals anticipate future higher taxes, then clearly this may 
lead policymakers to favour monetary tools.
Ultimately, the interaction of monetary and fiscal policies in practice is an empirical 
question, which we touched on earlier. In their detailed research paper using the IMF’S 
Global Integrated Monetary and Fiscal Model (IMF 2009), IMF researchers examined 
four forms of coordinated global fiscal loosening over a two-  year period, which will 
be reversed gradually after the two years are completed. These are:
■■an increase in social transfers to all households,

■■a decrease in tax on labour income,
■■a rise in government investment expenditure, and
■■a rise in transfers to the poorest in society.
The two types of monetary policy responses considered are:
■■no monetary accommodation, so rising aggregate demand leads to higher inter -
est rates immediately; or
■■interest rates are kept unchanged (accommodative policy) for the two years.
The following important policy conclusions from this study emphasize the role of 
policy interactions:
■■No monetary accommodation : Government spending increases have a much 
bigger effect (six times bigger) on GDP than similar size social transfers 
because the latter are not considered permanent, although real interest rates 
rise as monetary authorities react to rises in aggregate demand and inflation. 
Targeted social transfers to the poorest citizens have double the effect of the 
non-  targeted transfers, while labour tax reductions have a slightly bigger impact 
than the latter.

■■Monetary accommodation:  Except for the case of the cut in labour taxes, fiscal 
multipliers are now much larger than when there is no monetary accommoda -
tion. The cumulative multiplier (i.e., the cumulative effect on real GDP over the 
two years divided by the percentage of GDP , which is a fiscal stimulus) is now 
3.9 for government expenditure compared to 1.6 with no monetary accommo -
dation. The corresponding numbers for targeted social transfer payments are 
0.5 without monetary accommodation and 1.7 with it. The larger multiplier 
effects with monetary accommodation result from rises in aggregate demand 
and inflation, leading to falls in real interest rates and additional private sector 
spending (e.g., on investment goods). Labour tax cuts are less positive.
4.2 Quantitative Easing and Policy Interaction
What about the scenario of zero interest rates and deflation? Fiscal stimulus should

still raise demand and inflation, lowering real interest rates and stimulating private 
sector demand. We saw earlier that quantitative easing has been a feature of major 
economies during 2009–2010. This involves the purchase of government or private 
securities by the central bank from individuals, institutions, or banks and substitut -
ing central bank balances for those securities. The ultimate aim is that recipients will 
subsequently increase expenditures, lending or borrowing in the face of raised cash 
balances and lower interest rates.

The Relationship between Monetary and Fiscal Policy 321
If the central bank purchases government securities on a large scale, it is effectively 
funding the budget deficit and the independence of monetary policy is an illusion. 
This so-  called “printing of money” is feared by many economists as the monetization 
of the government deficit. Note that it is unrelated to the conventional inflation target 
of central banks, such as the Bank of England. Some economists question whether an 
independent central bank should engage in such activity.
4.3 The Importance of Credibility and Commitment
The IMF model implies that if governments run persistently high budget deficits, real 
interest rates rise and crowd out private investment, reducing each country’s produc -
tive potential. As individuals realize that deficits will persist, inflation expectations 
and longer-  term interest rates rise: This reduces the effect of the stimulus by half.

Further, if there is a real lack of commitment to fiscal discipline over the longer 
term, (e.g., because of aging populations) and the ratio of government debt to GDP 
rose by 10 percentage points permanently in the United States alone, then world real 
interest rates would rise by 0.14 percent—leading to a 0.6 percent permanent fall in 
world GDP .
EXAMPLE 19   
Interactions of Monetary and Fiscal Policy
1 In a world where Ricardian equivalence holds, governments would most 
likely  prefer to use monetary rather than fiscal policy because under 
Ricardian equivalence:
A real interest rates have a more powerful effect on the real economy.
B the transmission mechanism of monetary policy is better understood.
C the future impact of fiscal policy changes are fully discounted by eco -
nomic agents.
2 If fiscal policy is easy and monetary policy tight, then:
A interest rates would tend to fall, reinforcing the fiscal policy stance.
B the government sector would tend to shrink as a proportion of total

GDP .
C the government sector would tend to expand as a proportion of total 
GDP .
3 Which of the following has the greatest impact on aggregate demand 
according to an IMF study? A 1 percent of GDP stimulus in:
A government spending.
B rise in transfer benefits.
C cut in labour income tax across all income levels.
C is correct. If Ricardian equivalence holds, then economic agents anticipate 
that the consequence of any current tax cut will be future tax rises, which leads 
them to increase their saving in anticipation of this so that the tax cut has little 
effect on consumption and investment decisions. Governments would be forced 
to use monetary policy to affect the real economy on the assumption that money 
neutrality did not hold in the short term.

Reading 18 ■ Monetary and Fiscal Policy 322
C is correct. With a tight monetary policy, real interest rates should rise and 
reduce private sector activity, which could be at least partially offset by an 
expansion in government activity via the loosening of fiscal policy. The net 
effect, however, would be an expansion in the size of the public sector relative 
to the private sector.
A is correct. The study clearly showed that direct spending by the government 
leads to a larger impact on GDP than changes in taxes or benefits.
SUMMARY
In this reading, we have sought to explain the practices of both monetary and fiscal 
policy. Both can have a significant impact on economic activity, and it is for this reason 
that financial analysts need to be aware of the tools of both monetary and fiscal policy, 
the goals of the monetary and fiscal authorities, and most important the monetary 
and fiscal policy transmission mechanisms.

■■Governments can influence the performance of their economies by using com -
binations of monetary and fiscal policy. Monetary policy refers to central bank 
activities that are directed toward influencing the quantity of money and credit 
in an economy. By contrast, fiscal policy refers to the government’s decisions 
about taxation and spending. The two sets of policies affect the economy via 
different mechanisms.
■■Money fulfills three important functions: It acts as a medium of exchange, 
provides individuals with a way of storing wealth, and provides society with a 
convenient unit of account. Via the process of fractional reserve banking, the 
banking system can create money.
■■The amount of wealth that the citizens of an economy choose to hold in the 
form of money—as opposed to, for example, bonds or equities—is known 
as the demand for money. There are three basic motives for holding money: 
transactions-  related, precautionary, and speculative.

■■The addition of 1 unit of additional reserves to a fractional reserve banking sys -
tem can support an expansion of the money supply by an amount equal to the 
money multiplier, defined as 1/reserve requirement (stated as a decimal).
■■The nominal rate of interest is comprised of three components: a real required 
rate of return, a component to compensate lenders for future inflation, and a 
risk premium to compensate lenders for uncertainty (e.g., about the future rate 
of inflation).
■■Central banks take on multiple roles in modern economies. They are usually 
the monopoly supplier of their currency, the lender of last resort to the banking 
sector, the government’s bank and bank of the banks, and they often supervise 
banks. Although they may express their objectives in different ways, the overar -
ching objective of most central banks is price stability.
■■For a central bank to be able to implement monetary policy objectively, it

should have a degree of independence from government, be credible, and be 
transparent in its goals and objectives.

Summary 323
■■The ultimate challenge for central banks as they try to manipulate the supply 
of money to influence the economy is that they cannot control the amount of 
money that households and corporations put in banks on deposit, nor can they 
easily control the willingness of banks to create money by expanding credit. 
Taken together, this also means that they cannot always control the money sup -
ply. Therefore, there are definite limits to the power of monetary policy.
■■The concept of money neutrality is usually interpreted as meaning that money 
cannot influence the real economy in the long run. However, by the setting of 
its policy rate, a central bank hopes to influence the real economy via the policy 
rate’s impact on other market interest rates, asset prices, the exchange rate, and 
the expectations of economic agents.
■■Inflation targeting is the most common monetary policy—although exchange 
rate targeting is also used, particularly in developing economies. Quantitative

easing attempts to spur aggregate demand by drastically increasing the money 
supply.
■■Fiscal policy involves the use of government spending and revenue raising 
(taxation) to impact a number of aspects of the economy: the overall level of 
aggregate demand in an economy and hence the level of economic activity; the 
distribution of income and wealth among different segments of the population; 
and hence ultimately the allocation of resources between different sectors and 
economic agents.
■■The tools that governments use in implementing fiscal policy are related to 
the way in which they raise revenue and the different forms of expenditure. 
Governments usually raise money via a combination of direct and indirect 
taxes. Government expenditure can be current on goods and services or can 
take the form of capital expenditure, for example, on infrastructure projects.
■■As economic growth weakens, or when it is in recession, a government can

enact an expansionary fiscal policy—for example, by raising expenditure 
without an offsetting increase in taxation. Conversely, by reducing expenditure 
and maintaining tax revenues, a contractionary policy might reduce economic 
activity. Fiscal policy can therefore play an important role in stabilizing an 
economy.
■■Although both fiscal and monetary policy can alter aggregate demand, they 
work through different channels, the policies are therefore not interchangeable, 
and they conceivably can work against one another unless the government and 
central bank coordinate their objectives.

Reading 18 ■ Monetary and Fiscal Policy 324
Goodhart, Charles A.E. 1989. “The Conduct of Monetary Policy. ” 
Economic Journal , vol. 99, no. 396:293–346. 
Gray, Simon, and Nick Talbot. 2006. Monetary Operations . 
London: Bank of England (http://www.bankofengland.co.uk/
education/ccbs/handbooks/ccbshb24.htm).IMF (International Monetary Fund). 2009. “The Case for Global 
Fiscal Stimulus” (March): http://www.imf.org/external/pubs/
ft/spn/2009/spn0903.pdf.
Roger, Scott. 2010. “Inflation Targeting Turns 20. ” Finance and 
Development , vol. 47, no. 1:46–49 (March).
Truman, Edwin. 2003. Inflation Targeting in the World Economy . 
Washington, DC: Institute for International Economics.

Practice Problems 325
1 As the reserve requirement increases, the money multiplier:
2 Which is the most  accurate statement regarding the demand for money?
A Precautionary money demand is directly related to GDP .
B Transactions money demand is inversely related to returns on bonds.
C Speculative demand is inversely related to the perceived risk of other assets.
3 The following exhibit shows the supply and demand for money:
Quantity of mone yNominal rate of interes tMDMS
I1
I0
I2
M2 M0 M1
 There is an excess supply of money when the nominal rate of interest is:
A I0.
B I1.
C I2.
4 According to the theory of money neutrality, money supply growth does not 
affect variables such as real output and employment in:
A the long run.
B the short run.
C the long and short run.
5 Which of the following best describes a fundamental assumption when mone -
tary policy is used to influence the economy?
A Financial markets are efficient.

B Money is not neutral in the short run.
C Official rates do not affect exchange rates.
6 Monetarists are most likely  to believe:
A there is a causal relationship running from inflation to money.
B inflation can be affected by changing the money supply growth rate.

Reading 18 ■ Monetary and Fiscal Policy 326
C rapid financial innovation in the market increases the effectiveness of mone -
tary policy.
7 The proposition that the real interest rate is relatively stable is most  closely 
associated with:
A the Fisher effect.
B money neutrality.
C the quantity theory of money.
8 Which of the following equations is a consequence of the Fisher effect?
A Nominal interest rate = Real interest rate + Expected rate of inflation.
B Real interest rate = Nominal interest rate + Expected rate of inflation.
C Nominal interest rate = Real interest rate + Market risk premium.
9 Central banks would typically be most  concerned with costs of:
A low levels of inflation that are anticipated.
B moderate levels of inflation that are anticipated.
C moderate levels of inflation that are not anticipated.
10 Monetary policy is least likely  to include:
A setting an inflation rate target.
B changing an official interest rate.
C enacting a transfer payment program.

11 Which role is a central bank least likely  to assume?
A Lender of last resort.
B Sole supervisor of banks.
C Supplier of the currency.
12 Which is the most  accurate statement regarding central banks and monetary 
policy?
A Central bank activities are typically intended to maintain price stability.
B Monetary policies work through the economy via four independent 
channels.
C Commercial and interbank interest rates move inversely to official interest 
rates.
13 When a central bank announces a decrease in its official policy rate, the desired 
impact is an increase in:
A investment.
B interbank borrowing rates.
C the national currency’s value in exchange for other currencies.
14 Which action is a central bank least likely  to take if it wants to encourage busi -
nesses and households to borrow for investment and consumption purposes?
A Sell long-  dated government securities.
B Purchase long-  dated government treasuries.

C Purchase mortgage bonds or other securities.
15 A central bank that decides the desired levels of interest rates and inflation and 
the horizon over which the inflation objective is to be achieved is most  accu -
rately described as being:
A target independent and operationally independent.
B target independent but not operationally independent.

Practice Problems 327
C operationally independent but not target independent.
16 A country that maintains a target exchange rate is most likely  to have which 
outcome when its inflation rate rises above the level of the inflation rate in the 
target country?
A An increase in short-  term interest rates.
B An increase in the domestic money supply.
C An increase in its foreign currency reserves.
17 A central bank’s repeated open market purchases of government bonds:
A decreases the money supply.
B is prohibited in most countries.
C is consistent with an expansionary monetary policy.
18 In theory, setting the policy rate equal to the neutral interest rate should 
promote:
A stable inflation.
B balanced budgets.
C greater employment.
19 A prolonged period of an official interest rate very close to zero without an 
increase in economic growth most likely  suggests:
A quantitative easing must be limited to be successful.
B there may be limits to the effectiveness of monetary policy.

C targeting reserve levels is more important than targeting interest rates.
20 Raising the reserve requirement is most likely  an example of which type of mon -
etary policy?
A Neutral.
B Expansionary.
C Contractionary.
21 Which of the following is a limitation on the ability of central banks to stimu -
late growth in periods of deflation?
A Ricardian equivalence.
B The interaction of monetary and fiscal policy.
C The fact that interest rates cannot fall significantly below zero.
22 The least likely  limitation to the effectiveness of monetary policy is that central 
banks cannot:
A accurately determine the neutral rate of interest.
B regulate the willingness of financial institutions to lend.
C control amounts that economic agents deposit into banks.
23 Which of the following is the most likely  example of a tool of fiscal policy?
A Public financing of a power plant.
B Regulation of the payment system.
C Central bank’s purchase of government bonds.

24 The least likely  goal of a government’s fiscal policy is to:
A redistribute income and wealth.
B influence aggregate national output.
C ensure the stability of the purchasing power of its currency.

Reading 18 ■ Monetary and Fiscal Policy 328
25 Given an independent central bank, monetary policy actions are more likely  
than fiscal policy actions to be:
A implementable quickly.
B effective when a specific group is targeted.
C effective when combating a deflationary economy.
26 Which statement regarding fiscal policy is most  accurate?
A To raise business capital spending, personal income taxes should be 
reduced.
B Cyclically adjusted budget deficits are appropriate indicators of fiscal policy.
C An increase in the budget surplus is associated with expansionary fiscal 
policy.
27 The least likely  explanation for why fiscal policy cannot stabilize aggregate 
demand completely is that:
A private sector behavior changes over time.
B policy changes are implemented very quickly.
C fiscal policy focuses more on inflation than on unemployment.
28 Which of the following best represents a contractionary fiscal policy?
A Public spending on a high-  speed railway.
B A temporary suspension of payroll taxes.

C A freeze in discretionary government spending.
29 A “pay-  as- you-  go” rule, which requires that any tax cut or increase in entitle -
ment spending be offset by an increase in other taxes or reduction in other 
entitlement spending, is an example of which fiscal policy stance?
A Neutral.
30 Quantitative easing, the purchase of government or private securities by the 
central banks from individuals and/or institutions, is an example of which mon -
etary policy stance?
A Neutral.
31 The most likely  argument against high national debt levels is that:
A the debt is owed internally to fellow citizens.
B they create disincentives for economic activity.
C they may finance investment in physical and human capital.
32 Which statement regarding fiscal deficits is most  accurate?
A Higher government spending may lead to higher interest rates and lower 
private sector investing.

B Central bank actions that grow the money supply to address deflationary 
conditions decrease fiscal deficits.
C According to the Ricardian equivalence, deficits have a multiplicative effect 
on consumer spending.
33 Which policy alternative is most likely  to be effective for growing both the pub -
lic and private sectors?
A Easy fiscal/easy monetary policy.

Practice Problems 329
B Easy fiscal/tight monetary policy.
C Tight fiscal/tight monetary policy.

Reading 18 ■ Monetary and Fiscal Policy 330
SOLUTIONS
1 B is correct. There is an inverse relationship between the money multiplier 
and the reserve requirement. The money multiplier is equal to 1 divided by the 
reserve requirement.
2 A is correct. Precautionary money demand is directly related to GDP . 
Precautionary money balances are held to provide a buffer against unforeseen 
events that might require money. Precautionary balances tend to rise with the 
volume and value of transactions in the economy, and therefore rise with GDP .
3 B is correct. When the interest rate on bonds is I1 there is an excess supply of 
money (equal to M0 – M1 > 0). Economic agents would seek to buy bonds with 
their excess money balances, which would force the price of bonds up and the 
interest rate down to I0.
4 A is correct. According to the theory of money neutrality, an increase in the 
money supply ultimately leads to an increase in the price level and leaves real 
variables unaffected in the long run.

5 B is correct. If money were neutral in the short run, monetary policy would not 
be effective in influencing the economy.
6 B is correct. By definition, monetarists believe prices may be controlled by 
manipulating the money supply.
7 A is correct. The Fisher effect is based on the idea that the real interest rate is 
relatively stable. Changes in the nominal interest rate result from changes in 
expected inflation.
8 A is correct. The Fisher effect implies that changes in the nominal interest rate 
reflect changes in expected inflation, which is consistent with Nominal interest 
rate = Real interest rate + Expected rate of inflation.
9 C is correct. Low levels of inflation has higher economic costs than moderate 
levels, all else equal; unanticipated inflation has greater costs than anticipated 
10 C is correct. Transfer payment programs represent fiscal, not monetary policy.

11 B is correct. The supervision of banks is not a role that all central banks assume. 
When it is a central bank’s role, responsibility may be shared with one or more 
entities.
12 A is correct. Central bank activities are typically intended to maintain price 
stability. Concerning choice B, note that the transmission channels of monetary 
policy are not independent.
13 A is correct. Investment is expected to move inversely with the official policy 
rate.
14 A is correct. Such action would tend to constrict the money supply and increase 
interest rates, all else equal.
15 A is correct. The central bank described is target independent because it set 
its own targets (e.g., the target inflation rate) and operationally independent 
because it decides how to achieve its targets (e.g., the time horizon).
16 A is correct. Interest rates are expected to rise to protect the exchange rate 
target.
17 C is correct. The purchase of government bonds via open market operations

increases banking reserves and the money supply; it is consistent with an 
expansionary monetary policy.

Solutions 331
18 A is correct. The neutral rate of interest is that rate of interest that neither 
stimulates nor slows down the underlying economy. The neutral rate should be 
consistent with stable long-  run inflation.
19 B is correct. A central bank would decrease an official interest rate to stimulate 
the economy. The setting in which an official interest rate is lowered to zero (or 
even slightly below zero) without stimulating economic growth suggests that 
there are limits to monetary policy.
20 C is correct. Raising reserve requirements should slow money supply growth.
21 C is correct. Deflation poses a challenge to conventional monetary policy 
because once the central bank has cut nominal interest rates to zero (or slightly 
less than zero) to stimulate the economy, they cannot cut them further.
22 A is correct. The inability to determine exactly the neutral rate of interest does 
not necessarily limit the power of monetary policy.

23 A is correct. Public financing of a power plant could be described as a fiscal 
policy tool to stimulate investment.
24 C is correct. Ensuring stable purchasing power is a goal of monetary rather than 
fiscal policy. Fiscal policy involves the use of government spending and tax rev -
enue to affect the overall level of aggregate demand in an economy and hence 
the level of economic activity.
25 A is correct. Monetary actions may face fewer delays to taking action than fiscal 
policy, especially when the central bank is independent.
26 B is correct. Cyclically adjusted budget deficits are appropriate indicators of 
fiscal policy. These are defined as the deficit that would exist if the economy was 
at full employment (or full potential output).
27 B is correct. Fiscal policy is subject to recognition, action, and impact lags.
28 C is correct. A freeze in discretionary government spending is an example of a 
contractionary fiscal policy.

29 A is correct. A “pay-  as- you-  go” rule is a neutral policy because any increases in 
spending or reductions in revenues would be offset. Accordingly, there would 
be no net impact on the budget deficit/surplus.
30 B is correct. Quantitative easing is an example of an expansionary monetary 
policy stance. It attempts to spur aggregate demand by drastically increasing the 
31 B is correct. The belief is that high levels of debt to GDP may lead to higher 
future tax rates which may lead to disincentives to economic activity.
32 A is correct. Government borrowing may compete with private sector borrow -
ing for investment purposes.
33 A is correct. If both fiscal and monetary policies are “easy, ” then the joint impact 
will be highly expansionary, leading to a rise in aggregate demand, low interest 
rates, and growing private and public sectors.

International Trade and Capital Flows
by Usha Nair-  Reichert, PhD, and Daniel Robert Witschi, PhD, CFA
Usha Nair-  Reichert, PhD, is at Georgia Institute of Technology (USA). Daniel Robert 
Witschi, PhD, CFA (Switzerland).
a. compare gross domestic product and gross national product;
b. describe benefits and costs of international trade; 
c. distinguish between comparative advantage and absolute 
advantage;
d. compare the Ricardian and Heckscher–Ohlin models of trade and 
the source(s) of comparative advantage in each model;
e. compare types of trade and capital restrictions and their 
economic implications;
f. explain motivations for and advantages of trading blocs, common 
markets, and economic unions;
g. describe common objectives of capital restrictions imposed by 
governments;
h. describe the balance of payments accounts including their 
i. explain how decisions by consumers, firms, and governments

affect the balance of payments;
j. describe functions and objectives of the international 
organizations that facilitate trade, including the World Bank, the 
International Monetary Fund, and the World Trade Organization.
Global investors must address two fundamentally interrelated questions: where to 
invest and in what asset classes? Some countries may be attractive from an equity 
perspective because of their strong economic growth and the profitability of particular 
domestic sectors or industries. Other countries may be attractive from a fixed income 1READING
19

Reading 19 ■ International Trade and Capital Flows 334
perspective because of their interest rate environment and price stability. To identify 
markets that are expected to provide attractive investment opportunities, investors 
must analyze cross-  country differences in such factors as expected GDP growth 
rates, monetary and fiscal policies, trade policies, and competitiveness. From a longer 
term perspective investors also need to consider such factors as a country’s stage of 
economic and financial market development, demographics, quality and quantity of 
physical and human capital (accumulated education and training of workers), and its 
area(s) of comparative advantage.1
This reading provides a framework for analyzing a country’s trade and capital flows 
and their economic implications. International trade can facilitate economic growth 
by increasing the efficiency of resource allocation, providing access to larger capital

and product markets, and facilitating specialization based on comparative advantage. 
The flow of financial capital (funds available for investment) between countries with 
excess savings and those where financial capital is scarce can increase liquidity, raise 
output, and lower the cost of capital. From an investment perspective, it is important 
to understand the complex and dynamic nature of international trade and capital flows 
because investment opportunities are increasingly exposed to the forces of global 
competition for markets, capital, and ideas.
This reading is organized as follows. Section 2 defines basic terminology used in 
the reading and describes patterns and trends in international trade and capital flows. 
It also discusses the benefits of international trade, distinguishes between absolute and 
comparative advantage, and explains two traditional models of comparative advan -
tage. Section 3 describes trade restrictions and their implications and discusses the

motivation for, and advantages of, trade agreements. Section 4 describes the balance 
of payments and Section 5 discusses the function and objectives of international 
organizations that facilitate trade. A summary of key points and practice problems 
INTERNATIONAL TRADE
The following sections describe the role, importance, and possible benefits and costs 
of international trade. Before beginning those discussions, we define some basic ter -
minology used in this area.
2.1 Basic Terminology
The aggregate output of a nation over a specified time period is usually measured 
as its gross domestic product or its gross national product. Gross domestic product 
(GDP) measures the market value of all final goods and services produced by factors 
of production (such as labor and capital) located within a country/economy during 
a given period of time, generally a year or a quarter. Gross national product (GNP),

however, measures the market value of all final goods and services produced by 
factors of production (such as labor and capital) supplied by residents of a country, 
regardless of whether such production takes place within the country or outside of the 
country. The difference between a country’s GDP and its GNP is that GDP includes, 
and GNP excludes, the production of goods and services by foreigners within that 
country, whereas GNP includes, and GDP excludes, the production of goods and 2
1 Comparative advantage refers to a country’s ability to produce a good at a relatively lower cost than other 
goods it produces, as compared with another country. It will be more precisely defined and illustrated in 
Section 2.4.

International Trade 335
services by its citizens outside of the country. Countries that have large differences 
between GDP and GNP generally have a large number of citizens who work abroad 
(for example, Pakistan and Portugal), and/or pay more for the use of foreign-  owned 
capital in domestic production than they earn on the capital they own abroad (for 
example, Brazil and Canada). Therefore, GDP is more widely used as a measure of 
economic activity occurring within  the country, which, in turn, affects employment, 
growth, and the investment environment.
Imports  are goods and services that a domestic economy (i.e., households, firms, 
and government) purchases from other countries. For example, the US economy 
imports (purchases) cloth from India and wine from France. Exports  are goods 
and services that a domestic economy sells to other countries. For example, South 
Africa exports (sells) diamonds to the Netherlands, and China exports clothing to

the European Union. So how are services imported or exported? If a Greek shipping 
company transports the wine that the United States imports from France, the United 
States would classify the cost of shipping as an import of services from Greece and 
the wine would be classified as an import of goods from France. Similarly, when a 
British company provides insurance coverage to a South African diamond exporter, 
Britain would classify the cost of the insurance as an export of services to South Africa. 
Other examples of services exported/imported include engineering, consulting, and 
medical services.
The terms of trade  are defined as the ratio of the price of exports to the price of 
imports, representing those prices by export and import price indexes, respectively. 
The terms of trade capture the relative cost of imports in terms of exports. If the 
prices of exports increase relative to the prices of imports, the terms of trade have

improved because the country will be able to purchase more imports with the same 
amount of exports.2 For example, when oil prices increased during 2007–2008, major 
oil exporting countries experienced an improvement in their terms of trade because 
they had to export less oil in order to purchase the same amount of imported goods. 
In contrast, if the price of exports decreases relative to the price of imports, the terms 
of trade have deteriorated because the country will be able to purchase fewer imports 
with the same amount of exports. Because each country exports and imports a large 
number of goods and services, the terms of trade of a country are usually measured as 
an index number (normalized to 100 in some base year) that represents a ratio of the 
average price of exported goods and services to the average price of imported goods 
and services. Exhibit 1 shows the terms of trade reported in Salvatore (2010). A value

over (under) 100 indicates that the country, or group of countries, experienced better 
(worse) terms of trade relative to the base year of 2000.
Exhibit 1   Data on the Terms of Trade for Industrial and Developing Countries  
(Unit Export Value/Unit Import Value)
1990 1995 2000 2005 2006
Industrial countries 99.8 104.8 100 101.3 99
Developing countries 103 101.9 100 99.4 100.5
  Africa 100.4 102.8 100 107.9 105.2
  Asia 106.8 106.8 100 91.5 89.2
2 Although the prices of imports and exports are each stated in currency units, the currency units cancel 
out when we take the ratio, so the terms of trade reflect the relative price of imports and exports in real 
(i.e., quantity) terms: units of imports per unit of exports. To see this, note that if one unit of imports costs 
PM currency units and one unit of exports is priced at PX currency units, then the country can buy PX/PM 
(= Terms of trade) units of imports for each unit of exports.

Reading 19 ■ International Trade and Capital Flows 336
  Europe 68.7 105.5 100 102.1 99.8
  Middle East 109 68.4 100 140.4 155.9
  Western hemisphere 129.6 107.1 100 104.3 108.7
Source:  Salvatore (2010), case study 3–3. Base year 2000 = 100.
As an example, Exhibit 1 indicates that from 1990 to 2006 both of the broader 
groups, developing and industrial countries, experienced a slight decline in their 
terms of trade. Looking at the disaggregated data indicates that developing countries 
in Asia and the Western hemisphere experienced a considerable decline in terms of 
trade while those in Europe and the Middle East (which benefited from rising prices 
of their petroleum exports) experienced a substantial increase. Africa also experienced 
a small improvement in its terms of trade during this period.
Net exports  is the difference between the value of a country’s exports and the 
value of its imports (i.e., value of exports minus imports). If the value of exports equals

the value of imports, then trade is balanced. If the value of exports is greater (less) 
than the value of imports, then there is a trade surplus (deficit) . When a country 
has a trade surplus, it lends to foreigners or buys assets from foreigners reflecting 
the financing needed by foreigners running trade deficits with that country. Similarly, 
when a country has a trade deficit, it has to borrow from foreigners or sell some of its 
assets to foreigners. Section 4 on the balance of payments explains these relationships 
more fully.
Autarky  is a state in which a country does not trade with other countries. This 
means that all goods and services are produced and consumed domestically. The price of 
a good or service in such an economy is called its autarkic price . An autarkic economy 
is also known as a closed economy  because it does not trade with other countries. 
An open economy , in contrast, is an economy that trades with other countries. If

there are no restrictions on trade, then members of an open economy can buy and 
sell goods and services at the price prevailing in the world market, the world price . 
An open economy can provide domestic households with a larger variety of goods 
and services, give domestic companies access to global markets and customers, and 
offer goods and services that are more competitively priced. In addition, it can offer 
domestic investors access to foreign capital markets, foreign assets, and greater invest -
ment opportunities. For capital intensive industries, such as automobiles and aircraft, 
manufacturers can take advantage of economies of scale because they have access to 
a much larger market. Free trade  occurs when there are no government restrictions 
on a country’s ability to trade. Under free trade, global aggregate demand and supply 
determine the equilibrium quantity and price of imports and exports. Government

policies that impose restrictions on trade, such as tariffs and quotas (discussed later in 
the reading), are known as trade protection  and prevent market forces (demand and 
supply) from determining the equilibrium price and quantity for imports and exports. 
According to Deardorff, globalization  refers to the “increasing worldwide integration 
of markets for goods, services, and capital that began to attract special attention in the 
late 1990s. ”3 It also references “a variety of other changes that were perceived to occur 
at about the same time, such as an increased role for large corporations (multinational Exhibit 1   (Continued)
3 Deardorff, Alan. “Deardorff’s Glossary of International Economics” (www-  personal.umich.edu/~alandear/
glossary).

International Trade 337
corporations) in the world economy and increased intervention into domestic policies 
and affairs by international institutions, ” such as the International Monetary Fund, 
the World Trade Organization, and the World Bank.
The levels of aggregate demand and supply and the quantities of imports and 
exports in an economy are related to the concepts of excess demand  and excess supply . 
Exhibit 2 shows supply and demand curves for cars in the United Kingdom. E is the 
autarkic equilibrium at price PA and quantity QA, with the quantity of cars demanded 
equaling the quantity supplied. Now, consider a situation in which the country opens 
up to trade and the world price is P1. At this price, the quantity demanded domestically 
is QK while the quantity supplied is QJ. Hence excess demand is QJ QK. This quantity 
is satisfied by imports. For example, at a world price of $15,000, the quantity of cars

demanded in the United Kingdom might be 2 million and UK production of cars only 
1.5 million. As a result, the excess demand of 500,000 would be satisfied by imports. 
Returning to Exhibit 2, now consider a situation in which the world price is P2. The 
quantity demanded is QC while the quantity supplied is QD. Hence, the domestic excess 
supply at world price P2 is QC QD, which results in exports of QC QD.
Exhibit 2   Excess Demand, Excess Supply, Imports and Exports
Price of Cars
P1PAP2
0 QCQ  J QA QDQK CarsDomestic
Supply
C
D
E
KJExcess Supply = Exports
Domestic
DemandExcess Demand = Imports
2.2 Patterns and Trends in International Trade and Capital 
Flows
The importance of trade in absolute and relative terms (trade-  to- GDP ratio) is illus -
trated in Exhibits 3 through 5. Exhibit 3 shows that trade as a percentage of regional 
GDP increased in all regions of the world during 1970–2006. Developing countries 
in Asia had the fastest growth in trade, increasing from less than 20 percent of GDP

Reading 19 ■ International Trade and Capital Flows 338
Exhibit 3   Trade in Goods and Services (Percent of Regional GDP) 
Percent
140
120
100
80
60
40
20
0
79 88 97 76 85 94 03 06 00 73 70 82 91
Middle East and North Africa
Sub-Saharan Africa
Developing AsiaCEE and CIS
Latin AmericaAdvanced Economies
Note : CEE = Central and Eastern Europe; CIS = Commonwealth of Independent States
Source:  IMF Issues Brief “Globalization: A Brief Overview, ” 2008.
Exhibit 4 indicates that trade as a percentage of GDP and the GDP growth rate 
have increased in most regions of the world during 1990–2006. However, data for 
2008 (not shown) indicates a decline that, although consistent with the worldwide 
economic downturn, varied across country groups. High-  income countries that are 
members of the Organisation for Economic Co-  Operation and Development (OECD) 
experienced a growth rate of 2.4 percent during 2000–2006, but had a growth rate 
of only 0.3 percent in 2008. The corresponding numbers for growth in non-  OECD

high-  income countries are 5.0 percent and 3.2 percent, respectively; for lower-  middle-  
income countries, they are 7.7 percent and 7.5 percent, respectively. The 2009 World 
Development Report affirmed the link between trade and growth and noted evidence 
that all rich and emerging economies are oriented to being open to trade. More spe -
cifically, the report indicated:
…When exports are concentrated in labor-  intensive manufacturing, trade 
increases the wages for unskilled workers, benefiting poor people. It also 
encourages macroeconomic stability, again benefiting the poor, who are 
more likely to be hurt by inflation. And through innovation and factor 
accumulation, it enhances productivity and thus growth. There may be 
some empirical uncertainty about the strength of trade’s relationship with 
growth. But essentially all rich and emerging economies have a strong trade 
orientation. (World Bank 2009)

International Trade 339
Of course, trade is not the only factor that influences economic growth. Research 
has also identified such factors as the quality of institutions, infrastructure, and edu -
cation; economic systems; the degree of development; and global market conditions 
(World Trade Organization 2008).
Exhibit 4   Trade Openness and GDP Growth
Trade as Percent of GDP  
(averaged over the period) Average GDP growth (%)
Country Group 1980–1989 1990–1999 2000–2006 1980–1989 1990–1999 2000–2006
World 37.2 41.0 50.7 3.1 2.7 3.2
High income:
  All 38.1 40.3 49.5 3.1 2.6 2.5
  OECD 35.3 37.2 44.7 3.1 2.5 2.4
  Non-  OECD 120.0 128.1 172.5 3.9 4.5 5.0
Low and middle 
income:
  All 32.4 44.4 56.9 3.4 3.5 5.8
  Middle 32.4 44.5 57.1 3.4 3.5 5.8
  Upper middle 33.4 44.3 53.5 2.1 1.7 4.1
  Lower middle 31.4 44.8 61.4 6.0 6.1 7.7
  Low 32.5 39.9 51.7 2.6 2.7 4.8
Note : Averages indicate the average of the annual data for the period covered.
Source:  World Bank.

Exhibit 5 presents trade and foreign direct investment as a percentage of GDP 
for select countries for 1980–2007. Foreign direct investment  (FDI) refers to direct 
investment by a firm in one country (the source country ) in productive assets in a foreign 
country (the host country ). When a firm engages in FDI, it becomes a multinational 
corporation  (MNC) operating in more than one country or having subsidiary firms 
in more than one country. It is important to distinguish FDI from foreign portfolio 
investment  (FPI), which refers to shorter-  term investment by individuals, firms, and 
institutional investors (e.g., pension funds) in such foreign financial instruments as 
foreign stocks and foreign government bonds. Exhibit 5 shows that trade as a percent -
age of GDP for the world as a whole increased from 38 percent in 1980 to 57 percent 
in 2007. In Argentina, trade as a percentage of GDP increased from 12 percent in

1980 to 45 percent in 2007, while in India during this same period it increased from 
15.5 percent to 45 percent. Among the more advanced economies, trade expanded 
sharply in Germany (from 45 percent to 87 percent), but in the United States trade 
expanded more modestly (from 21 percent to 29 percent).
Exhibit 5   Increasing Global Interdependence  
FDI and Trade as a percentage of GDP
Country Type of Flow 1980 1990 2000 2007
World Trade 38.4 38.0 48.8 57.3
FDI: Net Inflows 0.6 1.0 5.1 4.3
FDI: Net Outflows 0.6 1.1 3.6 4.5

Reading 19 ■ International Trade and Capital Flows 340
Argentina Trade 11.5 15.0 22.4 45.0
FDI: Net Inflows –0.1 0.0 0.3 0.6
FDI: Net Outflows 0.9 1.3 3.7 2.5
Germany Trade 45.3 49.7 66.4 86.7
FDI: Net Inflows 0.5 1.4 3.1 4.9
FDI: Net Outflows 0.0 0.2 11.1 2.3
India Trade 15.6 15.7 27.4 45.2
FDI: Net Inflows 0.0 0.0 0.1 1.4
FDI: Net Outflows 0.0 0.1 0.8 2.0
United States Trade 20.8 20.5 25.9 28.7
FDI: Net Inflows 0.7 0.6 1.6 2.9
FDI: Net Outflows 0.6 0.8 3.2 1.9
Source:  World Development Indicators, World Bank.
The increasing importance of multinational corporations is also apparent in 
Exhibit 5. Net FDI inflows and outflows increased as a percentage of GDP between 
1980 and 2000 for each of the countries shown. Trade between multinational firms 
and their subsidiaries (i.e., intra-  firm trade) has become an important part of world 
trade. For example, 46 percent of US imports occur between related parties (Bernard,

Jensen, Redding, and Schott 2010). Globalization of production has increased the 
productive efficiency of manufacturing firms because they are able to decompose 
their value chain into individual components or parts, and then outsource their 
production to different locations where these components can be produced most 
efficiently.4 For example, Nintendo’s Wii remote is manufactured with components 
sourced from several locations around the world: the accelerometer is manufactured 
in the United States; the base memory chip in Italy; the data converter in the United 
States, Thailand, and India; the plastic casing is assembled in China and designed in 
Japan; the Bluetooth chip is manufactured in Taiwan and designed in California (US); 
and the rumble pack is manufactured in various locations in Asia.5 Foreign direct 
investment and outsourcing have increased business investment in these economies 
and provided smaller and less developed economies the opportunity to participate in

international trade. For example, the World Investment Report (2002) indicates that 
in January 2002 Intel had 13 fabrication plants and 11 assembly and testing sites in 
7 countries/regions. It was the leading national exporter from Ireland, Philippines, 
and Costa Rica, and 17th among foreign exporters from China. These trends indicate 
the increasing global interdependence of economies, although the degree of interde -
pendence varies. Greater interdependence also means that economies are now more 
exposed to global competition. As a result they must be more flexible in their produc -
tion structure in order to respond effectively to changes in global demand and supply.Exhibit 5   (Continued)
4 Hill and Hult (2019) explains the idea of the firm as a value chain: “The operations of the firms can be 
thought of as a value chain composed of a series of distinct value creation activities including produc -

tion, marketing and sales, materials management, R&D, human resources, information systems, and firm 
infrastructure. ” Production itself can be broken down into distinct components and each component 
outsourced separately.
5 http://money.cnn.com/magazines/fortune/storysupplement/wiiremote/index.htm.

International Trade 341
The complexity of trading relationships has also increased with the development of 
sophisticated global supply chains that include not only final goods but also interme -
diate goods and services. Increased global interdependence has changed the risk and 
return profiles of many economies. Economies that have greater international links are 
more exposed to, and affected by, economic downturns and crises occurring in other 
parts of the world. The contagion effect of the Asian financial crisis, which began in 
Thailand in July 1997, spread to many other markets, such as Indonesia, Malaysia, 
South Korea, Philippines, Hong Kong, Singapore, and Taiwan. It even affected Brazil 
and Russia to some degree, although there is less clarity about the mechanisms by 
which the crisis spread beyond Asia. Among the outward symptoms of the crisis 
were exchange rate problems, such as currency speculation and large depreciation of

currencies, capital flight, and financial and industrial sector bankruptcies. However, 
recovery was surprisingly swift and all these economies exhibited positive growth by 
the second quarter of 1999 (Gerber 2017).
2.3 Benefits and Costs of International Trade
The preceding sections have described the growth of world trade and the increasing 
interdependence of national economies. Has trade been beneficial? The benefits and 
costs of international trade have been widely debated. The most compelling arguments 
supporting international trade are: countries gain from exchange and specialization, 
industries experience greater economies of scale, households and firms have greater 
product variety, competition is increased, and resources are allocated more efficiently.
Gains from exchange occur when trade enables each country to receive a higher 
price for its exports (and greater profit) and/or pay a lower price for imported goods

instead of producing these goods domestically at a higher cost (i.e., less efficiently). 
This exchange, in turn, leads to a more efficient allocation of resources by increasing 
production of the export good and reducing production of the import good in each 
country (trading partner). This efficiency allows consumption of a larger bundle of 
goods, thus increasing overall welfare. The fact that trade increases overall welfare 
does not, of course, mean that every individual consumer and producer is better off. 
What it does mean is that the winners could, in theory, compensate the losers and 
still be better off .
Trade also leads to greater efficiency by fostering specialization based on com -
parative advantage. Traditional trade models, such as the Ricardian model and the 
Heckscher–Ohlin model, focus on specialization and trade according to comparative 
advantage arising from differences in technology and factor endowments, respectively. 
These models will be discussed in the next section.

Newer models of trade focus on the gains from trade that result from economies 
of scale, greater product variety, and increased competition. In an open economy, 
increased competition from foreign firms reduces the monopoly power of domestic 
firms and forces them to become more efficient, as compared to a closed economy. 
Industries that exhibit increasing returns to scale (for example, the automobile and 
steel industries) benefit from increased market size as a country starts trading because 
the average cost of production declines as output increases in these industries. 
Monopolistically competitive models of trade have been used to explain why there is 
significant two-  way trade (known as intra-  industry trade ) between countries within 
the same industry. Intra-  industry trade occurs when a country exports and imports 
goods in the same product category or classification.
In a monopolistically competitive industry, there are many firms; each firm produces

a unique or differentiated product, there are no exit or entry barriers, and long-  run 
economic profits are zero. In such a model, even though countries may be similar, they 
gain from trade because each country focuses on the production and export of one or 
more varieties of the good and imports other varieties of the good. For example, the

Reading 19 ■ International Trade and Capital Flows 342
European Union exports and imports different types of cars. Consumers gain from 
having access to a greater variety of final goods. Firms benefit from greater economies 
of scale because firms both within and outside the EU are able to sell their goods in 
both markets. Hence, scale economies allow firms to benefit from the larger market 
size and experience lower average cost of production as a result of trade.
Research suggests that trade liberalization can lead to increased real (that is, 
inflation-  adjusted) GDP although the strength of this relationship is still debated. 
The positive influence of trade on GDP can arise from more efficient allocation of 
resources, learning by doing, higher productivity, knowledge spillovers, and trade-  
induced changes in policies and institutions that affect the incentives for innovation.6 
In industries where there is “learning by doing, ” such as the semiconductor industry,

the cost of production per unit declines as output increases because of expertise and 
experience acquired in the process of production. Trade can lead to increased exchange 
of ideas, freer flow of technical expertise, and greater awareness of changing consumer 
tastes and preferences in global markets. It can also contribute to the development of 
higher quality and more effective institutions and policies that encourage domestic 
innovation. For example, Coe and Helpman (1995) show that foreign research and 
development (R&D) has beneficial effects on domestic productivity. These effects 
become stronger the more open an economy is to foreign trade. They estimate that 
about a quarter of the benefits of R&D investment in a G–7 country accrues to their 
trading partners.7 Hill (2007) discusses the case of Logitech, a Swiss company that 
manufactures computer mice. In order to win original equipment manufacturer (OEM)

contracts from IBM and Apple, Logitech needed to develop innovative designs and 
provide high-  volume production at a low cost. So in the late 1980s they moved to 
Taiwan, which had a highly qualified labor force, competent parts suppliers, a rapidly 
expanding local computer industry, and offered Logitech space in a science park at a 
very competitive rate. Soon thereafter, Logitech was able to secure the Apple contract.
Opponents of free trade point to the potential for greater income inequality and 
the loss of jobs in developed countries as a result of import competition. As a country 
moves toward free trade, there will be adjustments in domestic industries that are 
exporters as well as those that face import competition. Resources (investments) may 
need to be reallocated into or out of an industry depending on whether that industry 
is expanding (exporters) or contracting (i.e., facing import competition). As a result of

this adjustment process, less-  efficient firms may be forced to exit the industry, which 
may, in turn, lead to higher unemployment and the need for displaced workers to be 
retrained for jobs in expanding industries. The counter argument is that although there 
may be short-  term and even some medium-  term costs, these resources are likely to be 
more effectively (re-)employed in other industries in the long run. Nonetheless, the 
adjustment process is virtually certain to impose costs on some groups of stakeholders. 
For example, the US textile industry has undergone significant changes over the past 
30 years as a result of competition from lower-  priced imports produced in developing 
countries, including increased outsourcing of production by US firms. Example  1 
discusses recent developments and projections for future employment in the industry.
6 “Knowledge spillovers” occur when investments in knowledge creation generate benefits that extend

beyond the investing entity and facilitate learning and innovation by other firms or entities.
7 G–7 countries include Canada, France, Germany, Italy, Japan, the United Kingdom, and the United States.

International Trade 343
EXAMPLE 1   
The US Textile Industry
According to the US Bureau of Labor Statistics (BLS) the textile, textile product, 
and apparel manufacturing industry is very labor intensive and faces strong 
import competition. Changing trade regulations have a big impact on employment 
in this industry. In 2005, members of the World Trade Organization terminated 
the Multi Fiber Agreement that imposed quotas for apparel and textile products. 
This agreement included most US trading partners and, in particular, China. 
The expiration of quotas in 2005 has allowed more apparel and textile products 
to be imported into the United States. Although some bilateral quotas have 
been re-  imposed between the United States and China, imports have increased 
substantially. The low-  skilled, labor intensive parts of the industry, such as fab -
ric for apparel, have lost many jobs as firms shift their operations to countries

with very cheap labor costs. The more skill-  intensive jobs, such as design jobs 
and custom or high-  end items that are produced domestically, have not been 
as adversely affected by trade. Firms in the highly automated and innovative 
sectors of the industry, such as industrial fabrics, carpets, and specialty yarns, 
are competitive on a global scale, and it is expected that they will increase their 
exports as a result of the liberalization of trade in textiles.
The BLS estimates in Exhibit  6 indicate that in 2008 there were 497,100 
wage and salary workers in the textile, textile product, and apparel manufac -
turing industries. California, Georgia, and North Carolina together accounted 
for about 44 percent of these workers. The BLS also estimates that there will 
be a 47.9 percent decline in employment in this sector between 2008 and 2018. 
Increased labor productivity and foreign competition will both continue to 
contribute to this trend.

Exhibit 6   Employment in Textile, Textile Product, and Apparel 
Manufacturing by Industry Segment
2008 and Projected Change 2008–2018  
(Employment in Thousands)
Industry Segment2008  
Employment2008–2018  
Percent Change
Textile, textile product, and apparel 
manufacturing497.1 –47.9
Textile mills 151.1 –47.6
Textile product mills 147.6 –38.1
Apparel manufacturing 198.4 –55.4
Source:  BLS National Employment Matrix, 2008–2018.
The segment of the industry that remains in the United States has responded 
to competitive pressures by adopting new and more advanced technologies and 
becoming very labor efficient. Advanced technology includes computers and 
computer-  controlled equipment that aid in many functions, such as design, 
pattern making and cutting, wider looms, and the use of robotics to move mate -
rial within the plant. All these initiatives are boosting productivity, providing 
workers with increased training and new skills, and changing the nature of work

in the industry. Among the domestic industry’s advantages are its proximity to

Reading 19 ■ International Trade and Capital Flows 344
the domestic market and its ability to respond to fashion trends more rapidly 
than foreign competitors. The domestic industry is also better positioned to 
participate in retailers’ move to just-  in- time inventory management systems 
and electronic data exchange systems.
1 What are the key changes in trade policy that affected the US textile, tex -
tile product, and apparel manufacturing industry?
2 How did increased import competition affect the US industry?
The Multi Fiber Agreement that imposed quotas for apparel and textile products 
came to an end in 2005. This affected trade with most US trading partners and, 
in particular, China. The expiration of quotas in 2005 has allowed more apparel 
and textile products to be imported into the United States. Although some 
bilateral quotas have been re-  imposed between the United States and China, 
imports have increased substantially.

One of the main impacts was that many low-  skilled workers lost their jobs 
as firms moved production out of the United States to lower-  wage countries. 
The effect on more skill-  intensive jobs, such as those involved with design and 
domestically produced custom and high-  end items, has been less severe. The 
highly automated and innovative sectors of the industry, such as industrial fabrics, 
carpets, and specialty yarns, are competitive on a global scale. The industry has 
responded to competitive pressures by adopting new and advanced technologies 
and becoming very labor efficient.
EXAMPLE 2   
Benefits of Trade
Consider two countries that each produce two goods. Suppose the cost of pro -
ducing cotton relative to lumber is lower in Cottonland than in Lumberland.
1 How would trade between the two countries affect the lumber industry in 
Lumberland?
2 How would trade between the two countries affect the lumber industry in 
Cottonland?

3 What would happen to the lumber industry workers in Cottonland in the 
long run?
4 What is the meaning of the expression “gains from trade”?
5 What are some of the benefits from trade?
The lumber industry in Lumberland would benefit from trade. Because the cost 
of producing lumber relative to producing cotton is lower in Lumberland than 
in Cottonland (i.e., lumber is relatively cheap in Lumberland), Lumberland will 
export lumber and the industry will expand.

International Trade 345
The lumber industry in Cottonland would not benefit from trade, at least in the 
short run. Because lumber is relatively expensive to produce in Cottonland, the 
domestic lumber industry will shrink as lumber is imported from Lumberland.
The overall welfare effect in both countries is positive. However, in the short run, 
many lumber producers in Cottonland (and cotton producers in Lumberland) 
are likely to find themselves without jobs as the lumber industry in Cottonland 
and the cotton industry in Lumberland contract. Those with skills that are also 
needed in the other industry may find jobs fairly quickly. Others are likely to 
do so after some re-  training. In the long run, displaced workers should be able 
to find jobs in the expanding export industry. However, those who remain in 
the import-  competing industry may be permanently worse off because their

industry-  specific skills are now less valuable. Thus, even in the long run, trade 
does not necessarily make every stakeholder better off. But the winners could 
compensate the losers and still be better off, so the overall welfare effect of 
opening trade is positive.
Gains from trade imply that the overall benefits of trade outweigh the losses 
from trade. It does not mean that all stakeholders (producers, consumers, gov -
ernment) benefit (or benefit equally) from trade.
Some of the benefits from trade include: gains from exchange and specialization 
based on relative cost advantage; gains from economies of scale as the compa -
nies add new markets for their products; greater variety of products available to 
households and firms; greater efficiency from increased competition; and more 
efficient allocation of resources.
2.4 Comparative Advantage and the Gains from Trade
Up to this point, we have not been precise about what it means for a country to have

a comparative advantage in the production of specific goods and services. In this 
section, we define comparative advantage, distinguish it from the notion of absolute 
advantage, and demonstrate the gains from trading in accordance with comparative 
advantage. We then explain two traditional models of trade—the Ricardian and 
Heckscher–Ohlin models—and the source of comparative advantage in each model.
2.4.1  Gains from Trade: Absolute and Comparative Advantage
A country has an absolute advantage  in producing a good (or service) if it is able 
to produce that good at a lower cost or use fewer resources in its production than its 
trading partner. For example, suppose a worker in Brazil can produce either 20 pens 
or 40 pencils in a day. A worker in China can produce either 10 pens or 60 pencils. 
A Chinese worker produces 60 pencils a day while a Brazilian worker produces only 
40 pencils a day. Hence, China produces pencils at a lower cost than Brazil, and has

an absolute advantage in the production of pencils. Similarly, Brazil produces pens 
at a lower cost than China, and hence has an absolute advantage in the production of 
pens. A country has a comparative advantage  in producing a good if its opportunity 
cost of producing that good is less than that of its trading partner. In our example, the 
opportunity cost of producing an extra pen in China is 6 pencils. It is the opportunity 
foregone; namely, the number of pencils China would have to give up to produce an

Reading 19 ■ International Trade and Capital Flows 346
extra pen. If Brazil does not trade and has to produce both pens and pencils, it will 
have to give up 2 pencils in order to produce a pen. Similarly, in China each pen will 
cost 6 pencils. Hence, the opportunity cost of a pen in Brazil is 2 pencils, whereas in 
China it is 6 pencils. Brazil has the lower opportunity cost and thus a comparative 
advantage in the production of pens. China has a lower opportunity cost (1 pencil 
costs 1/6th of a pen) than Brazil (1 pencil costs ½ a pen) in the production of pencils 
and thus has a comparative advantage in the production of pencils. Example 3 further 
illustrates these concepts.
EXAMPLE 3   
Absolute and Comparative Advantages
Suppose there are only two countries, India and the United Kingdom. India 
exports cloth to the United Kingdom and imports machinery. The output per 
worker per day in each country is shown in Exhibit 7:
Exhibit 7   Output per Worker per Day
Machinery Cloth (yards)

United Kingdom 4 8
India 2 16
1 Which country has an absolute advantage in the production of:
A machinery?
B cloth?
2 Do the countries identified in Question 1 as having an absolute advantage 
in the production of A) machinery and B) cloth, also have a comparative 
advantage in those areas?
Solution to 1A: 
The United Kingdom has an absolute advantage in the production of machinery 
because it produces more machinery per worker per day than India.
Solution to 1B: 
India has an absolute advantage in the production of cloth because it produces 
more cloth per worker per day than the United Kingdom.
Solution to 2A and 2B: 
In both cases, the answer is “yes. ” In the case of machinery, the opportunity cost 
of a machine in the United Kingdom is 2 yards of cloth (8 ÷ 4 or 1 machine = 
2 yards cloth). This amount is the autarkic price of machines in terms of cloth

in the United Kingdom. In India, the opportunity cost of a machine is 8 yards 
of cloth (16 ÷ 2 or 1 machine = 8 yards cloth). Thus, the United Kingdom has a 
comparative advantage in producing machines. In contrast, the opportunity cost 
of a yard of cloth in the United Kingdom and in India is ½ and 1/8 of a machine, 
respectively. India has a lower opportunity cost (1/8 of a machine) and, therefore, 
a comparative advantage in the production of cloth.

International Trade 347
It is important to note that even if a country does not have an absolute advantage 
in producing any of the goods, it can still gain from trade by exporting the goods in 
which it has a comparative advantage. In Example 3, if India could produce only 6 
yards of cloth per day instead of 16 yards of cloth, the United Kingdom would have 
an absolute  advantage in both machines and cloth. However, India would still have 
a comparative  advantage in the production of cloth because the opportunity cost 
of a yard of cloth in India, 1/3 of a machine in this case, would still be less than the 
opportunity cost of a yard of cloth in the United Kingdom ( ½ of a machine as before).
Let us now illustrate the gains from trading according to comparative advantage. 
In Example  3, if the United Kingdom could sell a machine for more than 2 yards 
of cloth and if India could purchase a machine for less than 8 yards of cloth, both

countries would gain from trade. Although it is not possible to determine the exact 
world price without additional details regarding demand and supply conditions, both 
countries would gain from trade as long as the world price for machinery in terms 
of cloth is between the autarkic prices of the trading partners. In our example, this 
price corresponds to a price of between 2 and 8 yards of cloth for a machine. The 
further away the world price of a good or service is from its autarkic price in a given 
country, the more that country gains from trade.  For example, if the United Kingdom 
was able to sell a machine to India for 7 yards of cloth (i.e., closer to India’s autarkic 
price), it would gain 5 yards of cloth per machine sold to India compared with its 
own autarkic price (with no trade) of 1 machine for 2 yards of cloth. However, if the 
United Kingdom was able to sell a machine to India for only 3 yards of cloth (closer

to the UK autarkic price), it would gain only 1 yard of cloth per machine sold to India 
compared with its own autarkic price.
Exhibits 8 and 9 provide the production and consumption schedules of both coun -
tries at autarky and after trade has commenced. In autarky (Exhibit 8), the United 
Kingdom produces and consumes 200 machines and 400 yards of cloth (without 
trade, consumption of each product must equal domestic production). Similarly, 
India produces 100 machines and 800 yards of cloth in autarky. In a world economy 
consisting of only these two countries, total output for each commodity is the sum 
of production in both countries. Therefore, total world output is 300 machines and 
1,200 yards of cloth.
Exhibit 8   Production and Consumption in Autarky
Autarkic Production Autarkic Consumption
  Machinery (m) 200 200
  Cloth (yards) (c) 400 400
India
  Machinery 100 100
  Cloth (yards) 800 800
Total World:
  Machinery 300 300
  Cloth (yards) 1200 1200

Machinery 300 300
Now, assume that the United Kingdom and India start trading and that the world 
price of 1 machine is 4 yards of cloth (1m = 4c). This price is within the range of 
acceptable world trading prices discussed earlier because this price lies between 
the autarkic prices of the United Kingdom (1m = 2c) and India (1m = 8c). Exhibit 9

Reading 19 ■ International Trade and Capital Flows 348
shows that in an open economy, the United Kingdom would specialize in machines 
and India would specialize in cloth. As a result, the United Kingdom produces 400 
machines and no cloth, while India produces 1,600 yards of cloth and no machines. 
The United Kingdom exports 160 machines to India in exchange for 640 yards of cloth. 
After trade begins with India, the United Kingdom consumes 240 machines and 640 
yards of cloth. Consumption in the United Kingdom increases by 40 machines and 
240 yards of cloth. Similarly, India consumes 160 machines and 960 yards of cloth, an 
increase of 60 machines and 160 yards of cloth. World production and consumption is 
now 400 machines and 1,600 yards of cloth. Post-  trade production and consumption 
exceeds the autarkic situation by 100 machines and 400 yards of cloth.
Exhibit 9   Gains from Trade
Post-  trade 
ProductionPost-  trade 
ConsumptionChange in Consumption  
(compared with autarky)
UK

UK
  Machinery 400 240 +40
  Cloth (yards) 0 640 +240
India
  Machinery 0 160 +60
  Cloth (yards) 1600 960 +160
  Machinery 400 400 +100
  Cloth (yards) 1600 1600 +400
Exhibit 10 shows a more general case of gains from trade under increasing costs. 
In Panel A, the curve connecting the X and Y axes is the UK production possibilities 
frontier (PPF).8 That is, it represents the combinations of cloth and machinery that 
the United Kingdom can produce given its technology and resources (capital and 
labor). The slope of the PPF at any point is the opportunity cost of one good in terms 
of the other. The shape of the PPF indicates increasing opportunity cost in terms of 
machines as more cloth is produced and vice versa. To maximize the value of output, 
production occurs where the slope of the PPF equals the relative price of the goods. 
PA represents the autarkic price line, which is tangent to the PPF at A, the autarkic

equilibrium. The slope of the autarkic price line represents the opportunity cost 
before trade. In autarky, the United Kingdom produces and consumes 60 machines 
and 60  thousand yards cloth, and is on indifference curve I.9 When the United 
Kingdom starts trading with India, it faces the world price line P*. This new price line 
is tangent to the PPF at B. The change in relative prices of the goods encourages the 
United Kingdom to increase the production of the good in which it has comparative 
advantage (machines) and produce at B instead of A. We note that at B the United 
Kingdom has increased the production of machines to 120 units and reduced the 
production of cloth to 30 thousand yards. We also note that trade has expanded the 
UK consumption possibilities. The United Kingdom consumes at point E after trade, 
exports 80 machines to India and imports 80 thousand yards of cloth from India. Note 
that E is outside the PPF, but on the world price line that is tangent to the PPF at B.

8 Modified from Salvatore (2011).
9 An indifference curve represents the various combinations of goods (machines and cloth) that provide 
the same level of utility or welfare. Higher indifference curves represent higher levels of utility or welfare.

International Trade 349
This line is also the trading possibilities line because trade occurs along this line. The 
slope of this line is the opportunity cost of a machine in terms of cloth in the world 
market. The United Kingdom has clearly increased its welfare through trade because 
it is able to consume at point E, which is on a higher indifference curve (III) and thus 
represents a higher level of welfare compared with the autarkic consumption point 
A on indifference curve I.
Panel B shows the corresponding situation for India. When trade opens with the 
United Kingdom, India shifts production from A′ to B′, producing more cloth, the 
good in which it has a comparative advantage, and fewer machines. It now exports 
80 thousand yards of cloth to the United Kingdom and imports 80 machines from 
the United Kingdom. India now consumes at E′ which is on the world price line and 
also on a higher indifference curve, III ′, than the autarkic consumption point ( A′) on

indifference curve I ′. Thus, by specializing (incompletely, as is typically the case with 
increasing production costs) in the good in which it has a comparative advantage, each 
country increases its welfare. We should also note that P* is the price at which trade is 
balanced. At this relative world price, the export of cloth from India equals the import 
of cloth into the United Kingdom (80 thousand yards) and the export of machines 
from the United Kingdom equals the imports of machines into India (80 machines).
Exhibit 10   Graphical Depiction of Gains from Trade with Increasing Costs
Panel A. United Kingdom
Cloth (thousands of yards, Y)
Machines, X6080
40
20120
100
0
60 40 20 0 140 120 100 80E
III
P*B CAPA
I

Reading 19 ■ International Trade and Capital Flows 350
Panel B. India
40
20120140
100
0
60 40 20 0 140 120 100 80E′
P*B′
I′III′C′A′P*  A
A country’s comparative advantage can change over time as a result of structural 
shifts in its domestic economy, shifts in the global economy, the accumulation of 
physical or human capital, new technology, the discovery of such natural resources 
as oil, and so on. For example, an increase in skilled labor in China has led several 
multinational companies to establish R&D facilities in China to benefit from its highly 
educated workforce.
EXAMPLE 4   
Changes in Comparative Advantage
Exhibit  11 shows how Taiwan’s comparative advantage changed over time 
as a result of an export-  oriented development strategy it adopted during the 
1960s.10 The challenges of foreign competition created a “virtuous circle” that 
was self-  reinforcing. Taiwan’s changing comparative advantage was the result

of government policy, an increasingly skilled and productive workforce, and 
proactive firms that learned and adapted new technology.Exhibit 10   (Continued)
10 Prior to the 1960s, Taiwan had an import-  substitution policy—that is, a development policy aimed at 
replacing imports with domestic production that was supported by US aid. However, US aid ended in the 
1960s, forcing Taiwan toward export promotion policies.

International Trade 351
Exhibit 11   Changes in Structure of Taiwan’s Merchandise Exports, 1963–2003 (Percentage Shares)
Products 1963 1973 1983 1993 2003
Agricultural products 59.3 15.4 8.0 5.1 2.5
Mining products 2.7 0.9 2.4 1.7 3.5
Manufactures 38 83.6 89.1 93 93.7
  Iron and steel 3.0 1.3 2.5 1.6 3.9
  Chemicals 5.1 1.5 2.4 5.1 8.1
  Other semi-  manufactures 11.7 12.1 11.6 9.6 6.8
  Machinery and transport equipment 1.5 23.5 26.2 44.4 55.7
   Office and telecom equipment 0.3 16.3 13.9 23.8 35.8
   Electrical machinery and apparatus 0.3 2.7 3.6 6.5 8.1
  Textiles 11.7 12.8 7.2 9.6 6.2
  Clothing 3.0 16.1 11.9 4.4 1.4
  Other consumer goods 1.8 16.3 27.4 18.4 11.6
Source:  World Trade Report (2008).
1 How has Taiwan’s structure of exports changed over time?
2 How did increased foreign competition impact the economy?
3 What were the factors that helped to change Taiwan’s comparative 
advantage?
The economy moved from exporting agricultural products and textiles during

the 1960s to exporting clothes and other consumer goods during the 1970s and 
1980s to exporting office and telecommunications equipment in the 1990s. In 
1960, agriculture and manufacturing accounted for 59.3 percent and 38 per -
cent of Taiwan’s exports, respectively. By 2003, the corresponding figures were 
2.5 percent and 93.7 percent. The share of machinery and transport equipment 
(a subcategory of manufacturing) had increased from 1.5 percent in 1960 to 
55.7 percent in 2003.
The challenges of foreign competition created a “virtuous circle” that was self-  
reinforcing. Success in export markets increased the confidence of Taiwanese 
firms and led to greater success in exports through increased productivity, 
higher-  quality products, acquisition of new skills, and adoption of technologies.
The factors that helped change Taiwan’s comparative advantage included gov -
ernment policy, an increasingly skilled and productive workforce, and proactive

firms that learned and adapted new technology.
From an investment perspective, it is critical for analysts to be able to examine a 
country’s comparative and absolute advantages and to analyze changes in them. It is 
also important to understand changes in government policy and regulations, demo -
graphics, human capital, demand conditions, and other factors that may influence

Reading 19 ■ International Trade and Capital Flows 352
comparative advantage and production and trade patterns. This information can then 
be used to identify sectors, industries within those sectors, and companies within 
those industries that will benefit.
2.4.2  Ricardian and Heckscher–Ohlin Models of Comparative Advantage
A discussion of absolute and comparative advantage and the gains from specializa -
tion would be incomplete without a discussion of two important theories of trade, 
the Ricardian Model and the Heckscher–Ohlin Model. These models are based on 
cross-  country differences in technology and in factor endowments, respectively. These 
theoretical models are based on several assumptions, some of which may not be fully 
satisfied in the real world; nonetheless they provide extremely useful insights into the 
determinants and patterns of trade.
Adam Smith argued that a country could gain from trade if it had an absolute

advantage in the production of a good. David Ricardo extended Smith’s idea of the gains 
from trade by arguing that even if a country did not have an absolute advantage in the 
production of any good, it could still gain from trade if it had a comparative advantage 
in the production of a good. In the Ricardian model, labor is the only (variable) factor 
of production. Differences in labor productivity, reflecting underlying differences in 
technology, are the source of comparative advantage and hence the key driver of trade 
in this model. A country with a lower opportunity cost in the production of a good 
has a comparative advantage in that good and will specialize in its production. In 
our two-  country model, if countries vary in size, the smaller country may specialize 
completely, but may not be able to meet the total demand for the product. Hence, the 
larger country may be incompletely specialized, producing and exporting the good in

which it has a comparative advantage but still producing (and consuming) some of 
the good in which it has a comparative disadvantage. It is important to recognize that 
although differences in technology may be a major source of comparative advantage 
at a given point in time, other countries can close the technology gap or even gain a 
technological advantage. The shift of information technology services from developed 
countries to India is an example of comparative advantage shifting over time.11 This 
shift was facilitated by India’s growing pool of highly skilled and relatively low-  wage 
labor, the development and growth of its telecommunication infrastructure, and 
government policies that liberalized trade in the 1990s.
In the Heckscher–Ohlin Model (also known as the factor-  proportions theory), 
both capital and labor are variable factors of production. That is, each good can be 
produced with varying combinations of labor and capital. According to this model,

differences in the relative endowment of these factors are the source of a country’s 
comparative advantage. This model assumes that technology in each industry is the 
same among countries, but it varies between industries. According to the theory, a 
country has a comparative advantage in goods whose production is intensive in the 
factor with which it is relatively abundantly endowed, and would tend to specialize in 
and export that good. Capital is relatively more (less) abundant in a country if the ratio 
of its endowment of capital to labor is greater (less) than that of its trading partner.12 
This scenario means a country in which labor is relatively abundant would export rela -
tively labor-  intensive goods and import relatively capital-  intensive goods. For example, 
because the manufacture of textiles and clothing is relatively labor intensive, they are 
exported by such countries as China and India where labor is relatively abundant.

11 According to NASSCOM (India’s prominent IT-  BPO trade association), Indian firms offer a wide range 
of information technology services that include consulting, systems integration, IT outsourcing/managed 
services/hosting services, training, and support/maintenance. See www.nasscom.in.
12 Alternatively, factor abundance can be defined in terms of the relative factor prices that prevail in 
autarky. Under this definition, labor is more (less) abundant in a country if the cost of labor relative to the 
cost of capital is lower (higher) in that country.

International Trade 353
Relative factor intensities in production can be illustrated with the following 
example. In 2002, capital per worker in the Canadian paper industry was C$118,777, 
whereas in the clothing manufacturing sector it was C$8,954.13 These amounts indicate 
that manufacturing paper is more capital intensive than clothing production. Canada 
trades with Thailand and, being relatively capital abundant compared with Thailand, 
it exports relatively capital intensive paper to Thailand and imports relatively labor 
intensive clothing from Thailand.
Because the Heckscher–Ohlin model has two factors of production, labor and 
capital, (unlike the Ricardian model that has only labor), it allows for the possibility 
of income redistribution through trade. The demand for an input is referred to as a 
derived demand  because it is derived from the demand for the product it is used to 
produce. As a country opens up to trade, it has a favorable impact on the abundant

factor, and a negative impact on the scarce factor. This result is because trade causes 
output prices to change; more specifically, the price of the export good increases and 
the price of the import good declines. These price changes affect the demand for 
factors used to produce the import and export goods, and hence affect the incomes 
received by each factor of production.
To illustrate this point, consider again the opening of trade between the United 
Kingdom and India in Exhibit 10. When trade opened, the United Kingdom expanded 
production of machines—which are assumed to be the capital-  intensive industry—
and reduced production of clothing. India did the opposite. Machines became more 
expensive relative to clothing in the United Kingdom (line P* is steeper than line PA). 
The relative price change, along with the shift in output it induces, leads to a redistri -
bution of income from labor to capital in the United Kingdom. The opposite occurs

in India—machines become cheaper relative to clothing (line P* is flatter than PA′ ), 
production shifts toward clothing, and income is redistributed from capital to labor.
Note that in each country, the relatively cheap good and the relatively cheap factor 
of production both get more expensive when trade is opened. That raises an interest -
ing question: If free trade equalizes the prices of goods among countries, does it also 
equalize the prices of the factors of production? In the simple Heckscher–Ohlin world 
of homogeneous products, homogeneous inputs, and identical technologies among 
countries, the answer is yes: The absolute and relative factor prices are equalized in 
both countries if there is free trade. In the real world, we see that factor prices do not 
converge completely even if there is free trade because several assumptions of the 
models are not fully satisfied in the real world. Nonetheless, it is important to note

that with international trade factor prices display a tendency to move closer together 
in the long run.
Changes in factor endowments can cause changes in the patterns of trade and can 
create profitable investment opportunities. For example, in 1967 Japan had a com -
parative advantage in unskilled-  labor-  intensive goods, such as textiles, apparel, and 
leather. Meier (1998) notes that by 1980, Japan had greatly increased its skilled labor 
and consequently had a comparative advantage in skill-  intensive products, especially 
non-  electrical machinery.
It is important to note that technological differences, as emphasized in the Ricardian 
trade model, and differences in factor abundance, as emphasized in the Heckscher–
Ohlin model, are both important drivers of trade. They are complementary, not 
mutually exclusive. Tastes and preferences can also vary among countries and can 
change over time, leading to changes in trade patterns and trade flows.
13 Appleyard, Field, and Cobb (2010).

Reading 19 ■ International Trade and Capital Flows 354
TRADE AND CAPITAL FLOWS: RESTRICTIONS AND 
AGREEMENTS
Trade restrictions (or trade protection) are government policies that limit the ability 
of domestic households and firms to trade freely with other countries. Examples of 
trade restrictions include tariffs, import quotas, voluntary export restraints (VER), 
subsidies, embargoes, and domestic content requirements. Tariffs  are taxes that a 
government levies on imported goods. Quotas  restrict the quantity of a good that 
can be imported into a country, generally for a specified period of time. A voluntary 
export restraint is similar to a quota but is imposed by the exporting country. An 
export subsidy  is paid by the government to the firm when it exports a unit of a 
good that is being subsidized. The goal here is to promote exports, but it reduces 
welfare by encouraging production and trade that is inconsistent with comparative

advantage. Domestic content provisions  stipulate that some percentage of the value 
added or components used in production should be of domestic origin. Trade restric -
tions are imposed by countries for several reasons including protecting established 
domestic industries from foreign competition, protecting new industries from foreign 
competition until they mature (infant industry argument), protecting and increasing 
domestic employment, protecting strategic industries for national security reasons, 
generating revenues from tariffs (especially for developing countries), and retaliation 
against trade restrictions imposed by other countries.
Capital restrictions  are defined as controls placed on foreigners’ ability to own 
domestic assets and/or domestic residents’ ability to own foreign assets. Thus, in 
contrast with trade restrictions, which limit the openness of goods markets, capital 
restrictions limit the openness of financial markets. Sections 3.1 through 3.4 discuss

trade restrictions. Section 3.5 briefly addresses capital restrictions.
3.1 Tariffs
Tariffs  are taxes that a government levies on imported goods.14 The primary objective 
of tariffs is to protect domestic industries that produce the same or similar goods. 
They may also aim to reduce a trade deficit. Tariffs reduce the demand for imported 
goods by increasing their price above the free trade price. The economic impact of a 
tariff on imports in a small country is illustrated in Exhibit 12. In this context , a small 
country is not necessarily small in size, population, or GDP . Instead, a small country  
is one that is a price taker in the world market for a product and cannot influence 
the world market price. For example, by many measures Brazil is a large country, 
but it is a price taker in the world market for cars. A large country, however, is a 
large importer of the product and can exercise some influence on price in the world

market. When a large country imposes a tariff, the exporter reduces the price of the 
good to retain some of the market share it could lose if it did not lower its price. This 
reduction in price alters the terms of trade and represents a redistribution of income 
from the exporting country to the importing country. So, in theory it is possible for a 
large country to increase its welfare by imposing a tariff if 1) its trading partner does 
not retaliate and 2) the deadweight loss as a result of the tariff (see below) is smaller 
than the benefit of improving its terms of trade. However, there would still be a net 
reduction in global welfare—the large country cannot gain by imposing a tariff unless 
it imposes an even larger loss on its trading partner.3
14 Governments may also impose taxes on exports, although they are less common.

Trade and Capital Flows: Restrictions and Agreements 355
In Exhibit 12, the world price (free trade price) is P*. Under free trade, domestic 
supply is Q1, domestic consumption is Q4, and imports are Q1Q4. After the imposi -
tion of a per-  unit tariff t, the domestic price increases to Pt, which is the sum of the 
world price and the per-  unit tariff t. At the new domestic price, domestic production 
increases to Q2 and domestic consumption declines to Q3, resulting in a reduction 
in imports to Q2Q3.
The welfare effects can be summarized as follows:
■■Consumers suffer a loss of consumer surplus because of the increase in price.15 
This effect is represented by areas A + B + C + D in Exhibit 12.
■■Local producers gain producer surplus from a higher price for their output. This 
effect is represented by area A.
■■The government gains tariff revenue on imports Q2Q3. This effect is represented 
by area C.
The net welfare effect is the sum of these three effects. The loss in consumer surplus

is greater than the sum of the gain in producer surplus and government revenue and 
results in a deadweight loss to the country’s welfare of B + D.
Welfare Effects of an Import Tariff or Quota
Importing Country
Consumer surplus – (A + B + C + D)
Producer surplus +A
Tariff revenue or Quota rents +C
National welfare – B – D
Tariffs create deadweight loss because they give rise to inefficiencies on both the 
consumption and production side. B represents inefficiencies in production. Instead 
of being able to import goods at the world price P*, tariffs encourage inefficient pro -
ducers whose cost of production is greater than P* to enter (or remain in) the market, 
leading to an inefficient allocation of resources. On the consumption side, tariffs 
prevent mutually beneficial exchanges from occurring because consumers who were 
willing to pay more than P* but less than Pt are now unable to consume the good.

15 Consumer surplus, producer surplus, and deadweight loss are defined and discussed in the prerequi -
site reading “Demand and Supply Analysis: Introduction” available online in your Candidate Resources.

Reading 19 ■ International Trade and Capital Flows 356
Exhibit 12   Welfare Effects of Tariff and Import Quota
0AB CD
Q3 Q4 Quantit yDomestic
DemandDomestic
Supply
Q2 Q1Pt
P*Price
EXAMPLE 5   
Analysis of a Tariff
South Africa manufactures 110,000 tons of paper. However, domestic demand 
for paper is 200,000 tons. The world price for paper is $5 per ton. South Africa 
will import 90,000 tons of paper from the world market at free trade prices. If 
the South African government (a small country) decides to impose a tariff of 
20 percent on paper imports, the price of imported paper will increase to $6. 
Domestic production after the imposition of the tariff increases to 130,000 tons, 
while the quantity demanded declines to 170,000 tons.
1 Calculate the loss in consumer surplus arising from the imposition of the 
tariff.
2 Calculate the gain in producer surplus arising from the imposition of the 
tariff.
3 Calculate the gain in government revenue arising from the imposition of 
the tariff.

4 Calculate the deadweight loss arising from the imposition of the tariff.
The loss in consumer surplus = $1 × 170,000 + 1/2 × $1 × 30,000 = $185,000. 
This calculation is represented by areas A + B + C + D in Exhibit 12.
Gain in producer surplus = $1 × 110,000 + 1/2 × ($1 × 20,000) = $120,000; Area 
A in Exhibit 12.

Trade and Capital Flows: Restrictions and Agreements 357
Change in government revenue = $1 × 40,000 = $40,000; Area C in Exhibit 12.
Deadweight loss because of the tariff = 1/2 × $1 × 20,000 + 1/2 × $1 × 30,000 = 
$25,000; Areas B + D in Exhibit 12.
3.2 Quotas
A quota  restricts the quantity of a good that can be imported into a country, gener -
ally for a specified period of time. An import license  specifies the quantity that can 
be imported. For example, the European Union operates a system of annual import 
quotas for steel producers who are not members of the World Trade Organization. 
The 2010 quota was 0.2 million tons a year for Kazakhstan. In the case of Russia, the 
2010 quota of 3.2 million tons per year was a part of an EU–Russia agreement.16 A 
key difference between tariffs and quotas is that the government is able to collect the 
revenue generated from a tariff. This effect is uncertain under a quota. With quotas,

foreign producers can often raise the price of their goods and earn greater profits than 
they would without the quota. These profits are called quota rents . In Exhibit 12, if 
the quota is Q2Q3, the equivalent tariff that will restrict imports to Q2Q3 is t and the 
domestic price after the quota is Pt. This is the same as the domestic price after the 
tariff t was imposed. Area C, however, is now the quota rent or profits that are likely 
to be captured by the foreign producer rather than tariff revenue that is captured by 
the domestic government. If the foreign producer or foreign government captures the 
quota rent, C, then the welfare loss to the importing country, represented by areas 
B + D + C in Exhibit 12, under a quota is greater than under the equivalent tariff. If 
the government of the country that imposes the quota can capture the quota rents 
by auctioning the import licenses for a fee, then the welfare loss under the quota is

similar to that of a tariff, represented by areas B + D.
A voluntary export restraint  (VER) is a trade barrier under which the exporting 
country agrees to limit its exports of the good to its trading partners to a specific 
number of units. The main difference between an import quota and a VER is that 
the former is imposed by the importer, whereas the latter is imposed by the exporter. 
The VER allows the quota rent resulting from the decrease in trade to be captured 
by the exporter (or exporting country), whereas in the case of an import quota there 
is ambiguity regarding who captures the quota rents. Hence, a VER results in welfare 
loss in the importing country. For example, in 1981 the Japanese government imposed 
VERs on automobile exports to the United States.
3.3 Export Subsidies
An export subsidy is a payment by the government to a firm for each unit of a good 
that is exported. Its goal is to stimulate exports. But it interferes with the functioning

of the free market and may distort trade away from comparative advantage. Hence, 
it reduces welfare. Countervailing duties  are duties that are levied by the importing 
country against subsidized exports entering the country. As an example, agricultural 
subsidies in developed countries, notably the EU, have been a contentious issue in 
trade negotiations with less-  developed countries and developed countries that are 
agricultural exporters, such as New Zealand and Australia.
16 For more information, see http://ec.europa.eu/trade/creating-  opportunities/economic-  sectors/
industrial-  goods/steel/.

Reading 19 ■ International Trade and Capital Flows 358
In the case of an export subsidy, the exporter has the incentive to shift sales from 
the domestic to the export market because it receives the international price plus the 
per-  unit subsidy for each unit of the good exported. This scenario raises the price in 
the domestic market by the amount of the subsidy in the small country case (price 
before subsidy plus subsidy). In the large country case, the world price declines as the 
large country increases exports. The net welfare effect is negative in both the large 
and small country cases, with a larger decline in the large country case. This result 
is because in the large country case, the decline in world prices implies that a part 
of the subsidy is transferred to the foreign country, unlike in the small country case.
Exhibit 13 summarizes some of these effects.
Exhibit 13   
Panel A. Effects of Alternative Trade Policies
Tariff Import Quota Export Subsidy VER

Impact on Importing country Importing country Exporting country Importing country
Producer surplus Increases Increases Increases Increases
Consumer surplus Decreases Decreases Decreases Decreases
Government revenue Increases Mixed (depends on 
whether the quota 
rents are captured by 
the importing country 
through sale of licenses 
or by the exporters)Falls (government 
spending rises)No change (rent to 
foreigners)
National welfare Decreases in small 
country  
Could increase in 
large countryDecreases in small 
country  
Could increase in large 
countryDecreases Decreases
Panel B. Effects of Alternative Trade Policies on Price, Production, Consumption, and Trade
Price Increases Increases Increases Increases
Domestic consumption Decreases Decreases Decreases Decreases
Domestic production Increases Increases Increases Increases

Trade Imports decrease Imports decrease Exports increase Imports decrease
EXAMPLE 6   
Tariffs, Quotas, and VERs
Thailand, a small country, has to decide whether to impose a tariff or a quota 
on the import of computers. You are considering investing in a local firm that 
is a major importer of computers.
1 What will be the impact of a tariff on prices, quantity produced, and 
quantity imported in Thailand (the importing country)?
2 If Thailand imposes a tariff, what will the impact be on prices in the 
exporting country?

Trade and Capital Flows: Restrictions and Agreements 359
3 How would a tariff affect consumer surplus, producer surplus, and gov -
ernment revenue in Thailand?
4 Explain whether the net welfare effect of a tariff is the same as that of a 
quota.
5 Which policy, a tariff or a quota, would be most beneficial to the local 
importer in which you may invest and why?
6 If Thailand were to negotiate a VER with the countries from which it 
imports computers, would this be better or worse than an import quota 
for the local importing firm in which you may invest? Why?
A tariff imposed by a small country, such as Thailand, raises the price of com -
puters in the importing country, reduces the quantity imported, and increases 
domestic production.
A tariff imposed by a small country would not change the price of computers 
in the exporting country.
When a small country imposes a tariff, it reduces consumer surplus, increases

producer surplus, and increases government revenue in that country.
The quota can lead to a greater welfare loss than a tariff if the quota rents are 
captured by the foreign government or foreign firms.
A tariff will hurt importers because it will reduce their share of the computer 
market in Thailand. The impact of a quota depends on whether the importers 
can capture a share of the quota rents. Assuming importers can capture at least 
part of the rents, they will be better off with a quota.
The VER would not be better for the local importer than the import quota and 
would most likely be worse. Under the VER, all of the quota rents will be cap -
tured by the exporting countries whereas with an import quota at least part of 
the quota rents may be captured by local importers.
It is important to understand existing trade policies and the potential for policy 
changes that may impact return on investment. Changes in the government’s trade

policy can affect the pattern and value of trade and may result in changes in industry 
structure. These changes may have important implications for firm profitability and 
growth because they can affect the goods a firm can import/export, change demand 
for its products, impact its pricing policies, and create delays through increased 
paperwork, procurement of licenses, approvals, and so on. For example, changes in 
import policies that affect the ability of a firm to import vital inputs for production 
may increase the cost of production and reduce firm profitability.

Reading 19 ■ International Trade and Capital Flows 360
3.4 Trading Blocs, Common Markets, and Economic Unions
There has been a proliferation of trading blocs or regional trading agreements (RTA) in 
recent years. Important examples of regional integration include the North American 
Free Trade Agreement (NAFTA) and the European Union (EU). A regional trading 
bloc is a group of countries that have signed an agreement to reduce and progressively 
eliminate barriers to trade and movement of factors of production among the members 
of the bloc. It may or may not have common trade barriers against countries that are 
not members of the bloc.
There are many different types of regional trading blocs, depending on the level 
of integration that takes place. Free trade areas  (FTA) are one of the most prevalent 
forms of regional integration in which all barriers to the flow of goods and services 
among members have been eliminated. However, each country maintains its own

polices against non-  members. The North American Free Trade Agreement (NAFTA) 
among the United States, Canada, and Mexico is an example of a FTA. A customs 
union  extends the FTA by not only allowing free movement of goods and services 
among members but also creating a common trade policy against non-  members. In 
1947, Belgium, the Netherlands, and Luxemburg (“Benelux”) formed a customs union 
that became a part of the European Community in 1958. The common market  is the 
next level of economic integration that incorporates all aspects of the customs union 
and extends it by allowing free movement of factors of production among members. 
The Southern Cone Common Market (MERCOSUR) of Argentina, Brazil, Paraguay, 
and Uruguay is an example of a common market.17 An economic union  requires an 
even greater degree of integration. It incorporates all aspects of a common market and 
in addition requires common economic institutions and coordination of economic

policies among members. The European Community became the European Union 
in 1993. If the members of the economic union decide to adopt a common currency, 
then it is also a monetary union . For example, with the adoption of the euro, 19 EU 
member countries also formed a monetary union.18
EXAMPLE 7   
Trading Blocs
1 Chile and Australia have a free trade with each other but have separate 
trade barriers on imports from other countries. Chile and Australia are a 
part of a(n)
A FTA.
B Economic union.
C Customs union.
D Common market.
17 For more information, visit the OECD website, http://stats.oecd.org/glossary/.
18 On 1 January  1999, Austria, Belgium, Finland, France, Germany, Ireland, Italy, Luxembourg, the 
Netherlands, Portugal, and Spain adopted the euro. This adoption meant that these countries had to 
surrender control over their domestic monetary policy to the European Central Bank. Greece joined in

2001. Euro coins and notes went into circulation on 1 January 2002, and these countries gave up the last 
vestiges of their national currencies. Other members now include Slovenia (2007), Cyprus (2008), Malta 
(2008), Slovakia (2009), Estonia (2011), Latvia (2014), and Lithuania (2015). The eurozone (i.e., the monetary 
union) is only a subset of the EU membership because some EU members, notably the United Kingdom, 
have not adopted the euro.

Trade and Capital Flows: Restrictions and Agreements 361
2 An RTA that removes all tariffs on imports from member countries, has 
common external tariffs against all non-  members, but does not advance 
further in deepening economic integration is called a(n)
A FTA.
A is correct. Chile and Australia do not a have customs union because they 
do not have a common trade policy with respect to other trade partners (C is 
incorrect). A common market or a economic union entail even more integration 
(B and D are incorrect).
C is correct. A basic FTA does not entail common external tariffs (A is incorrect), 
whereas a common market and an economic union entail integration beyond 
common external tariffs (B and D are incorrect).
Regional integration is popular because eliminating trade and investment barriers 
among a small group of countries is easier, politically less contentious, and quicker

than multilateral trade negotiations under the World Trade Organization (WTO). The 
WTO is a negotiating forum that deals with the rules of global trade between nations 
and where member countries can go to sort out trade disputes. The latest rounds of 
trade negotiations launched by the WTO in 2001 at Doha, Qatar, included several 
contentious issues of specific concern to developing countries, such as the cost of 
implementing trade policy reform in developing countries, market access in developed 
countries for developing countries’ agricultural products, and access to affordable 
pharmaceuticals in developing countries. After nearly a decade of negotiations, very 
limited progress has been made on the major issues. Hence, it is not surprising to 
see a renewed interest in bilateral and multilateral trade liberalization on a smaller 
scale. Policy coordination and harmonization are also easier among a smaller group

of countries. Regional integration can be viewed as a movement toward freer trade.
Regional integration results in preferential treatment for members compared with 
non-  members and can lead to changes in the patterns of trade. Member countries 
move toward freer trade by eliminating or reducing trade barriers against each other, 
leading to a more efficient allocation of resources. But regional integration may also 
result in trade and production being shifted from a lower-  cost non-  member who still 
faces trade barriers to a higher-  cost member who faces no trade barriers. This shift 
leads to a less-  efficient allocation of resources and could reduce welfare. Hence, there 
are two static effects that are direct results of the formation of the customs union: 
trade creation and trade diversion.
Trade creation  occurs when regional integration results in the replacement of 
higher-  cost domestic production by lower-  cost imports from other members. For

example, consider two hypothetical countries, Qualor and Vulcan. Qualor produces 
10 million shirts annually and imports 2 million shirts from Vulcan, which has a lower 
cost of production. Qualor has 10 percent tariffs on imports from Vulcan. Qualor and 
Vulcan then agree to form a customs union. Qualor reduces its production of shirts 
to 7 million and now imports 11 million shirts from Vulcan. The decline in Qualor’s 
domestic production (from 10 million to 7 million shirts) is replaced by importing 
3 million additional shirts from the low-  cost producer, Vulcan. This scenario represents

Reading 19 ■ International Trade and Capital Flows 362
trade creation. The rest of the additional imports (6 million shirts) represent increased 
consumption by Qualor’s consumers because the price of shirts declines after forma -
tion of the custom union.
Trade diversion  occurs when lower-  cost imports from nonmember countries are 
replaced with higher-  cost imports from members. In the example in the preceding 
paragraph, suppose Qualor initially imposes a 10 percent tariff on imports from both 
Vulcan and Aurelia. Aurelia is the lowest-  cost producer of shirts, so Qualor initially 
imports 2 million shirts from Aurelia instead of from Vulcan. Qualor and Vulcan then 
form a customs union, which eliminates tariffs on imports from Vulcan but maintains 
a 10 percent tariff on imports from Aurelia. Now trade diversion could occur if the free 
trade price on imports from Vulcan is lower than the price on imports from Aurelia.

Even though Aurelia is the lowest-  cost producer, it may be a higher-  priced source 
of imports because of the tariff. If this is the case, then Qualor will stop importing 
from Aurelia, a non-  member, and divert its imports to Vulcan, a member of the RTA. 
Both trade creation and trade diversion are possible in an RTA. If trade creation is 
larger than trade diversion, then the net welfare effect is positive. However, there are 
concerns that this may not always be the case.
The benefits ascribed to free trade—greater specialization according to comparative 
advantage, reduction in monopoly power because of foreign competition, economies 
of scale from larger market size, learning by doing, technology transfer, knowledge 
spillovers, greater foreign investment, and better quality intermediate inputs at world 
prices—also apply to regional trading blocs. In addition, fostering greater interdepen -
dence among members of the regional trading bloc reduces the potential for conflict.

Members of the bloc also have greater bargaining power and political clout in the 
global economy by acting together instead of as individual countries.
The 2009 World Development Report points to spillover of growth across borders 
as one of the main benefits of regional integration (Collier and O’Connell 2007). There 
is evidence of considerable spillovers among OECD countries, which are highly inte -
grated both as a group and within their own geographic regions. The long-  run growth 
of integrated countries is interconnected because members have greater access to 
each other’s markets. Strong growth in any RTA country could have a positive impact 
on growth in other RTA member countries. RTAs also enhance the benefits of good 
policy and lead to convergence in living standards. For example, growth spillovers are 
likely to be much smaller among Sub-  Saharan African countries because of a lack of 
integration arising from deficiencies in RTAs and inadequate levels of transportation

and telecommunications infrastructure. Roberts and Deichmann (2008) estimated 
what the cumulative loss in real GDP between 1970 and 2000 would have been if 
Switzerland, which is landlocked and fully integrated with both its immediate neigh -
bors and the world economy, had been subject to the same level of spillovers as the 
Central African Republic. Under such a scenario, Switzerland’s GDP per capita in 
2000 would have been 9.3 percent lower. The cumulative GDP loss would have been 
$334 billion (constant US dollars, 2000), which was the equivalent of 162 percent of 
Switzerland’s real GDP in 2000.
Although regional integration has many advantages, it may impose costs on some 
groups. For example, there was significant concern in the United States that NAFTA 
and especially low-  skilled-  labor intensive imports from Mexico could hurt low-  skilled 
workers. Adjustment costs arose as import competition caused inefficient firms to

exit the market, and the workers in those firms were at least temporarily unemployed 
as they sought new jobs. However, the surviving firms experienced an increase in 
productivity, and US consumers benefited from the increase in product varieties 
imported from Mexico. Feenstra and Taylor (2008) estimated that the product varieties 
exported from Mexico to the United States had grown by an average of 2.2 percent 
a year across all industries. They estimated that NAFTA imposed private costs of 
nearly $5.4 billion a year in the United States during 1994–2002, but that these costs

Trade and Capital Flows: Restrictions and Agreements 363
were offset by an average welfare gain of $5.5 billion a year accruing from increased 
varieties imported from Mexico. Consumer gains from more varieties of products 
continued over time as long as the imports continued, while adjustment costs arising 
from job losses declined over time. In 2003, the gain from increased product varieties 
from Mexico was $11 billion, far exceeding the adjustment costs of $5.4 billion.19 
Their analysis concluded:
…Thus the consumer gains from increased product variety, when summed 
over the years, considerably exceed the private loss from displacement. This 
outcome is guaranteed to occur because the gains from expanded import 
varieties occur every year that the imports are available, whereas labor dis -
placement is a temporary phenomenon. (Feenstra and Taylor 2008, p. 208)
It is important to recognize, however, that workers displaced by regional inte -

gration may have to bear long-  term losses if they are unable to find jobs with wages 
comparable with the jobs they lost or they remain unemployed for a long period. For 
example, although import competition was certainly not the only factor that led to a 
dramatic contraction of the US automobile industry, the impact on employment in 
that industry is likely to be permanent and many former autoworkers, especially older 
workers, may never find comparable jobs.
Concerns regarding national sovereignty, especially where big and small nations 
may be part of the same bloc, have also been an impediment to the formation of FTAs. 
The proposal for a South Asian regional bloc has faced challenges regarding India’s 
role because it is one of the biggest economies in the region.
Regional integration is important from an investment perspective because it 
offers new opportunities for trade and investment. The cost of doing business in a

large, single, regional market is lower and firms can benefit from economies of scale. 
However, it is important to note that differences in tastes, culture, and competitive 
conditions still exist among members of a trading bloc. These differences may limit 
the potential benefits from investments within the bloc. In addition, depending on the 
level of integration and the safeguards in place, problems faced by individual member 
countries in an RTA may quickly spread to other countries in the bloc.
There are at least two challenges in the formation of an RTA and in its potential 
progression from a free trade area to deeper integration in the form of a customs 
union, common market, or economic union. First, cultural differences and historical 
considerations—for example, wars and conflicts—may complicate the social/political 
process of integration. Second, maintaining a high degree of economic integration 
limits the extent to which member countries can pursue independent economic and

social policies. Free trade and mobility of labor and capital tend to thwart policies 
aimed at controlling relative prices and/or quantities within a country, while balance 
of payments and fiscal credibility considerations limit the viability of divergent mac -
roeconomic policies. This situation is especially true in the case of a monetary union 
because monetary policy is not under the control of individual countries and currency 
devaluation/revaluation is not available as a tool to correct persistent imbalances.20 
When persistent imbalances do arise, they may lead to a crisis that spills over to other 
countries facing similar problems. A recent example is the fear of contagion caused 
by the Greek fiscal crisis in 2010. In May 2010, Standard & Poor’s reduced the credit 
ratings on Greece’s government from investment grade to junk status. It also down -
graded the government debt of Spain and Portugal. These countries were suffering

19 Feenstra and Taylor (2008) discuss in their book the data limitations and various assumptions they 
made in their analysis.
20 These limitations are inherent in any system with fixed exchange rates and a high degree of capital 
mobility. They are not unique to a monetary union (i.e., a common currency). For a discussion of currency 
regimes, see the Level I curriculum reading on Currency Exchange Rates.

Reading 19 ■ International Trade and Capital Flows 364
from a combination of high government deficits and slow GDP growth. The credit 
downgrades increased fears that Greece, in particular, would default on its debt and 
cause economic turmoil not only among the healthier countries in the EU but also 
in the United States and Asia. The EU and the International Monetary Fund (IMF) 
agreed on a USD145 billion (EUR110 billion) bailout for Greece in May 2010, and 
provided Ireland with a financing package of about USD113 billion (EUR85 billion) in 
November 2010. As of late 2010, there were continuing concerns about the financial 
health of Greece, Ireland, Portugal, and Spain. The EU, which created the European 
Financial Stability Facility (EFSF) in 2010 to help EU countries in need, has been 
debating the need for an expansion in the scope and financing capacity of the EFSF.
EXAMPLE 8   
Trade Agreements
Bagopia, Cropland, and Technopia decide to enter into an RTA. In the first stage,

they decide to sign a free trade agreement (FTA). After several successful years, 
they decide that it is time to form a common market.
1 Does an FTA make exporting firms in member countries more attractive 
as investment options?
2 How does the common market affect firms doing business in these coun -
tries compared with an FTA?
The first stage, where there is free movement of goods and services among RTA 
members, is called a free trade area. It makes exporting firms a more attractive 
investment proposition because they are able to serve markets in member 
countries without the additional costs imposed by trade barriers.
Unlike an FTA, a common market allows for free movement of factors of 
production, such as labor and capital, among the member economies. Like an 
FTA, it provides access to a much larger market and free movement of goods 
and services. But the common market can create more profitable opportunities

for firms than an FTA by allowing them to locate production in and purchase 
components from anywhere in the common market according to comparative 
advantage.
3.5 Capital Restrictions
There are many reasons for governments to restrict inward and outward flow of 
capital. For example, the government may want to meet some objective regarding 
employment or regional development, or it may have a strategic or defense-  related 
objective. Many countries require approval for foreigners to invest in their country 
and for citizens to invest abroad. Control over inward investment by foreigners 
results in restrictions on how much can be invested, and on the type of industries in 
which capital can be invested. For example, such strategic industries as defense and 
telecommunications are often subject to ownership restrictions. Outflow restrictions 
can include restrictions on repatriation of capital, interest, profits, royalty payments,

and license fees. Citizens are often limited in their ability to invest abroad, especially 
in foreign exchange–scarce economies, and there can be deadlines for repatriation 
of income earned from any investments abroad.

Trade and Capital Flows: Restrictions and Agreements 365
Economists consider free movement of financial capital to be beneficial because 
it allows capital to be invested where it will earn the highest return. Inflows of cap -
ital also allow countries to invest in productive capacity at a rate that is higher than 
could be achieved with domestic savings alone, and it can enable countries to achieve 
a higher rate of growth. Longer-  term investments by foreign firms that establish a 
presence in the local economy can bring in not only much needed capital but also 
new technology, skills, and advanced production and management practices as well 
as create spillover benefits for local firms. Investment by foreign firms can also create 
a network of local suppliers if they source some of their components locally. Such 
suppliers may receive advanced training and spillover benefits from a close working 
relationship with the foreign firms. On the one hand, increased competition from

foreign firms in the market may force domestic firms to become more efficient. On 
the other hand, it is possible that the domestic industry may be hurt because domestic 
firms that are unable to compete are forced to exit the market.
In times of macroeconomic crisis, capital mobility can result in capital flight out 
of the country, especially if most of the inflow reflects short-  term portfolio flows into 
stocks, bonds, and other liquid assets rather than foreign direct investment (FDI) in 
productive assets. In such circumstances, capital restrictions are often used in con -
junction with other policy instruments, such as fixed exchange rate targets. Capital 
restrictions and fixed exchange rate targets are complementary instruments because 
in a regime of perfect capital mobility, governments cannot achieve domestic and 
external policy objectives simultaneously using only standard monetary and fiscal 
policy tools.21 By limiting the free flow of capital, capital controls provide a way to

exercise control over a country’s external balance whereas more traditional macro-  
policy tools are used to address other objectives. 
Modern capital controls were developed by the belligerents in World War I as a 
method to finance the war effort. At the start of the war, all major powers restricted 
capital outflows (i.e., the purchase of foreign assets or loans abroad). These restric -
tions raised revenues by keeping capital in the domestic economy, facilitating the 
taxation of wealth, and producing interest income. Moreover, capital controls helped 
to maintain a low level of interest rates, reducing the government’s borrowing costs 
on its liabilities. Since WWI, controls on capital outflows have been used similarly 
in other countries, mostly developing nations, to generate revenue for governments 
or to permit them to allocate credit in the domestic economy without risking capital 
flight. In broad terms, a capital restriction is any policy designed to limit or redirect

capital flows. Such restrictions may take the form of taxes, price or quantity controls, 
or outright prohibitions on international trade in assets. Price controls may take the 
form of special taxes on returns to international investment, taxes on certain types 
of transactions, or mandatory reserve requirements—that is, a requirement forcing 
foreign parties wishing to deposit money in a domestic bank account to deposit some 
percentage of the inflow with the central bank for a minimum period at zero interest. 
Quantity restrictions on capital flows may include rules imposing ceilings or requir -
ing special authorization for new or existing borrowing from foreign creditors. Or 
there may be administrative controls on cross-  border capital movements in which a 
government agency must approve transactions for certain types of assets.
Effective implementation of capital restrictions may entail non-  trivial administra -

tion costs, particularly if the measures have to be broadened to close potential loop -
holes. There is also the risk that protecting the domestic financial markets by capital 
restrictions may postpone necessary policy adjustments or impede private-  sector 
21 Section 4.1 of the Level I curriculum reading on Currency Exchange Rates provides a concise discussion 
of the policy implications of capital mobility with fixed versus floating exchange rates.

Reading 19 ■ International Trade and Capital Flows 366
adaptation to changing international circumstances. Most importantly, controls may 
give rise to negative market perceptions, which may, in turn, make it more costly and 
difficult for the country to access foreign funds.
In a study on the effectiveness of capital controls, the International Monetary Fund 
considered restrictions on capital outflows and inflows separately.22 The authors con -
cluded that for restrictions on capital inflows to be effective (i.e., not circumvented), 
the coverage needs to be comprehensive and the controls need to be implemented 
forcefully. Considerable administrative costs are incurred in continuously extending, 
amending, and monitoring compliance with the regulations. Although controls on 
inflows appeared to be effective in some countries, it was difficult to distinguish the 
impact of the controls from the impact of other policies, such as strengthening of

prudential regulations, increased exchange rate flexibility, and adjustment of mone -
tary policy. In the case of capital outflows, the imposition of controls during episodes 
of financial crisis seems to have produced mixed results, providing only temporary 
relief of varying duration to some countries, while successfully shielding others (e.g., 
Malaysia) and providing them with sufficient time to restructure their economies.
EXAMPLE 9   
Capital Restrictions: Malaysia’s Capital Controls in 
1998–2001
After the devaluation of the Thai baht in July  1997, Southeast Asia suffered 
from significant capital outflows that led to falling local equity and real estate 
prices and declining exchange rates. To counter the outflows of capital, the 
IMF urged many of the countries in the region to increase interest rates, thus 
making their assets more attractive to foreign investors. Higher interest rates, 
however, weighed heavily on the domestic economies. In response to this

dilemma, Malaysia imposed capital controls on 1 September 1998. These con -
trols prohibited transfers between domestic and foreign accounts, eliminated 
credit facilities to offshore parties, prevented repatriation of investment until 
1 September 1999, and fixed the exchange rate of the Malaysian ringgit at 3.8 
per US dollar. In February 1999, a system of taxes on capital flows replaced the 
prohibition on repatriation of capital. Although the details were complex, the 
net effect was to discourage short-  term capital flows while permitting long-  term 
transactions. By imposing capital controls, Malaysia hoped to regain monetary 
independence, and to be able to cut interest rates without provoking a fall in 
the value of its currency as investors avoided Malaysian assets. The imposition 
of outflow controls indeed curtailed speculative capital outflows and allowed 
interest rates to be reduced substantially. At the same time, under the umbrella

of the capital controls, the authorities pursued bank and corporate restructuring 
and achieved a strong economic recovery in 1999 and 2000. With the restoration 
of economic and financial stability, administrative controls on portfolio outflows 
were replaced by a two-  tier, price-  based exit system in February 1999, which 
was finally eliminated in May  2001. Although Malaysia’s capital controls did 
contribute to a stabilization of its economy, they came with long-  term costs 
associated with the country’s removal from the MSCI developed equity market 
index, an important benchmark in the institutional asset management industry, 
and its relegation to the emerging market universe. The Malaysian market was 
no longer seen as on par with developed equity markets whose institutional 
22 Ariyoshi, et al. (2000).

The Balance of Payments 367
and regulatory frameworks provide a higher standard of safety for investors. As 
a consequence, it became more difficult for Malaysia to attract net long-  term 
capital inflows (Kawai and Takagi 2003).
1 Under what economic circumstances were Malaysia’s capital restrictions 
imposed?
2 What was the ultimate objective of Malaysia’s capital restrictions?
3 How successful were the country’s capital restrictions?
As a result of the Southeast Asian crisis, Malaysia suffered substantial net capital 
outflows pushing up the domestic interest rate level.
The restrictions were designed to limit and redirect capital flows to allow the gov -
ernment to reduce interest rates and pursue bank and corporate restructurings.
Although the capital controls helped stabilize Malaysia’s economy, they contrib -
uted to a change in investors’ perception of Malaysian financial markets and

removal of the Malaysian equity market from the MSCI benchmark universe of 
developed equity markets. This situation undermined international demand for 
Malaysian equities and made it more difficult to attract net long-  term capital 
inflows.
THE BALANCE OF PAYMENTS
The balance of payments  (BOP) is a double-  entry bookkeeping system that sum -
marizes a country’s economic transactions with the rest of the world for a particular 
period of time, typically a calendar quarter or year. In this context, a transaction is 
defined as “an economic flow that reflects the creation, transformation, exchange, 
or extinction of economic value and involves changes in ownership of goods and/or 
financial assets, the provision of services, or the provision of labour and capital. ”23 In 
other words, the BOP reflects payments for exports and imports as well as financial 
transactions and financial transfers. Analyzing the BOP is an important element in

assessing a country’s macroeconomic environment, its monetary and fiscal policies, 
and its long-  term growth potential. Investors use data on trade and capital flows to 
evaluate a country’s overall level of capital investment, profitability, and risk. The 
following section describes the balance of payments, the factors that influence it, and 
its impact on exchange rates, interest rates, and capital market transactions.
4.1 Balance of Payments Accounts
The BOP is a double-  entry system in which every transaction involves both a debit 
and credit. In principle, the sum of all debit entries should equal the sum of all credit 
entries, and the net balance of all entries on the BOP statement should equal zero. In 
practice, however, this is rarely the case because the data used to record balance of 
payments transactions are often derived from different sources.4
23 IMF Balance of Payments Handbook, chapter II, page 6.

Reading 19 ■ International Trade and Capital Flows 368
Debit entries reflect purchases of imported goods and services, purchases of foreign 
financial assets, payments received for exports, and payments (interest and principal) 
received from debtors. Credit entries reflect payments for imported goods and ser -
vices, payments for purchased foreign financial assets, and payments to creditors (see 
Exhibit 14, Panel A). Put differently, a debit represents an increase in a country’s assets 
(the purchase of foreign assets or the receipt of cash from foreigners) or a decrease in 
its liabilities (the amount owed to foreigners); a credit represents a decrease in assets 
(the sale of goods and services to foreigners or the payment of cash to foreigners) or 
an increase in liabilities (an amount owed to foreigners).
For example, as shown in Panel B of Exhibit 14, on 1 September Country A pur -
chases $1 million of goods from Country B and agrees to pay for these goods on 1

December. On 1 September, Country A would record in its BOP a $1 million debit 
to reflect the value of the goods purchased (i.e., increase in assets) and $1 million 
credit to reflect the amount owed to Country B. On 1 December, Country A would 
record in its BOP a $1 million debit to reflect a decrease in the amount owed (liabil -
ity) to Country B and $1 million a credit to reflect the actual payment to Country B 
(decrease in assets).
From Country B’s perspective, on 1 September it would record in its BOP a $1 mil -
lion debit to reflect the amount owed by Country A and a $1 million credit to reflect 
the sale of goods (exports). On 1 December, Country B would record a $1 million 
debit to reflect the cash received from Country A, and $1 million credit to reflect the 
fact that it is no longer owed $1 million by Country A.
Exhibit 14   Basic Entries in a BOP Context
Panel A
DEBITS CREDITS
Increase in Assets, Decrease in Liabilities Decrease in Assets, Increase in Liabilities

■■Value of imported goods and services
■■Purchases of foreign financial assets
■■Receipt of payments from foreigners
■■Increase in debt owed by foreigners
■■Payment of debt owed to foreigners■■Payments for imports of goods and services
■■Payments for foreign financial assets
■■Value of exported goods and services
■■Payment of debt by foreigners
■■Increase in debt owed to foreigners
Panel B
Country A Debits Credits
1 September $1 million  
Goods purchased from Country B  
(increase in real assets)$1 million  
Short-  term liability for goods purchased from 
Country B  
(increase in financial liabilities)
1 December $1 million  
Elimination of short-  term liability for goods 
purchased from Country B  
(decrease in financial liabilities)$1 million  
Payment for goods purchased from Country B  
(decrease in financial assets)

The Balance of Payments 369
Country B Debits Credits
Short-  term claim for goods delivered to 
Country A  
(increase in financial assets)$1 million  
Goods delivered to Country A  
(decrease in real assets)
Receipt of payment for goods delivered to 
Country A  
Elimination of claim for goods delivered to Country 
A 
4.2 Balance of Payment Components
The BOP is composed of the current account  that measures the flow of goods and 
services, the capital account  that measures transfers of capital, and the financial 
account  that records investment flows. These accounts are further disaggregated 
into sub-  accounts:
Current Account
The current account can be decomposed into four sub-  accounts:
1 Merchandise trade  consists of all commodities and manufactured goods 
bought, sold, or given away.
2 Services  include tourism, transportation, engineering, and business services,

such as legal services, management consulting, and accounting. Fees from 
patents and copyrights on new technology, software, books, and movies are also 
recorded in the services category.
3 Income receipts  include income derived from ownership of assets, such as 
dividends and interest payments; income on foreign investments is included in 
the current account because that income is compensation for services provided 
by foreign investments. When a German company builds a plant in China, for 
instance, the services the plant generates are viewed as a service export from 
Germany to China equal in value to the profits the plant yields for its German 
owner.
4 Unilateral transfers  represent one-  way transfers of assets, such as worker 
remittances from abroad to their home country and foreign direct aid or gifts.Exhibit 14   (Continued)

Reading 19 ■ International Trade and Capital Flows 370
Capital Account
The capital account consists of two sub-  accounts:
1 Capital transfers  include debt forgiveness and migrants’ transfers (goods and 
financial assets belonging to migrants as they leave or enter the country).24 
Capital transfers also include the transfer of title to fixed assets and the transfer 
of funds linked to the sale or acquisition of fixed assets, gift and inheritance 
taxes, death duties, uninsured damage to fixed assets, and legacies.
2 Sales and purchases of non-  produced, non-  financial assets , such as the 
rights to natural resources, and the sale and purchase of intangible assets, such 
as patents, copyrights, trademarks, franchises, and leases.
Financial Account
The financial account can be broken down in two sub-  accounts: financial assets abroad 
and foreign-  owned financial assets within the reporting country.
1 A country’s assets abroad are further divided into official reserve assets, gov -

ernment assets, and private assets. These assets include gold, foreign curren -
cies, foreign securities, the government’s reserve position in the International 
Monetary Fund,25 direct foreign investment, and claims reported by resident 
banks.
2 Foreign-  owned assets in the reporting country are further divided into offi -
cial assets and other foreign assets. These assets include securities issued by 
the reporting country’s government and private sectors (e.g., bonds, equities, 
mortgage-  backed securities), direct investment, and foreign liabilities reported 
by the reporting country’s banking sector.
EXAMPLE 10   
US Current Account Balance
Exhibit  15 shows a simplified version of the US balance of payments for 
1970–2009.
Exhibit 15   US International Transactions Accounts Data
(USD millions) 
(Credits+, Debits–) 1970 1980 1985 1990 2000 2009
Exports of goods and ser -
vices and income receipts68,387 344,440 387,612 706,975 1,421,515 2,159,000
  Exports of goods and

Exports of goods and 
services56,640 271,834 289,070 535,233 1,070,597 1,570,797
  Income receipts 11,748 72,606 98,542 171,742 350,918 588,203
Imports of goods and 
services and income 
payments–59,901 –333,774 –483,769 –759,290 –1,779,241 –2,412,489
24 Immigrants bring with them goods and financial assets already in their possession. Hence, these goods 
are imported on grounds other than commercial transactions.
25 These are in effect official currency reserves held with the International Monetary Fund.

The Balance of Payments 371
  Imports of goods and 
services–54,386 –291,241 –410,950 –616,097 –1,449,377 –1,945,705
  Income payments –5,515 –42,532 –72,819 –143,192 –329,864 –466,783
Unilateral current trans -
fers, net–6,156 –8,349 –21,998 –26,654 –58,645 –124,943
Capital account transac -
tions, net…. …. …. –7,220 –1 –140
US- owned assets abroad, 
ex derivatives (increase/
financial outflow (–))–9,337 –86,967 –44,752 –81,234 –560,523 –140,465
Foreign-  owned assets 
in the United States, ex 
derivatives (increase/
financial inflow (+))7,226 62,037 144,231 139,357 1,038,224 305,736
Financial derivatives, net NA NA NA NA NA 50,804
Statistical discrepancy 
(sum of above items with 
sign reversed)–219 22,613 18,677 28,066 –61,329 162,497
1 Calculate the current account balance for each year.
2 Calculate the financial account balance for each year.

3 Describe the long-  term change in the current account balance.
4 Describe the long-  term change in the financial account balance.
Current Account 2,330 2,317 –118,155 –78,969 –416,371 –378,432
Financial Account –2,111 –24,930 99,479 58,123 477,701 216,075
The United States had a current account surplus until 1980. After 1985, the US 
current account had an increasing deficit as a result of strong import growth.
Mirroring the growing US current account deficit, the US financial account, 
after 1985, registered increasing net capital inflows in similar proportions to 
the deficit in the current account.Exhibit 15   (Continued)

Reading 19 ■ International Trade and Capital Flows 372
4.3 Paired Transactions in the BOP Bookkeeping System
The following examples illustrate how some typical cross-  border transactions are 
recorded in the BOP framework outlined previously. They include commercial exports 
and imports, the receipt of income from foreign investments, loans made to borrowers 
abroad, and purchases of home-  country currency by foreign central banks. Exhibit 16 
illustrates the various individual bookkeeping entries from the perspective of an indi -
vidual country, in this case Germany.
Commercial Exports: Transactions (ia) and (ib)
A company in Germany sells technology equipment to a South Korean auto manu -
facturer for a total price of EUR50 million, including freight charges of EUR1 million 
to be paid within 90 days. The merchandise will be shipped via a German cargo ship. 
In this case, Germany is exporting two assets: equipment and transportation services.

The cargo shipped is viewed as being created in Germany and used by South Korean 
customers. In return for relinquishing these two assets, Germany acquires a financial 
asset—the promise by the South Korean manufacturer to pay for the equipment in 
90 days.
Germany would record a EUR50  million debit to an account called “private 
short-  term claims” to show an increase in this asset. It would also record a credit of 
EUR49 million to “goods” and another credit of EUR1 million to “services. ” Both credit 
entries are listed in the export category and show the decrease in assets available to 
German residents. These figures are entered as credits on lines 2 and 3 and as a debit 
on 19 in Exhibit 16 and are marked with (ia) to identify a typical commercial export 
transaction. To pay for the technology equipment purchased from Germany, the 
South Korean auto manufacturer may purchase euros from its local bank (i.e., a EUR

demand deposit held by the Korean bank in a German bank) and then transfer them 
to the German exporter. As a result, German liabilities to South Korean residents (i.e., 
South Korean private short-  term claims) would be debited. The respective entries, 
marked with (ib) are on lines 19 and 23 in Exhibit 16.
Commercial Imports: Transaction (ii)
A German utility company imports gas from Russia valued at EUR 45 million (ii), and 
agrees to pay the Russian company within three months. The imported gas generates 
a debit on line 6. The obligation pay is recorded as a credit to foreign private short-  
term claims on line 23.
Loans to Borrowers Abroad: Transaction (iii)
A German commercial bank purchases EUR 100 million in intermediate-  term bonds 
issued by a Ukrainian steel company. The bonds are denominated in euros, so payment 
is made in euros (i.e., by transferring EUR demand deposits). A debit entry on line 18 
records the increase in German holdings of Ukrainian bonds, and a credit entry on

line 23 records the increase in demand deposits held by Ukrainians in German banks.
Exhibit 16   Hypothetical Transactions between German Residents and Foreigners
Item no Account Debit Credit Balance
– + +/–
1 Exports of goods and services, income received 55
2 Goods 49 (ia) 49
3 Services 1 (ia) 1

The Balance of Payments 373
– + +/–
4 Income on residents’ investments abroad 5 (v) 5
5 Imports of goods and services, income paid –45
6 Goods 45 (ii) –45
7 Services
8 Income on foreign investments in home country
9 Unilateral transfers
10 Changes in residents’ claims on foreigners –105
11 Official reserve assets
12 Gold
13 Foreign currency balances
14 Other
15 Government claims
16 Private claims
17 Direct investments
18 Other private long-  term claims 100 (iii) –100
19 Private short-  term claims 50 (ia), 5 (v) 50 (ib) –5
20 Changes in foreign claims on residents 195
21 Foreign official claims 20 (iv) 20
22 Foreign private long-  term claims
23 Foreign private short-  term claims 20 (iv), 50 (ib) 45 (ii), 100 (iii), 
100 (vi)175
24 Other 100 (vi) –100
Total 270 370 270 370 0
Current Account : (1) + (5) + (9) 10
Capital Account : (24) –100
Financial Account : (10) + (20) 90
Purchases of Home-  Country Currency by Foreign Central Banks: Transaction (iv)

Private foreigners may not wish to retain euro balances acquired in earlier transac -
tions. Those who are holding foreign currency, in our example euro claims, typically 
do so for purposes of financing purchases from Germany (or other euro area member 
countries). Assume for instance, that Swiss residents attempt to sell EUR20 million 
in exchange for their native currency, the Swiss franc (CHF), but there is a lack of 
demand for EUR funds in Switzerland. In such circumstances, the CHF would appre -
ciate against the EUR. To prevent an undesired CHF appreciation, the Swiss National 
Bank (SNB) might sell CHF in exchange for EUR balances.
Suppose that the Swiss National Bank purchased EUR20 million, typically in the 
form of a EUR demand deposit held with a German bank, from local commercial 
banks in Switzerland. The German BOP would register an increase of EUR20 million in 
German liabilities held by foreign monetary authorities, the Swiss National Bank (line

21), and an equivalent decline in short-  term liabilities held by private foreigners (i.e., Exhibit 16   (Continued)

Reading 19 ■ International Trade and Capital Flows 374
Swiss private investors, line 23). It may be noteworthy that when the SNB purchases 
EUR funds from Swiss commercial banks, it also credits them the CHF equivalent 
of EUR20 million. The SNB’s liabilities to Swiss commercial banks arising from this 
transaction are in fact reserve deposits that Swiss banks can use when they expand 
their lending business and create new deposits. Currency interventions by central 
banks, therefore, can contribute to an increase in a country’s overall money supply, 
all else remaining unchanged.
Receipts of Income from Foreign Investments: Transaction (v)
Each year, residents of Germany receive billions of EUR in interest and dividends 
from capital invested in foreign securities and other financial claims. German resi -
dents receive these payments in return for allowing foreigners to use German capital 
that otherwise could be put to work in Germany. Foreign residents, in turn, receive

similar returns for their investments in Germany. Assume that a German firm has a 
long-  term capital investment in a profitable subsidiary abroad, and that the subsidiary 
transfers to its German parent EUR5 million in dividends in the form of funds held 
in a foreign bank. The German firm then has a new (or increased) demand deposit in 
a foreign bank as compensation for allowing its capital to be used by its subsidiary. 
A debit entry on line 19 shows German private short-  term claims on foreigners have 
increased by EUR5 million, and a credit entry on line 4 reflects the fact that German 
residents have given up an asset (the services of capital covered over the period) 
valued at EUR5 million.
Purchase of Non-  financial Assets: Transaction (vi)
In a move to safeguard its long-  term supply of uranium, a German utility company 
purchases the rights to exploit a uranium mine from the government of Kazakhstan.

It agrees to pay within three months. The respective entries are on lines 23 and 24. 
Because a non-  financial, non-  produced asset is involved in this transaction, it is 
recorded in Germany’s capital account.
Note that the sum of all BOP entries in Exhibit 16 is 0. Transactions (i)–(iv) produce 
a current account surplus of EUR10 million, a capital account deficit of EUR100 mil -
lion, and a financial account surplus of EUR90 million.
Although it is important to understand the detailed structure of official balance 
of payments accounts as described in the preceding paragraphs, this example is not 
necessarily how investment professionals think about the balance of payments day-  to- 
day. Practitioners often think of the current account as roughly synonymous with the 
trade balance (merchandise trade + services) and lump all the financing flows (financial 
account + capital account) into one category that is usually referred to simply as the

“capital account. ” They then think of the capital account as consisting of two types of 
flows—portfolio investment flows and foreign direct investment (FDI). The former 
are shorter-  term investments in foreign assets (stocks, bonds, etc.), whereas the latter 
are long-  term investments in production capacity abroad. Although not completely 
accurate, this way of thinking about the balance of payments focuses attention on the 
components—trade, portfolio flows, and FDI—that are most sensitive to, and most 
likely to affect, market conditions, prices of goods and services, asset prices, and 
exchange rates. In addition, this perspective fits well with the role that the balance of 
payments plays in the macroeconomy.

The Balance of Payments 375
4.4 National Economic Accounts and the Balance of Payments
In a closed economy, all output Y is consumed or invested by the private sector—
domestic households and businesses—or purchased by the government. Letting Y 
denote GDP , C private consumption, I investment, and G government purchases of 
goods and services, the national income identity for a closed economy is given by:
Y = C + I + G
Once foreign trade is introduced, however, some output is purchased by foreigners 
(exports) whereas some domestic spending is used for purchases of foreign goods and 
services (imports). The national income identity for an open economy is thus
Y = C + I + G + X – M
where X denotes exports and M denotes imports.
For most countries, exports rarely equal imports. Net exports or the difference 
between exports and imports ( X – M) is the equivalent of the current account balance 
from a BOP perspective.26 When a country’s imports exceed its exports, the current

account is in deficit. When a country’s exports exceed its imports, the current account 
is in surplus. As the right side of Equation  2 shows, a current account surplus or 
deficit can affect GDP (and also employment). The balance of the current account is 
also important because it measures the size and direction of international borrowing.
In order for the balance of payments to balance, a deficit or surplus in the current 
account must be offset by an opposite balance in the sum of the capital and financial 
accounts. This requirement means that a country with a current account deficit has 
to increase its net foreign debts by the amount of the current account deficit. For 
example, the United States has run current account deficits for many years while 
accumulating net foreign liabilities: The current account deficit was financed by net 
capital imports (i.e., direct investments by foreigners), loans by foreign banks, and

the sale of US equities and fixed-  income securities to foreign investors. By the same 
token, an economy with a current account surplus is earning more for its exports 
than it spends for its imports. Japan, Germany, and China are traditional current 
account surplus countries accumulating substantial net foreign claims, especially 
against the United States. An economy with a current account surplus finances the 
current account deficit of its trading partners by lending to them—that is, granting 
bank loans and investing in financial and real assets. As a result, the foreign wealth 
of a surplus country rises because foreigners pay for imports by issuing liabilities that 
they will eventually have to redeem.
By rearranging Equation 2, we can define the current account balance from the 
perspective of the national income accounts as:
CA = X – M = Y – (C + I + G)
Only by borrowing money from foreigners can a country have a current account

deficit and consume more output than it produces. If it consumes less output than it 
produces, it has a current account surplus and can (indeed must) lend the surplus to 
foreigners. International capital flows essentially reflect an inter-  temporal trade.  An 
economy with a current account deficit is effectively importing present consumption 
and exporting future consumption.(1)
(2)
(3)
26 Strictly speaking, net exports as defined here is the trade balance rather than the current account 
balance because it excludes income receipts and unilateral transfers. This distinction arises because we 
have defined income Y as GDP rather than GNP (see section 2.1). Because the trade balance is usually the 
dominant component of the current account, the terms “trade balance” and “current account” are often 
used interchangeably. We will do so here unless the distinction is important to the discussion.

Reading 19 ■ International Trade and Capital Flows 376
Let us now turn to the relationship between output Y and disposable income Yd. 
We have to recognize that part of income is spent on taxes T, and that the private 
sector receives net transfers R in addition to (national) income. Disposable income 
Yd is thus equal to income plus transfers minus taxes:
Yd = Y + R – T
Disposable income, in turn, is allocated to consumption and saving so that we can write
Yd = C + Sp
where Sp denotes private sector saving. Combining Equations 4 and 5 allows us to 
write consumption as income plus transfers minus taxes and saving.
C = Yd – Sp = Y + R – T – Sp
We can now use the right side of Equation 6 to substitute for C in Equation 3. With 
some rearrangement we obtain
CA = Sp – I + (T – G – R)
Because ( T – G – R) is taxes minus government spending and transfers, it is the gov -
ernment surplus, or put differently, government savings Sg. Equation 7 can therefore 
be restated as
Sp + Sg = I + CA

Equation 8 highlights an essential difference between open and closed economies: 
An open economy can use its saving for domestic investment or for foreign investment 
(i.e., by exporting its savings and acquiring foreign assets), while in a closed economy 
savings can only be used for domestic investment. Put another way, an open economy 
with promising investment opportunities is not constrained by its domestic savings rate 
in order to exploit these opportunities. As Equation 8 shows, it can raise investment 
by increasing foreign borrowing (a reduction in CA) without increasing domestic 
savings. For example, if India decides to build a network of high-  speed trains, it can 
import all the required materials it needs from France and then borrow the funds, 
perhaps also from France, to pay for the materials. This transaction increases India’s 
domestic investment because the imported materials contribute to the expansion in

the country’s capital stock. All else being equal, this transaction will also produce a 
current account deficit for India by an amount equal to the increase in investment. 
India’s savings does not have to increase, even though investment increases. This 
example can be interpreted as an inter-  temporal trade, in which India imports pres -
ent consumption (when it borrows to fund current expenditure) and exports future 
consumption (when it repays the loan).
Rearranging Equation 8, we can write
Sp = I + CA – Sg
Equation 9 states that an economy’s private savings can be used in three ways: (1) 
investment in domestic capital ( I), (2) purchases of assets from foreigners ( CA), and 
(3) net purchases (or redemptions) of government debt (– Sg).
Finally, we can rearrange Equation 8 again to illustrate the macroeconomic sources 
of a current account imbalance:
CA = Sp + Sg – I
A current account deficit tends to result from low private savings, high private invest -

ment, a government deficit ( Sg < 0), or a combination of the three. Alternatively, a 
current account surplus reflects high private savings, low private investment, or a 
government surplus.(4)
(5)
(6)
(7)
(8)
(9)
(10)

The Balance of Payments 377
As outlined above, trade deficits can result from a lack of private or government 
savings or booming investments. If trade deficits primarily reflect high private or 
government consumption (i.e., scarce savings = Sp + Sg), the deficit country’s capacity 
to repay its liabilities from future production remains unchanged. If a trade deficit 
primarily reflects strong investments ( I), however, the deficit country can increase its 
productive resources and its ability to repay its liabilities.
We can also see from Equation 3 that a current account deficit tends to reflect a 
strong domestic economy (elevated consumer, government, and investment spending), 
which is usually accompanied by elevated domestic credit demand and high interest 
rates. In such an environment, widening interest rate differentials vis-  à-vis other coun -
tries can lead to growing net capital imports and produce an appreciating currency.

In the long run, however, a persistent current account deficit leads to a permanent 
increase in the claims held by other countries against the deficit country. As a result, 
foreign investors may require rising risk premiums for such claims, a process that 
appears to lead to a depreciating currency.
EXAMPLE 11   
The United Kingdom Budget
A financial newspaper had the following item:
The UK’s budget deficit is the highest in the G–20; in Europe, only 
Ireland borrows more. These are the stark facts facing Chancellor of 
the Exchequer George Osborne as he plans his first Budget tomorrow. 
He intends to tackle the problem even if that involves severe spending 
cuts and large tax increases.
Source : Financial Times , 21 June 2010.
1 What are the likely consequences for the UK current account balance 
from the planned fiscal policy moves mentioned in the above article?
2 Describe the impact spending cuts and tax increases are likely to have on 
UK imports.

The combination of spending cuts and tax increases will, all else the same, lead 
to an improvement in the UK current account position.
UK imports are likely to be reduced by tax increases and spending cuts because 
government demand for foreign goods will fall and growth in private household 
income, which finances private imports, will be restricted as more household 
income goes to taxes.
EXAMPLE 12   
Global Current Account Imbalances since 1996
As a result of growing financial integration and trade liberalization, the world 
economy has entered a period of rapid growth in cross-  border trade since the 
late 1980s. In synch with surging international trade, current account imbalances

Reading 19 ■ International Trade and Capital Flows 378
widened substantially in the 1990s and the first decade of the new millennium. 
Exhibit  17 shows current account balances for 1996–2009 for four specific 
groups—the United States, oil exporters, Germany and Japan (DEU + JPN), 
China and emerging Asia (CHN + EMA)—and two broad categories: the rest of 
the world (ROW) and other current account deficit countries (OCADC), which 
includes Central and Eastern European countries, Australia, New Zealand, and 
a wide range of smaller developed and emerging countries. The United States 
ran a current account deficit in every year, and in every year its deficit repre -
sented most of the aggregate value of such deficits worldwide. Only in the wake 
of the 2007–2009 recession has the US deficit declined both in absolute terms 
and relative to the global aggregate of current account deficits. In the first half 
of the 1990s, Germany and Japan were the traditional current account surplus

countries, providing net exports of goods and services to and accumulating net 
claims against the United States. Since the late 1990s, among the largest current 
account surpluses are those of China and emerging Asia and the oil exporters.
Exhibit 17   Global Imbalances (Current Account Balance in Percent of 
World GDP) 
4
3
2
1
0
–1
–2
–3
96 98 02 04 06 09 08 00
Oil OCADC ROW CHN+EMA US DEU+JPN
Discrepancy
Note : CHN+EMA includes the following economies: China, Hong Kong SAR, Indonesia, 
Korea, Malaysia, Philippines, Singapore, Taiwan Region, Thailand.
Source:  IMF World Economic Outlook  April 2010, Chapter 4.
As illustrated in Equation 10, current account deficits or surpluses reflect 
imbalances between national savings (including government savings) and invest -
ments. Current account deficits are often related to expansionary fiscal policy 
and government deficits. In the 1980s, for instance, the growing deficit in the

Trade Organizations 379
US current account was widely seen as the consequence of tax cuts and rising 
defence spending adopted by the Reagan administration. Since the mid-  1990s, 
however, the current account imbalances depicted in Exhibit  17 appear to 
reflect other, more complex factors. Exhibit 18 illustrates US net savings ( S–I) 
for private domestic businesses, households, and the government (i.e., federal, 
state, and local) from 1996 to the second quarter of 2010. The exhibit indicates 
that business sector net savings and government net savings as a percentage of 
GDP have been near mirror-  images since 1996. During the technology bubble 
businesses invested heavily and ran progressively larger savings deficits while 
the government moved to a surplus. After the bubble burst the pattern reversed 
with businesses moving to net positive savings and the government fiscal balance 
deteriorating sharply. Meanwhile, the household sector gradually reduced its

savings rate. By 2006, each of the three sectors was dis-  saving roughly 2 percent 
of US GDP . From that point, the public and private sectors diverged sharply. In 
the wake of the global financial crisis, households and businesses cut spending 
and increased savings sharply while the government deficit exploded to more 
than 12 percent of GDP .
Exhibit 18   United States: Sectorial Saving–Investment Balance since 
1996 (Net Savings in Percent of GDP)
Percent
Domestic BusinessHouseholds
Government6
2
04
–4–2
–6
–8
–10
–12
–14
1/02 1/08 1/00 1/06 1/10 1/98 1/96 1/04
Source:  Federal Reserve Board, flow-  of- funds data.
TRADE ORGANIZATIONS
During the Great Depression in the 1930s, countries attempted to support their failing 
economies by sharply raising barriers to foreign trade, devaluing their currencies to 
compete against each other for export markets, and restricting their citizens’ freedom to 
hold foreign exchange. These attempts proved to be self-  defeating. World trade declined

dramatically and employment and living standards fell sharply in many countries. By 5

Reading 19 ■ International Trade and Capital Flows 380
the 1940s, it had become a wide-  spread conviction that the world economy was in 
need of organizations that would help promote international economic cooperation. 
In July 1944, during the United Nations Monetary and Financial Conference in Bretton 
Woods, New Hampshire, representatives of 45 governments agreed on a framework for 
international economic cooperation. Two crucial, multinational organizations emanated 
from this conference—the World Bank, which was founded during the conference, 
and the International Monetary Fund (IMF), which came into formal existence in 
December 1945. Although the IMF was founded with the goal to stabilize exchange 
rates and assist the reconstruction of the world’s international payment system, the 
World Bank was created to facilitate post-  war reconstruction and development.
A third institution, the International Trade Organization (ITO), was to be created

to handle the trade side of international economic cooperation, joining the other two 
“Bretton Woods” institutions. The draft ITO charter was ambitious, extending beyond 
world trade regulations to include rules on employment, commodity agreements, 
restrictive business practices, international investment, and services. The objective was 
to create the ITO at a United Nations Conference on Trade and Employment in Havana, 
Cuba in 1947. Meanwhile, 15 countries had begun negotiations in December 1945 
to reduce and regulate customs tariffs. With World War II only barely ended, they 
wanted to give an early boost to trade liberalization and begin to correct the legacy 
of protectionist measures that had remained in place since the early 1930s. The group 
had expanded to 23 nations by the time the deal was signed on 30 October 1947 and 
the General Agreement on Tariffs and Trade (GATT) was born. The Havana confer -
ence began on 21 November 1947, less than a month after GATT was signed. The

ITO charter was finally approved in Havana in March 1948, but ratification in some 
national legislatures proved impossible. The most serious opposition was in the US 
Congress, even though the US government had been one of the driving forces. In 
1950, the United States government announced that it would not seek congressional 
ratification of the Havana Charter, and the ITO was effectively dead. As a consequence, 
the GATT became the only multilateral instrument governing international trade from 
1948 until the World Trade Organization (WTO) was officially established in 1995.
5.1 International Monetary Fund
As we saw earlier, current account deficits reflect a shortage of net savings in an 
economy and can be addressed by policies designed to rein in domestic demand. This 
approach could, however, have adverse consequences for domestic employment. The 
IMF stands ready to lend foreign currencies to member countries to assist them during

periods of significant external deficits. A pool of gold and currencies contributed by 
members provides the IMF with the resources required for these lending operations. 
The funds are only lent under strict conditions and borrowing countries’ macro -
economic policies are continually monitored. The IMF’s main mandate is to ensure 
the stability of the international monetary system, the system of exchange rates and 
international payments that enables countries to buy goods and services from each 
other. More specifically, the IMF:
■■provides a forum for cooperation on international monetary problems;
■■facilitates the growth of international trade and promotes employment, eco -
nomic growth, and poverty reduction;
■■supports exchange rate stability and an open system of international payments; 
and
■■lends foreign exchange to members when needed, on a temporary basis 
and under adequate safeguards, to help them address balance of payments 
problems.

Trade Organizations 381
The global financial crisis of 2007–2009 demonstrated that domestic and inter -
national financial stability cannot be taken for granted, even in the world’s most 
developed countries. In light of these events, the IMF has redefined and deepened 
its operations by:27
■■enhancing its lending facilities : The IMF has upgraded its lending facilities to 
better serve its members. As part of a wide-  ranging reform of its lending prac -
tices, it has also redefined the way it engages with countries on issues related 
to structural reform of their economies. In this context, it has doubled member 
countries’ access to fund resources and streamlined its lending approach to 
reduce the stigma of borrowing for countries in need of financial help.
■■improving the monitoring of global, regional, and country economies : The IMF 
has taken several steps to improve economic and financial surveillance, which 
is its framework for providing advice to member countries on macroeconomic

policies and warning member countries of risks and vulnerabilities in their 
economies.
■■helping resolve global economic imbalances : The IMF’s analysis of global eco -
nomic developments provides finance ministers and central bank governors 
with a common framework for discussing the global economy.
■■analyzing capital market developments : The IMF is devoting more resources to 
the analysis of global financial markets and their links with macroeconomic pol -
icy. It also offers training to country officials on how to manage their financial 
systems, monetary and exchange regimes, and capital markets.
■■assessing financial sector vulnerabilities : Resilient, well-  regulated financial 
systems are essential for macroeconomic stability in a world of ever-  growing 
capital flows. The IMF and the World Bank jointly run an assessment program 
aimed at alerting countries to vulnerabilities and risks in their financial sectors.

From an investment perspective, the IMF helps to keep country-  specific market 
risk and global systemic risk under control. The Greek sovereign debt crisis, which 
threatened to destabilize the entire European banking system, is a recent example. In 
early 2010, the Greek sovereign debt rating was downgraded to non-  investment grade 
by leading rating agencies as a result of serious concerns about the sustainability of 
Greece’s public sector debt load. Yields on Greek government bonds rose substantially 
following the downgrading and the country’s ability to refinance its national debt was 
seriously questioned in international capital markets. Bonds issued by some other 
European governments fell and equity markets worldwide declined in response to 
spreading concerns of a Greek debt default. The downgrading of Greek sovereign debt 
was the ultimate consequence of persistent and growing budget deficits the Greek

government had run before and after the country had joined the European Monetary 
Union (EMU) in 2001. Most of the budget shortfalls reflected elevated outlays for 
public-  sector jobs, pensions, and other social benefits as well as persistent tax evasion. 
Reports that the Greek government had consistently and deliberately misreported the 
country’s official economic and budget statistics contributed to further erosion of con -
fidence in Greek government bonds in international financial markets. Facing default, 
the Greek government requested that a joint European Union/IMF bailout package be 
activated, and a loan agreement was reached between Greece, the other EMU member 
countries, and the IMF. The deal consisted of an immediate EUR45 billion in loans to 
be provided in 2010, with more funds available later. A total of EUR110 billion was 
agreed depending on strict economic policy conditions that included cuts in wages

and benefits, an increase in the retirement age for public-  sector employees, limits on 
27 Visit www.imf.org/ for more information.

Reading 19 ■ International Trade and Capital Flows 382
public pensions, increases in direct and indirect taxes, and a substantial reduction in 
state-  owned companies. By providing conditional emergency lending facilities to the 
Greek government and designing a joint program with the European Union on how 
to achieve fiscal consolidation, the IMF prevented a contagious wave of sovereign 
debt crises in global capital markets.
Another example of IMF activities is the East Asian Financial Crisis in the late 
1990s. It began in July 1997, when Thailand was forced to abandon its currency’s peg 
with the US dollar. Currency devaluation subsequently hit other East Asian countries 
that had similar balance of payment problems, such as South Korea, Malaysia, the 
Philippines, and Indonesia. They had run persistent and increasing current account 
deficits, financed mainly with short-  term capital imports, in particular, domestic

banks borrowing in international financial markets. External financing was popular 
because of the combination of lower foreign, especially US, interest rates and fixed 
exchange rates. Easy money obtained from abroad led to imprudent investment, 
which contributed to overcapacities in several industries and inflated prices on real 
estate and stock markets. The IMF came to the rescue of the affected countries with 
considerable loans, accompanied by policies designed to control domestic demand, 
which included fiscal austerity and tightened monetary reins.
5.2 World Bank Group
The World Bank’s main objective is to help developing countries fight poverty and 
enhance environmentally sound economic growth. For developing countries to grow 
and attract business, they have to
■■strengthen their governments and educate their government officials;
■■implement legal and judicial systems that encourage business;
■■protect individual and property rights and honour contracts;

■■develop financial systems robust enough to support endeavours ranging from 
micro credit to financing larger corporate ventures; and
■■combat corruption.
Given these targets, the World Bank provides funds for a wide range of projects 
in developing countries worldwide and financial and technical expertise aimed at 
helping those countries reduce poverty.
The World Bank’s two closely affiliated entities—the International Bank for 
Reconstruction and Development (IBRD) and the International Development 
Association (IDA)—provide low or no-  interest loans and grants to countries that 
have unfavourable or no access to international credit markets. Unlike private financial 
institutions, neither the IBRD nor the IDA operates for profit. The IBRD is market-  
based, and uses its high credit rating to pass the low interest it pays for funds on to 
its borrowers—developing countries. It pays for its own operating costs because it 
does not look to outside sources to furnish funds for overhead.

IBRD lending to developing countries is primarily financed by selling AAA-  rated 
bonds in the world’s financial markets. Although the IBRD earns a small margin on this 
lending, the greater proportion of its income comes from lending out its own capital. 
This capital consists of reserves built up over the years and money paid in from the 
Bank’s 185 member country shareholders. IBRD’s income also pays for World Bank 
operating expenses and has contributed to IDA and debt relief. IDA is the world’s 
largest source of interest-  free loans and grant assistance to the poorest countries. 
IDA’s funds are replenished every three years by 40 donor countries. Additional funds 
are regenerated through repayments of loan principal on 35-  to- 40- year, no-  interest

Trade Organizations 383
loans, which are then available for re-  lending. At the end of September  2010, the 
IBRD had net loans outstanding of USD125.5 billion, while its borrowings amounted 
to USD132 billion.
Besides acting as a financier, the World Bank also provides analysis, advice, and 
information to its member countries to enable them to achieve the lasting economic 
and social improvements their people need. Another of the Bank’s core functions is 
to increase the capabilities of its partners, people in developing countries, and its 
own staff. Links to a wide range of knowledge-  sharing networks have been set up by 
the Bank to address the vast need for information and dialogue about development.
From an investment perspective, the World Bank helps to create the basic economic 
infrastructure that is essential for the creation of domestic financial markets and a 
well-  functioning financial industry in developing countries. Moreover, the IBRD is one

of the most important supranational borrowers in the international capital markets. 
Because of its strong capital position and its very conservative financial, liquidity, and 
lending policies, it enjoys the top investment-  grade rating from the leading agencies 
and investors have confidence in its ability to withstand adverse events. As a result, 
IBRD bonds denominated in various major currencies are widely held by institutional 
and private investors.
5.3 World Trade Organization
The WTO provides the legal and institutional foundation of the multinational trading 
system. It is the only international organization that regulates cross-  border trade rela -
tionships among nations on a global scale. It was founded on 1 January 1995, replacing 
the General Agreement on Tariffs and Trade (GATT) that had come into existence 
in 1947. The GATT was the only multilateral body governing international trade 
from 1947 to 1995. It operated for almost half a century as a quasi-  institutionalized,

provisional system of multilateral treaties. Several rounds of negotiations took place 
under the GATT, of which the Tokyo round and the Uruguay round may have been 
the most far reaching. The Tokyo round was the first major effort to address a wide 
range of non-  tariff trade barriers, whereas the Uruguay round focused on the extension 
of the world trading system into several new areas, particularly trade in services and 
intellectual property, but also to reform trade in agricultural products and textiles. 
The GATT still exists in an updated 1994 version and is the WTO’s principal treaty for 
trade in goods. The GATT and the General Agreement on Trade in Services (GATS) 
are the major agreements within the WTO’s body of treaties that encompasses a total 
of about 60 agreements, annexes, decisions, and understandings.
In November 2001, the most recent and still ongoing round of negotiations was 
launched by the WTO in Doha, Qatar. The Doha round was an ambitious effort to

enhance globalization by slashing barriers and subsidies in agriculture and addressing 
a wide range of cross-  border services. So far, under GATS, which came into force in 
January 1995, banks, insurance companies, telecommunication firms, tour operators, 
hotel chains, and transport companies that want to do business abroad can enjoy the 
same principles of free and fair trade that had previously applied only to international 
trade in goods. No agreement has been reached in Doha so far, however, despite intense 
negotiations at several ministerial conferences and at other sessions. The Doha round 
nevertheless marks one of the most crucial events in global trade over the past several 
decades: China’s accession to the WTO in December 2001.
The WTO’s most important functions are the implementation, administration, and 
operation of individual agreements; acting as a platform for negotiations; and settling 
disputes. Moreover, the WTO has the mandate to review and propagate its members’

trade policies and ensure the coherence and transparency of trade policies through 
surveillance in a global policy setting. The WTO also provides technical cooperation 
and training to developing, least-  developed, and low-  income countries to assist with

Reading 19 ■ International Trade and Capital Flows 384
their adjustment to WTO rules. In addition, the WTO is a major source of economic 
research and analysis, producing ongoing assessments of global trade in its publications 
and research reports on special topics. Finally, the WTO is in close cooperation with 
the other two Bretton Woods institutions, the IMF and the World Bank.
From an investment perspective, the WTO’s framework of global trade rules 
provides the major institutional and regulatory base without which today’s global 
multinational corporations would be hard to conceive. Modern financial markets 
would look different without the large, multinational companies whose stocks and 
bonds have become key elements in investment portfolios. In the equity universe, for 
instance, investment considerations focusing on global sectors rather than national 
markets would make little sense without a critical mass of multinational firms com -

peting with each other in a globally defined business environment.
EXAMPLE 13   
Function and Objective of International Organizations
On 10 May 2010, the Greek government officially applied for emergency lending 
facilities extended by the International Monetary Fund. It sent the following 
letter to Dominique Strauss-  Kahn, the IMF’s Managing Director:
Request for Stand-  By Arrangement
This paper was prepared based on the information available at the time it was 
completed on Monday, May 10, 2010. The views expressed in this document are 
those of the staff team and do not necessarily reflect the views of the government 
of Greece or the Executive Board of the IMF. The policy of publication of staff 
reports and other documents by the IMF allows for the deletion of market-  
sensitive information.
Mr. Dominique Strauss-  Kahn Athens, May 3, 2010
Managing Director
International Monetary Fund
Washington DC
Dear Mr. Strauss-  Kahn:

Dear Mr. Strauss-  Kahn: 
The attached Memorandum of Economic and Financial Policies (MEFP)28 out-
lines the economic and financial policies that the Greek government and the 
Bank of Greece, respectively, will implement during the remainder of 2010 and 
in the period 2011–2013 to strengthen market confidence and Greece’s fiscal 
and financial position during a difficult transition period toward a more open 
and competitive economy. The government is fully committed to the policies 
stipulated in this document and its attachments, to frame tight budgets in the 
coming years with the aim to reduce the fiscal deficit to below 3 percent in 2014 
and achieve a downward trajectory in the public debt-  GDP ratio beginning in 
2013, to safeguard the stability of the Greek financial system, and to implement 
structural reforms to boost competitiveness and the economy’s capacity to pro -
duce, save, and export. (…) The government is strongly determined to lower the

fiscal deficit, (…) by achieving higher and more equitable tax collections, and con -
straining spending in the government wage bill and entitlement outlays, among 
28 The detailed memorandum is available from www.imf.org/external/pubs/ft/scr/2010/cr10111.pdf.

Trade Organizations 385
other items. In view of these efforts and to signal the commitment to effective 
macroeconomic policies, the Greek government requests that the Fund supports 
this multi-  year program under a Stand-  By Arrangement (SBA) for a period of 
36 months in an amount equivalent to SDR26.4 billion.29 (…) A parallel request 
for financial assistance to euro area countries for a total amount of €80 billion 
has been sent. The implementation of the program will be monitored through 
quantitative performance criteria and structural benchmarks as described in the 
attached MEFP and Technical Memorandum of Understanding (TMU). There 
will be twelve quarterly reviews of the program supported under the SBA by the 
Fund, (….) to begin with the first review that is expected to be completed in the 
course of the third calendar quarter of 2010, and then every quarter thereafter 
until the last quarterly review envisaged to be completed during the second

calendar quarter of 2013, to assess progress in implementing the program and 
reach understandings on any additional measures that may be needed to achieve 
its objectives. (….) The Greek authorities believe that the policies set forth in the 
attached memorandum are adequate to achieve the objectives of the economic 
program, and stand ready to take any further measures that may become appro -
priate for this purpose. The authorities will consult with the Fund in accordance 
with its policies on such consultations, (….) and in advance of revisions to the 
policies contained in the MEFP . All information requested by the Fund (….) to 
assess implementation of the program will be provided.
(….)
Sincerely, 
George Papaconstantinou George Provopoulos
Minister of Finance Governor of the Bank of Greece
1 What is the objective of the IMF’s emergency lending facilities?
2 What are the macroeconomic policy conditions under which the IMF pro -
vides emergency lending to Greece?

3 What is the amount Greece requests from the IMF as emergency funds?
The program seeks to safeguard the stability of the Greek financial system and 
to implement structural reforms to boost competitiveness and the economy’s 
capacity to produce, save and export.
The Greek government has to reduce the country’s fiscal deficit by achieving 
higher and more equitable tax collections as well as constrain spending in the 
government wage bill and entitlement outlays.
Greece applied for a standby arrangement in an amount equivalent to SDR26.4 bil -
lion (approximately USD39.5 billion, based on the 10 May 2010 exchange rate).
29 A SDR (special drawing right) is a basket of four leading currencies: Japanese yen (JPY), US dollar 
(USD), British pound (GBP), and euro (EUR). It consists of 18.4 yen, 0.6320 USD, 0.0903 GBP , and 0.41 
EUR. One SDR was worth 1.4975 USD or 1.1547 EUR on 10 May 2010.

Reading 19 ■ International Trade and Capital Flows 386
SUMMARY
and their economic implications. It examines basic models that explain trade based on 
comparative advantage and provides a basis for understanding how international trade 
can affect the rate and composition of economic growth as well as the attractiveness 
of investment in various sectors.
■■The benefits of trade include
■●gains from exchange and specialization;
■●gains from economies of scale as companies add new markets for their 
products;
■●greater variety of products available to households and firms; and
■●increased competition and more efficient allocation of resources.
■■A country has an absolute advantage in producing a good (or service) if it is 
able to produce that good at a lower absolute cost or use fewer resources in its 
production than its trading partner. A country has a comparative advantage in

producing a good if its opportunity cost  of producing that good is less than that 
of its trading partner.
■■Even if a country does not have an absolute advantage in the production of any 
good, it can gain from trade by producing and exporting the good(s) in which it 
has a comparative advantage and importing good(s) in which it has a compara -
tive disadvantage.
■■In the Ricardian model of trade, comparative advantage and the pattern of 
trade are determined by differences in technology between countries. In the 
Heckscher–Ohlin model of trade, comparative advantage and the pattern of 
trade are determined by differences in factor endowments between countries. 
In reality, technology and factor endowments are complementary, not mutually 
exclusive, determinants of trade patterns.
■■Trade barriers prevent the free flow of goods and services among countries. 
Governments impose trade barriers for various reasons including: to promote

specific developmental objectives, to counteract certain imperfections in the 
functioning of markets, or to respond to problems facing their economies.
■■For purposes of international trade policy and analysis, a small country is 
defined as one that cannot affect the world price of traded goods. A large coun -
try’s production and/or consumption decisions do alter the relative prices of 
trade goods.
■■In a small country, trade barriers generate a net welfare loss arising from dis -
tortion of production and consumption decisions and the associated inefficient 
allocation of resources.
■■Trade barriers can generate a net welfare gain in a large country if the gain from 
improving its terms of trade (higher export prices and lower import prices) 
more than offsets the loss from the distortion of resource allocations. However, 
the large country can only gain if it imposes an even larger welfare loss on its 
trading partner(s).

■■An import tariff and an import quota have the same effect on price, produc -
tion, and trade. With a quota, however, some or all of the revenue that would 
be raised by the equivalent tariff is instead captured by foreign producers (or 
the foreign government) as quota rents. Thus, the welfare loss suffered by the 
importing country is generally greater with a quota.

Summary 387
■■A voluntary export restraint is imposed by the exporting country. It has the 
same impact on the importing country as an import quota from which foreign -
ers capture all of the quota rents.
■■An export subsidy encourages firms to export their product rather than sell it 
in the domestic market. The distortion of production, consumption, and trade 
decisions generates a welfare loss. The welfare loss is greater for a large country 
because increased production and export of the subsidized product reduces its 
global price—that is, worsens the country’s terms of trade.
■■Capital restrictions are defined as controls placed on foreigners’ ability to own 
domestic assets and/or domestic residents’ ability to own foreign assets. In con -
trast to trade restrictions, which limit the openness of goods markets, capital 
restrictions limit the openness of financial markets.
■■A regional trading bloc is a group of countries who have signed an agreement to

reduce and progressively eliminate barriers to trade and movement of factors of 
production among the members of the bloc.
■●They may or may not have common trade barriers against those countries 
that are not members of the bloc. In a free trade area all barriers to the flow 
of goods and services among members are eliminated, but each country 
maintains its own polices against non-  members.
■●A customs union extends the FTA by not only allowing free movement of 
goods and services among members but also creating a common trade pol -
icy against non-  members.
■●A common market incorporates all aspects of a customs union and extends 
it by allowing free movement of factors of production among members.
■●An economic union incorporates all aspects of a common market and 
requires common economic institutions and coordination of economic poli -
cies among members.
■●Members of a monetary union adopt a common currency.
■■From an investment perspective, it is important to understand the complex and

dynamic nature of trading relationships because they can help identify potential 
profitable investment opportunities as well as provide some advance warning 
signals regarding when to disinvest in a market or industry.
■■The major components of the balance of payments are the
■●current account balance, which largely reflects trade in goods and services.
■●capital account balance, which mainly consists of capital transfers and net 
sales of non-  produced, non-  financial assets.
■●financial account, which measures net capital flows based on sales and pur -
chases of domestic and foreign financial assets.
■■Decisions by consumers, firms, and governments influence the balance of 
payments.
■●Low private savings and/or high investment tend to produce a current 
account deficit that must be financed by net capital imports; high private 
savings and/or low investment, however, produce a current account surplus, 
balanced by net capital exports.

■●All else the same, a government deficit produces a current account deficit 
and a government surplus leads to a current account surplus.
■●All else the same, a sustained current account deficit contributes to a rise in 
the risk premium for financial assets of the deficit country. Current account 
surplus countries tend to enjoy lower risk premiums than current account 
deficit countries.

Reading 19 ■ International Trade and Capital Flows 388
Appleyard, Dennis, Alfred Field, and Steven Cobb. 2010. 
International Economics . 7th edition. Boston: McGraw-Hill/
Irwin.
Ariyoshi, Akira, Karl Habermeier, Bernard Laurens, Inci Otker-  
Robe, Jorge Iván Canales-  Kriljenko, and Andrei Kirilenko. 
2000. ‘‘Capital Controls: Country Experiences with Their Use 
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and Peter K. Schott. 2010. “Intrafirm Trade and Product 
Contractibility. ” American Economic Review , vol. 100, no. 2 
(May):444–448. 
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Edition.
Coe, David T., and Elhanan Helpman. 1995. “International 
R&D Spillovers. ” European Economic Review , vol. 39, no. 5 
(May):859–887. 
Collier, Paul, and Stephen A. O’Connell. 2007. “Opportunities

and Choices. ” In The Political Economy of Economic Growth in 
Africa, 1960–2000 , vol. 1. Edited by Benno J. Ndulu, Stephen 
A. O’Connell, Robert H. Bates, Paul Collier, and Charles C. 
Soludo. Cambridge, U.K.: Cambridge University Press.
Feenstra, Robert C., and Alan M. Taylor. 2008. International 
Economics . New York: Worth Publishers.
Gerber, James. 2017. International Economics . 7th edition. New 
York: Prentice Hall.
Hill, Charles W.L., and G. Tomas M. Hult. 2019. International 
Business: Competing in the Global Marketplace . 12th edition. 
Boston: Irwin/McGraw-Hill.IMF. 2008. Globalization: A Brief Overview . Issues Brief, 
International Monetary Fund (May).
IMF. 2010a. Balance of Payments and International Investment 
Position Manual . 6th ed. Washington, DC: International 
Monetary Fund.
IMF. 2010b. World Economic Outlook : April 2010. Washington, 
DC: International Monetary Fund.
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(February): www.imf.org/external/np/exr/facts/glance.htm.
Kawai, Masahiro, and Shinji Takagi. 2003. “Rethinking Capital 
Controls: The Malaysian Experience. ” PRI Discussion Paper 
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Finance Japan, Tokyo (May).
Meier, Gerald M. 1998. The International Environment of 
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Roberts, Mark, and Uwe Deichmann. 2008. “Regional Spillover 
Estimation. ” Background paper for the World Development 
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Salvatore, Dominick. 2011. Introduction to International 
Economics . 3rd edition. Hoboken, NJ: John Wiley & Sons.
United Nations. 2002. World Investment Report 2002: 
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York: United Nations Conference on Trade and Development 
(UNCTAD).
World Bank. 2009. World Development Report 2009: Reshaping 
Economic Geography . Washington, DC: World Bank.

World Trade Organization. 2008. World Trade Report 2008: Trade 
in a Globalizing World . Geneva: World Trade Organization.■■Created after WWII, the International Monetary Fund, the World Bank, and 
the World Trade Organization are the three major international organizations 
that provide necessary stability to the international monetary system and facili -
tate international trade and development.
■●The IMF’s mission is to ensure the stability of the international monetary 
system, the system of exchange rates and international payments that 
enables countries to buy goods and services from each other. The IMF helps 
to keep country-  specific market risk and global systemic risk under control.
■●The World Bank helps to create the basic economic infrastructure essential 
for creation and maintenance of domestic financial markets and a well-  
functioning financial industry in developing countries.

■●The World Trade Organization’s mission is to foster free trade by providing 
a major institutional and regulatory framework of global trade rules without 
which today’s global multinational corporations would be hard to conceive.

Practice Problems 389
1 Which of the following statements best describes the benefits of international 
trade?
A Countries gain from exchange and specialization.
B Countries receive lower prices for their exports and pay higher prices for 
imports.
C Absolute advantage is required for a country to benefit from trade in the 
long term.
2 Which of the following statements best describes the costs of international 
trade?
A Countries without an absolute advantage in producing a good cannot bene -
fit significantly from international trade.
B Resources may need to be allocated into or out of an industry and less-  
efficient companies may be forced to exit an industry, which in turn may 
lead to higher unemployment.
C Loss of manufacturing jobs in developed countries as a result of import 
competition means that developed countries benefit far less than developing 
countries from trade.
3 Suppose the cost of producing tea relative to copper is lower in Tealand than in

Copperland. With trade, the copper industry in Copperland would most likely :
A expand.
B contract.
C remain stable.
4 A country has a comparative advantage in producing a good if:
A it is able to produce the good at a lower cost than its trading partner.
B its opportunity cost of producing the good is less than that of its trading 
partner.
C its opportunity cost of producing the good is more than that of its trading 
partner.
5 Suppose Mexico exports vegetables to Brazil and imports flashlights used 
for mining from Brazil. The output per worker per day in each country is as 
follows:
Flashlights Vegetables
Mexico 20 60
Brazil 40 80
 Which country has a comparative advantage in the production of vegetables 
and what is the most  relevant opportunity cost?
A Brazil: 2 vegetables per flashlight.
B Mexico: 1.5 vegetables per flashlight.
C Mexico: 1/3 flashlight per vegetable.
6 Suppose three countries produce rulers and pencils with output per worker per 
day in each country as follows:

Reading 19 ■ International Trade and Capital Flows 390
Rulers Pencils
Mexico 20 40
Brazil 30 90
China 40 160
 Which country has the greatest comparative advantage in the production of 
rulers?
A China.
B Brazil.
C Mexico.
7 In the Ricardian trade model, a country captures more of the gains from trade 
if:
A it produces all products while its trade partner specializes in one good.
B the terms of trade are closer to its autarkic prices than to its partner’s autar -
kic prices.
C the terms of trade are closer to its partner’s autarkic prices than to its autar -
8 Germany has much more capital per worker than Portugal. In autarky each 
country produces and consumes both machine tools and wine. Production of 
machine tools is relatively capital intensive whereas winemaking is labor inten -
sive. According to the Heckscher–Ohlin model, when trade opens:
A Germany should export machine tools and Portugal should export wine.
B Germany should export wine and Portugal should export machine tools.

C Germany should produce only machine tools and Portugal should produce 
only wine.
9 According to the Heckscher–Ohlin model, when trade opens:
A the scarce factor gains relative to the abundant factor in each country.
B the abundant factor gains relative to the scarce factor in each country.
C income is redistributed between countries but not within each country.
10 Which type of trade restriction would most likely  increase domestic govern -
ment revenue?
A Tariff.
B Import quota.
C Export subsidy.
11 Which of the following trade restrictions is likely to result in the greatest wel -
fare loss for the importing country?
A A tariff.
B An import quota.
C A voluntary export restraint.
12 A large country can:
A benefit by imposing a tariff.
B benefit with an export subsidy.
C not benefit from any trade restriction.
13 If Brazil and South Africa have free trade with each other, a common trade pol -
icy against all other countries, but no free movement of factors of production

A customs union.
B common market.
C free trade area (FTA).
14 Which of the following factors best explains why regional trading agreements 
are more popular than larger multilateral trade agreements?
A Minimal displacement costs.
B Trade diversions benefit members.
C Quicker and easier policy coordination.
15 The sale of mineral rights would be captured in which of the following balance 
of payments components?
A Capital account.
B Current account.
C Financial account.
16 Patent fees and legal services are recorded in which of the following balance of 
payments components?
17 During the most recent quarter, a steel company in South Korea had the follow -
ing transactions
■●Bought iron ore from Australia for AUD50 million.
■●Sold finished steel to the United States for USD65 million.
■●Borrowed AUD50 million from a bank in Sydney.
■●Received a USD10 million dividend from US subsidiary.

■●Paid KRW550 million to a Korean shipping company.
 Which of the following would be reflected in South Korea’s current account 
balance for the quarter?
A The loan.
B The shipping.
C The dividend.
18 Which of the following most likely  contributes to a current account deficit?
A High taxes.
B Low private savings.
C Low private investment.
19 Which of the following chronic deficit conditions is least  alarming to the deficit 
country’s creditors?
A High consumption.
B High private investment.
C High government spending.
20 Which of the following international trade organizations regulates cross-  border 
exchange among nations on a global scale?
A World Bank Group (World Bank).
B World Trade Organization (WTO).
C International Monetary Fund (IMF).

Reading 19 ■ International Trade and Capital Flows 392
21 Which of the following international trade organizations has a mission to help 
developing countries fight poverty and enhance environmentally sound eco -
nomic growth?
22 Which of the following organizations helps to keep global systemic risk under 
control by preventing contagion in scenarios such as the 2010 Greek sovereign 
debt crisis?
23 Which of the following international trade bodies was the only multilateral 
body governing international trade from 1948 to 1995?
A World Trade Organization (WTO).
B International Trade Organization (ITO).
C General Agreement on Tariffs and Trade (GATT).

Solutions 393
SOLUTIONS
1 A is correct. Countries gain from exchange when trade enables each country to 
receive a higher price for exported goods and/or pay a lower price for imported 
goods. This leads to more efficient resource allocation and allows consumption 
of a larger variety of goods.
2 B is correct. Resources may need to be reallocated into or out of an industry, 
depending on whether that industry is an exporting sector or an import-  
competing sector of that economy. As a result of this adjustment process, 
less-  efficient companies may be forced to exit the industry, which in turn may 
lead to higher unemployment and the need for retraining in order for displaced 
workers to find jobs in expanding industries.
3 A is correct. The copper industry in Copperland would benefit from trade. 
Because the cost of producing copper relative to producing tea is lower in 
Copperland than in Tealand, Copperland will export copper and the industry 
will expand.

4 B is correct. Comparative advantage is present when the opportunity cost of 
producing a good is less than that of a trading partner.
5 C is correct. While Brazil has an absolute advantage in the production of both 
flashlights and vegetables, Mexico has a comparative advantage in the pro -
duction of vegetables. The opportunity cost of vegetables in Mexico is 1/3 per 
flashlight, while the opportunity cost of vegetables in Brazil is ½ per flashlight.
6 C is correct. Mexico has the lowest opportunity cost to produce an extra ruler. 
The opportunity cost is 2 pencils per ruler in Mexico, 3 pencils per ruler in 
Brazil, and 4 pencils per ruler in China.
7 C is correct. A country gains if trade increases the price of its exports relative 
to its imports as compared to its autarkic prices, i.e. the final terms of trade 
are more favorable than its autarkic prices. If the relative price of exports and 
imports remains the same after trade opens, then the country will consume the

same basket of goods before and after trade opens, and it gains nothing from 
the ability to trade. In that case, its trade partner will capture all of the gains. Of 
course, the opposite is true if the roles are reversed. More generally, a country 
captures more of the gains from trade the more the final terms of trade differ 
from its autarkic prices.
8 A is correct. In the Heckscher–Ohlin model a country has a comparative 
advantage in goods whose production is intensive in the factor with which it 
is relatively abundantly endowed. In this case, capital is relatively abundant in 
Germany so Germany has a comparative advantage in producing the capital-  
intensive product: machine tools. Portugal is relatively labor abundant, hence 
should produce and export the labor-  intensive product: wine.
9 B is correct. As a country opens up to trade, it has a favorable impact on the 
abundant factor, and a negative impact on the scarce factor. This is because

trade causes the output mix to change and therefore changes the relative 
demand for the factors of production. Increased output of the export product 
increases demand for the factor that is used intensively in its production, while 
reduced output of the import product decreases demand for the factor used 
intensively in its production. Because the export (import) product uses the 
abundant (scarce) factor intensively, the abundant factor gains relative to the 
scarce factor in each country.

Reading 19 ■ International Trade and Capital Flows 394
10 A is correct. The imposition of a tariff will most likely increase domestic gov -
ernment revenue. A tariff is a tax on imports collected by the importing coun -
try’s government.
11 C is correct. With a voluntary export restraint, the price increase induced by 
restricting the quantity of imports (= quota rent for equivalent quota = tariff 
revenue for equivalent tariff) accrues to foreign exporters and/or the foreign 
12 A is correct. By definition, a large country is big enough to affect the world 
price of its imports and exports. A large country can benefit by imposing a tariff  
if its terms of trade improve by enough to outweigh the welfare loss arising 
from inefficient allocation of resources.
13 A is correct. A customs union extends a free trade area (FTA) by not only 
allowing free movement of goods and services among members, but also 
creating common trade policy against non-  members. Unlike a more integrated

common market, a customs union does not allow free movement of factors of 
production among members.
14 C is correct. Regional trading agreements are politically less contentious and 
quicker to establish than multilateral trade negotiations (for example, under the 
World Trade Organization). Policy coordination and harmonization is easier 
among a smaller group of countries.
15 A is correct. The capital account measures capital transfers and sale and pur -
chase of non-  produced, non-  financial assets such as mineral rights and intangi -
ble assets.
16 B is correct. The current account measures the flows of goods and services 
(including income from foreign investments). Patent fees and legal services are 
both captured in the services sub-  account of the current account.
17 C is correct. The current account includes income received on foreign invest -
ments. The Korean company effectively “exported” the use of its capital during

the quarter to its US subsidiary, and the dividend represents payment for those 
services.
18 B is correct. A current account deficit tends to result from low private saving, 
high private investment, a government deficit, or a combination of the three. 
Of the choices, only low private savings contributes toward a current account 
deficit.
19 B is correct. A current account deficit tends to result from low private saving, 
high private investment, low government savings, or a combination of the three. 
Of these choices, only high investments can increase productive resources and 
improve future ability to repay creditors.
20 B is correct. The WTO provides the legal and institutional foundation of the 
multinational trading system and is the only international organization that reg -
ulates cross-  border trade relations among nations on a global scale. The WTO’s 
mission is to foster free trade by providing a major institutional and regulatory

framework of global trade rules. Without such global trading rules, today’s 
global transnational corporations would be hard to conceive.
21 A is correct. The World Bank’s mission is to help developing countries fight 
poverty and enhance environmentally sound economic growth. The World 
Bank helps to create the basic economic infrastructure essential for creation 
and maintenance of domestic financial markets and a well-  functioning financial 
industry in developing countries.

Solutions 395
22 C is correct. From an investment perspective, the IMF helps to keep country-  
specific market risk and global systemic risk under control. The Greek sover -
eign debt crisis on 2010, which threatened to destabilize the entire European 
banking system, is a recent example. The IMF’s mission is to ensure the stability 
of the international monetary system, the system of exchange rates and interna -
tional payments which enables countries to buy goods and services from each 
other.
23 C is correct. The GATT was the only multilateral body governing international 
trade from 1948 to 1995. It operated for almost half a century as a quasi-  
institutionalized, provisional system of multilateral treaties and included several 
rounds of negotiations.

Currency Exchange Rates
by William A. Barker, PhD, CFA, Paul D. McNelis, and Jerry Nickelsburg
William A. Barker, PhD, CFA (Canada). Paul D. McNelis is at Gabelli School of Business, 
Fordham University (USA). Jerry Nickelsburg (USA).
a. define an exchange rate and distinguish between nominal and real 
exchange rates and spot and forward exchange rates;
b. describe functions of and participants in the foreign exchange 
market;
c. calculate and interpret the percentage change in a currency 
relative to another currency;
d. calculate and interpret currency cross-  rates;
e. convert forward quotations expressed on a points basis or in 
percentage terms into an outright forward quotation;
f. explain the arbitrage relationship between spot rates, forward 
rates, and interest rates;
g. calculate and interpret a forward discount or premium; 
h. calculate and interpret the forward rate consistent with the spot

rate and the interest rate in each currency;
i. describe exchange rate regimes;
j. explain the effects of exchange rates on countries’ international 
trade and capital flows.
Measured by daily turnover, the foreign exchange (FX) market—the market in which 
currencies are traded against each other—is by far the world’s largest market. Current 
estimates put daily turnover at approximately USD4 trillion for 2010. This is about 
10 to 15 times larger than daily turnover in global fixed-  income markets and about 1READING
20

Reading 20 ■ Currency Exchange Rates 398
50 times larger than global turnover in equities. Moreover, volumes in FX turnover 
continue to grow: Some predict that daily FX turnover will reach USD10 trillion by 
2020 as market participation spreads and deepens.
The FX market is also a truly global market that operates 24 hours a day, each 
business day. It involves market participants from every time zone connected through 
electronic communications networks that link players as large as multibillion-  dollar 
investment funds and as small as individuals trading for their own account—all brought 
together in real time. International trade would be impossible without the trade in 
currencies that facilitates it, and so too would cross-  border capital flows that connect 
all financial markets globally through the FX market.
These factors make foreign exchange a key market for investors and market partic -
ipants to understand. The world economy is increasingly transnational in nature, with

both production processes and trade flows often determined more by global factors 
than by domestic considerations. Likewise, investment portfolio performance increas -
ingly reflects global determinants because pricing in financial markets responds to the 
array of investment opportunities available worldwide, not just locally. All of these 
factors funnel through, and are reflected in, the foreign exchange market. As investors 
shed their “home bias” and invest in foreign markets, the exchange rate—the price at 
which foreign-  currency-  denominated investments are valued in terms of the domestic 
currency—becomes an increasingly important determinant of portfolio performance.
Even investors adhering to a purely “domestic” portfolio mandate are increasingly 
affected by what happens in the foreign exchange market. Given the globalization of 
the world economy, most large companies depend heavily on their foreign operations

(for example, by some estimates about 40  percent of S&P 500 Index earnings are 
from outside the United States). Almost all companies are exposed to some degree 
of foreign competition, and the pricing for domestic assets—equities, bonds, real 
estate, and others—will also depend on demand from foreign investors. All of these 
various influences on investment performance reflect developments in the foreign 
exchange market.
This reading introduces the foreign exchange market, providing the basic concepts 
and terminology necessary to understand exchange rates as well as some of the basics 
of exchange rate economics.
The reading is divided up as follows. Section 2 describes the organization of the 
foreign exchange market and discusses the major players—who they are, how they 
conduct their business, and how they respond to exchange rate changes. Section 
3 takes up the mechanics of exchange rates: definitions, quotes, and calculations.

This section shows that the reader has to pay close attention to conventions used in 
various foreign exchange markets around the world because they can vary widely. 
Sometimes exchange rates are quoted in the number of domestic currency units per 
unit of foreign currency, and sometimes they are quoted in the opposite way. The exact 
notation used to represent exchange rates can vary widely as well, and occasionally 
the same exchange rate notation will be used by different sources to mean completely 
different things. The notation used here may not be the same as that encountered 
elsewhere. Therefore, the focus should be on understanding the underlying concepts 
rather than relying on rote memorization of formulas. We also show how to calculate 
cross-  exchange rates and how to compute the forward exchange rate given either the 
forward points or the percentage forward premium or discount. In Section 4, we discuss

alternative exchange rate regimes operating throughout the world. Finally, in Section 
5, we discuss how exchange rates affect a country’s international trade (exports and 
imports) and capital flows. A summary and practice problems conclude the reading.

The Foreign Exchange Market 399
THE FOREIGN EXCHANGE MARKET
To understand the FX market, it is necessary to become familiar with some of its basic 
conventions. Individual currencies are often referred to by standardized three-  letter 
codes that the market has agreed upon through the International Organization for 
Standardization (ISO). Exhibit 1 lists some of the major global currencies and their 
identification codes.
Exhibit 1   Standard Currency Codes 
Three-  Letter Currency Code Currency
USD US dollar
EUR Euro
JPY Japanese yen
GBP British pound
CHF Swiss franc
CAD Canadian dollar
AUD Australian dollar
NZD New Zealand dollar
ZAR South African rand
SEK Swedish krona
NOK Norwegian krone
BRL Brazilian real
SGD Singapore dollar
MXN Mexican peso
CNY Chinese yuan
HKD Hong Kong dollar
INR Indian rupee
KRW South Korean won
RUB Russian ruble
It is important to understand that there is a difference between referring to an 
individual currency  and an exchange rate . One can hold an individual currency (for

example, in a EUR100 million deposit), but an exchange rate refers to the price of 
one currency in terms of another (for example, the exchange rate between the EUR 
and USD). An individual currency can be singular, but there are always two curren -
cies involved in an exchange rate: the price of one currency relative to another. The 
exchange rate is the number of units of one currency (called the price currency ) that 
one unit of another currency (called the base currency ) will buy. An equivalent way of 
describing the exchange rate is as the cost of one unit of the base currency in terms 
of the price currency.
This distinction between individual currencies and exchange rates is important 
because, as we will see in a later section, these three-  letter currency codes can be 
used both ways. (For example, when used as an exchange rate in the professional FX 
market, EUR is understood to be the exchange rate between the euro and US dollar).

But be aware of the context (either as a currency or as an exchange rate) in which 
these three-  letter currency codes are being used. To avoid confusion, this reading 
will identify exchange rates using the convention of “ A/B, ” referring to the number of 2

Reading 20 ■ Currency Exchange Rates 400
units of currency A that one unit of currency B will buy. For example, a USD/EUR 
exchange rate of 1.2875 means that 1 euro will buy 1.2875 US dollars (i.e., 1 euro costs 
1.2875 US dollars).1 In this case, the euro is the base currency and the US dollar is the 
price currency. A decrease in this exchange rate would mean that the euro costs less 
or that fewer US dollars are needed to buy one euro. In other words, a decline in this 
exchange rate indicates that the USD is appreciating  against the EUR or, equivalently, 
the EUR is depreciating  against the USD.
The exchange rates described above are referred to as nominal  exchange rates. This 
is to distinguish them from real exchange rates, which are indexes often constructed 
by economists and other market analysts to assess changes in the relative purchas -
ing power of one currency compared with another. Creating these indexes requires

adjusting the nominal exchange rate by using the price levels in each country of the 
currency pair (hence the name “real exchange rates”) in order to compare the relative 
purchasing power between countries.
In a world of homogenous goods and services and with no market frictions or trade 
barriers, the relative purchasing power across countries would tend to equalize: Why 
would you pay more, in real terms, domestically for a “widget” if you could import an 
identical “widget” from overseas at a cheaper price? This basic concept is the intu -
ition behind a theory known as “purchasing power parity” (PPP), which describes the 
long-  term equilibrium of nominal exchange rates. PPP asserts that nominal exchange 
rates adjust so that identical goods (or baskets of goods) will have the same price in 
different markets. Or, put differently, the purchasing power of different currencies is 
equalized for a standardized basket of goods.

In practice, the conditions required to enforce PPP are not satisfied: Goods and 
services are not identical across countries; countries typically have different baskets of 
goods and services produced and consumed; many goods and services are not traded 
internationally; there are trade barriers and transaction costs (e.g., shipping costs and 
import taxes); and capital flows are at least as important as trade flows in determin -
ing nominal exchange rates. As a result, nominal exchange rates exhibit persistent 
deviations from PPP . Moreover, relative purchasing power among countries displays 
a weak, if any, tendency toward long-  term equalization. A simple example of a cross-  
country comparison of the purchasing power of a standardized good is the “Big Mac” 
index produced by the Economist , which shows the relative price of this standardized 
hamburger in different countries. The Big Mac index shows that fast-  food hamburger

prices can vary widely internationally and that this difference in purchasing power is 
typical of most goods and services. Hence, movements in real exchange rates provide 
meaningful information about changes in relative purchasing power among countries.
Consider the case of an individual who wants to purchase goods from a foreign 
country. The individual would be able to buy fewer of these goods if the nominal 
spot exchange rate for the foreign currency appreciated or if the foreign price level 
increased. Conversely, the individual could buy more foreign goods if the individual’s 
domestic income increased. (For this example, we will assume that changes in the 
individual’s income are proportional to changes in the domestic price level.) Hence, 
in real purchasing power terms, the real exchange rate that an individual faces is an 
increasing function of the nominal exchange rate (quoted in terms of the number of

units of domestic currency per one unit of foreign currency) and the foreign price level 
and a decreasing function of the domestic price level. The higher  the real exchange 
1 This convention is consistent with the meaning of “/” in mathematics and the straightforward interpreta -
tion of “ A/B” as “ A per B” is helpful in understanding exchange rates as the price of one currency in terms 
of another. Nevertheless, other notation conventions exist. “B/A” and “B:A” are sometimes used to denote 
what this reading denotes as “ A/B. ” Careful attention to the context will usually make the convention clear.

The Foreign Exchange Market 401
rate that this individual faces, the fewer  foreign goods, in real terms, the individual 
can purchase and the lower  that individual’s relative purchasing power compared 
with the other country.
An equivalent way of viewing the real exchange rate is that it represents the relative 
price levels in the domestic and foreign countries. Mathematically, we can represent 
the foreign price level in terms of the domestic currency as:
Foreign price level in domestic currency = Sd/f × Pf
where Sd/f is the spot exchange rate (quoted in terms of the number of units of domestic 
currency per one unit of foreign currency) and Pf is foreign price level quoted in terms 
of the foreign currency. We can define the domestic price level, in terms of the domes -
tic currency, as Pd. Hence, the ratio between the foreign and domestic price levels is:
Real exchange rate(d/f) = (Sd/f × Pf)/Pd = Sd/f × (Pf/Pd)
For example, for a British consumer wanting to buy goods made in the Eurozone,

the real exchange rate (defined in GBP/EUR terms; note that the domestic currency for 
the United Kingdom is the price currency, not the base currency) will be an increasing 
function of the nominal spot exchange rate (GBP/EUR) and the Eurozone price level 
and a decreasing function of the UK price level. This is written as:
Real  exchange rat eGBP
EURGBP
EUReur
UKSCPI
CPI=×


Let’s examine the effect of movements in the domestic and foreign price levels, 
and the nominal spot exchange rate, on the real purchasing power of an individual in 
the United Kingdom wanting to purchase Eurozone goods. Assume that the nominal 
spot exchange rate (GBP/EUR) increases by 10 percent, the Eurozone price level by 
5 percent, and the UK price level by 2 percent. The change in the real exchange rate 
is then:
11
111 10 +∆ 



×+∆ 


+∆ 

−= +()S
SP
P
P
Pd
f
d
ff
f
d
d%× ×+
+−≈ +− ≈15
121105 21 3%
%%% %%
In this case, the real exchange rate for the UK-  based individual has increased  about

13 percent, meaning that it now costs more , in real terms, to buy Eurozone goods. Or 
put differently, the UK individual’s real purchasing power relative to Eurozone goods has 
declined  by about 13 percent. An easy way to remember this relationship is to consider 
the real exchange rate (stated with the domestic currency as the price currency) as 
representing the real price you face in order to purchase foreign goods and services: 
The higher  the price (real exchange rate), the lower  your relative purchasing power.
The real exchange rate for a currency can be constructed for the domestic currency 
relative to a single foreign currency or relative to a basket of foreign currencies. In 
either case, these real exchange rate indexes depend on the assumptions made by the 
analyst creating them. Several investment banks and central banks create proprietary 
measures of real exchange rates. It is important to note that real exchange rates are not

quoted or traded in global FX markets: They are only indexes created by analysts to 
understand the international competitiveness of an economy and the real purchasing 
power of a currency.
In this context, real exchange rates can be useful for understanding trends in 
international trade and capital flows and hence can be seen as one of the influences 
on nominal spot exchange rates. As an example, consider the exchange rate between 
the Chinese yuan and the US dollar. During 2010, the nominal yuan exchange rate 
against the US dollar (CNY/USD) declined by approximately 3 percent—meaning that

Reading 20 ■ Currency Exchange Rates 402
the US dollar depreciated against the yuan. However, the annual inflation rates in the 
United States and China were different during 2010—approximately 1.5 percent for 
the United States and 4.5 percent for China. This means that the real exchange rate 
(in CNY/USD terms) was depreciating more rapidly than the nominal CNY/USD 
exchange rate:
11
113 15 45 +∆



×+∆()
+∆()−≈ −+ −≈ %%
%%. %. % SP
PCNY
USDUS
China− −6%
This combination of a stronger yuan and a higher Chinese inflation rate meant that the 
real exchange rate faced by China was declining, thus increasing Chinese purchasing 
power in USD terms.
Movements in real exchange rates can have a similar effect as movements in nom -
inal exchange rates in terms of affecting relative prices and hence trade flows. Even if 
the nominal spot exchange rate does not move, differences in inflation rates between 
countries affect their relative competitiveness.

Although real exchange rates can exert some influence on nominal exchange rate 
movements, they are only one of many factors; it can be difficult to disentangle all 
of these inter-  relationships in a complex and dynamic FX market. As discussed ear -
lier, PPP is a poor guide to predicting future movements in nominal exchange rates 
because these rates can deviate from PPP equilibrium—and even continue to trend 
away from their PPP level—for years at a time. Hence, it should not be surprising that 
real exchange rates, which reflect changes in relative purchasing power, have a poor 
track record as a predictor of future nominal exchange rate movements.
EXAMPLE 1   
Nominal and Real Exchange Rates
An investment adviser located in Sydney, Australia, is meeting with a local client 
who is looking to diversify her domestic bond portfolio by adding investments 
in fixed-  rate, long-  term bonds denominated in HKD. The client frequently

visits Hong Kong, and many of her annual expenses are denominated in HKD. 
The client, however, is concerned about the foreign currency risks of offshore 
investments and whether the investment return on her HKD-  denominated 
investments will maintain her purchasing power—both domestically (i.e., for her 
AUD-  denominated expenses) and in terms of her foreign trips (i.e., denominated 
in HKD, for her visits to Hong Kong). The investment adviser explains the effect 
of changes in nominal and real exchange rates to the client and illustrates this 
explanation by making the following statements:
Statement 1  All else equal, an increase in the nominal AUD/HKD 
exchange rate will lead to an increase in the AUD-  
denominated value of your foreign investment.
Statement 2  All else equal, an increase in the nominal AUD/HKD 
exchange rate means that your relative purchasing power 
for your Hong Kong trips will increase (based on paying for 
your trip with the income from your HKD-  denominated 
bonds).

bonds).
Statement 3  All else equal, an increase in the Australian inflation rate 
will lead to an increase in the real exchange rate (AUD/
HKD). A higher real exchange rate means that the relative 
purchasing power of your AUD-  denominated income is 
higher.

The Foreign Exchange Market 403
Statement 4  All else equal, a decrease in the nominal exchange rate 
(AUD/HKD) will decrease the real exchange rate (AUD/
HKD) and increase the relative purchasing power of your 
AUD-  denominated income.
To demonstrate the effects of the changes in inflation and nominal exchange rates 
on relative purchasing power, the adviser uses the following scenario: “Suppose 
that the AUD/HKD exchange rate increases by 5 percent, the price of goods and 
services in Hong Kong goes up by 5 percent, and the price of Australian goods 
and services goes up by 2 percent. ”
1 Statement 1 is:
A correct.
B incorrect, because based on the quote convention the investment’s 
value would be decreasing in AUD terms.
C incorrect, because the nominal AUD value of the foreign investments 
will depend on movements in the Australian inflation rate.
2 Statement 2 is:
A correct.
B incorrect, because purchasing power is not affected in this case.

C incorrect, because based on the quote convention, the client’s relative 
purchasing power would be decreasing.
3 Statement 3 is:
A correct.
B incorrect with respect to the real exchange rate only.
C incorrect with respect to both the real exchange rate and the purchas -
ing power of AUD-  denominated income.
4 Statement 4 is:
A correct.
B incorrect with respect to the real exchange rate.
C incorrect with respect to the purchasing power of AUD-  denominated 
income.
5 Based on the adviser’s scenario and assuming that the HKD value of the 
HKD bonds remained unchanged, the nominal AUD value of the client’s 
HKD investments would:
A decrease by about 5 percent.
B increase by about 5 percent.
C remain approximately the same.
6 Based on the adviser’s scenario, the change in the relative purchasing 
power of the client’s AUD-  denominated income is closest  to:
A –8 percent.
B +8 percent.
C +12 percent.
A is correct. Given the quoting convention, an increase in the AUD/HKD rate

means that the base currency (HKD) is appreciating (one HKD will buy more 
AUD). This is increasing the nominal value of the HKD-  denominated investments 
when measured in AUD terms.

Reading 20 ■ Currency Exchange Rates 404
B is correct. When paying for HKD-  denominated expenses with HKD-  
denominated income, the value of the AUD/HKD spot exchange rate (or any 
other spot exchange rate) would not be relevant. In fact, this is a basic principle 
of currency risk management: reducing FX risk exposures by denominating 
assets and liabilities (or income and expenses) in the same currency.
C is correct. An increase in the Australian (i.e., domestic) inflation rate means 
that the real exchange rate (measured in domestic/foreign, or AUD/HKD, terms) 
would be decreasing, not increasing. Moreover, an increase in the real exchange 
rate ( RAUD/HKD ) would be equivalent to a reduction of the purchasing power of 
the Australian client: Goods and services denominated in HKD would cost more.
A is correct. As the spot AUD/HKD exchange rate decreases, the HKD is depre -
ciating against the AUD; or equivalently, the AUD is appreciating against the

HKD. This is reducing the real exchange rate ( RAUD/HKD ) and increasing the 
Australian client’s purchasing power.
B is correct. As the AUD/HKD spot exchange rate increases by 5 percent, the 
HKD is appreciating against the AUD by 5 percent and, all else equal, the value 
of the HKD-  denominated investment is increasing by 5 percent in AUD terms.
A is correct. The real exchange rate ( RAUD/HKD ) is expressed as:
RSP
PAUD
HKDAUD
HKDHKD
AUD=×
The information in the adviser’s scenario can be expressed as:
%% %% %% %% ∆≈ ∆+ ∆− ∆≈ ++ −≈ + RS PPAUD
HKDAUD
HKDHKDA UD 55 28
Because the real exchange rate (expressed in AUD/HKD terms) has gone up by 
about 8 percent, the real purchasing power of the investor based in Australia 
has declined by about 8 percent. This can be seen from the fact that HKD has 
appreciated against the AUD in nominal terms, and the Hong Kong price level 
has also increased. This increase in the cost of Hong Kong goods and services

(measured in AUD) is only partially offset by the small (2 percent) increase in 
the investor’s income (assumed equal to the change in the Australian price level).
2.1 Market Functions
FX markets facilitate international trade in goods and services, where companies 
and individuals need to make transactions in foreign currencies. This would cover 
everything from companies and governments buying and selling products in other 
countries, to tourists engaged in cross-  border travel (for example, a German tourist 
selling euros and buying sterling for a visit to London). Although this is an important 
dimension of FX markets, and despite the growth of global trade in recent years, an 
even larger proportion of the daily turnover in FX markets is accounted for by capital 
market transactions, where investors convert between currencies for the purpose of 
moving funds into (or out of) foreign assets. These types of transactions cover the

range from direct investments (for example, companies buying such fixed assets as

The Foreign Exchange Market 405
factories) in other countries to portfolio investments (the purchase of stocks, bonds, and 
other financial assets denominated in foreign currencies). Because capital is extremely 
mobile in modern financial markets, this ebb and flow of money across international 
borders and currencies generates a huge and growing volume of FX transactions.
Regardless of the underlying motivation for the FX transaction, it will eventually 
require that one currency be exchanged for another in the FX market. In advance of 
that required transaction, market participants are exposed to the risk that the exchange 
rate will move against them. Often they will try to reduce (hedge) this risk through a 
variety of FX instruments (described in more detail later). Conversely, market partic -
ipants may form opinions about future FX movements and undertake speculative FX 
risk exposures through a variety of FX instruments in order to profit from their views.

The distinction between hedging and speculative positions is not always clear cut. 
For example, consider the case of a corporation selling its products overseas. This cre -
ates an FX risk exposure because the revenue from foreign sales will ultimately need 
to be converted into the corporation’s home currency. This risk exposure is typically 
hedged, and corporate hedging often accounts for large FX flows passing through the 
market. The amount and timing of foreign revenue, however, are generally hard to 
predict with precision: They will depend on the pace of foreign sales, the sales prices 
realized, the pace at which foreign clients pay for their purchases, and so forth. In the 
face of this uncertainty, the corporate treasury will estimate the timing and amount 
of foreign revenue and will then hedge a portion of this estimated amount. Many 
corporate treasuries have hedging targets based on this estimate, but they also have

the flexibility to under-  hedge or over-  hedge based on their opinions about future FX 
rate movements. In order to judge the effectiveness of these discretionary trades, the 
performance of the corporate treasury is compared with a benchmark, usually stated 
in terms of a fixed amount hedged relative to total sales. (For example, the benchmark 
may be a 100 percent fully hedged position. The profitability of the hedge actually 
implemented—which, based on the treasury’s discretion, can vary above or below 
100 percent—is then compared with what would have been achieved with a passive, 
100 percent fully hedged position.) Treasury managers’ performance is judged based 
on gains or losses relative to the benchmark, just as an investment fund manager’s 
performance is benchmarked against performance targets.
At the other end of the spectrum between hedging and speculation, consider the 
archetypical speculative account: a hedge fund. Although it is true that hedge funds

will seek out, accept, and manage risk for profit, a hedge fund is, after all, a hedge 
fund: Strict risk control procedures are critical to the fund’s success, especially when 
leverage is involved. This mixture of speculative and hedging motives is common 
throughout the FX space as market participants shape their FX exposures to suit their 
market forecasts, operational mandates, and appetites for risk.
The FX market provides a variety of products that provide the flexibility to meet 
this varied and complex set of financial goals. Spot  transactions involve the exchange 
of currencies for immediate delivery. For most currencies, this corresponds to “T + 2” 
delivery, meaning that the exchange of currencies is settled two business days after the 
trade is agreed to by the two sides of the deal. (One exception is the Canadian dollar, 
for which spot settlement against the US dollar is on a T + 1 basis.) The exchange

rate used for these spot transactions is referred to as the spot exchange rate, and it is 
the exchange rate that most people refer to in their daily lives (for example, this is the 
exchange rate usually quoted by the financial press, on the evening news, and so forth).
It is important to realize, however, that spot transactions make up only a minority 
of total daily turnover in the global FX market: The rest is accounted for by trade in 
outright forward contracts, FX swaps, and FX options. Although these products will 
be covered in more depth in a subsequent section, and at Level II of the CFA curric -
ulum, we will provide a brief introduction to these products here.

Reading 20 ■ Currency Exchange Rates 406
Outright forward contracts  (often referred to simply as forwards) are agreements 
to deliver foreign exchange at a future date at an exchange rate agreed upon today. 
For example, suppose that a UK-  based company expects to receive a payment of 
100 million euros in 85 days. Although it could convert these euros to British pounds 
with a spot transaction (the spot rate would be the GBP/EUR rate in 83 days, because 
of T + 2 settlement), this future spot rate is currently unknown and represents a 
foreign exchange risk to the company. The company can avoid this risk by entering 
into a transaction with a foreign exchange dealer to sell 100 million euros against 
the British pound for settlement 85 days from today at a rate—the forward exchange 
rate—agreed upon today.
As such, forward contracts are any exchange rate transactions that occur with 
currency settlement longer than the usual T + 2 settlement for spot delivery. Each of

these contracts requires two specifications: the date at which the currencies are to be 
exchanged and the exchange rate to be applied on the settlement date. Accordingly, 
exchange rates for these transactions are called forward exchange rates  to distinguish 
them from spot rates.
Dealers will typically quote forward rates for a variety of standard forward settle -
ment dates (for example, one week, one month, or 90 days) on their dealing screens. In 
an over-  the- counter (OTC) market, however, traders can arrange forward settlement 
at any future date they agree upon, with the forward exchange rate scaled appropri -
ately for the specific term to settlement. Standard forward settlement dates (such as 
three months) are defined in terms of the spot settlement date, which is generally T 
+ 2. For example, if today is 18 October and spot settlement is for 20 October, then a 
three-  month forward settlement would be defined as 20 January of the following year.

Note as well that these standard forward settlement dates may not always be good 
business days: 20 January could be a weekend or a holiday. In that case, the forward 
settlement date is set to the closest good business day. Traders always confirm the 
exact forward settlement date when making these types of trades, and the forward 
rate is scaled by the exact number of days to settlement.
In an OTC market, the size of the forward contracts can also be any size that the 
two counterparties agree upon. In general, however, liquidity in forward markets 
declines the longer the term to maturity and the larger the trade size. The concept of 
the forward exchange rate and exchange hedging is developed further in Section 3.
Although the OTC market accounts for the majority of foreign exchange trades with 
future (i.e., greater than T + 2) settlement dates, there is also a deep, liquid market in 
exchange-  traded futures  contracts for currencies. Although there are technical differ -

ences between futures and forward contracts, the basic concept is the same: The price 
is set today for settlement on a specified future date. Futures contracts on currencies 
trade on several exchanges globally, but the majority of volume in exchange-  traded 
currency futures contracts is found on the International Monetary Market (IMM) 
division of the Chicago Mercantile Exchange (CME). Futures contracts differ from 
OTC forward contracts in several important ways: They trade on exchanges (such 
as the CME) rather than OTC; they are only available for fixed contract amounts 
and fixed settlement dates; the exchanges demand that a fixed amount of collateral 
be posted against the futures contract trade; and this collateral is marked-  to- market 
daily, with counterparties asked to post further collateral if their positions generate 
losses. On balance, futures contracts are somewhat less flexible than forward con -

tracts. Nonetheless, they provide deep, liquid markets for deferred delivery with a 
minimum of counterparty (i.e., default) risk—a proposition that many FX traders find 
attractive. Accordingly, daily turnover in FX futures contracts is huge. As of 2010, the 
average daily trading volume of FX futures on the CME alone was estimated to be 
about USD140 billion, which is almost comparable in size to the interbank volume 
of spot transactions.

The Foreign Exchange Market 407
Because forward contracts eventually expire, existing speculative positions or FX 
hedges that need to be extended must be rolled prior to their settlement dates. This 
typically involves a spot transaction to offset (settle) the expiring forward contract 
and a new forward contract to be set at a new, more distant settlement date. The 
combination of an offsetting spot transaction and a new forward contract is referred 
to as an FX swap .2
An FX swap is best illustrated by an example. Suppose that a trader sells 100 million 
euros with settlement 95 days from today at a forward exchange rate (USD/EUR) of 
1.2500. In 93 days, the forward contract is two days from settlement, specifically the T 
+ 2 days to spot settlement. To roll the forward contract, the trader will engage in the 
following FX swap. First, the trader will need to buy 100 million euros spot, for which 
T + 2 settlement will fall on day 95, the same day as the settlement of the expiring

forward contract. The purchase of the 100 million euros spot will be used to satisfy 
the delivery of the 100 million euros sold in the expiring forward contract. Because 
100 million euros are being both bought and sold on day 95, there is no exchange of 
euros between counterparties on that day: The amounts net to zero. However, there 
will be an exchange of US dollars, reflecting the movement in exchange rates between 
the date the forward contract was agreed to (day 0) and day 93. Suppose that on day 
93 the spot exchange rate for USD/EUR is 1.2400. This means that the trader will see 
a cash flow on day 95 of USD1,000,000. This is calculated as follows:
EUR100,000,000 × (1.2500 – 1.2400) = USD1,000,000
The trader receives USD1,000,000 from the counterparty because the euro was sold 
forward to day 95 at a price of 1.2500; it was bought  (on day 93) for spot settlement on 
day 95 at a price of 1.2400. This price  movement in the euro indicates a profit to the

trader, but because the euro quantities  exchanged on day 95 net to zero (100,000,000 
euros both bought and sold), this cash flow is realized in US dollars. The second leg 
of the FX swap is then to initiate a new forward sale of 100 million euros at the USD/
EUR forward exchange rate being quoted on day 93. This renews the forward position 
(a forward sale of the euro) to a new date.
FX swaps will be dealt with in more detail at Level II in the curriculum. For the 
purposes of this reading, it is only necessary to understand that (1) an FX swap consists 
of a simultaneous spot and forward transaction; (2) these swap transactions can extend 
(roll) an existing forward position to a new future date; and (3) rolling the position 
forward leads to a cash flow on settlement day. This cash flow can be thought of as a 
mark-  to- market on the forward position. FX swaps are a large component of daily FX 
market turnover because market participants have to roll over existing speculative or

hedging positions as the underlying forward contracts mature in order to extend the 
hedge or speculative position (otherwise, the position is closed out on the forward 
settlement date).
One other area where FX swaps are used in FX markets also bears mentioning: 
They are often used by market participants as a funding source (called swap funding). 
Consider the case of a UK-  based firm that needs to borrow GBP100 million for 90 days, 
starting 2 days from today. One way to do this is simply to borrow 90-  day money in 
GBP-  denominated funds starting at T + 2. An alternative is to borrow in US dollars and 
exchange these for British pounds in the spot FX market (both with T + 2 settlement) 
and then sell British pounds 90 days forward against the US dollar. (Recall that the 
maturity of a forward rate contract is defined in terms of the spot settlement date, so 
the 90-  day forward rate would be for settlement in 92 days from today.) The company

has the use of GBP100 million for 90 days, starting on T + 2, and at the end of this 
2 Note that an “FX swap” is not the same as a “currency swap. ” An FX swap is simply the combination of 
a spot and a forward FX transaction (i.e., only two settlement dates—spot and forward—are involved). A 
currency swap is generally used for multiple periods and payments.

Reading 20 ■ Currency Exchange Rates 408
period can pay off the US dollar loan at a known, pre-  determined exchange rate (the 
90- day forward rate). By engaging in simultaneous spot and forward transactions (i.e., 
an FX swap), the company has eliminated any FX risk from the foreign borrowing. 
The all-  in financing rate using an FX swap will typically be close to that of domestic 
borrowing, usually within a few basis points. This near equivalence is enforced by 
an arbitrage relationship that will be described in Section 3.3. On large borrowing 
amounts, however, even a small differential can add up to substantial cost savings.
Another way to hedge FX exposures, or implement speculative FX positions, is to 
use options on currencies. FX options are contracts that, for an upfront premium or 
fee, give the purchaser the right, but not the obligation, to make an FX transaction at 
some future date at an exchange rate agreed upon today (when the contract is agreed

to). The holder of an FX option will exercise the option only if it is advantageous to do 
so—that is, if the agreed upon exchange rate for the FX option contract is better than 
the FX rate available in the market at option expiry. As such, options are extremely 
flexible tools for managing FX exposures and account for a large percentage of daily 
turnover in the FX market.
Another concept to bear in mind is that spot, forward, swap, and option products 
are typically not used in isolation. Most major market participants manage their FX 
transactions and FX risk exposures through concurrent spot, forward, swap, and 
option positions. Taken together, these instruments (the building blocks of the FX 
market) provide an extremely flexible way for market participants to shape their 
FX risk exposures to match their operational mandate, risk tolerance, and market 
opinion. Moreover, FX transactions are often made in conjunction with transactions

in other financial markets—such as equities, fixed income, and commodities. These 
markets have a variety of instruments as well, and market participants jointly tailor 
their overall  position simultaneously using the building blocks of the FX market and 
these other markets.
EXAMPLE 2   
Spot and Forward Exchange Rates
The investment adviser based in Sydney, Australia, continues her meeting with 
the local client who has diversified her domestic bond portfolio by adding 
investments in fixed-  rate, long-  term bonds denominated in HKD. Given that 
the client spends most of the year in Australia, she remains concerned about the 
foreign exchange risk of her foreign investments and asks the adviser how these 
might be managed. The investment adviser explains the difference between spot 
and forward exchange rates and their role in determining foreign exchange risk 
exposures. The investment adviser suggests the following investment strategy

to the client: “You can exchange AUD for HKD in the spot exchange market, 
invest in a risk-  free, one-  year HKD-  denominated zero coupon bond, and use a 
one-  year forward contract for converting the proceeds back into AUD. ”
Spot exchange rate (AUD/HKD) 0.1429
One-  year HKD interest rate 7.00%
One-  year forward exchange rate (AUD/HKD) 0.1402
1 Which of the following statements is most  correct? Over a one-  year 
horizon, the exchange rate risk of the client’s investment in HKD-  
denominated bonds is determined by uncertainty over:
A today’s AUD/HKD forward rate.
B the AUD/HKD spot rate one year from now.

The Foreign Exchange Market 409
C the AUD/HKD forward rate one year from now.
2 To reduce the exchange rate risk of the Hong Kong investment, the client 
should:
A sell AUD spot.
B sell AUD forward.
C sell HKD forward.
3 Over a one-  year horizon, the investment proposed by the investment 
adviser is most  likely:
A risk free.
B exposed to interest rate risk.
C exposed to exchange rate risk.
4 To set up the investment proposed by the adviser, the client would need 
to:
A sell AUD spot; sell a one-  year, HKD-  denominated bond; and buy AUD 
forward.
B buy AUD spot; buy a one-  year, HKD-  denominated bond; and sell AUD 
forward.
C sell AUD spot; buy a one-  year, HKD-  denominated bond; and buy AUD 
forward.
5 The return (in AUD) on the investment proposed by the investment 
adviser is closest  to:
A 5.00 percent.
B 6.00 percent.
C 7.00 percent.
B is correct. The exchange rate risk (for an unhedged investment) is defined by

the uncertainty over future spot rates. In this case, the relevant spot rate is that 
which would prevail one year from now. Forward rates that would be in effect 
one year from now would be irrelevant, and the current forward rate is known 
with certainty.
C is correct. The Australian-  based investor owns HKD-  denominated bonds, 
meaning that she is long HKD exposure. To hedge this exposure, she could enter 
into a forward contract to sell the HKD against the AUD for future delivery (that 
is, match a long HKD exposure in the cash market with a short HKD exposure in 
the derivatives market). The forward rate is established at the time the forward 
contract is entered into, eliminating any uncertainty about what exchange rate 
would be used to convert HKD-  denominated cash flows back into AUD.
A is correct. The investment is risk free because the investment is based on 
a risk-  free, one-  year, zero coupon, HKD-  denominated bond—meaning there

is no default or reinvestment risk. The investment will mature in one-  year at 
par; there is no interest rate risk. The use of a forward contract to convert the 
HKD-  denominated proceeds back to AUD eliminates any exchange rate risk.

Reading 20 ■ Currency Exchange Rates 410
C is correct. To create the investment, the client needs to convert AUD to HKD 
in the spot exchange market, invest in (buy) the one-  year HKD bond, and sell 
the HKD forward/buy the AUD forward. Note that this process is directly com -
parable to the swap financing approach described in this section of the reading.
A is correct. Converting one AUD to HKD in the spot market gives the cli -
ent (1/0.1429) = HKD7.00. Investing this for one year leads to 7.00 × (1.07) = 
HKD7.49. Selling this amount of HKD at the forward rate gives 7.49 × 0.1402 = 
AUD1.05 (rounding to two decimal places). This implies an AUD-  denominated 
return of 5 percent.
2.2 Market Participants
We now turn to the counterparties that participate in FX markets. As mentioned 
previously, there is an extremely diverse range of market participants, ranging in size 
from multi-  billion-  dollar investment funds down to individuals trading for their own

account (including foreign tourists exchanging currencies at airport kiosks).
To understand the various market participants, it is useful to separate them into 
broad categories. One broad distinction is between what the market refers to as the buy 
side and the sell side . The sell side generally consists of large FX trading banks (such 
as Citigroup, UBS, and Deutsche Bank); the buy side consists of clients who use these 
banks to undertake FX transactions (i.e., buy FX products) from the sell-  side banks.
The buy side can be further broken down into several categories:
■■Corporate accounts : Corporations of all sizes undertake FX transactions during 
cross-  border purchases and sales of goods and services. Many of their FX flows 
can also be related to cross-  border investment flows—such as international 
mergers and acquisitions (M&A) transactions, investment of corporate funds in 
foreign assets, and foreign currency borrowing.

■■Real money accounts : These are investment funds managed by insurance 
companies, mutual funds, pension funds, endowments, exchange-  traded funds 
(ETFs), and other institutional investors. These accounts are referred to as real 
money because they are usually restricted in their use of leverage or financial 
derivatives. This distinguishes them from leveraged accounts (discussed next); 
although, many institutional investors often engage in some form of leverage, 
either directly through some use of borrowed funds or indirectly using financial 
■■Leveraged accounts : This category, often referred to as the professional trading 
community, consists of hedge funds, proprietary trading shops, commodity 
trading advisers (CTAs), high-  frequency algorithmic traders, and the propri -
etary trading desks at banks—and indeed, almost any active trading account 
that accepts and manages FX risk for profit. The professional trading commu -

nity accounts for a large and growing proportion of daily FX market turnover. 
These active trading accounts also have a wide diversity of trading styles. Some 
are macro-  hedge funds that take longer term FX positions based on their views 
of the underlying economic fundamentals of a currency. Others are high-  
frequency algorithmic traders that use technical trading strategies (such as 
those based on moving averages or Fibonacci levels) and whose trading cycles 
and investment horizons are sometimes measured in milliseconds.

The Foreign Exchange Market 411
■■Retail accounts : The simplest example of a retail account is the archetypical for -
eign tourist exchanging currency at an airport kiosk. However, it is important 
to realize that as electronic trading technology has reduced the barriers to entry 
into FX markets and the costs of FX trading, there has been a huge surge in 
speculative trading activity by retail accounts—consisting of individuals trading 
for their own accounts as well as smaller hedge funds and other active traders. 
This also includes households using electronic trading technology to move their 
savings into foreign currencies (this is relatively widespread among households 
in Japan, for example). It is estimated that retail trading accounts for as much as 
10 percent of all spot transactions in some currency pairs and that this propor -
tion is growing.
■■Governments : Public entities of all types often have FX needs, ranging from

relatively small (e.g., maintaining consulates in foreign countries) to large 
(e.g., military equipment purchases or maintaining overseas military bases). 
Sometimes these flows are purely transactional—the business simply needs 
to be done—and sometimes government FX flows reflect, at least in part, the 
public policy goals of the government. Some government FX business resem -
bles that of investment funds, although sometimes with a public policy mandate 
as well. In some countries, public sector pension plans and public insurance 
schemes are run by a branch of the government. One example is the Caisse de 
dépôt et placement du Québec, which was created by the Québec provincial 
government in Canada to manage that province’s public sector pension plans. 
The Caisse, as it is called, is a relatively large player in financial markets, with 
about CAD200 billion of assets under management as of 2010. Although it has

a mandate to invest these assets for optimal return, it is also called upon to help 
promote the economic development of Québec. It should be noted that many 
governments—both at the federal and provincial/state levels—issue debt in 
foreign currencies; this, too, creates FX flows. Such supranational agencies as 
the World Bank and the African Development Bank issue debt in a variety of 
currencies as well.
■■Central banks : These entities sometimes intervene in FX markets in order to 
influence either the level or trend in the domestic exchange rate. This often 
occurs when the central banks judge their domestic currency to be too weak 
and when the exchange rate has overshot any concept of equilibrium level (e.g., 
because of a speculative attack) to the degree that the exchange rate no longer 
reflects underlying economic fundamentals. Alternatively, central banks also 
intervene when the FX market has become so erratic and dysfunctional that

end-  users such as corporations can no longer transact necessary FX business. 
Conversely, sometimes central banks intervene when they believe that their 
domestic currency has become too strong, to the point that it undercuts that 
country’s export competitiveness. The Bank of Japan intervened against yen 
strength versus the US dollar in 2004 and again in September 2010. Similarly, 
in 2010 the Swiss National Bank intervened against strength in the Swiss 
franc versus the euro by selling the Swiss franc on the euro–Swiss (CHF/EUR) 
cross-  rate. Central bank reserve managers are also frequent participants in FX 
markets in order to manage their country’s FX reserves. In this context, they act 
much like real money investment funds—although generally with a cautious, 
conservative mandate to safeguard the value of their country’s foreign exchange 
reserves. The foreign exchange reserves of some countries are enormous, and

central bank participation in FX markets can sometimes have a material impact

Reading 20 ■ Currency Exchange Rates 412
on exchange rates even when these reserve managers are not intervening for 
public policy purposes. Exhibit 2 provides information on central bank reserve 
holdings as of the second quarter of 2010.3
Exhibit 2   Currency Composition of Official Foreign Exchange Reserves, as 
of 2nd Quarter 2010 (USD billion) 
Total foreign exchange holdings globally 8,422
Held by advanced economies 2,927
Held by emerging and developing economies 5,495
Percent of global holdings held in the US dollara62%
a This percentage is calculated using that amount of global currency reserves for which the currency 
composition can be identified.
Note that the amount of foreign exchange reserves now held by emerging econo -
mies comfortably exceeds those held by developed economies. This largely reflects the 
rapid growth in foreign reserves held by Asian central banks, because these countries 
typically run large current account surpluses with the United States and other devel -

oped economies. Reserve accumulation by energy exporting countries in the Middle 
East and elsewhere is also a factor. Most of the global currency reserves are held in 
US dollars; the percentage held in USD is more than twice the portion held in the 
euro, the second most widely held currency in central bank foreign exchange reserves.
■■Sovereign wealth funds (SWFs) : Many countries with large current account sur -
pluses have diverted some of the resultant international capital flows into SWFs 
rather than into foreign exchange reserves managed by central banks. Although 
SWFs are government entities, their mandate is usually more oriented to purely 
investment purposes rather than public policy purposes. As such, SWFs can be 
thought of as akin to real money accounts, although some SWFs can employ 
derivatives or engage in aggressive trading strategies. It is generally understood 
that SWFs use their resources to help fulfill the public policy mandate of their

government owners. The SWFs of many current account surplus countries 
(such as exporting countries in East Asia or oil-  exporting countries) are enor -
mous, and their FX flows can be an important determinant of exchange rate 
movements in almost all of the major currency pairs.
As mentioned, the sell side generally consists of the FX dealing banks that sell FX 
products to the buy side. Even here, however, distinctions can be made.
■■A large and growing proportion of the daily FX turnover is accounted for by 
the very largest dealing banks, such as Deutsche Bank, Citigroup, UBS, HSBC, 
and a few other multinational banking behemoths. Maintaining a competitive 
advantage in FX requires huge fixed-  cost investments in the electronic technol -
ogy that connects the FX market, and it also requires a broad, global client base. 
As a result, only the largest banks are able to compete successfully in providing 
competitive price quotes to clients across the broad range of FX products. In

fact, among the largest FX dealing banks, a large proportion of their business 
3 See International Monetary Fund (2010).

The Foreign Exchange Market 413
is crossed internally, meaning that these banks are able to connect buyers and 
sellers within their own extremely diverse client base and have no need to show 
these FX flows outside of the bank.
■■All other banks fall into the second and third tier of the FX market sell side. 
Many of these financial institutions are regional or local banks with well-  
developed business relationships, but they lack the economies of scale, broad 
global client base, or information technology (IT) expertise required to offer 
competitive pricing across a wide range of currencies and FX products. In many 
cases, these are banks in emerging markets that don’t have the business connec -
tions or credit lines required to access the FX market on a cost-  effective basis 
on their own. As a result, these banks often outsource FX services by forming 
business relationships with the larger tier-  one banks; otherwise, they depend on

the deep, competitive liquidity provided by the largest FX market participants.
The categories presented are based on functions that are closely associated with 
the named groups. However, in some cases, functions typifying a group may also be 
assumed by or shared with another group. For example, sell-  side banks provide FX 
price quotes. However, hedge funds and other large players may access the professional 
FX market on equal terms with the dealing banks and effectively act as market makers.
One of the most important ideas to draw from this categorization of market 
participants is that there is an extremely wide variety of FX market participants, 
reflecting a complex mix of trading motives and strategies that can vary with time. 
Most market participants reflect a combination of hedging and speculative motives 
in tailoring their FX risk exposures. Among public sector market participants, public 
policy motives may also be a factor. The dynamic, complex interaction of FX mar -

ket participants and their trading objectives makes it difficult to analyze or predict 
movements in FX rates with any precision, or to describe the FX market adequately 
with simple characterizations.
2.3 Market Size and Composition
In this section, we present a descriptive overview of the global FX market drawn from 
the 2010 Triennial Survey undertaken by the Bank for International Settlements (2010). 
The BIS is an umbrella organization for the world’s central banks. Every three years, 
participating central banks undertake a survey of the FX market in their jurisdictions, 
the results of which are aggregated and compiled at the BIS. The most recent survey, 
taken in April 2010, gives a broad indication of the current size and distribution of 
global FX market flows.
As of April 2010, the BIS estimates that average daily turnover in the traditional 
FX market (comprised of spot, outright forward, and FX swap transactions) totaled

approximately USD3.9 trillion. Exhibit 3 shows the approximate percentage allocation 
among FX product types, including both traditional FX products and exchange-  traded 
FX derivatives. Note that this table of percentage allocations adds exchange-  traded 
derivatives to the BIS estimate of average daily turnover of USD3.9 trillion; the “Spot” 
and “OTC forwards” categories include only transactions that are not executed as 
part of a swap transaction.
Exhibit 3   FX Turnover by Instrument
Spot 36%
OTC forwards 12
Exchange-  traded derivatives 4
Swapsa44

Reading 20 ■ Currency Exchange Rates 414
OTC optionsb4
Total 100%
a Includes both FX and currency swaps.
b Includes what the BIS categorizes as “other FX products. ”
The survey also provides a percentage breakdown of the average daily flows between 
sell-  side banks (called the interbank market), between banks and financial customers 
(all non-  bank financial entities, such as real money and leveraged accounts, SWFs, 
and central banks), and between banks and non-  financial customers (such as corpo -
rations, retail accounts, and governments). The breakdown is provided in Exhibit 4. 
It bears noting that the proportion of average daily FX flow accounted for by financial 
clients is much larger than that for non-  financial clients. The BIS also reports that 
the proportion of financial client flows has been growing rapidly, and as of 2010, it 
exceeded interbank trading volume for the first time. This underscores the fact that

only a minority of the daily FX flow is accounted for by corporations and individuals 
buying and selling foreign goods and services. Huge investment pools and professional 
traders are accounting for a large and growing proportion of the FX business.
Exhibit 4   FX Flows by Counterparty
Interbank 39%
Financial clients 48
Non-  financial clients 13
The 2010 BIS survey also identifies the top five currency pairs in terms of their 
percentage share of average daily global FX turnover. These are shown in Exhibit 5. 
Note that each of these most active pairs includes the US dollar (USD).
Exhibit 5   FX Turnover by Currency Pair
USD/EUR 28%
JPY/USD 14
USD/GBP 9
USD/AUD 6
CAD/USD 5
The largest proportion of global FX trading occurs in London, followed by New 
York. This means that FX markets are most active between approximately 8:00 a.m.  and 
11:30 a.m.  New York time, when banks in both cities are open. (The official London

close is at 11:00 a.m.  New York time, but London markets remain relatively active for 
a period after that.) Tokyo is the third-  largest FX trading hub.Exhibit 3   (Continued)

The Foreign Exchange Market 415
EXAMPLE 3   
Market Participants and Composition of Trades
The investment adviser based in Sydney, Australia, makes the following state -
ments to her client when describing some of the basic characteristics of the 
foreign exchange market:
Statement 1  “Foreign exchange transactions for spot settlement see 
the most trade volume in terms of average daily turnover 
because the FX market is primarily focused on settling 
international trade flows. ”
Statement 2  “The most important foreign exchange market participants 
on the buy side are corporations engaged in international 
trade; on the sell side they are the local banks that service 
their FX needs. ”
A correct.
B incorrect with respect to the importance of spot settlements.
C incorrect both with respect to the importance of spot settlements and 
international trade flows.
A correct.
B incorrect with respect to corporations engaged in international trade.

C incorrect with respect to both corporations and the local banks that 
service their trade needs.
C is correct. Although the media generally focus on the spot market when dis -
cussing foreign exchange, the majority of average daily trade volume involves the 
FX swap market as market participants either roll over or modify their existing 
hedging and speculative positions (or engage in FX swap financing). Although 
it is true that all international trade transactions eventually result in some form 
of spot settlement, this typically generates a great deal of hedging (and specula -
tive) activity in advance of spot settlement. Moreover, an important group of FX 
market participants engages in purely speculative positioning with no intention 
of ever delivering/receiving the principal amount of the trades. Most FX trading 
volume is not related to international trade: Portfolio flows (cross-  border capital 
movements) and speculative activities dominate.

C is correct. As of 2010, the most important foreign exchange market participants 
in terms of average daily turnover are found not among corporations engaged 
in international trade but among huge investment managers, both private (e.g., 
pension funds) and public (e.g., central bank reserve managers or sovereign wealth 
funds). A large and growing amount of daily turnover is also being generated by 
high-  frequency traders who use computer algorithms to automatically execute 
extremely high numbers of speculative trades (although their individual ticket 
sizes are generally small, they add up to large aggregate flows). On the sell side, 
the largest money center banks (e.g., Deutsche Bank, Citigroup, HSBC, UBS) are

Reading 20 ■ Currency Exchange Rates 416
increasingly dominating the amount of trading activity routed through dealers. 
Regional and local banks are increasingly being marginalized in terms of their 
share of average daily turnover in FX markets.
CURRENCY EXCHANGE RATE CALCULATIONS
3.1 Exchange Rate Quotations
Exchange rates represent the relative price of one currency in terms of another. This 
price can be represented in two ways: 1) currency A buys how many units of currency 
B; or 2) currency B buys how many units of currency A. Of course, these two prices 
are simply the inverse of each other.
To distinguish between these two prices, market participants sometimes distinguish 
between direct  and indirect  exchange rates. In the quoting convention A/B (where 
there is a certain number of units of currency A per one unit of currency B), we refer 
to currency A as the price currency  (or quote currency); currency B is referred to as

the base currency . (The reason for this choice of names will become clearer below.) 
The base currency is always set at a quantity of one. A direct  currency quote takes the 
domestic country as the price currency and the foreign country as the base currency. 
For example, for a Paris-  based trader, the domestic currency would be the euro (EUR) 
and a foreign currency would be the UK pound (GBP). For this Paris-  based trader, a 
direct  quote would be EUR/GBP . An exchange rate quote of EUR/GBP = 1.2225 means 
that 1 GBP costs 1.2225 EUR. For this Paris-  based trader, an indirect  quote has the 
domestic currency—the euro—as the base currency. An indirect quote of GBP/EUR 
= 0.8180 means that 1 EUR costs 0.8180 GBP . Direct and indirect quotes are just the 
inverse (reciprocal) of each other.
It can be confusing to describe exchange rates as either being direct or indirect 
because determining the domestic currency and the foreign currency depends on

where one is located. For a London-  based market participant, the UK pound (GBP) 
is the domestic currency and the euro (EUR) is a foreign currency. For a Paris-  based 
market participant, it would be the other way around.
To avoid confusion, the professional FX market has developed a set of market 
conventions that all market participants typically adhere to when making and asking 
for FX quotes. Exhibit 6 displays some of these for the major currencies: the currency 
code used for obtaining exchange rate quotes, how the market lingo refers to this 
currency pair, and the actual ratio—price currency per unit of base currency—rep -
resented by the quote.
Exhibit 6   Exchange Rate Quote Conventions
FX Rate Quote 
Convention Name ConventionActual Ratio  
(Price currency/Base currency)
EUR Euro USD/EUR
JPY Dollar–yen JPY/USD
GBP Sterling USD/GBP
CAD Dollar–Canada CAD/USD
AUD Aussie USD/AUD
NZD Kiwi USD/NZD
CHF Swiss franc CHF/USD3

Currency Exchange Rate Calculations 417
EURJPY Euro–yen JPY/EUR
EURGBP Euro–sterling GBP/EUR
EURCHF Euro–Swiss CHF/EUR
GBPJPY Sterling–yen JPY/GBP
EURCAD Euro–Canada CAD/EUR
CADJPY Canada–yen JPY/CAD
Several things should be noted in this exhibit. First, the three-  letter currency 
codes in the first column (for FX rate quotes) refer to what are considered the major 
exchange rates. Remember that an exchange rate is the price of one currency in terms 
of another: There are always two currencies involved in the price. This is different 
from referring to a single currency in its own right. For example, one can refer to the 
euro (EUR) as a currency ; but if we refer to a euro exchange rate  (EUR), it is always 
the price of the euro in terms of another currency, in this case the US dollar. This is 
because in the professional FX market, the three-  letter code EUR is always taken to

refer to the euro–US dollar exchange rate, which is quoted in terms of the number of 
US dollars per euro (USD/EUR). Second, where there are six-  letter currency codes 
in the first column, these refer to some of the major cross-  rates . This topic will be 
covered in the next section, but generally these are secondary exchange rates and 
they are not as common as the main exchange rates. (It can be noted that three-  letter 
codes are always in terms of an exchange rate involving the US dollar, while the six-  
letter codes are not.) Third, when both currencies are mentioned in the code or the 
name convention, the base currency is always mentioned first, the opposite order of 
the actual ratio (price currency/base currency).  Thus, the code for “Sterling–yen” is 
“GBPJPY, ” but the actual number quoted is the number of yen per sterling (JPY/GBP). 
It should also be noted that the codes may appear in a variety of formats that all mean

the same thing.  For example, GBPJPY might instead appear as GBP:JPY or GBP–JPY. 
Fourth, regardless of where a market participant is located, there is always a mix of 
direct and indirect quotes in common market usage. For example, a trader based in 
Toronto will typically refer to the euro–Canada and Canada–yen exchange rates—a 
mixture of direct (CAD/EUR) and indirect (JPY/CAD) quotes for a Canadian-  based 
trader. There is no overall consistency in this mixture of direct and indirect quoting 
conventions in the professional FX market; a market participant just has to get familiar 
with how the conventions are used.4
Another concept involving exchange rate quotes in professional FX markets is that 
of a two-  sided price . When a client asks a bank for an exchange rate quote, the bank 
will provide a “ bid” (the price at which the bank is willing to buy the currency) and 
an “offer ” (the price at which the bank is willing to sell the currency). But there are

two currencies involved in an exchange rate quote, which is always the price of one 
currency relative to the other. So, which one is being bought and sold in this two-  sided 
price quote? This is where the lingo involving the price currency (or quote currency) Exhibit 6   (Continued)
4 In general, however, there is a hierarchy for quoting conventions. For quotes involving the EUR, it serves 
as the base currency (e.g., GBP/EUR). Next in the priority sequence, for quotes involving the GBP (but not 
the EUR) it serves as the base currency (e.g., USD/GBP). Finally, for quotes involving the USD (but not the 
GBP or EUR) it serves as the base currency (e.g., CAD/USD). Exceptions among the major currencies are the 
AUD and NZD: they serve as the base currency when quoted against the USD (i.e., USD/AUD, USD/NZD).

Reading 20 ■ Currency Exchange Rates 418
and the base currency, explained above, becomes useful. The two-  sided price quoted by 
the dealer is in terms of buying/selling the base currency . It shows the number of units 
of the price  currency that the client will receive from the dealer for one unit of the 
base currency (the bid) and the number of units of the price currency that the client 
must sell to the dealer to obtain one unit of the base currency (the offer). Consider 
the case of a client that is interested in a transaction involving the Swiss franc (CHF) 
and the euro (EUR). As we have seen above, the market convention is to quote this 
as euro–Swiss (CHF/EUR). The EUR is the base currency, and the two-  sided quote 
(price) shows the number of units of the price currency (CHF) that must be paid 
or will be received for 1 euro. For example, a two-  sided price in euro–Swiss (CHF/
EUR) might look like: 1.3405–1.3407. The client will receive CHF1.3405 for selling

EUR1 to the dealer and must pay CHF1.3407 to the dealer to buy EUR1. Note that 
the price is shown in terms of the price currency  and that the bid is always less than 
the offer : The bank buys the base currency (EUR, in this case) at the low price and 
sells the base currency at the high price. Buying low and selling high is profitable for 
banks, and spreading clients—trying to widen the bid/offer spread—is how dealers 
try to increase their profit margins. However, it should be noted that the electronic 
dealing systems currently used in professional FX markets are extremely efficient in 
connecting buyers and sellers globally. Moreover, this worldwide competition for 
business has compressed most bid/offer spreads to very tight levels. For simplicity, 
in the remainder of this reading we will focus on exchange rates as a single number 
(with no bid/offer spread).
One last thing that can be pointed out in exchange rate quoting conventions is

that most major spot exchange rates are typically quoted to four decimal places. One 
exception among the major currencies involves the yen, for which spot exchange rates 
are usually quoted to two decimal places. (For example, using spot exchange rates from 
the middle of 2010, a USD/EUR quote would be expressed as 1.2875, while a JPY/
EUR quote would be expressed as 110.25.) This difference involving the yen comes 
from the fact that the units of yen per unit of other currencies is typically relatively 
large already, and hence extending the exchange rate quote to four decimal places is 
viewed as unnecessary.
Regardless of what quoting convention is used, changes in an exchange rate can 
be expressed as a percentage appreciation of one currency against the other: One 
simply has to be careful in identifying which currency is the price currency and which 
is the base currency. For example, let’s suppose the exchange rate for the euro (USD/

EUR) increases from 1.2500 to 1.3000. This represents an (un-  annualized) percentage 
change of:
1 3000
1 250014 00.
..% −=
This represents a 4 percent appreciation in the euro against the US dollar (and not an 
appreciation of the US dollar against the euro) because the USD/EUR exchange rate 
is expressed with the dollar as the price currency.
Note that this appreciation of the euro against the US dollar can also be expressed 
as a depreciation of the US dollar against the euro; but in this case, the depreciation is 
not equal to 4.0 percent. Inverting the exchange rate quote from USD/EUR to EUR/
USD, so that the euro is now the price currency, leads to:
1
1 3000
1
1 250011 2500
1 300013 85.
..
..%




−= −= −
Note that the US dollar depreciation is not the same, in percentage terms, as the euro 
appreciation. This will always be true; it is simply a matter of arithmetic.

Currency Exchange Rate Calculations 419
EXAMPLE 4   
Exchange Rate Conventions
A dealer based in New York City provides a spot exchange rate quote of 12.4035 
MXN/USD to a client in Mexico City. The inverse of 12.4035 is 0.0806.
1 From the perspective of the Mexican client, the most  accurate statement is 
that the:
A direct exchange rate quotation is equal to 0.0806.
B direct exchange rate quotation is equal to 12.4035.
C indirect exchange rate quotation is equal to 12.4035.
2 If the bid/offer quote from the dealer was 12.4020 ~ 12.4060 MXN/USD, 
then the bid/offer quote in USD/MXN terms would be closest  to:
A 0.08061 ~ 0.08063.
B 0.08063 ~ 0.08061.
C 0.08062 ~ 0.08062.
B is correct. A direct exchange rate uses the domestic currency as the price cur -
rency and the foreign currency as the base currency. For an MXN/USD quote, 
the MXN is the price currency; therefore, the direct quote for the Mexican 
client is 12.4035 (it costs 12.4035 pesos to purchase 1 US dollar). Another way

of understanding a direct  exchange rate quote is that it is the price of one unit 
of foreign currency in terms of your own currency. This purchase of a unit of 
foreign currency can be thought of as a purchase much like any other you might 
make; think of the unit of foreign currency as just another item that you might 
be purchasing with your domestic currency. For example, for someone based 
in Canada, a liter of milk currently costs about CAD1.25 and USD1 costs about 
CAD1.03. This direct  currency quote uses the domestic  currency (the Canadian 
dollar, in this case) as the price  currency and simply gives the price of a unit of 
foreign currency that is being purchased.
A is correct. An MXN/USD quote means the amount of MXN the dealer is bid -
ding (offering) to buy (sell) USD1. The dealer’s bid to buy USD1 at MXN12.4020 
is equivalent to the dealer paying MXN12.4020 to buy USD1. Dividing both terms

by 12.4020 means the dealer is paying (i.e., selling) MXN1 to buy USD0.08063. 
This is the offer in USD/MXN terms: The dealer offers to sell MXN1 at a price 
of USD0.08063. In USD/MXN terms, the dealer’s bid for MXN1 is 0.08061, 
calculated by inverting the offer of 12.4060 in MXN/USD terms (1/12.4060 = 
0.08061). Note that in any bid/offer quote, no matter what the base or price 
currencies, the bid is always lower than the offer.
3.2 Cross-  Rate Calculations
Given two exchange rates involving three currencies, it is possible to back out what 
the cross-  rate must be. For example, as we have seen, the FX market convention is 
to quote the exchange rate between the US dollar and the euro as euro–dollar (USD/
EUR). The FX market also quotes the exchange rate between the Canadian dollar

Reading 20 ■ Currency Exchange Rates 420
and US dollar as dollar–Canada (CAD/USD). Given these two exchange rates, it is 
possible to back out the cross-  rate between the euro and the Canadian dollar, which 
according to market convention is quoted as euro–Canada (CAD/EUR). This calcu -
lation is shown as:
CAD
USDUSD
EURCAD
USDUSD
EURCAD
EUR×= ×=
Hence, to get a euro–Canada (CAD/EUR) quote, we must multiply the dollar–
Canada (CAD/USD) quote by the euro–dollar (USD/EUR) quote. For example, assume 
the exchange rate for dollar–Canada is 1.0460 and the exchange rate for euro–dollar 
is 1.2880. Using these sample spot exchange rates, calculating the euro–Canada 
cross-  rate equals:
1.0460 × 1.2880 = 1.3472 CAD per EUR
It is best to avoid talking in terms of direct or indirect quotes because, as noted 
above, these conventions depend on where one is located and hence what the domes -
tic and foreign currencies are. Instead, focus on how the math works: Sometimes it

is necessary to invert one of the quotes in order to get the intermediary currency to 
cancel out in the equation to get the cross-  rate. For example, to get a Canada–yen 
(JPY/CAD) quote, one is typically using the dollar–Canada (CAD/USD) rate and 
dollar–yen (JPY/USD) rate, which are the market conventions. This Canada–yen 
calculation requires that the dollar–Canada rate (CAD/USD) be inverted to a USD/
CAD quote for the calculations to work, as shown below:
CAD
USDJPY
USDUSD
CADJPY
USDUSD
CADJPY
USDJPY
CAD

×=×= ×=−1
Hence, to get a Canada–yen (JPY/CAD) quote, we must first invert the dollar–
Canada (CAD/USD) quote before multiplying by the dollar–yen (JPY/USD) quote. 
As an example, let’s assume that we have spot exchange rates of 1.0460 for dollar–
Canada (CAD/USD) and 85.50 for dollar–yen (JPY/USD). The dollar–Canada rate of 
1.0460 inverts to 0.9560; multiplying this value by the dollar–yen quote of 85.50 gives 
a Canada–yen quote of:
0.9560 × 85.50 = 81.74 JPY per CAD

Market participants asking for a quote in a cross-  rate currency pair typically will 
not have to do this calculation themselves: Either the dealer or the electronic trading 
platform will provide a quote in the specified currency pair. (For example, a client 
asking for a quote in Canada–yen will receive that quote from the dealer; he will not be 
given separate dollar–Canada and dollar–yen quotes in order to do the math.) But be 
aware that dealers providing the quotes often have to do this calculation themselves if 
only because the dollar–Canada and dollar–yen currency pairs often trade on different 
trading desks and involve different traders. Electronic dealing machines used in both 
the interbank market and bank-  to- client markets often provide this mathematical 
operation to calculate cross-  rates automatically.
Because market participants can receive both a cross-  rate quote (for example,

Canada–yen) as well as the component underlying exchange rate quotes (for exam -
ple, dollar–Canada and dollar–yen), these cross-  rate quotes must be consistent with 
the above equation; otherwise, the market will arbitrage the mispricing. Extending 
our example above, we calculate a Canada–yen (JPY/CAD) rate of 81.74 based on 
underlying dollar–Canada (CAD/USD) and dollar–yen (JPY/USD) rates of 1.0460 and 
85.50, respectively. Now suppose that at the same time a misguided dealer quotes a 
Canada–yen rate of 82.00. This is a different price in JPY/CAD for an identical service: 
converting yen into Canadian dollars. Hence, any trader could buy CAD1 at the lower 
price of JPY81.74 and then turn around and sell CAD1 at JPY82.00 (recall our earlier

Currency Exchange Rate Calculations 421
discussion of how price and base currencies are defined). The riskless arbitrage profit 
is JPY0.26 per CAD1. The arbitrage—called triangular arbitrage , “tri-, ” because it 
involves three currencies—would continue until the price discrepancy was removed.
In reality, however, these discrepancies in cross-  rates almost never occur because 
both human traders and automatic trading algorithms are constantly on alert for 
any pricing inefficiencies. In practice, and for the purposes of this reading, we can 
consider cross-  rates as being consistent with their underlying exchange rate quotes 
and that given any two exchange rates involving three currencies, we can back out 
the third cross-  rate.
EXAMPLE 5   
Cross Exchange Rates and Percentage Changes
A research report produced by a dealer includes the following exhibit:
Spot Rate Expected Spot  
Rate in One Y ear
USD/EUR 1.3960 1.3863
CHF/USD 0.9585 0.9551
USD/GBP 1.5850 1.5794

1 The spot CHF/EUR cross-  rate is closest  to:
A 0.6866.
B 0.7473.
C 1.3381.
2 The spot GBP/EUR cross-  rate is closest  to:
A 0.8808.
B 1.1354.
C 2.2127.
3 Based on the exhibit, the euro is expected to appreciate by how much 
against the US dollar over the next year?
A –0.7 percent
B +0.7 percent
C +1.0 percent
4 Based on the exhibit, the US dollar is expected to appreciate by how much 
against the British pound over the next year?
A +0.6 percent
B –0.4 percent
C +0.4 percent
5 Over the next year, the Swiss franc is expected to:
A depreciate against the GBP .
B depreciate against the EUR.
C appreciate against the GBP , EUR, and USD.
6 Based on the exhibit, which of the following lists the three currencies 
from strongest to weakest over the next year?
A USD, GBP , EUR
B USD, EUR, GBP

Reading 20 ■ Currency Exchange Rates 422
C EUR, USD, GBP
7 Based on the exhibit, which of the following lists the three currencies in 
order of appreciating the most to appreciating the least (in percentage 
terms) against the USD over the next year?
A GBP , CHF, EUR
B CHF, GBP , EUR
C EUR, CHF, GBP
C is correct:
CHF
EURUSD
EURCHF
USD=×= ×= 1 3960 0 9585 1 3381.. .
A is correct:
GBP
EURUSD
EURUSD
GBPUSD
EURGBP
USD=×

 =×= =−11 3960
1 58500.
..8 8808
A is correct. The euro is the base currency in the USD/EUR quote, and the 
expected decrease in the USD/EUR rate indicates that the EUR is depreciating 
(in one year it will cost less USD to buy one EUR). Mathematically:
1 3863
1 396010 7.
..% −= −
C is correct. The GBP is the base currency in the USD/GBP quote, and the 
expected decrease in the USD/GBP rate means that the GBP is expected to 
depreciate against the USD. Or equivalently, the USD is expected to appreciate 
against the GBP . Mathematically:
1 5794

1 5794
1 585011 5850
1 579410 41.
..
..%

−= −= +−
C is correct: Because the question does not require calculating the magnitude 
of the appreciation or depreciation, we can work with CHF as either the price 
currency or the base currency. In this case, it is easiest to use it as the price 
currency. According to the table, CHF/USD is expected to decline from 0.9585 
to 0.9551, so CHF is expected to be stronger (i.e., it should appreciate against 
the USD). CHF/EUR is currently 1.3381 (see the solution to problem 1) and 
is expected to be 1.3241 (= 0.9551 × 1.3863), so CHF is expected to appreci -
ate against the EUR. CHF/GBP is currently 1.5192 (= 0.9585 × 1.5850) and is 
expected to be 1.5085 (= 0.9551 × 1.5794), so CHF is also expected to appreciate 
against the GBP .
Alternatively, we can derive this answer intuitively. The table shows that the 
CHF/USD rate is expected to decline: That is, the USD is expected to depreci -

ate against the CHF, or alternatively, the CHF is expected to appreciate against 
the USD. The table also shows that the USD/EUR and USD/GBP rates are also 
decreasing, meaning that the EUR and GBP are expected to depreciate against 
the USD, or alternatively, the USD is expected to appreciate against the EUR

Currency Exchange Rate Calculations 423
and GBP . If the CHF is expected to appreciate against the USD and the USD is 
expected to appreciate against both the EUR and GBP , it follows that the CHF 
is expected to appreciate against both the EUR and GBP .
A is correct. According to the table, USD/EUR is expected to decline from 1.3960 
to 1.3863, while USD/GBP is expected to decline from 1.5850 to 1.5794. So, the 
USD is expected to be stronger than both the EUR and GBP . GBP/EUR is cur -
rently 0.8808 [= (1.5850)–1 × 1.3960] and is expected to be 0.8777 [= (1.5794)–1 
× 1.3863], so the GBP is expected to be stronger than the EUR. 
B is correct. The USD/EUR rate depreciates by –0.7 percent (= [1.3863/1.3960] 
– 1), which is the depreciation of the base currency EUR against the USD. 
The USD/GBP rate declines –0.4 percent (= [1.5794/1.5850] – 1), which is the 
depreciation of the GBP against the USD. Inverting the CHF/USD rate to a USD/

CHF convention shows that the base currency CHF appreciates by +0.4 percent 
against the USD (= [1.0470/1.0433] – 1).
3.3 Forward Calculations
In professional FX markets, forward exchange rates are typically quoted in terms of 
points (also sometimes referred to as “pips”). The points on a forward rate quote are 
simply the difference between the forward exchange rate quote and the spot exchange 
rate quote, with the points scaled so that they can be related to the last decimal in the 
spot quote. When the forward rate is higher than the spot rate, the points are positive 
and the base currency is said to be trading at a forward premium . Conversely, if the 
forward rate is less than the spot rate, the points (forward rate minus spot rate) are 
negative and the base currency is said to be trading at a forward discount . Of course, if 
the base currency is trading at a forward premium, then the price currency is trading 
at a forward discount, and vice versa.

This can best be explained by means of an example. At one point during 2010, the 
spot euro–dollar exchange rate (USD/EUR) was 1.2875 and the one-  year forward rate 
was 1.28485. Hence, the forward rate was trading at a discount to the spot rate (the 
forward rate was smaller than the spot rate) and the one-  year forward points were 
quoted as –26.5. This –26.5 comes from:
1.28485 – 1.2875 = –0.00265
Recall that most non-  yen exchange rates are quoted to four decimal places, so in 
this case we would scale up by four decimal places (multiply by 10,000) so that this 
–0.00265 would be represented as –26.5 points. Notice that the points are scaled to 
the size of the last digit in the spot exchange rate quote—usually the fourth decimal 
place. Notice as well that points are typically quoted to one (or more) decimal places, 
meaning that the forward rate will typically be quoted to five or more decimal places.

The exception among the major currencies is the yen, which is typically quoted to 
two decimal places for spot rates. Here, forward points are scaled up by two decimal 
places—the last digit in the spot rate quote—by multiplying the difference between 
forward and spot rates by 100.

Reading 20 ■ Currency Exchange Rates 424
Typically, quotes for forward rates are shown as the number of forward points 
at each maturity.5 These forward points are also called swap points  because an FX 
swap consists of simultaneous spot and forward transactions. In the middle of 2010, 
a trader would have faced a spot rate and forward points in the euro–dollar (USD/
EUR) currency pair similar to those in Exhibit 7:
Exhibit 7   Sample Spot and Forward Quotes
Maturity Spot Rate or Forward Points
Spot 1.2875
One week –0.3
One month –1.1
Three months –5.5
Six months –13.3
Twelve months –26.5
Notice that the absolute number of points generally increases with maturity. This 
is because the number of points is proportional to the yield differential between the 
two countries (the Eurozone and the United States, in this case) scaled by the term 
to maturity. Given the interest rate differential, the longer the term to maturity, the

greater the absolute number of forward points. Similarly, given the term to maturity, 
a wider interest rate differential implies a greater absolute number of forward points. 
(This will be explained and demonstrated in more detail later in this section.)
To convert any of these quoted forward points into a forward rate, one would 
divide the number of points by 10,000 (to scale down to the fourth decimal place, 
the last decimal place in the spot quote) and then add the result to the spot exchange 
rate quote.6 For example, using the data in Exhibit 7, the three-  month forward rate 
in this case would be:
1 287555
10 0001 2875 0 00055 1 28695 ..
,.. . +−

=− =
Occasionally, one will see the forward rate or forward points represented as a per -
centage of the spot rate rather than as an absolute number of points. Continuing our 
example from above, the three-  month forward rate for USD/EUR can be represented as:
1 28750 0 00055
1 2875011 28695
1 2875010 043..
..
..%−−=

−= −

..
..%−−=

−= −
This shows that either the forward rate or the forward points can be used to 
calculate the percentage discount (or premium) in the forward market—in this case, 
–0.043  percent rounding to three decimal places. To convert a spot quote into a 
forward quote when the points are shown as a percentage, one simply multiples the 
spot rate by one plus the percentage premium or discount:
1.28750 × (1 – 0.043%) = 1.28750 × (1.0000 – 0.00043) ≈ 1.28695
5 As mentioned earlier, “maturity” is defined in terms of the time between spot settlement (usually T + 
2) and the settlement of the forward contract.
6 Because the JPY/USD exchange rate is only quoted to two decimal places, forward points for the dol -
lar–yen currency pair are divided by 100.

Currency Exchange Rate Calculations 425
Note that, rounded to the fifth decimal place, this is equal to our previous calcu -
lation. However, it is typically the case in professional FX markets that forward rates 
will be quoted in terms of pips rather than percentages.
We now turn to the relationship between spot rates, forward rates, and interest 
rates and how their relationship is derived. Forward exchange rates are based on 
an arbitrage relationship that equates the investment return on two alternative but 
equivalent investments. Consider the case of an investor with funds to invest. For 
simplicity, we will assume that there is one unit of the investor’s domestic currency to 
be invested for one period. One alternative is to invest for one period at the domestic 
risk-  free rate ( id); at the end of the period, the amount of funds held is equal to (1 
+ id). An alternative investment is to convert this one unit of domestic currency to

foreign currency using the spot rate of Sf/d (number of units of foreign currency per 
one unit of domestic currency). This can be invested for one period at the foreign 
risk-  free rate; at the end of the period, the investor would have Sf/d(1 + if) units of 
foreign currency. These funds must then be converted back to the investor’s domestic 
currency. If the exchange rate to be used for this end-  of- period conversion was pre-  
contracted at the start of the period (i.e., a forward rate was used), it would eliminate 
any foreign exchange risk from converting at a future, unknown spot rate. Given the 
assumed exchange rate convention here (foreign/domestic), the investor would obtain 
(1/Ff/d) units of the domestic currency for each unit of foreign currency sold forward. 
Note that this process of converting domestic funds in the spot FX market, investing 
at the foreign risk-  free rate, and then converting back to the domestic currency with

a forward rate is identical to the concept of swap financing described in an earlier 
section of this reading.
Hence, we have two alternative investments—both risk-  free because both are 
invested at risk-  free interest rates and because any foreign exchange risk was eliminated 
(hedged) by using a forward rate. Because these two investments are equal in risk 
characteristics, they must have the same return. Bearing in mind that the currency 
quoting convention is the number of foreign currency units per single domestic unit 
(f/d), this relationship can be stated as:
111+() =+ ()

iS iFdf df
fd
This is an arbitrage relationship because it describes two alternative investments 
(one on either side of the equal sign) that should have equal returns. If they do not, a 
riskless arbitrage opportunity exists because an investor can sell short the investment 
with the lower return and invest the funds in the investment with the higher return;

the difference between the two returns is pure profit.7
This formula is perhaps the easiest and most intuitive way to remember the for -
mula for the forward rate because it is based directly on the underlying intuition (the 
arbitrage relationship of two alternative but equivalent investments, one on either side 
of the equal sign). Also, the right-  hand side of the equation, for the hedged foreign 
investment alternative, is arranged in proper time sequence: a) convert domestic to 
foreign currency; then b) invest the foreign currency at the foreign interest rate; and 
finally c) convert the foreign currency back to the domestic currency.8
7 It is because of this arbitrage relationship that the all-  in financing rate using swap financing is close to 
the domestic interest rate.
8 Recall that this equation is based on an f/d exchange rate quoting convention. If the exchange rate data 
were presented in d/f form, one could either invert these quotes back to f/d form and use the above equa -

tion or use the following equivalent equation: (1 + id) = (1/ Sd/f)(1 + if)Fd/f. If this latter equation were used, 
remember that forward and spot exchange rates are now being quoted on a d/f convention.

Reading 20 ■ Currency Exchange Rates 426
This arbitrage equation can be re-  arranged as needs require. For example, to get 
the formula for the forward rate, the above equation can be restated as:
FSi
ifd fdf
d//=+
+

1
1
Another way of looking at this is, given the spot exchange rate and the domestic and 
foreign risk-  free interest rates, the forward rate is whatever value completes this equa -
tion and eliminates any arbitrage opportunity. For example, let’s assume that the spot 
exchange rate ( Sf/d) is 1.6535, the domestic 12-  month risk-  free rate is 3.50 percent, 
and the foreign 12-  month risk-  free rate is 5.00 percent. The 12-  month forward rate 
(Ff/d) must then be equal to:
1 65351 0500
1 03501 6775 ..
..

=
Suppose instead that, with the spot exchange rate and interest rates unchanged, 
you were given a quote on the 12-  month forward rate ( Ff/d) of 1.6900. Because this 
misquoted forward rate does not agree with the arbitrage equation, it would present

a riskless arbitrage opportunity. This can be seen by using the arbitrage equation to 
compute the return on the two alternative investment strategies. The return on the 
domestic-  only investment approach is the domestic risk-  free rate (3.50 percent). In 
contrast, the return on the hedged foreign investment when this misquoted forward 
rate is put into the arbitrage equation equals:
SiFfd f
fd111 6535 1051
1 69001 0273 +()

= ()

= ....
This defines a return of 2.73 percent. Hence, the investor could make riskless arbitrage 
profits by borrowing at the higher foreign risk-  free rate, selling the foreign currency at 
the spot exchange rate, hedging the currency exposure (buying the foreign currency 
back) at the misquoted forward rate, investing the funds at the lower domestic risk-  
free rate, and thereby getting a profit of 77 basis points (3.50% – 2.73%) for each unit 
of domestic currency involved—all with no upfront commitment of the investor’s own

capital. Any such opportunity in real-  world financial markets would be quickly “arbed” 
away. It is interesting to note that in this example, the investor actually borrows at 
the higher of the two interest rates but makes a profit because the foreign currency 
is underpriced in the forward market.
The underlying arbitrage equation can also be re-  arranged to show the forward 
rate as a percentage of the spot rate:
F
Si
ifd
fdf
d=+
+

1
1
This shows that, given an f/d quoting convention, the forward rate will be higher than 
(be at a premium to) the spot rate if foreign interest rates are higher than domestic 
interest rates. More generally, and regardless of the quoting convention, the currency 
with the higher (lower) interest rate will always trade at a discount (premium) in the 
forward market .
One context in which forward rates are quoted as a percentage of spot rates occurs 
when forward rates are interpreted as expected future spot rates, or:
FSt t= +1

Currency Exchange Rate Calculations 427
Substituting this expression into the previous equation and doing some re-  arranging 
leads to:
SSSii
it
ttfd
d ++ −= ∆=−
+

11 11%
This shows that if forward rates are interpreted as expected future spot rates, the 
expected percentage change in the spot rate is proportional to the interest rate dif -
ferential ( if – id).
It is intuitively appealing to see forward rates as expected future spot rates. 
However, this interpretation of forward rates should be used cautiously. First, the 
direction of the expected change in spot rates is somewhat counter-  intuitive. All else 
being equal, an increase in domestic interest rates (for example, the central bank 
tightens monetary policy) would typically be expected to lead to an increase in the 
value of the domestic currency. In contrast, the equation above indicates that, all else 
equal, a higher domestic interest rate implies slower expected appreciation (or greater

expected depreciation) of the domestic currency (recall that this equation is based 
on an f/d quoting convention).
More important, historical data show that forward rates are poor predictors of 
future spot rates. Although various econometric studies suggest that forward rates 
may be unbiased predictors of future spot rates (i.e., they do not systematically 
over- or under-  estimate future spot rates), this is not particularly useful information 
because the margin of error for these forecasts is so large. As we have seen in our 
introductory section, the FX market is far too complex and dynamic to be captured 
by a single variable, such as the level of the yield differential between countries. 
Moreover, as can be seen in the formula above for the forward rate, forward rates are 
based on domestic and foreign interest rates. This means that anything that affects the 
level and shape of the yield curve in either the domestic or foreign market will also

affect the relationship between spot and forward exchange rates. In other words, FX 
markets do not operate in isolation but will reflect almost all factors affecting other 
markets globally; anything that affects expectations or risk premia in these other 
markets will reverberate in forward exchange rates as well. Although the level of the 
yield differential is one factor that the market may look at in forming spot exchange 
rate expectations, it is only one of many factors. (Many traders look to the trend in 
the yield differential rather than the level of the differential.) Moreover, there is a lot 
of noise in FX markets that makes almost any model—no matter how complex—a 
relatively poor predictor of spot rates at any given point in the future. In practice, 
FX traders and market strategists do not base either their currency expectations or 
trading strategies solely on forward rates.
For the purposes of this reading, it is best to understand forward exchange rates

simply as a product of the arbitrage equation outlined earlier and forward points as 
being related to the (time-  scaled) interest rate differential between the two countries . 
Reading any more than that into forward rates or interpreting them as the “market 
forecast” can be potentially misleading.
To understand the relationship between maturity and forward points, we need to 
generalize our arbitrage formula slightly. Suppose the investment horizon is a fraction, 
τ, of the period for which the interest rates are quoted. Then the interest earned in 
the domestic and foreign markets would be ( id τ) and ( if τ), respectively. Substituting 
this into our arbitrage relationship and solving for the difference between the forward 
and spot exchange rates gives:
FS Sii
ifd fd fdfd
d−=−
+

1 ττ

Reading 20 ■ Currency Exchange Rates 428
This equation shows that forward points (appropriately scaled) are proportional to 
the spot exchange rate and to the interest rate differential and approximately (but not 
exactly) proportional to the horizon of the forward contract.
Let’s demonstrate this using an example. Suppose that we wanted to determine 
the 30-  day forward exchange rate given a 30-  day domestic risk-  free interest rate of 
2.00 percent per year, a 30-  day foreign risk-  free interest rate of 3.00 percent per year, 
and a spot exchange rate ( Sf/d) of 1.6555. The risk-  free assets used in this arbitrage 
relationship are typically bank deposits quoted using the London Interbank Offered 
Rate (Libor) for the currencies involved. The day count convention for Libor deposits 
is Actual/360.9 Incorporating the fractional period (τ) as above and inserting the data 
into the forward rate equation leads to a 30-  day forward rate of:
FSi
ifd fdf
d=+
+

=+


+1
11 655510 030030
360

ifd fdf
d=+
+

=+


+1
360
10 020τ
τ..
.0 030
3601 6569










=.
This means that, for a 30-  day term, forward rates are trading at a premium of 14 pips 
(1.6569 – 1.6555). This can also be calculated using the above formula for swap points:
FS Sii
ifd fd fdfd
d−=+

=−
+−
11 65550 0300 0 0200
10 0200ττ ...
.3 30
36030
3600 0014












=.
As should be clear from this expression, the absolute number of swap points will be 
closely related to the term of the forward contract (i.e., approximately proportional 
to τ = Actual/360). For example, leaving the spot exchange rate and interest rates 
unchanged, let’s set the term of the forward contract to 180 days:
FSfd fd// ...
.−=−
+







1 65550 0300 0 0200
10 0200180
360 



=180
3600 0082 .
This leads to the forward rate trading at a premium of 82 pips. The increase in the 
number of forward points is approximately proportional to the increase in the term

of the contract (from 30 days to 180 days). Note that although the term of the 180-  
day forward contract is six times longer than that of a 30-  day contract, the number 
of forward points is not exactly six times larger: 6 × 14 = 84.
Similarly, the number of forward points is proportional to the spread between 
foreign and domestic interest rates ( if – id). For example, with reference to the original 
30- day forward contract, let’s set the foreign interest rate to 4.00 percent leaving the 
domestic interest rate and spot exchange rate unchanged. This doubles the interest 
rate differential ( if – id) from 1.00 percent to 2.00 percent; it also doubles the forward 
points (rounding to four decimal places):
FSfd fd −=−
+









1 65550 0400 0 0200
10 020030
360...
.3 30
3600 0028

=.
9 This means that for interest calculation purposes, it is assumed that there are 360 days in the year.

However, the actual number of days the funds are on deposit is used to calculate the interest payable.

Currency Exchange Rate Calculations 429
EXAMPLE 6   
Forward Rates
A French company has recently finalized a sale of goods to a UK-  based client 
and expects to receive a payment of GBP50 million in 32 days. The corporate 
treasurer at the French company wants to hedge the foreign exchange risk of this 
transaction and receives the following exchange rate information from a dealer:
GBP/EUR spot rate 0.8752
One-  month forward points –1.4
1 Given the above data, the treasurer could hedge the foreign exchange risk 
by:
A buying EUR (selling GBP) at a forward rate of 0.87380.
B buying EUR (selling GBP) at a forward rate of 0.87506.
C selling EUR (buying GBP) at a forward rate of 0.87506.
2 The best interpretation of the forward discount shown is that:
A the euro is expected to depreciate over the next 30 days.
B one-  month UK interest rates are higher than those in the Eurozone.
C one-  month Eurozone interest rates are higher than those in the United 
Kingdom.

Kingdom.
3 If the 12-  month forward rate is 0.87295 GBP/EUR, then based on the data 
the 12-  month forward points are closest  to:
A –22.5.
B –2.25.
C –0.00225.
4 If a second dealer quotes GBP/EUR at a 12-  month forward discount of 
0.30 percent on the same spot rate, the French company could:
A trade with either dealer because the 12-  month forward quotes are 
equivalent.
B lock in a profit in 12 months by buying EUR from the second dealer 
and selling it to the original dealer.
C lock in a profit in 12 months by buying EUR from the original dealer 
and selling it to the second dealer.
5 If the 270-  day Libor rates (annualized) for the EUR and GBP are 1.370% 
and 1.325%, respectively, and the spot GBP/EUR exchange rate is 0.8489, 
then the number of forward points for a 270-  day forward rate ( FGBP/EUR ) 
A –22.8.
B –3.8.
C –2.8.
B is correct. The French company would want to convert the GBP to its domestic

currency, the EUR (it wants to sell GBP , buy EUR). The forward rate would be 
equal to: 0.8752 + (–1.4/10,000) = 0.87506.

Reading 20 ■ Currency Exchange Rates 430
C is correct. A forward discount indicates that interest rates in the base currency 
country (France in this case, which uses the euro) are higher than those in the 
price currency country (the United Kingdom).
A is correct. The number of forward points is equal to the scaled difference 
between the forward rate and the spot rate. In this case: 0.87295 – 0.87520 = 
–0.00225. This is then multiplied by 10,000 to convert to the number of forward 
points.
B is correct. A 0.30  percent discount means that the second dealer will sell 
euros 12 months forward at 0.8752 × (1 – 0.0030) = 0.87257, a lower price per 
euro than the original dealer’s quote of 0.87295. Buying euros at the cheaper 
12- month forward rate (0.87257) and selling the same amount of euros 12 
months forward at the higher 12-  month forward rate (0.87295) means a profit 
of (0.87295 – 0.87257 = GBP 0.00038) per euro transacted, receivable when both

forward contracts settle in 12 months.
C is correct, because the forward rate is calculated as:
FSiActual
iActualGBP
EURGBP
EURGBP
EUR=+


+

1360
1360  






=+


+
0 848910 01325270
360
10 01370270
360..
. 








=0 84862 .
This shows that the forward points are at a discount of: 0.84862 – 0.84890 = 
–0.00028, or –2.8 points. This can also be seen using the swap points formula:
FSGBP
EURGBP
EUR−=−
+

0 84890 01325 0 01370
360...
. 









=−270
3600 00028 .
The calculation of –3.8 points omits the day count (270/360), and –22.8 points 
gets the scaling wrong.
EXCHANGE RATE REGIMES
Highly volatile exchange rates create uncertainty that undermines the efficiency of 
real economic activity and the financial transactions required to facilitate that activity. 
Exchange rate volatility also has a direct impact on investment decisions because it is 
a key component of the risk inherent in foreign (i.e., foreign-  currency-  denominated)

assets. Exchange rate volatility is also a critical factor in selecting hedging strategies 
for foreign currency exposures.
The amount of foreign exchange rate volatility will depend, at least in part, on the 
institutional and policy arrangements associated with trade in any given currency. 
Virtually every exchange rate is managed to some degree by central banks. The policy 
framework that each central bank adopts is called an exchange rate regime . Although 4

Exchange Rate Regimes 431
there are many potential variations, these regimes fall into a few general categories. 
Before describing each of these types, we consider the possibility of an ideal regime 
and provide some historical perspective on the evolution of currency arrangements.
4.1 The Ideal Currency Regime
The ideal currency regime would have three properties. First, the exchange rate 
between any two currencies would be credibly fixed. This would eliminate currency-  
related uncertainty with respect to the prices of goods and services as well as real 
and financial assets. Second, all currencies would be fully convertible (i.e., curren -
cies could be freely exchanged for any purpose and in any amount). This condition 
ensures unrestricted flow of capital. Third, each country would be able to undertake 
fully independent monetary policy in pursuit of domestic objectives, such as growth 
and inflation targets.

Unfortunately, these three conditions are not consistent. If the first two conditions 
were satisfied—credibly fixed exchange rates and full convertibility—then there would 
really be only one currency in the world. Converting from one national currency to 
another would have no more significance (indeed less) than deciding whether to carry 
coins or paper currency in your wallet. Any attempt to influence interest rates, asset 
prices, or inflation by adjusting the supply of one currency versus another would be 
futile. Thus, it should be clear that independent monetary policy is not possible if 
exchange rates are credibly fixed and currencies are fully convertible. There can be 
no ideal currency regime .
The impact of the currency regime on a country’s ability to exercise independent 
monetary policy is a recurring theme in open-  economy macroeconomics. It will be 
covered in more detail in other readings; however, it is worthwhile to emphasize the

basic point by considering what would happen in an idealized world of perfect cap -
ital mobility. If the exchange rate were credibly fixed, then any attempt to decrease 
default-  free interest rates in one country below those in another—that is, to undertake 
independent, expansionary monetary policy—would result in a potentially unlimited 
outflow of capital because funds would seek the higher return. The central bank 
would be forced to sell foreign currency and buy domestic currency to maintain the 
fixed exchange rate. The loss of reserves and reduction in the domestic money supply 
would put upward pressure on domestic interest rates until rates were forced back to 
equality, negating the initial expansionary policy. Similarly, contractionary monetary 
policy (higher interest rates) would be thwarted by an inflow of capital.
The situation is quite different, however, with a floating exchange rate. A decrease

in the domestic interest rate would make the domestic currency less attractive. The 
resulting depreciation of the domestic currency would shift demand toward domesti -
cally produced goods (i.e., exports rise and imports fall), reinforcing the expansionary 
impact of the initial decline in the interest rate. Similarly, a contractionary increase 
in the interest rate would be reinforced by appreciation of the domestic currency.
In practice, of course, capital is not perfectly mobile and the impact on monetary 
policy is not so stark. The fact remains, however, that fixed exchange rates limit the 
scope for independent monetary policy and that national monetary policy regains 
potency and independence, at least to some degree, if the exchange rate is allowed to 
fluctuate and/or restrictions are placed on convertibility. In general, the more freely 
the exchange rate is allowed to float and the more tightly convertibility is controlled,

the more effective the central bank can be in addressing domestic macroeconomic 
objectives. The downside, of course, is the potential distortion of economic activity 
caused by exchange rate risk and inefficient allocation of financial capital.

Reading 20 ■ Currency Exchange Rates 432
4.2 Historical Perspective on Currency Regimes
How currencies exchange for one another has evolved over the centuries. At any 
point in time, different exchange rate systems may coexist; still, there tends to be 
one dominant system in the world economy. Throughout most of the 19th century 
and the early 20th century until the start of World War I, the US dollar and the UK 
pound sterling operated on the “classical gold standard. ” The price of each currency 
was fixed in terms of gold. Gold was the numeraire10 for each currency; therefore, 
it was indirectly the numeraire for all other prices in the economy. Many countries 
(e.g., the colonies of the United Kingdom) fixed their currencies relative to sterling 
and were therefore implicitly also operating on the classical gold standard.
The classical gold standard operated by what is called the price-  specie-  flow mech -
anism . This mechanism operated through the impact of trade imbalances on capital

flows, namely gold. As countries experienced a trade surplus, they accumulated gold 
as payment, their domestic money supply expanded by the amount dictated by the 
fixed parity, prices rose, and exports fell. Similarly, when a country ran a trade deficit, 
there was an automatic outflow of gold, a contraction of the domestic money supply, 
and a fall in prices leading to increased exports.
In this system, national currencies were backed by gold. A country could only print 
as much money as its gold reserve warranted. The system was limited by the amount 
of gold, but it was self-  adjusting and inspired confidence. With a fixed stock of gold, 
the price-  specie-  flow mechanism would work well. Still, new gold discoveries as well 
as more efficient methods of refining gold would enable a country to increase its gold 
reserves and increase its money supply apart from the effect of trade flows. In general, 
however, trade flows drove changes in national money supplies.11

There is much disagreement among economic historians about the effect of the 
classical gold standard on overall macroeconomic stability. Was it destabilizing? On 
the one hand, monetary policy was tied to trade flows, so a country could not engage 
in expansionary policies when there was a downturn in the non-  traded sector. On 
the other hand, it has been argued that tying monetary policy to trade flows kept 
inflation in check.
During the 1930s, the use of gold as a clearing device for settlement of trade imbal -
ances, combined with increasing protectionism on the part of economies struggling 
with depression as well as episodes of deflation and hyperinflation, created a chaotic 
environment for world trade. As a consequence of these factors, world trade dropped 
by over 50 percent and the gold standard was abandoned.
In the later stages of World War II, a new system of fixed exchange rates with 
periodic realignments was devised by John Maynard Keynes and Harry Dexter White,

representing the UK and US Treasuries, respectively. The Bretton Woods system, named 
after the town where it was negotiated, was adopted by 44 countries in 1944. From the 
end of the war until the collapse of the system in the early 1970s, the United States, 
Japan, and most of the industrialized countries of Europe maintained a system of fixed 
parities for exchange rates between currencies. When the parities were significantly 
and persistently out of line with the balancing of supply and demand, there would be a 
realignment of currencies with some appreciating in value and others depreciating in 
value. These periodic realignments were viewed as a part of standard monetary policy.
10 Economists refer to the unit of account in terms of which other goods, services, and assets are priced 
as the numeraire . Under the classical gold standard, the official value of each currency was expressed in 
ounces of gold.

11 The European inflation of the 17th century was an important exception. Discoveries of gold in South 
America led to an increase in the world gold stock and in prices throughout Europe. The impact was 
especially pronounced in Imperial Spain, the primary importing country. Historians have attributed the 
decline of the Spanish Empire, in part, to the loss of control of domestic prices.

Exchange Rate Regimes 433
By 1973, with chronic inflation taking hold throughout the world, most nations 
abandoned the Bretton Woods system in favor of a flexible exchange rate system 
under what are known as the Smithsonian Agreements. Milton Friedman had called 
for such a system as far back as the 1950s.12 His argument was that the fixed parity 
system with periodic realignments would become unsustainable. When the inevitable 
realignments were imminent, large speculative profit opportunities would appear. 
Speculators would force the hand of monetary policy authorities, and their actions 
would distort the data needed to ascertain appropriate trade-  related parities. It is 
better, he argued, to let the market, rather than central bank governors and treasury 
ministers, determine the exchange rate.
After 1973, most of the industrialized world changed to a system of flexible 
exchange rates. The original thinking was that the forces that caused exchange rate

chaos in the 1930s—poor domestic monetary policy and trade barriers—would not be 
present in a flexible exchange rate regime, and therefore exchange rates would move 
in response to the exchange of goods and services among countries. As it turned out, 
however, exchange rates moved around much more than anyone expected. Academic 
economists and financial analysts alike soon realized that the high degree of exchange 
rate volatility was the manifestation of a highly liquid, forward-  looking asset market.13 
Investment-  driven FX transactions—for both long-  term investment and short-  term 
speculation—mattered much more in setting the spot exchange rate than anyone had 
previously imagined.
There are costs, of course, to a high degree of exchange rate volatility. These include 
difficulty planning without hedging exchange rate risks—a form of insurance cost, 
domestic price fluctuations, uncertain costs of raw materials, and short-  term inter -

ruptions in financing transactions. For these reasons, in 1979 the European Economic 
Community opted for a system of limited flexibility, the European Exchange Rate 
Mechanism (ERM).
Initially, the system called for European currency values to fluctuate within a 
narrow band called “the snake. ” This did not last long. The end of the Cold War and 
the re-  unification of Germany created conditions ripe for speculative attack. In the 
early 1990s, the United Kingdom was in a recession and the government’s monetary 
policy leaned toward low interest rates to stimulate economic recovery. Germany 
was issuing large amounts of debt to pay for re-  unification, and the German central 
bank (the Deutsche Bundesbank) opted for high interest rates to ensure price stability. 
Capital began to flow from sterling to Deutsche marks to obtain the higher interest 
rate. The Bank of England tried to lean against these flows and maintain the exchange

rate within the Exchange Rate Mechanism, but eventually it began to run out of marks 
to sell. Because it was almost certain that devaluation would be required, holders of 
sterling rushed to purchase marks at the old rate and the speculative attack forced 
the United Kingdom out of the ERM in September 1992, only two years after it finally 
joined the system.
Despite these difficulties, 1999 saw the creation of a common currency for most 
Western European countries, without Switzerland or the United Kingdom, called 
the euro.14 The hope was that the common currency would increase transparency 
of prices across borders in Europe, enhance market competition, and facilitate more 
12 Friedman (1953).
13 Whether or not FX markets satisfy recognized definitions of market efficiency—correctly reflecting all 
available information—is debatable (e.g., some point to evidence of trending as a clear violation of efficiency).

However, there is no doubt that FX market participants attempt to incorporate new information, which is 
often lumpy and difficult to decipher, into their expectations about the future. Changing expectations—
accurate or otherwise—affect the value that investors place on holding different currencies and, in a highly 
liquid market, lead to rapid and sometimes violent exchange rate movements.
14 The number of European countries adopting the euro has continued to expand since its inception; the 
most recent country to join the euro was Lithuania, on 1 January 2015.

Reading 20 ■ Currency Exchange Rates 434
efficient allocation of resources. The drawback, of course, is that each member country 
lost the ability to manage its exchange rate and therefore to engage in independent 
monetary policy.
4.3 A Taxonomy of Currency Regimes
Although the pros and cons of fixed and flexible exchange rate regimes continue to be 
debated, regimes have been adopted that lie somewhere between these polar cases. In 
some cases, the driving force is the lack of credibility with respect to sound monetary 
policy. An economy with a history of hyperinflation may be forced to adopt a form of 
fixed-  rate regime because its promise to maintain a sound currency with a floating 
rate regime would not be credible. This has been a persistent issue in Latin America. 
In other cases, the driving force is as much political as economic. The decision to 
create the euro was strongly influenced by the desire to enhance political union within

the European Community, whose members had been at war with each other twice 
in the 20th century.
As of April 2008, the International Monetary Fund (IMF) classified exchange rate 
regimes into the eight categories shown in Exhibit 8.
Exhibit 8   Exchange Rate Regimes for Selected Economies15 As of 30 April 2008
Type of RegimeCurrency Anchor
USD EUR Basket/None
No separate legal tender
  Dollarized Ecuador, El Salvador, 
PanamaMontenegro, San Marino
Monetary union EMU: Austria, Belgium, 
Cyprus, Finland, France, 
Germany, Greece, Ireland, 
Italy, Luxembourg, Malta, 
Netherlands, Portugal, 
Slovenia, Spain
Currency board Antigua, Hong Kong Bosnia and Herzegovina, 
Bulgaria
Fixed parity Argentina, Belarus, 
Lebanon, Saudi Arabia, 
Venezuela, VietnamCroatia, Denmark Kuwait, Libya, Russia
Target zone Slovak Republic Syria
Crawling peg Bolivia, China, Iraq Iran
Crawling band Costa Rica Azerbaijan
15 The classifications are described in International Monetary Fund (2006). In some cases, the labels used

by the IMF do not clearly distinguish among the regimes. Hence, the names applied here to the regimes 
differ somewhat from the IMF’s original taxonomy.

Exchange Rate Regimes 435
Managed float Cambodia, Liberia, Ukraine Algeria, Colombia, Egypt, 
India, Indonesia, Malaysia, 
Peru, Singapore, Thailand
Independent float Australia, Canada, Chile, 
Hungary, Iceland, Israel, 
South Korea, Mexico, 
New Zealand, Norway, 
Philippines, Poland, South 
Africa, Sweden, Turkey, 
United Kingdom, Japan, 
Switzerland, United States
It should be noted that global financial markets are too complex and diverse to 
be fully captured by this (or any other) classification system. A government’s control 
over the domestic currency’s exchange rate will depend on many factors; for example, 
the degree of capital controls used to prevent the free flow of funds in and out of the 
economy. Also, even under an “independent float” regime monetary authorities will 
occasionally intervene in foreign exchange markets in order to influence the value 
of their domestic currency. Additionally, the specifics of exchange rate policy imple -

mentation are subject to change. 
This means that the classifications in Exhibit 8 are somewhat arbitrary and subject 
to interpretation, as well as change, over time. The important point to be drawn from 
this discussion is that the prices and flows in foreign exchange markets will, to varying 
degrees, reflect the legal and regulatory framework imposed by governments, not just 
“pure” market forces. Governments have a variety of motives and tools for attempting 
to manage exchange rates. The taxonomy in Exhibit 8 can be used to help understand 
the main distinctions among currency regimes and the rationales for adopting them, 
but the specific definitions should not be interpreted too rigidly. Instead, the focus 
should be on the diversity of foreign exchange markets globally as well as the impli -
cations of these various currency regimes for market pricing.
4.3.1  Arrangements with No Separate Legal Tender
The IMF identifies two types of arrangements in which a country does not have its

own legal tender. In the first, known as dollarization , the country uses the currency 
of another nation as its medium of exchange and unit of account. In the second, the 
country participates in a monetary union whose members share the same legal tender. 
In either case, the country gives up the ability to conduct its own monetary policy.
In principle, a country could adopt any currency as its medium of exchange and 
unit of account, but the main reserve currency, the US dollar, is an obvious choice—
hence the name dollarization. Many countries are dollarized: East Timor, El Salvador, 
Ecuador, and Panama, for example. By adopting another country’s currency as legal 
tender, a dollarized country inherits that country’s currency credibility, but not its 
credit-  worthiness. For example, although local banks may borrow, lend, and accept 
deposits in US dollars, they are not members of the US Federal Reserve System nor

are they backed by deposit insurance from the Federal Deposit Insurance Corporation. 
Thus, interest rates on US dollars in a dollarized economy need not be, and generally 
are not, the same as on dollar deposits in the United States.Exhibit 8   (Continued)

Reading 20 ■ Currency Exchange Rates 436
Dollarization imposes fiscal discipline by eliminating the possibility that the cen -
tral bank will be induced to monetize government debt (i.e., to persistently purchase 
government debt with newly created local currency). For countries with a history of 
fiscal excess or lack of monetary discipline, dollarizing the economy can facilitate 
growth of international trade and capital flows if it creates an expectation of economic 
and financial stability. In the process, however, it removes another potential source 
of stabilization—domestic monetary policy.
The European Economic and Monetary Union (EMU) is the most prominent 
example of the second type of arrangement lacking separate legal tender. Each EMU 
member uses the euro as its currency. Although member countries cannot have their 
own monetary policies, they jointly determine monetary policy through their rep -
resentation at the European Central Bank (ECB). As with dollarization, a monetary

union confers currency credibility on members with a history of fiscal excess and/or 
a lack of monetary discipline. However, as shown by the 2010 EMU sovereign debt 
crisis, monetary union alone cannot confer credit-  worthiness.
4.3.2  Currency Board System
The IMF defines a currency board system  (CBS) as:
A monetary regime based on an explicit legislative commitment to exchange 
domestic currency for a specified foreign currency at a fixed exchange rate, 
combined with restrictions on the issuing authority to ensure fulfillment of 
its legal obligation. This implies that domestic currency will be issued only 
against foreign exchange and it remains fully backed by foreign assets….16
Hong Kong is the leading example of a long-  standing (since 1983) currency board. 
US dollar reserves are held to cover, at the fixed parity, the entire monetary base —
essentially bank reserves plus all HKD notes and coins in circulation.17 Note that

HKD-  denominated bank deposits are not fully collateralized by US dollar reserves; 
to do so would mean that banks could not lend against their deposits. The Hong 
Kong Monetary Authority (HKMA) does not function as a traditional central bank 
under this system because the obligation to maintain 100 percent foreign currency 
reserves against the monetary base prevents it from acting as a lender-  of- last-  resort 
for troubled financial institutions. However, it can provide short-  term liquidity by 
lending against foreign currency collateral.
A CBS works much like the classical gold standard in that expansion and contraction 
of the monetary base are directly linked to trade and capital flows. As with the gold 
standard, a CBS works best if domestic prices and wages are very flexible, non-  traded 
sectors of the domestic economy are relatively small, and the global supply of the 
reserve asset grows at a slow, steady rate consistent with long-  run real growth with

stable prices. The first two of these conditions are satisfied in Hong Kong. Until and 
unless Hong Kong selects a new reserve asset, however, the third condition depends 
on US monetary policy.
In practice, the HKD exhibits modest fluctuations around the official parity of HKD/
USD = 7.80 because the HKMA buys (sells) USD at a pre-  announced level slightly 
below (above) the parity. Persistent flows on one side of this convertibility zone or the 
other result in interest rate adjustments rather than exchange rate adjustments. Inside 
the zone, however, the exchange rate is determined by the market and the HKMA is 
free to conduct limited monetary operations aimed at dampening transitory interest 
rate movements.
16 International Monetary Fund (2006).
17 For a description of Hong Kong’s currency board system, see Hong Kong Monetary Authority (2005).

Exchange Rate Regimes 437
One of the advantages of a CBS as opposed to dollarization is that the monetary 
authority can earn a profit by paying little or no interest on its liability—the monetary 
base—and can earn a market rate on its asset—the foreign currency reserves. This 
profit is called seigniorage .18 Under dollarization, the seigniorage goes to the monetary 
authority whose currency is used.
4.3.3  Fixed Parity
A simple fixed-  rate system differs from a CBS in two important respects. First, there 
is no legislative commitment to maintaining the specified parity. Thus, market partic -
ipants know that the country may choose to adjust or abandon the parity rather than 
endure other, potentially more painful, adjustments. Second, the target level of foreign 
exchange reserves is discretionary; it bears no particular relationship to domestic 
monetary aggregates. Thus, although monetary independence is ultimately limited

as long as the exchange peg is maintained, the central bank can carry out traditional 
functions, such as serving as lender of last resort.
In the conventional fixed-  rate system, the exchange rate may be pegged to a sin -
gle currency—for example, the US dollar—or to a basket index of the currencies of 
major trading partners. There is a band of up to ±1 percent around the parity level 
within which private flows are allowed to determine the exchange rate. The monetary 
authority stands ready to spend its foreign currency reserves, or buy foreign currency, 
in order to maintain the rate within these bands.
The credibility of the fixed parity depends on the country’s willingness and ability to 
offset imbalances in private sector demand for its currency. Both excess and deficient 
private demand for the currency can exert pressure to adjust or abandon the parity. 
Excess private demand for the domestic currency implies a rapidly growing stock of

foreign exchange reserves, expansion of the domestic money supply, and potentially 
accelerating inflation. Deficient demand for the currency depletes foreign exchange 
reserves and exerts deflationary pressure on the economy. If market participants believe 
the foreign exchange reserves are insufficient to sustain the parity, then that belief 
may be self-  fulfilling because the resulting speculative attack will drain reserves and 
may force an immediate devaluation. Thus, the level of reserves required to maintain 
credibility is a key issue for a simple fixed exchange rate regime.
4.3.4  Target Zone
A target zone regime has a fixed parity with fixed horizontal intervention bands that 
are somewhat wider—up to ±2 percent around the parity—than in the simple fixed 
parity regime. The wider bands provide the monetary authority with greater scope 
for discretionary policy.
4.3.5  Active and Passive Crawling Pegs
Crawling pegs for the exchange rate—usually against a single currency, such as the

US dollar—were common in the 1980s in Latin America, particularly Brazil, during 
the high inflation periods. To prevent a run on the US dollar reserves, the exchange 
rate was adjusted frequently (weekly or daily) to keep pace with the inflation rate. 
Such a system was called a passive crawl. An adaptation used in Argentina, Chile, and 
Uruguay was the active crawl: The exchange rate was pre-  announced for the coming 
weeks with changes taking place in small steps. The aim of the active crawl was to 
18 More generally, seigniorage is the profit earned when the value of money issued exceeds the cost of 
producing it. For physical currency, seigniorage arises when a coin is minted for a fraction of its face value 
and then issued (sold) at its face value.

Reading 20 ■ Currency Exchange Rates 438
manipulate expectations of inflation. Because the domestic prices of many goods 
were directly tied to import prices, announced changes in the exchange rate would 
effectively signal future changes in the inflation rate of these goods.
4.3.6  Fixed Parity with Crawling Bands
A country can also have a fixed central parity with crawling bands. Initially, a country 
may fix its rates to a foreign currency to anchor expectations about future inflation 
but then gradually permit more and more flexibility in the form of a pre-  announced 
widening band around the central parity. Such a system has the desirable property 
of allowing a gradual exit strategy from the fixed parity. A country might want to 
introduce greater flexibility and greater scope for monetary policy, but it may not 
yet have the credibility or financial infrastructure for full flexibility. So it maintains a 
fixed parity with slowly widening bands.
4.3.7  Managed Float

A country may simply follow an exchange rate policy based on either internal or 
external policy targets—intervening or not to achieve trade balance, price stability, 
or employment objectives. Such a policy, often called dirty floating,  invites trading 
partners to respond likewise with their exchange rate policy and potentially decreases 
stability in foreign exchange markets as a whole. The exchange rate target, in terms 
of either a level or a rate of change, is typically not explicit.
4.3.8  Independently Floating Rates
In this case, the exchange rate is left to market determination and the monetary 
authority is able to exercise independent monetary policy aimed at achieving such 
objectives as price stability and full employment. The central bank also has latitude 
to act as a lender of last resort to troubled financial institutions, if necessary.
It should be clear from recent experience that the concepts of float, managed

float, crawl, and target zone are not hard and fast rules. Central banks do occasion -
ally engage, implicitly or explicitly, in regime switches—even in countries nominally 
following an independently floating exchange rate regime. For example, when the US 
dollar appreciated in the mid-  1980s with record US trade deficits, then-  US Treasury 
Secretary James Baker engineered the Plaza Accord, in which Japan and Germany 
engineered an appreciation of their currencies against the US dollar. (The “Plaza 
Accord” is so named because it was negotiated at the Plaza Hotel in New York City.) 
This 1985 policy agreement involved a combination of fiscal and monetary policy 
measures by the countries involved as well as direct intervention in foreign exchange 
markets. The Plaza Accord was a clear departure from a pure independently floating 
exchange rate system.
There are more recent examples of government intervention in foreign exchange

markets. In September 2000, the European Central Bank, the Federal Reserve Board, 
the Bank of Japan, the Bank of England, and the Bank of Canada engaged in “concerted” 
intervention in order to support the value of the euro, a “freely floating” currency 
which was then under pressure within foreign exchange markets. (This intervention 
was described as “concerted” because it was pre-  arranged and coordinated among 
the central banks involved.) During 2010, many countries engaged in unilateral inter -
vention to prevent the rapid appreciation of their currencies against the US dollar. 
Several of these countries also employed various fiscal and regulatory measures (for 
example, taxes on capital inflows) in order to further affect exchange rate movements.
The important point to draw from this discussion is that exchange rates do not only 
reflect private sector market forces but will also, to varying degrees, be influenced by

the legal and regulatory framework (currency regimes) within which foreign exchange

Exchange Rate Regimes 439
markets operate. Moreover, they will occasionally be influenced by government polices 
(fiscal, monetary, and intervention) intended to manage exchange rates. All of these 
can vary widely among countries and are subject to change with time.
Nonetheless, the most widely traded currencies in foreign exchange markets (the 
US dollar, yen, euro, UK pound, Swiss franc, and the Canadian and Australian dollars) 
are typically considered to be free floating, although subject to relatively infrequent 
intervention.
EXAMPLE 7   
Currency Regimes
An investment adviser in Los Angeles, USA, is meeting with a client who wishes 
to diversify her portfolio by including more international investments. In order 
to evaluate the suitability of international diversification for the client, the adviser 
attempts to explain some of the characteristics of foreign exchange markets. 
The adviser points out that exchange rate regimes affect the performance of

domestic economies as well as the amount of foreign exchange risk posed by 
international investments.
The client and her adviser discuss potential investments in Hong Kong, 
Panama, and Canada. The adviser notes that the currency regimes of Hong 
Kong, Panama, and Canada are a currency board, dollarization, and a free float, 
respectively. The adviser tells his client that these regimes imply different degrees 
of foreign exchange risk for her portfolio.
The discussion between the investment adviser and his client then turns to 
potential investments in other markets with different currency regimes. The 
adviser notes that some markets are subject to fixed parity regimes against the 
US dollar. The client asks whether a fixed parity regime would imply less foreign 
currency risk for her portfolio than would a currency board. The adviser replies: 
“Yes, a fixed parity regime means a constant exchange rate and is more credible 
than a currency board. ”

The adviser goes on to explain that in some markets exchange rates are 
allowed to vary, although with different degrees of foreign exchange market 
intervention to limit exchange rate volatility. Citing examples, he notes that 
China has a crawling peg regime with reference to the US dollar, but the aver -
age daily percentage changes in the China/US exchange rate are very small 
compared with the average daily volatility for a freely floating currency. The 
adviser also indicates that Denmark has a target zone regime with reference 
to the euro, and South Korea usually follows a freely floating currency regime 
but sometimes switches to a managed float regime. The currencies of China, 
Denmark, and South Korea are the yuan renminbi (CNY), krone (DKK), and 
won (KRW), respectively.
1 Based solely on the exchange rate risk the client would face, what is the 
correct ranking (from most to least risky) of the following investment 
locations?
A Panama, Canada, Hong Kong.

B Canada, Hong Kong, Panama.
C Hong Kong, Panama, Canada.
2 Based solely on their foreign exchange regimes, which investment location 
is least likely to import inflation or deflation from the United States?
A Canada.
B Panama.

Reading 20 ■ Currency Exchange Rates 440
C Hong Kong.
3 The adviser’s statement about fixed parity regimes is incorrect with regard 
to:
A credibility.
B a constant exchange rate.
C both a constant exchange rate and credibility.
4 Based on the adviser’s categorization of China’s currency regime, if the 
USD is depreciating against the KRW, then it is most  likely correct that 
the CNY is:
A fixed against the KRW.
B appreciating against the KRW.
C depreciating against the KRW.
5 Based on the adviser’s categorization of Denmark’s currency regime, it 
would be most  correct to infer that the:
A krone is allowed to float against the euro within fixed bands.
B Danish central bank will intervene if the exchange rate strays from its 
target level.
C target zone will be adjusted periodically in order to manage inflation 
6 Based on the adviser’s categorization of South Korea’s currency policy, it 

A Korean central bank is engineering a gradual exit from a fixed-  rate 
regime.
B government is attempting to peg the exchange rate within a predefined 
zone.
C won is allowed to float, but with occasional intervention by the Korean 
central bank.
B is correct. The CAD/USD exchange rate is a floating exchange rate, and 
Canadian investments would therefore carry exchange rate risk for a US-  based 
investor. Although Hong Kong follows a currency board system, the HKD/USD 
exchange rate nonetheless does display some variation, albeit much less than in 
a floating exchange rate regime. In contrast, Panama has a dollarized economy 
(i.e., it uses the US dollar as the domestic currency); therefore, there is no foreign 
exchange risk for a US investor.
A is correct. The Canadian dollar floats independently against the US dollar 
leaving the Bank of Canada able to adjust monetary policy to maintain price

stability. Neither Hong Kong (currency board) nor Panama (dollarized) can exer -
cise independent monetary policy to buffer its economy from the inflationary/
deflationary consequences of US monetary policy.
C is correct. A fixed exchange rate regime does not mean that the exchange 
rate is rigidly fixed at a constant level. In practice, both a fixed-  rate regime 
and a currency board allow the exchange rate to vary within a band around 
the stated parity level. Thus, both regimes involve at least a modest amount of 
exchange rate risk. The fixed parity regime exposes the investor to the additional

Exchange Rates, International Trade, and Capital Flows 441
risk that the parity may not be maintained. In a fixed parity regime, the level 
of foreign currency reserves is discretionary and typically only a small fraction 
of the domestic money supply. With no legal obligation to maintain the parity, 
the monetary authority may adjust the parity (devalue or revalue its currency) 
or allow its currency to float if doing so is deemed to be less painful than other 
adjustment mechanisms (e.g., fiscal restraint). In contrast, a currency board 
entails a legal commitment to maintain the parity and to fully back the domestic 
currency with reserve currency assets. Hence, there is little risk that the parity 
will be abandoned.
C is correct. If the CNY is subject to a crawling peg with very small daily adjust -
ments versus the USD and the USD is depreciating against the KRW, then the 
CNY would most  likely be depreciating against the KRW as well. In fact, this was

an important issue in foreign exchange markets through the latter part of 2010: 
As the USD depreciated against most Asian currencies (and less so against the 
CNY), many Asian countries felt that they were losing their competitive export 
advantage because the CNY was so closely tied to the USD. This led many Asian 
countries to intervene in FX markets against the strength of their domestic 
currencies in order not to lose an export pricing advantage against China.
A is correct. A target zone means that the exchange rate between the euro and 
Danish krone (DKK) will be allowed to vary within a fixed band (as of 2010, the 
target zone for the DKK/EUR is a ±2.5 percent band). This does not mean that 
the DKK/EUR rate is fixed at a certain level (B is incorrect) or that the target 
zone will vary in order to manage inflation expectations (this is a description 
of a crawling peg, which makes C incorrect).

C is correct. Similar to the monetary authorities responsible for many of the 
world’s major currencies, the South Korean policy typically involves letting market 
forces determine the exchange rate (an independent floating rate regime). But 
this approach does not mean that market forces are the sole determinant of the 
won exchange rate. As with most governments, the South Korean policy is to 
intervene in foreign exchange markets when movements in the exchange rate 
are viewed as undesirable (a managed float). For example, during the later part 
of 2010, South Korea and many other countries intervened in foreign exchange 
markets to moderate the appreciation of their currencies against the US dollar. 
Answer A describes a fixed parity with a crawling bands regime, and B describes 
a target zone regime: Both answers are incorrect.
EXCHANGE RATES, INTERNATIONAL TRADE, AND 
CAPITAL FLOWS
Just as a family that spends more than it earns must borrow or sell assets to finance the

excess, a country that imports more goods and services than it exports must borrow 
from foreigners or sell assets to foreigners to finance the trade deficit. Conversely, a 
country that exports more goods and services than it imports must invest the excess 
either by lending to foreigners or by buying assets from foreigners. Thus, a trade deficit 5

Reading 20 ■ Currency Exchange Rates 442
(surplus) must be exactly matched by an offsetting capital account  surplus (deficit).19 
This implies that any factor that affects the trade balance must have an equal and oppo -
site impact on the capital account, and vice versa. To put this somewhat differently, 
the impact of exchange rates and other factors on the trade balance must be mirrored 
by their impact on capital flows : They cannot affect one without affecting the other.
Using a fundamental identity from macroeconomics, the relationship between the 
trade balance and expenditure/saving decisions can be expressed as:20
X – M = (S – I) + ( T – G)
where X represents exports, M is imports, S is private savings, I is investment in 
plant and equipment, T is taxes net of transfers, and G is government expenditure. 
From this relationship, we can see that a trade surplus ( X > M) must be reflected in 
a fiscal surplus ( T > G), an excess of private saving over investment ( S > I), or both.

Because a fiscal surplus can be viewed as government saving, we can summarize this 
relationship more simply by saying that a trade surplus means the country saves more 
than enough to fund its investment ( I) in plant and equipment. The excess saving 
is used to accumulate financial claims on the rest of the world. Conversely, a trade 
deficit means the country does not save enough to fund its investment spending ( I) 
and must reduce its net financial claims on the rest of the world.
Although this identity provides a key link between real expenditure/saving deci -
sions and the aggregate flow of financial assets into or out of a country, it does not 
tell us what type of financial assets will be exchanged or in what currency they will be 
denominated. All that can be said is that asset prices and exchange rates at home and 
abroad must adjust so that all financial assets are willingly held by investors.
If investors anticipate a significant change in an exchange rate, they will try to sell

the currency that is expected to depreciate and buy the currency that is expected to 
appreciate. This implies an incipient (i.e., potential) flow of capital from one country 
to the other, which must either be accompanied by a simultaneous shift in the trade 
balance or be discouraged by changes in asset prices and exchange rates. Because 
expenditure/saving decisions and prices of goods change much more slowly than 
financial investment decisions and asset prices, most of the adjustment usually occurs 
within the financial markets. That is, asset prices and exchange rates adjust so that 
the potential flow of financial capital is mitigated and actual capital flows remain 
consistent with trade flows . In a fixed exchange rate regime, the central bank offsets 
the private capital flows in the process of maintaining the exchange rate peg and the 
adjustment occurs in other asset prices, typically interest rates, until and unless the

central bank is forced to allow the exchange rate to adjust.21 In a floating exchange 
rate regime, the main adjustment is often a rapid change in the exchange rate that 
dampens an investor’s conviction that further movement will be forthcoming. Thus, 
capital flows—potential and actual—are the primary determinant of exchange rate 
movements in the short-  to- intermediate term . Trade flows become increasingly import -
ant in the longer term as expenditure/saving decisions and the prices of goods and 
services adjust.
19 In official balance of payments accounts, investment/financing flows are separated into two categories: 
the capital account and the financial account. Because the technical distinction is immaterial for present 
purposes, we will simply refer to the balance of investment/financing flows as the capital account. Similarly, 
we ignore the technical distinction between the trade balance and the current account  balance. The details

of balance of payments accounting are presented in the Level I curriculum reading on International Trade 
and Capital Flows.
20 This relationship is developed in the Level I curriculum reading on Aggregate Output, Prices, and 
Economic Growth.
21 A classic example of this occurred in September 1992, when the United Kingdom was forced to with -
draw from the European Exchange Rate Mechanism, the forerunner of the current European Economic 
and Monetary Union (EMU).

Exchange Rates, International Trade, and Capital Flows 443
With the correspondence between the trade balance and capital flows firmly 
established, we can now examine the impact of exchange rate changes on the trade 
balance from two perspectives. The first approach focuses on the effect of changing 
the relative price of domestic and foreign goods. This approach, which is called the 
elasticities approach , highlights changes in the composition of spending. The second 
approach, called the absorption approach , focuses on the impact of exchange rates 
on aggregate expenditure/saving decisions.
5.1 Exchange Rates and the Trade Balance: The Elasticities 
Approach
The effectiveness of devaluation (in a fixed system) or depreciation (in a flexible system) 
of the currency for reducing a trade deficit depends on well-  behaved demand and 
supply curves for goods and services. The condition that guarantees that devaluations

improve the trade balance is called the Marshall–Lerner condition. The usual statement 
of this condition assumes that trade is initially balanced. We will present a general -
ization of the condition that allows for an initial trade imbalance and hence is more 
useful in addressing whether exchange rate movements will correct such imbalances.
Recall from microeconomics that the price elasticity of demand is given by:22
ε=−= −%
%%
%change inquantity
change inpriceQ
P∆
∆
For example, a demand elasticity of 0.6 means that quantity demanded increases by 
6 percent if price declines by 10 percent. Note that the elasticity of demand is defined 
so that it is a positive number. Because expenditure ( R) equals price multiplied by 
quantity ( P × Q), by re-  arranging the above expression to solve and substitute for 
%ΔQ, we can see that:
%% %% % change inexpenditure RP QP == += −() ∆∆ ∆∆ 1ε
From this we can see that an increase in price decreases expenditure if ε > 1, but it

increases expenditure if ε < 1. By convention, if ε > 1 demand is described as being 
“elastic, ” while if ε < 1 demand is described as “inelastic. ”
The basic idea behind the Marshall–Lerner condition is that demand for imports 
and exports must be sufficiently price-  sensitive so that increasing the relative price 
of imports increases the difference between export receipts and import expenditures. 
The generalized Marshall–Lerner condition is:
ωXεX + ωM(εM – 1) > 0  
where ωX and ωM are the shares of exports and imports, respectively, in total trade 
(i.e., imports + exports) and εX and εM are the price elasticities of foreign demand for 
domestic country exports and domestic country demand for imports, respectively. 
Note that (ωX + ωM) = 1 and that an initial trade deficit implies ωM > ωX. If this con -
dition is satisfied, a devaluation/depreciation of the domestic currency will move the 
trade balance toward surplus.

The first term in the generalized Marshall–Lerner condition reflects the change in 
export receipts assuming the domestic currency price of exports is unchanged (i.e., 
foreigners are billed in the domestic currency). It will be positive as long as export 
demand is not totally insensitive to price. Depreciation of the domestic currency makes 
exports cheaper in foreign currency and induces an increase in the quantity demanded 
by foreigners. This is reflected by the elasticity εx. There is no direct price impact on 
domestic currency export revenue because the domestic currency price is assumed 
22 See the Level I curriculum reading Topics in Demand and Supply Analysis.

Reading 20 ■ Currency Exchange Rates 444
to be unchanged. Hence, the percentage change in export revenue corresponding to a 
1 percent depreciation of the currency is simply εx. The second term in the generalized 
Marshall–Lerner condition reflects the impact on import expenditures. Assuming 
that imports are billed in a foreign currency, the domestic currency price of imports 
rises as the domestic currency depreciates. The direct price effect increases import 
expenditures, while the induced reduction in the quantity of imports decreases import 
expenditures. The net effect depends on the elasticity of import demand, εM. Import 
expenditure declines only if import demand is elastic (i.e., εM > 1).
Examination of the generalized Marshall–Lerner condition indicates that more 
elastic demand—for either imports or exports—makes it more likely that the trade 
balance will improve. Indeed, if the demand for imports is elastic, εM > 1, then the

trade balance will definitely improve. It should also be clear that the elasticity of import 
demand becomes increasingly important, and the export elasticity less important, 
as the initial trade deficit gets larger—that is, as ωM increases. In the special case of 
initially balanced trade, ωX = ωM, the condition reduces to (εX + εM > 1), which is the 
classic Marshall–Lerner condition.
Exhibit 9 illustrates the impact of depreciation on the trade balance. For ease of 
reference, we assume the domestic currency is the euro. A 10 percent depreciation 
of the euro makes imports 10 percent more expensive in euro terms. With an import 
elasticity of 0.65, this induces a 6.5 percent reduction in the quantity of imports. But 
import expenditures increase by 3.5 percent [10% × (1 – 0.65)] or €21,000,000 because 
the drop in quantity is not sufficient to offset the increase in price. On the export side, 
the euro price of exports does not change but the foreign currency price of exports

declines by 10 percent. This induces a 7.5 percent increase in the quantity of exports 
given an elasticity of 0.75. The euro value of exports therefore increases by 7.5 percent 
or €30,000,000. The net effect is a €9,000,000 improvement in the trade balance and 
a €51,000,000 increase in total trade.
Exhibit 9   Marshall–Lerner Condition with a 10 Percent Depreciation of 
Domestic Currency (€)
Assumptions Exports Imports
Demand elasticity 0.75 0.65
Percent price change
  In domestic currency (€) 0 10%
  In foreign currency –10% 0
Results Initial value(€) Change(€)
Exports 400,000,000 30,000,000
Imports 600,000,000 21,000,000
Trade balance –200,000,000 9,000,000
Total trade 1,000,000,000 51,000,000
The balance of trade improves after the depreciation of the euro because the 
Marshall–Lerner condition is satisfied: The increase in the euro-  value of exports 
exceeds the increase in the value of imports. Based on the data in Exhibit 9, ωM = 0.6

(i.e., 600,000,000/1,000,000,000) and ωX = 0.4 (i.e., 1 – 0.6). Thus, the Marshall–Lerner 
equation is greater than zero:
ωXεX + ωM(εM – 1) = 0.4 × 0.75 + 0.6(0.65 – 1) = 0.09

Exchange Rates, International Trade, and Capital Flows 445
The elasticity of demand for any good or service depends on at least four factors: 
1) the existence or absence of close substitutes, 2) the structure of the market for that 
product (e.g., a monopoly or perfect competition), 3) its share in people’s budgets, 
and 4) the nature of the product and its role in the economy. Demand for a product 
with close substitutes is highly price-  sensitive, whereas demand for a unique product 
tends to be much less elastic. The demand curve faced by any producer also depends 
on the nature and level of competition among producers of that product. If there are 
many sellers of identical products, then each producer faces highly elastic demand 
for its output even if global demand for that product is insensitive to price. Producers 
who are able to differentiate their product, perhaps through branding, face somewhat 
less elastic demand. In markets with only a few sellers, each producer faces demand

that is highly dependent upon strategic maneuvers by its competitors. If competitors 
match price decreases but not increases, then the producer loses market share by 
raising his price but fails to gain market share by reducing his price.
Price changes have two effects on demand. The substitution effect  refers to changes 
in the composition of spending across different products. As a product gets more 
expensive (cheaper) relative to other products, customers demand less (more) of 
it. This is what people usually think of first when they consider the effect of a price 
change. The income effect  refers to the fact that price changes affect real purchasing 
power. When the price of a good rises (falls), people’s purchasing power is reduced 
(increased). The strength of this effect depends on the product’s share in people’s 
budgets—the more important the product, the stronger the income effect. The income 
effect also depends on the nature of the product. The demand for luxuries is highly

sensitive to income, whereas the demand for necessities is fairly insensitive to income.
To illustrate the differential impact of the two drivers of the income effect—share 
of expenditure and nature of the product—consider the demand for food. Clearly, food 
is a necessity. Based on this fact, we would expect demand to be inelastic. However, 
the share of expenditures that go to food varies across countries. In poor countries, 
food represents a much larger share of expenditure than in rich countries. Hence, all 
else being equal, we would expect the demand for food to be more price elastic in 
poorer countries. Of course, even in rich countries, the composition of spending on 
food may change considerably even if overall demand for food does not.
A significant portion of international trade occurs in intermediate products—prod -
ucts that are used as inputs into the production of other goods. Demand for these 
products derives from supply and demand decisions for the final products. However,

the same basic considerations apply for intermediate products as for final products. Are 
there close substitutes for it in the production process? If not, its demand will tend to 
be less elastic than would be the case if there were readily available substitutes. How 
important is it to the overall economy? All else equal, the larger its share in overall 
production costs for the economy, the bigger its impact on production decisions 
and therefore the more price-  elastic its derived demand. Oil is a classic example of a 
widely used input with few readily adoptable substitutes, at least in the short run. Lack 
of substitutes tends to make oil demand price-  inelastic. However, it is so important 
in modern industrial economies that changes in its price can induce expansion or 
contraction of aggregate output. This makes short-  run oil demand somewhat more 
elastic—at least for significant price changes. In the longer run, the feasibility of sub -

stitution among energy sources enhances the price sensitivity of oil demand.
Exhibit 10 shows estimates of demand elasticity for various products. The estimates 
range from essentially zero for pediatric doctor visits—a necessity for which there 
is virtually no substitute—to 3.8 for Coca-  Cola, a specific brand for which there are 
many substitutes. Note that the elasticity of demand for soft drinks in general is much 
lower than for Coca-  Cola, roughly 0.9. The elasticity of demand for rice in Japan versus 
in Bangladesh clearly illustrates the impact of expenditure share on price sensitivity. 
Similarly, although air travel for pleasure (a luxury) is quite price elastic, demand for

Reading 20 ■ Currency Exchange Rates 446
first-  class air travel is fairly insensitive to price. This is most likely because many first-  
class passengers are either traveling on business (presumably deemed to have high 
value added) or wealthy enough that the cost of first-  class airfare is inconsequential.
Exhibit 10   Estimates of Demand Elasticities
Product Description Elasticity Rationale/Comment
Travel and transport
  Airline travel (US)
   For pleasure 1.5 Luxury
   1st class 0.3 Business and wealthy travelers
  Car fuel (US, long term) 0.6
  Bus travel (US) 0.2
  Ford compact car 2.8 Large purchase; specific brand
Food and beverages
  Rice Necessity; staple food
   Bangladesh 0.8 Poor country
   Japan 0.3 Wealthy country
  Soft drinks
   All 0.8–1.0
   Coca-  Cola 3.8 Specific brand; competitive market
Medical care (US)
  Health insurance 0.3
  Pediatric doctor visit 0.0–0.1 No good substitute
Materials and energy Necessary inputs
  Steel 0.2–0.3
  Oil 0.4

Steel 0.2–0.3
  Oil 0.4
Sources:  Various studies cited in Wikipedia, “Price Elasticity of Demand, ” as of December 2010 
(http://en.wikipedia.org/wiki/Price_elasticity_of_demand).
In practice, most countries import and export a variety of products. Hence, the 
overall price elasticities of their imports and exports reflect a composite of the prod -
ucts they trade. In conjunction with the Marshall–Lerner condition, our review of 
the factors that determine price elasticities suggests that exchange rate changes will 
be a more-  effective mechanism for trade balance adjustment if a country imports and 
exports the following:
■■Goods for which there are good substitutes
■■Goods that trade in competitive markets
■■Luxury goods, rather than necessities
■■Goods that represent a large portion of consumer expenditures or a large por -
tion of input costs for final producers
Note that each of these conditions is associated with higher demand elasticities (εX 
and εM).

Exchange Rates, International Trade, and Capital Flows 447
Even when the Marshall–Lerner condition is satisfied, it is still possible that deval -
uation (in a fixed parity regime) or depreciation (in a floating regime) of the currency 
will initially make the trade balance worse before making it better. This effect, called 
the J-curve effect, is illustrated in Exhibit 11.
Exhibit 11   Trade Balance Dynamics: The J-Curve
Trade Balance
0
TimeDevaluation
In the very short run, the J-curve reflects the order delivery lags that take place in 
import and export transactions. Imagine a clothing importer in Washington. Orders 
are placed in January for French spring fashions. Market forces cause the dollar to 
depreciate in February, but contracts were already signed for payment in euros. When 
the fashions arrive in March, more dollars have to go out to pay for the order signed 
in euros. Thus, the trade balance gets worse. However, after the depreciation, the

clothing importer has to put in new orders for summer fashions. As a result of the 
currency depreciation, the French summer fashions are now more expensive, so the 
clothing store cuts the demand for imported clothes from France. The depreciation 
eventually improves the trade balance, even though it initially made it worse.
A J-curve pattern may also arise if short-  term price elasticities do not satisfy the 
Marshall–Lerner condition but long-  term elasticities do satisfy it. As noted above in 
the case of oil, significant changes in spending patterns often take time. Thus, the trade 
balance may worsen initially and then gradually improve following a depreciation of 
the currency as firms and consumers adapt.
5.2 Exchange Rates and the Trade Balance: The Absorption 
Approach
The elasticities approach focuses on the expenditure-  switching effect of changing the 
relative prices of imports and exports. It is essentially a microeconomic view of the

relationship between exchange rates and the trade balance. The absorption approach 
adopts an explicitly macroeconomic view of this relationship.
Recall from above that the trade balance is equal to the country’s saving, including 
the government fiscal balance, minus its investment in new plants and equipment. 
Equivalently, it is equal to the difference between income (GDP) and domestic 
expenditure, or absorption. Thus, in order to move the trade balance toward surplus,

Reading 20 ■ Currency Exchange Rates 448
a devaluation/depreciation of the domestic currency must increase income relative 
to expenditure or, equivalently, increase national saving relative to investment in 
physical capital.
If there is excess capacity in the economy, then by switching demand toward domes -
tically produced goods and services, depreciation of the currency can increase output/
income. Because some of the additional income will be saved, income rises relative to 
expenditure and the trade balance improves. If the economy is at full employment, 
however, the trade balance cannot improve unless domestic expenditure declines. 
If expenditure does not decline, then the depreciation will put upward pressure on 
domestic prices until the stimulative effect of the exchange rate change is negated by 
the higher price level and the trade balance reverts to its original level.
How might depreciation of the currency reduce domestic expenditure relative

to income? The main mechanism is a wealth effect. A weaker currency reduces the 
purchasing power of domestic-  currency-  denominated assets (including the present 
value of current and future earned income). Households respond by reducing expen -
diture and increasing saving in order to rebuild their wealth. Of course, as real wealth 
is rebuilt, the effect on saving is likely to be reversed—resulting in only a temporary 
improvement in the trade balance. Thus, in the absence of excess capacity in the 
economy, currency depreciation is likely to provide only a temporary solution for a 
chronic trade imbalance. Lasting correction of the imbalance requires more funda -
mental changes in expenditure/saving behavior (e.g., a policy shift that improves the 
fiscal balance or an increase in saving relative to capital investment induced by an 
increase in real interest rates).
The absorption approach also reminds us that currency depreciation cannot

improve the trade balance unless it also induces a corresponding change in the cap -
ital account. Not only must domestic saving increase, but that saving must also be 
willingly channeled into buying financial assets from foreigners. All else equal, this 
implies that foreign and domestic asset prices must change such that foreign assets 
become relatively more attractive and domestic assets relatively less attractive to both 
foreign and domestic investors.
EXAMPLE 8   
Exchange Rates and the Trade Balance
An analyst at a foreign exchange dealing bank is examining the exchange rate 
for the Australian dollar (AUD), which is a freely floating currency. Currently, 
Australia is running a trade surplus with the rest of the world, primarily reflecting 
strong demand for Australian resource exports generated by rapid growth in 
emerging market economies in the Western Pacific region. In turn, Australia 
imports food and energy from a variety of foreign countries that compete with

each other as well as with Australian producers of these products. The analyst 
uses data in the following table to estimate the effect of changes in the AUD 
exchange rate on Australia’s balance of trade.
Volume  
(AUD billions) Demand Elasticity
Exports 200 0.3
Imports 180 0.6
The analyst’s research report on this topic notes that the mix of products 
that Australia imports and exports seems to be changing and that this will affect 
the relation between the exchange rates and the trade surplus. The proportion 
of Australian exports accounted for by fine wines is increasing. These are

Exchange Rates, International Trade, and Capital Flows 449
considered a luxury good and must compete with increased wine exports from 
comparable-  producing regions (such as Chile and New Zealand). At the same 
time, rising income levels in Australia are allowing the country to increase the 
proportion of its imports accounted for by luxury goods, and these represent a 
rising proportion of consumer expenditures. The analyst’s report states: “Given 
the changing export mix, an appreciation of the currency will be more likely 
to reduce Australia’s trade surplus. In contrast, the changing import mix will 
have the opposite effect. ”
1 Given the data in the table, an appreciation in the AUD will:
A cause the trade balance to increase.
B cause the trade balance to decrease.
C have no effect on the trade balance.
2 All else equal, an appreciation in the AUD will be more  likely to reduce 
the trade surplus if the demand:
A elasticities for imports and exports increase.

B elasticity for exports and the export share in total trade decrease.
C elasticity for imports decreases and the import share in total trade 
3 All else equal, an appreciation in the AUD will be more  likely to reduce 
the trade surplus if it leads to an increase in Australian:
A tax receipts.
B private sector investment.
C government budget surpluses.
4 The report’s statement about the effect of changing import and export 
mixes is most  likely:
A correct.
B incorrect with respect to the import effect.
C incorrect with respect to the export effect.
5 Suppose the Australian government imposed capital controls that prohib -
ited the flow of financial capital into or out of the country. What impact 
would this have on the Australian trade balance?
A The trade surplus would increase.
B The trade balance would go to zero.
C The trade balance would not necessarily be affected.

6 Suppose the Australian government imposed capital controls that prohib -
ited the flow of financial capital into or out of the country. The impact on 
the trade balance, if any, would most likely take the form of:
A a decrease in private saving.
B a decrease in private investment.
C an increase in the government fiscal balance.
A is correct. As the AUD appreciates, the price of exports to offshore buyers  goes 
up and they demand fewer of them; hence, the AUD-  denominated revenue from 
exports decreases. (Although export demand is inelastic, or εX < 1, recall that 
the Australian  price of these exports is assumed not to have changed, so the 
amount of export revenue received by Australia, in AUD-  terms, unambiguously 
declines as the quantity of exports declines.) Australian expenditure for imports

Reading 20 ■ Currency Exchange Rates 450
also declines. Although the price of imports declines as the AUD appreciates, 
the Australians do not increase their import purchases enough to lead to higher 
expenditures. This is because import demand is also inelastic (εM < 1). This 
effect on import expenditure can be seen from: %Δ RM = (1 – εM)%ΔPM, where 
%ΔPM is negative (import prices are declining) and import demand is inelastic 
(so (1 – εM) > 0). With both import expenditures and export revenues declin -
ing, the net effect on the trade balance comes down to the relative size of the 
import and export weights (ωM and ωX, respectively). In this case, ωX = 0.53 (i.e., 
200/380) and ωM = 0.47 (i.e., 180/380). Putting this into the Marshall–Lerner 
equation leads to:
ωXεX + ωM(εM – 1) = 0.53 × 0.3 + 0.47(0.6 – 1) = –0.03  
Because the Marshall–Lerner condition is not satisfied, exchange rate move -
ments do not move the trade balance in the expected direction [i.e., appreciation

(depreciation) of the currency does not decrease (increase) the trade balance]. 
However, note that with different import/export weights and the same elastici -
ties, the Marshall–Lerner condition would be met. In particular, the condition 
would be met for any value of ωX greater than 4/7 (≈ 0.571).
A is correct. The basic intuition of the Marshall–Lerner condition is that in order 
for an exchange rate movement to rebalance trade, the demands for imports and 
exports must be sufficiently price-  sensitive (i.e., they must have sufficiently high 
elasticities). However, the relative share of imports and exports in total trade 
must also be considered. The generalized Marshall–Lerner condition requires: 
An increase in both εX and εM will clearly make this expression increase (A is 
correct). In contrast, a decrease in both ωX and εX tends to make the expression 
smaller (B is incorrect).23 If εM decreases and ωM increases, import demand

will respond less to an exchange rate movement and will have a larger role in 
determining the trade balance (C is incorrect).
B is correct. An Australian trade surplus means that Australia is spending less 
than it earns and is accumulating claims on foreigners. Equivalently, Australian 
saving, inclusive of both private saving and the government fiscal balance, is more 
than sufficient to fund Australian private sector investment. The relationship 
between the trade balance and expenditure/saving decisions is given by: 
X – M = (S – I) + ( T – G) > 0
For Australia’s trade balance to decline, it must save less ( S down), invest 
more ( I up), decrease its fiscal balance ( T – G down), or some combination of 
these. Increasing tax receipts ( T up) increases rather than decreases the fiscal 
balance, so answer A is incorrect. Similarly, answer C, increasing the government 
budget surplus, is incorrect. Increasing private investment ( I up) does decrease

the trade balance, so answer B is correct.
B is correct. As Australian exports become more dominated by luxury goods 
that face highly competitive market conditions, the elasticity of export demand 
(εX) is likely to be increasing. Increasing export elasticity makes the trade 
23 Because ωM = 1 – ωX and εM < 1 in this example, a decrease in ωX also decreases the second terms, 
ωM(εM – 1), in the Marshall–Lerner condition.

Summary 451
surplus more responsive to an AUD appreciation (the increase in εX will tend 
to increase the computed value for the Marshall–Lerner equation). Similarly, 
as Australian imports become more dominated by luxury goods that are an 
increasing proportion of household expenditure, import elasticity (εM) will 
most likely increase. This will also tend to increase the computed value for the 
Marshall–Lerner equation. 
B is correct. A trade deficit (surplus) must be exactly matched by an offsetting 
capital account surplus (deficit). Anything that impacts the trade balance must 
impact the capital account, and vice versa. If capital flows are prohibited, then 
both the capital account and the trade balance must be zero.
A is correct. The trade balance must go to zero. An increase in the fiscal balance 
implies an increase in the existing trade surplus, so answer C is incorrect. A 
decrease in private investment will also cause an increase in the trade surplus,

so answer B is incorrect. A decrease in private saving will decrease the trade 
surplus as required, so answer A is correct: A decrease in saving will most likely 
reflect a decline in national income, especially the profit component, as export 
demand is choked off by the inability to extend credit to foreigners.
SUMMARY
Foreign exchange markets are crucial for understanding both the functioning of the 
global economy as well as the performance of investment portfolios. In this reading, 
we have described the diverse array of FX market participants and have introduced 
some of the basic concepts necessary to understand the structure and functions of 
these markets. The reader should be able to understand how exchange rates—both spot 
and forward—are quoted and be able to calculate cross exchange rates and forward 
rates. We also have described the array of exchange rate regimes that characterize 
foreign exchange markets globally and how these regimes determine the flexibility of

exchange rates, and hence, the degree of foreign exchange rate risk that international 
investments are exposed to. Finally, we have discussed how movements in exchange 
rates affect international trade flows (imports and exports) and capital flows.
The following points, among others, are made in this reading:
■■Measured by average daily turnover, the foreign exchange market is by far the 
largest financial market in the world. It has important effects, either directly or 
indirectly, on the pricing and flows in all other financial markets.
■■There is a wide diversity of global FX market participants that have a wide vari -
ety of motives for entering into foreign exchange transactions.
■■Individual currencies are usually referred to by standardized three-  character 
codes. These currency codes can also be used to define exchange rates (the 
price of one currency in terms of another). There are a variety of exchange rate 
quoting conventions commonly used.

■■A direct currency quote takes the domestic currency as the price currency and 
the foreign currency as the base currency (i.e., Sd/f). An indirect quote uses the 
domestic currency as the base currency (i.e., Sf/d). To convert between direct

Reading 20 ■ Currency Exchange Rates 452
and indirect quotes, the inverse (reciprocal) is used. Professional FX markets 
use standardized conventions for how the exchange rate for specific currency 
pairs will be quoted.
■■Currencies trade in foreign exchange markets based on nominal exchange rates. 
An increase (decrease) in the exchange rate, quoted in indirect terms, means 
that the domestic currency is appreciating (depreciating) versus the foreign 
currency.
■■The real exchange rate, defined as the nominal exchange rate multiplied by the 
ratio of price levels, measures the relative purchasing power of the currencies. 
An increase in the real exchange rate ( Rd/f) implies a reduction in the relative 
purchasing power of the domestic currency.
■■Given exchange rates for two currency pairs—A/B and A/C—we can compute 
the cross-  rate (B/C) between currencies B and C. Depending on how the rates 
are quoted, this may require inversion of one of the quoted rates.

■■Spot exchange rates are for immediate settlement (typically, T + 2), while for -
ward exchange rates are for settlement at agreed-  upon future dates. Forward 
rates can be used to manage foreign exchange risk exposures or can be com -
bined with spot transactions to create FX swaps.
■■The spot exchange rate, the forward exchange rate, and the domestic and 
foreign interest rates must jointly satisfy an arbitrage relationship that equates 
the investment return on two alternative but equivalent investments. Given 
the spot exchange rate and the foreign and domestic interest rates, the forward 
exchange rate must take the value that prevents riskless arbitrage.
■■Forward rates are typically quoted in terms of forward (or swap) points. The 
swap points are added to the spot exchange rate in order to calculate the for -
ward rate. Occasionally, forward rates are presented in terms of percentages 
relative to the spot rate.

■■The base currency is said to be trading at a forward premium if the forward 
rate is above the spot rate (forward points are positive). Conversely, the base 
currency is said to be trading at a forward discount if the forward rate is below 
the spot rate (forward points are negative).
■■The currency with the higher (lower) interest rate will trade at a forward dis -
count (premium).
■■Swap points are proportional to the spot exchange rate and to the interest rate 
differential and approximately proportional to the term of the forward contract.
■■Empirical studies suggest that forward exchange rates may be unbiased predic -
tors of future spot rates, but the margin of error on such forecasts is too large 
for them to be used in practice as a guide to managing exchange rate exposures. 
FX markets are too complex and too intertwined with other global financial 
markets to be adequately characterized by a single variable, such as the interest 
rate differential.

■■Virtually every exchange rate is managed to some degree by central banks. 
The policy framework that each central bank adopts is called an exchange rate 
regime. These regimes range from using another country’s currency (dollariza -
tion), to letting the market determine the exchange rate (independent float). 
In practice, most regimes fall in between these extremes. The type of exchange 
rate regime used varies widely among countries and over time.
■■An ideal currency regime would have three properties: (1) the exchange rate 
between any two currencies would be credibly fixed; (2) all currencies would be 
fully convertible; and (3) each country would be able to undertake fully inde -
pendent monetary policy in pursuit of domestic objectives, such as growth and

Summary 453
inflation targets. However, these conditions are inconsistent. In particular, a 
fixed exchange rate and unfettered capital flows severely limit a country’s ability 
to undertake independent monetary policy. Hence, there cannot be an ideal 
currency regime.
■■The IMF identifies the following types of regimes: arrangements with no sepa -
rate legal tender (dollarization, monetary union), currency board, fixed parity, 
target zone, crawling peg, crawling band, managed float, and independent float. 
Most major currencies traded in FX markets are freely floating, albeit subject to 
occasional central bank intervention.
■■A trade surplus (deficit) must be matched by a corresponding deficit (surplus) 
in the capital account. Any factor that affects the trade balance must have an 
equal and opposite impact on the capital account, and vice versa.
■■A trade surplus reflects an excess of domestic saving (including the govern -

ment fiscal balance) over investment spending. A trade deficit indicates that the 
country invests more than it saves and must finance the excess by borrowing 
from foreigners or selling assets to foreigners.
■■The impact of the exchange rate on trade and capital flows can be analyzed 
from two perspectives. The elasticities approach focuses on the effect of chang -
ing the relative price of domestic and foreign goods. This approach highlights 
changes in the composition of spending. The absorption approach focuses on 
the impact of exchange rates on aggregate expenditure/saving decisions.
■■The elasticities approach leads to the Marshall–Lerner condition, which 
describes combinations of export and import demand elasticities such that 
depreciation (appreciation) of the domestic currency will move the trade bal -
ance toward surplus (deficit).
■■The idea underlying the Marshall–Lerner condition is that demand for imports

and exports must be sufficiently price-  sensitive so that an increase in the 
relative price of imports increases the difference between export receipts and 
import expenditures.
■■In order to move the trade balance toward surplus (deficit), a change in the 
exchange rate must decrease (increase) domestic expenditure (also called 
absorption) relative to income. Equivalently, it must increase (decrease) domes -
tic saving relative to domestic investment.
■■If there is excess capacity in the economy, then currency depreciation can 
increase output/income by switching demand toward domestically produced 
goods and services. Because some of the additional income will be saved, 
income rises relative to expenditure and the trade balance improves.
■■If the economy is at full employment, then currency depreciation must reduce 
domestic expenditure in order to improve the trade balance. The main mech -
anism is a wealth effect: A weaker currency reduces the purchasing power of

domestic-  currency-  denominated assets (including the present value of current 
and future earned income), and households respond by reducing expenditure 
and increasing saving.

Reading 20 ■ Currency Exchange Rates 454
Bank for International Settlements (BIS). 2010. “Triennial 
Central Bank Survey of Foreign Exchange and Derivatives 
Market Activity in 2010” (www.bis.org).
Friedman, Milton. 1953. “The Monetarist Theory of Flexible 
Exchange Rate Systems. ” In Essays in Positive Economics . 
Chicago: University of Chicago Press.
Hong Kong Monetary Authority (HKMA). 2005. HKMA 
Background Brief No. 1: Hong Kong’s Linked Exchange Rate 
System . 2nd ed. (November): www.info.gov.hk.International Monetary Fund (IMF). 2006. “De Facto 
Classification of Exchange Rate Regimes and Monetary Policy 
Framework” (www.imf.org).
International Monetary Fund (IMF). 2010. “Currency 
Composition of Official Foreign Exchange Reserves (COFER)” 
report (www.imf.org).

Practice Problems 455
1 An exchange rate:
A is most commonly quoted in real terms.
B is the price of one currency in terms of another.
C between two currencies ensures they are fully convertible.
2 A decrease in the real exchange rate (quoted in terms of domestic currency 
per unit of foreign currency) is most likely  to be associated with an increase in 
A Foreign price level.
B Domestic price level.
C Nominal exchange rate.
3 In order to minimize the foreign exchange exposure on a euro-  denominated 
receivable due from a German company in 100 days, a British company would 
most likely  initiate a:
A spot transaction.
B forward contract.
C real exchange rate contract.
4 Which of the following counterparties is most likely  to be considered a sell-  side 
foreign-  exchange market participant?
A A large corporation that borrows in foreign currencies.
B A sovereign wealth fund that influences cross-  border capital flows.

C A multinational bank that trades foreign exchange with its diverse client 
base.
5 What will be the effect on a direct exchange rate quote if the domestic currency 
appreciates?
A Increase
B Decrease
C No change
6 An executive from Switzerland checked into a hotel room in Spain and was 
told by the hotel manager that 1 EUR will buy 1.2983 CHF. From the executive’s 
perspective, an indirect exchange rate quote would be:
A 0.7702 EUR per CHF.
B 0.7702 CHF per EUR.
C 1.2983 EUR per CHF.
7 Over the past month, the Swiss Franc (CHF) has depreciated 12 percent against 
pound sterling (GBP). How much has the pound sterling appreciated against the 
Swiss Franc?
A 12%
B Less than 12%
C More than 12%
8 An exchange rate between two currencies has increased to 1.4500. If the base 
currency has appreciated by 8% against the price currency, the initial exchange 
rate between the two currencies was closest  to:

Reading 20 ■ Currency Exchange Rates 456
A 1.3340.
B 1.3426.
C 1.5660.
9–10
A dealer provides the following quotes:
Ratio Spot rate
CNY/HKD 0.8422
CNY/ZAR 0.9149
CNY/SEK 1.0218
9 The spot ZAR/HKD cross-  rate is closest  to:
A 0.9205.
B 1.0864.
C 1.2978.
10 Another dealer is quoting the ZAR/SEK cross-  rate at 1.1210. The arbitrage 
profit that can be earned is closest  to:
A ZAR 3671 per million SEK traded.
B SEK 4200 per million ZAR traded.
C ZAR 4200 per million SEK traded.
11 A BRL/MXN spot rate is listed by a dealer at 0.1378. The 6-  month forward rate 
is 0.14193. The 6-  month forward points are closest  to:
A –41.3.
B +41.3.
C +299.7.
12 A three-  month forward exchange rate in CAD/USD is listed by a dealer at 
1.0123. The dealer also quotes 3-  month forward points as a percentage at 6.8%. 
The CAD/USD spot rate is closest  to:
A 0.9478.
B 1.0550.
C 1.0862.
13 If the base currency in a forward exchange rate quote is trading at a forward

discount, which of the following statements is most  accurate?
A The forward points will be positive.
B The forward percentage will be negative.
C The base currency is expected to appreciate versus the price currency.
14 A forward premium indicates:
A an expected increase in demand for the base currency.
B the interest rate is higher in the base currency than in the price currency.
C the interest rate is higher in the price currency than in the base currency.

Practice Problems 457
15 The JPY/AUD spot exchange rate is 82.42, the JPY interest rate is 0.15%, and the 
AUD interest rate is 4.95%. If the interest rates are quoted on the basis of a 360-  
day year, the 90-  day forward points in JPY/AUD would be closest  to:
A –377.0.
B –97.7.
C 98.9.
16 Which of the following is not a condition of an ideal currency regime?
A Fully convertible currencies.
B Fully independent monetary policy.
C Independently floating exchange rates.
17 In practice, both a fixed parity regime and a target zone regime allow the 
exchange rate to float within a band around the parity level. The most likely  
rationale for the band is that the band allows the monetary authority to:
A be less active in the currency market.
B earn a spread on its currency transactions.
C exercise more discretion in monetary policy.
18 A fixed exchange rate regime in which the monetary authority is legally 
required to hold foreign exchange reserves backing 100% of its domestic cur -

rency issuance is best described as:
A dollarization.
B a currency board.
C a monetary union.
19 A country with a trade deficit will most likely :
A have an offsetting capital account surplus.
B save enough to fund its investment spending.
C buy assets from foreigners to fund the imbalance.
20 A large industrialized country has recently devalued its currency in an attempt 
to correct a persistent trade deficit. Which of the following domestic industries 
is most likely  to benefit from the devaluation?
A Luxury cars.
B Branded prescription drugs.
C Restaurants and live entertainment venues.
21 A country with a persistent trade surplus is being pressured to let its currency 
appreciate. Which of the following best describes the adjustment that must 
occur if currency appreciation is to be effective in reducing the trade surplus?
A Domestic investment must decline relative to saving.
B Foreigners must increase investment relative to saving.
C Global capital flows must shift toward the domestic market.

Reading 20 ■ Currency Exchange Rates 458
SOLUTIONS
1 B is correct. The exchange rate is the number of units of the price currency that 
1 unit of the base currency will buy. Equivalently, it is the number of units of 
the price currency required to buy 1 unit of the base currency.
2 B is correct. The real exchange rate (quoted in terms of domestic currency per 
unit of foreign currency) is given by:
Real exchange rate(d/f) = Sd/f × (Pf/Pd)
 An increase in the domestic price level ( Pd) decreases  the real exchange rate 
because it implies an increase  in the relative purchasing power of the domestic 
currency.
3 B is correct. The receivable is due in 100 days. To reduce the risk of currency 
exposure, the British company would initiate a forward contract to sell euros/
buy pounds at an exchange rate agreed to today. The agreed-  upon rate is called 
the forward exchange rate.
4 C is correct. The sell side generally consists of large banks that sell foreign

exchange and related instruments to buy-  side clients. These banks act as market 
makers, quoting exchange rates at which they will buy (the bid price) or sell (the 
offer price) the base currency.
5 B is correct. In the case of a direct exchange rate, the domestic currency is the 
price currency (the numerator) and the foreign currency is the base currency 
(the denominator). If the domestic currency appreciates, then fewer units of the 
domestic currency are required to buy 1 unit of the foreign currency and the 
exchange rate (domestic per foreign) declines. For example, if sterling (GBP) 
appreciates against the euro (EUR), then euro–sterling (GBP/EUR) might 
decline from 0.8650 to 0.8590.
6 A is correct. An indirect quote takes the foreign country as the price currency 
and the domestic country as the base currency. To get CHF—which is the exec -
utive’s domestic currency—as the base currency, the quote must be stated as

EUR/CHF. Using the hotel manager’s information, the indirect exchange rate is 
(1/1.2983) = 0.7702.
7 C is correct. The appreciation of sterling against the Swiss franc is simply the 
inverse of the 12% depreciation of the Swiss franc against Sterling: [1/(1 – 0.12)] 
– 1 = (1/0.88) – 1 = 0.1364, or 13.64%.
8 B is correct. The percentage appreciation of the base currency can be calculated 
by dividing the appreciated exchange rate by the initial exchange rate. In this 
case, the unknown is the initial exchange rate. The initial exchange is the value 
of X that satisfies the formula:
1.4500/ X = 1.08
 Solving for X leads to 1.45/1.08 = 1.3426.
9 A is correct. To get to the ZAR/HKD cross-  rate, it is necessary to take the 
inverse of the CNY/ZAR spot rate and then multiply by the CNY/HKD 
ZAR/HKD CNY/ ZARC NY/HKD =
==() ×()
() ×−1
109149 0 8422 0 9205/. ..

Solutions 459
10 C is correct. The ZAR/SEK cross-  rate from the original dealer is (1.0218/0.9149) 
= 1.1168, which is lower than the quote from the second dealer. To earn an 
arbitrage profit, a currency trader would buy SEK (sell ZAR) from the original 
dealer and sell SEK (buy ZAR) to the second dealer. On 1 million SEK the profit 
would be
SEK 1,000,000 × (1.1210 – 1.1168) = ZAR 4200  
11 B is correct. The number of forward points equals the forward rate minus 
the spot rate, or 0.14193 – 0.1378 = 0.00413, multiplied by 10,000: 10,000 × 
0.00413= 41.3 points. By convention, forward points are scaled so that ±1 for -
ward point corresponds to a change of ±1 in the last decimal place of the spot 
exchange rate.
12 A is correct. Given the forward rate and forward points as a percentage, the 
unknown in the calculation is the spot rate. The calculation is as follows:
Spot rate × (1 + Forward points as a percentage) = Forward rate
Spot rate × (1 + 0.068) = 1.0123
Spot = 1.0123/1.068 =0.9478

13 B is correct. The base currency trading at a forward discount means that 1 
unit of the base currency costs less for forward delivery than for spot delivery; 
i.e., the forward exchange rate is less than the spot exchange rate. The forward 
points, expressed either as an absolute number of points or as a percentage, are 
negative.
14 C is correct. To eliminate arbitrage opportunities, the spot exchange rate ( S), 
the forward exchange rate ( F), the interest rate in the base currency ( ib), and the 
interest rate in the price currency ( ip) must satisfy:
F
Si
ip
b=+
+

1
1
 According to this formula, the base currency will trade at forward premium 
(F > S) if, and only if, the interest rate in the price currency is higher than the 
interest rate in the base currency ( ip > ib).
15 B is correct. The forward exchange rate is given by
FSi
iJPYAUD JPYAUDJPY
AUD=+
+

=+

 1
182 421 001590
360 τ
τ..  
+










=× =1 049590
360
82 42 98815 81 443.
.. .









360
.. .
 The forward points are 100 × ( F – S) = 100 × (81.443 – 82.42) = 100 × (–0.977) 
= –97.7. Note that because the spot exchange rate is quoted with two decimal 
places, the forward points are scaled by 100.
16 C is correct. An ideal currency regime would have credibly fixed exchange rates 
among all currencies. This would eliminate currency-  related uncertainty with 
respect to the prices of goods and services as well as real and financial assets.
17 C is correct. Fixed exchange rates impose severe limitations on the exercise 
of independent monetary policy. With a rigidly fixed exchange rate, domestic 
interest rates, monetary aggregates (e.g., money supply), and credit conditions 
are dictated by the requirement to buy/sell the currency at the rigid parity. Even

Reading 20 ■ Currency Exchange Rates 460
a narrow band around the parity level allows the monetary authority to exer -
cise some discretionary control over these conditions. In general, the wider the 
band, the more independent control the monetary authority can exercise.
18 B is correct. With a currency board, the monetary authority is legally required 
to exchange domestic currency for a specified foreign currency at a fixed 
exchange rate. It cannot issue domestic currency without receiving foreign 
currency in exchange, and it must hold that foreign currency as a 100% reserve 
against the domestic currency issued. Thus, the country’s monetary base (bank 
reserves plus notes and coins in circulation) is fully backed by foreign exchange 
reserves.
19 A is correct. A trade deficit must be exactly matched by an offsetting capital 
account surplus to fund the deficit. A capital account surplus reflects borrow -
ing from foreigners (an increase in domestic liabilities) and/or selling assets to

foreigners (a decrease in domestic assets). A capital account surplus is often 
referred to as a “capital inflow” because the net effect is foreign investment in 
the domestic economy.
20 A is correct. A devaluation of the domestic currency means domestic producers 
are cutting the price faced by their foreign customers. The impact on their unit 
sales and their revenue depends on the elasticity of demand. Expensive luxury 
goods exhibit high price elasticity. Hence, luxury car producers are likely to 
experience a sharp increase in sales and revenue due to the devaluation.
21 C is correct. The trade surplus cannot decline unless the capital account deficit 
also declines. Regardless of the mix of assets bought and sold, foreigners must 
buy more assets from (or sell fewer assets to) domestic issuers/investors.

Index I-1
A
absolute advantage, 347–354
absorption approach to trade balance, 
449–450
accounting costs, 28
accounting profit, 28
accounts
balance of payments, 370–371, 377–379
in FX market, 412–413
action lag, 318
active crawling peg currency regime, 
439–440
activity ratio, 222
AD. see aggregate demand
AD curve. see aggregate demand curve
administrative costs, 368
advanced economies, trade-to-GDP 
ratio for, 340
AFC. see average fixed cost
Africa, terms of trade for, 337, 338. see 
also specific countries and regions
African Development Bank, 413
aggregate demand (AD), 137–148
and AD curve, 145–148
and business cycle, 204–205
defined, 136
and fiscal policy, 302–303
and global recession (2007-2009), 
165–167
and imports/exports, 338–339
and inflationary gap, 167–168
investment strategies for decrease in, 
164–165
investment strategies for increase in, 168
IS curve, 137–144
LM curve, 144–145
and recessionary gap, 163–167
shifts in, 150–157
capacity utilization, 153
consumer and business expectations, 
153
economic growth, 155

153
exchange rate, 155
fiscal policy, 153
household wealth, 151–152
monetary policy, 153–154
shifts in supply and, 170–173
aggregate demand curve (AD curve)
example, 147–148
features of, 145
interest rates and income effects, 
146–147
investment strategies based on, 171–172
aggregate expenditures, 119
aggregate income, 119–136
in economy, 119–120
and expenditures, 137–144
in gross domestic product, 120–136
components of, 127–131
external sector, 130–131
government sector, 129–130
household and business sectors, 128measuring, 120–123
nominal and real, 124–127
and other income measures, 131–136
values of goods and services, 123–124
real personal, 241
aggregate output, 119–136
household and business sectors, 128
measuring, 120–123
aggregate price, supply of money and, 
273–274

273–274
aggregate real personal income, 241
aggregate supply (AS)
and AS curve, 148–150
and global recession, 165–167
investment strategies for shifts in, 
169–170
long-run, 148–150, 159–161
in perfectly competitive market, 81
in real business cycle models, 218–219
shifts in, 150–151, 157–162
shifts in demand and, 170–173
short-run, 148–149, 157–158
and stagflation, 169–170
aggregate supply curve (AS curve)
about, 148–150
long-run, 148–150
agriculture industry, 68–69
AirTran Airways, 88
air transportation industry, 66
Algeria, 437
Amtrak, 104
Antigua, 436
antitrust policies, 92, 105–106
APC. see average propensity to consume
APL. see average product of labor
Apple, 344
appreciation, currency, 420
AR. see average revenue
arbitrage, triangular, 423
Archer Daniels Midland, 105
Argentina
exchange rate regime, 436, 439–440
foreign direct investment, 341, 342
MERCOSUR, 362

AS. see aggregate supply
AS curve. see aggregate supply curve
ASEAN. see Association of Southeast 
Asian Nations
Asia. see also  specific countries and regions
current account imbalance, 380effects of global recession, 165
financial crisis (1997-1998), 294, 343
natural resources, 178
terms of trade, 337
trade-to-GDP ratio, 340
asset prices, capital flows and, 444
Association of Southeast Asian Nations 
(ASEAN), 88
assumptions, Cournot, 90–91
ATC. see average total cost
AT&T, 105
Aussie exchange rate, 418
Australia
business investment, 177
current account imbalance, 380
cyclically adjusted budget deficit, 317
disinflation, 227
exchange rate regime, 437
export subsidies, 359
government liabilities/debt, 308
government revenues/expenditures, 
303, 304
inflation targeting, 287, 289
net borrowing/lending, 305
Australian dollar, 401
AUD/HKD exchange rate, 404–406, 
410–412
exchange rate quotes with, 418, 419n.4
trade balance and exchange rate for,

trade balance and exchange rate for, 
450–453
USD/AUD currency pair, 416
Australian Federal Reserve, 289
Austria
EU membership, 362n.18
exchange rate regime, 436
government debt, 262
public sector spending, 263
Austrian school of economic thought, 214
autarkic price, 338, 349
autarky, 338, 349
automatic stabilizers, 140, 304, 317–318
automobile industry, 86, 100, 122–123
AVC. see average variable cost
average bank prime lending rate, 241
Average Consumer Expectations for 
Business and Economic Conditions, 
241
average costs
average fixed cost, 31–35
average total cost
with economies of scale, 45–46
and other costs/output, 31–35
in perfect competition vs. monopoly, 
36–37
average variable cost
defined, 30
36–37
and shutdown decision, 39–40
in perfectly competitive markets, 
36–37, 79–80

I-2 Index
Average Duration of Unemployment, 241
average fixed cost (AFC), 31–35
average product of labor (AP L), 25–28
average propensity to consume (APC), 
139
average revenue (AR), 35
average total cost (ATC)
36–37
average variable cost (AVC)
36–37
average weekly claims for 
unemployment insurance, 240
average weekly hours, manufacturing, 240
Azerbaijan, 436
B
Bahamas, 295
Baker, James, 440
balanced budget multipliers, 315–316
balanced budgets, 304
balance of payments (BOP) system, 
369–381
accounts in, 370–371, 377–379
components of, 371–373
imbalances since 1996, 379–381
paired transactions in, 374–376
for United States, 372–373
balance of trade deficit, 130, 338
Bank for International Settlements, 
415–416
Banking and Finance Commission, 278
Bank of Canada, 185, 289, 440
Bank of England
in FX market, 440
independence of, 288

monetary policy, 276, 279, 289
quantitative easing, 298–299, 323
two-week repo rate, 284
Bank of Italy, 245, 278
Bank of Japan
in FX market, 413, 440
monetary policy, 292, 299–301
and money measures in Japan, 270
Bank of Korea, 281, 289
Bank of Netherlands, 279
banks
aggregate demand and reserves of, 
153–155
in FX market, 414–415
Barbados, 294
barriers to entry, market structure and, 
67, 97
barter economy, 123, 265
base currency, 401, 418
base rates, 284
BASF, 105
beer industry, 87, 88
behavior
consumer, 208–210
external trade sector, 211–213
housing sector, 210–211
“Beige Book, ” 244
Belarus, 436Belgium
banking supervision, 278
customs union, 362
in EU, 362n.18
Belize, 295
Bernanke, Ben, 298
biases, price index, 228
Big Mac index, 402
BLS. see US Bureau of Labor Statistics
BMW, 86
Bolivia, 436
bond market vigilantes, 297–298
boom phase (business cycle), 203, 205
BOP system. see balance of payments 
system

system
Bosnia and Herzegovina, 436
BP/Amoco/Arco, 107
brand loyalty, 84, 98
Brazil
absolute and comparative advantage, 
347–348
effects of Asian financial crisis, 343
exchange rate regimes, 439
GDP vs. GNP , 337
inflation targeting, 287
as small country, 356
Brazilian real, 401
breakeven analysis
and breakeven point of production, 
36–37
in shutdown analysis, 38–41
breakeven point, 36–40
Bretton Woods system, 434
British pound, 401
EUR/GBP exchange rate, 418, 419n.4
exchange rate quotes with, 418–420
GBP/EUR exchange rate, 403, 408
gold standard for, 434
USD/GBP currency pair, 416
broad measure of liquidity, 270
broad money, 269
budget constraints, price elasticity of 
demand and, 71
budget deficit (fiscal deficit), 304
and business cycles, 129
and fiscal policy, 317–318
and foreign capital, 138
and national debt, 307–309
and Ricardian equivalence, 316
budget surplus, 304
building permits, 240, 243
Bulgaria, 436

Burns, Wesley Clair, 200
business confidence, 153, 155
Business Cycle and Dating Committee, 203
business cycles, 199–258
defined, 200
economic indicators, 239–246
building permits as, 243
cyclical measures as, 244–245
diffusion index of, 244
leading, lagging, and coincident, 
239–243and external trade sector behavior, 
211–213
and GDP , 150
and housing sector behavior, 210–211
inflation, 225–239
cost-push, 233–235
deflation, hyperinflation, disinflation, 
226–227
demand-pull, 235–236
expectations, 236–237
price indexes, 227–233
types of, 233–236
phases of, 200–204
practice problems, 249–254
resource use, 204–210
capital spending, 205–207
consumer behavior, 208–210
inventory levels, 207–208
as short-term movements in economy, 
199–200
solutions to problems, 255–258
unemployment, 221–225
analyzing, 224–225
indicators, 224
rate of, 223–224
business cycle theories, 213–221
Austrian school, 214
Keynesian school, 214–215
Monetarist school, 217
Neoclassical school, 213–214

New Classical school, 217–221
business expectations, aggregate demand 
and, 153
business sector, in GDP , 128
business spending, 153, 202
business taxes, SRAS and, 158, 160
buyers. see consumer(s)
buy-side participants, FX market, 
412–414
C
Caisse de dépôt et placement du 
Québec, 413
Cambodia, 437
Canada
consumption expenditures, 139
expected inflation, 282
in FX market, 413
government spending, 129
gross domestic product, 121, 131–136
forecasts of, 184–185
GNP vs., 337
potential, 183, 184
labor productivity, 181
NAFTA, 362
national debt, 309
trade balance with US, 130, 131
underground economy, 124
Canada–yen exchange rate, 419, 
422–423
Canadian dollar, 401
CAD/USD currency pair, 416
in cross-rate calculations, 421–422
exchange rate quotes with, 419

Index  I-3
capacity utilization, aggregate demand 
and, 153, 155
capital
as factor of production, 24
financial
in Heckscher–Ohlin model, 354–355
and international trade, 336
in long-term economic growth, 175
human, 159, 176
physical
aggregate supply, 160
defined, 139
and economic growth, 176–177
and labor productivity, 180
and long-term aggregate supply, 159
capital account, BOP , 372, 444
capital consumption allowance (CCA), 
133
capital deepening investments, 175
capital expenditures, fiscal policy and, 
311
capital flows
and international trade, 356–369
and trade balance, 443–445
capital goods, 128
capital markets, 383, 406–407
capital restrictions, 356, 366–369
capital spending
cyclical use of resources, 205–207
and fiscal policy, 314
capital stock, 176–177
capital-to-labor ratio, 175
capital transfers sub-account, BOP , 372
Carnegie, Andrew, 96
cartels, 93, 96
cash flows, government, 303–306
CBS. see currency board system
CCA. see capital consumption 
allowance
Central African Republic, 364
Central Bank of Brazil, 280

central banks, 281
countercyclical policies of, 202
credibility of, 288–289
currency purchases by foreign, 
375–376
exchange rate regime switching by, 440
in FX market, 413–414
independence of, 288, 322
and inflation, 168, 226, 287–293
monetary policy by, 263n.1, 279
monetary transmission mechanism of, 
285–287, 297–298
objectives of, 280–281
policy rate of, 284
price index use by, 230
reserve requirements of, 268, 284–285
roles and responsibilities of, 277–280
transparency of, 289
Central Europe. see also  specific 
countries
Centre for Economic Policy Research 
(CEPR), 245
CFNAI. see Chicago Fed National 
Activity Index
Chamberlin, Edward H., 65
Chevron/Texaco, 107Chicago Fed National Activity Index 
(CFNAI), 244
Chicago Mercantile Exchange (CME), 
408
Chile, 287, 437, 439–440
China
capital goods expenditures, 128
central bank reserves, 413
comparative advantage, 347–348, 352
CPI, 229
current account, 377, 380

CPI, 229
economic growth, 179
economic indicators, 244
effects of global recession, 166
exchange rate regime, 436, 437, 441
exports from, 337, 342, 354
GDP , 121, 155
globalization of production, 342
housing sector, 211
labor supply, 176
Multi Fiber Agreement, 345
reserve requirements, 285
Chinese yuan, 401
CNY/USD exchange rate, 403–404
Citigroup, 412, 414
classical gold standard, 434
CLI. see Composite Leading Indicators
closed economy, 338, 377–378
CME. see Chicago Mercantile  
Exchange
Coca-Cola, 65, 71, 447, 448
coincident economic indicators,  
239, 241
Colombia, 287, 437
commercial loans, 241
Commission Bancaire, 278
common markets, 362–366
Commonwealth of Independent States, 
340
comparative advantage, 347–355
absolute advantage vs., 347–354
defined, 336n.1
Ricardian and Heckscher–Ohlin 
models, 354–355
as form of payment, 119
in GDP , 133
competition
imperfect
breakeven analysis, 40–41
marginal revenue, 29–30

revenue in perfect competition vs., 
35–36
monopolistic, 83–87
benefits of, 343–344
characteristics of, 67
defined, 65
demand analysis, 84–85
long-run equilibrium, 86–87
optimal price and output, 85
supply analysis, 85
non-price, 67
perfect, 68–83
breakeven point for firm, 38–39
defined, 65demand, average, and marginal costs, 
36–37
demand analysis, 69–76
and innovation, 83
long-run equilibrium, 81–82
and oligopoly, 96
optimal price, 77–81
output optimization, 77–81
revenue in imperfect competition vs., 
35–36
shutdown decision, 39–40
supply analysis, 76–77
and price collusion, 93
Competitive Strategy  (Porter), 68
complements
defined, 15
elasticity of demand and, 73
identifying, 16
Composite Leading Indicators (CLI), 239
concentration ratio, 106–108
Conference Board, 239, 240, 244
confidence, business and consumer, 153, 
155
consumer(s)
behavior of, 208–210
demand and supply analysis, 6–23
demand concepts, 6–8

elasticity of demand, 9–18
substitution and income effects, 
18–23
expectations of, 153
in microeconomics, 5
theory of the consumer, 5
consumer confidence, 153, 155
consumer installment debt, income and, 
242
consumer price index (CPI), 229, 230, 
242
consumer spending
and business cycles, 208–210
and expectations, 153
in phases of business cycle, 202
consumer surplus
and alternative trade policies, 357, 360
in monopoly, 102–104
in perfect competition, 74–76
and tariffs, 357
consumption
and aggregate demand, 138–139
and alternative trade policies, 360
in autarky, 349
average propensity to consume, 139
marginal propensity to consume, 139, 
314–316
wealth effect on, 152
consumption bundle (consumption 
basket), 227–229
consumption spending, 138–139
contractionary fiscal policy, 304, 317
contractionary monetary policy, 
296–297
contraction phase (business cycle), 
200–204. see also  recession
control, market structure and, 66–67
convergence, income, 175
copyright laws, 97
core inflation, 230–231

corporate accounts, in FX market, 412

I-4 Index
Costa Rica
exports from, 342
government spending, 130
cost function, 24
cost-push inflation, 233–235
costs
accounting, 28
administrative, 368
average, 36–37
average fixed, 31–35
average total, 31–37, 45–46
average variable, 30, 36–37, 39–40
economic, 28, 38, 77
fixed, 31–35, 41–42
of inflation, 281–283
of international trade, 343–347
labor, 158–160
long-run average, 102
long-run marginal, 102
marginal
and marginal revenue/profit 
maximization, 29–30
in monopolies, 36–37, 102
in perfect competition, 36–37
menu, 219–220, 282
opportunity, 24, 77
and output, 31–35
and production, 23–25
quasi-fixed, 33
shoe leather, 282
sunk, 28
total, 24, 31–35
total fixed, 31–35, 41–42
total variable, 31–35, 41–42
unit labor, 234, 241
variable, 30–35
cost structures
in monopolies, 99–100
countervailing duties, 359
Cournot, Augustin, 90
Cournot assumption, 90–91
Cournot equilibrium, 91, 93, 94
CPI. see consumer price index

CPI-U, 229, 230
crawling band currency regimes, 436, 
440
crawling peg currency regimes, 436, 
439–440
creative destruction theory,  
213–214
credibility
of central banks, 288–289
of monetary and fiscal policy  
mix, 323
credit crisis (2008), 303, 307, 308
credits, BOP system, 370–371
Croatia, 436
cross-price elasticity of demand
for consumers, 15–18
in perfect competition, 73
cross-rates, currency, 419, 421–425
cross-sectional regression analysis,  
106
crowding out, 309currency
in business cycles, 212
foreign central bank purchases of, 
375–376
FX conventions for, 401–402
currency board system (CBS), 436, 
438–439
currency codes, FX market, 401
currency exchange rates, 399–462
calculations, 418–432
cross-rate, 421–425
and exchange rate quotations, 
418–421
forward, 425–432
currency regimes, 432–443
active and passive crawling pegs, 
439–440
arrangements with no separate legal 
tender, 437–438
CBS, 438–439
fixed parity, 439
fixed parity with crawling bands, 440
free-floating, 440–441

historical perspective on, 434–436
ideal, 433
managed float, 440
target zone, 439
taxonomy of, 436–443
foreign exchange market, 399–418
about, 399–400
currency conventions, 401–402
functions, 406–412
nominal vs. real exchange rates, 
402–406
participants in, 412–415
size and composition of, 415–418
and international trade, 443–453
449–450
elasticities approach to trade balance, 
445–449
practice problems, 457–459
quotations, 418–421
solutions to problems, 460–462
currency quotes, 418–421
with crawling bands/pegs, 439–440
ideal, 433
currency reserves
foreign, 279, 294
requirements, 267, 268, 284–285, 367
current account, BOP , 371, 377–381
current government spending, 311
customers, segregation of, 103
cyclical companies, 165

cyclical economic indicators,  
244–245
Cyprus, 362n.18, 436
Czech Republic, 287D
deadweight loss, 356, 357
De Beers Consolidated Mines Limited, 97
debits, BOP system, 370–371
debt
government, 262, 316
national, 307–309
ratio of consumer installment debt to 
income, 242
debt burden, 308
decreasing returns to scale, 46
defensive companies, 165
deficit
budget (fiscal), 304
in current account, 377–381
trade, 130, 338
deflation
defined, 226
and inflation targeting, 290
and liquidity traps, 298
and quantitative easing, 298–299
Delta Air Lines, 88
demand
aggregate ( see aggregate demand [AD])
concepts, 6–8
derived, 355
elastic, 10, 12–14, 71
elasticity of demand, 8–18
calculating, from demand function, 
16–18
cross-price elasticity of demand, 15–18
defined, 8
income elasticity of demand, 14–16

defined, 8
own-price elasticity of demand, 9–14
excess, 339
inelastic, 10, 11, 13–14, 71
law of demand, 6, 18–19, 21, 75
long-run vs. short-run, 12
for money, 271–274
in monopolistic competition, 84–85
in monopoly, 36–37, 98–99
in oligopoly, 88–94
in perfect competition, 36–37, 69–76
perfectly elastic, 12
perfectly inelastic, 11
under perfect vs. imperfect 
competition, 36
unit elastic, 10
demand and supply analysis, 5–61
consumers, 6–23
substitution and income effects, 18–23
firms, 23–48
marginal returns, 23–28
scale and profit maximization, 43–48
shutdown analysis, 28–43
in microeconomics, 5–6
for money, 272–274
practice problems, 51–57
solutions to problems, 58–61
demand curves
aggregate, 145–148
defined, 8

Index  I-5
effect of income elasticity on, 15
elasticity of linear, 11
kinked, 89–90, 95
and law of demand, 18
of leaders in oligopoly, 95
as marginal value curve, 75
in monopolies, 98–99
negatively sloped, under imperfect 
competition, 40–41
in oligopolies, 88–90, 95
in perfect competition, 77–78
demand functions
defined, 6–7
elasticities from, 16–18
inverse, 8
demand-pull inflation, 233, 235–236
demand schedules, 71–73
demand shock to inflation rate, 297
demographics, housing sector and, 211
Denmark, 436, 441
in absorption approach, 450
currency, 420
and economic vs. accounting costs, 28
in elasticities approach, 445–449
depressions, 201
derived demand, 355
Detroit “Big Three” automakers, 100
Deutsche Bank, 412, 414
Deutsche Bundesbank, 278, 435
developed countries
business investment by, 177
foreign exchange reserves, 414
international trade and unemployment, 
344
developing countries
exchange rate targeting, 293–296

monetary policy of, 292–293
terms of trade for, 337–338
diffusion index, 242n.a, 244
diminishing marginal productivity, 
174–175
diminishing returns, law of, 79
direct currency quote, 418
direct exchange rate, 418
direct taxes, 311, 314
dirty floating, 440
discount rate, 284
discounts, forward, 425
discouraged worker, 223
discretionary goods, 12
diseconomies of scale, 44–47
disinflation, 226, 227
disposable income
and balance of payments, 378
defined, 209
and MPC, 315
personal, 134
dollar (Australia). see Australian dollar
dollar (Canada). see Canadian dollar
dollar (Hong Kong). see Hong Kong dollar
dollar (New Zealand), 401, 418, 419n.4
dollar (Singapore), 401dollar (United States). see US dollar
dollar–Canada exchange rate, 418, 
421–422
dollarization, 437–438
dollar–yen exchange rate, 418, 422–423
domestic content provisions, 356
double coincidence of wants, 265
Douglas, Roger, 287

downturn, 203–204
capital spending in, 206
housing sector in, 210
inventory–sales ratio in, 207
resource use in, 204–206
duopoly markets, 90–93
DuPont, 73
durable goods, 209
Duracell, 64
E
early expansion phase (business cycle), 
201–203
East Asian Financial Crisis (1990s), 384
Eastern Europe. see also  specific 
countries
East Timor, 437
easy fiscal policy, 321
easy monetary policy, 321
eBay, 98
ECB. see European Central Bank
econometric approach, in market 
structure identification, 106
economic activity, in business cycle, 
200–202
economic costs, 28, 38, 77
Economic Cycle Research Institute 
(ECRI), 239
economic depreciation. see depreciation
economic growth, 173–185
and aggregate demand, 155
in China, 179
in Mexico, 182
production function and potential 
GDP , 174–175
and real GDP , 173
RTAs and spillovers of, 364
sources of, 176–179
sustainable, 173, 179–185
and trade, 340–341
defined, 239

239–243
economic loss, 40
economic moat, 68
economic profit, 28, 29, 77, 85, 86
economics, 5
economic sectors
external trade, 130–131, 211–213
financial, 383
in GDP , 127–131
government, 129–130
household, 119–120, 128
housing, 210–211
information technology, 178
public sector spending, 263Economic sentiment index, 242
economic stabilization, fiscal policy and, 
304
economic unions, 362–366
economies of scale
from international trade, 343, 344
and monopolies, 97
for profit maximization, 44–47
economy
aggregate output and income in, 
119–120
barter, 123, 265
business cycles as short-term 
movements, 199–200
closed, 338, 377–378
and government debt, 262
IMF monitoring of, 382
influence of fiscal and monetary policy 
on, 262–264
open, 338, 343, 377, 378
underground, 123–124
ECRI. see Economic Cycle Research 
Institute
Ecuador, 436, 437
education, human capital and, 176
efficiency, of tax policy, 311

EFSF. see European Financial Stability 
Facility
Egypt, 437
elastic demand, 10, 12–14, 71
445–449
elasticity(-ies)
defined, 9
of demand, 8–18
and budget constraints, 71
16–18
cross-price, 15–18, 73
defined, 8
income, 14–16, 72–73
in oligopolies, 88
own-price, 9–14
in perfect competition, 70–74
and trade balance, 445–449
of linear demand curve, 11
of supply, 8
electric utilities, 66, 97
El Salvador, 436, 437
employed (term), 222
employees on non-agricultural payrolls, 
241
employment, business cycle and, 202, 
204–205
EMU. see European Economic and 
Monetary Union
endogeneity, problem of, 106
Energizer, 64
entry fee, 104
equilibrium
Cournot, 91, 93, 94
long-run
macroeconomic, 163
in monopolistic competition, 86–87
in monopoly, 104–105
in oligopoly, 96
in perfect competition, 81–82
in money market, 144–145
Nash, 92–93, 96

I-6 Index
equilibrium GDP , 163–173
inflationary gap, 167–168
long-run equilibrium, 163
recessionary gap, 163–167
stagflation, 169–170
equilibrium prices
for money, 272–273
77–78
ERM. see European Exchange Rate 
Mechanism
Essay on the Principle of Population  
(Malthus), 174
Estonia, 362n.18
Ethiopia, 166
euro, 401, 435–436
cross-rate calculations with, 421–422
as currency anchor, 436
EUR/GBP exchange rates, 418, 419n.4
forward calculations with, 425–426
intervention in FX market to support, 
440
USD/EUR currency pair, 416
USD/EUR exchange rate, 409
euro–Canada exchange rate, 419, 
421–422
Euro–Coin statistic, 245
euro–dollar exchange rate, 421–422, 
425–426
euro exchange rate, 418
Europe. see also  specific countries and 
regions
economic indicators, 245
interest rates, 298n.11
stagflation, 236
terms of trade, 338
trade balance with US, 130–131
European Central Bank (ECB)

CPI used by, 230
and currency regime of EMU, 438
and European Union, 362n.18
intervention in FX market, 440
monetary policy of, 185
money measures of, 270
objectives of, 280
European Commission, 105
European Community
currency regimes, 436
European Economic and Monetary 
Union (EMU), 383–384, 436, 438. 
see also  Eurozone
European Economic Community, 435
European Exchange Rate Mechanism 
(ERM), 294, 435
European Financial Stability Facility 
(EFSF), 366
European Union (EU)
economic indicators for, 239
EFSF of, 366
ERM of, 294
imports in, 337inflation targeting, 289
price index, 230
quotas from, 359
RTAs for, 362
underground economy, 124n.4
Eurostat, 230
euro–Sterling exchange rate, 419
Euro Stoxx Equity, 242
euro–Swiss exchange rate, 419, 420
euro–yen exchange rate, 419
Eurozone
economic indicators, 239, 242
and EU, 362n.18
money measures, 270
Eurozone Manufacturing Purchasing 
Managers Index, 242

Eurozone Service Sector Future Business 
Activity Expectations Index, 242
evaluation
of fiscal policy, 319–320
of monetary policy, 301–302
excess demand, 339
excess supply, 339
exchange, money as medium of, 265
exchange rate quotations, 418–421
exchange rate regimes, 432–443. see also  
currency regimes
exchange rates, 401. see also  currency 
exchange rates
and short-run aggregate supply, 158, 
160
exogenous policy tools, aggregate 
demand and, 140
expansionary fiscal policy, 302–304, 317
expansionary monetary policy, 154, 
296–297
expansion phase (business cycle), 
200–203. see also  recovery
inventory–sales ratio in, 208
investor preferences, 203
resource use in, 205
about future prices, 158, 160
about inflation, 236–237
and aggregate demand, 153
in economic indicators, 241
expected inflation, 281, 283
expenditure(s)
aggregate, 119
capital, 311
and consumer surplus, 74–76
government, 221, 303–306

personal consumption, 229
and price elasticity of demand, 
445–448
R&D, 178
total
and aggregate income, 137–144
and consumer surplus, 75–76
and own-price elasticity of demand, 
13–14
and trade balance, 444–445
expenditure approach to GDP , 120–122, 
127, 128, 131–133
exports
in balance of trade, 374in business cycles, 212
defined, 337
exchange rate and prices of, 155
net, 140, 338
voluntary export restraints, 356, 359
export subsidies, 356, 359–361
external competition, price collusion 
and, 93
external trade sector
cyclical behavior of, 211–212
in GDP , 130–131
Exxon Mobil, 107
F
Facebook, 98
factor markets, 128
factor-proportions theory, 354–355
factors of production (inputs), 23–24
fairness, of tax policy, 312
Fannie Mae, 299
FDI. see foreign direct investment
Federal Banking Supervisory Office, 278
Federal Commission, 279
Federal Deposit Insurance Corporation, 
279, 437–438
federal funds rate (fed funds rate), 241, 
284

284
Federal Open Market Committee 
(FOMC), 284
Federal Reserve Act, 292
Federal Reserve Bank of Chicago, 244
Fiat, 100
fiat money, 277
final goods, 121
final sales, 207
financial account, BOP , 372
financial assets abroad sub-account, 
BOP , 372
financial capital
278n.6
financial markets, in economy, 128
financial sector, IMF analysis of, 383
Financial Services Agency, 279
Financial Services Authority (FSA), 
277–279
Finland
firms
demand and supply analysis, 23–48
and market structure, 66–67
monopolist, 100–101
theory of the firm, 5
first-degree price discrimination, 
102–103
fiscal deficit. see budget deficit
fiscal multiplier, 314–315

Index  I-7
fiscal policy, 302–320
and aggregate demand, 153, 302–303
and deficits/national debt, 307–309
evaluating, 319–320
and government receipts/expenditures, 
303–306
implementation of, 316–319
and inflation, 168
influence on economy, 262–264
of Keynesian school, 215
and monetary policy, 320–324
roles and objectives, 302–310
and tax policy, 312
tools, 310–316
types of, 310
Fisher, Irving, 274
Fisher effect, 274–275
Fisher index, 228–229
average, 31–35
quasi-, 33
total, 31–35, 41–42
fixed-income investments, 184–185
fixed parity currency regimes, 436, 439
flexible exchange rates, 435
floating exchange rates, 433
FOMC. see Federal Open Market 
Committee
foreign currency reserves, at central 
banks, 279, 294
foreign direct investment (FDI), 341–342
foreign exchange market (FX market), 
399–418
402–406

402–406
foreign investments
direct, 341–342
income from, 376
portfolio, 341
foreign-owned financial assets sub-
account, BOP , 372
foreign portfolio investment (FPI), 341
forward discounts, 425
forward exchange rates, 408, 425–432
and spot rates, 410–412, 428–430
and swap/interest rates, 426–430
forward points, 425, 429–430
forward premiums, 425
forwards (forward contracts), in FX 
market, 408
FPI. see foreign portfolio investment
fractional reserve banking, 266–268
franc (Switzerland), 401, 418, 420
France
exchange rate regime, 436expected inflation, 282
exports of goods, 337
trade balance with US, 130
Freddie Mac, 299
free-floating currency regimes, 
440–441
free trade, 338, 343–344

440–441
free trade areas (FTAs), 362
frictionally unemployed (term), 222
Friedman, Milton, 217, 234, 435
Friedman, Thomas, 64
FSA. see Financial Services Authority
FTAs. see free trade areas
full employment, 164
full employment equilibrium GDP , 
163–164
full employment level of output, 150
functions, defined, 6
future prices, short-run aggregate supply 
and, 158, 160
futures (futures contracts), in FX 
FX market. see foreign exchange  
market
FX swaps, 409–410
G
G–7, 239, 344
G-10, 278–279
gains
from trade, 349–352
from voluntary exchange, 343
game theory, 92–94
Gary, Elbert, 96
gasoline market, concentration in, 107
GATS. see General Agreement on Trade 
in Services
GATT. see General Agreement on Tariffs 
and Trade
GDP deflator, 125–127
GE. see General Electric
General Agreement on Tariffs and Trade 
(GATT), 382, 385
General Agreement on Trade in Services 
(GATS), 385
General Electric (GE), 105
General Motors (GM), 46
Germany
automobile industry, 86

Germany
BOP paired transactions, 374–376
CPI, 229
currency regime, 435
current account imbalance, 377, 380
exchange rate regime, 436, 440
government liabilities/debt, 308government revenues/expenditures, 
303, 304
gross domestic product
forecasts, 184–185
potential, 183
hyperinflation, 226
investment spending, 140
leading economic indicator, 243
Ghana, 287
Giffen, Robert, 21
Giffen goods, 21
gilts, 298–299
global economic developments, IMF 
analysis of, 383
global financial crisis (2007-2009), 211, 
226, 236, 383
Global Integrated Monetary and Fiscal 
Model, 322
globalization, 338–339, 342–343
global supply chains, 343
GM. see General Motors

GNP . see gross national product
gold standard, 277, 434
goods
capital, 128
discretionary, 12
durable, 209
elasticity of demand for, 12
final, 121
Giffen, 21
inferior, 15, 19–23
intermediate, 121
manufacturers’ new orders for, 240
non-discretionary, 12
nondurable, 209
normal, 15, 19–23
substitution and income effects on, 
19–23
value of, 123–124
Veblen, 21
goods markets, 128
Google, 64
regulation of monopolies, 105–106
revenue from alternative trade policies, 
360
government-controlled authorization, 
97, 104
government debt, 262, 316. see also  
national debt
government expenditures
and business cycle theories, 221
and fiscal policy, 303–306
government receipts, fiscal policy and, 
303–306
government sector, in GDP , 129–130
government services, in GDP , 123
government spending, 129–130
and aggregate demand, 137–138, 155
current, 311
and fiscal policy, 153
and taxes, 314–315
Great Depression, 213, 226, 381–382

I-8 Index
Greece
exports of service, 337
fiscal crisis (2010), 365–366, 383–384, 
386–388
national debt, 307
Greenspan, Alan, 216
gross domestic product (GDP), 120–136
and cyclically adjusted budget deficit, 
317
equilibrium, 163–173
and foreign direct investment, 341–342
GNP vs., 336–337
and government liabilities/debt, 
308–309
and government revenues/
expenditures, 303–304
long-run growth rate vs. fluctuations 
in, 150–151
and net borrowing/lending, 305
nominal, 124–127
potential, 159
and demand-pull inflation, 235
and long-run equilibrium GDP , 163

measuring growth of, 179–181, 
183–184
production function of, 174–175
and price indexes, 231
and production function, 174–175
real, 124–127
and economic growth, 173
identifying recession with, 203–204
and international trade, 344
in Japan, 172–173
and shifts in aggregate supply/
demand, 170–173
sustainable growth in, 183–184
trade-to-GDP ratio, 339–342
gross investment, aggregate demand 
and, 139
gross national product (GNP), 120n.2, 
336–337
growth, economic. see economic growth
growth theory, 174–175
Guatemala, 287
H
Harley-Davidson, 84
harmonised index of consumer prices 
(HICP), 230
headline inflation, 230–231Heckscher–Ohlin model, 343, 354–355
hedging, in FX markets, 407
Herfindahl, O. C., 107
Herfindahl–Hirschman Index (HHI), 
107–108
H I C P.  see harmonised index of 
consumer prices
Hirschman, A. O., 107
HKMA. see Hong Kong Monetary 
Authority
Honda, 86
Honeywell, 105
Hong Kong SAR
Asian financial crisis, 343

exchange rate regime, 436, 438–439
exchange rate targeting, 294
Hong Kong dollar, 401
410–412
exchange rate regime for, 438–439
(HKMA), 438–439
horizontal demand schedule, 71–72
horizontal equity, 312
host country, for FDI, 341
hours worked, 224
household saving rate, 134, 152, 209
household sector, 119–120, 128
household wealth, aggregate demand 
and, 151–152
housing prices, 152, 155
housing sector, cyclical behavior of, 
210–211
HSBC, 414
human capital, 159, 160, 176
Hungary
hyperinflation, 226–227
I
IBM, 344
IBRD. see International Bank for 
Reconstruction and Development
Iceland, 287, 437
IDA. see International Development 
ideal currency regime, 433
ILO. see International Labour 
Organization
IMF. see International Monetary Fund
IMM. see International Monetary 
Market
impact lag, 318

Market
imperfect competition. see also  
monopolistic competition
breakeven analysis in, 40–41
marginal revenue in, 29–30
revenue in perfect vs., 35–36
implementation, fiscal policy, 316–319
implicit price deflator for GDP , 125–127
import license, 359
imports
in balance of trade, 374
in business cycles, 211, 212defined, 337
import-substitution policy, 352n.10
incentives
for monopolist firms, 100–101
in tax policy, 312
income
aggregate ( see aggregate income)
and consumer installment debt, 242
and consumer spending, 209
convergence of, 175
disposable, 134, 209, 315, 378
from foreign investments, 376
and GDP , 131–136
national, 133, 377
personal, 133–134
real, 18–19
income approach to GDP , 120, 131–133
income effects
on elasticity of demand, 12
on Giffen and Veblen goods, 21
and law of demand, 18–19
on normal and inferior goods, 19–23
in perfectly competitive markets, 69
with price decrease, 20–23
income elasticity of demand
calculating, 16

for consumers, 14–15
in perfect competition, 72–73
income inequality, 344
income sub-account, BOP , 371
increasing marginal returns, 23
increasing returns to scale, 45
independence, of central banks, 288, 
323
independent float currency regimes, 
437
Index of Leading Economic Indicators 
(LEI), 239, 242
India
comparative advantage, 348–352, 
354, 355
CPI, 229
exports from, 337, 354
trade balance with US, 131
Indian rupee, 401
indicators, economic. see economic 
indicators
indirect currency quote, 418
indirect exchange rate, 418
indirect taxes, 311, 313
Indonesia
industrial countries, terms of trade 
for, 337
industrial loans, 241

Index  I-9
Industrial Production Index, 241
inelastic demand, 71
defined, 10
perfectly inelastic demand, 11
price changes and total expenditure 
with, 13–14
infant industry argument, 356
inferior goods
defined, 15, 19
19–23
inflation
and business cycles, 205, 225–239
core, 230–231
cost-push (wage-push), 233–235
costs of, 281–283
defined, 167, 225
226–227
expectations about, 236–237
expected, 281, 283
and GDP deflator, 125–127
headline, 230–231
monetary policy and inflation rate, 
297
and New Classical school, 219
and nominal interest rates, 274–276
price indexes
constructing, 227–229
usage of, 229–231
in stagflation, 169–170
targets for, 289–290
and unemployment, 221–222
unexpected, 281–283
inflation rate, 167n.19, 225–226, 297
Inflation Reports, 289
inflation targeting, 287–293
exceptions to, 291–292

and independence of central banks, 
288
and monetary policy in developing 
countries, 292–293
transparency of, 289–291
by US Federal Reserve system, 292
inflation uncertainty, 282–283
information technology (IT) sector, 178
innovation
and perfect competition, 83
input prices, short-run aggregate supply 
input productivity, 23
inputs (factors of production), 23–24
Institute of Supply Management (ISM), 
244
Intel, 342
interbank FX market, 415–416
interest, 119, 296
and AD curve, 146–147
and equilibrium price for money, 
272–273
and housing sector behavior, 210
in monetary policy, 153–154and monetary transmission 
mechanism, 285–287
and money, 275
neutral, 296
nominal, 274–276
official, 284
real, 140
and swap rates/foreign exchange rates, 
426–430
intermediate goods, 121
International Bank for 
Reconstruction and Development 
(IBRD), 384–385
International Development Association 
(IDA), 384–385

International Labour Organization 
(ILO), 223
International Monetary Fund (IMF)
bailouts by, 383–384
capital restrictions study, 368
exchange rate regime classification, 
436
founding of, 382
and globalization, 339
Greek bailout, 366, 386–388
mandates of, 383
monetary and fiscal policy model,  
322
International Monetary Market 
(IMM), 408
International Organization for 
Standardization (ISO), 401
international trade, 335–398
balance of payments, 369–381
BOP accounts, 370–371, 377–379
paired transactions, 374–376
benefits and costs, 343–347
and capital flows, 356–369
absolute vs., 347–354
and currency exchange rates,  
443–453
449–450
445–449
global investors’ concerns, 335–336
patterns and trends, 339–343
practice problems, 392–395

solutions to problems, 396–398
terminology, 336–339
trade organizations, 381–388
function and objectives, 386–388
International Monetary Fund, 
382–384
World Bank Group, 384–385
World Trade Organization,  
385–386
trade restrictions/agreements, 
356–369
capital restrictions, 366–369
export subsidies, 359–361
quotas, 359tariffs, 356–361
trading blocs, common markets, and 
International Trade Organization (ITO), 
382
inter-temporal trade, 377, 378
intra-industry trade, 343
inventory
and business cycle, 204, 205
cyclical levels of, 207–208
and GDP , 127
inventory–sales ratio, 207–208, 241
inverse demand function, 8
investment
net, 139–140
saving–investment differential, 
141–143
investment spending, aggregate demand 
and, 139–140, 146–147
AD and AS curves as basis for, 
171–172
during decreases in aggregate demand, 
164–165
for inflationary gaps, 168
for shifts in aggregate supply, 169–170
iPod, 65
Iran, 436
Iraq, 436
Ireland

iPod, 65
Iran, 436
Iraq, 436
Ireland
budget deficit, 379
effects of Greek fiscal crisis, 366
wealth effect, 152
ISM. see Institute of Supply 
ISM new order index, 240
ISO. see International Organization for 
Standardization
Israel, 287, 437
Italy
government spending, 129, 130
ITO. see International Trade 
IT sector. see information technology 
sector

I-10  Index
J
Japan
aggregate demand and supply in, 
172–173
banking supervision, 279
budget deficit, 317
comparative advantage, 355
CPI, 229
deflation, 226, 298
economic indicators, 242–244
effects of global recession, 165, 166
exchange rate regime, 437, 440
government debt, 262, 308
government liabilities, 308
303, 304
gross domestic product, 155
potential, 183–184
and inflation targeting, 292
monetary policy, 299–301
VERs on exports, 359
Japanese yen, 401
cross-rate calculations with, 422–423
exchange rate quotes with, 418–419
JPY/USD currency pair, 416

J-curve effect, 449
Jordan, 294
K
Kazakhstan, 359
Kenya, 166
Keynes, John Maynard, 215, 216, 274, 
434
Keynesian school, 214–215, 303
kinked demand curve analysis, 
89–90, 95
Kiwi exchange rate, 418
krona (Sweden), 401
krone (Norway), 401
Kuwait, 436
Kydland, Finn E., 217
L
labor
average product of, 25–28
in Heckscher–Ohlin model, 354
marginal product of ( see marginal 
returns)
productivity of, 160, 180–184in Ricardian model, 354
supply of, 159, 160, 176
total product of, 25–28
labor costs
and aggregate supply, 158–160
unit, 234, 241
labor force, 176, 222
labor markets, 218
Laffer, Arthur, 312
lagging economic indicators, 239, 241–242
large country (term), 356
Laspeyres index, 228
late buying, in housing sector, 211
late expansion phase (business cycle), 
201–203
Latin America. see also  specific countries
exchange rate regimes, 439–440
Latvia, 362n.18
law of demand
defined, 6
exceptions for, 21

defined, 6
in perfect competition, 75
and substitution/income effects, 18–19
law of diminishing marginal returns, 23
law of diminishing returns, 79
layoffs, 223–224
Leading Credit Index, 240
leading economic indicators, 239–243
Lebanon, 294, 436
legal tender, 277, 436, 437
LEI. see Index of Leading Economic 
Indicators
lenders of last resort, 277
lending facilities, IMF, 383
leveraged accounts, in FX market, 412
Liberia, 437
Rate
Libya, 436
liquidity, broad measure of, 270
liquidity traps, 298
Lithuania, 362n.18, 435n.14
LMC. see long-run marginal cost
loans
to borrowers abroad, 374
commercial and industrial, 241
Logitech, 344
London Interbank Offered Rate (Libor), 
430
long-run aggregate supply, 159–161
defined, 148–149
and human capital, 159, 160
and labor, 159
and natural resources, 159–161
and physical capital, 159, 160
and productivity/technology, 160
long-run aggregate supply (LRAS) curve, 
148–150
long-run average cost (LRAC), 102

148–150
long-run average total cost (LRAC) 
curve, 44–48
long-run cost curves
average, 44–48
scale and profit maximization on, 
43–44, 47–48
time frame for, 43long-run demand, elasticity of, 12
long-run equilibrium
in monopolies, 104–105
in oligopolies, 96
long-run marginal cost (LMC), 30, 102
long-term unemployed (term), 222
loss
deadweight, 356, 357
economic, 40
LRAC. see long-run average cost
LRAC curve. see long-run average total 
cost curve
LRAS curve. see long-run aggregate 
supply curve
LRATC. see long-run average total cost 
curve
Luxembourg
M
M0 money measure, 270
M1 money measure, 269, 270
M2 money measure, 269, 270
M2 money supply, 242, 243
M3H money measure, 270
M3 money measure, 270
M4 money measure, 270
macroeconomics, 117–197
aggregate demand, 137–148
AD curve, 145–148

aggregate output and income, 119–136
aggregate supply
defined, 5
sources, 176–179
sustainable growth, 179–185
equilibrium GDP and prices, 163–173
business cycle and AD/AS curves, 
170–173
microeconomics vs., 118
new classical, 217
practice problems, 190–194
solutions to problems, 195–197
Malaysia
capital restrictions, 368–369
Maldives, 295
Malta, 362n.18, 436

Index  I-11
Malthus, Thomas, 174
managed float currency regimes, 437, 
440
manufacturers, new orders of, 240
manufacturing sales, 241
marginal costs (MC)
interactions of other costs and output 
with, 31–35
long-run, 30, 102
maximization, 30
marginal product, 23
marginal product of labor (MP L), 25–28. 
see also  marginal returns
marginal propensity to consume (MPC), 
139, 314–316
marginal propensity to save (MPS), 139, 
315
and definition of productivity, 23–25
increasing, 23
law of diminishing, 23
and total/average product of labor, 
25–28
marginal revenue (MR)
and marginal cost/profit maximization, 
29–30
in monopolies, 98–102
in monopolistic competition, 85–87
in oligopolies, 90, 91, 94, 96
in perfect competition, 70, 78–79
and price elasticity, 73–74
marginal value curve, 75
market concentration, 105–106
market demand function, 16
market functions, in FX markets, 
406–412

406–412
market power, 97, 105
markets
capital, 383, 406–407
common, 362–366
factor, 128
financial, 128
foreign exchange, 399–418
402–406
geographic limitations of, 64
goods, 128
labor, 218
over-the-counter, 408
market structures, 63–115
analysis of, 64–68
determining factors for, 66–68
identification of, 105–108
importance of, 63–64
monopolistic competition, 83–87
supply analysis, 85monopoly, 97–105
about, 97–98
demand analysis, 98–99
long-run equilibrium, 104–105
optimal price and output, 101–102
price discrimination and consumer 
surplus, 102–104
supply analysis, 99–100
oligopoly, 87–96
demand analysis and pricing 
strategies, 88–94
long-run equilibrium, 96
optimal price and output, 95–96
supply analysis, 94–95
perfect competition, 68–83

optimal price and output, 77–81
practice problems, 110–113
solutions to problems, 114–115
types of, 64–66
Marshall-Lerner condition, 445–449
maturity
of forward contracts, 426n.5
and forward points, 429–430
MC. see marginal costs
Medium Term Financial Strategy 
(MTFS), 276
menu costs, 219–220, 282
Mercedes, 86
merchandise trade sub-account, BOP , 
371
MERCOSUR. see Southern Cone 
Common Market
mergers, market concentration and, 
105–106
Mexican peso, 401, 421
Mexico
economic growth in, 182
effect of global recession, 166
NAFTA, 362, 364–365
microeconomics
defined, 5
demand and supply analysis in, 5–6
macroeconomics vs., 118
Microsoft, 98
Microsoft Word, network effects for, 98

Middle East. see also  specific countries
minimum efficient returns to scale, 46
Minsky, Hyman, 216
Minsky moment, 216
Mitchell, Arthur F., 200
MNCs. see multinational corporations
Monetarist school, 217, 271, 276, 303
monetary accommodation, 322monetary base, 438
monetary policy, 262–302
and aggregate demand, 153–154
central banks
roles and responsibilities, 277–280
tools of, 283–285
and concept of money, 264–276
contractionary and expansionary 
policies, 296–297
and currency regime, 433
of developing countries, 292–293
evaluating, 301–302
and fiscal policy, 320–324
central bank independence, 288
credibility, 288–289
exceptions to inflation-targeting rule, 
291–292
transparency, 289–291
limitations, 297–301

objectives, 280–283
of United Kingdom, 276
monetary transmission mechanism, 
monetary unions, 362, 365–366, 436
money, 264–276
creation process, 266–269
defined, 153, 269–270
demand for, 271–274
functions of, 265–266
and interest rates, 275
New Classical school models with, 
219–221
New Classical school models without, 
218–219
quantity theory of, 144, 270–271
supply and demand relationship, 
272–274
surplus of, 235–236
velocity of, 144, 236
money creation, 266–269
money market, equilibrium in,  
144–145
money multiplier, 268
money neutrality, 270–271, 274
money supply
and aggregate demand/supply, 154
changes in, 272–274
M2, 242, 243
real, 144–146
monopolist firms, 100–101
monopolistic competition, 83–87. see 
also imperfect competition
benefits of trade for, 343–344

I-12  Index
monopoly, 97–105
breakeven point in, 38–39
defined, 66
demand, average, and marginal costs 
under, 37
marginal revenue in, 29
Montenegro, 436
Morgan, J. P ., 96
mortgage crisis (2007-2008), 277–278
MPC. see marginal propensity to 
consume
MPL. see marginal product of labor
MPS. see marginal propensity to save
MR. see marginal revenue
MSCI developed equity market index, 
368–369
MTFS. see Medium Term Financial 
Strategy
multinational corporations (MNCs), 
341–342
N
NAFTA. see North American Free Trade 
Agreement
NAIRU. see non-accelerating inflation 
rate of unemployment
Napoleonic Wars, 307
narrow money, 269
NARU. see natural rate of 
unemployment
Nash, John, 92
Nash equilibrium, 92–93, 96
NASSCOM, 354n.11
National Bureau of Economic Research 
(NBER), 203, 240

National Bureau of Statistics of China, 
121
national debt, 307–309. see also  
government debt
national income, 133, 377
National Income and Product Accounts 
(NIPA), 120
nationalization, of monopolies, 104
national welfare
and export subsidies, 360
natural level of output, 150
natural monopolies, 97–98, 104
natural rate of unemployment (NARU), 
150, 234
natural resources. see also  raw 
materials
and aggregate supply, 160, 161
and economic growth, 178
NBER. see National Bureau of Economic 
Research
Neoclassical school of economic 
thought, 213–214
Neo-Keynesians, 219
net exports, 140, 338Netherlands
imports in, 337
Netherlands Antilles, 294
net investment, 139–140
Netscape, 98
net tax rate, 314
network effects, in monopolies, 98
neutral rate of interest, 296
new classical macroeconomics, 217
New Classical school of economic 
thought, 217–221
New Keynesians, 219
new product bias, of price index, 228

New Zealand
inflation targeting, 287, 289–291
Policy Targets Agreement, 290–291
New Zealand dollar, 401, 418, 419n.4
Nintendo, 342
NIPA. see National Income and Product 
Accounts
nominal exchange rates, 402–406
nominal GDP , 124–127
nominal interest rates, 274–276
nominal wages, 157, 160
non-accelerating inflation rate of 
unemployment (NAIRU), 234
non-discretionary goods, 12
nondurable goods, 209
nonfinancial assets, purchase of, 376
non-price competition, 67
non-renewable resources, 178
normal goods
19–23
normal profit, 33
North Africa, trade-to-GDP ratio, 340
North American Free Trade Agreement 
(NAFTA), 362, 364–365
Northern Rock Bank, 277–278
Norway, 287, 437
Norwegian krone, 401
numeraire, 434n.10
O
of central banks, 280–281
of monetary policy, 280–283
of trade organizations, 386–388

Co-Operation and Development
Currency, 279
Office of the Superintendent of Financial 
Institutions, 278
official interest rate (official policy rate), 
284
oil, supply and price of, 158
defined, 66demand analysis and pricing strategies, 
88–94
Oman, 295
OPEC. see Organization of Petroleum 
Exporting Countries
open economies, 338
benefits of trade, 343
investment in, 378
national income identity, 377
open market operations, 283
operational independence, 287, 288
opportunity costs, 24, 77
optimal output
in monopolies, 101–102
in monopolistic competition, 85
in oligopolies, 95–96
in perfect competition, 77–81
optimal price
options, in FX market, 410
orders, size/frequency of, 93

Co-Operation and Development 
(OECD)
economic indicators, 239
GDP reported by, 120
government liabilities/debt for, 308
government revenues/expenditures by, 
303, 304
net borrowing/lending by, 305
spillover effects for, 364
trade-to-GDP ratio, 340, 341
Organization of Petroleum Exporting 
Countries (OPEC), 88, 93
Osborne, George, 379
OTC markets. see over-the-counter 
markets
output
aggregate, 119–136
and costs, 31–35
full employment/natural level, 150
optimal
recessionary gap in, 205
value of final output method for GDP , 
121–122, 132
outsourcing, 342
overall payroll employment, 224
over-the-counter (OTC) markets, 408
own price (term), 7
calculating, 9–11
defined, 9
extremes of, 11–12
predicting, 12–13

defined, 9
and total expenditure, 13–14

Index  I-13
P
Paasche index, 229
paired transactions, in BOP system, 
374–376
Pakistan, 337
Panama, 436, 437
Papaconstantinou, George, 387
Paraguay, 362
participation ratio, 222
passive crawling peg currency regime, 
439
patents, 97
payments. see also  balance of payments 
(BOP) system
central banks in payments system, 279
forms of, 119
transfer, 129, 310–311
PCE. see personal consumption 
expenditures
PCE index, 229
PDI. see personal disposable income
peak phase (business cycle), 200–203, 
207
per capita real GDP , 124
under, 36–37
cross-price elasticity of demand, 73
elasticity of demand, 70–72
income elasticity of demand, 72–73
optimal price in, 77–81
output optimization in, 77–81
revenue in imperfect vs., 35–36
shutdown decision in, 39–40

perfectly elastic demand, 12
perfect price elasticity, 72
perfect price inelasticity, 72
personal consumption expenditures 
(PCE), 229
personal disposable income (PDI), 134
personal income, 133–134
Peru, 124, 287, 437
peso (Mexico), 401
Philippines
physical capital
and long-term aggregate supply, 159, 
160
pips, 425
Plaza Accord, 440
Poland, 287, 437policy rate, 284
Porsche, 86
Porter, Michael E., 68
Porter’s five forces, 68
portfolio demand for money, 271
Portugal
Greek fiscal crisis 2010, 365–366
potential GDP , 159
and long-run equilibrium  
GDP , 163

GDP , 163
183–184
pound (United Kingdom). see British 
pound
PPF. see production possibilities 
frontier
PPI. see producer price index
PPP . see purchasing power parity
PRA. see Prudential Regulation 
Authority
precautionary money balances, 271
premiums, forward, 425
Prescott, Edward C., 217
price(s)
aggregate, 273–274
asset, 444
autarkic, 338, 349
equilibrium, 77–78, 272–273
and equilibrium GDP , 163–173
aggregate supply and demand, 
170–173
harmonised index of, 230
housing, 152, 155
input, 158, 160
optimal
relative, 231
stability of, 280
of stock, 155
substitution and income effects with, 
20–23
two-sided, 419–420
world, 338, 339, 349
price collusion, 87–88, 93
price controls, 367

price currency, 401, 418
price discrimination, in monopolies, 
102–104
price elasticity of demand. see also  
in perfect competition, 70–72
and trade balance, 445–449price indexes, 227–233
sub-indexes, 231
price-specie-flow mechanism, 434
price takers, 66, 71–72
price wars, 88, 96
pricing
by dominant firms in oligopolies, 94–95
in oligopolies, 88–94
two-part tariff, 103–104
prime lending rate, average, 241
producer price index (PPI), 230
producer surplus, 357, 360
product differentiation
and market structure, 67
in monopolistic competition, 83–84
production
breakeven point of, 36–39
and costs, 23–25
globalization of, 342–343
scaling up vs. scaling down, 44
production function, 174–175
production possibilities frontier (PPF), 
350–351
productivity
and aggregate supply, 160

350–351
in cost-push inflation, 234–235
defined, 23–25
diminishing marginal, 174–175
and economic growth, 175
indicators of, 224
of labor, 160, 180–184
and long-term aggregate supply, 160
and marginal returns, 23
total factor, 174, 178
profit
economic, 28, 29, 77, 85, 86
in monopoly, 99–100, 102
normal, 33
profit maximization
under imperfect competition, 40–41
and marginal revenue/costs, 29–30
points of production for, 36–37
and scale, 43–48
promissory note, 266
Provopoulos, George, 387
Prudential Regulation Authority (PRA), 
278n.6
purchasing managers indexes, 244
purchasing power parity (PPP), 402, 404
Q
Qatar, 295
quality bias, 228
quantitative easing (QE), 322–323
and deflation, 298–299
in Japan, 300
quantity equation of exchange, 270
quantity theory of money, 144, 270–271
quasi-fixed costs, 33

I-14  Index
quota rents, 359
quotas, 359
defined, 356
and tariffs, 360–361
in textile industry, 345
R
rand (South Africa), 401
raw materials, 158, 160. see also  natural 
resources
Rayovac, 64
R&D. see research and development
real (Brazil), 401
real business cycle models (RBCs), 
218–220
real exchange rates, 402–406
real GDP , 124–127
and shifts in aggregate supply/demand, 
170–173
real income, 18–19
real interest rate, 140
real money accounts, in FX market, 412
real money supply, 144–146
receipts, government, 303–306
recession, 164n.16
defined, 201
identifying, 203–204
investor preferences, 202–203
recessionary gap, 163–167, 205
recognition lag, 318
recovery
unemployment rate in, 223
refinancing rate, 284
regional trading agreements (RTAs), 
362–366
regression analysis, 106
regulation, of monopolies, 105–106
relative price, 231
renewable resources, 178
rent
in GDP , 123

rent
in GDP , 123
repo rates, 284
repurchase agreements, 284
research and development (R&D), 178, 
344
reserve banking systems, 153–154, 
266–268
Reserve Bank of Australia, 280
Reserve Bank of India, 230
Reserve Bank of New Zealand, 287, 289, 
290
Reserve Bank of New Zealand Act, 287, 
290
reserve requirements, 367
of central banks, 268, 284–285
and monetary policy, 284–285
and money creation, 267
resources
consumer behavior and use of, 
208–210
cyclical use of, 204–210
inventory levels, 207–208natural, 159–161, 178
non-renewable, 178
renewable, 178
restrictions, trade. see trade restrictions
retail accounts, in FX market, 413
retail sales, consumer spending and, 209
retaliation, price collusion and, 93
returns
law of diminishing, 79
marginal, 23–28
law of diminishing marginal returns, 
23
25–28
to scale, 45, 46
revenue
average, 35
marginal
and marginal cost/profit 

total
in oligopoly, 90
under perfect and imperfect 
competition, 35–36
in shutdown analysis, 41–42
revenue sufficiency, of tax policy, 312
Rhone-Poulenc, 105
Ricardian equivalence, 316
Ricardian model, 343, 354–355
Ricardo, David, 316, 354
Riksbank, 289
risk premium, for inflation, 275
Robinson, Joan, 65
Roche, 105
Rolex, 98
Romania, 287
RTAs. see regional trading agreements
ruble (Russia), 401
rupee (Indian), 401
Russia, 343, 359, 436
Russian ruble, 401
S
sales
final, 207
inventory–sales ratio, 207, 241
manufacturing, 241
trade, 241
sales and purchases of non-produced, 
non-financial assets sub-account, 
BOP , 372
San Marino, 436
SATC curve. see short-run average total 
cost curve
Saudi Arabia, 294, 436
saving
household, 134, 137
marginal propensity to save, 139

saving–investment differential, 141–143saving rate, household, 134, 152, 209
Say, J. B., 213
Say’s law, 213
scale
diseconomies of, 44–47
economies of, 44–47
and profit maximization for firms, 
43–48
scaling down, 44
scaling up, 44
Schumpeter, Joseph A., 83, 213–214
Schwab, Charles M., 96
SDR. see special drawing right
second-degree price discrimination, 
103
second-order conditions, for profit 
sectors, economic. see economic  
sectors
seigniorage, 439
sellers, number/size of, 93
sell-side participants, FX market, 412, 
414–415
Serbia, 287
services
change in CPI for, 242
consumer spending on, 209
GDP and value of, 123–124
services sub-account, BOP , 371
Shell, 107
shoe leather costs, 282
short-run aggregate supply, 157–158
business taxes and subsidies, 158
exchange rate, 158
expectations about future prices, 158
input prices, 158
nominal wages, 157
short-run aggregate supply (SRAS) 
curve, 148–149, 157–158

short-run average total cost (SATC) 
curve, 44, 45
short-run cost curves
average total cost curve, 44, 45
profit maximization for firms on, 
43–44
time frame for, 43
total cost curve, 43–44
short-run cost schedule, in perfect 
competition, 80
short-run demand, elasticity of, 12
short-run equilibrium, in perfect 
competition, 81
short-run marginal cost (SMC), 30, 
36–37
short-run total cost (STC) curve,  
43–44
breakeven analysis, 38–41
economic vs. accounting cost, 28
interaction of costs and output, 31–35
marginal revenue, marginal cost, and 
profit maximization, 29–30
profit maximization, breakeven, and 
shutdown points, 36–37
revenue under perfect vs. imperfect 
shutdown point, 36–37, 40

Index  I-15
Singapore
external trade sector, 211
Singapore dollar, 401
Singha Co., 88
Slovak Republic, 362n.18, 436
Slovenia, 362n.18, 436
small country (term), 356
SMC. see short-run marginal cost
Smith, Adam, 354
Smithsonian Agreements, 435
social policies, taxes and, 313
Solow, Robert, 175
source country, FDI, 341
South Africa, 287, 337, 437
South African rand, 401
Southeast Asia, 368–369. see also  specific 
countries
Southern Cone Common Market 
(MERCOSUR), 362
South Korea
exchange rate regime, 437, 441
South Korean won, 401
sovereignty, regional trade agreements 
and, 365
sovereign wealth funds (SWFs), 414
earnings, 400
as leading indicator, 240, 242
Spain

Spain
gold standard for, 434n.11
special drawing right (SDR), 387n.29
specialization, international trade and, 
343
speculation, in FX markets, 407
speculative demand for money, 271
speculative money balances, 271
spending
business, 153, 202
capital, 205–207, 314
consumer, 153, 202, 208–210
consumption, 138–139
and taxes, 314–315investment, 139–140, 146–147
public sector, 263
spillover effect, of education, 176
spot exchange rates, 410–412, 428–430
spot transactions, in FX market, 407
SRAS curve. see short-run aggregate 
SRATC. see short-run average total cost 
curve
Stackelberg model, 94
stagflation
and aggregate supply, 169–170

and inflation expectations, 236
Standard & Poor’s, ratings of, 365
statistical discrepancies, in GDP , 132
Statistics Canada, 121, 132, 133
STC curve. see short-run total cost curve
Sterling exchange rate, 418
Sterling–yen exchange rate, 419
stock prices, aggregate demand and, 155
Strauss-Kahn, Dominique, 386
structural budget deficit, 317
Subaru, 86
sub-indexes, price, 231
growth spillovers, 364
subsidies
export, 356, 359–361
in monopolies, 104
and short-run aggregate supply, 158, 160
substitutes, 15, 16, 71, 73
substitution, import, 352n.10
substitution bias, 228
substitution effects
sum of value added method, for GDP , 
sunk costs, 28
supply. see also  demand and supply 
analysis
aggregate

analysis
aggregate
169–170
in real business models, 218–219
elasticity of, 8
money, 154
in monopolies, 99–100in monopolistic competition, 85
in oligopolies, 94–95
in perfect competition, 76–77
supply chains, global, 343
supply curves
aggregate, 148–150, 157–162, 171–172
supply shock to inflation rate, 297
surpluses
budget, 304
consumer
in current account, 377, 379–381
of money, 235–236
producer, 357, 360
trade, 338
Survey of Current Businesses  (US 
Department of Commerce), 121

sustainable growth, 173, 179–185
and fixed-income investments, 
184–185
and labor productivity, 181–182
measures of, 182
rate of growth in potential GDP , 
183–184
swap funding, 409–410
swap points, 426
swap rates, 426–430
swaps, FX, 409–410
swarming, 83
Sweden
Swedish Financial Supervisory 
Authority, 279
Swedish krona, 401
Swiss franc, 401, 418, 420
Swiss franc exchange rate, 418
Swiss National Bank, 413
Switzerland
growth spillover, 364
Syria, 436
T
Taiwan
comparative advantage, 352–353
Tankan Survey, 242, 244
target independence, 288
target zone currency regimes, 436, 439
tariffs, 356–361
analysis of, 358–359
GATT, 382, 385

and quotas/VERs, 360–361
two-part tariff pricing, 103–104

I-16  Index
taxes
and aggregate demand, 140, 153, 155
attributes of tax policy, 311–312
direct, 311, 314
and fiscal policy, 303–304, 312
and government spending, 314–315
indirect, 311, 313
and short-run aggregate supply, 
158, 160
and social policies, 313
tax reform, 312
TCs. see total costs
technology
and comparative advantage, 354
and economic growth, 175–178
telephone utilities, 100, 105
television broadcasting, 65
temporary workers, use of, 224
terms of trade, 337–338
textile industry, 345–346
TFC. see total fixed cost
TFP . see total factor productivity
ThaiBev, 88
Thailand
currency regime, 437
Thatcher, Margaret, 276
third-degree price discrimination,  
103
tight fiscal policy, 321
tight monetary policy, 321

TIPS. see Treasury Inflation-Protected 
tobacco industry, 87–88
total costs (TCs)
average
36–37
of production, 24
variable, 31–35, 41–42
total expenditure(s)
13–14
total factor productivity (TFP), 174, 
178
total fixed cost (TFC)
total product of labor, 25–28
total revenue (TR)
in oligopoly, 90under perfect and imperfect 
total value, consumer surplus and, 75
total variable cost (TVC)
Toyota, 86
TR. see total revenue
trade. see also  international trade

free, 338, 343–344
gains from, 349–352
inter-temporal, 377, 378
intra-industry, 343
terms of, 337–338
trade agreements
common markets, 362
economic unions, 362
trading blocs, 362–366
trade balance
absorption approach, 449–450
in business cycles, 211–212
and capital account, 444
elasticities approach, 445–449
and GDP , 130–131
and saving/expenditures, 444–445
trade creation, 363–364
trade diversion, 364
382–384
World Trade Organization, 385–386
trade protection, 338
trade restrictions, 356–369
quotas, 359–361
trade sales, 241
trade sector, 130–131, 211–212
trade surplus, 338
transactions, BOP , 369
transactions money balances, 271
transfer payments, 129, 310–311

transparency, of inflation targeting, 
289–291
Treasury Inflation-Protected Securities 
(TIPS), 230
triangular arbitrage, 423
trough phase (business cycle), 200,  
201
Turke y
turnover, in FX market, 415–416
TVC. see total variable cost
two-sided prices, 419–420
two-week repo rate, 284U
UBS, 412, 414
Ukraine, 226, 437
ULC. see unit labor cost
uncertainty, inflation, 282–283
underemployed, 222
underground economy, 123–124
unemployed, 222
and business cycles, 221–225
natural rate of, 150, 234
non-accelerating inflation rate of, 234
and overall payroll employment, 224
and real business cycle models, 218
and regional trade agreements, 
364–365
unemployment rate, 223–224
unexpected inflation, 281–283
unilateral transfers sub-account, BOP , 
371

371
comparative advantage, 348–351, 355
currency regime, 434, 435, 437
excess demand/supply of cars, 339
exchange rate targeting, 293, 294
fiscal policy, 314
government cash flows, 305–306
government liabilities/debt, 262, 308
303, 304
housing prices and saving rate, 152
inflation targeting, 287–289
monetary policy, 276, 293
national debt, 307, 309
United Nations Conference on Trade on 
Employment, 382
United Nations Monetary and Financial 
Conference, 382
antitrust violations, 105
balance of payments, 372–373

CPI, 229, 230
currency regime, 434, 437
current account deficit, 377, 380, 381
deflation/disinflation, 226, 227
economic indicators, 240–242, 
244–245

Index  I-17
external trade sector, 211–212
fiscal policy in 2009-2010, 314
global recession, 165–167
303, 304
gross domestic product, 120–121
and ITO charter, 382
money measures, 269
national income, 133n.7
natural monopolies, 104
quantitative easing, 298, 299
stagflation, 169, 236
unemployment rate, 223
VERs in, 359
US Bureau of Labor Statistics (BLS), 223, 
345
US Department of Commerce, 120–121
US dollar, 401

as currency anchor, 436–437, 439, 440
exchange rate quotes with, 418–421
as exchange rate target, 294
foreign exchange reserves, 413–414
USD/GBP currency pair, 416US Federal Reserve
banking supervision by, 279
CPI-U use by, 230
and dollarized currency regimes, 
437–438
inflation targeting by, 292
measures of money, 269
monetary policy, 153–154, 169, 185
quantitative easing by, 298, 299
in recession (2007-2009), 167
United States Steel Corporation (US 
Steel), 96
US Treasury, 167
US v. DuPont,  73n.4
unit elastic (unitary elastic), 71
unit elastic demand (unitary elastic 
demand), 10
unit labor cost (ULC), 234, 241
Uruguay, 362, 439–440
V
value

V
value
of goods and services in GDP , 123–124
measure of, 266
store of, 265–266
total, 75
value of final output method, 
average
36–37
variety, monopolistic competition and, 
86, 87
Veblen, Thorstein, 21
Veblen goods, 21
velocity of money, 144, 236
Venezuela, 436
VERs. see voluntary export restraints
vertical demand schedule, 72
vertical equity, 312
Vietnam, 436
virtuous circle, 352volatility, of exchange rates, 432, 435
Volkswagen, 86
voluntarily unemployed (term), 223
voluntary exchange, 343
voluntary export restraints (VERs), 356, 
359–361
von Hayek, F., 214
von Mises, L., 214
W
wage-push inflation (cost-push 
inflation), 233–235
wages, nominal, 157, 161
Wal-Mart, 46
wealth
household, 151–152
wealth effect, 151–152
White, Harry Dexter, 434
wholesale price index (WPI), 230
won (South Korea), 401
World Bank Group

foreign currency of, 413
and IMF, 382
mandates of, 384
World Development Report, 340
World Development Report, 340,  
364
World Investment Indictors, 342
The World Is Flat  (Friedman), 64
world price, 338, 339, 349
World Trade Organization (WTO)
agreements under, 363
functions of, 385–386
quotas on non-members, 359
termination of Multi Fiber Agreement, 
345
World War I, 226, 307, 367
World War II, 226, 307
WPI. see wholesale price index
WTO. see World Trade Organization
Y
yen (Japan). see Japanese yen
yuan (China). see Chinese yuan
Yugoslavia, 226
Z
Zimbabwe, 226–227

Equity Investments
STUDY SESSIONS 
Study Session 14 Equity Investments (1)
Study Session 15 Equity Investments (2)  
The candidate should be able to describe characteristics of equity investments, secu -
rity markets, and indexes. The candidate should also be able to analyze industries, 
companies, and equity securities and to describe and demonstrate the use of basic 
equity valuation models.
Global equities are an important asset class for meeting longer term growth and 
diversification objectives. Global equities also represent a substantial share of capital 
markets that has been expanding in breadth and depth as developing economies 
come to market for equity capital. As developed and emerging economies continue 
to open their markets to investment, their activity is expected to significantly change 
the composition of world equity markets.

Equity Investments (1)
This study session provides a structural overview of financial markets and their 
operating characteristics. Overview markets include equities, fixed income, deriva -
tives, and alternative investments. Various asset types, market participants, and how 
assets trade within these markets and ecosystems are described. Coverage of these 
core asset classes continues in subsequent Level I study sessions, laying the foundation 
for further study in Levels II and III. The study session then turns to the calculation, 
construction, and use of security market indexes. A discussion of market efficiency 
and the degree to which market prices may reflect available information concludes 
the session.
Reading 44 Market Organization and Structure  
by Larry Harris, PhD, CFA
Reading 45 Security Market Indexes  
by Paul D. Kaplan, PhD, CFA, and Dorothy C. Kelly, 
CFA
Reading 46 Market Efficiency  
by Sean Cleary, PhD, CFA, Howard J. Atkinson, CIMA,

ICD.D, CFA, and Pamela Peterson Drake, PhD, CFAEqUITY  INvEST mENTS
14

Market Organization and Structure
by Larry Harris, PhD, CFA
Larry Harris, PhD, CFA, is at the USC Marshall School of Business (USA).
a. explain the main functions of the financial system;
b. describe classifications of assets and markets;
c. describe the major types of securities, currencies, contracts, 
commodities, and real assets that trade in organized markets, 
including their distinguishing characteristics and major subtypes;
d. describe types of financial intermediaries and services that they 
provide;
e. compare positions an investor can take in an asset;
f. calculate and interpret the leverage ratio, the rate of return on a 
margin transaction, and the security price at which the investor 
would receive a margin call;
g. compare execution, validity, and clearing instructions;
h. compare market orders with limit orders;
i. define primary and secondary markets and explain how 
secondary markets support primary markets;

j. describe how securities, contracts, and currencies are traded in 
quote-  driven, order-  driven, and brokered markets;
k. describe characteristics of a well-  functioning financial system;
l. describe objectives of market regulation.READING
44

Reading 44 ■ Market Organization and Structure 6
Financial analysts gather and process information to make investment decisions, 
including those related to buying and selling assets. Generally, the decisions involve 
trading securities, currencies, contracts, commodities, and real assets such as real 
estate. Consider several examples:
■■Fixed income analysts evaluate issuer credit-  worthiness and macroeconomic 
prospects to determine which bonds and notes to buy or sell to preserve capital 
while obtaining a fair rate of return.
■■Stock analysts study corporate values to determine which stocks to buy or sell 
to maximize the value of their stock portfolios.
■■Corporate treasurers analyze exchange rates, interest rates, and credit condi -
tions to determine which currencies to trade and which notes to buy or sell to 
have funds available in a needed currency.
■■Risk managers work for producers or users of commodities to calculate how

many commodity futures contracts to buy or sell to manage inventory risks.
Financial analysts must understand the characteristics of the markets in which their 
decisions will be executed. This reading, by examining those markets from the analyst’s 
perspective, provides that understanding.
This reading is organized as follows. Section 2 examines the functions of the 
financial system. Section 3 introduces assets that investors, information-  motivated 
traders, and risk managers use to advance their financial objectives and presents ways 
practitioners classify these assets into markets. These assets include such financial 
instruments as securities, currencies, and some contracts; certain commodities; 
and real assets. Financial analysts must know the distinctive characteristics of these 
trading assets.
Section 4 is an overview of financial intermediaries (entities that facilitate the 
functioning of the financial system). Section 5 discusses the positions that can be

obtained while trading assets. You will learn about the benefits and risks of long and 
short positions, how these positions can be financed, and how the financing affects 
their risks. Section 6 discusses how market participants order trades and how mar -
kets process those orders. These processes must be understood to achieve trading 
objectives while controlling transaction costs.
Section 7 focuses on describing primary markets. Section 8 describes the struc -
tures of secondary markets in securities. Sections 9 and 10 close the reading with 
discussions of the characteristics of a well-  functioning financial system and of how 
regulation helps make financial markets function better. A summary reviews the 
reading’s major ideas and points, and practice problems conclude.
THE FUNCTIONS OF THE FINANCIAL SYSTEM
The financial system includes markets and various financial intermediaries that help 
transfer financial assets, real assets, and financial risks in various forms from one entity

to another, from one place to another, and from one point in time to another. These 
transfers take place whenever someone exchanges one asset or financial contract for 
another. The assets and contracts that people (people act on behalf of themselves, 
companies, charities, governments, etc., so the term “people” has a broad definition 
in this reading) trade include notes, bonds, stocks, exchange-  traded funds, currencies, 1
2

The Functions of the Financial System 7
forward contracts, futures contracts, option contracts, swap contracts, and certain 
commodities. When the buyer and seller voluntarily arrange their trades, as is usually 
the case, the buyer and the seller both expect to be better off.
People use the financial system for six main purposes:
1 to save money for the future;
2 to borrow money for current use;
3 to raise equity capital;
4 to manage risks;
5 to exchange assets for immediate and future deliveries; and
6 to trade on information.
The main functions of the financial system are to facilitate:
1 the achievement of the purposes for which people use the financial system;
2 the discovery of the rates of return that equate aggregate savings with aggregate 
borrowings; and
3 the allocation of capital to the best uses.
These functions are extremely important to economic welfare. In a well-  functioning 
financial system, transaction costs are low, analysts can value savings and investments,

and scarce capital resources are used well.
Sections 2.1 through 2.3 expand on these three functions. The six subsections of 
Section 2.1 cover the six main purposes for which people use the financial system and 
how the financial system facilitates the achievement of those purposes. Sections 2.2 and 
2.3 discuss determining rates of return and capital allocation efficiency, respectively.
2.1 Helping People Achieve Their Purposes in Using the 
Financial System
People often arrange transactions to achieve more than one purpose when using the 
financial system. For example, an investor who buys the stock of an oil producer may 
do so to move her wealth from the present to the future, to hedge the risk that she 
will have to pay more for energy in the future, and to exploit insightful research that 
she conducted that suggests the company’s stock is undervalued in the marketplace. 
If the investment proves to be successful, she will have saved money for the future,

managed her energy risk exposure, and obtained a return on her research.
The separate discussions of each of the six main uses of the financial system by 
people will help you better identify the reasons why people trade. Your ability to iden -
tify the various uses of the financial system will help you avoid confusion that often 
leads to poor financial decisions. The financial intermediaries that are mentioned in 
these discussions are explained further in Section 4.
2.1.1  Saving
People often have money that they choose not to spend now and that they want 
available in the future. For example, workers who save for their retirements need 
to move some of their current earnings into the future. When they retire, they will 
use their savings to replace the wages that they will no longer be earning. Similarly, 
companies save money from their sales revenue so that they can pay vendors when 
their bills come due, repay debt, or acquire assets (for example, other companies or

machinery) in the future.
To move money from the present to the future, savers buy notes, certificates of 
deposit, bonds, stocks, mutual funds, or real assets such as real estate. These alter -
natives generally provide a better expected rate of return than simply storing money.

Reading 44 ■ Market Organization and Structure 8
Savers then sell these assets in the future to fund their future expenditures. When 
savers commit money to earn a financial return, they commonly are called investors. 
They invest when they purchase assets, and they divest when they sell them.
Investors require a fair rate of return while their money is invested. The required 
fair rate of return compensates them for the use of their money and for the risk that 
they may lose money if the investment fails or if inflation reduces the real value of 
their investments.
The financial system facilitates savings when institutions create investment vehicles, 
such as bank deposits, notes, stocks, and mutual funds, that investors can acquire and 
sell without paying substantial transaction costs. When these instruments are fairly 
priced and easy to trade, investors will use them to save more.
2.1.2  Borrowing
People, companies, and governments often want to spend money now that they do

not have. They can obtain money to fund projects that they wish to undertake now by 
borrowing it. Companies can also obtain funds by selling ownership or equity interests 
(covered in Section 2.1.3). Banks and other investors provide those requiring funds 
with money because they expect to be repaid with interest or because they expect to 
be compensated with future disbursements, such as dividends and capital gains, as 
the ownership interest appreciates in value.
People may borrow to pay for such items as vacations, homes, cars, or education. 
They generally borrow through mortgages and personal loans, or by using credit cards. 
People typically repay these loans with money they earn later.
Companies often require money to fund current operations or to engage in new 
capital projects. They may borrow the needed funds in a variety of ways, such as 
arranging a loan or a line of credit with a bank, or selling fixed income securities to

investors. Companies typically repay their borrowing with income generated in the 
future. In addition to borrowing, companies may raise funds by selling ownership 
interests.
Governments may borrow money to pay salaries and other expenses, to fund 
projects, to provide welfare benefits to their citizens and residents, and to subsidize 
various activities. Governments borrow by selling bills, notes, or bonds. Governments 
repay their debt using future revenues from taxes and in some instances from the 
projects funded by these debts.
Borrowers can borrow from lenders only if the lenders believe that they will be 
repaid. If the lenders believe, however, that repayment in full with interest may not 
occur, they will demand higher rates of interest to cover their expected losses and 
to compensate them for the discomfit they experience wondering whether they will 
lose their money. To lower the costs of borrowing, borrowers often pledge assets as

collateral for their loans. The assets pledged as collateral often include those that will 
be purchased by the proceeds of the loan. If the borrowers do not repay their loans, 
the lenders can sell the collateral and use the proceeds to settle the loans.
Lenders often will not loan to borrowers who intend to invest in risky projects, 
especially if the borrowers cannot pledge other collateral. Investors may still be willing 
to supply capital for these risky projects if they believe that the projects will likely 
produce valuable future cash flows. Rather than lending money, however, they will 
contribute capital in exchange for equity in the projects.
The financial system facilitates borrowing. Lenders aggregate from savers the funds 
that borrowers require. Borrowers must convince lenders that they can repay their 
loans, and that, in the event they cannot, lenders can recover most of the funds lent. 
Credit bureaus, credit rating agencies, and governments promote borrowing; credit

bureaus and credit rating agencies do so by collecting and disseminating information 
that lenders need to analyze credit prospects and governments do so by establishing 
bankruptcy codes and courts that define and enforce the rights of borrowers and

The Functions of the Financial System 9
lenders. When the transaction costs of loans (i.e., the costs of arranging, monitoring, 
and collecting them) are low, borrowers can borrow more to fund current expenditures 
with credible promises to return the money in the future.
2.1.3  Raising Equity Capital
Companies often raise money for projects by selling (issuing) ownership interests (e.g., 
corporate common stock or partnership interests). Although these equity instruments 
legally represent ownership in companies rather than loans to the companies, selling 
equity to raise capital is simply another mechanism for moving money from the future 
to the present. When shareholders or partners contribute capital to a company, the 
company obtains money in the present in exchange for equity instruments that will 
be entitled to distributions in the future. Although the repayment of the money is 
not scheduled as it would be for loans, equity instruments also represent potential

claims on money in the future.
The financial system facilitates raising equity capital. Investment banks help com -
panies issue equities, analysts value the securities that companies sell, and regulatory 
reporting requirements and accounting standards attempt to ensure the production of 
meaningful financial disclosures. The financial system helps promote capital formation 
by producing the financial information needed to determine fair prices for equity. 
Liquid markets help companies raise capital. In these markets, shareholders can easily 
divest their equities as desired. When investors can easily value and trade equities, 
they are more willing to fund reasonable projects that companies wish to undertake.
EXAMPLE 1   
Financing Capital Projects
As a chief financial officer (CFO) of a large industrial firm, you need to raise 
cash within a few months to pay for a project to expand existing and acquire 
new manufacturing facilities. What are the primary options available to you?
Solution:

Solution:
Your primary options are to borrow the funds or to raise the funds by selling own -
ership interests. If the company borrows the funds, you may have the company 
pledge some or all of the project as collateral to reduce the cost of borrowing.
2.1.4  Managing Risks
Many people, companies, and governments face financial risks that concern them. 
These risks include default risk and the risk of changes in interest rates, exchange 
rates, raw material prices, and sale prices, among many other risks. These risks are 
often managed by trading contracts that serve as hedges for the risks.
For example, a farmer and a food processor both face risks related to the price of 
grain. The farmer fears that prices will be lower than expected when his grain is ready 
for sale whereas the food processor fears that prices will be higher than expected when 
she has to buy grain in the future. They both can eliminate their exposures to these

risks if they enter into a binding forward contract for the farmer to sell a specified 
quantity of grain to the food processor at a future date at a mutually agreed upon 
price. By entering into a forward contract that sets the future trade price, they both 
eliminate their exposure to changing grain prices.
In general, hedgers trade to offset or insure against risks that concern them. In 
addition to forward contracts, they may use futures contracts, option contracts, or 
insurance contracts to transfer risk to other entities more willing to bear the risks

Reading 44 ■ Market Organization and Structure 10
(these contracts will be covered in Section 3.4). Often the hedger and the other entity 
face exactly the opposite risks, so the transfer makes both more secure, as in the grain 
example.
The financial system facilitates risk management when liquid markets exist in which 
risk managers can trade instruments that are correlated (or inversely correlated) with 
the risks that concern them without incurring substantial transaction costs. Investment 
banks, exchanges, and insurance companies devote substantial resources to designing 
such contracts and to ensuring that they will trade in liquid markets. When such 
markets exist, people are better able to manage the risks that they face and often are 
more willing to undertake risky activities that they expect will be profitable.
2.1.5  Exchanging Assets for Immediate Delivery (Spot Market Trading)
People and companies often trade one asset for another that they rate more highly or,

equivalently, that is more useful to them. They may trade one currency for another 
currency, or money for a needed commodity or right. Following are some examples 
that illustrate these trades:
■■Volkswagen pays its German workers in euros, but the company receives dollars 
when it sells cars in the United States. To convert money from dollars to euros, 
Volkswagen trades in the foreign exchange markets.
■■A Mexican investor who is worried about the prospects for peso inflation or a 
potential devaluation of the peso may buy gold in the spot gold market. (This 
transaction may hedge against the risk of devaluation of the peso because the 
value of gold may increase with inflation.)
■■A plastic producer must buy carbon credits to emit carbon dioxide when 
burning fuel to comply with environmental regulations. The carbon credit is a 
legal right that the producer must have to engage in activities that emit carbon 
dioxide.
In each of these cases, the trades are considered spot market trades because

the instruments trade for immediate delivery. The financial system facilitates these 
exchanges when liquid spot markets exist in which people can arrange and settle 
trades without substantial transaction costs.
2.1.6  Information-  Motivated Trading
Information-  motivated traders  trade to profit from information that they believe 
allows them to predict future prices. Like all other traders, they hope to buy at low 
prices and sell at higher prices. Unlike pure investors, however, they expect to earn 
a return on their information in addition to the normal return expected for bearing 
risk through time.
Active investment managers are information-  motivated traders who collect and 
analyze information to identify securities, contracts, and other assets that their 
analyses indicate are under- or overvalued. They then buy those that they consider 
undervalued and sell those that they consider overvalued. If successful, they obtain a

greater return than the unconditional return that would be expected for bearing the 
risk in their positions. The return that they expect to obtain is a conditional return 
earned on the basis of the information in their analyses. Practitioners often call this 
process active portfolio management.
Note that the distinction between pure investors and information-  motivated 
traders depends on their motives for trading and not on the risks that they take or 
their expected holding periods. Investors trade to move wealth from the present to 
the future whereas information-  motivated traders trade to profit from superior infor -
mation about future values. When trading to move wealth forward, the time period 
may be short or long. For example, a bank treasurer may only need to move money

The Functions of the Financial System 11
overnight and might use money market instruments trading in an interbank funds 
market to accomplish that. A pension fund, however, may need to move money 30 
years forward and might do that by using shares trading in a stock market. Both are 
investors although their expected holding periods and the risks in the instruments 
that they trade are vastly different.
In contrast, information-  motivated traders trade because their information-  based 
analyses suggest to them that prices of various instruments will increase or decrease 
in the future at a rate faster than others without their information or analytical models 
would expect. After establishing their positions, they hope that prices will change 
quickly in their favor so that they can close their positions, realize their profits, and 
redeploy their capital. These price changes may occur almost instantaneously, or they

may take years to occur if information about the mispricing is difficult to obtain or 
understand.
The two categories of traders are not mutually exclusive. Investors also are often 
information-  motivated traders. Many investors who want to move wealth forward 
through time collect and analyze information to select securities that will allow them 
to obtain conditional returns that are greater than the unconditional returns expected 
for securities in their assets classes. If they have rational reasons to expect that their 
efforts will indeed produce superior returns, they are information-  motivated traders. 
If they consistently fail to produce such returns, their efforts will be futile, and they 
would have been better off simply buying and holding well-  diversified portfolios.
EXAMPLE 2   
Investing versus Information-  Motivated Trading
The head of a large labor union with a pension fund asks you, a pension consul -

tant, to distinguish between investing and information-  motivated trading. You 
are expected to provide an explanation that addresses the financial problems 
that she faces. How would you respond?
Solution:
The object of investing for the pension fund is to move the union’s pension assets 
from the present to the future when they will be needed to pay the union’s retired 
pensioners. The pension fund managers will typically do this by buying stocks, 
bonds, and perhaps other assets. The pension fund managers expect to receive a 
fair rate of return on the pension fund’s assets without paying excessive transac -
tion costs and management fees. The return should compensate the fund for the 
risks that it bears and for the time that other people are using the fund’s money.
The object of information-  motivated trading is to earn a return in excess of 
the fair rate of return. Information-  motivated traders analyze information that

they collect with the hope that their analyses will allow them to predict better 
than others where prices will be in the future. They then buy assets that they 
think will produce excess returns and sell those that they think will underperform. 
Active investment managers are information-  motivated traders.
The characteristic that most distinguishes investors from information-  
motivated traders is the return that they expect. Although both types of traders 
hope to obtain extraordinary returns, investors rationally expect to receive only 
fair returns during the periods of their investments. In contrast, information-  
motivated traders expect to make returns in excess of required fair rates of return. 
Of course, not all investing or information-  motivated trading is successful (in 
other words, the actual returns may not equal or exceed the expected returns).

Reading 44 ■ Market Organization and Structure 12
The financial system facilitates information-  motivated trading when liquid mar -
kets allow active managers to trade without significant transaction costs. Accounting 
standards and reporting requirements that produce meaningful financial disclosures 
reduce the costs of being well informed, but do not necessarily help informed traders 
profit because they often compete with each other. The most profitable well-  informed 
traders are often those that have the most unique insights into future values.
2.1.7  Summary  
People use the financial system for many purposes, the most important of which are 
saving, borrowing, raising equity capital, managing risk, exchanging assets in spot 
markets, and information-  motivated trading. The financial system best facilitates these 
uses when people can trade instruments that interest them in liquid markets, when 
institutions provide financial services at low cost, when information about assets and

about credit risks is readily available, and when regulation helps ensure that everyone 
faithfully honors their contracts.
2.2 Determining Rates of Return
Saving, borrowing, and selling equity are all means of moving money through time. 
Savers move money from the present to the future whereas borrowers and equity 
issuers move money from the future to the present.
Because time machines do not exist, money can travel forward in time only if an 
equal amount of money is travelling in the other direction. This equality always occurs 
because borrowers and equity sellers create the securities in which savers invest. For 
example, the bond sold by a company that needs to move money from the future to 
the present is the same bond bought by a saver who needs to move money from the 
present to the future.
The aggregate amount of money that savers will move from the present to the future 
is related to the expected rate of return on their investments. If the expected return

is high, they will forgo current consumption and move more money to the future. 
Similarly, the aggregate amount of money that borrowers and equity sellers will move 
from the future to the present depends on the costs of borrowing funds or of giving 
up ownership. These costs can be expressed as the rate of return that borrowers and 
equity sellers are expected to deliver in exchange for obtaining current funds. It is the 
same rate that savers expect to receive when delivering current funds. If this rate is 
low, borrowers and equity sellers will want to move more money to the present from 
the future. In other words, they will want to raise more funds.
Because the total money saved must equal the total money borrowed and received 
in exchange for equity, the expected rate of return depends on the aggregate supply 
of funds through savings and the aggregate demand for funds. If the rate is too high, 
savers will want to move more money to the future than borrowers and equity issuers

will want to move to the present. The expected rate will have to be lower to discourage 
the savers and to encourage the borrowers and equity issuers. Conversely, if the rate 
is too low, savers will want to move less money forward than borrowers and equity 
issuers will want to move to the present. The expected rate will have to be higher to 
encourage the savers and to discourage the borrowers and equity issuers. Between 
rates too high and too low, an expected rate of return exists, in theory, in which the 
aggregate supply of funds for investing (supply of funds saved) and the aggregate 
demand for funds through borrowing and equity issuing are equal.
Economists call this rate the equilibrium interest rate. It is the price for moving 
money through time. Determining this rate is one of the most important functions of 
the financial system. The equilibrium interest rate is the only interest rate that would

exist if all securities were equally risky, had equal terms, and were equally liquid. In 
fact, the required rates of return for securities vary by their risk characteristics, terms,

The Functions of the Financial System 13
and liquidity. For a given issuer, investors generally require higher rates of return for 
equity than for debt, for long-  term securities than for short-  term securities, and for 
illiquid securities than for liquid ones. Financial analysts recognize that all required 
rates of return depend on a common equilibrium interest rate plus adjustments for risk.
EXAMPLE 3   
Interest Rates
For a presentation to private wealth clients by your firm’s chief economist, you 
are asked to prepare the audience by explaining the most fundamental facts 
concerning the role of interest rates in the economy. You agree. What main 
points should you try to convey?
Solution:
Savers have money now that they will want to use in the future. Borrowers 
want to use money now that they do not have, but they expect that they will 
have money in the future. Borrowers are loaned money by savers and promise 
to repay it in the future.

The interest rate is the return that lenders, the savers, expect to receive from 
borrowers for allowing borrowers to use the savers’ money. The interest rate is 
the price of using money.
Interest rates depend on the total amount of money that people want to 
borrow and the total amount of money that people are willing to lend. Interest 
rates are high when, in aggregate, people value having money now substantially 
more than they value having money in the future. In contrast, if many people 
with money want to use it in the future and few people presently need more 
money than they have, interest rates will be low.
2.3 Capital Allocation Efficiency
Primary capital markets (primary markets)  are the markets in which companies and 
governments raise capital (funds). Companies may raise funds by borrowing money 
or by issuing equity. Governments may raise funds by borrowing money.
Economies are said to be allocationally efficient when their financial systems allocate

capital (funds) to those uses that are most productive. Although companies may be 
interested in getting funding for many potential projects, not all projects are worth 
funding. One of the most important functions of the financial system is to ensure 
that only the best projects obtain scarce capital funds; the funds available from savers 
should be allocated to the most productive uses.
In market-  based economies, savers determine, directly or indirectly, which proj -
ects obtain capital. Savers determine capital allocations directly by choosing which 
securities they will invest in. Savers determine capital allocations indirectly by giving 
funds to financial intermediaries that then invest the funds. Because investors fear 
the loss of their money, they will lend at lower interest rates to borrowers with the 
best credit prospects or the best collateral, and they will lend at higher rates to other 
borrowers with less secure prospects. Similarly, they will buy only those equities that

they believe have the best prospects relative to their prices and risks.
To avoid losses, investors carefully study the prospects of the various investment 
opportunities available to them. The decisions that they make tend to be well informed, 
which helps ensure that capital is allocated efficiently. The fear of losses by investors

Reading 44 ■ Market Organization and Structure 14
and by those raising funds to invest in projects ensures that only the best projects 
tend to be funded. The process works best when investors are well informed about 
the prospects of the various projects.
In general, investors will fund an equity project if they expect that the value of 
the project is greater than its cost, and they will not fund projects otherwise. If the 
investor expectations are accurate, only projects that should be undertaken will be 
funded and all such projects will be funded. Accurate market information thus leads 
to efficient capital allocation.
EXAMPLE 4   
Primary Market Capital Allocation
How can poor information about the value of a project result in poor capital 
allocation decisions?
Solution:
Projects should be undertaken only if their value is greater than their cost. If 
investors have poor information and overestimate the value of a project in which

its true value is less than its cost, a wealth-  diminishing project may be undertaken. 
Alternatively, if investors have poor information and underestimate the value 
of a project in which its true value is greater than its cost, a wealth-  enhancing 
project may not be undertaken.
ASSETS AND CONTRACTS
People, companies, and governments use many different assets and contracts to fur -
ther their financial goals and to manage their risks. The most common assets include 
financial assets (such as bank deposits, certificates of deposit, loans, mortgages, cor -
porate and government bonds and notes, common and preferred stocks, real estate 
investment trusts, master limited partnership interests, pooled investment products, 
and exchange-  traded funds), currencies, certain commodities (such as gold and oil), 
and real assets (such as real estate). The most common contracts are option, futures, 
forward, swap, and insurance contracts. People, companies, and governments use these

assets and contracts to raise funds, to invest, to profit from information-  motivated 
trading, to hedge risks, and/or to transfer money from one form to another.
3.1 Classifications of Assets and Markets
Practitioners often classify assets and the markets in which they trade by various 
common characteristics to facilitate communications with their clients, with each 
other, and with regulators.
The most actively traded assets are securities, currencies, contracts, and commod -
ities. In addition, real assets are traded. Securities generally include debt instruments, 
equities, and shares in pooled investment vehicles. Currencies  are monies issued by 
national monetary authorities. Contracts are agreements to exchange securities, cur -
rencies, commodities or other contracts in the future. Commodities include precious 
metals, energy products, industrial metals, and agricultural products. Real assets are

tangible properties such as real estate, airplanes, or machinery. Securities, currencies, 
and contracts are classified as financial assets whereas commodities and real assets 
are classified as physical assets.3

Assets and Contracts 15
Securities are further classified as debt or equity. Debt instruments (also called 
fixed-  income instruments) are promises to repay borrowed money. Equities represent 
ownership in companies. Pooled investment vehicle shares represent ownership of an 
undivided interest in an investment portfolio. The portfolio may include securities, 
currencies, contracts, commodities, or real assets. Pooled investment vehicles, such 
as exchange-  traded funds, which exclusively own shares in other companies, generally 
are also considered equities.
Securities are also classified by whether they are public or private securities. Public 
securities are those registered to trade in public markets, such as on exchanges or 
through dealers. In most jurisdictions, issuers must meet stringent minimum regu -
latory standards, including reporting and corporate governance standards, to issue 
publicly traded securities.

Private securities are all other securities. Often, only specially qualified investors 
can purchase private equities and private debt instruments. Investors may purchase 
them directly from the issuer or indirectly through an investment vehicle specifically 
formed to hold such securities. Issuers often issue private securities when they find 
public reporting standards too burdensome or when they do not want to conform 
to the regulatory standards associated with public equity. Venture capital is private 
equity that investors supply to companies when or shortly after they are founded. 
Private securities generally are illiquid. In contrast, many public securities trade in 
liquid markets in which sellers can easily find buyers for their securities.
Contracts are derivative contracts if their values depend on the prices of other 
underlying assets. Derivative contracts may be classified as physical or financial

depending on whether the underlying instruments are physical products or finan -
cial securities. Equity derivatives are contracts whose values depend on equities or 
indexes of equities. Fixed-  income derivatives are contracts whose values depend on 
debt securities or indexes of debt securities.
Practitioners classify markets by whether the markets trade instruments for 
immediate delivery or for future delivery. Markets that trade contracts that call for 
delivery in the future are forward or futures markets. Those that trade for immediate 
delivery are called spot markets  to distinguish them from forward markets that trade 
contracts on the same underlying instruments. Options markets trade contracts that 
deliver in the future, but delivery takes place only if the holders of the options choose 
to exercise them.
When issuers sell securities to investors, practitioners say that they trade in the 
primary market . When investors sell those securities to others, they trade in the

secondary market . In the primary market, funds flow to the issuer of the security 
from the purchaser. In the secondary market, funds flow between traders.
Practitioners classify financial markets as money markets or capital markets. Money 
markets  trade debt instruments maturing in one year or less. The most common 
such instruments are repurchase agreements (defined in Section 3.2.1), negotiable 
certificates of deposit, government bills, and commercial paper. In contrast, capital 
markets  trade instruments of longer duration, such as bonds and equities, whose 
values depend on the credit-  worthiness of the issuers and on payments of interest or 
dividends that will be made in the future and may be uncertain. Corporations generally 
finance their operations in the capital markets, but some also finance a portion of their 
operations by issuing short-  term securities, such as commercial paper.
Finally, practitioners distinguish between traditional investment markets  and

alternative investment markets . Traditional investments include all publicly traded 
debts and equities and shares in pooled investment vehicles that hold publicly traded 
debts and/or equities. Alternative investments include hedge funds , private equi -
ties (including venture capital), commodities, real estate securities and real estate 
properties, securitized debts, operating leases, machinery, collectibles, and precious 
gems. Because these investments are often hard to trade and hard to value, they may

Reading 44 ■ Market Organization and Structure 16
sometimes trade at substantial deviations from their intrinsic values. The discounts 
compensate investors for the research that they must do to value these assets and 
for their inability to easily sell the assets if they need to liquidate a portion of their 
The remainder of this section describes the most common assets and contracts 
that people, companies, and governments trade.
EXAMPLE 5   
Asset and Market Classification
The investment policy of a mutual fund only permits the fund to invest in pub -
lic equities traded in secondary markets. Would the fund be able to purchase:
1 Common stock of a company that trades on a large stock exchange?
2 Common stock of a public company that trades only through dealers?
3 A government bond?
4 A single stock futures contract?
5 Common stock sold for the first time by a properly registered public 
company?
6 Shares in a privately held bank with €10 billion of capital?

Yes. Common stock is equity. Those common stocks that trade on large exchanges 
invariably are public equities that trade in secondary markets.
Yes. Dealer markets are secondary markets and the security is a public equity.
No. Although government bonds are public securities, they are not equities. 
They are debt securities.
No. Although the underlying instruments for single stock futures are invariably 
public equities, single stock futures are derivative contracts, not equities.
No. The fund would not be able to buy these shares because a purchase from 
the issuer would be in the primary market. The fund would have to wait until 
it could buy the shares from someone other than the issuer.
No. These shares are private equities, not public equities. The public prominence 
of the company does not make its securities public securities unless they have 
been properly registered as public securities.
3.2 Securities

People, companies, and governments sell securities to raise money. Securities include 
bonds, notes, commercial paper, mortgages, common stocks, preferred stocks, warrants, 
mutual fund shares, unit trusts, and depository receipts. These can be classified broadly 
as fixed-  income instruments, equities, and shares in pooled investment vehicles. Note

Assets and Contracts 17
that the legal definition of a security varies by country and may or may not coincide 
with the usage here. Securities that are sold to the public or that can be resold to the 
public are called issues. Companies and governments are the most common issuers.
3.2.1  Fixed Income
Fixed-  income instruments contractually include predetermined payment schedules 
that usually include interest and principal payments. Fixed-  income instruments 
generally are promises to repay borrowed money but may include other instruments 
with payment schedules, such as settlements of legal cases or prizes from lotteries. 
The payment amounts may be pre-  specified or they may vary according to a fixed 
formula that depends on the future values of an interest rate or a commodity price. 
Bonds, notes, bills, certificates of deposit, commercial paper, repurchase agreements, 
loan agreements, and mortgages are examples of promises to repay money in the

future. People, companies, and governments create fixed-  income instruments when 
they borrow money.
Corporations and governments issue bonds and notes. Fixed-  income securities with 
shorter maturities are called “notes, ” those with longer maturities are called “bonds. ” 
The cutoff is usually at 10 years. In practice, however, the terms are generally used 
interchangeably. Both become short-  term instruments when the remaining time until 
maturity is short, usually taken to be one year or less.
Some corporations issue convertible bonds, which are typically convertible into 
stock, usually at the option of the holder after some period. If stock prices are high so 
that conversion is likely, convertibles are valued like stock. Conversely, if stock prices 
are low so that conversion is unlikely, convertibles are valued like bonds.
Bills, certificates of deposit, and commercial paper are respectively issued by 
governments, banks, and corporations. They usually mature within a year of being

issued; certificates of deposit sometimes have longer initial maturities.
Repurchase agreements (repos) are short-  term lending instruments. The term can 
be as short as overnight. A borrower seeking funds will sell an instrument—typically 
a high quality bond—to a lender with an agreement to repurchase it later at a slightly 
higher price based on an agreed upon interest rate.
Practitioners distinguish between short-  term, intermediate-  term, and long-  term 
fixed-  income securities. No general consensus exists about the definition of short-  
term, intermediate-  term, and long-  term. Instruments that mature in less than one 
to two years are considered short-  term instruments whereas those that mature in 
more than five to ten years are considered long-  term instruments. In the middle are 
intermediate-  term instruments.
Instruments trading in money markets are called money market instruments. Such 
instruments are traded debt instruments maturing in one year or less. Money market

funds and corporations seeking a return on their short-  term cash balances typically 
hold money market instruments.
3.2.2  Equities
Equities represent ownership rights in companies. These include common and pre -
ferred shares. Common shareholders own residual rights to the assets of the company. 
They have the right to receive any dividends declared by the boards of directors, and 
in the event of liquidation, any assets remaining after all other claims are paid. Acting 
through the boards of directors that they elect, common shareholders usually can 
select the managers who run the corporations.
Preferred shares are equities that have preferred rights (relative to common shares) 
to the cash flows and assets of the company. Preferred shareholders generally have 
the right to receive a specific dividend on a regular basis. If the preferred share is a 
cumulative preferred equity, the company must pay the preferred shareholders any

previously omitted dividends before it can pay dividends to the common shareholders.

Reading 44 ■ Market Organization and Structure 18
Preferred shareholders also have higher claims to assets relative to common share -
holders in the event of corporate liquidation. For valuation purposes, financial analysts 
generally treat preferred stocks as fixed-  income securities when the issuers will clearly 
be able to pay their promised dividends in the foreseeable future.
Warrants are securities issued by a corporation that allow the warrant holders to 
buy a security issued by that corporation, if they so desire, usually at any time before 
the warrants expire or, if not, upon expiration. The security that warrant holders can 
buy usually is the issuer’s common stock, in which case the warrants are considered 
equities because the warrant holders can obtain equity in the company by exercising 
their warrants. The warrant exercise price  is the price that the warrant holder must 
pay to buy the security.
EXAMPLE 6   

EXAMPLE 6   
What factors distinguish fixed-  income securities from equities?
Solution:
Fixed-  income securities generate income on a regular schedule. They derive 
their value from the promise to pay a scheduled cash flow. The most common 
fixed-  income securities are promises made by people, companies, and govern -
ments to repay loans.
Equities represent residual ownership in companies after all other claims—
including any fixed-  income liabilities of the company—have been satisfied. For 
corporations, the claims of preferred equities typically have priority over the 
claims of common equities. Common equities have the residual ownership in 
corporations.
3.2.3  Pooled Investments
Pooled investment vehicles are mutual funds, trusts, depositories, and hedge funds, 
that issue securities that represent shared ownership in the assets that these entities 
hold. The securities created by mutual funds, trusts, depositories, and hedge fund

are respectively called shares , units , depository receipts , and limited partnership 
interests  but practitioners often use these terms interchangeably. People invest in 
pooled investment vehicles to benefit from the investment management services of 
their managers and from diversification opportunities that are not readily available 
to them on an individual basis.
Mutual funds are investment vehicles that pool money from many investors for 
investment in a portfolio of securities. They are often legally organized as investment 
trusts or as corporate investment companies. Pooled investment vehicles may be 
open-  ended or closed-  ended. Open-  ended funds issue new shares and redeem existing 
shares on demand, usually on a daily basis. The price at which a fund redeems and 
sells the fund’s shares is based on the net asset value of the fund’s portfolio, which 
is the difference between the fund’s assets and liabilities, expressed on a per share

basis. Investors generally buy and sell open-  ended mutual funds by trading with the 
mutual fund.
In contrast, closed-  end funds issue shares in primary market offerings that the fund 
or its investment bankers arrange. Once issued, investors cannot sell their shares of 
the fund back to the fund by demanding redemption. Instead, investors in closed-  end 
funds must sell their shares to other investors in the secondary market. The secondary 
market prices of closed-  end funds may differ—sometimes quite significantly—from 
their net asset values. Closed-  end funds generally trade at a discount to their net asset

Assets and Contracts 19
values. The discount reflects the expenses of running the fund and sometimes investor 
concerns about the quality of the management. Closed-  end funds may also trade at 
a discount or a premium to net asset value when investors believe that the portfolio 
securities are overvalued or undervalued. Many financial analysts thus believe that 
discounts and premiums on closed-  end funds measure market sentiment.
Exchange-  traded funds (ETFs) and exchange-  traded notes (ETNs) are open-  ended 
funds that investors can trade among themselves in secondary markets. The prices at 
which ETFs trade rarely differ much from net asset values because a class of investors, 
known as authorized participants (APs), has the option of trading directly with the 
ETF. If the market price of an equity ETF is sufficiently below its net asset value, APs 
will buy shares in the secondary market at market price and redeem shares at net

asset value with the fund. Conversely, if the price of an ETF is sufficiently above its 
net asset value, APs will buy shares from the fund at net asset value and sell shares 
in the secondary market at market price. As a result, the market price and net asset 
values of ETFs tend to converge.
Many ETFs permit only in-  kind deposits and redemptions. Buyers who buy directly 
from such a fund pay for their shares with a portfolio of securities rather than with 
cash. Similarly, sellers receive a portfolio of securities. The transaction portfolio gen -
erally is very similar—often essentially identical—to the portfolio held by the fund. 
Practitioners sometimes call such funds “depositories” because they issue depository 
receipts for the portfolios that traders deposit with them. The traders then trade the 
receipts in the secondary market. Some warehouses holding industrial materials and 
precious metals also issue tradable warehouse receipts.

Asset-  backed securities are securities whose values and income payments are 
derived from a pool of assets, such as mortgage bonds, credit card debt, or car loans. 
These securities typically pass interest and principal payments received from the pool 
of assets through to their holders on a monthly basis. These payments may depend 
on formulas that give some classes of securities—called tranches—backed by the pool 
more value than other classes.
Hedge funds are investment funds that generally organize as limited partnerships. 
The hedge fund managers are the general partners. The limited partners are qualified 
investors who are wealthy enough and well informed enough to tolerate and accept 
substantial losses, should they occur. The regulatory requirements to participate in a 
hedge fund and the regulatory restrictions on hedge funds vary by jurisdiction. Most 
hedge funds follow only one investment strategy, but no single investment strategy

characterizes hedge funds as a group. Hedge funds exist that follow almost every 
imaginable strategy ranging from long–short arbitrage in the stock markets to direct 
investments in exotic alternative assets.
The primary distinguishing characteristic of hedge funds is their management 
compensation scheme. Almost all funds pay their managers with an annual fee that is 
proportional to their assets and with an additional performance fee that depends on 
the wealth that the funds generate for their shareholders. A secondary distinguishing 
characteristic of many hedge funds is the use of leverage to increase risk exposure 
and to hopefully increase returns.
3.3 Currencies
Currencies  are monies issued by national monetary authorities. Approximately 175 
currencies are currently in use throughout the world. Some of these currencies are 
regarded as reserve currencies. Reserve currencies are currencies that national central

banks and other monetary authorities hold in significant quantities. The primary reserve 
currencies are the US dollar and the euro. Secondary reserve currencies include the 
British pound, the Japanese yen, and the Swiss franc.

Reading 44 ■ Market Organization and Structure 20
Currencies trade in foreign exchange markets. In spot currency transactions, one 
currency is immediately or almost immediately exchanged for another. The rate of 
exchange is called the spot exchange rate. Traders typically negotiate institutional trades 
in multiples of large quantities, such as US$1 million or ¥100 million. Institutional 
trades generally settle in two business days.
Retail currency trades most commonly take place through commercial banks when 
their customers exchange currencies at a location of the bank, use ATM machines 
when travelling to withdraw a different currency than the currency in which their 
bank accounts are denominated, or use credit cards to buy items priced in different 
currencies. Retail currency trades also take place at airport kiosks, at store front 
currency exchanges, or on the street.
3.4 Contracts
A contract is an agreement among traders to do something in the future. Contracts

include forward, futures, swap, option, and insurance contracts. The values of most 
contracts depend on the value of an underlying  asset. The underlying asset may be 
a commodity, a security, an index representing the values of other instruments, a 
currency pair or basket, or other contracts.
Contracts provide for some physical or cash settlement in the future. In a phys -
ically settled contract, settlement occurs when the parties to the contract physically 
exchange some item, such as tomatoes, pork bellies, or gold bars. Physical settlement 
also includes the delivery of such financial instruments as bonds, equities, or futures 
contracts even though the delivery is electronic. In contrast, cash settled contracts 
settle through cash payments. The amount of the payment depends on formulas 
specified in the contracts.
Financial analysts classify contracts by whether they are physical or financial based 
on the nature of the underlying asset. If the underlying asset is a physical product,

the contract is a physical; otherwise, the contract is a financial. Examples of assets 
classified as physical include contracts for the delivery of petroleum, lumber, and gold. 
Examples of assets classified as financial include option contracts, and contracts on 
interest rates, stock indexes, currencies, and credit default swaps.
Contracts that call for immediate delivery are called spot contracts, and they trade 
in spot markets. Immediate delivery generally is three days or less, but depends on 
each market. All other contracts involve what practitioners call futurity. They derive 
their values from events that will take place in the future.
EXAMPLE 7   
Contracts for Difference
Contracts for difference (CFD) allow people to speculate on price changes for 
an underlying asset, such as a common stock or an index. Dealers generally 
sell CFDs to their clients. When the clients sell the CFDs back to their dealer, 
they receive any appreciation in the underlying asset’s price between the time

of purchase and sale (open and close) of the contract. If the underlying asset’s 
price drops over this interval, the client pays the dealer the difference.
1 Are contracts for difference derivative contracts?
2 Are contracts for difference based on copper prices cash settled or physi -
cally settled?

Assets and Contracts 21
Contracts for difference are derivative contracts because their values are derived 
from changes in the prices of the underlying asset on which they are based.
All contracts for difference are cash settled contracts regardless of the under -
lying asset on which they are based because they settle in cash and not in the 
underlying asset.
3.4.1  Forward Contracts
A forward contract  is an agreement to trade the underlying asset in the future at a 
price agreed upon today. For example, a contract for the sale of wheat after the harvest 
is a forward contract. People often use forward contracts to reduce risk. Before plant -
ing wheat, farmers like to know the price at which they will sell their crop. Similarly, 
before committing to sell flour to bakers in the future, millers like to know the prices 
that they will pay for wheat. The farmer and the miller both reduce their operating 
risks by agreeing to trade wheat forward.

Practitioners call such traders hedgers because they use their contractual com -
mitments to hedge their risks. If the price of wheat falls, the wheat farmer’s crop will 
drop in value on the spot market but he has a contract to sell wheat in the future at 
a higher fixed price. The forward contract has become more valuable to the farmer. 
Conversely, if the price of wheat rises, the miller’s future obligation to sell flour will 
become more burdensome because of the high price he would have to pay for wheat 
on the spot market, but the miller has a contract to buy wheat at a lower fixed price. 
The forward contract has become more valuable to the miller. In both cases, fluc -
tuations in the spot price are hedged by the forward contract. The forward contract 
offsets the operating risks that the hedgers face.
Consider a simple example of hedging. A tomato farmer in southern Ontario,

Canada, grows tomatoes for processing into tomato sauce. The farmer expects to harvest 
250,000 bushels and that the price at harvest will be $1.03. That price, however, could 
fluctuate significantly before the harvest. If the price of tomatoes drops to $0.75, the 
farmer would lose $0.28 per bushel ($1.03 – $0.75) relative to his expectations, or a 
total of $70,000. Now, suppose that the farmer can sell tomatoes forward to Heinz at 
$1.01 for delivery at the harvest. If the farmer sells 250,000 bushels forward, and the 
price of tomatoes drops to $0.75, the farmer would still be able to sell his tomatoes 
for $1.01, and thus would not suffer from the drop in price of tomatoes.
EXAMPLE 8   
Hedging Gold Production
An Indonesian gold producer invests in a mine expansion project on the expec -
tation that gold prices will remain at or above 35,000 rupiah per gram when the 
new project starts producing ore.
1 What risks does the gold producer face with respect to the price of gold?

2 How might the gold producer hedge its gold price risk?
The gold producer faces the risk that the price of gold could fall below 35,000 
rupiah before it can sell its new production. If so, the investment in the expan -
sion project will be less profitable than expected, and may even generate losses 
for the mine.

Reading 44 ■ Market Organization and Structure 22
The gold producer could hedge the gold price risk by selling gold forward, 
hopefully at a price near 35,000 rupiah. Even if the price of gold falls, the gold 
producer would get paid the contract price.
Forward contracts are very common, but two problems limit their usefulness for 
many market participants. The first problem is counterparty risk. Counterparty risk  
is the risk that the other party to a contract will fail to honor the terms of the contract. 
Concerns about counterparty risk ensure that generally only parties who have long-  
standing relationships with each other execute forward contracts. Trustworthiness 
is critical when prices are volatile because, after a large price change, one side or the 
other may prefer not to settle the contract.
The second problem is liquidity. Trading out of a forward contract is very difficult 
because it can only be done with the consent of the other party. The liquidity problem

ensures that forward contracts tend to be executed only among participants for whom 
delivery is economically efficient and quite certain at the time of contracting so that 
both parties will want to arrange for delivery.
The counterparty risk problem and the liquidity problem often make it difficult for 
market participants to obtain the hedging benefits associated with forward contract -
ing. Fortunately, futures contracts have been developed to mitigate these problems.
3.4.2  Futures Contracts
A futures contract  is a standardized forward contract for which a clearinghouse 
guarantees the performance of all traders. The buyer of a futures contract is the side 
that will take physical delivery or its cash equivalent. The seller of a futures contract 
is the side that is liable for the delivery or its cash equivalent. A clearinghouse  is an 
organization that ensures that no trader is harmed if another trader fails to honor

the contract. In effect, the clearinghouse acts as the buyer for every seller and as the 
seller for every buyer. Buyers and sellers, therefore, can trade futures without wor -
rying whether their counterparties are creditworthy. Because futures contracts are 
standardized, a buyer can eliminate his obligation to buy by selling his contract to 
anyone. A seller similarly can eliminate her obligation to deliver by buying a contact 
from anyone. In either case, the clearinghouse will release the trader from all future 
obligations if his or her long and short positions exactly offset each other.
To protect against defaults, futures clearinghouses require that all participants 
post with the clearinghouse an amount of money known as initial margin  when 
they enter a contract. The clearinghouse then settles the margin accounts on a daily 
basis. All participants who have lost on their contracts that day will have the amount

of their losses deducted from their margin by the clearinghouse. The clearinghouse 
similarly increases margins for all participants who gained on that day. Participants 
whose margins drop below the required maintenance margin  must replenish their 
accounts. If a participant does not provide sufficient additional margin when required, 
the participant’s broker will immediately trade to offset the participant’s position. 
These variation margin  payments ensure that the liabilities associated with futures 
contracts do not grow large.

Assets and Contracts 23
EXAMPLE 9   
Futures Margin
NYMEX’s Light Sweet Crude Oil futures contract specifies the delivery of 1,000 
barrels of West Texas Intermediate Crude Oil when the contract finally settles. 
A broker requires that its clients post an initial overnight margin of $7,763 per 
contract and an overnight maintenance margin of $5,750 per contract. A client 
buys ten contracts at $75 per barrel through this broker. On the next day, the 
contract settles for $72 per barrel. How much additional margin will the client 
have to provide to his broker?
Solution:
The client lost three dollars per barrel (he is the side committed to take delivery 
or its cash equivalent at $75 per barrel). This results in a $3,000 loss on each 
of his 10 contracts, and a total loss of $30,000. His initial margin of $77,630 is 
reduced by $30,000 leaving $47,630 in his margin account. Because his account 
has dropped below the maintenance margin requirement of $57,500, the client

will get a margin call. The client must provide an additional $30,000 = $77,630 
– $47,630 to replenish his margin account; the account is replenished to the 
amount of the initial margin. The client will only receive another margin call if 
his account drops to below $57,500 again.
Futures contracts have vastly improved the efficiency of forward contracting mar -
kets. Traders can trade standardized futures contracts with anyone without worrying 
about counterparty risk, and they can close their positions by arranging offsetting 
trades. Hedgers for whom the terms of the standard contract are not ideal generally 
still use the futures markets because the contracts embody most of the price risk that 
concerns them. They simply offset (close out) their futures positions, at the same time 
they enter spot contracts on which they make or take ultimate delivery.
EXAMPLE 10   
Forward and Futures Contracts
What feature most distinguishes futures contracts from forward contracts?
Solution:

Solution:
A futures contract is a standardized forward contract for which a clearinghouse 
guarantees the performance of all buyers and sellers. The clearinghouse reduces 
the counterparty risk problem. The clearinghouse allows a buyer who has bought 
a contract from one person and sold the same contract to another person to 
net out the two obligations so that she is no longer liable for either side of the 
contract; the positions are closed. The ability to trade futures contracts provides 
liquidity in futures contracts compared with forward contracts.
3.4.3  Swap Contracts
A swap contract  is an agreement to exchange payments of periodic cash flows that 
depend on future asset prices or interest rates. For example, in a typical interest rate 
swap , at periodic intervals, one party makes fixed cash payments to the counterparty 
in exchange for variable cash payments from the counterparty. The variable payments

are based on a pre-  specified variable interest rate such as the London Interbank Offered

Reading 44 ■ Market Organization and Structure 24
Rate (Libor). This swap effectively exchanges fixed interest payments for variable 
interest payments. Because the variable rate is set in the future, the cash flows for 
this contract are uncertain when the parties enter the contract.
Investment managers often enter interest rate swaps when they own a fixed long-  
term income stream that they want to convert to a cash flow that varies with current 
short-  term interest rates, or vice versa. The conversion may allow them to substantially 
reduce the total interest rate risk to which they are exposed. Hedgers often use swap 
contracts to manage risks.
In a commodity swap , one party typically makes fixed payments in exchange for 
payments that depend on future prices of a commodity such as oil. In a currency 
swap , the parties exchange payments denominated in different currencies. The pay -
ments may be fixed, or they may vary depending on future interest rates in the two

countries. In an equity swap , the parties exchange fixed cash payments for payments 
that depend on the returns to a stock or a stock index.
EXAMPLE 11   
Swap and Forward Contracts
What feature most distinguishes a swap contract from a cash-  settled forward 
contract?
Solution:
Both contracts provide for the exchange of cash payments in the future. A 
forward contract only has a single cash payment at the end that depends on an 
underlying price or index at the end. In contrast, a swap contract has several 
scheduled periodic payments, each of which depends on an underlying price or 
index at the time of the payment.
3.4.4  Option Contracts
An option contract  allows the holder (the purchaser) of the option  to buy or sell, 
depending on the type of option, an underlying instrument at a specified price at or 
before a specified date in the future. Those that do buy or sell are said to exercise  their 
contracts. An option to buy is a call option , and an option to sell is a put option. The

specified price is called the strike price (exercise price). If the holders can exercise 
their contracts only when they mature, they are European-  style  contracts. If they can 
exercise the contracts earlier, they are American-  style  contracts. Many exchanges list 
standardized option contracts on individual stocks, stock indexes, futures contracts, 
currencies, swaps, and precious metals. Institutions also trade many customized option 
contracts with dealers in the over-  the- counter derivative market.
Option holders generally will exercise call options if the strike price is below the 
market price of the underlying instrument, in which case, they will be able to buy at a 
lower price than the market price. Similarly, they will exercise put options if the strike 
price is above the underlying instrument price so that they sell at a higher price than 
the market price. Otherwise, option holders allow their options to expire as worthless.

The price that traders pay for an option is the option premium. Options can be 
quite expensive because, unlike forward and futures contracts, they do not impose 
any liability on the holder. The premium compensates the sellers of options—called 
option writers—for giving the call option holders the right to potentially buy below 
market prices and put option holders the right to potentially sell above market prices. 
Because the writers must trade if the holders exercise their options, option contracts 
may impose substantial liabilities on the writers.

Assets and Contracts 25
EXAMPLE 12   
Option and Forward Contracts
What feature most distinguishes option contracts from forward contracts?
Solution:
The holder of an option contract has the right, but not the obligation, to buy 
(for a call option) or sell (for a put option) the underlying instrument at some 
time in the future. The writer of an option contract must trade the underlying 
instrument if the holder exercises the option.
In contrast, the two parties to a forward contract must trade the underlying 
instrument (or its equivalent value for a cash-  settled contract) at some time in 
the future if either party wants to settle the contract.
3.4.5  Other Contracts
Insurance contracts pay their beneficiaries a cash benefit if some event occurs. Life, 
liability, and automobile insurance are examples of insurance contracts sold to retail 
clients. People generally use insurance contracts to compensate for losses that they

will experience if bad things happen unexpectedly. Insurance contracts allow them 
to hedge risks that they face.
Credit default swaps (CDS) are insurance contracts that promise payment of 
principal in the event that a company defaults on its bonds. Bondholders use credit 
default swaps to convert risky bonds into more secure investments. Other creditors 
of the company may also buy them to hedge against the risk they will not be paid if 
the company goes bankrupt.
Well-  informed traders who believe that a corporation will default on its bonds 
may buy credit default swaps written on the corporation’s bonds if the swap prices 
are sufficiently low. If they are correct, the traders will profit if the payoff to the swap 
is more than the cost of buying and maintaining the swap position.
People sometimes also buy insurance contracts as investments, especially in juris -
dictions where payouts from insurance contracts are not subject to as much taxation as

are payouts to other investment vehicles. They may buy these contracts directly from 
insurance companies, or they may buy already issued contracts from their owners. 
For example, the life settlements market trades life insurance contracts that people 
sell to investors when they need cash.
3.5 Commodities
Commodities include precious metals, energy products, industrial metals, agricul -
tural products, and carbon credits. Spot commodity markets trade commodities for 
immediate delivery whereas the forward and futures markets trade commodities for 
future delivery. Managers seeking positions in commodities can acquire them directly 
by trading in the spot markets or indirectly by trading forward and futures contracts.
The producers and processors of industrial metals and agricultural products are 
the primary users of the spot commodity markets because they generally are best 
able to take and make delivery and to store physical products. They undertake these

activities in the normal course of operating their businesses. Their ability to handle 
physical products and the information that they gather operating businesses also 
gives them substantial advantages as information-  motivated traders in these markets. 
Many producers employ financial analysts to help them analyze commodity market 
conditions so that they can best manage their inventories to hedge their operational 
risks and to speculate on future price changes.

Reading 44 ■ Market Organization and Structure 26
Commodities also interest information-  motivated traders and investment managers 
because they can use them as hedges against risks that they hold in their portfolios 
or as vehicles to speculate on future price changes. Most such traders take positions 
in the futures markets because they usually do not have facilities to handle most 
physical products nor can they easily obtain them. They also cannot easily cope with 
the normal variation in qualities that characterizes many commodities. Information-  
motivated traders and investment managers also prefer to trade in futures markets 
because most futures markets are more liquid than their associated spot markets 
and forward markets. The liquidity allows them to easily close their positions before 
delivery so that they can avoid handling physical products.
Some information-  motivated traders and investment managers, however, trade in

the spot commodity markets, especially when they can easily contract for low-  cost 
storage. Commodities for which delivery and storage costs are lowest are nonperish -
able products for which the ratio of value to weight is high and variation in quality is 
low. These generally include precious metals, industrial diamonds, such high-  value 
industrial metals as copper, aluminum, and mercury, and carbon credits.
3.6 Real Assets
Real assets include such tangible properties as real estate, airplanes, machinery, 
or lumber stands. These assets normally are held by operating companies, such as 
real estate developers, airplane leasing companies, manufacturers, or loggers. Many 
institutional investment managers, however, have been adding real assets to their 
portfolios as direct investments (involving direct ownership of the real assets) and 
indirect investments (involving indirect ownership, for example, purchase of securities

of companies that invest in real assets or real estate investment trusts). Investments 
in real assets are attractive to them because of the income and tax benefits that they 
often generate, and because changes in their values may have a low correlation with 
other investments that the managers hold.
Direct investments in real assets generally require substantial management to ensure 
that the assets are maintained and used efficiently. Investment managers investing in 
such assets must either hire personnel to manage them or hire outside management 
companies. Either way, management of real assets is quite costly.
Real assets are unique properties in the sense that no two assets are alike. An 
example of a unique property is a real estate parcel. No two parcels are the same 
because, if nothing else, they are located in different places. Real assets generally 
differ in their conditions, remaining useful lives, locations, and suitability for various

purposes. These differences are very important to the people who use them, so the 
market for a given real asset may be very limited. Thus, real assets tend to trade in 
very illiquid markets.
The heterogeneity of real assets, their illiquidity, and the substantial costs of man -
aging them are all factors that complicate the valuation of real assets and generally 
make them unsuitable for most investment portfolios. These same problems, however, 
often cause real assets to be misvalued in the market, so astute information-  motivated 
traders may occasionally identify significantly undervalued assets. The benefits from 
purchasing such assets, however, are often offset by the substantial costs of searching 
for them and by the substantial costs of managing them.
Many financial intermediaries create entities, such as real estate investment trusts 
(REITs) and master limited partnerships (MLPs), to securitize real assets and to facilitate

indirect investment in real assets. The financial intermediaries manage the assets and 
pass through the net benefits after management costs to the investors who hold these 
securities. Because these securities are much more homogenous and divisible than 
the real assets that they represent, they tend to trade in much more liquid markets. 
Thus, they are much more suitable as investments than the real assets themselves.

Assets and Contracts 27
Of course, investors seeking exposure to real assets can also buy shares in cor -
porations that hold and operate real assets. Although almost all corporations hold 
and operate real assets, many specialize in assets that particularly interest investors 
seeking exposure to specific real asset classes. For example, investors interested in 
owning aircraft can buy an aircraft leasing company such as Waha Capital (Abu Dhabi 
Securities Exchange) and Aircastle Limited (NYSE).
EXAMPLE 13   
Assets and Contracts
Consider the following assets and contracts:
Bank deposits Hedge funds
Certificates of deposit Master limited partnership interests
Common stocks Mortgages
Corporate bonds Mutual funds
Currencies Stock option contracts
Exchange-  traded funds Preferred stocks
Lumber forward contracts Real estate parcels
Crude oil futures contracts Interest rate swaps
Gold Treasury notes
1 Which of these represent ownership in corporations?
2 Which of these are debt instruments?

3 Which of these are created by traders rather than by issuers?
4 Which of these are pooled investment vehicles?
5 Which of these are real assets?
6 Which of these would a home builder most likely use to hedge construc -
tion costs?
7 Which of these would a corporation trade when moving cash balances 
among various countries?
Common and preferred stocks represent ownership in corporations.
Bank deposits, certificates of deposit, corporate bonds, mortgages, and Treasury 
notes are all debt instruments. They respectively represent loans made to banks, 
corporations, mortgagees (typically real estate owners), and the Treasury.
Lumber forward contracts, crude oil futures contracts, stock option contracts, 
and interest rate swaps are created when the seller sells them to a buyer.
Exchange-  traded funds, hedge funds, and mutual funds are pooled investment

vehicles. They represent shared ownership in a portfolio of other assets.
Real estate parcels are real assets.

Reading 44 ■ Market Organization and Structure 28
A builder would buy lumber forward contracts to lock in the price of lumber 
needed to build homes.
Corporations often trade currencies when moving cash from one country to 
another.
FINANCIAL INTERMEDIARIES
Financial intermediaries help entities achieve their financial goals. These intermedi -
aries include commercial, mortgage, and investment banks; credit unions, credit card 
companies, and various other finance corporations; brokers and exchanges; dealers 
and arbitrageurs; clearinghouses and depositories; mutual funds and hedge funds; 
and insurance companies. The services and products that financial intermediaries 
provide allow their clients to solve the financial problems that they face more effi -
ciently than they could do so by themselves. Financial intermediaries are essential to 
well-  functioning financial systems.
Financial intermediaries are called intermediaries because the services and prod -

ucts that they provide help connect buyers to sellers in various ways. Whether the 
connections are easy to identify or involve complex financial structures, financial 
intermediaries stand between one or more buyers and one or more sellers and help 
them transfer capital and risk between them. Financial intermediaries’ activities allow 
buyers and sellers to benefit from trading, often without any knowledge of the other.
This section introduces the main financial intermediaries that provide services and 
products in well-  developed financial markets. The discussion starts with those inter -
mediaries whose services most obviously connect buyers to sellers and then proceeds 
to those intermediaries whose services create more subtle connections. Because many 
financial intermediaries provide many different types of services, some are mentioned 
more than once. The section concludes with a general characterization of the various

ways in which financial intermediaries add value to the financial system.
4.1 Brokers, Exchanges, and Alternative Trading Systems
Brokers  are agents who fill orders for their clients. They do not trade with their clients. 
Instead, they search for traders who are willing to take the other side of their clients’ 
orders. Individual brokers may work for large brokerage firms, the brokerage arm of 
banks, or at exchanges. Some brokers match clients to clients personally. Others use 
specialized computer systems to identify potential trades and help their clients fill 
their orders. Brokers help their clients trade by reducing the costs of finding coun -
terparties for their trades.
Block brokers  provide brokerage service to large traders. Large orders are hard 
to fill because finding a counterparty willing to do a large trade is often quite difficult. 
A large buy order generally will trade at a premium to the current market price, and

a large sell order generally will trade at a discount to the current market price. These 
price concessions encourage other traders to trade with the large traders. They also 
make large traders reluctant, however, to expose their orders to the public before 
their trades are arranged because they do not want to move the market. Block bro -
kers, therefore, carefully manage the exposure of the orders entrusted to them, which 
makes filling them difficult.4

Financial Intermediaries 29
Investment banks  provide advice to their mostly corporate clients and help them 
arrange transactions such as initial and seasoned securities offerings. Their corporate 
finance divisions help corporations finance their business by issuing securities, such 
as common and preferred shares, notes, and bonds. Another function of corporate 
finance divisions is to help companies identify and acquire other companies (i.e., in 
mergers and acquisitions).
Exchanges  provide places where traders can meet to arrange their trades. 
Historically, brokers and dealers met on an exchange floor to negotiate trades. 
Increasingly, exchanges arrange trades for traders based on orders that brokers and 
dealers submit to them. Such exchanges essentially act as brokers. The distinction 
between exchanges and brokers has become quite blurred. Exchanges and brokers 
that use electronic order matching systems to arrange trades among their clients

are functionally indistinguishable in this respect. Examples of exchanges include the 
NYSE-  Euronext, Eurex, Deutsche Börse, the Chicago Mercantile Exchange, the Tokyo 
Stock Exchange, and the Singapore Exchange.
Exchanges are easily distinguished from brokers by their regulatory operations. 
Most exchanges regulate their members’ behavior when trading on the exchange, and 
sometimes away from the exchange.
Many securities exchanges regulate the issuers that list their securities on the 
exchange. These regulations generally require timely financial disclosure. Financial 
analysts use this information to value the securities traded at the exchange. Without 
such disclosure, valuing securities could be very difficult and market prices might 
not reflect the fundamental values of the securities. In such situations, well-  informed 
participants may profit from less-  informed participants. To avoid such losses, the

less-  informed participants may withdraw from the market, which can greatly increase 
corporate costs of capital.
Some exchanges also prohibit issuers from creating capital structures that would 
concentrate voting rights in the hands of a few owners who do not own a commen -
surate share of the equity. These regulations attempt to ensure that corporations are 
run for the benefit of all shareholders and not to promote the interests of controlling 
shareholders who do not have significant economic stakes in the company.
Exchanges derive their regulatory authority from their national or regional govern -
ments, or through the voluntary agreements of their members and issuers to subject 
themselves to the exchange regulations. In most countries, government regulators 
oversee the exchange rules and the regulatory operations. Most countries also impose 
financial disclosure standards on public issuers. Examples of government regulatory

bodies include the Japanese Financial Services Agency, the British Financial Services 
Authority, the German Bundesanstalt für Finanzdienstleistungsaufsicht, the US 
Securities and Exchange Commission, the Ontario Securities Commission, and the 
Mexican Comisión Nacional Bancaria y de Valores.
Alternative trading systems  (ATSs), also known as electronic communications 
networks  (ECNs) or multilateral trading facilities  (MTFs) are trading venues that 
function like exchanges but that do not exercise regulatory authority over their sub -
scribers except with respect to the conduct of their trading in their trading systems. 
Some ATSs operate electronic trading systems that are otherwise indistinguishable 
from the trading systems operated by exchanges. Others operate innovative trading 
systems that suggest trades to their customers based on information that their cus -
tomers share with them or that they obtain through research into their customers’

preferences. Many ATSs are known as dark pools  because they do not display the 
orders that their clients send to them. Large investment managers especially like these 
systems because market prices often move to their disadvantage when other traders 
know about their large orders. ATSs may be owned and operated by broker–dealers, 
exchanges, banks, or by companies organized solely for this purpose, many of which 
may be owned by a consortia of brokers–dealers and banks. Examples of ATSs include

Reading 44 ■ Market Organization and Structure 30
PureTrading (Canada), the Order Machine (Netherlands), Chi-  X Europe, BATS (United 
States), POSIT (United States), Liquidnet (United States), Baxter-  FX (Ireland), and 
Turquoise (Europe). Many of these ATSs provide services in many markets besides 
the ones in which they are domiciled.
4.2 Dealers
Dealers  fill their clients’ orders by trading with them. When their clients want to sell 
securities or contracts, dealers buy the instruments for their own accounts. If their 
clients want to buy securities, dealers sell securities that they own or have borrowed. 
After completing a transaction, dealers hope to reverse the transaction by trading 
with another client on the other side of the market. When they are successful, they 
effectively connect a buyer who arrived at one point in time with a seller who arrived 
at another point in time.
The service that dealers provide is liquidity. Liquidity  is the ability to buy or sell

with low transactions costs when you want to trade. By allowing their clients to trade 
when they want to trade, dealers provide liquidity to them. In over-  the- counter markets, 
dealers offer liquidity when their clients ask them to trade with them. In exchange 
markets, dealers offer liquidity to anyone who is willing to trade at the prices that 
the dealers offer at the exchange. Dealers profit when they can buy at prices that on 
average are lower than the prices at which they sell.
Dealers may organize their operations within proprietary trading houses, investment 
banks, and hedge funds, or as sole proprietorships. Some dealers are traditional dealers 
in the sense that individuals make trading decisions. Others use computerized trading 
to make all trading decisions. Examples of companies with large dealing operations 
include Deutsche Securities (Germany), RBC Capital Markets (Canada), Nomura 
(Japan), Timber Hill (United States), Knight Securities (United States), Goldman Sachs

(United States), and IG Group plc (United Kingdom). Almost all investment banks 
have large dealing operations.
Most dealers also broker orders, and many brokers deal to their customers. 
Accordingly, practitioners often use the term broker–dealer  to refer to dealers and 
brokers. Broker–dealers have a conflict of interest with respect to how they fill their 
customers’ orders. When acting as a broker, they must seek the best price for their 
customers’ orders. When acting as dealers, however, they profit most when they sell to 
their customers at high prices or buy from their customers at low prices. The problem 
is most serious when the customer allows the broker–dealer to decide whether to trade 
the order with another trader or to fill it as a dealer. Consequently, when trading with 
a broker–dealer, some customers specify how they want their orders filled. They may 
also trade only with pure agency brokers who do not also deal.

Primary dealers are dealers with whom central banks trade when conducting 
monetary policy. They buy bills, notes, and bonds when the central banks sell them 
to decrease the money supply. The dealers then sell these instruments to their clients. 
Similarly, when the central banks want to increase the money supply, the primary 
dealers buy these instruments from their clients and sell them to the central banks.
EXAMPLE 14   
Brokers and Dealers
What characteristic most likely  distinguishes brokers from dealers?

Financial Intermediaries 31
Solution:
Brokers are agents that arrange trades on behalf of their clients. They do not 
trade with their clients. In contrast, dealers are proprietary traders who trade 
with their clients.
4.3 Securitizers
Banks and investment companies create new financial products when they buy and 
repackage securities or other assets. For example, mortgage banks commonly originate 
hundreds or thousands of residential mortgages by lending money to homeowners. 
They then place the mortgages in a pool and sell shares of the pool to investors as 
mortgage pass-  through securities, which are also known as mortgage-  backed securi -
ties. All payments of principal and interest are passed through to the investors each 
month, after deducting the costs of servicing the mortgages. Investors who purchase 
these pass-  through securities obtain securities that in aggregate have the same net 
cash flows and associated risks as the pool of mortgages.

The process of buying assets, placing them in a pool, and then selling securities 
that represent ownership of the pool is called securitization.
Mortgage-  backed securities have the advantage that default losses and early 
repayments are much more predictable for a diversified portfolio of mortgages than 
they are for individual mortgages. They are also attractive to investors who cannot 
efficiently service mortgages but wish to invest in mortgages. By securitizing mortgage 
pools, the mortgage banks allow investors who are not large enough to buy hundreds 
of mortgages to obtain the benefits of diversification and economies of scale in loan 
servicing.
Securitization greatly improves liquidity in the mortgage markets because it allows 
investors in the pass-  through securities to buy mortgages indirectly that they otherwise 
would not buy. Because the financial risks associated with mortgage-  backed securities

(debt securities with specified claims on the cash flows of a portfolio of mortgages) 
are much more predictable than those of individual mortgages, mortgage-  backed 
securities are easier to price and thus easier to sell when investors need to raise cash. 
These characteristics make the market for mortgage-  backed securities much more 
liquid than the market for individual mortgages. Because investors value liquidity—the 
ability to sell when they want to—they will pay more for securitized mortgages than 
for individual mortgages. The homeowners benefit because higher mortgage prices 
imply lower interest rates.
The mortgage bank is a financial intermediary because it connects investors who 
want to buy mortgages to homeowners who want to borrow money. The homeowners 
sell mortgages to the bank when the bank lends them money.
Some mortgage banks form mortgage pools from mortgages that they buy from 
other banks that originate the loans. These mortgage banks are also financial inter -

mediaries because they connect sellers of mortgages to buyers of mortgage-  backed 
securities. Although the sellers of the mortgages are the originating lenders and not 
the borrowers, the benefits of creating liquid mortgage-  backed securities ultimately 
flow back to the borrowers.
The creation of the pass-  through securities generally takes place on the accounts of 
the mortgage bank. The bank buys mortgages and sells pass-  through securities whose 
values depend on the mortgage pool. The mortgages appear on the bank’s accounts 
as assets and the mortgage-  backed securities appear as liabilities.
In many securitizations, the financial intermediary avoids placing the assets and 
liabilities on its balance sheet by setting up a special corporation or trust that buys 
the assets and issues the securities. That corporation or trust is called a special pur -
pose vehicle  (SPV) or alternatively a special purpose entity  (SPE). Conducting a

Reading 44 ■ Market Organization and Structure 32
securitization through a special purpose vehicle is advantageous to investors because 
their interests in the asset pool are better protected in an SPV than they would be 
on the balance sheet of the financial intermediary if the financial intermediary were 
to go bankrupt.
Financial intermediaries securitize many assets. Besides mortgages, banks securitize 
car loans, credit card receivables, bank loans, and airplane leases, to name just a few 
assets. As a class, these securities are called asset-  backed securities.
When financial intermediaries securitize assets, they often create several classes 
of securities, called tranches, that have different rights to the cash flows from the 
asset pool. The tranches are structured so that some produce more predictable cash 
flows than do others. The senior tranches have first rights to the cash flow from the 
asset pool. Because the overall risk of a given asset pool cannot be changed, the more

junior tranches bear a disproportionate share of the risk of the pool. Practitioners 
often call the most junior tranche toxic waste because it is so risky. The complexity 
associated with slicing asset pools into tranches can make the resulting securities 
difficult to value. Mistakes in valuing these securities contributed to the financial 
crisis that started in 2007.
Investment companies also create pass-  through securities based on investment 
pools. For example, an exchange-  traded fund is an asset-  backed security that represents 
ownership in the securities and contracts held by the fund. The shareholders benefit 
from the securitization because they can buy or sell an entire portfolio in a single 
transaction. Because the transaction cost savings are quite substantial, exchange-  traded 
funds often trade in very liquid markets. The investment companies (and sometimes 
the arbitrageurs) that create exchange-  traded funds are financial intermediaries

because they connect the buyers of the funds to the sellers of the assets that make 
up the fund portfolios.
More generally, the creators of all pooled investment vehicles are financial inter -
mediaries that transform portfolios of securities and contracts into securities that 
represent undivided ownership of the portfolios. The investors in these funds thus 
indirectly invest in the securities held by the fund. They benefit from the expertise of 
the investment manager and from obtaining a portfolio that may be more diversified 
than one they might otherwise be able to hold.
4.4 Depository Institutions and Other Financial Corporations
Depository institutions  include commercial banks, savings and loan banks, credit 
unions, and similar institutions that raise funds from depositors and other investors 
and lend it to borrowers. The banks give their depositors interest and transaction 
services, such as check writing and check cashing, in exchange for using their money.

They may also raise funds by selling bonds or equity in the bank.
These banks are financial intermediaries because they transfer funds from their 
depositors and investors to their borrowers. The depositors and investors benefit 
because they obtain a return (in interest, transaction services, dividends, or capital 
appreciation) on their funds without having to contract with the borrowers and 
manage their loans. The borrowers benefit because they obtain the funds that they 
need without having to search for investors who will trust them to repay their loans.
Many other financial corporations provide credit services. For example, acceptance 
corporations, discount corporations, payday advance corporations, and factors pro -
vide credit to borrowers by lending them money secured by such assets as consumer 
loans, machinery, future paychecks, or accounts receivables. They finance these loans 
by selling commercial paper, bonds, and shares to investors. These corporations are

intermediaries because they connect investors to borrowers. The investors obtain 
investments secured by a diversified portfolio of loans while the borrowers obtain 
funds without having to search for investors.

Financial Intermediaries 33
Brokers also act as financial intermediaries when they lend funds to clients who 
want to buy securities on margin. They generally obtain the funds from other clients 
who deposit them in their accounts. Brokers who provide these services to hedge 
funds and other similar institutions are called prime brokers.
Banks, financial corporations, and brokers can only raise money from depositors and 
other lenders because their equity owners retain residual interests in the performance 
of the loans that they make. If the borrowers default, the depositors and other lenders 
have priority claims over the equity owners. If insufficient money is collected from 
the borrowers, shareholders’ equity is used to pay their depositors and other lenders. 
The risk of losing capital focuses the equity owners’ and management’s attention so 
that credit is not offered foolishly.
Because the ability of these companies to cover their credit losses is limited by the

capital that their owners invest in them, the depositors and other investors who lend 
them money pay close attention to how much money the owners have at risk. For 
example, if a finance corporation is poorly capitalized, its shareholders will lose little 
if its clients default on the loans that the finance corporation makes to them. In that 
case, the finance corporation will have little incentive to lend only to creditworthy 
borrowers and to effectively manage collection on those loans once they have been 
made. Worse, it may even choose to lend to borrowers with poor credit because the 
interest rates that they can charge such borrowers are higher. Until those loans default, 
the higher income will make the corporation appear to be more profitable than it actu -
ally is. Depositors and other investors are aware of these problems and generally pay 
close attention to them. Accordingly, poorly capitalized financial institutions cannot

easily borrow money to finance their operations at favorable rates.
Depository banks and financial corporations are similar to securitized asset pools 
that issue pass-  through securities. Their depositors and investors own securities 
that ultimately are backed by an asset pool consisting of their loan portfolios. The 
depositors generally hold the most senior tranche, followed by the other creditors. 
The shareholders hold the most junior tranche. In the event of bankruptcy, they are 
paid only if everyone else is paid.
EXAMPLE 15   
Commercial Banks
What services do commercial banks provide that make them financial 
intermediaries?
Solution:
Commercial banks collect deposits from investors and lend them to borrowers. 
They are intermediaries because they connect lenders to borrowers. Commercial 
banks also provide transaction services that make it easier for the banks’ depos -
itory customers to pay bills and collect funds from their own customers.
4.5 Insurance Companies

Insurance companies help people and companies offset risks that concern them. They 
do this by creating insurance contracts (policies) that provide a payment in the event 
that some loss occurs. The insured buy these contracts to hedge against potential losses. 
Common examples of insurance contracts include auto, fire, life, liability, medical, 
theft, and disaster insurance contracts.

Reading 44 ■ Market Organization and Structure 34
Credit default swaps are also insurance contracts, but historically they have not 
been subject to the same reserve requirements that most governments apply to more 
traditional insurance contracts. They may be sold by insurance companies or by other 
financial entities, such as investment banks or hedge funds.
Insurance contracts transfer risk from those who buy the contracts to those who sell 
them. Although insurance companies occasionally broker trades between the insured 
and the insurer, they more commonly provide the insurance themselves. In that case, 
the insurance company’s owners and creditors become the indirect insurers of the 
risks that the insurance company assumes. Insurance companies also often transfer 
risks that they do not wish to bear by buying reinsurance policies from reinsurers.
Insurers are financial intermediaries because they connect the buyers of their

insurance contracts with investors, creditors, and reinsurers who are willing to bear the 
insured risks. The buyers benefit because they can easily obtain the risk transfers that 
they seek without searching for entities that would be willing to assume those risks.
The owners, creditors, and reinsurers of the insurance company benefit because 
the company allows them to sell their tolerance for risk easily without having to 
manage the insurance contracts. Instead, the company manages the relationships with 
the insured—primarily collections and claims—and hopefully controls the various 
problems—fraud, moral hazard, and adverse selection—that often plague insurance 
markets. Fraud occurs when people deliberately cause or falsely report losses to col -
lect on insurance. Moral hazard occurs when people are less careful about avoiding 
insured losses than they would be if they were not insured so that losses occur more

often than they would otherwise. Adverse selection occurs when only those who are 
most at risk buy insurance so that insured losses tend to be greater than average.
Everyone benefits because insurance companies hold large diversified portfolios 
of policies. Loss rates for well-  diversified portfolios of insurance contracts are much 
more predictable than for single contracts. For such contracts as auto insurance in 
which losses are almost uncorrelated across policies, diversification ensures that the 
financial performance of a large portfolio of contracts will be quite predictable and so 
holding the portfolio will not be very risky. The insured benefit because they do not 
have to pay the insurers much to compensate them for bearing risk (the expected loss 
is quite predictable so the risk is relatively low). Instead, their insurance premiums 
primarily reflect the expected loss rate in the portfolio plus the costs of running and 
financing the company.
4.6 Arbitrageurs

Arbitrageurs  trade when they can identify opportunities to buy and sell identical or 
essentially similar instruments at different prices in different markets. They profit when 
they can buy in one market for less than they sell in another market. Arbitrageurs 
are financial intermediaries because they connect buyers in one market to sellers in 
another market.
The purest form of arbitrage involves buying and selling the same instrument in 
two different markets. Arbitrageurs who do such trades sell to buyers in one market 
and buy from sellers in the other market. They provide liquidity to the markets because 
they make it easier for buyers and sellers to trade when and where they want to trade.
Because dealers and arbitrageurs both provide liquidity to other traders, they 
compete with each other. The dealers connect buyers and sellers who arrive in the 
same market at different times whereas the arbitrageurs connect buyers and sellers

who arrive at the same time in different markets. In practice, traders who profit 
from offering liquidity rarely are purely dealers or purely arbitrageurs. Instead, most 
traders attempt to identify and exploit every opportunity they can to manage their 
inventories profitably.

Financial Intermediaries 35
If information about prices is readily available to market participants, pure arbi -
trages involving the same instrument will be quite rare. Traders who are well informed 
about market conditions usually route their orders to the market offering the best 
price so that arbitrageurs will have few opportunities to match traders across markets 
when they want to trade the exact same instrument.
Arbitrageurs often trade securities or contracts whose values depend on the same 
underlying factors. For example, dealers in equity option contracts often sell call options 
in the contract market and buy the underlying shares in the stock market. Because 
the values of the call options and of the underlying shares are closely correlated (the 
value of the call increases with the value of the shares), the long stock position hedges 
the risk in the short call position so that the dealer’s net position is not too risky.

Similar to the pure arbitrage that involves the same instrument in different mar -
kets, these arbitrage trades connect buyers in one market to sellers in another market. 
In this case, however, the buyers and sellers are interested in different instruments 
whose values are closely related. In the example, the buyer is interested in buying a 
call options contract, the value of which is a nonlinear function of the value of the 
underlying stock; the seller is interested in selling the underlying stock.
Options dealers buy stock and sell calls when calls are overpriced relative to the 
underlying stocks. They use complicated financial models to value options in relation 
to underlying stock values, and they use financial engineering techniques to control 
the risk of their portfolios. Successful arbitrageurs must know valuation relations well 
and they must manage the risk in their portfolios well to trade profitably. They profit

by buying the relatively undervalued instrument and selling the relatively overvalued 
instrument.
Buying a risk in one form and selling it another form involves a process called 
replication. Arbitrageurs use various trading strategies to replicate the returns to 
securities and contracts. If they can substantially replicate those returns, they can 
use the replication trading strategy to offset the risk of buying or selling the actual 
securities and contracts. The combined effect of their trading is to transform risk 
from one form to another. This process allows them to create or eliminate contracts 
in response to the excess demand for, and supply of, contracts.
For example, when traders want to buy more call contracts than are presently 
available, they push the call contract prices up so that calls become overvalued relative 
to the underlying stock. The arbitrageurs replicate calls by using a particular financial

engineering strategy to buy the underlying stock, and then create the desired call 
option contracts by selling them short. In contrast, if more calls have been created 
than traders want to hold, call prices will fall so that calls become undervalued relative 
to the underlying stock. The arbitrageurs will trade stocks and contracts to absorb the 
excess contracts. Arbitrageurs who use these strategies are financial intermediaries 
because they connect buyers and sellers who want to trade the same underlying risks 
but in different forms.
EXAMPLE 16   
Dealers and Arbitrageurs
With respect to providing liquidity to market participants, what characteristics 
most clearly distinguish dealers from arbitrageurs?

Reading 44 ■ Market Organization and Structure 36
Solution:
Dealers provide liquidity to buyers and sellers who arrive at the same market at 
different times. They move liquidity through time. Arbitrageurs provide liquid -
ity to buyers and sellers who arrive at different markets at the same time. They 
move liquidity across markets.
4.7 Settlement and Custodial Services
In addition to connecting buyers to sellers through a variety of direct and indirect 
means, financial intermediaries also help their customers settle their trades and ensure 
that the resulting positions are not stolen or pledged more than once as collateral.
Clearinghouses  arrange for final settlement of trades. In futures markets, they 
guarantee contract performance. In other markets, they may act only as escrow agents, 
transferring money from the buyer to the seller while transferring securities from the 
seller to the buyer.
The members of a clearinghouse are the only traders for whom the clearinghouse

will settle trades. To ensure that their members settle the trades that they present to 
the clearinghouse, clearinghouses require that their members have adequate capital 
and post-  performance bonds (margins). Clearinghouses also limit the aggregate net 
(buy minus sell) quantities that their members can settle.
Brokers and dealers who are not members of the clearinghouse must arrange to 
have a clearinghouse member settle their trades. To ensure that the non-  member 
brokers and dealers can settle their trades, clearinghouse members require that their 
customers (the non-  member brokers and dealers) have adequate capital and post-  
margins. They also limit the aggregate net quantities that their customers can settle 
and they monitor their customers’ trading to ensure that they do not arrange trades 
that they cannot settle.
Brokers and dealers similarly monitor the trades made by their retail and insti -
tutional customers, and regulate their customers to ensure that they do not arrange

trades that they cannot settle.
This hierarchical system of responsibility generally ensures that traders settle 
their trades. The brokers and dealers guarantee settlement of the trades they arrange 
for their retail and institutional customers. The clearinghouse members guarantee 
settlement of the trades that their customers present to them, and clearinghouses 
guarantee settlement of all trades presented to them by their members. If a clearing -
house member fails to settle a trade, the clearinghouse settles the trade using its own 
capital or capital drafted from the other members.
Reliable settlement of all trades is extremely important to a well-  functioning finan -
cial system because it allows strangers to confidently contract with each other without 
worrying too much about counterparty risk , the risk that their counterparties will 
not settle their trades. A secure clearinghouse system thus greatly increases liquidity

because it greatly increases the number of counterparties with whom a trader can 
safely arrange a trade.
In many national markets, clearinghouses clear all securities trades so that trad -
ers can trade securities through any exchange, broker, alternative trading system, or 
dealer. These clearinghouse systems promote competition among these exchange 
service providers.
In contrast, most futures exchanges have their own clearinghouses. These clear -
inghouses usually will not accept trades arranged away from their exchanges so that a 
competing exchange cannot trade another exchange’s contracts. Competing exchanges 
may create similar contracts, but moving traders from one established market to a 
new market is extraordinarily difficult because traders prefer to trade where other 
traders trade.

Financial Intermediaries 37
Depositories or custodians hold securities on behalf of their clients. These services, 
which are often offered by banks, help prevent the loss of securities through fraud, 
oversight, or natural disaster. Broker–dealers also often hold securities on behalf of 
their customers so that the customers do not have to hold the securities in certificate 
form. To avoid problems with lost certificates, securities increasingly are issued only 
in electronic form.
EXAMPLE 17   
Financial Intermediaries
As a relatively new member of the business community, you decide it would be 
advantageous to join the local lunch club to network with businessmen. Upon 
learning that you are a financial analyst, club members soon enlist you to give a 
lunch speech. During the question and answer session afterwards, a member of 
the audience asks, “I keep reading in the newspaper about the need to regulate 
‘financial intermediaries’ , but really don’t understand exactly what they are. Can

you tell me?” How do you answer?
Solution:
Financial intermediaries are companies that help their clients achieve their finan -
cial goals. They are called intermediaries because, in some way or another, they 
stand between two or more people who would like to trade with each other, but 
for various reasons find it difficult to do so directly. The intermediary arranges 
the trade for them, or more often, trades with both sides.
For example, a commercial bank is an intermediary that connects investors 
with money to borrowers who need money. The investors buy certificates of 
deposit from the bank, buy bonds or stock issued by the bank, or simply are 
depositors in the bank. The borrowers borrow this money from the bank when 
they arrange loans. Without the bank’s intermediation, the investors would have 
to find trustworthy borrowers themselves, which would be difficult, and the 
borrowers would have to find trusting lenders, which would also be difficult.

Similarly, an insurance company is an intermediary because it connects 
customers who want to insure risks with investors who are willing to bear those 
risks. The investors own shares or bonds issued by the insurance company, or 
they have sold reinsurance contracts to the insurance company. The insured 
benefit because they can more easily buy a policy from an insurance company 
than they can find counterparties who would be willing to bear their risks. The 
investors benefit because the insurance company creates a diversified portfolio of 
risks by selling insurance to thousands or millions of customers. Diversification 
ensures that the net risk borne by the insurance company and its investors will 
be predictable and thus financially manageable.
In both cases, the financial intermediary also manages the relationships 
with its customers and investors so that neither side has to worry about the 
credit-  worthiness or trust-  worthiness of its counterparties. For example, the

bank manages credit quality and collections on its loans and the insurance 
company manages risk exposure and collections on its policies. These services 
benefit both sides by reducing the costs of connecting investors to borrowers 
or of insured to insurers.
These are only two examples of financial intermediation. Many others involve 
firms engaged in brokerage, dealing, arbitrage, securitization, investment man -
agement, and the clearing and settlement of trades. In all cases, the financial

Reading 44 ■ Market Organization and Structure 38
intermediary stands between a buyer and a seller, offering them services that 
allow them to better achieve their financial goals in a cost effective and efficient 
manner.
4.8 Summary  
By facilitating transactions among buyers and sellers, financial intermediaries provide 
services essential to a well-  functioning financial system. They facilitate transactions 
the following ways:
1 Brokers, exchanges, and various alternative trading systems match buyers and 
sellers interested in trading the same instrument at the same place and time. 
These financial intermediaries specialize in discovering and organizing informa -
tion about who wants to trade.
2 Dealers and arbitrageurs connect buyers to sellers interested in trading the 
same instrument but who are not present at the same place and time. Dealers 
connect buyers to sellers who are present at the same place but at different

times whereas arbitrageurs connect buyers to sellers who are present at the 
same time but in different places. These financial intermediaries trade for their 
own accounts when providing these services. Dealers buy or sell with one client 
and hope to do the offsetting transaction later with another client. Arbitrageurs 
buy from a seller in one market while simultaneously selling to a buyer in 
3 Many financial intermediaries create new instruments that depend on the cash 
flows and associated financial risks of other instruments. The intermediaries 
provide these services when they securitize assets, manage investment funds, 
operate banks and other finance corporations that offer investments to investors 
and loans to borrowers, and operate insurance companies that pool risks. The 
instruments that they create generally are more attractive to their clients than 
the instruments on which they are based. The new instruments also may be

differentiated to appeal to diverse clienteles. Their efforts connect buyers of one 
or more instruments to sellers of other instruments, all of which in aggregate 
provide the same cash flows and risk exposures. Financial intermediaries thus 
effectively arrange trades among traders who otherwise would not trade with 
4 Arbitrageurs who conduct arbitrage among securities and contracts whose 
values depend on common factors convert risk from one form to another. Their 
trading connects buyers and sellers who want to trade similar risks expressed in 
different forms.
5 Banks, clearinghouses, and depositories provide services that ensure traders 
settle their trades and that the resulting positions are not stolen or pledged 
more than once as collateral.
POSITIONS
People generally solve their financial and risk management problems by taking positions 
in various assets or contracts. A position  in an asset is the quantity of the instrument

that an entity owns or owes. A portfolio consists of a set of positions.5

Positions 39
People have long positions  when they own assets or contracts. Examples of long 
positions include ownership of stocks, bonds, currencies, contracts, commodities, 
or real assets. Long positions benefit from an appreciation in the prices of the assets 
or contracts owned.
People have short positions  when they have sold assets that they do not own, 
or when they write and sell contracts. Short positions benefit from a decrease in the 
prices of the assets or contracts sold. Short sellers profit by selling at high prices and 
repurchasing at lower prices. Information-  motivated traders sell assets and contracts 
short positions when they believe that prices will fall.
Hedgers also often sell instruments short. They short securities and contracts when 
the financial risks inherent in the instruments are positively correlated with the risks 
to which they are exposed. For example, to hedge the risk associated with holding

copper inventories, a wire manufacturer would sell short copper futures. If the price 
of copper falls, the manufacturer will lose on his copper inventories but gain on his 
short futures position. (If the risk in an instrument is inversely correlated with a risk 
to which hedgers are exposed, the hedgers will hedge with long positions.)
Contracts have long sides and short sides. The long side of a forward or futures 
contract is the side that will take physical delivery or its cash equivalent. The short side 
of such contracts is the side that is liable for the delivery. The long side of a futures 
contract increases in value when the value of the underlying asset increases in value.
The identification of the two sides can be confusing for option contracts. The 
long side of an option contract is the side that holds the right to exercise the option. 
The short side is the side that must satisfy the obligation. Practitioners say that that

the long side holds  the option and the short side writes  the option, so the long side 
is the holder and the short side is the writer. The put contracts are the source of the 
potential confusion. The put contract holder has the right to sell the underlying to 
the writer. The holder will benefit if the price of the underlying falls, in which case 
the price of the put contract will rise. The holder is long the put contract and has 
an indirect short position in the underlying instrument. Analysts call the indirect 
short position short exposure to the underlying. The put contract holders have long 
exposure to their option contract and short exposure to the underlying instrument.
Exhibit 1   Option Positions and Their Associated Underlying Risk Exposures
Type of Option Option Position Exposure to Underlying Risk
Call Long Long
Call Short Short
Put Long Short
Put Short Long
The identification of the long side in a swap contract is often arbitrary because

swap contracts call for the exchange of contractually determined cash flows rather 
than for the purchase (or the cash equivalent) of some underlying instrument. In 
general, the side that benefits from an increase in the quoted price is the long side.
The identification of the long side in currency contracts also may be confusing. 
In this case, the confusion stems from symmetry in the contracts. The buyer of one 
currency is the seller of the other currency, and vice versa for the seller. Thus, a long 
forward position in one currency is a short forward position in the other currency. 
When practitioners describe a position, they generally will say, “I’m long the dollar 
against the yen, ” which means they have bought dollars and sold yen.

Reading 44 ■ Market Organization and Structure 40
5.1 Short Positions
Short sellers create short positions in contracts by selling contracts that they do not 
own. In a sense, they become the issuers of the contract when they create the liabilities 
associated with their contracts. This analogy will also help you better understand risk 
when you study corporate finance: Corporations create short positions in their bonds 
when they issue bonds in exchange for cash. Although bonds are generally considered 
to be securities, they are also contracts between the issuer and the bondholder.
Short sellers create short positions in securities by borrowing securities from secu -
rity lenders who are long holders. The short sellers then sell the borrowed securities 
to other traders. Short sellers close their positions by repurchasing the securities and 
returning them to the security lenders. If the securities drop in value, the short sellers

profit because they repurchase the securities at lower prices than the prices at which 
they sold the securities. If the securities rise in value, they will lose. Short sellers who 
buy to close their positions are said to cover their positions.
The potential gains in a long position generally are unbounded. For example, the 
stock prices of such highly successful companies as Yahoo! have increased more than 
50- fold since they were first publicly traded. The potential losses on long positions, 
however, are limited to no more than 100 percent—a complete loss—for long positions 
without any associated liabilities.
In contrast, the potential gains on a short position are limited to no more than 
100 percent whereas the potential losses are unbounded. The unbounded potential 
losses on short positions make short positions very risky in volatile instruments. For 
example, if you shorted 100 shares of Yahoo! in July 1996 at $20 and you kept your

position open for four years, you would have lost $148,000 on your $2,000 initial 
short position. During this period, Yahoo! rose 75-  fold to $1,500 on a split-  adjusted 
equivalent basis.
Although security lenders generally believe that they are long the securities that 
they lend, in fact, they do not actually own the securities during the periods of their 
loans. Instead, they own promises made by the short sellers to return the securities. 
These promises are memorialized in security lending agreements. These agreements 
specify that the short sellers will pay the long sellers all dividends or interest that they 
otherwise would have received had they not lent their securities. These payments are 
called payments-  in- lieu of dividends (or of interest), and they may have different tax 
treatments than actual dividends and interest. The security lending agreements also 
protect the lenders in the event of a stock split.

To secure the security loans, lenders require that the short seller leave the proceeds 
of the short sale on deposit with them as collateral for the stock loan. They invest the 
collateral in short-  term securities, and they rebate the interest to the short sellers at 
rates called short rebate rates. The short rebate rates are determined in the market 
and generally are available only to institutional short-  sellers and some large retail 
traders. If a security is hard to borrow, the rebate rate may be very small or even neg -
ative. Such securities are said to be on special. Otherwise, the rebate rate is usually 10 
basis points less than the overnight rate in the interbank funds market. Most security 
lending agreements require various margin payments to keep the credit risk among 
the parties from growing when prices change.
Securities lenders lend their securities because the short rebate rates they pay on

the collateral are lower than the interest rates they receive from investing the col -
lateral. The difference is because of the implicit loan fees that they receive from the 
borrowers for borrowing the stock. The difference also compensates lenders for risks 
that the lenders take when investing the collateral and for the risk that the borrowers 
will default if prices rise significantly.

Positions 41
EXAMPLE 18   
Short Positions in Securities and Contracts
How is the process of short selling shares of Siemens different from that of short 
selling a Siemens equity call option contract?
Solution:
To short sell shares of Siemens, the seller (or his broker) must borrow the 
shares from a long holder so that he can deliver them to the buyer. To short 
sell a Siemens equity call option contract, the seller simply creates the contract 
when he sells it to the buyer.
5.2 Leveraged Positions
In many markets, traders can buy securities by borrowing some of the purchase price. 
They usually borrow the money from their brokers. The borrowed money is called the 
margin loan , and they are said to buy on margin. The interest rate that the buyers pay 
for their margin loan is called the call money rate . The call money rate is above the 
government bill rate and is negotiable. Large buyers generally obtain more favorable

rates than do retail buyers. For institutional-  size buyers, the call money rate is quite 
low because the loans are generally well secured by securities held as collateral by 
the lender.
Trader’s equity is that portion of the security price that the buyer must supply. 
Traders who buy securities on margin are subject to minimum margin requirements. 
The initial margin requirement  is the minimum fraction of the purchase price that 
must be trader’s equity. This requirement may be set by the government, the exchange, 
or the exchange clearinghouse. For example, in the United States, the Federal Reserve 
Board sets the initial margin requirement through Regulation T. In Hong Kong, the 
Securities and Futures Commission sets the margin requirements. In all markets, 
brokers often require more equity than the government-  required minimum from 
their clients when lending to them.
Many markets allow brokers to lend their clients more money if the brokers use

risk models to measure and control the overall risk of their clients’ portfolios. This 
system is called portfolio margining.
Buying securities on margin can greatly increase the potential gains or losses for 
a given amount of equity in a position because the trader can buy more securities on 
margin than he could otherwise. The buyer thus earns greater profits when prices rise 
and suffers greater losses when prices fall. The relation between risk and borrowing 
is called financial leverage  (often simply called leverage). Traders leverage their 
positions when they borrow to buy more securities. A highly leveraged position is 
large relative to the equity that supports it.
The leverage ratio is the ratio of the value of the position to the value of the equity 
investment in it. The leverage ratio indicates how many times larger a position is than 
the equity that supports it. The maximum leverage ratio associated with a position

financed by the minimum margin requirement is one divided by the minimum margin 
requirement. If the requirement is 40 percent, then the maximum leverage ratio is 
2.5 = 100% position ÷ 40% equity.
The leverage ratio indicates how much more risky a leveraged position is relative 
to an unleveraged position. For example, if a stock bought on 40 percent margin rises 
10 percent, the buyer will experience a 25 percent (2.5 × 10%) return on the equity 
investment in her leveraged position. But if the stock falls by 10 percent, the return 
on the equity investment will be −25 percent (before the interest on the margin loan 
and before payment of commissions).

Reading 44 ■ Market Organization and Structure 42
Financial analysts must be able to compute the total return to the equity invest -
ment in a leveraged position. The total return depends on the price change of the 
purchased security, the dividends or interest paid by the security, the interest paid on 
the margin loan, and the commissions paid to buy and sell the security. The following 
example illustrates the computation of the total return to a leveraged purchase of 
stock that pays a dividend.
EXAMPLE 19   
Computing Total Return to a Leveraged Stock Purchase
A buyer buys stock on margin and holds the position for exactly one year, during 
which time the stock pays a dividend. For simplicity, assume that the interest on 
the loan and the dividend are both paid at the end of the year.
Purchase price $20/share
Sale price $15/share
Shares purchased 1,000
Leverage ratio 2.5
Call money rate 5%
Dividend $0.10/share
Commission $0.01/share
1 What is the total return on this investment?

2 Why is the loss greater than the 25 percent decrease in the market price?
To find the return on this investment, first determine the initial equity and then 
determine the equity remaining after the sale. The total purchase price is $20,000. 
The leverage ratio of 2.5 indicates that the buyer’s equity financed 40 percent = 
(1 ÷ 2.5) of the purchase price. Thus, the equity investment is $8,000 = 40% of 
$20,000. The $12,000 remainder is borrowed. The actual investment is slightly 
higher because the buyer must pay a commission of $10 = $0.01/share × 1,000 
shares to buy the stock. The total initial investment is $8,010.
At the end of the year, the stock price has declined by $5/share. The buyer 
lost $5,000 = $5/share × 1,000 shares as a result of the price change. In addition, 
the buyer has to pay interest at 5 percent on the $12,000 loan, or $600. The buyer

also receives a dividend of $0.10/share, or $100. The trader’s equity remaining 
after the sale is computed from the initial equity investment as follows:
Initial investment $8,010
Purchase commission –10
Trading gains/losses –5,000
Margin interest paid –600
Dividends received 100
Sales commission paid –10
Remaining equity $2,490
or
Proceeds on sale $15,000
Payoff loan –12,000

Positions 43
so that the return on the initial investment of $8,010 is (2,490 – 8,010)/8,010 = 
–68.9%.
The realized loss is substantially greater than the stock price return of ($15 – 
$20)/$20  = –25%. Most of the difference is because of the leverage with the 
remainder primarily the result of the interest paid on the loan. Based on the 
leverage alone and ignoring the other cash flows, we would expect that the return 
on the equity would be –62.5% = 2.5 leverage times the –25% stock price return.
In the above example, if the stock dropped more than the buyer’s original 40 per -
cent margin (ignoring commissions, interest, and dividends), the trader’s equity would 
have become negative. In that case, the investor would owe his broker more than the 
stock is worth. Brokers often lose money in such situations if the buyer does not repay 
the loan out of other funds.

To prevent such losses, brokers require that margin buyers always have a mini -
mum amount of equity in their positions. This minimum is called the maintenance 
margin requirement . It is usually 25 percent of the current value of the position, 
but it may be higher or lower depending on the volatility of the instrument and the 
policies of the broker.
If the value of the equity falls below the maintenance margin requirement, the 
buyer will receive a margin call , or request for additional equity. If the buyer does not 
deposit additional equity with the broker in a timely manner, the broker will close the 
position to prevent further losses and thereby secure repayment of the margin loan.
When you buy securities on margin, you must know the price at which you will 
receive a margin call if prices drop. The answer to this question depends on your 
initial equity and on the maintenance margin requirement.
EXAMPLE 20   
Margin Call Price

EXAMPLE 20   
A trader buys stock on margin posting 40 percent of the initial stock price of $20 
as equity. The maintenance margin requirement for the position is 25 percent. 
Below what price will a margin call occur?
Solution:
The trader’s initial equity is 40 percent of the initial stock price of $20, or $8 
per share. Subsequent changes in equity per share are equal to the share price 
change so that equity per share is equal to $8 + ( P – 20) where P is the current 
share price. The margin call takes place when equity drops below the 25 percent 
maintenance margin requirement. The price below which a margin call will take 
place is the solution to the following equation:
Equity /share
Price/shar e=+−=$%82 025P
P

Reading 44 ■ Market Organization and Structure 44
which occurs at P = 16. When the price drops below $16, the equity will be 
under $4/share, which is less than 25 percent of the price.
Traders who sell securities short are also subject to margin requirements because 
they have borrowed securities. Initially, the trader’s equity supporting the short posi -
tion must be at least equal to the margin requirement times the initial value of the 
short position. If prices rise, equity will be lost. At some point, the short seller will 
have to contribute additional equity to meet the maintenance margin requirement. 
Otherwise, the broker will buy the security back to cover the short position to prevent 
further losses and thereby secure repayment of the stock loan.
ORDERS
Buyers and sellers communicate with the brokers, exchanges, and dealers that arrange 
their trades by issuing orders . All orders specify what instrument to trade, how much

to trade, and whether to buy or sell. Most orders also have other instructions attached 
to them. These additional instructions may include execution instructions, validity 
instructions, and clearing instructions. Execution instructions  indicate how to fill 
the order, validity instructions  indicate when the order may be filled, and clearing 
instructions  indicate how to arrange the final settlement of the trade.
In this section, we introduce various order instructions and explain how traders use 
them to achieve their objectives. We discuss execution mechanisms—how exchanges, 
brokers and dealers fill orders—in the next section. To understand the concepts in 
this section, however, you need to know a little about order execution mechanisms.
In most markets, dealers and various other proprietary traders often are willing 
to buy from, or sell to, other traders seeking to sell or buy. The prices at which they

are willing to buy are called bid prices and those at which they are willing to sell are 
called ask prices, or sometimes offer  prices. The ask prices are invariably higher than 
the bid prices.
The traders who are willing to trade at various prices may also indicate the quan -
tities that they will trade at those prices. These quantities are called bid sizes  and ask 
sizes  depending on whether they are attached to bids or offers.
Practitioners say that the traders who offer to trade make a market. Those who 
trade with them take the market.
The highest bid in the market is the best bid , and the lowest ask in the market is 
the best offer . The difference between the best bid and the best offer is the market 
bid–ask spread . When traders ask, “What’s the market?” they want to know the best 
bid and ask prices and their associated sizes. Bid–ask spreads are an implicit cost of 
trading. Markets with small bid–ask spreads are markets in which the costs of trading

are small, at least for the sizes quoted. Dealers often quote both bid and ask prices, 
and in that case, practitioners say that they quote a two-  sided market. The market 
spread is never more than any dealer spread.
6.1 Execution Instructions
Market and limit orders convey the most common execution instructions. A market 
order  instructs the broker or exchange to obtain the best price immediately available 
when filling the order. A limit order  conveys almost the same instruction: Obtain the 
best price immediately available, but in no event accept a price higher than a specified 
limit price when buying or accept a price lower than a specified limit price when selling.6

Orders 45
Many people mistakenly believe that limit orders specify the prices at which the 
orders will trade. Although limit orders do often trade at their limit prices, remember 
that the first instruction is to obtain the best price available. If better prices are available 
than the limit price, brokers and exchanges should obtain those prices for their clients.
Market orders generally execute immediately if other traders are willing to take 
the other side of the trade. The main drawback with market orders is that they can 
be expensive to execute, especially when the order is placed in a market for a thinly 
traded security, or more generally, when the order is large relative to the normal trad -
ing activity in the market. In that case, a market buy order may fill at a high price, or 
a market sell order may fill at a low price if no traders are willing to trade at better 
prices. High purchase prices and low sale prices represent price concessions given

to other traders to encourage them to take the other side of the trade. Because the 
sizes of price concessions can be difficult to predict, and because prices often change 
between when a trader submits an order and when the order finally fills, the execution 
prices for market orders are often uncertain.
Buyers and sellers who are concerned about the possibility of trading at unaccept -
able prices add limit price instructions to their orders. The main problem with limit 
orders is that they may not execute. Limit orders do not execute if the limit price on 
a buy order is too low, or if the limit price on a sell order is too high. For example, if 
an investment manager submits a limit order to buy at the limit price of 20 (buy limit 
20) and nobody is willing to sell at or below 20, the order will not trade. If prices never 
drop to 20, the manager will never buy. If the price subsequently rises, the manager 
will have lost the opportunity to profit from the price rise.

Whether traders use market orders or limit orders when trying to arrange trades 
depends on their concerns about price, trading quickly, and failing to trade. On average, 
limit orders trade at better prices than do market orders, but they often do not trade. 
Traders generally regret when their limit orders fail to trade because they usually 
would have profited if they had traded. Limit buy orders do not fill when prices are 
rising, and limit sell orders do not fill when prices are falling. In both cases, traders 
would be better off if their orders had filled.
The probability that a limit order will execute depends on where the order is placed 
relative to market prices. An aggressively priced order is more likely to trade than is a 
less aggressively priced order. A limit buy order is aggressively priced when the limit 
price is high relative to the market bid and ask prices. If the limit price is placed above

the best offer, the buy order generally will partially or completely fill at the best offer 
price, depending on the size available at the best offer. Such limit orders are called 
marketable limit orders  because at least part of the order can trade immediately. A 
limit buy order with a very high price relative to the market is essentially a market order.
If the buy order is placed above the best bid but below the best offer, traders say the 
order makes a new market because it becomes the new best bid. Such orders generally 
will not immediately trade, but they may attract sellers who are interested in trading. 
A buy order placed at the best bid is said to make market. It may have to wait until 
all other buy orders at that price trade first. Finally, a buy order placed below the best 
bid is behind the market . It will not execute unless market prices drop. Traders call 
limit orders that are waiting to trade standing limit orders .

Sell limit orders are aggressively priced if the limit price is low relative to market 
prices. The limit price of a marketable sell limit order is below the best bid. A limit 
sell order placed between the best bid and the best offer makes a new market on the 
sell side, one placed at the best offer makes market, and one placed above the best 
offer is behind the market.
Exhibit 2 presents a simplified limit order book  in which orders are presented 
ranked by their limit prices for a hypothetical market. The market is “26 bid, offered 
at 28” because the best bid is 26 and the best offer (ask) is 28.

Reading 44 ■ Market Organization and Structure 46
Exhibit 2   Terms Traders Use to Describe Standing Limit Orders
Order Prices
Bids Offers (Asks)
The least aggressively priced sell orders are far 
from the market. 33
32
31 These sell orders are behind the market . We also say 
that they are away from the market . 30
29
28 The best offer  is at the market . 
The best bid and 
best offer make 
the market .The space between the current best bid and offer is 
inside the market . If a new limit order arrives here, it makes 
a new market .
26 The best bid  is at the market . 
25
24 These buy orders are behind the market . We also say that they 
are away from the market . 23
22
21 The least aggressively priced buy orders are far from the  
market .
Source:  Trading and Exchanges .
Harris, Larry. 2003. Trading and Exchanges: Market Microstructure for Practitioners . New York: Oxford University Press.
EXAMPLE 21   
Making and Taking
1 What is the difference between making a market and taking a market?

2 What order types are most likely associated with making a market and 
taking a market?
A trader makes a market when the trader offers to trade. A trader takes a market 
when the trader accepts an offer to trade.
Traders place standing limit orders to give other traders opportunities to trade. 
Standing limit orders thus make markets. In contrast, traders use market orders 
or marketable limit orders to take offers to trade. These marketable orders take 
the market.
A trade-  off exists between how aggressively priced an order is and the ultimate 
trade price. Although aggressively priced orders fill faster and with more certainty then 
do less aggressively priced limit orders, the prices at which they execute are inferior.

Orders 47
Buyers seeking to trade quickly must pay higher prices to increase the probability of 
trading quickly. Similarly, sellers seeking to trade quickly must accept lower prices to 
increase the probability of trading quickly.
Some order execution instructions specify conditions on size. For example, all- or- 
nothing (AON) orders  can only trade if their entire sizes can be traded. Traders can 
similarly specify minimum fill sizes. This specification is common when settlement 
costs depend on the number of trades made to fill an order and not on the aggregate 
size of the order.
Exposure instructions indicate whether, how, and perhaps to whom orders should 
be exposed. Hidden orders  are exposed only to the brokers or exchanges that receive 
them. These agencies cannot disclose hidden orders to other traders until they can fill 
them. Traders use hidden orders when they are afraid that other traders might behave

strategically if they knew that a large order was in the market. Traders can discover 
hidden size only by submitting orders that will trade with that size. Thus, traders can 
only learn about hidden size after they have committed to trading with it.
Traders also often indicate a specific display size  for their orders. Brokers and 
exchanges then expose only the display size for these orders. Any additional size is 
hidden from the public but can be filled if a suitably large order arrives. Traders some -
times call such orders iceberg orders  because most of the order is hidden. Traders 
specify display sizes when they do not want to display their full sizes, but still want 
other traders to know that someone is willing to trade at the displayed price. Traders 
on the opposite side who wish to trade additional size at that price can discover the 
hidden size only if they trade the displayed size, at which point the broker or exchange

will display any remaining size up to the display size. They also can discover the hidden 
size by submitting large orders that will trade with that size.
EXAMPLE 22   
Market versus Limit and Hidden versus Displayed Orders
You are the buy-  side trader for a very clever investment manager. The manager 
has hired a commercial satellite firm to take regular pictures of the parking lots 
in which new car dealers store their inventories. It has also hired some part-  time 
workers to count the cars on the lots. With this information and some econo -
metric analyses, the manager can predict weekly new car sale announcements 
more accurately than can most analysts. The manager typically makes a quarter 
percent each week on this strategy. Once a week, a day before the announcements 
are made, the manager gives you large orders to buy or sell car manufacturers 
based on his insights into their dealers’ sales. What primary issues should you 
consider when deciding whether to:

1 use market or limit orders to fill his orders?
2 display the orders or hide them?
The manager’s information is quite perishable. If his orders are not filled before 
the weekly sales are reported to the public, the manager will lose the opportunity 
to profit from the information as prices immediately adjust to the news. The 
manager, therefore, needs to get the orders filled quickly. This consideration 
suggests that the orders should be submitted as market orders. If submitted as 
limit orders, the orders might not execute and the firm would lose the oppor -
tunity to profit.

Reading 44 ■ Market Organization and Structure 48
Large market orders, however, can be very expensive to execute, especially 
if few people are willing to trade significant size on the other side of the market. 
Because transaction costs can easily exceed the expected quarter percent return, 
you should submit limit orders to limit the execution prices that you are willing 
to accept. It is better to fail to trade than to trade at losing prices.
Your large orders could easily move the market if many people were aware of 
them, and even more so if others were aware that you are trading on behalf of a 
successful information-  motivated trader. You thus should consider submitting 
hidden orders. The disadvantage of hidden orders is that they do not let people 
know that they can trade the other side if they want to.
6.2 Validity Instructions
Validity instructions indicate when an order may be filled. The most common validity

instruction is the day order . A day order is good for the day on which it is submitted. 
If it has not been filled by the close of business, the order expires unfilled.
Good-  till-  cancelled orders  (GTC) are just that. In practice, most brokers limit 
how long they will manage an order to ensure that they do not fill orders that their 
clients have forgotten. Such brokers may limit their GTC orders to a few months.
Immediate or cancel orders  (IOC) are good only upon receipt by the broker or 
exchange. If they cannot be filled in part or in whole, they cancel immediately. In 
some markets these orders are also known as fill or kill  orders. When searching for 
hidden liquidity, electronic algorithmic trading systems often submit thousands of 
these IOC orders for every order that they fill.
Good-  on- close  orders can only be filled at the close of trading. These orders often 
are market orders, so traders call them market-  on- close  orders. Traders often use on-

close orders when they want to trade at the same prices that will be published as the 
closing prices of the day. Mutual funds often like to trade at such prices because they 
value their portfolios at closing prices. Many traders also use good-  on- open  orders.
6.2.1  Stop Orders
A stop order  is an order in which a trader has specified a stop price condition. The 
stop order may not be filled until the stop price condition has been satisfied. For a sell 
order, the stop price condition suspends execution of the order until a trade occurs at 
or below the stop price. After that trade, the stop condition is satisfied and the order 
becomes valid for execution, subject to all other execution instructions attached to 
it. If the market price subsequently rises above the sell order’s stop price before the 
order trades, the order remains valid. Similarly, a buy order with a stop condition 
becomes valid only after a price rises above the specified stop price.

Traders often call stop orders stop-  loss orders  because many traders use them 
with the hope of stopping losses on positions that they have established. For example, 
a trader who has bought stock at 40 may want to sell the stock if the price falls below 
30. In that case, the trader might submit a “GTC, stop 30, market sell” order. If the 
price falls to or below 30, the market order becomes valid and it should immediately 
execute at the best price then available in the market. That price may be substantially 
lower than 30 if the market is falling quickly. The stop-  loss order thus does not guar -
antee a stop to losses at the stop price. If potential sellers are worried about trading at 
too low of a price, they can attach stop instructions to limit orders instead of market 
orders. In this example, if the trader is unwilling to sell below 25, the trader would 
submit a “GTC, stop 30, limit 25 sell” order.

Orders 49
If a trader wants to guarantee that he can sell at 30, the trader would buy a put 
option contract struck at 30. The purchase price of the option would include a premium 
for the insurance that the trader is buying. Option contracts can be viewed as limit 
orders for which execution is guaranteed at the strike price. A trader similarly might 
use a stop-  buy order or a call option to limit losses on a short position.
A portfolio manager might use a stop-  buy order when the manager believes that 
a security is undervalued but is unwilling to trade without market confirmation. For 
example, suppose that a stock currently trades for 50 RMB and a manager believes 
that it should be worth 100 RMB. Further, the manager believes that the stock will 
much more likely be worth 100 RMB if other traders are willing to buy it above 65 
RMB. To best take advantage of this information, the manager would consider issuing

a “GTC, stop 65 RMB, limit 100 RMB buy” order. Note that if the manager relies too 
much on the market when making this trading decision, however, he may violate CFA 
Standard of Professional Conduct V.A.2, which requires that all investment actions have 
a reasonable and adequate basis supported by appropriate research and investigation.
Because stop-  sell orders become valid when prices are falling and stop-  buy orders 
become valid when prices are rising, traders using stop orders contribute to market 
momentum as their sell orders push prices down further and their buy orders push 
prices up. Execution prices for stop orders thus are often quite poor.
EXAMPLE 23   
Limit and Stop Instructions
In what ways do limit and stop instructions differ?
Solution:
Although both limit and stop instructions specify prices, the role that these 
prices play in the arrangement of a trade are completely different. A limit price

places a limit on what trade prices will be acceptable to the trader. A buyer will 
accept prices only at or lower than the limit price whereas a seller will accept 
prices only at or above the limit price.
In contrast, a stop price indicates when an order can be filled. A buy order 
can only be filled once the market has traded at a price at or above the stop 
price. A sell order can only be filled once the market has traded at a price at or 
below the stop price.
Both order instructions may delay or prevent the execution of an order. A 
buy limit order will not execute until someone is willing to sell at or below the 
limit price. Similarly, a sell limit order will not execute until someone is willing to 
buy at or above the limit sell price. In contrast, a stop-  buy order will not execute 
if the market price never rises to the stop price. Similarly, a stop-  sell order will 
not execute if the market price never falls to the stop price.
6.3 Clearing Instructions

Clearing instructions  tell brokers and exchanges how to arrange final settlement 
of trades. Traders generally do not attach these instructions to each order—instead 
they provide them as standing instructions. These instructions indicate what entity 
is responsible for clearing and settling the trade. For retail trades, that entity is the 
customer’s broker. For institutional trades, that entity may be a custodian or another 
broker. When a client uses one broker to arrange trades and another broker to settle 
trades, traders say that the first broker gives up the trade to the other broker, who 
is often known as the prime broker. Institutional traders provide these instructions

Reading 44 ■ Market Organization and Structure 50
so they can obtain specialized execution services from different brokers while main -
taining a single account for custodial services and other prime brokerage services, 
such as margin loans.
An important clearing instruction that must appear on security sale orders is an 
indication of whether the sale is a long sale or a short sale. In either case, the broker 
representing the sell order must ensure that the trader can deliver securities for set -
tlement. For a long sale, the broker must confirm that the securities held are available 
for delivery. For a short sale, the broker must either borrow the security on behalf of 
the client or confirm that the client can borrow the security.
PRIMARY SECURITY MARKETS
When issuers first sell their securities to investors, practitioners say that the trades 
take place in the primary markets . An issuer makes an initial public offering  (IPO)—

sometimes called a placing—of a security issue when it sells the security to the public 
for the first time. A seasoned security is a security that an issuer has already issued. 
If the issuer wants to sell additional units of a previously issued security, it makes a 
seasoned offering  (sometimes called a secondary offering). Both types of offerings 
occur in the primary market  where issuers sell their securities to investors. Later, if 
investors trade these securities among themselves, they trade in secondary markets . 
This section discusses primary markets and the procedures that issuers use to offer 
their securities to the public.
7.1 Public Offerings
Corporations generally contract with an investment bank to help them sell their secu -
rities to the public. The investment bank then lines up subscribers who will buy the 
security. Investment bankers call this process book building . In London, the book 
builder is called the book runner. The bank tries to build a book of orders to which

they can sell the offering. Investment banks often support their book building by 
providing investment information and opinion about the issuer to their clients and to 
the public. Before the offering, the issuer generally makes a very detailed disclosure 
of its business, of the risks inherent in it, and of the uses to which the new funds will 
be placed.
When time is of the essence, issuers in Europe may issue securities through an 
accelerated book build , in which the investment bank arranges the offering in only 
one or two days. Such sales often occur at discounted prices.
The first public offering of common stock in a company consists of newly issued 
shares to be sold by the company. It may also include shares that the founders and 
other early investors in the company seek to sell. The initial public offering provides 
these investors with a means of liquidating their investments.
In an underwritten offering —the most common type of offering—the investment

bank guarantees the sale of the issue at an offering price that it negotiates with the 
issuer. If the issue is undersubscribed, the bank will buy whatever securities it cannot 
sell at the offering price. In the case of an IPO, the underwriter usually also promises to 
make a market in the security for about a month to ensure that the secondary market 
will be liquid and to provide price support, if necessary. For large issues, a syndicate of 
investment banks and broker–dealers helps the lead underwriter  build the book. The 
issuer usually pays an underwriting fee of about 7 percent for these various services. 
The underwriting fee is a placement cost of the offering.7

Primary Security Markets 51
In a best effort offering , the investment bank acts only as broker. If the offering 
is undersubscribed, the issuer will not sell as much as it hoped to sell.
For both types of offerings, the issuer and the bank usually jointly set the offering 
price following a negotiation. If they set a price that buyers consider too high, the 
offering will be undersubscribed, and they will fail to sell the entire issue. If they set 
the price too low, the offering will be oversubscribed, in which case the securities are 
often allocated to preferred clients or on a pro-  rata basis.
(Note that CFA Standard of Professional Conduct III.B—fair dealing—requires 
that the allocation be based on a written policy disclosed to clients and suggests that 
the securities be offered on a pro-  rata basis among all clients who have comparable 
relationships with their broker–dealers.)
Investment banks have a conflict of interest with respect to the offering price

in underwritten offerings. As agents for the issuers, they generally are supposed to 
select the offering price that will raise the most money. But as underwriters, they 
have strong incentives to choose a low price. If the price is low, the banks can allocate 
valuable shares to benefit their clients and thereby indirectly benefit the banks. If the 
price is too high, the underwriters will have to buy overvalued shares in the offering 
and perhaps also during the following month if they must support the price in the 
secondary market, which directly costs the banks. These considerations tend to lower 
initial offering prices so that prices in the secondary market often rise immediately 
following an IPO. They are less important in a seasoned offering because trading in 
the secondary market helps identify the proper price for the offering.
First time issuers generally accept lower offering prices because they and many

others believe that an undersubscribed IPO conveys very unfavorable information 
to the market about the company’s prospects at a time when it is most vulnerable to 
public opinion about its prospects. They fear that an undersubscribed initial public 
offering will make it substantially harder to raise additional capital in subsequent 
seasoned offerings.
EXAMPLE 24   
The Playtech Initial Public Offering
Playtech is a designer, developer, and licensor of software for the gambling 
industry. On 28 March 2006, Playtech raised approximately £265 million gross 
through an initial public offering of 103,142,466 ordinary shares at £2.57 per 
ordinary share. After the initial public offering, Playtech had 213,333,333 ordi -
nary shares issued and outstanding.
Playtech received gross proceeds of approximately £34.3  million and net 
proceeds of £31.8  million. The ordinary shares that were sold to the public 
represented approximately 48 percent of Playtech’s total issued ordinary shares.

The shares commenced trading at 8:00 AM on the AIM market of the London 
Stock Exchange where Playtech opened at £2.74, traded 37 million shares between 
£2.68 and £2.74, and closed at £2.73.
1 Approximately how many new shares were issued by the company and 
how many shares were sold by the company’s founders? What fraction of 
their holdings in the company did the founders sell?
2 Approximately what return did the subscribers who participated in the 
IPO make on the first day it traded?
3 Approximately how much did Playtech pay in placement costs as a per -
centage of the new funds raised?

Reading 44 ■ Market Organization and Structure 52
Playtech received gross proceeds of £34.3 million at £2.57 per share so the com -
pany issued and sold 13,346,304 shares (= £34.3 million/£2.57 per share). The total 
placement was for 103,142,466 shares, so the founders sold 89,796,162 shares 
(= 103,142,466 shares − 13,346,304 shares). Because approximately 200 million 
= 213.3 million – 13.3 million shares were outstanding before the placement, 
the founders sold approximately 45 percent (= 90 million/200 million) of the 
company.
The subscribers bought the stock for £2.57 per share and it closed at £2.73. The 
first day return thus was  622732 57
257100 .%..
.=−× .
Playtech obtained gross proceeds of £34.3 million, but only raised net proceeds 
of £31.8 million. The £2.5 million difference was the total cost of the placement 
to the firm, which is 7.9 percent of £31.8 million net proceeds.
7.2 Private Placements and Other Primary Market Transactions

Corporations sometimes issue their securities in private placements. In a private 
placement , corporations sell securities directly to a small group of qualified investors, 
usually with the assistance of an investment bank. Qualified investors have sufficient 
knowledge and experience to recognize the risks that they assume, and sufficient 
wealth to assume those risks responsibly. Most countries allow corporations to do 
private placements without nearly as much public disclosure as is required for public 
offerings. Private placements, therefore, may be cheaper than public offerings, but the 
buyers generally require higher returns (lower purchase prices) because they cannot 
subsequently trade the securities in an organized secondary market.
Corporations sometimes sell new issues of seasoned securities directly to the public 
on a piecemeal basis via a shelf registration. In a shelf registration , the corporation

makes all public disclosures that it would for a regular offering, but it does not sell the 
shares in a single transaction. Instead, it sells the shares directly into the secondary 
market over time, generally when it needs additional capital. Shelf registrations provide 
corporations with flexibility in the timing of their capital transactions, and they can 
alleviate the downward price pressures often associated with large secondary offerings.
Many corporations may also issue shares via dividend reinvestment plans (DRPs 
or DRIPs, for short) that allow their shareholders to reinvest their dividends in newly 
issued shares of the corporation (in particular, DRPs specify that the corporation issue 
new shares for the plan rather than purchase them on the open market). These plans 
sometimes also allow existing shareholders and other investors to buy additional stock 
at a slight discount to current prices.
Finally, corporations can issue new stock via a rights offering. In a rights offering,

the corporation distributes rights to buy stock at a fixed price to existing sharehold -
ers in proportion to their holdings. Because the rights need not be exercised, they 
are options. The exercise price, however, is set below the current market price of the 
stock so that buying stock with the rights is immediately profitable. Consequently, 
shareholders will experience dilution in the value of their existing shares. They can 
offset the dilution loss by exercising their rights or by selling the rights to others who 
will exercise them. Shareholders generally do not like rights offerings because they 
must provide additional capital (or sell their rights) to avoid losses through dilution. 
Financial analysts recognize that these securities, although called rights, are actually 
short-  term stock warrants and value them accordingly.

Secondary Security Market and Contract Market Structures 53
The national governments of financially strong countries generally issue their 
bonds, notes, and bills in public auctions organized by a government agency (usually 
associated with the finance ministry). They may also sell them directly to dealers.
Smaller and less financially secure national governments and most regional gov -
ernments often contract with investment banks to help them sell and distribute their 
securities. The laws of many governments, however, require that they auction their 
EXAMPLE 25   
Private and Public Placements
In what ways do private placements differ from public placements?
Solution:
Issuers make private placements to a limited number of investors that generally 
are financially sophisticated and well informed about risk. The investors gener -
ally have some relationship to the issuer. Issuers make public placements when

they sell securities to the general public. Public placements generally require 
substantially more financial disclosure than do private placements.
7.3 Importance of Secondary Markets to Primary Markets
Corporations and governments can raise money in the primary markets at lower cost 
when their securities will trade in liquid secondary markets. In a liquid market , trad -
ers can buy or sell with low transaction costs and small price concessions when they 
want to trade. Buyers value liquidity because they may need to sell their securities to 
meet liquidity needs. Investors thus will pay more for securities that they can easily 
sell than for those that they cannot easily sell. Higher prices translate into lower costs 
of capital for the issuers.
SECONDARY SECURITY MARKET AND CONTRACT 
MARKET STRUCTURES
Trading is the successful outcome to a bilateral search in which buyers look for sellers 
and sellers look for buyers. Many market structures have developed to reduce the costs

of this search. Markets are liquid when the costs of finding a suitable counterparty 
to a trade are low.
Trading in securities and contracts takes place in a variety of market structures. 
The structures differ by when trades can be arranged, who arranges the trades, how 
they do so, and how traders learn about possible trading opportunities and executed 
trades. This section introduces the various market structures used to trade securities 
and contracts. We first consider trading sessions, then execution mechanisms, and 
finally market information systems.8

Reading 44 ■ Market Organization and Structure 54
8.1 Trading Sessions
Markets are organized as call markets or as continuous trading markets. In a call 
market , trades can be arranged only when the market is called at a particular time 
and place. In contrast in a continuous trading market , trades can be arranged and 
executed anytime the market is open.
Buyers can easily find sellers and vice versa in call markets because all traders 
interested in trading (or orders representing their interests) are present at the same 
time and place. Call markets thus have the potential to be very liquid when they are 
called. But they are completely illiquid between trading sessions. In contrast, traders 
can arrange and execute their trades at anytime in continuous trading markets, but 
doing so can be difficult if the buyers and sellers (or their orders) are not both present 
at the same time.
Most call markets use single price auctions to match buyers to sellers. In these

auctions, the market constructs order books representing all buy orders and all seller 
orders. The market then chooses a single trade price that will maximize the total 
volume of trade. The order books are supply and demand schedules, and the point at 
which they cross determines the trade price.
Call markets usually are organized just once a day, but some markets organize 
calls at more frequent intervals.
Many continuous trading markets start their trading with a call market auction. 
During a pre-  opening period, traders submit their orders for the market call. At the 
opening, any possible trades are arranged and then trading continues in the contin -
uous trading session. Some continuous trading markets also close their trading with 
a call. In these markets, traders who are only interested in trading in the closing call 
submit market- or limit-  on- close orders.
EXAMPLE 26   
Call Markets and Continuous Trading Markets

1 What is the main advantage of a call market compared with a continuous 
trading market?
2 What is the main advantage of a continuous trading market compared 
with a call market?
By gathering all traders to the same place at the same time, a call market makes 
it easier for buyers to find sellers and vice versa. In contrast, if buyers and sellers 
(or their orders) are not present at the same time in a continuous market, they 
cannot trade.
In a continuous trading market, a willing buyer and seller can trade at any time 
the market is open. In contrast, in a call market trading can take place only 
when the market is called.
8.2 Execution Mechanisms
The three main types of market structures are quote-  driven markets (sometimes called 
price-  driven or dealer markets), order-  driven markets, and brokered markets. In quote-  
driven markets , customers trade with dealers. In order-  driven markets , an order

matching system run by an exchange, a broker, or an alternative trading system uses

Secondary Security Market and Contract Market Structures 55
rules to arrange trades based on the orders that traders submit. Most exchanges and 
ECNs organize order-  driven markets. In brokered markets , brokers arrange trades 
between their customers. Brokered markets are common for transactions of unique 
instruments, such as real estate properties, intellectual properties, or large blocks of 
securities. Many trading systems use more than one type of market structure.
8.2.1  Quote-  Driven Markets
Worldwide, most trading, other than in stocks, takes place in quote-  driven markets. 
Almost all bonds and currencies and most spot commodities trade in quote-  driven 
markets. Traders call them quote-  driven (or price-  driven or dealer) because custom -
ers trade at the prices quoted by dealers. Depending on the instrument traded, the 
dealers work for commercial banks, for investment banks, for broker–dealers, or for 
proprietary trading houses.

Quote-  driven markets also often are called over-  the- counter (OTC) markets 
because securities used to be literally traded over the dealer’s counter in the dealer’s 
office. Now, most trades in OTC markets are conducted over proprietary computer 
communications networks, by telephone, or sometimes over instant messaging systems.
8.2.2  Order-  Driven Markets
Order-  driven markets arrange trades using rules to match buy orders to sell orders. 
The orders may be submitted by customers or by dealers. Almost all exchanges use 
order-  driven trading systems, and every automated trading system is an order-  driven 
system.
Because rules match buyers to sellers, traders often trade with complete strangers. 
Order-  driven markets thus must have procedures to ensure that buyers and sellers per -
form on their trade contracts. Otherwise, dishonest traders would enter contracts that 
they would not settle if a change in market conditions made settlement unprofitable.

Two sets of rules characterize order-  driven market mechanisms: Order matching 
rules and trade pricing rules. The order matching rules match buy orders to sell orders. 
The trade pricing rules determine the prices at which the matched trades take place.
8.2.2.1  Order Matching Rules  Order-  driven trading systems match buyers to sellers 
using rules that rank the buy orders and the sell orders based on price, and often along 
with other secondary criteria. The systems then match the highest ranking buy order 
with the highest ranking sell order. If the buyer is willing to pay at least as much as 
the seller is willing to receive, the system will arrange a trade for the minimum of the 
buy and sell quantities. The remaining size, if any, is then matched with the next order 
on the other side and the process continues until no further trades can be arranged.
The order precedence hierarchy  determines which orders go first. The first rule is

price priority : The highest priced buy orders and the lowest priced sell orders go first. 
They are the most aggressively priced orders. Secondary precedence rules  determine 
how to rank orders at the same price. Most trading systems use time precedence to 
rank orders at the same price. The first order to arrive has precedence over other 
orders. In trading systems that permit hidden and partially hidden orders, displayed 
quantities at a given price generally have precedence over the undisplayed quantities. 
So the complete precedence hierarchy is given by price priority, display precedence 
at a given price, and finally time precedence among all orders with the same display 
status at a given price. These rules give traders incentives to improve price, display 
their orders, and arrive early if they want to trade quickly. These incentives increase 
market liquidity.

Reading 44 ■ Market Organization and Structure 56
8.2.2.2  Trade Pricing Rules  After the orders are matched, the trading system then 
uses its trade pricing rule to determine the trade price. The three rules that various 
order-  driven markets use to price their trades are the uniform pricing rule, the dis -
criminatory pricing rule, and the derivative pricing rule.
Call markets commonly use the uniform pricing rule. Under this rule, all trades 
execute at the same price. The market chooses the price that maximizes the total 
quantity traded.
Continuous trading markets use the discriminatory pricing rule . Under this rule, 
the limit price of the order or quote that first arrived—the standing order—determines 
the trade price. This rule allows a large arriving trader to discriminate among standing 
limit orders by filling the most aggressively priced orders first at their limit prices and 
then filling less aggressively priced orders at their less favorable (from the point of

view of the arriving trader) limit prices. If trading systems did not use this pricing rule, 
large traders would break their orders into pieces to price discriminate on their own.
EXAMPLE 27   
Filling a Large Order in a Continuous Trading Market
Before the arrival of a large order, a market has the following limit orders 
standing on its book:
Buyer Bid Size Limit Price(¥) Offer Size Seller
Takumi 15 100.1
Hiroto 8 100.2
Shou 10 100.3
100.4 4 Hina
100.5 6 Sakur
100.6 12 Miku
Buyer Tsubasa submits a day order to buy 15 contracts, limit ¥100.5. With whom 
does he trade, what is his average trade price, and what does the limit order 
book look like afterward?
Solution:
Tsubasa’s buy order first fills with the most aggressively priced sell order, which 
is Hina’s order for four contracts. A trade takes place at ¥100.4 for four contracts, 
Hina’s order fills completely, and Tsubasa still has 11 more contracts remaining.
The next most aggressively priced sell order is Sakur’s order for six contracts.

A second trade takes place at ¥100.5 for six contracts, Sakur’s order fills com -
pletely, and Tsubasa still has five more contracts remaining.
The next most aggressively priced sell order is Miku’s order at ¥100.6. No 
further trade is possible, however, because her limit sell price is above Tsubasa’s 
limit buy price. Tsubasa’s average trade price is  ¥¥ ¥100.5100 464 100 46
46..=×+ ×
+.
Because Tsubasa issued a day order, the remainder of his order is placed on 
the book on the buy side at ¥100.5. The following orders are then on the book:
Buyer Bid Size Limit Price (¥) Offer Size Seller

Secondary Security Market and Contract Market Structures 57
100.4
Tsubasa 5 100.5
If Tsubasa had issued an immediate-  or- cancel order, the remaining five 
contracts would have been cancelled.
Crossing networks use the derivative pricing rule. Crossing networks  are trading 
systems that match buyers and sellers who are willing to trade at prices obtained 
from other markets. Most systems cross their trades at the midpoint of the best bid 
and ask quotes published by the exchange at which the security primarily trades. 
This pricing rule is called a derivative pricing rule  because the price is derived from 
another market. In particular, the price does not depend on the orders submitted 
to the crossing network. Some crossing networks are organized as call markets and 
others as continuously trading markets. The most important crossing market is the 
equity trading system POSIT.
8.2.3  Brokered Markets

The third execution mechanism is the brokered market , in which brokers arrange 
trades among their clients. Brokers organize markets for instruments for which finding 
a buyer or a seller willing to trade is difficult because the instruments are unique and 
thus of interest only to a limited number of people or institutions. These instruments 
generally are also infrequently traded and expensive to carry in inventory. Examples 
of such instruments include very large blocks of stock, real estate properties, fine art 
masterpieces, intellectual properties, operating companies, liquor licenses, and taxi 
medallions. Because dealers generally are unable or unwilling to hold these assets 
in their inventories, they will not make markets in them. Organizing order-  driven 
markets for these instruments is not sensible because too few traders would submit 
orders to them.
Successful brokers in these markets try to know everyone who might now or in

the future be willing to trade. They spend most of their time on the telephone and in 
meetings building their networks.
EXAMPLE 28   
Quote-  Driven, Order-  Driven, and Brokered Markets
What are the primary advantages of quote-  driven, order-  driven, and brokered 
markets?
Solution:
In a quote-  driven market, dealers generally are available to supply liquidity. In 
an order-  driven market, traders can supply liquidity to each other. In a brokered 
market, brokers help find traders who are willing to trade when dealers would not 
be willing to make markets and when traders would not be willing to post orders.

Reading 44 ■ Market Organization and Structure 58
8.3 Market Information Systems
Markets vary in the type and quantity of data that they disseminate to the public. 
Traders say that a market is pre-  trade transparent if the market publishes real-  time 
data about quotes and orders. Markets are post-  trade transparent if the market pub -
lishes trade prices and sizes soon after trades occur.
Buy-  side traders value transparency because it allows them to better manage their 
trading, understand market values, and estimate their prospective and actual transac -
tion costs. In contrast, dealers prefer to trade in opaque markets because, as frequent 
traders, they have an information advantage over those who know less than they do. 
Bid–ask spreads tend to be wider and transaction costs tend to be higher in opaque 
markets because finding the best available price is harder for traders in such markets.
WELL-  FUNCTIONING FINANCIAL SYSTEMS

The financial system allows traders to solve financing and risk management problems. 
In a well-  functioning financial system:
■■investors can easily move money from the present to the future while obtaining 
a fair rate of return for the risks that they bear;
■■borrowers can easily obtain funds that they need to undertake current projects 
if they can credibly promise to repay the funds in the future;
■■hedgers can easily trade away or offset the risks that concern them; and
■■traders can easily trade currencies for other currencies or commodities that 
they need.
If the assets or contracts needed to solve these problems are available to trade, 
the financial system has complete markets . If the costs of arranging these trades are 
low, the financial system is operationally efficient . If the prices of the assets and 
contracts reflect all available information related to fundamental values, the financial 
system is informationally efficient.

Well-  functioning financial systems are characterized by:
■■the existence of well-  developed markets that trade instruments that help people 
solve their financial problems (complete markets);
■■liquid markets in which the costs of trading—commissions, bid–ask spreads, 
and order price impacts—are low (operationally efficient markets);
■■timely financial disclosures by corporations and governments that allow market 
participants to estimate the fundamental values of securities (support informa -
tionally efficient markets ); and
■■prices that reflect fundamental values so that prices vary primarily in response 
to changes in fundamental values and not to demands for liquidity made by 
uninformed traders (informationally efficient markets).
Such complete and operationally efficient markets are produced by financial inter -
mediaries who:
■■organize exchanges, brokerages, and alternative trading systems that match 
buyers to sellers;

■■provide liquidity on demand to traders;
■■securitize assets to produce investment instruments that are attractive to inves -
tors and thereby lower the costs of funds for borrowers;9

Well-  Functioning Financial Systems 59
■■run banks that match investors to borrowers by taking deposits and making 
loans;
■■run insurance companies that pool uncorrelated risks;
■■provide investment advisory services that help investors manage and grow their 
assets at low cost;
■■organize clearinghouses that ensure everyone settles their trades and contracts; 
and
■■organize depositories that ensure nobody loses their assets.
The benefits of a well-  functioning financial system are huge. In such systems, 
investors who need to move money to the future can easily connect with entrepreneurs 
who need money now to develop new products and services. Similarly, producers who 
would otherwise avoid valuable projects because they are too risky can easily transfer 
those risks to others who can better bear them. Most importantly, these transactions 
generally can take place among strangers so that the benefits from trading can be 
derived from an enormous number of potential matches.

In contrast, economies that have poorly functioning financial systems have great 
difficulties allocating capital among the many companies who could use it. Financial 
transactions tend to be limited to arrangements within families when people cannot 
easily find trustworthy counterparties who will honor their contracts. In such econ -
omies, capital is allocated inefficiently, risks are not easily shared, and production is 
inefficient.
An extraordinarily important byproduct of an operationally efficient financial 
system is the production of informationally efficient prices. Prices are information -
ally efficient when they reflect all available information about fundamental values. 
Informative prices are crucially important to the welfare of an economy because 
they help ensure that resources go where they are most valuable. Economies that use 
resources where they are most valuable are allocationally efficient . Economies that

do not use resources where they are most valuable waste their resources and conse -
quently often are quite poor.
Well-  informed traders make prices informationally efficient. When they buy assets 
and contracts that they think are undervalued, they tend to push the assets’ prices 
up. Similarly, when they sell assets and contracts that they think are overvalued, they 
tend to push the assets’ prices down. The effect of their trading thus causes prices to 
reflect their information about values.
How accurately prices reflect fundamental information depends on the costs of 
obtaining fundamental information and on the liquidity available to well-  informed 
traders. Accounting standards and reporting requirements that produce meaningful 
and timely financial disclosures reduce the costs of obtaining fundamental infor -
mation and thereby allow analysts to form more accurate estimates of fundamental 
values. Liquid markets allow well-  informed traders to fill their orders at low cost.

If filling orders is very costly, informed trading may not be profitable. In that case, 
information-  motivated traders will not commit resources to collect and analyze data 
and they will not trade. Without their research and their associated trading, prices 
would be less informative.

Reading 44 ■ Market Organization and Structure 60
EXAMPLE 29   
Well-  Functioning Financial Systems
As a financial analyst specializing in emerging market equities, you understand 
that a well-  functioning financial system contributes to the economic prosperity 
of a country. You are asked to start covering a new small market country. What 
factors will you consider when characterizing the quality of its financial markets?
Solution:
In general, you will consider whether:
■■the country has markets that allow its companies and residents to finance 
projects, save for the future, and exchange risk;
■■the costs of trading in those markets is low; and
■■prices reflect fundamental values.
You may specifically check to see whether:
■■fixed income and stock markets allow borrowers to easily obtain capital 
from investors;
■■corporations disclose financial and operating data on a timely basis in 
conformity to widely respected reporting standards, such as IFRS;

■■forward, futures, and options markets trade instruments that companies 
need to hedge their risks;
■■dealers and arbitrageurs allow traders to trade when they want to;
■■bid–ask spreads are small;
■■trades and contracts invariably settle as expected;
■■investment managers provide high-  quality management services for rea -
sonable fees;
■■banks and other financing companies are well capitalized and thus able to 
help investors provide capital to borrowers;
■■securitized assets are available and represent reasonable credit risks;
■■insurance companies are well capitalized and thus able to help those 
exposed to risks insure against them; and
■■price volatility appears consistent with changes in fundamental values.
MARKET REGULATION
Government agencies and practitioner organizations regulate many markets and the 
financial intermediaries that participate in them. The regulators generally seek to 
promote fair and orderly markets in which traders can trade at prices that accurately

reflect fundamental values without incurring excessive transaction costs. This section 
identifies the problems that financial regulators hope to solve and the objectives of 
their regulations.
Regrettably, some people will steal from each other if given a chance, especially if 
the probability of detection is low or if the penalty for being caught is low. The number 
of ways that people can steal or misappropriate wealth generally increases with the 
complexity of their relationships and with asymmetries in their knowledge. Because 10

Market Regulation 61
financial markets tend to be complex, and because customers are often much less 
sophisticated than the professionals that serve them, the potential for losses through 
various frauds can be unacceptably high in unregulated markets.
Regulators thus ensure that systems are in place to protect customers from fraud. 
In principle, the customers themselves would demand such systems as a condition of 
doing business. When customers are unsophisticated or poorly informed, however, they 
may not know how to protect themselves. When the costs of learning are large—as 
they often are in complex financial markets—having regulators look out for the public 
interest can be economically efficient.
More customer money is probably lost in financial markets through negligence 
than through outright fraud. Most customers in financial markets use various agents 
to help them solve problems that they do not understand well. These agents include

securities brokers, financial advisers, investment managers, and insurance agents. 
Because customers generally do not have much information about market condi -
tions, they find it extremely difficult to measure the added value they obtain from 
their agents. This problem is especially challenging when performance has a strong 
random component. In that case, determining whether agents are skilled or lucky is 
very difficult. Moreover, if the agent is a good salesman, the customer may not criti -
cally evaluate their agent’s performance. These conditions, which characterize most 
financial markets, ensure that customers cannot easily determine whether their agents 
are working faithfully for them. They tend to lose if their agents are unqualified or 
lazy, or if they unconsciously favor themselves and their friends over their clients, as 
is natural for even the most honest people.
Regulators help solve these agency problems by setting minimum standards of

competence for agents and by defining and enforcing minimum standards of practice. 
CFA Institute provides significant standard setting leadership in the areas of investment 
management and investment performance reporting through its Chartered Financial 
Analyst Program, in which you are studying, and its Global Investment Performance 
Standards. In principle, regulation would not be necessary if customers could identify 
competent agents and effectively measure their performance. In the financial markets, 
doing so is very difficult.
Regulators often act to level the playing field for market participants. For example, 
in many jurisdictions, insider trading in securities is illegal. The rule prevents corporate 
insiders and others with access to corporate information from trading on material 
information that has not been released to the public. The purpose of the rule is to 
reduce the profits that insiders could extract from the markets. These profits would

come from other traders who would lose when they trade with well-  informed insiders. 
Because traders tend to withdraw from markets when they lose, rules against insider 
trading help keep markets liquid. They also keep corporate insiders from hoarding 
Many situations arise in financial markets in which common standards benefit 
everyone involved. For example, having all companies report financial results on a 
common basis allows financial analysts to easily compare companies. Accordingly, 
the International Accounting Standards Board (IASB) and the US-  based Financial 
Accounting Standards Board, among many others, promulgate common financial stan -
dards to which all companies must report. The benefits of having common reporting 
standards has led to a very successful and continuing effort to converge all accounting 
standards to a single worldwide standard. Without such regulations, investors might

eventually refuse to invest in companies that do not report to a common standard, 
but such market-  based discipline is a very slow regulator of behavior, and it would 
have little effect on companies that do not need to raise new capital.
Regulators generally require that financial firms maintain minimum levels of capital. 
These capital requirements serve two purposes. First, they ensure that the compa -
nies will be able to honor their contractual commitments when unexpected market

Reading 44 ■ Market Organization and Structure 62
movements or poor decisions cause them to lose money. Second, they ensure that 
the owners of financial firms have substantial interest in the decisions that they make. 
Without a substantial financial interest in the decisions that they make, companies 
often take too many risks and exercise poor judgment about extending credit to others. 
When such companies fail, they impose significant costs on others. Minimum capital 
requirements reduce the probability that financial firms will fail and they reduce the 
disruptions associated with those failures that do occur. In principle, a firm’s custom -
ers and counterparties could require minimum capital levels as a condition of doing 
business with the firm, but they have more difficulty enforcing their contracts than 
do governments who can imprison people.
Regulators similarly regulate insurance companies and pension funds that make

long-  term promises to their clients. Such entities need to maintain adequate reserves 
to ensure that they can fund their liabilities. Unfortunately, their managers have a 
tendency to underestimate these reserves if they will not be around when the liabil -
ities come due. Again, in principle, policyholders and employees could regulate the 
behavior of their insurance funds and their employers by refusing to contract with 
them if they do not promise to adequately fund their liabilities. In practice, however, 
the sophistication, information, and time necessary to write and enforce contracts 
that control these problems are beyond the reach of most people. The government 
thus is a sensible regulator of such problems.
Many regulators are self-  regulating organizations (SROs) that regulate their 
members. Exchanges, clearinghouses, and dealer trade organizations are examples 
of self-  regulating organizations. In some cases, the members of these organizations

voluntarily subject themselves to the SRO’s regulations to promote the common good. 
In other cases, governments delegate regulatory and enforcement authorities to SROs, 
usually subject to the supervision of a government agency, such as a national securities 
and exchange authority. Exchanges, dealer associations, and clearing agencies often 
regulate their members with these delegated powers.
By setting high standards of behavior, SROs help their members obtain the confi -
dence of their customers. They also reduce the chance that members of the SRO will 
incur losses when dealing with other members of the SRO.
When regulators fail to solve the problems discussed here, the financial system 
does not function well. People who lose money stop saving and borrowers with good 
ideas cannot fund their projects. Similarly, hedgers withdraw from markets when the 
costs of hedging are high. Without the ability to hedge, producers become reluctant

to specialize because specialization generally increases risk. Because specialization 
also decreases costs, however, production becomes less efficient as producers chose 
safer technologies. Economies that cannot solve the regulatory problems described 
in this section tend to operate less efficiently than do better regulated economies, and 
they tend to be less wealthy.
To summarize, the objectives of market regulation are to:
1 control fraud;
2 control agency problems;
3 promote fairness;
4 set mutually beneficial standards;
5 prevent undercapitalized financial firms from exploiting their investors by mak -
ing excessively risky investments; and
6 ensure that long-  term liabilities are funded.
Regulation is necessary because regulating certain behaviors through market-  
based mechanisms is too costly for people who are unsophisticated and uninformed. 
Effectively regulated markets allow people to better achieve their financial goals.

Summary 63
EXAMPLE 30   
Bankrupt Traders
You are the chief executive officer of a brokerage that is a member of a clear -
inghouse. A trader who clears through your firm is bankrupt at midday, but you 
do not yet know it even though your clearing agreement with him explicitly 
requires that he immediately report significant losses. The trader knows that 
if he takes a large position, prices might move in his favor so that he will no 
longer be bankrupt. The trader attempts to do so and succeeds. You find out 
about this later in the evening.
1 Why does the clearinghouse regulate its members?
2 What should you do about the trader?
3 Why would the clearinghouse allow you to keep his trading profits?
The clearinghouse regulates its members to ensure that no member imposes 
costs on another member by failing to settle a trade.
You should immediately end your clearing relationship with the trader and

confiscate his trading profits. The trader was trading with your firm’s capital 
after he became bankrupt. Had he lost, your firm would have borne the loss.
If the clearinghouse did not permit you to keep his trading profits, other traders 
similarly situated might attempt the same strategy.
SUMMARY
This reading introduces how the financial system operates and explains how well-  
functioning financial systems lead to wealthy economies. Financial analysts need 
to understand how the financial system works because their analyses often lead to 
trading decisions.
The financial system consists of markets and the financial intermediaries that 
operate in them. These institutions allow buyers to connect with sellers. They may 
trade directly with each other when they trade the same instrument or they only 
may trade indirectly when a financial intermediary connects the buyer to the seller 
through transactions with each that appear on the intermediary’s balance sheet. The

buyer and seller may exchange instruments, cash flows, or risks.
The following points, among others, were made in this reading:
■■The financial system consists of mechanisms that allow strangers to contract 
with each other to move money through time, to hedge risks, and to exchange 
assets that they value less for those that they value more.
■■Investors move money from the present to the future when they save. They 
expect a normal rate of return for bearing risk through time. Borrowers 
move money from the future to the present to fund current projects and

Reading 44 ■ Market Organization and Structure 64
expenditures. Hedgers trade to reduce their exposure to risks they prefer not to 
take. Information-  motivated traders are active investment managers who try to 
identify under- and overvalued instruments.
■■Securities are first sold in primary markets by their issuers. They then trade in 
secondary markets.
■■People invest in pooled investment vehicles to benefit from the investment 
management services of their managers.
■■Forward contracts allow buyers and sellers to arrange for future sales at prede -
termined prices. Futures contracts are forward contracts guaranteed by clear -
inghouses. The guarantee ensures that strangers are willing to trade with each 
other and that traders can offset their positions by trading with anybody. These 
features of futures contract markets make them highly attractive to hedgers and 
information-  motivated traders.
■■Many financial intermediaries connect buyers to sellers in a given instru -

ment, acting directly as brokers and exchanges or indirectly as dealers and 
arbitrageurs.
■■Financial intermediaries create instruments when they conduct arbitrage, 
securitize assets, borrow to lend, manage investment funds, or pool insurance 
contracts. These activities all transform cash flows and risks from one form 
to another. Their services allow buyers and sellers to connect with each other 
through instruments that meet their specific needs.
■■Financial markets work best when strangers can contract with each other 
without worrying about whether their counterparts are able and willing to 
honor their contract. Clearinghouses, variation margins, maintenance margins, 
and settlement guarantees made by creditworthy brokers on behalf of their 
clients help manage credit risk and ultimately allow strangers to contract with 
■■Information-  motivated traders short sell when they expect that prices will fall.

Hedgers short sell to reduce the risks of a long position in a related contract or 
■■Margin loans allow people to buy more securities than their equity would 
otherwise permit them to buy. The larger positions expose them to more risk 
so that gains and losses for a given amount of equity will be larger. The leverage 
ratio is the value of a position divided by the value of the equity supporting it. 
The returns to the equity in a position are equal to the leverage ratio times the 
returns to the unleveraged position.
■■To protect against credit losses, brokers demand maintenance margin payments 
from their customers who have borrowed cash or securities when adverse price 
changes cause their customer’s equity to drop below the maintenance margin 
ratio. Brokers close positions for customers who do not satisfy these margin 
calls.
■■Orders are instructions to trade. They always specify instrument, side (buy or 
sell), and quantity. They usually also provide several other instructions.

■■Market orders tend to fill quickly but often at inferior prices. Limit orders gen -
erally fill at better prices if they fill, but they may not fill. Traders choose order 
submission strategies on the basis of how quickly they want to trade, the prices 
they are willing to accept, and the consequences of failing to trade.
■■Stop instructions are attached to other orders to delay efforts to fill them until 
the stop condition is satisfied. Although stop orders are often used to stop 
losses, they are not always effective.

Summary 65
■■Issuers sell their securities using underwritten public offerings, best efforts 
public offerings, private placements, shelf registrations, dividend reinvestment 
programs, and rights offerings. Investment banks have a conflict of interests 
when setting the initial offering price in an IPO.
■■Well-  functioning secondary markets are essential to raising capital in the pri -
mary markets because investors value the ability to sell their securities if they 
no longer want to hold them or if they need to disinvest to raise cash. If they 
cannot trade their securities in a liquid market, they will not pay as much for 
them.
■■Matching buyers and sellers in call markets is easy because the traders (or their 
orders) come together at the same time and place.
■■Dealers provide liquidity in quote-  driven markets. Public traders as well as deal -
ers provide liquidity in order-  driven markets.
■■Order-  driven markets arrange trades by ranking orders using precedence rules.

The rules generally ensure that traders who provide the best prices, display the 
most size, and arrive early trade first. Continuous order-  driven markets price 
orders using the discriminatory pricing rule. Under this rule, standing limit 
orders determine trade prices.
■■Brokers help people trade unique instruments or positions for which finding a 
buyer or a seller is difficult.
■■Transaction costs are lower in transparent markets than in opaque markets 
because traders can more easily determine market value and more easily man -
age their trading in transparent markets.
■■A well-  functioning financial system allows people to trade instruments that best 
solve their wealth and risk management problems with low transaction costs. 
Complete and liquid markets characterize a well-  functioning financial system. 
Complete markets are markets in which the instruments needed to solve invest -
ment and risk management problems are available to trade. Liquid markets are

markets in which traders can trade when they want to trade at low cost.
■■The financial system is operationally efficient when its markets are liquid. 
Liquid markets lower the costs of raising capital.
■■A well-  functioning financial system promotes wealth by ensuring that capital 
allocation decisions are well made. A well-  functioning financial system also 
promotes wealth by allowing people to share the risks associated with valuable 
products that would otherwise not be undertaken.
■■Prices are informationally efficient when they reflect all available information 
about fundamental values. Information-  motivated traders make prices infor -
mationally efficient. Prices will be most informative in liquid markets because 
information-  motivated traders will not invest in information and research if 
establishing positions based on their analyses is too costly.
■■Regulators generally seek to promote fair and orderly markets in which traders

can trade at prices that accurately reflect fundamental values without incur -
ring excessive transaction costs. Governmental agencies and self-  regulating 
organizations of practitioners provide regulatory services that attempt to make 
markets safer and more efficient.
■■Mandated financial disclosure programs for the issuers of publicly traded secu -
rities ensure that information necessary to estimate security values is available 
to financial analysts on a consistent basis.

Reading 44 ■ Market Organization and Structure 66
1 Akihiko Takabe has designed a sophisticated forecasting model, which predicts 
the movements in the overall stock market, in the hope of earning a return in 
excess of a fair return for the risk involved. He uses the predictions of the model 
to decide whether to buy, hold, or sell the shares of an index fund that aims to 
replicate the movements of the stock market. Takabe would best be character -
ized as a(n):
A hedger.
B investor.
C information-  motivated trader.
2 James Beach is young and has substantial wealth. A significant proportion 
of his stock portfolio consists of emerging market stocks that offer relatively 
high expected returns at the cost of relatively high risk. Beach believes that 
investment in emerging market stocks is appropriate for him given his ability 
and willingness to take risk. Which of the following labels most appropriately  
describes Beach?
A Hedger.
B Investor.
C Information-  motivated trader.

3 Lisa Smith owns a manufacturing company in the United States. Her company 
has sold goods to a customer in Brazil and will be paid in Brazilian real (BRL) 
in three months. Smith is concerned about the possibility of the BRL depreciat -
ing more than expected against the US dollar (USD). Therefore, she is planning 
to sell three-  month futures contracts on the BRL. The seller of such contracts 
generally gains when the BRL depreciates against the USD. If Smith were to sell 
these future contracts, she would most appropriately  be described as a(n):
A hedger.
4 Which of the following is not a function of the financial system?
A To regulate arbitrageurs’ profits (excess returns).
B To help the economy achieve allocational efficiency.
C To facilitate borrowing by businesses to fund current operations.
5 An investor primarily invests in stocks of publicly traded companies. The inves -

tor wants to increase the diversification of his portfolio. A friend has recom -
mended investing in real estate properties. The purchase of real estate would 
best be characterized as a transaction in the:
A derivative investment market.
B traditional investment market.
C alternative investment market.
6 A hedge fund holds its excess cash in 90-  day commercial paper and negotiable 
certificates of deposit. The cash management policy of the hedge fund is best 
described  as using:
A capital market instruments.

Practice Problems 67
B money market instruments.
C intermediate-  term debt instruments.
7 An oil and gas exploration and production company announces that it is offer -
ing 30 million shares to the public at $45.50 each. This transaction is most likely  
a sale in the:
A futures market.
B primary market.
C secondary market.
8 Consider a mutual fund that invests primarily in fixed-  income securities that 
have been determined to be appropriate given the fund’s investment goal. 
Which of the following is least likely  to be a part of this fund?
A Warrants.
B Commercial paper.
C Repurchase agreements.
9 A friend has asked you to explain the differences between open-  end and 
closed-  end funds. Which of the following will you most likely  include in your 
explanation?
A Closed-  end funds are unavailable to new investors.
B When investors sell the shares of an open-  end fund, they can receive a dis -
count or a premium to the fund’s net asset value.

C When selling shares, investors in an open-  end fund sell the shares back to 
the fund whereas investors in a closed-  end fund sell the shares to others in 
the secondary market.
10 The usefulness of a forward contract is limited by some problems. Which of the 
following is most likely  one of those problems?
A Once you have entered into a forward contract, it is difficult to exit from the 
contract.
B Entering into a forward contract requires the long party to deposit an initial 
amount with the short party.
C If the price of the underlying asset moves adversely from the perspective of 
the long party, periodic payments must be made to the short party.
11 Tony Harris is planning to start trading in commodities. He has heard about 
the use of futures contracts on commodities and is learning more about them. 
Which of the following is Harris least likely  to find associated with a futures 
contract?
A Existence of counterparty risk.

contract?
B Standardized contractual terms.
C Payment of an initial margin to enter into a contract.
12 A German company that exports machinery is expecting to receive $10 million 
in three months. The firm converts all its foreign currency receipts into euros. 
The chief financial officer of the company wishes to lock in a minimum fixed 
rate for converting the $10 million to euro but also wants to keep the flexibility 
to use the future spot rate if it is favorable. What hedging transaction is most 
likely  to achieve this objective?
A Selling dollars forward.
B Buying put options on the dollar.
C Selling futures contracts on dollars.

Reading 44 ■ Market Organization and Structure 68
13 A book publisher requires substantial quantities of paper. The publisher and a 
paper producer have entered into an agreement for the publisher to buy and the 
producer to supply a given quantity of paper four months later at a price agreed 
upon today. This agreement is a:
A futures contract.
C commodity swap.
14 The Standard & Poor’s Depositary Receipts (SPDRs) is an investment that 
tracks the S&P 500 stock market index. Purchases and sales of SPDRs during an 
average trading day are best described as:
A primary market transactions in a pooled investment.
B secondary market transactions in a pooled investment.
C secondary market transactions in an actively managed investment.
15 The Standard & Poor’s Depositary Receipts (SPDRs) is an exchange-  traded 
fund in the United States that is designed to track the S&P 500 stock market 
index. The current price of a share of SPDRs is $113. A trader has just bought

call options on shares of SPDRs for a premium of $3 per share. The call options 
expire in five months and have an exercise price of $120 per share. On the 
expiration date, the trader will exercise the call options (ignore any transaction 
costs) if and only if the shares of SPDRs are trading:
A below $120 per share.
B above $120 per share.
C above $123 per share.
16 Which of the following statements about exchange-  traded funds is most correct ?
A Exchange-  traded funds are not backed by any assets.
B The investment companies that create exchange-  traded funds are financial 
intermediaries.
C The transaction costs of trading shares of exchange-  traded funds are sub -
stantially greater than the combined costs of trading the underlying assets of 
the fund.
17 Jason Schmidt works for a hedge fund and he specializes in finding profit 
opportunities that are the result of inefficiencies in the market for convert -
ible bonds—bonds that can be converted into a predetermined amount of a

company’s common stock. Schmidt tries to find convertibles that are priced 
inefficiently relative to the underlying stock. The trading strategy involves the 
simultaneous purchase of the convertible bond and the short sale of the under -
lying common stock. The above process could best be described as:
A hedging.
B arbitrage.
C securitization.
18 Pierre-  Louis Robert just purchased a call option on shares of the Michelin 
Group. A few days ago he wrote a put option on Michelin shares. The call and 
put options have the same exercise price, expiration date, and number of shares 
underlying. Considering both positions, Robert’s exposure to the risk of the 
stock of the Michelin Group is:
A long.
B short.
C neutral.

Practice Problems 69
19 An online brokerage firm has set the minimum margin requirement at 55 per -
cent. What is the maximum leverage ratio associated with a position financed 
by this minimum margin requirement?
A 1.55.
B 1.82.
C 2.22.
20 A trader has purchased 200 shares of a non-  dividend-  paying firm on margin at 
a price of $50 per share. The leverage ratio is 2.5. Six months later, the trader 
sells these shares at $60 per share. Ignoring the interest paid on the borrowed 
amount and the transaction costs, what was the return to the trader during the 
six- month period?
A 20 percent.
B 33.33 percent.
C 50 percent.
21 Jason Williams purchased 500 shares of a company at $32 per share. The stock 
was bought on 75 percent margin. One month later, Williams had to pay inter -
est on the amount borrowed at a rate of 2 percent per month. At that time, 
Williams received a dividend of $0.50 per share. Immediately after that he sold

the shares at $28 per share. He paid commissions of $10 on the purchase and 
$10 on the sale of the stock. What was the rate of return on this investment for 
the one-  month period?
A −12.5 percent.
B –15.4 percent.
C –50.1 percent.
22 Caroline Rogers believes the price of Gamma Corp. stock will go down in the 
near future. She has decided to sell short 200 shares of Gamma Corp. at the 
current market price of €47. The initial margin requirement is 40 percent. 
Which of the following is an appropriate statement regarding the margin 
requirement that Rogers is subject to on this short sale?
A She will need to contribute €3,760 as margin.
B She will need to contribute €5,640 as margin.
C She will only need to leave the proceeds from the short sale as deposit and 
does not need to contribute any additional funds.
23 The current price of a stock is $25 per share. You have $10,000 to invest. You 
borrow an additional $10,000 from your broker and invest $20,000 in the stock.

If the maintenance margin is 30 percent, at what price will a margin call first 
occur?
A $9.62.
B $17.86.
C $19.71.
24 You have placed a sell market-  on- open order—a market order that would 
automatically be submitted at the market’s open tomorrow and would fill at the 
market price. Your instruction, to sell the shares at the market open, is a(n):
A execution instruction.
B validity instruction.
C clearing instruction.
25 A market has the following limit orders standing on its book for a particular 
stock. The bid and ask sizes are number of shares in hundreds.

Reading 44 ■ Market Organization and Structure 70
Bid Size Limit Price (€) Offer Size
5 9.73
12 9.81
4 9.84
6 9.95
10.02 5
10.10 12
10.14 8
 What is the market?
A 9.73 bid, offered at 10.14.
B 9.81 bid, offered at 10.10.
C 9.95 bid, offered at 10.02.
26 Consider the following limit order book for a stock. The bid and ask sizes are 
number of shares in hundreds.
Bid Size Limit Price (¥) Offer Size
3 122.80
8 123.00
4 123.35
123.80 7
124.10 6
124.50 7
 A new buy limit order is placed for 300 shares at ¥123.40. This limit order is 
said to:
A take the market.
B make the market.
C make a new market.
27 Currently, the market in a stock is “$54.62 bid, offered at $54.71. ” A new sell 
limit order is placed at $54.62. This limit order is said to:
28 Jim White has sold short 100 shares of Super Stores at a price of $42 per share. 
He has also simultaneously placed a “good-  till- cancelled, stop 50, limit 55 buy”

order. Assume that if the stop condition specified by White is satisfied and the 
order becomes valid, it will get executed. Excluding transaction costs, what is 
the maximum possible loss that White can have?
A $800.
B $1,300.
C Unlimited.
29 You own shares of a company that are currently trading at $30 a share. Your 
technical analysis of the shares indicates a support level of $27.50. That is, if the 
price of the shares is going down, it is more likely to stay above this level rather 
than fall below it. If the price does fall below this level, however, you believe 
that the price may continue to decline. You have no immediate intent to sell the

shares but are concerned about the possibility of a huge loss if the share price 
declines below the support level. Which of the following types of orders could 
you place to most appropriately address your concern?
A Short sell order.
B Good-  till- cancelled stop sell order.
C Good-  till- cancelled stop buy order.
30 In an underwritten offering, the risk that the entire issue may not be sold to the 
public at the stipulated offering price is borne by the:
A issuer.
B investment bank.
C buyers of the part of the issue that is sold.
31 A British company listed on the Alternative Investment Market of the London 
Stock Exchange, announced the sale of 6,686,665 shares to a small group of 
qualified investors at £0.025 per share. Which of the following best describes  
this sale?
A Shelf registration.
B Private placement.
C Initial public offering.
32 A German publicly traded company, to raise new capital, gave its existing share -

holders the opportunity to subscribe for new shares. The existing shareholders 
could purchase two new shares at a subscription price of €4.58 per share for 
every 15 shares held. This is an example of a(n):
A rights offering.
B private placement.
C initial public offering.
33 Consider an order-  driven system that allows hidden orders. The following four 
sell orders on a particular stock are currently in the system’s limit order book. 
Based on the commonly used order precedence hierarchy, which of these orders 
will have precedence over others?
Order Time of Arrival  
(HH:MM:SS)Limit Price  
(€)Special Instruction  
(If any)
I 9:52:01 20.33
II 9:52:08 20.29 Hidden order
III 9:53:04 20.29
IV 9:53:49 20.29
A Order I (time of arrival of 9:52:01).
B Order II (time of arrival of 9:52:08).
C Order III (time of arrival of 9:53:04).
34 Zhenhu Li has submitted an immediate-  or- cancel buy order for 500 shares of a 
company at a limit price of CNY 74.25. There are two sell limit orders standing

in that stock’s order book at that time. One is for 300 shares at a limit price of 
CNY 74.30 and the other is for 400 shares at a limit price of CNY 74.35. How 
many shares in Li’s order would get cancelled?
A None (the order would remain open but unfilled).
B 200 (300 shares would get filled).
C 500 (there would be no fill).

Reading 44 ■ Market Organization and Structure 72
35 A market has the following limit orders standing on its book for a particular 
stock:
BuyerBid Size  
(Number of Shares) Limit Price (£)Offer Size  
(Number of Shares) Seller
Keith 1,000 19.70
Paul 200 19.84
Ann 400 19.89
Mary 300 20.02
20.03 800 Jack
20.11 1,100 Margaret
20.16 400 Jeff
 Ian submits a day order to sell 1,000 shares, limit £19.83. Assuming that no 
more buy orders are submitted on that day after Ian submits his order, what 
would be Ian’s average trade price?
A £19.70.
B £19.92.
C £20.05.
36 A financial analyst is examining whether a country’s financial market is well 
functioning. She finds that the transaction costs in this market are low and 
trading volumes are high. She concludes that the market is quite liquid. In such 
a market:
A traders will find it hard to make use of their information.
B traders will find it easy to trade and their trading will make the market less 
informationally efficient.

C traders will find it easy to trade and their trading will make the market more 
37 The government of a country whose financial markets are in an early stage of 
development has hired you as a consultant on financial market regulation. Your 
first task is to prepare a list of the objectives of market regulation. Which of the 
following is least likely  to be included in this list of objectives?
A Minimize agency problems in the financial markets.
B Ensure that financial markets are fair and orderly.
C Ensure that investors in the stock market achieve a rate of return that is at 
least equal to the risk-  free rate of return.

SOLUTIONS
1 C is correct. Takabe is best characterized as an information-  motivated trader. 
Takabe believes that his model provides him superior information about the 
movements in the stock market and his motive for trading is to profit from this 
2 B is correct. Beach is an investor. He is simply investing in risky assets consis -
tent with his level of risk aversion. Beach is not hedging any existing risk or 
using information to identify and trade mispriced securities. Therefore, he is 
not a hedger or an information-  motivated trader.
3 A is correct. Smith is a hedger. The short position on the BRL futures contract 
offsets the BRL long position in three months. She is hedging the risk of the 
BRL depreciating against the USD. If the BRL depreciates, the value of the cash 
inflow goes down in USD terms but there is a gain on the futures contracts.
4 A is correct. Regulation of arbitrageurs’ profits is not a function of the financial

system. The financial system facilitates the allocation of capital to the best uses 
and the purposes for which people use the financial system, including borrow -
ing money.
5 C is correct. The purchase of real estate properties is a transaction in the alter -
native investment market.
6 B is correct. The 90-  day commercial paper and negotiable certificates of deposit 
are money market instruments.
7 B is correct. This transaction is a sale in the primary market. It is a sale of 
shares from the issuer to the investor and funds flow to the issuer of the secu -
rity from the purchaser.
8 A is correct. Warrants are least likely to be part of the fund. Warrant holders 
have the right to buy the issuer’s common stock. Thus, warrants are typically 
classified as equity and are least likely to be a part of a fixed-  income mutual 
fund. Commercial paper and repurchase agreements are short-  term fixed-  
income securities.

9 C is correct. When investors want to sell their shares, investors of an open-  end 
fund sell the shares back to the fund whereas investors of a closed-  end fund sell 
the shares to others in the secondary market. Closed-  end funds are available to 
new investors but they must purchase shares in the fund in the secondary mar -
ket. The shares of a closed-  end fund trade at a premium or discount to net asset 
value.
10 A is correct. Once you have entered into a forward contract, it is difficult to exit 
from the contract. As opposed to a futures contract, trading out of a forward 
contract is quite difficult. There is no exchange of cash at the origination of a 
forward contract. There is no exchange on a forward contract until the maturity 
11 A is correct. Harris is least likely to find counterparty risk associated with a 
futures contract. There is limited counterparty risk in a futures contract because

the clearinghouse is on the other side of every contract.
12 B is correct. Buying a put option on the dollar will ensure a minimum exchange 
rate but does not have to be exercised if the exchange rate moves in a favorable 
direction. Forward and futures contracts would lock in a fixed rate but would 
not allow for the possibility to profit in case the value of the dollar three months 
later in the spot market turns out to be greater than the value in the forward or 
futures contract.

Reading 44 ■ Market Organization and Structure 74
13 B is correct. The agreement between the publisher and the paper supplier to 
respectively buy and supply paper in the future at a price agreed upon today is a 
forward contract.
14 B is correct. SPDRs trade in the secondary market and are a pooled investment 
vehicle.
15 B is correct. The holder of the call option will exercise the call options if the 
price is above the exercise price of $120 per share. Note that if the stock price 
is above $120 but less than $123, the option would be exercised even though 
the net result for the option buyer after considering the premium is a loss. For 
example, if the stock price is $122, the option buyer would exercise the option 
to make $2 = $122 – $120 per share, resulting in a loss of $1 = $3 – $2 after 
considering the premium. It is better to exercise and have a loss of only $1, 
however, rather than not exercise and lose the entire $3 premium.

16 B is correct. The investment companies that create exchange-  traded funds 
(ETFs) are financial intermediaries. ETFs are securities that represent owner -
ship in the assets held by the fund. The transaction costs of trading shares of 
ETFs are substantially lower than the combined costs of trading the underlying 
assets of the ETF.
17 B is correct. The process can best be described as arbitrage because it involves 
buying and selling instruments, whose values are closely related, at different 
prices in different markets.
18 A is correct. Robert’s exposure to the risk of the stock of the Michelin Group is 
long. The exposure as a result of the long call position is long. The exposure as a 
result of the short put position is also long. Therefore, the combined exposure is 
long.
19 B is correct. The maximum leverage ratio is 1.82 = 100% position ÷ 55% equity. 
The maximum leverage ratio associated with a position financed by the mini -

mum margin requirement is one divided by the minimum margin requirement.
20 C is correct. The return is 50 percent. If the position had been unleveraged, the 
return would be 20% = (60 – 50)/50. Because of leverage, the return is 50% = 
2.5 × 20%.
 Another way to look at this problem is that the equity contributed by the trader 
(the minimum margin requirement) is 40% = 100% ÷ 2.5. The trader contrib -
uted $20 = 40% of $50 per share. The gain is $10 per share, resulting in a return 
of 50% = 10/20.
21 B is correct. The return is –15.4 percent.
Total cost of the purchase = $16,000 = 500 × $32
Equity invested = $12,000 = 0.75 × $16,000
Amount borrowed = $4,000 = 16,000 – 12,000
Interest paid at month end = $80 = 0.02 × $4,000
Dividend received at month end = $250 = 500 × $0.50
Proceeds on stock sale = $14,000 = 500 × $28
Total commissions paid = $20 = $10 + $10
Net gain/loss = −$1,850 = −16,000 − 80 + 250 + 14,000 − 20
Initial investment including commission on purchase = $12,010

22 A is correct. She will need to contribute €3,760 as margin. In view of the pos -
sibility of a loss, if the stock price goes up, she will need to contribute €3,760 = 
40% of €9,400 as the initial margin. Rogers will need to leave the proceeds from 
the short sale (€9,400 = 200 × €47) on deposit.
23 B is correct. A margin call will first occur at a price of $17.86. Because you have 
contributed half and borrowed the remaining half, your initial equity is 50 per -
cent of the initial stock price, or $12.50 = 0.50 × $25. If P is the subsequent 
price, your equity would change by an amount equal to the change in price. So, 
your equity at price P would be 12.50 + ( P – 25). A margin call will occur when 
the percentage margin drops to 30 percent. So, the price at which a margin call 
will occur is the solution to the following equation.
Equity /Share
Price/Shar e=+−=12 50 2530.%P
P
 The solution is P = $17.86.

P
24 B is correct. An instruction regarding when to fill an order is considered a 
validity instruction.
25 C is correct. The market is 9.95 bid, offered at 10.02. The best bid is at €9.95 and 
the best offer is €10.02.
26 C is correct. This order is said to make a new market. The new buy order is at 
¥123.40, which is better than the current best bid of ¥123.35. Therefore, the buy 
order is making a new market. Had the new order been at ¥123.35, it would be 
said to make the market. Because the new buy limit order is at a price less than 
the best offer of ¥123.80, it will not immediately execute and is not taking the 
market.
27 A is correct. This order is said to take the market. The new sell order is at 
$54.62, which is at the current best bid. Therefore, the new sell order will imme -
diately trade with the current best bid and is taking the market.
28 B is correct. The maximum possible loss is $1,300. If the stock price crosses $50,

the stop buy order will become valid and will get executed at a maximum limit 
price of $55. The maximum loss per share is $13 = $55 – $42, or $1,300 for 100 
shares.
29 B is correct. The most appropriate order is a good-  till- cancelled stop sell order. 
This order will be acted on if the stock price declines below a specified price (in 
this case, $27.50). This order is sometimes referred to as a good-  till- cancelled 
stop loss sell order. You are generally bullish about the stock, as indicated by no 
immediate intent to sell, and would expect a loss on short selling the stock. A 
stop buy order is placed to buy a stock when the stock is going up.
30 B is correct. The investment bank bears the risk that the issue may be undersub -
scribed at the offering price. If the entire issue is not sold, the investment bank 
underwriting the issue will buy the unsold securities at the offering price.
31 B is correct. This sale is a private placement. As the company is already publicly

traded, the share sale is clearly not an initial public offering. The sale also does 
not involve a shelf registration because the company is not selling shares to the 
public on a piecemeal basis.
32 A is correct. This offering is a rights offering. The company is distributing rights 
to buy stock at a fixed price to existing shareholders in proportion to their 
holdings.
33 C is correct. Order III (time of arrival of 9:53:04) has precedence. In the order 
precedence hierarchy, the first rule is price priority. Based on this rule, sell 
orders II, III, and IV get precedence over order I. The next rule is display

Reading 44 ■ Market Organization and Structure 76
precedence at a given price. Because order II is a hidden order, orders III and IV 
get precedence. Finally, order III gets precedence over order IV based on time 
priority at same price and same display status.
34 C is correct. The order for 500 shares would get cancelled; there would be no 
fill. Li is willing to buy at CNY 74.25 or less but the minimum offer price in the 
book is CNY 74.30; therefore, no part of the order would be filled. Because Li’s 
order is immediate-  or- cancel, it would be cancelled.
35 B is correct. Ian’s average trade price is:
££ 0.02 £19.89  £19.8419 92300 2 400 200
300 400 200.=×+ ×+ ×
++
 Ian’s sell order first fills with the most aggressively priced buy order, which is 
Mary’s order for 300 shares at £20.02. Ian still has 700 shares for sale. The next 
most aggressively priced buy order is Ann’s order for 400 shares at £19.89. This

order is filled. Ian still has 300 shares for sale. The next most aggressively priced 
buy order is Paul’s order for 200 shares at £19.84. A third trade takes place. Ian 
still has 100 shares for sale.
 The next buy order is Keith’s order for 1,000 shares at £19.70. However, this 
price is below Ian’s limit price of £19.83. Therefore, no more trade is possible.
36 C is correct. In such a market, well-  informed traders will find it easy to trade 
and their trading will make the market more informationally efficient. In a liq -
uid market, it is easier for informed traders to fill their orders. Their trading will 
cause prices to incorporate their information and the prices will be more in line 
with the fundamental values.
37 C is correct. Ensure that investors in the stock market achieve a rate of return 
that is at least equal to the risk-  free rate of return is least likely to be included as 
an objective of market regulation. Stocks are risky investments and there would

be occasions when a stock market investment would not only have a return less 
than the risk-  free rate but also a negative return. Minimizing agency costs and 
ensuring that financial markets are fair and orderly are objectives of market 

Security Market Indexes
by Paul D. Kaplan, PhD, CFA, and Dorothy C. Kelly, CFA
Paul D. Kaplan, PhD, CFA, is at Morningstar Research, Inc. (Canada). Dorothy C. Kelly, 
CFA, is at McIntire School of Commerce, University of Virginia (USA).
a. describe a security market index;
b. calculate and interpret the value, price return, and total return of 
an index;
c. describe the choices and issues in index construction and 
management;
d. compare the different weighting methods used in index 
construction;
e. calculate and analyze the value and return of an index given its 
weighting method;
f. describe rebalancing and reconstitution of an index; 
g. describe uses of security market indexes;
h. describe types of equity indexes;
i. describe types of fixed-  income indexes;
j. describe indexes representing alternative investments;
k. compare types of security market indexes.

Investors gather and analyze vast amounts of information about security markets on 
a continual basis. Because this work can be both time consuming and data intensive, 
investors often use a single measure that consolidates this information and reflects 
the performance of an entire security market.1READING
45

Reading 45 ■ Security Market Indexes 78
Security market indexes were first introduced as a simple measure to reflect the 
performance of the US stock market. Since then, security market indexes have evolved 
into important multi-  purpose tools that help investors track the performance of 
various security markets, estimate risk, and evaluate the performance of investment 
managers. They also form the basis for new investment products.
 
in·dex , noun  (pl. in·dex·es  or in·di·ces ) Latin indic-, index,  from indicare  to indicate: an 
indicator, sign, or measure of something.
ORIGIN OF MARKET INDEXES
Investors had access to regularly published data on individual security prices in London 
as early as 1698, but nearly 200 years passed before they had access to a simple indica -
tor to reflect security market information. To give readers a sense of how the US stock 
market in general performed on a given day, publishers Charles H. Dow and Edward D.

Jones introduced the Dow Jones Average, the world’s first security market index, in 1884. 
The index, which appeared in The Customers’ Afternoon Letter , consisted of the stocks 
of nine railroads and two industrial companies. It eventually became the Dow Jones 
Transportation Average. Convinced that industrial companies, rather than railroads, 
would be “the great speculative market” of the future, Dow and Jones introduced a 
second index in may 1896—the Dow Jones Industrial Average (DJIA). It had an initial 
value of 40.94 and consisted of 12 stocks from major US industries. Today, investors can 
choose from among thousands of indexes to measure and monitor different security 
markets and asset classes.
This reading is organized as follows. Section 2 defines a security market index and 
explains how to calculate the price return and total return of an index for a single 
period and over multiple periods. Section 3 describes how indexes are constructed

and managed. Section 4 discusses the use of market indexes. Sections 5, 6, and 7 dis -
cuss various types of indexes, and the final section summarizes the reading. Practice 
problems follow the conclusions and summary.
INDEX DEFINITION AND CALCULATIONS OF VALUE 
AND RETURNS
A security market index  represents a given security market, market segment, or asset 
class. Most indexes are constructed as portfolios of marketable securities.
The value of an index is calculated on a regular basis using either the actual or 
estimated market prices of the individual securities, known as constituent securities , 
within the index. For each security market index, investors may encounter two versions 
of the same index (i.e., an index with identical constituent securities and weights): 
one version based on price return and one version based on total return. As the name 
suggests, a price return index , also known as a price index , reflects only the prices of

the constituent securities within the index. A total return index , in contrast, reflects 
not only the prices of the constituent securities but also the reinvestment of all income 
received since inception.2

Index Definition and Calculations of Value and Returns 79
At inception, the values of the price and total return versions of an index are 
equal. As time passes, however, the value of the total return index, which includes 
the reinvestment of all dividends and/or interest received, will exceed the value of the 
price return index by an increasing amount. A look at how the values of each version 
are calculated over multiple periods illustrates why.
The value of a price return index is calculated as:
VPRI==∑nP
Dii
iN
1
where
 VPRI = the value of the price return index
 ni = the number of units of constituent security i held in the index portfolio
 N = the number of constituent securities in the index
 Pi = the unit price of constituent security i
 D = the value of the divisor
The divisor  is a number initially chosen at inception. It is frequently chosen so 
that the price index has a convenient initial value, such as 1,000. The index provider

then adjusts the value of the divisor as necessary to avoid changes in the index value 
that are unrelated to changes in the prices of its constituent securities. For example, 
when changing index constituents, the index provider may adjust the divisor so that 
the value of the index with the new constituents equals the value of the index prior 
to the changes.
Index return calculations, like calculations of investment portfolio returns, may 
measure price return or total return. Price return  measures only price appreciation 
or percentage change in price. Total return  measures price appreciation plus interest, 
dividends, and other distributions.
2.1 Calculation of Single-  Period Returns
For a security market index, price return can be calculated in two ways: either the 
percentage change in value of the price return index, or the weighted average of price 
returns of the constituent securities. The price return of an index can be expressed as:
PRIPRI PRI
PRIVV
V=−10
0
where

PRIPRI PRI
PRIVV
V=−10
0
where
 PRI = the price return of the index portfolio (as a decimal number, i.e., 
12 percent is 0.12)
 VPRI1 = the value of the price return index at the end of the period
 VPRI0 = the value of the price return index at the beginning of the period
Similarly, the price return of each constituent security can be expressed as: 
PRiii
iPP
P=−10
0
where
 PRi = the price return of constituent security i (as a decimal number)
 Pi1 = the price of constituent security i at the end of the period
 Pi0 = the price of constituent security i at the beginning of the period(1)
(2)
(3)

Reading 45 ■ Security Market Indexes 80
Because the price return of the index equals the weighted average of price returns of 
the individual securities, we can write: 
PR wPRwIi i ==− 


==∑∑
iN
i
iN
ii
iPP
P1110
0
where:
 PRI = the price return of index portfolio (as a decimal number)
 N = the number of individual securities in the index
 wi = the weight of security i (the fraction of the index portfolio allocated to 
security i)
 Pi0 = the price of constituent security i at the beginning of the period
Equation 4 can be rewritten simply as: 
PRI = w1PR1 + w2PR2 + … + wNPRN  
where
 N = the number of securities in the index

N = the number of securities in the index
Total return measures price appreciation plus interest, dividends, and other dis -
tributions. Thus, the total return  of an index is the price appreciation, or change in 
the value of the price return index, plus income (dividends and/or interest) over the 
period, expressed as a percentage of the beginning value of the price return index. 
The total return of an index can be expressed as:
TRIPRI PRI I
PRIVV
V=−+10
0Inc
where
 TRI = the total return of the index portfolio (as a decimal number)
 VPRI1= the value of the price return index at the end of the period
 IncI = the total income (dividends and/or interest) from all securities in the 
index held over the period
The total return of an index can also be calculated as the weighted average of total 
returns of the constituent securities. The total return of each constituent security in 
the index is calculated as:
TRiii i
iPP
P=−+10

TRiii i
iPP
P=−+10
0Inc
where
 TRi = the total return of constituent security i (as a decimal number)
 P1i = the price of constituent security i at the end of the period
 P0i = the price of constituent security i at the beginning of the period
 Inci = the total income (dividends and/or interest) from security i over the 
period(4)
(5)
(6)
(7)

Index Definition and Calculations of Value and Returns 81
Because the total return of an index can be calculated as the weighted average of 
total returns of the constituent securities, we can express total return as:
TR wTRwIi iInc==−+ 


==∑∑
iN
iii i
i iNPP
P110
0 1
Equation 8 can be rewritten simply as
TRI = w1TR1 + w2TR2 + … + wNTRN  
where
2.2 Calculation of Index Values over Multiple Time Periods
The calculation of index values over multiple time periods requires geometrically 
linking the series of index returns. With a series of price returns for an index, we can 
calculate the value of the price return index with the following equation:
VPRIT = VPRI 0(1 + PRI 1)(1 + PRI 2)…(1 + PRIT)  
where

where
 VPRI 0 = the value of the price return index at inception
 VPRIT = the value of the price return index at time t
 PRIT = the price return (as a decimal number) on the index over period t, t = 
1, 2, …, T
For an index with an inception value set to 1,000 and price returns of 5 percent 
and 3 percent for Periods 1 and 2 respectively, the values of the price return index 
would be calculated as follows:
Period Return (%) Calculation Ending Value
0 1,000(1.00) 1,000.00
1 5.00 1,000(1.05) 1,050.00
2 3.00 1,000(1.05)(1.03) 1,081.50
Similarly, the series of total returns for an index is used to calculate the value of 
the total return index with the following equation:
VTRIT  = VTRI 0(1 + TRI 1)(1 + TRI 2)…(1 + TRIT)  
where
 VTRI 0 = the value of the index at inception
 VTRIT  = the value of the total return index at time t
 TRIT = the total return (as a decimal number) on the index over period t, t = 
1, 2, …, T
Suppose that the same index yields an additional 1.5 percent return from income

in Period 1 and an additional 2.0 percent return from income in Period 2, bringing 
the total returns for Periods 1 and 2, respectively, to 6.5 percent and 5 percent. The 
values of the total return index would be calculated as follows:(8)
(9)
(10)
(11)

Reading 45 ■ Security Market Indexes 82
1 6.50 1,000(1.065) 1,065.00
2 5.00 1,000(1.065)(1.05) 1,118.25
As illustrated above, as time passes, the value of the total return index, which 
includes the reinvestment of all dividends and/or interest received, exceeds the value 
of the price return index by an increasing amount.
INDEX CONSTRUCTION AND MANAGEMENT
Constructing and managing a security market index is similar to constructing and 
managing a portfolio of securities. Index providers must decide the following:
1 Which target market should the index represent?
2 Which securities should be selected from that target market?
3 How much weight should be allocated to each security in the index?
4 When should the index be rebalanced?
5 When should the security selection and weighting decision be re-  examined?
3.1 Target Market and Security Selection
The first decision in index construction is identifying the target market, market seg -

ment, or asset class that the index is intended to represent. The target market may 
be defined very broadly or narrowly. It may be based on asset class (e.g., equities, 
fixed income, real estate, commodities, hedge funds); geographic region (e.g., Japan, 
South Africa, Latin America, Europe); the exchange on which the securities are traded 
(e.g., Shanghai, Toronto, Tokyo), and/or other characteristics (e.g., economic sector, 
company size, investment style, duration, or credit quality).
The target market determines the investment universe and the securities available 
for inclusion in the index. Once the investment universe is identified, the number of 
securities and the specific securities to include in the index must be determined. The 
constituent securities could be nearly all those in the target market or a representative 
sample of the target market. Some equity indexes, such as the S&P 500 Index and the

FTSE 100, fix the number of securities included in the index and indicate this number 
in the name of the index. Other indexes allow the number of securities to vary to 
reflect changes in the target market or to maintain a certain percentage of the target 
market. For example, the Tokyo Stock Price Index (TOPIX) represents and includes all 
of the largest stocks, known as the First Section, listed on the Tokyo Stock Exchange. 
To be included in the First Section—and thus the TOPIX—stocks must meet certain 
criteria, such as the number of shares outstanding, the number of shareholders, and 
market capitalization. Stocks that no longer meet the criteria are removed from the 
First Section and also the TOPIX. Objective or mechanical rules determine the con -
stituent securities of most, but not all, indexes. The Sensex of Bombay and the S&P 
500, for example, use a selection committee and more subjective decision-  making 
rules to determine constituent securities.3

Index Construction and Management 83
3.2 Index Weighting
The weighting decision determines how much of each security to include in the index 
and has a substantial impact on an index’s value. Index providers use a number of 
methods to weight the constituent securities in an index. Indexes can be price weighted, 
equal weighted, market-  capitalization weighted, or fundamentally weighted. Each 
weighting method has its advantages and disadvantages.
3.2.1  Price Weighting
The simplest method to weight an index and the one used by Charles Dow to construct 
the Dow Jones Industrial Average is price weighting . In price weighting, the weight 
on each constituent security is determined by dividing its price by the sum of all the 
prices of the constituent securities. The weight is calculated using the following formula:
wP
PP
Nii
i
i=
=∑
1
Exhibit  1 illustrates the values, weights, and single-  period returns following 
inception of a price-  weighted equity index with five constituent securities. The value

of the price-  weighted index is determined by dividing the sum of the security values 
(101.50) by the divisor, which is typically set at inception to equal the initial number 
of securities in the index. Thus, in our example, the divisor is 5 and the initial value 
of the index is calculated as 101.50 ÷ 5 = 20.30.
As illustrated in this exhibit, Security A, which has the highest price, also has the 
highest weighting and thus will have the greatest impact on the return of the index. 
Note how both the price return and the total return of the index are calculated on 
the basis of the corresponding returns on the constituent securities.
A property unique to price-  weighted indexes is that a stock split on one constit -
uent security changes the weights on all the securities in the index.1 To prevent the 
stock split and the resulting new weights from changing the value of the index, the 
index provider must adjust the value of the divisor as illustrated in Exhibit 2. Given

a 2- for- 1 split in Security A, the divisor is adjusted by dividing the sum of the con -
stituent prices after  the split (77.50) by the value of the index before  the split (21.00). 
This adjustment results in changing the divisor from 5 to 3.69 so that the index value 
is maintained at 21.00.
The primary advantage of price weighting is its simplicity. The main disadvantage 
of price weighting is that it results in arbitrary weights for each security. In particu -
lar, a stock split in any one security causes arbitrary changes in the weights of all the 
constituents’ securities.
Exhibit 2   Impact of 2-  for-  1 Split in Security A
Security Price before Split Weight before Split (%) Price after Split Weight after Split (%)
A 55.00 52.38 27.50 35.48
B 22.00 20.95 22.00 28.39
C 8.00 7.62 8.00 10.32
D 14.00 13.33 14.00 18.07(12)
1 A stock split is an increase in the number of shares outstanding and a proportionate decrease in the

price per share such that the total market value of equity, as well as investors’ proportionate ownership in 
the company, does not change.

Reading 45 ■ Security Market Indexes 84
Exhibit 1   Example of a Price-  Weighted Equity Index
SecurityShares 
in 
IndexBOP 
PriceValue 
(Shares 
× BOP 
Price)BOP 
Weight 
(%)EOP 
PriceDividends 
Per ShareValue 
(Shares 
× EOP 
Price)Total 
DividendsPrice 
Return 
(%)Total 
Return 
(%)BOP 
Weight 
× Price 
Return 
(%)BOP 
Weight 
× Total 
Return 
(%)EOP 
Weight 
(%)
A 1 50.00 50.00 49.26 55.00 0.75 55.00 0.75 10.00 11.50 4.93 5.66 52.38
B 1 25.00 25.00 24.63 22.00 0.10 22.00 0.10 −12.00 −11.60 −2.96 −2.86 20.95
C 1 12.50 12.50 12.32 8.00 0.00 8.00 0.00 −36.00 −36.00 −4.43 −4.43 7.62
D 1 10.00 10.00 9.85 14.00 0.05 14.00 0.05 40.00 40.50 3.94 3.99 13.33
E 1 4.00 4.00 3.94 6.00 0.00 6.00 0.00 50.00 50.00 1.97 1.97 5.72
Total 101.50 100.00 105.00 0.90 3.45 4.33 100.00
Index 
Value20.30 21.00 0.18 3.45 4.33
Divisor = 5
BOP = Beginning of period
EOP = End of period
Type of 
IndexBOP 
ValueReturn 
(%)EOP 
Value
Price 
Return20.30 3.45 21.00
Total 
Return20.30 4.33 21.18

Index Construction and Management 85
E 6.00 5.72 6.00 7.74
Total 105.00 100.00 77.50 100.00
Divisor 5.00 3.69
Index Value 21.00 21.00
3.2.2  Equal Weighting
Another simple index weighting method is equal weighting . This method assigns an 
equal weight to each constituent security at inception. The weights are calculated as:
wE
iN=1
where
 wi = fraction of the portfolio that is allocated to security i or weight of 
security  i
 N = number of securities in the index
To construct an equal-  weighted index from the five securities in Exhibit 1, the index 
provider allocates one-  fifth (20 percent) of the value of the index (at the beginning 
of the period) to each security. Dividing the value allocated to each security by each 
security’s individual share price determines the number of shares of each security to 
include in the index. Unlike a price-  weighted index, where the weights are arbitrarily

determined by the market prices, the weights in an equal-  weighted index are arbitrarily 
assigned by the index provider.
Exhibit  3 illustrates the values, weights, and single-  period returns following 
inception of an equal-  weighted index with the same constituent securities as those 
in Exhibit 1. This example assumes a beginning index portfolio value of 10,000 (i.e., 
an investment of 2,000 in each security). To set the initial value of the index to 1,000, 
the divisor is set to 10 (10,000 ÷ 10 = 1,000).
Exhibits 1 and 3 demonstrate how different weighting methods result in different 
returns. The 10.4 percent price return of the equal-  weighted index shown in Exhibit 3 
differs significantly from the 3.45 percent price return of the price-  weighted index 
in Exhibit 1.
Like price weighting, the primary advantage of equal weighting is its simplicity. 
Equal weighting, however, has a number of disadvantages. First, securities that con -

stitute the largest fraction of the target market value are underrepresented, and secu -
rities that constitute a small fraction of the target market value are overrepresented. 
Second, after the index is constructed and the prices of constituent securities change, 
the index is no longer equally weighted. Therefore, maintaining equal weights requires 
frequent adjustments (rebalancing) to the index.
3.2.3  Market-  Capitalization Weighting
In market-  capitalization weighting , or value weighting, the weight on each constit -
uent security is determined by dividing its market capitalization by the total market 
capitalization (the sum of the market capitalization) of all the securities in the index. 
Market capitalization or value is calculated by multiplying the number of shares out -
standing by the market price per share.(13)Exhibit 2   (Continued)

Reading 45 ■ Security Market Indexes 86
Exhibit 3   Example of an Equal-  Weighted Equity Index
SecurityShares in 
IndexBOP 
(Shares × 
BOP Price) Weight (%)EOP 
(Shares 
× EOP 
Return 
(%)Total 
Return 
(%)Weight 
× Price 
Return 
(%)Weight 
× Total 
Return 
(%)EOP 
Weight 
(%)
A 40 50.00 2,000 20.00 55.00 0.75 2,200 30 10.00 11.50 2.00 2.30 19.93
B 80 25.00 2,000 20.00 22.00 0.10 1,760 8 −12.00 −11.60 −2.40 −2.32 15.94
C 160 12.50 2,000 20.00 8.00 0.00 1,280 0 −36.00 −36.00 −7.20 −7.20 11.60
D 200 10.00 2,000 20.00 14.00 0.05 2,800 10 40.00 40.50 8.00 8.10 25.36
E 500 4.00 2,000 20.00 6.00 0.00 3,000 0 50.00 50.00 10.00 10.00 27.17
Total 10,000 100.00 11,040 48 10.40 10.88 100.00
Index 
Value1,000 1,104 4.80 10.40 10.88
Divisor = 10
Type of 
Index BOP ValueReturn 
(%) EOP Value
Price 
Return1,000.00 10.40 1,104.00
Total 
Return1,000.00 10.88 1,108.80

Index Construction and Management 87
The market-  capitalization weight of security i is:
wQP
QPM
iii
jj
jN=
=∑
1
where
security  i
 Qi = number of shares outstanding of security i
 Pi = share price of security i
Exhibit  4 illustrates the values, weights, and single-  period returns following 
inception of a market-  capitalization-  weighted index for the same five-  security market. 
Security A, with 3,000 shares outstanding and a price of 50 per share, has a market 
capitalization of 150,000 or 26.29  percent (150,000/570,500) of the entire index 
portfolio. The resulting index weights in the exhibit reflect the relative value of each 
security as measured by its market capitalization.
As shown in Exhibits 1, 3, and 4, the weighting method affects the index’s returns. 
The price and total returns of the market-  capitalization index in Exhibit 4 (1.49 percent

and 2.13 percent, respectively) differ significantly from those of the price-  weighted 
(3.45 percent and 4.33 percent, respectively) and equal-  weighted (10.40 percent and 
10.88  percent respectively) indexes. To understand the source and magnitude of 
the difference, compare the weights and returns of each security under each of the 
weighting methods. The weight of Security A, for example, ranges from 49.26 percent 
in the price-  weighted index to 20 percent in the equal-  weighted index. With a price 
return of 10 percent, Security A contributes 4.93 percent to the price return of the 
price-  weighted index, 2.00 percent to the price return of the equal-  weighted index, 
and 2.63 percent to the price return of the market-  capitalization-  weighted index. With 
a total return of 11.50 percent, Security A contributes 5.66 percent to the total return 
of the price-  weighted index, 2.30 percent to the total return of the equal-  weighted

index, and 3.02 percent to the total return of the market-  capitalization-  weighted index.
3.2.3.1  Float-  Adjusted Market-  Capitalization Weighting  In float-  adjusted market-  
capitalization weighting , the weight on each constituent security is determined by 
adjusting its market capitalization for its market float . Typically, market float is the 
number of shares of the constituent security that are available to the investing public. 
For companies that are closely held, only a portion of the shares outstanding are avail -
able to the investing public (the rest are held by a small group of controlling investors). 
In addition to excluding shares held by controlling shareholders, most float-  adjusted 
market-  capitalization-  weighted indexes also exclude shares held by other corporations 
and governments. Some providers of indexes that are designed to represent the invest -
ment opportunities of global investors further reduce the number of shares included

in the index by excluding shares that are not available to foreigner investors. The index 
providers may refer to these indexes as “free-  float-  adjusted market-  capitalization-  
weighted indexes. ”
Float-  adjusted market-  capitalization-  weighted indexes reflect the shares available 
for public trading by multiplying the market price per share by the number of shares 
available to the investing public (i.e., the float-  adjusted market capitalization) rather 
than the total number of shares outstanding (total market capitalization). Currently, 
most market-  capitalization-  weighted indexes are float adjusted. Therefore, unless oth -
erwise indicated, for the remainder of this reading, “market-  capitalization” weighting 
refers to float-  adjusted market-  capitalization weighting.(14)

Reading 45 ■ Security Market Indexes 88
Exhibit 4   Example of a Market-  Capitalization-  Weighted Equity Index
StockShares 
Out-  
standingBOP 
PriceBOP 
Market 
CapBOP 
Weight 
(%)EOP  
Per ShareEOP 
Market 
CapTotal 
Return 
(%)Total 
Return 
(%)BOP 
Weight 
× Price 
Return 
(%)BOP 
Weight 
× Total 
Return 
(%)EOP 
Weight 
(%)
A 3,000 50.00 150,000 26.29 55.00 0.75 165,000 2,250 10.00 11.50 2.63 3.02 28.50
B 10,000 25.00 250,000 43.82 22.00 0.10 220,000 1,000 −12.00 −11.60 −5.26 −5.08 38.00
C 5,000 12.50 62,500 10.96 8.00 0.00 40,000 0 −36.00 −36.00 −3.95 −3.95 6.91
D 8,000 10.00 80,000 14.02 14.00 0.05 112,000 400 40.00 40.50 5.61 5.68 19.34
E 7,000 4.00 28,000 4.91 6.00 0.00 42,000 0 50.00 50.00 2.46 2.46 7.25
Total 570,500 100.00 579,000 3,650 1.49 2.13 100.00
Index 
Value1,000 1,014.90 6.40 1.49 2.13
Divisor = 570.50
Type of 
IndexBOP 
(%)EOP 
Value
Price 
Return1,000.00 1.49 1,014.90
Total 
Return1,000.00 2.13 1,021.30

Index Construction and Management 89
The float-  adjusted market-  capitalization weight of security i is calculated as:
wfQP
fQPM
iii i
jj j
jN=
=∑
1
where
 fi = fraction of shares outstanding in the market float
security  i
Exhibit 5 illustrates the values, weights, and single-  period returns following incep -
tion of a float-  adjusted market-  capitalization-  weighted equity index using the same 
five securities as before. The low percentage of shares of Security D in the market 
float compared with the number of shares outstanding indicates that the security is 
closely held.
The primary advantage of market-  capitalization weighting (including float adjusted) 
is that constituent securities are held in proportion to their value in the target mar -

ket. The primary disadvantage is that constituent securities whose prices have risen 
the most (or fallen the most) have a greater (or lower) weight in the index (i.e., as 
a security’s price rises relative to other securities in the index, its weight increases; 
and as its price decreases in value relative to other securities in the index, its weight 
decreases). This weighting method leads to overweighting stocks that have risen in price 
(and may be overvalued) and underweighting stocks that have declined in price (and 
may be undervalued). The effect of this weighting method is similar to a momentum 
investment strategy in that over time, the securities that have risen in price the most 
will have the largest weights in the index.
3.2.4  Fundamental Weighting
Fundamental weighting  attempts to address the disadvantages of market-  capitalization 
weighting by using measures of a company’s size that are independent of its security

price to determine the weight on each constituent security. These measures include 
book value, cash flow, revenues, earnings, dividends, and number of employees.
Some fundamental indexes use a single measure, such as total dividends, to weight 
the constituent securities, whereas others combine the weights from several measures 
to form a composite value that is used for weighting.
Letting Fi denote a given fundamental size measure of company i, the fundamental 
weight on security i is:
wF
FF
ii
j
jN=
=∑
1
Relative to a market-  capitalization-  weighted index, a fundamental index with 
weights based on such an item as earnings will result in greater weights on constituent 
securities with earnings yields (earnings divided by price) that are higher than the 
earnings yield of the overall market-  weighted portfolio. Similarly, stocks with earnings 
yields less than the yield on the overall market-  weighted portfolio will have lower

weights. For example, suppose there are two stocks in an index. Stock A has a market 
capitalization of €200 million, Stock B has a market capitalization of €800 million, and 
their aggregate market capitalization is €1 billion (€1,000 million). Both companies (15)
(16)

Reading 45 ■ Security Market Indexes 90
Exhibit 5   Example of Float-  Adjusted Market-  Capitalization-  Weighted Equity Index
Out-  
standing% 
Shares 
in 
Market 
FloatShares 
in IndexBOP 
PriceBOP Float-  
Adjusted 
Market 
CapBOP 
Weight 
(%)EOP 
Per ShareEnding 
Float-  
Adjusted 
Market 
CapTotal 
Return 
(%)Total 
Return 
(%)BOP 
Weight 
× Price 
Return 
(%)BOP 
Weight 
× Total 
Return 
(%)EOP 
Weight 
(%)
A 3,000 100 3,000 50.00 150,000 35.40 55.00 0.75 165,000 2,250 10.00 11.50 3.54 4.07 39.61
B 10,000 70 7,000 25.00 175,000 41.31 22.00 0.10 154,000 700 −12.00 −11.60 −4.96 −4.79 36.97
C 5,000 90 4,500 12.50 56,250 13.28 8.00 0.00 36,000 0 −36.00 −36.00 −4.78 −4.78 8.64
D 8,000 25 2,000 10.00 20,000 4.72 14.00 0.05 28,000 100 40.00 40.50 1.89 1.91 6.72
E 7,000 80 5,600 4.00 22,400 5.29 6.00 0.00 33,600 0 50.00 50.00 2.65 2.65 8.06
Total 423,650 100.00 416,600 3,050 −1.66 −0.94 100.00
Index 
Value1,000 983.36 7.20 −1.66 −0.94
Divisor = 423.65

Type of 
IndexInitial 
(%)Ending 
Value
Price 
Return1,000.00 −1.66 983.36
Total 
Return1,000.00 −0.94 990.56

Index Construction and Management 91
have earnings of €20 million and aggregate earnings of €40 million. Thus, Stock A 
has an earnings yield of 10 percent (20/200) and Stock B has an earnings yield of 
2.5 percent (20/800). The earnings weight of Stock A is 50 percent (20/40), which is 
higher than its market-  capitalization weight of 20 percent (200/1,000). The earnings 
weight of Stock B is 50 percent (20/40), which is less than its market-  capitalization 
weight of 80  percent (800/1,000). Relative to the market-  cap-  weighted index, the 
earnings-  weighted index over-  weights the high-  yield Stock A and under-  weights the 
low-  yield Stock B.
The most important property of fundamental weighting is that it leads to indexes 
that have a “value” tilt. That is, a fundamentally weighted index has ratios of book 
value, earnings, dividends, etc. to market value that are higher than its market-  
capitalization-  weighted counterpart. Also, in contrast to the momentum “effect” of

market-  capitalization-  weighted indexes, fundamentally weighted indexes generally will 
have a contrarian “effect” in that the portfolio weights will shift away from securities 
that have increased in relative value and toward securities that have fallen in relative 
value whenever the portfolio is rebalanced.
3.3 Index Management: Rebalancing and Reconstitution
So far, we have discussed index construction. Index management entails the two 
remaining questions:
■■When should the index be rebalanced?
■■When should the security selection and weighting decisions be re-  examined?
3.3.1  Rebalancing
Rebalancing  refers to adjusting the weights of the constituent securities in the index. 
To maintain the weight of each security consistent with the index’s weighting method, 
the index provider rebalances the index by adjusting the weights of the constituent 
securities on a regularly scheduled basis (rebalancing dates)—usually quarterly.

Rebalancing is necessary because the weights of the constituent securities change 
as their market prices change. Note, for example, that the weights of the securities 
in the equal-  weighted index (Exhibit 3) at the end of the period are no longer equal 
(i.e., 20 percent):
Security A 19.93%
Security B 15.94
Security C 11.60
Security D 25.36
Security E 27.17
In rebalancing the index, the weights of Securities D and E (which had the highest 
returns) would be decreased and the weights of Securities A, B, and C (which had the 
lowest returns) would be increased. Thus, rebalancing creates turnover within an index.
Price-  weighted indexes are not rebalanced because the weight of each constitu -
ent security is determined by its price. For market-  capitalization-  weighted indexes, 
rebalancing is less of a concern because the indexes largely rebalance themselves. In 
our market-  capitalization index, for example, the weight of Security C automatically

declined from 10.96 percent to 6.91 percent, reflecting the 36 percent decline in its 
market price. Market-  capitalization weights are only adjusted to reflect mergers, 
acquisitions, liquidations, and other corporate actions between rebalancing dates.

Reading 45 ■ Security Market Indexes 92
3.3.2  Reconstitution
Reconstitution is the process of changing the constituent securities in an index. It is 
similar to a portfolio manager deciding to change the securities in his or her port -
folio. Reconstitution is part of the rebalancing cycle. The reconstitution date is the 
date on which index providers review the constituent securities, re-  apply the initial 
criteria for inclusion in the index, and select which securities to retain, remove, or 
add. Constituent securities that no longer meet the criteria are replaced with securities 
that do meet the criteria. Once the revised list of constituent securities is determined, 
the weighting method is re-  applied. Indexes are reconstituted to reflect changes in the 
target market (bankruptcies, de-  listings, mergers, acquisitions, etc.) and/or to reflect 
the judgment of the selection committee.
Reconstitution creates turnover in a number of different ways, particularly for

market-  capitalization-  weighted indexes. When one security is removed and another 
is added, the index provider has to change the weights of the other securities in order 
to maintain the market-  capitalization weighting of the index.
The frequency of reconstitution is a major issue for widely used indexes and their 
constituent securities. The Russell 2000 Index, for example, reconstitutes annually. 
It is used as a benchmark by numerous investment funds, and each year, prior to 
the index’s reconstitution, the managers of these funds buy stocks they think will be 
added to the index—driving those stocks’ prices up—and sell stocks they think will 
be deleted from the index—driving those stocks’ prices down. Exhibit 6 illustrates the 
potential impact of these decisions. Beginning in late April 2009, some managers began 
acquiring and bidding up the price of Uranium Energy Corporation (UEC) because 
they believed that it would be included in the reconstituted Russell 2000 Index. On

12 June, Russell listed UEC as a preliminary addition to the Russell 2000 Index and 
the Russell 3000 Index.2 By that time, the stock value had increased by more than 
300 percent. Investors continued to bid up the stock price in the weeks following the 
announcement, and the stock closed on the reconstitution date of 30 June at USD2.90, 
up nearly 400 percent for the quarter.
2 According to the press release, final membership in the index would be published after market close 
on Friday, 26 June.

Uses of Market Indexes 93
Exhibit 6   Three-  Month Performance of Uranium Energy Corporation and 
NASDAQ April through June 2009
+600%URANIUM ENERGY CORP
UEC
^IXIC+400%
+200%
0%
8.0
6.0Millions4.0
2.0
0.0Mar09 Apr0 9M ay09 Jun09 Jul09 Aug09
Volumeas of 12–Aug–2009
Source:  Yahoo! Finance and Capital IQ.
USES OF MARKET INDEXES
Indexes were initially created to give a sense of how a particular security market 
performed on a given day. With the development of modern financial theory, their 
uses in investment management have expanded significantly. Some of the major uses 
of indexes include:
■■gauges of market sentiment;
■■proxies for measuring and modeling returns, systematic risk, and risk-  adjusted 
performance;
■■proxies for asset classes in asset allocation models;
■■benchmarks for actively managed portfolios; and
■■model portfolios for such investment products as index funds and exchange-  
traded funds (ETFs).
Investors using security market indexes must be familiar with how various indexes are

constructed in order to select the index or indexes most appropriate for their needs.
4.1 Gauges of Market Sentiment
The original purpose of stock market indexes was to provide a gauge of investor 
confidence or market sentiment. As indicators of the collective opinion of market 
participants, indexes reflect investor attitudes and behavior. The Dow Jones Industrial 
Average has a long history, is frequently quoted in the media, and remains a popular 
gauge of market sentiment. It may not accurately reflect the overall attitude of inves -
tors or the “market, ” however, because the index consists of only 30 of the thousands 
of US stocks traded each day.4

Reading 45 ■ Security Market Indexes 94
4.2 Proxies for Measuring and Modeling Returns, Systematic 
Risk, and Risk-  Adjusted Performance
The capital asset pricing model (CAPM) defines beta as the systematic risk of a security 
with respect to the entire market. The market portfolio in the CAPM consists of all 
risky securities. To represent the performance of the market portfolio, investors use 
a broad index. For example, the Tokyo Price Index (TOPIX) and the S&P 500 often 
serve as proxies for the market portfolio in Japan and the United States, respectively, 
and are used for measuring and modeling systematic risk and market returns.
Security market indexes also serve as market proxies when measuring risk-  adjusted 
performance. The beta of an actively managed portfolio allows investors to form a 
passive alternative with the same level of systematic risk. For example, if the beta of 
an actively managed portfolio of global stocks is 0.95 with respect to the MSCI World

Index, investors can create a passive portfolio with the same systematic risk by investing 
95 percent of their portfolio in a MSCI World Index fund and holding the remaining 
5 percent in cash. Alpha, the difference between the return of the actively managed 
portfolio and the return of the passive portfolio, is a measure of risk-  adjusted return 
or investment performance. Alpha can be the result of manager skill (or lack thereof), 
transaction costs, and fees.
4.3 Proxies for Asset Classes in Asset Allocation Models
Because indexes exhibit the risk and return profiles of select groups of securities, they 
play a critical role as proxies for asset classes in asset allocation models. They provide 
the historical data used to model the risks and returns of different asset classes.
4.4 Benchmarks for Actively Managed Portfolios
Investors often use indiexs as benchmarks to evaluate the performance of active port -
folio managers. The index selected as the benchmark should reflect the investment

strategy used by the manager. For example, an active manager investing in global 
small-  capitalization stocks should be evaluated using a benchmark index, such as 
the FTSE Global Small Cap Index, which includes 4,600 small-  capitalization stocks 
across 48 countries.
The choice of an index to use as a benchmark is important because an inappropriate 
index could lead to incorrect conclusions regarding an active manager’s investment 
performance. Suppose that the small-  cap manager underperformed the small-  cap 
index but outperformed a broad equity market index. If investors use the broad market 
index as a benchmark, they might conclude that the small-  cap manager is earning 
his or her fees and should be retained or given additional assets to invest. Using the 
small-  cap index as a benchmark might lead to a very different conclusion.
4.5 Model Portfolios for Investment Products
Indexes also serve as the basis for the development of new investment products.

Using indexes as benchmarks for actively managed portfolios has led some investors 
to conclude that they should invest in the benchmarks instead. Based on the CAPM’s 
conclusion that investors should hold the market portfolio, broad market index funds 
have been developed to function as proxies for the market portfolio.

Equity Indexes 95
Investment management firms initially developed and managed index portfolios 
for institutional investors. Eventually, mutual fund companies introduced index funds 
for individual investors. Subsequently, investment management firms introduced 
exchange-  traded funds, which are managed the same way as index mutual funds but 
trade like stocks.
The first ETFs were based on existing indexes. As the popularity of ETFs increased, 
index providers created new indexes for the specific purpose of forming ETFs, leading 
to the creation of numerous narrowly defined indexes with corresponding ETFs. The 
Market Vectors Vietnam ETF, for example, allows investors to invest in the equity 
market of Vietnam.
The choice of indexes to meet the needs of investors is extensive. Index providers are 
constantly looking for opportunities to develop indexes to meet the needs of investors.
EQUITY INDEXES
A wide variety of equity indexes exist, including broad market, multi-  market, sector,

and style indexes.
5.1 Broad Market Indexes
A broad equity market index, as its name suggests, represents an entire given equity 
market and typically includes securities representing more than 90  percent of the 
selected market. For example, the Shanghai Stock Exchange Composite Index (SSE) is 
a market-  capitalization-  weighted index of all shares that trade on the Shanghai Stock 
Exchange. In the United States, the Wilshire 5000 Total Market Index is a market-  
capitalization-  weighted index that includes more than 6,000 equity securities and 
is designed to represent the entire US equity market.3 The Russell 3000, consisting 
of the largest 3,000 stocks by market capitalization, represents 99 percent of the US 
equity market.
5.2 Multi-  Market Indexes
Multi-  market indexes  usually comprise indexes from different countries and regions 
and are designed to represent multiple security markets. Multi-  market indexes may

represent multiple national markets, geographic regions, economic development 
groups, and, in some cases, the entire world. World indexes are of importance to 
investors who take a global approach to equity investing without any particular bias 
toward a particular country or region. A number of index providers publish families 
of multi-  market equity indexes.
MSCI Barra offers a number of multi-  market indexes. As shown in Exhibit 7, MSCI 
Barra classifies countries and regions along two dimensions: level of economic devel -
opment and geographic region. Developmental groups, which MSCI Barra refers to 
as market classifications, include developed markets, emerging markets, and frontier 
markets. The geographic regions are largely divided by longitudinal lines of the globe: 
the Americas, Europe with Africa, and Asia with the Pacific. MSCI Barra provides 
country- and region-  specific indexes for each of the developed and emerging markets 5

3 Despite its name, the Wilshire 5000 has no constraint on the number of securities that can be included. 
It included approximately 5,000 securities at inception.

Reading 45 ■ Security Market Indexes 96
within its multi-  market indexes. MSCI Barra periodically reviews the classifications of 
markets in its indexes for movement from frontier markets to emerging markets and 
from emerging markets to developed markets and reconstitutes the indexes accordingly.
Exhibit 7   MSCI International Equity Indexes Coverage (as of June 2009) 
Developed Markets
Americas Europe Pacific
Canada, United States Austria, Belgium, Denmark, Finland, 
France, Germany, Greece, Ireland, 
Italy, Netherlands, Norway, Portugal, 
Spain, Sweden, Switzerland, United 
KingdomAustralia, Hong Kong, Japan, New 
Zealand, Singapore
Emerging Markets
Americas Europe, Middle East, Africa Asia
Argentina1, Brazil, Chile, Colombia, 
Mexico, PeruCzech Republic, Egypt, Hungary, 
Israel, Jordan, Morocco, Poland, 
Russia, South Africa, TurkeyChina, India, Indonesia, South Korea, 
Malaysia, Pakistan2, Philippines, 
Taiwan, Thailand
Frontier Markets
AmericasCentral & Eastern 
Europe & CIS Africa Middle East Asia

Jamaica3, Trinidad & 
Tobago3Bulgaria, Croatia, 
Estonia, Lithuania, 
Kazakhstan, Romania, 
Serbia, Slovenia, 
UkraineBotswana4, Ghana4, 
Kenya, Mauritius, 
Nigeria, TunisiaLebanon, Bahrain, 
Kuwait, Oman, Qatar, 
United Arab Emirates, 
Saudi Arabia5Sri Lanka, Vietnam
1 The MSCI Argentina Index was reclassified from the MSCI Emerging Markets Index to the MSCI Frontier Markets Index at the end of 
May 2009 to coincide with the May 2009 Semi-  Annual Index Review.
2 The MSCI Pakistan Index was removed from the MSCI Emerging Markets Index as of the close of December 31, 2008 to reflect the dete -
rioration of investability conditions in the Pakistani equity market. In May 2009, the MSCI Pakistan Index was added to the MSCI Frontier 
Markets Index to coincide with the May 2009 Semi-  Annual Index Review.
3 In May 2009, the MSCI Trinidad & Tobago Index was added to the MSCI Frontier Markets Index. However, the MSCI Jamaica Index con -

tinues to be maintained as a stand-  alone country index because it does not meet the liquidity requirements of the Frontiers Market Index.
4 Botswana and Ghana currently stand-  alone and are not included in the MSCI Frontier Markets Index. The addition of these two countries 
to the MSCI Frontier Market Index is under consideration.
5 Saudi Arabia is currently not included in the MSCI Frontier Markets Index but is part of the MSCI GCC Countries Index.
Source:  MSCI Barra (www.mscibarra.com/products/indices/equity/index.jsp), June 2009.
5.2.1  Fundamental Weighting in Multi-  Market Indexes
Some index providers weight the securities within each country/region by market 
capitalization and then weight each country/region in the overall index in proportion 
to its relative GDP , effectively creating fundamental weighting in multi-  market indexes. 
GDP-  weighted indexes were some of the first fundamentally weighted indexes created.

Introduced in 1987 by MSCI to address the 60 percent weight of Japanese equities 
in the market-  capitalization-  weighted MSCI EAFE Index at the time, GDP-  weighted 
indexes reduced the allocation to Japanese equities by half.4
4 Steven A. Schoenfeld, Active Index Investing  (Hoboken, NJ: John Wiley & Sons, 2004):220.

Equity Indexes 97
5.3 Sector Indexes
Sector indexes  represent and track different economic sectors—such as consumer 
goods, energy, finance, health care, and technology—on either a national, regional, 
or global basis. Because different sectors of the economy behave differently over the 
course of the business cycle, some investors may seek to overweight or underweight 
their exposure to particular sectors.
Sector indexes are organized as families; each index within the family represents 
an economic sector. Typically, the aggregation of a sector index family is equivalent 
to a broad market index. Economic sector classification can be applied on a global, 
regional, or country-  specific basis, but no universally agreed upon sector classification 
method exists.
Sector indexes play an important role in performance analysis because they provide 
a means to determine whether a portfolio manager is more successful at stock selection

or sector allocation. Sector indexes also serve as model portfolios for sector-  specific 
ETFs and other investment products.
5.4 Style Indexes
Style indexes represent groups of securities classified according to market capital -
ization, value, growth, or a combination of these characteristics. They are intended 
to reflect the investing styles of certain investors, such as the growth investor, value 
investor, and small-  cap investor.
5.4.1  Market Capitalization
Market-  capitalization indexes represent securities categorized according to the major 
capitalization categories: large cap, midcap, and small cap. With no universal definition 
of these categories, the indexes differ on the distinctions between large cap and midcap 
and between midcap and small cap, as well as the minimum market-  capitalization 
size required to be included in a small-  cap index. Classification into categories can be 
based on absolute market capitalization (e.g., below €100 million) or relative market

capitalization (e.g., the smallest 2,500 stocks).
5.4.2  Value/Growth Classification
Some indexes represent categories of stocks based on their classifications as either 
value or growth stocks. Different index providers use different factors and valuation 
ratios (low price-  to- book ratios, low price-  to- earnings ratios, high dividend yields, 
etc.) to distinguish between value and growth equities.
5.4.3  Market Capitalization and Value/Growth Classification
Combining the three market-  capitalization groups with value and growth classifica -
tions results in six basic style index categories:
■■Large-  Cap Value ■■Large-  Cap Growth
■■Mid-  Cap Value ■■Mid-  Cap Growth
■■Small-  Cap Value ■■Small-  Cap Growth
Because indexes use different size and valuation classifications, the constituents 
of indexes designed to represent a given style, such as small-  cap value, may differ—
sometimes substantially.
Because valuation ratios and market capitalizations change over time, stocks

frequently migrate from one style index category to another on reconstitution dates. 
As a result, style indexes generally have much higher turnover than do broad market 
indexes.

Reading 45 ■ Security Market Indexes 98
FIXED-  INCOME INDEXES
A wide variety of fixed-  income indexes exists, but the nature of the fixed-  income 
markets and fixed-  income securities leads to some very important challenges to 
fixed-  income index construction and replication. These challenges are the number 
of securities in the fixed-  income universe, the availability of pricing data, and the 
liquidity of the securities.
6.1 Construction
The fixed-  income universe includes securities issued by governments, government 
agencies, and corporations. Each of these entities may issue a variety of fixed-  income 
securities with different characteristics. As a result, the number of fixed-  income 
securities is many times larger than the number of equity securities. To represent a 
specific fixed-  income market or segment, indexes may include thousands of different 
securities. Over time, these fixed-  income securities mature, and issuers offer new

securities to meet their financing needs, leading to turnover in fixed-  income indexes.
Another challenge in index construction is that fixed-  income markets are pre -
dominantly dealer markets. This means that firms (dealers) are assigned to specific 
securities and are responsible for creating liquid markets for those securities by pur -
chasing and selling them from their inventory. In addition, many securities do not 
trade frequently and, as a result, are relatively illiquid. As a result, index providers 
must contact dealers to obtain current prices on constituent securities to update the 
index or they must estimate the prices of constituent securities using the prices of 
traded fixed-  income securities with similar characteristics.
These challenges can result in indexes with dissimilar numbers of bonds rep -
resenting the same markets. As seen in Exhibit 8, the differences can be large. The 
large number of fixed-  income securities—combined with the lack of liquidity of some

securities—has made it more costly and difficult, compared with equity indexes, for 
investors to replicate fixed-  income indexes and duplicate their performance.
Exhibit 8   Comparison of Minimum Issue Size and Bond Holdings by Index
IndexBloomberg Barclays Markit iBoxx Morningstar
Min 
(Thousands)No. of 
BondsMin 
BondsMin 
Bonds
US agency 250,000 988 500,000 435 1,000,000 193
US corporate 250,000 3,134 500,000 1,694 500,000 1,862
UK corporate 250,000 916 100,000 713 225,000 303
Euro corporate 300,000 1,285 500,000 1,167 325,000 829
Source:  Morningstar.
6.2 Types of Fixed-  Income Indexes
The wide variety of fixed-  income securities, ranging from zero-  coupon bonds to 
bonds with embedded options (i.e., callable or putable bonds), results in a number of 
different types of fixed-  income indexes. Similar to equities, fixed-  income securities 6

Fixed-  Income Indexes 99
can be categorized according to the issuer’s economic sector, the issuer’s geographic 
region, or the economic development of the issuer’s geographic region. Fixed-  income 
securities can also be classified along the following dimensions:
■■type of issuer (government, government agency, corporation);
■■type of financing (general obligation, collateralized);
■■currency of payments;
■■maturity;
■■credit quality (investment grade, high yield, credit agency ratings); and
■■absence or presence of inflation protection.
Fixed-  income indexes are based on these various dimensions and can be catego -
rized as follows:
■■aggregate or broad market indexes;
■■market sector indexes;
■■style indexes;
■■economic sector indexes; and
■■specialized indexes such as high-  yield, inflation-  linked, and emerging market 
indexes.
The first fixed-  income index created, the Bloomberg Barclays US Aggregate Bond 
Index (formerly the Barclays Capital Aggregate Bond Index), is an example of a

single-  country aggregate index. Designed to represent the broad market of US fixed-  
income securities, it comprises more than 9,200 securities, including US Treasury, 
government-  related, corporate, mortgage-  backed, asset-  backed, and commercial 
mortgage-  backed securities.
Aggregate indexes can be subdivided by market sector (government, government 
agency, collateralized, corporate); style (maturity, credit quality); economic sector, or 
some other characteristic to create more narrowly defined indexes. A common dis -
tinction reflected in indexes is between investment grade (e.g., those with a Standard 
& Poor’s credit rating of BBB– or better) and high-  yield securities. Investment-  grade 
indexes are typically further subdivided by maturity (i.e., short, intermediate, or 
long) and by credit rating (e.g., AAA, BBB, etc.).5 The wide variety of fixed-  income 
indexes reflects the partitioning of fixed-  income securities on the basis of a variety 
of dimensions.

Exhibit 9 illustrates how the major types of fixed-  income indexes can be organized 
on the basis of various dimensions.
Exhibit 9   Dimensions of Fixed-  Income Indexes
MarketGlobal
Regional
Country or currency zone
Type CorporateCollateralized
agencyGovernment Securitized
Mortgage-  backed
5 Credit ratings are discussed in depth in the Level I CFA Program reading “Fundamentals of Credit Analysis. ”

Reading 45 ■ Security Market Indexes 100
Maturity For example, 1–3, 3–5, 5–7, 7–10, 10+ years; short-  term, medium-  
term, or long-  term
Credit quality For example, AAA, AA, A, BBB, etc.; Aaa, Aa, A, Baa, etc.; invest -
ment grade, high yield
All aggregate indexes include a variety of market sectors and credit ratings. The 
breakdown of the Bloomberg Barclays Global Aggregate Bond Index by market sectors 
and by credit rating is shown in Exhibit 10 and Exhibit 11, respectively.
Exhibit 10   Market Sector Breakdown of the Bloomberg Barclays Global 
Aggregate Bond Index
Treasu ry
49.0%
Government-
Related
14.3%
Corporate
15.3%Securiti zed
21.4%Sector Breakdown as of Oct 31 , 2008
Source:  Barclays, “The Benchmark in Fixed Income: Barclays Capital Indices” (December 2008).
Exhibit 11   Credit Breakdown of the Bloomberg Barclays Global Aggregate 
Bond Index
Aa
30.6% A
10.3%
Baa
4.3%Quality Breakdown as of Oct 31 , 2008
Aaa
54.8%

Aaa
54.8%
Source:  Barclays, “The Benchmark in Fixed Income: Barclays Capital Indices” (December 2008).Exhibit 9   (Continued)

Indexes for Alternative Investments 101
INDEXES FOR ALTERNATIVE INVESTMENTS
Many investors seek to lower the risk or enhance the performance of their portfolios 
by investing in assets classes other than equities and fixed income. Interest in alter -
native assets and investment strategies has led to the creation of indexes designed to 
represent broad classes of alternative investments. Three of the most widely followed 
alternative investment classes are commodities, real estate, and hedge funds.
7.1 Commodity Indexes
Commodity indexes consist of futures contracts on one or more commodities, such 
as agricultural products (rice, wheat, sugar), livestock (cattle, hogs), precious and 
common metals (gold, silver, copper), and energy commodities (crude oil, natural gas).
Although some commodity indexes may include the same commodities, the returns 
of these indexes may differ because each index may use a different weighting method.

Because commodity indexes do not have an obvious weighting mechanism, such as 
market capitalization, commodity index providers create their own weighting methods. 
Some indexes, such as the Commodity Research Bureau (CRB) Index, contain a fixed 
number of commodities that are weighted equally. The S&P GSCI uses a combination 
of liquidity measures and world production values in its weighting scheme and allo -
cates more weight to commodities that have risen in price. Other indexes have fixed 
weights that are determined by a committee.
The different weighting methods can also lead to large differences in exposure 
to specific commodities. The S&P GSCI, for example, has approximately double the 
energy-  sector weighting and one-  third the agriculture sector weighting of the CRB 
Index. These differences result in indexes with very different risk and return profiles. 
Unlike commodity indexes, broad equity and fixed-  income indexes that target the

same markets share similar risk and return profiles.
The performance of commodity indexes can also be quite different from their under -
lying commodities because the indexes consist of futures contracts on the commodities 
rather than the actual commodities. Index returns are affected by factors other than 
changes in the prices of the underlying commodities because futures contracts must 
be continually “rolled over” (i.e., replacing a contract nearing expiration with a new 
contract). Commodity index returns reflect the risk-  free interest rate, the changes in 
future prices, and the roll yield. Therefore, a commodity index return can be quite 
different from the return based on changes in the prices of the underlying commodities.
7.2 Real Estate Investment Trust Indexes
Real estate indexes represent not only the market for real estate securities but also the 
market for real estate—a highly illiquid market and asset class with infrequent trans -

actions and pricing information. Real estate indexes can be categorized as appraisal 
indexes, repeat sales indexes, and real estate investment trust (REIT) indexes.
REIT indexes consist of shares of publicly traded REITs. REITS are public or private 
corporations organized specifically to invest in real estate, either through ownership 
of properties or investment in mortgages. Shares of public REITs are traded on the 
world’s various stock exchanges and are a popular choice for investing in commercial 
real estate properties. Because REIT indexes are based on publicly traded REITs with 
continuous market pricing, the value of REIT indexes is calculated continuously.
The FTSE EPRA/NAREIT global family of REIT indexes shown in Exhibit 12 seeks 
to represent trends in real estate stocks worldwide and includes representation from 
the European Real Estate Association (EPRA) and the National Association of Real 
Estate Investment Trusts (NAREIT).7

Reading 45 ■ Security Market Indexes 102
Exhibit 12   The FTSE EPRA/NAREIT Global REIT Index Family
FTSE EPRA/NAREIT GIobal Real Estate Index Series
Europe, Middle
East, and Africa
Asia PacificAmericas Developed
EmergingSpecialty IndexesFTSE EPRA/NAREIT 
GIobal SeriesFTSE EPRA/NAREIT 
GIobal SeriesFTSE EPRA/NAREIT
GIobal Series
Source:  FTSE International, “FTSE EPRA/NAREIT Global & Global Ex US Indices” Factsheet 
2009). “FTSE®” is a trade mark of the London Stock Exchange Plc, “NAREIT®” is a trade mark 
of the National Association of Real Estate Investment Trusts (“NAREIT”) and “EPRA®” is a 
trade mark of the European Public Real Estate Association (“EPRA”) and all are used by FTSE 
International Limited (“FTSE”) under license.
7.3 Hedge Fund Indexes
Hedge fund indexes reflect the returns on hedge funds. Hedge funds  are private 
investment vehicles that typically use leverage and long and short investment strategies.
A number of research organizations maintain databases of hedge fund returns

and summarize these returns into indexes. These database indexes are designed to 
represent the performance of the hedge funds on a very broad global level (hedge 
funds in general) or the strategy level. Most of these indexes are equal weighted and 
represent the performance of the hedge funds within a particular database.
Most research organizations rely on the voluntary cooperation of hedge funds 
to compile performance data. As unregulated entities, however, hedge funds are not 
required to report their performance to any party other than their investors. Therefore, 
each hedge fund decides to which database(s) it will report its performance. As a 
result, rather than index providers determining the constituents, the constituents 
determine the index.
Frequently, a hedge fund reports its performance to only one database. The result 
is little overlap of funds covered by the different indexes. With little overlap between

their constituents, different global hedge fund indexes may reflect very different per -
formance for the hedge fund industry over the same period of time.
Another consequence of the voluntary performance reporting is the potential 
for survivorship bias and, therefore, inaccurate performance representation. This 
means that hedge funds with poor performance may be less likely to report their 
performance to the database or may stop reporting to the database, so their returns 
may be excluded when measuring the return of the index. As a result, the index may 
not accurately reflect actual hedge fund performance so much as the performance of 
hedge funds that are performing well.

Indexes for Alternative Investments 103
REPRESENTATIVE INDEXES WORLDWIDE
As indicated in this reading, the choice of indexes to meet the needs of investors 
is extensive. Investors using security market indexes must be careful in their 
selection of the index or indexes most appropriate for their needs. The following 
table illustrates the variety of indexes reflecting different asset classes, markets, 
and weighting methods.
Index RepresentingNumber of 
SecuritiesWeighting 
Method Comments
Dow Jones 
Industrial AverageUS blue chip 
companies30 Price The oldest and most widely known US 
equity index.  
Wall Street Journal  editors choose 30 
stocks from among large, mature blue-  
chip companies.
Nikkei Stock 
AverageJapanese blue chip 
companies225 Modified price Known as the Nikkei 225 and originally 
formulated by Dow Jones & Company. 
Because of extreme variation in price 
levels of component securities, some 
high-  priced shares are weighted as a 
fraction of share price. Index contains

fraction of share price. Index contains 
some illiquid stocks.
TOPIX All companies 
listed on the Tokyo 
Stock Exchange 
First SectionVaries Float-  adjusted 
market capRepresents about 93 percent of the 
market value of all Japanese equities. 
Contains a large number of very small, 
illiquid stocks, making exact replication 
difficult.
MSCI All Country 
World IndexStocks of 23 
developed and 22 
emerging marketsVaries Free-  float-  
adjusted 
market capComposed of companies representative 
of the market structure of developed 
and emerging market countries in the 
Americas, Europe/Middle East, and 
Asia/Pacific regions. Price return and 
total return versions available in both 
USD and local currencies.
S&P Developed 
Ex- US BMI 
Energy Sector 
IndexEnergy sector of 
developed global 
markets outside the 
United StatesVaries Float-  adjusted 
market capServes as a model portfolio for the 
SPDR® S&P Energy Sector Exchange-  
Traded Fund (ETF).
Bloomberg 
Barclays Global 
Aggregate Bond 
IndexInvestment-  grade

IndexInvestment-  grade 
bonds in the 
North American, 
European, and 
Asian marketsVaries Market cap Formerly known as Lehman Brothers 
Global Aggregate Bond Index.
Markit iBoxx Euro 
High-  Yield Bond 
IndexesSub-  investment-  
grade euro-  
denominated 
corporate bondsVaries Market cap 
and variationsRebalanced monthly. Represents 
tradable part of market. Price and total 
return versions available with such ana -
lytical values as yield, duration, modi -
fied duration, and convexity. Provides 
platform for research and structured 
products.
FTSE  
EPRA/NAREIT 
Global Real Estate 
IndexReal estate 
securities in the 
Asian markets335 Float-  adjusted 
market capThe stocks of REITs that constitute the 
index trade on public stock exchanges 
and may be constituents of equity 
market indexes.

Reading 45 ■ Security Market Indexes 104
HFRX Global 
Hedge Fund IndexOverall compo -
sition of the HFR 
databaseVaries Asset weighted Comprises all eligible hedge fund strat -
egies. Examples include convertible 
arbitrage, distressed securities, market 
neutral, event driven, macro, and 
relative value arbitrage. Constituent 
strategies are asset weighted on the 
basis of asset distribution within the 
hedge fund industry.
HFRX Equal 
Weighted 
Strategies EUR 
IndexOverall compo -
databaseVaries Equal weighted Denominated in euros and is con -
structed from the same strategies as 
the HFRX Global Hedge Fund Index.
Morningstar Style 
IndexesUS stocks classi -
fied by market cap 
and value/growth 
orientationVaries Float-  adjusted 
market capThe nine indexes defined by combi -
nations of market cap (large, mid, and 
small) and value/growth orientation 
(value, core, growth) have mutually 
exclusive constituents and are exhaus -

tive with respect to the Morningstar 
US Market Index. Each is a model 
portfolio for one of the iShares 
Morningstar ETFs.
SUMMARY
This reading explains and illustrates the construction, management, and uses of security 
market indexes. It also discusses various types of indexes. Security market indexes 
are invaluable tools for investors, who can select from among thousands of indexes 
representing a variety of security markets, market segments, and asset classes. These 
indexes range from those representing the global market for major asset classes to 
those representing alternative investments in specific geographic markets. To benefit 
from the use of security market indexes, investors must understand their construction 
and determine whether the selected index is appropriate for their purposes. Frequently, 
an index that is well suited for one purpose may not be well suited for other purposes.

Users of indexes must be familiar with how various indexes are constructed in order 
to select the index or indexes most appropriate for their needs.
Among the key points made in this reading are the following:
■■Security market indexes are intended to measure the values of different target 
markets (security markets, market segments, or asset classes).
■■The constituent securities selected for inclusion in the security market index are 
intended to represent the target market.
■■A price return index reflects only the prices of the constituent securities.
■■A total return index reflects not only the prices of the constituent securities but 
also the reinvestment of all income received since the inception of the index.
■■Methods used to weight the constituents of an index range from the very sim -
ple, such as price and equal weightings, to the more complex, such as market-  
capitalization and fundamental weightings.

Summary 105
■■Choices in index construction—in particular, the choice of weighting method—
affect index valuation and returns.
■■Index management includes 1) periodic rebalancing to ensure that the index 
maintains appropriate weightings and 2) reconstitution to ensure the index 
represents the desired target market.
■■Rebalancing and reconstitution create turnover in an index. Reconstitution can 
dramatically affect prices of current and prospective constituents.
■■Indexes serve a variety of purposes. They gauge market sentiment and serve as 
benchmarks for actively managed portfolios. They act as proxies for measuring 
systematic risk and risk-  adjusted performance. They also serve as proxies for 
asset classes in asset allocation models and as model portfolios for investment 
products.
■■Investors can choose from security market indexes representing various asset 
classes, including equity, fixed-  income, commodity, real estate, and hedge fund 
indexes.

indexes.
■■Within most asset classes, index providers offer a wide variety of indexes, 
ranging from broad market indexes to highly specialized indexes based on the 
issuer’s geographic region, economic development group, or economic sector or 
other factors.
■■Proper use of security market indexes depends on understanding their con -
struction and management.

Reading 45 ■ Security Market Indexes 106
1 A security market index represents the:
A risk of a security market.
B security market as a whole.
C security market, market segment, or asset class.
2 Security market indexes are:
A constructed and managed like a portfolio of securities.
B simple interchangeable tools for measuring the returns of different asset 
classes.
C valued on a regular basis using the actual market prices of the constituent 
3 When creating a security market index, an index provider must first determine 
the:
A target market.
B appropriate weighting method.
C number of constituent securities.
4 One month after inception, the price return version and total return version of 
a single index (consisting of identical securities and weights) will be equal if:
A market prices have not changed.
B capital gains are offset by capital losses.
C the securities do not pay dividends or interest.

5 The values of a price return index and a total return index consisting of identi -
cal equal-  weighted dividend-  paying equities will be equal:
A only at inception.
B at inception and on rebalancing dates.
C at inception and on reconstitution dates.
6 An analyst gathers the following information for an equal-  weighted index com -
prised of assets Able, Baker, and Charlie:
SecurityBeginning of  
Period Price (€)End of Period  
Price (€)Total  
Dividends (€)
Able 10.00 12.00 0.75
Baker 20.00 19.00 1.00
Charlie 30.00 30.00 2.00
 The price return of the index is:
A 1.7%.
B 5.0%.
C 11.4%.
7 An analyst gathers the following information for an equal-  weighted index com -

Practice Problems 107
 The total return of the index is:
A 5.0%.
B 7.9%.
C 11.4%.
8 An analyst gathers the following information for a price-  weighted index com -
prised of securities ABC, DEF, and GHI:
Period Price (£)End of Period  
Price (£)Total  
Dividends (£)
ABC 25.00 27.00 1.00
DEF 35.00 25.00 1.50
GHI 15.00 16.00 1.00
A –4.6%.
B –9.3%.
C –13.9%.
9 An analyst gathers the following information for a market-  capitalization-  
weighted index comprised of securities MNO, QRS, and XYZ:
Period Price (¥)End of Period  
Price (¥)Dividends  
per Share (¥)Shares  
MNO 2,500 2,700 100 5,000
QRS 3,500 2,500 150 7,500
XYZ 1,500 1,600 100 10,000
A –9.33%.
B –10.23%.
C –13.90%.

A –9.33%.
B –10.23%.
C –13.90%.
10 An analyst gathers the following information for a market-  capitalization-  
Per Share (¥)Shares  
A 1.04%.
B –5.35%.
C –10.23%.

Reading 45 ■ Security Market Indexes 108
11 When creating a security market index, the target market:
A determines the investment universe.
B is usually a broadly defined asset class.
C determines the number of securities to be included in the index.
12 An analyst gathers the following data for a price-  weighted index:
Beginning of Period End of Period
Security Price (€) Shares Price (€) Shares
A 20.00 300 22.00 300
B 50.00 300 48.00 300
C 26.00 2,000 30.00 2,000
 The price return of the index over the period is:
A 4.2%.
B 7.1%.
C 21.4%.
13 An analyst gathers the following data for a value-  weighted index:
Security Price (£) Shares Price (£) Shares
 The return on the value-  weighted index over the period is:
A 7.1%.
B 11.0%.
C 21.4%.
14 An analyst gathers the following data for an equally-  weighted index:
Security Price (¥) Shares Price (¥) Shares

 The return on the index over the period is:
A 4.2%.
B 6.8%.
C 7.1%.
15 Which of the following index weighting methods requires an adjustment to the 
divisor after a stock split?
A Price weighting.
B Fundamental weighting.
C Market-  capitalization weighting.
16 If the price return of an equal-  weighted index exceeds that of a market-  
capitalization-  weighted index comprised of the same securities, the most likely  
explanation is:

A stock splits.
B dividend distributions.
C outperformance of small-  market-  capitalization stocks.
17 A float-  adjusted market-  capitalization-  weighted index weights each of its con -
stituent securities by its price and:
A its trading volume.
B the number of its shares outstanding.
C the number of its shares available to the investing public.
18 Which of the following index weighting methods is most likely subject to a 
value tilt?
A Equal weighting.
19 Rebalancing an index is the process of periodically adjusting the constituent:
A securities’ weights to optimize investment performance.
B securities to maintain consistency with the target market.
C securities’ weights to maintain consistency with the index’s weighting 
method.
20 Which of the following index weighting methods requires the most frequent 
rebalancing?
B Equal weighting.

21 Reconstitution of a security market index reduces:
A portfolio turnover.
B the need for rebalancing.
C the likelihood that the index includes securities that are not representative 
of the target market.
22 Security market indexes are used as:
A measures of investment returns.
B proxies to measure unsystematic risk.
C proxies for specific asset classes in asset allocation models.
23 Uses of market indexes do not include serving as a:
A measure of systematic risk.
B basis for new investment products.
C benchmark for evaluating portfolio performance.
24 Which of the following statements regarding sector indexes is most  accurate? 
Sector indexes:
A track different economic sectors and cannot be aggregated to represent the 
equivalent of a broad market index.
B provide a means to determine whether an active investment manager is 
more successful at stock selection or sector allocation.
C apply a universally agreed upon sector classification system to identify the

constituent securities of specific economic sectors, such as consumer goods, 
energy, finance, health care.
25 Which of the following is an example of a style index? An index based on:

Reading 45 ■ Security Market Indexes 110
A geography.
B economic sector.
C market capitalization.
26 Which of the following statements regarding fixed-  income indexes is most  
accurate?
A Liquidity issues make it difficult for investors to easily replicate fixed-  
income indexes.
B Rebalancing and reconstitution are the only sources of turnover in fixed-  
C Fixed-  income indexes representing the same target market hold similar 
numbers of bonds.
27 An aggregate fixed-  income index:
A comprises corporate and asset-  backed securities.
B represents the market of government-  issued securities.
C can be subdivided by market or economic sector to create more narrowly 
defined indexes.
28 Fixed-  income indexes are least likely  constructed on the basis of:
A maturity.
B type of issuer.
C coupon frequency.
29 Commodity index values are based on:
A futures contract prices.
B the market price of the specific commodity.
C the average market price of a basket of similar commodities.

30 Which of the following statements is most  accurate?
A Commodity indexes all share similar weighting methods.
B Commodity indexes containing the same underlying commodities offer sim -
ilar returns.
C The performance of commodity indexes can be quite different from that of 
the underlying commodities.
31 Which of the following is not a real estate index category?
A Appraisal index.
B Initial sales index.
C Repeat sales index.
32 A unique feature of hedge fund indexes is that they:
A are frequently equal weighted.
B are determined by the constituents of the index.
C reflect the value of private rather than public investments.
33 The returns of hedge fund indexes are most likely :
A biased upward.
B biased downward.
C similar across different index providers.
34 In comparison to equity indexes, the constituent securities of fixed-  income 
indexes are:
A more liquid.

B easier to price.
C drawn from a larger investment universe.

Reading 45 ■ Security Market Indexes 112
SOLUTIONS
1 C is correct. A security market index represents the value of a given security 
market, market segment, or asset class.
2 A is correct. Security market indexes are constructed and managed like a port -
folio of securities.
3 A is correct. The first decision is identifying the target market that the index 
is intended to represent because the target market determines the investment 
universe and the securities available for inclusion in the index.
4 C is correct. The difference between a price return index and a total return 
index consisting of identical securities and weights is the income generated over 
time by the underlying securities. If the securities in the index do not generate 
income, both indexes will be identical in value.
5 A is correct. At inception, the values of the price return and total return ver -
sions of an index are equal.
6 B is correct. The price return is the sum of the weighted returns of each secu -

rity. The return of Able is 20 percent [(12 – 10)/10]; of Baker is –5 percent [(19 
– 20)/20]; and of Charlie is 0 percent [(30 – 30)/30]. The price return index 
assigns a weight of 1/3 to each asset; therefore, the price return is 1/3 × [20% + 
(–5%) + 0%] = 5%.
7 C is correct. The total return of an index is calculated on the basis of the change 
in price of the underlying securities plus the sum of income received or the 
sum of the weighted total returns of each security. The total return of Able is 
27.5 percent; of Baker is 0 percent; and of Charlie is 6.7 percent:
Able: (12 – 10 + 0.75)/10 = 27.5%
Baker: (19 – 20 + 1)/20 = 0%
Charlie: (30 – 30 + 2)/30 = 6.7%
 An equal-  weighted index applies the same weight (1/3) to each security’s return; 
therefore, the total return = 1/3 × (27.5% + 0% + 6.7%) = 11.4%.
8 B is correct. The price return of the price-  weighted index is the percentage 
change in price of the index: (68 – 75)/75 = –9.33%.
SecurityBeginning of Period  
Price (£)End of Period

Price (£)End of Period  
Price (£)
ABC 25.00 27.00
DEF 35.00 25.00
GHI 15.00 16.00
TOTAL 75.00 68.00
9 B is correct. The price return of the index is (48,250,000 – 
53,750,000)/53,750,000 = –10.23%.
SecurityBeginning 
of Period 
Price (¥)Shares 
OutstandingBeginning 
of Period 
Value (¥)End of 
Period 
Price (¥)End of Period 
Value (¥)
MNO 2,500 5,000 12,500,000 2,700 13,500,000
QRS 3,500 7,500 26,250,000 2,500 18,750,000

Solutions 113
of Period 
of Period 
Period 
Value (¥)
XYZ 1,500 10,000 15,000,000 1,600 16,000,000
Total 53,750,000 48,250,000
10 B is correct. The total return of the market-  capitalization-  weighted index is 
calculated below:
SecurityBeginning of 
Period Value 
(¥)End of Period 
Value (¥)Total  
Dividends 
(¥)Total Return 
(%)
MNO 12,500,000 13,500,000 500,000 12.00
QRS 26,250,000 18,750,000 1,125,000 –24.29
XYZ 15,000,000 16,000,000 1,000,000 13.33
Total 53,750,000 48,250,000 2,625,000 –5.35
11 A is correct. The target market determines the investment universe and the 
securities available for inclusion in the index.
12 A is correct. The sum of prices at the beginning of the period is 96; the sum at 
the end of the period is 100. Regardless of the divisor, the price return is 100/96 
– 1 = 0.042 or 4.2 percent.
13 B is correct. It is the percentage change in the market value over the period:

Market value at beginning of period: (20 × 300) + (50 × 300) + (26 × 2,000) 
= 73,000
Market value at end of period: (22 × 300) + (48 × 300) + (30 × 2,000) = 
81,000
Percentage change is 81,000/73,000 – 1 = 0.1096 or 11.0 percent with 
rounding.
14 C is correct. With an equal-  weighted index, the same amount is invested in 
each security. Assuming $1,000 is invested in each of the three stocks, the index 
value is $3,000 at the beginning of the period and the following number of 
shares is purchased for each stock:
Security A: 50 shares
Security B: 20 shares
Security C: 38.46 shares.
 Using the prices at the beginning of the period for each security, the index value 
at the end of the period is $3,213.8: ($22 × 50) + ($48 × 20) + ($30 × 38.46). The 
price return is $3,213.8/$3,000 – 1 = 7.1%.
15 A is correct. In the price weighting method, the divisor must be adjusted so the 
index value immediately after the split is the same as the index value immedi -
ately prior to the split.

16 C is correct. The main source of return differences arises from outperformance 
of small-  cap securities or underperformance of large-  cap securities. In an 
equal-  weighted index, securities that constitute the largest fraction of the mar -
ket are underrepresented and securities that constitute only a small fraction of 
the market are overrepresented. Thus, higher equal-  weighted index returns will 
occur if the smaller-  cap equities outperform the larger-  cap equities.
17 C is correct. “Float” is the number of shares available for public trading.

Reading 45 ■ Security Market Indexes 114
18 B is correct. Fundamental weighting leads to indexes that have a value tilt.
19 C is correct. Rebalancing refers to adjusting the weights of constituent securi -
ties in an index to maintain consistency with the index’s weighting method.
20 B is correct. Changing market prices will cause weights that were initially equal 
to become unequal, thus requiring rebalancing.
21 C is correct. Reconstitution is the process by which index providers review the 
constituent securities, re-  apply the initial criteria for inclusion in the index, and 
select which securities to retain, remove, or add. Constituent securities that 
no longer meet the criteria are replaced with securities that do. Thus, recon -
stitution reduces the likelihood that the index includes securities that are not 
representative of the target market.
22 C is correct. Security market indexes play a critical role as proxies for asset 
classes in asset allocation models.

23 A is correct. Security market indexes are used as proxies for measuring market 
or systematic risk, not as measures of systematic risk.
24 B is correct. Sector indexes provide a means to determine whether a portfolio 
manager is more successful at stock selection or sector allocation.
25 C is correct. Style indexes represent groups of securities classified according to 
market capitalization, value, growth, or a combination of these characteristics.
26 A is correct. The large number of fixed-  income securities—combined with the 
lack of liquidity of some securities—makes it costly and difficult for investors to 
replicate fixed-  income indexes.
27 C is correct. An aggregate fixed-  income index can be subdivided by market sec -
tor (government, government agency, collateralized, corporate), style (maturity, 
credit quality), economic sector, or some other characteristic to create more 
narrowly defined indexes.

28 C is correct. Coupon frequency is not a dimension on which fixed-  income 
indexes are based.
29 A is correct. Commodity indexes consist of futures contracts on one or more 
commodities.
30 C is correct. The performance of commodity indexes can be quite different 
from that of the underlying commodities because the indexes consist of futures 
contracts on the commodities rather than the actual commodities.
31 B is correct. It is not a real estate index category.
32 B is correct. Hedge funds are not required to report their performance to any 
party other than their investors. Therefore, each hedge fund decides to which 
database(s) it will report its performance. Thus, for a hedge fund index, con -
stituents determine the index rather than index providers determining the 
constituents.
33 A is correct. Voluntary performance reporting may lead to survivorship 
bias, and poorer performing hedge funds will be less likely to report their 

34 C is correct. The fixed-  income market has more issuers and securities than the 

Market Efficiency
by Sean Cleary, PhD, CFA, Howard J. Atkinson, CIMA, ICD.D, CFA, and 
Sean Cleary, PhD, CFA, is at Queen’s University (Canada). Howard J. Atkinson, CIMA, 
ICD.D, CFA, is at Horizons ETF Management (Canada) Inc. (Canada). Pamela Peterson 
Drake, PhD, CFA, is at James Madison University (USA).
a. describe market efficiency and related concepts, including their 
importance to investment practitioners;
b. distinguish between market value and intrinsic value;
c. explain factors that affect a market’s efficiency;
d. contrast weak-  form, semi-  strong-  form, and strong-  form market 
efficiency;
e. explain the implications of each form of market efficiency for 
fundamental analysis, technical analysis, and the choice between 
active and passive portfolio management;
f. describe market anomalies;
g. describe behavioral finance and its potential relevance to 
understanding market anomalies.

Market efficiency concerns the extent to which market prices incorporate available 
information. If market prices do not fully incorporate information, then opportunities 
may exist to make a profit from the gathering and processing of information. The 
subject of market efficiency is, therefore, of great interest to investment managers, 
as illustrated in Example 1.1READING
46

Reading 46 ■ Market Efficiency 116
EXAMPLE 1   
Market Efficiency and Active Manager Selection
The chief investment officer (CIO) of a major university endowment fund has 
listed eight steps in the active manager selection process that can be applied both 
to traditional investments (e.g., common equity and fixed-  income securities) and 
to alternative investments (e.g., private equity, hedge funds, and real assets). The 
first step specified is the evaluation of market opportunity:
What is the opportunity and why is it there? To answer this ques -
tion we start by studying capital markets and the types of managers 
operating within those markets. We identify market inefficiencies 
and try to understand their causes, such as regulatory structures or 
behavioral biases. We can rule out many broad groups of managers 
and strategies by simply determining that the degree of market inef -
ficiency necessary to support a strategy is implausible. Importantly,

we consider the past history of active returns meaningless unless we 
understand why markets will allow those active returns to continue 
into the future.1
The CIO’s description underscores the importance of not assuming that past 
active returns that might be found in a historical dataset will repeat themselves 
in the future. Active returns  refer to returns earned by strategies that do not 
assume that all information is fully reflected in market prices.
Governments and market regulators also care about the extent to which market 
prices incorporate information. Efficient markets imply informative prices—prices that 
accurately reflect available information about fundamental values. In market-  based 
economies, market prices help determine which companies (and which projects) obtain 
capital. If these prices do not efficiently incorporate information about a company’s 
prospects, then it is possible that funds will be misdirected. By contrast, prices that

are informative help direct scarce resources and funds available for investment to 
their highest-  valued uses.2 Informative prices thus promote economic growth. The 
efficiency of a country’s capital markets (in which businesses raise financing) is an 
important characteristic of a well-  functioning financial system.
The remainder of this reading is organized as follows. Section 2 provides specifics 
on how the efficiency of an asset market is described and discusses the factors affecting 
(i.e., contributing to and impeding) market efficiency. Section 3 presents an influential 
three-  way classification of the efficiency of security markets and discusses its implica -
tions for fundamental analysis, technical analysis, and portfolio management. Section 
4 presents several market anomalies (apparent market inefficiencies that have received 
enough attention to be individually identified and named) and describes how these

anomalies relate to investment strategies. Section 5 introduces behavioral finance and 
how that field of study relates to market efficiency. A summary concludes the reading.
1 The CIO is Christopher J. Brightman, CFA, of the University of Virginia Investment Management 
Company, as reported in Yau, Schneeweis, Robinson, and Weiss (2007, pp. 481–482).
2 This concept is known as allocative efficiency.

The Concept of Market Efficiency 117
THE CONCEPT OF MARKET EFFICIENCY
2.1 The Description of Efficient Markets
An informationally efficient market  (an efficient market ) is a market in which asset 
prices reflect new information quickly and rationally. An efficient market is thus a 
market in which asset prices reflect all past and present information.3
In this section we expand on this definition by clarifying the time frame required 
for an asset’s price to incorporate information as well as describing the elements of 
information releases assumed under market efficiency. We discuss the difference 
between market value and intrinsic value and illustrate how inefficiencies or discrep -
ancies between these values can provide profitable opportunities for active investment. 
As financial markets are generally not considered being either completely efficient or 
inefficient, but rather falling within a range between the two extremes, we describe a

number of factors that contribute to and impede the degree of efficiency of a financial 
market. Finally, we conclude our overview of market efficiency by illustrating how the 
costs incurred by traders in identifying and exploiting possible market inefficiencies 
affect how we interpret market efficiency.
Investment managers and analysts, as noted, are interested in market efficiency 
because the extent to which a market is efficient affects how many profitable trading 
opportunities (market inefficiencies) exist. Consistent, superior, risk-  adjusted returns 
(net of all expenses) are not achievable in an efficient market.4 In a highly efficient mar -
ket, a passive investment  strategy (i.e., buying and holding a broad market portfolio) 
that does not seek superior risk-  adjusted returns is preferred to an active investment  
strategy because of lower costs (for example, transaction and information-  seeking

costs). By contrast, in a very inefficient market, opportunities may exist for an active 
investment strategy to achieve superior risk-  adjusted returns (net of all expenses in 
executing the strategy) as compared with a passive investment strategy. In inefficient 
markets, an active investment strategy may outperform a passive investment strategy 
on a risk-  adjusted basis. Understanding the characteristics of an efficient market and 
being able to evaluate the efficiency of a particular market are important topics for 
investment analysts and portfolio managers.
An efficient market is a market in which asset prices reflect information quickly. But 
what is the time frame of “quickly”? Trades are the mechanism by which information 
can be incorporated into asset transaction prices. The time needed to execute trades 
to exploit an inefficiency may provide a baseline for judging speed of adjustment.5 
The time frame for an asset’s price to incorporate information must be at least as long

as the shortest time a trader needs to execute a transaction in the asset. In certain 
markets, such as foreign exchange and developed equity markets, market efficiency 
relative to certain types of information has been studied using time frames as short as 
one minute or less. If the time frame of price adjustment allows many traders to earn 
profits with little risk, then the market is relatively inefficient. These considerations 
lead to the observation that market efficiency can be viewed as falling on a continuum.2
3 This definition is convenient for making several instructional points. The definition that most simply 
explains the sense of the word efficient  in this context can be found in Fama (1976): “ An efficient capital 
market is a market that is efficient in processing information” (p. 134).
4 The technical term for superior  in this context is positive abnormal  in the sense of higher than expected

given the asset’s risk (as measured, according to capital market theory, by the asset’s contribution to the 
risk of a well-  diversified portfolio).
5 Although the original theory of market efficiency does not quantify this speed, the basic idea is that 
it is sufficiently swift to make it impossible to consistently earn abnormal profits. Chordia, Roll, and 
Subrahmanyam (2005) suggest that the adjustment to information on the New York Stock Exchange (NYSE) 
is between 5 and 60 minutes.

Reading 46 ■ Market Efficiency 118
Finally, an important point is that in an efficient market, prices should be expected 
to react only to the elements of information releases that are not anticipated fully 
by investors—that is, to the “unexpected” or “surprise” element of such releases. 
Investors process the unexpected information and revise expectations (for example, 
about an asset’s future cash flows, risk, or required rate of return) accordingly. The 
revised expectations enter or get incorporated in the asset price through trades in 
the asset. Market participants who process the news and believe that at the current 
market price an asset does not offer sufficient compensation for its perceived risk will 
tend to sell it or even sell it short. Market participants with opposite views should be 
buyers. In this way the market establishes the price that balances the various opinions 
after expectations are revised.
EXAMPLE 2   
Price Reaction to the Default on a Bond Issue

Suppose that a speculative-  grade bond issuer announces, just before bond markets 
open, that it will default on an upcoming interest payment. In the announce -
ment, the issuer confirms various reports made in the financial media in the 
period leading up to the announcement. Prior to the issuer’s announcement, 
the financial news media reported the following: 1) suppliers of the company 
were making deliveries only for cash payment, reducing the company’s liquidity; 
2) the issuer’s financial condition had probably deteriorated to the point that it 
lacked the cash to meet an upcoming interest payment; and 3) although public 
capital markets were closed to the company, it was negotiating with a bank for 
a private loan that would permit it to meet its interest payment and continue 
operations for at least nine months. If the issuer defaults on the bond, the con -
sensus opinion of analysts is that bondholders will recover approximately $0.36

to $0.38 per dollar face value.
1 If the market for the bond is highly efficient, the bond’s market price is 
most likely  to fully reflect the bond’s value after default:
A in the period leading up to the announcement.
B in the first trade prices after the market opens on the announcement 
day.
C when the issuer actually misses the payment on the interest payment 
date.
2 If the market for the bond is highly efficient, the piece of information that 
bond investors most likely  focused on in the issuer’s announcement was 
that the issuer:
A had failed in its negotiations for a bank loan.
B lacked the cash to meet the upcoming interest payment.
C had been required to make cash payments for supplier deliveries.
B is correct. The announcement removed any uncertainty about default. In the 
period leading up to the announcement, the bond’s market price incorporated 
a probability of default but the price would not have fully reflected the bond’s

value after default. The possibility that a bank loan might permit the company 
to avoid default was not eliminated until the announcement.

The Concept of Market Efficiency 119
A is correct. The failure of the loan negotiations first becomes known in this 
announcement. The failure implies default.
2.2 Market Value versus Intrinsic Value
Market value  is the price at which an asset can currently be bought or sold. Intrinsic 
value  (sometimes called fundamental value ) is, broadly speaking, the value that 
would be placed on it by investors if they had a complete understanding of the asset’s 
investment characteristics.6 For a bond, for example, such information would include 
its interest (coupon) rate, principal value, the timing of its interest and principal pay -
ments, the other terms of the bond contract (indenture), a precise understanding of 
its default risk, the liquidity of its market, and other issue-  specific items. In addition, 
market variables such as the term structure of interest rates and the size of various 
market premiums applying to the issue (for default risk, etc.) would enter into a dis -

counted cash flow estimate of the bond’s intrinsic value (discounted cash flow models 
are often used for such estimates). The word estimate  is used because in practice, 
intrinsic value can be estimated but is not known for certain.
If investors believe a market is highly efficient , they will usually accept market 
prices as accurately reflecting intrinsic values. Discrepancies between market price 
and intrinsic value are the basis for profitable active investment. Active investors seek 
to own assets selling below perceived intrinsic value in the marketplace and to sell or 
sell short assets selling above perceived intrinsic value.
If investors believe an asset market is relatively inefficient , they may try to develop 
an independent estimate of intrinsic value. The challenge for investors and analysts 
is estimating an asset’s intrinsic value. Numerous theories and models, including 
the dividend discount model, can be used to estimate an asset’s intrinsic value, but

they all require some form of judgment regarding the size, timing, and riskiness of 
the future cash flows associated with the asset. The more complex an asset’s future 
cash flows, the more difficult it is to estimate its intrinsic value. These complexities 
and the estimates of an asset’s market value are reflected in the market through the 
buying and selling of assets. The market value of an asset represents the intersection 
of supply and demand—the point that is low enough to induce at least one investor 
to buy while being high enough to induce at least one investor to sell. Because infor -
mation relevant to valuation flows continually to investors, estimates of intrinsic value 
change, and hence, market values change.
EXAMPLE 3   
Intrinsic Value
1 An analyst estimates that a security’s intrinsic value is lower than its mar -
ket value. The security appears to be:
A undervalued.
B fairly valued.
C overvalued.
2 A market in which assets’ market values are, on average, equal to or nearly

equal to intrinsic values is best described  as a market that is attractive for:
6 Intrinsic value is often defined as the present value of all expected future cash flows of the asset.

Reading 46 ■ Market Efficiency 120
A active investment.
B passive investment.
C both active and passive investment.
3 Suppose that the future cash flows of an asset are accurately estimated. 
The asset trades in a market that you believe is highly efficient based on 
most evidence. But your intrinsic value estimate exceeds market value by 
a moderate amount. The most likely  conclusion is that you have:
A overestimated the asset’s risk.
B underestimated the asset’s risk.
C identified a market inefficiency.
C is correct. The market is valuing the asset at more than its true worth.
B is correct because an active investment is not expected to earn superior risk-  
adjusted returns. The additional costs of active investment are not justified in 
such a market.
B is correct. If risk is underestimated, the discount rate being applied to find 
the present value of the expected cash flows (estimated intrinsic value) will be

too low and the intrinsic value estimate will be too high.
2.3 Factors Contributing to and Impeding a Market’s Efficiency
For markets to be efficient, prices should adjust quickly and rationally to the release of 
new information. In other words, prices of assets in an efficient market should “fully 
reflect” all information. Financial markets, however, are generally not classified at 
the two extremes as either completely inefficient or completely efficient but, rather, 
as exhibiting various degrees of efficiency. In other words, market efficiency should 
be viewed as falling on a continuum between extremes of completely efficient, at one 
end, and completely inefficient, at the other. Asset prices in a highly efficient market, 
by definition, reflect information more quickly and more accurately than in a less-  
efficient market. These degrees of efficiency also vary through time, across geographical 
markets, and by type of market. A number of factors contribute to and impede the

degree of efficiency in a financial market.
2.3.1  Market Participants
One of the most critical factors contributing to the degree of efficiency in a market 
is the number of market participants. Consider the following example that illustrates 
the relationship between the number of market participants and market efficiency.

The Concept of Market Efficiency 121
EXAMPLE 4   
Illustration of Market Efficiency
Assume that the shares of a small market capitalization (cap) company trade on 
a public stock exchange. Because of its size, it is not considered “blue-  chip” and 
not many professional investors follow the activities of the company.7 A small-  
cap fund analyst reports that the most recent annual operating performance 
of the company has been surprisingly good, considering the recent slump in 
its industry. The company’s share price, however, has been slow to react to the 
positive financial results because the company is not being recommended by the 
majority of research analysts. This mispricing implies that the market for this 
company’s shares is less than fully efficient. The small-  cap fund analyst recognizes 
the opportunity and immediately recommends the purchase of the company’s 
shares. The share price gradually increases as more investors purchase the shares

once the news of the mispricing spreads through the market. As a result, it takes 
a few days for the share price to fully reflect the information.
Six months later, the company reports another solid set of interim financial 
results. But because the previous mispricing and subsequent profit opportuni -
ties have become known in the market, the number of analysts following the 
company’s shares has increased substantially. As a result, as soon as unexpected 
information about the positive interim results are released to the public, a large 
number of buy orders quickly drive up the stock price, thereby making the market 
for these shares more efficient than before.
A large number of investors (individual and institutional) follow the major financial 
markets closely on a daily basis, and if mispricings exist in these markets, as illus -
trated by the example, investors will act so that these mispricings disappear quickly.

Besides the number of investors, the number of financial analysts who follow or ana -
lyze a security or asset should be positively related to market efficiency. The number 
of market participants and resulting trading activity can vary significantly through 
time. A lack of trading activity can cause or accentuate other market imperfections 
that impede market efficiency. In fact, in many of these markets, trading in many of 
the listed stocks is restricted for foreigners. By nature, this limitation reduces the 
number of market participants, restricts the potential for trading activity, and hence 
reduces market efficiency.
EXAMPLE 5   
Factors Affecting Market Efficiency
The expected effect on market efficiency of opening a securities market to trading 
by foreigners would be to:
A decrease market efficiency.
B leave market efficiency unchanged.
C increase market efficiency.
7 A “blue-  chip” share is one from a well-  recognized company that is considered to be high quality but

low risk. This term generally refers to a company that has a long history of earnings and paying dividends.

Reading 46 ■ Market Efficiency 122
Solution: 
C is correct. The opening of markets as described should increase market effi -
ciency by increasing the number of market participants.
2.3.2  Information Availability and Financial Disclosure
Information availability (e.g., an active financial news media) and financial disclo -
sure should promote market efficiency. Information regarding trading activity and 
traded companies in such markets as the New York Stock Exchange, the London 
Stock Exchange, and the Tokyo Stock Exchange is readily available. Many investors 
and analysts participate in these markets, and analyst coverage of listed companies is 
typically substantial. As a result, these markets are quite efficient. In contrast, trad -
ing activity and material information availability may be lacking in smaller securities 
markets, such as those operating in some emerging markets.
Similarly, significant differences may exist in the efficiency of different types of

markets. For example, many securities trade primarily or exclusively in dealer or over-  
the- counter (OTC) markets, including bonds, money market instruments, currencies, 
mortgage-  backed securities, swaps, and forward contracts. The information provided 
by the dealers that serve as market makers for these markets can vary significantly in 
quality and quantity, both through time and across different product markets.
Treating all market participants fairly is critical for the integrity of the market and 
explains why regulators place such an emphasis on “fair, orderly, and efficient mar -
k e t s .”8 A key element of this fairness is that all investors have access to the informa -
tion necessary to value securities that trade in the market. Rules and regulations that 
promote fairness and efficiency in a market include those pertaining to the disclosure 
of information and illegal insider trading.
For example, US Securities and Exchange Commission’s (SEC’s) Regulation FD

(Fair Disclosure) requires that if security issuers provide nonpublic information to 
some market professionals or investors, they must also disclose this information to 
the public.9 This requirement helps provide equal and fair opportunities, which is 
important in encouraging participation in the market. A related issue deals with illegal 
insider trading. The SEC’s rules, along with court cases, define illegal insider trading 
as trading in securities by market participants who are considered insiders “while in 
possession of material, nonpublic information about the security. ”10 Although these 
rules cannot guarantee that some participants will not have an advantage over others 
and that insiders will not trade on the basis of inside information, the civil and crim -
inal penalties associated with breaking these rules are intended to discourage illegal 
insider trading and promote fairness. In the European Union, insider trading laws are

generally enshrined in legislation and enforced by regulatory and judicial authorities.11
8 “The Investor’s Advocate: How the SEC Protects Investors, Maintains Market Integrity, and Facilitates 
Capital Formation, ” US Securities and Exchange Commission (www.sec.gov/about/whatwedo.shtml).
9 Regulation FD, “Selective Disclosure and Insider Trading, ” 17 CFR Parts 240, 243, and 249, effective 23 
October 2000.
10 Although not the focus of this particular reading, it is important to note that a party is considered an 
insider not only when the individual is a corporate insider, such as an officer or director, but also when the 
individual is aware that the information is nonpublic information [Securities and Exchange Commission, 
Rules 10b5-  1 (“Trading on the Basis of Material Nonpublic Information in Insider Trading Cases”) and 
Rule 10b5-  2 “Duties of Trust or Confidence in Misappropriation Insider Trading Cases”)].

11 See the European Union’s Market Abuse Regulation (Regulation (EU) no. 596/2014 of the European 
Parliament and of the Council of 16 April 2014 on market abuse) and Directive for Criminal Sanctions for 
Market Abuse (Directive 2014/57/EU of the European Parliament and of the Council of 16 April 2014 on 
criminal sanctions for market abuse).

The Concept of Market Efficiency 123
2.3.3  Limits to Trading
Arbitrage  is a set of transactions that produces riskless profits. Arbitrageurs are trad -
ers who engage in such trades to benefit from pricing discrepancies (inefficiencies) 
in markets. Such trading activity contributes to market efficiency. For example, if an 
asset is traded in two markets but at different prices, the actions of buying the asset 
in the market in which it is underpriced and selling the asset in the market in which 
it is overpriced will eventually bring these two prices together. The presence of these 
arbitrageurs helps pricing discrepancies disappear quickly. Obviously, market efficiency 
is impeded by any limitation on arbitrage resulting from operating inefficiencies, such 
as difficulties in executing trades in a timely manner, prohibitively high trading costs, 
and a lack of transparency in market prices.
Some market experts argue that restrictions on short selling limit arbitrage trading,

which impedes market efficiency. Short selling  is the transaction whereby an investor 
sells shares that he or she does not own by borrowing them from a broker and agreeing 
to replace them at a future date. Short selling allows investors to sell securities they 
believe to be overvalued, much in the same way they can buy those they believe to 
be undervalued. In theory, such activities promote more efficient pricing. Regulators 
and others, however, have argued that short selling may exaggerate downward market 
movements, leading to crashes in affected securities. In contrast, some researchers 
report evidence indicating that when investors are unable to borrow securities, that is to 
short the security, or when costs to borrow shares are high, market prices may deviate 
from intrinsic values.12 Furthermore, research suggests that short selling is helpful 
in price discovery (that is, it facilitates supply and demand in determining prices).13

2.4 Transaction Costs and Information-  Acquisition Costs
The costs incurred by traders in identifying and exploiting possible market inefficien -
cies affect the interpretation of market efficiency. The two types of costs to consider 
are transaction costs and information-  acquisition costs.
■■Transaction costs : Practically, transaction costs are incurred in trading to 
exploit any perceived market inefficiency. Thus, “efficient” should be viewed 
as efficient within the bounds of transaction costs. For example, consider a 
violation of the principle that two identical assets should sell for the same price 
in different markets. Such a violation can be considered to be a rather simple 
possible exception to market efficiency because prices appear to be inconsis -
tently processing information. To exploit the violation, a trader could arbitrage 
by simultaneously shorting the asset in the higher-  price market and buying the

asset in the lower-  price market. If the price discrepancy between the two mar -
kets is smaller than the transaction costs involved in the arbitrage for the lowest 
cost traders, the arbitrage will not occur, and both prices are in effect efficient 
within the bounds of arbitrage. These bounds of arbitrage are relatively narrow 
in highly liquid markets, such as the market for US Treasury bills, but could be 
wide in illiquid markets.
■■Information-  acquisition costs:  Practically, expenses are always associated with 
gathering and analyzing information. New information is incorporated in trans -
action prices by traders placing trades based on their analysis of information. 
Active investors who place trades based on information they have gathered and 
analyzed play a key role in market prices adjusting to reflect new information. 
The classic view of market efficiency is that active investors incur information 
12 See Deng, Mortal, and Gupta (2017) and references therein. ”

Reading 46 ■ Market Efficiency 124
acquisition costs but that money is wasted because prices already reflect all rel -
evant information. This view of efficiency is very strict in the sense of viewing 
a market as inefficient if active investing can recapture any part of the costs, 
such as research costs and active asset selection. Grossman and Stiglitz (1980) 
argue that prices must offer a return to information acquisition; in equilib -
rium, if markets are efficient, returns net of such expenses are just fair returns 
for the risk incurred. The modern perspective views a market as inefficient if, 
after deducting such costs, active investing can earn superior returns. Gross 
of expenses, a return should accrue to information acquisition in an efficient 
market.
In summary, a modern perspective calls for the investor to consider transaction 
costs and information-  acquisition costs when evaluating the efficiency of a market. A

price discrepancy must be sufficiently large to leave the investor with a profit (adjusted 
for risk) after taking account of the transaction costs and information-  acquisition costs 
to reach the conclusion that the discrepancy may represent a market inefficiency. 
Prices may somewhat less than fully reflect available information without there being 
a true market opportunity for active investors.
FORMS OF MARKET EFFICIENCY
Eugene Fama developed a framework for describing the degree to which markets 
are efficient.14 In his efficient market hypothesis, markets are efficient when prices 
reflect all relevant information at any point in time. This means that the market prices 
observed for securities, for example, reflect the information available at the time.
In his framework, Fama defines three forms of efficiency: weak, semi-  strong, and 
strong. Each form is defined with respect to the available information that is reflected 
in prices.
Market Prices Reflect:
Forms of Market EfficiencyPast

Forms of Market EfficiencyPast  
Market DataPublic 
InformationPrivate 
Weak form of market efficiency ✓
Semi-  strong form of market 
efficiency✓ ✓
Strong form of market efficiency ✓ ✓ ✓
A finding that investors can consistently earn abnormal returns  by trading on the 
basis of information is evidence contrary to market efficiency. In general, abnormal 
returns are returns in excess of those expected given a security’s risk and the market’s 
return. In other words, abnormal return equals actual return less expected return.3
14 Fama (1970).

Forms of Market Efficiency 125
3.1 Weak Form
In the weak-  form efficient market hypothesis , security prices fully reflect all past 
market data , which refers to all historical price and trading volume information. If 
markets are weak-  form efficient, past trading data are already reflected in current 
prices and investors cannot predict future price changes by extrapolating prices or 
patterns of prices from the past.15
Tests of whether securities markets are weak-  form efficient require looking at 
patterns of prices. One approach is to see whether there is any serial correlation in 
security returns, which would imply a predictable pattern.16 Although there is some 
weak correlation in daily security returns, there is not enough correlation to make 
this a profitable trading rule after considering transaction costs.
An alternative approach to test weak-  form efficiency is to examine specific trading 
rules that attempt to exploit historical trading data. If any such trading rule consis -

tently generates abnormal risk-  adjusted returns after trading costs, this evidence will 
contradict weak-  form efficiency. This approach is commonly associated with technical 
analysis , which involves the analysis of historical trading information (primarily pric -
ing and volume data) in an attempt to identify recurring patterns in the trading data 
that can be used to guide investment decisions. Many technical analysts, also referred 
to as “technicians, ” argue that many movements in stock prices are based, in large 
part, on psychology. Many technicians attempt to predict how market participants 
will behave, based on analyses of past behavior, and then trade on those predictions. 
Technicians often argue that simple statistical tests of trading rules are not conclusive 
because they are not applied to the more sophisticated trading strategies that can be 
used and that the research excludes the technician’s subjective judgment. Thus, it is

difficult to definitively refute this assertion because there are an unlimited number 
of possible technical trading rules.
Can technical analysts profit from trading on past trends? Overall, the evidence 
indicates that investors cannot consistently earn abnormal profits using past prices or 
other technical analysis strategies in developed markets.17 Some evidence suggests, 
however, that there are opportunities to profit on technical analysis in countries with 
developing markets, including Hungary, Bangladesh, and Turkey, among others.18
3.2 Semi-  Strong Form
In a semi-  strong-  form efficient market , prices reflect all publicly known and available 
information. Publicly available information includes financial statement data (such as 
earnings, dividends, corporate investments, changes in management, etc.) and financial 
market data (such as closing prices, shares traded, etc.). Therefore, the semi-  strong

form of market efficiency encompasses the weak form. In other words, if a market is 
semi-  strong efficient, then it must also be weak-  form efficient. A market that quickly 
incorporates all publicly available information into its prices is semi-  strong efficient.
In a semi-  strong market, efforts to analyze publicly available information are futile. 
That is, analyzing earnings announcements of companies to identify underpriced or 
overpriced securities is pointless because the prices of these securities already reflect 
all publicly available information. If markets are semi-  strong efficient, no single investor 
has access to information that is not already available to other market participants, 
15 Market efficiency should not be confused with the random walk hypothesis, in which price changes 
over time are independent of one another. A random walk model is one of many alternative expected return

generating models. Market efficiency does not require that returns follow a random walk.
16 Serial correlation is a statistical measure of the degree to which the returns in one period are related 
to the returns in another period.
17 Bessembinder and Chan (1998) and Fifield, Power, and Sinclair (2005).
18 Fifield, Power, and Sinclair (2005), Chen and Li (2006), and Mobarek, Mollah, and Bhuyan (2008).

Reading 46 ■ Market Efficiency 126
and as a consequence, no single investor can gain an advantage in predicting future 
security prices. In a semi-  strong efficient market, prices adjust quickly and accurately 
to new information. Suppose a company announces earnings that are higher than 
expected. In a semi-  strong efficient market, investors would not be able to act on this 
announcement and earn abnormal returns.
A common empirical test of investors’ reaction to information releases is the event 
study. Suppose a researcher wants to test whether investors react to the announce -
ment that the company is paying a special dividend. The researcher identifies a sample 
period and then those companies that paid a special dividend in the period and the 
date of the announcement. Then, for each company’s stock, the researcher calculates 
the expected return on the share for the event date. This expected return may be based

on many different models, including the capital asset pricing model, a simple market 
model, or a market index return. The researcher calculates the excess return as the 
difference between the actual return and the expected return. Once the researcher 
has calculated the event’s excess return for each share, statistical tests are conducted 
to see whether the abnormal returns are statistically different from zero. The process 
of an event study is outlined in Exhibit 1.
Exhibit 1   The Event Study Process
Identify the period of study
Identify the stocks associated with the event within the study period
Estimate the expected return for each company for the announcement 
Calculate the excess return for each company in the sample as the actual
return on the announcement date, less the expected return
Perform statistical analyses on the excess returns in the sample to see
whether these returns are different from zero
How do event studies relate to efficient markets? In a semi-  strong efficient mar -

ket, share prices react quickly and accurately to public information. Therefore, if the 
information is good news, such as better-  than-  expected earnings, one would expect 
the company’s shares to increase immediately at the time of the announcement; if it 
is bad news, one would expect a swift, negative reaction. If actual returns exceed what 
is expected in absence of the announcement and these returns are confined to the 
announcement period, then they are consistent with the idea that market prices react 
quickly to new information. In other words, the finding of excess returns at the time 
of the announcement does not necessarily indicate market inefficiency. In contrast, 
the finding of consistent excess returns following the announcement would suggest 
a trading opportunity. Trading on the basis of the announcement—that is, once the 
announcement is made—would not, on average, yield abnormal returns.

Forms of Market Efficiency 127
EXAMPLE 6   
Information Arrival and Market Reaction
Consider an example of a news item and its effect on a share’s price. In 
June 2008, the US Federal Trade Commission (FTC) began an investigation of 
Intel Corporation regarding non-  competitiveness, and on 16 December 2009, 
the FTC announced that it was suing Intel over non-  competitive issues. This 
announcement was made before the market opened for trading on 16 December.
Intel stock closed at $19.78 on 15 December 2009 but opened at $19.50 on 16 
December. The stock then traded in the range from $19.45 to $19.68 within the 
first half hour as the news of the suit and Intel’s initial response were spreading 
among investors. Exhibit 2 illustrates the price of Intel for the first 90 minutes 
of trading on 16 December.
Exhibit 2   Price of Intel: 16 December 2009
$19.70
$19.65
$19.60
$19.55
$19.50
$19.45
$19.40
$19.35
$19.30
$19.25
TimePrice per share
9:30
9:34
9:38
9:42
9:46
9:50
9:54
9:58
10:02
10:06
10:10
10:14
10:18
10:22
10:26
10:30

9:54
9:58
10:02
10:06
10:10
10:14
10:18
10:22
10:26
10:30
10:34
10:38
10:42
10:46
10:50
10:54
10:58
Source:  Yahoo! Finance.
Is the fact that the price of Intel moves up immediately and then comes down 
indicative of an inefficiency regarding information? Not necessarily. Does it mean 
that investors overreacted? Not necessarily. During the morning, both before 
and after the market opened, news flowed about the lawsuit and the company’s 
reaction to the lawsuit. The price of the shares reflects investors’ reactions to 
this news. Why didn’t Intel’s shares simply move to a new level and stay there? 
Because 1) information continued to flow during the day on Intel and inves -
tors’ estimate of the importance of this news on Intel’s stock value continued 
to change, and 2) other news, related to other events and issues (such as the 
economy), affected stock prices.
Researchers have examined many different company-  specific information events,

including stock splits, dividend changes, and merger announcements, as well as 
economy-  wide events, such as regulation changes and tax rate changes. The results

Reading 46 ■ Market Efficiency 128
of most research are consistent with the view that developed securities markets might 
be semi-  strong efficient. But some evidence suggests that the markets in developing 
countries may not be semi-  strong efficient.19
3.3 Strong Form
In a strong-  form efficient market , security prices fully reflect both public and 
private information. A market that is strong-  form efficient is, by definition, also 
semi-  strong- and weak-  form efficient. In the case of a strong-  form efficient market, 
insiders would not be able to earn abnormal returns from trading on the basis of 
private information. A strong-  form efficient market also means that prices reflect all 
private information, which means that prices reflect everything that the management 
of a company knows about the financial condition of the company that has not been 
publicly released. However, this is not likely because of the strong prohibitions against

insider trading that are found in most countries. If a market is strong-  form efficient, 
those with insider information cannot earn abnormal returns.
Researchers test whether a market is strong-  form efficient by testing whether 
investors can earn abnormal profits by trading on nonpublic information. The results 
of these tests are consistent with the view that securities markets are not strong-  form 
efficient; many studies have found that abnormal profits can be earned when nonpublic 
information is used.20
3.4 Implications of the Efficient Market Hypothesis
The implications of efficient markets to investment managers and analysts are import -
ant because they affect the value of securities and how these securities are managed. 
Several implications can be drawn from the evidence on efficient markets for devel -
oped markets:
■■Securities markets are weak-  form efficient, and therefore, investors cannot earn 
abnormal returns by trading on the basis of past trends in price.

■■Securities markets are semi-  strong efficient, and therefore, analysts who collect 
and analyze information must consider whether that information is already 
reflected in security prices and how any new information affects a security’s 
value.21
■■Securities markets are not strong-  form efficient because securities laws are 
intended to prevent exploitation of private information.
3.4.1  Fundamental Analysis
Fundamental analysis  is the examination of publicly available information and the 
formulation of forecasts to estimate the intrinsic value of assets. Fundamental analysis 
involves the estimation of an asset’s value using company data, such as earnings and 
sales forecasts, and risk estimates as well as industry and economic data, such as eco -
nomic growth, inflation, and interest rates. Buy and sell decisions depend on whether 
the current market price is less than or greater than the estimated intrinsic value.

19 See Gan, Lee, Hwa, and Zhang (2005) and Raja, Sudhahar, and Selvam (2009).
20 Evidence that finds that markets are not strong-  form efficient include Jaffe (1974) and Rozeff and 
Zaman (1988).
21 In the case of the Intel example, this implication would mean estimating how the actual filing of the 
lawsuit and the company’s reaction to the lawsuit affect the value of Intel, while keeping in mind that the 
expectation of a lawsuit was already impounded in Intel’s stock price.

Market Pricing Anomalies 129
The semi-  strong form of market efficiency says that all available public information 
is reflected in current prices. So, what good is fundamental analysis? Fundamental 
analysis is necessary in a well-  functioning market because this analysis helps the 
market participants understand the value implications of information. In other words, 
fundamental analysis facilitates a semi-  strong efficient market by disseminating value-  
relevant information. And, although fundamental analysis requires costly information, 
this analysis can be profitable in terms of generating abnormal returns if the analyst 
creates a comparative advantage with respect to this information.22
3.4.2  Technical Analysis
Investors using technical analysis  attempt to profit by looking at patterns of prices 
and trading volume. Although some price patterns persist, exploiting these patterns 
may be too costly and, hence, would not produce abnormal returns.

Consider a situation in which a pattern of prices exists. With so many investors 
examining prices, this pattern will be detected. If profitable, exploiting this pattern 
will eventually affect prices such that this pattern will no longer exist; it will be arbi -
traged away. In other words, by detecting and exploiting patterns in prices, technical 
analysts assist markets in maintaining weak-  form efficiency. Does this mean that 
technical analysts cannot earn abnormal profits? Not necessarily, because there may 
be a possibility of earning abnormal profits from a pricing inefficiency. But would it 
be possible to earn abnormal returns on a consistent basis from exploiting such a 
pattern? No, because the actions of market participants will arbitrage this opportunity 
quickly, and the inefficiency will no longer exist.
3.4.3  Portfolio Management
If securities markets are weak-  form and semi-  strong-  form efficient, the implication is

that active trading, whether attempting to exploit price patterns or public information, 
is not likely to generate abnormal returns. In other words, portfolio managers cannot 
beat the market on a consistent basis, so therefore, passive portfolio management 
should outperform active portfolio management. Researchers have observed that 
mutual funds do not, on average, outperform the market on a risk-  adjusted basis.23 
Mutual funds perform, on average, similar to the market before considering fees and 
expenses and perform worse than the market, on average, once fees and expenses are 
considered. Even if a mutual fund is not actively managed, there are costs to managing 
these funds, which reduces net returns.
So, what good are portfolio managers? The role of a portfolio manager is not nec -
essarily to beat the market but, rather, to establish and manage a portfolio consistent 
with the portfolio’s objectives, with appropriate diversification and asset allocation,

while taking into consideration the risk preferences and tax situation of the investor.
MARKET PRICING ANOMALIES
Although considerable evidence shows that markets are efficient, researchers have 
identified a number of apparent market inefficiencies or anomalies. These market 
anomalies, if persistent, are exceptions to the notion of market efficiency. Researchers 4
22 Brealey (1983).
23 See Malkiel (1995). One of the challenges to evaluating mutual fund performance is that the researcher 
must control for survivorship bias.

Reading 46 ■ Market Efficiency 130
conclude that a market anomaly  may be present if a change in the price of an asset 
or security cannot directly be linked to current relevant information known in the 
market or to the release of new information into the market. 
The validity of any evidence supporting the potential existence of a market inef -
ficiency or anomaly must be consistent  over reasonably long periods. Otherwise, a 
detected market anomaly may largely be an artifact of the sample period chosen. In the 
widespread search for discovering profitable anomalies, many findings could simply 
be the product of a process called data mining , also known as data snooping . In 
generally accepted research practice, an initial hypothesis is developed which is based 
on economic rationale. Tests are then conducted on objectively selected data to either 
confirm or reject the original hypothesis. However, with data mining the process is

typically reversed: data are examined with the intent to develop a hypothesis, instead 
of developing a hypothesis first. This is done by analyzing data in various manners, 
and even utilizing different empirical approaches until you find support for a desired 
result, in this case a profitable anomaly. 
Can researchers look back on data and find a trading strategy that would have 
yielded abnormal returns? Absolutely. Enough data snooping often can detect a trading 
strategy that would have worked in the past by chance alone. But in an efficient mar -
ket, such a strategy is unlikely to generate abnormal returns on a consistent basis in 
the future. Also, although identified anomalies may appear to produce excess returns, 
it is generally difficult to profitably exploit the anomalies after accounting for risk, 
trading costs, and so on.
Several well-  known anomalies are listed in Exhibit  3. This list is by no means

exhaustive, but it provides information on the breadth of the anomalies. A few of 
these anomalies are discussed in more detail in the following sections. The anomalies 
are placed into categories based on the research method that identified the anom -
aly. Time-  series anomalies were identified using time series of data. Cross-  sectional 
anomalies were identified based on analyzing a cross section of companies that differ 
on some key characteristics. Other anomalies were identified by a variety of means, 
including event studies.
Exhibit 3   Sampling of Observed Pricing Anomalies
Time Series Cross-  Sectional Other
January effect Size effect Closed-  end fund discount
Day-  of- the- week effect Value effect Earnings surprise
Weekend effect Book-  to- market ratios Initial public offerings
Turn-  of- the- month effect P/E ratio effect Distressed securities effect
Holiday effect Value Line enigma Stock splits
Time-  of- day effect Super Bowl
Momentum
Overreaction
4.1 Time-  Series Anomalies

Momentum
Two of the major categories of time-  series anomalies that have been documented are 
1) calendar anomalies and 2) momentum and overreaction anomalies.

Market Pricing Anomalies 131
4.1.1  Calendar Anomalies
In the 1980s, a number of researchers reported that stock market returns in January 
were significantly higher compared to the rest of the months of the year, with most 
of the abnormal returns reported during the first five trading days in January. Since 
its first documentation in the 1980s, this pattern, known as the January effect , has 
been observed in most equity markets around the world. This anomaly is also known 
as the turn-  of- the-  year effect , or even often referred to as the “small firm in January 
effect” because it is most frequently observed for the returns of small market capi -
talization stocks.24 
The January effect contradicts the efficient market hypothesis because excess 
returns in January are not attributed to any new and relevant information or news. A 
number of reasons have been suggested for this anomaly, including tax-  loss selling.

Researchers have speculated that, in order to reduce their tax liabilities, investors sell 
their “loser” securities in December for the purpose of creating capital losses, which 
can then be used to offset any capital gains. A related explanation is that these losers 
tend to be small-  cap stocks with high volatility.25 This increased supply of equities in 
December depresses their prices, and then these shares are bought in early January at 
relatively attractive prices. This demand then drives their prices up again. Overall, the 
evidence indicates that tax-  loss selling may account for a portion of January abnormal 
returns, but it does not explain all of it.
Another possible explanation for the anomaly is so-  called “window dressing” , a 
practice in which portfolio managers sell their riskier securities prior to 31 December. 
The explanation is as follows: many portfolio managers prepare the annual reports

of their portfolio holdings as of 31 December. Selling riskier securities is an attempt 
to make their portfolios appear less risky. After 31 December, a portfolio manager 
would then simply purchase riskier securities in an attempt to earn higher returns. 
However, similar to the tax-  loss selling hypothesis, the research evidence in support 
of the window dressing hypothesis explains some, but not all, of the anomaly.
Recent evidence for both stock and bond returns suggests that the January effect is 
not persistent and, therefore, is not a pricing anomaly. Once an appropriate adjustment 
for risk is made, the January “effect” does not produce abnormal returns.26
Several other calendar effects, including the day-  of- the- week and the weekend 
effects,27 have been found. These anomalies are summarized in Exhibit 4.28 But like the 
size effect, which will be described later, most of these anomalies have been eliminated

over time. One view is that the anomalies have been exploited such that the effect 
has been arbitraged away. Another view, however, is that increasingly sophisticated 
statistical methodologies fail to detect pricing inefficiencies.
24 There is also evidence of a January effect in bond returns that is more prevalent in high-  yield corporate 
bonds, similar to the small-  company effect for stocks.
25 See Roll (1983).
26 See, for example, Kim (2006).
27 For a discussion of several of these anomalous patterns, see Jacobs and Levy (1988).
28 The weekend effect consists of a pattern of returns around the weekend: abnormal positive returns 
on Fridays followed by abnormally negative returns on Mondays. This is a day-  of- the- week effect that 
specifically links Friday and Monday returns. It is interesting to note that in 2009, the weekend effect in 
the United States was inverted, with 80 percent of the gains from March 2009 onward coming from the 
first trading day of the week.

Reading 46 ■ Market Efficiency 132
Exhibit 4   Calendar-  Based Anomalies
Anomaly Observation
Turn-  of- the- month effect Returns tend to be higher on the last trading day of the 
month and the first three trading days of the next month.
Day-  of- the- week effect The average Monday return is negative and lower than 
the average returns for the other four days, which are all 
positive.
Weekend effect Returns on weekends tend to be lower than returns on 
weekdays.
Holiday effect Returns on stocks in the day prior to market holidays 
tend to be higher than other days.
4.1.2  Momentum and Overreaction Anomalies
Momentum anomalies relate to short-  term share price patterns. One of the earliest 
studies to identify this type of anomaly was conducted by Werner DeBondt and 
Richard Thaler, who argued that investors overreact to the release of unexpected 
public information.29 Therefore, stock prices will be inflated (depressed) for those

companies releasing good (bad) information. This anomaly has become known as 
the overreaction effect. Using the overreaction effect, they proposed a strategy that 
involved buying “loser” portfolios and selling “winner” portfolios. They defined stocks 
as winners or losers based on their total returns over the previous three- to five-  year 
period. They found that in a subsequent period, the loser portfolios outperformed 
the market, while the winner portfolios underperformed the market. Similar patterns 
have been documented in many, but not all, global stock markets as well as in bond 
markets. One criticism is that the observed anomaly may be the result of statistical 
problems in the analysis.
A contradiction to weak-  form efficiency occurs when securities that have expe -
rienced high returns in the short term tend to continue to generate higher returns 
in subsequent periods.30 Empirical support for the existence of momentum in stock

returns in most stock markets around the world is well documented. If investors 
can trade on the basis of momentum and earn abnormal profits, then this anomaly 
contradicts the weak form of the efficient market hypothesis because it represents a 
pattern in prices that can be exploited by simply using historical price information.31
Researchers have argued that the existence of momentum is rational and not 
contrary to market efficiency because it is plausible that there are shocks to the 
expected growth rates of cash flows to shareholders and that these shocks induce a 
serial correlation that is rational and short lived.32 In other words, having stocks with 
some degree of momentum in their security returns may not imply irrationality but, 
rather, may reflect prices adjusting to a shock in growth rates.
29 DeBondt and Thaler (1985).
30 Notice that this pattern lies in sharp contrast to DeBondt and Thaler’s reversal pattern that is displayed

over longer periods of time. In theory, the two patterns could be related. In other words, it is feasible that 
prices are bid up extremely high, perhaps too high, in the short term for companies that are doing well. 
In the longer term (three-  to- five years), the prices of these short-  term winners correct themselves and 
they do poorly.
31 Jegadeesh and Titman (2001).
32 Johnson (2002).

Market Pricing Anomalies 133
4.2 Cross-  Sectional Anomalies
Two of the most researched cross-  sectional anomalies in financial markets are the 
size effect and the value effect.
4.2.1  Size Effect
The size effect results from the observation that equities of small-  cap companies 
tend to outperform equities of large-  cap companies on a risk-  adjusted basis. Many 
researchers documented a small-  company effect soon after the initial research was 
published in 1981. This effect, however, was not apparent in subsequent studies.33 
Part of the reason that the size effect was not confirmed by subsequent studies may 
be because of the fact that if it were truly an anomaly, investors acting on this effect 
would reduce any potential returns. But some of the explanation may simply be that 
the effect as originally observed was a chance outcome and, therefore, not actually 
an inefficiency.
4.2.2  Value Effect
A number of global empirical studies have shown that value stocks, which are gen -

erally referred to as stocks that have below-  average price-  to- earnings (P/E) and 
market-  to- book (M/B) ratios, and above-  average dividend yields, have consistently 
outperformed growth stocks over long periods of time.34 If the effect persists, the value 
stock anomaly contradicts semi-  strong market efficiency because all the information 
used to categorize stocks in this manner is publicly available.
Fama and French developed a three-  factor model to predict stock returns.35 In 
addition to the use of market returns as specified by the capital asset pricing model 
(CAPM), the Fama and French model also includes the size of the company as mea -
sured by the market value of its equity and the company’s book value of equity divided 
by its market value of equity, which is a value measure. The Fama and French model 
captures risk dimensions related to stock returns that the CAPM model does not 
consider. Fama and French find that when they apply the three-  factor model instead

of the CAPM, the value stock anomaly disappears.
4.3 Other Anomalies
A number of additional anomalies has been documented in the financial markets, 
including the existence of closed-  end investment fund discounts, price reactions to 
the release of earnings information, returns of initial public offerings, and the pre -
dictability of returns based on prior information.
4.3.1  Closed-  End Investment Fund Discounts
A closed-  end investment fund issues a fixed number of shares at inception and does 
not sell any additional shares after the initial offering. Therefore, the fund capitalization 
is fixed unless a secondary public offering is made. The shares of closed-  end funds 
trade on stock markets like any other shares in the equity market (i.e., their prices are 
determined by supply and demand).
33 Although a large number of studies documents a small-  company effect, these studies are concentrated

in a period similar to that of the original research and, therefore, use a similar data set. The key to whether 
something is a true anomaly is persistence in out-  of- sample tests. Fama and French (2008) document that 
the size effect is apparent only in microcap stocks but not in small- and large-  cap stocks and these microcap 
stocks may have a significant influence in studies that document a size effect.
34 For example, see Capaul, Rowley, and Sharpe (1993) and Fama and French (1998).
35 Fama and French (1995).

Reading 46 ■ Market Efficiency 134
Theoretically, these shares should trade at a price approximately equal to their 
net asset value (NAV) per share, which is simply the total market value of the fund’s 
security holdings less any liabilities divided by the number of shares outstanding. An 
abundance of research, however, has documented that, on average, closed-  end funds 
trade at a discount from NAV. Most studies have documented average discounts in 
the 4–10 percent range, although individual funds have traded at discounts exceeding 
50 percent and others have traded at large premiums.36
The closed-  end fund discount presents a puzzle because conceptually, an investor 
could purchase all the shares in the fund, liquidate the fund, and end up making a 
profit. Some researchers have suggested that these discounts are attributed to man -
agement fees or expectations of the managers’ performance, but these explanations

are not supported by the evidence.37 An alternative explanation for the discount is 
that tax liabilities are associated with unrealized capital gains and losses that exist 
prior to when the investor bought the shares, and hence, the investor does not have 
complete control over the timing of the realization of gains and losses.38 Although the 
evidence supports this hypothesis to a certain extent, the tax effect is not large enough 
to explain the entire discount. Finally, it has often been argued that the discounts exist 
because of liquidity problems and errors in calculating NAV. The illiquidity explanation 
is plausible if shares are recorded at the same price as more liquid, publicly traded 
stocks; some evidence supports this assertion. But as with tax reasons, liquidity issues 
explain only a portion of the discount effect.
Can these discounts be exploited to earn abnormal returns if transaction costs

are taken into account? No. First, the transaction costs involved in exploiting the dis -
count—buying all the shares and liquidating the fund—would eliminate any profit.39 
Second, these discounts tend to revert to zero over time. Hence, a strategy to trade 
on the basis of these discounts would not likely be profitable.40
4.3.2  Earnings Surprise
Although most event studies have supported semi-  strong market efficiency, some 
researchers have provided evidence that questions semi-  strong market efficiency. 
One of these studies relates to the extensively examined adjustment of stock prices 
to earnings announcements.41 The unexpected part of the earnings announcement, 
or earnings surprise , is the portion of earnings that is unanticipated by investors 
and, according to the efficient market hypothesis, merits a price adjustment. Positive 
(negative) surprises should cause appropriate and rapid price increases (decreases).

Several studies have been conducted using data from numerous markets around the 
world. Most of the results indicate that earnings surprises are reflected quickly in stock 
prices, but the adjustment process is not always efficient. In particular, although a 
substantial adjustment occurs prior to and at the announcement date, an adjustment 
also occurs after the announcement.42
As a result of these slow price adjustments, companies that display the largest 
positive earnings surprises subsequently display superior stock return performance, 
whereas poor subsequent performance is displayed by companies with low or negative 
36 See Dimson and Minio-  Kozerski (1999) for a review of this literature.
37 See Lee, Sheifer, and Thaler (1990).
38 The return to owners of closed-  end fund shares has three parts: 1) the price appreciation or depreciation 
of the shares themselves, 2) the dividends earned and distributed to owners by the fund, and 3) the capital

gains and losses earned by the fund that are distributed by the fund. The explanation of the anomalous 
pricing has to do with the timing of the distribution of capital gains.
39 See, for example, the study by Pontiff (1996), which shows how the cost of arbitraging these discounts 
eliminates the profit.
40 See Pontiff (1995).
41 See Jones, Rendleman, and Latané (1984).
42 Not surprisingly, it is often argued that this slow reaction contributes to a momentum pattern.

Market Pricing Anomalies 135
earnings surprises.43 This finding implies that investors could earn abnormal returns 
using publicly available information by buying stocks of companies that had positive 
earnings surprises and selling those with negative surprises.
Although there is support for abnormal returns associated with earnings surprises, 
and some support for such returns beyond the announcement period, there is also 
evidence indicating that these observed abnormal returns are an artifact of studies 
that do not sufficiently control for transaction costs and risk.44
4.3.3  Initial Public Offerings (IPOs)
When a company offers shares of its stock to the public for the first time, it does so 
through an initial public offering (or IPO). This offering involves working with an 
investment bank that helps price and market the newly issued shares. After the offering 
is complete, the new shares trade on a stock market for the first time. Given the risk

that investment bankers face in trying to sell a new issue for which the true price is 
unknown, it is perhaps not surprising to find that, on average, the initial selling price 
is set too low and that the price increases dramatically on the first trading day. The 
percentage difference between the issue price and the closing price at the end of the 
first day of trading is often referred to as the degree of underpricing.
The evidence suggests that, on average, investors who are able to buy the shares 
of an IPO at their offering price may be able to earn abnormal profits. For example, 
during the internet bubble of 1995–2000, many IPOs ended their first day of trading 
up by more than 100 percent. Such performance, however, is not always the case. 
Sometimes the issues are priced too high, which means that share prices drop on 
their first day of trading. In addition, the evidence also suggests that investors buying

after the initial offering are not able to earn abnormal profits because prices adjust 
quickly to the “true” values, which supports semi-  strong market efficiency. In fact, the 
subsequent long-  term performance of IPOs is generally found to be below average. 
Taken together, the IPO underpricing and the subsequent poor performance suggests 
that the markets are overly optimistic initially (i.e., investors overreact).
Some researchers have examined closely why IPOs may appear to have anomalous 
returns. Because of the small size of the IPO companies and the method of equally 
weighting the samples, what appears to be an anomaly may simply be an artifact of 
the methodology.45
4.3.4  Predictability of Returns Based on Prior Information
A number of researchers have documented that equity returns are related to prior 
information on such factors as interest rates, inflation rates, stock volatility, and div -
idend yields.46 But finding that equity returns are affected by changes in economic

fundamentals is not evidence of market inefficiency and would not result in abnormal 
trading returns.47
43 A similar pattern has been documented in the corporate bond market, where bond prices react too 
slowly to new company earnings announcements as well as to changes in company debt ratings.
44 See Brown (1997) for a summary of evidence supporting the existence of this anomaly. See Zarowin 
(1989) for evidence regarding the role of size in explaining abnormal returns to surprises; Alexander, Goff, 
and Peterson (1989) for evidence regarding transaction costs and unexpected earnings strategies; and 
Kim and Kim (2003) for evidence indicating that the anomalous returns can be explained by risk factors.
45 See Brav, Geczy, and Gompers (1995).
46 See, for example, Fama and Schwert (1977) and Fama and French (1988).
47 See Fama and French (2008).

Reading 46 ■ Market Efficiency 136
Furthermore, the relationship between stock returns and the prior information is 
not consistent over time. For example, in one study, the relationship between stock 
prices and dividend yields changed from positive to negative in different periods.48 
Hence, a trading strategy based on dividend yields would not yield consistent abnor -
mal returns.
4.4 Implications for Investment Strategies
Although it is interesting to consider the anomalies just described, attempting to benefit 
from them in practice is not easy. In fact, most researchers conclude that observed 
anomalies are not violations of market efficiency but, rather, are the result of statis -
tical methodologies used to detect the anomalies. As a result, if the methodologies 
are corrected, most of these anomalies disappear.49 Another point to consider is that 
in an efficient market, overreactions may occur, but then so do under-  reactions.50

Therefore, on average, the markets are efficient. In other words, investors face chal -
lenges when they attempt to translate statistical anomalies into economic profits. 
Consider the following quote regarding anomalies from the Economist  (“Frontiers of 
Finance Survey, ” 9 October 1993):
Many can be explained away. When transactions costs are taken into 
account, the fact that stock prices tend to over-  react to news, falling back 
the day after good news and bouncing up the day after bad news, proves 
unexploitable: price reversals are always within the bid-  ask spread. Others 
such as the small-  firm effect, work for a few years and then fail for a few 
years. Others prove to be merely proxies for the reward for risk taking. Many 
have disappeared since (and because) attention has been drawn to them.
It is difficult to envision entrusting your retirement savings to a manager whose 
strategy is based on buying securities on Mondays, which tends to have negative returns

on average, and selling them on Fridays. For one thing, the negative Monday returns 
are merely an average, so on any given week, they could be positive. In addition, such 
a strategy would generate large trading costs. Even more importantly, investors would 
likely be uncomfortable investing their funds in a strategy that has no compelling 
underlying economic rationale.
BEHAVIORAL FINANCE
Behavioral finance  examines investor behavior to understand how people make deci -
sions, individually and collectively. Behavioral finance does not assume that people 
consider all available information in decision-  making and act rationally by maximizing 
utility within budget constraints and updating expectations consistent with Bayes’ 
formula. The resulting behaviors may affect what is observed in the financial markets. 
In a broader sense, behavioral finance attempts to explain why individuals make 
the decisions that they do, whether these decisions are rational or irrational. The focus

of much of the work in this area is on the behavioral biases that affect investment 
decisions. The behavior of individuals, in particular their behavioral biases, has been 
offered as a possible explanation for a number of pricing anomalies. 5
48 Schwert (2003, Chapter 15).
49 Fama (1998).
50 This point is made by Fama (1998).

Behavioral Finance 137
Most asset-  pricing models assume that markets are rational and that the intrinsic 
value of a security reflects this rationality. But market efficiency and asset-  pricing 
models do not require that each individual is rational—rather, only that the market 
is rational. If individuals deviate from rationality, other individuals are assumed to 
observe this deviation and respond accordingly. These responses move the market 
toward efficiency. If this does not occur in practice, it may be possible to explain some 
market anomalies referencing observed behaviors and behavioral biases. 
5.1 Loss Aversion
In most financial models, the assumption is that investors are risk averse. Risk aver -
sion  refers to the tendency of people to dislike risk and to require higher expected 
returns to compensate for exposure to additional risk. Behavioral finance allows for 
the possibility that the dissatisfaction resulting from a loss exceeds the satisfaction

resulting from a gain of the same magnitude. Loss aversion  refers to the tendency of 
people to dislike losses more than they like comparable gains. This results in a strong 
preference for avoiding losses as opposed to achieving gains.51 Some argue that 
behavioral theories of loss aversion can explain observed overreaction in markets. If 
loss aversion is more important than risk aversion, researchers should observe that 
investors overreact.52 Although loss aversion can explain the overreaction anomaly, 
evidence also suggests that under reaction is just as prevalent as overreaction, which 
counters these arguments.
5.2 Herding
Herding behavior has been advanced as a possible explanation of under reaction and 
overreaction in financial markets. Herding  occurs when investors trade on the same 
side of the market in the same securities, or when investors ignore their own private 
information and/or analysis and act as other investors do. Herding  is clustered trad -

ing that may or may not be based on information.53 Herding may result in under- or 
over-  reaction to information depending upon the direction of the herd. 
5.3 Overconfidence
A behavioral bias offered to explain pricing anomalies is overconfidence. If investors 
are overconfident, they overestimate their ability to process and interpret information 
about a security. Overconfident investors may not process information appropriately, 
and if there is a sufficient number of these investors, stocks will be mispriced.54 But 
most researchers argue that this mispricing is temporary, with prices correcting even -
tually. If it takes a sufficiently long time for prices to become correctly priced and the 
mispricing is predictable, it may be possible for investors to earn abnormal profits.
Evidence has suggested that overconfidence results in mispricing for US, UK, 
German, French, and Japanese markets.55 This overconfidence, however, is predom -

inantly in higher-  growth companies, whose prices react slowly to new information.56
51 See DeBondt and Thaler (1985) and Tversky and Kahneman (1981).
52 See Fama (1998).
53 The term used when there is herding without information is “spurious herding. ”
54 Another aspect to overconfidence is that investors who are overconfident in their ability to select 
investments and manage a portfolio tend to use less diversification, investing in what is most familiar. 
Therefore, investor behavior may affect investment results—returns and risk—without implications for 
the efficiency of markets.
55 Scott, Stumpp, and Xu (2003) and Boujelbene Abbes, Boujelbene, and Bouri (2009).
56 Scott, Stumpp, and Xu (2003).

Reading 46 ■ Market Efficiency 138
5.4 Information Cascades
An application of behavioral theories to markets and pricing focuses on the role of 
personal learning in markets. Personal learning is what investors learn by observing 
outcomes of trades and what they learn from “conversations”—ideas shared among 
investors about specific assets and the markets.57 Social interaction and the resultant 
contagion is important in pricing and may explain such phenomena as price changes 
without accompanying news and mistakes in valuation.
Biases that investors possess can lead to herding behavior or information cas -
cades. Herding and information cascades are related but not identical concepts. An 
information cascade  is the transmission of information from those participants who 
act first and whose decisions influence the decisions of others. Those who are acting 
on the choices of others may be ignoring their own preferences in favor of imitating

the choices of others. In particular, information cascades may occur with respect to 
the release of accounting information because accounting information may be diffi -
cult to interpret and may be noisy. For example, the release of earnings is difficult to 
interpret because it is necessary to understand how the number was arrived at and 
noisy because it is uncertain what the current earnings imply about future earnings.
Information cascades may result in serial correlation of stock returns, which is 
consistent with overreaction anomalies. Do information cascades result in correct 
pricing? Some argue that if a cascade is leading toward an incorrect value, this cascade 
is “fragile” and will be corrected because investors will ultimately give more weight 
to public information or the trading of a recognized informed trader.58 Information 
cascades, although documented in markets, do not necessarily mean that investors 
can exploit knowledge of them as profitable trading opportunities.

Are information cascades rational? If the informed traders act first and uninformed 
traders imitate the informed traders, this behavior is consistent with rationality. The 
imitation trading by the uninformed traders may help the market incorporate relevant 
information and improve market efficiency.59 However, the imitation trading may lead 
to an overreaction to information. The empirical evidence indicates that information 
cascades are greater for a stock when the information quality regarding the company 
is poor.60 Information cascades may enhance the information available to investors.
5.5 Other Behavioral Biases
Other behavioral biases that have been put forth to explain observed investor behavior 
■■representativeness —investors assess new information and probabilities of out -
comes based on similarity to the current state or to a familiar classification;
■■mental accounting —investors keep track of the gains and losses for different

investments in separate mental accounts and treat those accounts differently;
■■conservatism —investors tend to be slow to react to new information and con -
tinue to maintain their prior views or forecasts; and
■■narrow framing —investors focus on issues in isolation and respond to the 
issues based on how the issues are posed.61
57 Hirshleifer and Teoh (2009).
58 Avery and Zemsky (1999).
59 Another alternative is that the uninformed traders are the majority of the market participants and the 
imitators are imitating not because they agree with the actions of the majority but because they are looking 
to act on the actions of the uninformed traders.
60 Avery and Zemsky (1999) and Bikhchandani, Hirshleifer, and Welch (1992).
61 For a review of these behavioral issues, see Hirshleifer (2001).

Summary 139
The basic idea behind behavioral finance is that investors are humans and, there -
fore, imperfect. These observed less than rational behaviors may help explain observed 
pricing anomalies. The beliefs investors have about a given asset’s value may not be 
homogeneous. But an issue, which is controversial, is whether these insights can 
help someone identify and exploit any mispricing. In other words, can investors use 
knowledge of behavioral biases to predict how asset prices will be affected and act 
based on the predictions to earn abnormal profits?
5.6 Behavioral Finance and Investors
Behavior biases can affect all market participants, from the novice investor to the 
most experienced investment manager. An understanding of behavioral finance can 
help market participants recognize their own and others’ behavioral biases. As a 
result of this recognition, they may be able to respond and make improved decisions, 
individually and collectively.

5.7 Behavioral Finance and Efficient Markets
The use of behavioral finance to explain observed pricing is an important part of the 
understanding of how markets function and how prices are determined. Whether there 
is a behavioral explanation for market anomalies remains a debate. Pricing anomalies 
are continually being uncovered, and then statistical and behavioral explanations are 
offered to explain these anomalies.
On the one hand, if investors must be rational for efficient markets to exist, then 
all the imperfections of human investors suggest that markets cannot be efficient. 
On the other hand, if all that is required for markets to be efficient is that investors 
cannot consistently beat the market on a risk-  adjusted basis, then the evidence does 
support market efficiency.
SUMMARY
This reading has provided an overview of the theory and evidence regarding market 
efficiency and has discussed the different forms of market efficiency as well as the

implications for fundamental analysis, technical analysis, and portfolio management. 
The general conclusion drawn from the efficient market hypothesis is that it is not 
possible to beat the market on a consistent basis by generating returns in excess of 
those expected for the level of risk of the investment.
Additional key points include the following:
■■The efficiency of a market is affected by the number of market participants and 
depth of analyst coverage, information availability, and limits to trading.
■■There are three forms of efficient markets, each based on what is considered 
to be the information used in determining asset prices. In the weak form, asset 
prices fully reflect all market data, which refers to all past price and trading 
volume information. In the semi-  strong form, asset prices reflect all publicly 
known and available information. In the strong form, asset prices fully reflect all 
information, which includes both public and private information.

■■Intrinsic value refers to the true value of an asset, whereas market value refers 
to the price at which an asset can be bought or sold. When markets are effi -
cient, the two should be the same or very close. But when markets are not 
efficient, the two can diverge significantly.

Reading 46 ■ Market Efficiency 140
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Reading 46 ■ Market Efficiency 142
1 In an efficient market, the change in a company’s share price is most likely  the 
result of:
A insiders’ private information.
B the previous day’s change in stock price.
C new information coming into the market.
2 Regulation that restricts some investors from participating in a market will most 
likely :
A impede market efficiency.
B not affect market efficiency.
C contribute to market efficiency.
3 With respect to efficient market theory, when a market allows short selling, the 
efficiency of the market is most likely  to:
4 Which of the following regulations will most likely  contribute to market effi -
ciency? Regulatory restrictions on:
A short selling.
B foreign traders.
C insiders trading with nonpublic information.
5 Which of the following market regulations will most likely  impede market 
efficiency?
A Restricting traders’ ability to short sell.
B Allowing unrestricted foreign investor trading.

C Penalizing investors who trade with nonpublic information.
6 If markets are efficient, the difference between the intrinsic value and market 
value of a company’s security is:
B zero.
7 The intrinsic value of an undervalued asset is:
A less than the asset’s market value.
B greater than the asset’s market value.
C the value at which the asset can currently be bought or sold.
8 The market value of an undervalued asset is:
A greater than the asset’s intrinsic value.
B the value at which the asset can currently be bought or sold.
C equal to the present value of all the asset’s expected cash flows.
9 With respect to the efficient market hypothesis, if security prices reflect only 
past prices and trading volume information, then the market is:
A weak-  form efficient.

Practice Problems 143
B strong-  form efficient.
C semi-  strong-  form efficient.
10 Which one of the following statements best describes the semi-  strong form of 
A Empirical tests examine the historical patterns in security prices.
B Security prices reflect all publicly known and available information.
C Semi-  strong-  form efficient markets are not necessarily weak-  form efficient.
11 If markets are semi-  strong efficient, standard fundamental analysis will yield 
abnormal trading profits that are:
B equal to zero.
12 If prices reflect all public and private information, the market is best described 
as:
13 If markets are semi-  strong-  form efficient, then passive portfolio management 
strategies are most likely  to:
A earn abnormal returns.
B outperform active trading strategies.
C underperform active trading strategies.

14 If a market is semi-  strong-  form efficient, the risk-  adjusted returns of a passively 
managed portfolio relative to an actively managed portfolio are most likely :
A lower.
B higher.
C the same.
15 Technical analysts assume that markets are:
B weak-  form inefficient.
16 Fundamental analysts assume that markets are:
A weak-  form inefficient.
B semi-  strong-  form efficient.
C semi-  strong-  form inefficient.
17 If a market is weak-  form efficient but semi-  strong-  form inefficient, then which 
of the following types of portfolio management is most likely  to produce abnor -
mal returns?
A Passive portfolio management.
B Active portfolio management based on technical analysis.
C Active portfolio management based on fundamental analysis.
18 An increase in the time between when an order to trade a security is placed and

when the order is executed most likely  indicates that market efficiency has:
A decreased.
B remained the same.

Reading 46 ■ Market Efficiency 144
C increased.
19 With respect to efficient markets, a company whose share price reacts gradually 
to the public release of its annual report most likely  indicates that the market 
where the company trades is:
A semi-  strong-  form efficient.
B subject to behavioral biases.
C receiving additional information about the company.
20 Which of the following is least likely  to explain the January effect anomaly?
A Tax-  loss selling.
B Release of new information in January.
C Window dressing of portfolio holdings.
21 If a researcher conducting empirical tests of a trading strategy using time series 
of returns finds statistically significant abnormal returns, then the researcher 
has most likely  found:
A a market anomaly.
B evidence of market inefficiency.
C a strategy to produce future abnormal returns.
22 Which of the following market anomalies is inconsistent with weak-  form mar -
ket efficiency?
A Earnings surprise.
B Momentum pattern.
C Closed-  end fund discount.

23 Researchers have found that value stocks have consistently outperformed 
growth stocks. An investor wishing to exploit the value effect should purchase 
the stock of companies with above-  average:
A dividend yields.
B market-  to- book ratios.
C price-  to- earnings ratios.
24 With respect to rational and irrational investment decisions, the efficient mar -
ket hypothesis requires:
A only that the market is rational.
B that all investors make rational decisions.
C that some investors make irrational decisions.
25 Observed overreactions in markets can be explained by an investor’s degree of:
A risk aversion.
B loss aversion.
C confidence in the market.
26 Like traditional finance models, the behavioral theory of loss aversion assumes 
that investors dislike risk; however, the dislike of risk in behavioral theory is 
assumed to be:
A leptokurtic.
B symmetrical.
C asymmetrical.

Solutions 145
SOLUTIONS
1 C is correct. Today’s price change is independent of the one from yesterday, and 
in an efficient market, investors will react to new, independent information as it 
is made public.
2 A is correct. Reducing the number of market participants can accentuate mar -
ket imperfections and impede market efficiency (e.g., restrictions on foreign 
investor trading).
3 A is correct. According to theory, reducing the restrictions on trading will allow 
for more arbitrage trading, thereby promoting more efficient pricing. Although 
regulators argue that short selling exaggerates downward price movements, 
empirical research indicates that short selling is helpful in price discovery.
4 C is correct. Regulation to restrict unfair use of nonpublic information encour -
ages greater participation in the market, which increases market efficiency. 
Regulators (e.g., US SEC) discourage illegal insider trading by issuing penalties 
to violators of their insider trading rules.

5 A is correct. Restricting short selling will reduce arbitrage trading, which pro -
motes market efficiency. Permitting foreign investor trading increases market 
participation, which makes markets more efficient. Penalizing insider trading 
encourages greater market participation, which increases market efficiency.
6 B is correct. A security’s intrinsic value and market value should be equal when 
markets are efficient.
7 B is correct. The intrinsic value of an undervalued asset is greater than the mar -
ket value of the asset, where the market value is the transaction price at which 
an asset can be currently bought or sold.
8 B is correct. The market value is the transaction price at which an asset can be 
currently bought or sold.
9 A is correct. The weak-  form efficient market hypothesis is defined as a market 
where security prices fully reflect all market data, which refers to all past price 
and trading volume information.

10 B is correct. In semi-  strong-  form efficient markets, security prices reflect all 
publicly available information.
11 B is correct. If all public information should already be reflected in the market 
price, then the abnormal trading profit will be equal to zero when fundamental 
analysis is used.
12 B is correct. The strong-  form efficient market hypothesis assumes all informa -
tion, public or private, has already been reflected in the prices.
13 B is correct. Costs associated with active trading strategies would be difficult to 
recover; thus, such active trading strategies would have difficulty outperforming 
passive strategies on a consistent after-  cost basis.
14 B is correct. In a semi-  strong-  form efficient market, passive portfolio strategies 
should outperform active portfolio strategies on a risk-  adjusted basis.
15 B is correct. Technical analysts use past prices and volume to predict future

prices, which is inconsistent with the weakest form of market efficiency (i.e., 
weak-  form market efficiency). Weak-  form market efficiency states that investors 
cannot earn abnormal returns by trading on the basis of past trends in price 
and volume.

Reading 46 ■ Market Efficiency 146
16 C is correct. Fundamental analysts use publicly available information to esti -
mate a security’s intrinsic value to determine if the security is mispriced, which 
is inconsistent with the semi-  strong form of market efficiency. Semi-  strong-  
form market efficiency states that investors cannot earn abnormal returns by 
trading based on publicly available information.
17 C is correct. If markets are not semi-  strong-  form efficient, then fundamental 
analysts are able to use publicly available information to estimate a security’s 
intrinsic value and identify misvalued securities. Technical analysis is not able 
to earn abnormal returns if markets are weak-  form efficient. Passive portfolio 
managers outperform fundamental analysis if markets are semi-  strong-  form 
efficient.
18 A is correct. Operating inefficiencies reduce market efficiency.
19 C is correct. If markets are efficient, the information from the annual report is

reflected in the stock prices; therefore, the gradual changes must be from the 
release of additional information.
20 B is correct. The excess returns in January are not attributed to any new infor -
mation or news; however, research has found that part of the seasonal pattern 
can be explained by tax-  loss selling and portfolio window dressing.
21 A is correct. Finding significant abnormal returns does not necessarily indicate 
that markets are inefficient or that abnormal returns can be realized by applying 
the strategy to future time periods. Abnormal returns are considered market 
anomalies because they may be the result of the model used to estimate the 
expected returns or may be the result of underestimating transaction costs or 
other expenses associated with implementing the strategy, rather than because 
of market inefficiency.
22 B is correct. Trading based on historical momentum indicates that price 
patterns exist and can be exploited by using historical price information. A

momentum trading strategy that produces abnormal returns contradicts the 
weak form of the efficient market hypothesis, which states that investors cannot 
earn abnormal returns on the basis of past trends in prices.
23 A is correct. Higher than average dividend yield is a characteristic of a value 
stock, along with low price-  to- earnings and low market-  to- book ratios. Growth 
stocks are characterized by low dividend yields and high price-  to- earnings and 
high market-  to- book ratios.
24 A is correct. The efficient market hypothesis and asset-  pricing models only 
require that the market is rational. Behavioral finance is used to explain some  of 
the market anomalies as irrational decisions.
25 B is correct. Behavioral theories of loss aversion can explain observed overreac -
tion in markets, such that investors dislike losses more than comparable gains 
(i.e., risk is not symmetrical).
26 C is correct. Behavioral theories of loss aversion allow for the possibility that

the dislike for risk is not symmetrical, which allows for loss aversion to explain 
observed overreaction in markets such that investors dislike losses more than 
they like comparable gains.

Equity Investments (2)
This study session focuses on the characteristics, analysis, and valuation of equity 
securities. Various equity types including public and private equities are described. The 
various industry classification approaches for global equities and useful frameworks 
for conducting industry and individual company analysis are presented. Coverage 
of the three main equity valuation approaches (present value, multiplier, and asset 
based) conclude the session.
Reading 47 Overview of Equity Securities  
by Ryan C. Fuhrmann, CFA, and Asjeet S. Lamba, PhD, 
CFA
Reading 48 Introduction to Industry and Company Analysis  
by Patrick W. Dorsey, CFA, Anthony M. Fiore, CFA, and 
Ian Rossa O’Reilly, CFA
Reading 49 Equity Valuation: Concepts and Basic Tools  
by John J. Nagorniak, CFA, and Stephen E. Wilcox, PhD, 
CFAEqUITY  INvEST mENTS
15

Overview of Equity Securities
by Ryan C. Fuhrmann, CFA, and Asjeet S. Lamba, PhD, CFA
Ryan C. Fuhrmann, CFA, is at Fuhrmann Capital LLC (USA). Asjeet S. Lamba, PhD, CFA, 
is at the University of Melbourne (Australia).
a. describe characteristics of types of equity securities;
b. describe differences in voting rights and other ownership 
characteristics among different equity classes;
c. distinguish between public and private equity securities;
d. describe methods for investing in non-  domestic equity securities;
e. compare the risk and return characteristics of different types of 
equity securities;
f. explain the role of equity securities in the financing of a 
company’s assets;
g. distinguish between the market value and book value of equity 
securities;
h. compare a company’s cost of equity, its (accounting) return on 
equity, and investors’ required rates of return.

Equity securities represent ownership claims on a company’s net assets. As an asset 
class, equity plays a fundamental role in investment analysis and portfolio manage -
ment because it represents a significant portion of many individual and institutional 
investment portfolios.
The study of equity securities is important for many reasons. First, the decision 
on how much of a client’s portfolio to allocate to equities affects the risk and return 
characteristics of the entire portfolio. Second, different types of equity securities have 
different ownership claims on a company’s net assets, which affect their risk and return 1READING
47

Reading 47 ■ Overview of Equity Securities 150
characteristics in different ways. Finally, variations in the features of equity securities 
are reflected in their market prices, so it is important to understand the valuation 
implications of these features.
This reading provides an overview of equity securities and their different features 
and establishes the background required to analyze and value equity securities in a 
global context. It addresses the following questions:
■■What distinguishes common shares from preference shares, and what purposes 
do these securities serve in financing a company’s operations?
■■What are convertible preference shares, and why are they often used to raise 
equity for unseasoned or highly risky companies?
■■What are private equity securities, and how do they differ from public equity 
securities?
■■What are depository receipts and their various types, and what is the rationale 
for investing in them?

■■What are the risk factors involved in investing in equity securities?
■■How do equity securities create company value?
■■What is the relationship between a company’s cost of equity, its return on 
equity, and investors’ required rate of return?
The remainder of this reading is organized as follows. Section 2 provides an overview 
of global equity markets and their historical performance. Section 3 examines the 
different types and characteristics of equity securities, and Section 4 outlines the dif -
ferences between public and private equity securities. Section 5 provides an overview 
of the various types of equity securities listed and traded in global markets. Section 6 
discusses the risk and return characteristics of equity securities. Section 7 examines 
the role of equity securities in creating company value and the relationship between 
a company’s cost of equity, its return on equity, and investors’ required rate of return.

The final section summarizes the reading.
EQUITY SECURITIES IN GLOBAL FINANCIAL MARKETS
This section highlights the relative importance and performance of equity securities 
as an asset class. We examine the total market capitalization and trading volume of 
global equity markets and the prevalence of equity ownership across various geo -
graphic regions. We also examine historical returns on equities and compare them 
to the returns on government bonds and bills.
Exhibit  1 summarizes the contributions of selected countries and geographic 
regions to global gross domestic product (GDP) and global equity market capitalization. 
Analysts can examine the relationship between equity market capitalization and GDP 
as an indicator of whether the global equity market (or a specific country’s or region’s 
equity market) is under, over, or fairly valued. Global equity markets expanded at twice 
the rate of global GDP between 1993 and 2004. At the beginning of 2008, global GDP

and equity market capitalization were nearly equal at approximately US$55 trillion.1 
This implies an equity market capitalization to GDP ratio of 100 percent, which was 
almost twice the long-  run average of 50  percent and indicates that global equity 
markets were overvalued at that time.2
1 EconomyWatch.Com http://www.economywatch.com/gdp/world-  gdp/.

Equity Securities in Global Financial Markets 151
Exhibit 1 illustrates the significant value that investors attach to publicly traded 
equities relative to the sum of goods and services produced globally every year. It 
shows the continued significance, and the potential over-  representation, of US equity 
markets relative to their contribution to global GDP . That is, while US equity markets 
contribute around 43 percent to the total capitalization of global equity markets, their 
contribution to the global GDP is only around 21 percent. Following the stock market 
turmoil in 2008, however, the market capitalization to GDP ratio of the United States 
fell to 59 percent, which is significantly lower than its long-  run average of 79 percent.
As equity markets outside the United States develop and become increasingly 
global, their total capitalization levels are expected to grow closer to their respective 
world GDP contributions. Therefore, it is important to understand and analyze equity

securities from a global perspective.
Exhibit 1   Country and Regional Contributions to Global GDP and Equity Market Capitalization (2007) 
Japan
6.6%
Japan
10.8%United Kingdom
3.3%
8.3%Canada
2.0%
Canada
3.8%Other Asia
3.7%Contribution to World GDP Contri bution to Global Sto ck Market Capitalization
Other Asia
4.3%Other Europe
3.3%Other Europe
5.2%
United StatesUnited States
43.4%EU
16.1%
EU
13.3%
21.3%Emerging Ma rkets
43.7%Emerging Ma rkets
10.9%
Source:  MacroMavens, IMF World Economic Outlook 2008 , Standard & Poor’s BMI Global Index weights.
Exhibit 2 lists the top 10 equity markets at the end of 2008 based on total market 
capitalization (in billions of US dollars), trading volume, and the number of listed 
companies.2 Note that the rankings differ based on the criteria used. For example, the 
top three markets based on total market capitalization are the NYSE Euronext (US), 
Tokyo Stock Exchange Group, and NASDAQ OMX; however, the top three markets

based on total US dollar trading volume are the Nasdaq OMX, NYSE Euronext (US), 
and London Stock Exchange, respectively.3 
2 The market capitalization of an individual stock is computed as the share price multiplied by the number 
of shares outstanding. The total market capitalization of an equity market is the sum of the market capital -
izations of each individual stock listed on that market. Similarly, the total trading volume of an equity market 
is computed by value weighting the total trading volume of each individual stock listed on that market. Total 
dollar trading volume is computed as the average share price multiplied by the number of shares traded.
3 NASDAQ is the acronym for the National Association of Securities Dealers Automated Quotations.

Reading 47 ■ Overview of Equity Securities 152
Exhibit 2   Equity Markets Ranked by Total Market Capitalization at the End 
of 2008 (Billions of US Dollars)
Rank Name of MarketTotal US 
Dollar Market 
CapitalizationTotal US 
Dollar 
Trading 
VolumeNumber 
of Listed 
Companies
1 NYSE Euronext (US) $9,208.9 $33,638.9 3,011
2 Tokyo Stock Exchange 
Group$3,115.8 $5,607.3 2,390
3 NASDAQ OMX $2,396.3 $36,446.5 2,952
4 NYSE Euronext (Europe) $2,101.7 $4,411.2 1,002
5 London Stock Exchange $1,868.2 $6,271.5 3,096
6 Shanghai Stock Exchange $1,425.4 $2,600.2 864
7 Hong Kong Exchanges $1,328.8 $1,629.8 1,261
8 Deutsche Börse $1,110.6 $4,678.8 832
9 TSX Group $1,033.4 $1,716.2 3,841
10 BME Spanish Exchanges $948.4 $2,410.7 3,576
Source:  Adapted from the World Federation of Exchanges 2008 Report  (see http://www.world-  
exchanges.org). Note that market capitalization by company is calculated by multiplying its stock 
price by the number of shares outstanding. The market’s overall capitalization is the aggregate of

the market capitalizations of all companies traded on that market. The number of listed compa -
nies includes both domestic and foreign companies whose shares trade on these markets.
Exhibit 3 compares the real (or inflation-  adjusted) compounded returns on gov -
ernment bonds, government bills, and equity securities in 19 countries plus the world 
index (“Wld”), the world ex-  US (“WxU”), and Europe (“Eur”) during the 112 years 
1900–2011.4 In real terms, government bonds and bills have essentially kept pace 
with the inflation rate, earning annualized real returns of less than 2 percent in most 
countries.5 By comparison, real returns in equity markets have generally been above 
3.5 percent per year in most markets—with a world average return just over 5 percent 
and a world average return excluding the United States just under 5 percent. During 
this period, Australia and South Africa were the best performing markets followed 
by the United States, Sweden, and New Zealand.

4 The real return for a security is approximated by taking the nominal return and subtracting the observed 
inflation rate in that country.
5 The exceptions are Belgium, Italy, Germany, France, Japan, and England—where the average real returns 
on government bonds and/or bills have been negative. In general, that performance reflects the very high 
inflation rates in these countries during the World War years.

Equity Securities in Global Financial Markets 153
Exhibit 3   Real Returns on Global Equity Securities, Bonds, and Bills During 1900–2011
Equities Bonds BillsIta Bel Ger Fra Spa Jap Ire Nor Swi Eur Net Den U.K. Can NZ Swe SAf Aus Fin WxU4.8
Wld5.4
U.S.6.2
6
–4–2024
Source:  Dimson, Marsh, and Staunton (2012a). This chart is updated annually and can be found at www.tinyurl.com/DMSsourcebook.
Exhibit 4 focuses on the real compounded rates of return on equity securities in 
the same 19 countries over 1900–2011 Only the South African and Australian equity 
markets were better investments in real terms for the US investor than their own 
Exhibit 4   Real Annualized Equity Returns (%) in Local Currency and US Dollars, 1900–2011
7
–10123456
Local real return USD real return Real exchange rate vs. USDIta Fra Bel Ger Spa Ire Jap Nor Swi Fin Net U.K. Den NewZ Can SAf Aus U.S. Swe

The volatility in equity market returns is further highlighted in Exhibit 5, which 
shows the average performance of the worldwide equity index (in US dollars), bonds, 
and bills (bonds and bills are based on US data).

Reading 47 ■ Overview of Equity Securities 154
These observations and historical data are consistent with the concept that the 
return on securities is directly related to risk level. That is, equity securities have higher 
risk levels when compared with government bonds and bills, they earn higher rates 
of return to compensate investors for these higher risk levels, and they also tend to 
be more volatile over time.
Exhibit 5   Returns and Risk of Major Asset Classes since 1900
25
–505101520
Equities Bonds US BillsReal return (%) Nominal return (%) Standard deviation1.70.94.8
3.95.417.7
10.4
4.78.5
Source:  Dimson, Marsh, and Staunton (2012a). This chart is updated annually and can be found 
at www.tinyurl.com/DMSsourcebook.
Given the high risk levels associated with equity securities, it is reasonable to 
expect that investors’ tolerance for risk will tend to differ across equity markets. This 
is illustrated in Exhibit 6, which shows the results of a series of studies conducted by

the Australian Securities Exchange on international differences in equity ownership. 
During the 2000–2008 period, equity ownership as a percentage of the population was 
lowest in South Korea (averaging 7.5 percent), followed by Germany (16.6 percent) 
and Sweden (21 percent). In contrast, Australia, Canada, and the United States had 
the highest equity ownership as a percentage of the population (averaging almost 
50 percent). In addition, there has been a relative decline in share ownership in several 
countries over recent years, which is not surprising given the recent overall uncer -
tainty in global economies and the volatility in equity markets that this uncertainty 
has created.
Exhibit 6   International Comparisons of Stock Ownership: 2000–20086
2000 2002 2004 2006 2008
Australia – Direct/Indirect 52% 50% 55% 46% 41%
Canada – Shares/Funds 49 46 49 N/A N/A
Germany – Shares/Funds 19 18 16 16 14

6 The percentages reported in the exhibit are based on samples of the adult population in each country 
who own equity securities either directly or indirectly through investment or retirement funds. For example, 
41 percent of the adult population of Australia in 2008 (approximately 6.7 million people) owned equity 
securities either directly or indirectly. As noted in the study, it is not appropriate to make absolute com -
parisons across countries given the differences in methodology, sampling, timing, and definitions that have 
been used in different countries. However, trends across different countries can be identified.

Types and Characteristics of Equity Securities 155
New Zealand 24 N/A 23 26 N/A
South Korea – Shares 7 8 8 7 N/A
Switzerland – Shares/Funds 34 25 21 21 21
Sweden – Shares 22 23 22 20 18
United Kingdom – Shares/
Funds26 25 22 20 18
United States – Direct/
IndirectN/A 50 49 N/A 45
Source:  Adapted from the 2008 Australian Share Ownership Study  conducted by the Australian 
Securities Exchange (see http://www.asx.com.au). For Australia and the United States, the data 
pertain to direct and indirect ownership in equity markets; for other countries, the data pertain 
to direct ownership in shares and share funds. Data not available in specific years are shown as 
“N/A. ”
An important implication from the above discussion is that equity securities 
represent a key asset class for global investors because of their unique return and 
risk characteristics. We next examine the various types of equity securities traded on 
global markets and their salient characteristics.

TYPES AND CHARACTERISTICS OF EQUITY 
SECURITIES
Companies finance their operations by issuing either debt or equity securities. A key 
difference between these securities is that debt is a liability of the issuing company, 
whereas equity is not. This means that when a company issues debt, it is contractually 
obligated to repay the amount it borrows (i.e., the principal or face value of the debt) 
at a specified future date. The cost of using these funds is called interest, which the 
company is contractually obligated to pay until the debt matures or is retired.
When the company issues equity securities, it is not contractually obligated to repay 
the amount it receives from shareholders, nor is it contractually obligated to make 
periodic payments to shareholders for the use of their funds. Instead, shareholders 
have a claim on the company’s assets after all liabilities have been paid. Because of

this residual claim, equity shareholders are considered to be owners of the company. 
Investors who purchase equity securities are seeking total return (i.e., capital or price 
appreciation and dividend income), whereas investors who purchase debt securities 
(and hold until maturity) are seeking interest income. As a result, equity investors 
expect the company’s management to act in their best interest by making operating 
decisions that will maximize the market price of their shares (i.e., shareholder wealth).
In addition to common shares (also known as ordinary shares or common stock), 
companies may also issue preference shares (also known as preferred stock), the 
other type of equity security. The following sections discuss the different types and 
characteristics of common and preference securities.3Exhibit 6   (Continued)

Reading 47 ■ Overview of Equity Securities 156
3.1 Common Shares
Common shares  represent an ownership interest in a company and are the predomi -
nant type of equity security. As a result, investors share in the operating performance 
of the company, participate in the governance process through voting rights, and have 
a claim on the company’s net assets in the case of liquidation. Companies may choose 
to pay out some, or all, of their net income in the form of cash dividends to common 
shareholders, but they are not contractually obligated to do so.7
Voting rights provide shareholders with the opportunity to participate in major 
corporate governance decisions, including the election of its board of directors, the 
decision to merge with or take over another company, and the selection of outside 
auditors. Shareholder voting generally takes place during a company’s annual meet -
ing. As a result of geographic limitations and the large number of shareholders, it is

often not feasible for shareholders to attend the annual meeting in person. For this 
reason, shareholders may vote by proxy , which allows a designated party—such as 
another shareholder, a shareholder representative, or management—to vote on the 
shareholders’ behalf.
Regular shareholder voting, where each share represents one vote, is referred to as 
statutory voting . Although it is the common method of voting, it is not always the 
most appropriate one to use to elect a board of directors. To better serve shareholders 
who own a small number of shares, cumulative voting  is often used. Cumulative 
voting allows shareholders to direct their total voting rights to specific candidates, as 
opposed to having to allocate their voting rights evenly among all candidates. Total 
voting rights are based on the number of shares owned multiplied by the number of 
board directors being elected. For example, under cumulative voting, if four board

directors are to be elected, a shareholder who owns 100 shares is entitled to 400 votes 
and can either cast all 400 votes in favor of a single candidate or spread them across 
the candidates in any proportion. In contrast, under statutory voting, a shareholder 
would be able to cast only a maximum of 100 votes for each candidate.
The key benefit to cumulative voting is that it allows shareholders with a small 
number of shares to apply all of their votes to one candidate, thus providing the 
opportunity for a higher level of representation on the board than would be allowed 
under statutory voting.
Exhibit 7 describes the rights of Viacom Corporation’s shareholders. In this case, a 
dual-  share arrangement allows the founding chairman and his family to control more 
than 70 percent of the voting rights through the ownership of Class A shares. This 
arrangement gives them the ability to exert control over the board of director election

process, corporate decision making, and other important aspects of managing the 
company. A cumulative voting arrangement for any minority shareholders of Class 
A shares would improve their board representation.
7 It is also possible for companies to pay more than the current period’s net income as dividends. Such 
payout policies are, however, generally not sustainable in the long run.

Types and Characteristics of Equity Securities 157
Exhibit 7   Share Class Arrangements at Viacom Corporation8
Viacom has two classes of common stock: Class A, which is the voting stock, 
and Class B, which is the non-  voting stock. There is no difference between the 
two classes except for voting rights; they generally trade within a close price 
range of each other. There are, however, far more shares of Class B outstanding, 
so most of the trading occurs in that class.
■■Voting Rights —Holders of Class A common stock are entitled to one 
vote per share. Holders of Class B common stock do not have any voting 
rights, except as required by Delaware law. Generally, all matters to be 
voted on by Viacom stockholders must be approved by a majority of the 
aggregate voting power of the shares of Class A common stock present in 
person or represented by proxy, except as required by Delaware law.
■■Dividends —Stockholders of Class A common stock and Class B common

stock will share ratably in any cash dividend declared by the Board of 
Directors, subject to any preferential rights of any outstanding preferred 
stock. Viacom does not currently pay a cash dividend, and any decision to 
pay a cash dividend in the future will be at the discretion of the Board of 
Directors and will depend on many factors.
■■Conversion —So long as there are 5,000 shares of Class A common stock 
outstanding, each share of Class A common stock will be convertible at 
the option of the holder of such share into one share of Class B common 
stock.
■■Liquidation Rights —In the event of liquidation, dissolution, or wind -
ing- up of Viacom, all stockholders of common stock, regardless of class, 
will be entitled to share ratably in any assets available for distributions to 
stockholders of shares of Viacom common stock subject to the preferen -
tial rights of any outstanding preferred stock.
■■Split, Subdivision, or Combination —In the event of a split, subdivision,

or combination of the outstanding shares of Class A common stock or 
Class B common stock, the outstanding shares of the other class of com -
mon stock will be divided proportionally.
■■Preemptive Rights —Shares of Class A common stock and Class B com -
mon stock do not entitle a stockholder to any preemptive rights enabling 
a stockholder to subscribe for or receive shares of stock of any class or any 
other securities convertible into shares of stock of any class of Viacom.
As seen in Exhibit 7, companies can issue different classes of common shares (Class 
A and Class B shares), with each class offering different ownership rights.9 For exam -
ple, as shown in Exhibit 8, the Ford Motor Company has Class A shares (“Common 
Stock”), which are owned by the investing public. It also has Class B shares, which 
are owned only by the Ford family. The exhibit contains an excerpt from Ford’s 2008 
Annual Report  (p. 115). Class A shareholders have 60 percent voting rights, whereas

Class B shareholders have 40 percent. In the case of liquidation, however, Class B 
shareholders will not only receive the first US$0.50 per share that is available for 
8 This information has been adapted from Viacom’s investor relations website and its 10-  K filing with the 
US Securities and Exchange Commission; see www.viacom.com.
9 In some countries, including the United States, companies can issue different classes of shares, with 
Class A shares being the most common. The role and function of different classes of shares is described 
in more detail in Exhibit 8.

Reading 47 ■ Overview of Equity Securities 158
distribution (as will Class A shareholders), but they will also receive the next US$1.00 
per share that is available for distribution before Class A shareholders receive anything 
else. Thus, Class B shareholders have an opportunity to receive a larger proportion of 
distributions upon liquidation than do Class A shareholders.10
Exhibit 8   Share Class Arrangements at Ford Motor Company11
NOTE 21. CAPITAL STOCK AND AMOUNTS PER SHARE
All general voting power is vested in the holders of Common Stock and Class B 
Stock. Holders of our Common Stock have 60% of the general voting power and 
holders of our Class B Stock are entitled to such number of votes per share as 
will give them the remaining 40%. Shares of Common Stock and Class B Stock 
share equally in dividends when and as paid, with stock dividends payable in 
shares of stock of the class held. As discussed in Note 16, we are prohibited

from paying dividends (other than dividends payable in stock) under the terms 
of the Credit Agreement.
If liquidated, each share of Common Stock will be entitled to the first $0.50 
available for distribution to holders of Common Stock and Class B Stock, each 
share of Class B Stock will be entitled to the next $1.00 so available, each share 
of Common Stock will be entitled to the next $0.50 so available and each share 
of Common and Class B Stock will be entitled to an equal amount thereafter.
Common shares may also be callable or putable. Callable common shares  (also 
known as redeemable common shares) give the issuing company the option (or right), 
but not the obligation, to buy back shares from investors at a call price that is spec -
ified when the shares are originally issued. It is most common for companies to call 
(or redeem) their common shares when the market price is above the pre-  specified 
call price. The company benefits because it can buy back its shares below the current

market price and later resell them at a higher market price, and it can also reduce div -
idend payments to preserve capital, if required. Investors benefit because they receive 
a guaranteed return when their shares are called. Exhibit 9 provides an example of 
callable common shares issued by Genomic Solutions in the US market. The exhibit 
provides details on the creation of callable common shares used to consummate a 
strategic alliance between PerkinElmer and Genomic Solutions. The arrangement 
contains provisions more favorable to PerkinElmer because at the time it was a more 
established and better capitalized company than Genomic Solutions.
Exhibit 9   Callable Stock Arrangement from Genomic Solutions12
The following information assumes that the underwriters do not exercise the 
over-  allotment option granted by us to purchase additional shares in the offering:
10 For example, if US$2.00 per share is available for distribution, the Common Stock (Class A) shareholders

will receive US$0.50 per share, while the Class B shareholders will receive US$1.50 per share. However, if 
there is US$3.50 per share available for distribution, the Common Stock shareholders will receive a total 
of US$1.50 per share and the Class B shareholders will receive a total of US$2.00 per share.
11 Extracted from Ford Motor Company’s 2008 Annual Report  (virtual.stivesonline.com/
publication/?i=14030).
12 Genomic Solutions Form S-  1 as filed with the US SEC (14 May 2000); see www.edgar-  online.com.

Types and Characteristics of Equity Securities 159
Callable common stock offered by us: 7,000,000 shares
Callable common stock to be outstanding after the offering: 22,718,888 shares
Common stock to be outstanding after the offering: 1,269,841 shares
Proposed NASDAQ National Market symbol: GNSL
Use of proceeds: General corporate purposes and possible future acquisitions
For two years from the completion of this offering, we may require all holders 
of our callable common stock to sell their shares back to us. We must exercise 
this right at PerkinElmer’s direction. The price for repurchase of our callable 
common stock generally will be 20% over the market price. PerkinElmer also 
has a right to match any third party offer for our callable common stock or our 
business that our board of directors is prepared to accept.
Putable common shares  give investors the option or right to sell their shares (i.e., 
“put” them) back to the issuing company at a price that is specified when the shares are

originally issued. Investors will generally sell their shares back to the issuing company 
when the market price is below the pre-  specified put price. Thus, the put option feature 
limits the potential loss for investors. From the issuing company’s perspective, the put 
option facilitates raising capital because the shares are more appealing to investors.
Exhibit 10 provides an example of putable common shares issued by Dreyer’s, now 
a subsidiary of Switzerland-  based Nestlé. In this case, shareholders had the right to 
sell their shares to Dreyer’s for US$83.10, the pre-  specified put price.
Exhibit 10   Putable Stock Arrangement for Dreyer’s Grand Ice Cream13
Dreyer’s Grand Ice Cream Holdings, Inc. (“Dreyer’s”) announced today that 
the period during which holders of shares of Dreyer’s Class A Callable Putable 
Common Stock (the “Class A Shares”) could require Dreyer’s to purchase their 
Class A Shares (the “Put Right”) for a cash payment of $83.10 per Class A Share

(the “Purchase Price”) expired at 5:00 p.m. New York City time on January 13, 
2006 (the “Expiration Time”). According to the report of the depositary agent for 
the Put Right, holders of an aggregate of 30,518,885 Class A Shares (including 
1,792,193 shares subject to guaranteed delivery procedures) properly exercised 
the Put Right.
3.2 Preference Shares
Preference shares  (or preferred stock) rank above common shares with respect to 
the payment of dividends and the distribution of the company’s net assets upon liq -
uidation.14 However, preference shareholders generally do not share in the operating 
performance of the company and do not have any voting rights, unless explicitly 
allowed for at issuance. Preference shares have characteristics of both debt securities 
and common shares. Similar to the interest payments on debt securities, the divi -
dends on preference shares are fixed and are generally higher than the dividends on Exhibit 9   (Continued)

13 “Dreyer’s Announces Expiration of Put Period and Anticipated Merger with Nestle, ” Business Wire  (14 
January 2006): www.findarticles.com/p/articles/mi_m0EIN/is_2006_Jan_14/ai_n16001349.
14 Preference shares have a lower priority than debt in the case of liquidation. That is, debt holders have 
a higher claim on a firm’s assets in the event of liquidation and will receive what is owed to them first, 
followed by preference shareholders and then common shareholders.

Reading 47 ■ Overview of Equity Securities 160
common shares. However, unlike interest payments, preference dividends are not 
contractual obligations of the company. Similar to common shares, preference shares 
can be perpetual (i.e., no fixed maturity date), can pay dividends indefinitely, and can 
be callable or putable.
Exhibit 11 provides an example of callable preference shares issued by Goldman 
Sachs to raise capital during the credit crisis of 2008. In this case, Berkshire Hathaway, 
the purchaser of the shares, will receive an ongoing dividend from Goldman Sachs. If 
Goldman Sachs chooses to buy back the shares, it must do so at a 10 percent premium 
above their par value.
Exhibit 11   Callable Stock Arrangement between Goldman Sachs and 
Berkshire Hathaway15
New York, NY—September 23, 2008—The Goldman Sachs Group, Inc. announced 
today that it has reached an agreement to sell $5 billion of perpetual preferred

stock to Berkshire Hathaway, Inc. in a private offering. The preferred stock has 
a dividend of 10 percent and is callable at any time at a 10 percent premium. In 
conjunction with this offering, Berkshire Hathaway will also receive warrants to 
purchase $5 billion of common stock with a strike price of $115 per share, which 
are exercisable at any time for a five year term. In addition, Goldman Sachs is 
raising at least $2.5 billion in common equity in a public offering.
Dividends on preference shares can be cumulative, non-  cumulative, participat -
ing, non-  participating, or some combination thereof (i.e., cumulative participat -
ing, cumulative non-  participating, non-  cumulative participating, non-  cumulative 
non-  participating).
Dividends on cumulative preference shares  accrue so that if the company decides 
not to pay a dividend in one or more periods, the unpaid dividends accrue and must 
be paid in full before dividends on common shares can be paid. In contrast, non-

cumulative preference shares  have no such provision. This means that any dividends 
that are not paid in the current or subsequent periods are forfeited permanently and 
are not accrued over time to be paid at a later date. However, the company is still not 
permitted to pay any dividends to common shareholders in the current period unless 
preferred dividends have been paid first.
Participating preference shares  entitle the shareholders to receive the standard 
preferred dividend plus the opportunity to receive an additional dividend if the com -
pany’s profits exceed a pre-  specified level. In addition, participating preference shares 
can also contain provisions that entitle shareholders to an additional distribution of 
the company’s assets upon liquidation, above the par (or face) value of the preference 
shares. Non-  participating preference shares  do not allow shareholders to share in 
the profits of the company. Instead, shareholders are entitled to receive only a fixed

dividend payment and the par value of the shares in the event of liquidation. The use of 
participating preference shares is much more common for smaller, riskier companies 
where the possibility of future liquidation is more of a concern to investors.
15 Goldman Sachs, “Berkshire Hathaway to Invest $5 Billion in Goldman Sachs, ” (23 September 2008): 
www.goldmansachs.com/our-  firm/press/press-  releases/archived/2008/berkshire-  hathaway-  invest.html.

Types and Characteristics of Equity Securities 161
Preference shares can also be convertible. Convertible preference shares  entitle 
shareholders to convert their shares into a specified number of common shares. This 
conversion ratio is determined at issuance. Convertible preference shares have the 
following advantages:
■■They allow investors to earn a higher dividend than if they invested in the com -
pany’s common shares.
■■They allow investors the opportunity to share in the profits of the company.
■■They allow investors to benefit from a rise in the price of the common shares 
through the conversion option.
■■Their price is less volatile than the underlying common shares because the divi -
dend payments are known and more stable.
As a result, the use of convertible preference shares is a popular financing option 
in venture capital and private equity transactions in which the issuing companies are 
considered to be of higher risk and when it may be years before the issuing company

“goes public” (i.e., issues common shares to the public).
Exhibit 12 provides examples of the types and characteristics of preference shares 
as issued by DBS Bank of Singapore.
Exhibit 12   Examples of Preference Shares Issued by DBS Bank16
SINGAPORE, MAY 12—DBS Bank said today it plans to offer S$700 million in 
preference shares and make it available to both retail and institutional investors 
in Singapore. Called the DBS Preferred Investment Issue, it will yield investors 
a fixed non-  cumulative gross dividend rate of 6% for the first ten years and a 
floating rate thereafter. The DBS Preferred Investment Issue will be offered in two 
tranches, consisting of a S$100 million tranche to retail investors via ATMs and a 
S$600 million placement tranche available to both retail and institutional inves -
tors. Depending on investor demand, DBS could increase the offering amount.
Jackson Tai, President and Chief Operating Officer of DBS Group Holdings,

said that following the success of the hybrid Tier 1 issue in March, DBS decided 
to make this new issue available to the local retail investors. “We consider these 
issues as an important capital management tool. We were pleased with the success 
of our hybrid Tier 1 issue for institutional investors and wanted to introduce a 
capital instrument that would be available to retail investors as well. ”
DBS Preferred Investment Issues are perpetual securities, redeemable after ten 
years at the option of DBS Bank and at every dividend date thereafter subject to 
certain redemption conditions. They are issued by DBS Bank and are considered 
to be core Tier 1 capital under the Monetary Authority of Singapore and Bank 
of International Settlement's guidelines. They will be listed on the Singapore 
Exchange Securities Trading Limited and can be traded on the secondary market 
through a broker. Holders of the DBS Preferred Investment Issue will receive

the dividend net of the 24.5% income tax. Investors may claim the tax credit in 
their tax returns.
16 DBS Bank, “DBS Follows US$850 Million Offering of Subordinated Notes to International Markets with 
Singapore Dollar Market Financing” (12 May 2001): www.dbs.com/newsroom/2001/Pages/press010512.aspx.

Reading 47 ■ Overview of Equity Securities 162
PRIVATE VERSUS PUBLIC EQUITY SECURITIES
Our discussion so far has focused on equity securities that are issued and traded in 
public markets and on exchanges. Equity securities can also be issued and traded in 
private equity markets. Private equity securities  are issued primarily to institutional 
investors via non-  public offerings, such as private placements. Because they are not 
listed on public exchanges, there is no active secondary market for these securities. 
As a result, private equity securities do not have “market determined” quoted prices, 
are highly illiquid, and require negotiations between investors in order to be traded. 
In addition, financial statements and other important information needed to deter -
mine the fair value of private equity securities may be difficult to obtain because the 
issuing companies are typically not required by regulatory authorities to publish this 

There are three primary types of private equity investments: venture capital, lev -
eraged buyouts, and private investment in public equity. Venture capital  investments 
provide “seed” or start-  up capital, early-  stage financing, or mezzanine financing to 
companies that are in the early stages of development and require additional capital 
for expansion. These funds are then used to finance the company’s product devel -
opment and growth. Venture capitalists range from family and friends to wealthy 
individuals and private equity funds. Because the equity securities issued to venture 
capitalists are not publicly traded, they generally require a commitment of funds for 
a relatively long period of time; the opportunity to “exit” the investment is typically 
within 3 to 10 years from the initial start-  up. The exit return earned by these private 
equity investors is based on the price that the securities can be sold for if and when

the start-  up company first goes public, either via an initial public offering  (IPO) on 
the stock market or by being sold to other investors.
A leveraged buyout  (LBO) occurs when a group of investors (such as the com -
pany’s management or a private equity partnership) uses a large amount of debt to 
purchase all of the outstanding common shares of a publicly traded company. In 
cases where the group of investors acquiring the company is primarily comprised of 
the company’s existing management, the transaction is referred to as a management 
buyout  (MBO). After the shares are purchased, they cease to trade on an exchange 
and the investor group takes full control of the company. In other words, the company 
is taken “private” or has been privatized. Companies that are candidates for these 
types of transactions generally have large amounts of undervalued assets (which can 
be sold to reduce debt) and generate high levels of cash flows (which are used to make

interest and principal payments on the debt). The ultimate objective of a buyout (LBO 
or MBO) is to restructure the acquired company and later take it “public” again by 
issuing new shares to the public in the primary market.
The third type of private investment is a private investment in public equity , 
or PIPE.17 This type of investment is generally sought by a public company that is in 
need of additional capital quickly and is willing to sell a sizeable ownership position 
to a private investor or investor group. For example, a company may require a large 
investment of new equity funds in a short period of time because it has significant 
expansion opportunities, is facing high levels of indebtedness, or is experiencing a 
rapid deterioration in its operations. Depending on how urgent the need is and the 
size of the capital requirement, the private investor may be able to purchase shares in 
the company at a significant discount to the publicly-  quoted market price. Exhibit 13

contains a recent PIPE transaction for the electronics retailer hhgregg, which also 
included the issuance of additional common shares to the public.4
17 The term PIPE is widely used in the United States and is also used internationally, including in emerg -
ing markets.

Private versus Public Equity Securities 163
Exhibit 13   Example of a PIPE Transaction18
On July 20, 2009, hhgregg completed a public stock offering of 4,025,000 shares 
of its common stock at $16.50 per share. Concurrently with the public offering, 
investment funds affiliated with Freeman Spogli & Co. purchased an additional 
1,000,000 shares of common stock, in a private placement transaction, at the 
price per share paid by the public in the offering. Proceeds, net of underwriting 
fees, from the public stock offering and private placement, totaled approximately 
$78.6  million. These proceeds will be used for general corporate purposes, 
including funding the Company’s accelerated new store growth plans.
While the global private equity market is relatively small in comparison to the 
global public equity market, it has experienced considerable growth over the past three 
decades. According to a study of the private equity market sponsored by the World

Economic Forum  and spanning the period 1970–2007, approximately US$3.6 trillion 
in debt and equity were acquired in leveraged buyouts. Of this amount, approximately 
75 percent or US$2.7 trillion worth of transactions occurred during 2001–2007.19 
While the US and the UK markets were the focus of most private equity investments 
during the 1980s and 1990s, private equity investments outside of these markets have 
grown substantially in recent years. In addition, the number of companies operating 
under private equity ownership has also grown. For example, during the mid-  1990s, 
fewer than 2,000 companies were under LBO ownership compared to close to 14,000 
companies that were under LBO ownership globally at the beginning of 2007. The 
holding period for private equity investments has also increased during this time 
period from 3 to 5 years (1980s and 1990s) to approximately 10 years.20
The move to longer holding periods has given private equity investors the opportu -

nity to more effectively and patiently address any underlying operational issues facing 
the company and to better manage it for long-  term value creation. Because of the 
longer holding periods, more private equity firms are issuing convertible preference 
shares because they provide investors with greater total return potential through 
their dividend payments and the ability to convert their shares into common shares 
during an IPO.
In operating a publicly traded company, management often feels pressured to 
focus on short-  term results21 (e.g., meeting quarterly sales and earnings targets from 
analysts biased toward near-  term price performance) instead of operating the com -
pany to obtain long-  term sustainable revenue and earnings growth. By “going private, ” 
management can adopt a more long-  term focus and can eliminate certain costs that 
are necessary to operate a publicly traded company—such as the cost of meeting

regulatory and stock exchange filing requirements, the cost of maintaining investor 
relations departments to communicate with shareholders and the media, and the cost 
of holding quarterly analyst conference calls.
As described above, public equity markets are much larger than private equity 
networks and allow companies more opportunities to raise capital that is subsequently 
actively traded in secondary markets. By operating under public scrutiny, companies 
are incentivized to be more open in terms of corporate governance and executive 
compensation to ensure that they are acting for the benefit of shareholders. In fact, 
some studies have shown that private equity firms score lower in terms of corporate 
18 This information was obtained from hhgregg’s first quarter fiscal 2009 earnings report (http://ir.hhgregg.
com/releasedetail.cfm?ReleaseID=401980).
19 Stromberg (2008).
20 See, for example, Bailey, Wirth, and Zapol (2005).
21 See, for example, Graham, Harvey, and Rajgopal (2005).

Reading 47 ■ Overview of Equity Securities 164
governance effectiveness, which may be attributed to the fact that shareholders, 
analysts, and other stakeholders are able to influence management when corporate 
governance and other policies are public.
INVESTING IN NON-  DOMESTIC EQUITY SECURITIES
Technological innovations and the growth of electronic information exchanges 
(electronic trading networks, the internet, etc.) have accelerated the integration and 
growth of global financial markets. As detailed previously, global capital markets have 
expanded at a much more rapid rate than global GDP in recent years; both primary 
and secondary international markets have benefited from the enhanced ability to 
rapidly and openly exchange information. Increased integration of equity markets 
has made it easier and less expensive for companies to raise capital and to expand 
their shareholder base beyond their local market. Integration has also made it easier

for investors to invest in companies that are located outside of their domestic mar -
kets. This has enabled investors to further diversify and improve the risk and return 
characteristics of their portfolios by adding a class of assets with lower correlations 
to local country assets.
One barrier to investing globally is that many countries still impose “foreign 
restrictions” on individuals and companies from other countries that want to invest 
in their domestic companies. There are three primary reasons for these restrictions. 
The first is to limit the amount of control that foreign investors can exert on domestic 
companies. For example, some countries prevent foreign investors from acquiring a 
majority interest in domestic companies. The second is to give domestic investors the 
opportunity to own shares in the foreign companies that are conducting business in 
their country. For example, the Swedish home furnishings retailer IKEA abandoned

efforts to invest in parts of the Asia/Pacific region because local governments did not 
want IKEA to maintain complete ownership of its stores. The third reason is to reduce 
the volatility of capital flows into and out of domestic equity markets. For example, 
one of the main consequences of the Asian Financial Crisis in 1997–98 was the large 
outflow of capital from such emerging market countries as Thailand, Indonesia, and 
South Korea. These outflows led to dramatic declines in the equity markets of these 
countries and significant currency devaluations and resulted in many governments 
placing restrictions on capital flows. Today, many of these same markets have built 
up currency reserves to better withstand capital outflows inherent in economic con -
tractions and periods of financial market turmoil.
Studies have shown that reducing restrictions on foreign ownership has led to 
improved equity market performance over the long term.22 Although restrictions vary

widely, more countries are allowing increasing levels of foreign ownership. For exam -
ple, Australia has sought tax reforms as a means to encourage international demand 
for its managed funds in order to increase its role as an international financial center. 
Over the past two decades, three trends have emerged: a) an increasing number 
of companies have issued shares in markets outside of their home country; b) the 
number of companies whose shares are traded in markets outside of their home has 
increased; and c) an increasing number of companies are dual listed, which means that 
their shares are simultaneously issued and traded in two or more markets. Companies 
located in emerging markets have particularly benefited from these trends because 
they no longer have to be concerned with capital constraints or lack of liquidity in 
their domestic markets. These companies have found it easier to raise capital in the 5
22 See, for example, Henry and Chari (2004).

Investing in Non-  Domestic Equity Securities 165
markets of developed countries because these markets generally have higher levels of 
liquidity and more stringent financial reporting requirements and accounting standards. 
Being listed on an international exchange has a number of benefits. It can increase 
investor awareness about the company’s products and services, enhance the liquidity 
of the company’s shares, and increase corporate transparency because of the addi -
tional market exposure and the need to meet a greater number of filing requirements.
Technological advancements have made it easier for investors to trade shares 
in foreign markets. The German insurance company Allianz SE recently delisted its 
shares from the NYSE and certain European markets because international investors 
increasingly traded its shares on the Frankfurt Stock Exchange. Exhibit 14 illustrates 
the extent to which the institutional shareholder base at BASF, a large German chem -

ical corporation, has become increasingly global in nature.
Exhibit 14   Example of Increased Globalization of Share Ownership23
BASF is one of the largest publicly owned companies with around 460,000 
shareholders and a high free float. An analysis of the shareholder structure 
carried out in September 2008 showed that, at 22% of share capital, the United 
States and Canada made up the largest regional group of institutional investors. 
Institutional investors from Germany made up 13%. Shareholders from Great 
Britain and Ireland held 14% of BASF shares, while a further 14% are held by 
institutional investors from the rest of Europe. Around 28% of the company’s 
share capital is held by private investors, most of whom are resident in Germany.
German retail
investors2001 2008
investorsGerman institutional
investors
Rest of
World
Rest of
World 1%US & Canada
US & Canada Rest of EuropeRest of
EuropeNot
Identified
UK/IrelandUK/Ireland28% 28%
8%
22%14%14%
5%
9%12%37%13%
9%

8%
22%14%14%
5%
9%
5.1 Direct Investing
Investors can use a variety of methods to invest in the equity of companies outside of 
their local market. The most obvious is to buy and sell securities directly in foreign 
markets. However, this means that all transactions—including the purchase and sale of 
shares, dividend payments, and capital gains—are in the company’s, not the investor’s, 
domestic currency. In addition, investors must be familiar with the trading, clearing, 
and settlement regulations and procedures of that market. Investing directly often 
results in less transparency and more volatility because audited financial information 
may not be provided on a regular basis and the market may be less liquid. Alternatively, 
investors can use such securities as depository receipts and global registered shares, 
which represent the equity of international companies and are traded on local exchanges

23 Adapted from BASF’s investor relations website (www.basf.com). Free float  refers to the extent that 
shares are readily and freely tradable in the secondary market.

Reading 47 ■ Overview of Equity Securities 166
and in the local currencies. With these securities, investors have to worry less about 
currency conversions (price quotations and dividend payments are in the investor’s 
local currency), unfamiliar market practices, and differences in accounting standards. 
The sections that follow discuss various securities that investors can invest in outside 
of their home market.
5.2 Depository Receipts
A depository receipt24 (DR) is a security that trades like an ordinary share on a 
local exchange and represents an economic interest in a foreign company. It allows 
the publicly listed shares of a foreign company to be traded on an exchange outside 
its domestic market. A depository receipt is created when the equity shares of a for -
eign company are deposited in a bank (i.e., the depository) in the country on whose 
exchange the shares will trade. The depository then issues receipts that represent the

shares that were deposited. The number of receipts issued and the price of each DR is 
based on a ratio, which specifies the number of depository receipts to the underlying 
shares. Consequently, a DR may represent one share of the underlying stock, many 
shares of the underlying stock, or a fractional share of the underlying stock. The price 
of each DR will be affected by factors that affect the price of the underlying shares, 
such as company fundamentals, market conditions, analysts’ recommendations, and 
exchange rate movements. In addition, any short-  term valuation discrepancies between 
shares traded on multiple exchanges represent a quick arbitrage profit opportunity for 
astute traders to exploit. The responsibilities of the depository bank  that issues the 
receipts include acting as custodian and as a registrar. This entails handling dividend 
payments, other taxable events, stock splits, and serving as the transfer agent for the

foreign company whose securities the DR represents. The Bank of New York Mellon 
is the largest depository bank; however, Deutsche Bank, JPMorgan, and Citibank also 
offer depository services.25
A DR can be sponsored  or unsponsored . A sponsored DR is when the foreign 
company whose shares are held by the depository has a direct involvement in the 
issuance of the receipts. Investors in sponsored DRs have the same rights as the 
direct owners of the common shares (e.g., the right to vote and the right to receive 
dividends). In contrast, with an unsponsored DR, the underlying foreign company has 
no involvement with the issuance of the receipts. Instead, the depository purchases the 
foreign company’s shares in its domestic market and then issues the receipts through 
brokerage firms in the depository’s local market. In this case, the depository bank, not 
the investors in the DR, retains the voting rights. Sponsored DRs are generally subject

to greater reporting requirements than unsponsored DRs. In the United States, for 
example, sponsored DRs must be registered (meet the reporting requirements) with 
the US Securities and Exchange Commission (SEC). Exhibit 15 contains an example 
of a sponsored DR issued by Japan Airlines.
Exhibit 15   Sponsored versus Unsponsored Depository Receipts26
The Japan Airlines (JAL) Group, Asia’s biggest airline grouping, has picked the 
Bank of New York as the depository bank to make its previously unsponsored 
American depository receipts (ADRs) sponsored. By taking this action and by 
24 Note that the spellings depositary  and depository  are used interchangeably in financial markets. In this 
reading, we use the spelling depository  throughout.
25 Boubakri, Cosset, and Samet (2010).
26 Adapted from Japan Airlines Group’s investor relations website (www.jal.com/en/press/2004/082301/
img/ADRS.pdf).

Investing in Non-  Domestic Equity Securities 167
boosting investor relations activities in the United States, the JAL group aims to 
increase the number of overseas shareholders. The JAL Group’s sponsored ADRs 
became effective on August 19th, 2004 and dealing will start on August 25th. 
The JAL Group’s American depository receipts had been previously issued in 
the United States as unsponsored ADRs by several US depository banks since 
the 1970s. However, as unsponsored ADRs are issued without the involvement 
of the company itself, the company has difficulty in identifying ADR holders 
and controlling ADRs. From now, the JAL Group will be able to better serve 
its ADR holders and, at the same time, the JAL Group intends to increase its 
overseas investors.
There are two types of depository receipts: Global depository receipts (GDRs) and 
American depository receipts (ADRs), which are described below.
5.2.1  Global Depository Receipts

A global depository receipt  (GDR) is issued outside of the company’s home country 
and outside of the United States. The depository bank that issues GDRs is generally 
located (or has branches) in the countries on whose exchanges the shares are traded. 
A key advantage of GDRs is that they are not subject to the foreign ownership and 
capital flow restrictions that may be imposed by the issuing company’s home country 
because they are sold outside of that country. The issuing company selects the exchange 
where the GDR is to be traded based on such factors as investors’ familiarity with 
the company or the existence of a large international investor base. The London and 
Luxembourg exchanges were the first ones to trade GDRs. Some other stock exchanges 
trading GDRs are the Dubai International Financial Exchange and the Singapore Stock 
Exchange. Currently, the London and Luxembourg exchanges are where most GDRs

are traded because they can be issued in a more timely manner and at a lower cost. 
Regardless of the exchange they are traded on, the majority of GDRs are denominated 
in US dollars, although the number of GDRs denominated in pound sterling and euros 
is increasing. Note that although GDRs cannot be listed on US exchanges, they can 
be privately placed with institutional investors based in the United States.
5.2.2  American Depository Receipts
An American depository receipt  (ADR) is a US dollar-  denominated security that 
trades like a common share on US exchanges. First created in 1927, ADRs are the oldest 
type of depository receipts and are currently the most commonly traded depository 
receipts. They enable foreign companies to raise capital from US investors. Note that 
an ADR is one form of a GDR; however, not all GDRs are ADRs because GDRs cannot 
be publicly traded in the United States. The term American depository share  (ADS)

is often used in tandem with the term ADR. A depository share is a security that is 
actually traded in the issuing company’s domestic market. That is, while American 
depository receipts are the certificates that are traded on US markets, American 
depository shares are the underlying shares on which these receipts are based.
There are four primary types of ADRs, with each type having different levels of 
corporate governance and filing requirements. Level I Sponsored ADRs trade in the 
over-  the- counter (OTC) market and do not require full registration with the Securities 
and Exchange Commission (SEC). Level II and Level III Sponsored ADRs can trade 
on the New York Stock Exchange (NYSE), NASDAQ, and American Stock Exchange 
(AMEX). Level II and III ADRs allow companies to raise capital and make acquisitions 
using these securities. However, the issuing companies must fulfill all SEC requirements.Exhibit 15   (Continued)

Reading 47 ■ Overview of Equity Securities 168
The fourth type of ADR, an SEC Rule 144A or a Regulation S depository receipt, 
does not require SEC registration. Instead, foreign companies are able to raise capital 
by privately placing these depository receipts with qualified institutional investors 
or to offshore non-  US investors. Exhibit 16 summarizes the main features of ADRs.
Exhibit 16   Summary of the Main Features of American Depository Receipts
Level I  
(Unlisted) Level II  
(Listed)Level III  
(Listed)Rule 144A  
(Unlisted)
Objectives Develop and 
broaden US investor 
base with existing 
sharesDevelop and broaden 
US investor base with 
existing sharesDevelop and broaden 
existing/new sharesAccess qualified insti -
tutional buyers (QIBs)
Raising capital on US 
markets?No No Yes, through public 
offeringsYes, through private 
placements to QIBs
SEC registration Form F-  6 Form F-  6 Forms F-  1 and F-  6 None
Trading Over the counter 
(OTC)NYSE, NASDAQ, or

(OTC)NYSE, NASDAQ, or 
AMEXNYSE, NASDAQ, or 
AMEXPrivate offerings, 
resales, and trading 
through automated 
linkages such as 
PORTAL
Listing fees Low High High Low
Size and earnings 
requirementsNone Yes Yes None
Source:  Adapted from Boubakri, Cosset, and Samet (2010): Table 1.
More than 2,000 DRs, from over 80 countries, currently trade on US exchanges. 
Based on current statistics, the total market value of DRs issued and traded is esti -
mated at approximately US$2 trillion, or 15 percent of the total dollar value of equities 
traded in US markets.27
5.2.3  Global Registered Share
A global registered share  (GRS) is a common share that is traded on different stock 
exchanges around the world in different currencies. Currency conversions are not 
needed to purchase or sell them, because identical shares are quoted and traded in 
different currencies. Thus, the same share purchased on the Swiss exchange in Swiss

francs can be sold on the Tokyo exchange for Japanese yen. As a result, GRSs offer 
more flexibility than depository receipts because the shares represent an actual own -
ership interest in the company that can be traded anywhere and currency conversions 
are not needed to purchase or sell them. GRSs were created and issued by Daimler 
Chrysler in 1998.
5.2.4  Basket of Listed Depository Receipts
Another type of global security is a basket of listed depository receipts  (BLDR), 
which is an exchange-  traded fund (ETF) that represents a portfolio of depository 
receipts. An ETF is a security that tracks an index but trades like an individual share 
on an exchange. An equity-  ETF is a security that contains a portfolio of equities that 
tracks an index. It trades throughout the day and can be bought, sold, or sold short, 
27 JPMorgan Depositary Receipt Guide  (2005):4.

Risk and Return Characteristics of Equity Securities 169
just like an individual share. Like ordinary shares, ETFs can also be purchased on 
margin and used in hedging or arbitrage strategies. The BLDR is a specific class of 
ETF security that consists of an underlying portfolio of DRs and is designed to track 
the price performance of an underlying DR index. For example, the Asia 50 ADR 
Index Fund is a capitalization-  weighted ETF designed to track the performance of 
50 Asian market-  based ADRs.
RISK AND RETURN CHARACTERISTICS OF EQUITY 
Different types of equity securities have different ownership claims on a company’s 
net assets. The type of equity security and its features affect its risk and return char -
acteristics. The following sections discuss the different return and risk characteristics 
of equity securities.
6.1 Return Characteristics of Equity Securities
There are two main sources of equity securities’ total return: price change (or capital

gain) and dividend income. The price change represents the difference between the 
purchase price ( Pt–1) and the sale price ( Pt) of a share at the end of time t – 1 and t, 
respectively. Cash or stock dividends ( Dt) represent distributions that the company 
makes to its shareholders during period t. Therefore, an equity security’s total return 
is calculated as:
Total return, Rt = (Pt – Pt–1 + Dt)/Pt–1  
For non-  dividend-  paying stocks, the total return consists of price appreciation only. 
Companies that are in the early stages of their life cycle generally do not pay dividends 
because earnings and cash flows are reinvested to finance the company’s growth. In 
contrast, companies that are in the mature phase of their life cycle may not have as 
many profitable growth opportunities; therefore, excess cash flows are often returned 
to investors via the payment of regular dividends or through share repurchases.

For investors who purchase depository receipts or foreign shares directly, there is 
a third source of return: foreign exchange gains (or losses) . Foreign exchange gains 
arise because of the change in the exchange rate between the investor’s currency and 
the currency that the foreign shares are denominated in. For example, US investors 
who purchase the ADRs of a Japanese company will earn an additional return if the 
yen appreciates relative to the US dollar. Conversely, these investors will earn a lower 
total return if the yen depreciates relative to the US dollar. For example, if the total 
return for a Japanese company was 10 percent in Japan and the yen depreciated by 
10 percent against the US dollar, the total return of the ADR would be (approximately) 
0 percent. If the yen had instead appreciated by 10 percent against the US dollar, the 
total return of the ADR would be (approximately) 20 percent.
Investors that only consider price appreciation overlook an important source of

return: the compounding that results from reinvested dividends. Reinvested dividends 
are cash dividends that the investor receives and uses to purchase additional shares. 
As Exhibit 17 shows, in the long run total returns on equity securities are dramatically 
influenced by the compounding effect of reinvested dividends. Between 1900 and 2011, 
US$1 invested in US equities in 1900 would have grown in real terms to US$834 with 
dividends reinvested, but to just US$8.1 when taking only the price appreciation or 
capital gain into account. This corresponds to a real compounded return of 6.2 percent 
per year with dividends reinvested, versus only 1.9 percent per year without dividends 6
(1)

Reading 47 ■ Overview of Equity Securities 170
reinvested. The comparable ending real wealth for bonds and bills are US$9.30 and 
US$2.80, respectively. These ending real wealth figures correspond to annualized real 
compounded returns of 2.0 percent on bonds and 0.9 percent on bills. 
Exhibit 17   Impact of Reinvested Dividends on Cumulative Real Returns in the US and UK Equity Market: 
1900–2011
834
291
8.1
1.8
1900 10 20 30 40 50 60 70 80 90 2000 100.1
US real total return 6.2% p.a. UK real total return 5.2% p.a.
US real capital gain 1.9% p.a. UK real capital gain 0.5% p.a.
Source:  Dimson, Marsh, and Staunton (2012b). This chart is updated annually and can be found at www.tinyurl.com/DMSsourcebook.
6.2 Risk of Equity Securities
The risk of any security is based on the uncertainty of its future cash flows. The greater 
the uncertainty of its future cash flows, the greater the risk and the more variable or

volatile the security’s price. As discussed above, an equity security’s total return is 
determined by its price change and dividends. Therefore, the risk of an equity secu -
rity can be defined as the uncertainty of its expected (or future) total return. Risk is 
most often measured by calculating the standard deviation of the equity’s expected 
total return.
A variety of different methods can be used to estimate an equity’s expected total 
return and risk. One method uses the equity’s average historical return and the standard 
deviation of this return as proxies for its expected future return and risk. Another 
method involves estimating a range of future returns over a specified period of time, 
assigning probabilities to those returns, and then calculating an expected return and 
a standard deviation of return based on this information.
The type of equity security, as well as its characteristics, affects the uncertainty of

its future cash flows and therefore its risk. In general, preference shares are less risky 
than common shares for three main reasons:
1 Dividends on preference shares are known and fixed, and they account for 
a large portion of the preference shares’ total return. Therefore, there is less 
uncertainty about future cash flows.

Equity Securities and Company Value 171
2 Preference shareholders receive dividends and other distributions before com -
mon shareholders.
3 The amount preference shareholders will receive if the company is liquidated is 
known and fixed as the par (or face) value of their shares. However, there is no 
guarantee that investors will receive that amount if the company experiences 
financial difficulty.
With common shares, however, a larger portion of shareholders’ total return (or 
all of their total return for non-  dividend shares) is based on future price appreciation 
and future dividends are unknown. If the company is liquidated, common shareholders 
will receive whatever amount (if any) is remaining after the company’s creditors and 
preference shareholders have been paid. In summary, because the uncertainty sur -
rounding the total return of preference shares is less than common shares, preference 
shares have lower risk and lower expected return than common shares.

It is important to note that some preference shares and common shares can be 
riskier than others because of their associated characteristics. For example, from an 
investor’s point of view, putable common or preference shares are less risky than 
their callable or non-  callable counterparts because they give the investor the option 
to sell the shares to the issuer at a pre-  determined price. This pre-  determined price 
establishes a minimum price that investors will receive and reduces the uncertainty 
associated with the security’s future cash flow. As a result, putable shares generally 
pay a lower dividend than non-  putable shares.
Because the major source of total return for preference shares is dividend income, 
the primary risk affecting all preference shares is the uncertainty of future dividend 
payments. Regardless of the preference shares’ features (callable, putable, cumulative, 
etc.), the greater the uncertainty surrounding the issuer’s ability to pay dividends, the

greater risk. Because the ability of a company to pay dividends is based on its future 
cash flows and net income, investors try to estimate these amounts by examining past 
trends or forecasting future amounts. The more earnings and the greater amount of 
cash flow that the company has had, or is expected to have, the lower the uncertainty 
and risk associated with its ability to pay future dividends.
Callable common or preference shares are riskier than their non-  callable coun -
terparts because the issuer has the option to redeem the shares at a pre-  determined 
price. Because the call price limits investors’ potential future total return, callable 
shares generally pay a higher dividend to compensate investors for the risk that the 
shares could be called in the future. Similarly, putable preference shares have lower 
risk than non-  putable preference shares. Cumulative preference shares have lower 
risk than non-  cumulative preference shares because the cumulative feature gives

investors the right to receive any unpaid dividends before any dividends can be paid 
to common shareholders.
EQUITY SECURITIES AND COMPANY VALUE
Companies issue equity securities on primary markets to raise capital and increase 
liquidity. This additional liquidity also provides the corporation an additional “cur -
rency” (its equity), which it can use to make acquisitions and provide stock option-  
based incentives to employees. The primary goal of raising capital is to finance the 
company’s revenue-  generating activities in order to increase its net income and 
maximize the wealth of its shareholders. In most cases, the capital that is raised is 
used to finance the purchase of long-  lived assets, capital expansion projects, research 
and development, the entry into new product or geographic regions, and the acqui -
sition of other companies. Alternatively, a company may be forced to raise capital to 7

Reading 47 ■ Overview of Equity Securities 172
ensure that it continues to operate as a going concern. In these cases, capital is raised 
to fulfill regulatory requirements, improve capital adequacy ratios, or to ensure that 
debt covenants are met.
The ultimate goal of management is to increase the book value (shareholders’ 
equity on a company’s balance sheet) of the company and maximize the market value 
of its equity. Although management actions can directly affect the book value of the 
company (by increasing net income or by selling or purchasing its own shares), they 
can only indirectly affect the market value of its equity. The book value of a company’s 
equity—the difference between its total assets and total liabilities—increases when the 
company retains its net income. The more net income that is earned and retained, the 
greater the company’s book value of equity. Because management’s decisions directly

influence a company’s net income, they also directly influence its book value of equity.
The market value of the company’s equity, however, reflects the collective and 
differing expectations of investors concerning the amount, timing, and uncertainty 
of the company’s future cash flows. Rarely will book value and market value be equal. 
Although management may be accomplishing its objective of increasing the company’s 
book value, this increase may not be reflected in the market value of the company’s 
equity because it does not affect investors’ expectations about the company’s future 
cash flows. A key measure that investors use to evaluate the effectiveness of man -
agement in increasing the company’s book value is the accounting return on equity.
7.1 Accounting Return on Equity
Return on equity (ROE)  is the primary measure that equity investors use to determine 
whether the management of a company is effectively and efficiently using the capital

they have provided to generate profits. It measures the total amount of net income 
available to common shareholders generated by the total equity capital invested in the 
company. It is computed as net income available to ordinary shareholders (i.e., after 
preferred dividends have been deducted) divided by the average total book value of 
equity (BVE). That is:
ROENI
Average BV ENI
BVEB VEtt
tt
tt==+ () −12
where NIt is the net income in year t and the average book value of equity is computed 
as the book values at the beginning and end of year t divided by 2. Return on equity 
assumes that the net income produced in the current year is generated by the equity 
existing at the beginning of the year and any new equity that was invested during the 
year. Note that some formulas only use shareholders’ equity at the beginning of year  t 
(that is, the end of year t – 1) in the denominator. This assumes that only the equity

existing at the beginning of the year was used to generate the company’s net income 
during the year. That is:
ROENI
BVEtt
t=
−1
Both formulas are appropriate to use as long as they are applied consistently. For 
example, using beginning of the year book value is appropriate when book values 
are relatively stable over time or when computing ROE for a company annually over 
a period of time. Average book value is more appropriate if a company experiences 
more volatile year-  end book values or if the industry convention is to use average 
book values in calculating ROE.
One caveat to be aware of when computing and analyzing ROE is that net income 
and the book value of equity are directly affected by management’s choice of accounting 
methods, such as those relating to depreciation (straight line versus accelerated meth -
ods) or inventories (first in, first out versus weighted average cost). Different accounting (2)
(3)

Equity Securities and Company Value 173
methods can make it difficult to compare the return on equity of companies even if 
they operate in the same industry. It may also be difficult to compare the ROE of the 
same company over time if its accounting methods have changed during that time.
Exhibit 18 contains information on the net income and total book value of share -
holders’ equity for three blue chip  (widely held large market capitalization companies 
that are considered financially sound and are leaders in their respective industry or local 
stock market) pharmaceutical companies: Pfizer, Novartis AG, and GlaxoSmithKline. 
The data are for their financial years ending December 2006 through December 2008.28
Exhibit 18   Net Income and Book Value of Equity for Pfizer, Novartis AG, and 
GlaxoSmithKline (in Thousands of US Dollars)
Financial Y ear Ending
31 Dec 2008 31 Dec 2007 31 Dec 2006
Pfizer
Net income $8,104,000 $8,144,000 $19,337,000

Pfizer
Total stockholders’ equity $57,556,000 $65,010,000 $71,358,000
Novartis AG
Net income $8,233,000 $11,968,000 $5,264,000
Total stockholders’ equity $50,437,000 $49,396,000 $41,670,000
GlaxoSmithKline
Net income $6,822,505 $10,605,663 $8,747,382
Total stockholders’ equity $11,483,295 $19,180,072 $67,888,692
Using the average book value of equity, the return on equity for Pfizer for the years 
ending December 2007 and 2008 can be calculated as:
 
Return on equity for the year ending December 2007
ROENI
BVEB VE8,144,000
20072007
2006 2007 27 1 358 000 65 01=+ ()=+ ,, ,0 0 000 211 9,.%()=
Return on equity for the year ending December 2008
ROENI
BVEB VE8,104,000
20082008
2007 2008 26 5 010 000 57 55=+ ()=+ ,, ,6 6 000 213 2,.%()=
Exhibit 19 summarizes the return on equity for Novartis and GlaxoSmithKline in 
addition to Pfizer for 2007 and 2008.
28 Pfizer uses US GAAP to prepare its financial statements; Novartis and GlaxoSmithKline use International

Financial Reporting Standards. Therefore, it would be inappropriate to compare the ROE of Pfizer to that 
of Novartis or GlaxoSmithKline.

Reading 47 ■ Overview of Equity Securities 174
Exhibit 19   Return on Equity for Pfizer, Novartis AG, and 
31 Dec 2008 (%) 31 Dec 2007 (%)
Pfizer 13.2 11.9
Novartis AG 16.5 26.3
GlaxoSmithKline 44.5 24.4
In the case of Novartis, the ROE of 26.3 percent in 2007 indicates that the company 
was able to generate a return (profit) of US$0.263 on every US$1.00 of capital invested 
by shareholders. In 2008, its operating performance deteriorated because it was only 
able to generate a 16.5  percent return on its equity. In contrast, GlaxoSmithKline 
almost doubled its return on equity over this period, from 24.4 percent to 44.5 percent. 
Pfizer’s ROE remained relatively unchanged.
ROE can increase if net income increases at a faster rate than shareholders’ equity 
or if net income decreases at a slower rate than shareholders’ equity. In the case of 
Novartis, ROE fell in 2008 because its net income decreased by over 30 percent while

shareholders’ equity remained relatively stable. Stated differently, Novartis was less 
effective in using its equity capital to generate profits in 2008 than in 2007. In the case 
of GlaxoSmithKline, its ROE increased dramatically from 24.4 percent to 44.5 per -
cent in 2007 versus 2008 even though its net income fell over 35 percent because its 
average shareholder equity decreased dramatically from 2006–2007 to 2007–2008.
An important question to ask is whether an increasing ROE is always good. The 
short answer is, “it depends. ” One reason ROE can increase is if net income decreases 
at a slower rate than shareholders’ equity, which is not a positive sign. In addition, 
ROE can increase if the company issues debt and then uses the proceeds to repurchase 
some of its outstanding shares. This action will increase the company’s leverage and 
make its equity riskier. Therefore, it is important to examine the source of changes in

the company’s net income and shareholders’ equity over time. The DuPont formula, 
which is discussed in a separate reading, can be used to analyze the sources of changes 
in a company’s ROE.
The book value of a company’s equity reflects the historical operating and financ -
ing decisions of its management. The market value of the company’s equity reflects 
these decisions as well as investors’ collective assessment and expectations about the 
company’s future cash flows generated by its positive net present value investment 
opportunities. If investors believe that the company has a large number of these future 
cash flow-  generating investment opportunities, the market value of the company’s 
equity will exceed its book value. Exhibit 20 shows the market price per share, the total 
number of shares outstanding, and the total book value of shareholders’ equity for 
Pfizer, Novartis AG, and GlaxoSmithKline at the end of December 2008. This exhibit

also shows the total market value of equity (or market capitalization) computed as the 
number of shares outstanding multiplied by the market price per share.
Exhibit 20   Market Information for Pfizer, Novartis AG, and GlaxoSmithKline 
(in Thousands of US Dollars except market price)
Pfizer Novartis AG GlaxoSmithKline
Market price $16.97 $47.64 $35.84
Total shares outstanding 6,750,000 2,260,000 2,530,000

Equity Securities and Company Value 175
Total shareholders’ equity $57,556,000 $50,437,000 $11,483,295
Total market value of 
equity $114,547,500 $107,666,400 $90,675,200
Note that in Exhibit 20, the total market value of equity for Pfizer is computed as:
Market value of equity = Market price per share × Shares outstanding
Market value of equity = US$16.97 × 6,750,000 = US$114,547,500.
The book value of equity per share for Pfizer can be computed as:
Book value of equity per share = Total shareholders’ equity/Shares outstanding
Book value of equity per share = US$57,556,000/6,750,000 = US$8.53.
A useful ratio to compute is a company’s price-  to- book ratio, which is also referred 
to as the market-  to- book ratio. This ratio provides an indication of investors’ expec -
tations about a company’s future investment and cash flow-  generating opportunities. 
The larger the price-  to- book ratio (i.e., the greater the divergence between market

value per share and book value per share), the more favorably investors will view 
the company’s future investment opportunities. For Pfizer the price-  to- book ratio is:
Price-  to- book ratio = Market price per share/Book value of equity per share
Price-  to- book ratio = US$16.97/US$8.53 = 1.99
Exhibit 21 contains the market price per share, book value of equity per share, and 
price-  to- book ratios for Novartis and GlaxoSmithKline in addition to Pfizer.
Exhibit 21   Pfizer, Novartis AG, and GlaxoSmithKline
Market price per share $16.97 $47.64 $35.84
Book value of equity per share $8.53 $22.32 $4.54
Price-  to- book ratio 1.99 2.13 7.89
The market price per share of all three companies exceeds their respective book 
values, so their price-  to- book ratios are all greater than 1.00. However, there are 
significant differences in the sizes of their price-  to- book ratios. GlaxoSmithKline has

the largest price-  to- book ratio, while the price-  to- book ratios of Pfizer and Novartis 
are similar to each other. This suggests that investors believe that GlaxoSmithKline 
has substantially higher future growth opportunities than either Pfizer or Novartis.
It is not appropriate to compare the price-  to- book ratios of companies in different 
industries because their price-  to- book ratios also reflect investors’ outlook for the 
industry. Companies in high growth industries, such as technology, will generally have 
higher price-  to- book ratios than companies in slower growth (i.e., mature) industries, 
such as heavy equipment. Therefore, it is more appropriate to compare the price-  to- 
book ratios of companies in the same industry. A company with relatively high growth 
opportunities compared to its industry peers would likely have a higher price-  to- book 
ratio than the average price-  to- book ratio of the industry.Exhibit 20   (Continued)

Reading 47 ■ Overview of Equity Securities 176
Book value and return on equity are useful in helping analysts determine value but 
can be limited as a primary means to estimate a company’s true or intrinsic value, which 
is the present value of its future projected cash flows. In Exhibit 22, Warren Buffett, 
one of the most successful investors in the world and CEO of Berkshire Hathaway, 
provides an explanation of the differences between the book value of a company 
and its intrinsic value in a letter to shareholders. As discussed above, market value 
reflects the collective and differing expectations of investors concerning the amount, 
timing, and uncertainty of a company’s future cash flows. A company’s intrinsic value 
can only be estimated because it is impossible to predict the amount and timing of 
its future cash flows. However, astute investors—such as Buffett—have been able to 
profit from discrepancies between their estimates of a company’s intrinsic value and

the market value of its equity.
Exhibit 22   Book Value versus Intrinsic Value29
We regularly report our per-  share book value, an easily calculable number, though 
one of limited use. Just as regularly, we tell you that what counts is intrinsic value, 
a number that is impossible to pinpoint but essential to estimate.
For example, in 1964, we could state with certitude that Berkshire’s per-  
share book value was $19.46. However, that figure considerably overstated the 
stock’s intrinsic value since all of the company’s resources were tied up in a 
sub-  profitable textile business. Our textile assets had neither going-  concern nor 
liquidation values equal to their carrying values. In 1964, then, anyone inquiring 
into the soundness of Berkshire’s balance sheet might well have deserved the 
answer once offered up by a Hollywood mogul of dubious reputation: “Don’t 
worry, the liabilities are solid. ”
Today, Berkshire’s situation has reversed: Many of the businesses we control

are worth far more than their carrying value. (Those we don’t control, such as 
Coca-  Cola or Gillette, are carried at current market values.) We continue to give 
you book value figures, however, because they serve as a rough, understated, 
tracking measure for Berkshire’s intrinsic value.
We define intrinsic value as the discounted value of the cash that can be 
taken out of a business during its remaining life. Anyone calculating intrinsic 
value necessarily comes up with a highly subjective figure that will change both 
as estimates of future cash flows are revised and as interest rates move. Despite 
its fuzziness, however, intrinsic value is all-  important and is the only logical way 
to evaluate the relative attractiveness of investments and businesses.
To see how historical input (book value) and future output (intrinsic value) 
can diverge, let’s look at another form of investment, a college education. Think

of the education’s cost as its “book value. ” If it is to be accurate, the cost should 
include the earnings that were foregone by the student because he chose college 
rather than a job.
For this exercise, we will ignore the important non-  economic benefits of an 
education and focus strictly on its economic value. First, we must estimate the 
earnings that the graduate will receive over his lifetime and subtract from that 
figure an estimate of what he would have earned had he lacked his education. 
That gives us an excess earnings figure, which must then be discounted, at an 
appropriate interest rate, back to graduation day. The dollar result equals the 
intrinsic economic value of the education.
29 Extracts from Berkshire Hathaway’s 2008 Annual Report  (www.berkshirehathaway.com).

Equity Securities and Company Value 177
7.2 The Cost of Equity and Investors’ Required Rates of Return
When companies issue debt (or borrow from a bank) or equity securities, there is a 
cost associated with the capital that is raised. In order to maximize profitability and 
shareholder wealth, companies attempt to raise capital efficiently so as to minimize 
these costs.
When a company issues debt, the cost it incurs for the use of these funds is called 
the cost of debt. The cost of debt is relatively easy to estimate because it reflects the 
periodic interest (or coupon) rate that the company is contractually obligated to pay 
to its bondholders (lenders). When a company raises capital by issuing equity, the 
cost it incurs is called the cost of equity. Unlike debt, however, the company is not 
contractually obligated to make any payments to its shareholders for the use of their 
funds. As a result, the cost of equity is more difficult to estimate.

Investors require a return on the funds they provide to the company. This return 
is called the investor’s minimum required rate of return. When investors purchase 
the company’s debt securities, their minimum required rate of return is the periodic 
rate of interest they charge the company for the use of their funds. Because all of the 
bondholders receive the same periodic rate of interest, their required rate of return is 
the same. Therefore, the company’s cost of debt and the investors’ minimum required 
rate of return on the debt are the same.
When investors purchase the company’s equity securities, their minimum required 
rate of return is based on the future cash flows they expect to receive. Because these 
future cash flows are both uncertain and unknown, the investors’ minimum required 
rate of return must be estimated. In addition, the minimum required return may 
differ across investors based on their expectations about the company’s future cash

flows. As a result, the company’s cost of equity may be different from the investors’ 
minimum required rate of return on equity.30 Because companies try to raise capital 
at the lowest possible cost, the company’s cost of equity is often used as a proxy for 
the investors’ minimum  required rate of return.
In other words, the cost of equity can be thought of as the minimum expected rate 
of return that a company must offer its investors to purchase its shares in the primary 
market and to maintain its share price in the secondary market. If this expected rate 
of return is not maintained in the secondary market, then the share price will adjust 
so that it meets the minimum required rate of return demanded by investors. For 
example, if investors require a higher rate of return on equity than the company’s cost 
of equity, they would sell their shares and invest their funds elsewhere resulting in a 
decline in the company’s share price. As the share price declined, the cost of equity

would increase to reach the higher rate of return that investors require.
Two models commonly used to estimate a company’s cost of equity (or investors’ 
minimum required rate of return) are the dividend discount model (DDM) and the 
capital asset pricing model (CAPM). These models are discussed in detail in other 
curriculum readings.
The cost of debt (after tax) and the cost of equity (i.e., the minimum required 
rates of return on debt and equity) are integral components of the capital budgeting 
process because they are used to estimate a company’s weighted average cost of cap -
ital (WACC). Capital budgeting is the decision-  making process that companies use 
to evaluate potential long-  term investments. The WACC represents the minimum 
required rate of return that the company must earn on its long-  term investments to 
satisfy all providers of capital. The company then chooses among those long-  term 
investments with expected returns that are greater than its WACC.

30 Another important factor that can cause a firm’s cost of equity to differ from investors’ required rate 
of return on equity is the flotation cost associated with equity.

Reading 47 ■ Overview of Equity Securities 178
SUMMARY
Equity securities play a fundamental role in investment analysis and portfolio manage -
ment. The importance of this asset class continues to grow on a global scale because 
of the need for equity capital in developed and emerging markets, technological 
innovation, and the growing sophistication of electronic information exchange. Given 
their absolute return potential and ability to impact the risk and return characteristics 
of portfolios, equity securities are of importance to both individual and institutional 
investors.
This reading introduces equity securities and provides an overview of global equity 
markets. A detailed analysis of their historical performance shows that equity securities 
have offered average real annual returns superior to government bills and bonds, which 
have provided average real annual returns that have only kept pace with inflation. The

different types and characteristics of common and preference equity securities are 
examined, and the primary differences between public and private equity securities 
are outlined. An overview of the various types of equity securities listed and traded 
in global markets is provided, including a discussion of their risk and return charac -
teristics. Finally, the role of equity securities in creating company value is examined 
as well as the relationship between a company’s cost of equity, its accounting return 
on equity, investors’ required rate of return, and the company’s intrinsic value.
We conclude with a summary of the key components of this reading:
■■Common shares represent an ownership interest in a company and give inves -
tors a claim on its operating performance, the opportunity to participate in the 
corporate decision-  making process, and a claim on the company’s net assets in 
the case of liquidation.

■■Callable common shares give the issuer the right to buy back the shares from 
shareholders at a price determined when the shares are originally issued.
■■Putable common shares give shareholders the right to sell the shares back to the 
issuer at a price specified when the shares are originally issued.
■■Preference shares are a form of equity in which payments made to prefer -
ence shareholders take precedence over any payments made to common 
■■Cumulative preference shares are preference shares on which dividend pay -
ments are accrued so that any payments omitted by the company must be paid 
before another dividend can be paid to common shareholders. Non-  cumulative 
preference shares have no such provisions, implying that the dividend payments 
are at the company’s discretion and are thus similar to payments made to com -
■■Participating preference shares allow investors to receive the standard preferred

dividend plus the opportunity to receive a share of corporate profits above a 
pre-  specified amount. Non-  participating preference shares allow investors to 
simply receive the initial investment plus any accrued dividends in the event of 
liquidation.
■■Callable and putable preference shares provide issuers and investors with the 
same rights and obligations as their common share counterparts.
■■Private equity securities are issued primarily to institutional investors in private 
placements and do not trade in secondary equity markets. There are three types 
of private equity investments: venture capital, leveraged buyouts, and private 
investments in public equity (PIPEs).

References 179
Bailey, Elizabeth, Meg Wirth, and David Zapol. 2005. “Venture 
Capital and Global Health. ” Financing Global Health 
Ventures , Discussion Paper (September 2005): http://www.  
commonscapital.com/downloads/Venture_Capital_and_
Global_Health.pdf
Boubakri, Narjess, Jean-  Claude Cosset, and Anis Samet. 2010. 
“The Choice of ADRs. ” Journal of Banking and Finance , vol. 
34, no. 9:2077–2095.
Dimson, Elroy, Paul Marsh, and Mike Staunton. 2012a. Credit 
Suisse Global Investment Returns Sourcebook 2012 . Credit 
Suisse Research Institute.Dimson, Elroy, Paul Marsh, and Mike Staunton. 2012b. Credit 
Suisse Global Investment Returns Yearbook 2012 . Credit Suisse 
Research Institute.
Graham, John R., Campbell R. Harvey, and Shiva Rajgopal. 
2005. “The Economic Implications of Corporate Financial 
1–3:3–73.
Henry, Peter Blair, and Anusha Chari. 2004. “Risk Sharing and

Asset Prices: Evidence from a Natural Experiment. ” Journal of 
Finance , vol. 59, no. 3:1295–1324.
Strömberg, Per. 2008. “The New Demography of Private Equity. ” 
The Global Economic Impact of Private Equity Report 2008 , 
World Economic Forum.■■The objective of private equity investing is to increase the ability of the compa -
ny’s management to focus on its operating activities for long-  term value cre -
ation. The strategy is to take the “private” company “public” after certain profit 
and other benchmarks have been met.
■■Depository receipts are securities that trade like ordinary shares on a local 
exchange but which represent an economic interest in a foreign company. 
They allow the publicly listed shares of foreign companies to be traded on an 
exchange outside their domestic market.
■■American depository receipts are US dollar-  denominated securities trading 
much like standard US securities on US markets. Global depository receipts are

similar to ADRs but contain certain restrictions in terms of their ability to be 
resold among investors.
■■Underlying characteristics of equity securities can greatly affect their risk and 
return.
■■A company’s accounting return on equity is the total return that it earns on 
shareholders’ book equity.
■■A company’s cost of equity is the minimum rate of return that stockholders 
require the company to pay them for investing in its equity.

Reading 47 ■ Overview of Equity Securities 180
1 Which of the following is not a characteristic of common equity?
A It represents an ownership interest in the company.
B Shareholders participate in the decision-  making process.
C The company is obligated to make periodic dividend payments.
2 The type of equity voting right that grants one vote for each share of equity 
owned is referred to as:
A proxy voting.
B statutory voting.
C cumulative voting.
3 All of the following are characteristics of preference shares except :
A They are either callable or putable.
B They generally do not have voting rights.
C They do not share in the operating performance of the company.
4 Participating preference shares entitle shareholders to:
A participate in the decision-  making process of the company.
B convert their shares into a specified number of common shares.
C receive an additional dividend if the company’s profits exceed a pre-  
determined level.

5 Which of the following statements about private equity securities is incorrect ?
A They cannot be sold on secondary markets.
B They have market-  determined quoted prices.
C They are primarily issued to institutional investors.
6 Venture capital investments:
A can be publicly traded.
B do not require a long-  term commitment of funds.
C provide mezzanine financing to early-  stage companies.
7 Which of the following statements most accurately  describes one difference 
between private and public equity firms?
A Private equity firms are focused more on short-  term results than public 
firms.
B Private equity firms’ regulatory and investor relations operations are less 
costly than those of public firms.
C Private equity firms are incentivized to be more open with investors about 
governance and compensation than public firms.
8 Emerging markets have benefited from recent trends in international markets. 
Which of the following has not been a benefit of these trends?

A Emerging market companies do not have to worry about a lack of liquidity 
in their home equity markets.
B Emerging market companies have found it easier to raise capital in the mar -
kets of developed countries.

Practice Problems 181
C Emerging market companies have benefited from the stability of foreign 
exchange markets.
9 When investing in unsponsored depository receipts, the voting rights to the 
shares in the trust belong to:
A the depository bank.
B the investors in the depository receipts.
C the issuer of the shares held in the trust.
10 With respect to Level III sponsored ADRs, which of the following is least likely  
to be accurate? They:
A have low listing fees.
B are traded on the NYSE, NASDAQ, and AMEX.
C are used to raise equity capital in US markets.
11 A basket of listed depository receipts, or an exchange-  traded fund, would most 
likely  be used for:
A gaining exposure to a single equity.
B hedging exposure to a single equity.
C gaining exposure to multiple equities.
12 Calculate the total return on a share of equity using the following data:
 Purchase price: $50
 Sale price: $42
 Dividend paid during holding period: $2
A –12.0%
B –14.3%
C –16.0%

A –12.0%
B –14.3%
C –16.0%
13 If a US-  based investor purchases a euro-  denominated ETF and the euro subse -
quently depreciates in value relative to the dollar, the investor will have a total 
return that is:
A lower than the ETF’s total return.
B higher than the ETF’s total return.
C the same as the ETF’s total return.
14 Which of the following is incorrect  about the risk of an equity security? The risk 
of an equity security is:
A based on the uncertainty of its cash flows.
B based on the uncertainty of its future price.
C measured using the standard deviation of its dividends.
15 From an investor’s point of view, which of the following equity securities is the 
least  risky?
A Putable preference shares.
B Callable preference shares.
C Non-  callable preference shares.
16 Which of the following is least likely  to be a reason for a company to issue 
equity securities on the primary market?
A To raise capital.
B To increase liquidity.
C To increase return on equity.

Reading 47 ■ Overview of Equity Securities 182
17 Which of the following is not a primary goal of raising equity capital?
A To finance the purchase of long-  lived assets.
B To finance the company’s revenue-  generating activities.
C To ensure that the company continues as a going concern.
18 Which of the following statements is most accurate  in describing a company’s 
book value?
A Book value increases when a company retains its net income.
B Book value is usually equal to the company’s market value.
C The ultimate goal of management is to maximize book value.
19 Calculate the book value of a company using the following information:
Number of shares outstanding 100,000 
Price per share €52
Total assets €12,000,000
Total liabilities €7,500,000
Net Income €2,000,000
A €4,500,000.
B €5,200,000.
C €6,500,000.
20 Which of the following statements is least accurate  in describing a company’s 
market value?
A Management’s decisions do not influence the company’s market value.

B Increases in book value may not be reflected in the company’s market value.
C Market value reflects the collective and differing expectations of investors.
21 Calculate the 2009 return on equity (ROE) of a stable company using the fol -
lowing data:
Total sales £2,500,000
Net income £2,000,000
Beginning of year total assets £50,000,000
Beginning of year total liabilities £35,000,000
Number of shares outstanding at the end of 2009 1,000,000
Price per share at the end of 2009 £20
A 10.0%.
B 13.3%.
C 16.7%.
22 Holding all other factors constant, which of the following situations will most 
likely  lead to an increase in a company’s return on equity?
A The market price of the company’s shares increases.
B Net income increases at a slower rate than shareholders’ equity.
C The company issues debt to repurchase outstanding shares of equity.
23 Which of the following measures is the most difficult  to estimate?
A The cost of debt.
B The cost of equity.
C Investors’ required rate of return on debt.

Practice Problems 183
24 A company’s cost of equity is often used as a proxy for investors’:
A average required rate of return.
B minimum required rate of return.
C maximum required rate of return.

Reading 47 ■ Overview of Equity Securities 184
SOLUTIONS
1 C is correct. The company is not obligated to make dividend payments. It is at 
the discretion of the company whether or not it chooses to pay dividends.
2 B is correct. Statutory voting is the type of equity voting right that grants one 
vote per share owned.
3 A is correct. Preference shares do not have to be either callable or putable.
4 C is correct. Participating preference shares entitle shareholders to receive an 
additional dividend if the company’s profits exceed a pre-  determined level.
5 B is correct. Private equity securities do not have market-  determined quoted 
prices.
6 C is correct. Venture capital investments can be used to provide mezzanine 
financing to companies in their early stage of development.
7 B is correct. Regulatory and investor relations costs are lower for private equity 
firms than for public firms. There are no stock exchange, regulatory, or share -

holder involvements with private equity, whereas for public firms these costs 
can be high.
8 C is correct. The trends in emerging markets have not led to the stability of 
foreign exchange markets.
9 A is correct. In an unsponsored DR, the depository bank owns the voting rights 
to the shares. The bank purchases the shares, places them into a trust, and then 
sells shares in the trust—not the underlying shares—in other markets.
10 A is correct. The listing fees on Level III sponsored ADRs are high.
11 C is correct. An ETF is used to gain exposure to a basket of securities (equity, 
fixed income, commodity futures, etc.).
12 A is correct. The formula states Rt = (Pt – Pt–1 + Dt)/Pt–1. Therefore, total 
return = (42 – 50 + 2)/50 = –12.0%.
13 A is correct. The depreciated value of the euro will create an additional loss in 
the form of currency return that is lower than the ETF’s return.
14 C is correct. Some equity securities do not pay dividends, and therefore the

standard deviation of dividends cannot be used to measure the risk of all equity 
15 A is correct. Putable shares, whether common or preference, give the investor 
the option to sell the shares back to the issuer at a pre-  determined price. This 
pre- determined price creates a floor for the share’s price that reduces the uncer -
tainty of future cash flows for the investor (i.e., lowers risk relative to the other 
two types of shares listed).
16 C is correct. Issuing shares in the primary (and secondary) market reduces  a 
company’s return on equity because it increases the total amount of equity capi -
tal invested in the company (i.e., the denominator in the ROE formula).
17 C is correct. Capital is raised to ensure the company’s existence only when it is 
required. It is not a typical goal of raising capital.
18 A is correct. A company’s book value increases when a company retains its net 
income.
19 A is correct. The book value of the company is equal to total assets minus total

Solutions 185
20 A is correct. A company’s market value is affected by management’s decisions. 
Management’s decisions can directly affect the company’s book  value, which can 
then affect its market value.
21 B is correct. A company’s ROE is calculated as (NIt/BVEt–1). For 2009, the 
BVEt–1 is equal to the beginning total assets minus the beginning total liabili -
ties, which equals £50,000,000 – £35,000,000 = £15,000,000. Therefore, ROE2009 
= £2,000,000/£15,000,000 = 13.3%.
22 C is correct. A company’s ROE will increase if it issues debt to repurchase out -
standing shares of equity.
23 B is correct. The cost of equity is not easily determined. It is dependent on 
investors’ required rate of return on equity, which reflects the different risk 
levels of investors and their expectations about the company’s future cash flows.
24 B is correct. Companies try to raise funds at the lowest possible cost. Therefore, 
cost of equity is used as a proxy for the minimum required rate of return.

Introduction to Industry and 
Company Analysis
by Patrick W . Dorsey, CFA, Anthony M. Fiore, CFA, and 
Ian Rossa O’Reilly, CFA
Patrick W. Dorsey, CFA, is at Dorsey Asset Management (USA). Anthony M. Fiore, CFA, is 
at Silvercrest Asset Management (USA). Ian Rossa O’Reilly, CFA (Canada).
a. explain uses of industry analysis and the relation of industry 
analysis to company analysis;
b. compare methods by which companies can be grouped, current 
industry classification systems, and classify a company, given a 
description of its activities and the classification system;
c. explain the factors that affect the sensitivity of a company to 
the business cycle and the uses and limitations of industry and 
company descriptors such as “growth, ” “defensive, ” and “cyclical”;
d. explain how a company’s industry classification can be used to 
identify a potential “peer group” for equity valuation;

e. describe the elements that need to be covered in a thorough 
industry analysis;
f. describe the principles of strategic analysis of an industry;
g. explain the effects of barriers to entry, industry concentration, 
industry capacity, and market share stability on pricing power and 
price competition;
h. describe industry life cycle models, classify an industry as to life 
cycle stage, and describe limitations of the life-  cycle concept in 
forecasting industry performance;
i. compare characteristics of representative industries from the 
various economic sectors;
j. describe macroeconomic, technological, demographic, 
governmental, and social influences on industry growth, 
profitability, and risk;
k. describe the elements that should be covered in a thorough 
company analysis.READING
48

Reading 48 ■ Introduction to Industry and Company Analysis 188
Industry analysis  is the analysis of a specific branch of manufacturing, service, or 
trade. Understanding the industry in which a company operates provides an essential 
framework for the analysis of the individual company—that is, company analysis . 
Equity analysis and credit analysis are often conducted by analysts who concentrate 
on one or several industries, which results in synergies and efficiencies in gathering 
and interpreting information.
Among the questions we address in this reading are the following:
■■What are the similarities and differences among industry classification systems?
■■How does an analyst go about choosing a peer group of companies?
■■What are the key factors to consider when analyzing an industry?
■■What advantages are enjoyed by companies in strategically well-  positioned 
industries?
After discussing the uses of industry analysis in the next section, Sections 3 and

4 discuss, respectively, approaches to identifying similar companies and industry 
classification systems. Section 5 covers the description and analysis of industries. 
Also, Section 5, which includes an introduction to competitive analysis, provides a 
background to Section 6, which introduces company analysis. The reading ends with 
a summary, and practice problems follow the text.
USES OF INDUSTRY ANALYSIS
Industry analysis is useful in a number of investment applications that make use of 
fundamental analysis. Its uses include the following:
■■Understanding a company’s business and business environment . Industry 
analysis is often a critical early step in stock selection and valuation because it 
provides insights into the issuer’s growth opportunities, competitive dynamics, 
and business risks. For a credit analyst, industry analysis provides insights into 
the appropriateness of a company’s use of debt financing and into its ability to

meet its promised payments during economic contractions.
■■Identifying active equity investment opportunities . Investors taking a top-  down 
investing approach use industry analysis to identify industries with positive, 
neutral, or negative outlooks for profitability and growth. Generally, inves -
tors will then overweight, market weight, or underweight those industries 
(as appropriate to their outlooks) relative to the investor’s benchmark if the 
investor judges that the industry’s perceived prospects are not fully incorpo -
rated in market prices. Apart from security selection, some investors attempt 
to outperform their benchmarks by industry or sector rotation—that is, timing 
investments in industries in relation to an analysis of industry fundamentals 
and/or business-  cycle conditions (technical analysis may also play a role in such 
strategies). Several studies have underscored the importance of industry analy -

sis by suggesting that the industry factor in stock returns is at least as important 
as the country factor (e.g., Cavaglia, Diermeier, Moroz, and De Zordo, 2004). In 1
2

Approaches to Identifying Similar Companies 189
addition, industry membership has been found to account for about 20 percent 
of the variability of a company’s profitability in the United States (McGahan and 
Porter 1995).
■■Portfolio performance attribution.  Performance attribution, which addresses the 
sources of a portfolio’s returns, usually in relation to the portfolio’s benchmark, 
includes industry or sector selection. Industry classification schemes play a role 
in such performance attribution.
Later in this reading we explore the considerations involved in understanding 
a company’s business and business environment. The next section addresses how 
companies may be grouped into industries.
APPROACHES TO IDENTIFYING SIMILAR COMPANIES
Industry classification attempts to place companies into groups on the basis of 
commonalities. In the following sections, we discuss the three major approaches to 
industry classification:
■■products and/or services supplied;

■■business-  cycle sensitivities; and
■■statistical similarities.
3.1 Products and/or Services Supplied
Modern classification schemes are most commonly based on grouping companies by 
similar products and/or services. According to this perspective, an industry  is defined 
as a group of companies offering similar products and/or services. For example, major 
companies in the global heavy truck industry include Volvo, Daimler AG, Paccar, 
and Navistar, all of which make large commercial vehicles for the on-  highway truck 
market. Similarly, some of the large players in the global automobile industry are 
Toyota, General Motors, Volkswagen, Ford, Honda, Nissan, PSA Peugeot Citroën, and 
Hyundai, all of which produce light vehicles that are close substitutes for one another.
Industry classification schemes typically provide multiple levels of aggregation. The 
term sector  is often used to refer to a group of related industries. The health care sector,

for example, consists of a number of related industries, including the pharmaceutical, 
biotechnology, medical device, medical supply, hospital, and managed care industries.
These classification schemes typically place a company in an industry on the basis 
of a determination of its principal business activity. A company’s principal business 
activity  is the source from which the company derives a majority of its revenues and/
or earnings. For example, companies that derive a majority of their revenues from 
the sale of pharmaceuticals include Novartis AG, Pfizer Inc., Roche Holding AG, 
GlaxoSmithKline, and Sanofi-  aventis S.A., all of which could be grouped together as 
part of the global pharmaceutical industry. Companies that engage in more than one 
significant business activity usually report the revenues (and, in many cases, operating 
profits) of the different business segments in their financial statements.1
Examples of classification systems based on products and/or services include

the commercial classification systems that will be discussed later, namely, the Global 
Industry Classification Standard (GICS), Russell Global Sectors (RGS), and Industry 3
1 For more information, see International Financial Reporting Standard (IFRS) 8: Operating Segments. 
In IFRS 8, business segments  are called operating segments .

Reading 48 ■ Introduction to Industry and Company Analysis 190
Classification Benchmark. In addition to grouping companies by product and/or 
service, some of the major classification systems, including GICS and RGS, group 
consumer-  related companies into cyclical and non-  cyclical categories depending 
on the company’s sensitivity to the business cycle. The next section addresses how 
companies can be categorized on the basis of economic sensitivity.
3.2 Business-  Cycle Sensitivities
Companies are sometimes grouped on the basis of their relative sensitivity to the 
business cycle. This method often results in two broad groupings of companies—
cyclical and non-  cyclical.
A cyclical  company is one whose profits are strongly correlated with the strength 
of the overall economy. Such companies experience wider-  than-  average fluctuations 
in demand—high demand during periods of economic expansion and low demand

during periods of economic contraction—and/or are subject to greater-  than-  average 
profit variability related to high operating leverage (i.e., high fixed costs). Concerning 
demand, cyclical products and services are often relatively expensive and/or repre -
sent purchases that can be delayed if necessary (e.g., because of declining disposable 
income). Examples of cyclical industries are autos, housing, basic materials, industrials, 
and technology. A non-  cyclical  company is one whose performance is largely inde -
pendent of the business cycle. Non-  cyclical companies produce goods or services for 
which demand remains relatively stable throughout the business cycle. Examples of 
non-  cyclical industries are food and beverage, household and personal care products, 
health care, and utilities.
Although the classification systems we will discuss do not label their categories as 
cyclical or non-  cyclical, certain sectors tend to experience greater economic sensitivity

than others. Sectors that tend to exhibit a relatively high degree of economic sensi -
tivity include consumer discretionary, energy, financials, industrials, technology, and 
materials. In contrast, sectors that exhibit relatively less economic sensitivity include 
consumer staples, health care, telecommunications, and utilities.
EXAMPLE 1   
Descriptions Related to the Cyclical/Noncyclical 
Distinction
Analysts commonly encounter a number of labels related to the cyclical/non-  
cyclical distinction. For example, non-  cyclical industries have sometimes been 
sorted into defensive (or stable) versus growth. Defensive industries and com -
panies are those whose revenues and profits are least affected by fluctuations 
in overall economic activity. These industries/companies tend to produce staple 
consumer goods (e.g., bread), to provide basic services (grocery stores, drug 
stores, fast food outlets), or to have their rates and revenues determined by

contracts or government regulation (e.g., cost-  of- service, rate-  of- return regu -
lated public utilities). Growth industries would include industries with specific 
demand dynamics that are so strong that they override the significance of broad 
economic or other external factors and generate growth regardless of overall 
economic conditions, although their rates of growth may slow during an eco -
nomic downturn.2
2 Sometimes the “growth” label is attached to countries or regions in which economic growth is so strong 
that the fluctuations in local economic activity do not produce an actual decline in economic output, merely 
variation from high to low rates of real growth (e.g., China, India).

Approaches to Identifying Similar Companies 191
The usefulness of industry and company labels such as cyclical, growth, and 
defensive is limited. Cyclical industries as well as growth industries often have 
growth companies within them. A cyclical industry itself, although exposed to 
the effects of fluctuations in overall economic activity, may grow at an above-  
average rate for periods spanning multiple business cycles.3 Furthermore, when 
fluctuations in economic activity are large, as in the deep recession of 2008−2009, 
few companies escape the effects of the cyclical weakness in overall economic 
activity.
The defensive label is also problematic. Industries may include both companies 
that are growth and companies that are defensive in character, making the choice 
between a “growth” and a “defensive” label difficult. Moreover, “defensive” cannot 
be understood as necessarily being descriptive of investment characteristics.

Food supermarkets, for example, would typically be described as defensive but 
can be subject to profit-  damaging price wars. So-  called defensive industries/
companies may sometimes face industry dynamics that make them far from 
defensive in the sense of preserving shareholders’ capital.
One limitation of the cyclical/non-  cyclical classification is that business-  cycle 
sensitivity is a continuous spectrum rather than an “either/or” issue, so placement 
of companies in one of the two major groups is somewhat arbitrary. The impact of 
severe recessions usually reaches all parts of the economy, so non-  cyclical is better 
understood as a relative term.
Another limitation of a business-  cycle classification for global investing is that 
different countries and regions of the world frequently progress through the various 
stages of the business cycle at different times. While one region of the world may be 
experiencing economic expansion, other regions or countries may be in recession,

which complicates the application of a business-  cycle approach to industry analysis. 
For example, a jewelry retailer (i.e., a cyclical company) that is selling domestically into 
a weak economy will exhibit markedly different fundamental performance relative to 
a jewelry company operating in an environment where demand is robust. Comparing 
these two companies—that is, similar companies that are currently exposed to dif -
ferent demand environments—could suggest investment opportunities. Combining 
fundamental data from such companies, however, to establish industry benchmark 
values would be misleading.
3.3 Statistical Similarities
Statistical approaches to grouping companies are typically based on the correlations 
of past securities’ returns. For example, using the technique known as cluster analy -
sis, companies are separated (on the basis of historical correlations of stock returns) 
into groups in which  correlations are relatively high but between which  correlations

are relatively low. This method of aggregation often results in non-  intuitive groups of 
companies, and the composition of the groups may vary significantly by time period 
and region of the world. Moreover, statistical approaches rely on historical data, but 
analysts have no guarantee that past correlation values will continue in the future. 
In addition, such approaches carry the inherent dangers of all statistical methods, 
namely, 1) falsely indicating a relationship that arose because of chance or 2) falsely 
excluding a relationship that actually is significant.
3 The label growth cyclical  is sometimes used to describe companies that are growing rapidly on a long-  
term basis but that still experience above-  average fluctuation in their revenues and profits over the course 
of a business cycle.

Reading 48 ■ Introduction to Industry and Company Analysis 192
INDUSTRY CLASSIFICATION SYSTEMS
A well-  designed classification system often serves as a useful starting point for industry 
analysis. It allows analysts to compare industry trends and relative valuations among 
companies in a group. Classification systems that take a global perspective enable 
portfolio managers and research analysts to make global comparisons of companies in 
the same industry. For example, given the global nature of the automobile industry, a 
thorough analysis of the industry would include auto companies from many different 
countries and regions of the world.
4.1 Commercial Industry Classification Systems
Major index providers, including Standard & Poor’s, MSCI Barra, Russell Investments, 
Dow Jones, and FTSE, classify companies in their equity indexes into industry group -
ings. Most classification schemes used by these index providers contain multiple levels

of classification that start at the broadest level with a general sector grouping, then, 
in several further steps, subdivide or disaggregate the sectors into more “granular” 
(i.e., more narrowly defined) sub-  industry groups.
4.1.1  Global Industry Classification Standard
GICS was jointly developed by Standard & Poor’s and MSCI Barra, two of the largest 
providers of global equity indexes, in 1999. As the name implies, GICS was designed 
to facilitate global comparisons of industries, and it classifies companies in both 
developed and developing economies. Each company is assigned to a sub-  industry 
according to its principal business activity. Each sub-  industry belongs to a particular 
industry; each industry belongs to an industry group; and each group belongs to a 
sector. In June 2009, the GICS classification structure comprised four levels of detail 
consisting of 154 sub-  industries, 68 industries, 24 industry groups, and 10 sectors.

The composition of GICS has historically been adjusted over time to reflect changes 
in the global equity markets.
4.1.2  Russell Global Sectors
The RGS classification system uses a three-  tier structure to classify companies globally 
on the basis of the products or services a company produces. In June 2009, the RGS 
classification system consisted of 9 sectors, 32 subsectors, and 141 industries. Besides 
the number of tiers, another difference between the RGS and GICS classification sys -
tems is that the RGS system contains nine sectors, whereas GICS consists of ten. For 
example, the RGS system does not provide a separate sector for telecommunication 
service companies. Many companies that GICS classifies as “Telecommunication 
Services, ” including China Mobile Ltd., AT&T, and Telefonica, are assigned by RGS 
to its more broadly defined “Utilities” sector.
4.1.3  Industry Classification Benchmark
The Industry Classification Benchmark (ICB), which was jointly developed by Dow

Jones and FTSE, uses a four-  tier structure to categorize companies globally on the basis 
of the source from which a company derives the majority of its revenue. In June 2009, 
the ICB classification system consisted of 10 industries, 19 supersectors, 41 sectors, 
and 114 subsectors. Although the ICB is similar to GICS in the number of tiers and 
the method by which companies are assigned to particular groups, the two systems 
use significantly different nomenclature. For example, whereas GICS uses the term 
“sector” to describe its broadest grouping of companies, ICB uses the term “indus -
try. ” Another difference between the two systems is that ICB distinguishes between 4

Industry Classification Systems 193
consumer goods and consumer services companies, whereas both GICS and the RGS 
systems group consumer products companies and consumer services companies 
together into sectors on the basis of economic sensitivity. These stylistic distinctions 
tend to be less obvious at the more granular levels of the different hierarchies.
Despite these subtle differences, the three commercial classification systems use 
common methodologies for assigning companies to groups. Also, the broadest level 
of grouping for all three systems is quite similar. Specifically, GICS, the RGS, and the 
ICB each identify 9 or 10 broad groupings below which all other categories reside. 
Next, we describe sectors that are fairly representative of how the broadest level of 
industry classification is viewed by GICS, RGS, and ICB.
4.1.4  Description of Representative Sectors
Basic Materials and Processing:  companies engaged in the production of building

materials, chemicals, paper and forest products, containers and packaging, and metal, 
mineral, and mining companies.
Consumer Discretionary:  companies that derive a majority of revenue from the sale 
of consumer-  related products or services for which demand tends to exhibit a relatively 
high degree of economic sensitivity. Examples of business activities that frequently fall 
into this category are automotive, apparel, hotel, and restaurant businesses.
Consumer Staples:  consumer-  related companies whose business tends to exhibit 
less economic sensitivity than other companies; for example, manufacturers of food, 
beverage, tobacco, and personal care products.
Energy:  companies whose primary line of business involves the exploration, produc -
tion, or refining of natural resources used to produce energy; companies that derive a 
majority of revenue from the sale of equipment or through the provision of services 
to energy companies would also fall into this category.

Financial Services:  companies whose primary line of business involves banking, 
finance, insurance, real estate, asset management, and/or brokerage services.
Health Care:  manufacturers of pharmaceutical and biotech products, medical devices, 
health care equipment, and medical supplies and providers of health care services.
Industrial/Producer Durables:  manufacturers of capital goods and providers of 
commercial services; for example, business activities would include heavy machinery 
and equipment manufacture, aerospace and defense, transportation services, and 
commercial services and supplies.
Technology:  companies involved in the manufacture or sale of computers, soft -
ware, semiconductors, and communications equipment; other business activities that 
frequently fall into this category are electronic entertainment, internet services, and 
technology consulting and services.
Telecommunications:  companies that provide fixed-  line and wireless communication

services; some vendors prefer to combine telecommunication and utility companies 
together into a single “utilities” category.
Utilities:  electric, gas, and water utilities; telecommunication companies are some -
times included in this category.
 
To classify a company accurately in a particular classification scheme requires 
definitions of the classification categories, a statement about the criteria used in clas -
sification, and detailed information about the subject company. Example 2 introduces

Reading 48 ■ Introduction to Industry and Company Analysis 194
an exercise in such classification. In addressing the question, the reader can make use 
of the widely applicable sector descriptions just given and familiarity with available 
business products and services.
EXAMPLE 2   
Classifying Companies into Industries
The text defines 10 representative sectors, repeated here in Exhibit 1. Suppose the 
classification system is based on the criterion of a company’s principal business 
activity as judged primarily by source of revenue.
Exhibit 1   Ten Sectors
Sector
Basic Materials and Processing
Consumer Discretionary
Consumer Staples
Energy
Financial Services
Health Care
Industrial/Producer Durables
Technology
Telecommunications
Utilities
Based on the information given, determine an appropriate industry mem -
bership for each of the following hypothetical companies:
1 A natural gas transporter and marketer
2 A manufacturer of heavy construction equipment
3 A provider of regional telephone services

4 A semiconductor company
5 A manufacturer of medical devices
6 A chain of supermarkets
7 A manufacturer of chemicals and plastics
8 A manufacturer of automobiles
9 An investment management company
10 A manufacturer of luxury leather goods
11 A regulated supplier of electricity
12 A provider of wireless broadband services
13 A manufacturer of soaps and detergents
14 A software development company
15 An insurer
16 A regulated provider of water/wastewater services
17 A petroleum (oil) service company

Industry Classification Systems 195
18 A manufacturer of pharmaceuticals
19 A provider of rail transportation services
20 A metals mining company
Solution:
SectorCompany 
Number
Basic Materials and Processing 7, 20
Consumer Discretionary 8, 10
Consumer Staples 6, 13
Energy 1, 17
Financial Services 9, 15
Health Care 5, 18
Industrial/Producer Durables 2, 19
Technology 4, 14
Telecommunications 3, 12
Utilities 11, 16
Example 3 reviews some major concepts in industry classification.
EXAMPLE 3   
Industry Classification Schemes
1 The GICS classification system classifies companies on the basis of a com -
pany’s primary business activity as measured primarily by:
A assets.
B income.
C revenue.
2 Which of the following is least likely  to be accurately described as a cycli -
cal company? A(n):
A automobile manufacturer.
B producer of breakfast cereals.
C apparel company producing the newest trendy clothes for teenage 
girls.
3 Which of the following is the most accurate  statement? A statistical

approach to grouping companies into industries:
A is based on historical correlations of the securities’ returns.
B frequently produces industry groups whose composition is similar 
worldwide.
C emphasizes the descriptive statistics of industries consisting of compa -
nies producing similar products and/or services.
C is correct.

Reading 48 ■ Introduction to Industry and Company Analysis 196
B is correct. A producer of staple foods such as cereals is a classic example of 
a non-  cyclical company. Demand for automobiles is cyclical—that is, relatively 
high during economic expansions and relatively low during economic contrac -
tions. Also, demand for teenage fashions is likely to be more sensitive to the 
business cycle than demand for standard food items such as breakfast cereals. 
When budgets have been reduced, families may try to avoid expensive clothing 
or extend the life of existing wardrobes.
A is correct.
4.2 Governmental Industry Classification Systems
A number of classification systems in use by various governmental agencies today 
organize statistical data according to type of industrial or economic activity. A com -
mon goal of each government classification system is to facilitate the comparison of

data—both over time and among countries that use the same system. Continuity of the 
data is critical to the measurement and evaluation of economic performance over time.
4.2.1  International Standard Industrial Classification of All Economic Activities
The International Standard Industrial Classification of All Economic Activities (ISIC) 
was adopted by the United Nations in 1948 to address the need for international com -
parability of economic statistics. ISIC classifies entities into various categories on the 
basis of the principal type of economic activity the entity performs. ISIC is organized 
into 11 categories, 21 sections, 88 divisions, 233 groups, and more than 400 classes. 
According to the United Nations, a majority of the countries around the world have 
either used ISIC as their national activity classification system or have developed 
national classifications derived from ISIC. Some of the organizations currently using

the ISIC are the UN and its specialized agencies, the International Monetary Fund, 
the World Bank, and other international bodies.
4.2.2  Statistical Classification of Economic Activities in the European Community
Often regarded as the European version of ISIC, Statistical Classification of Economic 
Activities in the European Community (NACE) is the classification of economic 
activities that correspond to ISIC at the European level. Similar to ISIC, NACE clas -
sification is organized according to economic activity. NACE is composed of four 
levels—namely, sections (identified by alphabetical letters A through U), divisions 
(identified by two-  digit numerical codes 01 through 99), groups (identified by three-  
digit numerical codes 01.1 through 99.0), and classes (identified by four-  digit numerical 
codes 01.11 through 99.00).
4.2.3  Australian and New Zealand Standard Industrial Classification
The Australian and New Zealand Standard Industrial Classification (ANZSIC) was

jointly developed by the Australian Bureau of Statistics and Statistics New Zealand 
in 1993 to facilitate the comparison of industry statistics of the two countries and 
comparisons with the rest of the world. International comparability was achieved 
by aligning ANZSIC with the international standards used by ISIC. ANZSIC has a 
structure comprising five levels—namely, divisions (the broadest level), subdivisions, 
groups, classes, and at the most granular level, subclasses (New Zealand only).

Industry Classification Systems 197
4.2.4  North American Industry Classification System
Jointly developed by the United States, Canada, and Mexico, the North American 
Industry Classification System (NAICS) replaced the Standard Industrial Classification 
(SIC) system in 1997. NAICS distinguishes between establishments and enterprises. 
NAICS classifies establishments into industries according to the primary business 
activity of the establishment. In the NAICS system, an establishment  is defined as “a 
single physical location where business is conducted or where services or industrial 
operations are performed” (e.g., factory, store, hotel, movie theater, farm, office). An 
enterprise  may consist of more than one location performing the same or different 
types of economic activities. Each establishment of that enterprise is assigned a NAICS 
code on the basis of its own primary business activity.4
NAICS uses a two-  digit through six-  digit code to structure its categories into five

levels of detail. The greater the number of digits in the code, the more narrowly defined 
the category. The five levels of categories, from broadest to narrowest, are sector (sig -
nified by the first two digits of the code), subsector (third digit of the code), industry 
group (fourth digit), NAICS industry (fifth digit), and national industry (sixth digit). 
The five-  digit code is the level of greatest amount of comparability among countries; 
a six-  digit code provides for more country-  specific detail.
Although differences exist, the structures of ISIC, NACE, ANZSIC, and NAICS 
are similar enough that many of the categories from each of the different classification 
systems are compatible with one another. The US Census Bureau has published tables 
showing how the various categories of the classification systems relate to one another.5
4.3 Strengths and Weaknesses of Current Systems
Unlike commercial classification systems, most government systems do not disclose

information about a specific business or company, so an analyst cannot know all of 
the constituents of a particular category. For example, in the United States, federal 
law prohibits the Census Bureau from disclosing individual company activities, so, 
their NAICS and SIC codes are unknown.
Most government and commercial classification systems are reviewed and, if 
necessary, updated from time to time. Generally, commercial classification systems 
are adjusted more frequently than government classification systems, which may be 
updated only every five years or so. NAICS, for example, is reviewed for potential 
revisions every five years.
Government classification systems generally do not distinguish between small 
and large businesses, between for-  profit and not-  for- profit organizations, or between 
public and private companies. Many commercial classification systems have the abil -
ity to distinguish between large and small companies by virtue of association with a

particular equity index, and these systems include only for-  profit and publicly traded 
organizations.
Another limitation of current systems is that the narrowest classification unit 
assigned to a company generally cannot be assumed to be its peer group for the pur -
poses of detailed fundamental comparisons or valuation. A peer group  is a group 
of companies engaged in similar business activities whose economics and valuation 
are influenced by closely related factors. Comparisons of a company in relation to a 
well-  defined peer group can provide valuable insights into the company’s performance 
and its relative valuation.
4 For more information, see www.census.gov/eos/www/naics/faqs/faqs.html#q2.
5 For more information, see www.census.gov/eos/www/naics/concordances/concordances.html.

Reading 48 ■ Introduction to Industry and Company Analysis 198
4.4 Constructing a Peer Group
The construction of a peer group is a subjective process; the result often differs sig -
nificantly from even the most narrowly defined categories given by the commercial 
classification systems. However, commercial classification systems do provide a starting 
point for the construction of a relevant peer group because, by using such systems, an 
analyst can quickly discover the public companies operating in the chosen industry.
In fact, one approach to constructing a peer group is to start by identifying other 
companies operating in the same industry. Analysts who subscribe to one or more of 
the commercial classification systems that were discussed in Section 4.1 can quickly 
generate a list of other companies in the industry in which the company operates 
according to that particular service provider’s definition of the industry. An analyst

can then investigate the business activities of these companies and make adjustments 
as necessary to ensure that the businesses truly are comparable. The following lists 
of suggested steps and questions are given as practical aids to analysts in identifying 
peer companies.
Steps in constructing a preliminary list of peer companies
■■Examine commercial classification systems, if available to the analyst. These 
systems often provide a useful starting point for identifying companies operat -
ing in the same industry.
■■Review the subject company’s annual report for a discussion of the competitive 
environment. Companies frequently cite specific competitors.
■■Review competitors’ annual reports to identify other potential comparable 
■■Review industry trade publications to identify comparable companies.
■■Confirm that each comparable company derives a significant portion of its reve -
nue and operating profit from a business activity similar to the primary business

of the subject company.
Questions that may improve the list of peer companies
■■What proportion of revenue and operating profit is derived from business activ -
ities similar to those of the subject company? In general, a higher percentage 
results in a more meaningful comparison.
■■Does a potential peer company face a demand environment similar to that of 
the subject company? For example, a comparison of growth rates, margins, and 
valuations may be of limited value when comparing companies that are exposed 
to different stages of the business cycle. (As mentioned, such differences may be 
the result of conducting business in geographically different markets.)
■■Does a potential company have a finance subsidiary? Some companies operate 
a finance division to facilitate the sale of their products (e.g., Caterpillar Inc. 
and John Deere). To make a meaningful comparison of companies, the analyst 
should make adjustments to the financial statements to lessen the impact that

the finance subsidiaries have on the various financial metrics being compared.
Example 4 illustrates the process of identifying a peer group of companies and 
shows some of the practical hurdles to determining a peer group.

Industry Classification Systems 199
EXAMPLE 4   
An Analyst Researches the Peer Group of Brink’s Home 
Security
Suppose that an analyst needs to identify the peer group of companies for Brink’s 
Home Security for use in the valuation section of a company report. Brink’s 
is a provider of electronic security and alarm monitoring services primarily 
to residential customers in North America. The analyst starts by looking at 
Brink’s industry classification according to GICS. As previously discussed, the 
most narrowly defined category that GICS uses is the sub-  industry level, and in 
June 2009, Brink’s was in the GICS sub-  industry called Specialized Consumer 
Services, together with the companies listed here:
 
GICS Sector: Consumer Discretionary
  GICS Industry Group: Consumer Services
   GICS Industry: Diversified Consumer Services 
    GICS Sub-  Industry: Specialized Consumer Services 
     Brink’s Home Security Holdings, Inc.
     Coinstar, Inc.
     H&R Block, Inc. 
     Hillenbrand Inc.

H&R Block, Inc. 
     Mathews International Corporation
     Pre-  Paid Legal Services Inc.
     Regis Corporation 
     Service Corporation International 
     Sotheby’s
After looking over the list of companies, the analyst quickly realizes that some 
adjustments need to be made to the list to end up with a peer group of companies 
that are comparable to Brink’s. For example, Brink’s has little in common with 
the hair care salon services of Regis or, for that matter, with the funeral service 
operations of Hillenbrand, Mathews, or Service Corporation. In fact, after careful 
inspection, the analyst concludes that none of the other companies included in 
the GICS sub-  industry are particularly good “comparables” for Brink’s.
Next, the analyst reviews the latest annual report for Brink’s to find manage -
ment statements concerning its competitors. On p. 6 of Brink’s 2008 10-  K, in the 
section titled “Industry Trends and Competition, ” is a list of other companies

with comparable business activities: “We believe our primary competitors with 
national scope include: ADT Security Services, Inc., (part of Tyco International, 
Ltd.), Protection One, Inc., Monitronics International, Inc. and Stanley Security 
Solutions, (part of The Stanley Works). ” The analyst notes that Protection One 
on this list is another publicly held security services company and a likely can -
didate for inclusion in the peer group for Brink’s. Monitronics International is 
privately held, so the analyst excludes it from the peer group; up-  to- date, detailed 
fundamental data are not available for it.
The analyst discovers that ADT represents a significant portion of Tyco 
International’s sales and profits (more than 40 percent of 2008 sales and profits); 
therefore, an argument could be made to include Tyco International in the peer 
group. The analyst might also consider including Stanley Works in the peer group

because that company derived roughly a third of its revenue and close to half of 
its operating profit from its security division in 2008. Just as the analyst reviewed

Reading 48 ■ Introduction to Industry and Company Analysis 200
the latest annual report for Brink’s to identify additional potential comparables, 
the analyst should also scan the annual reports of the other companies listed 
to see if other comparables exist. In checking these three companies’ annual 
reports, the analyst finds that Protection One is the only one that cites specific 
competitors; Tyco and Stanley Works discuss competition only broadly.
After scanning all of the annual reports, the analyst finds no additional 
comparables.
The analyst decides that Brink’s peer group consists of ADT Security Services, 
Protection One, and Stanley Security Solutions but also decides to give extra 
weight to the comparison with Protection One in valuation because the com -
parison with Protection One has the fewest complicating factors.
In connection with this discussion, note that International Financial Reporting 
Standards and US GAAP require companies to disclose financial information

about their operating segments (subject to certain qualifications). Such disclo -
sures provide analysts with operational and financial information that can be 
helpful in peer-  group determination.
Although companies with limited lines of business may neatly be categorized into 
a single peer group, companies with multiple divisions may be included in more than 
one category. For example, Belgium-  based Anheuser-  Busch InBev primarily makes 
and sells various brands of beer. It can easily be grouped together with other beverage 
companies (the theme park business constitutes a relatively immaterial part of total 
revenue). However, US-  based Hewlett-  Packard Company (HP), a global provider of 
technology and software solutions, might reasonably be included in more than one 
category. Investors interested in the personal computer (PC) industry, for example, 
would probably include HP in their peer group, but investors constructing a peer

group of providers of information technology services would probably include HP 
in that group also.
In summary, analysts must distinguish between a company’s industry—as defined 
by one or more of the various classification systems—and its peer group. A compa -
ny’s peer group should consist of companies with similar business activities whose 
economic activity depends on similar drivers of demand and similar factors related to 
cost structure and access to financial capital. In practice, these necessities frequently 
result in a smaller group (even a different group) of companies than the most narrowly 
defined categories used by the common commercial classification systems. Example 5 
illustrates various aspects of developing and using peer groups.
EXAMPLE 5   
The Semiconductor Industry: Business-  Cycle Sensitivity 
and Peer-  Group Determination
The GICS semiconductor and semiconductor equipment industry (453010) has

two sub-  industries—the semiconductor equipment sub-  industry (45301010) and 
the semiconductors sub-  industry (45301020). Members of the semiconductor 
equipment sub-  industry include equipment suppliers such as Lam Research 
Corporation and ASML Holdings NV; the semiconductors sub-  industry includes 
integrated circuit manufacturers Intel Corporation and Taiwan Semiconductor 
Manufacturing Company Ltd.
Lam Research is a leading supplier of wafer fabrication equipment and 
services to the world’s semiconductor industry. Lam also offers wafer-  cleaning 
equipment that is used after many of the individual steps required to manu -
facture a finished wafer. Often, the technical advances that Lam introduces in

Industry Classification Systems 201
its wafer-  etching and wafer-  cleaning products are also available as upgrades to 
its installed base. This benefit provides customers with a cost-  effective way to 
extend the performance and capabilities of their existing wafer fabrication lines.
ASML describes itself as the world’s leading provider of lithography systems 
(etching and printing on wafers) for the semiconductor industry. ASML manufac -
tures complex machines that are critical to the production of integrated circuits 
or microchips. ASML designs, develops, integrates, markets, and services these 
advanced systems, which help chip makers reduce the size and increase the 
functionality of microchips and consumer electronic equipment. The machines 
are costly and thus represent a substantial capital investment for a purchaser.
Based on revenue, Intel is the world’s largest semiconductor chip maker and 
has the dominant share of microprocessors for the personal computer market.

Intel has made significant investments in research and development (R&D) to 
introduce and produce new chips for new applications.
Established in 1987, Taiwan Semiconductor Manufacturing (TSM) is one of 
the world’s largest dedicated semiconductor foundries (semiconductor fabrica -
tion plants that execute the designs of other companies). TSM describes itself as 
offering cutting-  edge process technologies, pioneering design services, manufac -
turing efficiency, and product quality. The company’s revenues represent about 
50 percent of the dedicated foundry segment in the semiconductor industry.
The questions that follow take the perspective of early 2009, when many 
economies around the world were in a recession. Based only on the information 
given, answer the following questions:
1 If the weak economy of early 2009 were to recover within the next 12–18 
months, which of the two sub-  industries of the semiconductor and semi -

conductor equipment industry would most likely be the first to experience 
a positive improvement in business?
2 Explain whether Intel and TSM should be considered members of the 
same peer group.
3 Explain whether Lam Research and ASML should be considered members 
of the same peer group.
In the most likely scenario, improvement in the business of the equipment makers 
(Lam and ASML) would lag that of semiconductor companies (Intel and TSM). 
Because of the weak economy of early 2009, excess manufacturing capacity 
should be available to meet increased demand for integrated circuits in the near 
term without additional equipment, which is a major capital investment. When 
semiconductor manufacturers believe the longer-  term outlook has improved, 
they should begin to place orders for additional equipment.
Solution to 2 :
Intel and TSM are not likely to be considered comparable members of the same 
peer group because they have different sets of customers and different business

models. Intel designs and produces its own proprietary semiconductors for direct 
sale to customers, such as personal computer makers. TSM provides design and 
production services to a diverse group of integrated circuit suppliers that gen -
erally do not have their own in-  house manufacturing capabilities. In mid-  2009, 
Standard & Poor’s did not group Intel and TSM in the same peer group; Intel 
was in the Semiconductors, Logic, Larger Companies group and TSM was in 
the Semiconductors, Foundry Services group.

Reading 48 ■ Introduction to Industry and Company Analysis 202
Both Lam Research and ASML are leading companies that design and manufac -
ture equipment to produce semiconductor chips. The companies are comparable 
because they both depend on the same economic factors that drive demand for 
their products. Their major customers are the semiconductor chip companies. 
In mid-  2009, Standard & Poor’s grouped both companies in the same peer 
group—Semiconductor Equipment, Larger Front End.
The next section addresses fundamental skills in describing and analyzing an 
industry.
DESCRIBING AND ANALYZING AN INDUSTRY
In their work, analysts study statistical relationships between industry trends and 
a range of economic and business variables. Analysts use economic, industry, and 
business publications and internet resources as sources of information. They also seek 
information from industry associations, from the individual subject companies they

are analyzing, and from these companies’ competitors, suppliers, and customers. An 
analyst with a superior knowledge about an industry’s characteristics, conditions, and 
trends has a competitive edge in evaluating the investment merits of the companies 
in the industry.
Analysts attempt to develop practical, reliable industry forecasts by using various 
approaches to forecasting. They often estimate a range of projections for a variable 
reflecting various possible scenarios. Analysts may seek to compare their projections 
with the projections of other analysts, partly to study differences in methodology and 
conclusions but also to identify differences between their forecasts and consensus 
forecasts. These latter differences are extremely important for uncovering investment 
opportunities because, to be the basis for superior investment performance, the forecast 
for a value-  relevant variable must be both correct and sufficiently different from the

consensus reflected in the price of publicly traded securities. Note that, although some 
information on analysts’ revenue projections, EPS estimates, and ratings are accessible 
in some markets, analysts may have limited access to details about other analysts’ work 
and assumptions because such details are kept confidential for competitive reasons.
Investment managers and analysts also examine industry performance 1) in relation 
to other industries to identify industries with superior/inferior returns and 2) over 
time to determine the degree of consistency, stability, and risk in the returns in the 
industry over time. The objective of this analysis is to identify industries that offer 
the highest potential for investment returns on a risk-  adjusted basis. The investment 
time horizon can be either long or short, as is the case for a rotation strategy in which 
portfolios are rotated into the industry groups that are expected to benefit from the 
next stage in the business cycle.

Often, analysts examine strategic groups  (groups sharing distinct business models 
or catering to specific market segments in an industry) almost as separate industries 
within industries. Criteria for selecting a strategic group might include the complexity 
of the product or service, its mode of delivery, and “barriers to entry. ” For example, 
charter airlines form a strategic group among “airlines” that is quite distinct from 
scheduled airlines; full-  service hotels form a strategic group that is separate from 
limited-  service or budget hotels; and companies that sell proprietary drugs (which are 5

Describing and Analyzing an Industry 203
protected by patents) would be in a separate group from companies that sell generic 
drugs (which do not have patent protection) partly because the two groups pursue 
different strategies and use different business models.
Analysts often consider and classify industries according to industry life-  cycle 
stage . The analyst determines whether an industry is in the embryonic, growth, shake -
out, mature, or declining stage of the industry life cycle. During the stages of the life 
cycle of a product or industry, its position on the experience curve is often analyzed. 
The experience curve  shows direct cost per unit of good or service produced or 
delivered as a typically declining function of cumulative output. The curve declines 1) 
because as the utilization of capital equipment increases, fixed costs (administration, 
overhead, advertising, etc.) are spread over a larger number of units of production,

2) because of improvements in labor efficiency and management of facilities, and 3) 
because of advances in production methods and product design. Examples exist in 
virtually all industries, but the experience curve is especially important in industries 
with high fixed overhead costs and/or repetitive production operations, such as elec -
tronics and appliance, automobile, and aircraft manufacturing. The industry life cycle 
is discussed in depth later in this reading.
Exhibit 2 provides a framework designed to help analysts check that they have 
considered the range of forces that may affect the evolution of an industry. It shows, 
at the macro level, macroeconomic, demographic, governmental, social, and techno -
logical influences affecting the industry. It then depicts how an industry is affected by 
the forces driving industry competition (threat of new entrants, substitution threats, 
customer and supplier bargaining forces), the competitive forces in the industry,

life- cycle issues, business-  cycle considerations, and position of the industry on the 
experience curve. Exhibit 2 summarizes and brings together pictorially topics and 
concepts discussed in this section.
Exhibit 2   A Framework for Industry Analysis

Reading 48 ■ Introduction to Industry and Company Analysis 204
5.1 Principles of Strategic Analysis
When analyzing an industry, the analyst must recognize that the economic fundamen -
tals can vary markedly among industries. Some industries are highly competitive, with 
most players struggling to earn adequate returns on capital, whereas other industries 
have attractive characteristics that allow almost all industry participants to generate 
healthy profits. Exhibit 3 makes this point graphically. It shows the average spread 
between return on invested capital (ROIC) and the cost of capital for 54 industries 
from 2006 through 2008.6 Industries earning positive spreads appear to be earning 
economic profits , in the sense that they are achieving returns on investment above 
the opportunity cost of funds. This result should create value—that is, should increase 
the wealth of the investors, who are the providers of capital. In contrast, industries that

are realizing negative spreads are destroying value. As can be seen, some industries 
struggled to generate positive economic returns (i.e., to create value) even during this 
period of synchronized global growth, while other industries did very well in earning 
such returns.
Exhibit 3   Some Industries Create Value, Others Destroy It: Average Industry ROIC Minus WACC, 2006–2008
Construction Machiner yData NetworkingMoney Management Data Processing Oil & Gas Services Tobacco Drugs Clothing Stores SoftwareSecurities Steel/Iron Medical Equipment Alcoholic Drinks Aerospace & Defense Beverage Mfg. Oil & Gas AdvertisingHousehold & Personal Products Semiconductors Machinery Discount Stores Publishing Specialty Retail Media Conglomerates Telecommunication Services Land Transport Coal Chemicals Food Mfg. Building Materials Department Stores Groceries Paper Auto Parts Air Transport Gold & Silver Home Building Forestry/Wood Biotechnology 
–40%–30%–20%–10%0%10%20%30%40%
Source:  Morningstar, Inc.

Differing competitive environments are often tied to the structural attributes of 
an industry, which is one reason industry analysis is a vital complement to company 
analysis. To thoroughly analyze a company itself, the analyst needs to understand 
6 Return on invested capital can be defined as net operating profit after tax divided by the sum of common 
and preferred equity, long-  term debt, and minority interests.

Describing and Analyzing an Industry 205
the context in which the company operates. Needless to say, industry analysis must 
be forward looking. Many of the industries in Exhibit 3 were very different 10 or 15 
years ago and would have been placed differently with respect to value creation; many 
will look very different 10 or 15 years from now. As analysts examine the competitive 
structure of an industry, they should always be thinking about what attributes could 
change in the future.
Analysis of the competitive environment with an emphasis on the implications 
of the environment for corporate strategy is known as strategic analysis . Michael 
Porter’s “five forces” framework is the classic starting point for strategic analysis;7 
although it was originally aimed more at internal managers of businesses than at 
external security analysts, the framework is useful to both.8
Porter (2008) identified the following five determinants of the intensity of com -
petition in an industry:

■■The threat of entry  to the industry, which depends on barriers to entry, or how 
difficult it would be for new competitors to enter the industry. Industries that 
are easy to enter will generally be more competitive than industries with high 
barriers to entry.
■■The power of suppliers , which may be able to raise prices or restrict the supply 
of key inputs to a company. For example, workers at a heavily unionized com -
pany may have greater bargaining power as suppliers of labor than workers at 
a comparable non-  unionized company. Suppliers of scarce or limited parts or 
elements often possess significant pricing power.
■■The power of buyers , which can affect the intensity of competition by exerting 
influence on suppliers regarding prices (and possibly other factors such as prod -
uct quality). For example, auto parts companies generally sell to a small number 
of auto manufacturers, which allows those customers, the auto manufacturers,

to be tough negotiators when it comes to setting prices.
■■The threat of substitutes , which can negatively affect demand if customers 
choose other ways of satisfying their needs. For example, consumers may trade 
down from premium beers to discount brands during recessions. Low-  priced 
brands may be close substitutes for premium brands, which, when consumer 
budgets are constrained, reduces the ability of premium brands to maintain or 
increase prices. Substitutes do not have to be similar but can satisfy a need with 
a very different product.
■■The rivalry among existing competitors , which is a function of the indus -
try’s competitive structure. Industries that are fragmented among many small 
competitors, have high fixed costs, provide undifferentiated (commodity-  like) 
products, or have high exit barriers usually experience more intense rivalry than 
industries without these characteristics.
Although all five of these forces merit attention, the first and fifth are particularly

recommended as a first focus for analysis. The two factors are broadly applicable 
because all companies have competitors and must worry about new entrants to their 
industries. Also, in investigating these two forces, the analyst may become familiar in 
detail with an industry’s incumbents and potential entrants, and all these companies’ 
relative competitive prospects.
7 See Porter (2008).
8 What aspects of a company are important may be different for internal and external analysts. Whether 
information about competitive positions is accurately reflected in market prices, for example, would be 
relatively more important to external analysts.

Reading 48 ■ Introduction to Industry and Company Analysis 206
Addressing the following questions should help the analyst evaluate the threat 
of new entrants and the level of competition in an industry and thereby provide an 
effective base for describing and analyzing the industry:
■■What are the barriers to entry? Is it difficult or easy for a new competitor to 
challenge incumbents? Relatively high (low) barriers to entry imply that the 
threat of new entrants is relatively low (high).
■■How concentrated is the industry? Do a small number of companies control 
a relatively large share of the market, or does the industry have many players, 
each with a small market share?
■■What are capacity levels? That is, based on existing investment, how much of 
the goods or services can be delivered in a given time frame? Does the industry 
suffer chronic over- or under-  capacity, or do supply and demand tend to come 
into balance reasonably quickly in the industry?

■■How stable are market shares? Do companies tend to rapidly gain or lose share, 
or is the industry stable?
■■Where is the industry in its life cycle? Does it have meaningful growth pros -
pects, or is demand stagnant/declining?
■■How important is price to the customer’s purchase decision?
The answers to these questions are elements of any thorough industry analysis.
5.1.1  Barriers to Entry
When a company is earning economic profits, the chances that it will be able to 
sustain them through time are greater, all else being equal, if the industry has high 
barriers to entry. The ease with which new competitors can challenge incumbents is 
often an important factor in determining the competitive landscape of an industry. 
If new competitors can easily enter the industry, the industry is likely to be highly 
competitive because high returns on invested capital will quickly be competed away by

new entrants eager to grab their share of economic profits. As a result, industries with 
low barriers to entry often have little pricing power because price increases that raise 
companies’ returns on capital will eventually attract new competitors to the industry.
If incumbents are protected by barriers to entry, the threat of new entrants is 
lower, and incumbents may enjoy a more benign competitive environment. Often, 
these barriers to entry can lead to greater pricing power, because potential competi -
tors would find it difficult to enter the industry and undercut incumbents’ prices. Of 
course, high barriers to entry do not guarantee pricing power, because incumbents 
may compete fiercely among each other.
A classic example of an industry with low barriers to entry is restaurants. Anyone 
with a modest amount of capital and some culinary skill can open a restaurant, and 
popular restaurants quickly attract competition. As a result, the industry is very com -

petitive, and many restaurants fail in their first few years of business.
At the other end of the spectrum of barriers to entry are the global credit card 
networks such as MasterCard and Visa, both of which often post operating margins 
greater than 30 percent. Such high profits should attract competition, but the barri -
ers to entry are extremely high. Capital costs are one hurdle; also, building a massive 
data-  processing network would not be cheap. Imagine for a moment that a venture 
capitalist was willing to fund the construction of a network that would replicate the 
physical infrastructure of the incumbents—the new card-  processing company would 
have to convince millions of consumers to use the new card and convince thousands 
of merchants to accept the card. Consumers would not want to use a card that 
merchants did not accept, and merchants would not want to accept a card that few

Describing and Analyzing an Industry 207
consumers carried. This problem would be difficult to solve, which is why the barriers 
to entering this industry are quite high. The barriers help preserve the profitability 
of the incumbent players.
One way of understanding barriers to entry is simply by thinking about what it 
would take for new players to compete in an industry. How much money would they 
need to spend? What kind of intellectual capital would they need to acquire? How 
easy would it be to attract enough customers to become successful?
Another way to investigate the issue is by looking at historical data. How often 
have new companies tried to enter the industry? Is a list of industry participants today 
markedly different from what it was five or ten years ago? These kinds of data can be 
very helpful because the information is based on the real-  world experience of many 
entrepreneurs and businesses making capital allocation decisions. If an industry has

seen a flood of new entrants over the past several years, odds are good that the bar -
riers are low; conversely, if the same ten companies that dominate an industry today 
dominated it ten years ago, barriers to entry are probably fairly high.
Do not confuse barriers to entry , however, with barriers to success . In some indus -
tries, entering may be easy but becoming successful enough to threaten the incumbents 
might be quite hard. For example, in the United States, starting a mutual fund requires 
a capital investment of perhaps US$150,000—not much of a barrier to an industry 
with historically high returns on capital. But once one has started a mutual fund, how 
does the company gather assets? Financial intermediaries are unlikely to sell a mutual 
fund with no track record. So, the fund may need to incur operational losses for a 
few years until it has established a good track record. Even with a track record, the

fund will be competing in a crowded marketplace against companies with massive 
advertising budgets and well-  paid salespeople. In this industry, good distribution 
can be even more valuable than good performance. So, although entering the asset 
management industry may be relatively easy, succeeding is another thing altogether.
Also, high barriers to entry do not automatically lead to good pricing power 
and attractive industry economics. Consider the cases of auto making, commercial 
aircraft manufacturing, and refining industries. Starting up a new company in any 
of these industries would be tremendously difficult. Aside from the massive capital 
costs, there would be significant other barriers to entry: A new automaker would 
need manufacturing expertise and a dealer network; an aircraft manufacturer would 
need a tremendous amount of intellectual capital; and a refiner would need process 
expertise and regulatory approvals.

Yet, all of these industries are quite competitive, with limited or nonexistent pricing 
power, and few industry participants reliably generate returns on capital in excess of 
their costs of capital. Among the reasons for this seeming paradox of high barriers to 
entry plus poor pricing power, two stand out.
■■First, price is a large component of the customer’s purchase decision when 
buying from these companies in these industries. In some cases, the reason is 
that the companies (e.g., refiners) sell a commodity; in some cases, the prod -
uct is expensive but has easily available substitutes. For example, most airlines 
choose between purchasing Boeing and Airbus airplanes not on brand but on 
cost-  related considerations: Airlines need to transport people and cargo at the 
lowest possible cost per mile because the airlines have limited ability to pass 
along higher costs to customers. That consideration makes price a huge compo -

nent of their purchase decision. Most airlines purchase whichever plane is the

Reading 48 ■ Introduction to Industry and Company Analysis 208
most cost efficient at any point in time. The result is that the Boeing Company 
and Airbus have limited ability to price their planes at a level that generates 
good returns on invested capital.9
■■Second, these industries all have high barriers to exit, which means they are 
prone to overcapacity. A refinery or automobile plant cannot be used for 
anything other than, respectively, refining oil or producing cars, which makes 
it hard to redeploy the capital elsewhere and exit the industry if conditions 
become unprofitable. This barrier gives owners of these types of assets a strong 
incentive to attempt to keep those loss-  making plants operating, which, of 
course, prolongs conditions of overcapacity.
A final consideration when analyzing barriers to entry is that they can change 
over time. Years ago, a potential new entrant to the semiconductor industry would

have needed the capital and expertise to build a “fab” (the industry term for a semi -
conductor manufacturing plant). Chip fabs are hugely expensive and technologically 
complex, which deterred potential new entrants. Starting in the mid-  1990s, however, 
the outsourcing of chip making to contract semiconductor manufacturers became 
feasible, which meant that designers of chips could challenge the manufacturers 
without the need to build their own plants. As a result, the industry became much 
more fragmented through the late 1990s and into the first decade of the 21st century.
So, in general, high barriers to entry can lead to better pricing and less competitive 
industry conditions, but important exceptions are worth bearing in mind.
5.1.2  Industry Concentration
Much like industries with barriers to entry, industries that are concentrated among 
a relatively small number of players often experience relatively less price competi -

tion. Again, there are important exceptions, so the reader should not automatically 
assume that concentrated industries always have pricing power or that fragmented 
industries do not.
An analysis of industry concentration should start with market share: What per -
centage of the market does each of the largest players have, and how large are those 
shares relative to each other and relative to the remainder of the market? Often, the 
relative  market shares of competitors matter as much as their absolute  market shares.
For example, the global market for long-  haul commercial aircraft is extremely 
concentrated—only Boeing and Airbus manufacture these types of planes. The two 
companies have roughly similar market shares, however, and control essentially the 
entire market. Because neither enjoys a scale advantage relative to its competitor and 
because any business gained by one is lost by the other, competition tends to be fierce.

This situation contrasts with the market for home improvement products in the 
United States, which is dominated by Home Depot and Lowe’s. These two companies 
have 11 percent and 7 percent market share, respectively, which doesn’t sound very 
large. However, the next largest competitor has only 2 percent of the market, and 
most market participants are tiny with miniscule market shares. Both Home Depot 
and Lowe’s have historically posted high returns on invested capital, in part because 
they could profitably grow by targeting smaller competitors rather than engaging in 
fierce competition with each other.
Fragmented industries tend to be highly price competitive for several reasons. 
First, the large number of companies makes coordination difficult because there are 
too many competitors for each industry member to monitor effectively. Second, each 
player has such a small piece of the market that even a small gain in market share can

9 Neither company’s commercial aircraft segment has reliably generated returns on capital comfortably in 
excess of the company’s cost of capital for many years. Boeing’s returns on capital have been respectable 
overall, but the company’s military segment is much more profitable than its commercial aircraft segment.

Describing and Analyzing an Industry 209
make a meaningful difference to its fortunes, which increases the incentive of each 
company to undercut prices and attempt to steal share. Finally, the large number of 
players encourages industry members to think of themselves individualistically rather 
than as members of a larger group, which can lead to fierce competitive behavior.
In concentrated industries, in contrast, each player can relatively easily keep track 
of what its competitors are doing, which makes tacit coordination much more feasible. 
Also, leading industry members are large, which means they have more to lose—and 
proportionately less to gain—by destructive price behavior. Large companies are 
also more tied to the fortunes of the industry as a whole, making them more likely to 
consider the long-  run effects of a price war on overall industry economics.
As with barriers to entry, the level of industry concentration is a guideline rather

than a hard and fast rule when thinking about the level of pricing power in an indus -
try. For example, Exhibit  4 shows a rough classification of industries compiled by 
Morningstar after asking its equity analysts whether industries were characterized 
by strong or weak pricing power and whether those industries were concentrated or 
fragmented. Examples of companies in industries are included in parentheses. In the 
upper right quadrant (“concentrated with weak pricing power”), those industries that 
are capital intensive and sell commodity-  like products are shown in boldface.
Exhibit 4   A Two-  Factor Analysis of Industries
Concentrated with Strong Pricing Power Concentrated with Weak Pricing Power
Soft Drinks (Coca-  Cola Co., PepsiCo)  
Orthopedic Devices (Zimmer, Smith & Nephew)  
Laboratory Services (Quest Diagnostics, LabCorp)  
Biotech (Amgen, Genzyme)  
Pharmaceuticals (Merck & Co., Novartis)  
Microprocessors (Intel, Advanced Micro Devices)

Microprocessors (Intel, Advanced Micro Devices)  
Industrial Gases (Praxair, Air Products and Chemicals)  
Enterprise Storage (EMC)  
Enterprise Networking (Cisco Systems)  
Integrated Shippers (UPS, FedEx, DHL International)  
US Railroads (Burlington Northern)  
US Defense (General Dynamics)  
Heavy Construction Equipment (Caterpillar, Komatsu)  
Seaborne Iron Ore (Vale, Rio Tinto)  
Confections (Cadbury, Mars/Wrigley)  
Credit Card Networks (MasterCard, Visa)  
Custody & Asset Administration (BNY Mellon, State Street)  
Investment Banking /Mergers &Acquisitions (Goldman 
Sachs, UBS)  
Futures Exchanges (Chicago Mercantile Exchange, 
Intercontinental Exchange)  
Canadian Banking (RBC Bank, TD Bank)  
Australian Banking  
Tobacco (Philip Morris, British American Tobacco)  
Alcoholic Beverages (Diageo, Pernod Ricard)Commercial Aircraft (Boeing, Airbus)  
Automobiles (General Motors, Toyota, Daimler)  
Memory (DRAM & Flash Product, Samsung, Hynix)  
Semiconductor Equipment (Applied Materials, Tokyo

Semiconductor Equipment (Applied Materials, Tokyo 
Electron)  
Generic Drugs (Teva Pharmaceutical Industries, Sandoz)  
Consumer Electronics (Sony Electronics, Koninklijke 
Philips Electronics)  
PCs (Dell, Acer, Lenovo)  
Printers/Office Machines (HP , Lexmark)  
Refiners (Valero, Marathon Oil)  
Major Integrated Oil (BP , ExxonMobil)  
Equity Exchanges (NYSE, Deutsche Börse Group)

Reading 48 ■ Introduction to Industry and Company Analysis 210
Fragmented with Strong Pricing Power Fragmented with Weak Pricing Power
Asset Management (BlackRock, Fidelity)  
For-  Profit Education (Apollo Group, DeVry University)  
Analog Chips (Texas Instruments, STMicroelectronics)  
Industrial Distribution (Fastenal, W.W. Grainger)  
Propane Distribution (AmeriGas, Ferrellgas)  
Private Banking (Northern Trust, Credit Suisse)Consumer Packaged Goods (Procter & Gamble, 
Unilever)  
Retail (Walmart, Carrefour Group)  
Marine Transportation (Maersk Line, Frontline)  
Solar Panels  
Homebuilding  
Airlines  
Mining (metals)  
Chemicals  
Engineering & Construction  
Metal Service Centers  
Commercial Printing  
Restaurants  
Radio Broadcasting  
Oil Services  
Life Insurance  
Reinsurance  
Exploration & Production (E&P)  
US Banking  
Specialty Finance  
Property/Casualty Insurance  
Household and Personal Products
Source:  Morningstar Equity Research.

The industries in the top right quadrant defy the “concentration is good for pric -
ing” guideline. We discussed the commercial aircraft manufacturing example in the 
preceding section, but many other industries are dominated by a small number of 
players yet have difficult competitive environments and limited pricing power.
When we examine these concentrated-  yet- competitive industries, a clear theme 
emerges: Many industries in this quadrant (the boldface ones) are highly capital inten -
sive and sell commodity-  like products. As we saw in the discussion of exit barriers, 
capital-  intensive industries can be prone to overcapacity, which mitigates the benefits 
of industry concentration. Also, if the industry sells a commodity product that is 
difficult—or impossible—to differentiate, the incentive to compete on price increases 
because a lower price frequently results in greater market share.10

The computer memory market is a perfect example of a concentrated-  yet- 
competitive industry. Dynamic random access memory (DRAM) is widely used in 
PCs, and the industry is concentrated, with about three-  quarters of global market share 
held by the top four companies. The industry is also highly capital intensive; a new fab 
costs upwards of US$3 billion. But one DRAM chip is much like another, and players 
in this market have a huge economic incentive to capture market share because of the 
large scale economies involved in running a semiconductor manufacturing plant. As 
a result, price competition tends to be extremely fierce and industry concentration is 
essentially a moot point in the face of these other competitive dynamics.Exhibit 4   (Continued)
10 There are a small number of concentrated and rational commodity industries, such as potash (a type 
of fertilizer) and seaborne iron ore. What sets these industries apart is that they are hyper -concentrated:

The top two players control 60 percent of the global potash market, and the top three players control two-  
thirds of the global market for seaborne iron ore.

Describing and Analyzing an Industry 211
The global soft drink market is also highly concentrated, of course, but capital 
requirements are relatively low and industry participants sell a differentiated product. 
Pepsi and Coca-  Cola do not own their own bottling facilities, so a drop in market share 
does not affect them as much as it would a memory-  chip maker. Moreover, although 
memory-  chip companies are assured of gaining market share and increasing sales 
volumes by cutting prices, a sizable proportion of consumers would not switch from 
Pepsi to Coke (or vice-  versa) even if one cost much less than the other.
Generally, industry concentration is a good indicator that an industry has pricing 
power and rational competition, but other factors may override the importance of 
concentration. Industry fragmentation is a much stronger signal that the industry is 
competitive with limited pricing power. Notice how few fragmented industries are in 
the bottom left quadrant in Exhibit 4.

The industry characteristics discussed here are guidelines meant to steer the ana -
lyst in a particular direction, not rules that should cause the analyst to ignore other 
relevant analytical factors.
5.1.3  Industry Capacity
The effect on pricing of industry capacity (the maximum amount of a good or service 
that can be supplied in a given time period) is clear: Tight, or limited, capacity gives 
participants more pricing power as demand for the product or service exceeds supply, 
whereas overcapacity leads to price cutting and a very competitive environment as 
excess supply chases demand. An analyst should think about not only current capacity 
conditions but future changes in capacity levels. How quickly can companies in the 
industry adjust to fluctuations in demand? How flexible is the industry in bringing 
supply and demand into balance? What will be the effect of that process on industry 
pricing power or on industry margins?

Generally, capacity is fixed in the short term and variable in the long term because 
capacity can be increased—e.g., new factories can be built—if time is sufficient. 
What is considered “sufficient” time—and, therefore, the duration of the short term, 
in which capacity cannot be increased—may vary dramatically among industries. 
Sometimes, adding capacity takes years to complete, as in the case of the construction 
of a “greenfield” (new) manufacturing plant for pharmaceuticals or for paper, which 
is complex and subject to regulatory requirements (e.g., relating to the plant’s waste). 
In other situations, capacity may be added or reduced relatively quickly, as is the case 
with service industries, such as advertising. In cyclical markets, such as commercial 
paper and paperboard, capacity conditions can change rapidly. Strong demand in 
the early stages of an economic recovery can result in the addition of supply. Given

the long lead times to build manufacturing plants, new supply may reach the market 
just as demand slows, rapidly changing capacity conditions from tight to loose. Such 
considerations underscore the importance of forecasting long-  term industry demand 
in evaluating industry investments in capacity.
One of the more dramatic examples of this process in recent years occurred in the 
market for maritime dry-  bulk shipping during the commodity boom of 2003–2008. 
Rapid industrialization in China—combined with synchronized global economic 
growth—increased demand for cargo ships that could transport iron ore, coal, grains, 
and other high-  volume/low-  value commodities. Given that the supply of cargo ships 
could not be increased very quickly (because ships take time to build and large com -
mercial shipyards typically have multi-  year backlogs), shippers naturally raised prices 
to take advantage of the tight global cargo capacity. In fact, the price to charter the

largest type of dry-  bulk vessel—a Capesize-  class ship too big to fit through the Panama 
Canal—increased more than fivefold in only a year, from approximately US$30,000 
per day in early 2006 to almost US$160,000 per day by late 2007.

Reading 48 ■ Introduction to Industry and Company Analysis 212
As one would expect, orders for new dry-  bulk carriers skyrocketed during this 
period as the industry scrambled to add shipping capacity to take advantage of 
seemingly insatiable demand and very favorable pricing. In early 2006, the number 
of dry-  bulk carriers on order from shipyards represented approximately 20 percent 
of the worldwide fleet. By late 2008, the number of bulk ships on order represented 
almost 70 percent of the global bulk fleet.11 Of course, the prospect of this additional 
capacity, combined with a dramatic slump in aggregate global demand for commod -
ities, caused a massive decline in shipping rates. Capesize charter rates plummeted 
from the US$160,000/day high of late 2007 to a low of under US$10,000 per day just 
one year later.
In this example, the conditions of tight supply that were driving strong dry-  bulk 
pricing were quite clear, and these high prices drove attractive returns on capital—and

share-  price performance—for dry-  bulk-  shipping companies. However, the careful 
analyst would have looked at future additions to supply in the form of new ships on 
order and would have forecasted that the tight supply conditions were not sustainable 
and thus that the pricing power of dry-  bulk shippers was short-  lived. These predictions 
are, in fact, precisely what occurred.
Note that capacity need not be physical. After Hurricane Katrina caused enormous 
damage to the southeastern United States in 2005, reinsurance rates quickly spiked 
as customers sought to increase their financial protection from future hurricanes. 
However, these high reinsurance rates enticed a flood of fresh capital into the rein -
surance market, and a number of new reinsurance companies were founded, which 
brought rates back down.
Generally, if new capacity is physical—for example, an auto manufacturing plant 
or a massive cargo ship—it will take longer for new capacity to come on line to meet

an increase in demand, resulting in a longer period of tight conditions. Unfortunately, 
capacity additions frequently overshoot long-  run demand, and because physical cap -
ital is often hard to re-  deploy, industries reliant on physical capacity may get stuck in 
conditions of excess capacity and diminished pricing power for an extended period.
Financial and human capital, in contrast, can be quickly shifted to new uses. In the 
reinsurance example, for instance, financial capital was quick to enter the reinsurance 
market and take advantage of tight capacity conditions, but if too much capital had 
entered the market, some portion of that capital could easily have left to seek higher 
returns elsewhere. Money can be used for many things, but massive bulk cargo vessels 
are not useful for much more than transporting heavy goods across oceans.
5.1.4  Market Share Stability
Examining the stability of industry market shares over time is similar to thinking

about barriers to entry and the frequency with which new players enter an industry. 
In fact, barriers to entry and the frequency of new product introductions, together 
with such factors as product differentiation—all affect market shares. Stable market 
shares typically indicate less competitive industries; unstable market shares often 
indicate highly competitive industries that have limited pricing power.
A comparison of two non-  commodity markets in the health care sector illustrates 
this point. Over the past decade, the orthopedic device industry—mainly artificial hips 
and knees—has been a relatively stable global oligopoly. As Exhibit 5 indicates, five 
companies control about 95 percent of the worldwide market, and the market shares 
of those companies have changed by only small amounts over the past several years.
11 From “RS Platou Monthly” (November  2008): www.platou.com/loadfileservlet/
loadfiledb?id=1228989312093PUBLISHER&key=1228989321421.

Describing and Analyzing an Industry 213
Exhibit 5   Market Share Stability in Global Orthopedic Devices (Entries Are 
Market Share)
Worldwide Knee/Hip Market 
Share 2005 (%) 2006 (%) 2007 (%) 2008 (%)
Zimmer 27.9 27.5 27.2 26.0
Johnson & Johnson (DePuy) 24.0 23.9 22.9 22.9
Stryker 21.6 21.4 21.5 21.3
Smith & Nephew 9.4 9.8 11.5 12.6
Biomet 11.5 10.9 10.9 11.3
Source:  Company reports and Morningstar estimates.
In contrast, although the US market for stents—small metal mesh devices used 
to prop open blocked arteries—is also controlled by a handful of companies, market 
shares recently have gone from being very stable to being marked by rapid change. 
Johnson & Johnson, which together with Boston Scientific, dominated the US stent 
market for many years, went from having about half the market in 2007 to having 
only 15 percent in early 2009; over the same period, Abbott Laboratories increased 
its market share from zero to 25 percent. The reason for this change was the launch

of new stents by Abbott and Medtronic, which took market share from Johnson & 
Johnson and Boston Scientific’s established stents.
Orthopedic device companies have experienced more stability in their market 
shares for two reasons. First, artificial hips and knees are complicated to implant, and 
each manufacturer’s products are slightly different. As a result, orthopedic surgeons 
become proficient at using one or several companies’ devices and may be reluctant 
to incur the time and cost of learning how to implant products from a competing 
company. The second reason is the relatively slow pace of innovation in the orthopedic 
device industry, which tends to be evolutionary rather than revolutionary, making the 
benefit of switching among product lines relatively low. In addition, the number of 
orthopedic device companies has remained fairly static over many years.
In contrast, the US stent market has experienced rapid shifts in market shares

because of several factors. First, interventional cardiologists seem to be more open 
than orthopedic surgeons to implanting stents from different manufacturers; that 
tendency may reflect lower switching costs for stents relative to orthopedic devices. 
More importantly, however, the pace of innovation in the stent market has become 
quite rapid, giving cardiologists added incentive to switch to newer stents, with 
potentially better patient outcomes, as they became available.
Low switching costs plus a relatively high benefit from switching caused market 
shares to change quickly in the stent market. High switching costs for orthopedic 
devices coupled with slow innovation resulted in a lower benefit from switching, 
which led to greater market share stability in orthopedic devices.
5.1.5  Industry Life Cycle
An industry’s life-  cycle position often has a large impact on its competitive dynamics, 
making this position an important component of the strategic analysis of an industry.

5.1.5.1  Description of an Industry Life-  Cycle Model  Industries, like individual com -
panies, tend to evolve over time, and usually experience significant changes in the rate 
of growth and levels of profitability along the way. Just as an investment in an individ -
ual company requires careful monitoring, industry analysis is a continuous process to 
identify changes that may be occurring or be likely to occur. A useful framework for

Reading 48 ■ Introduction to Industry and Company Analysis 214
analyzing the evolution of an industry is an industry life-  cycle model, which identifies the 
sequential stages that an industry typically goes through. The five stages of an industry 
life- cycle model are embryonic, growth, shakeout, mature, and decline. Each stage is 
characterized by different opportunities and threats.12 Exhibit 6 shows the model as a 
curve illustrating the level and growth rate of demand at each stage.
Exhibit 6   An Industry Life-  Cycle Model
TimeDemand
Shakeout
Slowing
growth
Intense
Declining
profitabilityDecline
Negative
growth
Excess
capacity
High
competitionMatu re
Little or no growth
Industry consolidation
High barriers to entryEmbryonic
Slow
growth
High prices
Significant
High riskGrowth
Rapidly
increasing
demand
Improving
Falling
prices
Low
Source:  Based on Figure 2.4 in Hill and Jones (2008).
Embryonic  An embryonic industry is one that is just beginning to develop. For exam -

ple, in the 1960s, the global semiconductor industry was in the embryonic stage (it has 
grown to become a US$249 billion industry in 2008)13 and in the early 1980s, the global 
mobile phone industry was in the embryonic stage (it now produces and sells more 
than a billion handsets annually). Characteristics of the embryonic stage include slow 
growth and high prices because customers tend to be unfamiliar with the industry’s 
product and volumes are not yet sufficient to achieve meaningful economies of scale. 
Increasing product awareness and developing distribution channels are key strategic 
initiatives of companies during this stage. Substantial investment is generally required, 
and the risk of failure is high. A majority of start-  up companies do not succeed.
Growth  A growth industry tends to be characterized by rapidly increasing demand, 
improving profitability, falling prices, and relativity low competition among companies

in the industry. Demand is fueled by new customers entering the market, and prices 
fall as economies of scale are achieved and as distribution channels develop. The threat 
12 Much of the discussion that follows regarding life-  cycle stages owes a debt to the discussion in Hill 
and Jones (2008).
13 Semiconductor Industry Association Factsheet: www.sia-  online.org/cs/industry_resources/
industry_fact_sheet.

Describing and Analyzing an Industry 215
of new competitors entering the industry is usually highest during the growth stage, 
when barriers to entry are relatively low. Competition tends to be relatively limited, 
however, because rapidly expanding demand provides companies with an opportunity to 
grow without needing to capture market share from competitors. Industry profitability 
improves as volumes rise and economies of scale are attained.
Shakeout  The shakeout stage is usually characterized by slowing growth, intense 
competition, and declining profitability. During the shakeout stage, demand approaches 
market saturation levels because few new customers are left to enter the market. 
Competition is intense as growth becomes increasingly dependent on market share 
gains. Excess industry capacity begins to develop as the rate at which companies con -
tinue to invest exceeds the overall growth of industry demand. In an effort to boost

volumes to fill excess capacity, companies often cut prices, so industry profitability 
begins to decline. During the shakeout stage, companies increasingly focus on reducing 
their cost structure (restructuring) and building brand loyalty. Marginal companies 
may fail or merge with others.
Mature  Characteristics of a mature industry include little or no growth, industry 
consolidation, and relatively high barriers to entry. Industry growth tends to be limited 
to replacement demand and population expansion because the market at this stage is 
completely saturated. As a result of the shakeout, mature industries often consolidate 
and become oligopolies. The surviving companies tend to have brand loyalty and rel -
atively efficient cost structures, both of which are significant barriers to entry. During 
periods of stable demand, companies in mature industries tend to recognize their 
interdependence and try to avoid price wars. Periodic price wars do occur, however,

most notably during periods of declining demand (such as during economic down -
turns). Companies with superior products or services are likely to gain market share 
and experience above-  industry-  average growth and profitability.
Decline  During the decline stage, industry growth turns negative, excess capacity 
develops, and competition increases. Industry demand at this stage may decline for a 
variety of reasons, including technological substitution (for example, the newspaper 
industry has been declining for years as more people turn to the internet and 24-  hour 
cable news networks for information), social changes, and global competition (for 
example, low-  cost foreign manufacturers pushing the US textile industry into decline). 
As demand falls, excess capacity in the industry forms and companies respond by 
cutting prices, which often leads to price wars. The weaker companies often exit the 
industry at this point, merge, or redeploy capital into different products and services.

When overall demand for an industry’s products or services is declining, the 
opportunity for individual companies to earn above-  average returns on invested 
capital tends to be less than when demand is stable or increasing, because of price 
cutting and higher per-  unit costs as production is cut back. Example 6 deals with 
industry life cycles.
EXAMPLE 6   
Industry Growth and Company Growth
US shipments of prefabricated housing (precut, modular housing) declined 
sharply in 1999–2004 as the abundant availability of low-  cost mortgage financ -
ing and other factors led individuals to purchase site-  built housing. In 1998, 
however, some forecasts had projected that prefabricated housing would gain 
market share at the expense of site-  built housing. What would have been the 
probable impact on market share of a typical company in the prefabricated 
housing industry under the 1998 optimistic forecast and under actual conditions?

Reading 48 ■ Introduction to Industry and Company Analysis 216
Solution:
Increasing industry demand as forecasted in 1998 would have given companies 
in the prefabricated housing industry the opportunity to grow without taking 
market share from one another, mitigating the intensity of competition in this 
industry. Under actual industry circumstances of declining demand and a shrink -
ing market, in contrast, revenue growth for a prefabricated housing company 
could happen only through market share gains from its competitors.
5.1.5.2  Using an Industry Life-  Cycle Model  In general, new industries tend to be 
more competitive (with lots of players entering and exiting) than mature industries, 
which often have stable competitive environments and players that are more inter -
ested in protecting what they have than in gaining lots of market share. However, as 
industries move from maturity to decline, competitive pressures may increase again

as industry participants perceive a zero-  sum environment and fight over pieces of an 
ever-  shrinking pie.
An important point for the analyst to think about is whether a company is “act -
ing its age” relative to where its industry sits in the life cycle. Companies in growth 
industries should be building customer loyalty as they introduce consumers to new 
products or services, building scale, and reinvesting heavily in their operations to 
capitalize on increasing demand. They are probably not focusing strongly on internal 
efficiency. These companies are rather like young adults, who are reinvesting their 
human and financial capital with the goal of becoming more successful in life. Growth 
companies typically reinvest their cash flows in new products and product platforms 
rather than returning cash flows to shareholders because these companies still have 
many opportunities to deploy their capital to make positive returns. Although this

analogy to the human life cycle is a helpful way to think about the model, the analyst 
should also be aware that the analogy is not exact in detail. Long-  established compa -
nies sometimes find a way to accelerate growth through innovation or by expansion 
into new markets. Humans cannot really move back to the days of youth. So, a more 
precise formulation may be “acting its stage” rather than acting its age.
Companies in mature industries are likely to be pursuing replacement demand 
rather than new buyers and are probably focused on extending successful product 
lines rather than introducing revolutionary new products. They are also probably 
focusing on cost rationalization and efficiency gains rather than on taking lots of 
market share. Importantly, these companies have fewer growth opportunities than in 
the previous stage, and thus more limited avenues for profitably reinvesting capital, 
but they often have strong cash flows. Given their strong cash flows and relatively

limited reinvestment opportunities, such companies should be, according to a com -
mon perspective, returning capital to shareholders via share repurchases or dividends. 
These companies are rather like middle-  aged adults who are harvesting the fruits of 
their success earlier in life.
What can be a concern is a middle-  aged company acting like a young, growth 
company and pouring capital into projects with low ROIC prospects in an effort to 
pursue size for its own sake. Many companies have a difficult time managing the 
transition from growth to maturity, and their returns on capital—and shareholder 
returns—may suffer until management decides to allocate capital in a manner more 
appropriate to the company’s life-  cycle stage.
For example, three large US retailers—Walmart, Home Depot, and McDonalds—all 
went through the transition to maturity in the first decade of the 21st century. At various 
times between 2002 and 2005, these companies realized that their size and industry

dominance meant that the days of double-  digit growth that was driven largely by new 
store (restaurant) openings were a thing of the past. All three reallocated capital away 
from opening new stores to other areas—namely, increased inventory efficiency (Home

Describing and Analyzing an Industry 217
Depot), improving the customer experience (McDonalds), and increased dividends 
and share repurchases (all three). As a result, returns on capital for each improved, 
as did shareholder returns.
5.1.5.3  Limitations of Industry Life-  Cycle Analysis  Although models can provide a 
useful framework for thinking about an industry, the evolution of an industry does not 
always follow a predictable pattern. Various external factors may significantly affect the 
shape of the pattern, causing some stages to be longer or shorter than expected and, 
in certain cases, causing some stages to be skipped altogether.
Technological changes may cause an industry to experience an abrupt shift from 
growth to decline, thus skipping the shakeout and mature stages. For example, tran -
sistors replaced vacuum tubes in the 1960s at a time when the vacuum tube industry 
was still in its growth stage; word processors replaced typewriters in the 1980s; and

today the movie rental industry is experiencing rapid change as consumers increas -
ingly turn to on-  demand services such as downloading movies from the internet or 
through their cable providers.
Regulatory changes can also have a profound impact on the structure of an indus -
try. A prime example is the deregulation of the US telecommunications industry in 
the 1990s, which transformed a monopolistic industry into an intensely competitive 
one. AT&T was broken into regional service providers, and many new long distance 
telephone service entrants, such as Sprint, emerged. The result was a wider range of 
product and service offerings and lower consumer prices. Changes in government 
reimbursement rates for health care products and services may (and have) affected 
the profitability of companies in the health care industry globally.
Social changes also have the ability to affect the profile of an industry. The casual

dining industry has benefited over the past 30 years from the increase in the number 
of dual-  income families, who often have more income but less time to cook meals 
to eat at home.
Demographics also play an important role. As the Baby Boom generation ages, for 
instance, industry demand for health care services is likely to increase.
Thus, life-  cycle models tend to be most useful for analyzing industries during peri -
ods of relative stability. They are less practical when the industry may be experiencing 
rapid change because of external or other special circumstances.
Another limiting factor of models is that not all companies in an industry experi -
ence similar performances. The key objective for the analyst is to identify the poten -
tial winners while avoiding potential losers. Highly profitable companies can exist in 
competitive industries with below-  average profitability—and vice versa. For example,

Nokia has historically been able to use its scale to generate levels of profitability that 
are well above average despite operating in a highly competitive industry. In contrast, 
despite the historically above-  average growth and profitability of the software industry, 
countless examples exist of software companies that failed to ever generate a profit 
and eventually went out of business.
EXAMPLE 7   
Industry Life Cycle
1 An industry experiencing slow growth and high prices is best character -
ized as being in the:
A mature stage.
B shakeout stage.
C embryonic stage.

Reading 48 ■ Introduction to Industry and Company Analysis 218
2 Which of the following statements about the industry life-  cycle model is 
least  accurate?
A The model is more appropriately used during a period of rapid change 
than during a period of relative stability.
B External factors may cause some stages of the model to be longer or 
shorter than expected, and in certain cases, a stage may be skipped 
entirely.
C Not all companies in an industry will experience similar performance, 
and very profitable companies can exist in an industry with below-  
average profitability.
C is correct. Both slow growth and high prices are associated with the embry -
onic stage. High price is not a characteristic of the mature or shakeout stages.
A is correct. The statement is the least accurate. The model is best used during 
a period of relative stability rather than during a period of rapid change.
5.1.6  Price Competition

A highly useful tool for analyzing an industry is attempting to think like a customer of 
the industry. Whatever factor most influences customer purchase decisions is likely to 
also be the focus of competitive rivalry in the industry. In general, industries for which 
price is a large factor in customer purchase decisions tend to be more competitive 
than industries in which customers value other attributes more highly.
Although this depiction may sound like the description of a commodity industry 
versus a non-  commodity industry, it is, in fact, a bit more subtle. Commercial aircraft 
and passenger cars are certainly more differentiated than lumps of coal or gallons of 
gasoline, but price nonetheless weighs heavily in the purchase decisions of buyers 
of aircraft and cars, because fairly good substitutes are easily available. If Airbus 
charges too much for an A320, an airline can buy a Boeing 737.14 If BMW’s price for

a four-  door luxury sedan rises too high, customers can switch to a Mercedes or other 
luxury brand with similar features. Similar switching can be expected as a result of a 
unilateral price increase in the case of most industries in the “Weak Pricing Power” 
column of Exhibit 4.
Contrast these industries with asset management, one of a handful of industries 
that is both fragmented and characterized by strong pricing power. Despite the well-  
documented impact of fees on future investment returns, the vast majority of asset 
management customers do not make decisions on the basis of price. Instead, asset 
management customers focus on historical returns, which allow this highly fragmented 
industry to maintain strong pricing power. Granted, the index fund arena is very price 
competitive, because any index fund is a perfect substitute for another fund tracking 
the same benchmark. But the active management segment of the industry has generally

been able to price its products in an implicitly cooperative fashion that enables most 
players to generate consistently high returns on capital, presumably because price is 
not uppermost in the mind of a prospective mutual fund investor.
14 A small amount of “path dependence” characterizes the airline industry, in that an airline with a large 
fleet of a particular Airbus model will be marginally more likely to stick with that model for a new purchase 
than it will be to buy a Boeing, but the aircraft manufacturers’ ability to exploit this likelihood is minimal.

Describing and Analyzing an Industry 219
Returning to a more capital-  intensive industry, consider heavy-  equipment manu -
facturers, such as Caterpillar, Deere, and Komatsu. A large wheel loader or combine 
harvester requires a large capital outlay, so price certainly plays a part in the buyers’ 
decisions. However, other factors are important enough to customers to allow these 
companies a small amount of pricing power. Construction equipment is typically used 
as a complement to other gear on a large project, which means that downtime for 
repairs increases costs because, for example, hourly laborers must wait for a bulldozer 
to be fixed. Broken equipment is also expensive for agricultural users, who may have 
only a few days in which to harvest a season’s crop. Because of the importance to users 
of their products’ reliability and their large service networks—which are important 
“differentiators” or factors bestowing a competitive advantage—Caterpillar, Komatsu,

and Deere have historically been able to price their equipment at levels that have 
generated solid returns on invested capital.
5.1.7  Industry Comparison
To illustrate how these elements might be applied, Exhibit 7 uses the factors discussed 
in this reading to examine three industries.
Exhibit 7   Elements of a Strategic Analysis for Three Industries
Branded Pharmaceuticals Oil Services Confections/Candy
Major Companies Pfizer, Novartis, Merck, 
GlaxoSmithKlineSchlumberger, Baker Hughes, 
HalliburtonCadbury, Hershey, Mars/
Wrigley, Nestle
Barriers to Entry Very High : Substantial 
financial and intellectual 
capital required to compete 
effectively. A potential new 
entrant would need to create 
a sizable R&D operation, a 
global distribution network, 
and large-  scale manufacturing 
capacity.Medium : Technological exper -
tise is required, but high level 
of innovation allows niche 
companies to enter the indus -
try and compete in specific 
areas.Very High : Low financial or 
technological hurdles, but

technological hurdles, but 
new players would lack the 
established brands that drive 
consumer purchase decisions.
Level of Concentration Concentrated : A small number 
of companies control the 
bulk of the global market 
for branded drugs. Recent 
mergers have increased level 
of concentration.Fragmented : Although only 
a small number of compa -
nies provide a full range of 
services, many smaller players 
compete effectively in specific 
areas. Service arms of national 
oil companies may control 
significant market share in 
their own countries, and some 
product lines are concentrated 
in the mature US market.Very Concentrated : Top four 
companies have a large pro -
portion of global market share. 
Recent mergers have increased 
level of concentration.
Impact of Industry 
CapacityNA: Pharmaceutical pricing 
is primarily determined by 
patent protection and regula -
tory issues, including govern -
ment approvals of drugs and 
of manufacturing facilities. 
Manufacturing capacity is of

Manufacturing capacity is of 
little importance.Medium/High : Demand can 
fluctuate quickly depending 
on commodity prices, and 
industry players often find 
themselves with too few (or 
too many) employees on the 
payroll.NA: Pricing is driven pri -
marily by brand strength. 
Manufacturing capacity has 
little effect.

Reading 48 ■ Introduction to Industry and Company Analysis 220
Industry Stability Stable : The branded pharma -
ceutical market is dominated 
by major companies and con -
solidation via mega-  mergers. 
Market shares shift quickly, 
however, as new drugs are 
approved and gain acceptance 
or lose patent protection.Unstable : Market shares may 
shift frequently depending 
on technology offerings and 
demand levels.Very Stable : Market shares 
change glacially.
Life Cycle Mature : Overall demand does 
not change greatly from year 
to year.Mature : Demand does fluc -
tuate with energy prices, but 
normalized revenue growth is 
only mid-  single digits.Very Mature : Growth is driven 
by population trends and 
pricing.
Price Competition Low/Medium : In the United 
States, price is a minimal fac -
tor because of consumer- and 
provider-  driven, de-  regulated 
health care system. Price is a 
larger part of the decision pro -
cess in single-  payer systems,

cess in single-  payer systems, 
where efficacy hurdles are 
higher.High : Price is a major factor 
in purchasers’ decisions. 
Some companies have modest 
pricing power because of 
a wide range of services or 
best-  in- class technology, but 
primary customers (major 
oil companies) can usually 
substitute with in-  house 
services if prices are too high. 
Also, innovation tends to 
diffuse quickly throughout the 
industry.Low: A lack of private-  label 
competition keeps pricing sta -
ble among established players, 
and brand/familiarity plays a 
much larger role in consumer 
purchase decisions than price.
Demographic 
InfluencesPositive : Populations of devel -
oped markets are aging, which 
slightly increases demand.NA NA
Government & 
Regulatory InfluencesVery High : All drugs must be 
approved for sale by national 
safety regulators. Patent 
regimes may differ among 
countries. Also, health care 
is heavily regulated in most 
countries.Medium : Regulatory frame -
works can affect energy 
demand at the margin.

demand at the margin. 
Also, governments play an 
important role in allocating 
exploration opportunities to 
E&P companies, which can 
indirectly affect the amount of 
work flowing down to service 
companies.Low: Industry is not regulated, 
but childhood obesity concerns 
in developed markets are a 
low-  level potential threat. Also, 
high-  growth emerging markets 
may block entry of established 
players into their markets, 
possibly limiting growth.
Social Influences NA NA NAExhibit 7   (Continued)

Describing and Analyzing an Industry 221
Technological 
InfluencesMedium/High : Biologic (large-  
molecule) drugs are pushing 
new therapeutic boundaries, 
and many large pharmaceuti -
cal companies have a relatively 
small presence in biotech.Medium/High : Industry is 
reasonably innovative, and 
players must re-  invest in 
R&D to remain competi -
tive. Temporary competitive 
advantages are possible via 
commercialization of new 
processes or exploitation of 
accumulated expertise.Very Low : Innovation does 
not play a major role in the 
industry.
Growth vs. Defensive 
vs. CyclicalDefensive : Demand for most 
health care services does not 
fluctuate with the economic 
cycle, but demand is not 
strong enough to be consid -
ered “growth. ”Cyclical : Demand is highly 
variable and depends on oil 
prices, exploration budgets, 
and the economic cycle.Defensive : Demand for candy 
and gum is extremely stable.

Note : “NA” in this exhibit stands for “not applicable. ”
Example 8 reviews some of the information presented in Exhibit 7.
EXAMPLE 8   
External Influences
1 Which of the following industries is most  affected by government 
regulation?
A Oil services.
B Pharmaceuticals.
C Confections and candy.
2 Which of the following industries is least  affected by technological 
innovation?
3 Which of the following statements about industry characteristics is least  
accurate?
A Manufacturing capacity has little effect on pricing in the confections/
candy industry.
B The branded pharmaceutical industry is considered to be defensive 
rather than a growth industry.
C With respect to the worldwide market, the oil services industry has a 
high level of concentration with a limited number of service providers.
B is correct. Exhibit 7 states that the pharmaceutical industry has high amount

Reading 48 ■ Introduction to Industry and Company Analysis 222
C is correct. Exhibit 7 states that innovation does not play a large role in the 
C is correct; it is a false statement. From a worldwide perspective, the industry 
is considered fragmented. Although a small number of companies provide the 
full range of services, competition by many smaller players occurs in niche areas. 
In addition, national oil service companies control significant market share in 
their home countries.
5.2 External Influences on Industry Growth, Profitability, 
and Risk
External factors affecting an industry’s growth include macroeconomic, technological, 
demographic, governmental, and social influences.
5.2.1  Macroeconomic Influences
Trends in overall economic activity generally have significant effects on the demand 
for an industry’s products or services. These trends can be cyclical (i.e., related to the

changes in economic activity caused by the business cycle) or structural (i.e., related 
to enduring changes in the composition or magnitude of economic activity). Among 
the economic variables that usually affect an industry’s revenues and profits are the 
■■gross domestic product or the measure of the value of goods and services 
produced by an economy, either in current or constant currency (inflation-  
adjusted) terms;
■■interest rates, which represent the cost of debt to consumers and businesses and 
are important ingredients in financial institutions’ revenues and costs;
■■the availability of credit, which affects business and consumer spending and 
financial solvency; and
■■inflation, which reflects the changes in prices of goods and services and influ -
ences costs, interest rates, and consumer and business confidence.
5.2.2  Technological Influences
New technologies create new or improved products that can radically change an

industry and can also change how other industries that use the products conduct 
their operations.
The computer hardware industry provides one of the best examples of how tech -
nological change can affect industries. The 1958 invention of the microchip (also 
known as an “integrated circuit, ” which is effectively a computer etched on a sliver of 
silicon) enabled the computer hardware industry to eventually create a new market of 
personal computing for the general public and radically extended the use of computers 
in business, government, and educational institutions.
Moore’s law states that the number of transistors that can be inexpensively placed 
on an integrated circuit doubles approximately every two years. Several other mea -
sures of digital technology have improved at exponential rates related to Moore’s law, 
including the size, cost, density and speed of components. As a result of these trends, 
the computer hardware industry encroached upon and, in time, came to dominate the

fields of hardware for word processing and many forms of electronic communication 
and home entertainment. The computing industry’s integrated circuit innovation

Describing and Analyzing an Industry 223
increased economies of scale and erected large barriers to new entrants because the 
capital costs of innovation and production became very high. Intel capitalized on 
both factors which allowed it to garner an industry market leadership position and 
to become the dominant supplier of the PC industry’s highest value component (the 
microprocessor). Thus, Intel became dominant because of its cost advantage, brand 
power, and access to capital.
Along the way, the computer hardware industry was supported and greatly assisted 
by the complementary industries of computer software and telecommunications 
(particularly in regard to development of the internet); also important were other 
industries—entertainment (television, movies, games), retailing, and the print media. 
Ever more powerful integrated circuits and advances in wireless technology, as well 
as the convergence of media, which the internet and new wireless technology have

facilitated, continue to reshape the uses and the roles of PC hardware in business and 
personal life. In the middle of the 20th century, few people in the world would have 
imagined they would ever have any use for a home computer. Today, the estimate is 
that about 1.6 billion people, or almost a quarter of the world’s population, have access 
to connected computing. For the United States, the estimate is at least 76 percent of 
the population; it is much less in emerging and underdeveloped countries. More than 
4 billion mobile cellular telephone subscriptions exist in the world today,15 and the 
advances of mobile telephony appear poised to increase this figure dramatically in the 
years ahead as mobile phone and computer hardware technologies merge to provide 
new hand-  held computing and communication capabilities.
Another example of the effects of technology on an industry is the impact of dig -
ital imaging technology on the photographic film industry. Digital imaging uses an

electronic image sensor to record an image as electronic data rather than as chemical 
changes on film. This difference allows a much greater degree of image processing and 
transmission than in film photography. Since their invention in 1981, digital cameras 
have become extremely popular and now widely outsell traditional film cameras 
(although many professional photographers continue to use film for esthetic reasons 
for certain applications). Digital cameras include such features as video and audio 
recording. The effects of this major change in photographic technology have caused 
film and camera manufacturers—including Kodak, Fujifilm, Nikon Corporation, and 
Pentax Imaging Company—to completely restructure and redesign their products to 
adapt to the new technology’s appeal to consumers.
5.2.3  Demographic Influences
Changes in population size, in the distributions of age and gender, and in other demo -
graphic characteristics may have significant effects on economic growth and on the

amounts and types of goods and services consumed.
The effects of demographics on industries are well exemplified by the impact of the 
post–World War II Baby Boom in North America on demand for goods and services. 
Born between 1946 and 1964, this bulge of 76 million people in the North American 
population has influenced the composition of numerous products and services it 
needs in its passage from the cradle through childhood, adolescence, early adulthood, 
middle age, and into retirement. The teenage pop culture of the late 1950s and 1960s 
and all the products (records, movies, clothes, and fashions associated with it), the 
surge in demand for housing in the 1970s and 1980s, and the increasing demand for 
retirement-  oriented investment products in the 1990s and early 2000s are all examples 
of the range of industries affected by this demographic bulge working its way through 
age categories of the population.
15 See www.itu.int/newsroom/press_releases/2009/39.html.

Reading 48 ■ Introduction to Industry and Company Analysis 224
Another example of the effects of demographics on industries is the impact of an 
aging population in Japan, which has one of the highest percentages of elderly residents 
(21 percent over the age of 65) and a very low birth rate. Japan’s ministry of health 
estimates that by 2055, the percentage of the population over 65 will rise to 40 per -
cent and the total population will fall by 25 percent. These demographic changes are 
expected by some observers to have negative effects on the overall economy because, 
essentially, they imply a declining workforce. However, some sectors of the economy 
stand to benefit from these trends—for example, the health care industry.
EXAMPLE 9   
The Post–World War II Baby Boom and Its Effects on the 
US Housing Industry
In the United States, Canada, and Australia, the end of World War II marked the 
beginning of a sustained period of elevated birth rates per thousand in the pop -

ulation. This rise reflected the relief from the hardships of the Great Depression 
of the 1930s and WWII, increased levels of immigration (immigrants tend to 
be younger and hence more fertile than average) and a protracted period of 
postwar economic prosperity. The rate of births in the United States rose from 
18.7 per thousand in 1935 and 20.4 per thousand in 1945 to 24.1 per thousand 
in 1950 and a peak of more than 25.0 per thousand in 1955–1957. Twenty years 
later, when the babies born during the period 1946–1964 entered adulthood, 
the housing industry experienced a surge in demand that led to a period of high 
sales of new homes. The rate of new housing starts in this period rose from 20.1 
per thousand of population in 1966 to a peak of 35.3 per thousand in 1972 and 
remained elevated, except during the economic recession of 1974–1975, until 
the end of the 1970s.
Another demographic effect on the housing industry arising from the post-

WWII Baby Boom came from the children of the Baby Boom generation (the 
so- called Echo Boomers). The Echo Boomers started to enter their most fertile 
years in the late 1970s and caused an increase in the number of births per thou -
sand from a post-  WWII low of 14.8 in 1975 to a peak of 16.7 in 1990. The Echo 
Boomers did not have as large an effect on housing demand 20 years later as 
their parents had had, but there was still a significant increase in new housing 
starts from 13.7 per thousand in 1995 to a high of 18.8 per thousand in 2005; 
easily available mortgage financing contributed to the increase.
5.2.4  Governmental Influences
Governmental influence on industries’ revenues and profits is pervasive and important. 
In setting tax rates and rules for corporations and individuals, governments affect profits 
and incomes, which in turn, affect corporate and personal spending. Governments 
are also major purchasers of goods and services from a range of industries.

Example 10 illustrates the sudden shifts in wealth that can occur when govern -
ments step in to support or quash a securities market innovation. In the example, an 
income trust  refers to a type of equity ownership vehicle established as a trust issuing 
ownership shares known as units. Income trusts became extremely popular among 
income-  oriented investors in Canada in the late 1990s and early 2000s because under 
then-  current regulation, such trusts could avoid taxation on income distributed to 
unit-  holders (investors)—that is, avoid double taxation (once at the corporate level 
and once at the investor level). As Example 10 describes, the tax advantage that reg -
ulations permitted was eventually removed.

Describing and Analyzing an Industry 225
EXAMPLE 10   
The Effects of Tax Increases on Income Trusts in Canada
On 31 October 2006, in an effort to halt the rapid growth of income trust struc -
tures in the Canadian stock market, Canada’s Minister of Finance James Flaherty 
announced that these tax-  exempt flow-  through entities would in the future be 
taxable on the income, with exemptions only for passive rent-  collecting real 
estate investment trusts. A five year hiatus was established for existing trusts to 
adapt. He stated that the government needed to clamp down on trusts because 
too many companies were converting to the high-  yield securities, primarily to 
save taxes. The S&P/TSX Capped Income Trust Index declined 12 percent on 
the day after the announcement, wiping out C$24 billion in market value.
Often, governments exert their influence indirectly by empowering other regu -
latory or self-  regulatory organizations (e.g., stock exchanges, medical associations,

utility rate setters, and other regulatory commissions) to govern the affairs of an 
industry. By setting the terms of entry into various sectors, such as financial services 
and health care, and the rules that companies and individuals must adhere to in these 
fields, governments control the supply, quality, and nature of many products and 
services and the public’s access to them. For example, in the financial industry, the 
acceptance of savings deposits from and the issuance of securities to the investing 
public are usually tightly controlled by governments and their agencies. This control 
is imposed through rules designed to protect investors from fraudulent operators and 
to ensure that investors receive adequate disclosure about the nature and risks of their 
investments. Another example is that medical patients in most developed countries 
are treated by doctors who are trained according to standards set by medical asso -

ciations acting as self-  regulatory organizations empowered under government laws. 
In addition, the medications that patients receive must be approved by government 
agencies. In a somewhat different vein, users of tobacco products purchase items for 
which the marketing and sales taxes are heavily controlled by governments in most 
developed countries and for which warnings to consumers about the dangers of smok -
ing are mandated by governments. In the case of industries that supply branches of 
government, such as the military, public works, and law enforcement departments, 
government contracts directly affect the revenues and profits of the suppliers.
EXAMPLE 11   
The Effects of Government Purchases on the Aerospace 
Industry
The aerospace, construction, and firearms industries are prime examples of 
industries for which governments are major customers and whose revenues and 
profits are significantly—in some cases, predominantly—affected by their sales

to governments. An example is the European Aeronautic Defence and Space 
Company (EADS), a global leader in aerospace, defense, and related services 
with head offices in Paris and Ottobrunn, Germany. In 2008, EADS generated 
revenues of €43.3  billion and employed an international workforce of about 
118,000. EADS includes Airbus, a leading manufacturer of commercial aircraft; 
Airbus Military, providing tanker, transport, and mission aircraft; Eurocopter, the 
world’s largest helicopter supplier; and EADS Astrium, the European leader in 
space programs, including Ariane and Galileo. Its Defence & Security Division 
is a provider of comprehensive systems solutions and makes EADS the major

Reading 48 ■ Introduction to Industry and Company Analysis 226
partner in the Eurofighter consortium and a stakeholder in missile systems pro -
vider MBDA. On 3 March 2008, EADS shares rose 9.2 percent after the US Air 
Force chose its Airbus A330 over Boeing’s 767 for an airborne refueling plane 
contract worth as much as US$35 billion.
5.2.5  Social Influences
Societal changes involving how people work, spend their money, enjoy their leisure 
time, and conduct other aspects of their lives can have significant effects on the sales 
of various industries.
Tobacco consumption in the United Kingdom provides a good example of the 
effects of social influences on an industry. Although the role of government in curbing 
tobacco advertising, legislating health warnings on the purchases of tobacco products, 
and banning smoking in public places (such as restaurants, bars, public houses, and 
transportation vehicles) probably has been the most powerful apparent instrument of

changes in tobacco consumption, the forces underlying that change have really been 
social in nature—namely, increasing consciousness on the part of the population of 
the damage to the health of tobacco users and those in their vicinity from smoking, 
the increasing cost to individuals and governments of the chronic illnesses caused by 
tobacco consumption, and the accompanying shift in public perception of smokers 
from socially correct to socially incorrect—even inconsiderate or reckless. As a result 
of these changes in society’s views of smoking, cigarette consumption in the United 
Kingdom declined from 102.5 billion cigarettes in 1990 to less than 65.0 billion in 
2009, placing downward pressure on tobacco companies’ unit sales.
EXAMPLE 12   
The Effects on Various Industries of More Women Entering 
the Workforce
In 1870, women accounted for only 15 percent of the workforce in the United 
States outside the home. By 1950, after two world wars and the Great Depression,

this figure had risen to 30 percent (it had been even higher temporarily during 
WWII because of high levels of war-  mandated production) and by 2008, to 
48 percent. Based on economic reasoning, identify four industries that should 
have benefitted from the social change that saw women shift from their most 
frequent historical roles in Western society as full-  time homemakers to becoming 
more frequently full-  time participants in the workforce.
Solution:
Industries include the following:
1 The restaurant business. The restaurant business stands to benefit from 
an increased demand given that women, because of their work responsi -
bilities, may not have the time and energy to prepare meals. Restaurant 
industry growth was actually high in this period: From accounting for only 
25 percent of every food dollar in the United States in 1950, the restaurant 
industry today consumes more than 44 percent of every food dollar, with

45 percent of current industry revenues arising from a category of restau -
rant that did not exist in 1950, namely, fast food.
2 Manufacturers of work clothing for women.
3 Home and child care services.

Describing and Analyzing an Industry 227
4 Automobile manufacturers. Extra vehicles became necessary to transport 
two members of the family to work, for instance, and children to school or 
day care.
5 Housing for the aging. With increasing workforce participation by women, 
aged family members requiring care or supervision became increasingly 
unable to rely on non-  working female family members to provide care in 
their homes.
EXAMPLE 13   
The Airline Industry: A Case Study of Many Influences
The global airline industry exemplifies many of the concepts and influences we 
have discussed.
Life-  Cycle Stage
The industry can be described as having some mature characteristics because 
average annual growth in global passenger traffic has remained relatively stable at 
4.5 percent in the 2000s (compared with 4.7 percent in the 1990s). Some market 
segments in the industry, however, are still in their growth phase—notably, the

markets of the Middle East and Asia, which are expected to grow at 6.5 percent 
compared with projected North American growth of 3.2 percent over the next 
20 years.
Sensitivity to Business Cycle
The airline industry is a cyclical industry; global economic activity produces 
swings in revenues and, especially, profitability, because of the industry’s high 
fixed costs and operating leverage. In 2009, for example, global passenger traffic is 
expected to have declined by approximately 8 percent and airlines are expected to 
report significant net losses—close to US$9.0 billion, which is down from a global 
industry profit of US$12.9 billion in 2007. The industry tends to respond early 
to upward and downward moves in economic cycles; depending on the region, 
air travel changes at 1.5 times to 2.0 times GDP growth. It is highly regulated, 
with governments and airport authorities playing a large role in allocating routes

and airport slots. Government agencies and the International Airline Transport 
Association set rules for aircraft and flight safety. Airline customers tend to have 
low brand loyalty (except at the extremes of high and low prices and service); 
leisure travelers focus mainly on price, and business travelers focus mostly on 
schedules and service. Product and service differentiation at particular price 
points is low because aircraft, cabin configuration, and catering tend to be quite 
similar in most cases. For leisure travelers, the price competition is intense and 
is led by low-  cost discount carriers, including Southwest Airlines in the United 
States, Ryanair in Europe, and Air Asia in Asia. For business travelers, the 
major scheduled airlines and a few service-  quality specialists, such as Singapore 
Airlines, are the main contenders. Fuel costs (typically more than 25 percent 
of total costs and highly volatile) and labor costs (around 10 percent of total

costs) have been the focus of management cost-  reduction efforts. The airline 
industry is highly unionized, and labor strife has frequently been a source of 
costly disruptions to the industry. Technology has always played a major role in 
the airline industry, from its origins with small propeller-  driven planes through 
the advent of the jet age to the drive for greater fuel efficiency since the oil price 
increases of the 1970s. Technology also poses a threat to the growth of business

Reading 48 ■ Introduction to Industry and Company Analysis 228
air travel in the form of improved telecommunications—notably, videoconfer -
encing and webcasting. Arguably, the airline industry has been a great force in 
shaping demography by permitting difficult-  to- access geographical areas to be 
settled with large populations. At the same time, large numbers of post-  WWII 
Baby Boomers have been a factor in generating the growth in demand for air 
travel in the past half-  century. In recent years, social issues have started to play 
a role in the airline industry; carbon emissions, for example, have come under 
scrutiny by environmentalists and governments.
COMPANY ANALYSIS
Company analysis includes an analysis of the company’s financial position, products 
and/or services, and competitive strategy  (its plans for responding to the threats and 
opportunities presented by the external environment). Company analysis takes place

after the analyst has gained an understanding of a company’s external environment—  
the macroeconomic, demographic, governmental, technological, and social forces 
influencing the industry’s competitive structure. The analyst should seek to determine 
whether the strategy is primarily defensive or offensive in its nature and how the 
company intends to implement the strategy.
Porter identifies two chief competitive strategies: a low-  cost strategy (cost lead -
ership) and a product/service differentiation strategy.
In a low-  cost strategy, companies strive to become the low-  cost producers and to 
gain market share by offering their products and services at lower prices than their 
competition while still making a profit margin sufficient to generate a superior rate 
of return based on the higher revenues achieved. Low-  cost strategies may be pursued 
defensively to protect market positions and returns or offensively to gain market

share and increase returns. Pricing also can be defensive (when the competitive envi -
ronment is one of low rivalry) or aggressive (when rivalry is intense). In the case of 
intense rivalry, pricing may even become predatory—that is, aimed at rapidly driving 
competitors out of business at the expense of near-  term profitability. The hope in 
such a strategy is that having achieved a larger market share, the company can later 
increase prices to generate higher returns than before. For example, the predatory 
strategy has been alleged by some analysts to have been followed by major airlines 
trying to protect lucrative routes from discount airlines. Although laws concerning 
anti-  competitive practices often prohibit predatory pricing to gain market share, in 
most cases, it is difficult to accurately ascribe the costs of products or services with 
sufficient precision to demonstrate that predatory pricing (as opposed to intense but

fair price competition) is occurring. Companies seeking to follow low-  cost strategies 
must have tight cost controls, efficient operating and reporting systems, and appro -
priate managerial incentives. In addition, they must commit themselves to painstaking 
scrutiny of production systems and their labor forces and to low-  cost designs and 
product distribution. They must be able to invest in productivity-  improving capital 
equipment and to finance that investment at a low cost of capital.
In differentiation strategies, companies attempt to establish themselves as the 
suppliers or producers of products and services that are unique either in quality, type, 
or means of distribution. To be successful, their price premiums must be above their 
costs of differentiation and the differentiation must be appealing to customers and 
sustainable over time. Corporate managers who successfully pursue differentiation 
strategies tend to have strong market research teams to identify and match customer

needs with product development and marketing. Such a strategy puts a premium on 
employing creative and inventive people.6

Company Analysis 229
6.1 Elements That Should be Covered in a Company Analysis
A thorough company analysis, particularly as presented in a research report, should
■■provide an overview of the company (corporate profile), including a basic 
understanding of its businesses, investment activities, corporate governance, 
and perceived strengths and weaknesses;
■■explain relevant industry characteristics;
■■analyze the demand for the company’s products and services;
■■analyze the supply of products and services, which includes an analysis of costs;
■■explain the company’s pricing environment; and
■■present and interpret relevant financial ratios, including comparisons over time 
and comparisons with competitors.
Company analysis often includes forecasting the company’s financial statements, 
particularly when the purpose of the analysis is to use a discounted cash flow method 
to value the company’s common equity.
Exhibit 8 provides a checklist of points to cover in a company analysis. The list

may need to be adapted to serve the needs of a particular company analysis and is 
not exhaustive.
Exhibit 8   A Checklist for Company Analysis
Corporate Profile
■■Identity of company’s major products and services, current position in 
industry, and history
■■Composition of sales
■■Product life-  cycle stages/experience curve effects16
■■Research & development activities
■■Past and planned capital expenditures
■■Board structure, composition, electoral system, anti-  takeover provisions, 
and other corporate governance issues
■■Management strengths, weaknesses, compensation, turnover, and corpo -
rate culture
■■Benefits, retirement plans, and their influence on shareholder value
■■Labor relations
■■Insider ownership levels and changes
■■Legal actions and the company’s state of preparedness
■■Other special strengths or weaknesses
Industry Characteristics
■■Stage in its life cycle
■■Business-  cycle sensitivity or economic characteristics

16 A product life cycle  relates to stages in the sales of a product. Experience curve effects  refer to the ten -
dency for the cost of producing a good or service to decline with cumulative output.

Reading 48 ■ Introduction to Industry and Company Analysis 230
■■Typical product life cycles in the industry (short and marked by tech -
nological obsolescence or long, such as pharmaceuticals protected by 
patents)
■■Brand loyalty, customer switching costs, and intensity of competition
■■Entry and exit barriers
■■Industry supplier considerations (concentration of sources, ability to 
switch suppliers or enter suppliers’ business)
■■Number of companies in the industry and whether it is, as determined by 
market shares, fragmented or concentrated
■■Opportunity to differentiate product/service and relative product/service 
price, cost, and quality advantages/disadvantages
■■Technologies used
■■Government regulation
■■State and history of labor relations
■■Other industry problems/opportunities
Analysis of Demand for Products/Services
■■Sources of demand
■■Product differentiation
■■Past record, sensitivities, and correlations with social, demographic, eco -
nomic, and other variables

■■Outlook—short, medium, and long term, including new product and 
business opportunities
Analysis of Supply of Products/Services
■■Sources (concentration, competition, and substitutes)
■■Industry capacity outlook—short, medium, and long term
■■Company’s capacity and cost structure
■■Import/export considerations
■■Proprietary products or trademarks
Analysis of Pricing
■■Past relationships among demand, supply, and prices
■■Significance of raw material and labor costs and the outlook for their cost 
and availability
■■Outlook for selling prices, demand, and profitability based on current and 
anticipated future trends
Financial Ratios and Measures
(in multi-  year spreadsheets with historical and forecast data)
 I. Activity ratios , measuring how efficiently a company performs such func -
tions as the collection of receivables and inventory management:
■●Days of sales outstanding (DSO)
■●Days of inventory on hand (DOH)Exhibit 8   (Continued)

Company Analysis 231
■●Days of payables outstanding (DPO)
 II. Liquidity ratios , measuring a company’s ability to meet its short-  term 
obligations:
■●Current ratio
■●Quick ratio
■●Cash ratio
■●Cash conversion cycle (DOH + DSO – DPO)
 III. Solvency ratios , measuring a company’s ability to meet its debt obli -
gations. (In the following, “net debt” is the amount of interest-  bearing 
liabilities after subtracting cash and cash equivalents.)
■●Net debt to EBITDA (earnings before interest, taxes, depreciation, and 
amortization)
■●Net debt to capital
■●Debt to assets
■●Debt to capital (at book and market values)
■●Financial leverage ratio (Average total assets/Average total equity)
■●Cash flow to debt
■●Interest coverage ratio
■●Off- balance-  sheet liabilities and contingent liabilities
■●Non-  arm’s-  length financial dealings
 IV. Profitability ratios , measuring a company’s ability to generate profitable 
sales from its resources (assets).
■●Gross profit margin
■●Operating profit margin

■●Pretax profit margin
■●Net profit margin
■●Return on invested capital or ROIC (Net operating profits after tax/
Average invested capital)
■●Return on assets or ROA (Net income/ Average total assets)
■●Return on equity or ROE (Net income/Average total equity)
 V. Financial Statistics and Related Considerations , quantities and facts 
about a company’s finances that an analyst should understand.
■●Growth rate of net sales
■●Growth rate of gross profit
■●EBITDA
■●Net income
■●Operating cash flow
■●EPS
■●Operating cash flow per share
■●Operating cash flow in relation to maintenance and total capital 
■●Expected rate of return on retained cash flow
■●Debt maturities and ability of company to refinance and/or repay debt

Reading 48 ■ Introduction to Industry and Company Analysis 232
■●Dividend payout ratio (Common dividends/Net income available to 
common shareholders)
To evaluate a company’s performance, the key measures presented in Exhibit 8 
should be compared over time and between companies (particularly peer companies). 
The following formula can be used to analyze how and why a company’s ROE differs 
from that of other companies or its own ROE in other periods by tracing the differences 
to changes in its profit margin, the productivity of its assets, or its financial leverage:
 ROE = (Net profit margin: Net earnings/Net sales) × (Asset turnover: Net sales/
Average total assets) × (Financial leverage: Average total assets/
Average common equity)
The financial statements of a company over time provide numerous insights into

the effects of industry conditions on its performance and the success or failure of its 
strategies. They also provide a framework for forecasting the company’s operating 
performance when given the analyst’s assumptions for numerous variables in the future. 
The financial ratios listed in Exhibit 8 are applicable to a wide range of companies and 
industries, but other statistics and ratios are often also used.
6.2 Spreadsheet Modeling
Spreadsheet modeling of financial statements to analyze and forecast revenues, oper -
ating and net income, and cash flows has become one of the most widely used tools in 
company analysis. Although spreadsheet models are a valuable tool for understanding 
past financial performance and forecasting future performance, the complexity of such 
models can at times be a problem. Because modeling requires the analyst to predict 
and input numerous items in financial statements, there is a risk of errors—either

in assumptions made or in formulas in the model—which can compound, leading to 
erroneous forecasts. Yet, those forecasts may seem precise because of the sheer com -
plexity of the model. The result is often a false sense of understanding and security 
on the part of those who rely on the models. To guard against this, before or after a 
model is completed, a “reality check” of the model is useful.
Such testing for reasonableness can be done by, first, asking what the few most 
important changes in income statement items are likely to be from last year to this 
year and the next year and, second, attempting to quantify the effects of these signif -
icant changes or “swing factors” on the bottom line. If an analyst cannot summarize 
in a few points what factors are realistically expected to change income from year to 
year and is not convinced that these assumptions are correct, then he or she does not 
really understand the output of the computer modeling efforts. In general, financial

models should be in a format that matches the company’s reporting of its financial 
results or supplementary disclosures or that can be accurately derived from these 
reports. Otherwise, there will be no natural reality check when the company issues 
its financial results and the analyst will not be able to compare his or her estimates 
with actual reported results.Exhibit 8   (Continued)

Summary 233
SUMMARY
In this reading, we have provided an overview of industry analysis and illustrated 
approaches that are widely used by analysts to examine an industry.
■■Company analysis and industry analysis are closely interrelated. Company and 
industry analysis together can provide insight into sources of industry revenue 
growth and competitors’ market shares and thus the future of an individual 
company’s top-  line growth and bottom-  line profitability.
■■Industry analysis is useful for:
■●understanding a company’s business and business environment;
■●identifying active equity investment opportunities;
■●formulating an industry or sector rotation strategy; and
■●portfolio performance attribution.
■■The three main approaches to classifying companies are:
■●products and/or services supplied;
■●business-  cycle sensitivities; and
■●statistical similarities.
■■Commercial industry classification systems include:
■●Global Industry Classification Standard;
■●Russell Global Sectors; and

■●Industry Classification Benchmark.
■■Governmental industry classification systems include:
■●International Standard Industrial Classification of All Economic Activities;
■●Statistical Classification of Economic Activities in the European 
Community;
■●Australian and New Zealand Standard Industrial Classification; and
■●North American Industry Classification System.
■■A limitation of current classification systems is that the narrowest classification 
unit assigned to a company generally cannot be assumed to constitute its peer 
group for the purposes of detailed fundamental comparisons or valuation.
■■A peer group is a group of companies engaged in similar business activities 
whose economics and valuation are influenced by closely related factors.
■■Steps in constructing a preliminary list of peer companies:
■●Examine commercial classification systems if available. These systems often 
provide a useful starting point for identifying companies operating in the

same industry.
■●Review the subject company’s annual report for a discussion of the competi -
tive environment. Companies frequently cite specific competitors.
■●Review competitors’ annual reports to identify other potential comparables.
■●Review industry trade publications to identify additional peer companies.
■●Confirm that each comparable or peer company derives a significant portion 
of its revenue and operating profit from a similar business activity as the 
subject company.

Reading 48 ■ Introduction to Industry and Company Analysis 234
■■Not all industries are created equal. Some are highly competitive, with many 
companies struggling to earn returns in excess of their cost of capital, and other 
industries have attractive characteristics that enable a majority of industry par -
ticipants to generate healthy profits.
■■Differing competitive environments are determined by the structural attributes 
of the industry. For this important reason, industry analysis is a vital com -
plement to company analysis. The analyst needs to understand the context in 
which a company operates to fully understand the opportunities and threats 
that a company faces.
■■The framework for strategic analysis known as “Porter’s five forces” can provide 
a useful starting point. Porter maintains that the profitability of companies in 
an industry is determined by five forces: 1) The threat of new entrants, which in

turn is determined by economies of scale, brand loyalty, absolute cost advan -
tages, customer switching costs, and government regulation; 2) the bargaining 
power of suppliers, which is a function of the feasibility of product substitution, 
the concentration of the buyer and supplier groups, and switching costs and 
entry costs in each case; 3) the bargaining power of buyers, which is a function 
of switching costs among customers and the ability of customers to produce 
their own product; 4) the threat of substitutes; and 5) the intensity of rivalry 
among existing competitors, which in turn is a function of industry competitive 
structure, demand conditions, cost conditions, and the height of exit barriers.
■■The concept of barriers to entry refers to the ease with which new competitors 
can challenge incumbents and can be an important factor in determining the 
competitive environment of an industry. If new competitors can easily enter the

industry, the industry is likely to be highly competitive because incumbents that 
attempt to raise prices will be undercut by newcomers. As a result, industries 
with low barriers to entry tend to have low pricing power. Conversely, if incum -
bents are protected by barriers to entry, they may enjoy a more benign compet -
itive environment that gives them greater pricing power over their customers 
because they do not have to worry about being undercut by upstarts.
■■Industry concentration is often, although not always, a sign that an industry 
may have pricing power and rational competition. Industry fragmentation is 
a much stronger signal, however, that the industry is competitive and pricing 
power is limited.
■■The effect of industry capacity on pricing is clear: Tight capacity gives partic -
ipants more pricing power because demand for products or services exceeds 
supply; overcapacity leads to price cutting and a highly competitive environ -

ment as excess supply chases demand. The analyst should think about not only 
current capacity conditions but also future changes in capacity levels—how 
long it takes for supply and demand to come into balance and what effect that 
process has on industry pricing power and returns.
■■Examining the market share stability of an industry over time is similar to 
thinking about barriers to entry and the frequency with which new players 
enter an industry. Stable market shares typically indicate less competitive indus -
tries, whereas unstable market shares often indicate highly competitive indus -
tries with limited pricing power.
■■An industry’s position in its life cycle often has a large impact on its compet -
itive dynamics, so it is important to keep this positioning in mind when per -
forming strategic analysis of an industry. Industries, like individual companies, 
tend to evolve over time and usually experience significant changes in the rate

of growth and levels of profitability along the way. Just as an investment in an

Summary 235
individual company requires careful monitoring, industry analysis is a contin -
uous process that must be repeated over time to identify changes that may be 
occurring.
■■A useful framework for analyzing the evolution of an industry is an industry 
life- cycle model, which identifies the sequential stages that an industry typically 
goes through. The five stages of an industry life cycle according to the Hill and 
Jones model are:
■●embryonic;
■●growth;
■●shakeout;
■●mature; and
■●decline.
■■Price competition and thinking like a customer are important factors that are 
often overlooked when analyzing an industry. Whatever factors most influence 
customer purchasing decisions are also likely to be the focus of competitive 
rivalry in the industry. Broadly, industries for which price is a large factor in 
customer purchase decisions tend to be more competitive than industries in 
which customers value other attributes more highly.

■■External influences on industry growth, profitability, and risk include:
■●technology;
■●demographics;
■●government; and
■●social factors.
■■Company analysis takes place after the analyst has gained an understanding of 
the company’s external environment and includes answering questions about 
how the company will respond to the threats and opportunities presented by 
the external environment. This intended response is the individual company’s 
competitive strategy. The analyst should seek to determine whether the strategy 
is primarily defensive or offensive in its nature and how the company intends to 
implement it.
■■Porter identifies two chief competitive strategies:
■●A low-  cost strategy (cost leadership) is one in which companies strive to 
become the low-  cost producers and to gain market share by offering their 
products and services at lower prices than their competition while still mak -
ing a profit margin sufficient to generate a superior rate of return based on

the higher revenues achieved.
■●A product/service differentiation strategy is one in which companies 
attempt to establish themselves as the suppliers or producers of products 
and services that are unique either in quality, type, or means of distribution. 
To be successful, the companies’ price premiums must be above their costs 
of differentiation and the differentiation must be appealing to customers and 
sustainable over time.
■■A checklist for company analysis includes a thorough investigation of:
■●corporate profile;
■●industry characteristics;
■●demand for products/services;
■●supply of products/services;
■●pricing; and

Reading 48 ■ Introduction to Industry and Company Analysis 236
Cavaglia, Stefano, Jeffrey Diermeier, Vadim Moroz, and Sonia De 
Zordo. 2004. “Investing in Global Equities. ” Journal of Portfolio 
Management , vol. 30, no. 3:88–94. 
Hill, Charles, and Gareth Jones. 2008. “External Analysis: 
The Identification of Opportunities and Threats. ” Strategic 
Management: An Integrated Approach . Boston, MA: 
Houghton Mifflin Co.McGahan, Anita M., and Michael E. Porter. 1997. “How Much 
Does Industry Matter, Really?” Strategic Management Journal , 
vol. 18, no. No. S1:15–30. 
Porter, Michael E. 2008. “The Five Competitive Forces That 
Shape Strategy. ” Harvard Business Review , vol. 86, no. 1:78–93.■●financial ratios.
■■Spreadsheet modeling of financial statements to analyze and forecast revenues, 
operating and net income, and cash flows has become one of the most widely 
used tools in company analysis. Spreadsheet modeling can be used to quantify

the effects of the changes in certain swing factors on the various financial state -
ments. The analyst should be aware that the output of the model will depend 
significantly on the assumptions that are made.

Practice Problems 237
1 Which of the following is least likely  to involve industry analysis?
A Sector rotation strategy.
B Top-  down fundamental investing.
C Tactical asset allocation strategy.
2 A sector rotation strategy involves investing in a sector by:
A making regular investments in it.
B investing in a pre-  selected group of sectors on a rotating basis.
C timing investment to take advantage of business-  cycle conditions.
3 Which of the following information about a company would most likely  depend 
on an industry analysis? The company’s:
A dividend policy.
B competitive environment.
C trends in corporate expenses.
4 Which industry classification system uses a three-  tier classification system?
A Russell Global Sectors.
B Industry Classification Benchmark.
C Global Industry Classification Standard.
5 In which sector would a manufacturer of personal care products be classified?
A Health care.
B Consumer staples.
C Consumer discretionary.

6 A automotive manufacturer is most likely classified in which of the following 
industry sectors?
A Consumer staples
B Industrial durables
C Consumer discretionary
7 Which of the following statements about commercial and government industry 
classification systems is most  accurate?
A Many commercial classification systems include private for-  profit 
B Both commercial and government classification systems exclude not-  for- 
profit companies.
C Commercial classification systems are generally updated more frequently 
than government classification systems.
8 Which of the following is not a limitation of the cyclical/non-  cyclical descrip -
tive approach to classifying companies?
A A cyclical company may have a growth component in it.
B Business-  cycle sensitivity is a discrete phenomenon rather than a continu -
ous spectrum.
C A global company can experience economic expansion in one part of the

world while experiencing recession in another part.

Reading 48 ■ Introduction to Industry and Company Analysis 238
9 A cyclical company is most likely  to: 
A have low operating leverage.
B sell relatively inexpensive products.
C experience wider-  than-  average fluctuations in demand.
10 A company that is sensitive to the business cycle would most likely :
A not have growth opportunities.
B experience below-  average fluctuation in demand.
C sell products that the customer can purchase at a later date if necessary.
11 Which of the following factors would most likely  be a limitation of applying 
business-  cycle analysis to global industry analysis?
A Some industries are relatively insensitive to the business cycle.
B Correlations of security returns between different world markets are rela -
tively low.
C One region or country of the world may experience recession while another 
region experiences expansion.
12 Which of the following statements about peer groups is most  accurate?

A Constructing a peer group for a company follows a standardized process.
B Commercial industry classification systems often provide a starting point 
for constructing a peer group.
C A peer group is generally composed of all the companies in the most 
narrowly defined category used by the commercial industry classification 
system.
13 With regard to forming a company’s peer group, which of the following state -
ments is not correct?
A Comments from the management of the company about competitors are 
generally not used when selecting the peer group.
B The higher the proportion of revenue and operating profit of the peer com -
pany derived from business activities similar to the subject company, the 
more meaningful the comparison.
C Comparing the company’s performance measures with those for a potential 
peer-  group company is of limited value when the companies are exposed to 
different stages of the business cycle.
14 When selecting companies for inclusion in a peer group, a company operating

in three different business segments would:
A be in only one peer group.
B possibly be in more than one peer group.
C not be included in any peer group.
15 An industry that most likely  has both high barriers to entry and high barriers to 
exit is the:
A restaurant industry.
B advertising industry.
C automobile industry.
16 Which factor is most likely  associated with stable market share?
A Low switching costs.
B Low barriers to entry.
C Slow pace of product innovation.

17 Which of the following companies most likely  has the greatest ability to quickly 
increase its capacity?
A Restaurant.
B Steel producer.
C Legal services provider.
18 A population that is rapidly aging would most likely  cause the growth rate of the 
industry producing eye glasses and contact lenses to:
C not change.
19 If over a long period of time a country’s average level of educational accom -
plishment increases, this development would most likely  lead to the country’s 
amount of income spent on consumer discretionary goods to:
20 If the technology for an industry involves high fixed capital investment, then 
one way to seek higher profit growth is by pursuing:
C removal of features that differentiate the product or service provided.
21 Which of the following life-  cycle phases is typically characterized by high 
prices?
A Mature.
B Growth.
C Embryonic.

prices?
A Mature.
B Growth.
22 In which of the following life-  cycle phases are price wars most likely  to be 
absent?
A Mature.
B Decline.
C Growth.
23 When graphically depicting the life-  cycle model for an industry as a curve, the 
variables on the axes are:
A price and time.
B demand and time.
C demand and stage of the life cycle.
24 Industry consolidation and high barriers to entry most likely  characterize which 
life- cycle stage? 
A Mature
B Growth
C Embryonic
25 Which of the following is most likely  a characteristic of a concentrated industry?
A Infrequent, tacit coordination.
B Difficulty in monitoring other industry members.
C Industry members attempting to avoid competition on price.

Reading 48 ■ Introduction to Industry and Company Analysis 240
26 Which of the following industry characteristics is generally least likely  to pro -
duce high returns on capital?
A High barriers to entry
B High degree of concentration
C Short lead time to build new plants
27 An industry with high barriers to entry and weak pricing power most likely  has:
A high barriers to exit.
B stable market shares.
C significant numbers of issued patents.
28 Economic value is created for an industry’s shareholders when the industry 
earns a return:
A below the cost of capital.
B equal to the cost of capital.
C above the cost of capital.
29 Which of the following industries is most likely  to be characterized as concen -
trated with strong pricing power?
A Asset management.
B Alcoholic beverages.
C Household and personal products.
30 With respect to competitive strategy, a company with a successful cost leader -
ship strategy is most likely  characterized by:
A a low cost of capital.
B reduced market share.

C the ability to offer products at higher prices than competitors.
31 When conducting a company analysis, the analysis of demand for a company’s 
product is least likely  to consider the:
A company’s cost structure.
B motivations of the customer base.
C product’s differentiating characteristics.
32 Which of the following statements about company analysis is most  accurate?
A The complexity of spreadsheet modeling ensures precise forecasts of finan -
B The interpretation of financial ratios should focus on comparing the compa -
ny’s results over time but not with competitors.
C The corporate profile would include a description of the company’s business, 
investment activities, governance, and strengths and weaknesses.

SOLUTIONS
1 C is correct. Tactical asset allocation involves timing investments in asset 
classes and does not make use of industry analysis.
2 C is correct. A sector rotation strategy is conducted by investors wishing to 
time investment in industries through an analysis of fundamentals and/or 
business-  cycle conditions.
3 B is correct. Determination of a company’s competitive environment depends 
on understanding its industry.
4 A is correct. The Russell system uses three tiers, whereas the other two systems 
are based on four tiers or levels.
5 B is correct. Personal care products are classified as consumer staples in the 
“Description of Representative Sectors. ”
6 C is correct. Automotive manufacturers are classified as consumer discretion -
ary. Consumer discretionary companies derive a majority of revenue from the 
sale of consumer-  related products for which demand tends to exhibit a high 
degree of economic sensitivity—that is, high demand during periods of eco -

nomic expansion and low demand during periods of contraction. 
7 C is correct. Commercial systems are generally updated more frequently than 
government systems, and include only publicly traded for-  profit companies.
8 B is correct. Business-  cycle sensitivity falls on a continuum and is not a discrete 
“either–or” phenomenon.
9 C is correct. Cyclical companies are sensitive to the business cycle, with low 
product demand during periods of economic contraction and high product 
demand during periods of economic expansion. They, therefore, experience 
wider-  than-  average fluctuations in product demand.
10 C is correct. Customers’ flexibility as to when they purchase the product makes 
the product more sensitive to the business cycle.
11 C is correct. Varying conditions of recession or expansion around the world 
would affect the comparisons of companies with sales in different regions of the 
world.
12 B is correct. Constructing a peer group is a subjective process, and a logical

starting point is to begin with a commercially available classification system. 
This system will identify a group of companies that may have properties compa -
rable to the business activity of interest.
13 A is correct because it is a false statement. Reviewing the annual report to find 
management’s discussion about the competitive environment and specific com -
petitors is a suggested step in the process of constructing a peer group.
14 B is correct. The company could be in more than one peer group depending on 
the demand drivers for the business segments, although the multiple business 
segments may make it difficult to classify the company.
15 C is correct. For the automobile industry, the high capital requirements and 
other elements mentioned in the reading provide high barriers to entry, and 
recognition that auto factories are generally only of use for manufacturing cars 
implies a high barrier to exit.
16 C is correct. A slow pace of product innovation often means that customers

prefer to stay with suppliers they know, implying stable market shares.

Reading 48 ■ Introduction to Industry and Company Analysis 242
17 C is correct. Capacity increases in providing legal services would not involve 
several factors that would be important to the other two industries, including 
the need for substantial fixed capital investments or, in the case of a restaurant, 
outfitting rental or purchased space. These requirements would tend to slow 
down, respectively, steel production and restaurant expansion.
18 B is correct. Vision typically deteriorates at advanced ages. An increased num -
ber of older adults implies more eyewear products will be purchased.
19 B is correct. As their educational level increases, workers are able to perform 
more skilled tasks, earn higher wages, and as a result, have more income left for 
discretionary expenditures.
20 A is correct. Seeking economies of scale would tend to reduce per-  unit costs 
and increase profit.
21 C is correct. The embryonic stage is characterized by slow growth and high 
prices.

prices.
22 C is correct. The growth phase is not likely to experience price wars because 
expanding industry demand provides companies the opportunity to grow even 
without increasing market share. When industry growth is stagnant, companies 
may only be able to grow by increasing market share, e.g., by engaging in price 
23 B is correct. The industry life-  cycle model shows how demand evolves through 
time as an industry passes from the embryonic stage through the stage of 
decline.
24 A is correct. Industry consolidation and relatively high barriers to entry are two 
characteristics of a mature-  stage industry.  
25 C is correct. The relatively few members of the industry generally try to avoid 
price competition.
26 C is correct. With short lead times, industry capacity can be rapidly increased 
to satisfy demand, but it may also lead to overcapacity and lower profits.
27 A is correct. An industry that has high barriers to entry generally requires sub -

stantial physical capital and/or financial investment. With weak pricing power 
in the industry, finding a buyer for excess capacity (i.e., to exit the industry) may 
be difficult.
28 C is correct. Economic profit is earned and value created for shareholders when 
the company earns returns above the company’s cost of capital.
29 B is correct. As displayed in Exhibit 4, the alcoholic beverage industry is con -
centrated and possesses strong pricing power.
30 A is correct. Companies with low cost strategies must be able to invest in 
productivity-  improving equipment and finance that investment at a low cost 
of capital. Market share and pricing depend on whether the strategy is pursued 
defensively or offensively.
31 A is correct. The cost structure is an appropriate element when analyzing the 
supply of the product, but analysis of demand relies on the product’s differenti -
ating characteristics and the customers’ needs and wants.

32 C is correct. The corporate profile would provide an understanding of these 
elements.

Equity Valuation: Concepts and Basic Tools
by John J. Nagorniak, CFA, and Stephen E. Wilcox, PhD, CFA
John J. Nagorniak, CFA (USA). Stephen E. Wilcox, PhD, CFA, is at Minnesota State 
University, Mankato (USA).
a. evaluate whether a security, given its current market price and a 
value estimate, is overvalued, fairly valued, or undervalued by the 
market;
b. describe major categories of equity valuation models;
c. describe regular cash dividends, extra dividends, stock dividends, 
stock splits, reverse stock splits, and share repurchases;
d. describe dividend payment chronology;
e. explain the rationale for using present value models to value 
equity and describe the dividend discount and free-  cash-  flow-  to- 
equity models;
f. calculate the intrinsic value of a non-  callable, non-  convertible 
g. calculate and interpret the intrinsic value of an equity security

based on the Gordon (constant) growth dividend discount model 
or a two-  stage dividend discount model, as appropriate;
h. identify characteristics of companies for which the constant 
growth or a multistage dividend discount model is appropriate;
i. explain the rationale for using price multiples to value equity, how 
the price to earnings multiple relates to fundamentals, and the 
use of multiples based on comparables;
j. calculate and interpret the following multiples: price to earnings, 
price to an estimate of operating cash flow, price to sales, and 
price to book value;
49

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 244
k. describe enterprise value multiples and their use in estimating 
equity value;
l. describe asset-  based valuation models and their use in estimating 
m. explain advantages and disadvantages of each category of 
valuation model.
Analysts gather and process information to make investment decisions, including 
buy and sell recommendations. What information is gathered and how it is processed 
depend on the analyst and the purpose of the analysis. Technical analysis uses such 
information as stock price and trading volume as the basis for investment decisions. 
Fundamental analysis uses information about the economy, industry, and company 
as the basis for investment decisions. Examples of fundamentals are unemployment 
rates, gross domestic product (GDP) growth, industry growth, and quality of and

growth in company earnings. Whereas technical analysts use information to predict 
price movements and base investment decisions on the direction of predicted change 
in prices, fundamental analysts use information to estimate the value of a security 
and to compare the estimated value to the market price and then base investment 
decisions on that comparison.
This reading introduces equity valuation models used to estimate the intrinsic value  
(synonym: fundamental value ) of a security; intrinsic value is based on an analysis 
of investment fundamentals and characteristics. The fundamentals to be considered 
depend on the analyst’s approach to valuation. In a top-  down approach, an analyst 
examines the economic environment, identifies sectors that are expected to prosper 
in that environment, and analyzes securities of companies from previously identified 
attractive sectors. In a bottom-  up approach, an analyst typically follows an industry or

industries and forecasts fundamentals for the companies in those industries in order 
to determine valuation. Whatever the approach, an analyst who estimates the intrinsic 
value of an equity security is implicitly questioning the accuracy of the market price 
as an estimate of value. Valuation is particularly important in active equity portfolio 
management, which aims to improve on the return–risk trade-  off of a portfolio’s 
benchmark by identifying mispriced securities.
This reading is organized as follows. Section 2 discusses the implications of dif -
ferences between estimated value and market price. Section 3 introduces three major 
categories of valuation model. Section 4 presents an overview of present value models 
with a focus on the dividend discount model. Section 5 describes and examines the 
use of multiples in valuation. Section 6 explains asset-  based valuation and demon -
strates how these models can be used to estimate value. Section 7 states conclusions

Estimated Value and Market Price 245
ESTIMATED VALUE AND MARKET PRICE
By comparing estimates of value and market price, an analyst can arrive at one of 
three conclusions: The security is undervalued , overvalued , or fairly valued  in the 
marketplace. For example, if the market price of an asset is $10 and the analyst esti -
mates intrinsic value at $10, a logical conclusion is that the security is fairly valued. 
If the security is selling for $20, the security would be considered overvalued. If the 
security is selling for $5, the security would be considered undervalued. Basically, by 
estimating value, the analyst is assuming that the market price is not necessarily the 
best estimate of intrinsic value. If the estimated value exceeds the market price, the 
analyst infers the security is undervalued . If the estimated value equals the market 
price, the analyst infers the security is fairly valued . If the estimated value is less than

the market price, the analyst infers the security is overvalued .
In practice, the conclusion is not so straightforward. Analysts must cope with 
uncertainties related to model appropriateness and the correct value of inputs. An 
analyst’s final conclusion depends not only on the comparison of the estimated value 
and the market price but also on the analyst’s confidence in the estimated value (i.e., 
in the model selected and the inputs used in it). One can envision a spectrum running 
from relatively high confidence in the valuation model and the inputs to relatively 
low confidence in the valuation model and/or  the inputs. When confidence is rela -
tively low, the analyst might demand a substantial divergence between his or her own 
value estimate and the market price before acting on an apparent mispricing. For 
instance, if the estimate of intrinsic value is $10 and the market price is $10.05, the 
analyst might reasonably conclude that the security is fairly valued and that the 1/2

of 1 percent market price difference from the estimated value is within the analyst’s 
confidence interval.
Confidence in the convergence of the market price to the intrinsic value over the 
investment time horizon relevant to the objectives of the portfolio must also be taken 
into account before an analyst acts on an apparent mispricing or makes a buy, sell, 
or hold recommendation: The ability to benefit from identifying a mispriced security 
depends on the market price converging to the estimated intrinsic value.
In seeking to identify mispricing and attractive investments, analysts are treating 
market prices with skepticism, but they are also treating market prices with respect. For 
example, an analyst who finds that many securities examined appear to be overvalued 
will typically recheck models and inputs before acting on a conclusion of overvalu -
ation. Analysts also often recognize and factor into recommendations that different

market segments—such as securities closely followed by analysts versus securities 
relatively neglected by analysts—may differ in how common or persistent mispricing 
is. Mispricing may be more likely in securities neglected by analysts.
EXAMPLE 1   
Valuation and Analyst Response
1 An analyst finds that all the securities analyzed have estimated values 
higher than their market prices. The securities all appear to be:
C fairly valued.2

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 246
2 An analyst finds that nearly all companies in a market segment have com -
mon shares which are trading at market prices above the analyst’s estimate 
of the shares’ values. This market segment is widely followed by analysts. 
Which of the following statements describes the analyst’s most appropri -
ate first action?
A Issue a sell recommendation for each share issue.
B Issue a buy recommendation for each share issue.
C Reexamine the models and inputs used for the valuations.
3 An analyst, using a number of models and a range of inputs, estimates a 
security’s value to be between ¥250 and ¥270. The security is trading at 
¥265. The security appears to be:
C fairly valued.
B is correct. The estimated intrinsic value for each security is greater than the 
market price. The securities all appear to be undervalued in the market. Note,

however, that the analyst may wish to reexamine the model and inputs to check 
that the conclusion is valid.
C is correct. It seems improbable that all the share issues analyzed are overvalued, 
as indicated by market prices in excess of estimated value—particularly because 
the market segment is widely followed by analysts. Thus, the analyst will not 
issue a sell recommendation for each issue. The analyst will most appropriately  
reexamine the models and inputs prior to issuing any recommendations. A 
buy recommendation is not an appropriate response to an overvalued security.
C is correct. The security’s market price of ¥265 is within the range estimated 
by the analyst. The security appears to be fairly valued.
Analysts often use a variety of models and inputs to achieve greater confidence 
in their estimates of intrinsic value. The use of more than one model and a range of 
inputs also helps the analyst understand the sensitivity of value estimates to different

models and inputs.
MAJOR CATEGORIES OF EQUITY VALUATION MODELS
Three major categories of equity valuation models are as follows:
■■Present value models  (synonym: discounted cash flow models ). These mod -
els estimate the intrinsic value of a security as the present value of the future 
benefits expected to be received from the security. In present value models, 
benefits are often defined in terms of cash expected to be distributed to share -
holders ( dividend discount models ) or in terms of cash flows available to 
be distributed to shareholders after meeting capital expenditure and working 
capital needs ( free-  cash-  flow-  to- equity models ). Many models fall within this 3

Major Categories of Equity Valuation Models 247
category, ranging from the relatively simple to the very complex. In Section 4, 
we discuss in detail two of the simpler models, the Gordon (constant) growth 
model and the two-  stage dividend discount models.
■■Multiplier models  (synonym: market multiple models ). These models are 
based chiefly on share price multiples or enterprise value multiples. The former 
model estimates intrinsic value of a common share from a price multiple for 
some fundamental variable, such as revenues, earnings, cash flows, or book 
value. Examples of the multiples include price to earnings (P/E, share price 
divided by earnings per share) and price to sales (P/S, share price divided by 
sales per share). The fundamental variable may be stated on a forward basis 
(e.g., forecasted EPS for the next year) or a trailing basis (e.g., EPS for the past 
year), as long as the usage is consistent across companies being examined. Price

multiples are also used to compare relative values. The use of the ratio of share 
price to EPS—that is, the P/E multiple—to judge relative value is an example of 
this approach to equity valuation.
Enterprise value  (EV) multiples have the form (Enterprise value)/(Value of a 
fundamental variable). Two possible choices for the denominator are earnings 
before interest, taxes, depreciation, and amortization (EBITDA) and total rev -
enue. Enterprise value, the numerator, is a measure of a company’s total mar -
ket value from which cash and short-  term investments have been subtracted 
(because an acquirer could use those assets to pay for acquiring the company). 
An estimate of common share value can be calculated indirectly from the EV 
multiple; the value of liabilities and preferred shares can be subtracted from the 
EV to arrive at the value of common equity.
■■Asset-  based valuation models . These models estimate intrinsic value of a

common share from the estimated value of the assets of a corporation minus 
the estimated value of its liabilities and preferred shares. The estimated mar -
ket value of the assets is often determined by making adjustments to the book 
value  (synonym: carrying value ) of assets and liabilities. The theory underlying 
the asset-  based approach is that the value of a business is equal to the sum of 
the value of the business’s assets.
As already mentioned, many analysts use more than one type of model to esti -
mate value. Analysts recognize that each model is a simplification of the real world 
and that there are uncertainties related to model appropriateness and the inputs to 
the models. The choice of model(s) will depend on the availability of information to 
input into the model(s) and the analyst’s confidence in the information and in the 
appropriateness of the model(s).
EXAMPLE 2   
Categories of Equity Valuation Models

EXAMPLE 2   
1 An analyst is estimating the intrinsic value of a new company. The analyst 
has one year of financial statements for the company and has calculated 
the average values of a variety of price multiples for the industry in which 
the company operates. The analyst plans to use at least one model from 
each of the three categories of valuation models. The analyst is least likely  
to rely on the estimate(s) from the:
A multiplier model(s).
B present value model(s).
C asset-  based valuation model(s).

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 248
2 Based on a company’s EPS of €1.35, an analyst estimates the intrinsic 
value of a security to be €16.60. Which type of model is the analyst most 
likely  to be using to estimate intrinsic value?
A Multiplier model.
B Present value model.
C Asset-  based valuation model.
B is correct. Because the company has only one year of data available, the analyst 
is least likely  to be confident in the inputs for a present value model. The values 
on the balance sheet, even before adjustment, are likely to be close to market 
values because the assets are all relatively new. The multiplier models are based 
on average multiples from the industry.
A is correct. The analyst is using a multiplier model based on the P/E multiple. 
The P/E multiple used was 16.60/1.35 = 12.3.
As you begin the study of specific equity valuation models in the next section, you

must bear in mind that any model of value is, by necessity, a simplification of the real 
world. Never forget this simple fact! You may encounter models much more complicated 
than the ones discussed here, but even those models will be simplifications of reality.
PRESENT VALUE MODELS: THE DIVIDEND DISCOUNT 
MODEL
Present value models follow a fundamental tenet of economics which states that 
individuals defer consumption—that is, they invest—for the future benefits expected. 
Individuals and companies make an investment because they expect thereby to earn a 
rate of return over the investment period. Logically, the value of an investment should 
be equal to the present value of the expected future benefits. For common shares, 
an analyst can equate benefits to the cash flows to be generated by the investment. 
The simplest present value model of equity valuation is the dividend discount model 
(DDM), which specifies cash flows from a common stock investment to be dividends.

The next section describes aspects of dividends that users of dividend discount 
models should understand.
4.1 Dividends: Background for the Dividend Discount Model
Generally, there are two sources of return from investing in equities: (1) cash divi -
dends received by an investor over his or her holding period and (2) the change in 
the market price of equities over that holding period.
A dividend  is a distribution paid to shareholders based on the number of shares 
owned, and a cash dividend is a cash distribution made to a company’s shareholders. 
Cash dividends are typically paid out regularly at known intervals; such dividends are 
known as regular cash dividends. By contrast, an extra dividend  or special dividend  
is a dividend paid by a company that does not pay dividends on a regular schedule or a 4

Present Value Models: The Dividend Discount Model 249
dividend that supplements regular cash dividends with an extra payment. Companies 
in cyclical industries and companies undergoing corporate and/or financial restruc -
turing are among those observed to use extra dividends.1
The payment of dividends is not a legal obligation: dividends must be declared 
(i.e., authorized) by a company’s board of directors; in some jurisdictions, they must 
also be approved by shareholders. Regular cash dividends are customarily declared 
and paid out quarterly in the United States and Canada; semiannually in Europe and 
Japan; and annually in some other countries, including China.
Dividend discount models address discounting expected cash dividends. A stock 
dividend  (also known as a bonus issue of shares ) is a type of dividend in which a 
company distributes additional shares of its common stock (typically, 2%–10% of the

shares then outstanding) to shareholders instead of cash. A stock dividend divides the 
“pie” (the market value of shareholders’ equity) into smaller pieces without affecting 
the value of the pie or any shareholder’s proportional ownership in the company. Thus, 
stock dividends are not relevant for valuation. Stock splits and reverse stock splits are 
similar to stock dividends in that they have no economic effect on the company or 
shareholders. A stock split  involves an increase in the number of shares outstanding 
with a consequent decrease in share price. An example of a stock split is a two-  for- 
one stock split in which each shareholder is issued an additional share for each share 
currently owned. A reverse stock split  involves a reduction in the number of shares 
outstanding with a corresponding increase in share price. In a one-  for- two reverse 
stock split, each shareholder would receive one new share for every two old shares

held, thereby reducing the number of shares outstanding by half.
In contrast to stock dividends and stock splits, share repurchases are an alternative 
to cash dividend payments. A share repurchase  (or buyback ) is a transaction in which 
a company uses cash to buy back its own shares. Shares that have been repurchased 
are not considered for dividends, voting, or computing earnings per share. A share 
repurchase is viewed as equivalent to the payment of cash dividends of equal value 
in terms of the effect on shareholders’ wealth, all other things being equal. Company 
managements have expressed several key reasons for engaging in share repurchases—
namely, (1) signaling a belief that their shares are undervalued (or, more generally, to 
support share prices), (2) flexibility in the amount and timing of distributing cash to 
shareholders, (3) tax efficiency in markets where tax rates on dividends exceed tax 
rates on capital gains, and (4) the ability to absorb increases in outstanding shares

because of the exercise of employee stock options.
The payout of regular cash dividends to common shareholders follows a fairly 
standard chronology that is set in motion once the company’s board of directors votes 
to pay the dividend. First is the declaration date , the day that the company issues 
a statement declaring a specific dividend. Next comes the ex- dividend date  (or ex-  
date), the first date that a share trades without (i.e., “ex”) the dividend. This is followed 
closely (one or two business days later) by the holder-  of- record date  (also called 
the owner-  of- record date, shareholder-  of- record date, record date, date of record, or 
date of book closure), the date that a shareholder listed on the company’s books will 
be deemed to have ownership of the shares for purposes of receiving the upcoming 
dividend; the amount of time between the ex-  date and the holder-  of- record date is 
linked to the trade settlement cycle in force. The final milestone is the payment date

(or payable date ), which is the day that the company actually mails out (or electron -
ically transfers) a dividend payment to shareholders.
1 Another type of dividend is a liquidating dividend, which is a return of capital rather than a distribution 
from earnings or retained earnings. Liquidating dividends are used when a company goes out of business 
and distributes its net assets, sells a portion of its business for cash and distributes the sale’s proceeds, or 
pays a dividend that exceeds its accumulated retained earnings.

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 250
EXAMPLE 3   
Total S.A. Dividend Payment Time Line
On 29 May 2015, Total S.A., one of the world’s largest integrated energy compa -
nies, declared an annual dividend of €2.44 per share, payable on a quarterly basis. 
The first quarterly dividend of €2.44/4 = €0.61 was payable on 21 October 2015. 
The holder-  of- record date was 29 September, and the ex-  dividend date was 28 
September. A timeline for the upcoming Total S.A. quarterly dividend is shown 
Exhibit 1   Timeline for Total S.A. Quarterly Dividend 
Declaration
DateEx-DateHolder-of-Record Date
Payment Date
29 May 28 September 29 September 21 October
Source:  Total S.A. website: www.total.com .
Because buyers of a company’s shares on the ex-  dividend date are no longer eligi -
ble to receive the upcoming dividend, all else being equal, on that day the company’s 
share price immediately decreases by the amount of the foregone dividend. Exhibit 2

illustrates the decrease in share price that occurs for a hypothetical company that has 
declared a $1.00 per share dividend as trading begins on its ex-  dividend date.
Exhibit 2   Stock Price Change for Hypothetical Company on Ex-  Dividend 
Date
Stock Price ($ per share)
20.50
20.25
20.00
19.75
19.50
19.25
19.00
18.75
18.50
0
Trading Days Ex-Date –1 Ex-Date +1 Record Date Ex-Date Ex-Date –2Last Trade on Ex-Date –1
Price: $20.00/share
First Trade on Ex-Date
Price: $19.00/share
Note : Assumes dividend declared is $1 per share and convention for stock trade settlement is T + 3.

Present Value Models: The Dividend Discount Model 251
4.2 The Dividend Discount Model: Description
If the issuing company is assumed to be a going concern, the intrinsic value of a share 
is the present value of expected future dividends. If a constant required rate of return is 
also assumed, then the DDM expression for the intrinsic value of a share is Equation 1:
VD
rt
t
t0
11=
+()=∞
∑
where
 V0 = value of a share of stock today, at t = 0
 Dt = expected dividend in year t, assumed to be paid at the end of the year
 r = required rate of return on the stock
At the shareholder level, cash received from a common stock investment includes 
any dividends received and the proceeds when shares are sold. If an investor intends 
to buy and hold a share for one year, the value of the share today is the present value 
of two cash flows—namely, the expected dividend plus the expected selling price in 
one year:
VDP
rD
rP
r011
11
11
111 1=+
+()=
+()+
+()
where P1 = the expected price per share at t = 1.

To estimate the expected selling price, P1, the analyst could estimate the price 
another investor with a one-  year holding period would pay for the share in one year. 
If V0 is based on D1 and P1, it follows that P1 could be estimated from D2 and P2:
PDP
r122
1=+
+()
Substituting the right side of this equation for P1 in Equation 2 results in V0 estimated as
VD
rDP
rD
rD
rP
r012 2
212
22
2 1 1 1 11=+()++
+()=+()+
+()+
+()
Repeating this process, we find the value for n holding periods is the present value 
of the expected dividends for the n periods plus the present value of the expected 
price in n periods:
VD
rD
rP
rn
nn
n01
111 1=
+()++
+()+
+()
Using summation notation to represent the present value of the n expected 
dividends, we arrive at the general expression for an n-period holding period or 
investment horizon:
VD
rP
rt
t
tn
n
n0
111=
+()+
+() =∑
The expected value of a share at the end of the investment horizon—in effect, the

expected selling price—is often referred to as the terminal stock value  (or terminal 
value ).(1)
(2)
(3)

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 252
EXAMPLE 4   
Estimating Share Value for a Three-  Year Investment 
Horizon
For the next three years, the annual dividends of a stock are expected to be 
€2.00, €2.10, and €2.20. The stock price is expected to be €20.00 at the end of 
three years. If the required rate of return on the shares is 10 percent, what is 
the estimated value of a share?
Solution: 
The present values of the expected future cash flows can be written as follows:
V012 33200
110210
110220
11020 00
110=
()+
()+
()+
().
..
..
..
.
Calculating and summing these present values gives an estimated share value 
of V0 = 1.818 + 1.736 + 1.653 + 15.026 = €20.23.
The three dividends have a total present value of €5.207, and the terminal 
stock value has a present value of €15.026, for a total estimated value of €20.23.
Extending the holding period into the indefinite future, we can say that a stock’s 
estimated value is the present value of all expected future dividends as shown in 
Equation 1.

Consideration of an indefinite future is valid because businesses established as 
corporations are generally set up to operate indefinitely. This general form of the DDM 
applies even in the case in which the investor has a finite investment horizon. For that 
investor, stock value today depends directly  on the dividends the investor expects to 
receive before the stock is sold and depends indirectly  on the expected dividends for 
periods subsequent to that sale, because those expected future dividends determine 
the expected selling price. Thus, the general expression given by Equation 1 holds 
irrespective of the investor’s holding period.
In practice, many analysts prefer to use a free-  cash-  flow-  to- equity (FCFE) valuation 
model. These analysts assume that dividend-  paying capacity  should be reflected in the 
cash flow estimates rather than expected dividends . FCFE is a measure of dividend-

paying capacity. Analysts may also use FCFE valuation models for a non-  dividend-  
paying stock. To use a DDM, the analyst needs to predict the timing and amount of 
the first dividend and all the dividends or dividend growth thereafter. Making these 
predictions for non-  dividend-  paying stock accurately is typically difficult, so in such 
cases, analysts often resort to FCFE models.
The calculation of FCFE starts with the calculation of cash flow from operations 
(CFO). CFO is simply defined as net income plus non-  cash expenses minus invest -
ment in working capital. FCFE is a measure of cash flow generated in a period that 
is available for distribution to common shareholders. What does “available for dis -
tribution” mean? The entire CFO is not available for distribution; the portion of the 
CFO needed for fixed capital investment (FCInv) during the period to maintain the 
value of the company as a going concern is not viewed as available for distribution to

common shareholders. Net amounts borrowed (borrowings minus repayments) are 
considered to be available for distribution to common shareholders. Thus, FCFE can 
FCFE = CFO – FCInv + Net borrowing  
The information needed to calculate historical FCFE is available from a company’s 
statement of cash flows and financial disclosures. Frequently, under the assumption 
that management is acting in the interest of maintaining the value of the company as (4)

Present Value Models: The Dividend Discount Model 253
a going concern, reported capital expenditure is taken to represent FCInv. Analysts 
must make projections of financials to forecast future FCFE. Valuation obtained by 
using FCFE involves discounting expected future FCFE by the required rate of return 
on equity; the expression parallels Equation 1:
V
rt
t
t0
11=
+()=∞
∑FCFE
EXAMPLE 5   
Present Value Models
1 An investor expects a share to pay dividends of $3.00 and $3.15 at the end 
of Years 1 and 2, respectively. At the end of the second year, the investor 
expects the shares to trade at $40.00. The required rate of return on the 
shares is 8 percent. If the investor’s forecasts are accurate and the market 
price of the shares is currently $30, the most likely  conclusion is that the 
shares are:
2 Two investors with different holding periods but the same expectations 
and required rate of return for a company are estimating the intrinsic

value of a common share of the company. The investor with the shorter 
holding period will most likely  estimate a:
A lower intrinsic value.
B higher intrinsic value.
C similar intrinsic value.
3 An equity valuation model that focuses on expected dividends rather than 
the capacity to pay dividends is the:
A dividend discount model.
B free cash flow to equity model.
C cash flow return on investment model.
B is correct.
V012 2300
108315
10840 00
10839 77 =
()+
()+
()=.
..
..
..
The value estimate of $39.77 exceeds the market price of $30, so the conclusion 
is that the shares are undervalued.
C is correct. The intrinsic value of a security is independent of the investor’s 
holding period.
A is correct. Dividend discount models focus on expected dividends.

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 254
How is the required rate of return for use in present value models estimated? To 
estimate the required rate of return on a share, analysts frequently use the capital 
asset pricing model (CAPM):
Required rate of return on share  C urrent expected ris k
fi=
−rree rate of retur n
 BetaM arket equity  risk prem ium + ()  i
Equation 5 states that the required rate of return on a share is the sum of the current 
expected risk-  free rate plus a risk premium that equals the product of the stock’s beta 
(a measure of non-  diversifiable risk) and the market risk premium (the expected return 
of the market in excess of the risk-  free return, where in practice, the “market” is often 
represented by a broad stock market index). However, even if analysts agree that the 
CAPM is an appropriate model, their inputs into the CAPM may differ. Thus, there 
is no uniquely correct answer to the question: What is the required rate of return?

Other common methods for estimating the required rate of return for the stock 
of a company include adding a risk premium that is based on economic judgments, 
rather than the CAPM, to an appropriate risk-  free rate (usually a government bond) 
and adding a risk premium to the yield on the company’s bonds. Good business and 
economic judgment is paramount in estimating the required rate of return. In many 
investment firms, required rates of return are determined by firm policy.
4.3 Preferred Stock Valuation
General dividend discount models are relatively easy to apply to preferred shares. 
In its simplest form, preferred stock  is a form of equity (generally, non-  voting) that 
has priority over common stock in the receipt of dividends and on the issuer’s assets 
in the event of a company’s liquidation. It may have a stated maturity date at which 
time payment of the stock’s par (face) value is made or it may be perpetual with no 
maturity date; additionally, it may be callable or convertible.

For a non-  callable, non-  convertible perpetual preferred share paying a level dividend 
D and assuming a constant required rate of return over time, Equation 1 reduces to 
the formula for the present value of a perpetuity. Its value is:
VD
r00=
For example, a $100 par value non-  callable perpetual preferred stock offers an 
annual dividend of $5.50. If its required rate of return is 6 percent, the value estimate 
would be $5.50/0.06 = $91.67.
For a non-  callable, non-  convertible preferred stock with maturity at time n, the 
estimated intrinsic value can be estimated by using Equation 3 but using the preferred 
stock’s par value, F, instead of Pn:
VD
rF
rt
t
tn
n0
111=
+()+
+() =∑
When Equation 7 is used, the most precise approach is to use values for n, r, and 
D that reflect the payment schedule of the dividends. This method is similar to the 
practice of fixed-  income analysts in valuing a bond. For example, a non-  convertible

preferred stock with a par value of £20.00, maturity in six years, a nominal required 
rate of return of 8.20 percent, and semiannual dividends of £2.00 would be valued 
by using an n of 12 , an r of 4.10 percent, a D of £2.00, and an F of £20.00. The result 
would be an estimated value of £31.01. Assuming payments are annual rather than 
semiannual (i.e., assuming that n = 6, r = 8.20 percent, and D = £4.00) would result 
in an estimated value of £30.84.(5)
(6)
(7)

Present Value Models: The Dividend Discount Model 255
Preferred stock issues are frequently callable (redeemable) by the issuer at some 
point prior to maturity, often at par value or at prices in excess of par value that decline 
to par value as the maturity date approaches. Such call options tend to reduce the 
value of a preferred issue to an investor because the option to redeem will be exercised 
by the issuer when it is in the issuer's favor and ignored when it is not. For example, 
if an issuer can redeem shares at par value that would otherwise trade (on the basis 
of dividends, maturity, and required rate of return) above par value, the issuer has 
motivation to redeem the shares.
Preferred stock issues can also include a retraction option that enables the holder of 
the preferred stock to sell the shares back to the issuer prior to maturity on prespecified 
terms. Essentially, the holder of the shares has a put option. Such put options tend to

increase the value of a preferred issue to an investor because the option to retract will 
be exercised by the investor when it is in the investor's favor and ignored when it is 
not. Although the precise valuation of issues with such embedded options is beyond 
the scope of this reading, Example 6 includes a case in which Equation 7 can be used 
to approximate the value of a callable, retractable preferred share.
EXAMPLE 6   
Preferred Share Valuation: Two Cases
Case 1 : Non-  callable, Non-  convertible, Perpetual Preferred 
Shares
The following facts concerning the Union Electric Company 4.75 percent per -
petual preferred shares are as follows:
■■Issuer: Union Electric Co. (owned by Ameren)
■■Par value: US$100
■■Dividend: US$4.75 per year
■■Maturity: perpetual
■■Embedded options: none
■■Credit rating: Moody’s Investors Service/Standard & Poor’s Ba1/BB
■■Required rate of return on Ba1/BB rated preferred shares as of valuation 
date: 7.5 percent.
A Estimate the intrinsic value of this preferred share.

B Explain whether the intrinsic value of this issue would be higher or lower 
if the issue were callable (with all other facts remaining unchanged).
Basing the discount rate on the required rate of return on Ba1/BB rated pre -
ferred shares of 7.5 percent gives an intrinsic value estimate of US$4.75/0.075 = 
US$63.33.
The intrinsic value would be lower if the issue were callable. The option to 
redeem or call the issue is valuable to the issuer because the call will be exercised 
when doing so is in the issuer’s interest. The intrinsic value of the shares to the 
investor will typically be lower if the issue is callable. In this case, because the 
intrinsic value without the call is much less than the par value, the issuer would 
be unlikely to redeem the issue if it were callable; thus, callability would reduce 
intrinsic value, but only slightly.

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 256
Case 2 : Retractable Term Preferred Shares
Retractable term preferred shares are a type of preferred share that has been 
issued by Canadian companies. This type of issue specifies a “retraction date” 
when the preferred shareholders have the option to sell back their shares to the 
issuer at par value (i.e., the shares are “retractable” or “putable” at that date).2 
At predetermined dates prior to the retraction date, the issuer has the option 
to redeem the preferred issue at predetermined prices (which are always at or 
above par value).
An example of a retractable term preferred share currently outstanding is 
YPG (Yellow Pages) Holdings, series 2, 5 percent first preferreds. YPG Holdings 
is Canada’s leading local commercial search provider and largest telephone 
directory publisher. The issue is in Canadian dollars. The shares have a $25 
par value and pay a quarterly dividend of $0.3125 [= (5 percent × $25)/4]. As

of 29 December 2008, shares were priced at $12.01 and carried ratings from 
Dominion Bond Rating Service (DBRS) and Standard & Poor’s of Pfd-  3H and 
P3, respectively. Thus, the shares are viewed by DBRS as having “adequate” 
credit quality, qualified by “H, ” which means relatively high quality within that 
group. The shares are redeemable at the option of YPG Holdings in June 2009 at 
$26.75, with redemption prices eventually declining to par value at later dates. 
The retraction date is 30 June 2017, or eight and half years (34 quarters) from 
the date (31 December 2008) the shares were being valued. Similarly rated pre -
ferred issues had an estimated nominal required rate of return of 15.5 percent 
(3.875 percent per quarter). Because the issue’s market price is so far below the 
prices at which YPG could redeem or call the issue, redemption is considered to 
be unlikely and the redemption option is assumed here to have minimal value 
for an investor.

A Assume that the issue will be retracted in June 2017; the holders of the 
shares will put the shares to the company in June 2017. Based on the 
information given, estimate the intrinsic value of a share.
An intrinsic value estimate of a share of this preferred issue is $12.71:
V020 3125
10 038750 3125
10 038=+()+
+()++
+$.
.$.
.$.
.
7 75
25
10 0387512 7134
34()




+
+()≈$
.$.
4.4 The Gordon Growth Model
A rather obvious problem when one is trying to implement Equation 1 for common 
equity is that it requires the analyst to estimate an infinite series of expected dividends. 
To simplify this process, analysts frequently make assumptions about how dividends 
will grow or change over time. The Gordon (constant) growth model (Gordon, 1962) 
is a simple and well-  recognized DDM. The model assumes dividends grow indefinitely 
at a constant rate.
2 “Retraction” refers to this option, which is a put option. The terminology is not completely settled:

The type of share being called “retractable term preferred” is also known as “hard retractable preferred, ” 
with “hard” referring to payment in cash rather than common shares at the retraction date. See the 2009 
ScotiaMcLeod report http://www.ritceyteam.com/pdf/guide_to_preferred_shares.pdf.

Present Value Models: The Dividend Discount Model 257
Because of its assumption of a constant growth rate, the Gordon growth model is 
particularly appropriate for valuing the equity of dividend-  paying companies that are 
relatively insensitive to the business cycle and in a mature growth phase. Examples 
might include an electric utility serving a slowly growing area or a producer of a staple 
food product (e.g., bread). A history of increasing the dividend at a stable growth rate 
is another practical criterion if the analyst believes that pattern will hold in the future.
With a constant growth assumption, Equation 1 can be written as Equation 8, 
where g is the constant growth rate:
VDg
rDg
rg
rg
rt
t00
02
21
11
11
11
1=+()
+()=+()
+()++()
+()+++()
+(∞
...
) )



∞
=∞
∑
t1
If required return r is assumed to be strictly greater than growth rate g, then 
the square-  bracketed term in Equation 8 is an infinite geometric series and sums to

[(1 + g)/(r – g)]. Substituting into Equation 8 produces the Gordon growth model as 
presented in Equation 9:
VDg
rgD
rg00 11=+()
−=−
For an illustration of the expression, suppose the current (most recent) annual 
dividend on a share is €5.00 and dividends are expected to grow at 4 percent per year. 
The required rate of return on equity is 8 percent. The Gordon growth model estimate 
of intrinsic value is, therefore, €5.00(1.04)/(0.08 – 0.04) = €5.20/0.04 = €130 per share. 
Note that the numerator is D1 not D0. (Using the wrong numerator is a common error.)
The Gordon growth model estimates intrinsic value as the present value of a 
growing perpetuity. If the growth rate, g, is assumed to be zero, Equation 8 reduces 
to the expression for the present value of a perpetuity, given earlier as Equation 6.
In estimating a long-  term growth rate, analysts use a variety of methods, including 
assessing the growth in dividends or earnings over time, using the industry median

growth rate, and using the relationship shown in Equation 10 to estimate the sus -
tainable growth rate:
g = b × ROE  
where
 g = dividend growth rate
 b = earnings retention rate = (1 – Dividend payout ratio)
 ROE = return on equity
Example 7 illustrates the application of the Gordon growth model to the shares of 
a large industrial manufacturing company. The analyst believes it will continue to grow 
at a rate that it achieved in the previous three years and remain stable in the future. 
The example asks how much the dividend growth assumption adds to the intrinsic 
value estimate. The question is relevant to valuation because if the amount is high on 
a percentage basis, a large part of the value of the share depends on the realization of 
the growth estimate. One can answer the question by subtracting from the intrinsic 
value estimate determined by Equation 9 the value determined by Equation 6, which 
assumes no dividend growth.3(8)
(9)
(10)

(9)
(10)
3 A related concept, the present value of growth opportunities (PVGO), is discussed in more advanced 
readings.

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 258
EXAMPLE 7   
Applying the Gordon Growth Model
Siemens AG operates in the capital goods and technology space. It is involved in 
the engineering, manufacturing, automation, power, and transportation sectors. 
It operates globally and is one of the largest companies in the sectors in which 
it operates. It is a substantial employer in both its original, domestic German 
market, as well as dozens of countries around the world. Selected financial 
information for Siemens appears in Exhibit 3.
Exhibit 3   Selected Financial Information for Siemens AG
Y ear 2017 2016 2015 2014 2013
EPS €7.45 €6.74 €8.85 €6.37 €5.08
DPS €3.7 €3.6 €3.5 €3.3 €3.0
Payout ratio 50% 53% 40% 52% 59%
ROE 15.6% 15.9% 22.3% 18.2% 14.6%
Share price
  (XETRA 
- Frankfurt) €119.2 €104.2 €79.94 €94.37 €89.06
Note : DPS stands for “dividends per share. ”
Source:  Morningstar, www.siemens.com.
The analyst estimates the growth rate to be approximately 5.4 percent based

on the dividend growth rate over the period 2013 to 2017 [3(1 + g)4 = 3.7, so g 
= 5.4%]. To verify that the estimated growth rate of 5.4 percent is feasible in the 
future, the analyst also uses the average of Siemens’s retention rate and ROE 
for the previous five years ( g ≈ 0.49 × 17.3% ≈ 8.5%) to estimate the sustainable 
growth rate.
Using a number of approaches, including adding a risk premium to a long-  
term German government bond and using the CAPM, the analyst estimates a 
required return of 7.5 percent. The most recent dividend of €3.70 is used for D0.
1 Use the Gordon growth model to estimate Siemens’s intrinsic value.
2 How much does the dividend growth assumption add to the intrinsic 
value estimate?
3 Based on the estimated intrinsic value, is a share of Siemens undervalued, 
overvalued, or fairly valued?
4 What is the intrinsic value if the growth rate estimate is lowered to 
4.4 percent?
5 What is the intrinsic value if the growth rate estimate is lowered to

4.4 percent and the required rate of return estimate is increased to 
8.5 percent?
V010 054
0 075 0 054=+()
−=¬3.70¬184.20.
..

Present Value Models: The Dividend Discount Model 259
¬184.20¬3.70
0.075¬134.87 −=
A share of Siemens appears to be undervalued. The analyst, before making a 
recommendation, might consider how realistic the estimated inputs are and 
check the sensitivity of the estimated value to changes in the inputs.
V010 044
0 075 0 044=+()
−=¬3.70¬124.61.
..
V010 044
0 085 0 044=+()
−=¬3.70¬94.21.
..
The Gordon growth model estimate of intrinsic value is extremely sensitive to 
the choice of required rate of return r and growth rate g. It is possible that the 
growth rate assumption and the required return assumption used initially were 
too high. Worldwide economic growth is typically in the low single digits, which 
may mean that a large company such as Siemens may struggle to grow dividends 
at 5.4 percent into perpetuity. Exhibit 4 presents a further sensitivity analysis of 
Siemens’s intrinsic value to the required return and growth estimates.

Exhibit 4   Sensitivity Analysis of the Intrinsic-  Value Estimate for 
Siemens AG
g = 2.5% g = 3.5% g = 4.5% g = 5.5% g = 6.5%
r = 6% €108.4 €153.2 €257.8 €780.7 —
r = 7% €84.3 €109.4 €154.7 €260.2 €788.1
r = 8% €69.0 €85.1 €110.5 €156.1 €262.7
r = 9% €58.3 €69.6 €85.9 €111.5 €157.6
r = 10% €50.6 €58.9 €70.3 €86.7 €112.6
Note that no value is shown when the growth rate exceeds the required rate 
of return. The Gordon growth model assumes that the growth rate cannot be 
greater than the required rate of return.
The assumptions of the Gordon model are as follows:
■■Dividends are the correct metric to use for valuation purposes.
■■The dividend growth rate is forever: It is perpetual and never changes.
■■The required rate of return is also constant over time.
■■The dividend growth rate is strictly less than the required rate of return.

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 260
An analyst might be dissatisfied with these assumptions for many reasons. The 
equities being examined might not currently pay a dividend. The Gordon assumptions 
might be too simplistic to reflect the characteristics of the companies being evaluated. 
Some alternatives to using the Gordon model are as follows:
■■Use a more robust DDM that allows for varying patterns of growth.
■■Use a cash flow measure other than dividends for valuation purposes.
■■Use some other approach (such as a multiplier method) to valuation.
Applying a DDM is difficult if the company being analyzed is not currently paying a 
dividend. A company may not be paying a dividend if 1) the investment opportunities 
the company has are all so attractive that the retention and reinvestment of funds is 
preferable, from a return perspective, to the distribution of a dividend to shareholders

or 2) the company is in such shaky financial condition that it cannot afford to pay a 
dividend. An analyst might still use a DDM to value such companies by assuming that 
dividends will begin at some future point in time. The analyst might further assume 
that constant growth occurs after that date and use the Gordon growth model for 
valuation. Extrapolating from no current dividend, however, generally yields highly 
uncertain forecasts. Analysts typically choose to use one or more of the alternatives 
instead of or as a supplement to the Gordon growth model.
EXAMPLE 8   
Gordon Growth Model in the Case of No Current Dividend
A company does not currently pay a dividend but is expected to begin to do 
so in five years (at t = 5). The first dividend is expected to be $4.00 and to be 
received five years from today. That dividend is expected to grow at 6 percent 
into perpetuity. The required return is 10 percent. What is the estimated current 
intrinsic value?
Solution:

Solution:
The analyst can value the share in two pieces:
1 The analyst uses the Gordon growth model to estimate the value at t = 5; 
in the model, the year-  ahead dividend is $4(1.06). Then the analyst finds 
the present value of this value as of t = 0.
2 The analyst finds the present value of the $4 dividend not “counted” in the 
estimate in Piece 1 (which values dividends from t = 6 onward). Note that 
the statement of the problem implies that D0, D1, D2, D3, and D4 are zero.
Piece 1: The value of this piece is $65.818:
VDg
rgD
rg
Vnn n=+()
−=−
=+()
−==+1
41 006
0100 06424
0041061
5$.
..$.
.$
V V05106
10 1065 818 =
+()=$
.$.
Piece 2: The value of this piece is $2.484:
V054
10 102 484 =
+()=$
.$.
The sum of the two pieces is $65.818 + $2.484 = $68.30.

Present Value Models: The Dividend Discount Model 261
Alternatively, the analyst could value the share at t = 4, the point at which 
dividends are expected to be paid in the following year and from which point 
they are expected to grow at a constant rate.
V
V4
04400
0100 06400
004100
100
10 1068 30=−==
=
+()=$.
..$.
.$
$
.$.
The next section addresses the application of the DDM with more flexible assump -
tions as to the dividend growth rate.
4.5 Multistage Dividend Discount Models
Multistage growth models are often used to model rapidly growing companies. The 
two-  stage DDM  assumes that at some point the company will begin to pay dividends 
that grow at a constant rate, but prior to that time the company will pay dividends 
that are growing at a higher rate than can be sustained in the long run. That is, the 
company is assumed to experience an initial, finite period of high growth, perhaps 
prior to the entry of competitors, followed by an infinite period of sustainable growth.

The two-  stage DDM thus makes use of two growth rates: a high growth rate for an 
initial, finite period followed by a lower, sustainable growth rate into perpetuity. The 
Gordon growth model is used to estimate a terminal value at time n that reflects the 
present value at time n of the dividends received during the sustainable growth period.
Equation 11 will be used here as the starting point for a two-  stage valuation model. 
The two-  stage valuation model is similar to Example 8 except that instead of assuming 
zero dividends for the initial period, the analyst assumes that dividends will exhibit a 
high rate of growth during the initial period. Equation 11 values the dividends over 
the short-  term period of high growth and the terminal value at the end of the period 
of high growth. The short-  term growth rate, gS, lasts for n years. The intrinsic value 
per share in year n, Vn, represents the year n value of the dividends received during

the sustainable growth period or the terminal value at time n. Vn can be estimated by 
using the Gordon growth model as shown in Equation 12, where gL is the long-  term 
or sustainable growth rate. The dividend in year n + 1, Dn+1, can be determined by 
using Equation 13:
VDg
rV
rSt
t
tn
n
n00
11
11=+()
+()+
+() =∑
VD
rgnn
L=−+1
DD ggnSn
L +=+ () +() 10 11
EXAMPLE 9   
Applying the Two-  Stage Dividend Discount Model
The current dividend, D0, is $5.00. Growth is expected to be 10 percent a year 
for three years and then 5  percent thereafter. The required rate of return is 
15 percent. Estimate the intrinsic value.(11)
(12)
(13)

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 262
Solution:
D1 = $5.00(1 + 0.10) = $5.50
D2 = $5.00(1 + 0.10)2 = $6.05
D3 = $5.00(1 + 0.10)3 = $6.655
D4 = $5.00(1 + 0.10)3(1 + 0.05) = $6.98775
V
V3
06 98775
0150 0569 8775
550
10 15605
10 15=−=
=+()+
+($.
..$.
$.
.$.
.) )+
+()+
+()≈23 36 655
10 1569 8775
10 1559 68$.
.$.
.$.
The DDM can be extended to as many stages as deemed appropriate. For most 
publicly traded companies (that is, companies beyond the start-  up stage), practitioners 
assume growth will ultimately fall into three stages: 1) growth, 2) transition, and 3) 
maturity. This assumption supports the use of a three-  stage DDM , which makes use 
of three growth rates: a high growth rate for an initial finite period, followed by a 
lower growth rate for a finite second period, followed by a lower, sustainable growth 
rate into perpetuity.
One can make the case that a three-  stage DDM would be most appropriate for a

fairly young company, one that is just entering the growth phase. The two-  stage DDM 
would be appropriate to estimate the value of an older company that has already 
moved through its growth phase and is currently in the transition phase (a period 
with a higher growth rate than the sustainable growth rate) prior to moving to the 
maturity phase (the period with a lower, sustainable growth rate).
However, the choice of a two-  stage DDM need not rely solely on the age of a 
company. Long-  established companies sometimes manage to restart above-  average 
growth through, for example, innovation, expansion to new markets, or acquisitions. 
Or a company’s long-  run growth rate may be interrupted by a period of subnormal 
performance. If growth is expected to moderate (in the first case) or improve (in the 
second case) toward some long-  term growth rate, a two-  stage DDM may be appro -
priate. Thus, we chose a two-  stage DDM to value Brown-  Forman in Example 10.
EXAMPLE 10

EXAMPLE 10   
Two-  Stage Dividend Discount Model: Brown-  Forman
Brown-  Forman Corporation is a diversified producer of wines and spirits. It was 
founded in 1870 by George Garvin Brown in Louisville, Kentucky, USA. His 
original brand, Old Forester Kentucky Straight Bourbon Whisky, was America's 
first bottled bourbon. Brown-  Forman, one of the largest American-  owned spirits 
and wine companies and among the top 10 largest global spirits companies, sells 
its brands in more than 135 countries and has offices in cities across the globe. In 
all, Brown-  Forman has more than 35 brands in its portfolio of wines and spirits.
The 30 January 2009 Value Line  report on Brown-  Forman appears in Exhibit 5. 
Brown-  Forman has increased its dividends every year except 2000, when the 
dividend remained at US$0.50 as it was in 1999. On the left side of the report, 
in the section titled “ Annual Rates, ” dividend growth is shown as 7.5 percent

for the past 10 years, 11 percent for the past 5 years, and estimated 5 percent 
for 2005–2007 to 2011–2013. After a period of growth through acquisition 
and merger, the pattern suggests that Brown-  Forman may be transitioning to 
a mature growth phase.

Present Value Models: The Dividend Discount Model 263
The two-  stage DDM is arguably a good choice for valuing Brown Forman 
because the company appears to be transitioning from a high-  growth phase 
(note the 11 percent dividend growth for the past 5 years) to a lower-  growth 
phase (note the forecast of 5 percent dividend growth to 2011–2013). The analyst 
discussion refers to the company facing “short-  term obstacles” and states that 
the company’s “capital appreciation potential for the 3- to 5-  year time frame is 
well below average. ”
The CAPM can be used to estimate the required return, r, for Brown-  Forman. 
The Value Line  report (in the upper left corner) estimates beta to be 0.70. Using 
the yield of about 3.1 percent on 10-  year US Treasury notes as a proxy for the 
risk-  free rate and assuming an equity risk premium of 5.0 percent, we find the 
estimate for r would be 6.6 percent [3.1% + 0.70(5.0%)].
To estimate the intrinsic value at the end of 2008, we use the 2008 dividend

of US$1.08 from the Value Line  report. The dividend is assumed to grow at a 
rate of 6.5 percent for two years and then 4.0 percent thereafter. The growth rate 
assumption for the first stage is consistent with the Value Line  forecast for 2008 
to 2009 growth. The assumption of a 4.0 percent perpetual growth rate produces 
a five-  year growth rate assumption near 5 percent,4 which is consistent with the 
Value Line  forecast of 5 percent growth to 2011–2013. Thus:
D2009 = US$1.08(1 + 0.065) = US$1.1502
D2010 = US$1.08(1 + 0.065)2 = US$1.224963
D2011 = US$1.08(1 + 0.065)2(1 + 0.04) = US$1.273962
V
V2010
20081 273962
0 066 00448 99854
1 1502
10=−=
=+USUS
US$.
..$.
$.
.0 0661 224963
10 06648 99854
10 06645 222()+
+()+
+()≈US USUS$.
.$.
.$. 8 8
Given a recent price of US$47.88, as noted at the top of the Value Line  
report, the intrinsic-  value estimate of US$45.28 suggests that Brown-  Forman 
is modestly overvalued.

4 The exact geometric average annual growth rate can be determined as [(1+0.065)  (1+0.065)  (1+0.04)  
(1+0.04)  (1.04)]1/5 – 1 = 0.049929 ≈ 5.0%.

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 264
Exhibit 5   Value Line  Report on Brown-  Forman
Source:  © 2009 Value Line, Inc. All Rights Reserved Worldwide. “Value Line” is a registered trademark of Value Line, Inc. Value 
Line Geometric and Arithmetic Indices calculated by Thomson Reuters. Information supplied by Thomson Reuters.

Multiplier Models 265
MULTIPLIER MODELS
The term price multiple  refers to a ratio that compares the share price with some 
sort of monetary flow or value to allow evaluation of the relative worth of a company’s 
stock. Some practitioners use price ratios as a screening mechanism. If the ratio falls 
below a specified value, the shares are identified as candidates for purchase, and if the 
ratio exceeds a specified value, the shares are identified as candidates for sale. Many 
practitioners use ratios when examining a group or sector of stocks and consider the 
shares for which the ratio is relatively low to be attractively valued securities.
Price multiples that are used by security analysts include the following:
■■Price-  to- earnings ratio (P/E). This measure is the ratio of the stock price to 
earnings per share. P/E is arguably the price multiple most frequently cited by 
the media and used by analysts and investors (Block 1999). The seminal works

of McWilliams (1966), Miller and Widmann (1966), Nicholson (1968), Dreman 
(1977), and Basu (1977) presented evidence of a return advantage to low-  P/E 
stocks.
■■Price-  to- book ratio (P/B). The ratio of the stock price to book value per share. 
Considerable evidence suggests that P/B multiples are inversely related to future 
rates of return (Fama and French 1995).
■■Price-  to- sales ratio (P/S). This measure is the ratio of stock price to sales per 
share. O’Shaughnessy (2005) provided evidence that a low P/S multiple is the 
most useful multiple for predicting future returns.
■■Price-  to- cash-  flow ratio (P/CF). This measure is the ratio of stock price to some 
per- share measure of cash flow. The measures of cash flow include free cash 
flow (FCF) and operating cash flow (OCF).
A common criticism of all of these multiples is that they do not consider the future. 
This criticism is true if the multiple is calculated from trailing or current values of the

divisor. Practitioners seek to counter this criticism by a variety of techniques, including 
forecasting fundamental values (the divisors) one or more years into the future. The 
resulting forward (leading or prospective) price multiples may differ markedly from 
the trailing price multiples. In the absence of an explicit forecast of fundamental val -
ues, the analyst is making an implicit forecast of the future when implementing such 
models. The choice of price multiple—trailing or forward—should be used consistently 
for companies being compared.
Besides the traditional price multiples used in valuation, just presented, analysts 
need to know how to calculate and interpret other ratios. Such ratios include those 
used to analyze business performance and financial condition based on data reported 
in financial statements. In addition, many industries have specialized measures of 
business performance that analysts covering those industries should be familiar with.

In analyzing cable television companies, for example, the ratio of total market value of 
the company to the total number of subscribers is commonly used. Another common 
measure is revenue per subscriber. In the oil industry, a commonly cited ratio is proved 
reserves per common share. Industry-  specific or sector-  specific ratios such as these 
can be used to understand the key business variables in an industry or sector as well 
as to highlight attractively valued securities.5

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 266
5.1 Relationships among Price Multiples, Present Value 
Models, and Fundamentals
Price multiples are frequently used independently of present value models. One price 
multiple valuation approach, the method of comparables, does not involve cash flow 
forecasts or discounting to present value. A price multiple is often related to funda -
mentals through a discounted cash flow model, however, such as the Gordon growth 
model. Understanding such connections can deepen the analyst’s appreciation of the 
factors that affect the value of a multiple and often can help explain reasons for differ -
ences in multiples that do not involve mispricing. The expressions that are developed 
can be interpreted as the justified value  of a multiple—that is, the value justified by 
(based on) fundamentals or a set of cash flow predictions. These expressions are an 
alternative way of presenting intrinsic-  value estimates.

As an example, using the Gordon growth model identified previously in Equation 9 
and assuming that price equals intrinsic value ( P0 = V0), we can restate Equation 9 
PD
rg01=−
To arrive at the model for the justified forward P/E given in Equation 14, we divide 
both sides of Equation 9.1 by a forecast for next year’s earnings, E1. In Equation 14, 
the dividend payout ratio, p, is the ratio of dividends to earnings:
P
EDE
rgp
rg0
111=−=−
Equation  14 indicates that the P/E is inversely related to the required rate of 
return and positively related to the growth rate; that is, as the required rate of return 
increases, the P/E declines, and as the growth rate increases, the P/E increases. The 
P/E and the payout ratio appear to be positively related. This relationship may not 
be true, however, because a higher payout ratio may imply a slower growth rate as a 
result of the company retaining a lower proportion of earnings for reinvestment. This

phenomenon is referred to as the dividend displacement of earnings.
EXAMPLE 11   
Value Estimate Based on Fundamentals
Petroleo Brasileiro SA, commonly known as Petrobras, was once labeled “the 
most expensive oil company” by Bloomberg.com. Data for Petrobras and the 
oil industry, including the trailing twelve-  month (TTM) P/E and payout ratios, 
appear below.
Petrobras Industry
P/E ratio (TTM) 11.77 7.23
Payout ratio (TTM) (%) 24.40 21.66
EPS 5-  year growth rate (%) 26.35 15.46
EPS (MRQ) vs. Qtr. 1 yr. ago (% change) −41.44 −127.53
Note : MRQ stands for “most recent quarter. ”
Source:  Reuters.
Explain how the information shown supports a higher P/E for Petrobras than 
for the industry.(9.1)
(14)

Multiplier Models 267
Solution: 
The data support a higher P/E for Petrobras because its payout ratio and five-  year 
EPS growth rate exceed those of the industry. Equation 14 implies a positive 
relationship between the payout ratio and the P/E multiple. A higher payout 
ratio supports a higher P/E. Furthermore, to the extent that higher EPS growth 
implies a high growth rate in dividends, the high EPS growth rate supports a 
high P/E. Although the Petrobras quarterly EPS have declined relative to EPS 
of a year ago, the decline is less than that of the industry.
EXAMPLE 12   
Determining Justified Forward P/E
Heinrich Gladisch, CFA, is estimating the justified forward P/E for Nestlé, one of 
the world’s leading nutrition and health companies. Gladisch notes that sales for 
2016 were SFr89.47 billion (US$90.4 billion) and that net income was SFr8.53 bil -
lion (US$8.62 billion). He organizes the data for EPS, dividends per share, and

the dividend payout ratio for the years 2012–2016 in the following table:
2012 2013 2014 2015 2016
Earnings per share SFr3.21 SFr3.14 SFr4.54 SFr2.90 SFr2.76
   Year over year % change –2.2% 44.6% –36.1% –4.8%
Dividend per share SFr2.05 SFr2.15 SFr2.2 SFr2.25 SFr2.3
   Year over year % change 4.9% 2.3% 2.3% 2.2%
Dividend payout ratio 63.9% 68.5% 48.5% 77.6% 83.3%
Gladisch calculates that ROE averaged 22 percent in the period 2012−2015 
but was below that level at 13.4 percent in 2016. In that year, however, Nestlé’s 
reported net income included a large nonrecurring component. The company 
reported 2016 “underlying earnings, ” which it defined as net income “from 
continuing operations before impairments, restructuring costs, results on dis -
posals and significant one-  off items, ” to be SFr3.40, giving an adjusted 17% ROE. 
Predicting increasing pressure on Nestlé’s profit margins from lower-  priced 
goods, particularly in developed markets, Gladisch estimates a long-  run ROE 
of 16 percent.

Gladisch decides that the dividend payout ratios of the 2012–2015 period—
averaging 64.6 percent—are more representative of Nestlé’s future payout ratio 
than is the high 2016 dividend payout ratio (when based on reported earnings). 
The dividend payout ratio in 2016 was higher because management apparently 
based the 2016 dividend on the components of net income that were expected 
to continue into the future. But basing a dividend on net income including 
non-  recurring items creates the potential need to increase dividends in the 
future. Rounding up the 2012−2016 average, Gladisch settles on an estimate of 
65 percent for the dividend payout ratio for use in calculating a justified forward 
P/E using Equation 14.
Gladisch’s firm estimates that the required rate of return for Nestlé’s shares 
is 9 percent per year. Gladisch also finds the following data at the opposite ends 
of the spectrum of external research analyst forecasts:

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 268
2017E 2018E
Most optimistic analyst forecast:
  EPS SFr3.69 SFr4.15
      Year over year % change 33.7% 12.5%
  P/E (based on a target price of SFr105) 28.5 25.3
Least optimistic analyst forecast:
  EPS SFr3.13 SFr3.42
      Year over year % change 13.4% 9.3%
  P/E (based on a target price of SFr68) 21.7 19.9
1 Based only on information and estimates developed by Gladisch and his 
firm, estimate Nestlé’s justified forward P/E.
2 Compare and contrast the justified forward P/E estimate from Question 
1 to the estimates from each end of the spectrum of external research ana -
lysts forecasts.
The estimate of the justified forward P/E is 19.1. The dividend growth rate can 
be estimated by using Equation 10 as (1 – Dividend payout ratio) × ROE = (1 – 
0.65) × 0.16 = 0.056, or 5.6 percent. Therefore,
P
Er g0
1065
0090 05619 1 =−=−=Payout .
...
The estimated justified forward P/E of 19.1 is lower than the justified 2017 P/E

estimates of 28.5 and 21.7 of the two analysts. Using a required rate of return 
of 8.5 percent rather than 9 percent results in a justified forward P/E estimate 
of 22.4 = 0.65/(0.085 – 0.056). Using an ROE of 22 percent (the average ROE of 
the 2012–2015 period) rather than 16 percent results in a justified forward P/E 
estimate of 50.0 = 0.65/[0.09 – (0.35)(0.22)] = 0.65/(0.09 – 0.077). The justified 
forward P/E is very sensitive to changes in the inputs.
Justified forward P/E estimates can be sensitive to small changes in assumptions. 
Therefore, analysts can benefit from carrying out a sensitivity analysis, as shown in 
Exhibit 6, which is based on Example 12. Exhibit 6 shows how the justified forward 
P/E varies with changes in the estimates for the dividend payout ratio (columns) and 
return on equity. The dividend growth rate (rows) changes because of changes in the 
retention rate (1 – Payout rate) and ROE. Recall g = ROE times retention rate.

Exhibit 6   Estimates for Nestlé’s Justified Forward P/E (Required Rate of 
Return = 9 Percent)
Constant Dividend 
Growth Rate (%)Dividend Payout Ratio
55% 60% 65% 70% 75%
4.0 11.0 12.0 13.0 14.0 15.0
4.5 12.2 13.3 14.4 15.6 16.7
5.0 13.8 15.0 16.3 17.5 18.8
5.5 15.7 17.1 18.6 20.0 21.4

Multiplier Models 269
6.0 18.3 20.0 21.7 23.3 25.0
6.5 22.0 24.0 26.0 28.0 30.0
7.0 27.5 30.0 32.5 35.0 37.5
7.5 36.7 40.0 43.3 46.7 50.0
5.2 The Method of Comparables
The method of comparables is the most widely used approach for analysts reporting 
valuation judgments on the basis of price multiples. This method essentially com -
pares relative values estimated using multiples or the relative values of multiples. The 
economic rationale underlying the method of comparables is the law of one price : 
Identical assets should sell for the same price. The methodology involves using a price 
multiple to evaluate whether an asset is fairly valued, undervalued, or overvalued in 
relation to a benchmark value of the multiple. Choices for the benchmark multiple 
include the multiple of a closely matched individual stock or the average or median 
value of the multiple for the stock’s industry. Some analysts perform trend or time-

series analyses and use past or average values of a price multiple as a benchmark.
Identifying individual companies or even an industry as the “comparable” may 
present a challenge. Many large corporations operate in several lines of business, 
so the scale and scope of their operations can vary significantly. When identifying 
comparables (sometimes referred to as “comps”), the analyst should be careful to 
identify companies that are most similar according to a number of dimensions. These 
dimensions include (but are not limited to) overall size, product lines, and growth 
rate. The type of analysis shown in Section 5.1 relating multiples to fundamentals 
is a productive way to identify the fundamental variables that should be taken into 
account in identifying comparables.
EXAMPLE 13   
Method of Comparables (1)
As noted previously, P/E is a price multiple frequently used by analysts. Using 
P/E in the method of comparables can be problematic, however, as a result of

business cycle effects on EPS. An alternative valuation tool that is useful during 
periods of economic slowdown or extraordinary growth is the P/S multiple. 
Although sales will decline during a recession and increase during a period of 
economic growth, the change in sales will be less than the change in earnings 
in percentage terms because earnings are heavily influenced by fixed operating 
and financing costs (operating and financial leverage).
The following data provide the P/S for most of the major automobile man -
ufacturers as at December 2017:
Company P/S
Peugeot 0.28
Ford Motor 0.33
General Motors 0.36
(continued)Exhibit 6   (Continued)

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 270
Nissan Motor 0.38
Honda Motor 0.46
Tata Motors 0.49
Daimler 0.55
BMW 0.57
Toyota Motor 0.80
Sources:  Morningstar and company websites.
Based on the data presented, which stock appears to be undervalued when 
compared with the others?
Solution:
The P/S analysis suggests that Peugeot shares offer the best value. An analyst 
must be alert for a range of potential explanations of apparently low or high 
multiples when performing comparables analysis, rather than just assuming a 
relative mispricing.
EXAMPLE 14   
Method of Comparables (2)
Incorporated in the Netherlands, Airbus is active in the aerospace and defense 
industry. It is a dominant aerospace company in Europe. Its largest business, 
Airbus Commercial Aircraft, is a manufacturing company with bases in several 
European countries and accounts for the majority of Airbus SE profits. Airbus 
and its primary competitor, Boeing, control most of the global commercial

airplane industry.
Comparisons are frequently made between Airbus and Boeing. As noted in 
Exhibit 7, the companies are broadly similar in size as measured by total rev -
enues. Converting total forecast revenues from euros to US dollars using the 
average exchange rate for 2017 of US$1.13/€ results in a value of $75.5 billion 
for Airbus’s total revenues. Thus, total revenues for Boeing are expected to be 
about a fifth higher than those for Boeing.
The companies do differ, however, in several important areas. Airbus derives 
a greater share of its revenue from commercial aircraft production than does 
Boeing, and the order backlog for Airbus is much higher than that for Boeing. 
Converting the Airbus order backlog from euros to US dollars using the quarter-  
end rate for September 2017 of $1.1813/€ results in a value of $1.12 billion for 
Airbus’s order backlog. Thus, the order backlog for Airbus is more than twice 
as high as the backlog for Boeing.5

5 Exchange rate data are available from FRED (Federal Reserve Economic Data) at http://research.stlouisfed.
org/fred2/. Each company uses slightly different methodology for calculating order backlog.

Multiplier Models 271
Exhibit 7   Data for EADS and Boeing
Airbus Boeing
Total revenues (billions, 2017) €66.8 $92.2
Annual revenue growth (2015–2017 
average) 1.8% –2.1%
Percent of revenues from commer -
cial aircraft 75% 69%
Order backlog (billions) €945 $474
Share price, 12/Dec/17 €86.96 $283.73
EPS (basic) €3.33 $10.18
DPS €1.48 $5.7
Dividend payout ratio 44% 56%
P/E ratio 26.1 27.9
Note : 2017 forecast data and YTD average exchange rate as of 12 December 2017. Order 
backlog as of 30 September 2017.
Sources:  Company websites: www.airbus.com and www.boeing.com, Financial Times .
What data shown in Exhibit 7 support a higher P/E for Boeing than for Airbus?
Solution:
Recall from Equation 14 and the discussion that followed it that P/E is directly 
related to the payout ratio and the dividend growth rate. The P/E is inversely 
related to the required rate of return. The only data presented in Exhibit 7 that 
support a higher P/E for Boeing is the company’s higher dividend payout ratio

(expected at 56 percent versus 44 percent for Airbus).
The following implicitly supports a higher P/E for Airbus: Airbus has higher 
revenue growth (as reported for 2016 and expected for 2017) and a higher backlog 
of orders, suggesting that it may have a higher future growth rate. 
EXAMPLE 15   
Method of Comparables (3)
Canon Inc. is a leading worldwide manufacturer of business machines, cameras, 
and optical products. Canon was founded in 1937 as a camera manufacturer 
and is incorporated in Tokyo. The corporate philosophy of Canon is kyosei  or 
"living and working together for the common good." The following data can be 
used to determine a P/E for Canon over the time period 2011–2016. Analyze 
the P/E of Canon over time and discuss the valuation of Canon.
Y earPrice  
(a)EPS  
(b)P/E 
(a) ÷ (b)
2012 ¥3,340 ¥191.3 17.5
2013 ¥3,330 ¥200.8 16.6
2014 ¥3,840.5 ¥229.0 16.8

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 272
Y earPrice  
(a)EPS  
(b)P/E 
(a) ÷ (b)
2015 ¥3,675 ¥201.7 18.2
2016 ¥3,295 ¥138 23.9
Sources:  EPS, year-  end prices, and P/E data are from Morningstar and the Financial 
Times . 
Solution:
Trend analysis of Canon’s P/E reveals a peak of 23.9 at the end of 2016. The 
2013 P/E of 16.6 is the lowest of the five years reported. This finding suggests 
that Canon’s share price may be overpriced as of year-  end 2016. A bearish case 
for Canon’s stock can be made if an analyst believes that P/E will return to its 
historical average (18.6 over this five-  year period) or be lower. Such a bearish 
prediction requires that a decrease in P/E not be offset by an increase in EPS. 
A bullish case can be made if the analyst believes the stock deserves re-  rating 
and an even higher than trend P/E.
5.3 Illustration of a Valuation Based on Price Multiples
Telefónica S.A., a world leader in the telecommunication sector, provides communi -

cation, information, and entertainment products and services in Europe, Africa, and 
Latin America. It has operated in its home country of Spain since 1924, but as of 2008, 
more than 60 percent of its business was outside its home market.
Deutsche Telekom AG provides network access, communication services, and 
value-  added services via fixed and mobile networks. It generates more than half of 
its revenues outside its home country, Germany.
Exhibit  8 provides comparable data for these two communication giants for 
2006–2008.
Exhibit 8   Data for Telefónica and Deutsche Telekom
Telefónica Deutsche Telekom
2008 2007 2006 2008 2007 2006
(1) Total assets (€ billions) 99.9 105.9 109.0 123.1 120.7 130.2
  Asset growth −5.7% −2.8% — 2.0% −7.3% —
(2) Net revenues (€ billions) 57.9 56.4 52.9 61.7 62.5 61.3
  Revenue growth 2.7% 6.6% — −1.3% 2.0% —
(3) Net cash flow from operating activities 
(€ billions)16.4 15.6 15.4 15.4 13.7 14.2
  Cash flow growth 5.1% 1.3% — 12.4% −3.5% —

Cash flow growth 5.1% 1.3% — 12.4% −3.5% —
(4) Book value of common shareholders’ equity 
(€ billions)19.6 22.9 20.0 43.1 45.2 49.7
  Debt ratio:  
   1 – [(4) ÷ (1)]80.4% 78.4% 81.7% 65.0% 62.6% 61.8%
(5) Net profit (€ billions) 7.8 9.1 6.6 1.5 0.6 3.2
  Earnings growth −14.3% 37.9% — 150.0% −81.3% —

Multiplier Models 273
(6) Weighted average number of shares out -
standing (millions)4,646 4,759 4,779 4,340 4,339 4,353
(7) Price per share (€) 15.85 22.22 16.22 10.75 15.02 13.84
  Price-  to- revenue ratio (P/R):  
   (7) ÷ [(2) ÷ (6)] 1.3 1.9 1.5 0.8 1.0 1.0
  P/CF:  
   (7) ÷ [(3) ÷ (6)] 4.5 6.8 5.0 3.0 4.8 4.2
  P/B:  
   (7) ÷ [(4) ÷ (6)] 3.8 4.6 3.9 1.1 1.4 1.2
  P/E:  
   (7) ÷ [(5) ÷ (6)] 9.4 11.6 11.7 31.1 108.6 18.8
Sources:  Company websites: www.telefonica.es and www.deutschetelekom.com .
Time-  series analysis of all price multiples in Exhibit 8 suggests that both companies 
are currently attractively valued. For example, the 2008 price-  to- revenue ratio (P/R) 
of 1.3 for Telefónica is below the 2006–2008 average for this ratio of approximately 
1.6. The 2008 P/CF of 3.0 for Deutsche Telekom is below the 2006–2008 average for 
this ratio of approximately 4.0.

A comparative analysis produces somewhat mixed results. The 2008 values for 
Deutsche Telekom for the P/R, P/CF, P/B multiples are lower than those for Telefónica. 
This result suggests that Deutsche Telekom is attractively valued when compared with 
Telefónica. The 2008 P/E for Telefónica, however, is much lower than for Deutsche 
Telekom.
An analyst investigating these contradictory results would look for information not 
reported in Exhibit 8. For example, the earnings before interest, taxes, depreciation, 
and amortization (EBITDA) for Telefónica was €22.9 billion in 2008. The EBITDA 
value for Deutsche Telekom was €18.0 billion in 2008. The 2008 price-  to- EBITDA 
ratio for Telefónica is [(15.85 × 4,646)/22,900] or [15.85/(22,900/4,646)] = 3.2, whereas 
the 2008 price-  to- EBITDA ratio for Deutsche Telekom is 2.6. Thus, the higher P/E for 
Deutsche Telekom may be explained by higher depreciation charges, higher interest 
costs, and/or a greater tax burden.

In summary, the major advantage of using price multiples is that they allow for 
relative comparisons, both cross-  sectional (versus the market or another comparable) 
and in time series. The approach can be especially beneficial for analysts who are 
assigned to a particular industry or sector and need to identify the expected best per -
forming stocks within that sector. Price multiples are popular with investors because 
the multiples can be calculated easily and many multiples are readily available from 
financial websites and newspapers.
Caution is necessary. A stock may be relatively undervalued when compared with 
its benchmarks but overvalued when compared with an estimate of intrinsic value 
as determined by one of the discounted cash flow methodologies. Furthermore, 
differences in reporting rules among different markets and in chosen accounting 
methods can result in revenues, earnings, book values, and cash flows that are not

easily comparable. These differences can, in turn, result in multiples that are not easily 
comparable. Finally, the multiples for cyclical companies may be highly influenced by 
current economic conditions.Exhibit 8   (Continued)

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 274
5.4 Enterprise Value
An alternative to estimating the value of equity is to estimate the value of the enter -
prise. Enterprise value is most frequently determined as market capitalization plus 
market value of preferred stock plus market value of debt minus cash and investments 
(cash equivalents and short-  term investments). Enterprise value is often viewed as 
the cost of a takeover: In the event of a buyout, the acquiring company assumes the 
acquired company’s debt but also receives its cash. Enterprise value is most useful 
when comparing companies with significant differences in capital structure.
Enterprise value (EV) multiples are widely used in Europe, with EV/EBITDA 
arguably the most common. EBITDA is a proxy for operating cash flow because it 
excludes depreciation and amortization. EBITDA may include other non-  cash expenses, 
however, and non-  cash revenues. EBITDA can be viewed as a source of funds to pay

interest, dividends, and taxes. Because EBITDA is calculated prior to payment to 
any of the company’s financial stakeholders, using it to estimate enterprise value is 
logically appropriate.
Using enterprise value instead of market capitalization to determine a multiple can 
be useful to analysts. Even where the P/E is problematic because of negative earnings, 
the EV/EBITDA multiple can generally be computed because EBITDA is usually 
positive. An alternative to using EBITDA in EV multiples is to use operating income.
In practice, analysts may have difficulty accurately assessing enterprise value if they 
do not have access to market quotations for the company’s debt. When current market 
quotations are not available, bond values may be estimated from current quotations for 
bonds with similar maturity, sector, and credit characteristics. Substituting the book 
value of debt for the market value of debt provides only a rough estimate of the debt’s

market value. This is because market interest rates change and investors’ perception 
of the issuer’s credit risk may have changed since the debt was issued.
EXAMPLE 16   
Estimating the Market Value of Debt and Enterprise Value
Cameco Corporation is one of the world's largest uranium producers; it accounts 
for 15 percent of world production from its mines in Canada and the United 
States. Cameco estimates it has about 226,796,185 kilograms of proven and 
probable reserves and holds premier land positions in the world's most promis -
ing areas for new uranium discoveries in Canada and Australia. Cameco is also 
a leading provider of processing services required to produce fuel for nuclear 
power plants. It generates 1,000 megawatts of electricity through a partnership 
in North America's largest nuclear generating station located in Ontario, Canada.
For simplicity of exposition in this example, we will present share counts in

thousands and all dollar amounts in thousands of Canadian dollars. In 2008, 
Cameco had 350,130 shares outstanding. Its 2008 year-  end share price was 
$20.99. Therefore, Cameco’s 2008 year-  end market capitalization was $7,349,229.
In its 2008 Annual Report (available at www.cameco.com), Cameco reported 
total debt and other liabilities of $2,716,475. The company presented the following 
schedule for long-  term debt payments:
Y ear Payment
2009 $10,175
2010 453,288
2011 13,272
2012 317,452

Multiplier Models 275
2013 16,325
Thereafter 412,645
Total $1,223,157
Cameco’s longest maturity debt matures in 2018. We will assume that the 
$412,645 to be paid “thereafter” will be paid in equal amounts of $82,529 over 
the 2014 to 2018 time period. A yield curve for zero-  coupon Canadian govern -
ment securities was available from the Bank of Canada. The yield-  curve data 
and assumed risk premiums in Exhibit 9 were used to estimate the market value 
of Cameco’s long-  term debt:
Exhibit 9   Estimated Market Value
Y earYield on 
Zero-  Coupon 
Security (%)Assumed 
Risk 
Premium 
(%)Discount  
Rate (%)Book 
ValueMarket 
Value
2009 0.89 0.50 1.39 $10,175 $10,036
2010 1.11 1.00 2.11 $453,288 $434,748
2011 1.39 1.50 2.89 $13,272 $12,185
2012 1.65 2.00 3.65 $317,452 $275,043
2013 1.88 2.50 4.38 $16,325 $13,175
2014 2.10 3.00 5.10 $82,529 $61,234
2015 2.30 3.50 5.80 $82,529 $55,617
2016 2.50 4.00 6.50 $82,529 $49,867
2017 2.71 4.50 7.21 $82,529 $44,105
2018 2.92 5.00 7.92 $82,529 $38,511

$1,223,157 $994,521
Note from Exhibit  9 that the book value of long-  term debt is $1,223,157 
and its estimated market value is $994,521. The book value of total debt and 
liabilities of $2,716,475 minus the book value of long-  term debt of $1,223,157 is 
$1,493,318. If we assume that the market value of that remaining debt is equal 
to its book value of $1,493,318, an estimate of the market value of total debt 
and liabilities is that amount plus the estimated market value of long-  term debt 
of $994,521 or $2,487,839.
At the end of 2008, Cameco had cash and equivalents of $269,176. Enterprise 
value can be estimated as the $7,349,229 market value of stock plus the $2,487,839 
market value of debt minus the $269,176 cash and equivalents, or $9,567,892. 
Cameco’s 2008 EBITDA was $1,078,606; an estimate of EV/EBITDA is, therefore, 
$9,567,892 divided by $1,078,606, or 8.9.

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 276
EXAMPLE 17   
EV/Operating Income
Exhibit 10 presents data for twelve major mining companies. Based only on the 
information in Exhibit 10, which two mining companies seem to be the most  
undervalued?
Exhibit 10   Data for Twelve Major Mining Companies
CompanyEV 
(US$ millions)Operating 
Income (OI)  
(US$ millions) EV/OI
BHP Billiton 119,712.3 11,753 10.19
Rio Tinto 93,856.1 6,471 14.5
Vale 82,051.2 6,366 12.89
Glencore 80,772.0 –549 –147.13
Southern Copper 37,817.0 1,564 24.18
Freeport-  McMoRan 33,452.0 –2,766 –12.09
Anglo American 32,870.3 2,562 12.83
Norilsk Nickel 22,483.0 3,377 6.66
Coal India 21,652.1 1,382 15.67
Barrick Gold 21,549.8 2,424 8.89
Newmont Mining 20,683.0 –65 –318.20
Goldcorp 12,986.7 369 35.19
Source:  www.miningfeeds.com, Morningstar.
Solution:
Norilsk Nickel and Barrick Gold have the lowest EV/OI and thus appear to be 
the most  undervalued or favorably priced on the basis of the EV/OI. Note the

negative ratio for Glencore, Freeport-  McMoRan, and Newmont Mining. Negative 
ratios are difficult to interpret, so other means are used to evaluate companies 
with negative ratios.
ASSET-  BASED VALUATION
An asset-  based valuation of a company uses estimates of the market or fair value of the 
company’s assets and liabilities. Thus, asset-  based valuations work well for companies 
that do not have a high proportion of intangible or “off the books” assets and that do 
have a high proportion of current assets and current liabilities. The analyst may be able 
to value these companies’ assets and liabilities in a reasonable fashion by starting with 
balance sheet items. For most companies, however, balance sheet values are different 
from market (fair) values, and the market (fair) values can be difficult to determine.6

Asset-  Based Valuation 277
Asset-  based valuation models are frequently used together with multiplier models 
to value private companies. As public companies increase reporting or disclosure of 
fair values, asset-  based valuation may be increasingly used to supplement present 
value and multiplier models of valuation. Important facts that the practitioner should 
realize are as follows:
■■Companies with assets that do not have easily determinable market (fair) val -
ues—such as those with significant property, plant, and equipment—are very 
difficult to analyze using asset valuation methods.
■■Asset and liability fair values can be very different from the values at which they 
are carried on the balance sheet of a company.
■■Some assets that are “intangible” are shown on the books of the company. Other 
intangible assets, such as the value from synergies or the value of a good busi -
ness reputation, may not be shown on the books. Because asset-  based valuation

may not consider some intangibles, it can give a “floor” value for a situation 
involving a significant amount of intangibles. When a company has significant 
intangibles, the analyst should prefer a forward-  looking cash flow valuation.
■■Asset values may be more difficult to estimate in a hyper-  inflationary 
We begin by discussing asset-  based valuation for hypothetical nonpublic companies 
and then move on to a public company example. Analysts should consider the difficul -
ties and rewards of using asset-  based valuation for companies that are suited to this 
measure. Owners of small privately held businesses are familiar with valuations arrived 
at by valuing the assets of the company and then subtracting any relevant liabilities.
EXAMPLE 18   
An Asset-  Based Valuation of a Family-  Owned Laundry
A family owns a laundry and the real estate on which the laundry stands. The 
real estate is collateral for an outstanding loan of $100,000. How can asset-  based

valuation be used to value this business?
Solution:
The analyst should get at least two market appraisals for the real estate (building 
and land) and estimate the cost to extinguish the $100,000 loan. This information 
would provide estimated values for everything except the laundry as a going 
concern. That is, the analyst has market values for the building and land and the 
loan but needs to value the laundry business. The analyst can value the assets 
of the laundry: the equipment and inventory. The equipment can be valued at 
depreciated value, inflation-  adjusted depreciated value, or replacement cost. 
Replacement cost in this case means the amount that would have to be spent 
to buy equivalent used machines. This amount is the market value of the used 
machines. The analyst will recognize that any intangible value of the laundry 
(prime location, clever marketing, etc.) is being excluded, which will result in 
an inaccurate asset-  based valuation.

Example 18 shows some of the subtleties present in applying asset-  based valuation 
to determine company value. It also shows how asset-  based valuation does not deal 
with intangibles. Example 19 emphasizes this point.

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 278
EXAMPLE 19   
An Asset-  Based Valuation of a Restaurant
The business being valued is a restaurant that serves breakfast and lunch. The 
owner/proprietor wants to sell the business and retire. The restaurant space is 
rented, not owned. This particular restaurant is hugely popular because of the 
proprietor’s cooking skills and secret recipes. How can the analyst value this 
business?
Solution:
Because of the intangibles, setting a value on this business is challenging. A 
multiple of income or revenue might be considered. But even those approaches 
overlook the fact that the proprietor may not be selling his secret recipes and, 
furthermore, does not intend to continue cooking. Some (or all) of the intangi -
ble assets may vanish when the business is sold. Asset-  based valuation for this 
restaurant would begin with estimating the value of the restaurant equipment

and inventory and subtracting the value of any liabilities. This approach will 
provide only a good baseline, however, for a minimum valuation.
For public companies, the assets will typically be so extensive that a piece-  by- piece 
analysis will be impossible, and the transition from book value to market value is a 
nontrivial task. The asset-  based valuation approach is most applicable when the market 
value of the corporate assets is readily determinable and the intangible assets, which 
are typically difficult to value, are a relatively small proportion of corporate assets. 
Asset-  based valuation has also been applied to financial companies, natural resource 
companies, and formerly going-  concerns that are being liquidated. Even for other 
types of companies, however, asset-  based valuation of tangible assets may provide a 
baseline for a minimal valuation.
EXAMPLE 20   
An Asset-  Based Valuation of an Airline

Consider the value of an airline company that has few routes, high labor and other 
operating costs, has stopped paying dividends, and is losing millions of dollars 
each year. Using most valuation approaches, the company will have a negative 
value. Why might an asset-  based valuation approach be appropriate for use by 
one of the company’s competitors that is considering acquisition of this airline?
Solution:
The airline’s routes, landing rights, leases of airport facilities, and ground equip -
ment and airplanes may have substantial value to a competitor. An asset-  based 
approach to valuing this company would value the company’s assets separately and 
aside from the money-  losing business in which they are presently being utilized.
Analysts recognizing the uncertainties related to model appropriateness and the 
inputs to the models frequently use more than one model or type of model in valuation

to increase their confidence in their estimates of intrinsic value. The choice of models 
will depend on the availability of information to put into the models. Example 21 
illustrates the use of three valuation methods.

Asset-  Based Valuation 279
EXAMPLE 21   
A Simple Example of the Use of Three Major Equity 
Valuation Models
Company data for dividend per share (DPS), earnings per share (EPS), share price, 
and price-  to- earnings ratio (P/E) for the most recent five years are presented 
in Exhibit 11. In addition, estimates (indicated by an “E” after the amount) of 
DPS and EPS for the next five years are shown. The valuation date is at the end 
of Year 5. The company has 1,000 shares outstanding.
Exhibit 11   Company DPS, EPS, Share Price, and P/E Data
Y ear DPS EPS Share Price TTM P/E
10 $3.10E $5.20E — —
9 $2.91E $4.85E — —
8 $2.79E $4.65E — —
7 $2.65E $4.37E — —
6 $2.55E $4.30E — —
5 $2.43 $4.00 $50.80 12.7
4 $2.32 $3.90 $51.48 13.2
3 $2.19 $3.65 $59.86 16.4
2 $2.14 $3.60 $54.72 15.2
1 $2.00 $3.30 $46.20 14.0
The company’s balance sheet at the end of Year 5 is given in Exhibit 12.
Exhibit 12   Balance Sheet as of End of Y ear 5
Cash $ 5,000
Accounts receivable 15,000
Inventories 30,000
Net fixed assets 50,000

Total assets $100,000
Accounts payable $ 3,000
Notes payable 17,000
Term loans 25,000
Common shareholders’ equity 55,000
Total liabilities and equity $100,000
1 Using a Gordon growth model, estimate intrinsic value. Use a discount 
rate of 10 percent and an estimate of growth based on growth in dividends 
over the next five years.

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 280
2 Using a multiplier approach, estimate intrinsic value. Assume that a rea -
sonable estimate of P/E is the average trailing twelve-  month (TTM) P/E 
ratio over Years 1 through 4.
3 Using an asset-  based valuation approach, estimate value per share from 
adjusted book values. Assume that the market values of accounts receiv -
able and inventories are as reported, the market value of net fixed assets 
is 110 percent of reported book value, and the reported book values of 
liabilities reflect their market values.
D5 (1 + g)5 = D102.43(1 + g)5 = 3.10
g ≈ 5.0%
Estimate of value = V5 = 2.55/(0.10 – 0.05) = $51.00
Average P/E = (14.0 + 15.2 + 16.4 + 13.2)/4 = 14.7
Estimate of value = $4.00 × 14.7 = $58.80
Market value of assets = 5,000 + 15,000 + 30,000 + 1.1(50,000) = $105,000
Market value of liabilities = $3,000 + 17,000 + 25,000 = $45,000
Adjusted book value = $105,000 – 45,000 = $60,000

Estimated value (adjusted book value per share) = $60,000 ÷ 1,000 shares = 
$60.00
Given the current share price of $50.80, the multiplier and the asset-  based val -
uation approaches indicate that the stock is undervalued. Given the intrinsic 
value estimated using the Gordon growth model, the analyst is likely to conclude 
that the stock is fairly priced. The analyst might examine the assumptions in 
the multiplier and the asset-  based valuation approaches to determine why their 
estimated values differ from the estimated value provided by the Gordon growth 
model and the market price.
SUMMARY
The equity valuation models used to estimate intrinsic value—present value models, 
multiplier models, and asset-  based valuation—are widely used and serve an import -
ant purpose. The valuation models presented here are a foundation on which to base 
analysis and research but must be applied wisely. Valuation is not simply a numerical

analysis. The choice of model and the derivation of inputs require skill and judgment.
When valuing a company or group of companies, the analyst wants to choose a 
valuation model that is appropriate for the information available to be used as inputs. 
The available data will, in most instances, restrict the choice of model and influence the 
way it is used. Complex models exist that may improve on the simple valuation models 
described in this reading; but before using those models and assuming that complexity 
increases accuracy, the analyst would do well to consider the “law of parsimony:” A

Summary 281
model should be kept as simple as possible in light of the available inputs. Valuation 
is a fallible discipline, and any method will result in an inaccurate forecast at some 
time. The goal is to minimize the inaccuracy of the forecast.
Among the points made in this reading are the following:
■■An analyst estimating intrinsic value is implicitly questioning the market’s esti -
mate of value.
■■If the estimated value exceeds the market price, the analyst infers the secu -
rity is undervalued . If the estimated value equals the market price, the analyst 
infers the security is fairly valued . If the estimated value is less than the market 
price, the analyst infers the security is overvalued . Because of the uncertainties 
involved in valuation, an analyst may require that value estimates differ mark -
edly from market price before concluding that a misvaluation exists.
■■Analysts often use more than one valuation model because of concerns about

the applicability of any particular model and the variability in estimates that 
result from changes in inputs.
■■Three major categories of equity valuation models are present value, multiplier, 
and asset-  based valuation models.
■■Present value models estimate value as the present value of expected future 
benefits.
■■Multiplier models estimate intrinsic value based on a multiple of some funda -
mental variable.
■■Asset-  based valuation models estimate value based on the estimated value of 
■■The choice of model will depend upon the availability of information to input 
into the model and the analyst’s confidence in both the information and the 
appropriateness of the model.
■■Companies distribute cash to shareholders using dividend payments and share 
■■Regular cash dividends are a key input to dividend valuation models.
■■Key dates in dividend chronology are the declaration date, ex-  dividend date, 
holder-  of- record date, and payment date.

■■In the dividend discount model, value is estimated as the present value of 
expected future dividends.
■■In the free cash flow to equity model, value is estimated as the present value of 
expected future free cash flow to equity.
■■The Gordon growth model, a simple DDM, estimates value as D1/(r – g).
■■The two stage dividend discount model estimates value as the sum of the pres -
ent values of dividends over a short-  term period of high growth and the present 
value of the terminal value at the end of the period of high growth. The terminal 
value is estimated using the Gordon growth model.
■■The choice of dividend model is based upon the patterns assumed with respect 
to future dividends.
■■Multiplier models typically use multiples of the form: P/ measure of fundamen -
tal variable or EV/ measure of fundamental variable.
■■Multiples can be based upon fundamentals or comparables.

■■Asset-  based valuations models estimate value of equity as the value of the assets 
less the value of liabilities.

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 282
Basu, S. 1977. “Investment Performance of Common Stocks in 
Relation to Their Price-  Earnings Ratios: A Test of the Efficient 
Market Hypothesis. ” Journal of Finance , vol. 32, no. 3:663–682. 
Block, S. 1999. “ A Study of Financial Analysts: Practice and 
Theory. ” Financial Analysts Journal , vol. 55, no. 4:86–95. 
Dreman, D. 1977. Psychology of the Stock Market . New York: 
AMACOM.
Fama, E., and K. French. 1995. “Size and Book-  to- Market Factors 
in Earnings and Returns. ” Journal of Finance , vol. 50, no. 
1:131–155. McWilliams, J. 1966. “Prices, Earnings and P-  E Ratios. ” Financial 
Analysts Journal , vol. 22, no. 3:137. 
Miller, P ., and E. Widmann. 1966. “Price Performance Outlook for 
High & Low P/E Stocks. ” 1966 Stock & Bond Issue, Commercial 
& Financial Chronicle : 26–28.
Nicholson, S. 1968. “Price Ratios in Relation to Investment 
Results. ” Financial Analysts Journal , vol. 24, no. 1:105–109.

O’Shaughnessy, J. 2005. What Works on Wall Street . New York: 
McGraw-Hill.

Practice Problems 283
1 An analyst estimates the intrinsic value of a stock to be in the range of €17.85 to 
€21.45. The current market price of the stock is €24.35. This stock is most likely :
2 An analyst determines the intrinsic value of an equity security to be equal to 
$55. If the current price is $47, the equity is most likely :
3 In asset-  based valuation models, the intrinsic value of a common share of stock 
is based on the:
A estimated market value of the company’s assets.
B estimated market value of the company’s assets plus liabilities.
C estimated market value of the company’s assets minus liabilities.
4 Which of the following is most likely  used in a present value model?
A Enterprise value.
B Price to free cash flow.
C Free cash flow to equity.
5 Book value is least likely  to be considered when using:
A a multiplier model.
B an asset-  based valuation model.
C a present value model.

6 An analyst is attempting to calculate the intrinsic value of a company and has 
gathered the following company data: EBITDA, total market value, and market 
value of cash and short-  term investments, liabilities, and preferred shares. The 
analyst is least likely  to use:
B a discounted cash flow model.
C an asset-  based valuation model.
7 An analyst who bases the calculation of intrinsic value on dividend-  paying 
capacity rather than expected dividends will most likely  use the:
C cash flow from operations model.
8 An investor expects to purchase shares of common stock today and sell them 
after two years. The investor has estimated dividends for the next two years, D1 
and D2, and the selling price of the stock two years from now, P2. According to 
the dividend discount model, the intrinsic value of the stock today is the present 
value of:
A next year’s dividend, D1.

value of:

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 284
B future expected dividends, D1 and D2.
C future expected dividends and price— D1, D2 and P2.
9 In the free cash flow to equity (FCFE) model, the intrinsic value of a share of 
stock is calculated as:
A the present value of future expected FCFE.
B the present value of future expected FCFE plus net borrowing.
C the present value of future expected FCFE minus fixed capital investment.
10 With respect to present value models, which of the following statements is most 
accurate ?
A Present value models can be used only if a stock pays a dividend.
B Present value models can be used only if a stock pays a dividend or is 
expected to pay a dividend.
C Present value models can be used for stocks that currently pay a dividend, 
are expected to pay a dividend, or are not expected to pay a dividend.
11 A Canadian life insurance company has an issue of 4.80 percent, $25 par value,

perpetual, non-  convertible, non-  callable preferred shares outstanding. The 
required rate of return on similar issues is 4.49 percent. The intrinsic value of a 
preferred share is closest to :
A $25.00.
B $26.75.
C $28.50.
12 Two analysts estimating the value of a non-  convertible, non-  callable, perpetual 
preferred stock with a constant dividend arrive at different estimated values. 
The most likely  reason for the difference is that the analysts used different:
A time horizons.
B required rates of return.
C estimated dividend growth rates.
13 The Beasley Corporation has just paid a dividend of $1.75 per share. If the 
required rate of return is 12.3 percent per year and dividends are expected to 
grow indefinitely at a constant rate of 9.2 percent per year, the intrinsic value of 
Beasley Corporation stock is closest  to:
A $15.54.
B $56.45.
C $61.65.
14 An investor is considering the purchase of a common stock with a $2.00 annual

dividend. The dividend is expected to grow at a rate of 4 percent annually. If the 
investor’s required rate of return is 7 percent, the intrinsic value of the stock is 
A $50.00.
B $66.67.
C $69.33.
15 An analyst gathers or estimates the following information about a stock:

Practice Problems 285
Current price per share €22.56
Current annual dividend per share €1.60
Annual dividend growth rate for Years 1–4 9.00%
Annual dividend growth rate for Years 5+ 4.00%
Required rate of return 12%
 Based on a dividend discount model, the stock is most likely :
16 An analyst is attempting to value shares of the Dominion Company. The com -
pany has just paid a dividend of $0.58 per share. Dividends are expected to 
grow by 20 percent next year and 15 percent the year after that. From the third 
year onward, dividends are expected to grow at 5.6 percent per year indefinitely. 
If the required rate of return is 8.3 percent, the intrinsic value of the stock is 
A $26.00.
B $27.00.
C $28.00.
17 Hideki Corporation has just paid a dividend of ¥450 per share. Annual divi -
dends are expected to grow at the rate of 4 percent per year over the next four 
years. At the end of four years, shares of Hideki Corporation are expected to

sell for ¥9000. If the required rate of return is 12 percent, the intrinsic value of a 
share of Hideki Corporation is closest  to:
A ¥5,850.
B ¥7,220.
C ¥7,670.
18 The Gordon growth model can be used to value dividend-  paying companies 
that are:
A expected to grow very fast.
B in a mature phase of growth.
C very sensitive to the business cycle.
19 The best model to use when valuing a young dividend-  paying company that is 
just entering the growth phase is most likely  the:
A Gordon growth model.
B two-  stage dividend discount model.
C three-  stage dividend discount model.
20 An equity analyst has been asked to estimate the intrinsic value of the com -
mon stock of Omega Corporation, a leading manufacturer of automobile 
seats. Omega is in a mature industry, and both its earnings and dividends are 
expected to grow at a rate of 3 percent annually. Which of the following is most 
likely  to be the best model for determining the intrinsic value of an Omega 
share?

share?
B Free cash flow to equity model.
C Multistage dividend discount model.

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 286
21 A price earnings ratio that is derived from the Gordon growth model is 
inversely related to the:
A growth rate.
B dividend payout ratio.
C required rate of return.
22 The primary difference between P/E multiples based on comparables and P/E 
multiples based on fundamentals is that fundamentals-  based P/Es take into 
account:
A future expectations.
B the law of one price.
C historical information.
23 An analyst makes the following statement: “Use of P/E and other multiples for 
analysis is not effective because the multiples are based on historical data and 
because not all companies have positive accounting earnings. ” The analyst’s 
statement is most likely :
A inaccurate with respect to both historical data and earnings.
B accurate with respect to historical data and inaccurate with respect to 
earnings.
C inaccurate with respect to historical data and accurate with respect to 
earnings.

earnings.
24 An analyst has prepared a table of the average trailing twelve-  month price-  to- 
earning (P/E), price-  to- cash flow (P/CF), and price-  to- sales (P/S) for the Tanaka 
Corporation for the years 2005 to 2008.
Y ear P/E P/CF P/S
2005 4.9 5.4 1.2
2006 6.1 8.6 1.5
2007 8.3 7.3 1.9
2008 9.2 7.9 2.3
 As of the date of the valuation in 2009, the trailing twelve-  month P/E, P/CF, and 
P/S are, respectively, 9.2, 8.0, and 2.5. Based on the information provided, the 
analyst may reasonably conclude that Tanaka shares are most likely :
25 An analyst has gathered the following information for the Oudin Corporation:
Expected earnings per share = €5.70
Expected dividends per share = €2.70
Dividends are expected to grow at 2.75 percent per year indefinitely
The required rate of return is 8.35 percent
 Based on the information provided, the price/earnings multiple for Oudin is 
A 5.7.
B 8.5.
C 9.4.

A 5.7.
B 8.5.
C 9.4.
26 An analyst gathers the following information about two companies:

Practice Problems 287
Alpha Corp. Delta Co.
Current price per share $57.32 $18.93
Last year’s EPS $3.82 $1.35
Current year’s estimated EPS $4.75 $1.40
 Which of the following statements is most accurate ?
A Delta has the higher trailing P/E multiple and lower current estimated P/E 
multiple.
B Alpha has the higher trailing P/E multiple and lower current estimated P/E 
multiple.
C Alpha has the higher trailing P/E multiple and higher current estimated P/E 
multiple.
27 An analyst gathers the following information about similar companies in the 
banking sector:
First 
BankPrime 
BankPioneer 
Trust
P/B 1.10 0.60 0.60
P/E 8.40 11.10 8.30
 Which of the companies is most likely  to be undervalued?
A First Bank.
B Prime Bank.
C Pioneer Trust.
28 The market value of equity for a company can be calculated as enterprise value:
A minus market value of debt, preferred stock, and short-  term investments.
B plus market value of debt and preferred stock minus short-  term 

C minus market value of debt and preferred stock plus short-  term 
29 Which of the following statements regarding the calculation of the enterprise 
value multiple is most likely  correct?
A Operating income may be used instead of EBITDA.
B EBITDA may not be used if company earnings are negative.
C Book value of debt may be used instead of market value of debt.
30 An analyst has determined that the appropriate EV/EBITDA for Rainbow 
Company is 10.2. The analyst has also collected the following forecasted infor -
mation for Rainbow Company:
EBITDA = $22,000,000
Market value of debt = $56,000,000
Cash = $1,500,000
 The value of equity for Rainbow Company is closest  to:
A $169 million.
B $224 million.
C $281 million.
31 Enterprise value is most often determined as market capitalization of common 
equity and preferred stock minus the value of cash equivalents plus the:

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 288
A book value of debt.
B market value of debt.
C market value of long-  term debt.
32 Asset-  based valuation models are best suited to companies where the capital 
structure does not have a high proportion of:
A debt.
B intangible assets.
C current assets and liabilities.
33 Which of the following is most likely  a reason for using asset-  based valuation?
A The analyst is valuing a privately held company.
B The company has a relatively high level of intangible assets.
C The market values of assets and liabilities are different from the balance 
sheet values.
34 A disadvantage of the EV method for valuing equity is that the following infor -
mation may be difficult to obtain:
A Operating income.
B Market value of debt.
C Market value of equity.
35 Which type of equity valuation model is most likely  to be preferable when one is 
comparing similar companies?
A A multiplier model.
B A present value model.
C An asset-  based valuation model.

36 Which of the following is most likely  considered a weakness of present value 
models?
A Present value models cannot be used for companies that do not pay 
dividends.
B Small changes in model assumptions and inputs can result in large changes 
in the computed intrinsic value of the security.
C The value of the security depends on the investor’s holding period; thus, 
comparing valuations of different companies for different investors is 

Solutions 289
SOLUTIONS
1 A is correct. The current market price of the stock exceeds the upper bound of 
the analyst’s estimate of the intrinsic value of the stock.
2 A is correct. The market price is less than the estimated intrinsic, or fundamen -
tal, value.
3 C is correct. Asset-  based valuation models calculate the intrinsic value of equity 
by subtracting liabilities from the market value of assets.
4 C is correct. FCFE can be used in a form of present value, or discounted cash 
flow, model. Both EV and price to free cash flow are forms of multiplier models.
5 C is correct. Multiplier valuation models (in the form of P/B) and asset-  based 
valuation models (in the form of adjustments to book value) use book value, 
whereas present value models typically discount future expected cash flows.
6 B is correct. To use a discounted cash flow model, the analyst will require FCFE 
or dividend data. In addition, the analyst will need data to calculate an appro -
priate discount rate.

7 B is correct. The FCFE model assumes that dividend-  paying capacity is reflected 
in FCFE.
8 C is correct. According to the dividend discount model, the intrinsic value of a 
stock today is the present value of all future dividends. In this case, the intrinsic 
value is the present value of D1, D2, and P2. Note that P2 is the present value at 
Period 2 of all future dividends from Period 3 to infinity.
9 A is correct. In the FCFE model, the intrinsic value of stock is calculated by 
discounting expected future FCFE to present value. No further adjustments are 
required.
10 C is correct. Dividend discount models can be used for a stock that pays a cur -
rent dividend or a stock that is expected to pay a dividend. FCFE can be used 
for both of those stocks and for stocks that do not, or are not expected to, pay 
dividends in the near future. Both of these models are forms of present value 
models.

models.
11 B is correct. The expected annual dividend is 4.80% × $25 = $1.20. The value of 
a preferred share is $1.20/0.0449 = $26.73.
12 B is correct. The required rate of return, r, can vary widely depending on the 
inputs and is not unique. A preferred stock with a constant dividend would not 
have a growth rate to estimate, and the investor’s time horizon would have no 
effect on the calculation of intrinsic value.
13 C is correct. P0 = D1/(r – g) = 1.75(1.092)/(0.123 – 0.092) = $61.65.
14 C is correct. According to the Gordon growth model, V0 = D1/(r – g). In this 
case, D1  = $2.00 × 1.04 = $2.08, so V0 = $2.08/(0.07 – 0.04) = $69.3333 = 
$69.33.
15 A is correct. The current price of €22.56 is less than the intrinsic value ( V0) of 
€24.64; therefore, the stock appears to be currently undervalued. According to 
the two-  stage dividend discount model:
VDg
rV
rSt
t
tn
n
n00
11
11=+()
+()+
+() =∑ and VD
rgnn
L=−+1
 Dn+1 = D0(1 + gS)n(1 + gL) 
 D1 = €1.60 × 1.09 = €1.744

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 290
 D2 = €1.60 × (1.09)2 = €1.901
 D3 = €1.60 × (1.09)3 = €2.072
 D4 = €1.60 × (1.09)4 = €2.259
 D5 = [€1.60 × (1.09)4](1.04) = €2.349
 V4 = €2.349/(0.12 – 0.04) = €29.363
 V0 = 1 744
1121 901
1122 072
1122 259
11229 363
1 234.
..
..
..
..
()+
()+
()+
()+
11124.()
  = 1.557 + 1.515 + 1.475 + 1.436 + 18.661
  = €24.64 (which is greater than the current price of €22.56)
VD
rD
rP
r012
22
2
21 11
070
1 083080
1 08331 2=+()+
+()+
+()
=()+
()+.
..
..9 9
1 083
02.
$.()
=28 1
 Note that D1 = 0.58(1.20) = 0.70, D2 = 0.58(1.20)(1.15) = 0.80, and P2 = D3/(k – 
g) = 0.80(1.056)/(0.083 – 0.056) = 31.29
17 B is correct.
VD
rD
rD
rD
rP
r012
23
34
44
4 1 11 11
468
1124=+()+
+()+
+()+
+()+
+()
=()+.8 86 72
112506 19
112526 44
1129000
112
7223 44.
..
..
..
¥,()+
()+
()+
()
= 2 20
18 B is correct. The Gordon growth model (also known as the constant growth 
model) can be used to value dividend-  paying companies in a mature phase of

growth. A stable dividend growth rate is often a plausible assumption for such 
19 C is correct. The Gordon growth model is best suited to valuing mature com -
panies. The two-  stage model is best for companies that are transitioning from a 
growth stage to a mature stage. The three-  stage model is appropriate for young 
companies just entering the growth phase.
20 A is correct. The company is a mature company with a steadily growing div -
idend rate. The two-  stage (or multistage) model is unnecessary because the divi -
dend growth rate is expected to remain stable. Although an FCFE model could 
be used, that model is more often chosen for companies that currently pay no 
21 C is correct. The justified forward P/E is calculated as follows:
P
ED
E
rg0
11
1=−
 P/E is inversely related to the required rate of return, r, and directly related to 
the growth rate, g, and the dividend payout ratio, D/E.

Solutions 291
22 A is correct. Multiples based on comparables are grounded in the law of one 
price and take into account historical multiple values. In contrast, P/E multiples 
based on fundamentals can be based on the Gordon growth model, which takes 
into account future expected dividends.
23 A is correct. The statement is inaccurate in both respects. Although multiples 
can be calculated from historical data, forecasted values can be used as well. For 
companies without accounting earnings, several other multiples can be used. 
These multiples are often specific to a company’s industry or sector and include 
price-  to- sales and price-  to- cash flow.
24 A is correct. Tanaka shares are most likely overvalued. As the table below 
shows, all the 2009 multiples are currently above their 2005–2008 averages.
Y ear P/E P/CF P/R
Average 7.1 7.3 1.7
25 B is correct.
P
ED
E
rg0
11
127
57
0 0835 0 027585 =−=−=.
.
...

P
ED
E
rg0
11
127
57
.
...
26 B is correct. P/E = Current price/EPS, and Estimated P/E = Current price/
Estimated EPS.
Alpha P/E = $57.32/$3.82 = 15.01
Alpha estimated P/E = $57.32/4.75 = 12.07
Delta P/E = $18.93/$1.35 = 14.02
Delta estimated P/E = $18.93/$1.40 = 13.52
27 C is correct. Relative to the others, Pioneer Trust has the lowest P/E multiple 
and the P/B multiple is tied for the lowest with Prime Bank. Given the law of 
one price, similar companies should trade at similar P/B and P/E levels. Thus, 
based on the information presented, Pioneer is most likely to be undervalued.
28 C is correct. Enterprise value is calculated as the market value of equity plus 
the market value of debt and preferred stock minus short-  term investments. 
Therefore, the market value of equity is enterprise value minus the market value 
of debt and preferred stock plus short-  term investments.
29 A is correct. Operating income may be used in place of EBITDA when calculat -

ing the enterprise value multiple. EBITDA may be used when company earnings 
are negative because EBITDA is usually positive. The book value of debt cannot 
be used in place of market value of debt.
30 A is correct.
EV = 10.2 × 22,000,000 = $224,400,000
 Equity value =  EV – Debt + Cash
  = 224,400,000 – 56,000,000 + 1,500,000
  = $169,900,000

Reading 49 ■ Equity Valuation: Concepts and Basic Tools 292
31 B is correct. The market value of debt must be calculated and taken out of the 
enterprise value. Enterprise value, sometimes known as the cost of a takeover, is 
the cost of the purchase of the company, which would include the assumption 
of the company’s debts at market value.
32 B is correct. Intangible assets are hard to value. Therefore, asset-  based valuation 
models work best for companies that do not have a high proportion of intangi -
33 A is correct. Asset-  based valuations are most often used when an analyst is 
valuing private enterprises. Both B and C are considerations in asset-  based 
valuations but are more likely to be reasons to avoid that valuation model rather 
than reasons to use it.
34 B is correct. According to the reading, analysts may have not have access to 
market quotations for company debt.
35 A is correct. Although all models can be used to compare various companies,

multiplier models have the advantage of reducing varying fundamental data 
points into a format that allows direct comparisons. As long as the analyst 
applies the data in a consistent manner for all the companies, this approach 
provides useful comparative data.
36 B is correct. Very small changes in inputs, such as required rate of return or 
dividend growth rate, can result in large changes to the valuation model output. 
Some present value models, such as FCFE models, can be used to value compa -
nies without dividends. Also, the intrinsic value of a security is independent of 
the investor’s holding period.

Study Session 16 Fixed Income (1)
Study Session 17 Fixed Income (2)
The candidate should be able to describe fixed-  income securities and their markets, 
yield measures, risk factors, and valuation measures and drivers. The candidate should 
also be able to calculate yields and values of fixed-  income securities.
Fixed-  income securities continue to represent the largest capital market segment 
in the financial ecosystem and the primary means in which institutions, governments, 
and other issuers raise capital globally. Institutions and individuals use fixed-  income 
investments in a wide range of applications including asset liability management, 
income generation, and principal preservation. Since the global financial crisis of 2008, 
evaluating risk—in particular, credit risk—for fixed-  income securities has become an 
increasingly important aspect for this asset class.

Fixed Income (1)
This study session introduces the unique attributes that define fixed-  income secu -
rities, then follows with an overview of global debt markets. Primary issuers, sectors, 
and bond types are explained. Key concepts for the calculation and interpretation of 
bond prices, yields, and spreads and coverage of interest rate risk and key related risk 
measures are presented. Securitization—the creation of fixed-  income securities backed 
by certain (typically less liquid) assets—including the various types, characteristics, 
and risks of these investments end the session.
Reading 50 Fixed-  Income Securities: Defining Elements  
by Moorad Choudhry, PhD, FRM, FCSI, and 
Stephen E. Wilcox, PhD, CFA
Reading 51 Fixed-  Income Markets: Issuance, Trading, and Funding  
by Moorad Choudhry, PhD, FRM, FCSI, Steven 
V. Mann, PhD, and Lavone F. Whitmer, CFA
Reading 52 Introduction to Fixed-  Income Valuation  
by James F. Adams, PhD, CFA, and Donald J. Smith, PhD

Reading 53 Introduction to Asset-  Backed Securities  
by Frank J. Fabozzi, PhD, CPA, CFAFIxED INCO mE
16

Fixed-  Income Securities: 
Defining Elements
by Moorad Choudhry, PhD, FRM, FCSI, and Stephen E. Wilcox, PhD, CFA
Moorad Choudhry, PhD, FRM, FCSI, is at the University of Kent (United Kingdom). 
Stephen E. Wilcox, PhD, CFA, is at Minnesota State University, Mankato (USA).
a. describe basic features of a fixed-  income security;
b. describe content of a bond indenture;
c. compare affirmative and negative covenants and identify examples 
of each;
d. describe how legal, regulatory, and tax considerations affect the 
issuance and trading of fixed-  income securities;
e. describe how cash flows of fixed-  income securities are structured;
f. describe contingency provisions affecting the timing and/or 
nature of cash flows of fixed-  income securities and identify 
whether such provisions benefit the borrower or the lender.
Judged by total market value, fixed-  income securities constitute the most prevalent

means of raising capital globally. A fixed-  income security is an instrument that allows 
governments, companies, and other types of issuers to borrow money from investors. 
Any borrowing of money is debt. The promised payments on fixed-  income securities 
are, in general, contractual (legal) obligations of the issuer to the investor. For com -
panies, fixed-  income securities contrast to common shares in not having ownership 
rights. Payment of interest and repayment of principal (amount borrowed) are a prior 
claim on the company’s earnings and assets compared with the claim of common 
shareholders. Thus, a company’s fixed-  income securities have, in theory, lower risk 
than that company’s common shares.1READING
50

Reading 50 ■ Fixed-  Income Securities: Defining Elements 298
In portfolio management, fixed-  income securities fulfill several important roles. 
They are a prime means by which investors—individual and institutional—can prepare 
to fund, with some degree of safety, known future obligations such as tuition payments 
or pension obligations. The correlations of fixed-  income securities with common 
shares vary, but adding fixed-  income securities to portfolios including common shares 
is usually an effective way of obtaining diversification benefits.
Among the questions this reading addresses are the following:
■■What set of features define a fixed-  income security, and how do these features 
determine the scheduled cash flows?
■■What are the legal, regulatory, and tax considerations associated with a fixed-  
income security, and why are these considerations important for investors?
■■What are the common structures regarding the payment of interest and repay -
ment of principal?

■■What types of provisions may affect the disposal or redemption of fixed-  income 
Embarking on the study of fixed-  income securities, please note that the terms 
“fixed-  income securities, ” “debt securities, ” and “bonds” are often used interchangeably 
by experts and non-  experts alike. We will also follow this convention, and where any 
nuance of meaning is intended, it will be made clear.1
The remainder of this reading is organized as follows. Section 2 describes, in 
broad terms, what an investor needs to know when investing in fixed-  income secu -
rities. Section 3 covers both the nature of the contract between the issuer and the 
bondholders as well as the legal, regulatory, and tax framework within which this 
contract exists. Section 4 presents the principal and interest payment structures that 
characterize fixed-  income securities. Section 5 discusses the contingency provisions

that affect the timing and/or nature of a bond’s cash flows. The final section provides 
a conclusion and summary of the reading.
OVERVIEW OF A FIXED-  INCOME SECURITY
A bond  is a contractual agreement between the issuer and the bondholders. There 
are three important elements that an investor needs to know about when investing 
in a bond:
■■The bond’s features, including the issuer, maturity, par value, coupon rate and 
frequency, and currency denomination. These features determine the bond’s 
scheduled cash flows and, therefore, are key determinants of the investor’s 
expected and actual return.
■■The legal, regulatory, and tax considerations that apply to the contractual agree -
ment between the issuer and the bondholders.
■■The contingency provisions that may affect the bond’s scheduled cash flows. 
These contingency provisions are options; they give the issuer or the bondhold -
ers certain rights affecting the bond’s disposal or redemption.2

1 Note that the term “fixed income” is not to be understood literally: Some fixed-  income securities have 
interest payments that change over time. Some experts include preference shares as a type of fixed-  income 
security, but none view them as a type of bond. Finally, in some contexts, bonds refer to the longer-  maturity 
form of debt securities in contrast to money market securities.

Overview of a Fixed-  Income Security 299
This section describes a bond’s basic features and introduces yield measures. The 
legal, regulatory, and tax considerations and contingency provisions are discussed in 
Sections 3 and 5, respectively.
2.1 Basic Features of a Bond
All bonds, whether they are “traditional” bonds or asset-  backed securities, are char -
acterized by the same basic features. Asset-  backed securities  (ABS) are created from 
a process called securitization, which involves moving assets from the owner of the 
assets into a special legal entity. This special legal entity then uses the securitized assets 
as guarantees to back (secure) a bond issue, leading to the creation of ABS. Assets 
that are typically used to create ABS include residential and commercial mortgage 
loans (mortgages), automobile (auto) loans, student loans, bank loans, and credit card 
debt, among others. Many elements discussed in this reading apply to both traditional

bonds and ABS. Considerations specific to ABS are discussed in the introduction to 
asset-  backed securities reading. 
2.1.1  Issuer
Many entities issue bonds: private individuals, such as the musician David Bowie; 
national governments, such as Singapore or Italy; and companies, such as BP , General 
Electric, or Tata Group.
Bond issuers are classified into categories based on the similarities of these issuers 
and their characteristics. Major types of issuers include the following:
■■Supranational organizations, such as the World Bank or the European 
Investment Bank;
■■Sovereign (national) governments, such as the United States or Japan;
■■Non-  sovereign (local) governments, such as the state of Minnesota in the 
United States, the region of Catalonia in Spain, or the city of Edmonton in 
Canada;
■■Quasi-  government entities (i.e., agencies that are owned or sponsored by gov -
ernments), such as postal services in many countries—for example, Correios in

Brazil, La Poste in France, or Pos in Indonesia;
■■Companies (i.e., corporate issuers). A distinction is often made between finan -
cial issuers (e.g., banks and insurance companies) and non-  financial issuers; and
■■Special legal entities that securitize assets to create ABS that are then sold to 
Market participants often classify fixed-  income markets by the type of issuer, 
which leads to the identification of three bond market sectors: the government and 
government-  related sector (i.e., the first four types of issuers listed above), the cor -
porate sector (the fifth type listed above), and the structured finance sector (the last 
type listed above).
Bondholders are exposed to credit risk—that is, the risk of loss resulting from 
the issuer failing to make full and timely payments of interest and/or repayments of 
principal. Credit risk is inherent to all debt investments. Bond markets are sometimes

classified into sectors based on the issuer’s creditworthiness as judged by credit rating 
agencies. One major distinction is between investment-  grade and non-  investment-  grade 
bonds, also called high-  yield or speculative bonds.2 Although a variety of considerations 
2 The three largest credit rating agencies are Moody’s Investors Service, Standard & Poor’s, and Fitch 
Ratings. Bonds rated Baa3 or higher by Moody’s and BBB– or higher by Standard & Poor’s and Fitch are 
considered investment grade.

Reading 50 ■ Fixed-  Income Securities: Defining Elements 300
enter into distinguishing the two sectors, the promised payments of investment-  grade 
bonds are perceived as less risky than those of non-  investment-  grade bonds because 
of profitability and liquidity considerations. Some regulated financial intermediaries, 
such as banks and life insurance companies, may face explicit or implicit limitations of 
holdings of non-  investment-  grade bonds. The investment policy statements of some 
investors may also include constraints or limits on such holdings. From the issuer’s 
perspective, an investment-  grade credit rating generally allows easier access to bond 
markets and at lower interest rates than does a non-  investment-  grade credit rating.3
2.1.2  Maturity
The maturity date of a bond refers to the date when the issuer is obligated to redeem 
the bond by paying the outstanding principal amount. The tenor  is the time remaining

until the bond’s maturity date. The tenor is an important consideration in the analysis 
of a bond. It indicates the period over which the bondholder can expect to receive the 
interest payments and the length of time until the principal is repaid in full.
Maturities typically range from overnight to 30 years or longer. Fixed-  income 
securities with maturities at issuance (original maturity) of one year or less are known 
as money market securities . Issuers of money market securities include governments 
and companies. Commercial paper and certificates of deposit are examples of money 
market securities. Fixed-  income securities with original maturities that are longer than 
one year are called capital market securities . Although very rare, perpetual bonds , 
such as the consols issued by the sovereign government in the United Kingdom, have 
no stated maturity date.
2.1.3  Par Value
The principal amount , principal value , or simply principal  of a bond is the amount

that the issuer agrees to repay the bondholders on the maturity date. This amount is 
also referred to as the par value, or simply par, face value, nominal value, redemption 
value, or maturity value. Bonds can have any par value.
In practice, bond prices are quoted as a percentage of their par value. For example, 
assume that a bond’s par value is $1,000. A quote of 95 means that the bond price is 
$950 (95% × $1,000). When the bond is priced at 100% of par, the bond is said to be 
trading at par. If the bond’s price is below 100% of par, such as in the previous example, 
the bond is trading at a discount. Alternatively, if the bond’s price is above 100% of 
par, the bond is trading at a premium.
2.1.4  Coupon Rate and Frequency
The coupon rate or nominal rate of a bond is the interest rate that the issuer agrees 
to pay each year until the maturity date. The annual amount of interest payments 
made is called the coupon. A bond’s coupon is determined by multiplying its coupon

rate by its par value. For example, a bond with a coupon rate of 6% and a par value of 
$1,000 will pay annual interest of $60 (6% × $1,000).
Coupon payments may be made annually, such as those for German government 
bonds or Bunds. Many bonds, such as government and corporate bonds issued in the 
United States or government gilts issued in the United Kingdom, pay interest semi-  
annually. Some bonds make quarterly or monthly interest payments. The acronyms 
QUIBS (quarterly interest bonds) and QUIDS (quarterly income debt securities) 
are used by Morgan Stanley and Goldman Sachs, respectively, for bonds that make 
quarterly interest payments. Many mortgage-  backed securities  (MBS), which are 
ABS backed by residential or commercial mortgages, pay interest monthly to match 
3 Several other distinctions among credit ratings are made. They are discussed in depth in the reading on 
fundamentals of credit analysis.

Overview of a Fixed-  Income Security 301
the cash flows of the mortgages backing these MBS. If a bond has a coupon rate of 
6% and a par value of $1,000, the periodic interest payments will be $60 if coupon 
payments are made annually, $30 if they are made semi-  annually, $15 if they are made 
quarterly, and $5 if they are made monthly.
A plain vanilla bond  or conventional bond  pays a fixed rate of interest. In this 
case, the coupon payment does not change during the bond’s life. However, there are 
bonds that pay a floating rate of interest; such bonds are called floating-  rate notes  
(FRNs) or floaters . The coupon rate of a FRN includes two components: a reference 
rate plus a spread. The spread, also called margin, is typically constant and expressed 
in basis points (bps). A basis point  is equal to 0.01%; put another way, there are 100 
basis points in 1%. The spread is set when the bond is issued based on the issuer’s

creditworthiness at issuance: The higher the issuer’s credit quality, the lower the spread. 
The reference rate, however, resets periodically. Thus, as the reference rate changes, 
the coupon rate and coupon payment change accordingly.
A widely used reference rate is the London interbank offered rate (Libor) . Libor is 
a collective name for a set of rates covering different currencies for different maturities 
ranging from overnight to one year. Other reference rates include the Euro interbank 
offered rate (Euribor), the Hong Kong interbank offered rate (Hibor), or the Singapore 
interbank offered rate (Sibor) for issues denominated in euros, Hong Kong dollars, 
and Singapore dollars, respectively. Euribor, Hibor, and Sibor are, like Libor, sets of 
rates for different maturities up to one year.
For example, assume that the coupon rate of a FRN that makes semi-  annual 
interest payments in June and December is expressed as the six-  month Libor + 150

bps. Suppose that in December 20X0, the six-  month Libor is 3.25%. The interest rate 
that will apply to the payment due in June 20X1 will be 4.75% (3.25% + 1.50%). Now 
suppose that in June 20X1, the six-  month Libor has decreased to 3.15%. The interest 
rate that will apply to the payment due in December 20X1 will decrease to 4.65% 
(3.15% + 1.50%). More details about FRNs are provided in Section 4.2.1.
All bonds, whether they pay a fixed or floating rate of interest, make periodic 
coupon payments except for zero-  coupon bonds . Such bonds do not pay interest, 
hence their name. Instead, they are issued at a discount to par value and redeemed 
at par; they are sometimes referred to as pure discount bonds . The interest earned 
on a zero-  coupon bond is implied and equal to the difference between the par value 
and the purchase price. For example, if the par value is $1,000 and the purchase price 
is $950, the implied interest is $50.
2.1.5  Currency Denomination

Bonds can be issued in any currency, although a large number of bond issues are made 
in either euros or US dollars. The currency of issue may affect a bond’s attractiveness. 
If the currency is not liquid or freely traded, or if the currency is very volatile relative 
to major currencies, investments in that currency will not appeal to many investors. 
For this reason, borrowers in developing countries often elect to issue bonds in a cur -
rency other than their local currency, such as in euros or US dollars, because doing so 
makes it easier to place the bond with international investors. Issuers may also choose 
to issue in a foreign currency if they are expecting cash flows in the foreign currency 
because the interest payments and principal repayments can act as a natural hedge, 
reducing currency risk. If a bond is aimed solely at a country’s domestic investors, it 
is more likely that the borrower will issue in the local currency.

Dual-  currency bonds  make coupon payments in one currency and pay the par 
value at maturity in another currency. For example, assume that a Japanese company 
needs to finance a long-  term project in the United States that will take several years to 
become profitable. The Japanese company could issue a yen/US dollar dual-  currency

Reading 50 ■ Fixed-  Income Securities: Defining Elements 302
bond. The coupon payments in yens can be made from the cash flows generated in 
Japan, and the principal can be repaid in US dollars using the cash flows generated 
in the United States once the project becomes profitable.
Currency option bonds  can be viewed as a combination of a single-  currency 
bond plus a foreign currency option. They give bondholders the right to choose the 
currency in which they want to receive interest payments and principal repayments. 
Bondholders can select one of two currencies for each payment.
Exhibit 1 brings all the basic features of a bond together and illustrates how these 
features determine the cash flow pattern for a plain vanilla bond. The bond is a five-  
year Japanese government bond (JGB) with a coupon rate of 0.4% and a par value of 
¥10,000. Interest payments are made semi-  annually. The bond is priced at par when 
it is issued and is redeemed at par.

Exhibit 1   Cash Flows for a Plain Vanilla Bond
¥10,000¥10,020
Semiannual
Time Periods¥20 ¥20 ¥20 ¥20 ¥20 ¥20 ¥20 ¥20 ¥20
The downward-  pointing arrow in Exhibit 1 represents the cash flow paid by the 
bond investor (received by the issuer) on the day of the bond issue—that is, ¥10,000. 
The upward-  pointing arrows are the cash flows received by the bondholder (paid by 
the issuer) during the bond’s life. As interest is paid semi-  annually, the coupon pay -
ment is ¥20 [(0.004 × ¥10,000) ÷ 2] every six months for five years—that is, 10 coupon 
payments of ¥20. The last payment is equal to ¥10,020 because it includes both the 
last coupon payment and the payment of the par value.
EXAMPLE 1   
1 An example of sovereign bond is a bond issued by:
A the World Bank.
B the city of New York.
C the federal German government.
2 The risk of loss resulting from the issuer failing to make full and timely 
payment of interest is called:
A credit risk.
B systemic risk.

C interest rate risk.
3 A money market security most likely  matures in:
A one year or less.

Overview of a Fixed-  Income Security 303
B between one and 10 years.
C over 10 years.
4 If the bond’s price is higher than its par value, the bond is trading at:
A par.
5 A bond has a par value of £100 and a coupon rate of 5%. Coupon pay -
ments are made semi-  annually. The periodic interest payment is:
A £2.50, paid twice a year.
B £5.00, paid once a year.
C £5.00, paid twice a year.
6 The coupon rate of a floating-  rate note that makes payments in June and 
December is expressed as six-  month Libor + 25 bps. Assuming that the 
six- month Libor is 3.00% at the end of June 20XX and 3.50% at the end 
of December 20XX, the interest rate that applies to the payment due in 
December 20XX is:
A 3.25%.
B 3.50%.
C 3.75%.
7 The type of bond that allows bondholders to choose the currency in which 
they receive each interest payment and principal repayment is a:
A pure discount bond.
B dual-  currency bond.
C currency option bond.

C is correct. A sovereign bond is a bond issued by a national government, such 
as the federal German government. A is incorrect because a bond issued by 
the World Bank is a supranational bond. B is incorrect because a bond issued 
by a local government, such as the city of New York, is a non-  sovereign bond.
A is correct. Credit risk is the risk of loss resulting from the issuer failing to 
make full and timely payments of interest and/or repayments of principal. B is 
incorrect because systemic risk is the risk of failure of the financial system. C is 
incorrect because interest rate risk is the risk that a change in market interest 
rate affects a bond’s value. Systemic risk and interest rate risk are defined in 
Sections 5.3 and 4.2.1, respectively.
A is correct. The primary difference between a money market security and a 
capital market security is the maturity at issuance. Money market securities

mature in one year or less, whereas capital market securities mature in more 
than one year.
C is correct. If a bond’s price is higher than its par value, the bond is trading at 
a premium. A is incorrect because a bond is trading at par if its price is equal 
to its par value. B is incorrect because a bond is trading at a discount if its price 
is lower than its par value.

Reading 50 ■ Fixed-  Income Securities: Defining Elements 304
A is correct. The annual coupon payment is 5% × £100 = £5.00. The coupon 
payments are made semi-  annually, so £2.50 paid twice a year.
A is correct. The interest rate that applies to the payment due in December 20XX 
is the six-  month Libor at the end of June 20XX plus 25 bps. Thus, it is 3.25% 
(3.00% + 0.25%).
C is correct. A currency option bond gives bondholders the right to choose the 
currency in which they want to receive each interest payment and principal 
repayment. A is incorrect because a pure discount bond is issued at a discount 
to par value and redeemed at par. B is incorrect because a dual-  currency bond 
makes coupon payments in one currency and pays the par value at maturity in 
another currency.
2.2 Yield Measures
There are several yield measures commonly used by market participants. The current

yield  or running yield  is equal to the bond’s annual coupon divided by the bond’s 
price, expressed as a percentage. For example, if a bond has a coupon rate of 6%, a 
par value of $1,000, and a price of $1,010, the current yield is 5.94% ($60 ÷ $1,010). 
The current yield is a measure of income that is analogous to the dividend yield for 
a common share.
The most commonly referenced yield measure is known as the yield to maturity , 
also called the yield to redemption  or redemption yield . The yield to maturity is 
the internal rate of return on a bond’s expected cash flows—that is, the discount rate 
that equates the present value of the bond’s expected cash flows until maturity with 
the bond’s price. The yield to maturity can be considered an estimate of the bond’s 
expected return; it reflects the annual return that an investor will earn on a bond if 
this investor purchases the bond today and holds it until maturity. There is an inverse

relationship between the bond’s price and its yield to maturity, all else being equal. 
That is, the higher the bond’s yield to maturity, the lower its price. Alternatively, the 
higher the bond’s price, the lower its yield to maturity. Thus, investors anticipating a 
lower interest rate environment (in which investors demand a lower yield-  to- maturity 
on the bond) hope to earn a positive return from price appreciation. The reading on 
understanding risk and return of fixed-  income securities covers these fundamentals 
and more.
LEGAL, REGULATORY , AND TAX CONSIDERATIONS
As a bond  is a contractual agreement between the issuer and the bondholders, it 
is subject to legal considerations. Investors in fixed-  income securities must also be 
aware of the regulatory and tax considerations associated with the bonds in which 
they invest or want to invest.3

Legal, Regulatory, and Tax Considerations 305
3.1 Bond Indenture
The trust deed  is the legal contract that describes the form of the bond, the obligations 
of the issuer, and the rights of the bondholders. Market participants frequently call 
this legal contract the bond indenture , particularly in the United States and Canada. 
The indenture is written in the name of the issuer and references the features of the 
bond issue, such as the principal value for each bond, the interest rate or coupon rate 
to be paid, the dates when the interest payments will be made, the maturity date when 
the bonds will be repaid, and whether the bond issue comes with any contingency 
provisions. The indenture also includes information regarding the funding sources 
for the interest payments and principal repayments, and it specifies any collaterals, 
credit enhancements, or covenants. Collaterals  are assets or financial guarantees

underlying the debt obligation above and beyond the issuer’s promise to pay. Credit 
enhancements  are provisions that may be used to reduce the credit risk of the bond 
issue. Covenants  are clauses that specify the rights of the bondholders and any actions 
that the issuer is obligated to perform or prohibited from performing.
Because it would be impractical for the issuer to enter into a direct agreement with 
each of many bondholders, the indenture is usually held by a trustee. The trustee is 
typically a financial institution with trust powers, such as the trust department of a 
bank or a trust company. It is appointed by the issuer, but it acts in a fiduciary capacity 
with the bondholders. The trustee’s role is to monitor that the issuer complies with 
the obligations specified in the indenture and to take action on behalf of the bond -
holders when necessary. The trustee’s duties tend to be administrative and usually

include maintaining required documentation and records; holding beneficial title to, 
safeguarding, and appraising collateral (if any); invoicing the issuer for interest pay -
ments and principal repayments; and holding funds until they are paid, although the 
actual mechanics of cash flow movements from the issuers to the trustee are typically 
handled by the principal paying agent. In the event of default, the discretionary powers 
of the trustee increase considerably. The trustee is responsible for calling meetings 
of bondholders to discuss the actions to take. The trustee can also bring legal action 
against the issuer on behalf of the bondholders.
For a plain vanilla bond, the indenture is often a standard template that is updated 
for the specific terms and conditions of a particular bond issue. For exotic bonds, the 
document is tailored and can often be several hundred pages.
When assessing the risk–reward profile of a bond issue, investors should be

informed by the content of the indenture. They should pay special attention to their 
rights in the event of default. In addition to identifying the basic bond features described 
earlier, investors should carefully review the following areas:
■■the legal identity of the bond issuer and its legal form;
■■the source of repayment proceeds;
■■the asset or collateral backing (if any);
■■the credit enhancements (if any); and
■■the covenants (if any).
We consider each of these areas in the following sections.
3.1.1  Legal Identity of the Bond Issuer and its Legal Form
The legal obligation to make the contractual payments is assigned to the bond issuer. 
The issuer is identified in the indenture by its legal name. For a sovereign bond, the 
legal issuer is usually the office responsible for managing the national budget, such 
as HM Treasury (Her Majesty’s Treasury) in the United Kingdom. The legal issuer

Reading 50 ■ Fixed-  Income Securities: Defining Elements 306
may be different from the body that administers the bond issue process. Using the 
UK example, the legal obligation to repay gilts lies with HM Treasury, but the bonds 
are issued by the UK Debt Management Office, an executive agency of HM Treasury.
For corporate bonds, the issuer is usually the corporate legal entity—for example, 
Wal-  Mart Stores Inc., Samsung Electronics Co. Ltd., or Volkswagen AG. However, 
bonds are sometimes issued by a subsidiary of a parent legal entity. In this case, investors 
should look at the credit quality of the subsidiary, unless the indenture specifies that 
the bond liabilities are guaranteed by the parent. When they are rated, subsidiaries 
often carry a credit rating that is lower than their parent, but this is not always the 
case. For example, in May 2012, Santander UK plc was rated higher by Moody’s than 
its Spanish parent, Banco Santander.

Bonds are sometimes issued by a holding company, which is the parent legal entity 
for a group of companies, rather than by one of the operating companies in the group. 
This issue is important for investors to consider because a holding company may be 
rated differently from its operating companies and investors may lack recourse to 
assets held by those companies. If the bonds are issued by a holding company that has 
fewer (or no) assets to call on should it default, investors face a higher level of credit 
risk than if the bonds were issued by one of the operating companies in the group.
For ABS, the legal obligation to repay the bondholders often lies with the special 
legal entity that was created by the financial institution in charge of the securitization 
process. The financial institution is known as the sponsor or originator. The special 
legal entity is most frequently referred to as a special purpose entity (SPE) in the United

States and a special purpose vehicle (SPV) in Europe, and it is also sometimes called 
a special purpose company (SPC). The legal form for the special legal entity may be 
a limited partnership, a limited liability company, or a trust. Typically, special legal 
entities are thinly capitalized, have no independent management or employees, and 
have no purpose other than the transactions for which they were created.
Through the securitization process, the sponsor transfers the assets to the special 
legal entity to carry out some specific transaction or series of transactions. One of the 
key reasons for forming a special legal entity is bankruptcy remoteness. The transfer of 
assets by the sponsor is considered a legal sale; once the assets have been securitized, 
the sponsor no longer has ownership rights. Any party making claims following the 
bankruptcy of the sponsor would be unable to recover the assets or their proceeds. As

a result, the special legal entity’s ability to pay interest and repay the principal should 
remain intact even if the sponsor were to fail—hence the reason why the special legal 
entity is also called a bankruptcy-  remote vehicle.
3.1.2  Source of Repayment Proceeds
The indenture usually describes how the issuer intends to service the debt (make 
interest payments) and repay the principal. Generally, the source of repayment for 
bonds issued by supranational organizations is either the repayment of previous 
loans made by the organization or the paid-  in capital from its members. National 
governments may also act as guarantors for certain bond issues. If additional sources 
of repayment are needed, the supranational organization can typically call on its 
members to provide funds.
Sovereign bonds are backed by the “full faith and credit” of the national govern -
ment and thus by that government’s ability to raise tax revenues and print money.

Sovereign bonds denominated in local currency are generally considered the safest of 
all investments because governments have the power to raise taxes to make interest 
payments and principal repayments. Thus, it is highly probable that interest and prin -
cipal will be paid fully and on time. As a consequence, the yields on sovereign bonds 
are typically lower than those for otherwise similar bonds from other local issuers.

Legal, Regulatory, and Tax Considerations 307
There are three major sources for repayment of non-  sovereign government debt 
issues, and bonds are usually classified according to these sources. The first source 
is through the general taxing authority of the issuer. The second source is from the 
cash flows of the project the bond issue is financing. The third source is from special 
taxes or fees established specifically for the purpose of funding interest payments and 
principal repayments.
The source of payment for corporate bonds is the issuer’s ability to generate cash 
flows, primarily through its operations. These cash flows depend on the issuer’s finan -
cial strength and integrity. Because corporate bonds carry a higher level of credit risk 
than otherwise similar sovereign and non-  sovereign government bonds, they typically 
offer a higher yield.
In contrast to corporate bonds, the source of payment for ABS does not depend

on the claims-  paying ability of an operating entity but on the cash flows generated 
by one or more underlying financial assets, such as mortgages or auto loans. Thus, 
investors in ABS must pay special attention to the quality of the assets backing the ABS.
3.1.3  Asset or Collateral Backing
Collateral backing is a way to alleviate credit risk. Investors should review where they 
rank compared with other creditors in the event of default and analyze the quality of 
the collateral backing the bond issue.
3.1.3.1  Seniority Ranking  Secured bonds  are backed by assets or financial guaran -
tees pledged to ensure debt repayment in the case of default. In contrast, unsecured 
bonds have no collateral; bondholders have only a general claim on the issuer’s assets 
and cash flows. Thus, unsecured bonds are paid after secured bonds in the event of 
default. By lowering credit risk, collateral backing increases the bond issue’s credit 
quality and decreases its yield.

A bond’s collateral backing might not specify an identifiable asset but instead may 
be described as the “general plant and infrastructure” of the issuer. In such cases, 
investors rely on seniority ranking—that is, the systematic way in which lenders are 
repaid in case of bankruptcy or liquidation. What matters to investors is where they 
rank compared with other creditors rather than whether there is an asset of sufficient 
quality and value in place to cover their claims. Senior debt is debt that has a priority 
claim over subordinated debt or junior debt. Financial institutions issue a large volume 
of both senior unsecured and subordinated bonds globally; it is not uncommon to see 
large as well as smaller banks issue such bonds. For example, in 2012, banks as diverse 
as Royal Bank of Scotland in the United Kingdom and Prime Bank in Bangladesh 
issued senior unsecured bonds to institutional investors.

Debentures  are a type of bond that can be secured or unsecured. In many juris -
dictions, debentures are unsecured bonds, with no collateral backing assigned to the 
bondholders. In contrast, bonds known as “debentures” in the United Kingdom and 
in other Commonwealth countries, such as India, are usually backed by an asset or 
pool of assets assigned as collateral support for the bond obligations and segregated 
from the claims of other creditors. Thus, it is important for investors to review the 
indenture to determine whether a debenture is secured or unsecured. If the debenture 
is secured, debenture holders rank above unsecured creditors of the company; they 
have a specific asset or pool of assets that the trustee can call on to realize the debt 
3.1.3.2  Types of Collateral Backing  There is a wide range of bonds that are secured 
by some form of collateral. Some companies issue collateral trust bonds and equipment

trust certificates. Collateral trust bonds  are secured by securities such as common 
shares, other bonds, or other financial assets. These securities are pledged by the issuer 
and typically held by the trustee. Equipment trust certificates  are bonds secured by

Reading 50 ■ Fixed-  Income Securities: Defining Elements 308
specific types of equipment or physical assets, such as aircraft, railroad cars, shipping 
containers, or oil rigs. They are most commonly issued to take advantage of the tax 
benefits of leasing. For example, suppose an airline finances the purchase of new aircraft 
with equipment trust certificates. The legal title to the aircraft is held by the trustee, 
which issues equipment trust certificates to investors in the amount of the aircraft 
purchase price. The trustee leases the aircraft to the airline and collects lease payments 
from the airline to pay the interest on the certificates. When the certificates mature, 
the trustee sells the aircraft to the airline, uses the proceeds to retire the principal, and 
cancels the lease.
One of the most common forms of collateral for ABS is mortgaged property. MBS 
are debt obligations that represent claims to the cash flows from pools of mortgage

loans, most commonly on residential property. Mortgage loans are purchased from 
banks, mortgage companies, and other originators and then assembled into pools by 
a governmental, quasi-  governmental, or private entity.
Financial institutions, particularly in Europe, issue covered bonds. A covered 
bond  is a debt obligation backed by a segregated pool of assets called a “cover pool” . 
Covered bonds are similar to ABS but offer bondholders additional protection if the 
financial institution defaults. A financial institution that sponsors ABS transfers the 
assets backing the bonds to a special legal entity. If the financial institution defaults, 
investors who hold bonds in the financial institution have no recourse against the 
special legal entity and its pool of assets because the special legal entity is a bankruptcy-  
remote vehicle; the only recourse they have is against the financial institution itself.

In contrast, in the case of covered bonds, the pool of assets remains on the financial 
institution’s balance sheet. In the event of default, bondholders have recourse against 
both the financial institution and the cover pool. Thus, the cover pool serves as col -
lateral. If the assets that are included in the cover pool become non-  performing (i.e., 
the assets are not generating the promised cash flows), the issuer must replace them 
with performing assets. Therefore, covered bonds usually carry lower credit risks and 
offer lower yields than otherwise similar ABS.
3.1.4  Credit Enhancements
Credit enhancements refer to a variety of provisions that can be used to reduce the 
credit risk of a bond issue. Thus, they increase the issue’s credit quality and decrease 
the bond’s yield. Credit enhancements are very often used when creating ABS.
There are two primary types of credit enhancements: internal and external. Internal

credit enhancement relies on structural features regarding the bond issue. External 
credit enhancement refers to financial guarantees received from a third party, often 
called a financial guarantor. We describe each type in the following sections.
3.1.4.1  Internal Credit Enhancement  The most common forms of internal credit 
enhancement are subordination, overcollateralization, and reserve accounts.
Subordination , also known as credit tranching , is the most popular internal credit 
enhancement technique. It relies on creating more than one bond class or tranche 
and ordering the claim priorities for ownership or interest in an asset between the 
tranches. The cash flows generated by the assets are allocated with different priority 
to tranches of different seniority. The ordering of the claim priorities is called a senior/
subordinated structure, where the tranches of highest seniority are called senior fol -

lowed by subordinated or junior tranches. The subordinated tranches function as credit 
protection for the more senior tranches, in the sense that the most senior tranche 
has the first claim on available cash flows. This type of protection is also commonly 
referred to as a waterfall structure because in the event of default, the proceeds from 
liquidating assets will first be used to repay the most senior creditors. Thus, if the 
issuer defaults, losses are allocated from the bottom up—that is, from the most junior

Legal, Regulatory, and Tax Considerations 309
to the most senior tranche. The most senior tranche is typically unaffected unless 
losses exceed the amount of the subordinated tranches, which is why the most senior 
tranche is usually rated Aaa/AAA.
Overcollateralization  refers to the process of posting more collateral than is needed 
to obtain or secure financing. It represents a form of internal credit enhancement 
because the additional collateral can be used to absorb losses. For example, if at issuance 
the principal amount of a bond issue is $100 million and the value of the collateral is 
$110 million, the amount of overcollateralization is $10 million. Over time, the amount 
of overcollateralization changes, for instance as a result of amortization, prepayments 
or defaults in the case of MBS. A major problem associated with overcollateralization 
is the valuation of the collateral. For example, one of the most significant contributors

to the 2007–2009 credit crisis was a valuation problem with the residential housing 
assets backing MBS. Many properties were originally valued in excess of the worth 
of the issued securities. But as property prices fell and homeowners started to default 
on their mortgages, the credit quality of many MBS declined sharply. The result was 
a rapid rise in yields and panic among investors in these securities.
Reserve accounts  or reserve funds  are another form of internal credit enhance -
ment, and come in two forms: a cash reserve fund and an excess spread account. A cash 
reserve fund is a deposit of cash that can be used to absorb losses. An excess spread 
account involves the allocation into an account of any amounts left over after paying 
out the interest to bondholders. The excess spread, sometimes called excess interest 
cash flow, is the difference between the cash flow received from the assets used to

secure the bond issue and the interest paid to bondholders. The excess spread can be 
retained and deposited into a reserve account that serves as a first line of protection 
against losses. In a process called turboing, the excess spread can be used to retire the 
principal, with the most senior tranche having the first claim on these funds.
3.1.4.2  External Credit Enhancement  The most common forms of external credit 
enhancement are bank guarantees and surety bonds, letters of credit, and cash collat -
eral accounts.
Bank guarantees and surety bonds  are very similar in nature because they both 
reimburse bondholders for any losses incurred if the issuer defaults. However, there 
is usually a maximum amount that is guaranteed, called the penal sum. The major 
difference between a bank guarantee and a surety bond is that the former is issued 
by a bank, whereas the latter is issued by a rated and regulated insurance company.

Insurance companies that specialize in providing financial guarantees are typically 
called monoline insurance companies or monoline insurers. Monoline insurers played 
an important role in securitization until the 2007–2009 credit crisis. But financial 
guarantees from monoline insurers have become a less common form of credit 
enhancement since the credit crisis as a consequence of the financial difficulties and 
credit rating downgrades that most monoline insurers experienced.
A letter of credit  from a financial institution is another form of external credit 
enhancement for a bond issue. The financial institution provides the issuer with a credit 
line to reimburse any cash flow shortfalls from the assets backing the issue. Letters of 
credit have also become a less common form of credit enhancement since the credit 
crisis as a result of the credit rating downgrades of several financial institutions that 
were providers of letters of credit.

Bank guarantees, surety bonds, and letters of credit expose the investor to third-  
party (or counterparty) risk—that is, the possibility that a guarantor cannot meet 
its obligations. A cash collateral account  mitigates this concern because the issuer 
immediately borrows the credit-  enhancement amount and then invests that amount, 
usually in highly rated short-  term commercial paper. Because a cash collateral account

Reading 50 ■ Fixed-  Income Securities: Defining Elements 310
is an actual deposit of cash rather than a pledge of cash, a downgrade of the cash 
collateral account provider will not necessarily result in a downgrade of the bond 
issue backed by that provider.
3.1.5  Covenants
Bond covenants are legally enforceable rules that borrowers and lenders agree on at the 
time of a new bond issue. An indenture will frequently include affirmative (or positive) 
and negative covenants. Affirmative covenants enumerate what issuers are required 
to do, whereas negative covenants specify what issuers are prohibited from doing.
Affirmative covenants are typically administrative in nature. For example, fre -
quently used affirmative covenants include what the issuer will do with the proceeds 
from the bond issue and the promise of making the contractual payments. The issuer 
may also promise to comply with all laws and regulations, maintain its current lines

of business, insure and maintain its assets, and pay taxes as they come due. These 
types of covenants typically do not impose additional costs to the issuer and do not 
materially constrain the issuer’s discretion regarding how to operate its business.
In contrast, negative covenants are frequently costly and do materially constrain the 
issuer’s potential business decisions. The purpose of negative covenants is to protect 
bondholders from such problems as the dilution of their claims, asset withdrawals 
or substitutions, and suboptimal investments by the issuer. Examples of negative 
covenants include the following:
■■Restrictions on debt  regulate the issue of additional debt. Maximum acceptable 
debt usage ratios (sometimes called leverage ratios or gearing ratios) and min -
imum acceptable interest coverage ratios are frequently specified, permitting 
new debt to be issued only when justified by the issuer’s financial condition.

■■Negative pledges  prevent the issuance of debt that would be senior to or rank in 
priority ahead of the existing bondholders’ debt.
■■Restrictions on prior claims  protect unsecured bondholders by preventing the 
issuer from using assets that are not collateralized (called unencumbered assets) 
to become collateralized.
■■Restrictions on distributions to shareholders  restrict dividends and other 
payments to shareholders such as share buy-  backs (repurchases). The restric -
tion typically operates by reference to the borrower’s profitability; that is, the 
covenant sets a base date, usually at or near the time of the issue, and permits 
dividends and share buy-  backs only to the extent of a set percentage of earnings 
or cumulative earnings after that date.
■■Restrictions on asset disposals  set a limit on the amount of assets that can be 
disposed by the issuer during the bond’s life. The limit on cumulative disposals

is typically set as a percentage of a company’s gross assets. The usual intent is to 
protect bondholder claims by preventing a break-  up of the company.
■■Restrictions on investments  constrain risky investments by blocking speculative 
investments. The issuer is essentially forced to devote its capital to its going-  
concern business. A companion covenant may require the issuer to stay in its 
present line of business.
■■Restrictions on mergers and acquisitions  prevent these actions unless the com -
pany is the surviving company or unless the acquirer delivers a supplemental 
indenture to the trustee expressly assuming the old bonds and terms of the old 
indenture. These requirements effectively prevent a company from avoiding its 
obligations to bondholders by selling out to another company.

Legal, Regulatory, and Tax Considerations 311
These are only a few examples of negative covenants. The common characteristic of 
all negative covenants is ensuring that the issuer will not take any actions that would 
significantly reduce its ability to make interest payments and repay the principal. 
Bondholders, however, rarely wish to be too specific about how an issuer should run 
its business because doing so would imply a degree of control that bondholders legally 
want to avoid. In addition, very restrictive covenants may not be in the bondholders’ 
best interest if they force the issuer to default when default is avoidable. For example, 
strict restrictions on debt may prevent the issuer from raising new funds that are 
necessary to meet its contractual obligations; strict restrictions on asset disposals may 
prohibit the issuer from selling assets or business units and obtaining the necessary 
liquidity to make interest payments or principal repayments; and strict restrictions on

mergers and acquisitions may prevent the issuer from being taken over by a stronger 
company that would be able to honor the issuer’s contractual obligations.
EXAMPLE 2   
1 The term most likely  used to refer to the legal contract under which a 
bond is issued is:
A indenture.
B debenture.
C letter of credit.
2 The individual or entity that most likely  assumes the role of trustee for a 
bond issue is:
A a financial institution appointed by the issuer.
B the treasurer or chief financial officer of the issuer.
C a financial institution appointed by a regulatory authority.
3 The individual or entity most likely  responsible for the timely payment of 
interest and repayment of principal to bondholders is the:
A trustee.
B primary or lead bank of the issuer.
C treasurer or chief financial officer of the issuer.
4 The major advantage of issuing bonds through a special legal entity is:
A bankruptcy remoteness.
B beneficial tax treatments.
C greater liquidity and lower issuing costs.

5 The category of bond most likely  repaid from the repayment of previous 
loans made by the issuer is:
A sovereign bonds.
B supranational bonds.
C non-  sovereign bonds.
6 The type of collateral used to secure collateral trust bonds is most likely :
B mortgages.
C physical assets.
7 The external credit enhancement that has the least  amount of third-  party 
risk is a:
A surety bond.

Reading 50 ■ Fixed-  Income Securities: Defining Elements 312
B letter of credit.
C cash collateral account.
8 An example of an affirmative covenant is the requirement:
A that dividends will not exceed 60% of earnings.
B to insure and perform periodic maintenance on financed assets.
C that the debt-  to- equity ratio will not exceed 0.4 and times interest 
earned will not fall below 8.0.
9 An example of a covenant that protects bondholders against the dilution 
of their claims is a restriction on:
A debt.
B investments.
C mergers and acquisitions.
A is correct. The contract between a bond issuer and the bondholders is very 
often called an indenture or deed trust. The indenture documents the terms of 
the issue, including the principal amount, the coupon rate, and the payments 
schedule. It also provides information about the funding sources for the contrac -
tual payments and specifies whether there are any collateral, credit enhancement,

or covenants. B is incorrect because a debenture is a type of bond. C is incorrect 
because a letter of credit is an external credit enhancement.
A is correct. The issuer chooses a financial institution with trust powers, such 
as the trust department of a bank or a trust company, to act as a trustee for the 
bond issue.
A is correct. Although the issuer is ultimately the source of the contractual 
payments, it is the trustee that ensures timely payments. Doing so is accom -
plished by invoicing the issuer for interest payments and principal repayments 
and holding the funds until they are paid.
A is correct. A special legal entity is a bankruptcy-  remote vehicle. Bankruptcy 
remoteness is achieved by transferring the assets from the sponsor to the special 
legal entity. Once this transfer is completed, the sponsor no longer has ownership 
rights. If the sponsor defaults, no claims can be made to recover the assets that

were transferred or the proceeds from the transfer to the special legal entity.
B is correct. The source of payment for bonds issued by supranational organi -
zations is either the repayment of previous loans made by the organization or 
the paid-  in capital of its member states. A is incorrect because national govern -
ments rely on their taxing authority and money creation to repay their debt. C 
is incorrect because non-  sovereign bonds are typically repaid from the issuer’s 
taxing authority or the cash flows of the project being financed.

Legal, Regulatory, and Tax Considerations 313
A is correct. Collateral trust bonds are secured by securities, such as common 
shares, other bonds, or other financial assets. B is incorrect because MBS are 
secured by mortgages. C is incorrect because equipment trust certificates are 
backed by physical assets such as aircraft, railroad cars, shipping containers, 
or oil rigs.
C is correct. The third-  party (or counterparty) risk for a surety bond and a letter 
of credit arises from both being future promises to pay. In contrast, a cash col -
lateral account allows the issuer to immediately borrow the credit-  enhancement 
amount and then invest it.
B is correct. Affirmative covenants indicate what the issuer “must do” and are 
administrative in nature. A covenant requiring the issuer to insure and perform 
periodic maintenance on financed assets is an example of affirmative covenant.

A and C are incorrect because they are negative covenants; they indicate what 
the issuer cannot do.
A is correct. A restriction on debt typically takes the form of a maximum accept -
able debt usage ratio or a minimum acceptable interest coverage ratio. Thus, it 
limits the issuer’s ability to issue new debt that would dilute the bondholders’ 
claims. B and C are incorrect because they are covenants that restrict the issu -
er’s business activities by preventing the company from making investments or 
being taken over, respectively.
3.2 Legal and Regulatory Considerations
Fixed-  income securities are subject to different legal and regulatory require -
ments depending on where they are issued and traded, as well as who holds them. 
Unfortunately, there are no unified legal and regulatory requirements that apply globally.
An important consideration for investors is where the bonds are issued and traded

because it affects the laws and regulation that apply. The global bond markets consist 
of national bond markets and the Eurobond market. A national bond market includes 
all the bonds that are issued and traded in a specific country, and denominated in 
the currency of that country. Bonds issued by entities that are incorporated in that 
country are called domestic bonds, whereas bonds issued by entities that are incor -
porated in another country are called foreign bonds. If Ford Motor Company issues 
bonds denominated in US dollars in the United States, these bonds will be classified 
as domestic. If Volkswagen Group or Toyota Motor Corporation (or their German 
or Japanese subsidiaries) issue bonds denominated in US dollars in the United States, 
these bonds will be classified as foreign. Foreign bonds very often receive nicknames. 
For example, foreign bonds are called “kangaroo bonds” in Australia, “maple bonds” in

Canada, “panda bonds” in China, “Samurai bonds” in Japan, “kimchi bonds” in South 
Korea, “matrioshka bonds” in Russia, “matador bonds” in Spain, “bulldog bonds” in 
the United Kingdom, and “Yankee bonds” in the United States. National regulators 
may make distinctions both between and among resident and non-  resident issuers, 
and they may have different requirements regarding the issuance process, the level 
of disclosures, or the restrictions imposed on the bond issuer and/or the investors 
who can purchase the bonds.

Reading 50 ■ Fixed-  Income Securities: Defining Elements 314
Governments and companies have issued foreign bonds in London since the 19th 
century, and foreign bond issues expanded in such countries as the United States, 
Japan, and Switzerland during the 1980s. But the 1960s saw the emergence of another 
bond market: the Eurobond market. The Eurobond market was created primarily to 
bypass the legal, regulatory, and tax constraints imposed on bond issuers and inves -
tors, particularly in the United States. Bonds issued and traded on the Eurobond 
market are called Eurobonds , and they are named after the currency in which they 
are denominated. For example, Eurodollar and Euroyen bonds are denominated in 
US dollars and Japanese yens, respectively. Bonds that are denominated in euros are 
called euro-  denominated Eurobonds.
Eurobonds are typically less regulated than domestic and foreign bonds because 
they are issued outside the jurisdiction of any single country. They are usually unse -

cured bonds and can be denominated in any currency, including the issuer’s domestic 
currency.4 They are underwritten by an international syndicate—that is, a group 
of financial institutions from different jurisdictions. Most Eurobonds are bearer 
bonds , meaning that the trustee does not keep records of who owns the bonds; only 
the clearing system knows who the bond owners are. In contrast, most domestic 
and foreign bonds are registered bonds  for which ownership is recorded by either 
name or serial number. Some investors may prefer bearer bonds to registered bonds, 
possibly for tax reasons.
A reference is sometimes made to global bonds. A global bond is issued simulta -
neously in the Eurobond market and in at least one domestic bond market. Issuing 
bonds in several markets at the same time ensures that there is sufficient demand for 
large bond issues, and that the bonds can be purchased by all investors, no matter

where these investors are located. For example, the World Bank is a regular issuer of 
global bonds. Many market participants refer to foreign bonds, Eurobonds, and global 
bonds as international bonds as opposed to domestic bonds.
The differences among domestic bonds, foreign bonds, Eurobonds, and global 
bonds matter to investors because these bonds are subject to different legal, regula -
tory, and as described in Section 3.3, tax requirements. They are also characterized by 
differences in the frequency of interest payments and the way the interest payment is 
calculated, which affect the bond’s cash flows and thus its price. Note, however, that 
the currency in which a bond is denominated has a stronger effect on its price than 
where the bond is issued or traded. This is because market interest rates have a strong 
influence on a bond’s price, and the market interest rates that affect a bond are those 
associated with the currency in which the bond is denominated.

As the emergence and growth of the Eurobond market illustrates, legal and regula -
tory considerations affect the dynamics of the global fixed-  income markets. Exhibit 2 
compares the amount of domestic and international debt outstanding for the 15 
countries that were the largest domestic debt issuers at the end of December 2011. 
The reported amounts are based on the residence of the issuer.
4 Eurobonds denominated in US dollars cannot be sold to US investors at the time of issue because they 
are not registered with the US Securities and Exchange Commission (SEC). Most Eurobonds are sold to 
investors in Europe, the Middle East, and Asia Pacific.

Legal, Regulatory, and Tax Considerations 315
Exhibit 2   Domestic and International Debt Securities by Residence of Issuer 
at the End of December 2011
IssuersDomestic Debt Securities  
(US$ billions)International Debt Securities  
 (US$ billions)
All issuers 69,912.7 28,475.4
United States 26,333.1 6,822.0
Japan 14,952.5 180.6
China 3,344.8 28.3
France 3,307.6 1,977.0
Italy 3,077.7 1,135.0
Germany 2,534.2 2,120.6
United Kingdom 1,743.8 3,671.4
Canada 1,547.7 710.9
Brazil 1,488.8 137.4
Spain 1,448.7 1,499.5
South Korea 1,149.0 154.6
Australia 1,023.4 586.4
Netherlands 955.5 2,019.7
Denmark 714.6 142.6
India 596.1 26.1
Source:  Based on data from the Bank of International Settlements, Tables 11 and 16A, available at 
www.bis.org/statistics/secstats.htm, (accessed 6 September 2012).
EXAMPLE 3   
1 An example of a domestic bond is a bond issued by:
A LG Group from South Korea, denominated in British pounds, and sold 
in the United Kingdom.
B the UK Debt Management Office, denominated in British pounds, and

sold in the United Kingdom.
C Wal-  Mart from the United States, denominated in US dollars, and sold 
in various countries in North America, Europe, the Middle East, and 
Asia Pacific.
2 A bond issued by Sony in Japan, denominated in US dollars but not reg -
istered with the SEC, and sold to an institutional investor in the Middle 
East, is most likely  an example of a:
A Eurobond.
B global bond.
C foreign bond.
B is correct. A domestic bond is issued by a local issuer, denominated in local 
currency, and sold in the domestic market. Gilts are British pound–  denominated 
bonds issued by the UK Debt Management Office in the United Kingdom. Thus, 
they are UK domestic bonds. A is incorrect because a bond issued by LG Group

Reading 50 ■ Fixed-  Income Securities: Defining Elements 316
from South Korea, denominated in British pounds, and sold in the United 
Kingdom, is an example of a foreign bond (bulldog bond). C is incorrect because 
a bond issued by Wal-  Mart from the United States, denominated in US dollars, 
and sold in various countries in North America, Europe, the Middle East, and 
Asia Pacific is most likely an example of a global bond, particularly if it is also 
sold in the Eurobond market.
A is correct. A Eurobond is a bond that is issued internationally, outside the 
jurisdiction of any single country. Thus, a bond issued by Sony from Japan, 
denominated in US dollars but not registered with the SEC, is an example of a 
Eurobond. B is incorrect because global bonds are bonds that are issued simul -
taneously in the Eurobond market and in at least one domestic bond market. C 
is incorrect because if Sony’s bond issue were a foreign bond (Yankee bond), it 
would be registered with the SEC.

3.3 Tax Considerations
Generally speaking, the income portion of a bond investment is taxed at the ordi -
nary income tax rate, which is typically the same tax rate that an individual would 
pay on wage or salary income. Tax-  exempt securities are the exception to this rule. 
For example, interest income received by holders of local government bonds called 
municipal bonds in the United States is often exempt from federal income tax and 
from the income tax of the state in which the bonds are issued. The tax status of bond 
income may also depend on where the bond is issued and traded. For example, some 
domestic bonds pay their interest net of income tax. Other bonds, including some 
Eurobonds, make gross interest payments.
In addition to earnings from interest, a bond investment may also generate a 
capital gain or loss. If a bond is sold before its maturity date, the price is likely to

have changed compared with the purchase price. This change will generate a capital 
gain if the bond price has increased or a capital loss if the bond price has decreased. 
From the stand point of taxes, a capital gain or loss is usually treated differently from 
taxable income. In addition, in some countries, there is a different tax rate for long-  
term and short-  term capital gains. For example, capital gains that are recognized 
more than 12 months after the original purchase date may be taxed at a long-  term 
capital gains tax rate, whereas capital gains that are recognized within 12 months of 
purchasing the investment may be taxed as a short-  term capital gain. Very often, the 
tax rate for long-  term capital gains is lower than the tax rate for short-  term capital 
gains, and the tax rate for short-  term capital gains is equal to the ordinary income tax 
rate, although there are exceptions. Not all countries, however, implement a capital

gains tax. Furthermore, differences in national and local legislation often result in a 
very diverse set of aggregate country capital gains tax rates.
For bonds issued at a discount, an additional tax consideration is related to the 
tax status of the original issue discount. The original issue discount is the difference 
between the par value and the original issue price. In some countries, such as the United 
States, a prorated portion of the discount must be included in interest income every 
tax year. This is not the case in other countries, such as Japan. Exhibit 3 illustrates 
the potential importance of this tax consideration.

Legal, Regulatory, and Tax Considerations 317
Exhibit 3   
Original Issue Discount Tax Provision
Assume a hypothetical country, Zinland, where the local currency is the zini 
(Z). The market interest rate in Zinland is 10%, and both interest income and 
capital gains are taxed. Companies A and B issue 20-  year bonds with a par value 
of Z1,000. Company A issues a coupon bond with an annual coupon rate of 10%. 
Investors buy Company A’s bonds for Z1,000. Every year, they receive and pay 
tax on their Z100 annual interest payments. When Company A’s bonds mature, 
bondholders receive the par value of Z1,000. Company B issues a zero-  coupon 
bond at a discount. Investors buy Company B’s bonds for Z148.64. They do not 
receive any cash flows until Company B pays the par value of Z1,000 when the 
bonds mature.
Company A’s bonds and Company B’s bonds are economically identical in the 
sense that they have the same maturity (20 years) and the same yield to maturity

(10%). Company A’s bonds make periodic payments, however, whereas Company 
B’s bonds defer payment until maturity. Investors in Company A’s bonds must 
include the annual interest payments in taxable income. When they receive 
their original Z1,000 investment back at maturity, they face no capital gain or 
loss. Without an original issue discount tax provision, investors in Company 
B’s bonds do not have any taxable income until the bonds mature. When they 
receive the par value at maturity, they face a capital gain on the original issue 
discount—that is, on Z851.36 (Z1,000 – Z148.64). The purpose of an original 
issue discount tax provision is to tax investors in Company B’s bonds the same 
way as investors in Company A’s bonds. Thus, a prorated portion of the Z851.36 
original issue discount is included in taxable income every tax year until maturity. 
This allows investors in Company B’s bonds to increase their cost basis in the 
bonds so that at maturity, they face no capital gain or loss.

Some jurisdictions also have tax provisions for bonds bought at a premium. They 
may allow investors to deduct a prorated portion of the amount paid in excess of the 
bond’s par value from their taxable income every tax year until maturity. For example, 
if an investor pays $1,005 for a bond that has a par value of $1,000 and matures five 
years later, she can deduct $1 from her taxable income every tax year for five years. 
But the deduction may not be required; the investor may have the choice either to 
deduct a prorated portion of the premium each year or to deduct nothing and declare 
a capital loss when the bond is redeemed at maturity.
EXAMPLE 4   
1 The coupon payment is most likely  to be taxed as:
A ordinary income.
B short-  term capital gain.
C long-  term capital gain.
2 Assume that a company issues bonds in the hypothetical country of 
Zinland, where the local currency is the zini (Z). There is an original 
issue discount tax provision in Zinland’s tax code. The company issues a

10- year zero-  coupon bond with a par value of Z1,000 and sells it for Z800. 
An investor who buys the zero-  coupon bond at issuance and holds it until 
maturity most likely :

Reading 50 ■ Fixed-  Income Securities: Defining Elements 318
A has to include Z20 in his taxable income every tax year for 10 years 
and has to declare a capital gain of Z200 at maturity.
B has to include Z20 in his taxable income every tax year for 10 years 
and does not have to declare a capital gain at maturity.
C does not have to include anything in his taxable income every tax year 
for 10 years but has to declare a capital gain of Z200 at maturity.
A is correct. Interest income is typically taxed at the ordinary income tax rate, 
which may be the same tax rate that individuals pay on wage and salary income.
B is correct. The original issue discount tax provision requires the investor to 
include a prorated portion of the original issue discount in his taxable income 
every tax year until maturity. The original issue discount is the difference between 
the par value and the original issue price—that is, Z1,000 – Z800 = Z200. The

bond’s maturity is 10 years. Thus, the prorated portion that must be included 
each year is Z200 ÷ 10 = Z20. The original issue discount tax provision allows the 
investor to increase his cost basis in the bond so that when the bond matures, 
the investor faces no capital gain or loss.
STRUCTURE OF A BOND’S CASH FLOWS
The most common payment structure by far is that of a plain vanilla bond, as depicted 
in Exhibit 1. These bonds make periodic, fixed coupon payments and a lump-  sum 
payment of principal at maturity. But there are other structures regarding both the 
principal repayment and the interest payments. This section discusses the major 
schedules observed in the global fixed-  income markets. Schedules for principal 
repayments and interest payments are typically similar for a particular type of bond, 
such as 10-  year US Treasury bonds. However, payment schedules vary considerably 
between types of bonds, such as government bonds versus corporate bonds.

4.1 Principal Repayment Structures
How the amount borrowed is repaid is an important consideration for investors 
because it affects the level of credit risk they face from holding the bonds. Any pro -
vision that periodically retires some of the principal amount outstanding is a way to 
reduce credit risk.
4.1.1  Bullet, Fully Amortized, and Partially Amortized Bonds
The payment structure of a plain vanilla bond has been used for nearly every govern -
ment bond ever issued as well as for the majority of corporate bonds. Such a bond is 
also known as a bullet bond because the entire payment of principal occurs at maturity.
In contrast, an amortizing bond  has a payment schedule that calls for periodic 
payments of interest and repayments of principal. A bond that is fully amortized is 
characterized by a fixed periodic payment schedule that reduces the bond’s outstanding 
principal amount to zero by the maturity date. A partially amortized bond also makes

fixed periodic payments until maturity, but only a portion of the principal is repaid 
by the maturity date. Thus, a balloon payment  is required at maturity to retire the 
bond’s outstanding principal amount.4

Structure of a Bond’s Cash Flows 319
Exhibit 4 illustrates the differences in the payment schedules for a bullet bond, a 
fully amortized bond, and a partially amortized bond. For the three bonds, the prin -
cipal amount is $1,000, the maturity is five years, the coupon rate is 6%, and interest 
payments are made annually. The market interest rate used to discount the bonds’ 
expected cash flows until maturity is assumed to be constant at 6%. The bonds are 
issued and redeemed at par. For the partially amortized bond, the balloon payment 
is $200 at maturity.5
Exhibit 4   Example of Payment Schedules for Bullet, Fully Amortized, and 
Partially Amortized Bonds
Bullet Bond
Y earInvestor Cash 
FlowsInterest 
PaymentPrincipal 
RepaymentOutstanding Principal 
at the End of the Y ear
0 –$1,000.00 $1,000.00
1 60.00 $60.00 $0.00 1,000.00
2 60.00 60.00 0.00 1,000.00
3 60.00 60.00 0.00 1,000.00
4 60.00 60.00 0.00 1,000.00
5 1,060.00 60.00 1,000.00 0.00
Fully Amortized Bond
FlowsInterest

0 –$1,000.00
1 237.40 $60.00 $177.40 $822.60
2 237.40 49.36 188.04 634.56
3 237.40 38.07 199.32 435.24
4 237.40 26.11 211.28 223.96
5 237.40 13.44 223.96 0.00
Partially Amortized Bond
1 201.92 $60.00 $141.92 $858.08
2 201.92 51.48 150.43 707.65
3 201.92 42.46 159.46 548.19
4 201.92 32.89 169.03 379.17
5 401.92 22.75 379.17 0.00
5 The examples in this reading were created in Microsoft Excel. Numbers may differ from the results 
obtained using a calculator because of rounding.

Reading 50 ■ Fixed-  Income Securities: Defining Elements 320
Investors pay $1,000 now to purchase any of the three bonds. For the bullet bond, 
they receive the coupon payment of $60 (6% × $1,000) every year for five years. The 
last payment is $1,060 because it includes both the last coupon payment and the 
principal amount.
For the fully amortized bond, the annual payment, which includes both the coupon 
payment and the principal repayment, is constant. Thus, this annual payment can be 
viewed as an annuity. This annuity lasts for five years; its present value, discounted 
at the market interest rate of 6%, is equal to the bond price of $1,000. Therefore, the 
annual payment is $237.40. The first year, the interest part of the payment is $60 (6% 
× $1,000), which implies that the principal repayment part is $177.40 ($237.40 – $60). 
This repayment leaves an outstanding principal amount, which becomes the basis for

the calculation of the interest the following year, of $822.60 ($1,000 – $177.40). The 
second year, the interest part of the payment is $49.36 (6% × $822.60), the principal 
repayment part is $188.04 ($237.40 – $49.36), and the outstanding principal amount 
is $634.56 ($822.60 – $188.04). The fifth year, the outstanding principal amount is 
fully repaid. Note that the annual payment is constant but, over time, the interest 
payment decreases and the principal repayment increases.
The partially amortized bond can be viewed as the combination of two elements: a 
five-  year annuity plus the balloon payment at maturity. The sum of the present values 
of these two elements is equal to the bond price of $1,000. As for the fully amortized 
bond, the discount rate is the market interest rate of 6%, making the constant amount 
for the annuity $201.92. This amount represents the annual payment for the first four 
years. For Years 1 through 4, the split between interest and principal is done the same

way as for the fully amortized bond. The interest part of the payment is equal to 6% 
multiplied by the outstanding principal at the end of the previous year; the principal 
repayment part is equal to $201.92 minus the interest part of the payment for the year; 
and the outstanding principal amount at the end of the year is equal to the outstanding 
principal amount at the end of the previous year minus the principal repayment for 
the year. In Year 5, investors receive $401.92; this amount is calculated either as the 
sum of the interest payment ($22.75) and the outstanding principal amount ($379.17) 
or as the constant amount of the annuity ($201.92) plus the balloon payment ($200). 
As for the fully amortized bond, the interest payment decreases and the principal 
repayment increases over time. Because the principal amount is not fully amortized, 
interest payments are higher for the partially amortized bond than for the fully amor -
tized bond, except the first year when they are equal.

Exhibit 4 does not address the complexity of the repayment structure for some 
bonds, such as many ABS. For example, MBS face prepayment risk, which is the 
possible early repayment of mortgage principal. Borrowers usually have the right to 
prepay mortgages, which typically occurs when a current homeowner purchases a 
new home or when homeowners refinance their mortgages because market interest 
rates have fallen. 
EXAMPLE 5   
1 The structure that requires the largest repayment of principal at maturity 
is that of a:
A bullet bond.
B fully amortized bond.
C partially amortized bond.

Structure of a Bond’s Cash Flows 321
2 A plain vanilla bond has a maturity of 10 years, a par value of £100, and 
a coupon rate of 9%. Interest payments are made annually. The market 
interest rate is assumed to be constant at 9%. The bond is issued and 
redeemed at par. The principal repayment the first year is closest  to:
A £0.00.
B £6.58.
C £10.00.
3 Relative to a fully amortized bond, the coupon payments of an otherwise 
similar partially amortized bond are:
A lower or equal.
B equal.
C higher or equal.
A is correct. The entire repayment of principal occurs at maturity for a bullet (or 
plain vanilla) bond, whereas it occurs over time for fully and partially amortized 
bonds. Thus, the largest repayment of principal at maturity is that of a bullet bond.
A is correct. A plain vanilla (or bullet) bond does not make any principal repay -
ment until the maturity date. B is incorrect because £6.58 would be the principal 
repayment for a fully amortized bond.

C is correct. Except at maturity, the principal repayments are lower for a 
partially amortized bond than for an otherwise similar fully amortized bond. 
Consequently, the principal amounts outstanding and, therefore, the amounts 
of interest payments are higher for a partially amortized bond than for a fully 
amortized bond, all else equal. The only exception is the first interest payment, 
which is the same for both repayment structures. This is because no principal 
repayment has been made by the time the first coupon is paid.
4.1.2  Sinking Fund Arrangements
A sinking fund arrangement  is another approach that can be used to achieve the same 
goal of periodically retiring the bond’s principal outstanding. The term sinking fund 
refers to an issuer’s plans to set aside funds over time to retire the bond. Originally, 
a sinking fund was a specified cash reserve that was segregated from the rest of the

issuer’s business for the purpose of repaying the principal. More generally today, a 
sinking fund arrangement specifies the portion of the bond’s principal outstanding, 
perhaps 5%, that must be repaid each year throughout the bond’s life or after a spec -
ified date. This repayment occurs whether or not an actual segregated cash reserve 
has been created.
Typically, the issuer will forward repayment proceeds to the bond’s trustee. The 
trustee will then either redeem bonds to this value or select by lottery the serial 
numbers of bonds to be paid off. The bonds for repayment may be listed in business 
newspapers, such as the Wall Street Journal  or the Financial Times .
As well as the standard  version described above, another type of sinking fund 
arrangement operates by redeeming a steadily increasing amount of the bond’s notional 
principal (total amount) each year. Any remaining principal is then redeemed at

Reading 50 ■ Fixed-  Income Securities: Defining Elements 322
maturity. It is common to find utility and energy companies in the United States, the 
United Kingdom, and the Commonwealth countries that issue bonds with sinking 
fund arrangements that incorporate such a provision.
Another common variation is for the bond issue to include a call provision, which 
gives the issuer the option to repurchase the bonds before maturity—callable bonds 
are discussed in Section 5.1. The issuer can usually repurchase the bonds at the market 
price, at par, or at a specified sinking fund price, whichever is the lowest. To allocate 
the burden of the call provision fairly among bondholders, the bonds to be retired are 
selected at random based on serial number. Usually, the issuer can repurchase only 
a small portion of the bond issue. Some indentures, however, allow issuers to use a 
doubling option to repurchase double the required number of bonds.

The benefit of a sinking fund arrangement is that it ensures that a formal plan is 
in place for retiring the debt. For an investor, a sinking fund arrangement reduces 
the risk the issuer will default when the principal is due, thereby reducing the credit 
risk of the bond issue. But investors experience potential disadvantages with sinking 
fund arrangements. First, investors face reinvestment risk, the risk associated with 
having to reinvest cash flows at an interest rate that may be lower than the current 
yield to maturity. If the serial number of an investor’s bonds is selected, the bonds 
will be repaid and the investor will have to reinvest the proceeds. If market interest 
rates have fallen since the investor purchased the bonds, he or she probably will not 
be able to purchase a bond offering the same return. Another potential disadvantage 
for investors occurs if the issuer has the option to repurchase bonds at below market

prices. For example, an issuer could exercise a call option to buy back bonds at par 
on bonds priced above par. In this case, investors would suffer a loss.
Exhibit 5 illustrates an example of a sinking fund arrangement.
Exhibit 5   
Example of a Sinking Fund Arrangement
The notional principal of the bond issue is £200  million. The sinking fund 
arrangement calls for 5% of the outstanding principal amount to be retired in 
Years 10 through 19, with the outstanding balance paid off at maturity in 20 years.
Y earOutstanding Principal  
at the Beginning  
of the Y ear  
(£ millions)Sinking 
Fund  
Payment  
(£ millions)Outstanding  
Principal at the  
End of the Y ear  
(£ millions)Final Principal  
Repayment  
(£ millions)
0 200.00
1 to 9 200.00 0.00 200.00
10 200.00 10.00 190.00
11 190.00 9.50 180.50
12 180.50 9.03 171.48
13 171.48 8.57 162.90
14 162.90 8.15 154.76
15 154.76 7.74 147.02
16 147.02 7.35 139.67
17 139.67 6.98 132.68
18 132.68 6.63 126.05
19 126.05 6.30 119.75
20 119.75 119.75

Structure of a Bond’s Cash Flows 323
There is no repayment of the principal during the first nine years. Starting the 
10th year, the sinking fund arrangement calls for 5% of the outstanding principal 
amount to be retired each year. In Year 10, £10 million (5% × £200 million) are 
paid off, which leaves an outstanding principal balance of £190 million. In Year 
11, the principal amount repaid is £9.50 million (5% × £190 million). The final 
repayment of the remaining balance (£119.75 million) is a balloon payment at 
maturity.
4.2 Coupon Payment Structures
A coupon is the interest payment that the bond issuer makes to the bondholder. A 
conventional bond pays a fixed periodic coupon over a specified time to maturity. 
Most frequently, the coupon is paid semi-  annually for sovereign and corporate bonds; 
this is the case in the United States, the United Kingdom, and Commonwealth coun -
tries such as Bangladesh, India, and New Zealand. Eurobonds usually pay an annual

coupon, although some Eurobonds make quarterly coupon payments. The norm for 
bonds issued in the eurozone is for an annual coupon, although there are exceptions.
Fixed-  rate coupons are not the only coupon payment structure, however. A wide 
range of coupon types is offered in the global fixed-  income markets. This variety exists 
to meet the differing needs of both issuers and investors.
4.2.1  Floating-  Rate Notes
Floating-  rate notes do not have a fixed coupon; instead, their coupon rate is linked 
to an external reference rate, such as Libor. Thus, a FRN’s interest rate will fluctuate 
periodically during the bond’s life, following the changes in the reference rate. As a 
consequence, the FRN’s cash flows are not known with certainty. Large issuers of 
FRNs include government-  sponsored enterprises (GSEs), such as the Federal Home 
Loan Banks (FHLB), the Federal National Mortgage Association (“Fannie Mae”), and

the Federal Home Loan Mortgage Corporation (“Freddie Mac”) in the United States, 
as well as banks and financial institutions in Europe and Asia Pacific. It is rare for 
national governments to issue FRNs because investors in sovereign bonds generally 
prefer fixed-  coupon bonds.
Almost all FRNs have quarterly coupons, although counter examples do exist. 
FRNs usually pay a fixed spread over the specified reference rate. A typical coupon 
rate may be the three-  month US dollar Libor + 20 bps (i.e., Libor + 0.20%) for a US 
dollar-  denominated bond or the three-  month Euribor + 20 bps for a euro-  denominated 
FRN. Occasionally the spread is not fixed; in this case, the bond is known as a variable-  
rate note .
Contrary to plain vanilla, fixed-  rate securities that decline in value in a rising 
interest rate environment, FRNs are less affected when interest rates increase because 
their coupon rates vary with market interest rates and are reset at regular, short-  term

intervals. Thus, FRNs have little interest rate risk—that is, the risk that a change in 
market interest rate affects a bond’s value. FRNs are frequently favored by investors 
who expect that interest rates will rise. That said, investors still face credit risk when 
investing in FRNs. If an issuer’s credit risk does not change from one coupon reset 
date to the next, the FRN’s price generally will stay close to the par value. However, 
if there is a change in the issuer’s credit quality that affects the perceived credit risk 
associated with the bond, the price of the FRN will deviate from its par value. A higher 
level of credit risk will lead to a lower price and a higher yield.Exhibit 5   (Continued)

Reading 50 ■ Fixed-  Income Securities: Defining Elements 324
Additional features observed in FRNs may include a floor or a cap. A floor (floored 
FRN) prevents the coupon from falling below a specified minimum rate. This feature 
benefits the bondholders, who are guaranteed that the interest rate will not fall below 
the specified rate during a time of falling interest rates. In contrast, a cap (capped 
FRN) prevents the coupon from rising above a specified maximum rate. This feature 
benefits the issuer, because it sets a limit to the interest rate paid on the debt during a 
time of rising interest rates. It is also possible to have a collared FRN, which includes 
both a cap and a floor.
An inverse or reverse FRN, or simply an inverse floater, is a bond whose coupon 
rate has an inverse relationship to the reference rate. The basic structure is the same 
as an ordinary FRN except for the direction in which the coupon rate is adjusted.

When interest rates fall, the coupon rate on an ordinary FRN decreases; in contrast, 
the coupon rate on a reverse FRN increases. Thus, inverse FRNs are typically favored 
by investors who expect interest rates to decline.
4.2.2  Step-  Up Coupon Bonds
The coupon of a step-  up coupon bond , which may be fixed or floating, increases by 
specified margins at specified dates. An example of a bond with a step-  up coupon 
is the FRN that was issued by the British bank HBOS plc in 2005. This FRN had a 
20- year maturity, and the coupon was linked to the three-  month Libor plus an initial 
spread of 50 bps. The spread was scheduled to increase to 250 bps over Libor in 2015 
for the bond’s tenor.
Bonds with step-  up coupons offer bondholders some protection against rising 
interest rates, and they may be an important feature for callable bonds. When inter -
est rates increase, there is a higher likelihood that the issuer will not call the bonds,

particularly if the bonds have a fixed rate of interest. The step-  up coupon allows 
bondholders to receive a higher coupon, in line with the higher market interest rates. 
Alternatively, when interest rates decrease or remain stable, the step-  up feature acts as 
an incentive for the issuer to call the bond before the spread increases and the interest 
expense rises. Thus, at issuance, most investors viewed the bond issued by HBOS as 
a 10-  year investment, given that they expected the issuer to redeem it after 10 years 
to avoid paying the higher coupon.
Redeeming the bond when the spread increases is not automatic, however; the 
issuer may choose to keep the bond despite its increasing cost. This may happen 
if refinancing the bond is necessary and alternatives are less advantageous for this 
issuer. For example, a financial crisis may make it difficult for the issuer to refinance. 
Alternatively, the issuer’s credit quality may have deteriorated, which would lead to a

higher spread, potentially making the coupon rate on the new bond more expensive 
than that on the existing bond despite the stepped-  up coupon. Although the issuer does 
not have to call the bond before the spread increases, there is an implicit expectation 
from investors that it will. Failure to do so may be viewed negatively by market par -
ticipants and reduce investors’ appetite for that particular issuer’s bonds in the future.
4.2.3  Credit-  Linked Coupon Bonds
A credit-  linked coupon bond  has a coupon that changes when the bond’s credit 
rating changes. An example of a bond with a credit-  linked coupon is one of British 
Telecom’s bonds maturing in 2020. It has a coupon rate of 9%, but the coupon will 
increase by 50 bps for every credit rating downgrade below the bond’s credit rating 
at the time of issuance and will decrease by 50 bps for every credit rating upgrade 
above the bond’s credit rating at the time of issuance.

Bonds with credit-  linked coupons are attractive to investors who are concerned 
about the future creditworthiness of the issuer. They may also provide some general 
protection against a poor economy because credit ratings tend to decline the most

Structure of a Bond’s Cash Flows 325
during recessions. A potential problem associated with these bonds is that increases 
in the coupon payments resulting from a downgrade may ultimately result in further 
deteriorations of the credit rating or even contribute to the issuer’s default.
4.2.4  Payment-  in- Kind Coupon Bonds
A payment-  in- kind (PIK) coupon bond typically allows the issuer to pay interest in 
the form of additional amounts of the bond issue rather than as a cash payment. Such 
bonds are favored by issuers who are concerned that the issuer may face potential cash 
flow problems in the future. They are used, for example, in financing companies that 
have a high debt burden, such as companies going through a leveraged buyout (a form 
of acquisition in which the financing consists primarily of debt). Because investors are 
aware of the additional credit risk associated with these bonds, they usually demand 
a higher yield for holding bonds with PIK coupons.

Other forms of PIK arrangements can also be found, such as paying the bond -
holders with common shares worth the amount of coupon due. With a PIK toggle 
note, the borrower has the option, for each interest period, to pay interest in cash, 
to make the interest payment in kind, or some mix of the two. Cash payments or 
payments in kind are frequently at the discretion of the borrower, but whether the 
payment is made in cash or in kind can be determined by an earnings or cash flow 
trigger identified in the indenture.
4.2.5  Deferred Coupon Bonds
A deferred coupon bond , sometimes called a split coupon bond , pays no coupons for 
its first few years but then pays a higher coupon than it otherwise normally would for 
the remainder of its life. Issuers of deferred coupon bonds are usually seeking ways to 
conserve cash in the years immediately following the bond issue, which may indicate

poorer credit quality. Deferred coupon bonds are also common in project financing 
when the assets being developed do not generate any income during the development 
phase. A deferred coupon bond allows the issuer to delay interest payments until the 
project is completed and the cash flows generated by the assets being financed can 
be used to service the debt.
One of the main advantages of investing in a deferred coupon bond is that these 
bonds are typically priced at significant discounts to par. Investors may also find the 
deferred coupon structure to be very helpful in managing taxes. If taxes due on the 
interest income can be delayed, investors may be able to minimize taxes. This tax 
advantage, however, depends on the jurisdiction concerned and how its tax rules 
apply to deferred coupon payments.
A zero-  coupon bond can be thought of as an extreme form of deferred coupon 
bond. These securities pay no interest to the investor and thus are issued at a deep

discount to par value. At maturity, the bondholder receives the par value of the bond 
as payment. Effectively, a zero-  coupon bond defers all interest payments until maturity.
4.2.6  Index-  Linked Bonds
An index-  linked bond  has its coupon payments and/or principal repayment linked to 
a specified index. In theory, a bond can be indexed to any published variable, includ -
ing an index reflecting prices, earnings, economic output, commodities, or foreign 
currencies. Inflation-  linked bonds  are an example of index-  linked bonds. They offer 
investors protection against inflation by linking a bond’s coupon payments and/or the 
principal repayment to an index of consumer prices such as the UK Retail Price Index 
(RPI) or the US Consumer Price Index (CPI). The advantage of using the RPI or CPI 
is that these indexes are well-  known, transparent, and published regularly.

Reading 50 ■ Fixed-  Income Securities: Defining Elements 326
Governments are large issuers of inflation-  linked bonds, also called linkers . The 
United Kingdom was one of the first developed countries to issue inflation-  linked 
bonds in 1981, offering gilts linked to the UK RPI, its main measure of the rate of 
inflation. In 1997, the US Treasury began introducing Treasury inflation-  indexed 
securities (TIIS) or Treasury inflation-  protected securities (TIPS) linked to the US CPI. 
Inflation-  linked bonds are now more frequently being offered by corporate issuers, 
including both financial and non-  financial companies.
A bond’s stated coupon rate represents the nominal interest rate received by 
the bondholders. But inflation reduces the actual value of the interest received. The 
interest rate that bondholders actually receive, net of inflation, is the real interest rate; 
it is approximately equal to the nominal interest rate minus the rate of inflation. By

increasing the coupon payments and/or the principal repayment in line with increases 
in the price index, inflation-  linked bonds reduce inflation risk. An example of an 
inflation-  linked bond is the 1.25% UK Treasury index-  linked gilt maturing in 2017: 
Bondholders receive a real interest rate of 1.25%, and the actual interest payments 
are adjusted in line with changes in the UK RPI.
Exhibit  6 shows the national governments that issue the largest amounts of 
inflation-  linked bonds. These sovereign issuers can be grouped into three categories. 
Countries such as Brazil, Chile, and Colombia have issued inflation-  linked bonds 
because they were experiencing extremely high rates of inflation when borrowing, and 
offering inflation-  linked bonds was their only available alternative to raise funds. The 
second category includes the United Kingdom, Australia, and Sweden. These countries 
have issued inflation-  linked bonds in an effort to add credibility to the government’s

commitment to disinflationary policies and also to capitalize on the demand from 
investors still concerned about inflation risk. The third category, which includes the 
United States, Canada, Germany, and France, consists of national governments that 
are most concerned about the social welfare benefits associated with inflation-  linked 
securities. Theoretically, inflation-  linked bonds provide investors the benefit of a 
long-  term asset with a fixed real return that is free from inflation risk.
Exhibit 6   Inflation-  Linked Bonds Outstanding by Market Value at the End 
of December 2011
US Dollars (billions)
800
700
600
500
400
300
200
100
0
South Africa
Chile
Argentina
Brazil
ColombiaAustralia
Canada
France
Germany
Italy
Japan
Sweden
South Ko rea
Mexico
Poland
Turkey
Israel
  
Source:  Based on data from Barclays.

Structure of a Bond’s Cash Flows 327
Different methods have been used for linking the cash flows of an index-  linked 
bond to a specified index; the link can be made via the interest payments, the prin -
cipal repayment, or both. The following examples describe how the link between the 
cash flows and the index is established, using inflation-  linked bonds as an illustration.
■■Zero-  coupon-  indexed bonds pay no coupon, so the inflation adjustment is 
made via the principal repayment only: The principal amount to be repaid at 
maturity increases in line with increases in the price index during the bond’s 
life. This type of bond has been issued in Sweden.
■■Interest-  indexed bonds pay a fixed nominal principal amount at maturity but 
an index-  linked coupon during the bond’s life. Thus, the inflation adjustment 
applies to the interest payments only. This type of bond was briefly issued by 
the Australian government in the late 1980s, but it never became a significant

part of the inflation-  linked bond market.
■■Capital-  indexed bonds  pay a fixed coupon rate but it is applied to a principal 
amount that increases in line with increases in the index during the bond’s life. 
Thus, both the interest payments and the principal repayment are adjusted for 
inflation. Such bonds have been issued by governments in Australia, Canada, 
New Zealand, the United Kingdom, and the United States.
■■Indexed-  annuity bonds are fully amortized bonds, in contrast to interest-  
indexed and capital-  indexed bonds that are non-  amortizing coupon bonds. The 
annuity payment, which includes both payment of interest and repayment of 
the principal, increases in line with inflation during the bond’s life. Indexed-  
annuity bonds linked to a price index have been issued by local governments in 
Australia, but not by the national government.
Exhibit 7 illustrates the different methods used for inflation-  linked bonds.
Exhibit 7   
Examples of Inflation-  Linked Bonds

Exhibit 7   
Assume a hypothetical country, Lemuria, where the currency is the lemming 
(L). The country issued 20-  year bonds linked to the domestic Consumer Price 
Index (CPI). The bonds have a par value of L1,000. Lemuria’s economy has been 
free of inflation until the most recent six months, when the CPI increased by 5%.
Suppose that the bonds are zero-  coupon-  indexed bonds. There will never 
be any coupon payments. Following the 5% increase in the CPI, the principal 
amount to be repaid increases to L1,050 [L1,000 × (1 + 0.05)] and will continue 
increasing in line with inflation until maturity.
Now, suppose that the bonds are coupon bonds that make semi-  annual inter -
est payments based on an annual coupon rate of 4%. If the bonds are interest-  
indexed bonds, the principal amount at maturity will remain L1,000 regardless 
of the CPI level during the bond’s life and at maturity. The coupon payments,

however, will be adjusted for inflation. Prior to the increase in inflation, the 
semi-  annual coupon payment was L20 [(0.04 × L1,000) ÷ 2]. Following the 5% 
increase in the CPI, the semi-  annual coupon payment increases to L21 [L20 × 
(1 + 0.05)]. Future coupon payments will also be adjusted for inflation.
If the bonds are capital-  indexed bonds, the annual coupon rate remains 4%, 
but the principal amount is adjusted for inflation and the coupon payment is 
based on the inflation-  adjusted principal amount. Following the 5% increase in 
the CPI, the inflation-  adjusted principal amount increases to L1,050 [L1,000 × 

Reading 50 ■ Fixed-  Income Securities: Defining Elements 328
(1 + 0.05)], and the new semi-  annual coupon payment is L21 [(0.04 × L1,050) ÷ 
2]. The principal amount will continue increasing in line with increases in the 
CPI until maturity, and so will the coupon payments.
If the bonds are indexed-  annuity bonds, they are fully amortized. Prior to 
the increase in inflation, the semi-  annual payment was L36.56—the annuity 
payment based on a principal amount of L1,000 paid back in 40 semi-  annual 
payments with an annual discount rate of 4%. Following the 5% increase in the 
CPI, the annuity payment increases to L38.38 [L36.56 × (1 + 0.05)]. Future annuity 
payments will also be adjusted for inflation in a similar manner.
EXAMPLE 6   
1 Floating-  rate notes most likely  pay:
A annual coupons.
B quarterly coupons.
C semi-  annual coupons.
2 A zero-  coupon bond can best be considered a:
A step-  up bond.
B credit-  linked bond.
C deferred coupon bond.

3 The bonds that do not offer protection to the investor against increases in 
market interest rates are:
A step-  up bonds.
B floating rate notes.
C inverse floating rate notes.
4 The US Treasury offers Treasury Inflation-  Protected Securities (TIPS). 
The principal of TIPS increases with inflation and decreases with deflation 
based on changes in the US Consumer Price Index. When TIPS mature, 
an investor is paid the original principal or inflation-  adjusted principal, 
whichever is greater. TIPS pay interest twice a year based on a fixed real 
coupon rate that is applied to the inflation-  adjusted principal. TIPS are 
most likely :
A capital-  indexed bonds.
B interest-  indexed bonds.
C indexed-  annuity bonds.
5 Assume a hypothetical country, Lemuria, where the national govern -
ment has issued 20-  year capital-  indexed bonds linked to the domestic 
Consumer Price Index (CPI). Lemuria’s economy has been free of inflation

until the most recent six months, when the CPI increased. Following the 
increase in inflation:
A the principal amount remains unchanged but the coupon rate 
increases.Exhibit 7   (Continued)

Bonds with Contingency Provisions 329
B the coupon rate remains unchanged but the principal amount 
C the coupon payment remains unchanged but the principal amount 
B is correct. Most FRNs pay interest quarterly and are tied to a three-  month 
reference rate such as Libor.
C is correct. Because interest is effectively deferred until maturity, a zero-  coupon 
bond can be thought of as a deferred coupon bond. A and B are incorrect because 
both step-  up bonds and credit-  linked bonds pay regular coupons. For a step-  up 
bond, the coupon increases by specified margins at specified dates. For a credit-  
linked bond, the coupon changes when the bond’s credit rating changes.
C is correct. The coupon rate on an inverse FRN has an inverse relationship 
to the reference rate. Thus, an inverse FRN does not offer protection to the 
investor when market interest rates increase but when they decrease. A and B

are incorrect because step-  up bonds and FRNs both offer protection against 
increases in market interest rates.
A is correct. TIPS have a fixed coupon rate, and the principal is adjusted based 
on changes in the CPI. Thus, TIPS are an example of capital-  indexed bonds. B 
is incorrect because with an interest-  index bond, it is the principal repayment 
at maturity that is fixed and the coupon that is linked to an index. C is incorrect 
because indexed-  annuity bonds are fully amortized bonds, not bullet bonds. The 
annuity payment (interest payment and principal repayment) is adjusted based 
on changes in an index.
B is correct. Following an increase in inflation, the coupon rate of a capital-  
indexed bond remains unchanged, but the principal amount is adjusted upward 
for inflation. Thus, the coupon payment, which is equal to the fixed coupon rate 
multiplied by the inflation-  adjusted principal amount, increases.
BONDS WITH CONTINGENCY PROVISIONS

A contingency refers to some future event or circumstance that is possible but not 
certain. A contingency provision  is a clause in a legal document that allows for some 
action if the event or circumstance does occur. For bonds, the term embedded option  
refers to various contingency provisions found in the indenture. These contingency 
provisions provide the issuer or the bondholders the right, but not the obligation, to 
take some action. These rights are called “options. ” These options are not independent 
of the bond and cannot be traded separately—hence the term “embedded. ” Some com -
mon types of bonds with embedded options include callable bonds, putable bonds, 
and convertible bonds. The options embedded in these bonds grant either the issuer 
or the bondholders certain rights affecting the disposal or redemption of the bond.5

Reading 50 ■ Fixed-  Income Securities: Defining Elements 330
5.1 Callable Bonds
The most widely used embedded option is the call provision. A callable bond  gives 
the issuer the right to redeem all or part of the bond before the specified maturity 
date. The primary reason why issuers choose to issue callable bonds rather than non-  
callable bonds is to protect themselves against a decline in interest rates. This decline 
can come either from market interest rates falling or from the issuer’s credit quality 
improving. If market interest rates fall or credit quality improves, the issuer of a callable 
bond has the right to replace an old, expensive bond issue with a new, cheaper bond 
issue. In other words, the issuer can benefit from a decline in interest rates by being 
able to refinance its debt at a lower interest rate. For example, assume that the market 
interest rate was 6% at the time of issuance and that a company issued a bond with a

coupon rate of 7%—the market interest rate plus a spread of 100 bps. Now assume that 
the market interest rate has fallen to 4% and that the company’s creditworthiness has 
not changed; it can still issue at the market interest rate plus 100 bps. If the original 
bond is callable, the company can redeem it and replace it with a new bond paying 
5% annually. If the original bond is non-  callable, the company must carry on paying 
7% annually and cannot benefit from the decline in market interest rates.
As illustrated in this example, callable bonds are advantageous to the issuer of 
the security. Put another way, the call option has value to the issuer . Callable bonds 
present investors with a higher level of reinvestment risk than non-  callable bonds; 
that is, if the bonds are called, bondholders have to reinvest funds in a lower interest 
rate environment. For this reason, callable bonds have to offer a higher yield and

sell at a lower price than otherwise similar non-  callable bonds. The higher yield and 
lower price compensate the bondholders for the value of the call option to the issuer.
Callable bonds have a long tradition and are commonly issued by corporate issuers. 
Although first issued in the US market, they are now frequently issued in every major 
bond market and in a variety of forms.
The details about the call provision are specified in the indenture. These details 
include the call price, which represents the price paid to bondholders when the bond 
is called. The call premium is the amount over par paid by the issuer if the bond is 
called. There may be restrictions on when the bond can be called, or the bond may 
have different call prices depending on when it is called. The call schedule specifies 
the dates and prices at which a bond may be called. Some callable bonds are issued 
with a call protection period, also called lockout period, cushion, or deferment period.

The call protection period prohibits the issuer from calling a bond early in its life and 
is often added as an incentive for investors to buy the bond. The earliest time that a 
bond might be called is known as the call date.
Make-  whole calls first appeared in the US corporate bond market in the mid-  1990s 
and have become more commonplace ever since. A typical make-  whole call requires 
the issuer to make a lump-  sum payment to the bondholders based on the present value 
of the future coupon payments and principal repayment not paid because of the bond 
being redeemed early. The discount rate used is usually some pre-  determined spread 
over the yield to maturity of an appropriate sovereign bond. The typical result is a 
redemption value that is significantly greater than the bond’s current market price. A 
make-  up call provision is less detrimental to bondholders than a regular call provision 
because it allows them to be compensated if the issuer calls the bond. Issuers, however,

rarely invoke this provision because redeeming a bond that includes a make-  whole 
provision before the maturity date is costly. Issuers tend to include a make-  whole 
provision as a “sweetener” to make the bond issue more attractive to potential buyers 
and allow them to pay a lower coupon rate.
Available exercise styles on callable bonds include the following:
■■American-  style call, sometimes referred to as continuously callable, for which 
the issuer has the right to call a bond at any time starting on the first call date.

Bonds with Contingency Provisions 331
■■European-  style call, for which the issuer has the right to call a bond only once 
on the call date.
■■Bermuda-  style  call, for which the issuer has the right to call bonds on specified 
dates following the call protection period. These dates frequently correspond to 
coupon payment dates.
EXAMPLE 7   
Assume a hypothetical 30-  year bond is issued on 15 August 2012 at a price of 
98.195 (as a percentage of par). Each bond has a par value of $1,000. The bond 
is callable in whole or in part every 15 August from 2022 at the option of the 
issuer. The call prices are shown below.
Y ear Call Price Y ear Call Price
2022 103.870 2028 101.548
2023 103.485 2029 101.161
2024 103.000 2030 100.774
2025 102.709 2031 100.387
2026 102.322 2032 and 
thereafter100.000
2027 101.955
1 The call protection period is:
A 10 years.
B 11 years.
C 20 years.
2 The call premium (per bond) in 2026 is closest  to:
A $2.32.
B $23.22.
C $45.14.
3 The call provision is most likely :
A a Bermuda call.

B a European call.
C an American call.
A is correct. The bonds were issued in 2012 and are first callable in 2022. The 
call protection period is 2022 – 2012 = 10 years.
B is correct. The call prices are stated as a percentage of par. The call price in 
2026 is $1,023.22 (102.322% × $1,000). The call premium is the amount paid 
above par by the issuer. The call premium in 2026 is $23.22 ($1,023.22 – $1,000).
A is correct. The bond is callable every 15 August from 2022—that is, on spec -
ified dates following the call protection period. Thus, the embedded option is 
a Bermuda call.

Reading 50 ■ Fixed-  Income Securities: Defining Elements 332
5.2 Putable Bonds
A put provision gives the bondholders the right to sell the bond back to the issuer 
at a pre-  determined price on specified dates. Putable bonds  are beneficial for the 
bondholder by guaranteeing a pre-  specified selling price at the redemption dates. If 
interest rates rise after the issue date, thus depressing the bond’s price, the bondholders 
can put the bond back to the issuer and get cash. This cash can be reinvested in bonds 
that offer higher yields, in line with the higher market interest rates.
Because a put provision has value to the bondholders , the price of a putable bond 
will be higher than the price of an otherwise similar bond issued without the put 
provision. Similarly, the yield on a bond with a put provision will be lower than the 
yield on an otherwise similar non-  putable bond. The lower yield compensates the 
issuer for the value of the put option to the investor.

The indenture lists the redemption dates and the prices applicable to the sale of 
the bond back to the issuer. The selling price is usually the par value of the bond. 
Depending on the terms set out in the indenture, putable bonds may allow buyers 
to force a sellback only once or multiple times during the bond’s life. Putable bonds 
that incorporate a single sellback opportunity include a European-  style put and are 
often referred to as one-  time put bonds. Putable bonds that allow multiple sellback 
opportunities include a Bermuda-  style put and are known as multiple put bonds. 
Multiple put bonds offer more flexibility for investors, so they are generally more 
expensive than one-  time put bonds.6 
Typically, putable bonds incorporate one- to five-  year put provisions. Their increas -
ing popularity has often been motivated by investors wanting to protect themselves 
against major declines in bond prices. One benefit of this rising popularity has been

an improvement in liquidity in some markets, because the put protection attracts 
more conservative classes of investors. The global financial crisis that started in 2008 
showed that these securities can often exacerbate liquidity problems, however, because 
they provide a first claim on the issuer’s assets. The put provision gives bondholders 
the opportunity to convert their claim into cash before other creditors.
5.3 Convertible Bonds
A convertible bond  is a hybrid security with both debt and equity features. It gives the 
bondholder the right to exchange the bond for a specified number of common shares 
in the issuing company. Thus, a convertible bond can be viewed as the combination of 
a straight bond (option-  free bond) plus an embedded equity call option. Convertible 
bonds can also include additional provisions, the most common being a call provision.
From the investor’s perspective, a convertible bond offers several advantages relative

to a non-  convertible bond. First, it gives the bondholder the ability to convert into 
equity in case of share price appreciation, and thus participate in the equity upside. At 
the same time, the bondholder receives downside protection; if the share price does 
not appreciate, the convertible bond offers the comfort of regular coupon payments 
and the promise of principal repayment at maturity. Even if the share price and thus 
the value of the equity call option decline, the price of a convertible bond cannot fall 
below the price of the straight bond. Consequently, the value of the straight bond acts 
as a floor for the price of the convertible bond.
Because the conversion provision is valuable to bondholders , the price of a con -
vertible bond is higher than the price of an otherwise similar bond without the con -
version provision. Similarly, the yield on a convertible bond is lower than the yield on

6 Although a bond could theoretically include an American-  type put, there is no such bond outstanding 
as of July 2014. The likely reason for the absence of continuously putable bonds is that issuers would not 
like to be surprised with having to raise cash to redeem the bonds at indeterminate times.

Bonds with Contingency Provisions 333
an otherwise similar non-  convertible bond. However, most convertible bonds offer 
investors a yield advantage; the coupon rate on the convertible bond is typically higher 
than the dividend yield on the underlying common share.
From the issuer’s perspective, convertible bonds offer two main advantages. The 
first is reduced interest expense. Issuers are usually able to offer below-  market coupon 
rates because of investors’ attraction to the conversion feature. The second advantage 
is the elimination of debt if the conversion option is exercised. But the conversion 
option is dilutive to existing shareholders.
Key terms regarding the conversion provision include the following:
■■The conversion price  is the price per share at which the convertible bond can 
be converted into shares.
■■The conversion ratio  is the number of common shares that each bond can be 
converted into. The indenture sometimes does not stipulate the conversion ratio

but only mentions the conversion price. The conversion ratio is equal to the par 
value divided by the conversion price. For example, if the par value is 1,000€ 
and the conversion price is 20€, the conversion ratio is 1,000€ ÷ 20€ = 50:1, or 
50 common shares per bond.
■■The conversion value , sometimes called the parity value, is the current share 
price multiplied by the conversion ratio. For example, if the current share price 
is 33€ and the conversion ratio is 30:1, the conversion value is 33€ × 30 = 990€.
■■The conversion premium is the difference between the convertible bond’s price 
and its conversion value. For example, if the convertible bond’s price is 1,020€ 
and the conversion value is 990€, the conversion premium is 1,020€ – 990€ = 
30€.
■■Conversion parity occurs if the conversion value is equal to the convertible 
bond’s price. Using the previous two examples, if the current share price is 34€ 
instead of 33€, then both the convertible bond’s price and the conversion value

are equal to 1,020€ (i.e., a conversion premium equal to 0). This condition is 
referred to as parity. If the common share is selling for less than 34€, the con -
dition is below parity. In contrast, if the common share is selling for more than 
34€, the condition is above parity.
Generally, convertible bonds have maturities of five to 10 years. First-  time or 
younger issuers are usually able to issue convertible bonds of up to three years in 
maturity only. Although it is common for convertible bonds to reach conversion 
parity before maturity, bondholders rarely exercise the conversion option before that 
time. Early conversion would eliminate the yield advantage of continuing to hold the 
convertible bond; investors would typically receive in dividends less than they would 
receive in coupon payments. For this reason, it is common to find convertible bonds 
that are also callable by the issuer on a set of specified dates. If the convertible bond

includes a call provision and the conversion value is above the current share price, 
the issuer may force the bondholders to convert their bonds into common shares 
before maturity. For this reason, callable convertible bonds have to offer a higher 
yield and sell at a lower price than otherwise similar non-  callable convertible bonds. 
Some indentures specify that the bonds can be called only if the share price exceeds 
a specified price, giving investors more predictability about the share price at which 
the issuer may force conversion.
Although somewhat similar in purpose to a conversion option, a warrant  is actu -
ally not an embedded option but rather an “attached” option. A warrant entitles the 
holder to buy the underlying stock of the issuing company at a fixed exercise price 
until the expiration date. Warrants are considered yield enhancements; they are fre -
quently attached to bond issues as a “sweetener. ” Warrants are actively traded in some

financial markets, such as the Deutsche Börse and the Hong Kong Stock Exchange.

Reading 50 ■ Fixed-  Income Securities: Defining Elements 334
Several European banks have been issuing a type of convertible bond called 
contingent convertible bonds. Contingent convertible bonds , nicknamed “CoCos, ” 
are bonds with contingent write-  down provisions. Two main features distinguish 
bonds with contingent write-  down provisions from the traditional convertible bonds 
just described. A traditional convertible bond is convertible at the option of the 
bondholder, and conversion occurs on the upside—that is, if the issuer’s share price 
increases. In contrast, bonds with contingent write-  down provisions are convertible 
on the downside. In the case of CoCos, conversion is automatic if a specified event 
occurs—for example, if the bank’s core Tier 1 capital ratio (a measure of the bank’s 
proportion of core equity capital available to absorb losses) falls below the minimum 
requirement set by the regulators. Thus, in the event that the bank experiences losses

that reduce its equity capital below the minimum requirement, CoCos are a way to 
reduce the bank’s likelihood of default and, therefore, systemic risk—that is, the risk 
of failure of the financial system. When the bank’s core Tier 1 capital falls below the 
minimum requirement, the CoCos immediately convert into equity, automatically 
recapitalizing the bank, lightening the debt burden, and reducing the risk of default. 
Because the conversion is not at the option of the bondholders but automatic, CoCos 
force bondholders to take losses. For this reason, CoCos must offer a higher yield than 
otherwise similar bonds.
Exhibit 8 shows the relative importance of plain vanilla (straight fixed-  rate), floating-  
rate, and equity-  related bonds to the total amount of international bonds outstanding. 
It indicates that the majority of bond issues are plain vanilla bonds.
Exhibit 8   Outstanding Bonds and Notes by Type of Interest Payment and 
Conversion Features at the End of March 2012

Type of BondAmount  
(US$ billions) Weight
Straight fixed-  rate issues 20,369.9 71.2%
Floating-  rate issues 7,749.6 27.1%
Equity-  related issues
  Convertibles 491.9 1.7%
  Warrants 2.3 0.0%
Total 28,613.7 100.0%
Source:  Based on data from the Bank of International Settlements, Table 13B, available at www.
bis.org/statistics/secstats.htm, (accessed 7 September 2012).
EXAMPLE 8   
1 Which of the following is not an example of an embedded option?
A Warrant
B Call provision
C Conversion provision
2 The type of bonds with an embedded option that would most likely  sell 
at a lower price than an otherwise similar bond without the embedded 
option is a:
A putable bond.
B callable bond.

Bonds with Contingency Provisions 335
C convertible bond.
3 The additional risk inherent to a callable bond is best described as:
B interest rate risk.
C reinvestment risk.
4 The put provision of a putable bond:
A limits the risk to the issuer.
B limits the risk to the bondholder.
C does not materially affect the risk of either the issuer or the 
bondholder.
5 Assume that a convertible bond issued in South Korea has a par value of 
₩1,000,000 and is currently priced at ₩1,100,000. The underlying share 
price is ₩40,000 and the conversion ratio is 25:1. The conversion condi -
tion for this bond is:
A parity.
B above parity.
C below parity.
A is correct. A warrant is a separate, tradable security that entitles the holder to 
buy the underlying common share of the issuing company. B and C are incorrect 
because the call provision and the conversion provision are embedded options.
B is correct. The call provision is an option that benefits the issuer. Because of

this, callable bonds sell at lower prices and higher yields relative to otherwise 
similar non-  callable bonds. A and C are incorrect because the put provision 
and the conversion provision are options that benefit the investor. Thus, putable 
bonds and convertible bonds sell at higher prices and lower yields relative to 
otherwise similar bonds that lack those provisions.
C is correct. Reinvestment risk refers to the effect that lower interest rates have 
on available rates of return when reinvesting the cash flows received from an 
earlier investment. Because bonds are typically called following a decline in 
market interest rates, reinvestment risk is particularly relevant for the holder 
of a callable bond. A is incorrect because credit risk refers to the risk of loss 
resulting from the issuer failing to make full and timely payments of interest 
and/or repayments of principal. B is incorrect because interest rate risk is the

risk that a change in market interest rate affects a bond’s value. Credit risk and 
interest rate risk are not inherent to callable bonds.
B is correct. A putable bond limits the risk to the bondholder by guaranteeing 
a pre-  specified selling price at the redemption dates.
C is correct. The conversion value of the bond is ₩40,000 × 25 = ₩1,000,000. 
The price of the convertible bond is ₩1,100,000. Thus, the conversion value of 
the bond is less than the bond’s price, and this condition is referred to as below 
parity.

Reading 50 ■ Fixed-  Income Securities: Defining Elements 336
SUMMARY
This reading provides an introduction to the salient features of fixed-  income securities 
while noting how these features vary among different types of securities. Important 
points include the following:
■■The three important elements that an investor needs to know when investing in 
a fixed-  income security are (1) the bond’s features, which determine its sched -
uled cash flows and thus the bondholder’s expected and actual return; (2) the 
legal, regulatory, and tax considerations that apply to the contractual agreement 
between the issuer and the bondholders; and (3) the contingency provisions 
that may affect the bond’s scheduled cash flows.
■■The basic features of a bond include the issuer, maturity, par value (or princi -
pal), coupon rate and frequency, and currency denomination.
■■Issuers of bonds include supranational organizations, sovereign governments,

non-  sovereign governments, quasi-  government entities, and corporate issuers.
■■Bondholders are exposed to credit risk and may use bond credit ratings to 
assess the credit quality of a bond.
■■A bond’s principal is the amount the issuer agrees to pay the bondholder when 
the bond matures.
■■The coupon rate is the interest rate that the issuer agrees to pay to the bond -
holder each year. The coupon rate can be a fixed rate or a floating rate. Bonds 
may offer annual, semi-  annual, quarterly, or monthly coupon payments depend -
ing on the type of bond and where the bond is issued.
■■Bonds can be issued in any currency. Bonds such as dual-  currency bonds and 
currency option bonds are connected to two currencies.
■■The yield to maturity is the discount rate that equates the present value of the 
bond’s future cash flows until maturity to its price. Yield to maturity can be con -
sidered an estimate of the market’s expectation for the bond’s return.

■■A plain vanilla bond has a known cash flow pattern. It has a fixed maturity date 
and pays a fixed rate of interest over the bond’s life.
■■The bond indenture or trust deed is the legal contract that describes the form 
of the bond, the issuer’s obligations, and the investor’s rights. The indenture is 
usually held by a financial institution called a trustee, which performs various 
duties specified in the indenture.
■■The issuer is identified in the indenture by its legal name and is obligated to 
make timely payments of interest and repayment of principal.
■■For asset-  backed securities, the legal obligation to repay bondholders often lies 
with a separate legal entity—that is, a bankruptcy-  remote vehicle that uses the 
assets as guarantees to back a bond issue.
■■How the issuer intends to service the debt and repay the principal should be 
described in the indenture. The source of repayment proceeds varies depending 
on the type of bond.

■■Collateral backing is a way to alleviate credit risk. Secured bonds are backed 
by assets or financial guarantees pledged to ensure debt payment. Examples of 
collateral-  backed bonds include collateral trust bonds, equipment trust certifi -
cates, mortgage-  backed securities, and covered bonds.

Summary 337
■■Credit enhancement can be internal or external. Examples of internal credit 
enhancement include subordination, overcollateralization, and reserve 
accounts. A bank guarantee, a surety bond, a letter of credit, and a cash collat -
eral account are examples of external credit enhancement.
■■Bond covenants are legally enforceable rules that borrowers and lenders agree 
on at the time of a new bond issue. Affirmative covenants enumerate what issu -
ers are required to do, whereas negative covenants enumerate what issuers are 
prohibited from doing.
■■An important consideration for investors is where the bonds are issued and 
traded, because it affects the laws, regulation, and tax status that apply. Bonds 
issued in a particular country in local currency are domestic bonds if they are 
issued by entities incorporated in the country and foreign bonds if they are 
issued by entities incorporated in another country. Eurobonds are issued inter -

nationally, outside the jurisdiction of any single country and are subject to a 
lower level of listing, disclosure, and regulatory requirements than domestic or 
foreign bonds. Global bonds are issued in the Eurobond market and at least one 
domestic market at the same time.
■■Although some bonds may offer special tax advantages, as a general rule, inter -
est is taxed at the ordinary income tax rate. Some countries also implement 
a capital gains tax. There may be specific tax provisions for bonds issued at a 
discount or bought at a premium.
■■An amortizing bond is a bond whose payment schedule requires periodic 
payment of interest and repayment of principal. This differs from a bullet bond, 
whose entire payment of principal occurs at maturity. The amortizing bond’s 
outstanding principal amount is reduced to zero by the maturity date for a fully 
amortized bond, but a balloon payment is required at maturity to retire the 
bond’s outstanding principal amount for a partially amortized bond.

■■Sinking fund agreements provide another approach to the periodic retirement 
of principal, in which an amount of the bond’s principal outstanding amount is 
usually repaid each year throughout the bond’s life or after a specified date.
■■A floating-  rate note or floater is a bond whose coupon is set based on some ref -
erence rate plus a spread. FRNs can be floored, capped, or collared. An inverse 
FRN is a bond whose coupon has an inverse relationship to the reference rate.
■■Other coupon payment structures include bonds with step-  up coupons, which 
pay coupons that increase by specified amounts on specified dates; bonds with 
credit-  linked coupons, which change when the issuer’s credit rating changes; 
bonds with payment-  in- kind coupons that allow the issuer to pay coupons 
with additional amounts of the bond issue rather than in cash; and bonds with 
deferred coupons, which pay no coupons in the early years following the issue 
but higher coupons thereafter.

■■The payment structures for index-  linked bonds vary considerably among coun -
tries. A common index-  linked bond is an inflation-  linked bond or linker whose 
coupon payments and/or principal repayments are linked to a price index. 
Index-  linked payment structures include zero-  coupon-  indexed bonds, interest-  
indexed bonds, capital-  indexed bonds, and indexed-  annuity bonds.
■■Common types of bonds with embedded options include callable bonds, 
putable bonds, and convertible bonds. These options are “embedded” in the 
sense that there are provisions provided in the indenture that grant either the 
issuer or the bondholder certain rights affecting the disposal or redemption of 
the bond. They are not separately traded securities.

Reading 50 ■ Fixed-  Income Securities: Defining Elements 338
■■Callable bonds give the issuer the right to buy bonds back prior to maturity, 
thereby raising the reinvestment risk for the bondholder. For this reason, call -
able bonds have to offer a higher yield and sell at a lower price than otherwise 
similar non-  callable bonds to compensate the bondholders for the value of the 
call option to the issuer.
■■Putable bonds give the bondholder the right to sell bonds back to the issuer 
prior to maturity. Putable bonds offer a lower yield and sell at a higher price 
than otherwise similar non-  putable bonds to compensate the issuer for the 
value of the put option to the bondholders.
■■A convertible bond gives the bondholder the right to convert the bond into 
common shares of the issuing company. Because this option favors the bond -
holder, convertible bonds offer a lower yield and sell at a higher price than 
otherwise similar non-  convertible bonds.

Practice Problems 339
1 A 10-  year bond was issued four years ago. The bond is denominated in US 
dollars, offers a coupon rate of 10% with interest paid semi-  annually, and is 
currently priced at 102% of par. The bond’s:
A tenor is six years.
B nominal rate is 5%.
C redemption value is 102% of the par value.
2 A sovereign bond has a maturity of 15 years. The bond is best described as a:
A perpetual bond.
B pure discount bond.
C capital market security.
3 A company has issued a floating-  rate note with a coupon rate equal to the 
three-  month Libor + 65 basis points. Interest payments are made quarterly on 
31 March, 30 June, 30 September, and 31 December. On 31 March and 30 June, 
the three-  month Libor is 1.55% and 1.35%, respectively. The coupon rate for the 
interest payment made on 30 June is:
A 2.00%.
B 2.10%.
C 2.20%.
4 The legal contract that describes the form of the bond, the obligations of the 
issuer, and the rights of the bondholders can be best described as a bond’s:

A covenant.
B indenture.
C debenture.
5 Which of the following is a type of external credit enhancement?
A Covenants
B A surety bond
C Overcollaterization
6 An affirmative covenant is most likely to stipulate:
A limits on the issuer’s leverage ratio.
B how the proceeds of the bond issue will be used.
C the maximum percentage of the issuer’s gross assets that can be sold.
7 Which of the following best describes a negative bond covenant? The issuer is:
A required to pay taxes as they come due.
B prohibited from investing in risky projects.
C required to maintain its current lines of business.
8 A South African company issues bonds denominated in pound sterling that are 
sold to investors in the United Kingdom. These bonds can be best described as:
A Eurobonds.
B global bonds.
C foreign bonds.
9 Relative to domestic and foreign bonds, Eurobonds are most likely  to be:

Reading 50 ■ Fixed-  Income Securities: Defining Elements 340
A bearer bonds.
B registered bonds.
C subject to greater regulation.
10 An investor in a country with an original issue discount tax provision purchases 
a 20-  year zero-  coupon bond at a deep discount to par value. The investor plans 
to hold the bond until the maturity date. The investor will most likely  report:
A a capital gain at maturity.
B a tax deduction in the year the bond is purchased.
C taxable income from the bond every year until maturity.
11 A bond that is characterized by a fixed periodic payment schedule that reduces 
the bond’s outstanding principal amount to zero by the maturity date is best 
described as a:
B plain vanilla bond.
C fully amortized bond.
12 If interest rates are expected to increase, the coupon payment structure most 
likely  to benefit the issuer is a:
A step-  up coupon.
B inflation-  linked coupon.
C cap in a floating-  rate note.

13 Investors who believe that interest rates will rise most likely  prefer to invest in:
A inverse floaters.
B fixed-  rate bonds.
C floating-  rate notes.
14 A 10-  year, capital-  indexed bond linked to the Consumer Price Index (CPI) is 
issued with a coupon rate of 6% and a par value of 1,000. The bond pays interest 
semi-  annually. During the first six months after the bond’s issuance, the CPI 
increases by 2%. On the first coupon payment date, the bond’s:
A coupon rate increases to 8%.
B coupon payment is equal to 40.
C principal amount increases to 1,020.
15 The provision that provides bondholders the right to sell the bond back to the 
issuer at a predetermined price prior to the bond’s maturity date is referred to 
as:
A a put provision.
B a make-  whole call provision.
C an original issue discount provision.
16 Which of the following provisions is a benefit to the issuer?
A Put provision

17 Relative to an otherwise similar option-  free bond, a:
A putable bond will trade at a higher price.
B callable bond will trade at a higher price.
C convertible bond will trade at a lower price.
18 Which type of bond most likely  earns interest on an implied basis?

Practice Problems 341
A Floater
B Conventional bond
C Pure discount bond
19 Clauses that specify the rights of the bondholders and any actions that the 
issuer is obligated to perform or is prohibited from performing are:
A covenants.
B collaterals. 
C credit enhancements.
20 Which of the following type of debt obligation most likely  protects bondholders 
when the assets serving as collateral are non-  performing?
A Covered bonds
B Collateral trust bonds
C Mortgage-  backed securities 
21 Which of the following best describes a negative bond covenant? The require -
ment to:
A insure and maintain assets.
B comply with all laws and regulations.
C maintain a minimum interest coverage ratio.
22 Relative to negative bond covenants, positive covenants are most likely :
A legally enforceable.
B cheaper for the issuers.
C enacted at the time of the bond issue.
23 A five-  year bond has the following cash flows:
£230.97 £230.97 £230.97 £230.97 £230.97
£1,000
 The bond can best be described as a:

24 Investors seeking some general protection against a poor economy are most 
likely  to select a:
A deferred coupon bond. 
B credit-  linked coupon bond.
C payment-  in- kind coupon bond.
25 The benefit to the issuer of a deferred coupon bond is most likely  related to:
A tax management. 
B cash flow management.
C original issue discount price.
26 Which of the following bond types provides the most benefit to a bondholder 
when bond prices are declining?
A Callable
B Plain vanilla
C Multiple put

Reading 50 ■ Fixed-  Income Securities: Defining Elements 342
27 Which type of call bond option offers the greatest  flexibility as to when the 
issuer can exercise the option?
A A Bermuda call
B A European call
C An American call
28 Which of the following best describes a convertible bond’s conversion 
premium? 
A Bond price minus conversion value 
B Par value divided by conversion price
C Current share price multiplied by conversion ratio

Solutions 343
SOLUTIONS
1 A is correct. The tenor of the bond is the time remaining until the bond’s matu -
rity date. Although the bond had a maturity of 10 years at issuance (original 
maturity), it was issued four years ago. Thus, there are six years remaining until 
the maturity date.
 B is incorrect because the nominal rate is the coupon rate, i.e., the interest rate 
that the issuer agrees to pay each year until the maturity date. Although interest 
is paid semi-  annually, the nominal rate is 10%, not 5%. C is incorrect because 
it is the bond’s price, not its redemption value (also called principal amount, 
principal value, par value, face value, nominal value, or maturity value), that is 
equal to 102% of the par value.
2 C is correct. A capital market security has an original maturity longer than one 
year.
 A is incorrect because a perpetual bond does not have a stated maturity date. 
Thus, the sovereign bond, which has a maturity of 15 years, cannot be a perpet -

ual bond. B is incorrect because a pure discount bond is a bond issued at a dis -
count to par value and redeemed at par. Some sovereign bonds (e.g., Treasury 
bills) are pure discount bonds, but others are not.
3 C is correct. The coupon rate that applies to the interest payment due on 30 
June is based on the three-  month Libor rate prevailing on 31 March. Thus, the 
coupon rate is 1.55% + 0.65% = 2.20%.
4 B is correct. The indenture, also referred to as trust deed, is the legal contract 
that describes the form of the bond, the obligations of the issuer, and the rights 
of the bondholders.
 A is incorrect because covenants are only one element of a bond’s indenture. 
Covenants are clauses that specify the rights of the bondholders and any actions 
that the issuer is obligated to perform or prohibited from performing. C is 
incorrect because a debenture is a type of bond. 
5 B is correct. A surety bond is an external credit enhancement, i.e., a guarantee

received from a third party. If the issuer defaults, the guarantor who provided 
the surety bond will reimburse investors for any losses, usually up to a maxi -
mum amount called the penal sum.
 A is incorrect because covenants are legally enforceable rules that borrowers 
and lenders agree upon when the bond is issued. C is incorrect because over -
collateralization is an internal, not external, credit enhancement. Collateral is 
a guarantee underlying the debt above and beyond the issuer’s promise to pay, 
and overcollateralization refers to the process of posting more collateral than 
is needed to obtain or secure financing. Collateral, such as assets or securities 
pledged to ensure debt payments, is not provided by a third party. Thus, over -
collateralization is not an external credit enhancement.
6 B is correct. Affirmative (or positive) covenants enumerate what issuers are 
required to do and are typically administrative in nature. A common affirmative

covenant describes what the issuer intends to do with the proceeds from the 
 A and C are incorrect because imposing a limit on the issuer’s leverage ratio 
or on the percentage of the issuer’s gross assets that can be sold are negative 
covenants. Negative covenants prevent the issuer from taking actions that could 
reduce its ability to make interest payments and repay the principal.

Reading 50 ■ Fixed-  Income Securities: Defining Elements 344
7 B is correct. Prohibiting the issuer from investing in risky projects restricts the 
issuer’s potential business decisions. These restrictions are referred to as nega -
tive bond covenants.
 A and C are incorrect because paying taxes as they come due and maintaining 
the current lines of business are positive covenants.
8 C is correct. Bonds sold in a country and denominated in that country’s cur -
rency by an entity from another country are referred to as foreign bonds.
 A is incorrect because Eurobonds are bonds issued outside the jurisdiction of 
any single country. B is incorrect because global bonds are bonds issued in the 
Eurobond market and at least one domestic country simultaneously.
9 A is correct. Eurobonds are typically issued as bearer bonds, i.e., bonds for 
which the trustee does not keep records of ownership. In contrast, domes -
tic and foreign bonds are typically registered bonds for which ownership is

recorded by either name or serial number.
 B is incorrect because Eurobonds are typically issued as bearer bonds, not reg -
istered bonds. C is incorrect because Eurobonds are typically subject to lower, 
not greater, regulation than domestic and foreign bonds.
10 C is correct. The original issue discount tax provision requires the investor to 
every tax year until maturity. The original issue discount is equal to the differ -
ence between the bond’s par value and its original issue price.
 A is incorrect because the original issue discount tax provision allows the 
he faces no capital gain or loss. B is incorrect because the original issue dis -
count tax provision does not require any tax deduction in the year the bond is 
purchased or afterwards.
11 C is correct. A fully amortized bond calls for equal cash payments by the bond’s

issuer prior to maturity. Each fixed payment includes both an interest payment 
component and a principal repayment component such that the bond’s out -
standing principal amount is reduced to zero by the maturity date.
 A and B are incorrect because a bullet bond or plain vanilla bond only make 
interest payments prior to maturity. The entire principal repayment occurs at 
maturity.
12 C is correct. A cap in a floating-  rate note (capped FRN) prevents the coupon 
rate from increasing above a specified maximum rate. This feature benefits the 
issuer in a rising interest rate environment because it sets a limit to the interest 
rate paid on the debt.
 A is incorrect because a bond with a step-  up coupon is one in which the cou -
pon, which may be fixed or floating, increases by specified margins at specified 
dates. This feature benefits the bondholders, not the issuer, in a rising interest 
rate environment because it allows bondholders to receive a higher coupon in

line with the higher market interest rates. B is incorrect because inflation-  linked 
bonds have their coupon payments and/or principal repayment linked to an 
index of consumer prices. If interest rates increase as a result of inflation, this 
feature is a benefit for the bondholders, not the issuer.
13 C is correct. In contrast to fixed-  rate bonds that decline in value in a rising 
interest rate environment, floating-  rate notes (FRNs) are less affected when 
interest rates increase because their coupon rates vary with market interest 
rates and are reset at regular, short-  term intervals. Consequently, FRNs are 
favored by investors who believe that interest rates will rise.

Solutions 345
 A is incorrect because an inverse floater is a bond whose coupon rate has 
an inverse relationship to the reference rate, so when interest rates rise, the 
coupon rate on an inverse floater decreases. Thus, inverse floaters are favored 
by investors who believe that interest rates will decline, not rise. B is incorrect 
because fixed rate-  bonds decline in value in a rising interest rate environment. 
Consequently, investors who expect interest rates to rise will likely avoid invest -
ing in fixed-  rate bonds.
14 C is correct. Capital-  indexed bonds pay a fixed coupon rate that is applied to 
a principal amount that increases in line with increases in the index during 
the bond’s life. If the consumer price index increases by 2%, the coupon rate 
remains unchanged at 6%, but the principal amount increases by 2% and the 
coupon payment is based on the inflation-  adjusted principal amount. On the 
first coupon payment date, the inflation-  adjusted principal amount is 1,000 ×

(1 + 0.02) = 1,020 and the semi-  annual coupon payment is equal to (0.06 × 
1,020) ÷ 2 = 30.60.
15 A is correct. A put provision provides bondholders the right to sell the bond 
back to the issuer at a predetermined price prior to the bond’s maturity date.
 B is incorrect because a make-  whole call provision is a form of call provision; 
i.e., a provision that provides the issuer the right to redeem all or part of the 
bond before its maturity date. A make-  whole call provision requires the issuer 
to make a lump sum payment to the bondholders based on the present value 
of the future coupon payments and principal repayments not paid because of 
the bond being redeemed early by the issuer. C is incorrect because an original 
issue discount provision is a tax provision relating to bonds issued at a discount 
to par value. The original issue discount tax provision typically requires the 
bondholders to include a prorated portion of the original issue discount (i.e.,

the difference between the par value and the original issue price) in their tax -
able income every tax year until the bond’s maturity date.
16 B is correct. A call provision (callable bond) gives the issuer the right to redeem 
all or part of the bond before the specified maturity date. If market interest 
rates decline or the issuer’s credit quality improves, the issuer of a callable bond 
can redeem it and replace it by a cheaper bond. Thus, the call provision is bene -
ficial to the issuer.
 A is incorrect because a put provision (putable bond) is beneficial to the bond -
holders. If interest rates rise, thus lowering the bond’s price, the bondholders 
have the right to sell the bond back to the issuer at a predetermined price on 
specified dates. C is incorrect because a conversion provision (convertible 
bond) is beneficial to the bondholders. If the issuing company’s share price 
increases, the bondholders have the right to exchange the bond for a specified

number of common shares in the issuing company.
17 A is correct. A put feature is beneficial to the bondholders. Thus, the price of a 
putable bond will typically be higher than the price of an otherwise similar non-  
putable bond.
 B is incorrect because a call feature is beneficial to the issuer. Thus, the price of 
a callable bond will typically be lower, not higher, than the price of an otherwise 
similar non-  callable bond. C is incorrect because a conversion feature is bene -
ficial to the bondholders. Thus, the price of a convertible bond will typically be 
higher, not lower, than the price of an otherwise similar non-  convertible bond.
18 C is correct. A zero-  coupon, or pure discount, bond pays no interest; instead, it 
is issued at a discount to par value and redeemed at par. As a result, the inter -
est earned is implied and equal to the difference between the par value and the 

Reading 50 ■ Fixed-  Income Securities: Defining Elements 346
19 A is correct. Covenants specify the rights of the bondholders and any actions 
that the issuer is obligated to perform or is prohibited from performing. 
20 A is correct. A covered bond is a debt obligation backed by a segregated pool of 
assets called a “cover pool. ” When the assets that are included in the cover pool 
become non-  performing (i.e., the assets are not generating the promised cash 
flows), the issuer must replace them with performing assets. 
21 C is correct. Negative covenants enumerate what issuers are prohibited from 
doing. Restrictions on debt, including maintaining a minimum interest cov -
erage ratio or a maximum debt usage ratio, are typical examples of negative 
covenants. 
22 B is correct. Positive (or affirmative) covenants are typically administrative in 
nature and do not impose additional costs on the issuer, whereas negative cove -
nants are frequently costly.

23 B is correct. A bond that is fully amortized is characterized by a fixed periodic 
payment schedule that reduces the bond’s outstanding principal amount to zero 
by the maturity date. The stream of £230.97 payments reflects the cash flows of 
a fully amortized bond with a coupon rate of 5% and annual interest payments.
24 B is correct. A credit-  linked coupon bond has a coupon that changes when the 
bond’s credit rating changes. Because credit ratings tend to decline the most 
during recessions, credit-  linked coupon bonds may thus provide some general 
protection against a poor economy by offering increased coupon payments 
when credit ratings decline.
25 B is correct. Deferred coupon bonds pay no coupon for their first few years but 
then pay higher coupons than they otherwise normally would for the remainder 
of their life. Deferred coupon bonds are common in project financing when the 
assets being developed may not generate any income during the development

phase, thus not providing cash flows to make interest payments. A deferred 
coupon bond allows the issuer to delay interest payments until the project is 
completed and the cash flows generated by the assets can be used to service the 
debt.
26 C is correct. A putable bond is beneficial for the bondholder by guaranteeing a 
prespecified selling price at the redemption date, thus offering protection when 
interest rates rise and bond prices decline. Relative to a one-  time put bond that 
incorporates a single sellback opportunity, a multiple put bond offers more fre -
quent sellback opportunities, thus providing the most benefit to bondholders. 
27 C is correct. An American call option gives the issuer the right to call the bond 
at any time starting on the first call date.
28 A is correct. The conversion premium is the difference between the convertible 
bond’s price and its conversion value.

Fixed-  Income Markets: Issuance, 
Trading, and Funding
by Moorad Choudhry, PhD, FRM, FCSI, Steven V . Mann, PhD, and 
Lavone F. Whitmer, CFA
Moorad Choudhry, PhD, FRM, FCSI, is at the University of Kent (United Kingdom). Steven 
V. Mann, PhD, is at the University of South Carolina (USA). Lavone F. Whitmer, CFA, is at 
Federal Home Loan Bank of Indianapolis (USA).
a. describe classifications of global fixed-  income markets;
b. describe the use of interbank offered rates as reference rates in 
floating-  rate debt;
c. describe mechanisms available for issuing bonds in primary 
markets;
d. describe secondary markets for bonds;
e. describe securities issued by sovereign governments; 
f. describe securities issued by non-  sovereign governments, quasi-  
government entities, and supranational agencies;
g. describe types of debt issued by corporations;
h. describe structured financial instruments;

i. describe short-  term funding alternatives available to banks;
j. describe repurchase agreements (repos) and the risks associated 
with them.
Global fixed-  income markets represent the largest subset of financial markets in terms 
of number of issuances and market capitalization. These markets bring borrowers and 
lenders together to allocate capital globally to its most efficient uses. Fixed-  income 
markets include not only publicly traded securities, such as commercial paper, notes, 
and bonds, but also non-  publicly traded loans. At the end of 2010, the total amount of 1READING
51

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 348
debt and equity outstanding was about $212 trillion globally.1 The global fixed-  income 
market represented approximately 75% of this total; simply put, global debt markets 
are three times larger than global equity markets.
Understanding how fixed-  income markets are structured and how they operate is 
important for debt issuers and investors. Debt issuers have financing needs that must 
be met. For example, a government may need to finance an infrastructure project, a 
new hospital, or a new school. A company may require funds to expand its business. 
Financial institutions also have funding needs, and they are among the largest issuers 
of fixed-  income securities. Fixed income is an important asset class for both individual 
and institutional investors. Thus, investors need to understand the characteristics of 
fixed-  income securities including how these securities are issued and traded.

■■What are the key bond market sectors?
■■How are bonds sold in primary markets and traded in secondary markets?
■■What types of bonds are issued by governments, government-  related entities, 
financial companies, and non-  financial companies?
■■What additional sources of funds are available to banks?
The remainder of this reading is organized as follows. Section 2 presents an overview 
of global fixed-  income markets and how these markets are classified, including some 
descriptive statistics on the size of the different bond market sectors. Section 2 also 
identifies the major issuers of and investors in fixed-  income securities and presents 
fixed-  income indexes. Section 3 discusses how fixed-  income securities are issued in 
primary markets, and how these securities are then traded in secondary markets. 
Sections 4 to 7 examine different bond market sectors. Section 8 discusses additional

short-  term funding alternatives available to banks, including repurchase agreements. 
Section 9 concludes and summarizes the reading.
OVERVIEW OF GLOBAL FIXED-  INCOME MARKETS
Although there is no standard classification of fixed-  income markets, many investors 
and market participants use criteria to structure fixed-  income markets and identify 
bond market sectors. This section starts by describing the most widely used ways of 
classifying fixed-  income markets.
2.1 Classification of Fixed-  Income Markets
Common criteria used to classify fixed-  income markets include the type of issuer; 
the bonds’ credit quality, maturity, currency denomination, and type of coupon; and 
where the bonds are issued and traded.
2.1.1  Classification by Type of Issuer
One way of classifying fixed-  income markets is by type of issuer, which usually leads 
to the identification of three bond market sectors: the government and government-

related sector, the corporate sector, and the structured finance sector. The government 2
1 Charles Roxburgh, Susan Lund, and John Piotowski, “Mapping Global Capital Markets, ” McKinsey & 
Company (2011). The $212 trillion amount is based on a sample of 79 countries and includes the market 
capitalization of stock markets; the principal amount outstanding of bonds issued by governments, financial, 
and non-  financial companies; securitized debt instruments; and the book value of the loans held on the 
balance sheets of banks and other financial institutions.

Overview of Global Fixed-  Income Markets 349
and government-  related sector includes the bonds issued by supranational (interna -
tional) organizations, such as the World Bank; sovereign (national) governments; 
non-  sovereign (local) governments, such as provinces, regions, states, or cities; and 
quasi-  government entities that are either owned or sponsored by governments, such 
as rail services or utilities in many countries. The corporate sector refers to the bonds 
issued by financial and non-  financial companies. The structured finance sector includes 
bonds created by securitization, a process that transforms private transactions between 
borrowers and lenders into securities traded in public markets. 
Exhibit 1 presents data on global capital markets at the end of December 2010. 
As mentioned in the introduction, the combined sectors of the global debt markets 
are three times larger than the global equity markets. Exhibit 1 also indicates that

the largest issuers of bonds are governments and financial institutions. However, the 
last column shows that in the immediate aftermath of the global financial crisis that 
started in 2008, the amount of bonds issued by governments increased, whereas the 
amount of bonds issued by financial institutions decreased. In addition, the last two 
columns of Exhibit 1 show that the sector that grew the fastest between 1990 and 2009 
was securitized debt instruments, but it was also the sector that shrank the most after 
2008. Securitized debt instruments, also called asset-  backed securities, are created 
by securitization. Securitization involves transferring ownership of assets from the 
original owners into a special legal entity. The special legal entity then issues securities 
backed by the assets, and the assets’ cash flows are used to pay interest and repay the 
principal owed to the holders of the securities. Assets that are typically used to create

securitized debt instruments include loans (such as mortgage loans) and receivables 
(such as credit card receivables). Securitized debt instruments are not discussed in 
this reading but rather in the reading on asset-  backed securities.
The last row is a reminder that although the focus of many market participants 
and this reading is on publicly traded securities, bank loans remain an important 
component of global capital markets. In many countries, bank loans are the primary 
source of capital, particularly for small and medium-  size companies.
Exhibit 1   Global Debt and Equity Outstanding by Sector at the End of 
December 2010
SectorAmount  
(US$ trillions) WeightCompound 
Annual  
Growth Rate  
1990–2009Annual  
2009–2010
Stock markets $54 26% 7.2% 5.6%
Bonds issued by 
governments41 19 7.8 11.9
Bonds issued by financial 
companies42 20 9.5 –3.3
Bonds issued by nonfinan -
cial companies10 5 6.7 9.7
Securitized debt instruments 15 7 12.7 –5.6
Bank loans 49 23 4.1 5.9

Notes : Data include 79 countries. The amounts reflect the market capitalization of stock markets; 
the principal amount outstanding of bonds issued by governments, financial, and non-  financial 
companies; securitized debt instruments; and the book value of the loans held on the balance sheets 
of banks and other financial institutions.
Source:  Data from Exhibit E1 in Charles Roxburgh, Susan Lund, and John Piotowski, “Mapping 
Global Capital Markets, ” McKinsey & Company (2011):4.

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 350
Exhibit 2 shows the amounts of debt and equity outstanding and the total cap -
ital as a percentage of GDP for various countries and economic areas at the end of 
December 2010. It indicates that financial markets relative to GDP are much smaller 
in emerging countries than in developed countries. Debt and equity capital represent 
more than 400% of GDP in the United States, Japan, and Western Europe, versus less 
than 200% in Central and Eastern Europe (CEE), the Commonwealth of Independent 
States (CIS), Latin America, and the Middle East and Africa. 
Exhibit 2   Global Debt and Equity Outstanding for Various Countries and Economic Areas at the End of 
December 2010 (US$ trillions)
Economic 
AreaBank 
LoansSecuritized 
Debt 
InstrumentsBonds 
Issued by 
Nonfinancial 
CompaniesBonds 
Issued by 
Financial 
Issued by 
GovernmentsStock 
MarketsTotal 
Capital as a 
GDP
United States $44 $77 $31 $116 $75 $119 462%

GDP
Japan 106 10 18 31 220 72 457
Western 
Europe110 15 19 115 72 69 400
Other 
Developed91 29 20 47 49 152 388
China 127 2 10 16 28 97 280
India 60 4 1 7 44 93 209
Middle East 
and Africa66 2 5 6 15 96 190
Other Asia 54 1 10 7 34 62 168
Latin 
America27 3 3 20 38 57 148
CEE and CIS 62 0 2 6 24 48 142
Note : CEE and CIS stand for Central and Eastern Europe and Commonwealth of Independent States, respectively.
Source:  Data are from Exhibit E2 in Charles Roxburgh, Susan Lund, and John Piotowski, “Mapping Global Capital Markets, ” McKinsey & 
Company (2011):8.
2.1.2  Classification by Credit Quality
Investors who hold bonds are exposed to credit risk, which is the risk of loss resulting 
from the issuer failing to make full and timely payments of interest and/or principal. 
Bond markets can be classified based on the issuer’s creditworthiness as judged by credit 
rating agencies. Ratings of Baa3 or above by Moody’s Investors Service or BBB– or

above by Standard & Poor’s (S&P) and Fitch Ratings are considered investment grade. 
In contrast, ratings below these levels are referred to as non-  investment grade, high 
yield, speculative, or “junk. ” An important point to understand is that credit ratings 
are an assessment of the issuer’s creditworthiness at a certain point in time; they are 
not a recommendation to buy or sell the issuer’s securities. In addition, credit ratings 
are not static; they will change if a credit rating agency perceives that the probability 
of default for an issuer has changed.
One of the reasons why the distinction between investment-  grade and high-  yield 
bond markets matters is because institutional investors may be prohibited from 
investing in, or restricted in their exposure to, lower-  quality or lower-  rated securities. 
Prohibition or restriction in high-  yield bond holdings generally arise because of a more

restrictive risk–reward profile that forms part of the investor’s investment objectives 
and constraints. For example, regulated banks and life insurance companies are usually

Overview of Global Fixed-  Income Markets 351
limited to investing in very highly rated securities. In contrast, the sovereign wealth 
funds of both Qatar and Kuwait have no formal restrictions on what type of assets 
they can hold or on the percentage split between bond market sectors. Globally, 
investment-  grade bond markets tend to be more liquid than high-  yield bond markets.
2.1.3  Classification by Maturity
Fixed-  income securities can also be classified by the original maturity of the bonds 
when they are issued. Securities that are issued with a maturity at issuance (original 
maturity) ranging from overnight to one year are money market securities. Some 
of these securities are issued by sovereign governments, such as Treasury bills. The 
corporate sector also issues fixed-  income securities with short maturities. Examples 
include commercial paper and negotiable certificates of deposit, which are discussed

in Sections 6.2 and 7.2.3, respectively. In contrast, capital market securities are secu -
rities that are issued with an original maturity longer than one year.
2.1.4  Classification by Currency Denomination
One of the critical ways to distinguish among fixed-  income securities is by currency 
denomination. The currency denomination of the bond’s cash flows influences which 
interest rates affect a bond’s price. For example, if a bond is denominated in yen, 
its price will be primarily driven by the credit quality of the issuer and by Japanese 
Exhibit  3 presents data on the currency denomination of international bonds, 
which are bonds issued by entities outside their home market, either in their domestic 
currency or in a foreign currency. It shows that approximately 79% of international 
bonds are denominated either in Euros or in US dollars.
Exhibit 3   Amounts of International Bonds Outstanding 
by Currency Denomination at the End of 
December 2011
CurrencyAmount

CurrencyAmount  
Euro (EUR) $9,665.9 46.0%
US Dollar (USD) 6,900.8 32.9
British Pound Sterling (GBP) 2,052.3 9.8
Japanese Yen (JPY) 762.0 3.6
Swiss Franc (CHF) 393.4 1.9
Australian Dollar (AUD) 317.2 1.5
Canadian Dollar (CAD) 313.1 1.5
Swedish Krona (SEK) 103.0 0.5
Norwegian Krone (NOK) 86.4 0.4
Hong Kong Dollar (HKD) 63.5 0.3
Yuan Renminbi (CNY) 38.9 0.2
Other Currencies 305.0 1.5
Total 21,001.5 100.0%
Source:  Based on data from Bank of International Settlements, Tables 
13A and 13B, available at www.bis.org/statistics/secstats.htm (accessed 12 
December 2012).

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 352
2.1.5  Classification by Type of Coupon
Another way of classifying fixed-  income markets is by type of coupon. Some bonds pay 
a fixed rate of interest; others, called floating-  rate bonds, floating-  rate notes (FRNs) 
or floaters, pay a rate of interest that adjusts to market interest rates at regular, short-  
term intervals (e.g., quarterly).
2.1.5.1  Demand and Supply of Fixed-  Rate vs. Floating-  Rate Debt  Balance sheet risk 
management considerations explain much of the demand and supply of floating-  rate 
debt. For instance, the funding of banks—that is, the money banks raise to make loans 
to companies and individuals—is often short term and issued at rates that change or 
reset frequently. When there is a mismatch between the interest paid on the liabilities 
(money the bank borrowed) and the interest received on the assets (money the bank lent

or invested), banks are exposed to interest rate risk—that is, the risk associated with a 
change in interest rate. In an effort to limit the volatility of their net worth resulting from 
interest rate risk, banks that issue floating-  rate debt often prefer to make floating-  rate 
loans and invest in floating-  rate bonds or in other adjustable-  rate assets. In addition 
to institutions with short-  term funding needs, demand for floating-  rate bonds comes 
from investors who believe that interest rates will rise. In that case, investors will benefit 
from holding floating-  rate investments compared with fixed-  rate ones.
On the supply side, issuance of floating-  rate debt comes from institutions needing 
to finance short-  term loans, such as consumer finance companies. Corporate borrowers 
also view floating-  rate bonds as an alternative to using bank liquidity facilities (e.g., 
lines of credit), particularly when they are a lower cost option, and as an alternative

to borrowing long-  term at fixed rates when they expect interest rates will fall.
2.1.5.2  Reference Rates  The coupon rate of a floating rate bond is typically expressed 
as a reference rate plus a spread or margin. The spread is usually set when the bond 
is issued and remains constant until maturity. It is primarily a function of the issuer’s 
credit risk at issuance: the lower the issuer’s credit quality (the higher its credit risk), 
the higher the spread. The reference rate, however, resets periodically. Therefore, the 
coupon rate adjusts to the level of market interest rates each time the reference rate is 
reset. The choice of the reference rate is critical because the reference rate is the primary 
driver of a bond’s coupon rate. Thus, the issuer’s cost of financing and the investor’s 
return from investing in the bonds depend on the reference rate.
Different reference rates are used depending on where the bonds are issued and

their currency denomination. The London interbank offered rate (Libor)  is the ref -
erence rate for many floating-  rate bonds, in particular those issued in the Eurobond 
market. For example, a typical coupon rate for a floater denominated in British sterling 
that pays coupons semi-  annually is the sterling six-  month Libor plus a spread. The 
coupon rate that is paid at the end of a six-  month period is set based on the sterling 
six- month Libor at the beginning of the period, and it remains constant throughout 
the six months. Every six months, the coupon rate is reset in line with the sterling 
six- month Libor prevailing on the reset date. For floating-  rate bonds denominated 
in US dollars, the reference rate is usually the US dollar Libor—the US dollar three-  
month Libor if the coupons are paid quarterly or the US dollar 12-  month Libor if the 
coupons are paid annually.
As illustrated in these examples, “Libor” is a collective name for multiple rates.

Libor rates reflect the rates at which a panel of banks believe they could borrow unse -
cured funds from other banks in the London interbank money market for different 
currencies and different borrowing periods ranging from overnight to one year—the 
interbank money market  or interbank market  is the market of loans and deposits 
between banks for maturities up to one year. The sidebar describes how the Libor 
rates are determined and identifies some of the issues associated with Libor.

Overview of Global Fixed-  Income Markets 353
Administration of Libor
As of the time of this writing in late 2012, the process by which Libor rates are set is in 
transition. Historically, Libor rates were set by the British Bankers’ Association (BBA). Every 
business day, a select group of 18 banks would submit to the BBA the rates at which 
they believed they could borrow from other banks in the London interbank market for 
10 currencies and 15 borrowing periods.2 The submitted rates would be ranked from 
highest to lowest, and the upper and lower four submissions would be discarded. The 
arithmetic mean of the remaining 10 rates became the Libor rates for a particular com -
bination of currency and maturity. The 150 Libor rates would then be communicated to 
market participants for use as reference rates in many different types of debt, including 
floating-  rate bonds.
One of the advantages of Libor has been its prevalence of use. The shortcoming of

Libor as historically set was that Libor rates were not based on readily observable market 
rates but on banks’ own estimates of their borrowing rates. Because the rates at which 
a bank can borrow money are an indication of its credit risk, banks had an incentive to 
understate their reported borrowing rates. A scandal emerged in 2012 as it was recognized 
that, at times, Libor rates drifted away from the underlying reality. How the Libor rates 
are set will certainly evolve going forward. In September 2012, the Financial Services 
Authority (FSA), at that time the regulator of all the providers of financial services in the 
United Kingdom, announced that the BBA would be relieved of oversight of Libor.3 It is 
also possible that over time, market rates may emerge as an alternative way of setting 
Libor and other reference rates.
Although there are Libor rates for currencies such as the euro and the yen, 
alternative interbank offered rates may be used for floating-  rate debt issued in these

currencies, such as the Euro interbank offered rate (Euribor) and the Tokyo interbank 
offered rate (Tibor), respectively. Similar sets of interbank offered rates exist in other 
markets, for instance, the Singapore interbank offered rate (Sibor), the Hong Kong 
interbank offered rate (Hibor), the Mumbai interbank offered rate (Mibor), or the 
Korea interbank offered rate (Koribor) for floating-  rate debt issued in Singapore dollar, 
Hong Kong dollar, Indian rupee, or the Korean won, respectively. All these different 
interbank offered rates are sets of rates for borrowing periods of various maturities 
of up to one year. The processes to determine them are similar, except that the sets 
of banks and organizations fixing the daily rates are different.
The use of these interbank offered rates extends beyond setting coupon rates for 
floating-  rate debt. These rates are also used as reference rates for other debt instru -

ments including mortgages, derivatives such as interest rate and currency swaps, and 
many other financial contracts and products. As of November 2012, it is estimated 
that nearly $300 trillion of financial instruments are tied to Libor.
2 The question asked is, “ At what rate could you borrow funds, were you to do so by asking for and then 
accepting interbank offers in a reasonable market size just prior to 11am?” Since Libor was established 
in 1986, the number of currencies has increased from three to 10, and the number of periods has also 
increased from 12 to 15, resulting in 150 rates as of 2012. But the number of rates is likely to go down in 
2013 with the elimination of some of the currencies and maturities.
3 In 2013, the Financial Services Authority (FSA) was replaced by two new regulatory authorities, the 
Prudential Regulation Authority (PRA), responsible for the prudential regulation and supervision of

the banking system, and the Financial Conduct Authority (FCA), the regulator for all other providers of 
financial services.

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 354
2.1.6  Classification by Geography
A distinction is very often made between the domestic bond, foreign bond, and 
Eurobond markets. Bonds issued in a specific country, denominated in the currency 
of that country, and sold in that country are classified as domestic bonds if they are 
issued by an issuer domiciled in that country and foreign bonds if they are issued by 
an issuer domiciled in another country. Domestic and foreign bonds are subject to 
the legal, regulatory, and tax requirements that apply in that particular country. In 
contrast, a Eurobond is issued internationally, outside the jurisdiction of the country 
in whose currency the bond is denominated. The Eurobond market has traditionally 
been characterized by less reporting, regulatory and tax constraints than domestic 
and foreign bond markets. These fewer constraints explain why approximately 80%

of entities that issue bonds outside their country of origin choose to do so in the 
Eurobond market rather than in a foreign bond market. In addition, Eurobonds are 
attractive for issuers because it gives them the ability to reach out to more investors 
globally. Access to a wider pool of investors often allows issuers to raise more capital 
and usually at a lower cost.
Exhibit 4 presents data on the residence of issuers and a breakdown of the amount 
of bonds outstanding between the government, financial, and non-  financial sectors. 
It shows that 59% of issuers are located in the United States and Japan, and that the 
residents of 10 countries account for 90% of the global bond markets. Exhibit 4 also 
indicates that the split between the three sectors varies among countries. For example, 
the government sector represents 74% of the amount of bonds outstanding in Japan, 
but non-  financial corporate issuers only account for 7% of the $15.7 trillion of bonds

outstanding. In contrast, the corporate sector is the largest sector in countries such 
as the Netherlands, Spain, the United Kingdom, or the United States, although the 
majority of bonds are issued by financial rather than non-  financial companies.
Exhibit 4   Amount of Bonds Outstanding by Residence of Issuer and Type of Issuer at the End of 
December 2011 (US$ billions)
CountryAll Issuers Government Financial Non-  Financial
AmountGlobal 
Weight AmountSector 
Weight
United States $33,582 40% $12,954 39% $14,938 44% $5,690 17%
Japan 15,700 19 11,552 74 3,111 20 1,038 7
United Kingdom 5,275 6 2,040 39 2,537 48 699 13
Germany 4,383 5 2,079 47 2,175 50 129 3
France 4,382 5 1,910 44 1,947 44 525 12
Italy 3,686 4 2,078 56 1,492 40 116 3
Spain 2,307 3 871 38 1,416 61 19 1
Netherlands 2,246 3 401 18 1,730 77 116 5
Canada 1,899 2 1,178 62 399 21 322 17
Australia 1,847 2 479 26 1,186 64 182 10
Rest of the world 8,748 10 3,184 36 4,830 55 734 8

Total $84,055 100% $38,726 46% $35,761 43% $9,570 11%
Source:  Based on data from Bank of International Settlements, Tables 13A and 13B, available from www.bis.org/statistics/secstats.htm 
(accessed 12 December 2012).

Overview of Global Fixed-  Income Markets 355
Investors make a distinction between countries with established capital markets 
(developed markets) and countries where the capital markets are in earlier stages of 
development (emerging markets). For emerging bond markets, a further distinction is 
made between bonds issued in local currency and bonds issued in a foreign currency, 
such as the euro or the US dollar.
Emerging bond markets are much smaller than developed bond markets, which 
is the reason why they do not appear in Exhibit 4. But as demand from local and 
international investors has increased, issuance and trading of emerging market bonds 
have risen in volume and value. International investors’ interest in emerging market 
bonds has been triggered by a desire to diversify risk across several jurisdictions in the 
belief that investment returns across markets are not closely correlated. In addition, 
emerging market bonds usually offer higher yields (return) than developed market

bonds because of the higher perceived risk. Emerging countries typically lag developed 
countries in the areas of political stability, property rights, and contract enforcement, 
which often leads to a higher credit risk and higher yields. Many emerging countries, 
however, are less indebted than their developed counterparts and benefit from higher 
growth prospects, which appeals to many investors.
2.1.7  Other Classifications of Fixed-  Income Markets
There are various other ways of classifying fixed-  income markets. Market participants 
may classify fixed-  income markets based on some specific characteristics associ -
ated with the fixed-  income securities. Specific market sectors that are of interest 
to some investors are inflation-  linked bonds and, in some jurisdictions, tax-  exempt 
bonds. Issuance of either type of bond tends to be limited to certain types of issuers. 
Inflation-  linked bonds or linkers are typically issued by governments, government-

related entities, and corporate issuers that have an investment-  grade rating. They 
offer investors protection against inflation by linking the coupon payment and/or the 
principal repayment to an index of consumer prices.
Tax-  exempt bonds can only be issued in those jurisdictions that recognize such 
tax exemption. In the United States for example, there is an income tax exemption 
for some of the bonds issued by governments or by some non-  profit organizations. 
In particular, local governments can issue municipal bonds  (or munis ) that are tax 
exempt (they can also issue taxable municipal bonds, although tax-  exempt munis 
are more frequently issued than taxable munis). Tax-  exempt municipal bonds are of 
interest to investors who are subject to income tax because the interest income on 
these bonds is typically exempt from federal income tax and from income tax of the 
state where the bonds are issued, subject to certain restrictions. The coupon rate on a

tax- exempt municipal bond is typically lower than that on an otherwise similar taxable 
bond to reflect the implied income tax rate. Investors are willing to accept a lower 
coupon rate on a tax-  exempt municipal bond compared with an otherwise similar 
taxable bond because the income received from municipal bonds is not taxable. Tax-  
exempt bonds also exist in other jurisdictions. For example, the National Highways 
Authority of India (NHAI) issues tax-  exempt bonds. In countries that implement a 
capital gains tax, there may be tax exemptions for some types of bonds. In the United 
Kingdom for example, government gilts are not subject to capital gains tax.
EXAMPLE 1   
Classification of Fixed-  Income Markets
1 Which of the following is most likely  an issuer of bonds?
A Hedge fund
B Pension fund

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 356
C Local government
2 A bond issued by a city would most likely  be classified as a:
A supranational bond.
B quasi-  government bond.
C non-  sovereign government bond.
3 A fixed-  income security issued with a maturity at issuance of nine months 
is most likely  classified as a:
A capital market security.
B money market security.
C securitized debt instrument.
4 The price of a bond issued in the United States by a British company and 
denominated in US dollars is most likely  to:
A change as US interest rates change.
B change as British interest rates change.
C be unaffected by changes in US and British interest rates.
5 Interbank offered rates are best described as the rates at which a panel of 
banks can:
A issue short-  term debt.
B borrow unsecured funds from other major banks.
C borrow from other major banks against some form of collateral.
6 A company issues floating-  rate bonds. The coupon rate is expressed as the

three-  month Libor plus a spread. The coupon payments are most likely  to 
increase as:
A Libor increases.
B the spread increases.
C the company’s credit quality decreases.
C is correct. Major issuers of bonds include sovereign (national) governments, 
non-  sovereign (local) governments, quasi-  government agencies, supranational 
organizations, and financial and non-  financial companies. A and B are incorrect 
because hedge funds and pension funds are typically investors in, not issuers 
of, bonds.
C is correct. Non-  sovereign (local) government bond issuers include provinces, 
regions, states, and cities. A is incorrect because supranational bonds are issued 
by international organizations. B is incorrect because quasi-  government bonds 
are issued by agencies that are either owned or sponsored by governments.
B is correct. Money market securities are issued with a maturity at issuance

(original maturity) ranging from overnight to one year. A is incorrect because 
capital market securities are issued with an original maturity longer than one year. 
C is incorrect because securitization, which leads to the creation of securitized 
debt instruments, does not relate to a bond’s maturity but to the process that 
transforms private transactions between borrowers and lenders into securities 
traded in public markets.

Overview of Global Fixed-  Income Markets 357
A is correct. The currency denomination of a bond’s cash flows influences which 
country’s interest rates affect a bond’s price. The price of a bond issued by a British 
company and denominated in US dollars will be affected by US interest rates.
B is correct. Interbank offered rates represent a set of interest rates at which 
major banks believe they could borrow unsecured funds from other major banks 
in the interbank money market for different currencies and different borrowing 
periods ranging from overnight to one year.
A is correct. The coupon payments of a floating-  rate bond that is tied to the 
three-  month Libor will reset every three months, based on changes in Libor. 
Thus, as Libor increases, so will the coupon payments. B is incorrect because 
the spread on a floating-  rate bond is typically constant; it is set when the bond is

issued and does not change afterward. C is incorrect because the issuer’s credit 
quality affects the spread and thus the coupon rate that serves as the basis for 
the calculation of the coupon payments, but only when the spread is set—that 
is, at issuance.
2.2 Fixed-  Income Indexes
A fixed-  income index is a multi-  purpose tool used by investors and investment man -
agers to describe a given bond market or sector, as well as to evaluate the performance 
of investments and investment managers. Most fixed-  income indexes are constructed 
as portfolios of securities that reflect a particular bond market or sector. The index 
construction—that is, the security selection and the index weighting—varies among 
indexes.4 Index weighting may be based on price or value (market capitalization).
There are literally dozens of fixed-  income indexes globally, capturing different 
aspects of the fixed-  income markets discussed earlier. One of the most popular set

of indexes is the Bloomberg Barclays Global Aggregate Bond Index, which represents 
a broad-  based measure of the global investment-  grade fixed-  rate bond market. It has 
an index history beginning on 1 January 1990 and contains three important compo -
nents: the US Aggregate Bond Index (formerly Lehman Aggregate Bond Index), the 
Pan-  European Aggregate Bond Index, and the Asian-  Pacific Aggregate Bond Index. 
These indexes reflect the investment-  grade sectors of the US, European, and Asian-  
Pacific bond markets, respectively.
With respect to emerging markets, one of the most widely followed indexes is the 
J.P . Morgan Emerging Market Bond Index (EMBI) Global, which includes US dollar-  
denominated Brady bonds (bonds issued primarily by Latin American countries in 
the late 1980s under a debt restructuring plan aimed at converting bank loans into 
tradable securities), Eurobonds and loans issued by sovereign and quasi-  sovereign 
entities in several emerging markets.

Another popular set of indexes is the FTSE Global Bond Index Series, which has 
been set up to provide coverage of different classes of securities related to the govern -
ment and corporate bond markets. It includes indexes of global government bonds, 
euro-  denominated government bonds from emerging markets, sterling- and euro-  
denominated investment-  grade corporate bonds, and covered bonds from Germany 
and other European Union issuers. Covered bonds are debt obligations issued by 
banks and backed (secured) by a segregated pool of assets.
4 Fixed-  income indexes are discussed in greater details in the reading on security market indexes.

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 358
Many other fixed-  income indexes are available to investors and investment man -
agers to measure and report performance.
2.3 Investors in Fixed-  Income Securities
The overview of fixed-  income markets has so far focused on the supply side. Before 
discussing bond issuers in greater detail, it is important to consider the demand side 
because demand for a particular type of bond or issuer may affect supply. After all, 
market prices are the result of the interaction between demand and supply; neither 
one can be considered in isolation. For example, an increase in demand for inflation-  
linked bonds as a result of investors’ desire to protect the value of their portfolios 
against inflation risk may lead governments to issue a greater quantity of this type of 
bond. By issuing relatively more inflation-  linked bonds for which there is demand, a

government not only manages to sell its bond issue and get the funds required, but 
it may also benefit from a lower cost of financing.
There are different types of investors in fixed-  income securities. Major categories 
of bond investors include central banks, institutional investors, and retail investors. 
The first two typically invest directly in fixed-  income securities. In contrast, retail 
investors often invest indirectly through fixed-  income mutual funds or exchange-  
Central banks use open market operations to implement monetary policy. Open 
market operations  refer to the purchase or sale of bonds, usually sovereign bonds 
issued by the national government. By purchasing (selling) domestic bonds, central 
banks increase (decrease) the monetary base in the economy. Central banks may also 
purchase and sell bonds denominated in foreign currencies as part of their efforts to

manage the relative value of the domestic currency and their country’s foreign reserves.
Institutional investors, including pension funds, hedge funds, charitable foundations 
and endowments, insurance companies, and banks, represent the largest groups of 
investors in fixed-  income securities. Another major group of investors is sovereign 
wealth funds, which are state-  owned investment funds that tend to have very long 
investment horizons and aim to preserve or create wealth for future generations.
Finally, retail investors often invest heavily in fixed-  income securities because of 
the attractiveness of relatively stable prices and steady income production.
Fixed-  income markets are dominated by institutional investors in part because of 
the high informational barriers to entry and high minimum transaction sizes. Fixed-  
income securities are far more diverse than equity securities because of the variety of

types of issuers and securities. In addition, unlike common shares that are primarily 
issued and traded in organized markets, the issuance and trading of bonds very often 
occurs in over-  the-  counter (OTC) markets . Thus, fixed-  income securities are more 
difficult to access than equity securities. For these reasons, institutional investors tend 
to invest directly in bonds, whereas most retail investors prefer to use investment 
vehicles, such as mutual funds and ETFs.
EXAMPLE 2   
Investors in Fixed-  Income Securities
1 Open market operations describe the process used by central banks to 
buy and sell bonds to:
A implement fiscal policy.
B control the monetary base.
C issue and repay government debt.

Primary and Secondary Bond Markets 359
2 Retail investors most often :
A do not invest in fixed-  income securities.
B invest directly in fixed-  income securities.
C invest indirectly in fixed-  income securities through mutual funds or 
exchange-  traded funds.
B is correct. Open market operations refer to the purchase or sale of bonds, 
usually sovereign bonds issued by the national government, as a means of imple -
menting monetary policy. By purchasing (selling) bonds, central banks increase 
(decrease) the monetary base in the economy, thus controlling the money supply. 
A is incorrect because open market operations help facilitate monetary policy, 
not fiscal policy (which is the taxing and spending by the national government). 
C is incorrect because although Treasury departments and some central banks 
may facilitate the issuance and repayment of government debt, open market 
operations specifically refer to the implementation of monetary policy.

C is correct. Retail investors often invest in fixed-  income securities because 
of the attractiveness of relatively stable prices and steady income production. 
However, because most retail investors lack the expertise to value fixed-  income 
securities and are not large enough investors to buy and sell them directly, they 
usually invest in fixed income indirectly through mutual funds and exchange-  
traded funds.
PRIMARY AND SECONDARY BOND MARKETS
Primary bond markets  are markets in which issuers initially sell bonds to investors 
to raise capital. In contrast, secondary bond markets  are markets in which existing 
bonds are subsequently traded among investors. As with all financial markets, primary 
and secondary bond markets are regulated within the framework of the overall finan -
cial system. An established independent regulatory authority is usually responsible for 
overseeing both the structure of the markets and the credentials of market participants.

3.1 Primary Bond Markets
Issuances in primary bond markets are frequent. Exhibit 5 presents data on net bond 
issuances (i.e., the difference between new bond issuances and bond repayments). It 
shows that during the year 2011, the amount of new bond issuances exceeded the 
amount of bond repayments by $3.8 trillion globally, a growth rate of approximately 
4%. In all the largest bond markets, there were more new bond issuances than bond 
repayments in value.3

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 360
Exhibit 5   Amounts of Bonds Outstanding at the End 
of December 2011 and Amounts of Net Bond 
Issuances in 2011 by Residence of the Issuer (US$ 
billions)
CountryAmount of Bonds 
Outstanding Net Bond Issuances
United States $33,582 $559.7
Japan 15,700 457.5
United Kingdom 5,275 77.2
Germany 4,383 25.5
France 4,382 322.1
Italy 3,686 197.6
Spain 2,307 64.2
Netherlands 2,246 65.2
Canada 1,899 111.7
Australia 1,847 100.8
Rest of the world 8,748 1,796.2
Total $84,055 $3,777.7
Source:  Based on data from Bank of International Settlements, Tables 14A, 
14B, and 16A, available at www.bis.org/statistics/secstats.htm (accessed 30 
October 2012).
In the remainder of this section, we discuss the process for issuing bonds in pri -
mary markets. Different bond issuing mechanisms are used depending on the type of 
issuer and the type of bond issued. A bond issue can be sold via a public offering  (or

public offer ), in which any member of the public may buy the bonds, or via a private 
placement , in which only a selected investor, or group of investors, may buy the bonds.
3.1.1  Public Offerings
Investment banks play a critical role in bond issuance by assisting the issuer in access -
ing the primary market and by providing an array of financial services. The most 
common bond issuing mechanisms are underwritten offerings, best effort offerings, 
and auctions. In an underwritten offering , also called a firm commitment offering , 
the investment bank guarantees the sale of the bond issue at an offering price that is 
negotiated with the issuer. Thus, the investment bank, called the underwriter , takes 
the risk associated with selling the bonds. In contrast, in a best effort offering , the 
investment bank only serves as a broker. It only tries to sell the bond issue at the 
negotiated offering price if it is able to for a commission. Thus, the investment bank

has less risk and correspondingly less incentive to sell the bonds in a best effort 
offering than in an underwritten offering. An auction  is a bond issuing mechanism 
that involves bidding.
3.1.1.1  Underwritten Offerings  Underwritten offerings are typical bond issuing 
mechanisms for corporate bonds, some local government bonds (such as municipal 
bonds in the United States), and some asset-  backed securities (such as mortgage-  backed 
securities). The underwriting process typically includes six phases.
The underwriting process starts with the determination of the funding needs. 
Often with the help of an adviser or advisers, the issuer must determine how much 
money must be raised, the type of bond offering, and whether the bond issue should 
be underwritten.

Primary and Secondary Bond Markets 361
Once the issuer has decided that the bond issue should be underwritten, it must 
select the underwriter, which is typically an investment bank. The underwriter of a 
bond issue takes the risk of buying the newly issued bonds from the issuer, and then 
resells them to investors or to dealers who then sell them to investors. The difference 
between the purchase price of the new bond issue and the reselling price to investors 
is the underwriter’s revenue. A relatively small-  size bond issue may be underwritten 
by a single investment bank. It is more common for larger bond issues, however, to 
be underwritten by a group, or syndicate, of investment banks. In this case, the bond 
issue is referred to as a syndicated offering . There is a lead underwriter that invites 
other investment banks to join the syndicate and that coordinates the effort. The 
syndicate is collectively responsible for determining the pricing of the bond issue and

for placing (selling) the bonds with investors.
The third phase of an underwritten offering is to structure the transaction. Before 
the bond issue is announced, the issuer and the lead underwriter discuss the terms of 
the bond issue, such as the bond’s notional principal (total amount), the coupon rate, 
and the expected offering price. The underwriter or the syndicate typically organizes 
the necessary regulatory filings and prepares the offering circular or prospectus that 
provides information about the terms of the bond issue. The issuer must also choose 
a trustee, which is typically a trust company or the trust department of a bank, to 
oversee the master bond agreement. The bond offering is formally launched the day 
the transaction is announced, usually in the form of a press release. The announcement 
specifies the new bond issue’s terms and conditions, including the bond’s features, 
such as the maturity date, the currency denomination, and the expected coupon range,

as well as the expected offering price. The issuer also releases the offering circular 
or prospectus. The final terms may differ from these terms as a result of changes in 
market conditions between the announcement day and the pricing day.
The success of the bond issue depends on the underwriter or syndicate’s discern -
ment in assessing market conditions and in pricing the bond issue accordingly. The 
pricing of the bond issue is, therefore, an important phase of an underwritten offering. 
Ideally, the bond issue should be priced so that the amount of bonds available is equal to 
the demand for the bonds by investors. If the offering price is set too high, the offering 
will be undersubscribed—that is, there will be insufficient demand for the bond issue. 
As a consequence, the underwriter or syndicate will fail to sell the entire bond issue. 
Alternatively, if the offering price is set too low, the offering will be oversubscribed.

Underwriters may aim at a small oversubscription because it reduces the risk of being 
unable to sell the entire bond issue. But a large oversubscription indicates that the 
offering terms were probably unfavorable to the issuer in that the issuer might have 
raised the desired amount of capital at a lower coupon rate.
Between the announcement of a bond issue and the end of the subscription 
period, the underwriter or syndicate must gauge what the demand for the bond issue 
is and at what price the bond should be offered to ensure that the entire bond issue is 
placed without running the risk of a large oversubscription. There are different ways 
for underwriters to do so. The bond issue is usually marketed to potential investors. 
This may be by an indirect approach, such as an advertisement in a newspaper, a 
commonly used approach for bond issued by household names, or through direct 
marketing and road shows, aimed at institutional investors such as pension funds

and insurance companies. The underwriter or syndicate may also approach large 
institutional investors and discuss with them the kind of bond issues they are willing 
to buy. These buyers are known as the “anchor. ” For some, but not all, bond issues, 
the grey market is another way for underwriters to gauge investor’s interest. The grey 
market , also called “when issued” market, is a forward market for bonds about to 
be issued. Trading in the grey market helps underwriters determine what the final 
offering price should be.

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 362
The pricing day is the last day when investors can commit to buy the bond issue, 
and it is also the day when the final terms of the bond issue are agreed on. The fol -
lowing day, called the “offering day, ” the underwriting agreement that includes the 
bond issue’s final terms is signed. The underwriting process then enters the issuing 
phase. The underwriter or the syndicate purchases the entire bond issue from the 
issuer, delivers the proceeds, and starts reselling the bonds through its sales network.
The underwriting process comes to an end about 14 days later, on the closing 
day, when the bonds are delivered to investors. Investors no longer receive a paper 
settlement; instead, the bond itself is represented by a global note that is typically 
held by the paying agent.
3.1.1.2  Shelf Registration  A shelf registration  allows certain authorized issuers

to offer additional bonds to the general public without having to prepare a new and 
separate offering circular for each bond issue. Rather, the issuer prepares a single, 
all- encompassing offering circular that describes a range of future bond issuances, all 
under the same document. This master prospectus may be in place for years before 
it is replaced or updated, and it may be used to cover multiple bond issuances. For 
example, the British retailer Tesco used a shelf registration in 2010 for a series of issues 
under a universal aggregate $10 billion of bonds. The company could have elected to 
issue the entire size at once. Instead, it has issued smaller notional amounts at different 
intervals since 2010.
Under a shelf registration, each individual offering is prefaced with a short issue 
announcement document. This document must confirm that there has been no change 
to material elements of the issuer’s business, or otherwise describe any changes to the

issuer’s financial condition since the master prospectus was filed. Because shelf issu -
ances are subject to a lower level of scrutiny compared with standard public offerings, 
they are only an option for well-  established issuers that have convinced the regulatory 
authorities of their financial strength. Additionally, certain jurisdictions may only 
allow shelf registrations to be purchased by “qualified” institutional investors—that 
is, institutional investors that meet a set of criteria set forth by the regulators.
3.1.1.3  Auctions  An auction is a method that involves bidding. It is helpful in provid -
ing price discovery (i.e., it facilitates supply and demand in determining prices) and in 
allocating securities. In many countries, most sovereign bonds are sold to the public via 
a public auction. For example, in 2011, the United States conducted 269 public auctions 
and issued approximately $7.5 trillion of new securities such as Treasury bills, notes,

bonds, and Treasury Inflation-  Protected Securities (TIPS). The public auction process 
used in the United States is a single-  price auction through which all the winning bid -
ders pay the same price and receive the same coupon rate for the bonds. In contrast, 
the public auction process used in Canada and Germany is a multiple-  price auction 
process, which generates multiple prices and coupon rates for the same bond issue.
The US sovereign bond market is one of the largest and most liquid bond markets 
globally, so we will illustrate the US single-  price auction process. This process includes 
three phases: announcement, bidding, and issuance. First, the US Treasury announces 
the auction and provides information about the bond issue, such as the amount of 
securities being offered, the auction date, the issue date, the maturity date, bidding 
close times, and other pertinent information.
After the auction announcement is made, dealers, institutional investors, and indi -

vidual investors may enter competitive or non-  competitive bids. With competitive bids, 
a bidder specifies the rate (yield) that is considered acceptable; if the rate determined 
at auction is lower than the rate specified in the competitive bid, the investor will not 
be offered any securities. In contrast, with non-  competitive bids, a bidder agrees to 
accept the rate determined at auction; non-  competitive bidders always receive their 
securities. At the close of the auction, the US Treasury accepts all non-  competitive

Primary and Secondary Bond Markets 363
bids and competitive bids in ascending order of their rates (lowest to highest) until the 
amount of bids is equal to the amount the issuer requires. All bidders receive the same 
rate, based on the highest accepted bid. This single-  price auction process encourages 
aggressive bidding and potentially results in a lower cost of funds (i.e., lower coupon 
rate) for the U.S Treasury because all the winning bidders pay the same price.
On the issue day, the US Treasury delivers the securities to the winning bidders 
and collects the proceeds from investors. After the auction process is complete, the 
securities are traded in secondary markets like other securities.
Exhibit 6 shows the results of a US Treasury public auction.
Exhibit 6   Results of a US Treasury Public Auction on 16 October 2012
Term and Type of Security 28- Day Bill
CUSIP Number 9127955L1
High ratea0.125%
Allotted at high 21.85%
Price 99.990278
Investment rateb0.127%
Median ratec0.115%

Low rated0.100%
Issue date 18 October 2012
Maturity date 15 November 2012
Tendered Accepted
Competitive $160,243,967,000 $39,676,092,000
Non-  competitive 224,607,300 224,607,300
FIMA (non-  competitive) 100,000,000 100,000,000
Subtotale$160,568,574,300 $40,000,699,300f
SOMA $0 $0
Total $160,568,574,300 $40,000,699,300
Primary Dealerg$137,250,000,000 $26,834,200,000
Direct Bidderh13,450,000,000 4,079,425,000
Indirect Bidderi9,543,967,000 8,762,467,000
Total Competitive $160,243,967,000 $39,676,092,000
a All tenders at lower rates were accepted in full.
b Equivalent coupon-  issue yield.
c 50% of the amount of accepted competitive tenders was tendered at or below that rate.
d 5% of the amount of accepted competitive tenders was tendered at or below that rate.
e Bid-  to- cover ratio: $160,568,574,300/$40,000,699,300 = 4.01.
f Awards to combined Treasury Direct systems = $134,591,900.

g Primary dealers as submitters bidding for their own house accounts.
h Non-  primary dealer submitters bidding for their own house accounts.

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 364
i Customers placing competitive bids through a direct submitter, including Foreign and International 
Monetary Authorities placing bids through the Federal reserve Bank of New York.
Note : FIMA stands for Foreign and International Monetary Authority and reflects the non-  competitive 
bids made by investors from foreign countries. SOMA stands for System Open Market Account 
and reflects the Federal Reserve’s open market operations.
Source:  Based on information from www.treasurydirect.gov.
The rate determined at auction was 0.125%. T-  bills are pure discount bonds; they 
are issued at a discount to par value and redeemed at par. Investors paid 99.990278% 
of par—that is, approximately $999.90. The US Treasury received bids for $160.6 bil -
lion, but only raised $40.0 billion. All the non-  competitive bids ($324.6 million) were 
accepted, but only a quarter ($39.7 of the $160.2  billion) of competitive bids was

accepted. Note that half the competitive bids were submitted with a rate lower than 
0.115%. All bidders, however, received the rate of 0.125%.
Exhibit  6 also identifies the types of bidders. Most US Treasury securities are 
bought at auction by primary dealers. Primary dealers  are financial institutions that 
are authorized to deal in new issues of US Treasury securities. They have established 
business relationships with the Federal Reserve Bank of New York (New York Fed), 
which implements US monetary policy. Primary dealers serve primarily as trading 
counterparties of the New York Fed and are required to participate meaningfully in 
open market operations and in all auctions of US Treasury securities. They also provide 
the New York Fed with market information. Institutional investors and central banks 
are the largest investors in US Treasury securities; only a very small amount of these 
bonds is purchased directly by individual investors.
3.1.2  Private Placements

A private placement is typically a non-  underwritten, unregistered offering of bonds 
that are sold only to an investor or a small group of investors. Typical investors in 
privately placed bonds are large institutional investors. A private placement can be 
accomplished directly between the issuer and the investor(s) or through an investment 
bank. Because privately placed bonds are unregistered and may be restricted securities 
that can only be purchased by some types of investors, there is usually no active second -
ary market to trade them. However, trading may be possible under certain conditions. 
For example, restricted securities issued under Rule 144A in the United Sates cannot 
be sold to the public, but they can be traded among qualified institutional investors. 
Even if trading is possible, privately placed bonds typically exhibit lower liquidity than 
publicly issued bonds. Insurance companies and pension funds are major buyers of

privately placed bonds because they do not need every security in their portfolio to 
be liquid and they often value the additional yield offered by these bonds.
Private placements sometimes represent a step in the company’s financing evolution 
between syndicated loans  (loans from a group of lenders to a single borrower further 
discussed in Section 6.1) and public offerings. Privately placed bonds are often issued 
in small aggregate amounts, at times by unknown issuers. Many investors may not be 
willing to undertake the credit analysis that is required for a new name, in particular if 
the offering amount is small. Unlike in a public offering in which the bonds are often 
sold to investors on a take-  it- or- leave-  it basis, investors in a private placement can 
influence the structure of the bond issue, including such considerations as asset and 
collateral backing, credit enhancements, and covenants. It is common for privately

placed bonds to have more customized and restrictive covenants than publicly issued 
ones. In addition to being able to negotiate the terms of the bonds and align them Exhibit 6   (Continued)

Primary and Secondary Bond Markets 365
with their needs, investors in private placements are rewarded by getting the bonds, 
which is not always the case in public offerings in which investors cannot know for sure 
when the issue will become available and how many securities they will be allocated.
Private placements are also offered by regular bond issuers, in particular for smaller 
amounts of capital raised in major currencies, such as US dollars, euros, or sterling. 
Private placements are usually more flexible than public offerings and allow regular 
issuers to tailor the bond issue to their own needs.
3.2 Secondary Bond Markets
Secondary markets, also called the “aftermarket, ” are where existing securities are 
traded among investors. Securities can be traded directly from investor to investor, 
or through a broker or dealer to facilitate the transaction. The major participants in 
secondary bond markets globally are large institutional investors and central banks.

The presence of retail investors in secondary bonds markets is limited, unlike in 
secondary equity markets.
The key to understanding how secondary bond markets are structured and 
function is to understand liquidity. Liquidity refers to the ability to trade (buy or 
sell) securities quickly and easily at prices close to their fair market value. Liquidity 
involves much more than “how quickly one can turn a bond into cash. ” This statement 
implicitly assumes a long position, but some market participants need to buy quickly 
when covering a short position. The other aspect of liquidity that is often ignored is 
that speed of trading alone does not constitute a liquid market. One can always buy 
something quickly by offering a very high price or sell something quickly by accepting 
a very low price. In a liquid market, trading takes place quickly at prices close to the 
security’s fair market value.
There are two main ways for secondary markets to be structured: as an organized

exchange or as an over-  the- counter market. An organized exchange  provides a place 
where buyers and sellers can meet to arrange their trades. Although buy or sell orders 
may come from anywhere, the transaction must take place at the exchange accord -
ing to the rules imposed by the exchange. In contrast, with OTC markets, buy and 
sell orders initiated from various locations are matched through a communications 
network. Thus, OTC markets need electronic trading platforms over which users 
submit buy and sell orders. Bloomberg Fixed Income Electronic Trading platform is 
an example of such a platform through which dealers stand ready to trade in multiple 
bond markets globally. Although there is some trading of government bonds and very 
active corporate bonds on many stock exchanges around the world, the vast majority 
of bonds are traded in OTC markets.
The liquidity demands of fixed-  income investors have evolved since the early

1990s. The type of investors who would buy and hold a bond to maturity that once 
dominated the fixed-  income markets has been supplanted by institutional investors 
who trade actively. The dynamics of global fixed-  income markets reflect this change 
in the relative demand for liquidity.
We will illustrate how secondary markets work by using the example of Eurobonds. 
The most important Eurobond trading center by volume is in London, although a 
large number of market participants are also based in Brussels, Frankfurt, Zurich, and 
Singapore. Liquidity is supplied by Eurobond market makers, of which approximately 
35 are registered with the International Capital Market Association (ICMA). ICMA 
is an association of banks and other financial institutions that provides a regulatory 
framework for international bond markets and that is behind much of the established 
uniform practices that are observed by all market participants in the Eurobond market.

The level of commitment to the different sectors of the market varies among 
market makers. The bid–offer spread  or bid–ask spread , which reflects the prices 
at which dealers will buy from a customer (bid) and sell to a customer (offer or ask),

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 366
is very often used as an indicator of liquidity. It can be as low as 5 bps for very liquid 
bond issues, such as issues of the World Bank, to no price quoted for illiquid issues. 
A reasonable spread is of the order of 10−12 bps, whereas an illiquid spread may be 
in excess of 50 bps. When there is no bid or offer price, the issue is completely illiquid 
for trading purposes.
Settlement  is the process that occurs after the trade is made. The bonds are passed 
to the buyer and payment is received by the seller. Secondary market settlement for 
government and quasi-  government bonds typically takes place either on a cash basis 
or on a T + 1 basis. With cash settlement, trading and settlement occur on the same 
day. With T + 1 settlement, settlement takes place the day after the trade date. In 
contrast, corporate bonds usually settle on a T + 2 or T + 3 basis, although settlement

can extend to T + 7 in some jurisdictions. Trades clear within either or both of the 
two main clearing systems, Euroclear and Clearstream. Settlement occurs by means 
of a simultaneous exchange of bonds for cash on the books of the clearing system. 
An electronic bridge connecting Euroclear and Clearstream allows transfer of bonds 
from one system to the other, so it is not necessary to have accounts at both systems. 
Both systems operate on a paperless, computerized book-  entry basis, although a bond 
issue is still represented by a physical document, the global note mentioned earlier. 
All participants in either system will have their own internal account set up, and they 
may also act as agent for buyers or sellers who do not possess an account.
EXAMPLE 3   
Bond Markets
1 Which of the following best describes a primary market for bonds? A 
market:
A in which bonds are issued for the first time to raise capital.
B that has a specific location where the trading of bonds takes place.

C in which existing bonds are traded among individuals and institutions.
2 US Treasury bonds are typically sold to the public via a(n):
A auction.
B primary dealer.
C secondary bond market.
3 In a single-  price bond auction, an investor who places a competitive bid 
and specifies a rate that is above the rate determined at auction will most 
likely :
A not receive any bonds.
B receive the bonds at the rate determined at auction.
C receive the bonds at the rate specified in the investor’s competitive bid.
4 A bond purchased in a secondary market is most likely  purchased from:
A the bond’s issuer.
B the bond’s lead underwriter.
C another investor in the bond.
5 Corporate bonds will most likely  settle:
A on the trade date.
B on the trade date plus one day.
C by the trade date plus three days.

Sovereign Bonds 367
A is correct. Primary bond markets are markets in which bonds are issued for 
the first time to raise capital. B is incorrect because having a specific location 
where the trading of bonds takes place is not a requirement for a primary bond 
market. C is incorrect because a market in which existing bonds are traded among 
individuals and institutions is the definition of a secondary, not primary, market.
A is correct. US Treasury bonds are typically sold to the public via an auction. 
B is incorrect because primary dealers are often bidders in the auction; they are 
financial institutions that are active in trading US Treasury bonds. C is incorrect 
because any bond issue coming directly to the market is considered to be in the 
primary, not the secondary, market.
A is correct. In a single-  price bond auction, a bidder that enters a competitive 
bid specifies the rate (yield) that is considered acceptable. If the rate specified in

the competitive bid is above the coupon rate determined at auction, the investor 
will not be offered any securities.
C is correct. Secondary bond markets are where bonds are traded among 
investors. A and B are incorrect because a bond purchased from the bond’s 
issuer or from the bond’s lead underwriter would happen in the primary, not 
secondary, market.
C is correct. Corporate bonds typically settle on a T + 2 or T + 3 basis—that 
is, two or three days after the trade date—although settlement can extend to T 
+ 7 in some jurisdictions. A and B are incorrect because it is government and 
quasi-  government bonds, not corporate bonds, that typically settle either on a 
cash basis or on a T + 1 basis.
SOVEREIGN BONDS
National governments issue bonds primarily for fiscal reasons—to fund spending 
when tax revenues are insufficient to cover expenditures. To meet their spending 
goals, national governments issue bonds in various types and amounts. This section

discusses bonds issued by national governments, often referred to as sovereign 
bonds  or sovereigns .
4.1 Characteristics of Sovereign Bonds
Sovereign bonds denominated in local currency have different names in different 
countries. For example, they are named US Treasuries in the United States, Japanese 
government bonds (JGBs) in Japan, gilts in the United Kingdom, Bunds in Germany, 
and obligations assimilables du Trésor (OATs) in France. Some investors or market 
participants may refer to sovereign bonds as Treasury securities or Treasuries for 
short, on the principle that the national Treasury department is often in charge of 
managing a national government’s funding needs.4

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 368
Names may also vary depending on the original maturity of the sovereign bond. For 
example, US government bonds are named Treasury bills (T-  bills) when the original 
maturity is one year or shorter, Treasury notes (T-  notes) when the original maturity 
is longer than one year and up to 10 years, and Treasury bonds (T-  bonds) when the 
original maturity is longer than 10 years; in Spain, the sovereigns issued by Tesoro 
Público are named letras del Tesoro, bonos del Estado, and obligaciones del Estado 
depending on the sovereign’s original maturity, one year or shorter, longer than one 
year and up to five years, or longer than five years, respectively. Although very rare, 
some bonds, such as the consols in the United Kingdom, have no stated maturity date.
The majority of the trading in secondary markets is of sovereign securities that

were most recently issued. These securities are called on- the-  run. The latest sovereign 
bond issue for a given maturity is also referred to as a benchmark issue  because it 
serves as a benchmark against which to compare bonds that have the same features 
(i.e., maturity, coupon type and frequency, and currency denomination) but that are 
issued by another type of issuer (e.g., non-  sovereign, corporate). As a general rule, as 
sovereign securities age, they trade less frequently.
One salient difference between money market securities, such as T-  bills, and 
capital market securities, such as T-  notes and T-  bonds, is the interest provision. As 
illustrated in Exhibit 6, T-  bills are pure discount bonds; they are issued at a discount 
to par value and redeemed at par. The difference between the par value and the issue 
price is the interest paid on the borrowing. In contrast, capital market securities are

typically coupon (or coupon-  bearing) bonds; these securities make regular coupon 
payments and repay the par value at maturity. Bunds pay coupons annually, whereas 
US Treasuries, JGBs, gilts, and OATs make semi-  annual coupon payments.
4.2 Credit Quality of Sovereign Bonds
Sovereign bonds are usually unsecured obligations of the sovereign issuer—that is, they 
are not backed by collateral but by the taxing authority of the national government. 
When a national government runs a budget surplus, excess tax revenues over expen -
ditures is the primary source of funds for making interest payments and repaying the 
principal. In contrast, when a country runs a budget deficit, the source of the funds 
used for the payment of interest and repayment of principal comes from tax revenues 
and also by “rolling over” (refinancing) existing debt into new debt.
Highly rated sovereign bonds denominated in local currency are virtually free of

credit risk. Credit rating agencies assign ratings to sovereign bonds, and these rat -
ings are called “sovereign ratings. ” The highest rating (i.e., highest credit quality and 
lowest credit risk) is AAA by S&P and Fitch and Aaa by Moody’s. As of late 2012, 
only a handful of sovereign issuers were rated at this (theoretically) risk-  free level by 
these three credit rating agencies, including Germany, Singapore, Switzerland, the 
Netherlands, and the United Kingdom. The global financial crisis that started in 2008 
resulted in many national governments reaching potentially unsustainable levels of 
debt, with the pace of spending far exceeding tax revenues. Many of these national 
governments suffered downgrades from the AAA/Aaa level, including Ireland in 
2009, Spain in 2010, and the United States, which was downgraded by S&P in 2011.
Credit rating agencies make a distinction between bonds issued in the sovereign’s

local currency and bonds issued in a foreign currency. In theory, a government can 
make interest payments and repay the principal by generating cash flows from its 
unlimited power (in the short run at least) to tax its citizens. A national government 
also has the ability to print its own currency, whereas it is restricted in being able to 
pay in a foreign currency only what it earns in exports or can exchange in financial 
markets. Thus, it is common to observe a higher credit rating for sovereign bonds 
issued in local currency than for those issued in a foreign currency. But there are 
limits to a government’s ability to reduce the debt burden. As the sovereign debt crisis

Sovereign Bonds 369
that followed the global financial crisis has shown, taxing citizens can only go so far 
in paying down debt before the taxation becomes an economic burden. Additionally, 
printing money only serves to weaken a country’s currency relative to other curren -
cies over time.
The national government of a country that has a strong domestic savings base has 
the luxury of being able to issue bonds in its local currency and sell them to domestic 
investors. If the local currency is liquid and freely traded, the sovereign issuer may 
also attract foreign investors who may want to hold that sovereign issuer’s bonds and 
have exposure to that country’s local currency. A national government may also issue 
debt in a foreign currency when there is demand for the sovereign issuer’s bonds, but 
not necessarily in the sovereign’s local currency. For example, demand from overseas 
investors has caused national governments such as Switzerland and Sweden to issue

sovereign bonds in US dollars and euros. Emerging market countries may also have 
to issue in major currencies because international investors may be willing to accept 
the credit risk but not the foreign exchange (currency) risk associated with emerging 
market bonds. When a sovereign issuer raises debt in a foreign currency, it usually 
swaps the proceeds into its local currency.
4.3 Types of Sovereign Bonds
National governments issue different types of bonds, some of them paying a fixed 
rate of interest and others paying a floating rate, including inflation-  linked bonds.
4.3.1  Fixed-  Rate Bonds
Fixed-  rate bonds (i.e., bonds that pay a fixed rate of interest) are by far the most 
common type of sovereign bond. National governments routinely issue two types of 
fixed-  rate bonds: zero-  coupon bonds (or pure discount bonds) and coupon bonds. 
A zero-  coupon bond does not pay interest. Instead, it is issued at a discount to par

value and redeemed at par at maturity. Coupon bonds are issued with a stated rate of 
interest and make interest payments periodically, such as semi-  annually or annually. 
They have a terminal cash flow equal to the final interest payment plus the par value. 
As mentioned earlier, most sovereign bonds with an original maturity of one year or 
less are zero-  coupon bonds, whereas bonds with an original maturity longer than one 
year are typically issued as coupon bonds.
4.3.2  Floating-  Rate Bonds
The price of a bond changes in the opposite direction from the change in interest 
rates, a relationship that is fully explained in the reading on understanding the risk 
and return of fixed-  income securities. Thus, investors who hold fixed-  rate bonds are 
exposed to interest rate risk: As interest rates increase, bond prices decrease, which 
lowers the value of their portfolio. In response to public demand for less interest rate

risk, some national governments around the world issue bonds with a floating rate 
of interest that resets periodically based on changes in the level of a reference rate 
such as Libor. Although interest rate risk still exists on floating-  rate bonds, it is far 
less pronounced than that on fixed-  rate bonds.
Examples of countries where the national government issues floating-  rate bonds 
include Germany, Spain, and Belgium in developed markets and Brazil, Turkey, Mexico, 
Indonesia, and Poland in emerging markets. The largest sovereign issuer, the United 
States, began issuing floating-  rate bonds in January 2014. Two other large sovereign 
issuers, Japan and the United Kingdom, have never issued bonds whose coupon rate 
is tied to a reference rate.

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 370
4.3.3  Inflation-  Linked Bonds
Fixed-  income investors are exposed to inflation risk. The cash flows of fixed-  rate bonds 
are fixed by contract. If a particular country experiences an inflationary episode, the 
purchasing power of the fixed cash flows is eroded over time. Thus, to respond to 
the demand for less inflation risk, many national governments issue inflation-  linked 
bonds, or linkers, whose cash flows are adjusted for inflation. First issuers of inflation-  
linked bonds were the governments of Argentina, Brazil, and Israel. The United 
States introduced inflation-  linked securities in January 1997, calling them Treasury 
Inflation-  Protected Securities (TIPS). Other countries where the national government 
has issued inflation-  linked bonds include the United Kingdom, Sweden, Australia, and 
Canada in developed markets and Brazil, South Africa, and Chile in emerging markets.

As explained in the reading on fixed-  income securities, the index to which the 
coupon payments and/or principal repayments are linked is typically an index of 
consumer prices. Inflation-  linked bonds can be structured a variety of ways: The 
inflation adjustment can be made via the coupon payments, the principal repay -
ment, or both. In the United States, the index used is the Consumer Price Index for 
All Urban Consumers (CPI-  U). In the United Kingdom, it is the Retail Price Index 
(RPI) (All Items). In France, there are two inflation-  linked bonds with two different 
indexes: the French consumer price index (CPI) (excluding tobacco) and the Eurozone’s 
Harmonized Index of Consumer Prices (HICP) (excluding tobacco). Although linking 
the cash flow payments to a consumer price index reduces inflation risk, it does not 
necessarily eliminate the effect of inflation completely because the consumer price 
index may be an imperfect proxy for inflation.
EXAMPLE 4   
Sovereign Bonds

EXAMPLE 4   
1 Sovereign debt with a maturity at issuance shorter than one year are most 
likely :
A floating-  rate instruments.
B zero-  coupon instruments.
C coupon-  bearing instruments.
2 Floating-  rate bonds are issued by national governments as the best way to 
reduce:
B inflation risk.
3 Sovereign bonds whose coupon payments and/or principal repayments 
are adjusted by a consumer price index are most likely  known as:
A linkers.
B floaters.
C consols.
B is correct. Most debt issued by national governments with a maturity at issu -
ance (original maturity) shorter than one year takes the form of zero-  coupon 
instruments. A and C are incorrect because floating-  rate and coupon-  bearing 
instruments are typically types of sovereign debt with maturities longer than 
one year.

Non-  Sovereign Government, Quasi-  Government, and Supranational Bonds 371
C is correct. The coupon rates of floating-  rate bonds are reset periodically based 
on changes in the level of a reference rate such as Libor, which reduces interest 
rate risk. A is incorrect because credit risk, although low for sovereign bonds, 
cannot be reduced by linking the coupon rate to a reference rate. B is incorrect 
because although inflation risk is lower for floating-  rate bonds than for fixed-  
rate bonds, floating-  rate bonds are not as good as inflation-  linked bonds to 
reduce inflation risk.
A is correct because sovereign bonds whose coupon payments and/or principal 
repayment are adjusted by a consumer price index are known as inflation-  linked 
bonds or linkers. B is incorrect because floaters describe floating-  rate bonds 
that have a coupon rate tied to a reference rate such as Libor. C is incorrect

because consols are sovereign bonds with no stated maturity date issued by 
the UK government.
NON-  SOVEREIGN GOVERNMENT, QUASI-  
GOVERNMENT, AND SUPRANATIONAL BONDS
This section covers the bonds issued by local governments and by government-  related 
entities.
5.1 Non-  Sovereign Bonds
Levels of government below the national level such as provinces, regions, states, 
and cities issue bonds called non-  sovereign government bonds  or non-  sovereign 
bonds . These bonds are typically issued to finance public projects, such as schools, 
motorways, hospitals, bridges, and airports. The sources for paying interest and 
repaying the principal include the taxing authority of the local government, the cash 
flows of the project the bond issue is financing, or special taxes and fees established 
specifically for the purpose of making interest payments and principal repayments. 
Non-  sovereign bonds are typically not guaranteed by the national government.

As mentioned in Section 2.1.7, bonds issued by state and local governments in 
the United States are known as municipal bonds, and they often offer income tax 
exemptions. In the United Kingdom, non-  sovereign bonds are known as local authority 
bonds. Other non-  sovereign bonds include those issued by state authorities such as 
the 16 Lander  in Germany.
Credit ratings for non-  sovereign bonds vary widely because of the differences in 
credit and collateral quality. Because default rates of non-  sovereign bonds are histor -
ically low, they very often receive high credit ratings. However, non-  sovereign bonds 
usually trade at a higher yield and lower price than sovereign bonds with similar char -
acteristics. The additional yield depends on the credit quality, the liquidity of the bond 
issue, and the implicit or explicit level of guarantee or funding commitment from the 
national government. The additional yield is the lowest for non-  sovereign bonds that

have high credit quality, are liquid, and are guaranteed by the national government.5

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 372
5.2 Quasi-  Government Bonds
National governments establish organizations that perform various functions for them. 
These organizations often have both public and private sector characteristics, but they 
are not actual governmental entities. They are referred to as quasi-  government entities, 
although they take different names in different countries. These quasi-  government 
entities often issue bonds to fund specific financing needs. These bonds are known 
as quasi-  government bonds  or agency bonds .
Examples of quasi-  government entities include government-  sponsored enterprises 
(GSEs) in the United States, such as the Federal National Mortgage Association 
(“Fannie Mae”), the Federal Home Loan Mortgage Corporation (“Freddie Mac”), 
and the Federal Home Loan Bank (FHLB). GSEs were among the largest issuers 
of bonds before the global financial crisis that started in 2008. Other examples of

quasi-  government entities that issue bonds include Hydro Quebec in Canada or the 
Japan Bank for International Cooperation (JBIC). In the case of JBIC’s bonds, timely 
payments of interest and repayment of principal are guaranteed by the Japanese gov -
ernment. Most quasi-  government bonds, however, do not offer an explicit guarantee 
by the national government, although investors often perceive an implicit guarantee.
Because a quasi-  government entity typically does not have direct taxing authority, 
bonds are repaid from the cash flows generated by the entity or from the project the 
bond issue is financing. Quasi-  government bonds may be backed by collateral, but 
this is not always the case. Quasi-  government bonds are usually rated very high by 
the credit rating agencies because historical default rates are extremely low. Bonds 
that are guaranteed by the national government receive the highest ratings and trade

at a lower yield and higher price than otherwise similar bonds that are not backed by 
the sovereign government’s guarantee.
5.3 Supranational Bonds
A form of often highly rated bonds is issued by supranational agencies, also referred 
to as multilateral agencies. The most well-  known supranational agencies are the 
International Bank for Reconstruction and Development (the World Bank), the 
International Monetary Fund (IMF), the European Investment Bank (EIB), the Asian 
Development Bank (ADB), and the African Development Bank (AFDB). Bonds issued 
by supranational agencies are called supranational bonds .
Supranational bonds are typically plain vanilla bonds, although floating-  rate bonds 
and callable bonds are sometimes issued. Highly rated supranational agencies, such 
as the World Bank, frequently issue large-  size bond issues that are often used as 
benchmarks issues when there is no liquid sovereign bond available.
EXAMPLE 5   
Non-  Sovereign Government, Quasi-  Government, and

Supranational Bonds
1 Relative to sovereign bonds, non-  sovereign bonds with similar character -
istics most likely  trade at a yield that is:
A lower.
B the same.
C higher.
2 Bonds issued by a governmental agency are most likely :
A repaid from the cash flows generated by the agency.

Corporate Debt 373
B guaranteed by the national government that sponsored the agency.
C backed by the taxing power of the national government that sponsored 
the agency.
C is correct. Non-  sovereign bonds usually trade at a higher yield and lower price 
than sovereign bonds with similar characteristics. The higher yield is because of 
the higher credit risk associated with non-  sovereign issuers relative to sovereign 
issuers, although default rates of local governments are historically low and 
their credit quality is usually high. The higher yield may also be a consequence 
of non-  sovereign bonds being less liquid than sovereign bonds with similar 
A is correct. Most bonds issued by a governmental agency are repaid from the 
cash flows generated by the agency or from the project the bond issue is financ -
ing. B and C are incorrect because although some bonds issued by governmental

agencies are guaranteed by the national government or are backed by the taxing 
power of the national government that sponsored the agency, bonds are most 
likely repaid first from the cash flows generated by the agency.
CORPORATE DEBT
Companies differ from governments and government-  related entities in that their 
primary goal is profit; they must be profitable to stay in existence. Thus, profitability 
is an important consideration when companies make decisions, including financing 
decisions. Companies routinely raise debt as part of their overall capital structure, both 
to fund short-  term spending needs (e.g., working capital) as well as long-  term capital 
investments. We have so far focused on publicly issued debt, but loans from banks 
and other financial institutions are a significant part of the debt raised by companies. 
For example, it is estimated that European companies traditionally meet 70% of their

borrowing needs from banks and only 30% from financial markets.5 However, as banks 
have been deleveraging and reducing the amount of loans to companies following 
the global financial crisis that started in 2008, companies, in particular those with 
high credit quality, have turned to financial markets to issue bonds. They have been 
taking advantage of the low interest rate environment and the increased appetite of 
investors for corporate bonds.
6.1 Bank Loans and Syndicated Loans
A bilateral loan  is a loan from a single lender to a single borrower. Companies rou -
tinely use bilateral loans from their banks, and these bank loans are governed by the 
bank loan documents. Bank loans are the primary source of debt financing for small 
and medium-  size companies as well as for large companies in countries where bond 
markets are either under-  developed or where most bond issuances are from govern -
ment, government-  related entities, and financial institutions. Access to bank loans

depends not only on the characteristics and financial health of the company, but also 
on market conditions and bank capital availability.6
5 Neil O’Hara, “In or Out of MTNs?” FTSE Global Markets , no. 65 (October 2012):32−34.

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 374
A syndicated loan is a loan from a group of lenders, called the “syndicate, ” to a 
single borrower. A syndicated loan is a hybrid between relational lending and publicly 
traded debt. Syndicated loans are primarily originated by banks, and the loans are 
extended to companies but also to governments and government-  related entities. The 
coordinator, or lead bank, originates the loan, forms the syndicate, and processes the 
payments. In addition to banks, a variety of lenders participate in the syndicate, such 
as pension funds, insurance companies, and hedge funds. Syndicated loans are a way 
for these institutional investors to participate in corporate lending while diversifying 
the credit risk among a group of lenders.
In recent years, a secondary market in syndicated loans has developed. These 
loans are often packaged and securitized, and the securities created are then sold in 
secondary markets to investors.

Most bilateral and syndicated loans are floating-  rate loans, and the interest rate 
is based on a reference rate plus a spread. The reference rate may be Libor, a sover -
eign rate (e.g., the T-  bill rate), or the prime lending rate, also called the “prime rate. ” 
The prime rate formerly reflected the interest rate at which banks lent to their most 
creditworthy customers, but it now tends to be driven by the overnight rate at which 
banks lend to each other. Bank loans can be customized to the borrower’s needs. 
They can have different maturities, as well as different interest payment and prin -
cipal repayment structures. The frequency of interest payments varies among bank 
loans. Some loans are bullet loans, in which the entire payment of principal occurs at 
maturity, and others are amortizing loans, in which the principal is repaid over time.
For highly rated companies, both bilateral and syndicated loans can be more expen -

sive than bonds issued in financial markets. Thus, companies often turn to money and 
capital markets to raise funds, which allows them to diversify their sources of financing.
6.2 Commercial Paper
Commercial paper  is a short-  term, unsecured promissory note issued in the public 
market or via a private placement that represents a debt obligation of the issuer. 
Commercial paper was first issued in the United States more than a century ago. It 
later appeared in the United Kingdom, in other European countries, and then in the 
rest of the world.
6.2.1  Characteristics of Commercial Paper
Commercial paper is a valuable source of flexible, readily available, and relatively low-  
cost short-  term financing. It is a source of funding for working capital and seasonal 
demands for cash. It is also a source of bridge financing —that is, interim financing 
that provides funds until permanent financing can be arranged. Suppose a company

wants to build a new distribution center in southeast China and wants to finance this 
investment with an issuance of long-  term bonds. The market conditions for issuing 
long-  term bonds may currently be volatile, which would translate into a higher cost 
of borrowing. Rather than issuing long-  term bonds immediately, the company may 
opt to raise funds with commercial paper and wait for a more favorable environment 
in which to sell long-  term bonds.
The largest issuers of commercial paper are financial institutions, but some non-  
financial companies are also regular issuers of commercial paper. Although the focus 
of this section is on corporate borrowers, sovereign governments and supranational 
agencies routinely issue commercial paper as well.
The maturity of commercial paper can range from overnight to one year, but a 
typical issue matures in less than three months.

Corporate Debt 375
6.2.2  Credit Quality of Commercial Paper
Traditionally, only the largest, most stable companies issued commercial paper. 
Although only the strongest, highest-  rated companies issue low-  cost commercial 
paper, issuers from across the risk spectrum can issue commercial paper with higher 
yields than higher-  rated companies. Thus, investors in commercial paper are exposed 
to various levels of credit risk depending on the issuer’s creditworthiness. Many inves -
tors perform their own credit analysis, but most investors also assess a commercial 
paper’s credit quality by using the ratings provided by credit rating agencies. Exhibit 7 
presents the range of commercial paper ratings from the main credit rating agencies. 
Commercial paper rated adequate or above (shaded area of Exhibit 7) is called “prime 
paper, ” and it is typically considered investment grade by investors.
Exhibit 7   Commercial Paper Ratings
Credit Quality Moody’s S&P Fitch
Superior P1 A1+/A1 F1+/F1

Satisfactory P2 A2 F2
Adequate P3 A3 F3
Speculative NP B/C F4
Defaulted NP D F5
In most cases, maturing commercial paper is paid with the proceeds of new 
issuances of commercial paper, a practice referred to as “rolling over the paper. ” This 
practice creates a risk that the issuer will be unable to issue new paper at maturity, 
referred to as rollover risk. As a safeguard against rollover risk, credit rating agencies 
often require that commercial paper issuers secure backup lines of credit  from banks. 
The purpose of the backup lines of credit is to ensure that the issuer will have access 
to sufficient liquidity to repay maturing commercial paper if rolling over the paper is 
not a viable option. This is why backup lines of credit are sometimes called “liquidity 
enhancement” or “backup liquidity lines. ” Issuers of commercial paper may be unable 
to roll over the paper as a result of either market-  wide or company-  specific events.

For example, financial markets could be in the midst of a financial crisis that would 
make it difficult to roll over the paper. A company could also experience some sort of 
financial distress such that it could only issue new commercial paper at significantly 
higher rates. In this case, the company could draw on its credit lines instead of rolling 
over its paper. Most commercial paper issuers maintain 100% backing, although some 
large, high credit quality issues carry less than 100% backing. Backup lines of credit 
typically contain a “material adverse change” provision that allows the bank to cancel 
the backup line of credit if the financial condition of the issuer deteriorates substantially.
Historically, defaults on commercial paper have been relatively rare, primarily 
because commercial paper has a short maturity. Each time existing paper matures, 
investors have the opportunity to assess the issuer’s financial position, and they can

refuse to buy the new paper if they estimate that the issuer’s credit risk is too high. 
Thus, the commercial paper market is quicker in withdrawing financing when an issuer’s 
credit quality deteriorates than markets for longer-  term securities. This reduces the 
exposure of the commercial paper market to defaults. In addition, corporate managers 
realize that defaulting on commercial paper would likely prevent any future issuance 
of this valuable financing alternative.
The combination of short-  dated maturity, relatively low credit risk, and a large 
number of issuers makes commercial paper attractive to a diverse range of institutional 
investors, including money market mutual funds, bank liquidity desks, corporate

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 376
treasury departments, and institutional investors that have liquidity constraints. 
Most commercial paper investors hold their position to maturity. The result is little 
secondary market trading except for the largest issues. Investors who wish to sell 
commercial paper prior to maturity can either sell the paper back to the dealer, to 
another investor, or in some cases, directly back to the issuer.
The yield on commercial paper is typically higher than that on short-  term sov -
ereign bonds of the same maturity for two main reasons. First, commercial paper is 
exposed to credit risk unlike most highly rated sovereign bonds. Second, commercial 
paper markets are generally less liquid than short-  term sovereign bond markets. Thus, 
investors require higher yields to compensate for the lower liquidity. In the United 
States, the yield on commercial paper also tends to be higher than that on short-  term

municipal bonds for tax reasons. Income generated by investments in commercial 
paper is usually subject to income taxes, whereas income from many municipal bonds 
is tax exempt. Thus, to attract taxable investors, bonds that are subject to income taxes 
must offer higher yields than those that are tax exempt.
6.2.3  US Commercial Paper vs. Eurocommercial Paper
The US commercial paper (USCP) market is the largest commercial paper market in the 
world, although there are other active commercial paper markets in other countries. 
Commercial paper issued in the international market is known as Eurocommercial 
paper (ECP). Although ECP is a similar instrument to USCP , there are some differences 
between the two. These differences are shown in Exhibit 8.
Exhibit 8   USCP vs. ECP
Feature US Commercial Paper Eurocommercial Paper
Currency US dollar Any currency
Maturity Overnight to 270 daysaOvernight to 364 days
Interest Discount basis Interest-  bearing or discount basis

Settlement T + 0 (trade date) T + 2 (trade date plus two days)
Negotiable Can be sold to another party Can be sold to another party
a In the United States, securities with an original maturity in excess of 270 days must be registered 
with the Securities and Exchange Commission (SEC). To avoid the time and expense associated 
with a SEC registration, issuers of US commercial paper rarely offer maturities longer than 270 days.
A difference between USCP and ECP is related to the interest provision. USCP 
is typically issued on a discount basis—that is, USCP is issued at a discount to par 
value and pays full par value at maturity. The difference between the par value and 
the issue price is the interest paid on the borrowing. In contrast, ECP may be issued 
at, and trade on, an interest-  bearing or yield basis or a discount basis. The distinction 
between the discount and the interest-  bearing basis is illustrated in Exhibit 9. Some

aspects of the calculation, such as the day count convention, are discussed in the 
introduction to fixed-  income valuation reading.
Exhibit 9   
Interest Calculation: Discount vs. Interest-  Bearing Basis
A US bank and a German industrial company both issue $50 million of 180-  day, 
5% commercial paper. The US bank issues its commercial paper domestically, 
and the German industrial company issues Eurocommercial paper.

Corporate Debt 377
US bank:
Issues $50,000,000 180-  day USCP .
Interest is $1,250,000 [$50,000,000 × 0.05 × (180/360)].
Interest on USCP is on a discount basis. Proceeds received are 
$48,750,000 [$50,000,000 − $1,250,000].
At maturity, the bank repays the par value of $50,000,000.
German industrial company:
Issues $50,000,000 180-  day ECP .
Interest on ECP is on an interest-  bearing basis. Proceeds received are the 
par value of $50,000,000.
At maturity, the company repays $51,250,000 [$50,000,000 + $1,250,000].
The amount of interest is the same for both companies. In the case of USCP , 
investors receive the interest by getting a discount on the par value when the 
commercial paper is issued. In the case of ECP , investors receive the interest by 
getting an additional payment (or add-  on) to the par value when the commercial 
paper is repaid. However, note that the investors’ return is not the same. Investors

earn 2.56% on their 180-  day investment in USCP ($1,250,000 ÷ $48,750,000) 
versus 2.50% on their 180-  day investment in ECP ($1,250,000 ÷ $50,000,000).
Typical transaction sizes in ECP are also much smaller than in USCP , and it is 
difficult to place longer-  term ECP with investors. The ECP market also exhibits less 
liquidity than the USCP market.
6.3 Corporate Notes and Bonds
Companies are active participants in global capital markets and regularly issue corpo -
rate notes and bonds. These securities can be placed directly with specific investors 
via private placements or sold in public securities markets. This section discusses 
various characteristics of corporate notes and bonds.
6.3.1  Maturities
There is no universally accepted taxonomy as to what constitutes short-, medium-, and 
long-  term maturities. For our purposes, short term refers to original maturities of five 
years or less; intermediate term to original maturities longer than five years and up to

12 years; and long term to original maturities longer than 12 years. Those securities 
with maturities between 1 and 12 years are often considered notes, whereas securi -
ties with maturities greater than 12 years are considered bonds. It is not uncommon, 
however, to refer to bonds for all securities, irrespective of their original maturity.
In practice, most corporate bonds range in term to maturity between 1 and 30 
years. In Europe, however, there are also bond issues with maturities of 40 and 50 
years. In addition, during the 1990s a number of corporate bonds were issued in the 
United States with maturities of 100 years; these bonds are called “century bonds. ” 
The first century bond was issued by the Walt Disney Company in 1993 as part of its 
medium-  term note program.Exhibit 9   (Continued)

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 378
Medium-  term note  (MTN) is a misnomer. As the century bond example above 
illustrates, MTNs can have very long maturities. From the perspective of the issuer, 
the initial purpose of MTNs was to fill the funding gap between commercial paper 
and long-  term bonds. It is for this reason that they are referred to as “medium term. ” 
The MTN market can be broken into three segments: short-  term securities that carry 
floating or fixed rates, medium- to long-  term securities that primarily bear a fixed 
rate of interest, and structured notes. MTNs have the unique characteristic of being 
securities that are offered continuously to investors by an agent of the issuer. This 
feature gives the borrower maximum flexibility for issuing securities on a continuous 
basis. Financial institutions are the primary issuers of MTNs, in particular short-  term

ones. Life insurance companies, pension funds, and banks are among the largest buyers 
of MTNs because they can customize the bond issue to their needs and stipulate the 
amount and characteristics of the securities they want to purchase. These investors are 
often willing to accept less liquidity than they would get with a comparable publicly 
issued bond because the yield is slightly higher. The cost savings in registration and 
underwriting often makes MTNs a lower cost option for the issuer.
6.3.2  Coupon Payment Structures
Corporate notes and bonds have a range of coupon payment structures. Financial and 
non-  financial companies issue conventional coupon bonds that pay a fixed periodic 
coupon during the bond’s life. They also issue bonds for which the periodic coupon 
payments adjust to changes in market conditions and/or changes to the issuer’s credit 
quality. Such bonds typically offer investors the opportunity to reduce their exposure

to a particular type of risk. For example, FRNs, whose coupon payments adjust to 
changes in the level of market interest rates, are a way to limit interest rate risk; some 
of the inflation-  linked bonds whose coupon payments adjust to changes in the level 
of a consumer price index offer a protection against inflation risk; credit-  linked cou -
pon bonds, whose coupon payments adjust to changes in the issuer’s credit quality, 
are a way to reduce credit risk. Whether the periodic coupon is fixed or not, coupon 
payments can be made quarterly, semi-  annually, or annually depending on the type 
of bond and where the bonds are issued and traded.
Other coupon payment structures exist. Zero-  coupon bonds pay no coupon. 
Deferred coupon bonds pay no coupon initially, but then offer a higher coupon. 
Payment-  in- kind (PIK) coupon bonds make periodic coupon payments, but not nec -
essarily in cash; the issuer may pay interest in the form of securities, such as bonds or

common shares. These types of coupon payment structures give issuers more flexibility 
regarding the servicing of their debt.
6.3.3  Principal Repayment Structures
Corporate note or bond issues have either a serial or a term maturity structure. With 
a serial maturity structure , the maturity dates are spread out during the bond’s life; 
a stated number of bonds mature and are paid off each year before final maturity. 
With a term maturity structure , the bond’s notional principal is paid off in a lump 
sum at maturity. Because there is no regular repayment of the principal outstanding 
throughout the bond’s life, a term maturity structure carries more credit risk than a 
serial maturity structure.
A sinking fund arrangement is a way to reduce credit risk by making the issuer 
set aside funds over time to retire the bond issue. For example, a corporate bond 
issue may require a specified percentage of the bond’s outstanding principal amount

to be retired each year. The issuer may satisfy this requirement in one of two ways. 
The most common approach is for the issuer to make a random call for the specified 
percentage of bonds that must be retired and to pay the bondholders whose bonds 
are called the sinking fund price, which is typically par. Alternatively, the issuer can 
deliver bonds to the trustee with a total amount equal to the amount that must be

Corporate Debt 379
retired. To do so, the issuer may purchase the bonds in the open market. The sinking 
fund arrangement on a term maturity structure accomplishes the same goal as the 
serial maturity structure—that is, both result in a portion of the bond issue being 
paid off each year. With a serial maturity structure, however, the bondholders know 
which bonds will mature and will thus be paid off each year. In contrast, the bonds 
retired annually with a sinking fund arrangement are designated by a random drawing.
6.3.4  Asset or Collateral Backing
Unlike most highly rated sovereign bonds, all corporate debt is exposed to varying 
degrees of credit risk. Thus, corporate debt is structured with this risk in mind. An 
important consideration for investors is seniority ranking—that is, the systematic way 
in which lenders are repaid if the issuer defaults. In the case of secured debt, there 
is some form of collateral pledged to ensure payment of the debt. In contrast, in the

case of unsecured debt, claims are settled by the general assets of the company in 
accordance with the priority of payments that applies either legally or contractually 
and as described in the bond indenture. Within each category of debt (secured and 
unsecured), there are finer gradations of rankings, which are discussed in the reading 
on credit analysis.
There is a wide range of bonds that are secured by some form of collateral. 
Companies that need to finance equipment or physical assets may issue equipment 
trust certificates. Corporate issuers also sell collateral trust bonds that are secured by 
securities, such as common shares, bonds, or other financial assets. Banks, particularly 
in Europe, may issue covered bonds, which are a type of debt obligation that is secured 
by a segregated pool of assets. Asset-  backed securities are also secured forms of debt.
Companies can and do default on their debt. Debt secured by collateral may still

experience losses, but investors in secured debt usually fare better than in unsecured 
debt in bankruptcy proceedings. Investors who face a higher level of credit risk typi -
cally require a higher yield than investors exposed to very little credit risk.
6.3.5  Contingency Provisions
Contingency provisions are clauses in the indenture that provide the issuer or the 
bondholders rights that affect the disposal or redemption of the bond. The three 
commonly used contingency provisions are call, put, and conversion provisions.
Callable bonds give issuers the ability to retire debt prior to maturity. The most 
compelling reason for them to do so is to take advantage of lower borrowing rates. 
By calling the bonds before their maturity date, the issuer can substitute a new, lower 
cost bond issue for an older, higher cost one. In addition, companies may also retire 
debt to eliminate restrictive covenants or to alter their capital structure to improve

flexibility. Because the call provision is a valuable option for the issuer, investors 
demand compensation ex ante (before investing in the bond). Thus, other things equal, 
investors require a higher yield (and thus pay a lower price) for a callable bond than 
for an otherwise similar non-  callable bond.
Companies also issue putable bonds, which give the bondholders the right to sell 
the bond back to the issuer at a predetermined price on specified dates before matu -
rity. Most putable bonds pay a fixed rate of interest, although some bonds may have 
step-  up coupons that increase by specified margins at specified dates. Because the put 
provision is a valuable option for the bondholders, putable bonds offer a lower yield 
(and thus have a higher price) than otherwise similar non-  putable bonds. The main 
corporate issuers of putable bonds are investment-  grade companies. Putable bonds 
may offer them a cheaper way of raising capital, in particular if the company estimates

that the benefit of a lower coupon outweighs the risk associated with the put provision.
A convertible bond is a hybrid security that lies on a continuum between debt and 
equity. It consists of a long position in an option-  free bond and a conversion option 
that gives the bondholder the right to convert the bond into a specified number of

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 380
shares of the issuer’s common shares. From the point of view of the issuer, convertible 
bonds make it possible to raise funds that may not be possible without the incentive 
associated with the conversion option. The more common issuers of convertibles 
bonds are newer companies that have not established a presence in debt capital mar -
kets but who are able to present a more attractive package to institutional investors 
by including an equity upside potential. Established issuers of bonds may also prefer 
to issue convertible bonds because they are usually sold at a lower coupon rate than 
otherwise similar non-  convertible bonds as a result of investors’ attraction to the 
conversion provision. However, there is a potential equity dilution effect if the bonds 
are converted. From the investor’s point of view, convertible bonds represent a means

of accessing the equity upside potential of the issuer but at a lower risk–reward profile 
because there is the floor of the coupon payments in the meantime.
6.3.6  Issuance, Trading, and Settlement
In the era before electronic settlement, there were some differences in the processes 
of issuing and settling corporate bonds depending on where the securities were reg -
istered. This is no longer the case; the processes of issuing and settling bonds are now 
essentially the same globally. New corporate bond issues are usually sold to investors 
by investment banks acting as underwriters in the case of underwritten offerings or 
brokers in the case of best effort offerings. They are then settled via the local settle -
ment system. These local systems typically possess a “bridge” to the two Eurobond 
systems, Euroclear and Clearstream. As for Eurobonds from the corporate sector, 
they are all issued, traded, and settled in the same way, irrespective of the issuer and 
its local jurisdiction.

Most bond prices are quoted in basis points. The vast majority of corporate bonds 
are traded in OTC markets through dealers who “make a market” in bonds and sell 
from their inventory. Dealers do not typically charge a commission or a transaction 
fee. Instead, they earn a profit from the bid–offer spread.
For corporate bonds, settlement differences exist primarily between new bond 
issues and the secondary trading of bonds. The issuing phase for an underwritten 
offering usually takes several days. Thus, settlement takes longer for new bond issued 
than for the secondary trading of bonds, for which settlement is typically on a T + 2 
or T + 3 basis.
EXAMPLE 6   
Corporate Debt
1 A loan made by a group of banks to a private company is most likely :
A a bilateral loan.
B a syndicated loan.
C a securitized loan.
2 Which of the following statements relating to commercial paper is most 
accurate ? Companies issue commercial paper:
A only for funding working capital.

B only as an interim source of financing.
C both for funding working capital and as an interim source of funding.
3 Maturities of Eurocommercial paper range from:
A overnight to three months.
B overnight to one year.

Structured Financial Instruments 381
C three months to one year.
4 A bond issue that has a stated number of bonds that mature and are paid 
off each year before final maturity most likely  has a:
A term maturity.
B serial maturity.
C sinking fund arrangement.
B is correct. A loan from a group of lenders to a single borrower is a syndicated 
loan. A is incorrect because a bilateral loan is a loan from a single lender to a 
single borrower. C is incorrect because securitization involves moving assets, 
such as loans, from the owner of the assets into a special legal entity.
C is correct. Companies use commercial paper as a source of funding working 
capital and seasonal demand for cash, as well as an interim source of financing 
until permanent financing can be arranged.
B is correct. Eurocommercial paper ranges in maturity from overnight to 364 days.
B is correct. With a serial maturity structure, a stated number of bonds mature

and are paid off each year before final maturity. A is incorrect because a bond 
issue with a term maturity structure is paid off in one lump sum at maturity. C 
is incorrect because a sinking fund arrangement, like a serial maturity structure, 
results in a portion of the bond issue being paid off every year. However, with a 
serial maturity structure, the bonds are paid off because the maturity dates are 
spread out during the life of the bond and the bonds that are retired are matur -
ing; the bondholders know in advance which bonds will be retired. In contrast, 
the bonds retired annually with a sinking fund arrangement are designated by 
a random drawing.
STRUCTURED FINANCIAL INSTRUMENTS
Structured financial instruments  represent a broad sector of financial instruments. 
This sector includes asset-  backed securities (ABS) and collateralized debt obligations 
(CDOs). CDOs are securities backed by a diversified pool of one or more debt obli -

gations, and like ABS, they are discussed in the reading on asset-  backed securities. 
A common attribute of all these financial instruments is that they repackage and 
redistribute risks. 
Our focus in this section is on structured financial instruments apart from ABS 
and CDOs. These instruments typically have customized structures that often combine 
a bond and at least one derivative. Some of these instruments are called structured 
products. The use of derivatives gives the holder of the structured financial instrument 
exposure to one or more underlying assets, such as equities, bonds, and commodities. 
The redemption value and often the coupons of structured financial instruments are 
linked via a formula to the performance of the underlying asset(s). Thus, the bond’s 
payment features are replaced with non-  traditional payoffs that are derived not from 
the issuer’s cash flows but from the performance of the underlying asset(s). While 7

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 382
there is no universally accepted taxonomy used to categorize structured financial 
instruments, we will present four broad categories of instruments in this reading: 
capital protected, yield enhancement, participation, and leveraged instruments.
7.1 Capital Protected Instruments
Suppose an investor has $100,000 to invest. The investor buys zero-  coupon bonds issued 
by a sovereign issuer that will pay off $100,000 one year from now. Also suppose the 
cost of buying the zero-  coupon bonds is $99,000. The investor can use the $1,000 left 
over from the purchase of the zero-  coupon bond to buy a call option on some under -
lying asset that expires one year from now. Buying a call option gives the investor the 
right to buy the underlying asset in one year at a pre-  determined price. The investor 
will receive $100,000 when the zero-  coupon bond matures and may also gain from

the upside potential of the call option, if any. This combination of the zero-  coupon 
bond and the call option can be prepackaged as a structured financial instrument 
called a guarantee certificate . The zero-  coupon bond provides the investor capital 
protection; at maturity, the investor will receive 100% of the capital invested even if 
the call option expires worthless. The call option provides upside potential if the price 
of the underlying asset rises and a limited downside if the price of the underlying asset 
falls. The downside is limited to the price, often called the premium, paid for the call 
option. In our example, the maximum loss the investor faces is $1,000, which is the 
price paid for the call option.
Capital protected instruments offer different levels of capital protection. A guar -
antee certificate offers full capital protection. Other structured financial instruments 
may offer only partial capital protection. Note that the capital protection is only as

good as the issuer of the instrument. Should the issuer of guarantee certificates go 
bankrupt, investors may lose their entire capital.
7.2 Yield Enhancement Instruments
Yield enhancement refers to increasing risk exposure in the hope of realizing a higher 
expected return. A credit-  linked note (CLN)  is an example of a yield enhancement 
instrument. Specifically, it is a type of bond that pays regular coupons but whose 
redemption value depends on the occurrence of a well-  defined credit event, such as a 
rating downgrade or the default of an underlying asset, called the reference asset. If the 
specified credit event does not occur, the investor receives the par value of the CLN at 
maturity. But if the specified credit event occurs, the investor receives the par value of 
the CLN minus the nominal value of the reference asset to which the CLN is linked.
A CLN allows the issuer to transfer the effect of a particular credit event to inves -

tors. Thus, the issuer is the protection buyer and the investor is the protection seller. 
Investors are willing to buy CLNs because these securities offer higher coupons than 
otherwise similar bonds. In addition, CLNs are usually issued at a discount. Thus, if 
the specified credit event does not occur, investors will realize a significant capital 
gain on the purchase of the CLN. 
7.3 Participation Instruments
As the name suggests, a participation instrument is one that allows investors to 
participate in the return of an underlying asset. Floating-  rate bonds can be viewed 
as a type of participation instrument. As discussed earlier, floaters differ from fixed-  
rate bonds in that their coupon rate adjusts periodically according to a pre-  specified 
formula. The coupon formula is usually expressed as a reference rate adjusted for a 
spread. A floater has almost zero interest rate risk because changes in the cash flows

Structured Financial Instruments 383
limit the effect of changes in interest rates on the floater’s price. Thus, floaters give 
investors the opportunity to participate in movements of interest rates. For example, 
the Italian government issued in June 2005 floaters set to mature in June 2020. The 
coupon payments are delivered annually and determined by the formula of 85% of 
the 10-  year constant maturity swap rate, a widely-  used type of interest rate. Thus, 
investors who hold these floaters participate partially in movements of the 10-  year 
constant maturity swap rate.
Most participation instruments are designed to give investors indirect exposure 
to a particular index or asset price. For example, investors who are precluded from 
investing in equity directly may get indirect equity exposure by investing in participa -
tion instruments that are linked via a formula to the performance of equity indexes.

Many structured products sold to individuals are participation instruments linked to 
an equity index. In contrast to capital protected instruments that offer equity exposure, 
these participation instruments usually do not offer capital protection.
7.4 Leveraged Instruments
Leveraged instruments are structured financial instruments created to magnify returns 
and offer the possibility of high payoffs from small investments. An inverse floater  is 
an example of a leveraged instrument. As the name suggests, an inverse floater is the 
opposite of a traditional floater. The cash flows are adjusted periodically and move 
in the opposite direction of changes in the reference rate. So when the reference rate 
decreases, the coupon payment of an inverse floater increases.
A general formula for an inverse floater’s coupon rate is:
Inverse floater coupon rate = C – (L × R)
where C is the maximum coupon rate reached if the reference rate is equal to zero,

L is the coupon leverage, and R is the reference rate on the reset date. Note that the 
coupon leverage indicates the multiple that the coupon rate will change in response 
to a 100 basis points (bps) change in the reference rate. For example, if the coupon 
leverage is three, the inverse floater’s coupon rate will decrease by 300 bps when the 
reference rate increases by 100 bps.
Inverse floaters with a coupon leverage greater than zero but lower than one are 
called deleveraged inverse floaters. Inverse floaters with a coupon leverage greater 
than one are called leveraged inverse floaters. For example, the Royal Bank of Scotland 
PLC issued a leveraged inverse floater set to mature in February 2020. The coupon 
payments are delivered quarterly and are determined by the formula of 8% minus 
the euro 3-  month Libor. In this case, the coupon leverage is one. Thus, for a 100 bps 
increase in the euro 3-  month Libor, the coupon rate of the leveraged inverse floater

will decrease by 100 bps. Inverse floaters often have a floor that specifies a minimum 
coupon rate; for example, a floor may be set at zero to avoid the possibility of a neg -
ative interest rate. 
EXAMPLE 7   
Structured Financial Instruments
1 If an investor holds a credit-  linked note and the credit event does not 
occur, the investor receives:
A all promised cash flows as scheduled.
B all coupon payments as scheduled but not the par value at maturity.

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 384
C all coupon payments as scheduled and the par value minus the nom -
inal value of the reference asset to which the credit-  linked note is 
linked at maturity.
2 A structured financial instrument whose coupon rate is determined by the 
formula 5% – (0.5 × Libor) is most likely :
A a leveraged inverse floater.
B a participation instrument.
C a deleveraged inverse floater.
A is correct. If the credit event does not occur, the issuer must make all prom -
ised cash flows as scheduled—that is, the regular coupon payments and the par 
value at maturity.
C is correct. A structured financial instrument whose coupon rate moves in the 
opposite direction of the reference rate is called an inverse floater. Because the 
coupon leverage (0.5) is greater than zero but lower than one, the structured 
financial instrument is a deleveraged inverse floater. In this example, if the

reference rate increases by 100 bps, the coupon rate decreases by 50 bps. A is 
incorrect because the coupon leverage would have to be higher than one for the 
structured financial instrument to be a leveraged inverse floater. B is incorrect 
because a participation instrument is designed to give investors indirect exposure 
to a particular underlying asset.
SHORT-  TERM FUNDING ALTERNATIVES AVAILABLE 
TO BANKS
Funding refers to the amount of money or resources necessary to finance some specific 
project or enterprise. Accordingly, funding markets are markets in which debt issuers 
borrow to meet their financial needs. Companies have a range of funding alternatives, 
including bank loans, commercial paper, notes, and bonds. Financial institutions such as 
banks have larger financing needs than non-  financial companies because of the nature 
of their operations. This section discusses the additional funding alternatives that are

available to them. The majority of these funding alternatives have short maturities.
Banks, such as deposit-  taking (or depositary) institutions, typically have access to 
funds obtained from the retail market—that is, deposit accounts from their customers. 
However, it is quite common for banks to originate more loans than they have retail 
deposits. Thus, whenever the amount of retail deposits is insufficient to meet their 
financial needs, banks also need to raise funds from the wholesale market. Wholesale 
funds include central bank funds, interbank deposits, and certificates of deposit. In 
addition to filling the gaps between loans and deposits, banks raise wholesale funds 
to minimize their funding cost. At the margin, wholesale funds may be less expensive 
(in terms of interest expense) than deposit funding. Finally, financial institutions may 
raise wholesale funds as a balance sheet risk management tool to reduce interest rate 
risk, as discussed in Section 2.1.5.1.8

Short-  Term Funding Alternatives Available to Banks 385
8.1 Retail Deposits
One of the primary sources of funding for deposit-  taking banks is their retail deposit 
base, which includes funds from both individual and commercial depositors. There 
are several types of retail deposit accounts. Demand deposits, also known as checking 
accounts, are available to customers “on demand. ” Depositors have immediate access 
to the funds in their deposit accounts and use the funds as a form of payment for 
transactions. Because the funds are available immediately, deposit accounts typically 
pay no interest. In contrast, savings accounts pay interest and allow depositors to 
accumulate wealth in a very liquid form, but they do not offer the same transactional 
convenience as demand deposits. Money market accounts were originally designed to 
compete with money market mutual funds. They offer money market rates of return 
and depositors can access funds at short or no notice. Thus, money market accounts

are, for depositors, an intermediate between demand deposit and savings accounts.
8.2 Short-  Term Wholesale Funds
Wholesale funds available for banks include reserve funds, interbank funds, and 
certificates of deposit.
8.2.1  Reserve Funds
Many countries require deposit-  taking banks to place a reserve balance with the national 
central bank. The reserve funds help to ensure sufficient liquidity should depositors 
require withdrawal of funds. When a bank cannot obtain short-  term funding, most 
countries allow that bank to borrow from the central bank. In aggregate, the reserve 
funds act as a liquidity buffer providing comfort to depositors and investors that the 
central bank can act as lender of last resort.
Treatment of interest on reserve funds varies among countries, from a low interest 
payment, to no interest payment, to charges for keeping reserve funds. Additionally, 
there is an opportunity cost to the banks for holding reserves with the central bank in

that these funds cannot be invested with higher interest or loaned out to consumers or 
commercial enterprises. Some banks have an excess over the minimum required funds 
to be held in reserve. At the same time, other banks run short of required reserves. 
This imbalance is solved through the central bank funds market , which allows banks 
that have a surplus of funds to loan money to banks that need funds for maturities of 
up to one year. These funds are known as central bank funds and are called “overnight 
funds” when the maturity is one day and “term funds” when the maturity ranges from 
two days to one year. The interest rates at which central bank funds are bought (i.e., 
borrowed) and sold (i.e., lent) are short-  term interest rates determined by the markets 
but influenced by the central bank’s open market operations. These rates are termed 
the central bank funds rates .
In the United States, the central bank is the Federal Reserve (Fed). The central

bank funds and funds rate are called Fed funds and Fed funds rates, respectively. 
Other short-  term interest rates, such as the yields on Treasury bills, are highly cor -
related with the Fed funds rate. The most widely followed rate is known as the Fed 
funds effective rate, which is the volume-  weighted average of rates for Fed fund trades 
arranged throughout the day by the major New York City brokers. Fed funds are traded 
between banks and other financial institutions globally and may be transacted directly 
or through money market brokers.
8.2.2  Interbank Funds
The interbank market is the market of loans and deposits between banks. The term to 
maturity of an interbank loan or deposit ranges from overnight to one year. The rate 
on an interbank loan or deposit can be quoted relative to a reference rate, such as an

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 386
interbank offered rate or as a fixed interest rate. An interbank deposit is unsecured, so 
banks placing deposits with another bank need to have an interbank line of credit in 
place for that institution. Usually, a large bank will make a two-  way price, indicating 
the rate at which it will lend funds and the rate at which it will borrow funds for a 
specific maturity, on demand. Interest on the deposit is payable at maturity. Much 
interbank dealing takes place on the Reuters electronic dealing system, so that the 
transaction is done without either party speaking to the other.
Because the market is unsecured, it is essentially based on confidence in the banking 
system. At times of stress, such as in the aftermath of the Lehman Brothers’ bankruptcy 
in 2008, the market is prone to “dry up” as banks withdraw from funding other banks.
8.2.3  Large-  Denomination Negotiable Certificates of Deposit

A certificate of deposit  (CD) is an instrument that represents a specified amount of 
funds on deposit for a specified maturity and interest rate. CDs are an important source 
of funds for financial institutions. A CD may take one of two forms: non-  negotiable 
or negotiable. If the CD is non-  negotiable, the deposit plus the interest are paid to 
the initial depositor at maturity. A withdrawal penalty is imposed if the depositor 
withdraws funds prior to the maturity date.
Alternatively, a negotiable CD allows any depositor (initial or subsequent) to sell 
the CD in the open market prior to the maturity date. Negotiable CDs were intro -
duced in the United States in the early 1960s when various types of deposits were 
constrained by interest rate ceilings. At the time, bank deposits were not an attractive 
investment because investors earned a below-  market interest rate unless they were 
prepared to commit their capital for an extended period of time. The introduction of

negotiable CDs enabled bank customers to buy a three-  month or longer negotiable 
instrument yielding a market interest rate and to recover their investment by selling 
it in the market. This innovation helped banks increase the amount of funds raised in 
the money markets. It also fostered competition among deposit-  taking institutions.
There are two types of negotiable CDs: large-  denomination CDs and small-  
denomination CDs. Thresholds between small- and large-  denomination CDs vary 
among countries. For example, in the United States, large-  denomination CDs are 
usually issued in denominations of $1 million or more. Small-  denomination CDs are 
a retail-  oriented product, and they are of secondary importance as a funding alterna -
tive. Large-  denomination CDs, in contrast, are an important source of wholesale funds 
and are typically traded among institutional investors.
Like other money market securities, CDs are available in domestic bond markets

as well as in the Eurobond market. Most CDs have maturities shorter than one year 
and pay interest at maturity. CDs with longer maturities are called “term CDs. ”
Yields on CDs are driven primarily by the credit risk of the issuing bank and to a 
lesser extent by the term to maturity. The spread attributable to credit risk will vary 
with economic conditions and confidence in the banking system in general and in the 
issuing bank in particular. As with all debt instruments, spreads widen during times 
of financial turmoil as a result of an increase in risk aversion.
8.3 Repurchase and Reverse Repurchase Agreements
Repurchase agreements are another important source of funding not only for banks 
but also for other market participants. A repurchase agreement  or repo  is the sale 
of a security with a simultaneous agreement by the seller to buy the same security 
back from the purchaser at an agreed-  on price and future date.6 In practical terms,

a repurchase agreement can be viewed as a collateralized loan in which the security 
6 Repurchase agreements can be structured such that the transaction is terminable on demand.

Short-  Term Funding Alternatives Available to Banks 387
sold and subsequently repurchased represents the collateral posted. One party is bor -
rowing money and providing collateral for the loan at an interest rate that is typically 
lower than on an otherwise similar bank loan. The other party is lending money while 
accepting a security as collateral for the loan.
Repurchase agreements are a common source of money market funding for dealer 
firms in many countries. An active market in repurchase agreements underpins every 
liquid bond market. Financial and non-  financial companies participate actively in 
the market as both sellers and buyers of collateral depending on their circumstances. 
Central banks are also active users of repurchase agreements in their daily open 
market operations; they either lend to the market to increase the supply of funds or 
withdraw surplus funds from the market.
8.3.1  Structure of Repurchase and Reverse Repurchase Agreements

Suppose a government securities dealer purchases a 2.25% UK gilt that matures in 
three years. The dealer wants to fund the position overnight through the end of the 
next business day. The dealer could finance the transaction with its own funds, which 
is what other market participants, such as insurance companies or pension funds, may 
do in similar circumstances. But a securities dealer typically uses leverage (debt) to 
fund the position. Rather than borrowing from a bank, the dealer uses a repurchase 
agreement to obtain financing by using the gilt as collateral for the loan.
A repurchase agreement may be constructed as follows: The dealer sells the 2.25% 
UK gilt that matures in three years to a counterparty for cash today. At the same time, 
the dealer makes a promise to buy the same gilt the next business day for an agreed-  on 
price. The price at which the dealer repurchases the gilt is known as the repurchase

price . The date when the gilt is repurchased, the next business day in this example, 
is called the repurchase date . When the term of a repurchase agreement is one day, 
it is called an “overnight repo. ” When the agreement is for more than one day, it is 
called a “term repo. ” An agreement lasting until the final maturity date is known as 
a “repo to maturity. ”
As in any borrowing or lending transaction, the interest rate of the loan must be 
negotiated in the agreement. The interest rate on a repurchase agreement is called 
the repo rate . Several factors affect the repo rate:
■■The risk associated with the collateral. Repo rates are typically lower for highly 
rated collaterals, such as highly rated sovereign bonds. They increase with the 
level of credit risk associated with the collateral underlying the transaction.
■■The term  of the repurchase agreement. Repo rates generally increase with 
maturity because long-  term rates are typically higher than short-  term rates in

normal circumstances.
■■The delivery requirement  for the collateral. Repo rates are usually lower when 
delivery to the lender is required.
■■The supply and demand conditions  of the collateral. The more scarce a specific 
piece of collateral, the lower the repo rate against it because the borrower has 
a security that lenders of cash want for specific reasons, perhaps because the 
underlying issue is in great demand. The demand for such collateral means that 
it considered to be “on special. ” Collateral that is not special is known as “gen -
eral collateral. ” The party that has a need for collateral that is on special is typi -
cally required to lend funds at a below-  market repo rate to obtain the collateral.
■■The interest rates of alternative financing  in the money market.
The interest on a repurchase agreement is paid on the repurchase date—that is, at 
the termination of the agreement. Note that any coupon paid by the security during the

repurchase agreement belongs to the seller of the security (i.e., the borrower of cash).

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 388
When a repurchase agreement is viewed through the lens of the cash lending 
counterparty, the transaction is referred to as a reverse repurchase agreement  or 
reverse repo . In the above example, the counterparty agrees to buy the 2.25% UK 
gilt that matures in three years and promises to sell it back the next business day at 
the agreed-  on price. The counterparty is making a collateralized loan to the dealer. 
Reverse repurchase agreements are very often used to borrow securities to cover 
short positions.
The question of whether a particular transaction is labeled a repurchase agreement 
or a reverse repurchase agreement depends on one’s point of view. Standard practice 
is to view the transaction from the dealer’s perspective. If the dealer is borrowing cash 
from a counterparty and providing securities as collateral, the transaction is termed

a repurchase agreement. If the dealer is borrowing securities and lending cash to the 
counterparty, the transaction is termed a reverse repurchase agreement.
8.3.2  Credit Risk Associated with Repurchase Agreements
Each market participant in a repurchase agreement is exposed to the risk that the 
counterparty defaults, regardless of the collateral exchanged. Credit risk is present 
even if the collateral is a highly rated sovereign bond. Suppose that a dealer (i.e., the 
borrower of cash) defaults and is not in a position to repurchase the collateral on the 
specified repurchase date. The lender of funds takes possession of the collateral and 
retains any income owed to the borrower. The risk is that the price of the collateral has 
fallen following the inception of the repurchase agreement, causing the market value 
of the collateral to be lower than the unpaid repurchase price. Conversely, suppose 
the investor (i.e., the lender of cash) defaults and is unable to deliver the collateral

on the repurchase date. The risk is that the price of the collateral has risen since the 
inception of the repurchase agreement, resulting in the dealer now holding an amount 
of cash lower than the market value of the collateral. In this case, the investor is liable 
for any excess of the price paid by the dealer for replacement of the securities over 
the repurchase price.
Although both parties to a repurchase agreement are subject to credit risk, 
the agreement is structured as if the lender of funds is the most vulnerable party. 
Specifically, the amount lent is lower than the collateral’s market value. The difference 
between the market value of the security used as collateral and the value of the loan 
is known as the repo margin , although the term haircut  is more commonly used, 
particularly in the United States. The repo margin allows for some worsening in 
market value, and thus provides the cash lender a margin of safety if the collateral’s

market value declines. Repo margins vary by transaction and are negotiated bilaterally 
between the counterparties. The level of margin is a function of the following factors:
■■The length  of the repurchase agreement. The longer the repurchase agreement, 
the higher the repo margin.
■■The quality  of the collateral. The higher the quality of the collateral, the lower 
the repo margin.
■■The credit quality  of the counterparty. The higher the creditworthiness of the 
counterparty, the lower the repo margin.
■■The supply and demand  conditions  of the collateral. Repo margins are lower if 
the collateral is in short supply or if there is a high demand for it.
EXAMPLE 8   
Short-  Term Funding Alternatives Available to Banks
1 Which of the following are not considered wholesale funds?

Short-  Term Funding Alternatives Available to Banks 389
A Interbank funds
B Central bank funds
C Repurchase agreements
2 A large-  denomination negotiable certificate of deposit most likely :
A is traded in the open market.
B is purchased by retail investors.
C has a penalty for early withdrawal of funds.
3 From the dealer’s viewpoint, a repurchase agreement is best described as a 
type of:
A collateralized short-  term lending.
B collateralized short-  term borrowing.
C uncollateralized short-  term borrowing.
4 The interest on a repurchase agreement is known as the:
A repo rate.
B repo yield.
C repo margin.
5 The level of repo margin is higher:
A the higher the quality of the collateral.
B the higher the credit quality of the counterparty.
C the longer the length of the repurchase agreement.
C is correct. Wholesale funds refer to the funds that financial institutions lend to 
and borrow from each other. They include central bank funds, interbank funds,

and certificates of deposit. Although repurchase agreements are an important 
source of funding for banks, they are not considered wholesale funds.
A is correct. Large-  denomination negotiable certificates of deposit (CDs) can 
be traded in the open market. B is incorrect because it is small-  denomination, 
not large-  denomination, negotiable CDs that are primarily purchased by retail 
investors. C is incorrect because it is non-  negotiable, not negotiable, CDs that 
have a penalty for early withdrawal of funds.
B is correct. In a repurchase agreement, a security is sold with a simultaneous 
agreement by the seller to buy the same security back from the purchaser later 
at a higher price. Thus, a repurchase agreement is similar to a collateralized 
short-  term borrowing in which the security sold and subsequently repurchased 
represents the collateral posted. A is incorrect because collateralized short-

term lending is a description of a reverse repurchase agreement. C is incorrect 
because a repurchase agreement involves collateral. Thus, it is a collateralized, 
not uncollateralized, short-  term borrowing.
A is correct. The repo rate is the interest rate on a repurchase agreement. B 
is incorrect because the interest on a repurchase agreement is known as the 
repo rate, not repo yield. C is incorrect because the repo margin refers to the 
difference between the market value of the security used as collateral and the 
value of the loan.

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 390
C is correct. The longer the length of the repurchase agreement, the higher the 
repo margin (haircut). A is incorrect because the higher the quality of the col -
lateral, the lower the repo margin. B is incorrect because the higher the credit 
quality of the counterparty, the lower the repo margin.
SUMMARY
Debt financing is an important source of funds for governments, government-  related 
entities, financial institutions, and non-  financial companies. Well-  functioning fixed-  
income markets help ensure that capital is allocated efficiently to its highest and best 
use globally. Important points include the following:
■■The most widely used ways of classifying fixed-  income markets include the type 
of issuer; the bonds’ credit quality, maturity, currency denomination, and type 
of coupon; and where the bonds are issued and traded.

■■Based on the type of issuer, the three major bond market sectors are the gov -
ernment and government-  related sector, the corporate sector, and the struc -
tured finance sector. The major issuers of bonds globally are governments and 
financial institutions.
■■Investors make a distinction between investment-  grade and high-  yield bond 
markets based on the issuer’s credit quality.
■■Money markets are where securities with original maturities ranging from 
overnight to one year are issued and traded, whereas capital markets are where 
securities with original maturities longer than one year are issued and traded.
■■The majority of bonds are denominated in either euros or US dollars.
■■Investors make a distinction between bonds that pay a fixed rate versus a float -
ing rate of interest. The coupon rate of floating-  rate bonds is often expressed 
as a reference rate plus a spread. Interbank offered rates, such as Libor, are the

most commonly used reference rates for floating-  rate debt and other financial 
■■Interbank offered rates are sets of rates that reflect the rates at which banks 
believe they could borrow unsecured funds from other banks in the interbank 
market for different currencies and different maturities.
■■Based on where the bonds are issued and traded, a distinction is made between 
domestic and international bond markets. The latter includes the Eurobond 
market, which falls outside the jurisdiction of any single country and is charac -
terized by less reporting, regulatory and tax constraints. Investors also make a 
distinction between developed and emerging bond markets.
■■Fixed-  income indexes are used by investors and investment managers to 
describe bond markets or sectors and to evaluate performance of investments 
and investment managers.
■■The largest investors in bonds include central banks; institutional investors,

such as pension funds, hedge funds, charitable foundations and endowments, 
insurance companies, mutual funds and ETFs, and banks; and retail investors, 
typically by means of indirect investments.

Summary 391
■■Primary markets are markets in which issuers first sell bonds to investors to 
raise capital. Secondary markets are markets in which existing bonds are subse -
quently traded among investors.
■■There are two mechanisms for issuing a bond in primary markets: a public 
offering, in which any member of the public may buy the bonds, or a private 
placement, in which only an investor or small group of investors may buy the 
bonds either directly from the issuer or through an investment bank.
■■Public bond issuing mechanisms include underwritten offerings, best effort 
offerings, shelf registrations, and auctions.
■■When an investment bank underwrites a bond issue, it buys the entire issue and 
takes the risk of reselling it to investors or dealers. In contrast, in a best efforts 
offering, the investment bank serves only as a broker and sells the bond issue 
only if it is able to do so. Underwritten and best effort offerings are frequently 
used in the issuance of corporate bonds.

■■The underwriting process typically includes six phases: the determination of the 
funding needs, the selection of the underwriter, the structuring and announce -
ment of the bond offering, pricing, issuance, and closing.
■■A shelf registration is a method for issuing securities in which the issuer files a 
single document with regulators that describes and allows for a range of future 
issuances.
■■An auction is a public offering method that involves bidding, and that is helpful 
in providing price discovery and in allocating securities. It is frequently used in 
the issuance of sovereign bonds.
■■Most bonds are traded in over-  the- counter (OTC) markets, and institutional 
investors are the major buyers and sellers of bonds in secondary markets.
■■Sovereign bonds are issued by national governments primarily for fiscal rea -
sons. They take different names and forms depending on where they are issued,

their maturities, and their coupon types. Most sovereign bonds are fixed-  rate 
bonds, although some national governments also issue floating-  rate bonds and 
inflation-  linked bonds.
■■Local governments, quasi-  government entities, and supranational agencies issue 
bonds, which are named non-  sovereign, quasi-  government, and supranational 
bonds, respectively.
■■Companies raise debt in the form of bilateral loans, syndicated loans, commer -
cial paper, notes, and bonds.
■■Commercial paper is a short-  term unsecured security that is used by companies 
as a source of short-  term and bridge financing. Investors in commercial paper 
are exposed to credit risk, although defaults are rare. Many issuers roll over 
their commercial paper on a regular basis.
■■Corporate bonds and notes take different forms depending on the maturities, 
coupon payment, and principal repayment structures. Important considerations 
also include collateral backing and contingency provisions.

■■Medium-  term notes are securities that are offered continuously to investors by 
an agent of the issuer. They can have short-  term or long-  term maturities.
■■The structured finance sector includes asset-  backed securities, collateralized 
debt obligations, and other structured financial instruments. All of these seem -
ingly disparate financial instruments share the common attribute of repackaging 
risks.

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 392
■■Many structured financial instruments are customized instruments that often 
combine a bond and at least one derivative. The redemption and often the cou -
pons of these structured financial instruments are linked via a formula to the 
performance of the underlying asset(s). Thus, the bond’s payment features are 
replaced with non-  traditional payoffs that are derived not from the issuer’s cash 
flows but from the performance of the underlying asset(s). Capital protected, 
yield enhancement, participation and leveraged instruments are typical exam -
ples of structured financial instruments.
■■Financial institutions have access to additional sources of funds, such as retail 
deposits, central bank funds, interbank funds, large-  denomination negotiable 
certificates of deposit, and repurchase agreements.
■■A repurchase agreement is similar to a collateralized loan. It involves the sale

of a security (the collateral) with a simultaneous agreement by the seller (the 
borrower) to buy the same security back from the purchaser (the lender) at an 
agreed-  on price in the future. Repurchase agreements are a common source of 
funding for dealer firms and are also used to borrow securities to implement 

1 In most countries, the bond market sector with the smallest amount of bonds 
outstanding is most likely  the:
A government sector.
B financial corporate sector.
C non-  financial corporate sector.
2 The distinction between investment grade debt and non-  investment grade debt 
is best described by differences in:
A tax status.
B credit quality.
C maturity dates.
3 A bond issued internationally, outside the jurisdiction of the country in whose 
currency the bond is denominated, is best described as a:
B foreign bond.
C municipal bond.
4 When classified by type of issuer, asset-  backed securities are part of the:
A corporate sector.
B structured finance sector.
C government and government-  related sector. 
5 Compared with developed markets bonds, emerging markets bonds most likely :
A offer lower yields.
B exhibit higher risk.
C benefit from lower growth prospects.
6 With respect to floating-  rate bonds, a reference rate such as the London inter -

bank offered rate (Libor) is most likely  used to determine the bond’s:
A spread.
B coupon rate.
C frequency of coupon payments.
7 The variability of the coupon rate on a Libor-  based floating-  rate bond is most 
likely  due to:
A periodic resets of the reference rate.
B market-  based reassessments of the issuer’s creditworthiness.
C changing estimates by the Libor administrator of borrowing capacity.
8 Which of the following statements is most accurate ? An interbank offered rate:
A is a single reference rate.
B applies to borrowing periods of up to 10 years.
C is used as a reference rate for interest rate swaps.
9 An investment bank that underwrites a bond issue most likely :
A buys and resells the newly issued bonds to investors or dealers.
B acts as a broker and receives a commission for selling the bonds to investors.

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 394
C incurs less risk associated with selling the bonds than in a best efforts 
offering.
10 In major developed bond markets, newly issued sovereign bonds are most  often 
sold to the public via a(n):
A auction.
C best efforts offering.
11 Which of the following describes privately placed bonds? 
A They are non-  underwritten and unregistered.
B They usually have active secondary markets.
C They are less customized than publicly offered bonds.
12 A mechanism by which an issuer may be able to offer additional bonds to the 
general public without preparing a new and separate offering circular best 
describes:
A the grey market.
B a shelf registration.
C a private placement.
13 Which of the following statements related to secondary bond markets is most 
accurate ?
A Newly issued corporate bonds are issued in secondary bond markets.
B Secondary bond markets are where bonds are traded between investors.

C The major participants in secondary bond markets globally are retail 
14 A bond market in which a communications network matches buy and sell 
orders initiated from various locations is best described as an:
A organized exchange.
B open market operation.
C over-  the- counter market.
15 A liquid secondary bond market allows an investor to sell a bond at:
A the desired price.
B a price at least equal to the purchase price.
C a price close to the bond’s fair market value.
16 Corporate bond secondary market trading most often  occurs:
A on a book-  entry basis.
B on organized exchanges.
C prior to settlement at T + 1. 
17 Sovereign bonds are best described as:
A bonds issued by local governments.
B secured obligations of a national government.
C bonds backed by the taxing authority of a national government.
18 Which factor is associated with a more favorable quality sovereign bond credit 
rating? 
A Issued in local currency, only
B Strong domestic savings base, only

C Issued in local currency of country with strong domestic savings base

19 Which type of sovereign bond has the lowest interest rate risk for an investor?
A Floaters
B Coupon bonds
C Discount bonds
20 Agency bonds are issued by:
A local governments.
B national governments.
C quasi-  government entities.
21 The type of bond issued by a multilateral agency such as the International 
Monetary Fund (IMF) is best described as a:
A sovereign bond.
B supranational bond.
C quasi-  government bond.
22 A bond issued by a local government authority, typically without an explicit 
funding commitment from the national government, is most likely  classified as 
a:
B quasi-  government bond 
23 Which of the following statements relating to commercial paper is most 
accurate ?
A There is no secondary market for trading commercial paper.
B Only the strongest, highly rated companies issue commercial paper.
C Commercial paper is a source of interim financing for long-  term projects.
24 Eurocommerical paper is most likely :

A negotiable.
B denominated in euro.
C issued on a discount basis.
25 For the issuer, a sinking fund arrangement is most similar  to a:
A term maturity structure. 
B serial maturity structure.
C bondholder put provision.
26 When issuing debt, a company may use a sinking fund arrangement as a means 
of reducing:
27 Which of the following is a source of wholesale funds for banks?
A Demand deposits
B Money market accounts
C Negotiable certificates of deposit
28 A characteristic of negotiable certificates of deposit is:
A they are mostly available in small denominations.
B they can be sold in the open market prior to maturity.
C a penalty is imposed if the depositor withdraws funds prior to maturity.

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 396
29 A repurchase agreement is most  comparable to a(n):
A interbank deposit.
B collateralized loan.
C negotiable certificate of deposit.
30 The repo margin is:
A negotiated between counterparties.
B established independently of market-  related conditions.
C structured on an agreement assuming equal credit risks to all 
counterparties.
31 The repo margin on a repurchase agreement is most likely  to be lower when:
A the underlying collateral is in short supply.
B the maturity of the repurchase agreement is long.
C the credit risk associated with the underlying collateral is high.

Solutions 397
SOLUTIONS
1 C is correct. In most countries, the largest issuers of bonds are the national and 
local governments as well as financial institutions. Thus, the bond market sector 
with the smallest amount of bonds outstanding is the non-  financial corporate 
sector.
2 B is correct. The distinction between investment grade and non-  investment 
grade debt relates to differences in credit quality, not tax status or maturity 
dates. Debt markets are classified based on the issuer’s creditworthiness as 
judged by the credit ratings agencies. Ratings of Baa3 or above by Moody’s 
Investors Service or BBB– or above by Standard & Poor’s and Fitch Ratings are 
considered investment grade, whereas ratings below these levels are referred to 
as non-  investment grade (also called high yield, speculative, or junk).
3 A is correct. Eurobonds are issued internationally, outside the jurisdiction of 
any single country. B is incorrect because foreign bonds are considered inter -

national bonds, but they are issued in a specific country, in the currency of 
that country, by an issuer domiciled in another country. C is incorrect because 
municipal bonds are US domestic bonds issued by a state or local government.
4 B is correct. Asset-  backed securities (ABS) are securitized debt instruments 
created by securitization, a process that involves transferring ownership of 
assets from the original owners to a special legal entity. The special legal 
entity then issues securities backed by the transferred assets. The assets’ cash 
flows are used to pay interest and repay the principal owed to the holders of 
the securities. Assets that are typically used to create securitized debt instru -
ments include loans (such as mortgage loans) and receivables (such as credit 
card receivables). The structured finance sector includes such securitized debt 
instruments (also called asset-  backed securities).

5 B is correct. Many emerging countries lag developed countries in the areas of 
political stability, property rights, and contract enforcement. Consequently, 
emerging market bonds usually exhibit higher risk than developed markets 
bonds. A is incorrect because emerging markets bonds typically offer higher 
(not lower) yields than developed markets bonds to compensate investors for 
the higher risk. C is incorrect because emerging markets bonds usually benefit 
from higher (not lower) growth prospects than developed markets bonds.
6 B is correct. The coupon rate of a floating-  rate bond is expressed as a reference 
rate plus a spread. Different reference rates are used depending on where the 
bond is issued and its currency denomination, but one of the most widely used 
set of reference rates is Libor. A and C are incorrect because a bond’s spread 
and frequency of coupon payments are typically set when the bond is issued 
and do not change during the bond’s life.

7 A is correct. Changes in the coupon rate of interest on a floating-  rate bond that 
uses a Libor reference rate are due to changes in the reference rate (for example, 
90- day Libor), which resets periodically. “Therefore, the coupon rate adjusts to 
the level of market interest rates (plus the spread) each time the reference rate 
is reset. ” 
8 C is correct. Interbank offered rates are used as reference rates not only for 
floating-  rate bonds, but also for other debt instruments including mortgages, 
derivatives such as interest rate and currency swaps, and many other financial 
contracts and products. A and B are incorrect because an interbank offered rate 
such as Libor or Euribor is a set of reference rates (not a single reference rate) 
for different borrowing periods of up to one year (not 10 years).

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 398
9 A is correct. In an underwritten offering (also called firm commitment offer -
ing), the investment bank (called the underwriter) guarantees the sale of the 
bond issue at an offering price that is negotiated with the issuer. Thus, the 
underwriter takes the risk of buying the newly issued bonds from the issuer, and 
then reselling them to investors or to dealers who then sell them to investors. 
B and C are incorrect because the bond issuing mechanism where an invest -
ment bank acts as a broker and receives a commission for selling the bonds to 
investors, and incurs less risk associated with selling the bonds, is a best efforts 
offering (not an underwritten offering).
10 A is correct. In major developed bond markets, newly issued sovereign bonds 
are sold to the public via an auction. B and C are incorrect because sovereign 
bonds are rarely issued via private placements or best effort offerings.

11 A is correct. Private placements are typically non-  underwritten, unregis -
tered bond offerings that are sold only to a single investor or a small group of 
investors. 
12 B is correct. A shelf registration allows certain authorized issuers to offer addi -
tional bonds to the general public without having to prepare a new and separate 
offering circular. The issuer can offer multiple bond issuances under the same 
master prospectus, and only has to prepare a short document when additional 
bonds are issued. A is incorrect because the grey market is a forward market for 
bonds about to be issued. C is incorrect because a private placement is a non-  
underwritten, unregistered offering of bonds that are not sold to the general 
public but directly to an investor or a small group of investors.
13 B is correct. Secondary bond markets are where bonds are traded between 
investors. A is incorrect because newly issued bonds (whether from corporate

issuers or other types of issuers) are issued in primary (not secondary) bond 
markets. C is incorrect because the major participants in secondary bond 
markets globally are large institutional investors and central banks (not retail 
investors).
14 C is correct. In over-  the- counter (OTC) markets, buy and sell orders are 
initiated from various locations and then matched through a communications 
network. Most bonds are traded in OTC markets. A is incorrect because on 
organized exchanges, buy and sell orders may come from anywhere, but the 
transactions must take place at the exchange according to the rules imposed by 
the exchange. B is incorrect because open market operations refer to central 
bank activities in secondary bond markets. Central banks buy and sell bonds, 
usually sovereign bonds issued by the national government, as a means to 
implement monetary policy.
15 C is correct. Liquidity in secondary bond markets refers to the ability to buy or

sell bonds quickly at prices close to their fair market value. A and B are incor -
rect because a liquid secondary bond market does not guarantee that a bond 
will sell at the price sought by the investor, or that the investor will not face a 
loss on his or her investment.
16 A is correct. The vast majority of corporate bonds are traded in over-  the- 
counter (OTC) markets that use electronic trading platforms through which 
users submit buy and sell orders. Settlement of trades in the OTC markets 
occurs by means of a simultaneous exchange of bonds for cash on the books of 
the clearing system “on a paperless, computerized book-  entry basis. ” 
17 C is correct. Sovereign bonds are usually unsecured obligations of the national 
government issuing the bonds; they are not backed by collateral, but by the tax -
ing authority of the national government. A is incorrect because bonds issued

Solutions 399
by local governments are non-  sovereign (not sovereign) bonds. B is incorrect 
because sovereign bonds are typically unsecured (not secured) obligations of a 
national government.
18 C is correct. Bonds issued in the sovereign’s currency and a strong domes -
tic savings base are both favorable sovereign rating factors. It is common to 
observe a higher credit rating for sovereign bonds issued in local currency 
because of the sovereign’s ability to tax its citizens and print its own currency. 
Although there are practical limits to the sovereign’s taxing and currency-  
printing capacities, each tends to support a sovereign’s ability to repay debt. A 
strong domestic savings base is advantageous because it supports the sover -
eign’s ability to issue debt in local currency to domestic investors. 
19 A is correct. Floaters are bonds with a floating rate of interest that resets 
periodically based on changes in the level of a reference rate, such as Libor.

Because changes in the reference rate reflect changes in market interest rates, 
price changes of floaters are far less pronounced than those of fixed-  rate bonds, 
such as coupon bonds and discount bonds. Thus, investors holding floaters are 
less exposed to interest rate risk than investors holding fixed-  rate discount or 
coupon bonds. 
20 C is correct. Agency bonds are issued by quasi-  government entities. These enti -
ties are agencies and organizations usually established by national governments 
to perform various functions for them. A and B are incorrect because local and 
national governments issue non-  sovereign and sovereign bonds, respectively.
21 B is correct. The IMF is a multilateral agency that issues supranational bonds. A 
and C are incorrect because sovereign bonds and quasi-  government bonds are 
issued by national governments and by entities that perform various functions 
for national governments, respectively.

22 C is correct. Bonds issued by levels of government below the national level—
such as provinces, regions, states, cities, and local government authorities—are 
classified as non-  sovereign government bonds. These bonds are typically not 
guaranteed by the national government. 
23 C is correct. Companies use commercial paper not only as a source of funding 
working capital and seasonal demand for cash, but also as a source of interim 
financing for long-  term projects until permanent financing can be arranged. A 
is incorrect because there is a secondary market for trading commercial paper, 
although trading is limited except for the largest issues. B is incorrect because 
commercial paper is issued by companies across the risk spectrum, although 
only the strongest, highly rated companies issue low-  cost commercial paper.
24 A is correct. Commercial paper, whether US commercial paper or

Eurocommercial paper, is negotiable—that is, investors can buy and sell com -
mercial paper on secondary markets. B is incorrect because Eurocommercial 
paper can be denominated in any currency. C is incorrect because 
Eurocommercial paper may be issued on an interest-  bearing (or yield) basis or a 
discount basis.
25 B is correct. With a serial maturity structure, a stated number of bonds mature 
and are paid off on a pre-  determined schedule before final maturity. With a 
sinking fund arrangement, the issuer is required to set aside funds over time to 
retire the bond issue. Both result in a pre-  determined portion of the issue being 
paid off according to a pre-  determined schedule. 
26 A is correct. A sinking fund arrangement is a way to reduce credit risk by 
making the issuer set aside funds over time to retire the bond issue. B and C are 
incorrect because a sinking fund arrangement has no effect on inflation risk or 
interest rate risk.

Reading 51 ■ Fixed-  Income Markets: Issuance, Trading, and Funding 400
27 C is correct. Wholesale funds available for banks include central bank funds, 
interbank funds, and negotiable certificates of deposit. A and B are incorrect 
because demand deposits (also known as checking accounts) and money market 
accounts are retail deposits (not wholesale funds).
28 B is correct. A negotiable certificate of deposit (CD) allows any depositor (initial 
or subsequent) to sell the CD in the open market prior to maturity. A is incor -
rect because negotiable CDs are mostly available in large (not small) denomina -
tions. Large-  denomination negotiable CDs are an important source of whole -
sale funds for banks, whereas small-  denomination CDs are not. C is incorrect 
because a penalty is imposed if the depositor withdraws funds prior to maturity 
for non-  negotiable (instead of negotiable) CDs.
29 B is correct. A repurchase agreement (repo) can be viewed as a collateralized

loan where the security sold and subsequently repurchased represents the col -
lateral posted. A and C are incorrect because interbank deposits and negotiable 
certificates of deposit are unsecured deposits—that is, there is no collateral 
backing the deposit.
30 A is correct. Repo margins vary by transaction and are negotiated bilaterally 
between the counterparties. 
31 A is correct. The repo margin (the difference between the market value of the 
underlying collateral and the value of the loan) is a function of the supply and 
demand conditions of the collateral. The repo margin is typically lower if the 
underlying collateral is in short supply or if there is a high demand for it. B and 
C are incorrect because the repo margin is usually higher (not lower) when the 
maturity of the repurchase agreement is long and when the credit risk associ -
ated with the underlying collateral is high.

Introduction to Fixed-  Income Valuation
by James F. Adams, PhD, CFA, and Donald J. Smith, PhD
James F. Adams, PhD, CFA, is at J.P. Morgan (USA). Donald J. Smith, PhD, is at Boston 
University Questrom School of Business (USA).
a. calculate a bond’s price given a market discount rate;
b. identify the relationships among a bond’s price, coupon rate, 
maturity, and market discount rate (yield-  to- maturity);
c. define spot rates and calculate the price of a bond using spot 
rates;
d. describe and calculate the flat price, accrued interest, and the full 
price of a bond;
e. describe matrix pricing;
f. calculate and interpret yield measures for fixed-  rate bonds, 
floating-  rate notes, and money market instruments;
g. define and compare the spot curve, yield curve on coupon bonds, 
par curve, and forward curve;
h. define forward rates and calculate spot rates from forward rates, 
forward rates from spot rates, and the price of a bond using

forward rates;
i. compare, calculate, and interpret yield spread measures.
Globally, the fixed-  income market is a key source of financing for businesses and 
governments. In fact, the total market value outstanding of corporate and government 
bonds is significantly larger than that of equity securities. Similarly, the fixed-  income 
market, which is also called the debt market or bond market, represents a significant 
investing opportunity for institutions as well as individuals. Pension funds, mutual 
funds, insurance companies, and sovereign wealth funds, among others, are major 
fixed-  income investors. Retirees who desire a relatively stable income stream often hold 1READING
52

Reading 52 ■ Introduction to Fixed-  Income Valuation 402
fixed-  income securities. Clearly, understanding how to value fixed-  income securities 
is important to investors, issuers, and financial analysts. This reading focuses on the 
valuation of traditional (option-  free) fixed-  rate bonds, although other debt securities, 
such as floating-  rate notes and money market instruments, are also covered.
Section 2 describes and illustrates basic bond valuation, which includes pricing 
a bond using a market discount rate for each of the future cash flows and pricing a 
bond using a series of spot rates. Valuation using spot rates allows for each future 
cash flow to be discounted at a rate associated with its timing. This valuation meth -
odology for future cash flows has applications well beyond the fixed-  income market. 
Relationships among a bond’s price, coupon rate, maturity, and market discount rate 
(yield-  to- maturity) are also described and illustrated.

Section 3 describes how bond prices and yields are quoted and calculated in prac -
tice. When bonds are actively traded, investors can observe the price and calculate 
various yield measures. However, these yield measures differ by the type of bond. In 
practice, different measures are used for fixed-  rate bonds, floating-  rate notes, and 
money market instruments. When a bond is not actively traded, matrix pricing is 
often used to estimate the value based on comparable securities.
Section 4 addresses the maturity or term structure of interest rates. This discussion 
involves an analysis of yield curves, which illustrates the relationship between yields-  
to- maturity and times-  to- maturity on bonds with otherwise similar characteristics. 
Various types of yield curves are described.
Section 5 focuses on yield spreads over benchmark interest rates. When investors 
want relatively higher yields, they have to be prepared to bear more risk. Yield spreads

are measures of how much additional yield over the benchmark security (usually a 
government bond) investors expect for bearing additional risk. A summary of key 
points and practice problems conclude the reading.
BOND PRICES AND THE TIME VALUE OF MONEY
Bond pricing is an application of discounted cash flow analysis. The complexity of 
the pricing depends on the particular bond’s features and rate (or rates) used to do 
the discounting. This section starts with using a single discount factor for all future 
cash flows and concludes with the most general approach to bond valuation. The 
general approach to bond valuation is to use a series of spot rates that correspond to 
the timing of the future cash flows.
2.1 Bond Pricing with a Market Discount Rate
On a traditional (option-  free) fixed-  rate bond, the promised future cash flows are a 
series of coupon interest payments and repayment of the full principal at maturity. The

coupon payments are on regularly scheduled dates, for example, an annual payment 
bond might pay interest on 15 June of each year for five years. The final coupon typically 
is paid together with the full principal on the maturity date. The price of the bond at 
issuance is the present value of the promised cash flows. The market discount rate  is 
used in the time-  value-  of- money calculation to obtain the present value. The market 
discount rate is the rate of return required by investors given the risk of the invest -
ment in the bond. It is also called the required yield , or the required rate of return .2

Bond Prices and the Time Value of Money 403
For example, suppose the coupon rate on a bond is 4% and the payment is made 
once a year. If the time-  to- maturity is five years and the market discount rate is 6%, 
the price of the bond is 91.575 per 100 of par value . The par value is the amount of 
principal on the bond.
4
1064
1064
1064
106104
106
3 774 3 5601 2345.. .. .
..()+
()+
()+
()+
()=
++ ++ += 3 358 3 168 77 715 91 575.. ..
The final cash flow of 104 is the redemption of principal (100) plus the coupon pay -
ment for that date (4). The price of the bond is the sum of the present values of the 
five cash flows. The price per 100 of par value may be interpreted as the percentage 
of par value. If the par value is USD100,000, the coupon payments are USD4,000 
each year and the price of the bond is USD91,575. Its price is 91.575% of par value. 
This bond is described as trading at a discount  because the price is below par value.

Suppose that another five-  year bond has a coupon rate of 8% paid annually. If the 
market discount rate is again 6%, the price of the bond is 108.425.
8
1068
1068
1068
106108
106
7 547 7 1201 2345.. .. .
..()+
()+
()+
()+
()=
++ +++ = 6 717 6 337 80 704 108 425.. ..
This bond is trading at a premium  because its price is above par value.
If another five-  year bond pays a 6% annual coupon and the market discount rate 
still is 6%, the bond would trade at par value.
6
1066
1066
1066
106106
106
5 660 5 3401 2345.. .. .
..()+
()+
()+
()+
()=
++ ++ += 5 038 4 753 79 209 100 000.. ..
The coupon rate indicates the amount the issuer promises to pay the bondholders 
each year in interest. The market discount rate reflects the amount investors need 
to receive in interest each year in order to pay full par value for the bond. Therefore, 
assuming that these three bonds have the same risk, which is consistent with them 
having the same market discount rate, the 4% bond offers a “deficient” coupon rate.

The amount of the discount below par value is the present value of the deficiency, 
which is 2% of par value each year. The present value of the deficiency, discounted 
using the market discount rate, is –8.425.
−
()+−
()+−
()+−
()+−
()=−2
1062
1062
1062
1062
1068 4251 2345.. .. ..
The price of the 4% coupon bond is 91.575 (= 100 – 8.425). In the same manner, 
the 8% bond offers an “excessive” coupon rate given the risk because investors require 
only 6%. The amount of the premium is the present value of the excess cash flows, 
which is +8.425. The price of the 8% bond is 108.425 (= 100 + 8.425).
These examples demonstrate that the price of a fixed-  rate bond, relative to par 
value, depends on the relationship of the coupon rate to the market discount rate. 
Here is a summary of the relationships:
■■When the coupon rate is less than the market discount rate, the bond is priced 
at a discount below par value.
■■When the coupon rate is greater than the market discount rate, the bond is

priced at a premium above par value.
■■When the coupon rate is equal to the market discount rate, the bond is priced 
at par value.

Reading 52 ■ Introduction to Fixed-  Income Valuation 404
At this point, it is assumed that the bond is priced on a coupon payment date. If the 
bond is between coupon payment dates, the price paid will include accrued interest, 
which is interest that has been earned but not yet paid. Accrued interest is discussed 
in detail in Section 3.1.
Equation  1 is a general formula for calculating a bond price given the market 
discount rate:
PVPMT
rPMT
rPMTF V
rN=
+()+
+()+++
+() 11 112
where
 PV = present value, or the price of the bond
 PMT  = coupon payment per period
 FV = future value paid at maturity, or the par value of the bond
 r = market discount rate, or required rate of return per period
 N = number of evenly spaced periods to maturity
The examples so far have been for an annual payment bond, which is the convention 
for most European bonds. Asian and North American bonds generally make semiannual 
payments, and the stated rate is the annual coupon rate. Suppose the coupon rate on

a bond is stated to be 8% and the payments are made twice a year (semiannually) on 
15 June and 15 December. For each 100 in par value ( FV = 100), the coupon payment 
per period is 4 ( PMT  = 4). If there are three years to maturity, there are six evenly 
spaced semiannual periods ( N = 6). If the market discount rate is 3% per semiannual 
period ( r = 0.03), the price of the bond is 105.417 per 100 of par value.
4
1034
1034
1034
1034
103104
103101 23456.. .. .. ()+
()+
()+
()+
()+
()= 5 5 417 .
If the actual par value of the bond investment is in Singapore dollars—for instance, 
SGD 100,000—the price is SGD 105,417. This bond is trading at a premium above par 
value because the coupon rate of 4% per period  is greater than the market discount 
rate of 3% per period . Usually, those interest rates are annualized by multiplying the 
rate per period by the number of periods in a year. Therefore, an equivalent statement 
is that the bond is priced at a premium because its stated annual  coupon rate of 8%

is greater than the stated annual  market discount rate of 6%. Interest rates, unless 
stated otherwise, are typically quoted as annual rates.
EXAMPLE 1   
Bonds Trading at a Discount, at a Premium, and at Par
Identify whether each of the following bonds is trading at a discount, at par 
value, or at a premium. Calculate the prices of the bonds per 100 in par value 
using Equation 1. If the coupon rate is deficient or excessive compared with 
the market discount rate, calculate the amount of the deficiency or excess per 
100 of par value.
BondCoupon 
Payment  
per PeriodNumber of Periods  
to MaturityMarket Discount Rate  
per Period
A 2 6 3%
B 6 4 4%(1)

Bond Prices and the Time Value of Money 405
Payment  
per Period
C 5 5 5%
D 0 10 2%
Bond A
2
1032
1032
1032
1032
103102
103941 23456.. .. .. ()+
()+
()+
()+
()+
()= . .583
Bond A is trading at a discount. Its price is below par value because the coupon 
rate per period (2%) is less than the required yield per period (3%). The defi -
ciency per period is the coupon rate minus the market discount rate, times the 
par value: (0.02 – 0.03) × 100 = –1. The present value of deficiency is –5.417, 
discounted using the required yield (market discount rate) per period.
−
()+−
()+−
()+−
()+−
()+−
()1
1031
1031
1031
1031
1031
1031 2345.. .. ..6 65 417=− .
The amount of the deficiency can be used to calculate the price of the bond; the 
price is 94.583 (= 100 – 5.417).
Bond B
6
1046
1046
104106
104107 2601 234.. ...
()+
()+
()+
()=
Bond B is trading at a premium because the coupon rate per period (6%) is

greater than the market discount rate per period (4%). The excess per period is 
the coupon rate minus market discount rate, times the par value: (0.06 – 0.04) 
× 100 = +2. The present value of excess is +7.260, discounted using the required 
yield per period.
2
1042
1042
1042
1047 2601 234.. ...
()+
()+
()+
()=
The price of the bond is 107.260 (= 100 + 7.260).
Bond C
5
1055
1055
1055
105105
105100 0001 2345.. .. ..
()+
()+
()+
()+
()=
Bond C is trading at par value because the coupon rate is equal to the market 
discount rate. The coupon payments are neither excessive nor deficient given 
the risk of the bond.
Bond D
100
10282 03510..
()=

Reading 52 ■ Introduction to Fixed-  Income Valuation 406
Bond D is a zero-  coupon bond, which always will trade at a discount below par 
value (as long as the required yield is greater than zero). The deficiency in the 
coupon payments is –2 per period: (0 – 0.02) × 100 = –2.
−
()+−
()+−
()+−
()+−
()+
−
()2
1022
1022
1022
1022
102
2
1021 2345.. .. .
.667 89 102
1022
1022
1022
10217 965 +−
()+−
()+−
()+−
()=−
.. ...
The price of the bond is 82.035 (= 100 – 17.965).
2.2 Yield-  to- Maturity
If the market price of a bond is known, Equation 1 can be used to calculate its yield 
to maturity  (sometimes called the redemption yield or yield-  to- redemption). The 
yield-  to- maturity is the internal rate of return on the cash flows—the uniform interest 
rate such that when the future cash flows are discounted at that rate, the sum of the 
present values equals the price of the bond. It is the implied  market discount rate.
The yield-  to- maturity is the rate of return on the bond to an investor given three

critical assumptions:
1 The investor holds the bond to maturity.
2 The issuer makes all of the coupon and principal payments in the full amount 
on the scheduled dates. Therefore, the yield-  to- maturity is the promised  yield—
the yield assuming the issuer does not default on any of the payments.
3 The investor is able to reinvest coupon payments at that same yield. This is a 
characteristic of an internal rate of return.
For example, suppose that a four-  year, 5% annual coupon payment bond is priced 
at 105 per 100 of par value. The yield-  to- maturity is the solution for the rate, r, in 
this equation:
1055
15
15
1105
11 234=
+()+
+()+
+()+
+() rr rr
Solving by trial-  and-  error search, or using the time-  value-  of- money keys on a financial 
calculator, obtains the result that r = 0.03634. The bond trades at a premium because 
its coupon rate (5%) is greater than the yield that is required by investors (3.634%).
Yields-  to- maturity do not depend on the actual amount of par value in a fixed-

income portfolio. For example, suppose a Japanese institutional investor owns a 
three-  year, 2.5% semiannual payment bond having a par value of JPY100 million. The 
bond currently is priced at JPY98,175,677. The yield per semiannual period can be 
obtained by solving this equation for r:
98 175677125
1125
1125
1125
1125
1 234... .. .=
+()+
+()+
+()+
+()+
rr rr 1 1101 25
156+()+
+() rr.
The yield per semiannual period turns out to be 1.571% ( r = 0.01571), which can 
be annualized to be 3.142% (0.01571 × 2 = 0.03142). In general, a three-  year, 2.5% 
semiannual bond for any amount of par value has an annualized yield-  to- maturity of 
3.142% if it is priced at 98.175677% of par value.

Bond Prices and the Time Value of Money 407
EXAMPLE 2   
Yields-  to- Maturity for a Premium, Discount, and Zero-  
Coupon Bond
Calculate the yields-  to- maturity for the following bonds. The prices are stated 
per 100 of par value.
Payment  
per PeriodNumber of 
Periods  
to Maturity Price
A 3.5 4 103.75
B 2.25 6 96.50
C 0 60 22.375
Bond A
103 7535
135
135
1103 5
101 234... ... =
+()+
+()+
+()+
+()=
rr rrr,     0 02503
Bond A is trading at a premium, so its yield-  to- maturity per period (2.503%) 
must be lower than its coupon rate per period (3.5%).
Bond B
96 50225
1225
1225
1225
1
225
11 234... ..
.=
+()+
+()+
+()+
+()+
+rr rr
r 
(()+
+()=56102 25
10 02894..
rr,     
Bond B is trading at a discount, so the yield-  to- maturity per period (2.894%) 
must be higher than the coupon rate per period (2.25%).
Bond C
22 375100
10 0252760.. =
+()=
rr,     
Bond C is a zero-  coupon bond trading at a significant discount below par value. 
Its yield-  to- maturity is 2.527% per period.

2.3 Relationships between the Bond Price and Bond 
Characteristics
The price of a fixed-  rate bond will change whenever the market discount rate changes. 
Four relationships about the change in the bond price given the market discount rate are
1 The bond price is inversely related to the market discount rate. When the mar -
ket discount rate increases, the bond price decreases (the inverse effect).
2 For the same coupon rate and time-  to- maturity, the percentage price change is 
greater (in absolute value, meaning without regard to the sign of the change) 
when the market discount rate goes down than when it goes up (the convexity 
effect).

Reading 52 ■ Introduction to Fixed-  Income Valuation 408
3 For the same time-  to- maturity, a lower-  coupon bond has a greater percentage 
price change than a higher-  coupon bond when their market discount rates 
change by the same amount (the coupon effect).
4 Generally, for the same coupon rate, a longer-  term bond has a greater percent -
age price change than a shorter-  term bond when their market discount rates 
change by the same amount (the maturity effect).
Exhibit 1 illustrates these relationships using nine annual coupon payment bonds. 
The bonds have different coupon rates and times-  to- maturity but otherwise are the 
same in terms of risk. The coupon rates are 10%, 20%, and 30% for bonds having 10, 
20, and 30 years to maturity. At first, the bonds are all priced at a market discount 
rate of 20%. Equation 1 is used to determine the prices. Then the market discount 
rate is decreased by 1 percentage point, from 20% to 19%, and next, it is increased 
from 20% to 21%.

Exhibit 1   Relationships between Bond Prices and Bond Characteristics
Rate MaturityPrice at 
20%Discount Rates  
Go DownDiscount Rates  
Go Up
Price at 
19%% 
ChangePrice at 
21%% 
Change
A 10.00% 10 58.075 60.950 4.95% 55.405 –4.60%
B 20.00% 10 100.000 104.339 4.34% 95.946 –4.05%
C 30.00% 10 141.925 147.728 4.09% 136.487 –3.83%
D 10.00% 20 51.304 54.092 5.43% 48.776 –4.93%
E 20.00% 20 100.000 105.101 5.10% 95.343 –4.66%
F 30.00% 20 148.696 156.109 4.99% 141.910 –4.56%
G 10.00% 30 50.211 52.888 5.33% 47.791 –4.82%
H 20.00% 30 100.000 105.235 5.23% 95.254 –4.75%
I 30.00% 30 149.789 157.581 5.20% 142.716 –4.72%
The first relationship is that the bond price and the market discount rate move 
inversely. All bond prices in Exhibit 1 go up when the rates go down from 20% to 19%, 
and all prices go down when the rates go up from 20% to 21%. This happens because 
of the fixed cash flows on a fixed-  rate bond. The numerators in Equation 1 do not

change when the market discount rate in the denominators rises or falls. Therefore, 
the price ( PV) moves inversely with the market discount rate ( r).
The second relationship reflects the convexity effect. In Exhibit 1, the percentage 
price changes are calculated using this equation:
% ChangeNew pric eO ld pric e
Old price=−
For example, when the market discount rate falls on Bond A, the price rises from 
58.075 to 60.950. The percentage price increase is 4.95%.
% Change =−=60 950 58 075
58 0750 0495..
..

Bond Prices and the Time Value of Money 409
For each bond, the percentage price increases are greater in absolute value  than 
the percentage price decreases. This implies that the relationship between bond prices 
and the market discount rate is not linear; instead, it is curved. It is described as being 
“convex. ” The convexity effect is shown in Exhibit 2 for a 10%, 10-  year bond.
Exhibit 2   The Convex Relationship between the Market Discount Rate and 
the Price of a 10-  Y ear, 10% Annual Coupon Payment Bond
Price
200
180
160
140
120
100
80
60
40
20
0
0 20 5 10 15
Market Discount Rate (%)
The third relationship is the coupon effect. Consider Bonds A, B, and C, which 
have 10 years to maturity. For both the decrease and increase in the yield-  to- maturity, 
Bond A has a larger percentage price change than Bond B, and Bond B has a larger 
change than C. The same pattern holds for the 20-  year and 30-  year bonds. Therefore,

lower-  coupon bonds have more price volatility than higher-  coupon bonds, other 
things being equal.
The fourth relationship is the maturity effect. Compare the results for Bonds A 
and D, for Bonds B and E, and for Bonds C and F. The 20-  year bonds have greater 
percentage price changes than the 10-  year bonds for either an increase or a decrease 
in the market discount rate. In general, longer-  term bonds have more price volatility 
than shorter-  term bonds, other things being equal.
There are exceptions to the maturity effect. That is why the word “generally” 
appears in the statement of the relationship at the beginning of this section. Compare 
the results in Exhibit  1 for Bonds D and G, for Bonds E and H, and for Bonds F 
and I. For the higher-  coupon bonds trading at a premium, Bonds F and I, the usual 
property holds—the 30-  year bonds have greater percentage price changes than the 
20- year bonds. The same pattern holds for Bonds E and H, which are priced initially

at par value. The exception is illustrated in the results for Bonds D and G, which are 
priced at a discount because the coupon rate is lower than the market discount rate. 
The 20-  year, 10% bond has a greater percentage price change than the 30-  year, 10% 
bond. Exceptions to the maturity effect are rare in practice. They occur only for low-  
coupon (but not zero-  coupon), long-  term bonds trading at a discount. The maturity 
effect always holds on zero-  coupon bonds, as it does for bonds priced at par value or 
at a premium above par value.

Reading 52 ■ Introduction to Fixed-  Income Valuation 410
One final point to note in Exhibit 1 is that Bonds B, E, and H, which have coupon 
rates of 20%, all trade at par value when the market discount rate is 20%. A bond having 
a coupon rate equal to the market discount rate is priced at par value on a coupon 
payment date, regardless of the number of years to maturity.
EXAMPLE 3   
Bond Percentage Price Changes Based on Coupon and 
Time-  to- Maturity
An investor is considering the following six annual coupon payment govern -
ment bonds:
RateTime-  to- 
MaturityYield-  to- 
Maturity
A 0% 2 years 5.00%
B 5% 2 years 5.00%
C 8% 2 years 5.00%
D 0% 4 years 5.00%
E 5% 4 years 5.00%
F 8% 4 years 5.00%
1 Based on the relationships between bond prices and bond characteristics, 
which bond will go up in price the most  on a percentage basis if all yields 
go down from 5.00% to 4.90%?
2 Based on the relationships between the bond prices and bond characteris -

tics, which bond will go down in price the least  on a percentage basis if all 
yields go up from 5.00% to 5.10%?
Bond D will go up in price the most on a percentage basis because it has the 
lowest coupon rate (the coupon effect) and the longer time-  to- maturity (the 
maturity effect). There is no exception to the maturity effect in these bonds 
because there are no low-  coupon bonds trading at a discount.
Bond C will go down in price the least on a percentage basis because it has the 
highest coupon rate (the coupon effect) and the shorter time-  to- maturity (the 
maturity effect). There is no exception to the maturity effect because Bonds C 
and F are priced at a premium above par value.
Exhibit 2 demonstrates the impact on a bond price assuming the time-  to- maturity 
does not change. It shows an instantaneous  change in the market discount rate from 
one moment to the next.
But bond prices change as time passes even if the market discount rate remains

the same. As time passes, the bondholder comes closer to receiving the par value at 
maturity. The constant-  yield price trajectory  illustrates the change in the price of a 
fixed-  income bond over time. This trajectory shows the “pull to par” effect on the price 
of a bond trading at a premium or a discount to par value. If the issuer does not default, 
the price of a bond approaches par value as its time-  to- maturity approaches zero.

Bond Prices and the Time Value of Money 411
Exhibit 3 shows the constant-  yield price trajectories for 4% and 12% annual cou -
pon payment, 10-  year bonds. Both bonds have a market discount rate of 8%. The 
4% bond’s initial price is 73.160 per 100 of par value. The price increases each year 
and approaches par value as the maturity date nears. The 12% bond’s initial price is 
126.840, and it decreases each year, approaching par value as the maturity date nears. 
Both prices are “pulled to par. ”
Exhibit 3   Constant-  Yield Price Trajectories for 4% and 12% Annual Coupon 
Payment, 10-  Y ear Bonds at a Market Discount Rate of 8%
Price
12% (Premium) Bond
4% (Discount) Bond140
120
100
80
60
40
20
Discount Bond
Premium Bond0
2
77.013
122.981
75.012
124.980
73.160
126.843
79.175
120.824
81.508
118.496
86.751
113.247
89.692
110.309
96.296
103.7010
100.00
100.005
84.029
115.978
92.867
107.13Year
2.4 Pricing Bonds with Spot Rates
When a fixed-  rate bond is priced using the market discount rate, the same discount

rate is used for each cash flow. A more fundamental approach to calculate the price 
of a bond is to use a sequence of market discount rates that correspond to the cash 
flow dates. These market discount rates are called spot rates . Spot rates are yields-  
to- maturity on zero-  coupon bonds maturing at the date of each cash flow. Sometimes 
these are called “zero rates. ” Bond price (or value) determined using the spot rates is 
sometimes referred to as the bond’s “no-  arbitrage value. ” If a bond’s price differs from its 
no- arbitrage value, an arbitrage opportunity exists in the absence of transaction costs.
Suppose that the one-  year spot rate is 2%, the two-  year spot rate is 3%, and the 
three-  year spot rate is 4%. Then, the price of a three-  year bond that makes a 5% annual 
coupon payment is 102.960.
5
1025
103105
104
4 902 4 713 93 345 102 96012 3.. .
.. ..()+
()+
()=
++ =

Reading 52 ■ Introduction to Fixed-  Income Valuation 412
This three-  year bond is priced at a premium above par value, so its yield-  to- maturity 
must be less than 5%. Using Equation 1, the yield-  to- maturity is 3.935%.
102 9605
15
1105
10 0393512 3.. =
+()+
+()+
+()=
rr rr,     
When the coupon and principal cash flows are discounted using the yield-  to- maturity, 
the same price is obtained.
5
1 039355
1 03935105
1 03935
4 811 4 629 93 520 112 3.. .
.. .()+
()+
()=
++ =0 02 960 .
Notice that the present values of the individual cash flows discounted using spot 
rates differ from those using the yield-  to- maturity. The present value of the first 
coupon payment is 4.902 when discounted at 2%, but it is 4.811 when discounted at 
3.935%. The present value of the final cash flow, which includes the redemption of 
principal, is 93.345 at 4% and 93.520 at 3.935%. Nevertheless, the sum of the present 
values using either approach is 102.960.

Equation 2 is a general formula for calculating a bond price given the sequence 
of spot rates:
PVPMT
ZPMT
ZPMTF V
ZNN=
+()+
+()+++
+() 11 111
22
where
 Z1 = spot rate, or the zero-  coupon yield, or zero rate, for Period 1
 Z2 = spot rate, or the zero-  coupon yield, or zero rate, for Period 2
 ZN = spot rate, or the zero-  coupon yield, or zero rate, for Period N
EXAMPLE 4   
Bond Prices and Yields-  to- Maturity Based on Spot Rates
Calculate the price (per 100 of par value) and the yield-  to- maturity for a four-  year, 
3% annual coupon payment bond given the following two sequences of spot rates.
Time-  to- Maturity Spot Rates A Spot Rates B
1 year 0.39% 4.08%
2 years 1.40% 4.01%
3 years 2.50% 3.70%
4 years 3.60% 3.50%
Solution:
Spot Rates A
3
1 00393
1 01403
1 0250103
1 0360
2 988 2 9181 234.. ..
..()+
()+
()+
()=
++ 2 2 786 89 412 98 104.. . +=
Given spot rates A, the four-  year, 3% bond is priced at 98.104.
98 1043
13
13
1103
10 035161 234.. =
+()+
+()+
+()+
+()=
rr rrr,     (2)

Prices and Yields: Conventions for Quotes and Calculations 413
The yield-  to- maturity is 3.516%.
Spot Rates B
3
1 04083
1 04013
1 0370103
1 0350
2 882 2 7731 234.. ..
..()+
()+
()+
()=
++ 2 2 690 89 759 98 104.. . +=
98 1043
13
13
1103
+()+
+()+
+()+
+()=
rr rrr,     
Given spot rates B, the four-  year, 3% bond is again priced at 98.104 to yield 3.516%.
This example demonstrates that two very different sequences of spot rates can 
result in the same bond price and yield-  to- maturity. Spot rates A are increasing 
for longer maturities, whereas spot rates B are decreasing.
PRICES AND YIELDS: CONVENTIONS FOR QUOTES 
AND CALCULATIONS
When investors purchase shares, they pay the quoted price. For bonds, however, there 
can be a difference between the quoted price and the price paid. This section explains 
why this difference occurs and how to calculate the quoted price and the price that 
will be paid. It also describes how prices are estimated for bonds that are not actively

traded, and demonstrates how yield measures are calculated for fixed-  rate bonds, 
floating-  rate notes, and money market instruments.
3.1 Flat Price, Accrued Interest, and the Full Price
When a bond is between coupon payment dates, its price has two parts: the flat price  
(PVFlat) and the accrued interest  (AI). The sum of the parts is the full price  (PVFull), 
which also is called the invoice or “dirty” price. The flat price, which is the full price 
minus the accrued interest, is also called the quoted or “clean” price.
PVFull = PVFlat + AI  
The flat price usually is quoted by bond dealers. If a trade takes place, the accrued 
interest is added to the flat price to obtain the full price paid by the buyer and received 
by the seller on the settlement date . The settlement date is when the bond buyer 
makes cash payment and the seller delivers the security.
The reason for using the flat price for quotation is to avoid misleading investors

about the market price trend for the bond. If the full price were to be quoted by deal -
ers, investors would see the price rise day after day even if the yield-  to- maturity did 
not change. That is because the amount of accrued interest increases each day. Then, 
after the coupon payment is made, the quoted price would drop dramatically. Using 
the flat price for quotation avoids that misrepresentation. It is the flat price that is 
“pulled to par” along the constant-  yield price trajectory shown in Exhibit 3.
Accrued interest is the proportional share of the next coupon payment. Assume 
that the coupon period has “ T” days between payment dates and that “ t” days have 
gone by since the last payment. The accrued interest is calculated using Equation 4:
AIt
TPMT =×3
(3)
(4)

Reading 52 ■ Introduction to Fixed-  Income Valuation 414
where
 t = number of days from the last coupon payment to the settlement date
 T = number of days in the coupon period
 t/T = fraction of the coupon period that has gone by since the last payment
Notice that the accrued interest part of the full price does not depend on the yield-  to- 
maturity. Therefore, it is the flat price that is affected by a market discount rate change.
There are different conventions used in bond markets to count days. The two 
most common day-  count conventions are actual/actual and 30/360. For the actual/
actual method, the actual number of days is used, including weekends, holidays, and 
leap days. For example, a semiannual payment bond pays interest on 15 May and 
15 November of each year. The accrued interest for settlement on 27 June would be 
the actual number of days between 15 May and 27 June ( t = 43 days) divided by the

actual number of days between 15 May and 15 November ( T = 184 days), times the 
coupon payment. If the stated coupon rate is 4.375%, the accrued interest is 0.511209 
AI=× =43
1844 375
20 511209..
Day-  count conventions vary from market to market. However, actual/actual is most 
common for government bonds.
The 30/360 day-  count convention often is used on corporate bonds. It assumes  that 
each month has 30 days and that a full year has 360 days. Therefore, for this method, 
there are assumed to be 42 days between 15 May and 27 June: 15 days between 15 May 
and 30 May and 27 days between 1 June and 27 June. There are assumed to be 180 
days in the six-  month period between 15 May and 15 November. The accrued interest 
on a 4.375% semiannual payment corporate bond is 0.510417 per 100 of par value.
AI=× =42
1804 375
20 510417..
The full price of a fixed-  rate bond between coupon payments given the market 
discount rate per period ( r) can be calculated with Equation 5:
PVPMT

PVPMT
rPMT
rPMTF V
rFull
tT tT Nt T=
+()+
+()+++
+()−− −11 112
This is very similar to Equation 1. The difference is that the next coupon payment 
(PMT ) is discounted for the remainder of the coupon period, which is 1 – t/T. The 
second coupon payment is discounted for that fraction plus another full period, 2 – t/T.
Equation 5 is simplified by multiplying the numerator and denominator by the 
expression (1 + r)t/T. The result is Equation 6:
PVPMT
rPMT
rPMTF V
rrFull
NtT=
+()+
+()+++
+()



×+()
=11 1112
PPV rtT×+()1
An advantage to Equation 6 is that PV, the expression in the brackets, is easily obtained 
using the time-  value-  of- money keys on a financial calculator because there are N 
evenly spaced periods. PV here is identical to Equation 1 and is not the same as PVFlat.
For example, consider a 5% semiannual coupon payment government bond that 
matures on 15 February 2024. Accrued interest on this bond uses the actual/actual

day-  count convention. The coupon payments are made on 15 February and 15 August 
of each year. The bond is to be priced for settlement on 14 May 2015. That date is 
88 days into the 181-  day period. There are actually 88 days from the last coupon on (5)
(6)

Prices and Yields: Conventions for Quotes and Calculations 415
15 February to 14 May and 181 days between 15 February and the next coupon on 
15 August. The annual yield-  to- maturity is stated to be 4.80%. That corresponds to 
a market discount rate of 2.40% per semiannual period. As of the beginning of the 
coupon period on 15 February 2015, there would be 18 evenly spaced semiannual 
periods until maturity. The first step is to solve for PV using Equation 1, whereby 
PMT  = 2.5, N = 18, FV = 100, and r = 0.0240.
PV =
()+
()++
()=25
1 024025
1 0240102 5
1 0240101 44779012 18.
..
..
.. 
The price of the bond would be 101.447790 per 100 of par value if its yield-  to- maturity 
is 2.40% per period on the last coupon payment date. This is not the actual price for 
the bond on that date. It is a “what-  if” price using the required yield that corresponds 
to the settlement date of 14 May 2015.
Equation 6 can be used to get the full price for the bond.
PVFull = 101.447790 × (1.0240)88/181 = 102.624323

The full price is 102.624323 per 100 of par value. The accrued interest is 1.215470 
AI=× =88
18125 1 215470 ..
The flat price is 101.408853 per 100 of par value.1
PVFlat = PVFull – AI = 102.624323 – 1.215470 = 101.408853
EXAMPLE 5   
Calculating the Full Price, Accrued Interest, and Flat Price 
for a Bond
A 6% German corporate bond is priced for settlement on 18 June 2015. The 
bond makes semiannual coupon payments on 19 March and 19 September of 
each year and matures on 19 September  2026. The corporate bond uses the 
30/360 day-  count convention for accrued interest. Calculate the full price, the 
accrued interest, and the flat price per EUR100 of par value for three stated 
annual yields-  to- maturity: (A) 5.80%, (B) 6.00%, and (C) 6.20%.
Solution:
Given the 30/360 day-  count convention assumption, there are 89 days between 
the last coupon on 19 March 2015 and the settlement date on 18 June 2015 (11

days between 19 March and 30 March, plus 60 days for the full months of April 
and May, plus 18 days in June). Therefore, the fraction of the coupon period 
that has gone by is assumed to be 89/180. At the beginning of the period, there 
are 11.5 years (and 23 semiannual periods) to maturity.
1 Microsoft Excel users can obtain the flat price using the PRICE financial function: PRICE (“5/14/2015, ” 
“2/15/2024, ” 0.05, 0.0480, 100, 2, 1). The inputs are the settlement date, maturity date, annual coupon rate 
as a decimal, annual yield-  to- maturity as a decimal, par value, number of periods in the year, and the code 
for the day-  count (0 for 30/360, 1 for actual/actual).

Reading 52 ■ Introduction to Fixed-  Income Valuation 416
(A) Stated annual yield-  to- maturity of 5.80%, or 2.90% per semiannual 
period:
The price at the beginning of the period is 101.661589 per 100 of par value.
PV =
()+
()++
()=3
1 02903
1 0290103
1 0290101 66158912 23.. .. 
The full price on 18 June is EUR103.108770.
PVFull = 101.661589 × (1.0290)89/180 = 103.108770
The accrued interest is EUR1.483333, and the flat price is EUR101.625437.
AI=× =89
18031 4833333 .
PVFlat = 103.108770 – 1.483333 = 101.625437
(B) Stated annual yield-  to- maturity of 6.00%, or 3.00% per semiannual 
period:
The price at the beginning of the period is par value, as expected, because the 
coupon rate and the market discount rate are equal.
PV =
()+
()++
()=3
1 03003
1 0300103
1 0300100 00000012 23.. .. 
The full price on 18 June is EUR101.472251.
PVFull = 100.000000 × (1.0300)89/180 = 101.472251
The accrued interest is EUR1.483333, and the flat price is EUR99.988918.
AI=× =89

AI=× =89
PVFlat = 101.472251 – 1.483333 = 99.988918
The flat price of the bond is a little below par value, even though the coupon 
rate and the yield-  to- maturity are equal, because the accrued interest does not 
take into account the time value of money. The accrued interest is the interest 
earned by the owner of the bond for the time between the last coupon payment 
and the settlement date, 1.483333 per 100 of par value. However, that interest 
income is not received until the next coupon date. In theory, the accrued interest 
should be the present value  of 1.483333. In practice, however, accounting and 
financial reporting need to consider issues of practicality and materiality. For 
those reasons, the calculation of accrued interest in practice neglects the time 
value of money. Therefore, compared to theory, the reported accrued interest is 
a little “too high” and the flat price is a little “too low. ” The full price, however,

is correct because it is the sum of the present values of the future cash flows, 
discounted using the market discount rate.
(C) Stated annual yield-  to- maturity of 6.20%, or 3.10% per semiannual 
period:
The price at the beginning of the period is 98.372607 per 100 of par value.
PV =
()+
()++
()=3
1 03103
1 0310103
1 031098 37260712 23.. .. 
The full price on 18 June is EUR99.868805.
PVFull = 98.372607 × (1.0310)89/180 = 99.868805

Prices and Yields: Conventions for Quotes and Calculations 417
The accrued interest is EUR1.483333, and the flat price is EUR98.385472.
AI=× =89
PVFlat = 99.868805 – 1.483333 = 98.385472
The accrued interest is the same in each case because it does not depend on 
the yield-  to- maturity. The differences in the flat prices indicate the differences 
in the rate of return that is required by investors. 
3.2 Matrix Pricing
Some fixed-  rate bonds are not actively traded. Therefore, there is no market price 
available to calculate the rate of return required by investors. The same problem occurs 
for bonds that are not yet issued. In these situations, it is common to estimate the 
market discount rate and price based on the quoted or flat prices of more frequently 
traded comparable bonds. These comparable bonds have similar times-  to- maturity, 
coupon rates, and credit quality. This estimation process is called matrix pricing .

For example, suppose that an analyst needs to value a three-  year, 4% semiannual 
coupon payment corporate bond, Bond X. Assume that Bond X is not actively traded 
and that there are no recent transactions reported for this particular security. However, 
there are quoted prices for four corporate bonds that have very similar credit quality:
■■Bond A: two-  year, 3% semiannual coupon payment bond trading at a price of 
98.500
■■Bond B: two-  year, 5% semiannual coupon payment bond trading at a price of 
102.250
■■Bond C: five-  year, 2% semiannual coupon payment bond trading at a price of 
90.250
■■Bond D: five-  year, 4% semiannual coupon payment bond trading at a price of 
99.125
The bonds are displayed in a matrix according to the coupon rate and the time-  
to- maturity. This matrix is shown in Exhibit 4.
Exhibit 4   Matrix Pricing Example
2% 
Coupon3% 
Coupon4% 
Coupon5% 
Coupon
Two Years 98.500 102.250
3.786% 3.821%
Three Years Bond X
Four Years
Five Years 90.250 99.125
4.181% 4.196%

Reading 52 ■ Introduction to Fixed-  Income Valuation 418
In Exhibit 4, below each bond price is the yield-  to- maturity. It is stated as the yield 
per semiannual period times two. For example, the yield-  to- maturity on the two-  year, 
3% semiannual coupon payment corporate bond is 3.786%.
98 50015
115
115
1101 5
+()+
+()+
+()+
+()=
rr rrr,     0 01893 20 03786 ,    ×= .
Next, the analyst calculates the average yield for each year: 3.8035% for the two-  
year bonds and 4.1885% for the five-  year bonds.
0 03786 0 03821
20 038035...+=
0 04181 0 04196
20 041885...+=
The estimated three-  year market discount rate can be obtained with linear inter -
polation. The interpolated yield is 3.9318%.
0 03803532
520 041885 0 038035 0 039318 .. .. +−
−

×−() =
Using 3.9318% as the estimated three-  year annual market discount rate, the 
three-  year, 4% semiannual coupon payment corporate bond has an estimated price 
of 100.191 per 100 of par value.
2
1 0196592
1 0196592
1 0196592
1 0196592

2
1 0196592
1 0196592
1 0196592
1 0196592
1 0191 234.. .. . ()+
()+
()+
()+
6 659
102
1 019659100 1915
6()+
()=
..
Notice that 3.9318% is the stated annual rate. It is divided by two to get the yield 
per semiannual period: (0.039318/2 = 0.019659).
Matrix pricing also is used in underwriting new bonds to get an estimate of the 
required yield spread  over the benchmark rate . The benchmark rate typically is 
the yield-  to- maturity on a government bond having the same, or close to the same, 
time-  to- maturity. The spread is the difference between the yield-  to- maturity on the 
new bond and the benchmark rate. The yield spread is the additional compensation 
required by investors for the difference in the credit risk, liquidity risk, and tax status of 
the bond relative to the government bond. This spread is sometimes called the spread 
over the benchmark . Yield spreads are often stated in terms of basis points (bps),

where one basis point  equals one-  hundredth of a percentage point. For example, if a 
yield-  to- maturity is 2.25% and the benchmark rate is 1.50%, the yield spread is 0.75%, 
or 75 bps. Yield spreads are covered in more detail later in this reading.
Suppose that a corporation is about to issue a five-  year bond. The corporate issuer 
currently has a four-  year, 3% annual coupon payment debt liability on its books. The 
price of that bond is 102.400 per 100 of par value. This is the full price, which is the 
same as the flat price because the accrued interest is zero. This implies that the coupon 
payment has just been made and there are four full years to maturity. The four-  year 
rate of return required by investors for this bond is 2.36%.
102 4003
13
13
1103
10 02361 234.. =
+()+
+()+
+()+
+()=
rr rrr,     
Suppose that there are no four-  year government bonds to calculate the yield spread 
on this security. However, there are three-  year and five-  year government bonds that

have yields-  to- maturity of 0.75% and 1.45%, respectively. The average of the two

Prices and Yields: Conventions for Quotes and Calculations 419
yields-  to- maturity is 1.10%, which is the estimated yield for the four-  year government 
bond. Therefore, the estimated yield spread is 126 bps over the implied benchmark 
rate (0.0236 – 0.0110 = 0.0126).
There usually is a different yield spread for each maturity and for each credit rating. 
The term structure of “risk-  free” rates, which is discussed further in Section 4, is the 
relationship between yields-  to- maturity on “risk-  free” bonds and times-  to- maturity. 
The quotation marks around “risk-  free” indicate that no bond is truly without risk. 
The primary component of the yield spread for many bonds is compensation for 
credit risk, not for time-  to- maturity, and as a result, the yield spreads reflect the term 
structure of credit spreads . The term structure of credit spreads is the relationship 
between the spreads over the “risk-  free” (or benchmark) rates and times-  to- maturity.

These term structures are covered in more detail in later readings.
The issuer now has an estimate of the four-  year yield spread, 126 bps. This spread 
is a reference point for estimating the five-  year spread for the newly issued bond. 
Suppose that the term structure of credit spreads for bonds of the corporate issuer’s 
quality indicates that five-  year spreads are about 25 bps higher than four-  year spreads. 
Therefore, the estimated five-  year required yield spread is 151 bps (0.0126 + 0.0025 = 
0.0151). Given the yield-  to- maturity of 1.45% on the five-  year government bond, the 
expected market discount rate for the newly issued bond is 2.96% (0.0145 + 0.0151 = 
0.0296). The corporation might set the coupon rate to be 3% and expect that the bond 
can be sold for a small premium above par value.
EXAMPLE 6   
Using Matrix Pricing to Estimate Bond Price
An analyst needs to assign a value to an illiquid four-  year, 4.5% annual coupon

payment corporate bond. The analyst identifies two corporate bonds that have 
similar credit quality: One is a three-  year, 5.50% annual coupon payment bond 
priced at 107.500 per 100 of par value, and the other is a five-  year, 4.50% annual 
coupon payment bond priced at 104.750 per 100 of par value. Using matrix 
pricing, the estimated price of the illiquid bond per 100 of par value is closest  to:
A 103.895.
B 104.991.
C 106.125.
Solution:
B is correct. The first step is to determine the yields-  to- maturity on the observed 
bonds. The required yield on the three-  year, 5.50% bond priced at 107.500 is 
2.856%.
107 500550
1550
1105 50
10 0285612 3... .. =
+()+
+()+
+()=
rr rr,     
The required yield on the five-  year, 4.50% bond priced at 104.750 is 3.449%.
104 750450
1450
1450
1450
1104 50
1 234.. ... .=
+()+
+()+
+()+
+()+
rr rr 1 10 034495+()=
rr,     .
The estimated market discount rate for a four-  year bond having the same 
credit quality is the average of two required yields:
0 02856 0 03449

Reading 52 ■ Introduction to Fixed-  Income Valuation 420
Given an estimated yield-  to- maturity of 3.1525%, the estimated price of the 
illiquid four-  year, 4.50% annual coupon payment corporate bond is 104.991 per 
450
1 031525450
1 031525104 50
10312 3.
..
..
..
. ()+
()+
()+
1 15251049914()= .
3.3 Yield Measures for Fixed-  Rate Bonds
There are many ways to measure the rate of return on a fixed-  rate bond investment. 
Consider a five-  year, zero-  coupon government bond. The purchase price today is 80. 
The investor receives 100 at redemption in five years. One possible yield measure is 
25%—the gain of 20 divided by the amount invested, 80. However, investors want a 
yield measure that is standardized  to allow for comparison between bonds that have 
different times-  to- maturity. Therefore, yield measures typically are annualized . A 
possible annual rate for this zero-  coupon bond is 5% per year—25% divided by five

years. But for bonds maturing in more than one year, investors want an annualized 
and compounded  yield-  to- maturity. Money market rates on instruments maturing in 
one year or less typically are annualized but not compounded . They are stated on a 
simple interest basis. This concept is covered later in this reading.
In general, an annualized and compounded yield on a fixed-  rate bond depends 
on the assumed number of periods in the year, which is called the periodicity  of the 
annual rate. Typically, the periodicity matches the frequency of coupon payments. A 
bond that pays semiannual coupons has a stated annual yield-  to- maturity for a peri -
odicity of two—the rate per semiannual period times two. A bond that pays quarterly 
coupons has a stated annual yield for a periodicity of four—the rate per quarter times 
four. It is always important to know the periodicity of a stated annual rate.
The periodicity of the annual market discount rate for a zero-  coupon bond is

arbitrary  because there are no coupon payments. For semiannual compounding, the 
annual yield-  to- maturity on the five-  year, zero-  coupon bond priced at 80 per 100 of 
par value is stated to be 4.5130%. This annual rate has a periodicity of two.
80100
10 022565 20 04513010=
+()=× =
rr,     ,    ..
For quarterly compounding, the annual yield-  to- maturity is stated to be 4.4880%. This 
annual rate has a periodicity of four.
80100
10 011220 40 04488020=
+()=× =
rr,     ,    ..
For monthly compounding, the annual yield-  to- maturity is stated to be 4.4712%. This 
annual rate has a periodicity of 12.
80100
10 003726 12 0 04471260=
+()=× =
rr,     ,    ..
For annual compounding, the yield-  to- maturity is stated to be 4.5640%. This annual 
rate has a periodicity of one.
80100
10 045640 10 0456405=
+()=× =
rr,     ,    ..
This is known as an effective annual rate . An effective annual rate has a periodicity 
of one because there is just one compounding period in the year.

Prices and Yields: Conventions for Quotes and Calculations 421
In this zero-  coupon bond example, 2.2565% compounded two times a year, 
1.1220% compounded four times a year, and 0.3726% compounded twelve times a 
year are all equivalent to an effective annual rate of 4.5640%. The compounded total 
return is the same for each expression for the annual rate. They differ in terms of the 
number of compounding periods per year—that is, in terms of the periodicity  of the 
annual rate. For a given pair of cash flows, the stated annual rate and the periodicity 
are inversely related.
The most common periodicity for USD-  denominated bond yields is two because 
most bonds in the USD market make semiannual coupon payments. An annual rate 
having a periodicity of two is known as a semiannual bond basis yield , or semian -
nual bond equivalent yield . Therefore, a semiannual bond basis yield is the yield 
per semiannual period times two. It is important to remember that “semiannual bond

basis yield” and “yield per semiannual period” have different meanings. For example, 
if a bond yield is 2% per semiannual period, its annual yield is 4% when stated on a 
semiannual bond basis.
An important tool used in fixed-  income analysis is to convert an annual yield from 
one periodicity to another. These are called periodicity, or compounding, conversions. 
A general formula to convert an annual percentage rate for m periods per year, denoted 
APRm, to an annual percentage rate for n periods per year, APRn, is Equation 7.
11+

=+

APR
mAPR
nmm
nn
For example, suppose that a three-  year, 5% semiannual coupon payment corporate 
bond is priced at 104 per 100 of par value. Its yield-  to- maturity is 3.582%, quoted on 
a semiannual bond basis for a periodicity of two: 0.01791 × 2 = 0.03582.
10425
125
125
125
125
1102
1 2345=
+()+
+()+
+()+
+()+
+()+. ... ..
rr rr r5 5
10 017916+()=
rr,     .
To compare this bond with others, an analyst converts this annualized yield-  to- maturity

to quarterly and monthly compounding. That entails using Equation 7 to convert from 
a periodicity of m = 2 to periodicities of n = 4 and n = 12.
10 03582
2140 035662
44
4 +

=+

=..APRAPR,     
10 03582
21120 035562
1212
12 +

=+

An annual yield-  to- maturity of 3.582% for semiannual compounding provides the same 
rate of return as annual yields of 3.566% and 3.556% for quarterly and monthly com -
pounding, respectively. A general rule for these periodicity conversions is compounding 
more frequently at a lower annual rate corresponds to compounding less frequently at a 
higher annual rate . This rule can be used to check periodicity conversion calculations.(7)

Reading 52 ■ Introduction to Fixed-  Income Valuation 422
EXAMPLE 7   
Yield Conversion Based on Periodicity
A five-  year, 4.50% semiannual coupon payment government bond is priced at 98 
per 100 of par value. Calculate the annual yield-  to- maturity stated on a semian -
nual bond basis, rounded to the nearest basis point. Convert that annual yield to:
A an annual rate that can be used for direct comparison with otherwise 
comparable bonds that make quarterly  coupon payments and
B an annual rate that can be used for direct comparison with otherwise 
comparable bonds that make annual  coupon payments.
Solution:
The stated annual yield-  to- maturity on a semiannual bond basis is 4.96% (0.0248 × 
2 = 0.0496).
98225
1225
1225
1225
1225
11 2345=
+()+
+()+
+()+
+()+
+()+.. .. .
rr rr r2225
1
225
1225
1225
1102 26
78 9.
.. ..+()+
+()+
+()+
+()+r
rr r        5 5
10 024810+()=
rr,     .
A Convert 4.96% from a periodicity of two to a periodicity of four:
10 0496
2140 04932
44
4 +

=+

=..APRAPR,

2140 04932
44
4 +

=+

 The annual percentage rate of 4.96% for compounding semiannually com -
pares with 4.93% for compounding quarterly. That makes sense because 
increasing the frequency of compounding lowers the annual rate.
B Convert 4.96% from a periodicity of two to a periodicity of one:
10 0496
2110 05022
11
1 +

=+

 The annual rate of 4.96% for compounding semiannually compares with 
an effective annual rate of 5.02%. Converting from more frequent to less 
frequent compounding entails raising the annual percentage rate.
An important concern for quoting and calculating bond yields-  to- maturity is the 
actual timing of the cash flows. Consider a 6% semiannual payment corporate bond 
that matures on 15 March 2022. Suppose that for settlement on 23 January 2014, the 
bond is priced at 98.5 per 100 of par value to yield 6.236% quoted on a semiannual 
bond basis. Its coupon payments are scheduled for 15 March and 15 September of each

year. The yield calculation implicitly assumes that the payments are made on those 
dates. It neglects the reality that 15 March 2015 is a Sunday and 15 September 2018 
is a Saturday. In fact, the coupon payments will be made to investors on the following 
Monday.
Yield measures that neglect weekends and holidays are quoted on what is called 
street convention . The street convention yield-  to- maturity is the internal rate of 
return on the cash flows assuming the payments are made on the scheduled dates. 
This assumption simplifies bond price and yield calculations and commonly is used 
in practice. Sometimes the true yield  is also quoted. The true yield-  to- maturity is the

Prices and Yields: Conventions for Quotes and Calculations 423
internal rate of return on the cash flows using the actual calendar of weekends and 
bank holidays. The true yield is never higher than the street convention yield because 
weekends and holidays delay the time to payment. The difference is typically small, 
no more than a basis point or two. Therefore, the true yield is not commonly used in 
practice. Sometimes, a government equivalent yield  is quoted for a corporate bond. 
A government equivalent yield restates a yield-  to- maturity based on 30/360 day-  count 
to one based on actual/actual. The government equivalent yield on a corporate bond 
can be used to obtain the spread over the government yield. Doing so keeps the yields 
stated on the same day-  count convention basis.
Another yield measure that is commonly quoted for fixed-  income bonds is the 
current yield , also called the income or interest yield. The current yield is the sum

of the coupon payments received over the year divided by the flat price. For example, 
a 10-  year, 2% semiannual coupon payment bond is priced at 95 per 100 of par value. 
Its current yield is 2.105%.
2
950 02105=.
The current yield is a crude measure of the rate of return to an investor because it 
neglects the frequency of coupon payments in the numerator and any accrued interest 
in the denominator. It focuses only on interest income. In addition to collecting and 
reinvesting coupon payments, the investor has a gain if the bond is purchased at a 
discount and is redeemed at par value. The investor has a loss if the bond is purchased 
at a premium and is redeemed at par value. Sometimes the simple yield  on a bond is 
quoted. It is the sum of the coupon payments plus the straight-  line amortized share 
of the gain or loss, divided by the flat price. Simple yields are used mostly to quote 
Japanese government bonds, known as “JGBs. ”
EXAMPLE 8   
Comparing Yields for Different Periodicities

An analyst observes these reported statistics for two bonds.
Bond A Bond B
Annual Coupon Rate 8.00% 12.00%
Coupon Payment Frequency Semiannually Quarterly
Years to Maturity 5 Years 5 Years
Price (per 100 of par value) 90 105
Current Yield 8.889% 11.429%
Yield-  to- Maturity 10.630% 10.696%
1 Confirm the calculation of the two yield measures for the two bonds.
2 The analyst believes that Bond B has a little more risk than Bond A. How 
much additional compensation, in terms of a higher yield-  to- maturity, 
does a buyer of Bond B receive for bearing this risk compared with 
Bond A?
Current Yield for Bond A
8
900 08889=.

Reading 52 ■ Introduction to Fixed-  Income Valuation 424
Yield-  to- Maturity for Bond A
904
14
1104
10 05315 20 1012 10=
+()+
+()++
+()=× =
rr rr  ,     ,    .. 6 630
Current Yield for Bond B
12
1050 11429=.
Yield-  to- Maturity for Bond B
1053
13
1103
10 02674 40 112 20=
+()+
+()++
+()=× =
rr rr  ,     ,    .. 0 0696
The yield-  to- maturity on Bond A of 10.630% is an annual rate for compounding 
semiannually. The yield-  to- maturity on Bond B of 10.696% is an annual rate for 
compounding quarterly. The difference in the yields is not 6.6 bps (0.10696 – 
0.10630 = 0.00066). It is essential to compare the yields for the same periodicity 
to make a statement about relative value.
10.630% for a periodicity of two converts to 10.492% for a periodicity of four:
10 10630
2140 104922
44
4 +

=+

10.696% for a periodicity of four converts to 10.839% for a periodicity of two:
10 10696
4120 108394
22
2 +

=+


22
2 +

=+

The additional compensation for the greater risk in Bond B is 20.9 bps 
(0.10839 – 0.10630 = 0.00209) when the yields are stated on a semiannual bond 
basis. The additional compensation is 20.4 bps (0.10696 – 0.10492 = 0.00204) 
when both are annualized for quarterly compounding.
If a fixed-  rate bond contains an embedded option , other yield measures are 
used. An embedded option is part of the security and cannot be removed and sold 
separately. For example, a callable bond  contains an embedded call option that gives 
the issuer the right to buy the bond back from the investor at specified prices on pre-  
determined dates. The preset dates usually coincide with coupon payment dates after 
a call protection  period. A call protection period is the time during which the issuer 
of the bond is not allowed to exercise the call option.
Suppose that a seven-  year, 8% annual coupon payment bond is first callable in

four years. That gives the investor four years of protection against the bond being 
called. After the call protection period, the issuer might exercise the call option if 
interest rates decrease or the issuer’s credit quality improves. Those circumstances 
allow the issuer to refinance the debt at a lower cost of funds. The preset prices that 
the issuer pays if the bond is called often are at a premium above par. For example, 
the “call schedule” for this bond might be that it is first callable at 102 (per 100 of par 
value) on the coupon payment date in four years, callable at 101 in five years, and at 
par value on coupon payment dates thereafter.

Prices and Yields: Conventions for Quotes and Calculations 425
The yield-  to- maturity on this seven-  year, 8% callable bond is just one of several 
traditional yield measures for the investment. Others are yield-  to- first-  call, yield-  to- 
second-  call, and so on. If the current price for the bond is 105 per 100 of par value, 
the yield-  to- first-  call in four years is 6.975%.
1058
18
18
18 102
10 069751 234=
+()+
+()+
+()++
+()=
rr rrr,     .
The yield-  to- second-  call in five years is 6.956%.
1058
18
18
18
18 101
1001 2345=
+()+
+()+
+()+
+()++
+()=
rr rr rr,     .66956
The yield-  to- third-  call is 6.953%.
1058
18
18
18
18
18 100
11 23456=
+()+
+()+
+()+
+()+
+()++
+() rr rr rr,      r=0 06953 .
Finally, the yield-  to- maturity is 7.070%.
1058
18
18
18
18
18
1
8 100
11 23456=
+()+
+()+
+()+
+()+
+()+
+()+
+rr rr rr
+ +()=
rr70 07070 ,     .
Each calculation is based on Equation 1, whereby the call price (or par value) is 
used for F V. The lowest of the sequence of yields-  to- call and the yield-  to- maturity

is known as the yield-  to- worst . In this case, it is the yield-  to- third-  call of 6.953%. 
The intent of this yield measure is to provide to the investor the most conservative 
assumption for the rate of return.
The yield-  to- worst is a commonly cited yield measure for fixed-  rate callable bonds 
used by bond dealers and investors. However, a more precise approach is to use an 
option pricing model and an assumption about future interest rate volatility to value 
the embedded call option. The value of the embedded call option is added to the flat 
price of the bond to get the option-  adjusted price . The investor bears the call risk 
(the bond issuer has the option to call), so the embedded call option reduces the 
value of the bond from the investor’s perspective. The investor pays a lower price for 
the callable bond than if it were option-  free. If the bond were non-  callable, its price 
would be higher. The option-  adjusted price is used to calculate the option-  adjusted

yield . The option-  adjusted yield is the required market discount rate whereby the 
price is adjusted for the value of the embedded option. The value of the call option is 
the price of the option-  free bond minus the price of the callable bond.
3.4 Yield Measures for Floating-  Rate Notes
Floating-  rate notes  are very different from a fixed-  rate bond. The interest payments 
on a floating-  rate note, which often is called a floater or an FRN, are not fixed. Instead, 
they vary from period to period depending on the current level of a reference interest 
rate. The interest payments could go up or down; that is why they “float. ” The intent of 
an FRN is to offer the investor a security that has less market price risk than a fixed-  
rate bond when market interest rates fluctuate. In principle, a floater has a stable price 
even in a period of volatile interest rates. With a traditional fixed-  income security,

interest rate volatility affects the price because the future cash flows are constant. With 
a floating-  rate note, interest rate volatility affects future interest payments.
The reference rate on a floating-  rate note usually is a short-  term money market 
rate, such as three-  month Libor (the London Interbank Offered Rate). The principal 
on the floater typically is non-  amortizing and is redeemed in full at maturity. The

Reading 52 ■ Introduction to Fixed-  Income Valuation 426
reference rate is determined at the beginning of the period, and the interest payment 
is made at the end of the period. This payment structure called “in arrears. ” The 
most common day-  count conventions for calculating accrued interest on floaters are 
actual/360 and actual/365.
Although there are many varieties of FRNs, only the most common and traditional 
floaters are covered here. On these floaters, a specified yield spread is added to, or 
subtracted from, the reference rate. For example, the floater might reset its interest 
rate quarterly at three-  month Libor plus 0.50%. This specified yield spread over the 
reference rate is called the quoted margin  on the FRN. The role of the quoted margin 
is to compensate the investor for the difference in the credit risk of the issuer and that 
implied by the reference rate. For example, a company with a stronger credit rating

than that of the banks included in Libor may be able to obtain a “sub-  Libor” cost of 
borrowed funds, which results in a negative quoted margin. An AAA rated company 
might be able to issue an FRN that pays three-  month Libor minus 0.25%.
The required margin  is the yield spread over, or under, the reference rate such that 
the FRN is priced at par value on a rate reset date. Suppose that a traditional floater is 
issued at par value and pays three-  month Libor plus 0.50%. The quoted margin is 50 
bps. If there is no change in the credit risk of the issuer, the required margin remains 
at 50 bps. On each quarterly reset date, the floater will be priced at par value. Between 
coupon dates, its flat price will be at a premium or discount to par value if Libor goes 
down or up. However, if the required margin continues to be the same as the quoted 
margin, the flat price is “pulled to par” as the next reset date nears. At the reset date,

any change in Libor is included in the interest payment for the next period.
Changes in the required margin usually come from changes in the issuer’s credit 
risk. Changes in liquidity or tax status also could affect the required margin. Suppose 
that on a reset date, the required margin goes up to 75 bps because of a downgrade 
in the issuer’s credit rating. A floater having a quoted margin of 50 bps now pays its 
investors a “deficient” interest payment. This FRN will be priced at a discount below 
par value. The amount of the discount is the present value of the deficient future cash 
flows. That annuity is 25 bps per period for the remaining life of the bond. It is the 
difference between the required and quoted margins. If the required margin goes 
down from 50 bps to 40 bps, the FRN will be priced at a premium. The amount of the 
premium is the present value of the 10 bp annuity for the “excess” interest payment 
each period.

Fixed-  rate and floating-  rate bonds are essentially the same with respect to changes 
in credit risk. With fixed-  rate bonds, the premium or discount arises from a difference 
in the fixed coupon rate and the required yield-  to- maturity. With floating-  rate bonds, 
the premium or discount arises from a difference in the fixed quoted margin and the 
required margin. However, fixed-  rate and floating-  rate bonds are very different with 
respect to changes in benchmark interest rates.
The valuation of a floating-  rate note needs a pricing model. Equation 8 is a sim -
plified FRN pricing model. Following market practice, the required margin is called 
the discount margin .
PVQM FV
m
DM
mQM FV
m=+ () ×
++ 

++ () ×
++Index
IndexIndex
Index111DDM
m
QM FV
mFV
DM
mN

++
+ () ×+
++ 

2
1
 Index
Index(8)

Prices and Yields: Conventions for Quotes and Calculations 427
where
 PV = present value, or the price of the floating-  rate note
 Index = reference rate, stated as an annual percentage rate
 QM = quoted margin, stated as an annual percentage rate
 m = periodicity of the floating-  rate note, the number of payment periods 
per year
 DM = discount margin, the required margin stated as an annual percentage 
rate
This equation is similar to Equation 1, which is the basic pricing formula for a fixed-  
rate bond given the market discount rate. In Equation 1, PMT  is the coupon payment 
per period . Here, annual  rates are used. The first interest payment is the annual rate 
for the period (Index + QM) times the par value ( FV) and divided by the number of 
periods in the year ( m). In Equation 1, the market discount rate per period ( r) is used

to discount the cash flows. Here, the discount rate per period is the reference rate 
plus the discount margin (Index + DM) divided by the periodicity ( m).
This is a simplified FRN pricing model for several reasons. First, PV is for a rate 
reset date when there are N evenly spaced periods to maturity. There is no accrued 
interest so that the flat price is the full price. Second, the model assumes a 30/360 
day-  count convention so that the periodicity is an integer. Third, and most important, 
the same reference rate (Index) is used for all payment periods in both the numerators 
and denominators. More complex FRN pricing models use projected future rates for 
Index in the numerators and spot rates in the denominators. Therefore, the calculation 
for DM depends on the simplifying assumptions in the pricing model.
Suppose that a two-  year FRN pays six-  month Libor plus 0.50%. Currently, six-  
month Libor is 1.25%. In Equation 8, Index = 0.0125, QM = 0.0050, and m = 2. The

numerators in Equation 8, ignoring the repayment of principal, are 0.875.
Index + () ×=+ () ×=QM FV
m0 0125 0 0050 100
20 875...
Suppose that the yield spread required by investors is 40 bps over the reference rate, 
DM = 0.0040. The assumed discount rate per period is 0.825%.
Index +=+=DM
m0 0125 0 0040
20 00825...
Using Equation 8 for N = 4, the FRN is priced at 100.196 per 100 of par value.
0 875
10 008250 875
10 00825087
12 3.
..
..
..
+()+
+()+
+()+5 5 100
10 00825100 1964+
+()=
..
This floater is priced at a premium above par value because the quoted margin is 
greater than the discount margin.
A similar calculation is to estimate the discount margin given the market price of 
the floating-  rate note. Suppose that a five-  year FRN pays three-  month Libor plus 0.75% 
on a quarterly basis. Currently, three-  month Libor is 1.10%. The price of the floater 
is 95.50 per 100 of par value, a discount below par value because of a downgrade in 
the issuer’s credit rating.

Reading 52 ■ Introduction to Fixed-  Income Valuation 428
In Equation 8, use PV = 95.50 and N = 20.
95 500 4625
10 0110
40 4625
10 0110
412..
..
.=
++ 

+
++ 

+
DM DM ++
++ 

0 4625 100
10 0110
420.
. DM
This has the same format as Equation 1, which can be used to solve for the market 
discount rate per period, r = 0.7045%.
95 500 4625
10 4625
10 4625 100
112 20... .=
+()+
+()+++
+() rr rr  ,     = =0 007045 .
This can be used to solve for DM = 1.718%.
0 0070450 0110
40 01718 ... =+=DMDM,     
If this FRN was issued at par value, investors required at that time a spread of only 
75 bps over three-  month Libor. Now, after the credit downgrade, investors require an 
estimated  discount margin of 171.8 bps. The floater trades at a discount because the 
quoted margin remains fixed at 75 bps. The calculated discount margin is an estimate 
because it is based on a simplified FRN pricing model.
EXAMPLE 9   
Calculating the Discount Margin for a Floating-  Rate Note

A four-  year French floating-  rate note pays three-  month Euribor (Euro Interbank 
Offered Rate, an index produced by the European Banking Federation) plus 1.25%. 
The floater is priced at 98 per 100 of par value. Calculate the discount margin 
for the floater assuming that three-  month Euribor is constant at 2%. Assume 
the 30/360 day-  count convention and evenly spaced periods.
Solution:
By assumption, the interest payment each period is 0.8125 per 100 of par value.
m0 0200 0 0125 100
40 8125...
The discount margin can be estimated by solving for DM in this equation.
980 8125
10 0200
40 8125
10 0200
412=
++ 

+
++ 

++.
..
. DM DM
 0 0 8125 100
10 0200
416.
.+
++ 

DM
The solution for the discount rate per period is 0.9478%.
980 8125
10 8125
10 8125 100
1012 16=
+()+
+()+++
+()=.. ..
rr rr  ,     0 009478
Therefore, DM = 1.791%.
0 0094780 0200
40 01791 ... =+=DMDM,

Prices and Yields: Conventions for Quotes and Calculations 429
The quoted margin is 125 bps over the Euribor reference rate. Using the 
simplified FRN pricing model, it is estimated that investors require a 179.1 bp 
spread for the floater to be priced at par value.
3.5 Yield Measures for Money Market Instruments
Money market instruments are short-  term debt securities. They range in time-  to- 
maturity from overnight sale and repurchase agreements (repos) to one-  year bank 
certificates of deposit. Money market instruments also include commercial paper, 
government issues of less than one year, bankers’ acceptances, and time deposits 
based on such indexes as Libor and Euribor. Money market mutual funds are a major 
investor in such securities. These mutual funds can invest only in certain eligible 
money market securities.
There are several important differences in yield measures between the money 
market and the bond market:

1 Bond yields-  to- maturity are annualized and compounded. Yield measures in the 
money market are annualized but not compounded. Instead, the rate of return 
on a money market instrument is stated on a simple interest basis.
2 Bond yields-  to- maturity can be calculated using standard time-  value-  of- money 
analysis and with formulas programmed into a financial calculator. Money mar -
ket instruments often are quoted using nonstandard interest rates and require 
different pricing equations than those used for bonds.
3 Bond yields-  to- maturity usually are stated for a common periodicity for all 
times-  to- maturity. Money market instruments having different times-  to- 
maturity have different periodicities for the annual rate.
In general, quoted money market rates are either discount rates  or add-  on rates . 
Although market conventions vary around the world, commercial paper, Treasury bills

(a US government security issued with a maturity of one year or less), and bankers’ 
acceptances often are quoted on a discount rate basis. Bank certificates of deposit, 
repos, and such indexes as Libor and Euribor are quoted on an add-  on rate basis. It 
is important to understand that “discount rate” has a unique meaning in the money 
market. In general, discount rate means “interest rate used to calculate a present 
value”—for instance, “market discount rate” as used in this reading. In the money 
market, however, discount rate is a specific type of quoted rate. Some examples will 
clarify this point.
Equation  9 is the pricing formula for money market instruments quoted on a 
discount rate basis.
PV FV DR =× −×

 1Days
Year
where
 PV = present value, or the price of the money market instrument
 FV = future value paid at maturity, or the face value of the money market 
instrument
 Days = number of days between settlement and maturity
 Year = number of days in the year

Year = number of days in the year
 DR = discount rate, stated as an annual percentage rate(9)

Reading 52 ■ Introduction to Fixed-  Income Valuation 430
Suppose that a 91-  day US Treasury bill (T-  bill) with a face value of USD10 million is 
quoted at a discount rate of 2.25% for an assumed 360-  day year. Enter FV = 10,000,000, 
Days = 91, Year = 360, and DR = 0.0225. The price of the T-  bill is USD9,943,125.
PV =× −×

= 10 000 000 191
3600 0225 9 943 125 ,, ., ,
The unique characteristics of a money market discount rate can be examined 
with Equation 10, which transforms Equation 9 algebraically to isolate the DR term.
DRFV PV
FV=

×− 

Year
Days
The first term, Year/Days, is the periodicity of the annual rate. The second term 
reveals the odd character of a money market discount rate. The numerator, FV – PV , 
is the interest earned on the T-  bill, USD56,875 (= 10,000,000 – 9,943,125), over the 
91 days to maturity. However, the denominator is FV, not PV. In theory, an interest 
rate is the amount earned divided by the investment amount ( PV)—not divided by

the total return at maturity, which includes the earnings ( FV). Therefore, by design, 
a money market discount rate understates  the rate of return to the investor, and it 
understates  the cost of borrowed funds to the issuer. That is because PV is less than 
FV (as long as DR is greater than zero).
Equation 11 is the pricing formula for money market instruments quoted on an 
add-  on rate basis.
PVFV
AOR=
+×

 1Days
Year
where
 PV = present value, principal amount, or the price of the money market 
 FV = future value, or the redemption amount paid at maturity including 
interest
 AOR  = add-  on rate, stated as an annual percentage rate
Suppose that a Canadian pension fund buys a 180-  day banker’s acceptance (BA) 
with a quoted add-  on rate of 4.38% for a 365-  day year. If the initial principal amount 
is CAD10 million, the redemption amount due at maturity is found by re-  arranging

Equation 11 and entering PV = 10,000,000, Days = 180, Year = 365, and AOR  = 0.0438.
FV =+ ××

= 10 000 000 10 000 000180
3650 0438 10 216 000 ,, ,, ., ,
At maturity, the pension fund receives CAD10,216,000, the principal of CAD10 mil -
lion plus interest of CAD216,000. The interest is calculated as the principal times 
the fraction of the year times the annual add-  on rate. It is added to the principal to 
determine the redemption amount.
Suppose that after 45 days, the pension fund sells the BA to a dealer. At that time, 
the quoted add-  on rate for a 135-  day BA is 4.17%. The sale price for the BA can be 
calculated using Equation 11 for FV = 10,216,000, Days = 135, Year = 365, and AOR  
= 0.0417. The sale price is CAD10,060,829.
PV =
+×

=10 216 000
1135
3650 041710 060 829,,
.,,(10)
(11)

Prices and Yields: Conventions for Quotes and Calculations 431
The characteristics of an add-  on rate can be examined with Equation 12, which 
transforms Equation 11 algebraically to isolate the AOR  term.
AORFV PV
PV=

×− 

Year
Days
This equation indicates that an add-  on rate is a reasonable yield measure for a money 
market investment. The first term, Year/Days, is the periodicity of the annual rate. 
The second term is the interest earned, FV – PV , divided by PV, the amount invested.
The pension fund’s rate of return on its 45-  day investment in the banker’s acceptance 
can be calculated with Equation 12. Enter Year = 365, Days = 45, FV = 10,060,829, and 
PV = 10,000,000. Notice that FV here is the sale price, not the redemption amount.
AOR=

×− 

=365
4510 060 829 10 000 000
10 000 000004,, ,,
,,.9934
The rate of return, stated on a 365-  day add-  on rate basis, is 4.934%. This result is 
an annual rate for a periodicity of 8.11 (= 365/45). Implicitly, this assumes that the

investment can be replicated 8.11 times over the year.
Investment analysis is made difficult for money market securities because (1) some 
instruments are quoted on a discount rate basis and others on an add-  on rate basis 
and (2) some are quoted for a 360-  day year and others for a 365-  day year. Another 
difference is that the “amount” of a money market instrument quoted on a discount 
rate basis typically is the face value paid at maturity. However, the “amount” when 
quoted on an add-  on rate basis usually is the principal, the price at issuance. To 
make money market investment decisions, it is essential to compare instruments on 
a common basis. An example illustrates this point.
Suppose that an investor is comparing two money market instruments: (A) 90-  day 
commercial paper quoted at a discount rate of 5.76% for a 360-  day year and (B) 90-  
day bank time deposit quoted at an add-  on rate of 5.90% for a 365-  day year. Which

offers the higher expected rate of return assuming that the credit risks are the same? 
The price of the commercial paper is 98.560 per 100 of face value, calculated using 
Equation 9 and entering FV = 100, Days = 90, Year = 360, and DR = 0.0576.
PV =× −×

= 100 190
3600 0576 98 560..
Next, use Equation 12 to solve for the AOR  for a 365-  day year, whereby Year  = 365, 
Days  = 90, FV = 100, and PV = 98.560.
AOR=

×− 

=365
90100 98 560
98 5600 05925.
..
The 90-  day commercial paper discount rate of 5.76% converts to an add-  on rate for 
a 365-  day year of 5.925%. This converted rate is called a bond equivalent yield , or 
sometimes just an “investment yield. ” A bond equivalent yield is a money market rate 
stated on a 365-  day add-  on rate basis. If the risks are the same, the commercial paper 
offers 2.5 bps more in annual return than the bank time deposit.
EXAMPLE 10   
Comparing Money Market Instruments Based on Bond 
Equivalent Yields

Suppose that a money market investor observes quoted rates on the following 
four 180-  day money market instruments:(12)

Reading 52 ■ Introduction to Fixed-  Income Valuation 432
Money Market 
InstrumentQuotation  
BasisAssumed Number of 
Days in the Y ear Quoted Rate
A Discount Rate 360 4.33%
B Discount Rate 365 4.36%
C Add-  On Rate 360 4.35%
D Add-  On Rate 365 4.45%
Calculate the bond equivalent yield for each instrument. Which instrument 
offers the investor the highest rate of return if the credit risk is the same?
Solution:
A Use Equation 9 to get the price per 100 of par value, where FV = 100, 
Days  = 180, Year = 360, and DR = 0.0433.
PV =× −×

= 100 1180
3600 0433 97 835..
 Use Equation 12 to get the bond equivalent yield, where Year = 365, Days 
= 180, FV = 100, and PV = 97.835.
AOR=

×− 

=365
180100 97 835
97 8350 04487.
..
 The bond equivalent yield for Bond A is 4.487%.
B Use Equation 9 to get the price per 100 of face value, where FV = 100, 
Days = 180, Year = 365, and DR = 0.0436.
PV =× −×

3650 0436 97 850..
 Use Equation 12 to get the bond equivalent yield, where Year = 365, Days

= 180, FV = 100, and PV = 97.850.
AOR=

×− 

=365
180100 97 850
97 8500 04456.
..
 The bond equivalent yield for Bond B is 4.456%.
C First, determine the redemption amount per 100 of principal ( PV = 100), 
where Days = 180, Year = 360, and AOR  = 0.0435.
FV =+ ××

= 100 100180
3600 0435 102 175..
= 180, FV = 102.175, and PV = 100.
AOR=

×− 

=365
180102 175 100
1000 04410..
 The bond equivalent yield for Bond C is 4.410%.
 Another way to get the bond equivalent yield for Bond C is to observe 
that the AOR  of 4.35% for a 360-  day year can be obtained using 
Equation 12 for Year = 360, Days = 180, FV = 102.175, and PV = 100.
AOR=

×− 

=360
1000 0435..

The Maturity Structure of Interest Rates 433
 Therefore, an add-  on rate for a 360-  day year only needs to be multiplied 
by the factor of 365/360 to get the 365-  day year bond equivalent yield.
365
3600 0435 0 04410×=..
D The quoted rate for Bond D of 4.45% is a bond equivalent yield, which is 
defined as an add-  on rate for a 365-  day year.
If the risk of these money market instruments is the same, Bond A offers the 
highest rate of return on a bond equivalent yield basis, 4.487%.
The third difference between yield measures in the money market and the bond 
market is the periodicity of the annual rate. Because bond yields-  to- maturity are 
computed using interest rate compounding, there is a well-  defined periodicity. For 
instance, bond yields-  to- maturity for semiannual compounding are annualized for a 
periodicity of two. Money market rates are computed using simple interest without 
compounding. In the money market, the periodicity is the number of days in the year

divided by the number of days to maturity. Therefore, money market rates for different 
times-  to- maturity have different periodicities.
Suppose that an analyst prefers to convert money market rates to a semiannual 
bond basis so that the rates are directly comparable to yields on bonds that make 
semiannual coupon payments. The quoted rate for a 90-  day money market instrument 
is 10%, quoted as a bond equivalent yield, which means its periodicity is 365/90. Using 
Equation 7, the conversion is from m = 365/90 to n = 2 for APR365/90  = 0.10.
1010
365 90120 10127365 90
22
2 +

 =+

Therefore, 10% for a periodicity of 365/90 corresponds to 10.127% for a periodicity 
of two. The difference is significant—12.7 bps. In general, the difference depends on 
the level of the annual percentage rate. When interest rates are lower, the difference 
between the annual rates for any two periodicities is reduced.
THE MATURITY STRUCTURE OF INTEREST RATES

There are many reasons why the yields-  to- maturity on any two bonds are different. 
Suppose that the yield-  to- maturity is higher on Bond X than on Bond Y. The following 
are some possible reasons for the difference between the yields:
■■Currency—Bond X could be denominated in a currency with a higher expected 
rate of inflation than the currency in which Bond Y is denominated.
■■Credit risk—Bond X could have a non-  investment-  grade rating of BB, and Bond 
Y could have an investment-  grade rating of AA.
■■Liquidity—Bond X could be illiquid, and Bond Y could be actively traded.
■■Tax Status—Interest income on Bond X could be taxable, whereas interest 
income on Bond Y could be exempt from taxation.
■■Periodicity—Bond X could make a single annual coupon payment, and its 
yield-  to- maturity could be quoted for a periodicity of one. Bond Y could make 
monthly coupon payments, and its yield-  to- maturity could be annualized for a 
periodicity of 12.4

Reading 52 ■ Introduction to Fixed-  Income Valuation 434
Obviously, another reason is that Bond X and Bond Y could have different times-  to- 
maturity. This factor explaining the differences in yields is called the maturity structure , 
or term structure , of interest rates. It involves the analysis of yield curves, which are 
relationships between yields-  to- maturity and times-  to- maturity. There are different 
types of yield curves, depending on the characteristics of the underlying bonds.
In theory, maturity structure should be analyzed for bonds that have the same 
properties other than time-  to- maturity. The bonds should be denominated in the same 
currency and have the same credit risk, liquidity, and tax status. Their annual rates 
should be quoted for the same periodicity. Also, they should have the same coupon 
rate so that they each have the same degree of coupon reinvestment risk. In practice,

maturity structure is analyzed for bonds for which these strong assumptions rarely hold.
The ideal dataset would be yields-  to- maturity on a series of zero-  coupon  govern -
ment bonds for a full range of maturities. This dataset is the government bond spot 
curve , sometimes called the zero or “strip” curve (because the coupon payments are 
“stripped” off of the bonds). The spot, zero, or strip curve is a sequence of yields-  to- 
maturity on zero-  coupon bonds. Often, these government spot rates are interpreted 
as the “risk-  free” yields; in this context, “risk-  free” refers only to default risk. There still 
could be a significant amount of inflation risk to the investor, as well as liquidity risk.
A government bond spot curve is illustrated in Exhibit 5 for maturities ranging 
from 1 to 30 years. The annual yields are stated on a semiannual bond basis, which 
facilitates comparison to coupon-  bearing bonds that make semiannual payments.
Exhibit 5   A Government Bond Spot Curve

Yield-to-Maturity (%)
6
5
4
3
2
1
0
0 30 5 15 20 10 25
Time-to-Maturity (years)
This spot curve is upward sloping and flattens for longer times-  to- maturity. 
Longer-  term government bonds usually have higher yields than shorter-  term bonds. 
This pattern is typical under normal market conditions. Sometimes, a spot curve is 
downward sloping in that shorter-  term yields are higher than longer-  term yields. 
This downward sloping spot curve is called an inverted yield curve. The theories that 
attempt to explain the shape of the yield curve and its implications for future financial 
market conditions are covered in later readings.

The Maturity Structure of Interest Rates 435
This hypothetical spot curve is ideal for analyzing maturity structure because 
it best meets the “other things being equal” assumption. These government bonds 
presumably have the same currency, credit risk, liquidity, and tax status. Most impor -
tantly, they have no coupon reinvestment risk because there are no coupons to rein -
vest. However, most actively traded government and corporate bonds make coupon 
payments. Therefore, analysis of maturity structure usually is based on price data on 
government bonds that make coupon payments. These coupon bonds might not have 
the same liquidity and tax status. Older (“seasoned”) bonds tend to be less liquid than 
newly issued debt because they are owned by “buy-  and-  hold” institutional and retail 
investors. Governments issue new debt for regular times-  to- maturity—for instance, 
5- year and 10-  year bonds. The current 6-  year bond could be a 10-  year bond that was

issued four years ago. Also, as interest rates fluctuate, older bonds are priced at a dis -
count or premium to par value, which can lead to tax differences. In some countries, 
capital gains have different tax treatment than capital losses and interest income.
Analysts usually use only the most recently issued and actively traded government 
bonds to build a yield curve. These bonds have similar liquidity, and because they are 
priced closer to par value, they have fewer tax effects. A problem is that there are 
limited data for the full range of maturities. Therefore, it is necessary to interpolate  
between observed yields. Exhibit  6 illustrates a yield curve for a government that 
issues 2-  year, 3-  year, 5-  year, 7-  year, 10-  year, and 30-  year bonds that make semiannual 
coupon payments. Straight-  line interpolation is used between those points on the 
yield curve for coupon bonds.

Reading 52 ■ Introduction to Fixed-  Income Valuation 436
Exhibit 6   A Government Bond Yield Curve
3.0
2.5
2.0
1.5
1.0
0.5
0
0 30 5 10 15 20 25
0.20
0.15
0.10
0.05
0
12 1 3 6
Time-to-Maturit y (months)Yield-to-Maturity (%)
Exhibit 6 also includes yields for short-  term government securities having 1 month, 
3 months, 6 months, and 12 months to maturity. Although these money market instru -
ments might have been issued and traded on a discount rate basis, they typically are 
reported as bond equivalent yields. It is important for the analyst to know whether they 
have been converted to the same periodicity as the longer-  term government bonds. 
If not, the observed yield curve can be misleading because the number of periods in 
the year is not the same.
In addition to the yield curve on coupon bonds and the spot curve on zero-  coupon 
bonds, maturity structure can be assessed using a par curve . A par curve is a sequence

of yields-  to- maturity such that each bond is priced at par value. The bonds, of course, 
are assumed to have the same currency, credit risk, liquidity, tax status, and annual 
yields stated for the same periodicity. Between coupon payment dates, the flat price 
(not the full price) is assumed to be equal to par value.

The Maturity Structure of Interest Rates 437
The par curve is obtained from a spot curve. On a coupon payment date, the fol -
lowing equation can be used to calculate a par rate given the sequence of spot rates.
100
11100
111
22=
+()+
+()+++
+()PMT
zPMT
zPMT
zNN
This equation is very similar to Equation 2 whereby PV = FV = 100. The problem is 
to solve for PMT  algebraically. Then, PMT /100 is equal to the par rate per period .
An example illustrates the calculation of the par curve given a spot curve. Suppose 
the spot rates on government bonds are 5.263% for one year, 5.616% for two years, 
6.359% for three years, and 7.008% for four years. These are effective annual rates. 
The one-  year par rate is 5.263%.
100100
1 052635 2631=+
()=PMTPMT
.. ,     
The two-  year par rate is 5.606%.
100
1 05263100
1 056165 60612=
()++
()=PMTP MTPMT
... ,     
The three-  year and four-  year par rates are 6.306% and 6.899%, respectively.
100
1 05263 1 05616100
1 0635912 3=
()+
()++
()PMTP MT PMTPMT
.. .,     = =6 306 .
100

()+
()++
100
1 05263 1 05616 1 06359100
1 07012 3=
()+
()+
()++ PMTP MT PMTP MT
.. .. 0 086 8994()= ,     PMT .
The fixed-  income securities covered so far have been cash market securities . 
Money market securities often are settled on a “same day, ” or “cash settlement, ” basis. 
Other securities have a difference between the trade date and the settlement date. For 
instance, if a government bond trades on a T + 1 basis, there is a one-  day difference 
between the trade date and the settlement date. If a corporate bond trades on a T + 
3 basis, the seller delivers the bond and the buyer makes payment in three business 
days. Cash markets are also called spot markets, which can be confusing because spot 
rate can have two meanings. It can mean the “rate on a bond traded in the spot, or 
cash, market. ” It can also mean “yield on a zero-  coupon bond, ” which is the meaning 
of spot rate used in this reading.

A forward market  is for future delivery, beyond the usual settlement time period 
in the cash market. Agreement to the terms for the transaction is on the trade date, 
but delivery of the security and payment for it is deferred to a future date. A forward 
rate  is the interest rate on a bond or money market instrument traded in a forward 
market. For example, suppose that in the cash market, a five-  year zero-  coupon bond 
is priced at 81 per 100 of par value. Its yield-  to- maturity is 4.2592%, stated on a 
81100
10 021296 20 04259210=
+()=× =
rr,     ,    ..
Suppose that a dealer agrees to deliver a five-  year bond two years into the future 
for a price of 75 per 100 of par value. The credit risk, liquidity, and tax status of this 
bond traded in the forward market are the same as the one in the cash market. The 
forward rate is 5.8372%.
75100
10 029186 20 05837210=
+()=× =
rr,     ,    ..(13)

Reading 52 ■ Introduction to Fixed-  Income Valuation 438
The notation for forward rates is important to understand. Although finance 
textbook authors use varying notation, the most common market practice is to name 
this forward rate the “2y5y” . This is pronounced “the two-  year into five-  year rate, ” or 
simply “the 2’s, 5’s. ” The idea is that the first number (two years) refers to the length of 
the forward period in years from today and the second number (five years) refers to 
the tenor  of the underlying bond. The tenor is the time-  to- maturity for a bond (or a 
derivative contract). Therefore, 5.8372% is the “2y5y” forward rate for the zero-  coupon 
bond—the five-  year yield two years into the future. Note that the bond that will be a 
five-  year zero in two years currently has seven years to maturity. In the money mar -
ket, the forward rate usually refers to months. For instance, an analyst might inquire

about the “1m6m” forward rate on Euribor, which is the rate on six-  month Euribor 
one month into the future.
Implied forward rates  (also known as forward yields) are calculated from spot 
rates. An implied forward rate is a break-  even reinvestment rate. It links the return on 
an investment in a shorter-  term zero-  coupon bond to the return on an investment in 
a longer-  term zero-  coupon bond. Suppose that the shorter-  term bond matures in A 
periods and the longer-  term bond matures in B periods. The yields-  to- maturity per 
period on these bonds are denoted zA and zB. The first is an A-period zero-  coupon 
bond trading in the cash market. The second is a B-period zero-  coupon cash market 
bond. The implied forward rate between period A and period B is denoted IFRA,B–A. 
It is a forward rate on a security that starts in period A and ends in period B. Its tenor 
is B – A  periods.
Equation 14 is a general formula for the relationship between the two spot rates

and the implied forward rate.
(1 + zA)A × (1 + IFRA,B–A)B–A = (1 + zB)B  
Suppose that the yields-  to- maturity on three-  year and four-  year zero-  coupon bonds 
are 3.65% and 4.18%, respectively, stated on a semiannual bond basis. An analyst would 
like to know the “3y1y” implied forward rate, which is the implied one-  year forward 
yield three years into the future. Therefore, A = 6 (periods), B = 8 (periods), B – A = 
2 (periods), z6 = 0.0365/2 (per period), and z8 = 0.0418/2 (per period).
10 0365
2110 0418
26
6228
62 +

×+() =+

 =..
,,IFRI FR ,     0 0 02889
20 05778.
.,
    ×=
The “3y1y” implied forward yield is 5.778%, annualized for a periodicity of two.
Equation  14 can be used to construct a forward curve . A forward curve is a 
series of forward rates, each having the same time frame. These forward rates might 
be observed on transactions in the derivatives market. Often, the forward rates are 
implied from transactions in the cash market. Exhibit 7 displays the forward curve

that is calculated from the government bond spot curve shown in Exhibit 5. These 
are one-  year forward rates stated on a semiannual bond basis.(14)

The Maturity Structure of Interest Rates 439
Exhibit 7   A Government Bond Spot Curve and Forward Curve
Spot CurveForward Curve7
6
5
4
3
2
1
0
0 35 10 20 30 5 15 25
A forward rate can be interpreted as an incremental, or marginal, return for 
extending the time-  to- maturity for an additional time period. Suppose an investor 
has a four-  year investment horizon and is choosing between buying a three-  year zero-  
coupon bond that is priced to yield 3.65% and a four-  year zero that is priced to yield 
4.18%. The incremental, or marginal, return for the fourth year is 5.778%, the “3y1y” 
implied forward rate. If the investor’s view on future bond yields is that the one-  year 
yield in three years is likely to be less than 5.778%, the investor might prefer to buy 
the four-  year bond. However, if the investor’s view is that the one-  year yield will be 
more than the implied forward rate, the investor might prefer the three-  year bond and

the opportunity to reinvest at the expected higher rate. That explains why an implied 
forward rate is the breakeven reinvestment rate . Implied forward rates are very useful 
to investors as well as bond issuers in making maturity decisions.
EXAMPLE 11   
Computing Forward Rates
Suppose that an investor observes these prices and yields-  to- maturity on zero-  
coupon government bonds:
Maturity Price Yield-  to- Maturity
1 year 97.50 2.548%
2 years 94.25 2.983%
3 years 91.75 2.891%
The prices are per 100 of par value. The yields-  to- maturity are stated on a 
1 Compute the “1y1y” and “2y1y” implied forward rates, stated on a semian -
nual bond basis.

Reading 52 ■ Introduction to Fixed-  Income Valuation 440
2 The investor has a three-  year investment horizon and is choosing between 
(1) buying the two-  year zero and reinvesting in another one-  year zero in 
two years and (2) buying and holding to maturity the three-  year zero. The 
investor decides to buy the two-  year bond. Based on this decision, which 
of the following is the minimum yield-  to- maturity the investor expects on 
one-  year zeros two years from now?
A 2.548%
B 2.707%
C 2.983%
The “1y1y” implied forward rate is 3.419%. In Equation 14, A = 2 (periods), B = 
4 (periods), B – A = 2 (periods), z2 = 0.02548/2 (per period), and z4 = 0.02983/2 
(per period).
10 02548
2110 02983
22
2224
2 +

×+() =+

..
,,IFRI FR ,     2 2 0 017095
20 03419=
×=.
.,
    
The “2y1y” implied forward rate is 2.707%. In Equation 14, A = 4 (periods), 
B = 6 (periods), B – A  = 2 (periods), z4 = 0.02983/2 (per period), and z6 = 
0.02891/2 (per period).
10 02983
2110 02891
24
4226
4 +

×+() =+

10 02983
2110 02891
24
4226
4 +

×+() =+

..
,,IFRI FR ,     2 2 0 013536
20 02707=
×=.
.,
    
B is correct. The investor’s view is that the one-  year yield in two years will be 
greater than or equal to 2.707%.
The “2y1y” implied forward rate of 2.707% is the breakeven reinvestment 
rate. If the investor expects the one-  year rate in two years to be less than that, 
the investor would prefer to buy the three-  year zero. If the investor expects the 
one-  year rate in two years to be greater than 2.707%, the investor might prefer 
to buy the two-  year zero and reinvest the cash flow.
The forward curve has many applications in fixed-  income analysis. Forward rates 
are used to make maturity choice decisions. They are used to identify arbitrage oppor -
tunities between transactions in the cash market for bonds and in derivatives markets. 
Forward rates are important in the valuation of derivatives, especially interest rate swaps

and options. Those applications for the forward curve are covered in other readings.
Forward rates can be used to value a fixed-  income security in the same manner as 
spot rates because they are interconnected. The spot curve can be calculated from the 
forward curve, and the forward curve can be calculated from the spot curve. Either 
curve can be used to value a fixed-  rate bond. An example will illustrate this process.
Suppose the current forward curve for one-  year rates is the following:
Time Period Forward Rate
0y1y 1.88%
1y1y 2.77%
2y1y 3.54%
3y1y 4.12%

Yield Spreads 441
These are annual rates stated for a periodicity of one. They are effective annual rates. 
The first rate, the “0y1y, ” is the one-  year spot rate. The others are one-  year forward 
rates. Given these rates, the spot curve can be calculated as the geometric average  of 
the forward rates.
The two-  year implied spot rate is 2.3240%.
(1.0188 × 1.0277) = (1 + z2)2, z2 = 0.023240
The following are the equations for the three-  year and four-  year implied spot rates.
(1.0188 × 1.0277 × 1.0354) = (1 + z3)3, z3 = 0.027278
(1.0188 × 1.0277 × 1.0354 × 1.0412) = (1 + z4)4, z4 = 0.030741
The three-  year implied spot rate is 2.7278%, and the four-  year spot rate is 3.0741%.
Suppose that an analyst needs to value a four-  year, 3.75% annual coupon payment 
bond that has the same risks as the bonds used to obtain the forward curve. Using the 
implied spot rates, the value of the bond is 102.637 per 100 of par value.
375
1 0188375
1 023240375
1 027278103 75
1 030712 3.
..
..
..
. ()+
()+
()+

1 030712 3.
..
..
..
. ()+
()+
()+
4 41102 6374()= .
The bond also can be valued using the forward curve.
375
1 0188375
1 0188 1 0277375
1 0188 1 0277 1 0354.
..
...
.. . ()+× ()+×× ( ) )
+×× × ()=  103 75
1 0188 1 0277 1 0354 1 0412102 637.
.. ...
YIELD SPREADS
A yield spread, in general, is the difference in yield between different fixed income 
securities. This section describes a number of yield spread measures.
5.1 Yield Spreads over Benchmark Rates
In fixed-  income security analysis, it is important to understand why bond prices and 
yields-  to- maturity change. To do this, it is useful to separate a yield-  to- maturity into 
two components: the benchmark  and the spread . The benchmark yield for a fixed-  
income security with a given time-  to- maturity is the base rate, often a government bond 
yield. The spread is the difference between the yield-  to- maturity and the benchmark.
The reason for this separation is to distinguish between macroeconomic and

microeconomic factors that affect the bond price and, therefore, its yield-  to- maturity. 
The benchmark captures the macroeconomic factors: the expected rate of inflation 
in the currency in which the bond is denominated, general economic growth and the 
business cycle, foreign exchange rates, and the impact of monetary and fiscal policy. 
Changes in those factors impact all bonds in the market, and the effect is seen mostly 
in changes in the benchmark yield. The spread captures the microeconomic factors 
specific to the bond issuer and the bond itself: credit risk of the issuer and changes in 
the quality rating on the bond, liquidity and trading in comparable securities, and the 
tax status of the bond. It should be noted, however, that general yield spreads across 
issuers can widen and narrow with changes in macroeconomic factors.
Exhibit 8 illustrates the building blocks of the yield-  to- maturity, starting with the

benchmark and the spread. The benchmark is often called the risk-  free rate of return. 
Also, the benchmark can be broken down into the expected real rate and the expected 5

Reading 52 ■ Introduction to Fixed-  Income Valuation 442
inflation rate in the economy. The yield spread is called the risk premium over the 
“risk-  free” rate of return. The risk premium provides the investor with compensation 
for the credit and liquidity risks, and possibly the tax impact of holding a specific bond.
Exhibit 8   Yield-  to- Maturity Building Blocks
Spread
BenchmarkRisk Premium
“Risk-Free” Rate of
ReturnLiquidityTaxation
Credit Risk
Expected Inflation
Rate
Expected Real
Rate
The benchmark varies across financial markets. Fixed-  rate bonds often use a 
government benchmark security with the same time-  to- maturity as, or the closest 
time-  to- maturity to, the specified bond. This benchmark is usually the most recently 
issued government bond and is called the on- the-  run security. The on-  the- run gov -
ernment bond is the most actively traded security and has a coupon rate closest to 
the current market discount rate for that maturity. That implies that it is priced close

to par value. Seasoned government bonds are called off-  the-  run. On-  the- run bonds 
typically trade at slightly lower yields-  to- maturity than off-  the- run bonds having the 
same or similar times-  to- maturity because of differences in demand for the securities 
and, sometimes, differences in the cost of financing the government security in the 
repo market.
A frequently used benchmark for floating-  rate notes is Libor. As a composite 
interbank rate, it is not a risk-  free rate. The yield spread over a specific benchmark 
is referred to as the benchmark spread  and is usually measured in basis points. If 
no benchmark exists for a specific bond’s tenor or a bond has an unusual maturity, 
interpolation is used to derive an implied benchmark. Also, bonds with very long 
tenors are priced over the longest available benchmark bond. For example, 100-  year 
bonds (often called “century bonds”) in the United States are priced over the 30-  year 
US Treasury benchmark rate.

In the United Kingdom, the United States, and Japan, the benchmark rate for 
fixed-  rate bonds is a government bond yield. The yield spread in basis points over an 
actual or interpolated government bond is known as the G- spread . The spread over 
a government bond is the return for bearing greater credit, liquidity, and other risks 
relative to the sovereign bond. Euro-  denominated corporate bonds are priced over a 
EUR interest rate swap benchmark. For example, a newly issued five-  year EUR bond 
might be priced at a rate of “mid-  swaps” plus 150 bps, where “mid-  swaps” is the aver -
age of the bid and offered swap rates. The yield spread is over a five-  year EUR swap 
rate rather than a government benchmark. Note that the government bond yield or 
swap rate used as the benchmark for a specific corporate bond will change over time 
as the remaining time-  to- maturity changes.

Yield Spreads 443
The yield spread of a specific bond over the standard swap rate in that currency of 
the same tenor is known as the I- spread  or interpolated spread  to the swap curve. 
This yield spread over Libor allows comparison of bonds with differing credit and 
liquidity risks against an interbank lending benchmark. Issuers often use the Libor 
spread to determine the relative cost of fixed-  rate bonds versus floating-  rate alternatives, 
such as an FRN or commercial paper. Investors use the Libor spread as a measure of 
a bond’s credit risk. Whereas a standard interest rate swap involves an exchange of 
fixed for floating cash flows based on a floating index, an asset swap  converts the 
periodic fixed coupon of a specific bond to a Libor plus or minus a spread. If the bond 
is priced close to par, this conversion approximates the price of a bond’s credit risk 
over the Libor index. Exhibit 9 illustrates these yield spreads using the Bloomberg

Fixed Income Relative Value (FIRV) page.
This example is for the 5.70% IBM bond that matures on 14 September 2017. The 
spreads are in the top-  left corner of the page. The bond’s flat price was 120.878 per 
100 of par value on 1 May 2012, and its yield-  to- maturity was 1.618%. On that date, 
the yield spread over a particular Treasury benchmark was 85 bps. Its G-  spread over 
an interpolated government bond yield was 77 bps. These two spreads typically differ 
by a few basis points, especially if the benchmark is on-  the- run and has a somewhat 
different maturity date. The bond’s I-  spread was 50 bps. That Libor spread is smaller 
than the G-  spread because five-  year Treasury yields were lower than five-  year Libor 
swap rates at that time. The use of these spreads in investor strategies will be covered 
in more detail in later readings. In general, an analyst will track these spreads relative 
to their averages and historical highs and lows in an attempt to identify relative value.

5.2 Yield Spreads over the Benchmark Yield Curve
A yield curve shows the relationship between yields-  to- maturity and times-  to- maturity 
for securities with the same risk profile. For example, the government bond yield 
curve is the relationship between the yields of on-  the- run government bonds and 
their times-  to- maturity. The swap yield curve shows the relationship between fixed 
Libor swap rates and their times-  to- maturity.
Each of these yield curves represents the term structure of benchmark interest rates, 
whether for “risk-  free” government yields or “risky” fixed swap rates. Benchmark yield 
curves tend to be upward-  sloping because investors typically demand a premium for 
holding longer-  term securities. In general, investors face greater price risk for a given 
change in yield for longer-  term bonds. This topic is covered further in the reading 
“Understanding Fixed-  Income Risk and Return. ” The term structure of interest rates

is dynamic, with short-  term rates driven by central bank policy and longer-  term rates 
affected by long-  term growth and inflation expectations.
Isolating credit risk over varying times-  to- maturity gives rise to a term structure of 
credit spreads that is distinct for each borrower. The G-  spread and I-  spread each use 
the same discount rate for each cash flow. Another approach is to calculate a constant 
yield spread over a government (or interest rate swap) spot curve instead. This spread 
is known as the zero volatility spread (Z-  spread)  of a bond over the benchmark rate. 
In Exhibit 9, the Z-  spread for the IBM bond was reported to be 52 bps.
The Z-  spread over the benchmark spot curve can be calculated with Equation 15:
PVPMT
zZPMT
zZPMTF V
zZNN=
++()+
++()+++
++() 11 111
22
The benchmark spot rates— z1, z2, …, zN—are derived from the government yield 
curve (or from fixed rates on interest rate swaps). Z is the Z-  spread per period and

is the same for all time periods. In Equation 15, N is an integer, so the calculation 
is on a coupon date when the accrued interest is zero. Sometimes, the Z-  spread is (15)

Reading 52 ■ Introduction to Fixed-  Income Valuation 444
Exhibit 9   Bloomberg FIRV Page for the 5.70% IBM Bond
Used with permission of Bloomberg Businessweek Copyright © 2013. All rights reserved.

Yield Spreads 445
called the static spread because it is constant (and has zero volatility). In practice, the 
Z- spread is usually calculated in a spreadsheet using a goal seek function or similar 
solver function.
The Z-  spread is also used to calculate the option-  adjusted spread  (OAS) on a 
callable bond. The OAS, like the option-  adjusted yield, is based on an option-  pricing 
model and an assumption about future interest rate volatility. Then, the value of the 
embedded call option, which is stated in basis points per year, is subtracted from the 
yield spread. In particular, it is subtracted from the Z-  spread:
OAS = Z-  spread – Option value (in basis points per year)
This important topic is covered in later readings.
EXAMPLE 12   
The G-  Spread and the Z-  Spread
A 6% annual coupon corporate bond with two years remaining to maturity is 
trading at a price of 100.125. The two-  year, 4% annual payment government

benchmark bond is trading at a price of 100.750. The one-  year and two-  year 
government spot rates are 2.10% and 3.635%, respectively, stated as effective 
annual rates.
1 Calculate the G-  spread, the spread between the yields-  to- maturity on the 
corporate bond and the government bond having the same maturity.
2 Demonstrate that the Z-  spread is 234.22 bps.
The yield-  to- maturity for the corporate bond is 5.932%.
100 1256
1106
10 0593212.. =
+()+
+()=
rrr,     
The yield-  to- maturity for the government benchmark bond is 3.605%.
100 7504
1104
10 0360512.. =
+()+
+()=
rrr,     
The G-  spread is 232.7 bps: 0.05932 – 0.03605 = 0.02327.
Solve for the value of the corporate bond using z1 = 0.0210, z2 = 0.03635, and 
Z = 0.023422:
6
10 0210 0 023422106
10 03635 0 023422
6
1 04442212++()+
++()
=
(.. ..
. 
) )+
()=12106
1 059772100 125
..

Reading 52 ■ Introduction to Fixed-  Income Valuation 446
SUMMARY
This reading covers the principles and techniques that are used in the valuation of 
fixed-  rate bonds, as well as floating-  rate notes and money market instruments. These 
building blocks are used extensively in fixed-  income analysis. The following are the 
main points made in the reading:
■■The market discount rate is the rate of return required by investors given the 
risk of the investment in the bond.
■■A bond is priced at a premium above par value when the coupon rate is greater 
than the market discount rate.
■■A bond is priced at a discount below par value when the coupon rate is less 
■■The amount of any premium or discount is the present value of the “excess” or 
“deficiency” in the coupon payments relative to the yield-  to- maturity.
■■The yield-  to- maturity, the internal rate of return on the cash flows, is the 
implied market discount rate given the price of the bond.

■■A bond price moves inversely with its market discount rate.
■■The relationship between a bond price and its market discount rate is convex.
■■The price of a lower-  coupon bond is more volatile than the price of a higher-  
coupon bond, other things being equal.
■■Generally, the price of a longer-  term bond is more volatile than the price of 
shorter-  term bond, other things being equal. An exception to this phenome -
non can occur on low-  coupon (but not zero-  coupon) bonds that are priced at a 
discount to par value.
■■Assuming no default, premium and discount bond prices are “pulled to par” as 
maturity nears.
■■A spot rate is the yield-  to- maturity on a zero-  coupon bond.
■■A yield-  to- maturity can be approximated as a weighted average of the underly -
ing spot rates.
■■Between coupon dates, the full (or invoice, or “dirty”) price of a bond is split 
between the flat (or quoted, or “clean”) price and the accrued interest.

■■Flat prices are quoted to not misrepresent the daily increase in the full price as 
a result of interest accruals.
■■Accrued interest is calculated as a proportional share of the next coupon pay -
ment using either the actual/actual or 30/360 methods to count days.
■■Matrix pricing is used to value illiquid bonds by using prices and yields on 
comparable securities having the same or similar credit risk, coupon rate, and 
maturity.
■■The periodicity of an annual interest rate is the number of periods in the year.
■■A yield quoted on a semiannual bond basis is an annual rate for a periodicity of 
two. It is the yield per semiannual period times two.
■■The general rule for periodicity conversions is that compounding more fre -
quently at a lower annual rate corresponds to compounding less frequently at a 
higher annual rate.
■■Street convention yields assume payments are made on scheduled dates, 
neglecting weekends and holidays.

■■The current yield is the annual coupon payment divided by the flat price, 
thereby neglecting as a measure of the investor’s rate of return the time value 
of money, any accrued interest, and the gain from buying at a discount and the 
loss from buying at a premium.
■■The simple yield is like the current yield but includes the straight-  line amortiza -
tion of the discount or premium.
■■The yield-  to- worst on a callable bond is the lowest of the yield-  to- first-  call, 
yield-  to- second-  call, and so on, calculated using the call price for the future 
value and the call date for the number of periods.
■■The option-  adjusted yield on a callable bond is the yield-  to- maturity after add -
ing the theoretical value of the call option to the price.
■■A floating-  rate note (floater, or FRN) maintains a more stable price than a fixed-  
rate note because interest payments adjust for changes in market interest rates.

■■The quoted margin on a floater is typically the specified yield spread over or 
under the reference rate, which often is Libor.
■■The discount margin on a floater is the spread required by investors, and to 
which the quoted margin must be set, for the FRN to trade at par value on a 
■■Money market instruments, having one year or less time-  to- maturity, are 
quoted on a discount rate or add-  on rate basis.
■■Money market discount rates understate the investor’s rate of return (and the 
borrower’s cost of funds) because the interest income is divided by the face 
value or the total amount redeemed at maturity, and not by the amount of the 
■■Money market instruments need to be converted to a common basis for 
analysis.
■■A money market bond equivalent yield is an add-  on rate for a 365-  day year.
■■The periodicity of a money market instrument is the number of days in the 
year divided by the number of days to maturity. Therefore, money market

instruments with different times-  to- maturity have annual rates for different 
periodicities.
■■In theory, the maturity structure, or term structure, of interest rates is the rela -
tionship between yields-  to- maturity and times-  to- maturity on bonds having the 
same currency, credit risk, liquidity, tax status, and periodicity.
■■A spot curve is a series of yields-  to- maturity on zero-  coupon bonds.
■■A frequently used yield curve is a series of yields-  to- maturity on coupon bonds.
■■A par curve is a series of yields-  to- maturity assuming the bonds are priced at 
par value.
■■In a cash market, the delivery of the security and cash payment is made on a 
settlement date within a customary time period after the trade date—for exam -
ple, “ T + 3. ”
■■In a forward market, the delivery of the security and cash payment is made on a 
predetermined future date.
■■A forward rate is the interest rate on a bond or money market instrument 
traded in a forward market.

■■An implied forward rate (or forward yield) is the breakeven reinvestment rate 
linking the return on an investment in a shorter-  term zero-  coupon bond to the 
return on an investment in a longer-  term zero-  coupon bond.
■■An implied forward curve can be calculated from the spot curve.

Reading 52 ■ Introduction to Fixed-  Income Valuation 448
■■Implied spot rates can be calculated as geometric averages of forward rates.
■■A fixed-  income bond can be valued using a market discount rate, a series of 
spot rates, or a series of forward rates.
■■A bond yield-  to- maturity can be separated into a benchmark and a spread.
■■Changes in benchmark rates capture macroeconomic factors that affect all 
bonds in the market—inflation, economic growth, foreign exchange rates, and 
monetary and fiscal policy.
■■Changes in spreads typically capture microeconomic factors that affect the par -
ticular bond—credit risk, liquidity, and tax effects.
■■Benchmark rates are usually yields-  to- maturity on government bonds or fixed 
rates on interest rate swaps.
■■A G-  spread is the spread over or under a government bond rate, and an 
I- spread is the spread over or under an interest rate swap rate.
■■A G-  spread or an I-  spread can be based on a specific benchmark rate or on a

rate interpolated from the benchmark yield curve.
■■A Z-  spread (zero-  volatility spread) is based on the entire benchmark spot curve. 
It is the constant spread that is added to each spot rate such that the present 
value of the cash flows matches the price of the bond.
■■An option-  adjusted spread (OAS) on a callable bond is the Z-  spread minus the 
theoretical value of the embedded call option.

Practice Problems 449
1 A portfolio manager is considering the purchase of a bond with a 5.5% coupon 
rate that pays interest annually and matures in three years. If the required rate 
of return on the bond is 5%, the price of the bond per 100 of par value is closest  
to:
A 98.65.
B 101.36.
C 106.43.
2 A bond with two years remaining until maturity offers a 3% coupon rate with 
interest paid annually. At a market discount rate of 4%, the price of this bond 
per 100 of par value is closest  to:
A 95.34.
B 98.00.
C 98.11.
3 An investor who owns a bond with a 9% coupon rate that pays interest semian -
nually and matures in three years is considering its sale. If the required rate of 
return on the bond is 11%, the price of the bond per 100 of par value is closest  
to:
A 95.00.
B 95.11.
C 105.15.
4 A bond offers an annual coupon rate of 4%, with interest paid semiannually. The 
bond matures in two years. At a market discount rate of 6%, the price of this

bond per 100 of par value is closest  to:
A 93.07.
B 96.28.
C 96.33.
5 A bond offers an annual coupon rate of 5%, with interest paid semiannually. The 
bond matures in seven years. At a market discount rate of 3%, the price of this 
A 106.60.
B 112.54.
C 143.90.
6 A zero-  coupon bond matures in 15 years. At a market discount rate of 4.5% per 
year and assuming annual compounding, the price of the bond per 100 of par 
value is closest  to:
A 51.30.
B 51.67.
C 71.62.
7 Consider the following two bonds that pay interest annually:

Reading 52 ■ Introduction to Fixed-  Income Valuation 450
Bond Coupon Rate Time-  to- Maturity
A 5% 2 years
B 3% 2 years
 At a market discount rate of 4%, the price difference between Bond A and Bond 
B per 100 of par value is closest  to:
A 3.70.
B 3.77.
C 4.00.
The following information relates to Questions 8 
and 9
Bond Price Coupon Rate Time-  to- Maturity
A 101.886 5% 2 years
B 100.000 6% 2 years
C 97.327 5% 3 years
8 Which bond offers the lowest yield-  to- maturity?
A Bond A
B Bond B
C Bond C
9 Which bond will most likely experience the smallest percent change in price if 
the market discount rates for all three bonds increase by 100 basis points?
A Bond A
B Bond B
C Bond C
10 Suppose a bond’s price is expected to increase by 5% if its market discount rate 
decreases by 100 basis points. If the bond’s market discount rate increases by 
100 basis points, the bond price is most likely  to change by:
A 5%.
B less than 5%.
C more than 5%.

The following information relates to Questions 11 
and 12
Bond Coupon Rate Maturity (years)
A 6% 10
B 6% 5
C 8% 5
All three bonds are currently trading at par value.
11 Relative to Bond C, for a 200 basis point decrease in the required rate of return, 
Bond B will most likely  exhibit a(n):
A equal percentage price change.
B greater percentage price change.
C smaller percentage price change.
12 Which bond will most likely experience the greatest percentage change in price 
if the market discount rates for all three bonds increase by 100 basis points?
A Bond A
B Bond B
C Bond C
13 An investor considers the purchase of a 2-  year bond with a 5% coupon rate, 
with interest paid annually. Assuming the sequence of spot rates shown below, 
the price of the bond is closest  to:
Time-  to- Maturity Spot Rates
1 year 3%
2 years 4%
A 101.93.
B 102.85.
C 105.81.
14 A 3-  year bond offers a 10% coupon rate with interest paid annually. Assuming

the following sequence of spot rates, the price of the bond is closest  to:
1 year 8.0%
2 years 9.0%
3 years 9.5%
A 96.98.
B 101.46.
C 102.95.

Reading 52 ■ Introduction to Fixed-  Income Valuation 452
15–17
Bond Coupon Rate Time-  to- Maturity Time-  to- Maturity Spot Rates
X 8% 3 years 1 year 8%
Y 7% 3 years 2 years 9%
Z 6% 3 years 3 years 10%
All three bonds pay interest annually.
15 Based upon the given sequence of spot rates, the price of Bond X is closest  to:
A 95.02.
B 95.28.
C 97.63.
16 Based upon the given sequence of spot rates, the price of Bond Y is closest  to:
A 87.50.
B 92.54.
C 92.76.
17 Based upon the given sequence of spot rates, the yield-  to- maturity of Bond Z is 
A 9.00%.
B 9.92%.
C 11.93%
18 Bond dealers most often quote the:
A flat price.
B full price.
C full price plus accrued interest.
19–21
Bond G, described in the exhibit below, is sold for settlement on 16 June 2014.
Annual Coupon 5%
Coupon Payment Frequency Semiannual
Interest Payment Dates 10 April and 10 October
Maturity Date 10 October 2016

Day Count Convention 30/360
Annual Yield-  to- Maturity 4%
19 The full price that Bond G will settle at on 16 June 2014 is closest  to:
A 102.36.
B 103.10.

Practice Problems 453
C 103.65.
20 The accrued interest per 100 of par value for Bond G on the settlement date of 
16 June 2014 is closest  to:
A 0.46.
B 0.73.
C 0.92.
21 The flat price for Bond G on the settlement date of 16 June 2014 is closest  to:
A 102.18.
B 103.10.
C 104.02.
22 Matrix pricing allows investors to estimate market discount rates and prices for 
bonds:
A with different coupon rates.
B that are not actively traded.
C with different credit quality.
23 When underwriting new corporate bonds, matrix pricing is used to get an esti -
mate of the:
A required yield spread over the benchmark rate.
B market discount rate of other comparable corporate bonds.
C yield-  to- maturity on a government bond having a similar time-  to- maturity.
24 A bond with 20 years remaining until maturity is currently trading for 111 per 
100 of par value. The bond offers a 5% coupon rate with interest paid semiannu -
ally. The bond’s annual yield-  to- maturity is closest  to:
A 2.09%.
B 4.18%.
C 4.50%.

A 2.09%.
B 4.18%.
C 4.50%.
25 The annual yield-  to- maturity, stated for with a periodicity of 12, for a 4-  year, 
zero-  coupon bond priced at 75 per 100 of par value is closest to:
A 6.25%.
B 7.21%.
C 7.46%.
26 A 5-  year, 5% semiannual coupon payment corporate bond is priced at 104.967 
per 100 of par value. The bond’s yield-  to- maturity, quoted on a semiannual 
bond basis, is 3.897%. An analyst has been asked to convert to a monthly peri -
odicity. Under this conversion, the yield-  to- maturity is closest to :
A 3.87%.
B 4.95%.
C 7.67%.

Reading 52 ■ Introduction to Fixed-  Income Valuation 454
27–30
A bond with 5 years remaining until maturity is currently trading for 101 per 100 of 
par value. The bond offers a 6% coupon rate with interest paid semiannually. The bond 
is first callable in 3 years, and is callable after that date on coupon dates according to 
the following schedule:
End of Y ear Call Price
3 102
4 101
5 100
27 The bond’s annual yield-  to- maturity is closest  to:
A 2.88%.
B 5.77%.
C 5.94%.
28 The bond’s annual yield-  to- first-  call is closest  to:
A 3.12%.
B 6.11%.
C 6.25%.
29 The bond’s annual yield-  to- second-  call is closest  to:
A 2.97%.
B 5.72%.
C 5.94%.
30 The bond’s yield-  to- worst is closest  to:
A 2.88%.
B 5.77%.
C 6.25%.
31 A two-  year floating-  rate note pays 6-  month Libor plus 80 basis points. The 
floater is priced at 97 per 100 of par value. Current 6-  month Libor is 1.00%. 
Assume a 30/360 day-  count convention and evenly spaced periods. The dis -

count margin for the floater in basis points (bps) is closest  to:
A 180 bps.
B 236 bps.
C 420 bps.
32 An analyst evaluates the following information relating to floating rate notes 
(FRNs) issued at par value that have 3-  month Libor as a reference rate:
Floating Rate Note Quoted Margin Discount Margin
X 0.40% 0.32%
Y 0.45% 0.45%
Z 0.55% 0.72%

 Based only on the information provided, the FRN that will be priced at a pre -
mium on the next reset date is:
A FRN X.
B FRN Y.
C FRN Z.
33 A 365-  day year bank certificate of deposit has an initial principal amount of 
USD 96.5 million and a redemption amount due at maturity of USD 100 mil -
lion. The number of days between settlement and maturity is 350. The bond 
equivalent yield is closest  to:
A 3.48%.
B 3.65%.
C 3.78%.
34 The bond equivalent yield of a 180-  day banker’s acceptance quoted at a discount 
rate of 4.25% for a 360-  day year is closest to:
A 4.31%.
B 4.34%.
C 4.40%.
35 Which of the following statements describing a par curve is incorrect ?
A A par curve is obtained from a spot curve.
B All bonds on a par curve are assumed to have different credit risk.
C A par curve is a sequence of yields-  to- maturity such that each bond is 
priced at par value.
36 A yield curve constructed from a sequence of yields-  to- maturity on zero-  
coupon bonds is the:
A par curve.

B spot curve.
C forward curve.
37 The rate, interpreted to be the incremental return for extending the time-  to- 
maturity of an investment for an additional time period, is the:
A add-  on rate.
B forward rate.
C yield-  to- maturity.
The following information relates to Questions 38 
and 39
“0y1y” 0.80%
“1y1y” 1.12%
“2y1y” 3.94%
“3y1y” 3.28%
“4y1y” 3.14%

Reading 52 ■ Introduction to Fixed-  Income Valuation 456
All rates are annual rates stated for a periodicity of one (effective annual rates).
38 The 3-  year implied spot rate is closest  to:
A 1.18%.
B 1.94%.
C 2.28%.
39 The value per 100 of par value of a two-  year, 3.5% coupon bond, with interest 
payments paid annually, is closest to:
A 101.58.
B 105.01.
C 105.82.
40 The spread component of a specific bond’s yield-  to- maturity is least likely  
impacted by changes in:
A its tax status.
B its quality rating.
C inflation in its currency of denomination.
41 The yield spread of a specific bond over the standard swap rate in that currency 
of the same tenor is best described as the:
A I- spread.
B Z- spread.
C G- spread.
The following information relates to Question 42
Bond Coupon Rate Time-  to- Maturity Price
UK Government Benchmark 
Bond2% 3 years 100.25
UK Corporate Bond 5% 3 years 100.65
Both bonds pay interest annually. The current three-  year EUR interest rate swap 
benchmark is 2.12%.

42 The G-  spread in basis points (bps) on the UK corporate bond is closest  to:
A 264 bps.
B 285 bps.
C 300 bps.
43 A corporate bond offers a 5% coupon rate and has exactly 3 years remaining to 
maturity. Interest is paid annually. The following rates are from the benchmark 
spot curve:

Time-  to- Maturity Spot Rate
1 year 4.86%
2 years 4.95%
3 years 5.65%
 The bond is currently trading at a Z-  spread of 234 basis points. The value of the 
bond is closest to :
A 92.38.
B 98.35.
C 106.56.
44 An option-  adjusted spread (OAS) on a callable bond is the Z-  spread:
A over the benchmark spot curve.
B minus the standard swap rate in that currency of the same tenor.
C minus the value of the embedded call option expressed in basis points per 
year.

Reading 52 ■ Introduction to Fixed-  Income Valuation 458
SOLUTIONS
1 B is correct. The bond price is closest to 101.36. The price is determined in the 
following manner:
PVPMT
rPMT
rPMTF V
r=
+()+
+()++
+() 11 112 3
 where:
 
PV =
+()+
+()++
+()55
10 0555
10 0555 100
10 0512 3.
..
..
.
PV = 5.24 + 4.99 + 91.13 = 101.36
2 C is correct. The bond price is closest to 98.11. The formula for calculating the 
price of this bond is:
PVPMT
rPMTF V
r=
+()++
+() 1112
 where:
 
PV =
+()++
+()=+ =3
10 043 100
10 042889 5239 81112.... .
3 A is correct. The bond price is closest to 95.00. The bond has six semiannual

periods. Half of the annual coupon is paid in each period with the required rate 
of return also being halved. The price is determined in the following manner:
PVPMT
rPMT
rPMT
rPMT
rPMT
rPMTF=
+()+
+()+
+()+
+()+
+()++
11 11 11 2345V V
r16+()
 where:

PV =
+()+
+()+
+()+
+()45
10 05545
10 05545
10 05545
10 0551 234.
..
..
..
.+ +
+()++
+()45
10 05545 100
10 05556.
..
.
PV = 4.27 + 4.04 + 3.83 + 3.63 + 3.44 + 75.79 = 95.00
4 B is correct. The bond price is closest to 96.28. The formula for calculating this 
bond price is:
PVPMT
rPMT
rPMT
rPMTF V
r=
+()+
+()+
+()++
+() 11 1112 34
 where:
 
PV =
+()+
+()+
+()++
+()2
10 032
10 032
10 032 100
10 031 234.. ..
PV = 1.94 + 1.89 + 1.83 + 90.62 = 96.28
5 B is correct. The bond price is closest to 112.54.The formula for calculating this 
PVPMT
rPMT
rPMT
rPMTF V
r=
+()+
+()+
+()+++
+() 11 1112 31 4
 where:
 
PV =

PV =
+()+
+()+
+()++
+(25
10 01525
10 01525
10 01525
10 01512 3.
..
..
..
.
) )++
+()13 1425 100
10 015.
.
PV = 2.46 + 2.43 + 2.39 + … + 2.06 + 83.21 = 112.54
6 B is correct. The price of the zero-  coupon bond is closest to 51.67. The price is 
determined in the following manner:
PV
rN=
+()100
1
 where:

Reading 52 ■ Introduction to Fixed-  Income Valuation 460
 
PV =
+()100
10 04515.
PV = 51.67
7 B is correct. The price difference between Bonds A and B is closest to 3.77. One 
method for calculating the price difference between two bonds with an identical 
term to maturity is to use the following formula:
PVPMT
rPMT
r=
+()+
+() 1112
 where:
 PV = price difference
 PMT  = coupon difference per period
 In this case the coupon difference is (5% – 3%), or 2%.
PV =
+()+
+()=+=2
10 042
10 041921 85 37712.... .
8 A is correct. Bond A offers the lowest yield-  to- maturity. When a bond is priced 
at a premium above par value the yield-  to- maturity (YTM), or market discount 
rate is less than the coupon rate. Bond A is priced at a premium, so its YTM is 
below its 5% coupon rate. Bond B is priced at par value so its YTM is equal to 
its 6% coupon rate. Bond C is priced at a discount below par value, so its YTM 
is above its 5% coupon rate.

9 B is correct. Bond B will most likely experience the smallest percent change in 
price if market discount rates increase by 100 basis points. A higher-  coupon 
bond has a smaller percentage price change than a lower-  coupon bond when 
their market discount rates change by the same amount (the coupon effect). 
Also, a shorter-  term bond generally has a smaller percentage price change 
than a longer-  term bond when their market discount rates change by the same 
amount (the maturity effect). Bond B will experience a smaller percent change 
in price than Bond A because of the coupon effect. Bond B will also experience 
a smaller percent change in price than Bond C because of the coupon effect and 
the maturity effect.
10 B is correct. The bond price is most likely to change by less than 5%. The rela -
tionship between bond prices and market discount rate is not linear. The per -
centage price change is greater in absolute value when the market discount rate

goes down than when it goes up by the same amount (the convexity effect). If a 
100 basis point decrease in the market discount rate will cause the price of the 
bond to increase by 5%, then a 100 basis point increase in the market discount 
rate will cause the price of the bond to decline by an amount less than 5%.
11 B is correct. Generally, for two bonds with the same time-  to- maturity, a lower 
coupon bond will experience a greater percentage price change than a higher 
coupon bond when their market discount rates change by the same amount. 
Bond B and Bond C have the same time-  to- maturity (5 years); however, Bond 
B offers a lower coupon rate. Therefore, Bond B will likely experience a greater 
percentage change in price in comparison to Bond C.

Solutions 461
12 A is correct. Bond A will likely experience the greatest percent change in price 
due to the coupon effect and the maturity effect. For two bonds with the same 
time-  to- maturity, a lower-  coupon bond has a greater percentage price change 
than a higher-  coupon bond when their market discount rates change by the 
same amount. Generally, for the same coupon rate, a longer-  term bond has a 
greater percentage price change than a shorter-  term bond when their market 
discount rates change by the same amount. Relative to Bond C, Bond A and 
Bond B both offer the same lower coupon rate of 6%; however, Bond A has a 
longer time-  to- maturity than Bond B. Therefore, Bond A will likely experience 
the greater percentage change in price if the market discount rates for all three 
bonds increase by 100 basis points.
13 A is correct. The bond price is closest to 101.93. The price is determined in the 
PVPMT
ZPMTF V
Z=
+()++
+() 1111
22
 where:

PVPMT
ZPMTF V
Z=
+()++
+() 1111
22
 where:
 Z1 = spot rate, or the zero-  coupon yield, for Period 1
 Z2 = spot rate, or the zero-  coupon yield, for Period 2
 
PV =
+()++
+()5
10 035 100
10 0412..
PV = 4.85 + 97.08 = 101.93
14 B is correct. The bond price is closest to 101.46. The price is determined in the 
PVPMT
ZPMT
ZPMTF V
Z=
+()+
+()++
+() 11 111
22
33
 where:
 Z1 = spot rate, or the zero-  coupon yield, or zero rate, for period 1
 Z2 = spot rate, or the zero-  coupon yield, or zero rate, for period 2
 Z3 = spot rate, or the zero-  coupon yield, or zero rate, for period 3
 
PV =
+()+
+()++
+()10
10 0810
10 0910 100
10 09512 3.. .
PV = 9.26 + 8.42 + 83.78 = 101.46

Reading 52 ■ Introduction to Fixed-  Income Valuation 462
15 B is correct. The bond price is closest to 95.28. The formula for calculating this 
PVPMT
ZPMT
ZPMTF V
Z=
+()+
+()++
+() 11 111
22
33
 where:
 
PV =
+()+
+()++
+()8
10 088
10 098 100
10 1012 3.. .
PV = 7.41 + 6.73 + 81.14 = 95.28
16 C is correct. The bond price is closest to 92.76. The formula for calculating this 
PVPMT
ZPMT
ZPMTF V
Z=
+()+
+()++
+() 11 111
22
33
 where:

Z1 = spot rate, or the zero-  coupon yield, or zero rate, for period 1
 
PV =
+()+
+()++
+()7
10 087
10 097 100
PV = 6.48 + 5.89 + 80.39 = 92.76
17 B is correct. The yield-  to- maturity is closest to 9.92%. The formula for calculat -
ing the price of Bond Z is:
PVPMT
ZPMT
ZPMTF V
Z=
+()+
+()++
+() 11 111
22
33
 where:

Solutions 463
 
PV =
+()+
+()++
+()6
10 086
10 096 100
PV = 5.56 + 5.05 + 79.64 = 90.25
 Using this price, the bond’s yield-  to- maturity can be calculated as:
PVPMT
rPMT
rPMTF V
r=
+()+
+()++
+() 11 112 3
90 256
16
16 100
112 3.=
+()+
+()++
+() rr r
r = 9.92%
18 A is correct. Bond dealers usually quote the flat price. When a trade takes place, 
the accrued interest is added to the flat price to obtain the full price paid by the 
buyer and received by the seller on the settlement date. The reason for using 
the flat price for quotation is to avoid misleading investors about the market 
price trend for the bond. If the full price were to be quoted by dealers, inves -
tors would see the price rise day after day even if the yield-  to- maturity did not 
change. That is because the amount of accrued interest increases each day. Then 
after the coupon payment is made the quoted price would drop dramatically. 
Using the flat price for quotation avoids that misrepresentation. The full price,

flat price plus accrued interest, is not usually quoted by bond dealers. Accrued 
interest is included in not added to the full price and bond dealers do not gen -
erally quote the full price.
19 B is correct. The bond’s full price is 103.10. The price is determined in the fol -
lowing manner:
 As of the beginning of the coupon period on 10 April 2014, there are 2.5 
years (5 semiannual periods) to maturity. These five semiannual periods occur 
on 10 October 2014, 10 April 2015, 10 October 2015, 10 April 2016 and 10 
October 2016.
PVPMT
rPMT
rPMT
rPMT
rPMTF V
r=
+()+
+()+
+()+
+()++
+() 11 11 11 234 5
 where:
 PV = present value
 
PV =
+()+
+()+
+()+
+()+25
10 0225
10 0225
10 0225
10 0225
1 234.
..
..
..
..+ +
+()100
10 025.
PV = 2.45 + 2.40 + 2.36 + 2.31 + 92.84 = 102.36

Reading 52 ■ Introduction to Fixed-  Income Valuation 464
 The accrued interest period is identified as 66/180. The number of days between 
10 April 2014 and 16 June 2014 is 66 days based on the 30/360 day count con -
vention. (This is 20 days remaining in April + 30 days in May + 16 days in June 
= 66 days total). The number of days between coupon periods is assumed to be 
180 days using the 30/360 day convention.
PVFull = PV × (1 + r)66/180
PVFull = 102.36 × (1.02)66/180 = 103.10
20 C is correct. The accrued interest per 100 of par value is closest to 0.92. The 
accrued interest is determined in the following manner: The accrued interest 
period is identified as 66/180. The number of days between 10 April 2014 and 
16 June 2014 is 66 days based on the 30/360 day count convention. (This is 20 
days remaining in April + 30 days in May + 16 days in June = 66 days total). The 
number of days between coupon periods is assumed to be 180 days using the 
30/360 day convention.
Accrued interes t=×t
TPMT

TPMT
 where:
 t = number of days from the last coupon payment to the settlement 
date
 t/T = fraction of the coupon period that has gone by since the last 
payment
 
Accrued interes t=× =66
180500
2092..
21 A is correct. The flat price of 102.18 is determined by subtracting the accrued 
interest (from question 20) from the full price (from question 19).
PVFlat = PVFull – Accrued Interest
PVFlat = 103.10 – 0.92 = 102.18
22 B is correct. For bonds not actively traded or not yet issued, matrix pricing is a 
price estimation process that uses market discount rates based on the quoted 
prices of similar bonds (similar times-  to- maturity, coupon rates, and credit 
quality).
23 A is correct. Matrix pricing is used in underwriting new bonds to get an esti -
mate of the required yield spread over the benchmark rate. The benchmark rate

is typically the yield-  to- maturity on a government bond having the same, or 
close to the same, time-  to- maturity. The spread is the difference between the 
yield-  to- maturity on the new bond and the benchmark rate. The yield spread 
is the additional compensation required by investors for the difference in the 
credit risk, liquidity risk, and tax status of the bond relative to the government 
bond.
 In matrix pricing, the market discount rates of comparable bonds and the 
yield-  to- maturity on a government bond having a similar time-  to- maturity are 
not estimated. Rather they are known and used to estimate the required yield 
spread of a new bond.

Solutions 465
24 B is correct. The formula for calculating this bond’s yield-  to- maturity is:
PVPMT
rPMT
rPMT
rPMT
rPMTF V
r=
+()+
+()+
+()++
+()++
+() 11 11 112 33 940 0
 where:
 
11125
125
125
125
125 100
112 33 9=
+()+
+()+
+()++
+()++
+(.. .. .
rr rr r
) )40
r = 0.0209
 To arrive at the annualized yield-  to- maturity, the semiannual rate of 2.09% must 
be multiplied by two. Therefore, the yield-  to- maturity is equal to 2.09% × 2 = 
4.18%.
25 B is correct. The annual yield-  to- maturity, stated for a periodicity of 12, is 
7.21%. It is calculated as follows:
PVFV
rN=
+()1
75100
1412=
+()



×r
100
75148=+() r
1.33333 = (1 + r)48
[1.33333]1/48 = [(1 + r)48]1/48
1.3333302083 = (1 + r)
1.00601 = (1 + r)
1.00601 – 1 = r
0.00601 = r
r × 12 = 0.07212, or approximately 7.21%

26 A is correct. The yield-  to- maturity, stated for a periodicity of 12 (monthly 
periodicity), is 3.87%.The formula to convert an annual percentage rate (annual 
yield-  to- maturity) from one periodicity to another is as follows:
11+

=+

APR
mAPR
nmm
nn
10 03897
21122
1212
+

=+

. APR

Reading 52 ■ Introduction to Fixed-  Income Valuation 466
1 01949 1122 1212
.() =+

APR
103935 1121212
. =+

APR
1 03935 112112 1212112
.() =+





APR
100322 11212. =+

APR
100322 11212. −=

APR
APR12 = 0.00322 × 12 = 0.03865, or approximately 3.87%.
27 B is correct. The yield-  to- maturity is 5.77%. The formula for calculating this 
bond’s yield-  to- maturity is:
PVPMT
rPMT
rPMT
rPMT
rPMTF V
r=
+()+
+()+
+()++
+()++
+() 11 11 112 39 10
 where:
 
1013
13
13
13
13 100
112 39 10=
+()+
+()+
+()++
+()++
+() rr rr r
r = 0.02883
 To arrive at the annualized yield-  to- maturity, the semiannual rate of 2.883% 
must be multiplied by two. Therefore, the yield-  to- maturity is equal to 2.883% × 
2 = 5.77% (rounded).

28 C is correct. The yield-  to- first-  call is 6.25%. Given the first call date is exactly 
three years away, the formula for calculating this bond’s yield-  to- first-  call is:
PVPMT
rPMT
rPMT
rPMT
rPMTF V
r=
+()+
+()+
+()++
+()++
+() 11 11 112 35 6
 where:
 FV = call price paid at call date

Solutions 467
 
1013
13
13
13
13 102
112 35 6=
+()+
+()+
+()++
+()++
+() rr rr r
r = 0.03123
 To arrive at the annualized yield-  to- first-  call, the semiannual rate of 3.123% 
must be multiplied by two. Therefore, the yield-  to- first-  call is equal to 3.123% × 
2 = 6.25% (rounded).
29 C is correct. The yield-  to- second-  call is 5.94%. Given the second call date is 
exactly four years away, the formula for calculating this bond’s yield-  to- second-  
call is:
PVPMT
rPMT
rPMT
rPMT
rPMTF V
r=
+()+
+()+
+()++
+()++
+() 11 11 112 37 8
 where:
 
1013
13
13
13
13 101
112 37 8=
+()+
+()+
+()+
+()++
+() rr rr r
r = 0.0297
 To arrive at the annualized yield-  to- second-  call, the semiannual rate of 2.97% 
must be multiplied by two. Therefore, the yield-  to- second-  call is equal to 2.97% 
× 2 = 5.94%.

× 2 = 5.94%.
30 B is correct. The yield-  to- worst is 5.77%. The bond’s yield-  to- worst is the lowest 
of the sequence of yields-  to- call and the yield-  to- maturity. From above, we have 
the following yield measures for this bond:
 Yield-  to- first-  call: 6.25%
 Yield-  to- second-  call: 5.94%
 Yield-  to- maturity: 5.77%
 Thus, the yield-  to- worst is 5.77%.
31 B is correct. The discount or required margin is 236 basis points. Given the 
floater has a maturity of two years and is linked to 6-  month Libor, the formula 
for calculating discount margin is:
PVQM FV
m
DM
mQM FV
m=+ () ×
++ 

++ () ×
++Index
mQM FV
mFV
DM
m

+++ () ×+
++ 

24
1Index
Index
 where:
 PV = present value, or the price of the floating-  rate note = 97
 Index =  reference rate, stated as an annual percentage rate = 0.01
 QM = quoted margin, stated as an annual percentage rate = 0.0080

Reading 52 ■ Introduction to Fixed-  Income Valuation 468
 FV = future value paid at maturity, or the par value of the bond = 100
 m = periodicity of the floating-  rate note, the number of payment peri -
ods per year = 2
 DM = discount margin, the required margin stated as an annual percent -
age rate
 Substituting given values in:
970010 0080 100
2
1001
20010 0080 100
2
11=+ () ×
++ 

++ () × ..
...
DM+ ++ 

+++ () ×+
++ 

001
2100
1001
22...
. DM DM4 4
97090
1001
2090
1001
2090
100112=
++ 

+
++ 

+
++.
..
..
. DM DM DDM DM
2090 100
1001
234

++
++ 

.
.
 To calculate DM, begin by solving for the discount rate per period:
97090
1090
1090
1090 100
112 34=
+()+
+()+
+()++
+().. ..
rr rr
r = 0.0168
 Now, solve for DM:
001
20 0168..+=DM
DM = 0.0236
 The discount margin for the floater is equal to 236 basis points.
32 A is correct. FRN X will be priced at a premium on the next reset date because 
the quoted margin of 0.40% is greater than the discount or required margin of

0.32%. The premium amount is the present value of the extra or “excess” inter -
est payments of 0.08% each quarter (0.40% – 0.32%). FRN Y will be priced at 
par value on the next reset date since there is no difference between the quoted 
and discount margins. FRN Z will be priced at a discount since the quoted mar -
gin is less than the required margin.
33 C is correct. The bond equivalent yield is closest to 3.78%. It is calculated as:
AORFV PV
PV=

×− 

Year
Days
 where:
interest
 Days =  number of days between settlement and maturity
 Year =  number of days in the year
 AOR  = add-  on rate, stated as an annual percentage rate (also, called bond 
equivalent yield).

Solutions 469
 
AOR=

×− 

365
350100 96 5
96 5.
.
AOR  = 1.04286 × 0.03627
AOR  = 0.03783 or approximately 3.78%
34 C is correct. The bond equivalent yield is closest to 4.40%. The present value of 
the banker’s acceptance is calculated as:

 1Days
Year
 where:
 PV = present value, or price of the money market instrument
 FV = future value paid at maturity, or face value of the money market 
 DR = discount rate, stated as an annual percentage rate
 
PV DR =× −×

 100 1Days
Year
PV =× −×

 100 1180
3600 0425 .
PV = 100 × (1 – 0.02125) 
PV = 100 × 0.97875
PV = 97.875
 The bond equivalent yield (AOR) is calculated as:
AORFV PV
PV=

×− 

Year
Days
 where:
interest

Year =  number of days in the year
 AOR  = add-  on rate (bond equivalent yield), stated as an annual percent -
age rate
 
AORPV
PV=

×− 

365
180100

Reading 52 ■ Introduction to Fixed-  Income Valuation 470
AOR=

×− 

365
180100 97 875
97 875.
.
AOR  = 2.02778 × 0.02171
AOR  = 0.04402, or approximately 4.40%
 Note that the PV is calculated using an assumed 360-  day year and the AOR 
(bond equivalent yield) is calculated using a 365-  day year.
35 B is correct. All bonds on a par curve are assumed to have similar, not differ -
ent, credit risk. Par curves are obtained from spot curves and all bonds used 
to derive the par curve are assumed to have the same credit risk, as well as the 
same periodicity, currency, liquidity, tax status, and annual yields. A par curve 
is a sequence of yields-  to- maturity such that each bond is priced at par value.
36 B is correct. The spot curve, also known as the strip or zero curve, is the yield 
curve constructed from a sequence of yields-  to- maturities on zero-  coupon 
bonds. The par curve is a sequence of yields-  to- maturity such that each bond is

priced at par value. The forward curve is constructed using a series of forward 
rates, each having the same timeframe.
37 B is correct. The forward rate can be interpreted to be the incremental or 
marginal return for extending the time-  to- maturity of an investment for an 
additional time period. The add-  on rate (bond equivalent yield) is a rate quoted 
for money market instruments such as bank certificates of deposit and indexes 
such as Libor and Euribor. Yield-  to- maturity is the internal rate of return on the 
bond’s cash flows—the uniform interest rate such that when the bond’s future 
cash flows are discounted at that rate, the sum of the present values equals the 
price of the bond. It is the implied market discount rate.
38 B is correct. The 3 year implied spot rate is closest to 1.94%. It is calculated as 
the geometric average of the one-  year forward rates:
(1.0080 × 1.0112 × 1.0394) = (1 + z3)3
1.05945 = (1 + z3)3
[1.05945]1/3 = [(1 + z3)3]1/3
1.01944 = 1 + z3
1.01944 – 1 = z3

0.01944 = z3, z3 = 1.944% or approximately 1.94%
39 B is correct. The value per 100 of par value is closest to105.01. Using the for -
ward curve, the bond price is calculated as follows:
35
1 0080103 5
1 0080 1 0112347 101 54 105 01.
..
.... . +× ()=+ =
40 C is correct. The spread component of a specific bond’s yield-  to- maturity is 
least likely impacted by changes in inflation of its currency of denomination. 
The effect of changes in macroeconomic factors, such as the expected rate of 
inflation in the currency of denomination, is seen mostly in changes in the 
benchmark yield. The spread or risk premium component is impacted by micro -
economic factors specific to the bond and bond issuer including tax status and 
quality rating.

Solutions 471
41 A is correct. The I-  spread, or interpolated spread, is the yield spread of a spe -
cific bond over the standard swap rate in that currency of the same tenor. The 
yield spread in basis points over an actual or interpolated government bond is 
known as the G-  spread. The Z-  spread (zero-  volatility spread) is the constant 
spread such that is added to each spot rate such that the present value of the 
cash flows matches the price of the bond.
42 B is correct. The G-  spread is closest to 285 bps. The benchmark rate for UK 
fixed-  rate bonds is the UK government benchmark bond. The Euro interest 
rate spread benchmark is used to calculate the G-  spread for Euro-  denominated 
corporate bonds, not UK bonds. The G-  spread is calculated as follows:
 Yield-  to- maturity on the UK corporate bond:
100 655
15
1105
10 04762 47612 3., . =
+()+
+()+
+()=
rr rr    or  bps
 Yield-  to- maturity on the UK government benchmark bond:
100 252
12
1102
10 01913 19112 3., . =
+()+
+()+
+()=
rr rr    or  bps

+()+
+()+
+()=
rr rr    or  bps
 The G-  spread is 476 – 191 = 285 bps.
43 A is correct. The value of the bond is closest to 92.38. The calculation is:
PVPMT
zZPMT
zZPMTF V
zZ=
++()+
++()++
++()
=
++11 1
5
10 0486 0011
22
33
.. 2 2345
10 0495 0 0234105
10 0565 0 0234
5
1 072012 3()+
++()+
++()
=+.. ..
.5 5
1 15111105
1 259364664 34 83 38 92 38.... .. += ++ =
44 C is correct. The option value in basis points per year is subtracted from the 
Z- spread to calculate the option-  adjusted spread (OAS). The Z-  spread is the 
constant yield spread over the benchmark spot curve. The I-  spread is the yield 
spread of a specific bond over the standard swap rate in that currency of the 
same tenor.

Introduction to Asset-  Backed Securities
by Frank J. Fabozzi, PhD, CPA, CFA
Frank J. Fabozzi, PhD, CPA, CFA, is at EDHEC Business School (France).
a. explain benefits of securitization for economies and financial 
markets;
b. describe securitization, including the parties involved in the 
process and the roles they play;
c. describe typical structures of securitizations, including credit 
tranching and time tranching;
d. describe types and characteristics of residential mortgage loans 
that are typically securitized;
e. describe types and characteristics of residential mortgage-  backed 
securities, including mortgage pass-  through securities and 
collateralized mortgage obligations, and explain the cash flows 
and risks for each type;
f. define prepayment risk and describe the prepayment risk of 
mortgage-  backed securities;
g. describe characteristics and risks of commercial mortgage-  backed 

h. describe types and characteristics of non-  mortgage asset-  backed 
securities, including the cash flows and risks of each type;
i. describe collateralized debt obligations, including their cash flows 
and risks.
Previous readings examined risk characteristics of various fixed-  income instruments 
and the relationships among maturity, coupon, and interest rate changes. This read -
ing introduces an additional level of complexity—that of fixed-  income instruments 
created through a process known as securitization . This process involves transferring 
ownership of assets from the original owners into a special legal entity. The special 1READING
53

Reading 53 ■ Introduction to Asset-  Backed Securities 474
legal entity then issues securities backed by these assets, and the assets’ cash flows 
are used to pay interest and repay the principal owed to the holders of the securities. 
These securities are referred to generically as asset-  backed securities  (ABS); the pool 
of securitized assets from which the ABS’s cash flows are generated is called the col -
lateral. Assets that are used to create ABS are called securitized assets . These assets 
are typically loans and receivables and include, among others, residential mortgage 
loans (mortgages), commercial mortgages, automobile (auto) loans, student loans, 
bank loans, accounts receivables, and credit card receivables. Advances and innova -
tions in securitization have led to securities backed, or collateralized, by all kinds of 
income-  yielding assets, including airport landing slots and toll roads.
This reading discusses the benefits of securitization, describes securitization, and

explains the investment characteristics of different types of ABS. The terminology 
regarding ABS varies by jurisdiction. Mortgage-  backed securities  (MBS) are ABS 
backed by a pool of mortgages, and a distinction is sometimes made between MBS 
and ABS backed by non-  mortgage assets. This distinction is common in the United 
States, for example, where typically the term “mortgage-  backed securities” refers to 
securities backed by high-  quality real estate mortgages and the term “asset-  backed 
securities” refers to securities backed by other types of assets. Because the US ABS 
market is the largest in the world, much of the discussion and many examples in this 
reading refer to the United States. Note, however, that many non-  US investors hold 
US ABS, including MBS, in their portfolios.
To underline the importance of securitization from a macroeconomic perspec -
tive, Section 2 discusses of the benefits of securitization for economies and financial

markets. In Section 3, the reading describes securitization and identifies the parties 
involved in the process and their roles. Section 3 also discusses typical structures of 
securitizations, including credit tranching and time tranching. Sections 4–6 discuss 
securities backed by mortgages for real estate property. Many types of residential 
mortgage designs around the world are described in Section 4. Sections 5 and 6 
focus on residential MBS and commercial MBS, respectively. Section 7 discusses ABS 
based on two types of non-  mortgage loans that are typically securitized throughout 
the world: auto loans and credit card receivables. Collateralized debt obligations are 
covered in Section 8. Section 9 concludes the reading with a summary.
BENEFITS OF SECURITIZATION FOR ECONOMIES AND 
FINANCIAL MARKETS
The securitization of pools of loans and receivables into multiple securities provides 
economies and financial markets with a number of benefits.1

Traditionally, the purchase of such assets as houses and autos has been financed by 
loans originated by financial institutions, such as commercial banks. For investors to 
gain exposure to these loans, they must hold some combination of deposits, debt, or 
common equity issued by banks. This creates an additional intermediary (that is, the 
bank) between the borrowers and the investors. In addition, by being constrained to 
hold bank deposits and securities, investors cannot gain exposure to loans only; they 
are also affected by economic risks undertaken in other bank activities.
Securitization solves a number of these problems. It allows investors to achieve 
more direct legal claims on loans and portfolios of receivables and enables these 
investors to tailor interest rate and credit risk exposures to suit their needs. Because 2
1 For a more detailed discussion, see Fabozzi and Kothari (2008).

Benefits of Securitization for Economies and Financial Markets 475
of disintermediation (that is, lessening the role of intermediaries), the costs paid by 
borrowers can be effectively lowered while the risk-  adjusted returns to investors can 
be enhanced. At the same time, banks can improve their profitability by increasing 
loan origination and the related fees. They can lend more than they would be able to 
lend if they were able to engage in only those activities they could finance themselves 
with their own deposits, debt, and equity. By allowing banks to increase the amount 
of funds available to lend, securitization ultimately benefits individuals, governments, 
and companies that need to borrow.
Securitization also has benefits for investors. Securitization enables financial inno -
vation, which allows investors to access securities with profiles that match their risk, 
return, and maturity needs that are otherwise not directly available. For example, a

pension fund with a long-  term horizon can gain access to long-  term real estate loans 
by investing in residential MBS without having to invest in bank bonds or stocks. 
Although few institutional or individual investors are willing to make or purchase 
real estate loans, auto loans, or credit card receivables directly, they may invest in a 
security backed by such loans or receivables. The ABS that are created by pooling these 
loans and receivables have characteristics similar to those of a standard bond and do 
not require the specialized resources and expertise needed to originate, monitor, and 
collect the payments from the underlying loans and receivables. As a result, investors 
can add to their portfolios exposure to the risk–return characteristics provided by a 
wider range of assets if they so desire. Note that in many countries, the sale of ABS 
and similar instruments is restricted to investors who meet certain qualifications, 
such as those pertaining to net worth.

Securitization allows for the creation of tradable securities with better liquidity 
than that of the original loans on the bank’s balance sheet. In making loans and receiv -
ables tradable, securitization makes financial markets more efficient. It also improves 
liquidity, which reduces liquidity risk in the financial system. In fact, an adviser to the 
People’s Bank of China gave this very reason for the country’s plans to launch a pilot 
securitization program in March 2012 that would permit certain Chinese commercial 
lenders to securitize such assets as auto loans. The adviser stated that securitiza -
tion could help banks in China transform illiquid assets on their books into liquid 
assets.2 How securitization improves liquidity will become clear when securitization 
is described in more detail in Section 3.
An important benefit of securitization for companies is that ABS provide an alter -

native means of funding operations that can be considered alongside bond, preferred 
equity, and common equity issuance. Companies that originate loans and receivables 
that can be securitized often compare the funding costs associated with each of these 
sources of financing and choose the optimal one. As discussed in Section 3.4, securi -
tization is often cheaper than a corporate bond issue secured by the same collateral 
as the securitization.
For these reasons, securitization is beneficial to economies and financial markets, 
and many sovereign governments throughout the world have embraced securitiza -
tion. For example, the Italian government has used securitization since the late 1990s 
for privatizing public assets. In emerging markets, securitization is widely used. For 
example, in South America, companies and banks with high credit ratings have used 
securitization to sell receivables on exports, such as oil, to lower their funding costs.

Although securitization brings many benefits to economies, it is not without 
risks, and some of these risks are widely attributed to have precipitated the turmoil 
in financial markets during 2007–2009. Broadly, those risks fall into two categories: 
risks that relate primarily to the timing of the ABS’s cash flows, such as contraction 
2 “China Revives Giant Securitization Program” (2012), p. 6.

Reading 53 ■ Introduction to Asset-  Backed Securities 476
risk and extension risk, and risks related to the inherent credit risk of the loans and 
receivables backing the ABS. This reading describes these risks and also discusses 
some of the structures used to mitigate them as well as redistribute them.
EXAMPLE 1   
Re- establishing Sustainable Securitization Markets
The following appeared in the July 2011 publication by the Joint Forum titled 
“Report on Securitization Incentives” and published by the Bank for International 
Settlements:
Re- establishing sustainable securitization markets has been high on 
the agenda of the Group of Twenty (G-  20), the Financial Stability 
Board (FSB, an international body established to coordinate and 
promote implementation of the work of financial authorities and 
standard setting bodies), and other international organizations and 
national governments since the onset of the crisis.
The FSB’s November 20, 2010, report to the G-  20 leaders noted,

in particular, that “Re-  establishing securitization on a sound basis 
remains a priority in order to support provision of credit to the real 
economy and improve banks’ access to funding in many jurisdictions. ”
Explain what is meant by the quotation in the FSB’s November 20 report.
Solution:
Funding via securitization is a means by which non-  bank entities can provide 
investment funds to various sectors of the economy without those sectors rely -
ing exclusively on banks. Securitization allows banks to originate, monitor, and 
collect loans beyond what they could do if limited to their own deposits and 
capital. Thus, securitization allows the non-  bank and bank sectors to provide 
credit to the real economy more cheaply and efficiently than would otherwise 
be available only from banks.
HOW SECURITIZATION WORKS
When assets are securitized, several legal and regulatory conditions must be satisfied. 
A number of parties participate in the process to facilitate the transaction and ensure

these conditions are met. In this section, a typical securitization is described by way 
of a hypothetical example. The example describes the parties involved in a securiti -
zation and their roles. It also introduces the typical structures of securitizations, such 
as credit tranching and time tranching.
3.1 An Example of a Securitization
Mediquip, a hypothetical company, is a manufacturer of medical equipment that ranges 
in cost from US$50,000 to US$300,000. The majority of Mediquip’s sales are made 
through loans granted by the company to its customers, and the medical equipment 
serves as collateral for the loans. These loans, which represent an asset to Mediquip, 
have maturities of five years and carry a fixed interest rate. They are fully amortizing 
with monthly payments; that is, the borrowers make equal payments each month 3

How Securitization Works 477
consisting of interest payment and principal repayment. The total principal repaid 
from the 60 loan payments (12 months × 5 years) is such that the amount borrowed 
is fully repaid at the end of the term.
Mediquip’s credit department makes the decision about whether to extend credit 
to customers and services the loans that are made. Loan servicing refers to adminis -
tering any aspect of a loan, including collecting payments from borrowers, notifying 
borrowers who may be delinquent, and recovering and disposing of the medical 
equipment if the borrower does not make the scheduled payments by a specified time. 
If one of its customers defaults, Mediquip can seize the medical equipment and sell 
it to try to recoup the remaining principal on the loan. Although the servicer of such 
loans need not be the originator of the loans, the assumption in this example is that 
Mediquip is the servicer.

The following is an illustration of how these loans can be securitized. Assume 
that Mediquip has US$200  million of loans. This amount is shown on Mediquip’s 
balance sheet as an asset. Assume also that Mediquip wants to raise US$200 mil -
lion, which happens to be the amount of the loans. Because Mediquip’s treasurer is 
aware of the potentially lower funding costs of securitization, he decides to raise the 
US$200 million by securitizing the loans on the medical equipment rather than by 
issuing corporate bonds.
To do so, Mediquip sets up a separate legal entity called Medical Equipment Trust 
(MET), to which it sells the loans on the medical equipment. Such a legal entity is 
referred to as a special purpose entity  (SPE) and sometimes also called a special 
purpose vehicle (SPV) or a special purpose company. The legal form of the SPE 
varies by jurisdiction, but in almost all cases, the ultimate owner of the loans—MET

in our example—is legally independent and is considered bankruptcy remote from 
the seller of the loans. Setting up a separate legal entity ensures that if Mediquip, the 
originator of the loans, files for bankruptcy, the loans backing the ABS that are issued 
by MET are secure within the SPE and creditors of Mediquip have no claim on them. 
Note that in some jurisdictions, the SPE may, in turn, transfer the loans to a trust or 
a limited company.
A securitization is diagramed in Exhibit 1. The SPE set up by Mediquip is called 
MET. The top of Exhibit 1 reflects Mediquip’s business model as described above—
that is, the sale of medical equipment financed by loans (first oval). Mediquip sells to 
MET US$200 million of loans (second oval) and receives from MET US$200 million 
in cash (third oval); in this simplified example, the costs associated with the securi -
tization are ignored. MET issues and sells securities that are backed by the pool of

securitized loans (fourth oval) and receives cash (fifth oval). These securities are the 
ABS mentioned earlier, and the US$200 million of loans represent the collateral. The 
periodic cash payments that are received from the collateral—that is, the monthly 
payments made by Mediquip’s customers that include both interest payment and 
principal repayment (sixth oval)—are used to make the periodic cash payments to 
the security holders—the investors who bought the ABS (seventh oval).

Reading 53 ■ Introduction to Asset-  Backed Securities 478
Exhibit 1   Mediquip’s Securitization 
Mediquip1.
Sale of medical 
equipment financed 
by loansCustomers
2.
Sale of the loans3.
Cash payments for
the loans6.
Periodic cash 
payments
4.
Issuance and sale 
of securities5.
Cash payment
for securities7.
Periodic cash
payments
InvestorsMedical Equipment Trust
(MET)
3.2 Parties to a Securitization and Their Roles
Securitization requires the publication of a prospectus, a document that contains 
information about the securitization.3 The three main parties to a securitization are:
■■the seller of the collateral, sometimes called the depositor (Mediquip in our 
example);
■■the SPE that purchases the loans or receivables and uses them as collateral to 
issue the ABS—MET in our example. (The SPE is often referred to as the issuer 
in the prospectus because it is the entity that issues the securities; it may also 
be called the trust if the SPE is set up as a trust); and

■■the servicer of the loans (Mediquip in our example).
Other parties are also involved in a securitization: independent accountants, law -
yers/attorneys, trustees, underwriters, rating agencies, and financial guarantors. All 
these parties, including the servicer when it is different from the seller of the collateral, 
are referred to as third parties to the securitization.
A significant amount of legal documentation is involved in a securitization. Lawyers/
attorneys are responsible for preparing the legal documents. An important legal docu -
ment is the purchase agreement between the seller of the collateral and the SPE, which 
3 To be more precise, in the United States, a “base prospectus” and a “supplementary prospectus” are 
typically filed with the Securities and Exchange Commission. The base prospectus provides definitions, 
information about the parties to the securitization, and certain information about securities to be offered

in the future—the types of assets that may be securitized, the types of structures that will be used, and the 
types of credit enhancement (the last two are discussed in Section 5.3). The supplementary prospectus 
provides the details of a specific securitization.

How Securitization Works 479
sets forth the representations and warranties that the seller makes about the assets 
sold. These representations and warranties assure investors about the quality of the 
assets, an important consideration when assessing the risks associated with the ABS.
Another important legal document is the prospectus, which describes the structure 
of the securitization, including the priority and amount of payments to be made to the 
servicer, administrators, and the ABS holders. Securitizations often use several forms of 
credit enhancements, which are documented in the prospectus. Credit enhancements 
are provisions that are used to reduce the credit risk of a bond issue. They include (1) 
internal credit enhancements, such as subordination, overcollateralization and reserve 
accounts, and (2) external credit enhancements, such as financial guarantees by banks 
or insurance companies, letters of credit, and cash collateral accounts. Securitizations

often use subordination, which is further discussed in Section 4. Prior to the 2007–2009 
credit crisis, many securitizations included financial guarantees by a third party. The 
most common third-  party financial guarantors are monoline insurance companies or 
monoline insurers. A monoline insurer is a private insurance company whose business 
is restricted to providing guarantees for financial instruments such as ABS. Following 
the financial difficulties and downgrading of the major monoline insurers as a result 
of the financial crisis that began in the mortgage market in mid-  2007, few structures 
in recent years have used financial guarantees from a monoline insurer.
A trustee or trustee agent is typically a financial institution with trust powers that 
safeguards the assets after they have been sold to the SPE, holds the funds due to the 
ABS holders until they are paid, and provides periodic information to the ABS holders.

The information is provided in the form of remittance reports, which may be issued 
monthly, quarterly, or as agreed to in the terms of the prospectus.
Underwriters and rating agencies perform the same functions in a securitization 
as they do in a standard bond offering.
EXAMPLE 2   
A Securitization by Harley-  Davidson
Harley-  Davidson, Inc. manufactures and markets motorcycles. The follow -
ing information is taken from a filing with the US Securities and Exchange 
Commission for a securitization related to the purchase of Harley-  Davidson 
motorcycles:
Issuer: Harley-  Davidson Motorcycle Trust 2005-  2
Seller and Servicer: Harley-  Davidson Credit Corp.
Underwriters: J.P . Morgan Securities Inc., ABN AMRO Inc., BNP Paribas 
Securities Corp., Citigroup Global Markets Inc., and Wachovia Capital 
Markets, LLC
Rating Agencies: Standard & Poor’s Ratings Services and Moody’s 
Investor Services
Notes:
US$487,000,000 3.79% Harley-  Davidson motorcycle contract backed Class 
A- 1 notes, rated AAA/Aaa

US$251,180,000 4.07% Harley-  Davidson motorcycle contract backed Class 
A- 2 notes, rated AAA/Aaa
US$36,820,000 4.27% Harley-  Davidson motorcycle contract backed Class 
B notes, rated A/A3

Reading 53 ■ Introduction to Asset-  Backed Securities 480
Contracts: The assets underlying the notes are fixed-  rate, simple interest, 
motorcycle conditional sales agreements, promissory notes, and security 
agreements relating to the purchase of new or used motorcycles manufac -
tured by one or more subsidiaries of Harley-  Davidson, Inc.
1 The collateral for this securitization is:
A Harley-  Davidson motorcycle contract backed Class A-  1, Class A-  2, 
and Class B notes. 
B new or used motorcycles manufactured by one or more subsidiaries of 
Harley-  Davidson, Inc.
C fixed-  rate, simple interest, motorcycle conditional sales agreements, 
promissory notes, and security agreements relating to the purchase of 
new or used motorcycles manufactured by one or more subsidiaries of 
2 The special purpose entity in this securitization is:
A Harley-  Davidson, Inc.
B Harley-  Davidson Credit Corp.
C Harley-  Davidson Motorcycle Trust 2005-  2.

3 Harley-  Davidson Credit Corp. is responsible for:
A selling the collateral and collecting payments from borrowers.
B selling the new and used motorcycles to customers and collecting 
payments from borrowers.
C selling the motorcycle contract backed Class A-  1, Class A-  2, and Class 
B notes to investors and making the cash payments to them.
C is correct. The collateral is the pool of securitized assets from which the cash 
flows will be generated. It is the “contracts”—that is, the debt obligations that 
have been securitized. These contracts are basically loans provided to purchas -
ers of new or used motorcycles manufactured by Harley-  Davidson, Inc. and 
its subsidiaries. These loans go by different names, such as conditional sales 
agreements, promissory notes, and security agreements.
C is correct. Harley-  Davidson Motorcycle Trust 2005-  2 is the issuer of the ABS

and, thus, the SPE. We might have expected the SPE to purchase the contracts 
that became the collateral from Harley-  Davidson, Inc., the manufacturer, but 
it is Harley-  Davidson Credit Corp. that originates the loans and is, therefore, 
the seller of the collateral. Harley-  Davidson Credit Corp. is also the servicer of 
the contracts.
A is correct. Harley-  Davidson Credit Corp. is the seller of the collateral. As the 
servicer, it is responsible for collecting payments from borrowers, notifying 
borrowers who may be delinquent, and if necessary, recovering and disposing 
of the motorcycles if the borrower defaults.

How Securitization Works 481
3.3 Structure of a Securitization
A simple securitization may involve the sale of only one class of bond or ABS. Let us 
call this class Bond Class A. Returning to the Mediquip and MET example, MET may 
raise US$200 million by issuing 200,000 certificates for Bond Class A with a par value 
of US$1,000 per certificate. Thus, each certificate holder is entitled to 1/200,000 of 
the payments from the collateral after payment of servicing and other administrative 
fees; what these fees represent is discussed in Section 5.1.1.
The structure of the securitization is often more complicated than a single class 
of ABS. As mentioned earlier, it is common for securitizations to include a form of 
internal credit enhancement called subordination , also referred to as credit tranching . 
In such a structure, there is more than one bond class or tranche, and the bond classes 
differ as to how they will share any losses resulting from defaults of the borrowers

whose loans are in the collateral. The bond classes are classified as senior bond classes 
or subordinated bond classes—hence, the reason this structure is also referred to as a 
senior/subordinated structure. The subordinated bond classes are sometimes called 
“non-  senior bond classes” or “junior bond classes. ” They function as credit protection 
for the more senior bond classes; that is, losses are realized by the subordinated bond 
classes before any losses are realized by the senior bond classes. This type of protection 
is also commonly referred to as a waterfall structure because of the cascading flow of 
payments between bond classes in the event of default.
For example, suppose MET issues two bond classes with a total par value of 
US$200 million: Bond Class A, the senior bond class, with a par value of US$120 million, 
and Bond Class B, the subordinated bond class, with a par value of US$80 million. In

this senior/subordinated structure, also referred to as credit tranching, Bond Class B 
will absorb losses up to US$80 million. Thus, as long as defaults by Mediquip’s custom -
ers do not exceed US$80 million, Bond Class A will be fully repaid its US$120 million. 
The purpose of this structure is to redistribute the credit risk associated with the 
collateral. The creation of a set of bond classes allows investors to choose the level of 
credit risk that they prefer to bear.
More than one subordinated bond class may be created. Suppose MET issues the 
following structure:
Bond Class Par Value (US$ millions)
A (senior) 180
B (subordinated) 14
C (subordinated) 6
 Total 200
In this structure, Bond Class A is the senior bond class whereas both Bond Class 
B and Bond Class C are subordinated bond classes from the perspective of Bond 
Class A. The rules for the distribution of losses are as follows. All losses on the col -
lateral are absorbed by Bond Class C before any losses are realized by Bond Class B

and then Bond Class A. Consequently, if the losses on the collateral do not exceed 
US$6  million, no losses will be realized by Bond Class A or Bond Class B. If the 
losses exceed US$6 million, Bond Class B must absorb the losses up to an additional 
US$14 million. For example, if the total loss on the collateral is US$16 million, Bond 
Class C loses its entire par value of US$6 million and Bond Class B realizes a loss of 
US$10 million of its par value of US$14 million. Bond Class A does not realize any 
loss in this scenario. Clearly, Bond Class A realizes a loss only if the total loss on the 
collateral exceeds US$20 million.
The structure of a securitization may also allow the redistribution of another type 
of risk, called “prepayment risk, ” among bond classes. Prepayment risk  is the uncer -
tainty that the cash flows will be different from the scheduled cash flows as set forth

Reading 53 ■ Introduction to Asset-  Backed Securities 482
in the loan agreement because of the borrowers’ ability to alter payments, usually to 
take advantage of interest rate movements. For example, when interest rates decline, 
borrowers tend to pay off part or all of their loans and refinance at lower interest rates. 
The creation of bond classes that possess different expected maturities is referred to 
as time tranching  and is further discussed in Section 5.2.
It is possible, and quite common, for a securitization to have structures with both 
credit tranching and time tranching.
EXAMPLE 3   
Bond Classes and Tranching
Return to the Harley-  Davidson securitization described in Example 2. Based on 
the information provided, the form of credit enhancement that the transaction 
most likely  includes is:
A time tranching.
B credit tranching.
C a financial guarantee.
Solution:
B is correct. The Harley-  Davidson securitization includes three bond classes:

Class A-  1, Class A-  2, and Class B. Each bond class has a fixed but different 
interest rate; the interest rate increases from 3.79% for Class A-  1 notes to 4.27% 
for Class B notes. Thus, it is likely that the transaction has credit tranching and 
that the three bond classes display a senior/subordinated structure, with Class 
A- 1 notes being senior to Class A-  2 notes, and both Classes A-  1 and A-  2 notes 
being senior to Class B notes, the subordinated bond class. As the credit risk 
increases from the Class A-  1 notes to the Class B notes, so does the interest 
rate to reflect the additional compensation investors require for bearing the 
additional credit risk. The information provided does not give any indication 
of either time tranching or a financial guarantee.
3.4 Key Role of the Special Purpose Entity
The SPE plays a pivotal role in securitization. In fact, the setup of a legal entity that 
plays the same role as an SPE in terms of protecting the rights of ABS holders is a

prerequisite in any country that wants to allow securitization. Indeed, without a pro -
vision in a country’s legal system for the equivalent of an SPE, the benefits of using 
securitization by an entity seeking to raise funds would not exist. Let us explain why 
by returning to our example involving Mediquip and MET.
Assume that Mediquip has a credit rating from a credit-  rating agency, such as 
Standard & Poor’s, Moody’s Investors Service, or Fitch Ratings. A credit rating reflects 
the opinion of a credit-  rating agency about the creditworthiness of an entity and/or the 
debt securities the entity issues. Suppose that the credit rating assigned to Mediquip 
is BB or Ba2. Such a credit rating means that Mediquip is below what is referred to 
as an investment-  grade credit rating.
Assume again that Mediquip’s treasurer wants to raise US$200 million and is con -
templating doing so by issuing a five-  year corporate bond rather than by securitizing

the loans. The treasurer is, of course, concerned about the funding cost and would 
like the lowest possible interest rate available relative to some benchmark interest rate. 
The difference between the interest rate paid on the five-  year corporate bond and the 
benchmark interest rate is the spread. The spread reflects the compensation investors

How Securitization Works 483
require for buying the corporate bond, which is riskier than the bonds issued at the 
benchmark interest rate. The major factor affecting the spread is the issuer’s credit 
rating—hence, the reason the spread is called a “credit spread. ”
Another factor that will influence the credit spread is whether the bond is backed 
by collateral. A corporate bond that has collateral is often referred to as a secured 
bond. The collateral usually reduces the credit spread, making the credit spread of a 
secured bond lower than that of an otherwise identical unsecured bond. In our exam -
ple, Mediquip’s treasurer can use the loans on the medical equipment as collateral 
for the secured corporate bond issue. Thus, if Mediquip issues a five-  year corporate 
bond to raise US$200 million, the credit spread will reflect its credit rating primarily 
and the collateral slightly. We will soon explain why the collateral affects the credit 
spread only slightly.

Now suppose that instead of using the loans as collateral for a secured corporate 
bond issue, Mediquip sells the loan contracts in an arm’s length transaction to MET, 
the SPE. After the sale is completed, it is MET, not Mediquip, that legally owns them. 
As a result, if Mediquip is forced into bankruptcy while the loans are still outstanding, 
Mediquip’s creditors cannot recover them because they are legally owned by another 
entity. Note that it is possible, however, that transfers made to bankruptcy-  remote 
vehicles can be challenged as fraudulent conveyances and potentially unwound. The 
legal implication of setting up MET is that investors contemplating the purchase of 
any bond class backed by the cash flows from the pool of loans on the medical equip -
ment will evaluate the credit risk associated with collecting the payments due on the 
receivables independently of Mediquip’s credit rating.

Credit ratings are assigned to each of the various bond classes created in the secu -
ritization. They depend on the quality of the collateral—that is, how the rating agencies 
evaluate the credit risk of the pool of securitized loans or receivables. Depending on 
the structure of the securitization, each bond class receives a credit rating that reflects 
its credit risk, and some of the bond classes may have a better credit rating than the 
company that is seeking to raise funds. As a consequence, in aggregate, the funding 
cost of a securitization may be lower than that of a corporate bond issue. Access to 
lower funding cost is a key role of the SPE in a securitization.
A fair question is why a securitization can be cheaper than a corporate bond issue 
secured by the same collateral as the securitization. The reason is that the SPE would 
not be affected by the bankruptcy of the seller of the collateral. As mentioned above,

the assets belong to the SPE, not to the entity that sold the assets to the SPE. In the 
United States and other countries, when a company is liquidated, creditors receive 
distributions based on the absolute priority rule to the extent that assets are available. 
The absolute priority rule is the principle that senior creditors are paid in full before 
subordinated creditors are paid anything. The absolute priority rule also guarantees 
the seniority of creditors relative to equity holders.
Whereas the absolute priority rule generally holds in liquidations, it has not always 
been upheld by the courts in reorganizations. Thus, although investors in the debt of 
a company may believe they have priority over the equity holders and priority over 
other classes of creditors, the actual outcome of a reorganization may be far differ -
ent from the terms stated in the debt agreement; that is, there is no assurance that

if the corporate bond has collateral, the rights of the bondholders will be respected. 
For this reason, the credit spread for a corporate bond backed by collateral does not 
decrease dramatically.
In the case of a securitization, the courts have in most jurisdictions no discretion 
to change seniority because the bankruptcy of a company does not affect the SPE. The 
rules set forth in the legal document, which describes how losses are to be absorbed 
by each bond class, are unaffected by the company’s bankruptcy. This important 
decoupling of the credit risk of the entity needing funds from the bond classes issued 
by the SPE explains why the SPE’s legal role is critical.

Reading 53 ■ Introduction to Asset-  Backed Securities 484
The SPE is bankruptcy remote from the seller of the collateral, which means that 
the bankruptcy of the seller of the collateral will not affect the holders of securities 
issued by the SPE and backed by the collateral. The security holders face credit risk 
only to the extent that the borrowers whose claims the SPE has purchased default on 
their loans. The SPE’s ability to make cash payments to the security holders remains 
intact as long as the borrowers make the interest payments and/or the principal 
repayments on their loans.
However, all countries do not have the same legal framework. Impediments have 
arisen in some countries with respect to the issuance of ABS because the concept of 
trust law is not as well developed globally as it is in the United States and many other 
developed countries.4 Thus, investors should be aware of the legal considerations that 
apply in the jurisdictions where they purchase ABS.
EXAMPLE 4

EXAMPLE 4   
Special Purpose Entity and Bankruptcy
Agnelli Industries (Agnelli), a manufacturer of industrial machine tools based 
in Bergamo, Italy, has €500  million of corporate bonds outstanding. These 
bonds have a credit rating below investment grade. Agnelli has €400 million of 
receivables on its balance sheet that it would like to securitize. The receivables 
represent payments Agnelli expects to receive for machine tools it has sold to 
various customers in Europe. Agnelli sells the receivables to Agnelli Trust, a 
special purpose entity. Agnelli Trust then issues ABS, backed by the pool of 
receivables, with the following structure:
Bond Class Par Value (€ millions)
A (senior) 280
B (subordinated) 60
C (subordinated) 60
 Total 400
Bond Class A is given an investment-  grade credit rating by the credit-  rating 
agencies.
1 Why does Bond Class A have a higher credit rating than the corporate 
bonds?
2 If Agnelli Industries files for bankruptcy after the issuance of the asset-  
backed security:

A Bond Classes A, B, and C will be unaffected.
B Bond Classes A, B, and C will lose their entire par value.
C losses will be realized by Bond Class C first, then by Bond Class B, and 
then by Bond Class A.
3 If one of Agnelli’s customers defaults on its €60 million loan:
A Bond Classes A, B, and C will realize losses of €20 million each.
4 In many EU countries, the creditors are protected in the recognition of the securitization as a true sale. 
The SPE has full legal ownership of the securitized assets, which are de-  recognized from the seller’s balance 
sheet. In the event of default of the originator/servicer, the SPE can appoint a substitute company to the 
service role and continue to pay bondholders from the income stream of the securitized assets without the 
other creditors of the initial originator/servicer being able to have any recourse or claim to these assets.

Residential Mortgage Loans 485
B Bond Class C will realize losses of €60 million, but Bond Classes A and 
B will be unaffected.
C Bond Classes B and C will realize losses of €30 million each, but Bond 
Class A will be unaffected.
Bond Class A are issued by Agnelli Trust, an SPE that is bankruptcy remote from 
Agnelli. Thus, the investors who hold Agnelli’s bonds and/or common shares 
have no legal claim on the cash flows from the securitized receivables that are 
the collateral for the ABS. As long as Agnelli’s customers make the interest 
payments and/or principal repayments on their loans, Agnelli Trust will be able 
to make cash payments to the ABS investors. Because of the credit tranching, 
even if some of Agnelli’s customers were to default on their loans, the losses 
would be realized by the subordinated Bond Classes B and C before any losses 
are realized by the senior Bond Class A. The credit risk associated with Bond

Class A is, therefore, lower than that of Bond Classes B and C and the corporate 
bonds, justifying the investment-  grade credit rating.
A is correct. The ABS have been issued by Agnelli Trust, an SPE that is bank -
ruptcy remote from Agnelli. If the securitization is viewed as resulting in a true 
sale, the fact that Agnelli files for bankruptcy does not affect the ABS holders. 
These ABS holders face credit risk only to the extent that Agnelli’s customers 
who bought the machine tools do not make the obligatory payments on their 
loans. As long as the customers continue to make payments, all three bond 
classes will receive their expected cash flows. These cash flows are completely 
and legally independent of anything that happens to Agnelli itself.
B is correct. The rules for the distribution of losses are as follows. All losses on 
the collateral are absorbed by Bond Class C before any losses are realized by

Bond Class B and then Bond Class A. Consequently, if the losses on the collateral 
are €60 million, which is the par value of Bond Class C, Bond Class C loses its 
entire par value, but Bond Classes A and B are unaffected.
RESIDENTIAL MORTGAGE LOANS
Before describing the various types of residential mortgage-  backed securities, this 
section briefly discusses the fundamental features of the underlying assets: residential 
mortgage loans. The mortgage designs described in this section are those that are 
typically securitized.
A mortgage loan , or simply mortgage , is a loan secured by the collateral of some 
specified real estate property that obliges the borrower (often someone wishing to 
buy a home) to make a predetermined series of payments to the lender (often initially 
a bank or mortgage company). The mortgage gives the lender the right to foreclose 
on the loan if the borrower defaults; that is, a foreclosure  allows the lender to take

possession of the mortgaged property and then sell it in order to recover funds toward 
satisfying the debt obligation.
Typically, the amount of the loan advanced to buy the property is less than the 
property’s purchase price. The borrower makes a down payment, and the amount 
borrowed is the difference between the property’s purchase price and the down 4

Reading 53 ■ Introduction to Asset-  Backed Securities 486
payment. When the loan is first taken out, the borrower’s equity in the property is 
equal to the down payment. Over time, as the market value of the property changes, 
the borrower’s equity also changes. It also changes as the borrower makes mortgage 
payments that include principal repayment.
The ratio of the amount of the mortgage to the property’s value is called the loan-  
to- value ratio  (LTV). The lower the LTV, the higher the borrower’s equity. From the 
lender’s perspective, the higher the borrower’s equity, the less likely the borrower 
is to default. Moreover, the lower the LTV, the more protection the lender has for 
recovering the amount loaned if the borrower does default and the lender repossesses 
and sells the property.
In the United States, market participants typically identify two types of mort -
gages based on the credit quality of the borrower: prime loans and subprime loans.

Generally, for a loan to be considered prime, the borrower must be viewed as having 
high credit quality; that is, the borrower must have strong employment and credit 
histories, income sufficient to pay the loan obligation, and substantial equity in the 
underlying property. If the borrower has lower credit quality or if the loan is not a 
first lien on the property (that is, a party other than the current potential lender has 
a prior claim on the underlying property), the loan is treated as subprime.
Throughout the world, there are a considerable number of mortgage designs. 
Mortgage design means the specification of (1) the maturity of the loan, (2) how the 
interest rate is determined, (3) how the principal is to be repaid (that is, the amor -
tization schedule), (4) whether the borrower has the option to prepay and, in such 
cases, whether any prepayment penalties might be imposed, and (5) the rights of the 
lender in a foreclosure.

A study by Lea (2010) provides an excellent review of mortgage designs in Australia, 
Canada, Denmark, Ireland, Japan, Germany, the Netherlands, South Korea, Spain, the 
United Kingdom, and the United States.5 This section draws on this study to describe 
the five specifications of a mortgage design.
4.1 Maturity
In the United States, the typical maturity of a mortgage ranges from 15 to 30 years. 
For most countries in Europe, a residential mortgage typically has a maturity between 
20 and 40 years, but in some countries, such as France and Spain, it can be as long as 
50 years. Japan is an extreme case; the maturity of a mortgage can be 100 years.6 Note 
that what is called the term of a mortgage means the number of years to maturity.
4.2 Interest Rate Determination
The interest rate on a mortgage is called the mortgage rate , contract rate , or note 
rate . How the mortgage rate is determined varies considerably among countries. The

four basic ways that the mortgage rate can be specified are as follows:
■■Fixed rate:  The mortgage rate remains the same during the life of the mortgage. 
The United States and France have a high proportion of this type of interest rate 
determination. Although fixed-  rate mortgages are not the dominant form in 
Germany, they do exist there.
5 Lea (2010, Table 2, p. 17).
6 The term of residential mortgages is usually in line with the age of the borrower at the end of the loan 
maturity period, with the borrower’s retirement age being a usual upper limit.

Residential Mortgage Loans 487
■■Adjustable or variable rate:  The mortgage rate is reset periodically—daily, 
weekly, monthly, or annually. The determination of the new mortgage rate for 
an adjustable-  rate mortgage (ARM) at the reset date may be based on some 
reference rate or index (in which case, it is called an indexed-  referenced ARM) 
or a rate determined at the lender’s discretion (in which case, it is called a 
reviewable ARM). Residential mortgages in Australia, Ireland, South Korea, 
Spain, and the United Kingdom are dominated by adjustable-  rate mortgages. In 
Australia, Ireland, and the United Kingdom, the reviewable ARM is standard. 
In South Korea and Spain, the indexed-  referenced ARM is the norm. Canada 
and the United States have ARMs that are typically tied to an index or reference 
rate, although this type of mortgage rate is not the dominant form of interest 
rate determination. An important feature of an ARM is that it will usually have

a maximum interest rate by which the mortgage rate can change at a reset date 
and a maximum interest rate that the mortgage rate can reach during the mort -
gage’s life.
■■Initial period fixed rate:  The mortgage rate is fixed for some initial period and 
is then adjusted. The adjustment may call for a new fixed rate or for a variable 
rate. When the adjustment calls for a fixed rate, the mortgage is referred to as a 
rollover or renegotiable mortgage. This mortgage design is dominant in Canada, 
Denmark, Germany, the Netherlands, and Switzerland. When the mortgage 
starts out with a fixed rate and then switches to an adjustable rate after a 
specified initial term, the mortgage is referred to as a hybrid mortgage. Hybrid 
mortgages are popular in the United Kingdom.
■■Convertible : The mortgage rate is initially either a fixed rate or an adjustable 
rate. At some point, the borrower has the option to convert the mortgage to a

fixed rate or an adjustable rate for the remainder of the mortgage’s life. Almost 
half of the mortgages in Japan are convertible.
4.3 Amortization Schedule
In most countries, residential mortgages are amortizing loans . The amortization of 
a loan means the gradual reduction of the amount borrowed over time. Assuming 
no prepayments are made by the borrower, the periodic mortgage payments made by 
the borrower consist of interest payments and scheduled principal repayments. The 
scheduled principal repayment is the amount of reduction of the outstanding mort -
gage balance and is thus referred to as the amortization. As discussed in a previous 
reading, there are two types of amortizing loans: fully amortizing loans and partially 
amortizing loans. In a fully amortizing loan, the sum of all the scheduled principal 
repayments during the mortgage’s life is such that when the last mortgage payment 
is made, the loan is fully repaid. Most residential mortgages in the United States are

fully amortizing loans. In a partially amortizing loan, the sum of all the scheduled 
principal repayments is less than the amount borrowed. The last payment that has 
to be made is then the unpaid mortgage balance, and that last payment is said to be 
a “balloon” payment.
If no scheduled principal repayment is specified for a certain number of years, the 
loan is said to be an interest-  only mortgage . Interest-  only mortgages are available 
in Australia, Denmark, Finland, France, Germany, Greece, Ireland, the Netherlands, 
Portugal, South Korea, Spain, Switzerland, and the United Kingdom.7 Interest-  only 
mortgages are also available to a limited extent in the United States. A special type of 
interest-  only mortgage is one in which there are no scheduled principal repayments 
7 See Table 7 in Scanlon, Lunde, and Whitehead (2008).

Reading 53 ■ Introduction to Asset-  Backed Securities 488
over the entire life of the loan. In this case, the balloon payment is equal to the original 
loan amount. These mortgages, referred to as “interest-  only lifetime mortgages” or 
“bullet mortgages, ” are available in Denmark, the Netherlands, and the United Kingdom.
4.4 Prepayment Options and Prepayment Penalties
A prepayment is any payment toward the repayment of principal that is in excess of the 
scheduled principal repayment. A mortgage may entitle the borrower to prepay all or 
part of the outstanding mortgage principal prior to the scheduled due date when the 
principal must be repaid. This contractual provision is referred to as a prepayment 
option  or an early repayment option . From the lender’s or investor’s viewpoint, the 
effect of a prepayment option is that the amount and timing of the cash flows from 
a mortgage cannot be known with certainty. This risk was referred to as prepayment

risk in Section 3. Prepayment risk affects all mortgages that allow prepayment, not 
just the level-  payment, fixed-  rate, fully amortizing mortgages.
The mortgage may stipulate some sort of monetary penalty when a borrower 
prepays within a certain time period after the mortgage is originated, and this time 
period may extend for the full life of the loan. Such mortgage designs are referred to 
as prepayment penalty mortgages . The purpose of the prepayment penalty is to 
compensate the lender for the difference between the contract rate and the prevailing 
mortgage rate if the borrower prepays when interest rates decline. Hence, the prepay -
ment penalty is effectively a mechanism that provides for yield maintenance for the 
lender. The method for calculating the penalty varies. Prepayment penalty mortgages 
are common in Europe. Although the proportion of prepayment penalty mortgages 
in the United States is small, they do exist.
4.5 Rights of the Lender in a Foreclosure

A mortgage can be a recourse loan or a non-  recourse loan. When the borrower fails to 
make the contractual loan payments, the lender can repossess the property and sell it, 
but the proceeds received from the sale of the property may be insufficient to recoup 
the losses. In a recourse loan , the lender has a claim against the borrower for the 
shortfall between the amount of the outstanding mortgage balance and the proceeds 
received from the sale of the property. In a non-  recourse loan , the lender does not 
have such a claim and thus can look only to the property to recover the outstanding 
mortgage balance. In the United States, recourse is typically determined by the state, 
and residential mortgages are non-  recourse loans in many states. In contrast, resi -
dential mortgages in most European countries are recourse loans.
The recourse/non-  recourse feature of a mortgage has implications for projecting the

likelihood of defaults by borrowers, particularly in the case of what is sometimes called 
“underwater mortgages”—that is, mortgages for which the value of the property has 
declined below the amount owed by the borrower. For example, in the United States, 
where mortgages are typically non-  recourse, the borrower may have an incentive to 
default on an underwater mortgage and allow the lender to foreclose on the property, 
even if resources are available to continue to make mortgage payments. This type of 
default by a borrower is referred to as a “strategic default. ” A strategic default, how -
ever, has negative consequences for the borrower, who will then have a lower credit 
score and a reduced ability to borrow in the future. Thus, not all borrowers faced 
with underwater mortgages will default. In countries where residential mortgages are 
recourse loans, a strategic default is less likely because the lender can seek to recover

Residential Mortgage Loans 489
Now that the basics of a residential mortgage have been set out, we can turn our 
attention to how these mortgages are securitized—that is, transformed into MBS. In 
the following sections, we focus on the US residential mortgage sector because it is 
the largest in the world and many non-  US investors hold US MBS in their portfolios.
EXAMPLE 5   
Residential Mortgage Designs 
1 In an interest-  only mortgage, the borrower:
A does not have to repay the principal as long as she pays the interest.
B does not have to make principal repayments for a certain number of 
years, after which she starts paying down the original loan amount.
C does not have to make principal repayments over the entire life of 
the mortgage and pays down the original loan amount as a balloon 
payment.
2 A bank advertises a mortgage with the following interest rate: 2.99% 
(12- month Euribor + 2.50%), resetting once a year. The mortgage is most 
likely :
A a hybrid mortgage.

likely :
B an adjustable-  rate mortgage.
C an initial period fixed-  rate mortgage.
3 If the borrower fails to make the contractual mortgage payments on a 
non-  recourse mortgage, the lender:
A cannot foreclose the property.
B can only recover the outstanding mortgage balance through the sale of 
the property.
C can recover the outstanding mortgage balance through the sale of the 
property and the borrower’s other assets and/or income.
B is correct. In an interest-  only mortgage, there is no scheduled principal 
repayment for a certain number of years, so the borrower starts paying down 
the original loan amount only after an initial period of interest-  only payments. 
Some, but not all, interest-  only mortgages do not have scheduled principal 
repayments over the entire life of the loan. These mortgages are called interest-  
only lifetime mortgages or bullet mortgages, and they require the borrower to 
pay back the original loan amount at maturity.

B is correct. An adjustable-  rate mortgage is one for which the mortgage rate 
is typically based on some reference rate or index (indexed-  referenced ARM) 
or a rate determined at the lender’s discretion (reviewable ARM) and is reset 
periodically. A mortgage rate of 12-  month Euribor + 2.50%, resetting once per 
year, suggests that the mortgage is an index-  referenced ARM. The 2.99% rate 
is the current mortgage rate (that is, 12-  month Euribor of 0.49% + 2.50%) and 
should not be taken as an indication that it is a fixed-  rate, initial period fixed-  
rate, or hybrid mortgage.

Reading 53 ■ Introduction to Asset-  Backed Securities 490
B is correct. In the case of a non-  recourse mortgage, the lender can foreclose 
the property if the borrower fails to make the contractual mortgage payments. 
However, the lender can use only the proceeds from the property to recover the 
outstanding mortgage balance.
RESIDENTIAL MORTGAGE-  BACKED SECURITIES
The bonds created from the securitization of mortgages related to the purchase of 
residential properties are residential mortgage-  backed securities (RMBS). In such 
countries as the United States, Canada, Japan, and South Korea, a distinction is often 
made between securities that are guaranteed by the government or a quasi-  government 
entity and securities that are not. Quasi-  government entities are usually created by 
governments to perform various functions for them. Examples of quasi-  government 
entities include government-  sponsored enterprises (GSEs) such as Fannie Mae (pre -

viously the Federal National Mortgage Association) and Freddie Mac (previously 
the Federal Home Loan Mortgage Corporation) in the United States and the Japan 
Housing Finance Agency (JHF).
In the United States, securities backed by residential mortgages are divided into 
three sectors: (1) those guaranteed by a federal agency, (2) those guaranteed by a 
GSE, and (3) those issued by private entities and that are not guaranteed by a federal 
agency or a GSE. The first two sectors are referred to as agency RMBS , and the third 
sector as non-  agency RMBS . A significant amount of space in this section is devoted 
to US agency and non-  agency RMBS because these securities represent a large sector 
of the investment-  grade bond market and are included in the portfolios of many US 
as well as non-  US investors.
Agency RMBS include securities issued by federal agencies, such as the Government 
National Mortgage Association, popularly referred to as Ginnie Mae. This entity is a

federally related institution because it is part of the US Department of Housing and 
Urban Development. As a result, the RMBS that it guarantees carry the full faith and 
credit of the US government with respect to timely payment of interest and repay -
ment of principal.
Agency RMBS also include RMBS issued by GSEs, such as Fannie Mae and 
Freddie Mac. RMBS issued by GSEs do not carry the full faith and credit of the US 
government.8 Agency RMBS issued by GSEs differ from non-  agency RMBS in two 
ways. First, the credit risk of the RMBS issued by Fannie Mae and Freddie Mac is 
reduced by the guarantee of the GSE itself, which charges a fee for insuring the 
issue. In contrast, non-  agency RMBS use credit enhancements to reduce credit risk, 
which is further discussed in Section 5.3. The second way in which RMBS issued by 
GSEs differ from non-  agency RMBS is with regard to the pool of securitized loans. 
For a loan to be included in a pool of loans backing an agency RMBS, it must meet

specific underwriting standards established by various government agencies. These 
standards set forth the maximum size of the loan, the loan documentation required, 
the maximum loan-  to- value ratio, and whether or not insurance is required. If a loan 
satisfies the underwriting standards for inclusion as collateral for an agency RMBS, it 
is called a “conforming mortgage. ” If a loan fails to satisfy the underwriting standards, 
it is called a “non-  conforming mortgage. ”5
8 In September 2008, both GSEs were placed in conservatorship. In a conservatorship, a judge appoints 
an entity to take charge of the financial affairs of another entity.

Residential Mortgage-  Backed Securities 491
This section starts with a discussion of agency RMBS, which include mortgage 
pass-  through securities and collateralized mortgage obligations. We then discuss 
non-  agency RMBS.9
5.1 Mortgage Pass-  Through Securities
A mortgage pass-  through security  is a security created when one or more holders 
of mortgages form a pool of mortgages and sell shares or participation certificates 
in the pool. A pool can consist of several thousand or only a few mortgages. When a 
mortgage is included in a pool of mortgages that is used as collateral for a mortgage 
pass-  through security, the mortgage is said to be securitized.
5.1.1  Characteristics
The cash flows of a mortgage pass-  through security depend on the cash flows of the 
underlying pool of mortgages. The cash flows consist of monthly mortgage payments 
representing interest, the scheduled repayment of principal, and any prepayments.

Cash payments are made to security holders each month. Neither the amount nor the 
timing of the cash flows from the pool of mortgages, however, is necessarily identical 
to that of the cash flow passed through to the security holders. In fact, the monthly 
cash flows of a mortgage pass-  through security are less than the monthly cash flow 
of the underlying pool of mortgages by an amount equal to the servicing and other 
administrative fees.
The servicing fee is the charge related to servicing the mortgages. Servicing involves 
collecting monthly payments from borrowers, forwarding proceeds to owners of the 
loan, sending payment notices to borrowers, reminding borrowers when payments 
are overdue, maintaining records of the outstanding mortgage balance, initiating 
foreclosure proceedings if necessary, and providing tax information to borrowers 
when applicable. The servicing fee is typically a portion of the mortgage rate. The

other administrative fees are those charged by the issuer or financial guarantor of the 
mortgage pass-  through security for guaranteeing the issue.
A mortgage pass-  through security’s coupon rate is called the pass-  through rate . 
The pass-  through rate is lower than the mortgage rate on the underlying pool of 
mortgages by an amount equal to the servicing and other administrative fees. The 
pass-  through rate that the investor receives is said to be “net interest” or “net coupon. ”
Not all of the mortgages that are included in a pool of securitized mortgages have 
the same mortgage rate and the same maturity. Consequently, for each mortgage 
pass-  through security, a weighted average coupon rate  (WAC) and a weighted 
average maturity  (WAM) are determined. The WAC is calculated by weighting the 
mortgage rate of each mortgage in the pool by the percentage of the outstanding 
mortgage balance relative to the outstanding amount of all the mortgages in the pool.

Similarly, the WAM is calculated by weighting the remaining number of months to 
maturity of each mortgage in the pool by the outstanding mortgage balance relative 
to the outstanding amount of all the mortgages in the pool. Example 6 illustrates the 
calculation of the WAC and WAM.
9 A popular bond market index, the Bloomberg Barclays US Aggregate Bond Index, has a sector called 
the “mortgage sector. ” In the mortgage sector, Bloomberg Barclays includes only agency RMBS that are 
mortgage pass-  through securities.

Reading 53 ■ Introduction to Asset-  Backed Securities 492
EXAMPLE 6   
Weighted Average Coupon Rate and Weighted Average 
Maturity
Assume that a pool includes three mortgages with the following characteristics:
MortgageOutstanding 
Mortgage Balance 
(US$)Coupon Rate 
(%)Number of Months 
to Maturity
1 1,000 5.1 34
2 3,000 5.7 76
3 6,000 5.3 88
The outstanding amount of three mortgages is US$10,000. Thus, the weights 
of Mortgages 1, 2, and 3 are 10%, 30%, and 60 %, respectively.
The WAC is:
10% × 5.1% + 30% × 5.7% + 60% × 5.3% = 5.4%
The WAM is:
10% × 34 + 30% × 76 + 60% × 88 = 79 months
5.1.2  Prepayment Risk
An investor who owns mortgage pass-  through securities does not know what the 
future cash flows will be because these future cash flows depend on actual prepay -
ments. As we noted earlier, this risk is called prepayment risk. This prepayment risk 
has two components: contraction risk and extension risk, both of which largely reflect 
changes in the general level of interest rates.

Contraction risk  is the risk that when interest rates decline, actual prepayments will 
be higher than forecasted because homeowners will refinance at now-  available lower 
interest rates. Thus, a security backed by mortgages will have a shorter maturity than 
was anticipated at the time of purchase. Holding a security whose maturity becomes 
shorter when interest rates decline has two adverse consequences for investors. First, 
investors must reinvest the proceeds at lower interest rates. Second, if the security 
is prepayable or callable, its price appreciation is not as great as that of an otherwise 
identical bond that does not have a prepayment or call option.
In contrast, extension risk  is the risk that when interest rates rise, prepayments 
will be lower than forecasted because homeowners are reluctant to give up the ben -
efits of a contractual interest rate that now looks low. As a result, a security backed

by mortgages will typically have a longer maturity than was anticipated at the time of 
purchase. From the investors’ perspective, the value of the security has fallen because 
the higher interest rates translate into a lower price for the security, and the income 
investors receive (and can potentially reinvest) is typically limited to the interest 
payment and scheduled principal repayments.
5.1.3  Prepayment Rate Measures
In describing prepayments, market participants refer to the prepayment rate or 
prepayment speed. The two key prepayment rate measures are the single monthly 
mortality rate (SMM), a monthly measure, and its corresponding annualized rate, the 
conditional prepayment rate (CPR).

Residential Mortgage-  Backed Securities 493
The SMM reflects the dollar amount of prepayment for the month as a fraction of 
the balance on the mortgage after accounting for the scheduled principal repayment 
for the month. It is calculated as follows:
SMMPrepay ment for the month
Beginning outstanding m ortgag e=  balance for the mont h
Schedul ed principa l repayment for − tthe m onth


Note that the SMM is typically expressed as a percentage.
When market participants describe the assumed prepayment for a pool of resi -
dential mortgages, they refer to the annualized SMM, which is the CPR. A CPR of 
6%, for example, means that approximately 6% of the outstanding mortgage balance 
at the beginning of the year is expected to be prepaid by the end of the year.
A key factor in the valuation of a mortgage pass-  through security and other 
products derived from a pool of mortgages is forecasting the future prepayment rate.

This task involves prepayment modeling. Prepayment modeling uses characteristics 
of the mortgage pool and other factors to develop a statistical model for forecasting 
future prepayments.
In the United States, market participants describe prepayment rates in terms of 
a prepayment pattern or benchmark over the life of a mortgage pool. This pattern is 
the Public Securities Association (PSA) prepayment benchmark, which is produced 
by the Securities Industry and Financial Markets Association (SIFMA). The PSA 
prepayment benchmark is expressed as a series of monthly prepayment rates. Based 
on historical patterns, it assumes that prepayment rates are low for newly originated 
mortgages and then speed up as the mortgages become seasoned. Slower or faster 
prepayment rates are then referred to as some percentage of the PSA prepayment 
benchmark. Rather than going into the details of the PSA prepayment benchmark, this

discussion will rely on some PSA assumptions. What is important to remember is that 
the standard for the PSA model is 100 PSA; that is, at 100 PSA, investors can expect 
prepayments to follow the PSA prepayment benchmark—for example, an increase of 
prepayment rates of 0.20% for the first 30 months until they peak at 6% in Month 30. 
A PSA assumption greater than 100 PSA means that prepayments are assumed to be 
faster than the standard model. In contrast, a PSA assumption lower than 100 PSA 
means that prepayments are assumed to be slower than the standard model.
5.1.4  Cash Flow Construction
Let us see how to construct the monthly cash flow for a hypothetical mortgage pass-  
through security. We assume the following:
■■The underlying pool of mortgages has a par value of US$800 million.
■■The mortgages are fixed-  rate, level-  payment, and fully amortizing loans.
■■The WAC for the mortgages in the pool is 6%.
■■The WAM for the mortgages in the pool is 357 months.

■■The pass-  through rate is 5.5%.
Exhibit 2 shows the cash flows to the mortgage pass-  through security holders for 
selected months assuming a prepayment rate of 165 PSA. The SMM in Column 3 
and mortgage payments in Column 4 are given. The net interest payment in Column 
5 is the amount available to pay security holders after servicing and other adminis -
trative fees. This amount is equal to the beginning outstanding mortgage balance in 
Column 2 multiplied by the pass-  through rate of 5.5% and then divided by 12. The 
scheduled principal repayment in Column 6 is the difference between the mortgage 
payment in Column 4 and the gross interest payment. The gross interest payment is 
equal to the beginning outstanding mortgage balance in Column 2 multiplied by the 
WAC of 6% and then divided by 12. The prepayment in Column 7 is calculated by (1)

Reading 53 ■ Introduction to Asset-  Backed Securities 494
applying Equation 1, using the SMM provided in Column 3, the beginning outstanding 
mortgage balance in Column 2, and the scheduled principal repayment in Column 
6.10 The total principal repayment in Column 8 is the sum of the scheduled principal 
repayment in Column 6 and the prepayments in Column 7. Subtracting this amount 
from the beginning outstanding mortgage balance for the month gives the beginning 
outstanding mortgage balance for the following month. Finally, the projected cash flow 
for this mortgage pass-  through security in Column 9 is the sum of the net interest 
payment in Column 5 and the total principal repayment in Column 8.
Exhibit 2   Monthly Cash Flow to Bondholders for a US$800 Million Mortgage Pass-  Through Security with a 
WAC of 6.0%, a WAM of 357 Months, and a Pass-  Through Rate of 5.5%, Assuming a Prepayment 
Rate of 165 PSA
(1) (2) (3) (4) (5) (6) (7) (8) (9)
MonthBeginning 
Outstanding 
Mortgage 
Balance

Mortgage 
Balance 
(US$)SMM  
(%)Mortgage 
Payment 
(US$)Net 
Interest 
Payment 
(US$)Scheduled 
Principal 
Repayment 
(US$)Prepayment 
(US$)Total 
Principal 
Repayment 
(US$)Projected 
Cash Flow 
(US$)
1 800,000,000 0.111 4,810,844 3,666,667 810,844 884,472 1,695,316 5,361,982
2 798,304,684 0.139 4,805,520 3,658,896 813,996 1,104,931 1,918,927 5,577,823
3 796,385,757 0.167 4,798,862 3,650,101 816,933 1,324,754 2,141,687 5,791,788
⋮
29 674,744,235 0.865 4,184,747 3,092,578 811,026 5,829,438 6,640,464 9,733,042
30 668,103,771 0.865 4,148,550 3,062,142 808,031 5,772,024 6,580,055 9,642,198
⋮
100 326,937,929 0.865 2,258,348 1,498,466 623,659 2,822,577 3,446,236 4,944,702
101 323,491,693 0.865 2,238,814 1,482,670 621,355 2,792,788 3,414,143 4,896,814
⋮
200 103,307,518 0.865 947,322 473,493 430,784 889,871 1,320,655 1,794,148
201 101,986,863 0.865 939,128 467,440 429,193 878,461 1,307,654 1,775,094
⋮
300 19,963,930 0.865 397,378 91,501 297,559 170,112 467,670 559,172

301 19,496,260 0.865 393,941 89,358 296,460 166,076 462,536 551,893
⋮
356 484,954 0.865 244,298 2,223 241,873 2,103 243,976 246,199
357 240,978 0.865 242,185 1,104 240,980 0 240,980 242,084
Note : Since the WAM is 357 months, the underlying mortgage pool is seasoned an average of three months, and therefore based on a 165 
PSA, the CPR is 0.132% in month 1 (seasoned month 4), and the pool seasons at 6% in month 27.
10 The SMM in Column 3 is rounded, which results in some rounding error in the calculation of the 
prepayments in Column 7 and, thus, of the total principal repayments and the projected cash flows in 
Columns 8 and 9, respectively.

Residential Mortgage-  Backed Securities 495
5.1.5  Weighted Average Life
A standard practice in the bond market is to refer to the maturity of a bond. This 
practice is not followed for MBS because principal repayments (scheduled princi -
pal repayments and prepayments) are made over the life of the security. Although 
an MBS has a “legal maturity, ” which is the date when the last scheduled principal 
repayment is due, the legal maturity does not reveal much about the actual principal 
repayments and the interest rate risk associated with the MBS. For example, a 30-  
year, option-  free, corporate bond and an MBS with a 30-  year legal maturity with the 
same coupon rate are not equivalent in terms of interest rate risk. Effective duration 
can be calculated for both the corporate bond and the MBS to assess the sensitivity 
of the securities to interest rate movements. But a measure widely used by market 
participants for MBS is the weighted average life  or simply the average life  of the

MBS. This measure gives investors an indication of how long they can expect to hold 
the MBS before it is paid off assuming interest rates stay at current levels and, thus, 
expected prepayments are realized. In other words, the average life of the MBS is the 
convention-  based average time to receipt of all the projected principal repayments 
(scheduled principal repayments and projected prepayments).
A mortgage pass-  through security’s average life depends on the prepayment 
assumption, as illustrated in the following table. This table provides the average life 
of the mortgage pass-  through security used in Exhibit 2 for various prepayment rates. 
Note that at the assumed prepayment rate of 165 PSA, the mortgage pass-  through 
security has an average life of 8.6 years. The average life extends when the prepay -
ment rate goes down and contracts rapidly as the prepayment rate goes up. So, at a 
prepayment rate of 600 PSA, the average life of the mortgage pass-  through security

is only 3.2 years.
PSA assumption 100 125 165 250 400 600
Average life (years) 11.2 10.1 8.6 6.4 4.5 3.2
EXAMPLE 7   
Mortgage Pass-  Through Securities
1 A non-  conforming mortgage:
A cannot be used as collateral in a mortgage-  backed security.
B does not satisfy the underwriting standards for inclusion as collateral 
for an agency residential mortgage-  backed security.
C does not give the lender a claim against the borrower for the shortfall 
between the amount of the outstanding mortgage balance and the 
proceeds from the sale of the property in the event that the borrower 
defaults on the mortgage.
2 The monthly cash flows of a mortgage pass-  through security most likely :
A are constant.
B change when interest rates decline.
C are equal to the cash flows of the underlying pool of mortgages.
3 A prepayment rate of 80 PSA means that investors can expect:
A 80% of the par value of the mortgage pass-  through security to be 
repaid prior to the security’s maturity.

Reading 53 ■ Introduction to Asset-  Backed Securities 496
B 80% of the borrowers whose mortgages are included in the collat -
eral backing the mortgage pass-  through security to prepay their 
mortgages.
C the prepayment rate of the mortgages included in the collateral 
backing the mortgage pass-  through security to be 80% of the monthly 
prepayment rates forecasted by the PSA model.
4 All else being equal, when interest rates decline:
A investors in mortgage pass-  through securities face extension risk.
B the weighted average maturity of a mortgage pass-  through security 
lengthens.
C the increase in the price of a mortgage pass-  through security is less 
than the increase in the price of an otherwise identical bond with no 
prepayment option.
B is correct. A non-  conforming mortgage is one that does not satisfy the under -
writing standards for inclusion as collateral for an agency RMBS. The standards 
specify the maximum size of the loan, the loan documentation required, the

maximum loan-  to- value ratio, and whether or not insurance is required for the 
loans in the pool.
B is correct. The monthly cash flows of a mortgage pass-  through security depend 
on the cash flows of the underlying pool of mortgages, but their amount and 
timing cannot be known with certainty because of prepayments. When inter -
est rates decline, borrowers are likely to prepay all or part of their outstanding 
mortgage balance, which will affect the monthly cash flows of the mortgage 
pass-  through security. Remember that the fees related to servicing and guaran -
teeing the mortgages reduce the monthly cash flows of a mortgage pass-  through 
security relative to those of the underlying pool of mortgages.
C is correct. A prepayment rate of 80 PSA means that investors can expect the 
prepayment rate of the mortgages included in the collateral backing the mortgage 
pass-  through security to be 80% of the monthly prepayment rates forecasted by

the PSA model. For example, if the PSA model forecasts an increase in prepay -
ment rates of 0.20% for the first 30 months until they peak at 6% in Month 30, 
80 PSA would assume an increase in prepayment rates of 0.16% (80% × 0.20%) 
for the first 30 months until they peak at 4.80% (80% × 6%) in Month 30. Thus, 
investors can expect slower prepayments than the PSA prepayment benchmark.
C is correct. When interest rates decline, the prepayment rate on a mortgage 
pass-  through security goes up because homeowners refinance at now-  available 
lower interest rates. As a result, investors face contraction risk; that is, they 
receive payments faster than anticipated. Investors who decide to retain the 
security face the prospect of having to reinvest those payments at relatively low 
interest rates. Investors who decide to sell the security would have to do so at a 
price lower than that of an otherwise identical bond with no prepayment option 
and thus no prepayment risk.

Residential Mortgage-  Backed Securities 497
5.2 Collateralized Mortgage Obligations
As noted in the previous section, prepayment risk is an important consideration 
when investing in mortgage pass-  through securities. Some institutional investors are 
concerned with extension risk and others with contraction risk. The structuring of a 
securitization can help redistribute the cash flows of mortgage-  related products (mort -
gage pass-  through securities or pools of loans) to different bond classes or tranches, 
which leads to the creation of securities that have different exposures to prepayment 
risk and thus different risk–return patterns relative to the mortgage-  related product 
from which they were created.
When the cash flows of mortgage-  related products are redistributed to various 
tranches, the resulting securities are called collateralized mortgage obligations  
(CMOs). The mortgage-  related products from which the cash flows are obtained are

considered the collateral. Note that in contrast to a mortgage pass-  through security, 
the collateral is not a pool of mortgages but a mortgage pass-  through security. In fact, 
in practice, the collateral is usually a pool of mortgage pass-  through securities—hence 
the reason market participants sometimes use the terms “collateral” and “mortgage 
pass-  through securities” interchangeably.
The creation of a CMO cannot eliminate or change prepayment risk; it can only 
distribute the various forms of this risk among different bond classes. The CMO’s 
major financial innovation is that securities can be created to closely satisfy the asset/
liability needs of institutional investors, thereby broadening the appeal of mortgage-  
backed products.
A wide range of CMO structures exists. The major ones are reviewed in the fol -
lowing subsections.
5.2.1  Sequential-  Pay CMO Structures
The first CMO was structured so that each tranche would be retired sequentially. Such

structures are called “sequential-  pay CMOs. ” The rule for the monthly distribution 
of the principal repayments (scheduled principal repayment plus prepayments) to 
the tranches in this structure is as follows. First, distribute all principal payments to 
Tranche 1 until the principal balance for Tranche 1 is zero. After Tranche 1 is paid off, 
distribute all principal payments to Tranche 2 until the principal balance for Tranche 
2 is zero. And so on.
To illustrate a sequential-  pay CMO, let us use a hypothetical transaction called 
CMO-  01. Assume that the collateral for CMO-  01 is the mortgage pass-  through 
security described in Exhibit 2 in Section 5.1.4. Recall that the total par value of the 
collateral is US$800 million, the pass-  through coupon rate is 5.5%, the WAC is 6%, 
and the WAM is 357 months. From this US$800 million of collateral, four tranches are 
created, as shown in Exhibit 3. In this simple structure, the coupon rate is the same

for each tranche and also the same as the mortgage pass-  through security’s coupon 
rate. This feature is for simplicity; typically, the coupon rate varies by tranche.11
11 Keep in mind that the coupon rate for a tranche is affected by the term structure of interest rates (that 
is, basically, the yield curve). Typically, yield increases as maturity increases. A CMO has tranches with 
different average lives. Usually, the longer the average life, the higher the coupon rate should be. So, in 
the hypothetical four-  tranche sequential-  pay structure shown in Exhibit 3, Tranche A might have a 4.2% 
coupon rate, Tranche B a 4.8% coupon rate, Tranche C a 5.2% coupon rate, and Tranche D a 5.5% coupon 
rate. In any event, investors evaluate each tranche on the basis of its perceived risk and price it accordingly. 
Consequently, investors pay a price for the tranche that reflects the yield they expect to receive given the

particular coupon rate. Separately, the difference between the coupon rate paid by the underlying pool of 
mortgages net of servicing and other administrative fees (that is, the net coupon—5.5% in our example) 
and the coupon rate paid to each of the tranches that has a coupon rate of less than the net coupon is used 
to create securities called “structured interest-  only tranches. ” A discussion of these tranches is beyond the 
scope of this reading.

Reading 53 ■ Introduction to Asset-  Backed Securities 498
Exhibit 3   CMO-  01: Sequential-  Pay CMO Structure with Four Tranches
Tranche Par Amount (US$ millions) Coupon Rate (%)
A 389 5.5
B 72 5.5
C 193 5.5
D 146 5.5
  Total 800
Payment rules: For payment of monthly coupon interest:  Disburse monthly coupon interest to each 
tranche on the basis of the amount of principal outstanding for each tranche at the beginning of the 
month. For disbursement of principal payments:  Disburse principal payments to Tranche A until it is 
completely paid off. After Tranche A is completely paid off, disburse principal payments to Tranche 
B until it is completely paid off. After Tranche B is completely paid off, disburse principal payments 
to Tranche C until it is completely paid off. After Tranche C is completely paid off, disburse principal 
payments to Tranche D until it is completely paid off.
Remember that a CMO is created by redistributing the cash flows—interest pay -

ments and principal repayments—to the various tranches on the basis of a set of pay -
ment rules. The payment rules at the bottom of Exhibit 3 describe how the cash flows 
from the mortgage pass-  through security are to be distributed to the four tranches. 
CMO-  01 has separate rules for the interest payment and the principal repayment, 
the latter being the sum of the scheduled principal repayment and the prepayments.
Although the payment rules for the distribution of the principal repayments are 
known, the precise amount of the principal repayment in each month is not. This 
amount will depend on the cash flow of the collateral, which depends on the actual 
prepayment rate of the collateral. The assumed prepayment rate (165 PSA in Exhibit 2) 
allows determining only the projected, not the actual, cash flow.
Consider what has been accomplished by creating the sequential-  pay CMO-  01 
structure. Earlier, we saw that with a prepayment rate of 165 PSA, the mortgage pass-

through security’s average life was 8.6 years. Exhibit 4 reports the average life of the 
collateral and the four tranches assuming various actual prepayment rates. Note that 
the four tranches have average lives that are shorter or longer than the collateral, 
thereby attracting investors who have preferences for different average lives. For 
example, a pension fund that needs cash only after a few years because it expects a 
significant increase in the number of retirements after that time may opt for a tranche 
with a longer average life.
Exhibit 4   Average Life of the Collateral and the Four Tranches of CMO-  01 
for Various Actual Prepayment Rates
Prepayment 
RateAverage Life (years)
Collateral Tranche A Tranche B Tranche C Tranche D
100 PSA 11.2 4.7 10.4 15.1 24.0
125 PSA 10.1 4.1 8.9 13.2 22.4
165 PSA 8.6 3.4 7.3 10.9 19.8
250 PSA 6.4 2.7 5.3 7.9 15.2
400 PSA 4.5 2.0 3.8 5.3 10.3
600 PSA 3.2 1.6 2.8 3.8 7.0

Residential Mortgage-  Backed Securities 499
A major problem that remains is the considerable variability of the average lives 
of the tranches. How this problem can be handled is shown in the next section, but 
at this point, note that some protection against prepayment risk is provided for each 
tranche. The protection arises because prioritizing the distribution of principal (that 
is, establishing the payment rule for the principal repayment) effectively protects the 
shorter-  term tranche (A in this structure) against extension risk. This protection must 
come from somewhere; it actually comes from the longer-  term tranches. Similarly, 
Tranches C and D provide protection against extension risk for Tranches A and B. 
At the same time, Tranches C and D benefit because they are provided protection 
against contraction risk; this protection comes from Tranches A and B. Thus, the 
sequential-  pay CMO-  01 structure allows investors concerned about extension risk

to invest in Tranches A or B and those concerned about contraction risk to invest in 
Tranches C or D.
5.2.2  CMO Structures Including Planned Amortization Class and Support Tranches
A common structure in CMOs is to include planned amortization class (PAC) 
tranches , which offer greater predictability of the cash flows as long as the prepayment 
rate is within a specified band over the collateral’s life. Remember that the creation of 
an MBS, whether it is a mortgage pass-  through or a CMO, cannot make prepayment 
risk disappear. So where does the reduction of prepayment risk (both extension risk 
and contraction risk) that PAC tranches offer investors come from? The answer is 
that it comes from the existence of non-  PAC tranches, called support tranches  or 
companion tranches. The structure of the CMO makes the support tranches absorb 
prepayment risk first. Because PAC tranches have limited (but not complete) protection

against both extension risk and contraction risk, they are said to provide two-  sided 
prepayment protection.
The greater predictability of the cash flows for the PAC tranches occurs because 
a principal repayment schedule must be satisfied. As long as the prepayment rate is 
within the specified band, called the PAC band, all prepayment risk is absorbed by 
the support tranche. If the collateral prepayments are slower than forecasted, the sup -
port tranches do not receive any principal repayment until the PAC tranches receive 
their scheduled principal repayment. This rule reduces the extension risk of the PAC 
tranches. Similarly, if the collateral prepayments are faster than forecasted, the sup -
port tranches absorb any principal repayments in excess of the scheduled principal 
repayments. This rule reduces the contraction risk of the PAC tranches. Even if the 
prepayment rate is outside the PAC band, prepayment risk is first absorbed by the

support tranche. Thus, the key to the prepayment protection that PAC tranches offer 
investors is the amount of support tranches outstanding. If the support tranches are 
paid off quickly because of faster-  than-  expected prepayments, they no longer provide 
any protection for the PAC tranches.
Support tranches expose investors to the highest level of prepayment risk. Therefore, 
investors must be particularly careful in assessing the cash flow characteristics of 
support tranches in order to reduce the likelihood of adverse portfolio consequences 
resulting from prepayments.
To illustrate how to create CMO structures including PAC and support tranches, 
we use again the US$800 million mortgage pass-  through security described in Exhibit 2 
in Section 5.1.4, with a pass-  through coupon rate of 5.5%, a WAC of 6%, and a WAM 
of 357 months as collateral. The creation of PAC tranches requires the specification 
of two PSA prepayment rates: a lower  PSA prepayment assumption and an upper

PSA prepayment assumption. The lower and upper PSA prepayment assumptions are 
called the “initial PAC collar” or the “initial PAC band. ” The PAC collar for a CMO 
is typically dictated by market conditions. In our example, we assume that the lower 
and upper PSA prepayment assumptions are 100 PSA and 250 PSA, respectively, so 
the initial PAC collar is 100–250 PSA.

Reading 53 ■ Introduction to Asset-  Backed Securities 500
Exhibit 5 shows a CMO structure called CMO-  02 that contains only two tranches: 
a 5.5% coupon PAC tranche created assuming an initial PAC collar of 100–250 PSA 
and a support tranche.
Exhibit 5   CMO-  02: CMO Structure with One PAC Tranche and One Support 
Tranche
Tranche Par Amount (US$ million) Coupon Rate (%)
P (PAC) 487.6 5.5
S (support) 312.4 5.5
  Total 800.0
tranche on the basis of the amount of principal outstanding for each tranche at the beginning of 
the month. For disbursement of principal payments:  Disburse principal payments to Tranche P on 
the basis of its schedule of principal repayments. Tranche P has priority with respect to current and 
future principal payments to satisfy the schedule. Any excess principal payments in a month over

the amount necessary to satisfy the schedule for Tranche P are paid to Tranche S. When Tranche S 
is completely paid off, all principal payments are to be made to Tranche P regardless of the schedule.
Exhibit 6 reports the average life of the PAC and support tranches in CMO-  02 
assuming various actual prepayment rates. Note that between 100 PSA and 250 PSA, 
the average life of the PAC tranche is constant at 7.7 years. At slower or faster PSA 
rates, however, the schedule is broken and the average life changes—extending when 
the prepayment rate is less than 100 PSA and contracting when it is greater than 250 
PSA. Even so, there is much less variability for the average life of the PAC tranche 
compared with that of the support tranche.
Exhibit 6   Average Life of the PAC Tranche and the Support Tranche of CMO-  
02 for Various Actual Prepayment Rates and an Initial PAC Collar 
of 100–250 PSA
Prepayment RateAverage Life (years)
PAC Tranche (P) Support Tranche (S)
50 PSA 10.2 24.9
75 PSA 8.6 22.7

100 PSA 7.7 20.0
165 PSA 7.7 10.7
250 PSA 7.7 3.3
400 PSA 5.5 1.9
600 PSA 4.0 1.4
Most CMO structures including PAC and support tranches have more than 
one PAC tranche. A sequence of six PAC tranches (that is, PAC tranches paid off  
in sequence as specified by a principal repayment schedule) is not uncommon. For 
example, consider CMO-  03 in Exhibit 7, which contains four sequential PAC tranches 
(P- A, P-  B, P-  C, and P-  D) and one support tranche. The total par amount of the PAC 
and support tranches is the same as for CMO-  02 in Exhibit 5. The difference is that 
instead of one PAC tranche with a schedule, there are four PAC tranches with sched -
ules. As described in the payment rules, the PAC tranches are paid off in sequence.

Residential Mortgage-  Backed Securities 501
Exhibit 7   CMO-  03: CMO Structure with Sequential PAC Tranches and One 
Support Tranche
P- A (PAC) 287.6 5.5
P- B (PAC) 90.0 5.5
P- C (PAC) 60.0 5.5
P- D (PAC) 50.0 5.5
month. For disbursement of principal payments:  Disburse principal payments to Tranche P-  A on the 
basis of its schedule of principal repayments. Tranche P-  A has priority with respect to current and 
future principal payments to satisfy the schedule. Any excess principal payments in a month over 
the amount necessary to satisfy the schedule while P-  A is outstanding is paid to Tranche S. Once 
P- A is paid off, disburse principal payments to Tranche P-  B on the basis of its schedule of principal

repayments. Tranche P-  B has priority with respect to current and future principal payments to satisfy 
the schedule. Any excess principal payments in a month over the amount necessary to satisfy the 
schedule while P-  B is outstanding are paid to Tranche S. The same rule applies for P-  C and P-  D. 
When Tranche S is completely paid off, all principal payments are to be made to the outstanding 
PAC tranches regardless of the schedule.
5.2.3  Other CMO Structures
Often, there is a demand for tranches that have a floating rate. Although the collateral 
pays a fixed rate, it is possible to create a tranche with a floating rate. This is done by 
constructing a floater and an inverse floater combination from any of the fixed-  rate 
tranches in the CMO structure. Because the floating-  rate tranche pays a higher rate 
when interest rates go up and the inverse floater pays a lower rate when interest rates 
go up, they offset each other. Thus, a fixed-  rate tranche can be used to satisfy the

demand for a floating-  rate tranche.
In a similar vein, other types of tranches to satisfy the various needs of investors 
are possible.
EXAMPLE 8   
Collateralized Mortgage Obligations
1 A collateralized mortgage obligation:
A eliminates prepayment risk.
B is created from a pool of conforming loans.
C redistributes various forms of prepayment risk among different bond 
classes.
2 The variability in the average life of the PAC tranche of a CMO relative to 
the average life of the mortgage pass-  through securities from which the 
CMO is created is:
A lower.
B the same.
C higher.

Reading 53 ■ Introduction to Asset-  Backed Securities 502
3 Referring to Exhibit 7, the tranche of CMO-  03 that is most suitable  for an 
investor concerned about contraction risk is:
A P- A (PAC).
B P- D (PAC).
C S (support).
4 The tranche of a collateralized mortgage obligation that is most suitable  
for an investor who expects a fall in interest rates is:
A a fixed-  rate tranche.
B an inverse floating-  rate tranche.
C a PAC tranche.
5 The investment that is most suitable  for an investor who is willing and 
able to accept significant prepayment risk is:
A a mortgage pass-  through security.
B the support tranche of a collateralized mortgage obligation.
C the inverse floating-  rate tranche of a collateralized mortgage 
obligation.
C is correct. CMOs are created by redistributing the cash flows of mortgage-  
related products, including mortgage pass-  through securities, to different bond 
classes or tranches on the basis of a set of payment rules.

A is correct. The purpose of creating different bond classes in a CMO is to provide 
a risk–return profile that is more suitable to investors than the risk-  return profile 
of the mortgage pass-  through securities from which the CMO is created. The 
PAC tranche has considerably less variability in average life than the mortgage 
pass-  through securities. In contrast, the support tranche has more variability 
in average life than the mortgage pass-  through securities.
B is correct. Contraction risk is the risk that when interest rates decline, pre -
payments will be higher than expected and the security’s maturity will become 
shorter than was anticipated at the time of purchase. PAC tranches offer investors 
protection against contraction risk (and extension risk). The PAC tranche that is 
most suitable for an investor concerned about contraction risk is P-  D because 
it is the latest-  payment PAC tranche; that is, any principal repayments in excess

of the scheduled principal repayments are absorbed sequentially by the support 
tranche, then P-  A, P-  B, and, finally, P-  D.
B is correct. The tranche of a CMO that is most suitable for an investor who 
expects a fall in interest rates is an inverse floating-  rate tranche. The inverse 
floater pays a coupon rate that is inversely related to prevailing interest rates. 
Thus, if interest rates fall, the CMO’s coupon rate will rise.
B is correct. The investment that is most suitable to an investor who is willing 
and able to accept significant prepayment risk is the support tranche of a col -
lateralized mortgage obligation. Because the PAC tranche has a stable average 
life at prepayment rates within the PAC band, all prepayment risk is absorbed 
by the support tranche for prepayment rates within the band. Even at rates

Commercial Mortgage-  Backed Securities 503
outside the PAC band, prepayment risk is first absorbed by the support tranche. 
Investors will be compensated for bearing prepayment risk in the sense that, if 
properly priced, the support tranche will have a higher expected rate of return 
than the PAC tranche.
5.3 Non-  agency Residential Mortgage-  Backed Securities
Agency RMBS are those issued by Ginnie Mae, Fannie Mae, and Freddie Mac. RMBS 
issued by any other entity are non-  agency RMBS. Entities that issue non-  agency RMBS 
are typically thrift institutions, commercial banks, and private conduits. Private con -
duits may purchase non-  conforming mortgages, pool them, and then sell mortgage 
pass-  through securities whose collateral is the underlying pool of non-  conforming 
mortgages. Because they are not guaranteed by the government or by a GSE, credit 
risk is an important consideration when investing in non-  agency RMBS.

Non-  agency RMBS share many features and structuring techniques with agency 
CMOs. However, because non-  agency RMBS are not guaranteed by the US govern -
ment or by a GSE that can provide protection against losses in the pool, some form 
of internal or external credit enhancement is necessary to make these securities 
attractive to investors. These credit enhancements allow investors to reduce credit 
risk or transfer credit risk between bond classes, thus enabling investors to choose 
the risk–return profile that best suits their needs. Credit enhancements also play an 
important role in obtaining favorable credit ratings, which make non-  agency RMBS 
more marketable to investors. The level of credit enhancement is usually determined 
relative to a specific credit rating desired by the issuer for a security. Note that one of 
the consequences of the 2007–2009 credit crisis has been an overall increase in the 
level of credit enhancement.

As mentioned in Section 3.3, subordination, or credit tranching, is a common 
form of credit enhancement. The subordination levels (that is, the amount of credit 
protection for a bond class) are set at the time of issuance. However, the subordina -
tion levels change over time, as voluntary prepayments and defaults occur. To protect 
investors in non-  agency RMBS, a securitization is designed to keep the amount of 
credit enhancement from deteriorating over time. If the credit enhancement for senior 
tranches deteriorates because of poor performance of the collateral, a mechanism 
called the “shifting interest mechanism” locks out subordinated bond classes from 
receiving payments for a period of time. Many non-  agency RMBS also include other 
credit enhancements, such as overcollateralization and reserve accounts.
When forecasting the future cash flows of non-  agency RMBS, investors must con -

sider two important components. The first is the assumed default rate for the collateral. 
The second is the recovery rate, because even though the collateral may default, not 
all of the outstanding mortgage balance may be lost. The repossession and subsequent 
sale of the recovered property may provide cash flows that will be available to pay 
bondholders. That amount is based on the assumed amount that will be recovered.
The focus in Section 5 is on securities backed by a pool of residential mortgages. 
The next section discusses securities backed by a pool of commercial mortgages.
COMMERCIAL MORTGAGE-  BACKED SECURITIES
Commercial mortgage-  backed securities (CMBS) are backed by a pool of commer -
cial mortgages on income-  producing property, such as multifamily properties (e.g., 
apartment buildings), office buildings, industrial properties (including warehouses), 6

Reading 53 ■ Introduction to Asset-  Backed Securities 504
shopping centers, hotels, and health care facilities (e.g., senior housing care facilities). 
The collateral is a pool of commercial loans that were originated either to finance a 
commercial purchase or to refinance a prior mortgage obligation.
6.1 Credit Risk
In the United States and other countries where commercial mortgages are non-  recourse 
loans, the lender can look only to the income-  producing property backing the loan 
for interest payments and principal repayments. If a default occurs, the lender can 
foreclose the commercial property but it can only use the proceeds from the sale 
of that property to recover the principal outstanding, and it has no recourse to the 
borrower’s other assets and/or income for any unpaid balance. The lender must view 
each property individually, and lenders evaluate each property using measures that 
have been found useful in assessing credit risk.

Two measures that have been found to be key indicators of potential credit per -
formance are the loan-  to- value ratio (LTV), which was discussed in Section 4, and the 
debt-  service-  coverage (DSC) ratio, sometimes referred to as DSCR. The DSC ratio is 
equal to the property’s annual net operating income (NOI) divided by the debt service 
(that is, the annual amount of interest payments and principal repayments). The NOI 
is defined as the rental income reduced by cash operating expenses and a non-  cash 
replacement reserve reflecting the depreciation of the property over time. A DSC 
ratio that exceeds 1.0 indicates that the cash flows from the property are sufficient 
to cover the debt service while maintaining the property in its initial state of repair. 
The higher the DSC ratio, the more likely it is that the borrower will be able to meet 
debt-  servicing requirements from the property’s cash flows.
6.2 CMBS Structure

A credit-  rating agency determines the level of credit enhancement necessary to 
achieve a desired credit rating. For example, if specific loan-  to- value and DSC ratios 
are needed and those ratios cannot be met at the loan level, subordination is used to 
achieve the desired credit rating.
Interest on the principal outstanding is paid to all tranches. Losses arising from loan 
defaults are charged against the outstanding principal balance of the CMBS tranche 
with the lowest priority. This tranche may not be rated by credit-  rating agencies; in 
this case, this unrated tranche is called the “first-  loss piece, ” “residual tranche, ” or 
“equity tranche. ” The total loss charged includes the amount previously advanced and 
the actual loss incurred in the sale of the loan’s underlying property.
Two characteristics that are usually specific to CMBS structures are the presence 
of a call protection and a balloon maturity provision.
6.2.1  Call Protection

A critical investment feature that distinguishes CMBS from RMBS is the protection 
against early prepayments available to investors’ known as a call protection . An investor 
in an RMBS is exposed to considerable prepayment risk because the borrower has the 
right to prepay a loan, in whole or in part, before the scheduled principal repayment 
date. As explained in Section 4.4, a borrower in the United States usually does not pay 
any penalty for prepayment. The discussion of CMOs highlighted how investors can 
purchase certain types of tranches (e.g., sequential-  pay and PAC tranches) to modify 
or reduce prepayment risk.
With CMBS, investors have considerable call protection. In fact, it is this protec -
tion that results in CMBS trading in the market more like corporate bonds than like 
RMBS. The call protection comes either at the structure level or at the loan level.

Commercial Mortgage-  Backed Securities 505
Structural call protection is achieved when CMBS are structured to have sequential-  
pay tranches, by credit rating. A lower-  rated tranche cannot be paid down until the 
higher-  rated tranche is completely retired, so the AAA rated bonds must be paid off  
before the AA rated bonds are, and so on. Principal losses resulting from defaults, 
however, are affected from the bottom of the structure upward.
At the loan level, four mechanisms offer investors call protection:
■■A prepayment lockout, which is a contractual agreement that prohibits any 
prepayments during a specified period of time.
■■Prepayment penalty points, which are predetermined penalties that a borrower 
who wants to refinance must pay to do so—a point is equal to 1% of the out -
standing loan balance.
■■A yield maintenance charge, also called a “make-  whole charge, ” which is a 
penalty paid by the borrower that makes refinancing solely to get a lower

mortgage rate uneconomical for the borrower. In its simplest terms, a yield 
maintenance charge is designed to make the lender indifferent as to the timing 
of prepayments.
■■Defeasance, for which the borrower provides sufficient funds for the servicer to 
invest in a portfolio of government securities that replicates the cash flows that 
would exist in the absence of prepayments. The cash payments that must be 
met by the borrower are projected on the basis of the terms of the loan. Then, a 
portfolio of government securities is constructed in such a way that the interest 
payments and the principal repayments from the portfolio will be sufficient to 
pay off each obligation when it comes due. When the last obligation is paid off, 
the value of the portfolio is zero (that is, there are no funds remaining). The 
cost of assembling such a portfolio is the cost of defeasing the loan that must be 
repaid by the issuer.12
6.2.2  Balloon Maturity Provision

Many commercial loans backing CMBS are balloon loans that require a substantial 
principal repayment at maturity of the loan. If the borrower fails to make the balloon 
payment, the borrower is in default. The lender may extend the loan over a period 
of time called the “workout period. ” In doing so, the lender may modify the original 
terms of the loan and charge a higher interest rate, called the “default interest rate, ” 
during the workout period.
The risk that a borrower will not be able to make the balloon payment because 
either the borrower cannot arrange for refinancing or cannot sell the property to 
generate sufficient funds to pay off the outstanding principal balance is called “balloon 
risk. ” Because the life of the loan is extended by the lender during the workout period, 
balloon risk is a type of extension risk.
12 This portfolio strategy for paying off liabilities is used by insurance companies. In the United States, it

has also been used by municipal bond issuers; the resulting bonds are referred to as “pre-  refunded bonds. ”

Reading 53 ■ Introduction to Asset-  Backed Securities 506
EXAMPLE 9   
An Example of a Commercial Mortgage-  Backed Security
The following information is taken from a filing with the US Securities and 
Exchange Commission about a CMBS issued in April  2013 by Citigroup 
Commercial Mortgage Trust 2013-  GCJ11. The collateral for this CMBS is a pool 
of 72 fixed-  rate mortgages secured by first liens (first claims) on various types 
of commercial, multifamily, and manufactured housing community properties.
Classes of Offered 
CertificatesInitial Principal Amount 
(US$)Initial Pass-  Through 
Rate (%)
A- 1 75,176,000 0.754
A- 2 290,426,000 1.987
A- 3 150,000,000 2.815
A- 4 236,220,000 3.093
A- AB 92,911,000 2.690
X- A 948,816,000 1.937
A- S 104,083,000 3.422
B 75,423,000 3.732
C 42,236,000
The filing includes the following statements:
If you acquire Class B certificates, then your rights to receive 
distributions of amounts collected or advanced on or in respect of

the mortgage loans will be subordinated to those of the holders of 
the Class A-  1, Class A-  2, Class A-  3, Class A-  4, Class A-  AB, Class 
X- A, and Class A-  S certificates. If you acquire Class C certificates, 
then your rights to receive distributions of amounts collected or 
advanced on or in respect of the mortgage loans will be subordinated 
to those of the holders of the Class B certificates and all other classes 
of offered certificates.
“Prepayment Penalty Description” or “Prepayment Provision” 
means the number of payments from the first due date through and 
including the maturity date for which a mortgage loan is, as appli -
cable, (i) locked out from prepayment, (ii) provides for payment of 
a prepayment premium or yield maintenance charge in connection 
with a prepayment, (iii) permits defeasance.
1 Based on the information provided, this CMBS:
A does not include any credit enhancement. 
B includes an internal credit enhancement.
C includes an external credit enhancement.

2 Based on the information provided, investors in this CMBS have prepay -
ment protection at:
A the loan level. 
B the structure level.
C both the loan and structure levels.
3 Defeasance can be best described as:
A a predetermined penalty that a borrower who wants to refinance must 
pay to do so.

Commercial Mortgage-  Backed Securities 507
B a contractual agreement that prohibits any prepayments during a 
specified period of time. 
C funds that the borrower must provide to replicate the cash flows that 
would exist in the absence of prepayments.
4 A risk that investors typically face when holding CMBS is:
A call risk
B balloon risk.
C contraction risk.
5 The credit risk of a commercial mortgage-  backed security is lower:
A the lower the DSC ratio and the lower the LTV.
B the lower the DSC ratio and the higher the LTV.
C the higher the DSC ratio and the lower the LTV.
B is correct. The CMBS includes a senior/subordinated structure, which is a 
form of internal credit enhancement. Class B provides protection for all of the 
bond classes listed above it. Similarly, Class C provides protection for all other 
bond classes, including Class B; it is the first-  loss piece, also called the residual 
tranche or equity tranche. Note that because it is the residual tranche, Class C

has no specific pass-  through rate. Investors in Class C will price it on the basis 
of some expected residual rate of return, but they could do better or worse than 
expected depending on how interest rate movements and default rates affect 
the performance of the other tranches.
C is correct. This CMBS offers investors prepayment protection at both the 
structure and loan levels. The structural call protection is achieved thanks to the 
sequential-  pay tranches. At the loan level, the CMBS includes three of the four 
types of call protection—namely, a prepayment lockout, a yield maintenance 
charge, and defeasance.
C is correct. Defeasance is a call protection at the loan level that requires the 
borrower to provide sufficient funds for the servicer to invest in a portfolio 
of government securities that replicates the cash flows that would exist in the 
absence of prepayments.
B is correct. Because many commercial loans backing CMBS require a balloon

payment, investors in CMBS typically face balloon risk—that is, the risk that if 
the borrower cannot arrange for refinancing or cannot sell the property to make 
the balloon payment, the CMBS may extend in maturity because the lender has 
to wait to obtain the outstanding principal until the borrower can make the 
balloon amount. Balloon risk is a type of extension risk.
C is correct. The DSC ratio and the LTV are key indicators of potential credit 
performance and thus allow investors to assess the credit risk of a CMBS. The 
DSC ratio is equal to the property’s annual NOI divided by the annual amount 
of interest payments and principal repayments. So the higher the DSC ratio, the

Reading 53 ■ Introduction to Asset-  Backed Securities 508
lower the CMBS’s credit risk. The LTV is equal to the amount of the mortgage 
divided by the property’s value. So the lower the LTV, the lower the CMBS’s 
credit risk.
To this point, this reading has addressed the securitization of real estate property, 
both residential and commercial. Section 7 discusses the securitization of debt obli -
gations in which the underlying asset is not real estate.
NON-  MORTGAGE ASSET-  BACKED SECURITIES
Numerous types of non-  mortgage assets have been used as collateral in securitization. 
The largest in most countries are auto loan and lease receivables, credit card receiv -
ables, personal loans, and commercial loans. What is important to keep in mind is 
that, regardless of the type of asset, ABS that are not guaranteed by a government or 
a quasi-  government entity are subject to credit risk.
ABS can be categorized on the basis of the way the collateral repays—that is,

whether the collateral is amortizing or non-  amortizing. Traditional residential mort -
gages and auto loans are examples of amortizing loans. The cash flows for an amortizing 
loan include interest payments, scheduled principal repayments and any prepayments, 
if permissible. If the loan has no schedule for paying down the principal, it is a non-  
amortizing loan. Because a non-  amortizing loan does not involve scheduled principal 
repayments, an ABS backed by non-  amortizing loans is not affected by prepayment risk. 
Credit card receivable ABS are an example of ABS backed by non-  amortizing loans.
Consider an ABS backed by a pool of 1,000 amortizing loans with a total par value 
of US$100 million. Over time, some of the loans will be paid off; the amounts received 
from the scheduled principal repayment and any prepayments will be distributed 
to the bond classes on the basis of the payment rule. Consequently, over time, the

number of loans in the collateral will drop from 1,000 and the total par value will fall 
to less than US$100 million.
Now, what happens if the collateral of the ABS is 1,000 non-  amortizing loans? 
Some of these loans will be paid off in whole or in part before the maturity of the 
ABS. When those loans are paid off, what happens depends on whether the loans were 
paid off during the lockout period or after it. The lockout period or revolving period 
is the period during which the principal repaid is reinvested to acquire additional 
loans with a principal equal to the principal repaid. The reinvestment in new loans 
can result in the collateral including more or less than 1,000 loans, but the loans will 
still have a total par value of US$100 million. When the lockout period is over, any 
principal that is repaid will not be used to reinvest in new loans but will instead be 
distributed to the bond classes.
This reading cannot cover all types of non-  mortgage ABS. It focuses on the two

popular non-  mortgage ABS in most countries: auto loan ABS and credit card receiv -
able ABS.
7.1 Auto Loan ABS
Auto loan ABS are backed by auto loans and lease receivables. The focus in this section 
is on the largest type of auto securitizations—that is, auto loan-  backed securities. In 
some countries, auto loan-  backed securities represent the largest or second largest 
sector of the securitization market.7

Non-  Mortgage Asset-  Backed Securities 509
The cash flows for auto loan-  backed securities consist of scheduled monthly 
payments (that is, interest payments and scheduled principal repayments) and any 
prepayments. For securities backed by auto loans, prepayments result from sales 
and trade-  ins requiring full payoff of the loan, repossession and subsequent resale 
of autos, insurance proceeds received upon loss or destruction of autos, and early 
payoffs of the loans.
All auto loan-  backed securities have some form of credit enhancement, often a 
senior/subordinated structure. In addition, many auto loan-  backed securities come 
with overcollateralization and a reserve account, often an excess spread account. Recall 
from a previous reading that the excess spread, sometimes called excess interest cash 
flow, is an amount that can be retained and deposited into a reserve account and that 
can serve as a first line of protection against losses.

To illustrate the typical structure of auto loan-  backed securities, let us use the 
example of securities issued by Fideicomiso Financiero Autos VI. The collateral is a 
pool of 827 auto loans denominated in Argentine pesos (ARS).The loans were originated 
by BancoFinansur. The structure of the securitization includes three bond classes:
Bond ClassOutstanding 
Principal Balance at 
the end of 2012 (ARS)
Class A Floating-  Rate Debt Securities 22,700,000
Class B Floating-  Rate Debt Securities 1,970,000
Certificates 5,988,245
Total 30,658,245
The certificates provide credit protection for Class B, and Class B provides credit 
protection for Class A. Further credit enhancement comes from overcollateralization 
and the presence of an excess spread account. The reference rate for the floating-  rate 
debt securities is BADLAR (Buenos Aires Deposits of Large Amount Rate), the bench -
mark rate for loans in Argentina. This reference rate is the average rate on 30-  day

deposits of at least ARS1 million. For Class A, the interest rate is BADLAR plus 450 bps, 
with a minimum rate of 18% and a maximum rate of 26%; for Class B, it is BADLAR 
plus 650 bps, with 20% and 28% as the minimum and maximum rates, respectively. 
EXAMPLE 10   
An Example of an Auto Loan ABS
The following information is from the prospectus supplement for US$877,670,000 
of auto loan ABS issued by AmeriCredit Automobile Receivables Trust 2013–4:
The collateral for this securitization is a pool of sub-  prime automobile 
loan contracts secured for new and used automobiles and light-  duty 
trucks and vans.
The issuing entity will issue seven sequential-  pay classes of asset-  
backed notes pursuant to the indenture. The notes are designated as 
the “Class A-  1 Notes, ” the “Class A-  2 Notes, ” the “Class A-  3 Notes, ” 
the “Class B Notes, ” the “Class C Notes, ” the “Class D Notes, ” and 
the “Class E Notes. ” The Class A-  1 Notes, the Class A-  2 Notes, and

the Class A-  3 Notes are the “Class A Notes. ” The Class A Notes, the 
Class B Notes, the Class C Notes, and the Class D Notes are being 
offered by this prospectus supplement and are sometimes referred 
to as the publicly offered notes. The Class E Notes are not being

Reading 53 ■ Introduction to Asset-  Backed Securities 510
offered by this prospectus supplement and will initially be retained 
by the depositor or an affiliate of the depositor. The Class E Notes 
are sometimes referred to as the privately placed notes .
Each class of notes will have the initial note principal balance, 
interest rate, and final scheduled distribution date listed in the fol -
lowing tables:
Publicly Offered Notes
ClassInitial Note  
Principal Balance  
(US$)Interest Rate  
(%)Final Scheduled  
Distribution Date
A- 1 (senior) 168,000,000 0.25 8 August 2014
A- 2 (senior) 279,000,000 0.74 8 November 2016
A- 3 (senior) 192,260,000 0.96 9 April 2018
B (subordinated) 68,870,000 1.66 10 September 2018
C (subordinated) 85,480,000 2.72 9 September 2019
D (subordinated) 84,060,000 3.31 8 October 2019
Privately Placed Notes
E (subordinated) 22,330,000 4.01 8 January 2021

Interest on each class of notes will accrue during each interest 
period at the applicable interest rate.
The overcollateralization amount represents the amount by which 
the aggregate principal balance of the automobile loan contracts 
exceeds the principal balance of the notes. On the closing date, the 
initial amount of overcollateralization is approximately US$49,868,074 
or 5.25% of the aggregate principal balance of the automobile loan 
contracts as of the cutoff date.
On the closing date, 2.0% of the expected initial aggregate principal 
balance of the automobile loan contracts will be deposited into the 
reserve account, which is approximately US$18,997,361.
1 The reference to sub-  prime means that:
A the asset-  backed notes are rated below investment grade. 
B the automobile (auto) loan contracts were made to borrowers who do 
not have or cannot document strong credit.
C some of the auto loan contracts are secured by autos of low quality

that may be difficult to sell in case the borrower defaults.
2 Based on the information provided, if on the first distribution date there 
are losses on the loans of US$10 million:
A none of the classes of notes will incur losses. 
B Class E notes will incur losses of US$10 million.
C Classes B, C, D, and E will incur losses pro rata of their initial note 
principal balances.

Non-  Mortgage Asset-  Backed Securities 511
3 Based on the information provided, if the first loss on the loans is 
US$40 million over and above the protection provided by the internal 
credit enhancements and occurs in January 2014, which class(es) of notes 
realize losses?
A Class E and then Class D
B Each class of subordinated notes in proportion to its principal balance
C Class E and then each class of subordinated notes in proportion to its 
principal balance
B is correct. A subprime loan is one granted to borrowers with lower credit 
quality, who have typically experienced prior credit difficulties or who cannot 
otherwise document strong credit.
A is correct. The amount of the loss (US$10 million) is lower than the combined 
amount of overcollateralization and the reserve account (US$49,868,074  + 
US$18,997,361 = US$68,865,435). Therefore, none of the classes of notes will 
incur losses.

A is correct. Once the amount of losses exceeds the amount of protection pro -
vided by the overcollateralization and the reserve account, losses are absorbed 
by the bond classes. Because it is a sequential-  pay structure, Class E notes are 
the first ones to absorb losses, up to the principal amount of US$22,330,000. It 
means that there is still US$17,670,000 to be absorbed by another bond class, 
which would be the Class D notes.
7.2 Credit Card Receivable ABS
When a purchase is made on a credit card, the issuer of the credit card (the lender) 
extends credit to the cardholder (the borrower). Credit cards are issued by banks, 
credit card companies, retailers, and travel and entertainment companies. At the time 
of purchase, the cardholder agrees to repay the amount borrowed (that is, the cost of 
the item purchased) plus any applicable finance charges. The amount that the card -

holder agrees to pay the issuer of the credit card is a receivable from the perspective 
of the issuer of the credit card. Credit card receivables are used as collateral for the 
issuance of credit card receivable ABS.
For a pool of credit card receivables, the cash flows consist of finance charges 
collected, fees, and principal repayments. Finance charges collected represent the 
periodic interest the credit card borrower is charged on the unpaid balance after 
the grace period. The interest rate may be fixed or floating. The floating rate may be 
capped; that is, it may have an upper limit because some countries have usury rate 
laws that impose a cap on interest rates. Fees include late payment fees and any annual 
membership fees.
Interest is paid to holders of credit card receivable ABS periodically (e.g., monthly, 
quarterly, or semiannually). As noted earlier, the collateral of credit card receivable 
ABS is a pool of non-  amortizing loans. These loans have lockout periods during which

the cash flows that are paid out to security holders are based only on finance charges 
collected and fees. When the lockout period is over, the principal that is repaid by the 
cardholders is no longer reinvested but instead is distributed to investors.

Reading 53 ■ Introduction to Asset-  Backed Securities 512
Some provisions in credit card receivable ABS require early amortization of the 
principal if specific events occur. Such provisions are referred to as “early amortization” 
or “rapid amortization” provisions and are included to safeguard the credit quality of 
the issue. The only way the principal cash flows can be altered is by the triggering of 
the early amortization provision.
To illustrate the typical structure of credit card receivable ABS, consider the GE 
Capital Credit Card Master Note Trust Series 2013-  1 issued in March  2013. The 
originator of the credit card receivables is GE Capital Retail Bank, now known as 
Synchrony Bank, and the servicer is GE Capital Corporation. The collateral is a pool 
of credit card receivables from several private-  label and co-  branded credit card issu -
ers, including JCPenney, Lowe’s Home Improvement, Sam’s Club, Walmart, Gap, and

Chevron. The structure of the US$969,085,000 securitization is as follows: Class A 
notes for US$800,000,000, Class B notes for US$100,946,373, and Class C notes for 
US$68,138,802. Thus, the issue has a senior/subordinate structure. The Class A notes 
are the senior notes and were rated Aaa by Moody’s and AAA by Fitch. The Class B 
notes were rated A2 by Moody’s and A+ by Fitch. The Class C notes were rated Baa2 
by Moody’s and BBB+ by Fitch.
EXAMPLE 11   
Credit Card Receivable ABS vs. Auto Loan ABS
Credit card receivable asset-  backed securities (ABS) differ from auto loan ABS 
in the following way:
A credit card loans are recourse loans, whereas auto loans are non-  recourse 
loans.
B the collateral for credit card receivable-  backed securities is a pool of non-  
amortizing loans, whereas the collateral for auto loan ABS is a pool of 
amortizing loans. 
C credit card receivable-  backed securities have regular principal repay -

ments, whereas auto loan ABS include a lockout period during which the 
cash proceeds from principal repayments are reinvested in additional loan 
Solution:
B is correct. A main difference between credit card receivable ABS and auto 
loan ABS is the type of loans that back the securities. For credit card receivable 
ABS, the collateral is a pool of non-  amortizing loans. During the lockout period, 
the cash proceeds from principal repayments are reinvested in additional credit 
card receivables. When the lockout period is over, principal repayments are 
used to pay off the outstanding principal. For auto loan-  backed securities, the 
collateral is a pool of amortizing loans. Security holders receive regular principal 
repayments. As a result, the outstanding principal balance declines over time. 
COLLATERALIZED DEBT OBLIGATIONS
Collateralized debt obligation  (CDO) is a generic term used to describe a security

backed by a diversified pool of one or more debt obligations: CDOs backed by corporate 
and emerging market bonds are collateralized bond obligations (CBOs); CDOs backed 8

Collateralized Debt Obligations 513
by leveraged bank loans are collateralized loan obligations (CLOs); CDOs backed by 
ABS, RMBS, CMBS, and other CDOs are structured finance CDOs; CDOs backed by 
a portfolio of credit default swaps for other structured securities are synthetic CDOs.
8.1 CDO Structure
A CDO involves the creation of an SPE. In a CDO, there is a need for a CDO manager, 
also called “ collateral manager , ” to buy and sell debt obligations for and from the 
CDO’s collateral (that is, the portfolio of assets) to generate sufficient cash flows to 
meet the obligations to the CDO bondholders.
The funds to purchase the collateral assets for a CDO are obtained from the issuance 
of debt obligations. These debt obligations are bond classes or tranches and include 
senior bond classes, mezzanine bond classes (that is, bond classes with credit ratings 
between senior and subordinated bond classes), and subordinated bond classes, often

referred to as the residual or equity tranches. The motivation for investors to invest in 
senior or mezzanine bond classes is to earn a potentially higher yield than that on a 
comparably rated corporate bond by gaining exposure to debt products that they may 
not otherwise be able to purchase. Investors in equity tranches have the potential to 
earn an equity-  type return, thereby offsetting the increased risk from investing in the 
subordinated class. The key to whether or not a CDO is viable is whether a structure 
can be created that offers a competitive return for the subordinated tranche.
The basic economics of the CDO is that the funds are raised by the sale of the bond 
classes and the CDO manager invests those funds in assets. The CDO manager seeks 
to earn a rate of return higher than the aggregate cost of the bond classes. The return 
in excess of what is paid out to the bond classes accrues to the holders of the equity

tranche and to the CDO manager. In other words, a CDO is a leveraged transaction 
in which those who invest in the equity tranche use borrowed funds (the bond classes 
issued) to generate a return above the funding cost.
As with ABS, each CDO bond class is structured to provide a specific level of risk 
for investors. The CDO is constructed so as to impose restrictions on the CDO man -
ager via various tests and limits that must be satisfied for the CDO to meet investors’ 
varying risk appetites while still providing adequate protection for the senior bond 
class. If the CDO manager fails pre-  specified tests, a provision is triggered that requires 
the payoff of the principal to the senior bond class until the tests are satisfied. This 
process effectively deleverages the CDO because the cheapest funding source for the 
CDO, the senior bond class, is reduced.
The ability of the CDO manager to make the interest payments and principal

repayments depends on the performance of the collateral. The proceeds to meet the 
obligations to the CDO bond classes can come from one or more of the following 
sources: interest payments from collateral assets, maturing of collateral assets, and 
sale of collateral assets. The cash flows and credit risks of a CDO are best illustrated 
by an example.
8.2 An Example of a CDO Transaction
Although various motivations may prompt a sponsor to create a CDO, the following 
example uses a CDO for which the purpose is to capture what market participants 
mistakenly label a CDO arbitrage transaction. The term “arbitrage” is not used here 
in the traditional sense—that is, a risk-  free transaction that earns an expected posi -
tive net profit but requires no net investment of money. In this context, arbitrage is 
used in a loose sense to describe a transaction in which the motivation is to capture 
a spread between the return that could potentially be earned on the collateral and 
the funding cost.

Reading 53 ■ Introduction to Asset-  Backed Securities 514
To understand the structure of a CDO transaction and its risks, consider the 
following US$100 million issue:
Tranche Par Value (US$ million) Coupon Rate
Senior 80 Libora + 70 bps
Mezzanine 10 10- year US Treasury rate + 200 bps
Equity 10 —
a Libor is the dollar London Interbank Offered Rate, a commonly used reference rate for floating-  
rate debt.
Suppose that the collateral consists of bonds that all mature in 10 years and that 
the coupon rate for every bond is the 10-  year US Treasury rate plus 400 bps. Because 
the collateral pays a fixed rate (the 10-  year US Treasury rate plus 400 bps) but the 
senior tranche requires a floating-  rate payment (Libor plus 70 bps), the CDO manager 
enters into an interest rate swap agreement with another party. An interest rate swap 
is simply an agreement to periodically exchange interest payments. The payments 
are calculated based on a notional amount. This amount is not exchanged between

the two parties but is simply used to determine the amount of interest payment for 
each party. By construction, the notional amount of the interest rate swap is the par 
value of the senior tranche—that is, US$80 million in this example. Let us suppose 
that through the interest rate swap, the CDO manager agrees to do the following: (1) 
pay a fixed rate each year equal to the 10-  year US Treasury rate plus 100 bps and (2) 
receive Libor.
Assume that the 10-  year US Treasury rate at the time this CDO is issued is 7%. 
Now, consider the annual cash flow for the first year. First, let us look at the collateral. 
Assuming no default, the collateral will pay an interest rate equal to the 10-  year US 
Treasury rate of 7% plus 400 bps—that is, 11%. So, the interest payment is 11% × 
US$100,000,000 = US$11,000,000.
Now, let us determine the interest that must be paid to the senior and mezzanine 
tranches. For the senior tranche, the interest payment is US$80,000,000 × (Libor +

70 bps). For the mezzanine tranche, the coupon rate is the 10-  year US Treasury rate 
plus 200 bps—that is, 9%. So, the interest payment for the mezzanine tranche is 9% 
× US$10,000,000 = US$900,000.
Finally, consider the interest rate swap. In this agreement, the CDO manager 
agreed to pay the swap counterparty the 10-  year US Treasury rate plus 100 bps—
that is, 8%—based on a notional amount of US$80 million. So, the amount paid to 
the swap counterparty is 8% × US$80,000,000  = US$6,400,000 the first year. The 
amount received from the swap counterparty is Libor based on a notional amount of 
US$80 million—that is, Libor × US$80,000,000.
All of this information can now be put together. The cash inflows for the CDO are
Interest from collateral $11,000,000
Interest from swap counterparty $80,000,000 × Libor
  Total interest received $11,000,000 + $80,000,000 × Libor
The cash outflows for the CDO are
Interest to senior tranche $80,000,000 × (Libor + 70 bps)
Interest to mezzanine tranche $900,000

Interest to swap counterparty $6,400,000
  Total interest paid $7,300,000 + $80,000,000 × (Libor + 70 bps)

Collateralized Debt Obligations 515
Netting the total interest received ($11,000,000 + $80,000,000 × Libor) and the 
total interest paid ($7,300,000 + $80,000,000 × [Libor + 70 bps]) leaves a net interest 
of $3,700,000 – $80,000,000 × 70 bps = US$3,140,000. From this amount, any fees—
including the CDO manager’s fees—must be paid. The balance is then the amount 
available to pay the equity tranche. Suppose the CDO manager’s fees are US$640,000. 
The cash flow available to the equity tranche for the first year is US$2.5  million 
($3,140,000 − $640,000). Because the equity tranche has a par value of US$10 million 
and is assumed to be sold at par, the annual return is 25%.
Obviously, some simplifying assumptions have been made in this example. For 
instance, it is assumed that no defaults would occur. Furthermore, it is assumed that 
all of the securities purchased by the CDO manager are non-  callable and, thus, that

the coupon rate would not decline because of securities being called. Despite these 
simplifying assumptions, the example does demonstrate the economics of an arbitrage 
CDO transaction, the need for the use of an interest rate swap, and how the equity 
tranche will realize a return.
In practice, CDOs are subject to risks that investors should be aware of. For exam -
ple, in the case of defaults in the collateral, there is a risk that the manager will fail to 
earn a return sufficient to pay off the investors in the senior and mezzanine tranches, 
resulting in a loss for these investors. Investors in the equity tranche risk the loss of 
their entire investment. Even if payments are made to these investors, the return they 
realize may not be the return expected at the time of purchase.
Moreover, after some period, the CDO manager must begin repaying principal 
to the senior and mezzanine tranches. The interest rate swap must be structured to

take this requirement into account because the entire amount of the senior tranche 
is not outstanding for the life of the collateral.
EXAMPLE 12   
Collateralized Debt Obligations
An additional risk of an investment in an arbitrage collateralized debt 
obligation relative to an investment in an asset-  backed security is:
A the default risk on the collateral assets. 
B the risk that the CDO manager fails to earn a return sufficient to pay 
off the investors in the senior and the mezzanine tranches.
C the risk due to the mismatch between the collateral making fixed-  rate 
payments and the bond classes making floating-  rate payments.
Solution:
B is correct. In addition to the risks associated with investments in ABS, such 
as the default risk on the collateral assets and the risk due to the potential mis -
match between the collateral making fixed-  rate payments and the bond classes 
making floating-  rate payments, investors in CDOs face the risk that the CDO

manager fails to earn a return sufficient to pay off the investors in the senior 
and the mezzanine tranches. With an ABS, the cash flows from the collateral are 
used to pay off the holders of the bond classes without the active management 
of the collateral—that is, without a manager altering the composition of the 
debt obligations in the pool that is backing the securitization. In contrast, in an 
arbitrage CDO, a CDO manager buys and sells debt obligations with the dual 
purpose of not only paying off the holders of the bond classes but also generating 
an attractive/competitive return for the equity tranche and for the manager.

Reading 53 ■ Introduction to Asset-  Backed Securities 516
SUMMARY
■■Securitization involves pooling debt obligations, such as loans or receivables, 
and creating securities backed by the pool of debt obligations called asset-  
backed securities (ABS). The cash flows of the debt obligations are used to make 
interest payments and principal repayments to the holders of the ABS.
■■Securitization has several benefits. It allows investors direct access to liquid 
investments and payment streams that would be unattainable if all the financing 
were performed through banks. It enables banks to increase loan originations at 
economic scales greater than if they used only their own in-  house loan port -
folios. Thus, securitization contributes to lower costs of borrowing for entities 
raising funds, higher risk-  adjusted returns to investors, and greater efficiency 
and profitability for the banking sector.
■■The parties to a securitization include the seller of the collateral (pool of loans),

the servicer of the loans, and the special purpose entity (SPE). The SPE is bank -
ruptcy remote, which plays a pivotal role in the securitization.
■■A common structure in a securitization is subordination, which leads to the 
creation of more than one bond class or tranche. Bond classes differ as to how 
they will share any losses resulting from defaults of the borrowers whose loans 
are in the collateral. The credit ratings assigned to the various bond classes 
depend on how the credit-  rating agencies evaluate the credit risks of the collat -
eral and any credit enhancements.
■■The motivation for the creation of different types of structures is to redistribute 
prepayment risk and credit risk efficiently among different bond classes in the 
securitization. Prepayment risk is the uncertainty that the actual cash flows will 
be different from the scheduled cash flows as set forth in the loan agreements 
because borrowers may choose to repay the principal early to take advantage of

■■Because of the SPE, the securitization of a company’s assets may include some 
bond classes that have better credit ratings than the company itself or its corpo -
rate bonds. Thus, the company’s funding cost is often lower when raising funds 
through securitization than when issuing corporate bonds.
■■A mortgage is a loan secured by the collateral of some specified real estate 
property that obliges the borrower to make a predetermined series of payments 
to the lender. The cash flow of a mortgage includes (1) interest, (2) scheduled 
principal payments, and (3) prepayments (any principal repaid in excess of the 
scheduled principal payment).
■■The various mortgage designs throughout the world specify (1) the maturity of 
the loan; (2) how the interest rate is determined (i.e., fixed rate versus adjust -
able or variable rate); (3) how the principal is repaid (i.e., whether the loan is 
amortizing and if it is, whether it is fully amortizing or partially amortizing with

a balloon payment); (4) whether the borrower has the option to prepay and if 
so, whether any prepayment penalties might be imposed; and (5) the rights of 
the lender in a foreclosure (i.e., whether the loan is a recourse or non-  recourse 
loan).
■■In the United States, there are three sectors for securities backed by residen -
tial mortgages: (1) those guaranteed by a federal agency (Ginnie Mae) whose 
securities are backed by the full faith and credit of the US government, (2) those 
guaranteed by a GSE (e.g., Fannie Mae and Freddie Mac) but not by the US 
government, and (3) those issued by private entities that are not guaranteed by

Summary 517
a federal agency or a GSE. The first two sectors are referred to as agency resi -
dential mortgage-  backed securities (RMBS), and the third sector as non-  agency 
RMBS.
■■A mortgage pass-  through security is created when one or more holders of 
mortgages form a pool of mortgages and sell shares or participation certificates 
in the pool. The cash flow of a mortgage pass-  through security depends on the 
cash flow of the underlying pool of mortgages and consists of monthly mort -
gage payments representing interest, the scheduled repayment of principal, and 
any prepayments, net of servicing and other administrative fees.
■■Market participants measure the prepayment rate using two measures: the 
single monthly mortality rate (SMM) and its corresponding annualized rate—
namely, the conditional prepayment rate (CPR). For MBS, a measure widely 
used by market participants to assess is the weighted average life or simply the 
average life of the MBS.

■■Market participants use the Public Securities Association (PSA) prepayment 
benchmark to describe prepayment rates. A PSA assumption greater than 100 
PSA means that prepayments are assumed to occur faster than the benchmark, 
whereas a PSA assumption lower than 100 PSA means that prepayments are 
assumed to occur slower than the benchmark.
■■Prepayment risk includes two components: contraction risk and extension risk. 
The former is the risk that when interest rates decline, the security will have a 
shorter maturity than was anticipated at the time of purchase because home -
owners will refinance at the new, lower interest rates. The latter is the risk that 
when interest rates rise, fewer prepayments will occur than what was antici -
pated at the time of purchase because homeowners are reluctant to give up the 
benefits of a contractual interest rate that now looks low.
■■The creation of a collateralized mortgage obligation (CMO) can help manage

prepayment risk by distributing the various forms of prepayment risk among 
different classes of bondholders. The CMO’s major financial innovation is that 
the securities created more closely satisfy the asset/liability needs of institu -
tional investors, thereby broadening the appeal of mortgage-  backed products.
■■The most common types of CMO tranches are sequential-  pay tranches, planned 
amortization class (PAC) tranches, support tranches, and floating-  rate tranches.
■■Non-  agency RMBS share many features and structuring techniques with agency 
CMOs. However, they typically include two complementary mechanisms. First, 
the cash flows are distributed by rules that dictate the allocation of interest 
payments and principal repayments to tranches with various degrees of prior -
ity/seniority. Second, there are rules for the allocation of realized losses, which 
specify that subordinated bond classes have lower payment priority than senior 
classes.

classes.
■■In order to obtain favorable credit ratings, non-  agency RMBS and non-  
mortgage ABS often require one or more credit enhancements. The most com -
mon forms of internal credit enhancement are senior/subordinated structures, 
reserve funds, and overcollateralization. In external credit enhancement, credit 
support in the case of defaults resulting in losses in the pool of loans is pro -
vided in the form of a financial guarantee by a third party to the transaction.
■■Commercial mortgage-  backed securities (CMBS) are securities backed by a 
pool of commercial mortgages on income-  producing property.
■■Two key indicators of the potential credit performance of CMBS are the debt-  
service-  coverage (DSC) ratio and the loan-  to- value ratio (LTV). The DSC ratio 
is the property’s annual net operating income divided by the debt service.

Reading 53 ■ Introduction to Asset-  Backed Securities 518
“China Revives Giant Securitization Program. ” 2012. Asset-  
Backed Alert  (23 March).
Fabozzi, Frank J., and Vinod Kothari. 2008. Introduction to 
Securitization . Hoboken, NJ: John Wiley & Sons: 284–290.Lea, Michael. 2010. “International Comparison of Mortgage 
Product Offerings. ” Special report published jointly by the 
Research Institute for Housing America and the American 
Bankers Association (September).
Scanlon, Kathleen, Jens Lunde, and Christine Whitehead. 2008. 
“Mortgage Product Innovation in Advanced Economies: More 
Choice, More Risk. ” European Journal of Housing Policy , vol. 8, 
no. 2 (June): 109–131. ■■CMBS have considerable call protection, which allows CMBS to trade in 
the market more like corporate bonds than like RMBS. This call protection 
comes in two forms: at the structure level and at the loan level. The creation 
of sequential-  pay tranches is an example of call protection at the structure

level. At the loan level, four mechanisms offer investors call protection: pre -
payment lockouts, prepayment penalty points, yield maintenance charges, and 
defeasance.
■■ABS are backed by a wide range of asset types. The most popular non-  mortgage 
ABS are auto loan ABS and credit card receivable ABS. The collateral is amor -
tizing for auto loan ABS and non-  amortizing for credit card receivable ABS. 
As with non-  agency RMBS, these ABS must offer credit enhancement to be 
appealing to investors.
■■A collateralized debt obligation (CDO) is a generic term used to describe a 
security backed by a diversified pool of one or more debt obligations (e.g., 
corporate and emerging market bonds, leveraged bank loans, ABS, RMBS, and 
CMBS).
■■A CDO involves the creation of an SPE. The funds necessary to pay the bond 
classes come from a pool of loans that must be serviced. A CDO requires a col -
lateral manager to buy and sell debt obligations for and from the CDO’s portfo -

lio of assets to generate sufficient cash flows to meet the obligations of the CDO 
bondholders and to generate a fair return for the equity holders.
■■The structure of a CDO includes senior, mezzanine, and subordinated/equity 
bond classes.

Practice Problems 519
1 Securitization is beneficial for banks because it:
A repackages bank loans into simpler structures.
B increases the funds available for banks to lend.
C allows banks to maintain ownership of their securitized assets.
2 Securitization benefits financial markets by:
A increasing the role of intermediaries.
B establishing a barrier between investors and originating borrowers.
C allowing investors to tailor credit risk and interest rate risk exposures to 
meet their individual needs.
3 A benefit of securitization is the:
A reduction in disintermediation.
B simplification of debt obligations.
C creation of tradable securities with greater liquidity than the original loans.
4 In a securitization, the special purpose entity (SPE) is responsible for the:
A issuance of the asset-  backed securities.
B collection of payments from the borrowers.
C recovery of underlying assets from delinquent borrowers.

5 A special purpose entity issues asset-  backed securities in the following 
A (senior) 200
B (subordinated) 20
C (subordinated) 5
 At which of the following amounts of default in par value would Bond Class A 
experience a loss?
A €20 million
B €25 million
C €26 million
6 In a securitization, time tranching provides investors with the ability to choose 
between:
A extension and contraction risks.
B senior and subordinated bond classes.
C fully amortizing and partially amortizing loans.
7 The last payment in a partially amortizing residential mortgage loan is best 
referred to as a:
A waterfall.
B principal repayment.
C balloon payment.
8 If a mortgage borrower makes prepayments without penalty to take advantage 
of falling interest rates, the lender will most likely  experience:

Reading 53 ■ Introduction to Asset-  Backed Securities 520
A extension risk.
B contraction risk.
C yield maintenance.
9 Which of the following characteristics of a residential mortgage loan would best 
protect the lender from a strategic default by the borrower?
A Recourse
B A prepayment option
C Interest-  only payments
10 William Marolf obtains a 5 million EUR mortgage loan from Bank Nederlandse. 
A year later the principal on the loan is 4 million EUR and Marolf defaults on 
the loan. Bank Nederlandse forecloses, sells the property for 2.5 million EUR, 
and is entitled to collect the 1.5 million EUR shortfall, from Marolf. Marolf most 
likely  had a:
A bullet loan.
B recourse loan.
C non-  recourse loan.
11 Fran Martin obtains a non-  recourse mortgage loan for $500,000. One year later, 
when the outstanding balance of the mortgage is $490,000, Martin cannot make 
his mortgage payments and defaults on the loan. The lender forecloses on the

loan and sells the house for $315,000. What amount is the lender entitled to 
claim from Martin?
A $0.
B $175,000.
C $185,000.
12 Which of the following describes a typical feature of a non-  agency residential 
mortgage-  backed security (RMBS)?
A Senior/subordinated structure
B A pool of conforming mortgages as collateral
C A guarantee by a government-  sponsored enterprise
13 If interest rates increase, an investor who owns a mortgage pass-  through secu -
rity is most likely  affected by:
B extension risk.
14 Which of the following is most likely an advantage of collateralized mortgage 
obligations (CMOs)? CMOs can
A eliminate prepayment risk.
B be created directly from a pool of mortgage loans.
C meet the asset/liability requirements of institutional investors.
15 The longest-  term tranche of a sequential-  pay CMO is most likely  to have the 
lowest:
A average life.

Practice Problems 521
16 The tranches in a collateralized mortgage obligation (CMO) that are most likely  
to provide protection for investors against both extension and contraction risk 
are:
A planned amortization class (PAC) tranches.
B support tranches.
C sequential-  pay tranches.
17 Support tranches are most appropriate for investors who are:
A concerned about their exposure to extension risk.
B concerned about their exposure to concentration risk.
C willing to accept prepayment risk in exchange for higher returns.
18 In the context of mortgage-  backed securities, a conditional prepayment rate 
(CPR) of 8% means that approximately 8% of the outstanding mortgage pool 
balance at the beginning of the year is expected to be prepaid:
A in the current month.
B by the end of the year.
C over the life of the mortgages.
19 For a mortgage pass-  through security, which of the following risks most likely  
increases as interest rates decline?
A Balloon
B Extension
C Contraction

A Balloon
20 Credit risk is an important consideration for commercial mortgage-  backed 
securities (CMBS) if the CMBS are backed by mortgage loans that:
A are non-  recourse.
B have call protection.
C haveprepayment penalty points.
21 Which commercial mortgage-  backed security (CMBS) characteristic causes a 
CMBS to trade more like a corporate bond than a residential mortgage-  backed 
security (RMBS)?
A Call protection
B Internal credit enhancement
C Debt-  service coverage ratio level
22 A commercial mortgage-  backed security (CMBS) does not meet the debt-  to- 
service coverage at the loan level necessary to achieve a desired credit rating. 
Which of the following features would most  likely  improve the credit rating of 
the CMBS?
A Subordination
B Call protection
C Balloon payments
23 If a default occurs in a non-  recourse commercial mortgage-  backed security 
(CMBS), the lender will most likely :
A recover prepayment penalty points paid by the borrower to offset losses.

B use only the proceeds received from the sale of the property to recover 
losses.
C initiate a claim against the borrower for any shortfall resulting from the sale 
of the property.

Reading 53 ■ Introduction to Asset-  Backed Securities 522
24 Which of the following investments is least subject to prepayment risk?
A Auto loan receivable–backed securities
B Commercial mortgage-  backed securities (CMBSs)
C Non-  agency residential mortgage-  backed securities (RMBSs)
25 An excess spread account incorporated into a securitization is designed to limit:
26 Which of the following best describes the cash flow that owners of credit card 
receivable asset-  backed securities receive during the lockout period?
A No cash flow
B Only principal payments collected
C Only finance charges collected and fees
27 Collateralized mortgage obligations (CMOs) are designed to:
A eliminate contraction risk in support tranches.
B distribute prepayment risk to various tranches.
C eliminate extension risk in planned amortization tranches.

Solutions 523
SOLUTIONS
1 B is correct. Securitization increases the funds available for banks to lend 
because it allows banks to remove loans from their balance sheets and issue 
bonds that are backed by those loans. Securitization repackages relatively sim -
ple debt obligations, such as bank loans, into more complex, not simpler, struc -
tures. Securitization involves transferring ownership of assets from the original 
owner—in this case, the banks—into a special legal entity. As a result, banks do 
not maintain ownership of the securitized assets.
2 C is correct. By removing the wall between ultimate investors and originating 
borrowers, investors can achieve better legal claims on the underlying mort -
gages and portfolios of receivables. This transparency allows investors to tailor 
interest rate risk and credit risk to their specific needs.
3 C is correct. Securitization allows for the creation of tradable securities with

greater liquidity than the original loans on a bank’s balance sheet. Securitization 
results in lessening the roles of intermediaries, which increases disintermedia -
tion. Securitization is a process in which relatively simple debt obligations, such 
as loans, are repackaged into more complex structures.
4 A is correct. In a securitization, the special purpose entity (SPE) is the special 
legal entity responsible for the issuance of the asset-  backed securities. The 
servicer, not the SPE, is responsible for both the collection of payments from 
the borrowers and the recovery of underlying assets if the borrowers default on 
their loans.
5 C is correct. The first €25 (€5 + €20) million in default are absorbed by the 
subordinated classes (C and B). The senior Class A bonds will only experience a 
loss when defaults exceed €25 million.
6 A is correct. Time tranching is the process in which a set of bond classes or 
tranches is created that allow investors a choice in the type of prepayment risk,

extension or contraction, that they prefer to bear. Senior and subordinated bond 
classes are used in credit tranching. Credit tranching structures allow investors 
to choose the amount of credit risk that they prefer to bear. Fully and partially 
amortizing loans are two types of amortizing loans.
7 C is correct. In a partially amortizing loan, the sum of all the scheduled princi -
pal repayments is less than the amount borrowed. The last payment is for the 
remaining unpaid mortgage balance and is called the “balloon payment. ”
8 B is correct. Contraction risk is the risk that when interest rates decline, actual 
prepayments will be higher than forecasted. Extension risk is the risk that when 
interest rates rise, prepayments will be lower than forecasted. Yield mainte -
nance results from prepayment penalties; the lender is protected from loss in 
yield by the imposition of prepayment penalties.
9 A is correct. In a recourse loan, the lender has a claim against the borrower

for the shortfall between the amount of the mortgage balance outstanding and 
the proceeds received from the sale of the property. A prepayment option is a 
benefit to the borrower and would thus not offer protection to the lender. An 
interest-  only mortgage requires no principal repayment for a number of years 
and will not protect the lender from strategic default by the borrower.
10 B is correct. Bank Nederlandse has a claim against Marolf for 1.5 million EUR, 
the shortfall between the amount of the mortgage balance outstanding and the 
proceeds received from the sale of the property. This indicates that the mort -
gage loan is a recourse loan. The recourse/non-  recourse feature indicates the

Reading 53 ■ Introduction to Asset-  Backed Securities 524
rights of a lender in foreclosure. If Marolf had a non-  recourse loan, the bank 
would have only been entitled to the proceeds from the sale of the underlying 
property, or 2.5 million EUR. A bullet loan is a special type of interest-  only 
mortgage for which there are no scheduled principal payments over the entire 
term of the loan. Since the unpaid balance is less than the original mortgage 
loan, it is unlikely that Marolf has an interest only mortgage.
11 A is correct. Because the loan has a non-  recourse feature, the lender can only 
look to the underlying property to recover the outstanding mortgage balance 
and has no further claim against the borrower. The lender is simply entitled to 
foreclose on the home and sell it.
12 A is correct. Non-  agency RMBS are credit enhanced, either internally or 
externally, to make the securities more attractive to investors. The most com -

mon forms of internal credit enhancements are senior/subordinated structures, 
reserve accounts, and overcollateralization. Conforming mortgages are used as 
collateral for agency (not non-  agency) mortgage pass-  through securities. An 
agency RMBS, rather than a non-  agency RMBS, issued by a GSE (government 
sponsored enterprise), is guaranteed by the respective GSE.
13 B is correct. Extension risk is the risk that when interest rate rise, fewer pre -
payments will occur. Homeowners will be reluctant to give up the benefit of a 
contractual interest rate that is lower. As a result, the mortgage pass-  through 
security becomes longer in maturity than anticipated at the time of purchase.
14 C is correct. Using CMOs, securities can be created to closely satisfy the asset/
liability needs of institutional investors. The creation of a CMO cannot elimi -
nate prepayment risk; it can only distribute the various forms of this risk among

various classes of bondholders. The collateral of CMOs are mortgage-  related 
products, not the mortgages themselves.
15 C is correct. For a CMO with multiple sequential-  pay tranches, the longest-  
term tranche will have the lowest contraction (prepayments greater than 
forecasted) risk because of the protection against this risk offered by the other 
tranches. The longest-  term tranche is likely to have the highest average life and 
extension risk because it is the last tranche repaid in a sequential-  pay tranche.
16 A is correct. PAC tranches have limited (but not complete) protection against 
both extension risk and contraction risk. This protection is provided by the 
support tranches. A sequential-  pay tranche can protect against either extension 
risk or contraction risk but not both of these risks. The CMO structure with 
sequential-  pay tranches allows investors concerned about extension risk to 
invest in shorter-  term tranches and those concerned about contraction risk to

invest in the longer-  term tranches.
17 C is correct. The greater predictability of cash flows provided in the planned 
amortization class (PAC) tranches comes at the expense of support tranches. As 
a result, investors in support tranches are exposed to higher extension risk and 
contraction risk than investors in PAC tranches. Investors will be compensated 
for bearing this risk because support tranches have a higher expected return 
than PAC tranches.
18 B is correct. CPR is an annualized rate, which indicates the percentage of the 
outstanding mortgage pool balance at the beginning of the year that is expected 
to be prepaid by the end of the year.
19 C is correct. When interest rates decline, a mortgage pass-  through security is 
subject to contraction risk. Contraction risk is the risk that when interest rates 
decline, actual prepayments will be higher than forecasted because borrowers

Solutions 525
will refinance at now-  available lower interest rates. Thus, a security backed by 
mortgages will have a shorter maturity than was anticipated when the security 
was purchased.
20 A is correct. If commercial mortgage loans are non-  recourse loans, the lender 
can only look to the income-  producing property backing the loan for interest 
and principal repayment. If there is a default, the lender looks to the proceeds 
from the sale of the property for repayment and has no recourse against the 
borrower for any unpaid mortgage loan balance. Call protection and prepay -
ment penalty points protect against prepayment risk.
21 A is correct. With CMBS, investors have considerable call protection. An inves -
tor in a RMBS is exposed to considerable prepayment risk, but with CMBS, call 
protection is available to the investor at the structure and loan level. The call 
protection results in CMBS trading in the market more like a corporate bond

than a RMBS. Both internal credit enhancement and the debt-  service-  coverage 
(DSC) ratio address credit risk, not prepayment risk.
22 A is correct. If specific ratios of debt to service coverage are needed, and those 
ratios cannot be met at the loan level, subordination is used to achieve the 
desired credit rating. Call protection protects investors against prepayment risk. 
Balloon payments increase the risk of the underlying loans.
23 B is correct. In a non-  recourse CMBS, the lender can look only to the income-  
producing property backing the loan for interest and principal repayment. If a 
default occurs, the lender can use only the proceeds from the sale of the prop -
erty for repayment and has no recourse to the borrower for any unpaid balance.
24 B is correct. A critical feature that differentiates CMBSs from RMBSs is the call 
protection provided to investors. An investor in a RMBS is exposed to consid -
erable prepayment risk because the borrower has the right to prepay the loan

before maturity. CMBSs provide investors with considerable call protection that 
comes either at the structure level or at the loan level.
25 A is correct. An excess spread account, sometimes called excess interest cash 
flow, is a form of internal credit enhancement that limits credit risk. It is an 
amount that can be retained and deposited into a reserve account and that can 
serve as a first line of protection against losses. An excess spread account does 
not limit prepayment risk, extension, or contraction.
26 C is correct. During the lockout period, the cash flow that is paid out to owners 
of credit card receivable asset-  backed securities is based only on finance charges 
collected and fees.
27 B is correct. CMOs are designed to redistribute cash flows of mortgage-  related 
products to different bond classes or tranches through securitization. Although 
CMOs do not eliminate prepayment risk, they distribute prepayment risk 
among various classes of bondholders.

Fixed Income (2)
This study session examines the fundamental elements underlying bond returns and 
risks with a specific focus on interest rate and credit risk. Duration, convexity, and 
other key measures for assessing a bond’s sensitivity to interest rate risk are intro -
duced. An explanation of credit risk and the use of credit analysis for risky bonds 
concludes the session.
Reading 54  Understanding Fixed-  Income Risk and Return  
by James F. Adams, PhD, CFA, and 
Donald J. Smith, PhD
Reading 55 Fundamentals of Credit Analysis  
by Christopher L. Gootkind, CFAFIxED INCO mE
17

Understanding Fixed -Income 
Risk and Return
a. calculate and interpret the sources of return from investing in a 
fixed-  rate bond;
b. define, calculate, and interpret Macaulay, modified, and effective 
durations;
c. explain why effective duration is the most appropriate measure of 
interest rate risk for bonds with embedded options;
d. define key rate duration and describe the use of key rate durations 
in measuring the sensitivity of bonds to changes in the shape of 
the benchmark yield curve;
e. explain how a bond’s maturity, coupon, and yield level affect its 
interest rate risk;
f. calculate the duration of a portfolio and explain the limitations of 
portfolio duration;
g. calculate and interpret the money duration of a bond and price

value of a basis point (PVBP);
h. calculate and interpret approximate convexity and distinguish 
between approximate and effective convexity;
i. estimate the percentage price change of a bond for a specified 
change in yield, given the bond’s approximate duration and 
convexity;
j. describe how the term structure of yield volatility affects the 
interest rate risk of a bond;
k. describe the relationships among a bond’s holding period return, 
its duration, and the investment horizon;
l. explain how changes in credit spread and liquidity affect yield-  to- 
maturity of a bond and how duration and convexity can be used 
to estimate the price effect of the changes.READING
54

Reading 54 ■ Understanding Fixed -Income Risk and Return 530
It is important for analysts to have a well-  developed understanding of the risk and 
return characteristics of fixed-  income investments. Beyond the vast worldwide market 
for publicly and privately issued fixed-  rate bonds, many financial assets and liabilities 
with known future cash flows may be evaluated using the same principles. The start -
ing point for this analysis is the yield-  to- maturity, or internal rate of return on future 
cash flows, which was introduced in the fixed-  income valuation reading. The return 
on a fixed-  rate bond is affected by many factors, the most important of which is the 
receipt of the interest and principal payments in the full amount and on the scheduled 
dates. Assuming no default, the return is also affected by changes in interest rates that 
affect coupon reinvestment and the price of the bond if it is sold before it matures.

Measures of the price change can be derived from the mathematical relationship used 
to calculate the price of the bond. The first of these measures (duration) estimates the 
change in the price for a given change in interest rates. The second measure (convexity) 
improves on the duration estimate by taking into account the fact that the relationship 
between price and yield-  to- maturity of a fixed-  rate bond is not linear.
Section 2 uses numerical examples to demonstrate the sources of return on an 
investment in a fixed-  rate bond, which includes the receipt and reinvestment of cou -
pon interest payments and the redemption of principal if the bond is held to maturity. 
The other source of return is capital gains (and losses) on the sale of the bond prior 
to maturity. Section 2 also shows that fixed-  income investors holding the same bond 
can have different exposures to interest rate risk if their investment horizons differ.

Discussion of credit risk, although critical to investors, is postponed to Section 5 so 
that attention can be focused on interest rate risk.
Section 3 provides a thorough review of bond duration and convexity, and shows 
how the statistics are calculated and used as measures of interest rate risk. Although 
procedures and formulas exist to calculate duration and convexity, these statistics 
can be approximated using basic bond-  pricing techniques and a financial calculator. 
Commonly used versions of the statistics are covered, including Macaulay, modified, 
effective, and key rate durations. The distinction is made between risk measures that 
are based on changes in the bond’s yield-  to- maturity (i.e., yield  duration and convexity) 
and on benchmark yield curve changes (i.e., curve  duration and convexity).
Section 4 returns to the issue of the investment horizon. When an investor has 
a short-  term horizon, duration (and convexity) are used to estimate the change in

the bond price. In this case, yield volatility matters. In particular, bonds with varying 
times-  to- maturity have different degrees of yield volatility. When an investor has a 
long-  term horizon, the interaction between coupon reinvestment risk and market 
price risk matters. The relationship among interest rate risk, bond duration, and the 
investment horizon is explored.
Section 5 discusses how the tools of duration and convexity can be extended to 
credit and liquidity risks and highlights how these different factors can affect a bond’s 
return and risk.
A summary of key points and practice problems in the CFA Institute multiple-  
choice format conclude the reading.
SOURCES OF RETURN
An investor in a fixed-  rate bond has three sources of return: (1) receipt of the promised 
coupon and principal payments on the scheduled dates, (2) reinvestment of coupon 
payments, and (3) potential capital gains or losses on the sale of the bond prior to 1
2

Sources of Return 531
maturity. In this section, it is assumed that the issuer makes the coupon and principal 
payments as scheduled. This reading focuses primarily on interest rate risk (the risk 
that interest rates will change), which affects the reinvestment of coupon payments 
and the market price if the bond is sold prior to maturity. Credit risk is considered 
in Section 5 of this reading and is the primary subject of the reading “Fundamentals 
of Credit Analysis. ”
When a bond is purchased at a premium or a discount, it adds another aspect to 
the rate of return. Recall from the reading on fixed-  income valuation that a discount 
bond offers the investor a “deficient” coupon rate, or one below the market discount 
rate. The amortization of the discount in each period brings the return in line with 
the market discount rate as the bond’s carrying value is “pulled to par. ” For a premium 
bond, the coupon rate exceeds the market discount rate and the amortization of the

premium adjusts the return to match the market discount rate. Through amortization, 
the bond’s carrying value reaches par value at maturity.
A series of examples will demonstrate the effect of a change in interest rates on 
two investors’ realized rate of returns. Interest rates are the rates at which coupon 
payments are reinvested and the market discount rates at the time of purchase and 
at the time of sale if the bond is not held to maturity. In Examples 1 and 2, interest 
rates are unchanged. The two investors, however, have different time horizons for 
holding the bond. Examples 3 and 4 show the impact of an increase in interest rates 
on the two investors’ total return. Examples 5 and 6 show the impact of a decrease 
in interest rates. In each of the six examples, an investor initially buys a 10-  year, 8% 
annual coupon payment bond at a price of 85.503075 per 100 of par value. The bond’s 
yield-  to- maturity is 10.40%.
85 5030758
18
18
18
18
1
8
11 2345
6. =
+()+
+()+
+()+
+()+
+()+
+()rr rr r
r + +

18
1
8
11 2345
6. =
+()+
+()+
+()+
+()+
+()+
+()rr rr r
r + +
+()+
+()+
+()+
+()=8
18
18
1108
10 104078 91 0rr rrr,     .
EXAMPLE 1   
A “buy-  and-  hold” investor purchases a 10-  year, 8% annual coupon payment bond 
at 85.503075 per 100 of par value and holds it until maturity. The investor receives 
the series of 10 coupon payments of 8 (per 100 of par value) for a total of 80, 
plus the redemption of principal (100) at maturity. In addition to collecting the 
coupon interest and the principal, the investor has the opportunity to reinvest 
the cash flows. If the coupon payments are reinvested at 10.40%, the future value 
of the coupons on the bond’s maturity date is 129.970678 per 100 of par value.
81 1040 81 1040 81 1040 8198 7×()

+× ()

+× ()

+× .. .. 1 1040
81 1040 81 1040 81 1046
54()

+
×()

+× ()

+× .. .008 1 1040
81 1040 8 129 970632
1()

+× ()

+
×()

+=.
.. 7 78
The first coupon payment of 8 is reinvested at 10.40% for nine years until

maturity, the second is reinvested for eight years, and so forth. The future value 
of the annuity is obtained easily on a financial calculator, using 8 for the payment 
that is received at the end of each of the 10 periods. The amount in excess of 
the coupons, 49.970678 (= 129.970678 – 80), is the “interest-  on- interest” gain 
from compounding.

Reading 54 ■ Understanding Fixed -Income Risk and Return 532
The investor’s total return is 229.970678, the sum of the reinvested coupons 
(129.970678) and the redemption of principal at maturity (100). The realized 
rate of return is 10.40%.
85 503075229 970678
10 104010... =
+()=
rr,     
Example 1 demonstrates that the yield-  to- maturity at the time of purchase measures 
the investor’s rate of return under three assumptions: (1) The investor holds the bond 
to maturity, (2) there is no default by the issuer, and (3) the coupon interest payments 
are reinvested at that same rate of interest.
Example 2 considers another investor who buys the 10-  year, 8% annual coupon 
payment bond and pays the same price. This investor, however, has a four-  year invest -
ment horizon. Therefore, coupon interest is only reinvested for four years, and the 
bond is sold immediately after receiving the fourth coupon payment.
EXAMPLE 2   
A second investor buys the 10-  year, 8% annual coupon payment bond and sells

the bond after four years. Assuming that the coupon payments are reinvested 
at 10.40% for four years, the future value of the reinvested coupons is 37.347111 
81 1040 81 1040 81 1040 83 732 1×()

+× ()

+× ()

+= .. .. .347111
The interest-  on- interest gain from compounding is 5.347111 (= 37.347111 
– 32). After four years, when the bond is sold, it has six years remaining until 
maturity. If the yield-  to- maturity remains 10.40%, the sale price of the bond is 
89.668770.
8
1 10408
1 10408
1 10408
1 1040
8
1 10401081 234
5.. ..
.()+
()+
()+
()+
()+
1 1 104089 6687706..
()=
The total return is 127.015881 (= 37.347111 + 89.668770) and the realized 
85 503075127 015881
10 10404... =
+()=
rr,     
In Example 2, the investor’s horizon yield  is 10.40%. A horizon yield is the inter -
nal rate of return between the total return (the sum of reinvested coupon payments 
and the sale price or redemption amount) and the purchase price of the bond. The

horizon yield on a bond investment is the annualized holding-  period rate of return.
Example  2 demonstrates that the realized horizon yield matches the original 
yield-  to- maturity if (1) coupon payments are reinvested at the same interest rate as 
the original yield-  to- maturity, and (2) the bond is sold at a price on the constant-  yield 
price trajectory, which implies that the investor does not have any capital gains or 
losses when the bond is sold.

Sources of Return 533
Capital gains arise if a bond is sold at a price above its constant-  yield price tra -
jectory and capital losses occur if a bond is sold at a price below its constant-  yield 
price trajectory. This trajectory is based on the yield-  to- maturity when the bond is 
purchased. The trajectory is shown in Exhibit 1 for a 10-  year, 8% annual payment 
bond purchased at a price of 85.503075 per 100 of par value.
Exhibit 1   Constant-  Yield Price Trajectory for a 10-  Y ear, 8% Annual Payment 
Bond
Price
Capital Gain if
the Bond Is Sold
at a Price Above
the Trajectory
Capital Loss if
at a Price Below
the Trajectory102
100
98
96
94
92
90
88
86
84
01 0 2 4 6 8
Year
Note:  Price is price per 100 of par value
A point on the trajectory represents the carrying value  of the bond at that time. 
The carrying value is the purchase price plus the amortized amount of the discount 
if the bond is purchased at a price below par value. If the bond is purchased at a

price above par value, the carrying value is the purchase price minus the amortized 
amount of the premium.
The amortized amount for each year is the change in the price between two points 
on the trajectory. The initial price of the bond is 85.503075 per 100 of par value. Its 
price (the carrying value) after one year is 86.393394, calculated using the original 
yield-  to- maturity of 10.40%. Therefore, the amortized amount for the first year is 
0.890319 (= 86.393394 – 85.503075). The bond price in Example 2 increases from 
85.503075 to 89.668770, and that increase over the four years is movement along  the 
constant-  yield price trajectory. At the time the bond is sold, its carrying value is also 
89.668770, so there is no capital gain or loss.
Examples 3 and 4 demonstrate the impact on investors’ realized horizon yields if 
interest rates go up by 100 basis points (bps). The market discount rate on the bond

increases from 10.40% to 11.40%. Coupon reinvestment rates go up by 100 bps as well.

Reading 54 ■ Understanding Fixed -Income Risk and Return 534
EXAMPLE 3   
The buy-  and-  hold investor purchases the 10-  year, 8% annual payment bond at 
85.503075. After the bond is purchased and before the first coupon is received, 
interest rates go up to 11.40%. The future value of the reinvested coupons at 
11.40% for 10 years is 136.380195 per 100 of par value.
81 1140 81 1140 81 1140 8198 7×()

+× ()

+× ()

+× .. .. 1 1140
81 1140 81 1140 81 1146
54()

+
×()

+× ()

+× .. .008 1 1140
81 1140 8 136 380132
1()

+× ()

+
×()

+=.
.. 9 95
The total return is 236.380195 (= 136.380195 + 100). The investor’s realized 
rate of return is 10.70%.
85 503075236 380195
10 107010... =
+()=
rr,     
In Example 3, the buy-  and-  hold investor benefits from the higher coupon rein -
vestment rate. The realized horizon yield is 10.70%, 30 bps higher than the outcome in 
Example 1, when interest rates are unchanged. There is no capital gain or loss because

the bond is held until maturity. The carrying value at the maturity date is par value, 
the same as the redemption amount.
EXAMPLE 4   
The second investor buys the 10-  year, 8% annual payment bond at 85.503075 
and sells it in four years. After the bond is purchased, interest rates go up to 
11.40%. The future value of the reinvested coupons at 11.40% after four years is 
37.899724 per 100 of par value.
81 1140 81 1140 81 1140 83 732 1×()

+× ()

+× ()

+= .. .. .899724
The sale price of the bond after four years is 85.780408.
8
1 11408
1 11408
1 11408
1 1140
8
1 11401081 234
5.. ..
.()+
()+
()+
()+
()+
1 1 114085 7804086..
()=
The total return is 123.680132 (= 37.899724  + 85.780408), resulting in a 
realized four-  year horizon yield of 9.67%.
85 503075123 680132
10 09674... =
+()=
rr,     
In Example 4, the second investor has a lower realized rate of return compared with 
the investor in Example 2, in which interest rates are unchanged. The future value of

reinvested coupon payments goes up by 0.552613 (= 37.899724 – 37.347111) per 100 
of par value because of the higher interest rates. But there is a capital loss  of 3.888362 
(= 89.668770 – 85.780408) per 100 of par value. Notice that the capital loss is mea -
sured from the bond’s carrying value, the point on the constant-  yield price trajectory,

Sources of Return 535
and not from the original purchase price. The bond is now sold at a price below the 
constant-  yield price trajectory. The reduction in the realized four-  year horizon yield 
from 10.40% to 9.67% is a result of the capital loss being greater than the gain from 
reinvesting coupons at a higher rate, which reduces the investor’s total return.
Examples 5 and 6 complete the series of rate-  of- return calculations for the two 
investors. Interest rates decline by 100 bps. The required yield on the bond falls from 
10.40% to 9.40% after the purchase of the bond. The interest rates at which the coupon 
payments are reinvested fall as well.
EXAMPLE 5   
The buy-  and-  hold investor purchases the 10-  year bond at 85.503075 and holds 
the security until it matures. After the bond is purchased and before the first 
coupon is received, interest rates go down to 9.40%. The future value of reinvesting 
the coupon payments at 9.40% for 10 years is 123.888356 per 100 of par value.

81 0940 81 0940 81 0940 8198 7×()

+× ()

+× ()

+× .. .. 0 0940
81 0940 81 0940 81 0946
54()

+
×()

+× ()

+× .. .008 1 0940
81 0940 8 123 888332
1()

+× ()

+
×()

+=.
.. 5 56
The total return is 223.888356, the sum of the future value of reinvested 
coupons and the redemption of par value. The investor’s realized rate of return 
is 10.10%.
85 503075223 888356
10 101010... =
+()=
rr,     
In Example 5, the buy-  and-  hold investor suffers from the lower coupon reinvestment 
rates. The realized horizon yield is 10.10%, 30 bps lower than the result in Example 1, 
when interest rates are unchanged. There is no capital gain or loss because the bond 
is held until maturity. Examples 1, 3, and 5 indicate that the interest rate risk for a 
buy-  and-  hold investor arises entirely from changes in coupon reinvestment rates.
EXAMPLE 6   
The second investor buys the 10-  year bond at 85.503075 and sells it in four years.

After the bond is purchased, interest rates go down to 9.40%. The future value 
of the reinvested coupons at 9.40% is 36.801397 per 100 of par value.
81 0940 81 0940 81 0940 83 632 1×()

+× ()

+× ()

+= .. .. .801397
This reduction in future value is offset by the higher sale price of the bond, 
which is 93.793912 per 100 of par value.
8
1 09408
1 09408
1 09408
1 0940
8
1 09401081 234
5.. ..
.()+
()+
()+
()+
()+
1 1 094093 7939126..
()=

Reading 54 ■ Understanding Fixed -Income Risk and Return 536
The total return is 130.595309 (= 36.801397 + 93.793912), and the realized 
yield is 11.17%.
85 503075130 595309
10 11174... =
+()=
rr,     
The investor in Example 6 has a capital gain of 4.125142 (= 93.793912 – 89.668770). 
The capital gain is measured from the carrying value, the point on the constant-  yield 
price trajectory. That gain offsets the reduction in the future value of reinvested cou -
pons of 0.545714 (= 37.347111 – 36.801397). The total return is higher than that in 
Example 2, in which the interest rate remains at 10.40%.
In these examples, interest income for the investor is the return associated with 
the passage of time . Therefore, interest income includes the receipt of coupon inter -
est, the reinvestment of those cash flows, and the amortization of the discount from 
purchase at a price below par value (or the premium from purchase at a price above

par value) to bring the return back in line with the market discount rate. A capital 
gain or loss is the return to the investor associated with the change in the value  of 
the security. On the fixed-  rate bond, a change in value arises from a change in the 
yield-  to- maturity, which is the implied market discount rate. In practice, the manner 
in which interest income and capital gains and losses are calculated and reported on 
financial statements depends on financial and tax accounting rules.
This series of examples illustrates an important point about fixed-  rate bonds: 
The investment horizon  is at the heart of understanding interest rate risk and return. 
There are two offsetting types of interest rate risk that affect the bond investor: cou -
pon reinvestment risk and market price risk. The future value of reinvested coupon 
payments (and in a portfolio, the principal on bonds that mature before the horizon

date) increases  when interest rates go up and decreases  when rates go down. The 
sale price on a bond that matures after the horizon date (and thus needs to be sold) 
decreases  when interest rates go up and increases  when rates go down. Coupon rein -
vestment risk matters more when the investor has a long-  term horizon relative to the 
time-  to- maturity of the bond. For instance, a buy-  and-  hold investor only has coupon 
reinvestment risk. Market price risk matters more when the investor has a short-  term 
horizon relative to the time-  to- maturity. For example, an investor who sells the bond 
before the first coupon is received has only market price risk. Therefore, two investors 
holding the same bond (or bond portfolio) can have different exposures to interest 
rate risk if they have different investment horizons.
EXAMPLE 7   
An investor buys a four-  year, 10% annual coupon payment bond priced to yield

5.00%. The investor plans to sell the bond in two years once the second coupon 
payment is received. Calculate the purchase price for the bond and the horizon 
yield assuming that the coupon reinvestment rate after the bond purchase and 
the yield-  to- maturity at the time of sale are (1) 3.00%, (2) 5.00%, and (3) 7.00%.
Solution:
The purchase price is 117.729753.
10
1 050010
1 050010
1 0500110
1 0500117 729751 234.. ...
()+
()+
()+
()= 3 3
1 3.00%: The future value of reinvested coupons is 20.300.
(10 × 1.0300) + 10 = 20.300

Interest Rate Risk on Fixed-  Rate Bonds 537
 The sale price of the bond is 113.394288.
10
1 0300110
1 0300113 39428812...
()+
()=
 Total return: 20.300 + 113.394288 = 133.694288.
 If interest rates go down from 5.00% to 3.00%, the realized rate of return 
over the two-  year investment horizon is 6.5647%, higher than the original 
yield-  to- maturity of 5.00%.
117 729753133 694288
10 0656472... =
+()=
rr,     
2 5.00%: The future value of reinvested coupons is 20.500.
(10 × 1.0500) + 10 = 20.500
 The sale price of the bond is 109.297052.
10
1 0500110
1 0500109 29705212...
()+
()=
 Total return: 20.500 + 109.297052 = 129.797052.
 If interest rates remain 5.00% for reinvested coupons and for the required 
yield on the bond, the realized rate of return over the two-  year investment 
horizon is equal to the yield-  to- maturity of 5.00%.
117 729753129 797052
10 0500002... =
+()=
rr,     
3 7.00%: The future value of reinvested coupons is 20.700.
(10 × 1.0700) + 10 = 20.700
 The bond is sold at 105.424055.
10
1 0700110

The bond is sold at 105.424055.
10
1 0700110
1 0700105 42405512...
()+
()=
 Total return: 20.700 + 105.424055 = 126.124055.
117 729753126 124055
10 0350372... =
+()=
rr,     
 If interest rates go up from 5.00% to 7.00%, the realized rate of return 
over the two-  year investment horizon is 3.5037%, lower than the yield-  to- 
maturity of 5.00%.
INTEREST RATE RISK ON FIXED-  RATE BONDS
This section covers two commonly used measures of interest rate risk: duration and 
convexity. It distinguishes between risk measures based on changes in a bond’s own 
yield to maturity (yield duration and convexity) and those that affect the bond based 
on changes in a benchmark yield curve (curve duration and convexity).3

Reading 54 ■ Understanding Fixed -Income Risk and Return 538
3.1 Macaulay, Modified, and Approximate Duration
The duration of a bond measures the sensitivity of the bond’s full price (including 
accrued interest) to changes in the bond’s yield-  to- maturity or, more generally, to 
changes in benchmark interest rates. Duration estimates changes in the bond price 
assuming that variables other than the yield-  to- maturity or benchmark rates are held 
constant. Most importantly, the time-  to- maturity is unchanged. Therefore, duration 
measures the instantaneous  (or, at least, same-  day) change in the bond price. The 
accrued interest is the same, so it is the flat price that goes up or down when the full 
price changes. Duration is a useful measure because it represents the approximate 
amount of time a bond would have to be held for the market discount rate at pur -
chase to be realized if there is a single change in interest rate. If the bond is held for

the duration period, an increase from reinvesting coupons is offset by a decrease in 
price if interest rates increase and a decrease from reinvesting coupons is offset by 
an increase in price if interest rates decrease.
There are several types of bond duration. In general, these can be divided into 
yield duration  and curve duration . Yield duration is the sensitivity of the bond price 
with respect to the bond’s own yield-  to- maturity. Curve duration is the sensitivity of 
the bond price (or more generally, the market value of a financial asset or liability) 
with respect to a benchmark yield curve. The benchmark yield curve could be the 
government yield curve on coupon bonds, the spot curve, or the forward curve, but 
in practice, the government par curve is often used. Yield duration statistics used in 
fixed-  income analysis include Macaulay duration, modified duration, money duration, 
and the price value of a basis point (PVBP). A curve duration statistic often used is

effective duration. Effective duration is covered in Section 3.2.
Macaulay duration  is named after Frederick Macaulay, the Canadian economist 
who first wrote about the statistic in a book published in 1938.1 Equation 1 is a general 
formula to calculate the Macaulay duration (MacDur) of a traditional fixed-  rate bond.
MacDur =
−() ×
+()+−() ×
+()++−() ×
−−1
12
112tT PMT
rtT PMT
rNt TP M
tT tTTTF V
r
PMT
rPMT
rPMTF V
rNtT
tT tT Nt+ ()
+()
+()+
+()+++
+()−
−− −1
11 112T T










where
 t = the number of days from the last coupon payment to the settlement 
date
 T = the number of days in the coupon period
 t/T = the fraction of the coupon period that has gone by since the last 
payment
 PMT  = the coupon payment per period
 FV = the future value paid at maturity, or the par value of the bond
 r = the yield-  to- maturity, or the market discount rate, per period
 N = the number of evenly spaced periods to maturity as of the beginning of 
the current period(1)

1 Frederick R. Macaulay, Some Theoretical Problems Suggested by the Movements of Interest Rates, Bond Yields 
and Stock Prices in the United States since 1856  (New York: National Bureau of Economic Research, 1938).

Interest Rate Risk on Fixed-  Rate Bonds 539
The denominator in Equation 1 is the full price ( PVFull) of the bond including accrued 
interest. It is the present value of the coupon interest and principal payments, with 
each cash flow discounted by the same market discount rate, r.
PVPMT
rPMT
rPMTF V
rFull
tT tT Nt T=
+()+
+()+++
Equation  3 combines Equations 1 and 2 to reveal an important aspect of the 
Macaulay duration: Macaulay duration is a weighted average of the time to receipt of 
the bond’s promised payments, where the weights are the shares of the full price that 
correspond to each of the bond’s promised future payments.
MacDur =−()+()









+−()+−
11211
tTPMT
r
PVtTPMT
rtT
Full(()









++
−()+
+()−
−2
1tT
Full
Nt T
FullPV
Nt TPMTF V
r
PV
 































The time to receipt of cash flow measured in terms of time periods are 1 – t/T, 
2 – t /T, …, N – t/T. The weights are the present values of the cash flows divided by

the full price. Therefore, Macaulay duration is measured in terms of time periods. A 
couple of examples will clarify this calculation.
Consider first the 10-  year, 8% annual coupon payment bond used in Examples 
1–6. The bond’s yield-  to- maturity is 10.40%, and its price is 85.503075 per 100 of par 
value. This bond has 10 evenly spaced periods to maturity. Settlement is on a cou -
pon payment date so that t/T = 0. Exhibit 2 illustrates the calculation of the bond’s 
Macaulay duration.
Exhibit 2   Macaulay Duration of a 10-  Y ear, 8% Annual Payment Bond
Period Cash Flow Present Value Weight Period × Weight
1 8 7.246377 0.08475 0.0847
2 8 6.563747 0.07677 0.1535
3 8 5.945423 0.06953 0.2086
4 8 5.385347 0.06298 0.2519
5 8 4.878032 0.05705 0.2853
6 8 4.418507 0.05168 0.3101
7 8 4.002271 0.04681 0.3277
8 8 3.625245 0.04240 0.3392
9 8 3.283737 0.03840 0.3456
10 108 40.154389 0.46963 4.6963
85.503075 1.00000 7.0029(2)
(3)

Reading 54 ■ Understanding Fixed -Income Risk and Return 540
The first two columns of Exhibit 2 show the number of periods to the receipt of 
the cash flow and the amount of the payment per 100 of par value. The third column 
is the present value of the cash flow. For example, the final payment is 108 (the last 
coupon payment plus the redemption of principal) and its present value is 40.154389.
108
1 104040 15438910..
()=
The sum of the present values is the full price of the bond. The fourth column is the 
weight, the share of total market value corresponding to each cash flow. The final 
payment of 108 per 100 of par value is 46.963% of the bond’s market value.
40 154389
85 5030750 46963.
..=
The sum of the weights is 1.00000. The fifth column is the number of periods to the 
receipt of the cash flow (the first column) multiplied by the weight (the fourth column). 
The sum of that column is 7.0029, which is the Macaulay duration of this 10-  year, 8%

annual coupon payment bond. This statistic is sometimes reported as 7.0029 years,  
although the time frame is not needed in most applications.
Now consider an example between  coupon payment dates. A 6% semiannual 
payment corporate bond that matures on 14 February 2022 is purchased for settle -
ment on 11 April 2014. The coupon payments are 3 per 100 of par value, paid on 
14 February and 14 August of each year. The yield-  to- maturity is 6.00% quoted on a 
street-  convention semiannual bond basis. The full price of this bond comprises the 
flat price plus accrued interest. The flat price for the bond is 99.990423 per 100 of par 
value. The accrued interest is calculated using the 30/360 method to count days. This 
settlement date is 57 days into the 180-  day semiannual period, so t/T = 57/180. The 
accrued interest is 0.950000 (= 57/180 × 3) per 100 of par value. The full price for the 
bond is 100.940423 (= 99.990423 + 0.950000). Exhibit 3 shows the calculation of the

bond’s Macaulay duration.
Exhibit 3   Macaulay Duration of an Eight-  Y ear, 6% Semiannual Payment 
Bond Priced to Yield 6.00%
Period Time to Receipt Cash Flow Present Value Weight Time × Weight
1 0.6833 3 2.940012 0.02913 0.019903
2 1.6833 3 2.854381 0.02828 0.047601
3 2.6833 3 2.771244 0.02745 0.073669
4 3.6833 3 2.690528 0.02665 0.098178
5 4.6833 3 2.612163 0.02588 0.121197
6 5.6833 3 2.536080 0.02512 0.142791
7 6.6833 3 2.462214 0.02439 0.163025
8 7.6833 3 2.390499 0.02368 0.181959
9 8.6833 3 2.320873 0.02299 0.199652
10 9.6833 3 2.253275 0.02232 0.216159
11 10.6833 3 2.187645 0.02167 0.231536
12 11.6833 3 2.123927 0.02104 0.245834
13 12.6833 3 2.062065 0.02043 0.259102
14 13.6833 3 2.002005 0.01983 0.271389
15 14.6833 3 1.943694 0.01926 0.282740

Interest Rate Risk on Fixed-  Rate Bonds 541
16 15.6833 103 64.789817 0.64186 10.066535
100.940423 1.00000 12.621268
There are 16 semiannual periods to maturity between the last coupon payment 
date of 14 February  2014 and maturity on 14 February  2022. The time to receipt 
of cash flow in semiannual periods is in the second column: 0.6833 = 1 – 57/180, 
1.6833 = 2 – 57/180, etc. The cash flow for each period is in the third column. The 
annual yield-  to- maturity is 6.00%, so the yield per semiannual period is 3.00%. When 
that yield is used to get the present value of each cash flow, the full price of the bond 
is 100.940423, the sum of the fourth column. The weights, which are the shares of 
the full price corresponding to each cash flow, are in the fifth column. The Macaulay 
duration is the sum of the items in the sixth column, which is the weight multiplied

by the time to receipt of each cash flow. The result, 12.621268, is the Macaulay dura -
tion on an eight-  year, 6% semiannual payment bond for settlement on 11 April 2014 
measured in semiannual periods . Similar to coupon rates and yields-  to- maturity, 
duration statistics invariably are annualized in practice. Therefore, the Macaulay 
duration typically is reported as 6.310634 years  (= 12.621268/2).2 (Such precision for 
the duration statistic is not needed in practice. Typically, “6.31 years” is enough. The 
full precision is shown here to illustrate calculations.)
Another approach to calculating the Macaulay duration is to use a closed-  form 
equation derived using calculus and algebra. Equation  4 is a general closed-  form 
formula for determining the Macaulay duration of a fixed-  rate bond, where c is the 
coupon rate per period ( PMT/FV ).3
MacDur =+−++ ×−() 
×+() −

+



−1 1
11r
rrN cr
cr rtTN(()

×+() −

+



−1 1
11r
rrN cr
cr rtTN(()
The Macaulay duration of the 10-  year, 8% annual payment bond is calculated by 
entering r = 0.1040, c = 0.0800, N = 10, and t/T = 0 into Equation 4.
MacDur =+−++ ×−()  10 1040
0 104010 1040 10 0 0800 0 1040
0 080.
... .
.001 0 1040 10 10407 002910×+() −

+=
...
Therefore, the weighted average time to receipt of the interest and principal payments 
that will result in realization of the initial market discount rate on this 10-  year bond 
is 7.00 years.(4)Exhibit 3   (Continued)
2 Microsoft Excel users can obtain the Macaulay duration using the DURATION financial function: 
DURATION (“4/11/2014, ” “2/14/2022, ” 0.06, 0.06, 2, 0). The inputs are the settlement date, maturity date, 
annual coupon rate as a decimal, annual yield-  to- maturity as a decimal, periodicity, and the code for the 
day count (0 for 30/360, 1 for actual/actual).
3 The step-  by- step derivation of this formula is in Donald J. Smith, Bond Math: The Theory behind the

Reading 54 ■ Understanding Fixed -Income Risk and Return 542
The Macaulay duration of the 6% semiannual payment bond maturing on 14 
February 2022 is obtained by entering r = 0.0300, c = 0.0300, N = 16, and t/T = 57/180 
into Equation 4.
MacDur =+−++ ×−()  10 0300
0 030010 0300 16 0 0300 0 0300
0 030.
... .
.001 0 0300 10 030057 180
12 62126816×+() −

+





−()
=..
.
Equation  4 uses the yield-  to- maturity per period , the coupon rate per period , the 
number of periods  to maturity, and the fraction of the current period  that has gone 
by. Its output is the Macaulay duration in terms of periods . It is converted to annual 
duration by dividing by the number of periods in the year.
The calculation of the modified duration  (ModDur) statistic of a bond requires a 
simple adjustment to Macaulay duration. It is the Macaulay duration statistic divided 
by one plus the yield per period.
ModDurMacDur=+1r
For example, the modified duration of the 10-  year, 8% annual payment bond is 6.3432.

ModDur= =7 0029
1 10406 3432.
..
The modified duration of the 6% semiannual payment bond maturing on 14 
February 2022 is 12.253658 semiannual periods.
ModDur= =12 621268
1 030012 253658.
..
The annualized modified duration of the bond is 6.126829 (= 12.253658/2).4
Although modified duration might seem to be just a Macaulay duration with minor 
adjustments, it has an important application in risk measurement: Modified duration 
provides an estimate of the percentage price change for a bond given a change in its 
yield-  to- maturity.
%ΔPVFull ≈ –AnnModDur × ΔYield  
The percentage price change refers to the full price, including accrued interest. The 
AnnModDur term in Equation 6 is the annual  modified duration, and the ΔYield term 
is the change in the annual  yield-  to- maturity. The ≈ sign indicates that this calculation 
is an estimation. The minus sign indicates that bond prices and yields-  to- maturity 
move inversely.
If the annual yield on the 6% semiannual payment bond that matures on 14

February 2022 jumps by 100 bps, from 6.00% to 7.00%, the estimated loss in value 
for the bond is 6.1268%.
%ΔPVFull ≈ –6.126829 × 0.0100 = –0.061268
If the yield-  to- maturity were to drop by 100 bps to 5.00%, the estimated gain in value 
is also 6.1268%.
%ΔPVFull ≈ –6.126829 × –0.0100 = 0.061268
Modified duration provides a linear  estimate of the percentage price change. In 
terms of absolute value, the change is the same for either an increase or decrease in 
the yield-  to- maturity. Recall from “Introduction to Fixed-  Income Valuation” that for (5)
(6)
4 Microsoft Excel users can obtain the modified duration using the MDURATION financial function: 
MDURATION (“4/11/2014, ” “2/14/2022, ” 0.06, 0.06, 2, 0). The inputs are the same as for the Macaulay 
duration in Footnote 2.

Interest Rate Risk on Fixed-  Rate Bonds 543
a given coupon rate and time-  to- maturity, the percentage price change is greater (in 
absolute value) when the market discount rate goes down than when it goes up. Later 
in this reading, a “convexity adjustment” to duration is introduced. It improves the 
accuracy of this estimate, especially when a large change in yield-  to- maturity (such 
as 100 bps) is considered.
The modified duration statistic for a fixed-  rate bond is easily obtained if the 
Macaulay duration is already known. An alternative approach is to approximate  mod -
ified duration directly. Equation 7 is the approximation formula for annual modified 
duration.
ApproxModDurYield=() −()
×() ×()−+PV PV
PV 20 ∆
The objective of the approximation is to estimate the slope of the line tangent to the 
price–yield curve. The slope of the tangent and the approximated slope are shown 
in Exhibit 4.
Exhibit 4   Approximate Modified Duration
PV0
PV+Price
PV–
∆ Yield ∆ YieldPrice–Yield Curve

PV0
PV+Price
PV–
Approximation for the
Line Tangent to the
Price–Yield Curve
Line T angent to the
Yield-to-Maturity
To estimate the slope, the yield-  to- maturity is changed up and down by the same 
amount—the ΔYield. Then the bond prices given the new yields-  to- maturity are 
calculated. The price when the yield is increased is denoted PV+. The price when the 
yield-  to- maturity is reduced is denoted PV−. The original price is PV0. These prices 
are the full prices, including accrued interest. The slope of the line based on PV+ and 
PV− is the approximation for the slope of the line tangent to the price–yield curve. 
The following example illustrates the remarkable accuracy of this approximation. In 
fact, as ΔYield approaches zero, the approximation approaches AnnModDur.
Consider the 6% semiannual coupon payment corporate bond maturing on 14 
February 2022. For settlement on 11 April 2014, the full price ( PV0) is 100.940423

given that the yield-  to- maturity is 6.00%.
PV012 1657 180 3
1033
103103
1031031 0 =
()+
()++
()



×() =
.. ..  0 0 940423 .(7)

Reading 54 ■ Understanding Fixed -Income Risk and Return 544
Raise the annual yield-  to- maturity by five bps, from 6.00% to 6.05%. This increase 
corresponds to an increase in the yield-  to- maturity per semiannual period of 2.5 bps, 
from 3.00% to 3.025% per period. The new full price ( PV+) is 100.631781.
PV+=
()+
()++
()



×3
1 030253
1 03025103
1 030251 03012 16.. ..  2 25 100 63178157 180() = .
Lower the annual yield-  to- maturity by five bps, from 6.00% to 5.95%. This decrease 
corresponds to a decrease in the yield-  to- maturity per semiannual period of 2.5 bps, 
from 3.00% to 2.975% per period. The new full price ( PV−) is 101.250227.
PV−=
()+
()++
()



×3
1 029753
1 02975103
1 029751 02912 16.. ..  7 75 101 25022757 180() = .
Enter these results into Equation 7 for the 5 bp change in the annual yield-  to- maturity, 
or ΔYield = 0.0005:
ApproxModDur =−
××=101 250227 100 631781
20 0005 100 940423612..
...66842

...66842
The “exact” annual modified duration for this bond is 6.126829 and the “approxi -
mation” is 6.126842—virtually identical results. Therefore, although duration can 
be calculated using the approach in Exhibits 2 and 3—basing the calculation on the 
weighted average time to receipt of each cash flow—or using the closed-  form formula 
as in Equation 4, it can also be estimated quite accurately using the basic bond-  pricing 
equation and a financial calculator. The Macaulay duration can be approximated as 
well—the approximate modified duration multiplied by one plus the yield per period.
ApproxMacDur = ApproxModDur × (1 + r)  
The approximation formulas produce results for annualized  modified and Macaulay 
durations. The frequency of coupon payments and the periodicity of the yield-  to- 
maturity are included in the bond price calculations.
EXAMPLE 8   
Assume that the 3.75% US Treasury bond that matures on 15 August 2041 is

priced to yield 5.14% for settlement on 15 October  2014. Coupons are paid 
semiannually on 15 February and 15 August. The yield-  to- maturity is stated on 
a street-  convention semiannual bond basis. This settlement date is 61 days into a 
184-  day coupon period, using the actual/actual day-  count convention. Compute 
the approximate modified duration and the approximate Macaulay duration for 
this Treasury bond assuming a 5 bp change in the yield-  to- maturity.
Solution:
The yield-  to- maturity per semiannual period is 0.0257 (= 0.0514/2). The coupon 
payment per period is 1.875 (= 3.75/2). At the beginning of the period, there 
are 27 years (54 semiannual periods) to maturity. The fraction of the period 
that has passed is 61/184. The full price at that yield-  to- maturity is 80.501507 
PV012 541 875
1 02571 875
1 0257101 875
1 0257=
()+
()++
()

.
..
..
.
 
×() = 1 0257 80 50150761 184..(8)

Interest Rate Risk on Fixed-  Rate Bonds 545
Raise the yield-  to- maturity from 5.14% to 5.19%—therefore, from 2.57% to 2.595% 
per semiannual period, and the price becomes 79.886293 per 100 of par value.
PV+=
()+
()++
()
1 875
1 025951 875
1 02595101 875
1 0259512 54.
..
..
.  


×()
=1 02595
79 88629361 184.
.
Lower the yield-  to- maturity from 5.14% to 5.09%—therefore, from 2.57% to 
2.545% per semiannual period, and the price becomes 81.123441 per 100 of 
par value.
PV−=
()+
()++
()
1 875
1 025451 875
1 02545101 875
1 0254512 54.
..
..
.  


×()
=1 02545
81 12344161 184.
.
The approximate annualized modified duration for the Treasury bond is 15.368.
××=81 123441 79 886293
20 0005 80 50150715 368..
...
The approximate annualized Macaulay duration is 15.763.
ApproxMacDur = 15.368 × 1.0257 = 15.763
Therefore, from these statistics, the investor knows that the weighted average 
time to receipt of interest and principal payments is 15.763 years (the Macaulay

duration) and that the estimated loss in the bond’s market value is 15.368% (the 
modified duration) if the market discount rate were to suddenly go up by 1% 
from 5.14% to 6.14%.
3.2 Effective Duration
Another approach to assess the interest rate risk of a bond is to estimate the percentage 
change in price given a change in a benchmark yield curve—for example, the govern -
ment par curve. This estimate, which is very similar to the formula for approximate 
modified duration, is called the effective duration . The effective duration of a bond is 
the sensitivity of the bond’s price to a change in a benchmark yield curve. The formula 
to calculate effective duration (EffDur) is Equation 9.
EffDurCurve=() −()
PV 20 ∆
The difference between approximate modified duration and effective duration is 
in the denominator. Modified duration is a yield duration  statistic in that it measures 
interest rate risk in terms of a change in the bond’s own yield-  to- maturity (ΔYield).

Effective duration is a curve duration  statistic in that it measures interest rate risk in 
terms of a parallel shift in the benchmark yield curve (ΔCurve).
Effective duration is essential to the measurement of the interest rate risk of a 
complex bond, such as a bond that contains an embedded call option. The duration 
of a callable bond is not the sensitivity of the bond price to a change in the yield-  to- 
worst (i.e., the lowest of the yield-  to- maturity, yield-  to- first-  call, yield-  to- second-  call, 
and so forth). The problem is that future cash flows are uncertain because they are 
contingent on future interest rates. The issuer’s decision to call the bond depends on 
the ability to refinance the debt at a lower cost of funds. In brief, a callable bond does 
not have a well-  defined internal rate of return (yield-  to- maturity). Therefore, yield 
duration statistics, such as modified and Macaulay durations, do not apply; effective

Reading 54 ■ Understanding Fixed -Income Risk and Return 546
The specific option-  pricing models that are used to produce the inputs to effective 
duration for a callable bond are covered in later readings. However, as an example, 
suppose that the full price of a callable bond is 101.060489 per 100 of par value. The 
option-  pricing model inputs include (1) the length of the call protection period, (2) 
the schedule of call prices and call dates, (3) an assumption about credit spreads over 
benchmark yields (which includes any liquidity spread as well), (4) an assumption 
about future interest rate volatility, and (5) the level of market interest rates (e.g., 
the government par curve). The analyst then holds the first four inputs constant 
and raises and lowers the fifth input. Suppose that when the government par curve 
is raised and lowered by 25 bps, the new full prices for the callable bond from the 
model are 99.050120 and 102.890738, respectively. Therefore, PV0 = 101.060489, PV+

= 99.050120, PV− = 102.890738, and ΔCurve = 0.0025. The effective duration for the 
callable bond is 7.6006.
EffDur =−
××=102 890738 99 050120
20 0025 101 0604897 6006..
...
This curve duration measure indicates the bond’s sensitivity to the benchmark yield 
curve—in particular, the government par curve—assuming no change in the credit 
spread. In practice, a callable bond issuer might be able to exercise the call option and 
obtain a lower cost of funds if (1) benchmark yields fall and the credit spread over 
the benchmark is unchanged or (2) benchmark yields are unchanged and the credit 
spread is reduced (e.g., because of an upgrade in the issuer’s rating). A pricing model 
can be used to determine a “credit duration” statistic—that is, the sensitivity of the 
bond price to a change in the credit spread. On a traditional fixed-  rate bond, modified 
duration estimates the percentage price change for a change in the benchmark yield

and/or the credit spread. For bonds that do not have a well-  defined internal rate of 
return because the future cash flows are not fixed—for instance, callable bonds and 
floating-  rate notes—pricing models are used to produce different statistics for changes 
in benchmark interest rates and for changes in credit risk.
Another fixed-  income security for which yield duration statistics, such as modified 
and Macaulay durations, are not relevant is a mortgage-  backed bond. These securities 
arise from a residential (or commercial) loan portfolio securitization. The key point 
for measuring interest rate risk on a mortgage-  backed bond is that the cash flows are 
contingent on homeowners’ ability to refinance their debt at a lower rate. In effect, 
the homeowners have call options on their mortgage loans.
A practical consideration in using effective duration is in setting the change in the 
benchmark yield curve. With approximate modified duration, accuracy is improved by

choosing a smaller yield-  to- maturity change. But the pricing models for more-  complex 
securities, such as callable and mortgage-  backed bonds, include assumptions about 
the behavior of the corporate issuers, businesses, or homeowners. Rates typically need 
to change by a minimum amount to affect the decision to call a bond or refinance a 
mortgage loan because issuing new debt involves transaction costs. Therefore, estimates 
of interest rate risk using effective duration are not necessarily improved by choosing 
a smaller change in benchmark rates. Effective duration has become an important 
tool in the financial analysis of not only traditional bonds but also financial liabilities. 
Example 9 demonstrates such an application of effective duration.
EXAMPLE 9   
Defined-  benefit pension schemes typically pay retirees a monthly amount 
based on their wage level at the time of retirement. The amount could be fixed 
in nominal terms or indexed to inflation. These programs are referred to as

“defined-  benefit pension plans” when US GAAP or IFRS accounting standards 
are used. In Australia, they are called “superannuation funds. ”

Interest Rate Risk on Fixed-  Rate Bonds 547
A British defined-  benefit pension scheme seeks to measure the sensitivity of 
its retirement obligations to market interest rate changes. The pension scheme 
manager hires an actuarial consultancy to model the present value of its liabilities 
under three interest rate scenarios: (1) a base rate of 5%, (2) a 100 bp increase 
in rates, up to 6%, and (3) a 100 bp drop in rates, down to 4%.
The actuarial consultancy uses a complex valuation model that includes 
assumptions about employee retention, early retirement, wage growth, mortality, 
and longevity. The following chart shows the results of the analysis.
Interest Rate Assumption Present Value of Liabilities
4% GBP973.5 million
5% GBP926.1 million
6% GBP871.8 million
Compute the effective duration of the pension scheme’s liabilities.
Solution:
PV0 = 926.1, PV+ = 871.8, PV− = 973.5, and ΔCurve = 0.0100. The effective 
duration of the pension scheme’s liabilities is 5.49.
EffDur =−
××=973 5 871 8

EffDur =−
20 0100 926 1549..
...
This effective duration statistic for the pension scheme’s liabilities might be 
used in asset allocation decisions to decide the mix of equity, fixed income, 
and alternative assets.
Although effective duration is the most appropriate interest rate risk measure for 
bonds with embedded options, it also is useful with traditional bonds to supplement 
the information provided by the Macaulay and modified yield durations. Exhibit 5 
displays the Bloomberg Yield and Spread (YAS) Analysis page for the 0.625% US 
Treasury note that matures on 31 May 2017.

Reading 54 ■ Understanding Fixed -Income Risk and Return 548
Exhibit 5   Bloomberg YAS Page for the 0.625% US Treasury Note
In Exhibit 5, the quoted (flat) price for the bond is 99 – 16¾, which is equal to 
99 and 16¾ 32nds per 100 of par value for settlement on 22 June 2012. Most bond 
prices are stated in decimals, but US Treasuries are usually quoted in fractions. As a 
decimal, the flat price is 99.523438. The accrued interest uses the actual/actual day-  
count method. That settlement date is 22 days into a 183-  day semiannual coupon 
payment period. The accrued interest is 0.037568 per 100 of par value (= 22/183 × 
0.00625/2 × 100). The full price of the bond is 99.561006. The yield-  to- maturity of the 
bond is 0.723368%, stated on a street-  convention semiannual bond basis.
The modified duration for the bond is shown in Exhibit 5 to be 4.853, which is

the conventional yield  duration statistic. Its curve  duration, however, is 4.882, which 
is the price sensitivity with respect to changes in the US Treasury par curve. On 
Bloomberg, the effective duration is called the “OAS duration” because it is based on 
the option-  pricing model that is also used to calculate the option-  adjusted spread. The 
small difference arises because the government yield curve is not flat. When the par 
curve is shifted in the model, the government spot curve is also shifted, although not 
in the same “parallel” manner. Therefore, the change in the bond price is not exactly 
the same as it would be if its own yield-  to- maturity changed by the same amount as 
the change in the par curve. In general, the modified duration and effective duration 
on a traditional option-  free bond are not identical. The difference narrows when the 
yield curve is flatter, the time-  to- maturity is shorter, and the bond is priced closer to

par value (so that the difference between the coupon rate and the yield-  to- maturity 
is smaller). The modified duration and effective duration on an option-  free bond are 
identical only in the rare circumstance of an absolutely flat yield curve.
Above, the effective duration for a sample callable bond was calculated as:
EffDur =−
...
This duration measure indicates the bond’s sensitivity to the benchmark yield 
curve assuming that all yields change by the same amount.

Interest Rate Risk on Fixed-  Rate Bonds 549
3.3 Key Rate Duration
Key rate duration provides further insight into a bond’s sensitivity to changes in the 
benchmark yield curve. A key rate duration  (or partial duration ) is a measure of 
a bond’s sensitivity to a change in the benchmark yield curve at a specific maturity 
segment. In contrast to effective duration, key rate durations help identify “shaping 
risk” for a bond—that is, a bond’s sensitivity to changes in the shape of the benchmark 
yield curve (e.g., the yield curve becoming steeper or flatter).
The previous illustration of effective duration assumed a parallel shift of 25 bps at 
all maturities. However, the analyst may want to know how the price of the callable 
bond is expected to change if benchmark rates at short maturities (say up to 2 years) 
shifted up by 25 bps but longer maturity benchmark rates remained unchanged. This 
scenario would represent a flattening of the yield curve, given that the yield curve

is upward sloping. Using key rate durations, the expected price change would be 
approximately equal to minus the key rate duration for the short maturity segment 
times the 0.0025 interest rate shift at that segment. Of course, for parallel shifts in 
the benchmark yield curve, key rate durations will indicate the same interest rate 
sensitivity as effective duration.
3.4 Properties of Bond Duration
The Macaulay and modified yield duration statistics for a traditional fixed-  rate bond 
are functions of the input variables: the coupon rate or payment per period, the yield-  
to- maturity per period, the number of periods to maturity (as of the beginning of 
the period), and the fraction of the period that has gone by. The properties of bond 
duration are obtained by changing one of these variables while holding the others 
constant. Because duration is the basic measure of interest rate risk on a fixed-  rate 
bond, these properties are important to understand.

The closed-  form formula for Macaulay duration, presented as Equation  4 and 
again here, is useful in demonstrating the characteristics of the bond duration statistic.
×+() −

+



−1 1
11r
rrN cr
cr rtTN(()
The same characteristics hold for modified duration. Consider first the fraction of 
the period that has gone by ( t/T). Macaulay and modified durations depend on the 
day-  count basis used to obtain the yield-  to- maturity. The duration of a bond that uses 
the actual/actual method to count days is slightly different from that of an otherwise 
comparable bond that uses the 30/360 method. The key point is that for a constant 
yield-  to- maturity ( r), the expression in braces is unchanged as time passes during the 
period. Therefore, the Macaulay duration decreases smoothly as t goes from t = 0 to 
t = T, which creates a “saw-  tooth” pattern. This pattern for a typical fixed-  rate bond 
is illustrated in Exhibit 6.

Reading 54 ■ Understanding Fixed -Income Risk and Return 550
Exhibit 6   Macaulay Duration between Coupon Payments with a Constant 
Yield-  to- Maturity
Macaulay
Duration
Time-to-Maturity
Coupon Payment Dates
As times passes during the coupon period (moving from right to left in the dia -
gram), the Macaulay duration declines smoothly and then jumps upward after the 
coupon is paid.
The characteristics of bond duration related to changes in the coupon rate, the 
yield-  to- maturity, and the time-  to- maturity are illustrated in Exhibit 7.
Exhibit 7   Properties of the Macaulay Yield Duration
Macaulay
Duration
Time-to-MaturityZero-Coupon Bond
Premium BondPerpetuityl + r
r
Exhibit 7 shows the graph for coupon payment dates when t/T = 0, thus not dis -
playing the saw-  tooth pattern between coupon payments. The relationship between the 
Macaulay duration and the time-  to- maturity for a zero-  coupon bond is the 45-  degree

line: MacDur = N when c = 0 (and t/T = 0). Therefore, the Macaulay duration of a 
zero-  coupon bond is its time-  to- maturity.
A perpetuity  or perpetual bond, which also is called a consol, is a bond that does 
not mature. There is no principal to redeem. The investor receives a fixed coupon 
payment forever, unless the bond is callable. Non-  callable perpetuities are rare, but 
they have an interesting Macaulay duration: MacDur = (1  + r)/r as N approaches 
infinity. In effect, the second expression within the braces approaches zero as the 
number of periods to maturity increases because N in the numerator is a coefficient 
but N in the denominator is an exponent and the denominator increases faster than 
the numerator as N grows larger.
Typical fixed-  rate coupon bonds with a stated maturity date are portrayed in 
Exhibit 7 as the premium and discount bonds. The usual pattern is that longer times-  
to- maturity correspond to higher Macaulay duration statistics. This pattern always

holds for bonds trading at par value or at a premium above par. In Equation 4, the 
second expression within the braces is a positive number for premium and par bonds.

Interest Rate Risk on Fixed-  Rate Bonds 551
The numerator is positive because the coupon rate ( c) is greater than or equal to the 
yield-  to- maturity ( r), whereas the denominator is always positive. Therefore, the 
Macaulay duration is always less than (1 + r)/r, and it approaches that threshold from 
below as the time-  to- maturity increases.
The curious result displayed in Exhibit  7 is in the pattern for discount bonds. 
Generally, the Macaulay duration increases for a longer time-  to- maturity. But at 
some point when the time-  to- maturity is high enough, the Macaulay duration exceeds 
(1  + r)/r, reaches a maximum, and then approaches the threshold from above. In 
Equation 4, such a pattern develops when the number of periods ( N) is large and the 
coupon rate ( c) is below the yield-  to- maturity ( r). Then the numerator of the second 
expression within the braces can become negative. The implication is that on long-

term discount bonds, the interest rate risk can actually be less than on a shorter-  term 
bond, which explains why the word “generally” is needed in describing the maturity 
effect for the relationship between bond prices and yields-  to- maturity. Generally, 
for the same coupon rate, a longer-  term bond has a greater percentage price change 
than a shorter-  term bond when their yields-  to- maturity change by the same amount. 
The exception is when the longer-  term bond actually has a lower duration statistic.
Coupon rates and yields-  to- maturity are both inversely related to the Macaulay 
duration. In Exhibit  7, for the same time-  to- maturity and yield-  to- maturity, the 
Macaulay duration is higher for a zero-  coupon bond than for a low-  coupon bond 
trading at a discount. Also, the low-  coupon bond trading at a discount has a higher 
duration than a high-  coupon bond trading at a premium. Therefore, all else being

equal, a lower-  coupon bond has a higher duration and more interest rate risk than a 
higher-  coupon bond. The same pattern holds for the yield-  to- maturity. A higher yield-  
to- maturity reduces the weighted average of the time to receipt of cash flow. More 
weight is on the cash flows received in the near term, and less weight is on the cash 
flows received in the more-  distant future periods if those cash flows are discounted 
at a higher rate.
In summary, the Macaulay and modified duration statistics for a fixed-  rate bond 
depend primarily on the coupon rate, yield-  to- maturity, and time-  to- maturity. A 
higher coupon rate or a higher yield-  to- maturity reduces the duration measures. A 
longer time-  to- maturity usually  leads to a higher duration. It always  does so for a 
bond priced at a premium or at par value. But if the bond is priced at a discount, a 
longer time-  to- maturity might  lead to a lower duration. This situation only occurs if the

coupon rate is low (but not zero) relative to the yield and the time-  to- maturity is long.
EXAMPLE 10   
A hedge fund specializes in investments in emerging market sovereign debt. 
The fund manager believes that the implied default probabilities are too high, 
which means that the bonds are viewed as “cheap” and the credit spreads are too 
high. The hedge fund plans to take a position on one of these available bonds.
BondTime-  to- 
MaturityCoupon 
Rate PriceYield-  to- 
Maturity
(A) 10 years 10% 58.075279 20%
(B) 20 years 10% 51.304203 20%
(C) 30 years 10% 50.210636 20%

Reading 54 ■ Understanding Fixed -Income Risk and Return 552
The coupon payments are annual. The yields-  to- maturity are effective annual 
rates. The prices are per 100 of par value.
1 Compute the approximate modified duration of each of the three bonds 
using a 1 bp change in the yield-  to- maturity and keeping precision to six 
decimals (because approximate duration statistics are very sensitive to 
rounding).
2 Which of the three bonds is expected to have the highest percentage price 
increase if the yield-  to- maturity on each decreases by the same amount—
for instance, by 10 bps from 20% to 19.90%?
Bond A:
PV0 = 58.075279
PV+= 58.047598
10
1 200110
1 2001110
1 200158 04759812 10.. ..
()+
()++
()= 
PV−= 58.102981
10
1 199910
1 1999110
1 199958 10298112 10.. ..
()+
()++
()= 
The approximate modified duration of Bond A is 4.768.
××=58 102981 58 047598
20 0001 58 0752794 768..
...
Bond B:
PV0 = 51.304203
PV+= 51.277694
10
1 200110
1 2001110
1 200151 27769412 20.. ..
()+
()++
()= 

1 2001110
()+
()++
()= 
PV−= 51.330737
10
1 199910
1 1999110
1 199951 33073712 20.. ..
()+
()++
()= 
The approximate modified duration of Bond B is 5.169. 
××=51 330737 51 277694
20 0001 51 3042035 169..
...
Bond C:
PV0 = 50.210636
PV+= 50.185228
10
1 200110
1 2001110
1 200150 18522812 30.. ..
()+
()++
()= 
PV−= 50.236070

Interest Rate Risk on Fixed-  Rate Bonds 553
10
1 199910
1 1999110
1 199950 23607012 30.. ..
()+
()++
()= 
The approximate modified duration of Bond C is 5.063.
××=50 236070 50 185228
20 0001 50 2106365 063..
...
Despite the significant differences in times-  to- maturity (10, 20, and 30 years), 
the approximate modified durations on the three bonds are fairly similar (4.768, 
5.169, and 5.063). Because the yields-  to- maturity are so high, the additional time 
to receipt of interest and principal payments on the 20- and 30-  year bonds have 
low weight. Nevertheless, Bond B, with 20 years to maturity, has the highest 
modified duration. If the yield-  to- maturity on each is decreased by the same 
amount—for instance, by 10 bps, from 20% to 19.90%—Bond B would be expected 
to have the highest percentage price increase because it has the highest mod -
ified duration. This example illustrates the relationship between the Macaulay

duration and the time-  to- maturity on discount bonds in Exhibit 7. The 20-  year 
bond has a higher duration than the 30-  year bond.
Callable bonds require the use of effective duration because Macaulay and modi -
fied yield duration statistics are not relevant. The yield-  to- maturity for callable bonds 
is not well-  defined because future cash flows are uncertain. Exhibit 8 illustrates the 
impact of the change in the benchmark yield curve (ΔCurve) on the price of a callable 
bond price compared with that on a comparable non-  callable bond. The two bonds 
have the same credit risk, coupon rate, payment frequency, and time-  to- maturity. The 
vertical axis is the bond price. The horizontal axis is a particular benchmark yield—for 
instance, a point on the par curve for government bonds.
Exhibit 8   Interest Rate Risk Characteristics of a Callable Bond
PV0
PV+Price
PV–
∆ Curve ∆ CurveValue of the Embedded Call Option
Callable BondNon-Callable Bond
Benchmark Yield

As shown in Exhibit 8, the price of the non-  callable bond is always greater than 
that of the callable bond with otherwise identical features. The difference is the value 
of the embedded call option. Recall that the call option is an option to the issuer and 
not the holder of the bond. When interest rates are high compared with the coupon 
rate, the value of the call option is low. When rates are low, the value of the call option

Reading 54 ■ Understanding Fixed -Income Risk and Return 554
is much greater because the issuer is more likely to exercise the option to refinance 
the debt at a lower cost of funds. The investor bears the “call risk” because if the bond 
is called, the investor must reinvest the proceeds at a lower interest rate.
Exhibit 8 shows the inputs for calculating the effective duration of the callable bond. 
The entire benchmark curve is raised and lowered by the same amount, ΔCurve. The 
key point is that when benchmark yields are high, the effective durations of the callable 
and non-  callable bonds are very similar. Although the exhibit does not illustrate it, 
the slopes of the lines tangent to the price–yield curve are about the same in such a 
situation. But when interest rates are low, the effective duration of the callable bond 
is lower than that of the otherwise comparable non-  callable bond. That is because 
the callable bond price does not increase as much when benchmark yields fall. The

slope of the line tangent to the price–yield curve would be flatter. The presence of the 
call option limits price appreciation. Therefore, an embedded call option reduces the 
effective duration of the bond, especially when interest rates are falling and the bond 
is more likely to be called. The lower effective duration can also be interpreted as a 
shorter expected life—the weighted average of time to receipt of cash flow is reduced.
Exhibit 9 considers another embedded option—a put option.
Exhibit 9   Interest Rate Risk Characteristics of a Putable Bond
PV0
PV+Price
PV–
∆ Curve ∆ CurveValue of the Embedded Put OptionPutable Bond
Non-Putable Bond
A putable bond allows the investor to sell the bond back to the issuer prior to 
maturity, usually at par value, which protects the investor from higher benchmark 
yields or credit spreads that otherwise would drive the bond to a discounted price. 
Therefore, the price of a putable bond is always higher than that of an otherwise com -

parable non-  putable bond. The price difference is the value of the embedded put option.
An embedded put option reduces the effective duration of the bond, especially 
when rates are rising. If interest rates are low compared with the coupon rate, the 
value of the put option is low and the impact of a change in the benchmark yield on 
the bond’s price is very similar to the impact on the price of a non-  putable bond. But 
when benchmark interest rates rise, the put option becomes more valuable to the 
investor. The ability to sell the bond at par value limits the price depreciation as rates 
rise. In summary, the presence of an embedded option reduces the sensitivity of the 
bond price to changes in the benchmark yield curve, assuming no change in credit risk.

Interest Rate Risk on Fixed-  Rate Bonds 555
3.5 Duration of a Bond Portfolio
Similar to equities, bonds are typically held in a portfolio. There are two ways to cal -
culate the duration of a bond portfolio: (1) the weighted average of time to receipt of 
the aggregate  cash flows and (2) the weighted average of the individual bond durations 
that comprise the portfolio. The first method is the theoretically correct approach, 
but it is difficult to use in practice. The second method is commonly used by fixed-  
income portfolio managers, but it has its own limitations. The differences in these two 
methods to compute portfolio duration can be examined with a numerical example.
Suppose an investor holds the following portfolio of two zero-  coupon  bonds:
Bond Maturity Price YieldMacaulay 
DurationModified 
Duration Par ValueMarket 
Value Weight
(X) 1 year 98.00 2.0408% 1 0.980 10,000,000 9,800,000 0.50
(Y) 30 years 9.80 8.0503% 30 27.765 100,000,000 9,800,000 0.50

The prices are per 100 of par value. The yields-  to- maturity are effective annual rates. 
The total market value for the portfolio is 19,600,000. The portfolio is evenly weighted 
in terms of market value between the two bonds.
The first approach views the portfolio as a series of aggregated cash flows. Its cash 
flow yield  is 7.8611%. A cash flow yield is the internal rate of return on a series of 
cash flows, usually used on a complex security such as a mortgage-  backed bond (using 
projected cash flows based on a model of prepayments as a result of refinancing) or a 
portfolio of fixed-  rate bonds. It is the solution for r in the following equation.
19 600 00010 000 000
10
10
1100 000 000
12 29,,,, ,,=
+()+
+()++
+()+
rr r
1 10 07861130+()=
rr,     .
The Macaulay duration of the portfolio in this approach is the weighted average 
of time to receipt of aggregated cash flow. The cash flow yield is used to obtain the

weights. This calculation is similar to Equation 1, and the portfolio duration is 16.2825.
MacDur =×
()+×
()110 000 000
1 07861130 100 000 000
1 078611
113 0,,
.,,
.
0 0 000 000
1 078611100 000 000
1 07861113 0,,
.,,
. ()+
()









 =16 2825 .
There are just two future cash flows in the portfolio—the redemption of principal 
on the two zero-  coupon bonds. In more complex portfolios, a series of coupon and 
principal payments may occur on some dates, with an aggregated cash flow composed 
of coupon interest on some bonds and principal on those that mature.
The modified duration of the portfolio is the Macaulay duration divided by one 
plus the cash flow yield per period (here, the periodicity is 1).
ModDur= =16 2825
1 07861115 0958.
..
The modified duration for the portfolio is 15.0958. That statistic indicates the percent -
age change in the market value given a change in the cash flow yield. If the cash flow 
yield increases or decreases by 100 bps, the market value of the portfolio is expected

to increase or decrease by about 15.0958%.
Although this approach is “theoretically correct, ” it is difficult to use in practice. 
First, the cash flow yield is not commonly calculated for bond portfolios. Second, 
the amount and timing of future coupon and principal payments are uncertain if the 
portfolio contains callable or putable bonds or floating-  rate notes. Third, interest rate 
risk is usually expressed as a change in benchmark interest rates, not as a change in the 
cash flow yield. Fourth, the change in the cash flow yield is not necessarily the same

Reading 54 ■ Understanding Fixed -Income Risk and Return 556
amount as the change in the yields-  to- maturity on the individual bonds. For instance, 
if the yields-  to- maturity on the two zero-  coupon bonds in this portfolio both increase 
or decrease by 10 bps, the cash flow yield increases or decreases by only 9.52 bps.
In practice, the second approach to portfolio duration is commonly used. The 
Macaulay and modified durations for the portfolio are calculated as the weighted 
average of the statistics for the individual bonds. The shares of overall portfolio market 
value are the weights. This weighted average is an approximation of the “theoretically 
correct” portfolio duration, which is obtained using the first approach. This approxi -
mation becomes more accurate when the differences in the yields-  to- maturity on the 
bonds in the portfolio are smaller. When the yield curve is flat, the two approaches 
produce the same portfolio duration.

Given the equal “50/50” weights in this simple numerical example, this version of 
portfolio duration is easily computed.
 Average Macaulay duration = (1 × 0.50) + (30 × 0.50) = 15.50
 Average modified duration = (0.980 × 0.50) + (27.765 × 0.50) = 14.3725
Note that 0.980 = 1/1.020404 and 27.765 = 30/1.080503. An advantage of the second 
approach is that callable bonds, putable bonds, and floating-  rate notes can be included 
in the weighted average using the effective durations for these securities.
The main advantage to the second approach is that it is easily used as a measure of 
interest rate risk. For instance, if the yields-  to- maturity on the bonds in the portfolio 
increase by 100 bps, the estimated drop in the portfolio value is 14.3725%. However, 
this advantage also indicates a limitation: This measure of portfolio duration implicitly 
assumes a parallel shift  in the yield curve. A parallel yield curve shift implies that

all rates change by the same amount in the same direction. In reality, interest rate 
changes frequently result in a steeper or flatter yield curve. Yield volatility is discussed 
later in this reading.
EXAMPLE 11   
An investment fund owns the following portfolio of three fixed-  rate government 
bonds:
Bond A Bond B Bond C
Par value EUR25,000,000 EUR25,000,000 EUR50,000,000
Coupon rate 9% 11% 8%
Time-  to- maturity 6 years 8 years 12 years
Yield-  to- maturity 9.10% 9.38% 9.62%
Market value EUR24,886,343 EUR27,243,887 EUR44,306,787
Macaulay duration 4.761 5.633 7.652
The total market value of the portfolio is EUR96,437,017. Each bond is on 
a coupon date so that there is no accrued interest. The market values are the 
full prices given the par value. Coupons are paid semiannually. The yields-  to- 
maturity are stated on a semiannual bond basis, meaning an annual rate for a 
periodicity of 2. The Macaulay durations are annualized.

1 Calculate the average (annual) modified duration for the portfolio using 
the shares of market value as the weights.
2 Estimate the percentage loss in the portfolio’s market value if the (annual) 
yield-  to- maturity on each bond goes up by 20 bps.

Interest Rate Risk on Fixed-  Rate Bonds 557
The average (annual) modified duration for the portfolio is 6.0495.
4 761
10 0910
224 886 343
96 437 0175 633
100.
.,,
,,.
.+×





+
+9 938
227 243 887
96 437 017
7 652
10 0962
244 3×





+
+×,,
,,
.
.,0 06 787
96 437 0176 0495,
,,.





=
Note that the annual modified duration for each bond is the annual Macaulay 
duration, which is given, divided by one plus the yield-  to- maturity per semi -
annual period.
The estimated decline in market value if each yield rises by 20 bps is 1.21%: 
−6.0495 × 0.0020 = −0.0121.
3.6 Money Duration of a Bond and the Price Value of a Basis 
Point
Modified duration is a measure of the percentage price change  of a bond given a change 
in its yield-  to- maturity. A related statistic is money duration . The money duration 
of a bond is a measure of the price change  in units of the currency in which the bond 
is denominated. The money duration can be stated per 100 of par value or in terms

of the actual position size of the bond in the portfolio. In the United States, money 
duration is commonly called “dollar duration. ”
Money duration (MoneyDur) is calculated as the annual modified duration times 
the full price ( PVFull) of the bond, including accrued interest.
MoneyDur = AnnModDur × PVFull  
The estimated change in the bond price in currency units is calculated using 
Equation 11, which is very similar to Equation 6. The difference is that for a given 
change in the annual yield-  to- maturity (ΔYield), modified duration estimates the 
percentage price change and money duration estimates the change in currency units.
ΔPVFull ≈ –MoneyDur × ΔYield  
For an example of money duration, consider the 6% semiannual coupon payment 
bond that matures on 14 February 2022 and is priced to yield 6.00% for settlement 
on 11 April  2014. The full price of the bond is 100.940423 per 100 of par value, 
and the annual modified duration is 6.1268. Suppose that a Hong Kong–based life

insurance company has a position in the bond for a par value of HKD100,000,000. 
The market value of the investment is HKD100,940,423. The money duration of this 
bond is HKD618,441,784 (= 6.1268 × HKD100,940,423). Therefore, if the yield-  to- 
maturity rises by 100 bps—from 6.00% to 7.00%—the expected loss is approximately 
HKD6,184,418 (= HKD618,441,784 × 0.0100). On a percentage basis, that expected 
loss is approximately 6.1268%. The “convexity adjustment” introduced in the next 
section makes these estimates more accurate.(10)
(11)

Reading 54 ■ Understanding Fixed -Income Risk and Return 558
Another version of money duration is the price value of a basis point  (PVBP) for 
the bond. The PVBP is an estimate of the change in the full price given a 1 bp change 
in the yield-  to- maturity. The PVBP can be calculated using a formula similar to that 
for the approximate modified duration. Equation 12 is the formula for the PVBP .
PVBP=() −() −+PV PV
2
PV− and PV+ are the full prices calculated by decreasing and increasing the yield-  
to- maturity by 1 bp. The PVBP is also called the “PV01, ” standing for the “price value 
of an 01”or “present value of an 01, ” where “01” means 1 bp. In the United States, it is 
commonly called the “DV01, ” or the “dollar value of a 01. ” A related statistic, some -
times called a “basis point value” (or BPV), is the money duration times 0.0001 (1 bp).
For a numerical example of the PVBP calculation, consider the 0.625% semiannual

coupon payment US Treasury note that matures on 31 May 2017. In Exhibit 5, the PVBP 
for the Treasury note is shown to be 0.04831. Its yield-  to- maturity is 0.723368%, and 
the settlement date is 22 days into a 183-  day period. To confirm this result, calculate 
the new prices by increasing and decreasing the yield-  to- maturity. First, increase the 
yield by 1 bp (0.01%), from 0.723368% to 0.733368%, to solve for a PV+ of 99.512707.
PV+=
+

++
+
0 3125
10 00733368
2100 3125
21.
..
.
 









×+


=1022 183
2
99 512707.
.
Then, decrease the yield-  to- maturity by 1 bp, from 0.723368% to 0.713368%, to solve 
for a PV− of 99.609333.
PV−=
+

++
+
0 3125
10 00713368
2100 3125
21.
..
.
 









×+


=1022 183
2
99 609333.
.
The PVBP is obtained by substituting these results into Equation 12.
PVBP=−=99 609333 99 512707
20 04831...
Another money duration statistic reported on the Bloomberg YAS page is “risk. ” It is

shown to be 4.831. Bloomberg’s risk statistic is simply the PVBP (or PV01) times 100.
EXAMPLE 12   
A life insurance company holds a USD10 million (par value) position in a 4.50% 
ArcelorMittal bond that matures on 25 February 2017. The bond is priced (flat) 
at 98.125 per 100 of par value to yield 5.2617% on a street-  convention semian -
nual bond basis for settlement on 27 June 2014. The total market value of the 
position, including accrued interest, is USD9,965,000, or 99.650 per 100 of par 
value. The bond’s (annual) Macaulay duration is 2.4988.
1 Calculate the money duration per 100 in par value for the ArcelorMittal 
bond.
2 Using the money duration, estimate the loss on the position for each 1 bp 
increase in the yield-  to- maturity for that settlement date.(12)

Interest Rate Risk on Fixed-  Rate Bonds 559
The money duration is the annual modified duration times the full price of the 
bond per 100 of par value.
2 4988
10 052617
299 650 242 62.
...
+





×=USDU SD
For each 1 bp increase in the yield-  to- maturity, the loss is estimated to be 
USD0.024262 per 100 of par value: USD242.62 × 0.0001 = USD0.024262.
Given a position size of USD10 million in par value, the estimated loss per 
basis-  point increase in the yield is USD2,426.20. The money duration is per 100 
of par value, so the position size of USD10 million is divided by 100.
USDUSDUSD 0 02426210 000 000
1002 426 20 .,,,. ×=
3.7 Bond Convexity
Modified duration measures the primary effect on a bond’s percentage price change 
given a change in the yield-  to- maturity. A secondary effect is measured by the convexity 
statistic, which is illustrated in Exhibit 10 for a traditional (option-  free) fixed-  rate bond.

Exhibit 10   Convexity of a Traditional (Option-  Free) Fixed-  Rate Bond
Price
Convex Price–Yield Curve
Estimated Change Due to Convexity
Estimated Change Due to Duration
The true relationship between the bond price and the yield-  to- maturity is the 
curved (convex) line shown in Exhibit 10. This curved line shows the actual bond price 
given its market discount rate. Duration (in particular, money duration) estimates the 
change in the bond price along the straight line that is tangent to the curved line. For 
small yield-  to- maturity changes, there is little difference between the lines. But for 
larger changes, the difference becomes significant.

Reading 54 ■ Understanding Fixed -Income Risk and Return 560
The convexity statistic for the bond is used to improve the estimate of the percent -
age price change provided by modified duration alone. Equation 13 is the convexity-  
adjusted estimate of the percentage change in the bond’s full price.5
%∆
∆∆PVFull≈
−×() +× ×()
AnnModDur YieldA nnConvexity Yield1
22
 
The first bracketed expression, the “first-  order” effect, is the same as Equation 6. 
The (annual) modified duration, AnnModDur, is multiplied by the change in the 
(annual) yield-  to- maturity, ΔYield. The second bracketed expression, the “second-  
order” effect, is the convexity adjustment . The convexity adjustment is the annual 
convexity statistic, AnnConvexity, times one-  half, multiplied by the change in the 
yield-  to- maturity squared . This additional term is a positive amount on a traditional 
(option-  free) fixed-  rate bond for either an increase or decrease in the yield. In

Exhibit 10, this amount adds to the linear estimate provided by the duration alone, 
which brings the adjusted estimate very close to the actual price on the curved line. 
But it still is an estimate, so the ≈ sign is used.
Similar to the Macaulay and modified durations, the annual convexity statistic can 
be calculated in several ways. It can be calculated using tables, such as Exhibits 2 and 
3. It also is possible to derive a closed-  form equation for the convexity of a fixed-  rate 
bond on and between coupon payment dates using calculus and algebra.6 But like 
modified duration, convexity can be approximated with accuracy. Equation 14 is the 
formula for the approximate convexity statistic, ApproxCon .
ApproxCon
Yield=() +() −× () 
() ×()−+PV PV PV
PV20
2
0 ∆
This equation uses the same inputs as Equation  7 for ApproxModDur. The new 
price when the yield-  to- maturity is increased is PV+. The new price when the yield

is decreased by the same amount is PV−. The original price is PV0. These are the full 
prices, including accrued interest, for the bond.
The accuracy of this approximation can be demonstrated with the special case 
of a zero-  coupon bond. The absence of coupon payments simplifies the interest rate 
risk measures. The Macaulay duration of a zero-  coupon bond is N – t/T  in terms of 
periods to maturity. The exact convexity statistic of a zero-  coupon bond, also in terms 
of periods, is calculated with Equation 15.
Convexity  (of a zero- coupon bond) =−() ×+ −() Nt TN tT 1
1+ +()r2
N is the number of periods to maturity as of the beginning of the current period, t/T 
is the fraction of the period that has gone by, and r is the yield-  to- maturity per period.
For an example of this calculation, consider a long-  term, zero-  coupon US Treasury 
bond. The bond’s Bloomberg YAS page is shown in Exhibit 11.(13)
(14)
(15)

(14)
(15)
5 Readers who have studied calculus will recognize this equation as the first two terms of a Taylor series 
expansion. The first term, the modified duration, includes the first derivative of the bond price with respect 
to a change in the yield. The second term, the convexity, includes the second derivative.
6 The step-  by- step derivation for a closed-  form equation for convexity on and between coupon payment dates 
is in Donald J. Smith, Bond Math: The Theory behind the Formulas  (Hoboken, NJ: John Wiley & Sons, 2011).

Interest Rate Risk on Fixed-  Rate Bonds 561
Exhibit 11   Bloomberg YAS Page for the Zero-  Coupon US Treasury Bond
The bond matures on 15 May 2042 and was priced at 41.483611 per 100 of par 
value for settlement on 8 June  2012. Its yield-  to- maturity was 2.961% stated on a 
street-  convention semiannual bond basis. Even though it is a zero-  coupon bond, its 
yield-  to- maturity is based on the actual/actual day-  count convention. That settlement 
date was 24 days into a 184-  day period. The annual modified duration was 29.498.
For this bond, N = 60, t/T = 24/184, and r = 0.02961/2. Entering these variables 
into Equation 15 produces a convexity of 3,538.68 in terms of semiannual periods.
60 24 184 60 12 4 184
10 02961
23 538 682−() ×+ −() 
+

=
.,.
As with the other statistics, convexity is annualized in practice and for use in the

convexity adjustment in Equation 13. It is divided by the periodicity squared . The 
yield-  to- maturity on this zero-  coupon bond is stated on a semiannual bond basis, 
meaning a periodicity of 2. Therefore, the annualized convexity statistic is 884.7.
3 538 68
4884 7,..=
For example, suppose that the yield-  to- maturity is expected to fall by 10 bps, 
from 2.961% to 2.861%. Given the (annual) modified duration of 29.498 and (annual) 
convexity of 884.7, the expected percentage price gain is 2.9940%.
%. .. .
.∆PVFull≈− ×− [] +× ×−()


=29 498 0 00101
288470 0010
0 0292
4 498 0 000442
0 029940+
=.
.
Modified duration alone (under)estimates the gain to be 2.9498%. The convexity 
adjustment adds 4.42 bps.

Reading 54 ■ Understanding Fixed -Income Risk and Return 562
The long-  term, zero-  coupon bond of Exhibit 11 demonstrates the significant dif -
ference between yield  duration and convexity and curve  duration and convexity, even 
on an option-  free bond. Its modified duration is 29.498, whereas its effective duration 
is 34.198. Its yield convexity is reported on the Bloomberg page to be 8.847, and its 
effective convexity is 10.998. (Note that Bloomberg scales the convexity statistics by 
dividing by 100.) In general, the differences are heightened when the benchmark yield 
curve is not flat, when the bond has a long time-  to- maturity, and the bond is priced 
at a significant discount or premium.
To obtain the ApproxCon for this long-  term, zero-  coupon bond, calculate PV0, 
PV+, and PV− for yields-  to- maturity of 2.961%, 2.971%, and 2.951%, respectively. For 
this exercise, ΔYield = 0.0001.
PV06024 184100
10 02961
210 02961
241 483617 =
+

×+

 =
...
PV+=
+

×+

 =100
10 02971


×+

 =
...
PV+=
+

×+

 =100
10 02971
210 02971
241 3614316024 184
...
PV−=
+

×+

 =100
10 02951
210 02951
241 6061696024 184
...
The price of the zero-  coupon bond is actually 41.483611, not 41.483617. In this cal -
culation, PV0 is slightly different because the quoted yield-  to- maturity is rounded.7 
It is appropriate to use the calculated PV0 to be consistent with the change in the 
Using these results, first calculate ApproxModDur using Equation 7 to confirm 
that these inputs are correct. In Exhibit 11, modified duration is stated to be 29.498.
××=41 606169 41 361431
20 0001 41 48361729 498..
...
Using Equation 14, ApproxCon is 882.3.
ApproxCon =+− ×()
() ×41 606169 41 361431 24 1 483617
0 0001 41 482.. .
.. 3 3617882 3= .
This result, 882.3, is an approximation for annualized  convexity. The number of periods 
in the year is included in the price calculations. This approximation is quite close to the

“exact” result using the closed-  form equation for the special case of the zero-  coupon 
bond, 884.7. The difference is not likely to be meaningful for practical applications.
Because this is an individual zero-  coupon bond, it is easy to calculate the new 
price if the yield-  to- maturity does go down by 10 bps, to 2.861%.
100
10 02861
210 02861
2427258416024 184
+

×+

 =
...
Therefore, the actual percentage price increase is 2.9945%.
42 725841 41 483611
41 4836110 029945..
..−=
7 Given the price of 41.483611, the yield-  to- maturity is 2.96100046%.

Interest Rate Risk on Fixed-  Rate Bonds 563
The convexity-  adjusted estimation of 2.9940% is very close to the actual change. Using 
the approximate convexity of 882.3 instead of the exact convexity of 884.7 would not 
have had a meaningful impact.
%. .. .
.∆PVFull≈− ×− () +× ×−()


288230 0010
0 0292
4 498 0 000441
0 029939+
=.
.
The “exact” convexity adjustment is 4.42 bps. The “approximate” convexity adjustment 
is 4.41 bps.
EXAMPLE 13   
An Italian bank holds a large position in a 7.25% annual coupon payment cor -
porate bond that matures on 4 April 2029. The bond’s yield-  to- maturity is 7.44% 
for settlement on 27 June 2014, stated as an effective annual rate. That settlement 
date is 83 days into the 360-  day year using the 30/360 method of counting days.
1 Calculate the full price of the bond per 100 of par value.
2 Calculate the approximate modified duration and approximate convexity 
using a 1 bp increase and decrease in the yield-  to- maturity.

3 Calculate the estimated convexity-  adjusted percentage price change 
resulting from a 100 bp increase in the yield-  to- maturity.
4 Compare the estimated percentage price change with the actual change, 
assuming the yield-  to- maturity jumps to 8.44% on that settlement date.
There are 15 years from the beginning of the current period on 4 April 2014 to 
maturity on 4 April 2029.
1 The full price of the bond is 99.956780 per 100 of par value.
PV011 583 360 725
1 0744107 25
1 07441 0744 =
()++
()



×().
..
..  = =99 956780 .
2 PV+ = 99.869964, and PV− = 100.043703.
PV+=
()++
()



×()725
1 0745107 25
1 07451 074511 583 360 .
..
..  = =99 869964 .
PV−=
()++
()



×()725
1 0743107 25
1 07431 074311 583 360 .
..
..  = =100 043703 .
 The approximate modified duration is 8.6907.
××=100 043703 99 869964
20 0001 99 9567808 6907..
...
 The approximate convexity is 107.046.
() ×100 043703 99 869964 29 9 956780
0 0001 99 92.. .
.. 5 56780107 046= .

Reading 54 ■ Understanding Fixed -Income Risk and Return 564
3 The convexity-  adjusted percentage price drop resulting from a 100 bp 
increase in the yield-  to- maturity is estimated to be 8.1555%. Modified 
duration alone estimates the percentage drop to be 8.6907%. The convex -
ity adjustment adds 53.52 bps.
%. .. .
.∆PVFull≈− × () +× ×()


=−8 6907 0 01001
2107 046 0 0100
0082
6 6907 0 005352
0 081555+
=−.
.
4 The new full price if the yield-  to- maturity goes from 7.44% to 8.44% on 
that settlement date is 91.780921.
PVFull=
()++
()



×()725
1 0844107 25
1 08441 084411 583 .
..
.. 3 36091 780921= .
%..
.. ∆PVFull=−=−91 780921 99 956780
99 9567800 081794
 The actual percentage change in the bond price is –8.1794%. The 
convexity-  adjusted estimate is –8.1555%, whereas the estimated change 
using modified duration alone is –8.6907%.
The money duration of a bond indicates the first-  order effect on the full price 
of a bond in units of currency given a change in the yield-  to- maturity. The money

convexity  statistic (MoneyCon) is the second-  order effect. The money convexity of 
the bond is the annual convexity multiplied by the full price, such that
∆∆ ∆ PVFull≈− × () +× ×()

Mone yDur YieldM oneyCon Yield1
22
For a money convexity example, consider again the Hong Kong–based life insur -
ance company that has a HKD100,000,000 position in the 6.00% bond that matures 
on 14 February 2022. In Section 3.5, using the money duration alone, the estimated 
loss is HKD6,184,418 if the yield-  to- maturity increases by 100 bps. The money dura -
tion for the position is HKD618,441,784. That estimation is improved by including 
the convexity adjustment. In Section 3.1, these inputs are calculated to obtain the 
approximate modified duration of 6.1268 for a 5 bp change in the yield-  to- maturity 
(ΔYield = 0.0005): PV0 = 100.940423, PV+ = 100.631781, and PV− = 101.250227. Enter 
these into Equation 14 to calculate the approximate convexity.

() ×101 250227 100 631781 2 100 940423
0 0005 102.. .
. 0 0 94042346 047
.. =
The money convexity is 46.047 times the market value of the position, HKD100,940,423. 
The convexity-  adjusted loss given a 100 bp jump in the yield-  to- maturity is 
HKD5,952,018.
−×() × +
××6 1268 100 940 423 0 0100
1
246 047 100 940 4., ,.
., ,HKD
HKD 2 23 0 0100
6 184 418 232 400
5 952 02() ×()


=− +
=−.
,, ,
,,HKD HKD
HKD 1 18(16)

Interest Rate Risk on Fixed-  Rate Bonds 565
The factors that lead to greater convexity are the same as for duration. A fixed-  rate 
bond with a longer time-  to- maturity, a lower coupon rate, and a lower yield-  to- 
maturity has greater convexity than a bond with a shorter time-  to- maturity, a higher 
coupon rate, and a higher yield-  to- maturity. Another factor is the dispersion of cash 
flows, meaning the degree to which payments are spread out over time. If two bonds 
have the same duration, the one that has the greater dispersion of cash flows has 
the greater convexity. The positive attributes of greater convexity for an investor are 
shown in Exhibit 12.
Exhibit 12   The Positive Attributes of Greater Bond Convexity on a 
Traditional (Option-  Free) Bond
Price
More Convex Bond
Less Convex Bond
The two bonds in Exhibit 12 are assumed to have the same price, yield-  to- maturity,

and modified duration. Therefore, they share the same line tangent to their price–
yield curves. The benefit of greater convexity occurs when their yields-  to- maturity 
change. For the same decrease in yield-  to- maturity, the more convex bond appreciates 
more  in price. And for the same increase in yield-  to- maturity, the more convex bond 
depreciates less  in price. The conclusion is that the more convex bond outperforms 
the less convex bond in both bull (rising price) and bear (falling price) markets. This 
conclusion assumes, however, that this positive attribute is not “priced into” the 
bond. To the extent that it is included, the more convex bond would have a higher 
price (and lower yield-  to- maturity). That does not diminish the value of convexity. It 
only suggests that the investor has to pay for it. As economists say, “There is no such 
thing as a free lunch. ”
EXAMPLE 14   
The investment manager for a UK defined-  benefit pension scheme is considering

two bonds about to be issued by a large life insurance company. The first is a 
30- year, 4% semiannual coupon payment bond. The second is a 100-  year, 4% 
semiannual coupon payment “century” bond. Both bonds are expected to trade 
at par value at issuance.
Calculate the approximate modified duration and approximate convexity for 
each bond using a 5 bp increase and decrease in the annual yield-  to- maturity. 
Retain accuracy to six decimals per 100 of par value.

Reading 54 ■ Understanding Fixed -Income Risk and Return 566
Solution:
In the calculations, the yield per semiannual period goes up by 2.5 bps to 2.025% 
and down by 2.5 bps to 1.975%. The 30-  year bond has an approximate modified 
duration of 17.381 and an approximate convexity of 420.80.
PV+=
()++
()=2
1 02025102
1 0202599 13621416 0... 
PV−=
()++
()=2
1 01975102
1 01975100 87430616 0... 
××=100 874306 99 136214
20 0005 10017 381..
..
() ×=100 874306 99 136214 2 100
0 0005 100420 802..
..
The 100-  year century bond has an approximate modified duration of 24.527 and 
an approximate convexity of 1,132.88.
PV+=
()++
()=2
1 02025102
1 0202598 7878291 200... 
PV−=
()++
()=2
1 01975102
1 01975101 2404931 200... 
××=101 240493 98 787829
20 0005 10024 527..
..
() ×=101 240493 98 787829 2 100
0 0005 10011322..
.,. 8 88
The century bond offers a higher modified duration—24.527 compared with

17.381—and a much greater degree of convexity—1,132.88 compared with 420.80.
In the same manner that the primary, or first-  order, effect of a shift in the bench -
mark yield curve is measured by effective duration, the secondary, or second-  order, 
effect is measured by effective convexity . The effective convexity of a bond is a curve 
convexity  statistic that measures the secondary effect of a change in a benchmark yield 
curve. A pricing model is used to determine the new prices when the benchmark 
curve is shifted upward ( PV+) and downward ( PV−) by the same amount (ΔCurve). 
These changes are made holding other factors constant—for example, the credit 
spread. Then, Equation 17 is used to calculate the effective convexity (EffCon) given 
the initial price ( PV0).
EffCon
Curve=() +() −× () 
PV20
2
0 ∆
This equation is very similar to Equation  14, for approximate yield  convexity. The

difference is that in Equation 14, the denominator includes the change in the yield-  
to- maturity squared, (ΔYield)2. Here, the denominator includes the change in the 
benchmark yield curve squared, (ΔCurve)2.(17)

Interest Rate Risk and the Investment Horizon 567
Consider again the callable bond example in Section 3.2. It is assumed that an 
option-  pricing model is used to generate these callable bond prices: PV0 = 101.060489, 
PV+ = 99.050120, PV− = 102.890738, and ΔCurve = 0.0025. The effective duration for 
the callable bond is 7.6006.
EffDur =−
...
Using these inputs in Equation 17, the effective convexity is –285.17.
EffCon =+− ×()
() ×102 890738 99 050120 2 101 060489
0 0025 101 062.. .
.. 0 0489285 17=− .
Negative convexity, which could be called “concavity, ” is an important feature of 
callable bonds. Putable bonds, on the other hand, always have positive convexity. As 
a second-  order effect, effective convexity indicates the change in the first-  order effect 
(i.e., effective duration) as the benchmark yield curve is changed. In Exhibit 8, as the 
benchmark yield goes down, the slope of the line tangent to the curve for the non-

callable bond steepens, which indicates positive convexity. But the slope of the line 
tangent to the callable bond flattens as the benchmark yield goes down. Technically, it 
reaches an inflection point, which is when the effective convexity shifts from positive 
to negative.
In summary, when the benchmark yield is high and the value of the embedded call 
option is low, the callable and the non-  callable bonds experience very similar effects 
from interest rate changes. They both have positive convexity. But as the benchmark 
yield is reduced, the curves diverge. At some point, the callable bond moves into the 
range of negative convexity, which indicates that the embedded call option has more 
value to the issuer and is more likely to be exercised. This situation limits the potential 
price appreciation of the bond arising from lower interest rates, whether because of 
a lower benchmark yield or a lower credit spread.

Another way to understand why a callable bond can have negative convexity is to 
rearrange Equation 17.
EffCon
Curve=() −() −() −() 
() ×()−+PV PV PV PV
PV00
2
0 ∆
In the numerator, the first bracketed expression is the increase in price when the 
benchmark yield curve is lowered. The second expression is the decrease in price when 
the benchmark yield curve is raised. On a non-  callable bond, the increase is always 
larger than the decrease (in absolute value). This result is the “convexity effect” for 
the relationship between bond prices and yields-  to- maturity. On a callable bond, the 
increase can be smaller than the decrease (in absolute value). That creates negative 
convexity, as illustrated in Exhibit 8.
INTEREST RATE RISK AND THE INVESTMENT 
HORIZON
This section explores the effect of yield volatility on the investment horizon, and 
on the interaction between the investment horizon, market price risk, and coupon 
reinvestment risk.4

Reading 54 ■ Understanding Fixed -Income Risk and Return 568
4.1 Yield Volatility
An important aspect in understanding the interest rate risk and return characteristics 
of an investment in a fixed-  rate bond is the time horizon. This section considers a 
short-  term horizon. A primary concern for the investor is the change in the price of 
the bond given a sudden (i.e., same-  day) change in its yield-  to- maturity. The accrued 
interest does not change, so the impact of the change in the yield is on the flat price 
of the bond. Section 4.2 considers a long-  term horizon. The reinvestment of coupon 
interest then becomes a key factor in the investor’s horizon yield.
Bond duration is the primary measure of risk arising from a change in the yield-  
to- maturity. Convexity is the secondary risk measure. In the discussion of the impact 
on the bond price, the phrase “for a given  change in the yield-  to- maturity” is used

repeatedly. For instance, the given change in the yield-  to- maturity could be 1 bp, 25 
bps, or 100 bps. In comparing two bonds, it is assumed that the “given change” is 
the same for both securities. When the government bond par curve is shifted up or 
down by the same amount to calculate effective duration and effective convexity, the 
events are described as “parallel” yield curve shifts. Because yield curves are rarely (if 
ever) straight lines, this shift may also be described as a “shape-  preserving” shift to 
the yield curve. The key assumption is that all yields-  to- maturity under consideration 
rise or fall by the same amount across the curve.
Although the assumption of a parallel shift in the yield curve is common in fixed-  
income analysis, it is not always realistic. In reality, the shape of the yield curve changes 
based on factors affecting the supply and demand of shorter-  term versus longer-  term

securities. In fact, the term structure of bond yields (also called the “term structure 
of interest rates”) is typically upward sloping. However, the term structure of yield 
volatility  may have a different shape depending on a number of factors. The term 
structure of yield volatility is the relationship between the volatility of bond yields-  
to- maturity and times-  to- maturity.
For example, a central bank engaging in expansionary monetary policy might cause 
the yield curve to steepen by reducing short-  term interest rates. But this policy might 
cause greater volatility  in short-  term bond yields-  to- maturity than in longer-  term 
bonds, resulting in a downward-  sloping term structure of yield volatility. Longer-  
term bond yields are mostly determined by future inflation and economic growth 
expectations. Those expectations often tend to be less volatile.
The importance of yield volatility in measuring interest rate risk is that bond price

changes are products of two factors: (1) the impact per basis-  point change in the 
yield-  to- maturity and (2) the number  of basis points in the yield-  to- maturity change. 
The first factor is duration or the combination of duration and convexity, and the 
second factor is the yield volatility. For example, consider a 5-  year bond with a mod -
ified duration of 4.5 and a 30-  year bond with a modified duration of 18.0. Clearly, for 
a given  change in yield-  to- maturity, the 30-  year bond represents more much more 
interest rate risk to an investor who has a short-  term horizon. In fact, the 30-  year 
bond appears to have four times  the risk given the ratio of the modified durations. 
But that assumption neglects the possibility that the 30-  year bond might have half 
the yield volatility of the 5-  year bond.
Equation 13, restated here, summarizes the two factors.
%∆∆ ∆ PVFull≈− × () +× ×()
22
 

22
 
The estimated percentage change in the bond price depends on the modified duration 
and convexity as well as on the yield-  to- maturity change. Parallel shifts between two 
bond yields and along a benchmark yield curve are common assumptions in fixed-  
income analysis. However, an analyst must be aware that non-  parallel shifts frequently 
occur in practice.

Interest Rate Risk and the Investment Horizon 569
EXAMPLE 15   
A fixed-  income analyst is asked to rank three bonds in terms of interest rate 
risk. Interest rate risk here means the potential price decrease on a percentage 
basis given a sudden change in financial market conditions. The increases in the 
yields-  to- maturity represent the “worst case” for the scenario being considered.
Bond Modified Duration Convexity ΔYield
A 3.72 12.1 25 bps
B 5.81 40.7 15 bps
C 12.39 158.0 10 bps
The modified duration and convexity statistics are annualized. ΔYield is the 
increase in the annual yield-  to- maturity. Rank the bonds in terms of interest 
rate risk.
Solution:
Calculate the estimated percentage price change for each bond:
Bond A:

=− 3720 00251
21210 0025 0 0092622.. .. .
Bond B:

=− 5810 00151
24070 0015 0 0086692.. .. .
Bond C:

=− 12 39 0 00101
215800 0010 0 0123112.. .. .
Based on these assumed changes in the yield-  to- maturity and the modified

duration and convexity risk measures, Bond C has the highest degree of interest 
rate risk (a potential loss of 1.2311%), followed by Bond A (a potential loss of 
0.9262%) and Bond B (a potential loss of 0.8669%).
4.2 Investment Horizon, Macaulay Duration, and Interest Rate 
Risk
Although short-  term interest rate risk is a concern to some investors, other investors 
have a long-  term horizon. Day-  to- day changes in bond prices cause unrealized  capital 
gains and losses. Those unrealized gains and losses might need to be accounted for in 
financial statements. This section considers a long-  term investor concerned only with 
the total return over the investment horizon. Therefore, interest rate risk is important 
to this investor. The investor faces coupon reinvestment risk as well as market price 
risk if the bond needs to be sold prior to maturity.
Section 2 included examples of interest rate risk using a 10-  year, 8% annual coupon

payment bond that is priced at 85.503075 per 100 of par value. The bond’s yield-  to- 
maturity is 10.40%. A key result in Example 3 is that an investor with a 10-  year time 
horizon is concerned only with coupon reinvestment risk. This situation assumes, of 
course, that the issuer makes all of the coupon and principal payments as scheduled. 
The buy-  and-  hold investor has a higher total return if interest rates rise (see Example 3) 
and a lower total return if rates fall (see Example 5). The investor in Examples 4 and

Reading 54 ■ Understanding Fixed -Income Risk and Return 570
6 has a four-  year horizon. This investor faces market price risk in addition to coupon 
reinvestment risk. In fact, the market price risk dominates because this investor has 
a higher total return if interest rates fall (see Example 6) and a lower return if rates 
rise (see Example 4).
Now, consider a third investor who has a seven-  year time horizon. If interest 
rates remain at 10.40%, the future value of reinvested coupon interest is 76.835787 
81 1040 81 1040 81 1040 8165 4×()

+× ()

+× ()

81 1040 81 1040 87 6833
21()

+
×()

+× ()

+= .. .55787
The bond is sold for a price of 94.073336, assuming that the bond stays on the constant-  
yield price trajectory and continues to be “pulled to par. ”
8
1 10408
1 1040108
1 104094 07333612 3.. ..
()+
()+
()=
The total return is 170.909123 (= 76.835787 + 94.073336) per 100 of par value, and 
the horizon yield, as expected, is 10.40%.

85 503075170 909123
10 10407... =
+()=
rr,     
Following Examples 3 and 4, assume that the yield-  to- maturity on the bond rises 
to 11.40%. Also, coupon interest is now reinvested each year at 11.40%. The future 
value of reinvested coupons becomes 79.235183 per 100 of par value.
81 1140 81 1140 81 1140 8165 4×()

+× ()

+× ()

81 1140 81 1140 87 9233
21()

+
×()

+× ()

+= .. .55183
After receiving the seventh coupon payment, the bond is sold. There is a capital loss 
because the price, although much higher than at purchase, is below the constant-  yield 
price trajectory.
8
1 11408
1 1140108
1 114091 74883312 3.. ..
()+
()+
()=
The total return is 170.984016 (= 79.235183 + 91.748833) per 100 of par value and 
the holding-  period rate of return is 10.407%.
85 503075170 984016
10 104077... =
+()=
rr,     
Following Examples 5 and 6, assume that the coupon reinvestment rates and

the bond yield-  to- maturity fall to 9.40%. The future value of reinvested coupons is 
74.512177.
81 0940 81 0940 81 0940 8165 4+()

++ ()

++ ()

++ .. .. 0 0940
81 0940 81 0940 87 4523
21()

+
+()

++ ()

+= .. .1177
The bond is sold at a capital gain because the price is above the constant-  yield price 
trajectory.
8
1 09408
1 0940108
1 094096 48129912 3.. ..
()+
()+
()=

Interest Rate Risk and the Investment Horizon 571
The total return is 170.993476 (= 74.512177 + 96.481299) per 100 of par value, and 
the horizon yield is 10.408%.
85 503075170 993476
10 104087... =
+()=
rr,     
These results are summarized in the following table to reveal the remarkable out -
come: The total returns and horizon yields are virtually the same. The investor with 
the 7-  year horizon, unlike those having a 4- or 10-  year horizon, achieves the same 
holding-  period rate of return whether interest rates rise, fall, or remain the same. 
Note that the terms “horizon yield” and “holding-  period rate of return” are used 
interchangeably in this reading. Sometimes “horizon yield” refers to yields on bonds 
that need to be sold at the end of the investor’s holding period.
Interest 
RateFuture Value of 
Reinvested Coupon Sale Price Total Return Horizon Yield
9.40% 74.512177 96.481299 170.993476 10.408%
10.40% 76.835787 94.073336 170.909123 10.400%
11.40% 79.235183 91.748833 170.984016 10.407%

This particular bond was chosen as an example to demonstrate an important 
property of Macaulay duration: For a particular assumption about yield volatility, 
Macaulay duration indicates the investment horizon for which coupon reinvestment 
risk and market price risk offset each other. In Section 3.1, the Macaulay duration of 
this 10-  year, 8% annual payment bond is calculated to be 7.0029 years. This is one of 
the applications for duration in which “years” is meaningful and in which Macaulay 
duration is used rather than modified duration. The particular assumption about yield 
volatility is that there is a one-  time “parallel” shift in the yield curve that occurs before 
the next coupon payment date. Exhibit 13 illustrates this property of bond duration, 
assuming that the bond is initially priced at par value.

Reading 54 ■ Understanding Fixed -Income Risk and Return 572
Exhibit 13   Interest Rate Risk, Macaulay Duration, and the Investment 
Horizon
Initial
Date
Maturity
DateMoney
DurationMacaulay DurationGain on the Future Value
of Reinvested CouponsA. Interest Rates Rise
Gains
Losses
Loss on the Sale of the Bond
Money
Duration
Macaulay
DurationLoss on the Future Value
of Reinvested CouponsB. Interest Rates Fall
Gains
LossesGain on the Sale of the Bond
As demonstrated in Panel A of Exhibit 13, when interest rates rise, duration mea -
sures the immediate drop in value. In particular, the money duration indicates the 
change in price. Then as time passes, the bond price is “pulled to par. ” The gain in the 
future value of reinvested coupons starts small but builds over time as more coupons 
are received. The curve indicates the additional future value of reinvested coupons 
because of the higher interest rate. At some point in the lifetime of the bond, those

two effects offset each other and the gain on reinvested coupons is equal to the loss 
on the sale of the bond. That point in time is the Macaulay duration statistic.
The same pattern is displayed in the Panel B when interest rates fall, which leads to 
a reduction in the bond yield and the coupon reinvestment rate. There is an immediate 
jump in the bond price, as measured by the money duration, but then the “pulled 
to par” effect brings the price down as time passes. The impact from reinvesting at 
a lower rate starts small but then becomes more significant over time. The loss on 
reinvested coupons is with respect to the future value if interest rates had not fallen. 
Once again, the bond’s Macaulay duration indicates the point in time when the two 
effects offset each other and the gain on the sale of the bond matches the loss on 
coupon reinvestment.
The earlier numerical example and Exhibit 13 allow for a statement of the general

relationships among interest rate risk, the Macaulay duration, and the investment 
horizon.
1 When the investment horizon is greater than the Macaulay duration of a bond, 
coupon reinvestment risk dominates market price risk. The investor’s risk is to 
lower interest rates.

Interest Rate Risk and the Investment Horizon 573
2 When the investment horizon is equal to the Macaulay duration of a bond, 
coupon reinvestment risk offsets market price risk.
3 When the investment horizon is less than the Macaulay duration of the bond, 
market price risk dominates coupon reinvestment risk. The investor’s risk is to 
higher interest rates.
In the numerical example, the Macaulay duration of the bond is 7.0 years. Statement 
1 reflects the investor with the 10-  year horizon; Statement 2, the investor with the 
7- year horizon; and Statement 3, the investor with the 4-  year horizon.
The difference between the Macaulay duration of a bond and the investment horizon 
is called the duration gap . The duration gap is a bond’s Macaulay duration minus the 
investment horizon. The investor with the 10-  year horizon has a negative duration 
gap and currently is at risk of lower rates. The investor with the 7-  year horizon has a

duration gap of zero and currently is hedged against interest rate risk. The investor 
with the 4-  year horizon has a positive duration gap and currently is at risk of higher 
rates. The word “currently” is important because interest rate risk is connected to an 
immediate  change in the bond’s yield-  to- maturity and the coupon reinvestment rates. 
As time passes, the investment horizon is reduced and the Macaulay duration of the 
bond also changes. Therefore, the duration gap changes as well.
EXAMPLE 16   
An investor plans to retire in 10 years. As part of the retirement portfolio, the 
investor buys a newly issued, 12-  year, 8% annual coupon payment bond. The 
bond is purchased at par value, so its yield-  to- maturity is 8.00% stated as an 
effective annual rate.
1 Calculate the approximate Macaulay duration for the bond, using a 1 bp 
increase and decrease in the yield-  to- maturity and calculating the new 
prices per 100 of par value to six decimal places.

2 Calculate the duration gap at the time of purchase.
3 Does this bond at purchase entail the risk of higher or lower interest 
rates? Interest rate risk here means an immediate, one-  time, parallel yield 
curve shift.
The approximate modified duration of the bond is 7.5361. PV0 = 100, PV+ = 
99.924678, and PV− = 100.075400.
PV+=
()++
()=8
1 0801108
1 080199 92467811 2... 
PV−=
()++
()=8
1 0799108
1 0799100 07540011 2... 
××=100 075400 99 924678
20 0001 1007 5361..
..
The approximate Macaulay duration is 8.1390 (= 7.5361 × 1.08).
Given an investment horizon of 10 years, the duration gap for this bond at 
purchase is negative: 8.1390 – 10 = –1.8610.

Reading 54 ■ Understanding Fixed -Income Risk and Return 574
A negative duration gap entails the risk of lower interest rates. To be precise, 
the risk is an immediate, one-  time, parallel, downward yield curve shift because 
coupon reinvestment risk dominates market price risk. The loss from reinvesting 
coupons at a rate lower than 8% is larger than the gain from selling the bond at 
a price above the constant-  yield price trajectory.
CREDIT AND LIQUIDITY RISK
The focus of this reading is to demonstrate how bond duration and convexity estimate 
the bond price change, either in percentage terms or in units of currency, given an 
assumed yield-  to- maturity change. This section addresses the source  of the change in 
the yield-  to- maturity. In general, the yield-  to- maturity on a corporate bond is composed 
of a government benchmark  yield and a spread  over that benchmark. A change in the

bond’s yield-  to- maturity can originate in either component or a combination of the two.
The key point is that for a traditional (option-  free) fixed-  rate bond, the same dura -
tion and convexity statistics apply for a change in the benchmark yield as for a change 
in the spread. The “building blocks” approach from “Introduction to Fixed-  Income 
Valuation” shows that these yield-  to- maturity changes can be broken down further. A 
change in the benchmark yield can arise from a change in either the expected inflation 
rate or the expected real rate of interest. A change in the spread can arise from a change 
in the credit risk of the issuer or in the liquidity of the bond. Therefore, for a fixed-  rate 
bond, the “inflation duration, ” the “real rate duration, ” the “credit duration, ” and the 
“liquidity duration” are all the same number. The inflation duration would indicate 
the change in the bond price if expected inflation were to change by a certain amount.

In the same manner, the real rate duration would indicate the bond price change if 
the real rate were to go up or down. The credit duration and liquidity duration would 
indicate the price sensitivity that would arise from changes in those building blocks 
in the yield-  to- maturity. A bond with a modified duration of 5.00 and a convexity of 
32.00 will appreciate in value by about 1.26% if its yield-  to- maturity goes down by 
25 bps: (–5.00 × –0.0025) + [1/2 × 32.00 × (–0.0025)2] = + 0.0126, regardless of the 
source  of the yield-  to- maturity change.
Suppose that the yield-  to- maturity on a corporate bond is 6.00%. If the bench -
mark yield is 4.25%, the spread is 1.75%. An analyst believes that credit risk makes up 
1.25% of the spread and liquidity risk, the remaining 0.50%. Credit risk includes the 
probability of default as well as the recovery of assets if default does occur. A credit 
rating downgrade or an adverse change in the ratings outlook for a borrower reflects

a higher risk of default. Liquidity risk refers to the transaction costs associated with 
selling a bond. In general, a bond with greater frequency of trading and a higher vol -
ume of trading provides fixed-  income investors with more opportunity to purchase 
or sell the security and thus has less liquidity risk. In practice, there is a difference 
between the bid (or purchase) and the offer  (or sale) price. This difference depends 
on the type of bond, the size of the transaction, and the time of execution, among 
other factors. For instance, government bonds often trade at just a few basis points 
between the purchase and sale prices. More thinly traded corporate bonds can have 
a much wider difference between the bid and offer prices.
The problem for a fixed-  income analyst is that it is rare for the changes in the 
components of the overall yield-  to- maturity to occur in isolation. In practice, the 
analyst is concerned with the interaction  between changes in benchmark yields and

spreads, between changes in expected inflation and the expected real rate, and between 
changes in credit and liquidity risk. For example, during a financial crisis, a “flight 5

Summary 575
to quality” can cause government benchmark yields to fall as credit spreads widen. 
An unexpected credit downgrade on a corporate bond can result in greater credit as 
well as liquidity risk.
EXAMPLE 17   
The (flat) price on a fixed-  rate corporate bond falls one day from 92.25 to 91.25 
per 100 of par value because of poor earnings and an unexpected ratings down -
grade of the issuer. The (annual) modified duration for the bond is 7.24. Which 
of the following is closest  to the estimated change in the credit spread on the 
corporate bond, assuming benchmark yields are unchanged?
A 15 bps
B 100 bps
C 108 bps
Solution:
Given that the price falls from 92.25 to 91.25, the percentage price decrease is 
1.084%.
91 25 92 25
92 250 01084..
..−=−
Given an annual modified duration of 7.24, the change in the yield-  to- maturity 
is 14.97 bps.
–0.01084 ≈ –7.24 × ΔYield, ΔYield = 0.001497
Therefore, the answer is A. The change in price reflects a credit spread increase 
on the bond of about 15 bps.

SUMMARY
This reading covers the risk and return characteristics of fixed-  rate bonds. The focus 
is on the widely used measures of interest rate risk—duration and convexity. These 
statistics are used extensively in fixed-  income analysis. The following are the main 
points made in the reading:
■■The three sources of return on a fixed-  rate bond purchased at par value are (1) 
receipt of the promised coupon and principal payments on the scheduled dates, 
(2) reinvestment of coupon payments, and (3) potential capital gains, as well as 
losses, on the sale of the bond prior to maturity.
■■For a bond purchased at a discount or premium, the rate of return also includes 
the effect of the price being “pulled to par” as maturity nears, assuming no 
default.
■■The total return is the future value of reinvested coupon interest payments and 
the sale price (or redemption of principal if the bond is held to maturity).

■■The horizon yield (or holding period rate of return) is the internal rate of return 
between the total return and purchase price of the bond.
■■Coupon reinvestment risk increases with a higher coupon rate and a longer 
reinvestment time period.

Reading 54 ■ Understanding Fixed -Income Risk and Return 576
■■Capital gains and losses are measured from the carrying value of the bond and 
not from the purchase price. The carrying value includes the amortization of 
the discount or premium if the bond is purchased at a price below or above par 
value. The carrying value is any point on the constant-  yield price trajectory.
■■Interest income on a bond is the return associated with the passage of time. 
Capital gains and losses are the returns associated with a change in the value of 
a bond as indicated by a change in the yield-  to- maturity.
■■The two types of interest rate risk on a fixed-  rate bond are coupon reinvestment 
risk and market price risk. These risks offset each other to a certain extent. An 
investor gains from higher rates on reinvested coupons but loses if the bond is 
sold at a capital loss because the price is below the constant-  yield price trajec -

tory. An investor loses from lower rates on reinvested coupon but gains if the 
bond is sold at a capital gain because the price is above the constant-  yield price 
■■Market price risk dominates coupon reinvestment risk when the investor has a 
short-  term horizon (relative to the time-  to- maturity on the bond).
■■Coupon reinvestment risk dominates market price risk when the investor has a 
long-  term horizon (relative to the time-  to- maturity)—for instance, a buy-  and-  
hold investor.
■■Bond duration, in general, measures the sensitivity of the full price (including 
accrued interest) to a change in interest rates.
■■Yield duration statistics measuring the sensitivity of a bond’s full price to the 
bond’s own yield-  to- maturity include the Macaulay duration, modified duration, 
money duration, and price value of a basis point.
■■Curve duration statistics measuring the sensitivity of a bond’s full price to the 
benchmark yield curve are usually called “effective durations. ”

■■Macaulay duration is the weighted average of the time to receipt of coupon 
interest and principal payments, in which the weights are the shares of the full 
price corresponding to each payment. This statistic is annualized by dividing 
by the periodicity (number of coupon payments or compounding periods in a 
year).
■■Modified duration provides a linear estimate of the percentage price change for 
a bond given a change in its yield-  to- maturity.
■■Approximate modified duration approaches modified duration as the change in 
the yield-  to- maturity approaches zero.
■■Effective duration is very similar to approximate modified duration. The dif -
ference is that approximate modified duration is a yield duration statistic that 
measures interest rate risk in terms of a change in the bond’s own yield-  to- 
maturity, whereas effective duration is a curve duration statistic that measures 
interest rate risk assuming a parallel shift in the benchmark yield curve.

■■Key rate duration is a measure of a bond’s sensitivity to a change in the bench -
mark yield curve at specific maturity segments. Key rate durations can be used 
to measure a bond’s sensitivity to changes in the shape of the yield curve.
■■Bonds with an embedded option do not have a meaningful internal rate of 
return because future cash flows are contingent on interest rates. Therefore, 
effective duration is the appropriate interest rate risk measure, not modified 
duration.
■■The effective duration of a traditional (option-  free) fixed-  rate bond is its sensi -
tivity to the benchmark yield curve, which can differ from its sensitivity to its 
own yield-  to- maturity. Therefore, modified duration and effective duration on a 
traditional (option-  free) fixed-  rate bond are not necessarily equal.

Summary 577
■■During a coupon period, Macaulay and modified durations decline smoothly 
in a “saw-  tooth” pattern, assuming the yield-  to- maturity is constant. When the 
coupon payment is made, the durations jump upward.
■■Macaulay and modified durations are inversely related to the coupon rate and 
the yield-  to- maturity.
■■Time-  to- maturity and Macaulay and modified durations are usually  positively 
related. They are always  positively related on bonds priced at par or at a pre -
mium above par value. They are usually  positively related on bonds priced at a 
discount below par value. The exception is on long-  term, low-  coupon bonds, on 
which it is possible to have a lower duration than on an otherwise comparable 
shorter-  term bond.
■■The presence of an embedded call option reduces a bond’s effective duration 
compared with that of an otherwise comparable non-  callable bond. The reduc -
tion in the effective duration is greater when interest rates are low and the

issuer is more likely to exercise the call option.
■■The presence of an embedded put option reduces a bond’s effective duration 
compared with that of an otherwise comparable non-  putable bond. The reduc -
tion in the effective duration is greater when interest rates are high and the 
investor is more likely to exercise the put option.
■■The duration of a bond portfolio can be calculated in two ways: (1) the weighted 
average of the time to receipt of aggregate  cash flows and (2) the weighted aver -
age of the durations of individual bonds that compose the portfolio.
■■The first method to calculate portfolio duration is based on the cash flow yield, 
which is the internal rate of return on the aggregate cash flows. It cannot be 
used for bonds with embedded options or for floating-  rate notes.
■■The second method is simpler to use and quite accurate when the yield curve 
is relatively flat. Its main limitation is that it assumes a parallel shift in the

yield curve in that the yields on all bonds in the portfolio change by the same 
amount.
■■Money duration is a measure of the price change in terms of units of the cur -
rency in which the bond is denominated.
■■The price value of a basis point (PVBP) is an estimate of the change in the full 
price of a bond given a 1 bp change in the yield-  to- maturity.
■■Modified duration is the primary, or first-  order, effect on a bond’s percentage 
price change given a change in the yield-  to- maturity. Convexity is the second -
ary, or second-  order, effect. It indicates the change in the modified duration as 
the yield-  to- maturity changes.
■■Money convexity is convexity times the full price of the bond. Combined with 
money duration, money convexity estimates the change in the full price of a 
bond in units of currency given a change in the yield-  to- maturity.
■■Convexity is a positive attribute for a bond. Other things being equal, a more

convex bond appreciates in price more than a less convex bond when yields fall 
and depreciates less when yields rise.
■■Effective convexity is the second-  order effect on a bond price given a change in 
the benchmark yield curve. It is similar to approximate convexity. The differ -
ence is that approximate convexity is based on a yield-  to- maturity change and 
effective convexity is based on a benchmark yield curve change.
■■Callable bonds have negative effective convexity when interest rates are low. The 
increase in price when the benchmark yield is reduced is less in absolute value 
than the decrease in price when the benchmark yield is raised.

Reading 54 ■ Understanding Fixed -Income Risk and Return 578
■■The change in a bond price is the product of (1) the impact per basis-  point 
change in the yield-  to- maturity and (2) the number of basis points in the yield 
change. The first factor is estimated by duration and convexity. The second 
factor depends on yield volatility.
■■The investment horizon is essential in measuring the interest rate risk on a 
fixed-  rate bond.
■■For a particular assumption about yield volatility, the Macaulay duration indi -
cates the investment horizon for which coupon reinvestment risk and market 
price risk offset each other. The assumption is a one-  time parallel shift to the 
yield curve in which the yield-  to- maturity and coupon reinvestment rates 
■■When the investment horizon is greater than the Macaulay duration of the 
bond, coupon reinvestment risk dominates price risk. The investor’s risk is to

lower interest rates. The duration gap is negative.
■■When the investment horizon is equal to the Macaulay duration of the bond, 
coupon reinvestment risk offsets price risk. The duration gap is zero.
■■When the investment horizon is less than the Macaulay duration of the bond, 
price risk dominates coupon reinvestment risk. The investor’s risk is to higher 
interest rates. The duration gap is positive.
■■Credit risk involves the probability of default and degree of recovery if default 
occurs, whereas liquidity risk refers to the transaction costs associated with 
selling a bond.
■■For a traditional (option-  free) fixed-  rate bond, the same duration and convexity 
statistics apply if a change occurs in the benchmark yield or a change occurs in 
the spread. The change in the spread can result from a change in credit risk or 
liquidity risk.
■■In practice, there often is interaction between changes in benchmark yields and 
in the spread over the benchmark.

Practice Problems 579
1 A “buy-  and-  hold” investor purchases a fixed-  rate bond at a discount and holds 
the security until it matures. Which of the following sources of return is least 
likely to contribute to the investor’s total return over the investment horizon, 
assuming all payments are made as scheduled?
A Capital gain
B Principal payment
C Reinvestment of coupon payments
2 Which of the following sources of return is most likely exposed to interest rate 
risk for an investor of a fixed-  rate bond who holds the bond until maturity?
A Capital gain or loss
B Redemption of principal
3 An investor purchases a bond at a price above par value. Two years later, the 
investor sells the bond. The resulting capital gain or loss is measured by com -
paring the price at which the bond is sold to the:
A carrying value.
B original purchase price.
C original purchase price value plus the amortized amount of the premium.

The following information relates to Problems 
4–6
An investor purchases a nine-  year, 7% annual coupon payment bond at a price equal 
to par value. After the bond is purchased and before the first coupon is received, 
interest rates increase to 8%. The investor sells the bond after five years. Assume that 
interest rates remain unchanged at 8% over the five-  year holding period.
4 Per 100 of par value, the future value of the reinvested coupon payments at the 
end of the holding period is closest  to:
A 35.00.
B 40.26.
C 41.07.
5 The capital gain/loss per 100 of par value resulting from the sale of the bond at 
the end of the five-  year holding period is closest  to a:
A loss of 8.45.
B loss of 3.31.
C gain of 2.75.
6 Assuming that all coupons are reinvested over the holding period, the investor’s 
five-  year horizon yield is closest  to:
A 5.66%.

Reading 54 ■ Understanding Fixed -Income Risk and Return 580
B 6.62%.
C 7.12%.
7 An investor buys a three-  year bond with a 5% coupon rate paid annually. The 
bond, with a yield-  to- maturity of 3%, is purchased at a price of 105.657223 per 
100 of par value. Assuming a 5-  basis point change in yield-  to- maturity, the 
bond’s approximate modified duration is closest  to:
A 2.78.
B 2.86.
C 5.56.
8 Which of the following statements about duration is correct? A bond’s:
A effective duration is a measure of yield duration.
B modified duration is a measure of curve duration.
C modified duration cannot be larger than its Macaulay duration.
9 An investor buys a 6% annual payment bond with three years to maturity. The 
bond has a yield-  to- maturity of 8% and is currently priced at 94.845806 per 100 
of par. The bond’s Macaulay duration is closest  to:
A 2.62.
B 2.78.
C 2.83.
10 The interest rate risk of a fixed-  rate bond with an embedded call option is best 
measured by:
A effective duration.

B modified duration.
C Macaulay duration.
11 Which of the following is most  appropriate for measuring a bond’s sensitivity to 
shaping risk?
A key rate duration
B effective duration
C modified duration
12 A Canadian pension fund manager seeks to measure the sensitivity of her 
pension liabilities to market interest rate changes. The manager determines the 
present value of the liabilities under three interest rate scenarios: a base rate of 
7%, a 100 basis point increase in rates up to 8%, and a 100 basis point drop in 
rates down to 6%. The results of the manager’s analysis are presented below:
6% CAD 510.1 million
7% CAD 455.4 million
8% CAD 373.6 million
 The effective duration of the pension fund’s liabilities is closest  to:
A 1.49.
B 14.99.
C 29.97.
13 Which of the following statements about Macaulay duration is correct?

Practice Problems 581
A A bond’s coupon rate and Macaulay duration are positively related.
B A bond’s Macaulay duration is inversely related to its yield-  to- maturity.
C The Macaulay duration of a zero-  coupon bond is less than its 
14 Assuming no change in the credit risk of a bond, the presence of an embedded 
put option:
A reduces the effective duration of the bond.
B increases the effective duration of the bond.
C does not change the effective duration of the bond.
15 A bond portfolio consists of the following three fixed-  rate bonds. Assume 
annual coupon payments and no accrued interest on the bonds. Prices are per 
Bond MaturityMarket 
Value Price CouponYield-  to- 
MaturityModified 
Duration
A 6 years 170,000 85.0000 2.00% 4.95% 5.42
B 10 years 120,000 80.0000 2.40% 4.99% 8.44
C 15 years 100,000 100.0000 5.00% 5.00% 10.38
 The bond portfolio’s modified duration is closest  to:
A 7.62.
B 8.08.
C 8.20.

A 7.62.
B 8.08.
C 8.20.
16 A limitation of calculating a bond portfolio’s duration as the weighted average 
of the yield durations of the individual bonds that compose the portfolio is that 
it:
A assumes a parallel shift to the yield curve.
B is less accurate when the yield curve is less steeply sloped.
C is not applicable to portfolios that have bonds with embedded options.
17 Using the information below, which bond has the greatest  money duration per 
100 of par value assuming annual coupon payments and no accrued interest?
MaturityPrice Per 100 of 
Par ValueCoupon 
RateYield-  to- 
Duration
A 6 years 85.00 2.00% 4.95% 5.42
B 10 years 80.00 2.40% 4.99% 8.44
C 9 years 85.78 3.00% 5.00% 7.54
A Bond A
B Bond B
C Bond C
18 A bond with exactly nine years remaining until maturity offers a 3% coupon 
rate with annual coupons. The bond, with a yield-  to- maturity of 5%, is priced 
at 85.784357 per 100 of par value. The estimated price value of a basis point for

Reading 54 ■ Understanding Fixed -Income Risk and Return 582
19 The “second-  order” effect on a bond’s percentage price change given a change in 
yield-  to- maturity can be best described as:
A duration.
B convexity.
C yield volatility.
20 A bond is currently trading for 98.722 per 100 of par value. If the bond’s yield-  
to- maturity (YTM) rises by 10 basis points, the bond’s full price is expected to 
fall to 98.669. If the bond’s YTM decreases by 10 basis points, the bond’s full 
price is expected to increase to 98.782. The bond’s approximate convexity is 
A 0.071.
B 70.906.
C 1,144.628.
21 A bond has an annual modified duration of 7.020 and annual convexity 
of 65.180. If the bond’s yield-  to- maturity decreases by 25 basis points, the 
expected percentage price change is closest  to:
A 1.73%.
B 1.76%.
C 1.78%.
22 A bond has an annual modified duration of 7.140 and annual convexity of 
66.200. The bond’s yield-  to- maturity is expected to increase by 50 basis points.

The expected percentage price change is closest  to:
A –3.40%.
B –3.49%.
C –3.57%.
23 Which of the following statements relating to yield volatility is most  accurate? If 
the term structure of yield volatility is downward sloping, then:
A short-  term rates are higher than long-  term rates.
B long-  term yields are more stable than short-  term yields.
C short-  term bonds will always experience greater price fluctuation than long-  
term bonds.
24 The holding period for a bond at which the coupon reinvestment risk offsets the 
market price risk is best approximated by:
A duration gap.
25 When the investor’s investment horizon is less than the Macaulay duration of 
the bond she owns:
A the investor is hedged against interest rate risk.
B reinvestment risk dominates, and the investor is at risk of lower rates.
C market price risk dominates, and the investor is at risk of higher rates.
26 An investor purchases an annual coupon bond with a 6% coupon rate and

exactly 20 years remaining until maturity at a price equal to par value. The 
investor’s investment horizon is eight years. The approximate modified duration 
of the bond is 11.470 years. The duration gap at the time of purchase is closest 
to:
A –7.842.

Practice Problems 583
B 3.470.
C 4.158.
27 A manufacturing company receives a ratings upgrade and the price increases on 
its fixed-  rate bond. The price increase was most likely  caused by a(n):
A decrease in the bond’s credit spread.
B increase in the bond’s liquidity spread.
C increase of the bond’s underlying benchmark rate.

Reading 54 ■ Understanding Fixed -Income Risk and Return 584
SOLUTIONS
1 A is correct. A capital gain is least likely to contribute to the investor’s total 
return. There is no capital gain (or loss) because the bond is held to matu -
rity. The carrying value of the bond at maturity is par value, the same as the 
redemption amount. When a fixed-  rate bond is held to its maturity, the investor 
receives the principal payment at maturity. This principal payment is a source of 
return for the investor. A fixed-  rate bond pays periodic coupon payments, and 
the reinvestment of these coupon payments is a source of return for the inves -
tor. The investor’s total return is the redemption of principal at maturity and the 
sum of the reinvested coupons.
2 C is correct. Because the fixed-  rate bond is held to maturity (a “buy-  and-  hold” 
investor), interest rate risk arises entirely from changes in coupon reinvestment 
rates. Higher interest rates increase income from reinvestment of coupon pay -

ments, and lower rates decrease income from coupon reinvestment. There will 
not be a capital gain or loss because the bond is held until maturity. The carry -
ing value at the maturity date is par value, the same as the redemption amount. 
The redemption of principal does not expose the investor to interest rate risk. 
The risk to a bond’s principal is credit risk.
3 A is correct. Capital gains (losses) arise if a bond is sold at a price above (below) 
its constant-  yield price trajectory. A point on the trajectory represents the 
carrying value of the bond at that time. That is, the capital gain/loss is measured 
from the bond’s carrying value, the point on the constant-  yield price trajectory, 
and not from the original purchase price. The carrying value is the original pur -
chase price plus the amortized amount of the discount if the bond is purchased 
at a price below par value. If the bond is purchased at a price above par value,

the carrying value is the original purchase price minus (not plus) the amortized 
amount of the premium. The amortized amount for each year is the change in 
the price between two points on the trajectory.
4 C is correct. The future value of reinvested cash flows at 8% after five years is 
closest to 41.07per 100 of par value.
71 08 71 08 71 08 71 08432 1×()

+× ()

+× ()

+× ().... 
+=74 1 0662 .
 The 6.07 difference between the sum of the coupon payments over the five-  year 
holding period (35) and the future value of the reinvested coupons (41.07) rep -
resents the “interest-  on- interest” gain from compounding.
5 B is correct. The capital loss is closest to 3.31 per 100 of par value. After five 
years, the bond has four years remaining until maturity and the sale price of the 
bond is 96.69, calculated as:
7
1087
1087
108107
10896 691 234.. ...
()+
()+
()+
()=
 The investor purchased the bond at a price equal to par value (100). Because the

bond was purchased at a price equal to its par value, the carrying value is par 
value. Therefore, the investor experienced a capital loss of 96.69 – 100 = –3.31.

Solutions 585
6 B is correct. The investor’s five-  year horizon yield is closest to 6.62%. After five 
years, the sale price of the bond is 96.69 (from problem 5) and the future value 
of reinvested cash flows at 8% is 41.0662 (from problem 4) per 100 of par value. 
The total return is 137.76 (= 41.07 + 96.69), resulting in a realized five-  year 
horizon yield of 6.62%:
100 00137 76
10 06625... =
+()=
rr,     
7 A is correct. The bond’s approximate modified duration is closest to 2.78. 
Approximate modified duration is calculated as:
PV 20 ∆
 Lower yield-  to- maturity by 5 bps to 2.95%:
PV−=
+()+
+()++
+()=5
10 02955
10 02955 100
10 0295105 80423212 3.. ..
 Increase yield-  to- maturity by 5 bps to 3.05%:
PV+=
+()+
+()++
+()=5
10 03055
10 03055 100
10 0305105 51049412 3.. ..
PV0 = 105.657223, ΔYield  = 0.0005
××=105 804232 105 510494
20 0005 105 657223278..
...
8 C is correct. A bond’s modified duration cannot be larger than its Macaulay

duration. The formula for modified duration is:
 where r is the bond’s yield-  to- maturity per period. A bond’s yield-  to- maturity 
has an effective lower bound of 0, and thus the denominator 1 + r term has a 
lower bound of 1. Therefore, ModDur will typically be less than MacDur .
 Effective duration is a measure of curve duration. Modified duration is a mea -
sure of yield duration.
9 C is correct. The bond’s Macaulay duration is closest to 2.83. Macaulay dura -
tion (MacDur) is a weighted average of the times to the receipt of cash flow. 
The weights are the shares of the full price corresponding to each coupon and 
principal payment.
1 6 5.555556 0.058575 0.058575
2 6 5.144033 0.054236 0.108472
3 106 84.146218 0.887190 2.661570
94.845806 1.000000 2.828617
 Thus, the bond’s Macaulay duration (MacDur) is 2.83.

Reading 54 ■ Understanding Fixed -Income Risk and Return 586
 Alternatively, Macaulay duration can be calculated using the following closed-  
form formula:
×+() −

+



−1 1
11r
rrN cr
cr rtTN(()
MacDur =−+× − () 
×() −

108
0081083 0060 08
0061 08 13.
... .
.. + +



−
0080
.
MacDur = 13.50 − 10.67 = 2.83
10 A is correct. The interest rate risk of a fixed-  rate bond with an embedded call 
option is best measured by effective duration. A callable bond’s future cash 
flows are uncertain because they are contingent on future interest rates. The 
issuer’s decision to call the bond depends on future interest rates. Therefore, the 
yield-  to- maturity on a callable bond is not well defined. Only effective duration, 
which takes into consideration the value of the call option, is the appropriate 
interest rate risk measure. Yield durations like Macaulay and modified durations 
are not relevant for a callable bond because they assume no changes in cash

flows when interest rates change.
11 A is correct. Key rate duration is used to measure a bond’s sensitivity to a shift 
at one or more maturity segments of the yield curve which result in a change to 
yield curve shape. Modified and effective duration measure a bond’s sensitivity 
to parallel shifts in the entire curve.
12 B is correct. The effective duration of the pension fund’s liabilities is closest to 
14.99. The effective duration is calculated as follows:
PV 20 ∆
PV0 = 455.4, PV+ = 373.6, PV− = 510.1, and ΔCurve = 0.0100.
EffDur =−
××=510 1 373 6
20 0100 455 414 99..
...
13 B is correct. A bond’s yield-  to- maturity is inversely related to its Macaulay 
duration: The higher the yield-  to- maturity, the lower its Macaulay duration 
and the lower the interest rate risk. A higher yield-  to- maturity decreases the 
weighted average of the times to the receipt of cash flow, and thus decreases the 

 A bond’s coupon rate is inversely related to its Macaulay duration: The lower 
the coupon, the greater the weight of the payment of principal at maturity. This 
results in a higher Macaulay duration. Zero-  coupon bonds do not pay periodic 
coupon payments; therefore, the Macaulay duration of a zero-  coupon bond is 
its time-  to- maturity.
14 A is correct. The presence of an embedded put option reduces the effective 
duration of the bond, especially when rates are rising. If interest rates are low 
compared with the coupon rate, the value of the put option is low and the 
impact of the change in the benchmark yield on the bond’s price is very similar 
to the impact on the price of a non-  putable bond. But when benchmark interest 
rates rise, the put option becomes more valuable to the investor. The ability to

Solutions 587
sell the bond at par value limits the price depreciation as rates rise. The pres -
ence of an embedded put option reduces the sensitivity of the bond price to 
changes in the benchmark yield, assuming no change in credit risk.
15 A is correct. The portfolio’s modified duration is closest to 7.62.Portfolio dura -
tion is commonly estimated as the market-  value-  weighted average of the yield 
durations of the individual bonds that compose the portfolio.
 The total market value of the bond portfolio is 170,000 + 120,000 + 100,000 = 
390,000.
 The portfolio duration is 5.42 × (170,000/390,000) + 8.44 × (120,000/390,000) + 
10.38 × (100,000/390,000) = 7.62.
16 A is correct. A limitation of calculating a bond portfolio’s duration as the 
weighted average of the yield durations of the individual bonds is that this mea -
sure implicitly assumes a parallel shift to the yield curve (all rates change by the 
same amount in the same direction). In reality, interest rate changes frequently

result in a steeper or flatter yield curve. This approximation of the “theoreti -
cally correct” portfolio duration is more  accurate when the yield curve is flatter 
(less steeply sloped). An advantage of this approach is that it can be used with 
portfolios that include bonds with embedded options. Bonds with embedded 
options can be included in the weighted average using the effective durations 
for these securities.
17 B is correct. Bond B has the greatest money duration per 100 of par value. 
Money duration (MoneyDur) is calculated as the annual modified duration 
(AnnModDur ) times the full price ( PVFull) of the bond including accrued inter -
est. Bond B has the highest money duration per 100 of par value.
MoneyDur = AnnModDur × PVFull
MoneyDur of Bond A = 5.42 × 85.00 = 460.70
MoneyDur of Bond B = 8.44 × 80.00 = 675.20
MoneyDur of Bond C = 7.54 × 85.78 = 646.78
18 B is correct. The PVBP is closest to 0.0648. The formula for the price value of a 
basis point is:
2
 where:

2
 where:
 PVBP =  price value of a basis point
 PV– = full price calculated by lowering the yield-  to- maturity by one basis 
point
 PV+ = full price calculated by raising the yield-  to- maturity by one basis 
point
 Lowering the yield-  to- maturity by one basis point to 4.99% results in a bond 
price of 85.849134:
PV−=
+()+++
+()=3
10 04993 100
10 049985 84913419... 

Reading 54 ■ Understanding Fixed -Income Risk and Return 588
 Increasing the yield-  to- maturity by one basis point to 5.01% results in a bond 
price of 85.719638:
PV+=
+()+++
+()=3
10 05013 100
10 050185 71963819... 
PVBP=−=85 849134 85 719638
20 06475...
 Alternatively, the PVBP can be derived using modified duration:
PV 20 ∆
××=85 849134 85 719638
20 0001 85 7843577 548..
...
PVBP = 7.548 × 85.784357 × 0.0001 = 0.06475
19 B is correct. Convexity measures the “second order” effect on a bond’s percent -
age price change given a change in yield-  to- maturity. Convexity adjusts the per -
centage price change estimate provided by modified duration to better approx -
imate the true relationship between a bond’s price and its yield-  to- maturity 
which is a curved line (convex).
 Duration estimates the change in the bond’s price along the straight line that 
is tangent to this curved line (“first order” effect). Yield volatility measures the

magnitude of changes in the yields along the yield curve.
20 B is correct. The bond’s approximate convexity is closest to 70.906. Approximate 
convexity (ApproxCon) is calculated using the following formula:
ApproxCon = [ PV– + PV+ – (2 × PV0)]/(∆Yield2 × PV0)
 where:
 PV_ = new price when the yield-  to- maturity is decreased
 PV+ = new price when the yield-  to- maturity is increased
 PV0 = original price
 ∆Yield =  change in yield-  to- maturity
 ApproxCon =  [98.782 + 98.669 – (2 × 98.722)]/(0.0012 × 98.722) = 
70.906
21 C is correct. The expected percentage price change is closest to 1.78%. The 
convexity-  adjusted percentage price change for a bond given a change in the 
yield-  to- maturity is estimated by:
%∆PVFull ≈ [–AnnModDur × ∆Yield] + [0.5 × AnnConvexity × (∆Yield)2]
%∆PVFull ≈ [–7.020 × (–0.0025)] + [0.5 × 65.180 × (–0.0025)2] = 0.017754, 
or 1.78%
22 B is correct. The expected percentage price change is closest to −3.49%. The

%∆PVFull ≈ [–7.140 × 0.005] + [0.5 × 66.200 × (0.005)2] = –0.034873, or 
–3.49%

Solutions 589
23 B is correct. If the term structure of yield volatility is downward-  sloping, then 
short-  term bond yields-  to- maturity have greater volatility than for long-  term 
bonds. Therefore, long-  term yields are more stable than short-  term yields. 
Higher volatility in short-  term rates does not necessarily mean that the level of 
short-  term rates is higher than long-  term rates. With a downward-  sloping term 
structure of yield volatility, short-  term bonds will not always experience greater 
price fluctuation than long-  term bonds. The estimated percentage change in a 
bond price depends on the modified duration and convexity as well as on the 
yield-  to- maturity change.
24 C is correct. When the holder of a bond experiences a one-  time parallel shift in 
the yield curve, the Macaulay duration statistic identifies the number of years 
necessary to hold the bond so that the losses (or gains) from coupon reinvest -

ment offset the gains (or losses) from market price changes. The duration gap 
is the difference between the Macaulay duration and the investment horizon. 
Modified duration approximates the percentage price change of a bond given a 
25 C is correct. The duration gap is equal to the bond’s Macaulay duration minus 
the investment horizon. In this case, the duration gap is positive, and price risk 
dominates coupon reinvestment risk. The investor risk is to higher rates.
 The investor is hedged against interest rate risk if the duration gap is zero; that 
is, the investor’s investment horizon is equal to the bond’s Macaulay duration. 
The investor is at risk of lower rates only if the duration gap is negative; that is, 
the investor’s investment horizon is greater than the bond’s Macaulay duration. 
In this case, coupon reinvestment risk dominates market price risk.
26 C is correct. The duration gap is closest to 4.158. The duration gap is a bond’s

Macaulay duration minus the investment horizon. The approximate Macaulay 
duration is the approximate modified duration times one plus the yield-  to- 
maturity. It is 12.158 (= 11.470 × 1.06).
 Given an investment horizon of eight years, the duration gap for this bond at 
purchase is positive: 12.158 – 8 = 4.158. When the investment horizon is less 
than the Macaulay duration of the bond, the duration gap is positive, and price 
risk dominates coupon reinvestment risk.
27 A is correct. The price increase was most likely caused by a decrease in the 
bond’s credit spread. The ratings upgrade most likely reflects a lower expected 
probability of default and/or a greater level of recovery of assets if default 
occurs. The decrease in credit risk results in a smaller credit spread. The 
increase in the bond price reflects a decrease in the yield-  to- maturity due to a 
smaller credit spread. The change in the bond price was not due to a change in 
liquidity risk or an increase in the benchmark rate.

Fundamentals of Credit Analysis
by Christopher L. Gootkind, CFA
Christopher L. Gootkind, CFA, is at Loomis Sayles & Company, LP (USA).
a. describe credit risk and credit-  related risks affecting corporate 
bonds;
b. describe default probability and loss severity as components of 
credit risk;
c. describe seniority rankings of corporate debt and explain the 
potential violation of the priority of claims in a bankruptcy 
proceeding;
d. distinguish between corporate issuer credit ratings and issue 
credit ratings and describe the rating agency practice of 
“notching”;
e. explain risks in relying on ratings from credit rating agencies;
f. explain the four Cs (Capacity, Collateral, Covenants, and 
Character) of traditional credit analysis;
g. calculate and interpret financial ratios used in credit analysis;
h. evaluate the credit quality of a corporate bond issuer and a bond 
of that issuer, given key financial ratios of the issuer and the 
industry;

industry;
i. describe factors that influence the level and volatility of yield 
spreads;
j. explain special considerations when evaluating the credit of high 
yield, sovereign, and non-  sovereign government debt issuers and 
issues.READING
55
The author would like to thank several of his Fixed Income Research colleagues at Loomis, Sayles & 
Company for their assistance with this reading: Paul Batterton, Diana Leader-  Cramer, Diana Monteith, 
Shannon O’Mara, CFA, and Laura Sarlo, CFA.

Reading 55 ■ Fundamentals of Credit Analysis 592
With bonds outstanding worth many trillions of US dollars, the debt markets play 
a critical role in the global economy. Companies and governments raise capital in 
the debt market to fund current operations; buy equipment; build factories, roads, 
bridges, airports, and hospitals; acquire assets, and so on. By channeling savings into 
productive investments, the debt markets facilitate economic growth. Credit analysis 
has a crucial function in the debt capital markets—efficiently allocating capital by 
properly assessing credit risk, pricing it accordingly, and repricing it as risks change. 
How do fixed-  income investors determine the riskiness of that debt, and how do they 
decide what they need to earn as compensation for that risk?
This reading covers basic principles of credit analysis, which may be broadly defined 
as the process by which credit risk is evaluated. Readers will be introduced to the

definition of credit risk, the interpretation of credit ratings, the four Cs of traditional 
credit analysis, and key financial measures and ratios used in credit analysis. The 
reading explains, among other things, how to compare bond issuer creditworthiness 
within a given industry as well as across industries and how credit risk is priced in 
the bond market.
The reading focuses primarily on analysis of corporate debt; however, credit anal -
ysis of sovereign and non-  sovereign, particularly municipal, government bonds will 
also be addressed. Structured finance, a segment of the debt markets that includes 
securities backed by pools of assets, such as residential and commercial mortgages 
as well as other consumer loans, will not be covered here.
The key components of credit risk—default probability and loss severity—are 
introduced in the next section along with such credit-  related risks as spread risk, credit

migration risk, and liquidity risk. Section 3 discusses the relationship between credit 
risk and the capital structure of the firm. Credit ratings and the role of credit rating 
agencies are addressed in Section 4. Section 5 focuses on the process of analyzing the 
credit risk of corporations, whereas Section 6 examines the impact of credit spreads 
on risk and return. Special considerations applicable to the analysis of (i) high-  yield 
(low-  quality) corporate bonds and (ii) government bonds are presented in Section 7. 
Section 8 gives a brief summary, and a set of review questions concludes the reading.
CREDIT RISK
Credit risk is the risk of loss resulting from the borrower (issuer of debt) failing to make 
full and timely payments of interest and/or principal. Credit risk has two components. 
The first is known as default risk , or default probability , which is the probability 
that a borrower defaults—that is, fails to meet its obligation to make full and timely

payments of principal and interest, according to the terms of the debt security. The 
second component is loss severity  (also known as “loss given default”) in the event of 
default—that is, the portion of a bond’s value (including unpaid interest) an investor 
loses. A default can lead to losses of various magnitudes. In most instances, in the 
event of default, bondholders will recover some value, so there will not be a total loss 
on the investment. Thus, credit risk is reflected in the distribution of potential losses 
that may arise if the investor is not paid in full and on time. Although it is sometimes 1
2

Credit Risk 593
important to consider the entire distribution of potential losses and their respective 
probabilities,1 it is often convenient to summarize the risk with a single default prob -
ability and loss severity and to focus on the expected loss :
Expected loss = Default probability × Loss severity given default
The loss severity, and hence the expected loss, can be expressed as either a 
monetary amount (e.g., €450,000) or as a percentage of the principal amount (e.g., 
45 percent). The latter form of expression is generally more useful for analysis because 
it is independent of the amount of investment. Loss severity is often expressed as (1 
– Recovery rate), where the recovery rate is the percentage of the principal amount 
recovered in the event of default.
Because default risk (default probability) is quite low for most high-  quality debt 
issuers, bond investors tend to focus primarily on assessing this probability and devote

less effort to assessing the potential loss severity arising from default. However, as an 
issuer’s default risk rises, investors will focus more on what the recovery rate might 
be in the event of default. This issue will be discussed in more detail later. Important 
credit-  related risks include the following: 
■■Spread risk . Corporate bonds and other “credit-  risky” debt instruments typi -
cally trade at a yield premium, or spread, to bonds that have been considered 
“default-  risk free, ” such as US Treasury bonds or German government bonds. 
Yield spreads, expressed in basis points, widen based on two primary factors: 
(1) a decline in an issuer’s creditworthiness, sometimes referred to as credit 
migration or downgrade risk, and (2) an increase in market liquidity risk . 
These two risks are separate but frequently related.
■■Credit migration risk  or downgrade risk . This is the risk that a bond issuer’s 
creditworthiness deteriorates, or migrates lower, leading investors to believe

the risk of default is higher and thus causing the yield spreads on the issuer’s 
bonds to widen and the price of its bonds to fall. The term “downgrade” refers 
to action by the major bond rating agencies, whose role will be covered in more 
detail in Section 4.
■■Market liquidity risk . This is the risk that the price at which investors can actu -
ally transact—buying or selling—may differ from the price indicated in the mar -
ket. To compensate investors for the risk that there may not be sufficient market 
liquidity for them to buy or sell bonds in the quantity they desire, the spread or 
yield premium on corporate bonds includes a market liquidity component, in 
addition to a credit risk component. Unlike stocks, which trade on exchanges, 
most markets bonds trade primarily over the counter, through broker–dealers 
trading for their own accounts. Their ability and willingness to make markets, as 
reflected in the bid–ask spread, is an important determinant of market liquidity

risk. The two main issuer-  specific factors that affect market liquidity risk are (1) 
the size of the issuer (that is, the amount of publicly traded debt an issuer has 
outstanding) and (2) the credit quality of the issuer. In general, the less debt an 
issuer has outstanding, the less frequently its debt trades, and thus the higher 
the market liquidity risk. And the lower the quality of the issuer, the higher the 
market liquidity risk.
1 As an example, careful attention to the full distribution of potential losses is important in analyzing credit 
risk in structured finance products because the various tranches usually share unequally in the credit losses 
on the underlying loans or securities. A particular tranche typically bears none of the losses up to some 
level of underlying losses, then it bears all of the underlying losses until the tranche is wiped out. Losses 
on a “thin” tranche are very likely to be either 0 percent or 100 percent, with relatively small probabilities

on intermediate loss severities. This situation is not well described by a single “average” loss severity.

Reading 55 ■ Fundamentals of Credit Analysis 594
During times of financial stress or crisis, such as in late 2008, market liquidity 
can decline sharply, causing yield spreads on corporate bonds, and other credit-  risky 
debt, to widen and their prices to drop. Some research has been done on trying to 
quantify market liquidity risk,2 and more is likely to be done in the aftermath of the 
EXAMPLE 1   
Defining Credit Risk
1 Which of the following best defines credit risk?
A The probability of default times the severity of loss given default
B The loss of principal and interest payments in the event of bankruptcy
C The risk of not receiving full interest and principal payments on a 
timely basis
2 Which of the following is the best measure of credit risk?
A The expected loss
B The severity of loss
C The probability of default
3 Which of the following is NOT credit or credit-  related risk?
A Default risk
B Interest rate risk
C Downgrade or credit migration risk

C is correct. Credit risk is the risk that the borrower will not make full and 
timely payments.
A is correct. The expected loss captures both of the key components of credit 
risk: (the product of) the probability of default and the loss severity in the event 
of default. Neither component alone fully reflects the risk.
B is correct. Bond price changes due to general interest rate movements are not 
considered credit risk.
2 For example, see Francis A. Longstaff, Sanjay Mithal, and Eric Neis, “Corporate Yield Spreads: Default 
Risk or Liquidity? New Evidence from the Credit-  Default Swap Market, ” Journal of Finance, vol. 60, no. 5, 
October 2005:2213–2253.

Capital Structure, Seniority Ranking, and Recovery Rates 595
CAPITAL STRUCTURE, SENIORITY RANKING, AND 
RECOVERY RATES
The various debt obligations of a given borrower will not necessarily all have the same 
seniority ranking , or priority of payment. In this section, we will introduce the topic 
of an issuer’s capital structure and discuss the various types of debt claims that may 
arise from that structure, as well as their ranking and how those rankings can influence 
recovery rates in the event of default.
3.1 Capital Structure
The composition and distribution across operating units of a company’s debt and 
equity—including bank debt, bonds of all seniority rankings, preferred stock, and 
common equity—is referred to as its capital structure . Some companies and industries 
have straightforward capital structures, with all the debt equally ranked and issued 
by one main operating entity. Other companies and industries, due to their frequent

acquisitions and divestitures (e.g., media companies or conglomerates) or high levels of 
regulation (e.g., banks and utilities), tend to have more complicated capital structures. 
Companies in these industries often have many different subsidiaries, or operating 
companies, that have their own debt outstanding and parent holding companies that 
also issue debt, with different levels or rankings of seniority. Similarly, the cross-  
border operations of multi-  national corporations tend to increase the complexity of 
their capital structures.
3.2 Seniority Ranking
Just as borrowers can issue debt with many different maturity dates and coupons, 
they can also have many different rankings in terms of seniority. The ranking refers to 
the priority of payment, with the most senior or highest-  ranking debt having the first 
claim on the cash flows and assets of the issuer. This level of seniority can affect the

value of an investor’s claim in the event of default and restructuring. Broadly, there is 
secured debt  and unsecured debt . Secured debt means the debtholder has a direct 
claim—a pledge from the issuer—on certain assets and their associated cash flows. 
Unsecured bondholders have only a general claim on an issuer’s assets and cash flow. 
In the event of default, unsecured debtholders’ claims rank below (i.e., get paid after) 
those of secured creditors3 under what’s known as the priority of claims .3
3 The term “creditors” is used throughout this reading to mean holders of debt instruments, such as bonds 
and bank loans. Unless specifically stated, it does not include such obligations as trade credit, tax liens, or 
employment-  related obligations.

Reading 55 ■ Fundamentals of Credit Analysis 596
Exhibit 1   Seniority Ranking
Subordinate dSenior Su bordinate dSenior Unsecu redSecond Lien Loan – Secu redFirst Lien Loan – S enior Secu red
Junior Su bordinate d
Within each category of debt, there are finer gradations of types and rankings. 
Within secured debt, there is first mortgage and first lien debt, which are the highest-  
ranked debt in terms of priority of repayment. First mortgage debt  or loan refers to 
the pledge of a specific property (e.g., a power plant for a utility or a specific casino 
for a gaming company). First lien debt  or loan refers to a pledge of certain assets 
that could include buildings but might also include property and equipment, licenses, 
patents, brands, and so on. There can also be second lien , or even third lien, secured 
debt, which, as the name implies, has a secured interest in the pledged assets but ranks 
below first lien debt in both collateral protection and priority of payment.

Within unsecured debt, there can also be finer gradations and seniority rankings. 
The highest-  ranked unsecured debt is senior unsecured debt. It is the most common 
type of all corporate bonds outstanding. Other, lower-  ranked debt includes subor -
dinated debt  and junior subordinated debt. Among the various creditor classes, 
these obligations have among the lowest priority of claims and frequently have little 
or no recovery in the event of default. That is, their loss severity can be as high as 
100 percent. (See Exhibit 1 for a sample seniority ranking.) For regulatory and cap -
ital purposes, banks in Europe and the United States have issued debt and debt-  like 
securities that rank even lower than subordinated debt4 and are intended to provide a 
capital cushion in times of financial distress. Many of them did not work as intended 
during the financial crisis that began in 2008, and most were phased out, potentially

to be replaced by more effective instruments that automatically convert to equity in 
certain circumstances.
There are many reasons why companies issue—and investors buy—debt with 
different seniority rankings. Issuers are interested in optimizing their cost of cap -
ital—finding the right mix of the various types of both debt and equity—for their 
industry and type of business. Issuers may offer secured debt because that is what the 
market (i.e., investors) may require, given a company’s perceived riskiness, or because 
secured debt is generally lower cost due to the reduced credit risk inherent in its higher 
4 These have various names such as hybrids, trust preferred, and upper and lower Tier 2 securities. In 
some cases, the non-  payment or deferral of interest does not constitute an event of default, and in other 
cases, they might convert into perpetual securities—that is, securities with no maturity date.

Capital Structure, Seniority Ranking, and Recovery Rates 597
priority of claims. Or, issuers may offer subordinated debt because (1) they believe it 
is less expensive than issuing equity5 (and doesn’t dilute existing shareholders) and is 
typically less restrictive than issuing senior debt and (2) investors are willing to buy it 
because they believe the yield being offered is adequate compensation for the risk they 
perceive. Credit risk versus return will be discussed in more detail later in the reading.
EXAMPLE 2   
Seniority Ranking
The Acme Company has senior unsecured bonds as well as both first and second 
lien debt in its capital structure. Which ranks higher with respect to priority of 
claims: senior unsecured bonds or second lien debt?
Solution:
Second lien debt ranks higher than senior unsecured bonds because of its 
secured position.
3.3 Recovery Rates
All creditors at the same level of the capital structure are treated as one class; thus,

a senior unsecured bondholder whose debt is due in 30 years has the same pro rata 
claim in bankruptcy as one whose debt matures in six months. This provision is 
referred to as bonds ranking pari passu  (“on an equal footing”) in right of payment.
Defaulted debt will often continue to be traded by investors and broker–dealers 
based on their assessment that either in liquidation of the bankrupt company’s assets 
or in reorganization, the bonds will have some recovery value. In the case of reorgani -
zation, or restructuring (whether through formal bankruptcy or on a voluntary basis), 
new debt, equity, cash, or some combination thereof could be issued in exchange for 
the original defaulted debt.
As discussed, recovery rates vary by seniority of ranking in a company’s capital 
structure, under the priority of claims treatment in bankruptcy. Over many decades, 
there have been enough defaults to generate statistically meaningful historical data

on recovery rates by seniority ranking. Exhibit 2 provides recovery rates by seniority 
ranking for North American non-  financial companies.6 For example, as shown in 
Exhibit 2, investors on average recovered 51.6 percent of the value of senior unsecured 
debt that defaulted in 2009 but only 28.0 percent of the value of senior subordinated 
issues that defaulted that year.
5 Debtholders require a lower return than equity holders because they have prior claims to an issuer’s 
cash flow and assets. That is, the cost of debt is lower than the cost of equity. In most countries, this cost 
differential is even greater due to the tax deductibility of interest payments.
6 The recovery rates shown for default years 2009 and 2010 should be viewed as preliminary because 
some of the numbers are based on the relatively small number of defaults for which final recovery had 
been determined at the time of the Moody’s study. For example, the 2010 senior unsecured recovery rate 
reflects only two bonds.

Reading 55 ■ Fundamentals of Credit Analysis 598
Exhibit 2   Average Corporate Debt Recovery Rates Measured by Ultimate 
Recoveries
Emergence Y ear* Default Y ear
Seniority ranking 2010 2009 1987–2010 2010 2009 1987–2010
Senior secured 64.4% 59.0% 63.5% 56.3% 65.6% 63.5%
Senior unsecured 51.0% 48.3% 49.2% 26.5% 51.6% 49.2%
Senior subordinated 20.5% 26.2% 29.4% 21.7% 28.0% 29.4%
Subordinated 53.4% 34.3% 29.3% 0.0% 58.3% 29.3%
Junior subordinated NA 0.5% 18.4% NA 0.0% 18.4%
* Emergence year is typically the year the defaulted company emerges from bankruptcy. Default year 
data refer to the recovery rate of debt that defaulted in that year (i.e., 2009 and 2010) or range of years 
(i.e., 1987–2010). Data are for North American nonfinancial companies. NA indicates not available. 
Source:  Based on data from Moody’s Investors Service, Inc. ’s Ultimate Recovery Database.
There are a few things worth noting:
1 Recovery rates can vary widely by industry . Companies that go bankrupt

in industries that are in secular decline (e.g., newspaper publishing) will most 
likely have lower recovery rates than those that go bankrupt in industries 
merely suffering from a cyclical economic downturn.
2 Recovery rates can also vary depending on when they occur in a credit 
cycle .7 As shown in Exhibit 3, at or near the bottom of a credit cycle—which 
is almost always closely linked with an economic cycle—recoveries will tend 
to be lower than at other times in the credit cycle. This is because there will be 
many companies closer to, or already in, bankruptcy, causing valuations to be 
depressed.
7 Credit cycles describe the changing availability—and pricing—of credit. When the economy is strong or 
improving, the willingness of lenders to extend credit, and on favorable terms, is high. Conversely, when 
the economy is weak or weakening, lenders pull back, or “tighten” credit, by making it less available and

more expensive. This frequently contributes to asset values, such as real estate, declining, causing further 
economic weakness and higher defaults. Central banks frequently survey banks to assess how “tight” or 
“loose” their lending standards are. This information, as well as the level and direction of corporate bond 
default rates, helps provide a good sense of where one is in the credit cycle.

Capital Structure, Seniority Ranking, and Recovery Rates 599
Exhibit 3   Global Recovery Rates by Seniority Ranking, 1990–2010
Senior Unsecured Senior SubordinatedFirst Lien Loan US RecessionRecovery (%)
100
80
60
40
20
0
92 90 94 96 98 00 02 04 06 08 10
3 These recovery rates are averages . In fact, there can be large variability, both 
across industries, as noted above, as well as across companies within a given 
industry. Factors might include composition and proportion of debt across an 
issuer’s capital structure. An abundance of secured debt will lead to smaller 
recovery rates on lower-  ranked debt.
Understanding recovery rates is important because they are a key component of 
credit analysis and risk. Recall that the best measure of credit risk is expected loss—
that is, probability of default times loss severity given default. And loss severity equals

(1 – Recovery rate). Having an idea how much one can lose in the event of default is a 
critical factor in valuing credit, particularly lower-  quality credit, as the default risk rises.
Priority of claims: Not always absolute . The priority of claims in bankruptcy—the 
idea that the highest-  ranked creditors get paid out first, followed by the next level, 
and on down, like a waterfall—is well established and is often described as “absolute. ” 
In principle, in the event of bankruptcy or liquidation:
■■Creditors with a secured claim have the right to the value of that specific prop -
erty before any other claim. If the value of the pledged property is less than the 
amount of the claim, then the difference becomes a senior unsecured claim.
■■Unsecured creditors have a right to be paid in full before holders of equity 
interests (common and preferred shareholders) receive value on their interests.
■■Senior unsecured creditors take priority over all subordinated creditors. A cred -

itor is senior unsecured unless expressly subordinated.
In practice, however, creditors with lower seniority and even shareholders may 
receive some consideration without more senior creditors being paid in full. Why 
might this be the case? In bankruptcy, there are different classes of claimants, and all 
classes that are impaired (that is, receive less than full claim) get to vote to confirm 
the plan of reorganization. This vote is subject to the absolute priority of claims. 
Either by consent of the various parties or by the judge’s order, however, absolute 
priority may not be strictly enforced in the final plan. There may be disputes over 
the value of various assets in the bankruptcy estate (e.g., what is a plant, or a patent

Reading 55 ■ Fundamentals of Credit Analysis 600
portfolio, worth?) or the present value or timing of payouts. For example, what is the 
value of the new debt I’m receiving for my old debt of a reorganized company before 
it emerges from bankruptcy?
Resolution of these disputes takes time, and cases can drag on for months and 
years. In the meantime, during bankruptcy, substantial expenses are being incurred 
for legal and accounting fees, and the value of the company may be declining as key 
employees leave, customers go elsewhere, and so on. Thus, to avoid the time, expense, 
and uncertainty over disputed issues, such as the value of property in the estate, the 
legality of certain claims, and so forth, the various claimants have an incentive to 
negotiate and compromise. This frequently leads to creditors with lower seniority 
and other claimants (e.g., even shareholders) receiving more consideration than they 
are legally entitled to.

It’s worth noting that in the United States, the bias is toward reorganization and 
recovery of companies in bankruptcy, whereas in other jurisdictions, such as the United 
Kingdom, the bias is toward liquidation of companies in bankruptcy and maximizing 
value to the banks and other senior creditors. It’s also worth noting that bankruptcy 
and bankruptcy laws are very complex and can vary greatly by country, so it is difficult 
to generalize about how creditors will fare. As shown in the earlier chart, there is huge 
variability in recovery rates for defaulted debt. Every case is different.
EXAMPLE 3   
Priority of Claims
1 Under which circumstance is a subordinated bondholder most likely  to 
recover some value in a bankruptcy without a senior creditor getting paid 
in full? When:
A absolute priority rules are enforced.
B the various classes of claimants agree to it.
C the company is liquidated rather than reorganized.

2 In the event of bankruptcy, claims at the same level of the capital struc -
ture are:
A on an equal footing, regardless of size, maturity, or time outstanding.
B paid in the order of maturity from shortest to longest, regardless of 
size or time outstanding.
C paid on a first-  in, first-  out (FIFO) basis so that the longest-  standing 
claims are satisfied first, regardless of size or maturity.
B is correct. All impaired classes get to vote on the reorganization plan. 
Negotiation and compromise are often preferable to incurring huge legal and 
accounting fees in a protracted bankruptcy process that would otherwise reduce 
the value of the estate for all claimants. This process may allow junior creditors 
(e.g., subordinated bondholders) to recover some value even though more senior 
creditors do not get paid in full.
A is correct. All claims at the same level of the capital structure are pari passu 
(on an equal footing).

Ratings Agencies, Credit Ratings, and Their Role in the Debt Markets 601
RATINGS AGENCIES, CREDIT RATINGS, AND THEIR 
ROLE IN THE DEBT MARKETS
The major credit ratings agencies—Moody’s Investors Service (“Moody’s”), Standard & 
Poor’s (“S&P”), and Fitch Ratings (“Fitch”)—play a central, if somewhat controversial, 
role in the credit markets. For the vast majority of outstanding bonds, at least two of 
the agencies provide ratings: a symbol-  based measure of the potential risk of default 
of a particular bond or issuer of debt. In the public and quasi-  public bond markets,8 
issuers won’t offer, and investors won’t buy, bonds that do not carry ratings from 
Moody’s, S&P , or Fitch. This practice applies for all types of bonds—government or 
sovereign, government related,9 supranational,10 corporate, non-  sovereign govern -
ment, and mortgage- and asset-  backed debt. How did the ratings agencies attain such 
a dominant position in the credit markets? What are credit ratings, and what do they

mean? How does the market use credit ratings? What are the risks of relying solely 
or excessively on credit ratings?
The history of the major ratings agencies goes back more than 100 years. John 
Moody began publishing credit analysis and opinions on US railroads in 1909. S&P 
published its first ratings in 1916. They have grown in size and prominence since 
then. Many bond investors like the fact that there are independent analysts who meet 
with the issuer and often have access to material, non-  public information, such as 
financial projections that investors cannot receive, to aid in the analysis. What has 
also proven very attractive to investors is that credit ratings provide direct and easy 
comparability of the relative credit riskiness of all bond issuers, within and across 
industries and bond types, although there is some debate about ratings comparability 
across the types of bonds.11
Several factors have led to the near universal use of credit ratings in the bond

markets and the dominant role of the major credit rating agencies. These factors 
■■Independent assessment of credit risk
■■Ease of comparison across bond issuers, issues, and market segments
■■Regulatory and statutory reliance and usage12
■■Issuer payment for ratings134
8 That is, underwritten by investment banks, as opposed to privately placed on a “best efforts” basis.
9 These are government agencies or instrumentalities that may have implicit or explicit guarantees from 
the government. Examples include Ginnie Mae in the United States and Pfandbriefe  in Germany.
10 Supranationals are international financial institutions, such as the International Bank for Reconstruction 
and Development (“World Bank”), the Asian Development Bank, and the European Investment Bank, that 
are established by treaty and owned by several member governments.
11 Investigations conducted after the late 2008/early 2009 financial crisis suggested that, for a given rating

category, municipal bonds have experienced a lower historical incidence of default than corporate debt. 
12 It is common for regulations to make reference to ratings issued by recognized credit ratings agencies. 
In light of the role played by the agencies in the sub-  prime mortgage crisis, however, some jurisdictions 
(e.g., the United States) are moving to remove such references. Nonetheless, the so-  called Basel III global 
framework for bank supervision developed beginning in 2009 retains such references. 
13 The “issuer pay” model allows the distribution of ratings to a broad universe of investors and undoubt -
edly facilitated widespread reliance on ratings. It is controversial, however, because some believe it creates 
a conflict of interest among the rating agency, the investor, and the issuer. Studies suggest, however, that 
ratings are not biased upward and alternate payment models, such as “investor pays, ” have their own short -

comings, including the “free rider” problem inherent in a business where information is widely available 
and freely shared. So, despite its potential problems, and some calls for a new payment model, the “issuer 
pay” model remains entrenched in the market.

Reading 55 ■ Fundamentals of Credit Analysis 602
■■Huge growth of debt markets
■■Development and expansion of bond portfolio management and the accompa -
nying bond indexes.
However, in the aftermath of the financial crisis of 2008–2009, when the rating 
agencies were blamed for contributing to the crisis with their overly optimistic ratings 
on securities backed by subprime mortgages, there were attempts to reduce the role 
and dominant positions of the major credit rating agencies. New rules, regulations, 
and legislation were passed to require the agencies to be more transparent, reduce 
conflicts of interest, and stimulate more competition. Challenging the dominance 
of Moody’s, S&P , and Fitch, additional credit rating agencies have emerged. Some 
credit rating agencies that are well-  established in their home markets but are not so 
well known globally, such as Dominion Bond Rating Service (DBRS) in Canada and

Mikuni & Co. in Japan, have tried to raise their profiles. The market dominance of 
the biggest credit rating agencies, however, remains largely intact.
4.1 Credit Ratings
The three major global credit rating agencies—Moody’s, S&P , and Fitch—use similar, 
symbol-  based ratings that are basically an assessment of a bond issue’s risk of default. 
Exhibit 4 shows their long-  term ratings ranked from highest to lowest.14
Exhibit 4   Long-  Term Ratings Matrix: Investment Grade vs. Non-  Investment 
Grade
Moody's S&P Fitch
Investment GradeHigh-  Quality 
GradeAaa AAA AAA
Aa1 AA+ AA+
Aa2 AA AA
Aa3 AA– AA–
Upper-  Medium 
GradeA1 A+ A+
A2 A A
A3 A– A–
Low-  Medium 
GradeBaa1 BBB+ BBB+
Baa2 BBB BBB
Baa3 BBB– BBB–
14 The rating agencies also provide ratings on short-  term debt instruments, such as bank deposits and 
commercial paper. However, they use different scales: From the highest to lowest rating, Moody’s uses P-  1,

P- 2, P-  3; S&P uses A-  1+, A-  1, A-  2, A-  3; Fitch uses F-  1, F-  2, F-  3. Below that is not prime. Short-  term ratings 
are typically used by money market funds, with the vast majority of the instruments they own rated in the 
highest (or in the case of S&P , the highest or second-  highest) category. These top ratings basically map to 
a single-  A or higher long-  term rating.

Ratings Agencies, Credit Ratings, and Their Role in the Debt Markets 603
Non-  Investment Grade 
“Junk” or “High Yield”Low Grade or 
Speculative 
GradeBa1 BB+ BB+
Ba2 BB BB
Ba3 BB– BB–
B1 B+ B+
B2 B B
B3 B– B–
Caa1 CCC+ CCC+
Caa2 CCC CCC
Caa3 CCC– CCC–
Ca CC CC
C C C
Default C D D
Bonds rated triple-  A (Aaa or AAA) are said to be “of the highest quality, with 
minimal credit risk”15 and thus have extremely low probabilities of default. Double-  A 
(Aa or AA) rated bonds are referred to as “high-  quality grade” and are also regarded as 
having very low default risk. Bonds rated single-  A are referred to as “upper-  medium 
grade. ” Baa (Moody’s) or BBB (S&P and Fitch) are called “low-  medium grade. ” Bonds 
rated Baa3/BBB– or higher are called “investment grade. ” Bonds rated Ba1 or lower 
by Moody’s and BB+ or lower by S&P and Fitch, respectively, have speculative credit 
characteristics and increasingly higher default risk. As a group, these bonds are referred

to in a variety of ways: “low grade, ” “speculative grade, ” “non-  investment grade, ” “below 
investment grade, ” “high yield, ” and, in an attempt to reflect the extreme level of risk, 
some observers refer to these bonds as “junk bonds. ” The D rating is reserved for 
securities that are already in default in S&P’s and Fitch’s scales. For Moody’s, bonds 
rated C are likely, but not necessarily, in default. Generally, issuers of bonds rated 
investment grade are more consistently able to access the debt markets and can borrow 
at lower interest rates than those rated below investment grade.
In addition, rating agencies will typically provide outlooks on their respective 
ratings—positive, stable, or negative—and may provide other indicators on the poten -
tial direction of their ratings under certain circumstances, such as “On Review for a 
Downgrade” or “On CreditWatch for an Upgrade. ”16 It should also be noted that, in

support of the ratings they publish, the rating agencies also provide extensive writ -
ten commentary and financial analysis on the obligors they rate, as well as summary 
industry statistics.
4.2 Issuer vs. Issue Ratings
Rating agencies will typically provide both issuer and issue ratings, particularly as they 
relate to corporate debt. Terminology used to distinguish between issuer and issue 
ratings includes corporate family rating (CFR) and corporate credit rating (CCR) or 
issuer credit rating and issue credit rating. An issuer credit rating is meant to address Exhibit 4   (Continued)
15 Moody’s Investors Service, “Ratings Symbols and Definitions” (July 2011).
16 Additional detail on their respective ratings definitions, methodologies, and criteria can be found on each 
of the major rating agency’s websites: www.moodys.com, www.standardandpoors.com, and www.fitch.com.

Reading 55 ■ Fundamentals of Credit Analysis 604
an obligor’s overall creditworthiness—its ability and willingness to make timely pay -
ments of interest and principal on its debt. The issuer credit rating usually applies to 
its senior unsecured debt.
Issue ratings refer to specific financial obligations of an issuer and take into consid -
eration such factors as ranking in the capital structure (e.g., secured or subordinated). 
Although cross-  default provisions , whereby events of default such as non-  payment 
of interest17 on one bond trigger default on all outstanding debt,18 implies the same 
default probability for all issues, specific issues may be assigned different credit rat -
ings—higher or lower—due to a ratings adjustment methodology known as notching .
Notching.  For the rating agencies, likelihood of default—default risk—is the primary 
factor in assigning their ratings. However, there are secondary factors as well. These

factors include the priority of payment in the event of a default (e.g., secured versus 
senior unsecured versus subordinated) as well as potential loss severity in the event 
of default. Another factor considered by rating agencies is structural subordination , 
which can arise when a corporation with a holding company structure has debt at both 
its parent holding company and operating subsidiaries. Debt at the operating subsid -
iaries will get serviced by the cash flow and assets of the subsidiaries before funds can 
be passed (“upstreamed”) to the holding company to service debt at that level.
Recognizing these different payment priorities, and thus the potential for higher 
(or lower) loss severity in the event of default, the rating agencies have adopted a 
notching process whereby their credit ratings on issues can be moved up or down 
from the issuer rating, which is usually the rating applied to its senior unsecured debt.

As a general rule, the higher the senior unsecured rating, the smaller the notching 
adjustment will be. The reason behind this is that the higher the rating, the lower the 
perceived risk of default, so the need to “notch” the rating to capture the potential 
difference in loss severity is greatly reduced. For lower-  rated credits, however, the risk 
of default is greater and thus the potential difference in loss from a lower (or higher) 
priority ranking is a bigger consideration in assessing an issue’s credit riskiness. Thus, 
the rating agencies will typically apply larger rating adjustments. For example, S&P 
applies the following notching guidelines:
As default risk increases, the concern over what can be recovered takes on 
greater relevance and, therefore, greater rating significance. Accordingly, 
the LGD [Loss Given Default] aspect of ratings is given more weight as 
one moves down the rating spectrum. For example, subordinated debt can

be rated up to two notches below a noninvestment grade corporate credit 
rating, but one notch at most if the corporate credit rating is investment 
grade. (In the same vein, issues of companies with an ‘ AAA’ rating need 
not be notched at all.)19
Exhibit 5 is an example of S&P’s notching criteria, as applied to United Rentals, 
Inc. (URI). URI is a US-  based equipment rental company whose corporate credit—and 
senior unsecured—rating is single-  B. Note how the company’s subordinated debt is 
rated two notches lower, at CCC+.
17 This issue will be covered in greater detail in the section on covenants.
18 Nearly all bonds have a cross-  default provision. Rare exceptions to this cross-  default provision include 
the deeply subordinated, debt-  like securities referenced earlier in this reading.
19 Standard & Poor’s, “Rating Each Issue, ” in Corporate Ratings Criteria 2008  (New York: Standard and 
Poor’s, 2008):89.

Ratings Agencies, Credit Ratings, and Their Role in the Debt Markets 605
Exhibit 5   URI’s S&P Ratings Detail, 27 May 2011
Corporate credit rating B/Stable/–
Preferred stock (1 issue) CCC
Senior unsecured (2 issues) B
Subordinated (4 issues) CCC+
Source:  Based on data from Standard & Poor’s Financial Services, LLC.
4.3 Risks in Relying on Agency Ratings
The dominant position of the rating agencies in the global debt markets, and the 
near-  universal use of their credit ratings on debt securities, suggests that investors 
believe they do a good job assessing credit risk. In fact, with a few exceptions (e.g., 
too high ratings on US subprime mortgage-  backed securities issued in the mid-  2000s, 
which turned out to be much riskier than expected), their ratings have proved quite 
accurate as a relative measure of default risk. For example, Exhibit 6 shows historical 
S&P one-  year global corporate default rates by rating category from 1991 to 2010.20

Exhibit 6   Global Corporate Annual Default Rates by Rating Category (%)
AAA AA A BBB BB B CCC/C
1991 0.00 0.00 0.00 0.55 1.68 13.84 33.87
1992 0.00 0.00 0.00 0.00 0.00 6.99 30.19
1993 0.00 0.00 0.00 0.00 0.70 2.62 13.33
1994 0.00 0.00 0.14 0.00 0.27 3.08 16.67
1995 0.00 0.00 0.00 0.17 0.98 4.59 28.00
1996 0.00 0.00 0.00 0.00 0.67 2.91 4.17
1997 0.00 0.00 0.00 0.25 0.19 3.49 12.00
1998 0.00 0.00 0.00 0.41 0.97 4.61 42.86
1999 0.00 0.17 0.18 0.19 0.95 7.28 32.35
2000 0.00 0.00 0.26 0.37 1.25 7.73 34.12
2001 0.00 0.00 0.35 0.33 3.13 11.24 44.55
2002 0.00 0.00 0.00 1.01 2.81 8.11 44.12
2003 0.00 0.00 0.00 0.23 0.56 4.01 32.93
2004 0.00 0.00 0.08 0.00 0.53 1.56 15.33
2005 0.00 0.00 0.00 0.07 0.20 1.73 8.94
2006 0.00 0.00 0.00 0.00 0.30 0.81 12.38
2007 0.00 0.00 0.00 0.00 0.19 0.25 15.09
2008 0.00 0.38 0.38 0.48 0.78 3.98 26.26
2009 0.00 0.00 0.22 0.54 0.72 10.38 48.68
2010 0.00 0.00 0.00 0.00 0.55 0.80 22.27
Mean 0.00 0.03 0.08 0.23 0.87 5.00 25.91

20 S&P uses a static pool methodology here. It measures the percentage of issues that defaulted in a given 
calendar year based on how they were rated at the beginning of the year.

Reading 55 ■ Fundamentals of Credit Analysis 606
Max 0.00 0.38 0.38 1.01 3.13 13.84 48.68
Min 0.00 0.00 0.00 0.00 0.00 0.25 4.17
Source:  Based on data from Standard & Poor's Financial Services, LLC.
As Exhibit 6 shows, the highest-  rated bonds have extremely low default rates. With 
very few exceptions, the lower the rating, the higher the annual rate of default, with 
bonds rated CCC and lower experiencing the highest default rates by far.
There are limitations and risks, however, to relying on credit rating agency ratings, 
including the following:
■■Credit ratings can change over time . Over a long time period (e.g., many 
years), credit ratings can migrate—move up or down—significantly from what 
they were at the time of bond issuance. Using Standard & Poor’s data, Exhibit 7 
shows the average three-  year migration (or “transition”) by rating from 1981 
to 2010. Note that the higher the credit rating, the greater the ratings stability.

Even for AAA rated credits, however, only about 70 percent (70 percent in the 
United States and 68 percent globally) of the time did ratings remain in that rat -
ing category over a three-  year period. (Of course, AAA rated credits can have 
their ratings move in only one direction—down.) A very small fraction of AAA 
rated credits became non-  investment grade or defaulted within three years. For 
single-  B rated credits, only about 40 percent (40 percent in the United States 
and 39 percent globally) of the time did ratings remain in that rating category 
over three-  year periods. This observation about how credit ratings can change 
over time isn’t meant to be a criticism of the rating agencies. It is meant to 
demonstrate that creditworthiness can and does change—up or down—and that 
bond investors should not assume an issuer’s credit rating will remain the same 
from time of purchase through the entire holding period.

Exhibit 7   Average Three-  Y ear Corporate Transition Rates, 1981–2010 (%)
From/To AAA AA A BBB BB B CCC/C D NR*
United States  
AAA 69.75 16.60 2.47 0.38 0.21 0.13 0.13 0.17 10.15
AA 1.32 65.46 17.75 2.52 0.47 0.42 0.04 0.20 11.82
A 0.11 4.34 67.32 12.05 1.79 0.69 0.14 0.42 13.16
BBB 0.04 0.47 8.61 62.21 8.03 2.47 0.35 1.22 16.60
BB 0.02 0.10 0.78 10.95 43.95 13.59 1.40 5.60 23.61
B 0.01 0.06 0.42 1.08 10.06 40.27 4.94 15.79 27.37
CCC/C 0.00 0.00 0.38 0.98 1.97 12.19 13.47 43.98 27.02
Global  
AAA 68.09 18.85 2.46 0.34 0.14 0.08 0.11 0.14 9.78
AA 1.30 65.78 18.59 2.24 0.37 0.26 0.03 0.15 11.29
A 0.08 4.53 67.31 11.84 1.42 0.57 0.12 0.34 13.80
BBB 0.03 0.41 8.90 61.42 7.44 2.12 0.36 1.20 18.12
BB 0.01 0.07 0.67 11.31 43.97 12.06 1.37 5.17 25.37Exhibit 6   (Continued)

Ratings Agencies, Credit Ratings, and Their Role in the Debt Markets 607
B 0.01 0.05 0.34 1.08 10.90 38.93 4.61 15.25 28.84
CCC/C 0.00 0.00 0.29 0.91 2.05 16.04 12.39 40.47 27.85
* NR means not rated—that is, certain corporate issuers were no longer rated by S&P . This could occur for a variety of reasons, including 
issuers paying off their debt and no longer needing ratings.
■■Credit ratings tend to lag the market’s pricing of credit risk . Bond prices and 
credit spreads frequently move more quickly because of changes in perceived 
creditworthiness than rating agencies change their ratings (or even outlooks) 
up or down. Bond prices and relative valuations can move every day, whereas 
bond ratings, appropriately, don’t change that often. Even over long time peri -
ods, however, credit ratings can badly lag changes in bond prices. Exhibit 8

shows the price and Moody’s rating of a bond from US automaker Ford Motor 
Company before, during, and after the financial crisis in 2008. Note how the 
bond’s price moved down sharply well before Moody’s downgraded its credit 
rating—multiple times—and also how the bond’s price began to recover—and 
kept recovering—well before Moody’s upgraded its credit rating on Ford debt.
Exhibit 8   Ford Motor Company Senior Unsecured Debt: Price vs. Moody’s 
Rating Since 2005
Ford 6.5% Due 2018Price ($)
Baa3
Ba3
B2
B3
Caa1
Caa2
Ca
Caa2
Caa1
B3
B2
Ba3110
100
90
80
70
60
50
40
30
20
10
0
05 06 08 07 10 09 11
Sources:  Data based on Bloomberg Finance L.P . and Moody’s Investors Service.
Moreover, particularly for certain speculative-  grade credits, two bonds with 
similar ratings may trade at very different valuations. This is partly a result of 
the fact that credit ratings primarily try to assess the risk of default, whereas for

low-  quality credits, the market begins focusing more on expected loss (default Exhibit 7   (Continued)

Reading 55 ■ Fundamentals of Credit Analysis 608
probability times loss severity). So, bonds from two separate issuers with 
comparable (high) risk of default but different recovery rates may have similar 
ratings but trade at significantly different dollar prices.21
Thus, bond investors who wait for rating agencies to change their ratings before 
making buy and sell decisions in their portfolios may be at risk of underper -
forming other investors who make portfolio decisions in advance of—or not 
solely based on—rating agency changes.
■■Rating agencies may make mistakes . The mis-  rating of billions of dollars of 
subprime-  backed mortgage securities is one example. Other examples include 
the mis-  ratings of US companies Enron and WorldCom and European issuer 
Parmalat. Like many investors, the rating agencies did not see the accounting 
fraud being committed in those companies.
■■Some risks are difficult to capture in credit ratings . Examples include litiga -

tion risk, such as that which can affect tobacco companies, or environmental 
and business risks faced by chemical companies and utility power plants. This 
would also include such unpredictable events as the earthquake and tsunami 
that hit Japan in March 2011 and its credit impact on debt issuer Tokyo Electric 
Power Company (TEPCO). Leveraged transactions, such as debt-  financed 
acquisitions and large stock buybacks (share repurchases), are often difficult to 
anticipate and thus to capture in credit ratings.
As described, there are risks in relying on credit rating agency ratings when invest -
ing in bonds. Thus, while the credit rating agencies will almost certainly continue to 
play a significant role in the bond markets, it is important for investors to perform 
their own credit analyses and draw their own conclusions regarding the credit risk 
of a given debt issue or issuer.
EXAMPLE 4   
Credit Ratings
1 Using the S&P ratings scale, investment grade bonds carry which of the

following ratings?
A AAA to EEE
B BBB– to CCC
C AAA to BBB–
2 Using both Moody’s and S&P ratings, which of the following pairs of 
ratings is considered high yield, also known as “below investment grade, ” 
“speculative grade, ” or “junk”?
A Baa1/BBB–
B B3/CCC+
C Baa3/BB+
3 What is the difference between an issuer rating and an issue rating?
A The issuer rating applies to all of an issuer’s bonds, whereas the issue 
rating considers a bond’s seniority ranking.
B The issuer rating is an assessment of an issuer’s overall creditworthi -
ness, whereas the issue rating is always higher than the issuer rating.
21 See Christopher L. Gootkind, “Improving Credit Risk Analysis, ” in Fixed-  Income Management for the 
21st Century  (Charlottesville, VA: Association for Investment Management and Research, 2002).

Ratings Agencies, Credit Ratings, and Their Role in the Debt Markets 609
C The issuer rating is an assessment of an issuer’s overall creditwor -
thiness, typically reflected as the senior unsecured rating, whereas 
the issue rating considers a bond’s seniority ranking (e.g., secured or 
subordinated).
4 Based on the practice of notching by the rating agencies, a subordinated 
bond from a company with an issuer rating of BB would likely carry what 
rating?
A B+
B BB
C BBB–
5 The fixed-  income portfolio manager you work with asked you why a 
bond from an issuer you cover didn’t rise in price when it was upgraded 
by Fitch from B+ to BB. Which of the following is the most likely  
A Bond prices never react to rating changes.
B The bond doesn’t trade often so the price hasn’t adjusted to the rating 
change yet.
C The market was expecting the rating change, and so it was already 
“priced in” to the bond.
6 Amalgamated Corp. and Widget Corp. each have bonds outstanding with

similar coupons and maturity dates. Both bonds are rated B2, B–, and B 
by Moody’s, S&P , and Fitch, respectively. The bonds, however, trade at 
very different prices—the Amalgamated bond trades at €89, whereas the 
Widget bond trades at €62. What is the most likely  explanation of the 
price (and yield) difference?
A Widget’s credit ratings are lagging the market’s assessment of the com -
pany’s credit deterioration.
B The bonds have similar risks of default (as reflected in the ratings), but 
the market believes the Amalgamated bond has a higher expected loss 
C The bonds have similar risks of default (as reflected in the ratings), but 
the market believes the Widget bond has a higher expected recovery 
rate in the event of default.
B is correct. Note that issuers with ratings such as Baa3/BB+ (answer C) are 
called “crossovers” because one rating is investment grade (the Moody’s rating

of Baa3) and the other is high yield (the S&P rating of BB+).
A is correct. The subordinated bond would have its rating notched lower than 
the company’s BB rating, probably by two notches, reflecting the higher weight 
given to loss severity for below-  investment-  grade credits.

Reading 55 ■ Fundamentals of Credit Analysis 610
C is correct. The market was anticipating the rating upgrade and had already 
priced it in. Bond prices often do react to rating changes, particularly multi-  notch 
ones. Even if bonds don’t trade, their prices adjust based on dealer quotations 
given to bond pricing services.
A is correct. Widget’s credit ratings are probably lagging behind the market’s 
assessment of its deteriorating creditworthiness. Answers B and C both state the 
situation backwards. If the market believed that the Amalgamated bond had a 
higher expected loss given default, then that bond would be trading at a lower, 
not a higher, price. Similarly, if the market believed that the Widget bond had a 
higher expected recovery rate in the event of default, then that bond would be 
trading at a higher, not a lower, price.
TRADITIONAL CREDIT ANALYSIS: CORPORATE DEBT 

The goal of credit analysis is to assess an issuer’s ability to satisfy its debt obligations, 
including bonds and other indebtedness, such as bank loans. These debt obligations 
are contracts, the terms of which specify the interest rate to be paid, the frequency 
and timing of payments, the maturity date, and the covenants that describe the 
permissible and required actions of the borrower. Because corporate bonds are con -
tracts, enforceable by law, credit analysts generally assume an issuer’s willingness to 
pay and concentrate instead on assessing its ability to pay. Thus, the main focus in 
credit analysis is to understand a company’s ability to generate cash flow over the 
term of its debt obligations. In so doing, analysts must assess both the credit quality 
of the company and the fundamentals of the industry in which the company operates. 
Traditional credit analysis considers the sources, predictability, and sustainability of

cash generated by a company to service its debt obligations. This section will focus 
on corporate credit analysis; in particular, it will emphasize non-  financial companies. 
Financial institutions have very different business models and funding profiles from 
industrial and utility companies.
5.1 Credit Analysis vs. Equity Analysis: Similarities and 
The above description of credit analysis suggests credit and equity analyses should 
be very similar; in many ways, they are. There are motivational differences, however, 
between equity and fixed-  income investors that are an important aspect of credit 
analysis. Strictly speaking, management works for the shareholders of a company. Its 
primary objective is to maximize the value of the company for its owners. In contrast, 
management’s legal duty to its creditors—including bondholders—is to meet the terms 
of the governing contracts. Growth in the value of a corporation from rising profits

and cash flow accrues to the shareholders, while the best outcome for bondholders 
is to receive full, timely payment of interest and repayment of principal when due. 
Conversely, shareholders are more exposed to the decline in value if a company’s 
earnings and cash flow decline because bondholders have a prior claim on cash flow 
and assets. But if a company’s earnings and cash flow decline to the extent that it can 
no longer make its debt payments, then bondholders are at risk of loss as well.5

Traditional Credit Analysis: Corporate Debt Securities 611
In summary, in exchange for a prior claim on cash flow and assets, bondholders 
do not share in the growth in value of a company (except to the extent that its cred -
itworthiness improves) but have downside risk in the event of default. In contrast, 
shareholders have theoretically unlimited upside opportunity, but in the event of default, 
their investment is typically wiped out before the bondholders suffer a loss. This is 
very similar to the type of payoff patterns seen in financial options. In fact, in recent 
years, credit risk models, have been developed based on the insights of option pricing 
theory. Although it is beyond the scope of this present introduction to the subject, 
it is an expanding area of interest to both institutional investors and rating agencies.
Thus, although the analysis is similar in many respects for both equity and credit,

equity analysts are interested in the strategies and investments that will increase a 
company’s value and grow earnings per share. They then compare that earnings and 
growth potential with that of other companies in a given industry. Credit analysts 
will look more at the downside risk by measuring and assessing the sustainability of 
a company’s cash flow relative to its debt levels and interest expense. Importantly for 
credit analysts, the balance sheet will show the composition of an issuer’s debt—the 
overall amount, how much is coming due and when, and the distribution by seniority 
ranking. In general, equity analysts will focus more on income and cash flow state -
ments, whereas credit analysts tend to focus more on the balance sheet and cash 
flow statements.
5.2 The Four Cs of Credit Analysis: A Useful Framework
Traditionally, many analysts evaluated creditworthiness based on what is often called 
the “four Cs of credit analysis”:22
■■Capacity
■■Collateral
■■Covenants
■■Character

Capacity  refers to the ability of the borrower to make its debt payments on time; 
this is the focus of this section. Collaterals  refers to the quality and value of the assets 
supporting the issuer’s indebtedness. Covenants  are the terms and conditions of 
lending agreements that the issuer must comply with. Character  refers to the quality 
of management. Each of these will now be covered in greater detail.
5.2.1  Capacity
Capacity is the ability of a borrower to service its debt. To determine that, credit 
analysis, in a process similar to equity analysis, starts with industry analysis and then 
turns to examination of the specific issuer (company analysis).
22 There is no unique list of Cs. In addition to those listed here, one may see “capital” and/or “conditions” 
on a particular author’s list of four (or five) Cs. Conditions typically refers to overall economic conditions.

Capital refers to the company’s accumulated capital and its specific capital assets and is essentially sub -
sumed within the categories of capacity and collateral. Keep in mind that the list of Cs is a convenient way 
to summarize the important aspects of the analysis, not a checklist to be applied mechanically.

Reading 55 ■ Fundamentals of Credit Analysis 612
Industry structure.  A useful framework for analyzing industry structure was devel -
oped by business school professor and consultant Michael Porter.23 The framework 
considers the effects of five competitive forces on an industry:
1 Threat of entry.  Threat of entry depends on the extent of barriers to entry 
and the expected response from incumbents to new entrants. Industries with 
high entry barriers tend to be more profitable and have lower credit risk than 
industries with low entry barriers because incumbents do not need to hold 
down prices or take other steps to deter new entrants. High entry barriers can 
take many forms, including high capital investment, such as in aerospace; large, 
established distribution systems, such as in auto dealerships; patent protection, 
such as in technology or pharmaceutical industries; or a high degree of regula -
tion, such as in utilities.

2 Power of suppliers.  An industry that relies on just a few suppliers tends to be 
less profitable and to have greater credit risk than an industry that has multi -
ple suppliers. Industries and companies with just a few suppliers have limited 
negotiating power to keep the suppliers from raising prices, whereas industries 
that have many suppliers can play them off against each other to keep prices in 
check.
3 Power of buyers/customers.  Industries that rely heavily on just a few main 
customers have greater credit risk because the negotiating power lies with the 
buyers. For example, a toolmaker that sells 50 percent of its products to one 
large global retailer has limited negotiating power with its principal customer.
4 Threat of substitutes.  Industries (and companies) that offer products and 
services that provide great value to their customers, and for which there are 
not good or cost-  competitive substitutes, typically have strong pricing power,

generate substantial cash flows, and represent less credit risk than other indus -
tries or companies. Certain (patent-  protected) drugs are an example. Over time, 
however, disruptive technologies and inventions can increase substitution risk. 
For example, years ago, airplanes began displacing many trains and steamships. 
Newspapers were considered to have a nearly unassailable market position until 
television and then the internet became substitutes for how people received 
news and information. Over time, recorded music has shifted from records to 
tapes, to compact discs, to mp3s and other forms of digital media.
5 Rivalry among existing competitors.  Industries with strong rivalry—because 
of numerous competitors, slow industry growth, or high barriers to exit—tend 
to have less cash flow predictability and, therefore, higher credit risk than 
industries with less competition. Regulation can affect the extent of rivalry and

competition. For example, regulated utilities typically have a monopoly position 
in a given market, which results in relatively stable and predictable cash flows. 
It is important to consider how companies in an industry generate revenues and 
earn profits. Is it an industry with high fixed costs and capital investment or one 
with modest fixed costs? These structures generate revenues and earn profits in very 
different ways. Two examples of industries with high fixed costs, also referred to as 
“having high operating leverage, ” are airlines and hotels. Many of their operating costs 
are fixed—running a hotel, flying a plane—so they cannot easily cut costs. If an insuf -
ficient number of people stay at a hotel or fly in a plane, fixed operating costs may not 
be covered and losses may result. With higher occupancy of a hotel or plane, revenues 
are higher, and it is more likely that fixed costs will be covered and profits earned.

23 Porter, Michael E. 2008. “The Five Competitive Forces That Shape Strategy. ” Harvard Business Review , 
vol. 86, no. 1:78–93.

Traditional Credit Analysis: Corporate Debt Securities 613
Industry fundamentals.  After understanding an industry’s structure, the next step 
is to assess its fundamentals, including its sensitivity to macroeconomic factors, its 
growth prospects, its profitability, and its business need—or lack thereof—for high 
credit quality. Judgments about these can be made by looking at the following:
■■Cyclical or non-  cyclical . This is a crucial assessment because industries that are 
cyclical—that is, have greater sensitivity to broader economic performance—
have more volatile revenues, margins, and cash flows and thus are inherently 
riskier than non-  cyclical industries. Consumer product and health care com -
panies are typically considered non-  cyclical, whereas auto and steel companies 
can be very cyclical. Companies in cyclical industries should carry lower levels 
of debt relative to their ability to generate cash flow over an economic cycle

than companies in less-  cyclical or non-  cyclical industries.
■■Growth prospects . Although growth is typically a greater focus for equity 
analysts than for credit analysts, bond investors have an interest in growth as 
well. Industries that have little or no growth tend to consolidate via mergers 
and acquisitions. Depending upon how these are financed (e.g., using stock or 
debt) and the economic benefits (or lack thereof) of the merger, they may or 
may not be favorable to corporate bond investors. Weaker competitors in slow-  
growth industries may begin to struggle financially, adversely affecting their 
creditworthiness.
■■Published industry statistics . Analysts can get an understanding of an industry’s 
fundamentals and performance by researching statistics that are published by 
and available from a number of different sources, including the rating agencies, 
investment banks, industry publications, and frequently, government agencies.

Company fundamentals.  Following analysis of an industry’s structure and funda -
mentals, the next step is to assess the fundamentals of the company: the corporate 
borrower. Analysts should examine the following:
■■Competitive position
■■Track record/operating history
■■Management’s strategy and execution
■■Ratios and ratio analysis
Competitive position.  Based on their knowledge of the industry structure and fun -
damentals, analysts assess a company’s competitive position within the industry. What 
is its market share? How has it changed over time: Is it increasing, decreasing, holding 
steady? Is it well above (or below) its peers? How does it compare with respect to cost 
structure? How might it change its competitive position? What sort of financing might 
that require?
Track record/Operating history.  How has the company performed over time? It’s 
useful to go back several years and analyze the company’s financial performance, per -

haps during times of both economic growth and contraction. What are the trends in 
revenues, profit margins, and cash flow? Capital expenditures represent what percent 
of revenues? What are the trends on the balance sheet—use of debt versus equity? Was 
this track record developed under the current management team? If not, when did the 
current management team take over?
Management’s strategy and execution.  What is management’s strategy for the 
company: to compete and to grow? Does it make sense, and is it plausible? How risky 
is it, and how differentiated is it from its industry peers? Is it venturing into unrelated 
businesses? Does the analyst have confidence in management’s ability to execute? What

Reading 55 ■ Fundamentals of Credit Analysis 614
is management’s track record, both at this company and at previous ones? Credit analysts 
also want to know and understand how management’s strategy will affect its balance 
sheet. Does management plan to manage the balance sheet prudently, in a manner that 
doesn’t adversely affect bondholders? Analysts can learn about management’s strategy 
from reading comments, discussion, and analysis that are included with financial state -
ments filed with appropriate regulators, listening to conference calls about earnings 
or other big announcements (e.g., acquisitions), going to company websites to find 
earnings releases and copies of slides of presentations at various industry conferences, 
visiting and speaking with the company, and so on.
EXAMPLE 5   
Industry and Company Analysis
1 Given a hotel company, a chemical company, and a consumer products 
company, which is most likely  to be able to support a high debt load over 
an economic cycle?

A The hotel company, because people need a place to stay when they 
travel.
B The chemical company, because chemicals are a key input to many 
products.
C The consumer products company, because consumer products are 
typically resistant to recessions.
2 Heavily regulated monopoly companies, such as utilities, often carry high 
debt loads. Which of the following statements about such companies is 
most  accurate?
A Regulators require them to carry high debt loads.
B They generate strong and stable cash flows, enabling them to support 
high levels of debt.
C They are not very profitable and need to borrow heavily to maintain 
their plant and equipment.
3 XYZ Corp. manufactures a commodity product in a highly competitive 
industry in which no company has significant market share and where 
there are low barriers to entry. Which of the following best describes 
XYZ’s ability to take on substantial debt?
A Its ability is very limited because companies in industries with those

characteristics generally cannot support high debt loads.
B Its ability is high because companies in industries with those charac -
teristics generally have high margins and cash flows that can support 
significant debt.
C We don’t have enough information to answer the question.
C is correct. Consumer products companies are considered non-  cyclical, whereas 
hotel and chemical companies are more cyclical and thus more vulnerable to 
economic downturns.
B is correct. Because such monopolies’ financial returns are generally dictated 
by the regulators, they generate consistent cash flows and are, therefore, able 
to support high debt levels.

Traditional Credit Analysis: Corporate Debt Securities 615
A is correct. Companies in industries with those characteristics typically have 
low margins and limited cash flow and thus cannot support high debt levels.
Ratios and ratio analysis.  To provide context to the analysis and understanding of a 
company’s fundamentals—based on the industry in which it operates, its competitive 
position, its strategy and execution—a number of financial measures derived from the 
company’s principal financial statements are examined. Credit analysts calculate a num -
ber of ratios to assess the financial health of a company, identify trends over time, and 
compare companies across an industry to get a sense of relative creditworthiness. Note 
that typical values of these ratios vary widely from one industry to another because of 
different industry characteristics previously identified: competitive structure, economic 
cyclicality, regulation, and so on.

We will categorize the key credit analysis measures into three different groups:
■■Profitability and cash flow
■■Leverage
■■Coverage
Profitability and cash flow measures.  It is from profitability and cash flow generation 
that companies can service their debt. Credit analysts typically look at operating profit 
margins and operating income to get a sense of a company’s underlying profitability 
and see how it varies over time. Operating income is defined as operating revenues 
minus operating expenses and is commonly referred to as “earnings before interest 
and taxes” (EBIT). Credit analysts focus on EBIT because it is useful to determine a 
company’s performance prior to costs arising from its capital structure (i.e., how much 
debt it carries versus equity). And “before taxes” is used because interest expense is 
paid before income taxes are calculated.
There are several measures of cash flow used in credit analysis; some are more

conservative than others because they make certain adjustments for cash that gets used 
in managing and maintaining the business or in making payments to shareholders. The 
cash flow measures and leverage and coverage ratios discussed below are non-  IFRS 
in the sense that they do not have official IFRS definitions; the concepts, names, and 
definitions given should be viewed as one usage among several possible, in most cases. 
■■Earnings before interest, taxes, depreciation, and amortization (EBITDA).  
EBITDA is a commonly used measure of cash flow that takes operating income 
and adds back depreciation and amortization expense because those are non-  
cash items. This is a somewhat crude measure of cash flow because it excludes 
certain cash-  related expenses of running a business, such as capital expendi -
tures and changes in (non-  cash) working capital. Thus, despite its popularity as 
a cash flow measure, analysts look at other measures in addition to EBITDA.

■■Funds from operations (FFO).  Standard & Poor’s defines funds from opera -
tions as net income from continuing operations plus depreciation, amortization, 
deferred income taxes, and other non-  cash items.24
24 The funds from operations differs only slightly from the better known cash flow from operations in 
that it excludes working capital changes. The idea behind using FFO in credit analysis is to take out the 
near-  term swings and seasonality in working capital that can potentially distort the amount of operating 
cash flow a business is generating. Over time, the working capital swings are expected to even out. Analysts 
tend to look at both FFO and cash flow from operations, particularly for businesses with large working 
capital swings (e.g., very cyclical manufacturing companies).

Reading 55 ■ Fundamentals of Credit Analysis 616
■■Free cash flow before dividends (FCF before dividends).25 This measures 
excess cash flow generated by the company (excluding non-  recurring items) 
before payments to shareholders or that could be used to pay down debt or pay 
dividends. It can be calculated as net income (excluding non-  recurring items) 
plus depreciation and amortization minus increase (plus decrease) in non-  cash 
working capital minus capital expenditures. This is, depending upon the treat -
ment of dividends and interest in the cash flow statement, approximated by the 
cash flow from operating activities minus capital expenditures. Companies that 
have negative free cash flow before payments to shareholders will be consuming 
cash they have or will need to rely on additional financing—from banks, bond 
investors, or equity investors. This obviously represents higher credit risk.
■■Free cash flow after dividends (FCF after dividends).  This measure just takes

free cash flow before dividends and subtracts dividend payments. If this number 
is positive, it represents cash that could be used to pay down debt or build up 
cash on the balance sheet. Either action may be viewed as deleveraging, which 
is favorable from a credit risk standpoint. Some credit analysts will calculate net 
debt by subtracting balance sheet cash from total debt, although they shouldn’t 
assume the cash will be used to pay down debt. Actual debt paid down from 
free cash flow is a better indicator of deleveraging. Some analysts will also 
deduct stock buybacks to get the “truest” measure of free cash flow that can be 
used to de-  lever on either a gross or net debt basis; however, others view stock 
buybacks (share repurchases) as more discretionary and as having less certain 
timing than dividends, and thus treat those two types of shareholder payments 
differently when calculating free cash flow.

Leverage ratios.  There are a few measures of leverage used by credit analysts. The 
most common are the debt/capital, debt/EBITDA, and measures of funds or cash 
flows/debt ratios. Note that many analysts adjust a company’s reported debt levels for 
debt-  like liabilities, such as underfunded pensions and other retiree benefits, as well as 
operating leases. When adjusting for leases, analysts will typically add back the imputed 
interest or rent expense to various cash flow measures.
■■Debt/capital . Capital is calculated as total debt plus shareholders equity. This 
ratio shows the percent of a company’s capital base that is financed with debt. 
A lower percentage of debt indicates lower credit risk. This traditional ratio 
is generally used for investment-  grade corporate issuers. Where goodwill or 
other intangible assets are significant (and subject to obsolescence, depletion,

or impairment), it is often informative to also compute the debt to capital ratio 
after assuming a write-  down of the after-  tax value of such assets.
■■Debt/EBITDA.  This ratio is a common leverage measure. Analysts use it on a 
“snapshot” basis, as well as to look at trends over time and at projections and to 
compare companies in a given industry. Rating agencies often use it as a trigger 
for rating actions, and banks reference it in loan covenants. A higher ratio indi -
cates more leverage and thus higher credit risk. Note that this ratio can be very 
volatile for companies with high cash flow variability, such as those in cyclical 
industries and with high operating leverage (fixed costs).
25 This is similar to free cash flow to the firm (FCFF), referred to in the Level I CFA Program reading 
“Understanding Cash Flow Statements. ”

Traditional Credit Analysis: Corporate Debt Securities 617
■■FFO/debt.  Credit rating agencies often use this leverage ratio. They publish key 
median and average ratios, such as this one, by rating category so analysts can 
get a sense of why an issuer is assigned a certain credit rating, as well as where 
that rating may migrate based on changes to such key ratios as this one. A 
higher ratio indicates greater ability to pay debt by funds from operations.
■■FCF after dividends/debt . A higher ratio indicates that a greater amount of 
debt can be paid off from free cash flow after dividend payments.
Coverage ratios.  Coverage ratios measure an issuer’s ability to meet—to “cover”—its 
interest payments. The two most common are the EBITDA/interest expense and EBIT/
interest expense ratios.
■■EBITDA/interest expense.  This measurement of interest coverage is a bit more 
liberal than the one that uses EBIT because it does not subtract out the impact

of (non-  cash) depreciation and amortization expense. A higher ratio indicates 
higher credit quality.
■■EBIT/interest expense.  Because EBIT does not include depreciation and 
amortization, it is considered a more conservative measure of interest coverage. 
This ratio is now used less frequently than EBITDA/interest expense.
Exhibit 9 is an example of key average credit ratios by rating category for industrial 
companies over a three-  year period, as published by Standard & Poor’s.
Exhibit 9   Industrial Comparative Ratio Analysis 
Credit 
RatingEBITDA 
Margin  
(%)Return on  
 Capital  
(%)EBIT 
Interest 
Coverage  
(x)EBITDA 
Interest 
Coverage  
(x)FFO/Debt  
(%)Free Operations  
Cash Flow/Debt  
(%)Debt/  
EBITDA  
(x)Debt/Debt  
plus Equity  
(%)
AAA
US 29.6 36.8 60.2 68.0 251.1 197.0 0.4 15.7
EMEA NA NA NA NA NA NA NA NA
AA
US 24.6 24.5 16.8 20.5 69.9 52.3 1.2 36.0
EMEA 25.2 21.7 14.4 17.6 163.9 82.5 0.9 23.7
A
US 24.2 21.0 22.0 29.0 96.7 65.9 1.5 36.0
EMEA 21.5 17.1 9.0 12.3 92.8 60.1 1.6 34.5
BBB

BBB
US 21.8 16.1 8.8 12.2 54.0 32.8 2.7 46.3
EMEA 19.7 13.1 5.3 7.9 52.1 23.7 2.6 44.9
BB
US 23.4 11.8 4.1 6.2 35.7 13.6 3.3 54.9
EMEA 20.3 11.0 5.3 7.2 31.8 9.7 3.3 51.0
B
US 19.4 8.0 1.6 2.9 17.5 5.1 6.6 84.0
EMEA 20.5 6.8 1.7 3.4 19.1 2.2 7.0 78.4
Notes : Data are as of 24 August 2011. EMEA is Europe, Middle East, and Africa.

Reading 55 ■ Fundamentals of Credit Analysis 618
Comments on issuer liquidity.  An issuer’s access to liquidity is also an important 
consideration in credit analysis. Companies with high liquidity represent lower credit 
risk than those with weak liquidity, other factors being equal. The financial crisis of 
2008–2009 showed that access to liquidity via the debt and equity markets should not 
be taken for granted, particularly for companies that do not have strong balance sheets 
or steady operating cash flow.
When assessing an issuer’s liquidity, credit analysts tend to look at the following:
■■Cash on the balance sheet.  Cash holdings provide the greatest assurance of 
having sufficient liquidity to make promised payments.
■■Net working capital.  The big US automakers used to have enormous nega -
tive working capital, despite having high levels of cash on the balance sheet. 
This proved disastrous when the financial crisis hit in 2008 and the economy

contracted sharply. Auto sales—and thus revenues—fell, the auto companies 
cut production, and working capital consumed billions of dollars in cash as 
accounts payable came due when the companies most needed liquidity.
■■Operating cash flow.  Analysts will project this figure out a few years and con -
sider the risk that it may be lower than expected.
■■Committed bank lines.  Committed but untapped lines of credit provide con -
tingent liquidity in the event that the company is unable to tap other, potentially 
cheaper, financing in the public debt markets.
■■Debt coming due and committed capital expenditures in the next one to 
two years.  Analysts will compare the sources of liquidity with the amount of 
debt coming due as well as with committed capital expenditures to ensure that 
companies can repay their debt and still invest in the business if the capital 
markets are somehow not available.
As will be discussed in more detail in the section on special considerations for

high-  yield credits, issuer liquidity is a bigger consideration for high-  yield companies 
than for investment grade companies.
EXAMPLE 6   
Watson Pharmaceuticals, Inc. (Watson) is a US-  based specialty health care com -
pany. As a credit analyst, you have been asked to assess its creditworthiness—on 
its own, compared to a competitor in its overall industry, and compared with a 
similarly rated company in a different industry. Using the financial statements 
provided in Exhibits 10 through 12 for the three years ending 31 December 2008, 
2009, and 2010, address the following:
1 Calculate Watson’s operating profit margin, EBITDA, and free cash flow 
after dividends. (Note: The company did not pay dividends in 2008–2010.) 
Comment on what these measures indicate about Watson’s profitability 
and cash flow.
2 Determine Watson’s leverage ratios: debt/EBITDA, debt/capital, free cash 
flow after dividends/debt. Comment on what these leverage ratios indicate 
about Watson’s creditworthiness.

3 Calculate Watson’s interest coverage using both EBIT and EBITDA. 
Comment on what these coverage ratios indicate about Watson’s 
4 Using the credit ratios provided in Exhibit 11 on Johnson & Johnson, 
compare the creditworthiness of Watson relative to Johnson & Johnson.

Traditional Credit Analysis: Corporate Debt Securities 619
5 Compare the Exhibit 12 credit ratios of Luxembourg-  based ArcelorMittal, 
one of the world’s largest global steelmakers, with those of Watson. 
Comment on the volatility of the credit ratios of the two companies. 
Which company looks to be more cyclical? What industry factors might 
explain some of the differences? In comparing the creditworthiness of 
these two companies, what other factors might be considered to offset 
greater volatility of credit ratios?
Exhibit 10A    Watson Pharmaceuticals’ Financial Statements
Consolidated Statements of Operations Y ears Ended December 31
(dollars in millions except per share 
amounts) 2008 2009 2010
Net revenues 2,535.5 2,793.0 3,566.9
 
Operating expenses:  
Cost of sales (excludes amortization) 1,502.8 1,596.8 1,998.5
Research and development 170.1 197.3 296.1
Selling and marketing 232.9 263.1 320.0
General and administrative 190.5 257.1 436.1
Amortization 80.7 92.6 180.0

Loss on asset sales and impairments 0.3 2.2 30.8
Total operating expenses 2,177.3 2,409.1 3,261.5
 
Operating income 358.2 383.9 305.4
Other (expense) income:  
Interest income 9.0 5.0 1.6
Interest expense (28.2) (34.2) (84.1)
Other income 19.3 7.9 27.7
Total other (expense) income, net 0.1 (21.3) (54.8)
 
Income before income taxes and noncon -
trolling interest358.3 362.6 250.6
 
Provision for income taxes 119.9 140.6 67.3
 
Net income 238.4 222.0 183.3
Loss attributable to noncontrolling interest — — 1.1
 
Net income attributable to common 
shareholders238.4 222.0 184.4
Source:  Based on data from Watson Pharmaceuticals’ Company Annual Report (2010).

Reading 55 ■ Fundamentals of Credit Analysis 620
Exhibit 10B   Watson Pharmaceuticals’ Financial Statements
Consolidated Balance Sheets Y ears Ended December 31
(dollars in millions) 2008 2009 2010
ASSETS
Cash and cash equivalents 507.6 201.4 282.8
Marketable securities 13.2 13.6 11.1
Accounts receivable 305.0 517.4 560.9
Inventories, net 473.1 692.3 631.0
Prepaid expenses and other current assets 48.5 213.9 134.2
Deferred tax assets 111.0 130.9 179.4
Total current assets 1,458.4 1,769.5 1,799.4
 
Property and equipment, net 658.5 694.2 642.3
Investments and other assets 80.6 114.5 84.5
Deferred tax assets 52.3 110.8 141.0
Product rights and other intangibles, net 560.0 1,713.5 1,632.0
Goodwill 868.1 1,501.0 1,528.1
Total assets 3,677.9 5,903.5 5,827.3
 
LIABILITIES AND EQUITY  
Current liabilities:  
Accounts payable and accrued expenses 381.3 614.3 741.1
Income taxes payable 15.5 78.4 39.9
Short-  term debt and current portion of 
long-  term debt53.2 307.6 —

Deferred tax liabilities 15.9 31.3 20.8
Deferred revenue 16.1 16.3 18.9
Total current liabilities 482.0 1,047.9 820.7
 
Long-  term debt 824.7 1,150.2 1,016.1
Deferred revenue 30.1 31.9 18.2
Other long-  term liabilities 4.9 118.7 183.1
Other taxes payable 53.3 76.0 65.1
Deferred tax liabilities 174.3 455.7 441.5
Total liabilities 1,569.3 2,880.4 2,544.7
 
Equity:  
Preferred stock — — —
Common stock 0.4 0.4 0.4
Additional paid-  in capital 995.9 1,686.9 1,771.8
Retained earnings 1,418.1 1,640.1 1,824.5
Accumulated other comprehensive (loss) 
income(3.2) 1.9 (2.5)

Traditional Credit Analysis: Corporate Debt Securities 621
Treasury stock, at cost (9.7 and 9.6 shares 
held, respectively)(302.6) (306.2) (312.5)
Total stockholders' equity 2,108.6 3,023.1 3,281.7
Noncontrolling interest — — 0.9
Total equity 2,108.6 3,023.1 3,282.6
 
Total liabilities and equity 3,677.9 5,903.5 5,827.3
Exhibit 10C   Watson Pharmaceuticals’ Financial Statements
Consolidated Statements of Cash Flow Y ears Ended December 31
Reconciliation to net cash provided by operat -
ing activities: 
Depreciation 90.0 96.4 101.9
Provision for inventory reserve 45.7 51.0 50.0
Share-  based compensation 18.5 19.1 23.5
Deferred income tax (benefit) provision 3.5 (19.0) (118.3)

(Gain) loss on sale of securities (9.6) 1.1 (27.3)
Loss on asset sales and impairment 0.3 2.6 29.8
Increase in allowance for doubtful accounts 1.2 3.4 9.5
Accretion of preferred stock and contingent 
payment consideration— 2.2 38.4
Other, net (13.9) (7.6) 11.3
Changes in working capital (38.2) (87.0) 88.9
Net cash provided by operating activities 416.6 376.8 571.0
 
Cash flows from investing activities:  
Additions to property and equipment (63.5) (55.4) (56.6)
Additions to product rights and other 
intangibles(37.0) (16.5) (10.9)
Additions to marketable securities (8.2) (8.0) (5.5)
Additions to long-  term investments — — (43.7)
Proceeds from sale of property and equipment — 3.0 2.7
Proceeds from sale of marketable securities 6.7 9.0 9.5
Proceeds from sale of investments 8.2 — 95.4
(continued)Exhibit 10B   (Continued)

Reading 55 ■ Fundamentals of Credit Analysis 622
Acquisition of business, net of cash acquired — (968.2) (67.5)
Other investing activities, net 0.4 — 2.5
Net cash used in investing activities (93.4) (1,036.1) (74.1)
 
Cash flows from financing activities:  
Proceeds from issuance of long-  term debt — 1,109.9 —
Principal payments on debt (95.6) (786.6) (459.7)
Proceeds from borrowings on short-  term debt 67.9 — —
Proceeds from stock plans 8.4 33.4 54.7
Repurchase of common stock (0.9) (3.6) (6.3)
activities(20.2) 353.1 (411.3)
 
Effect of currency exchange rate changes — — (4.2)
 
Net increase (decrease) in cash and cash 
equivalents303.0 (306.2) 81.4
period204.6 507.6 201.4
Cash and cash equivalents at end of period 507.6 201.4 282.8

Exhibit 11   Johnson & Johnson’s Credit Ratios
2008 2009 2010
Operating profit margin 25.1% 25.2% 26.8%
Debt/EBITDA 0.6x 0.8x 0.9x
EBITDA/Interest 43.3x 40.7x 42.8x
FCF after dividends/Debt 58.1% 61.1% 48.9%
Debt/Capital 21.8% 22.3% 22.9%
Source:  Company Filings, Loomis, Sayles & Company.
Exhibit 12   ArcelorMittal Credit Ratios
Operating profit margin 10.2% –2.4% 4.6%
Debt/EBITDA 2.0x 8.0x 3.3x
EBITDA/Interest 7.4x 1.1x 3.6xExhibit 10C   (Continued)

Traditional Credit Analysis: Corporate Debt Securities 623
FCF after dividends/Debt 20.0% 13.0% –2.1%
Debt/Capital 36.5% 27.5% 28.2%
1 Operating profit margin (%) = Operating income/Revenue
2008: 358.2/2535.5 = 0.141 or 14.1 percent
2009: 383.9/2793.0 = 0.137 or 13.7 percent
2010: 305.4/3566.9 = 0.086 or 8.6 percent
 EBITDA = Operating income + Depreciation + Amortization
2008: 358.2 + 90.0 + 80.7 = 528.9
2009: 383.9 + 96.4 + 92.6 = 572.9
2010: 305.4 + 101.9 + 180.0 = 587.3
 FCF after dividends = Cash flow from operations – Capital expenditures 
– Dividends
2008: 416.6 – (63.5 + 37.0 – 0.0) – 0 = 316.1
2009: 376.8 – (55.4 + 16.5 – 3.0) – 0 = 307.9
2010: 571.0 – (56.6 + 10.9 – 2.7) – 0 = 506.2
 where
Capital expenditures = Additions to property and equipment + 
Additions to product rights and intangibles – Proceeds of sale of prop -
erty and equipment
 Note that “ Additions to product rights and intangibles” is included in cap -

ital expenditures here because such activities are likely to be both material 
and recurring for a health care/drug company. For other types of busi -
nesses, the analyst might elect to exclude this item from capital expendi -
tures when calculating FCF.
 Both EBITDA and FCF after dividends increased from 2008 to 2010. 
Operating profit margin declined over the same time period. Sales 
increased by 40.7% and operating expenses increased by 49.8% from 
2008 to 2010. As a result operating profit margin declined even though 
EBITDA and FCF after dividends increased.
2 Debt/EBITDA
Total debt = Short-  term debt and Current portion of long-  term debt + 
Long-  term debt
2008: Debt: 53.2 + 824.7 = 877.9
Debt/EBITDA: 877.9/528.9 = 1.7x
2009: Debt: 307.6 + 1150.2 = 1457.8
Debt/EBITDA: 1457.8/572.9 = 2.5x
2010: Debt: 0 + 1016.1 = 1016.1
Debt/EBITDA: 1016.1/587.3 = 1.7xExhibit 12   (Continued)

Reading 55 ■ Fundamentals of Credit Analysis 624
 Debt/Capital (%)
Capital = Debt + Equity
2008: Capital: 877.9 + 2108.6 = 2986.5
Debt/Capital: 877.9/2986.5 = 29.4 percent
2009: Capital: 1457.8 + 3023.1 = 4480.9
Debt/Capital: 1457.8/4480.9 = 32.5 percent
2010: Capital: 1016.1 + 3282.6 = 4298.7
Debt/Capital: 1016.1/4298.7 = 23.6 percent
 FCF after dividends/Debt (%)
2008: 316.1/877.9 = 36.0 percent
2009: 307.9/1457.8 = 21.1 percent
2010: 506.2/1016.1 = 49.8 percent
 These leverage ratios indicate volatility in the capital structure. Watson’s 
creditworthiness in 2010 compared to 2009 is likely higher. It has less debt 
in its capital structure, debt is a lower multiple of EBITDA, and the FCF 
after dividends to debt ratio is higher. 
3 EBIT/Interest expense
2008: 358.2/28.2 = 12.7x
2009: 383.9/34.2 = 11.2x
2010: 305.4/84.1 = 3.6x
 EBITDA/Interest expense
2008: 528.9/28.2 = 18.8x
2009: 572.9/34.2 = 16.8x
2010: 587.3/84.1 = 7.0x
 Based on these coverage ratios, Watson’s creditworthiness declined

from 2008 to 2010. EBIT and EBITDA as a multiple of interest expense 
declined each year from 2008 to 2010. 
4 Johnson & Johnson (J&J) has a higher operating profit margin, better 
leverage ratios—lower Debt/EBITDA, higher FCF after dividends/debt 
over the three years (though slightly lower in 2010), lower debt/capital 
(although about equal in 2010), and better interest coverage as measured 
by EBITDA/interest. Collectively, those ratios suggest J&J has higher 
credit quality than Watson. 
Watson Pharmaceuticals’ Credit Ratios 2008 2009 2010
Operating profit margin 14.1% 13.7% 8.6%
Debt/EBITDA 1.7x 2.5x 1.7x
FCF after dividends/Debt 36.0% 21.1% 49.8%
Debt/Capital 29.4% 32.5% 23.6%
EBITDA/Interest 18.8x 16.8x 7.0x
Johnson & Johnson’s Credit Ratios 2008 2009 2010

Traditional Credit Analysis: Corporate Debt Securities 625
5 Watson has a higher and less volatile operating profit margin than 
ArcelorMittal (Arcelor), better leverage ratios (except debt/capital in 
2009), and higher interest coverage. Based on the volatility of its cash flow 
and operating profit margin, Arcelor appears to be a much more cyclical 
credit. Coupled with its higher debt levels, one would expect Arcelor to 
have a lower credit rating. 
 A steelmaker likely has a significant amount of long-  term assets financed 
by debt. It is a highly competitive industry with little ability to distinguish 
products from other competitors. To mitigate the impact of its more vol -
atile credit ratios, Arcelor might maintain high levels of liquidity. Its size 
and global diversity may also be a “plus. ” It may be able to negotiate favor -

able supplier and customer contracts and to keep costs down through 
ArcelorMittal’s Credit Ratios 2008 2009 2010
EBITDA/Interest 7.4x 1.1x 3.6x
5.2.2  Collateral
Collateral, or asset value, analysis is typically emphasized more with lower credit 
quality companies. As discussed earlier, credit analysts focus primarily on probability 
of default, which is mostly about an issuer’s ability to generate sufficient cash flow to 
support its debt payments, as well as its ability to refinance maturing debt. Only when 
the default probability rises to a sufficient level do analysts typically consider asset or

collateral value in the context of loss severity in the event of default.
Analysts do think about the value and quality of a company’s assets; however, these 
are difficult to observe directly. Factors to consider include the nature and amount 
of intangible assets on the balance sheet. Some assets, such as patents, are clearly 
valuable and can be sold if necessary to cover liabilities. Goodwill, on the other hand, 
is not considered a high-  quality asset. In fact, sustained weak financial performance 
most likely implies that a company’s goodwill will be written down, reinforcing its 
poor quality. Another factor to consider is the amount of depreciation an issuer takes 
relative to its capital expenditures: Low capital expenditures relative to depreciation

Reading 55 ■ Fundamentals of Credit Analysis 626
expense could imply that management is insufficiently investing in its business, which 
will lead to lower-  quality assets, potentially reduced future operating cash flow, and 
higher loss severity in the event of default.
A market-  based signal that credit analysts use to impute the quality of a publicly 
traded company’s assets, and its ability to support its debt, is equity market capi -
talization. For instance, a company whose stock trades below book value may have 
lower-  quality assets than is suggested by the amount reported on the balance sheet.
As economies become more service- and knowledge-  based and those types of 
companies issue debt, it’s important to understand that these issuers rely more on 
human and intellectual capital than on “hard assets. ” In generating profits and cash 
flow, these companies are not as asset intensive. One example would be software

companies. Another example would be investment management firms. Human- and 
intellectual- capital-  based companies may generate a lot of cash flow, but their col -
lateral value is questionable, unless there are patents and other types of intellectual 
property and “intangible capital” that may not appear directly on the balance sheet 
but could be valuable in the event of financial distress or default.
Regardless of the nature of the business, the key point of collateral analysis is to 
assess the value of the assets relative to the issuer’s level—and seniority ranking—of 
debt.
5.2.3  Covenants
Covenants are meant to protect creditors while also giving management sufficient 
flexibility to operate its business on behalf of and for the benefit of the shareholders. 
They are integral to credit agreements, whether they are bonds or bank loans, and 
they spell out what the issuer’s management is (1) obligated to do and (2) limited in

doing. The former are called “affirmative covenants, ” whereas the latter are called 
“negative” or “restrictive covenants. ” Obligations would include such duties as making 
interest and principal payments and filing audited financial statements on a timely 
basis. Covenants might also require a company to redeem debt in the event of the 
company being acquired26 or to keep the ratio of debt to EBITDA below some pre -
scribed amount. The limitations might include a cap on the amount of cash that can be 
paid out to shareholders relative to earnings, or perhaps on the amount of additional 
secured debt that can be issued. Covenant violations are a breach of contract and can be 
considered default events unless they are cured in a short time or a waiver is granted.
For corporate bonds, covenants are described in the bond prospectus , the doc -
ument that is part of a new bond issue. The prospectus describes the terms of the

bond issue, as well as supporting financial statements, to help investors perform 
their analyses and make investment decisions as to whether or not to submit orders 
to buy the new bonds. Actually, the trust deed  or bond indenture  is the governing 
legal credit agreement and is typically incorporated by reference in the prospectus.
Covenants are an important but underappreciated part of credit analysis. Strong 
covenants protect bond investors from the possibility of management taking actions 
that would hurt an issuer’s creditworthiness. For example, without appropriate cove -
nants management might pay large dividends, undertake stock buybacks well in excess 
of free cash flow, sell the company in a leveraged buyout,27 or take on a lot of secured 
debt that structurally subordinates unsecured bondholders. All of these actions would 
enrich shareholders at the expense of bondholders. Recall that management works for 
26 This is often referred to as a “change of control” covenant.

27 A leveraged buyout (LBO) is an acquisition of a company by private investors using high levels of debt 
and relatively little equity.

Traditional Credit Analysis: Corporate Debt Securities 627
the shareholders and that bonds are contracts, with management’s only real obligation 
to creditors being to uphold the terms of the contract. The inclusion of covenants in 
the contract is intended to protect bondholders.
The bond-  buying investor base is very large and diverse, particularly for investment-  
grade debt. It includes institutional investors such as insurance companies, investment 
management firms, pension funds, mutual funds, hedge funds, sovereign wealth funds, 
and so on. Although there are some very large institutional investors, the buyer base 
is fragmented and does not—and legally cannot—act as a syndicate. Thus, bondhold -
ers are generally not able to negotiate strong covenants on most new bond issues. 
Covenants on new bond issues tend to be stronger during weak economic or market 
conditions because investors seek more protection during such times. There are a

few organized institutional investor groups focused on strengthening covenants: the 
Credit Roundtable28 in the United States and the European Model Covenant Initiative 
Covenant language is often very technical and written in “legalese, ” so it can be 
helpful to have an in-  house person with a legal background to review and interpret 
the specific covenant terms and wording. One might also use a third-  party service 
specializing in covenant analysis, such as Covenant Review.29
We will go into more detail on specific covenants in the section on special con -
siderations for high-  yield bonds.
5.2.4  Character
The character of a corporate borrower can be difficult to observe. The analysis of 
character as a factor in credit analysis dates to when loans were made to compa -
nies owned by individuals. Most corporate bond issuers are now publicly owned 
by shareholders or privately owned by pools of capital, such as private equity firms.

Management often has little ownership in a corporation, so analysis and assessment 
of character is different than it would be for owner-  managed firms. Credit analysts 
can make judgments about management’s character in the following ways:
■■An assessment of the soundness of management’s strategy.
■■Management’s track record in executing past strategies, particularly if they led 
to bankruptcy or restructuring. A company run by executives whose prior posi -
tions/ventures resulted in significant distress might still be able to borrow in the 
debt markets, but it would likely have to borrow on a secured basis and/or pay a 
higher rate of interest.
■■Use of aggressive accounting policies and/or tax strategies. Examples might 
include using a significant amount of off-  balance-  sheet financing, capitalizing 
versus immediately expensing items, recognizing revenue prematurely, and/or 
frequently changing auditors. These are potential warning flags to other behav -

iors or actions that may adversely impact an issuer’s creditworthiness.
■■Any history of fraud or malfeasance—a major warning flag to credit analysts.
■■Previous poor treatment of bondholders—for example, management actions 
that resulted in major credit rating downgrades. These actions might include a 
debt-  financed acquisition, a large special dividend to shareholders, or a major 
debt-  financed stock buyback program.
28 See www.creditroundtable.org.
29 See www.covenantreview.com.

Reading 55 ■ Fundamentals of Credit Analysis 628
EXAMPLE 7   
The Four Cs
1 Which of the following would not be a bond covenant?
A The issuer must file financial statements with the bond trustee on a 
timely basis.
B The company can buy back as much stock as it likes.
C If the company offers security to any creditors, it must offer security to 
this bond issue.
2 Why should credit analysts be concerned if a company’s stock trades 
below book value?
A It means the company is probably going bankrupt.
B It means the company will probably incur lots of debt to buy back its 
undervalued stock.
C It’s a signal that the company’s asset value on its balance sheet may 
be impaired and have to be written down, suggesting less collateral 
protection for creditors.
3 If management is of questionable character, how can investors incorporate 
this assessment into their credit analysis and investment decisions?
A They can choose not to invest based on the increased credit risk.

B They can insist on getting collateral (security) and/or demand a higher 
return.
C They can choose not to invest or insist on additional security and/or 
higher return.
B is correct. Covenants describe what the borrower is (1) obligated to do or (2) 
limited in doing. It’s the absence of covenants that would permit a company 
to buy back as much stock as it likes. A requirement that the company offer 
security to this bond issue if it offers security to other creditors (answer C) is 
referred to as a “negative pledge. ”
C is correct. Investors can always say no if they are not comfortable with the 
credit risk presented by a bond or issuer. They may also decide to lend to a 
borrower with questionable character only on a secured basis and/or demand 
a higher return for the perceived higher risk.
CREDIT RISK VS. RETURN: YIELDS AND SPREADS
The material in this section applies to all bonds subject to credit risk. For

simplicity, in what follows all such bonds are sometimes referred to as 
“corporate” bonds.6

Credit Risk vs. Return: Yields and Spreads 629
As in other types of investing, taking more risk in credit offers higher potential return, 
but with more volatility and less certainty of earning that return. Using credit ratings 
as a proxy for risk, Exhibit 13 shows the composite yield to maturity30 for bonds of 
all maturities within each rating category in the US and European bond markets 
according to Barclays, one of the largest providers of fixed-  income market indexes.
Exhibit 13   Corporate Yields by Rating Category as of 30 June 2011
Bloomberg Barclays 
IndicesInvestment Grade Non-  Investment Grade
AAA (%) AA (%) A (%) BBB (%) BB (%) B (%) CCC (%) CC (%) D (%)
US 3.09 3.10 3.64 4.35 6.50 7.93 10.27 14.11 22.73
Pan European 3.33 3.58 4.14 4.98 6.90 8.67 17.12 13.81 54.80
Note that the lower the credit quality, the higher the quoted yield. The realized 
yield, or return, will almost always be different because of changes in interest rates

and the credit-  related risks discussed earlier. For example, in the aggregate credit 
losses will “eat up” some of the yield premium offered by lower-  quality bonds versus 
higher-  quality credits. Trailing 12-  month returns by credit rating category, and the 
volatility (standard deviation) of those returns, are shown in Exhibit 14.
30 High-  yield bonds are often quoted on a “yield to call” (YTC) or “yield to worst” (YTW) basis because 
so many of them are callable before maturity, whereas most investment-  grade bonds are non-  callable, or 
at least callable at such punitive premiums that issuers are not likely to exercise that option.

Reading 55 ■ Fundamentals of Credit Analysis 630
Exhibit 14   US Trailing 12-  Month Returns by Rating Category, 31 
December 1996–30 June 2011
Return (%)
120
6080100
2040
0
–20
–40
–60
Aa A Aaa Baa Ba B Caa 
Avg. Return: 6.18% 6.63% 6.52% 7.33% 8.58% 6.93% 8.10%
Max. Return: 16.08% 19.30% 29.39% 36.43% 50.80% 52.10% 97.47%
Min. Return: –4.17% –5.47% –14.98% –15.70% –22.12% –31.47% –44.35%
Avg. Volatility: 4.02% 4.45% 5.18% 5.51% 6.31% 8.11% 12.63%
Source:  Based on data from Barclays and Loomis, Sayles & Company.
As shown in the exhibit, the higher the credit risk, the greater the return potential 
and the higher the volatility of that return. This pattern is consistent with other types 
of investing that involves risk and return (although average returns on single-  B rated 
bonds appear anomalous in this example).
For extremely liquid bonds that are deemed to have virtually no default risk (e.g., 
German government bonds, or Bunds ), the yield is a function of real interest rates

plus an expected inflation rate and a maturity premium. Of course, those factors are 
present in corporate bonds as well. In addition, the yield on corporate bonds will 
include a liquidity premium and a credit spread intended to compensate investors 
for these additional risks as well as for the expected level of credit losses. Thus, the 
yield on a corporate bond can be decomposed as
 Yield on corporate bond = Real risk-  free interest rate + Expected inflation rate 
+ Maturity premium + Liquidity premium + Credit 
spread
Changes in any of these components will alter the yield, price, and return on the bond.
Investors in corporate bonds focus primarily on the yield spread relative to a 
comparable, default-  free bond, which is composed of the liquidity premium and the 
credit spread:
Yield spread = Liquidity premium + Credit spread

Credit Risk vs. Return: Yields and Spreads 631
The market’s willingness to bear risk will affect each of these components. In general, 
however, it is not possible to directly observe the market’s assessment of the compo -
nents separately—analysts can only observe the total yield spread.
Spreads on all corporate bonds can be affected by a number of factors, with lower-  
quality issuers typically experiencing greater spread volatility. These factors, which 
are frequently linked, include the following:
■■Credit cycle.  As the credit cycle improves, credit spreads will narrow. 
Conversely, a deteriorating credit cycle will cause credit spreads to widen. 
Spreads are tightest at or near the top of the credit cycle, when financial mar -
kets believe risk is low, whereas they are widest at or near the bottom of the 
credit cycle, when financial markets believe risk is high.
■■Broader economic conditions.  Not surprisingly, weakening economic con -

ditions will push investors to desire a greater risk premium and drive overall 
credit spreads wider. Conversely, a strengthening economy will cause credit 
spreads to narrow because investors anticipate credit measures will improve 
due to rising corporate cash flow, thus reducing the risk of default.
■■Financial market performance overall, including equities.  In weak financial 
markets, credit spreads will widen, whereas in strong markets, credit spreads 
will narrow. In a steady, low-  volatility environment, credit spreads will typically 
also narrow, as investors tend to “reach for yield. ”
■■Broker–dealers’ willingness to provide sufficient capital for market mak -
ing. Bonds trade primarily over the counter, so investors need broker–dealers 
to commit capital for market-  making purposes. During the financial crisis in 
2008–2009, several large broker–dealer counterparties either failed or were 
taken over by another. This, combined with financial and regulatory stresses

faced by virtually all the other broker–dealers, greatly reduced the total capital 
available for making markets and the willingness to buy/sell credit-  risky bonds. 
Future regulatory reform may well lead to persistent or even permanent reduc -
tions in broker-  provided capital.
■■General market supply and demand.  In periods of heavy new issue supply, 
credit spreads will widen if there is insufficient demand. In periods of high 
demand for bonds, spreads will move tighter.
Each of the first four factors played a role during the financial crisis of 2008–2009, 
causing spreads to widen dramatically, as shown in Exhibit 15, before narrowing sharply 
as governments intervened and markets stabilized. This is shown in two panels—one 
for investment grade, another for high yield—because of the much greater spread 
volatility in high-  yield bonds, particularly CCC rated credits. This spread volatility is 
reflected in the different spread ranges on the y-axes. OAS is option-  adjusted spread,

which incorporates the value of the embedded call option in certain corporate bonds 
that issuers have the right to exercise before maturity.31
31 The details of valuing bonds with embedded options and the calculation of OAS are covered in Level 
II of the CFA curriculum.

Reading 55 ■ Fundamentals of Credit Analysis 632
Exhibit 15   US Investment-  Grade and High-  Yield Corporate Spreads
Aa A Baa Aaa US RecessionOAS (bps)
800
700
600
400
200300
100500
0
97 95 99 01 03 05 07 09 11A. Investment-Grade Corporate Spreads
B Ba Caa US RecessionOAS (bps)
3,000
2,500
2,000
1,000
5001,500
0
97 95 99 01 03 05 07 09 11B. High-Yield Corporate Spreads
Sources:  Based on data from Barclays and Loomis Sayles & Company.
EXAMPLE 8   
Yield Spreads
1 Which bonds are likely to exhibit the greatest spread volatility?
A Bonds from issuers rated AA
B Bonds from issuers rated BB
C Bonds from issuers rated A
2 If investors become increasingly worried about the economy—say, as 
shown by declining stock prices—what is the most likely  impact on credit 
spreads?
A There will be no change to credit spreads. They aren’t affected by 
equity markets.

Credit Risk vs. Return: Yields and Spreads 633
B Narrower spreads will occur. Investors will move out of equities into 
debt securities.
C Wider spreads will occur. Investors are concerned about weaker 
B is correct. Lower-  quality bonds exhibit greater spread volatility than higher-  
quality bonds. All of the factors that affect spreads—the credit cycle, economic 
conditions, financial performance, market-  making capacity, and supply/demand 
conditions—will tend to have a greater impact on the pricing of lower-  quality 
credits.
C is correct. Investors will require higher yields as compensation for the greater 
credit losses that are likely to occur in a weakening economy.
We have discussed how yield spreads on credit-  risky debt obligations, such as 
corporate bonds, can fluctuate based on a number of factors, including changes in 
the market’s view of issuer-  specific or idiosyncratic risk. The next question to ask is

how these spread changes affect the price of and return on these bonds.
Although bond investors do concern themselves with default risks, recall that the 
probability of default for higher-  quality bonds is typically very low: For investment-  
grade bonds, annual defaults are nearly always well below 1 percent (recall Exhibit 6). 
On the other hand, default rates can be very high for lower-  quality issuers, although 
they can vary widely depending upon the credit cycle, among other things. What most 
investors in investment-  grade debt focus on more than default risk is spread risk—that 
is, the effect on prices and returns from changes in spreads.
The price impact from spread changes is driven by two main factors: the modified 
duration (price sensitivity with respect to changes in interest rates) of the bond and 
the magnitude of the spread change. The effect on return to the bondholder depends 
on the holding period used for calculating the return.

The simplest example is that of a small, instantaneous change in the yield spread. 
In this case, the price impact, i.e., the percentage change in price (including accrued 
interest), can be approximated by
Price impact ≈ – MDur × ∆Spread
where MDur is the modified duration. The negative sign in this equation reflects the 
fact that because bond prices and yields move in opposite directions, narrower spreads 
have a positive impact on bond prices and thus returns, whereas wider spreads have a 
negative impact on bond returns. Note that if the spread change is expressed in basis 
points, then the price impact will also be in basis points, whereas if the spread change 
is expressed as a decimal, the price impact will also be expressed as a decimal. Either 
way, the result is easily re-  expressed as a percent.
For larger spread changes (and thus larger yield changes), the impact of convexity 
needs to be incorporated into the approximation:
Price impact ≈ –(MDur × ∆Spread) + ½Cvx × (∆Spread)2

In this case, one must be careful to ensure that convexity (denoted by Cvx) is appropri -
ately scaled to be consistent with the way the spread change is expressed. In general, 
for bonds without embedded options, one can scale convexity so that it has the same 
order of magnitude as the duration squared and then express the spread change as a

Reading 55 ■ Fundamentals of Credit Analysis 634
decimal. For example, for a bond with duration of 5.0 and reported convexity of 0.235, 
one would re-  scale convexity to 23.5 before applying the formula. For a 1 percent (i.e., 
100 bps) increase in spread, the result would be
Price impact = (–5.0 × 0.01) + ½ × 23.5 × (0.01)2 = –0.048825 or 
–4.8825 percent
The price impact of instantaneous spread changes is illustrated in Exhibit 16 using 
two bonds from British Telecom, the UK telecommunications company. The bonds, 
denominated in British pounds, are priced to provide a certain spread over British 
government bonds (gilts) of a similar maturity. From the starting spread, in increments 
of 25 bps and for both wider and narrower spreads, the new price and actual return 
for each spread change are calculated. In addition, the exhibit shows the approximate 
returns with and without the convexity term. As can be seen, the approximation using

only duration is reasonably accurate for small spread changes but for larger changes, 
the convexity term generally provides a meaningful improvement.
Exhibit 16   Impact of Duration on Price for a Given Change in Spread
Issuer: British Telecom, 8.625%, maturing on 26 March 2020
Price: £129.475 Modified Duration: 6.084 Spread to Gilt Curve: 248 b.p.
Accrued interest: 6.3 Convexity: 47.4 YTM: 4.31
Scenarios
Spread ∆ (b.p.) –100 –75 –50 –25 0 25 50 75 100
Spread (b.p.) 148 173 198 223 248 273 298 323 348
New Price (£) 137.90 135.73 133.60 131.52 129.48 127.47 125.51 123.59 121.71
New Price + Accrued 
(£)144.20 142.03 139.90 137.82 135.78 133.77 131.81 129.89 128.01
Price ∆ (£) 8.43 6.26 4.13 2.05 0.00 –2.01 –3.96 –5.88 –7.77
Return (%)                  
  Actual 6.21% 4.61% 3.04% 1.51% 0.00% –1.48% –2.92% –4.33% –5.72%
  Approx: Dur only 6.08% 4.56% 3.04% 1.52% 0.00% –1.52% –3.04% –4.56% –6.08%
  Approx: Dur & Cvx 6.32% 4.70% 3.10% 1.54% 0.00% –1.51% –2.98% –4.43% –5.85%

Issuer: British Telecom, 6.375%, maturing on 23 June 2037
Price: £110.093 Modified Duration: 13.064 Spread to Gilt Curve: 247 b.p.
Accrued interest: 3.117 Convexity: 253.5 YTM: 5.62
Scenarios
Spread (b.p.) 147 172 197 222 247 272 297 322 347
New Price (£) 125.99 121.72 117.65 113.78 110.09 106.58 103.23 100.04 97.00
(£)129.11 124.84 120.77 116.90 113.21 109.70 106.35 103.16 100.11
Price ∆ (£) 15.90 11.63 7.56 3.69 0.00 –3.51 –6.86 –10.05 –13.10
Return (%)                  
  Actual 14.04% 10.27% 6.68% 3.26% 0.00% –3.10% –6.06% –8.88% –11.57%

Credit Risk vs. Return: Yields and Spreads 635
Scenarios
  Approx: Dur only 13.06% 9.80% 6.53% 3.27% 0.00% –3.27% –6.53% –9.80% –13.06%
  Approx: Dur & Cvx 14.33% 10.51% 6.85% 3.35% 0.00% –3.19% –6.22% –9.09% –11.80%
Source:  Based on data from Bloomberg Finance, L.P . (settle date is 19 December 2011).
Note that the price change for a given spread change is higher for the longer-  
duration bond—in this case, the 2037 maturity British Telecom bond—than for the 
shorter-  duration bond. Longer-  duration corporate bonds are referred to as having 
“higher spread sensitivity”; that is, their prices, and thus returns, are more volatile 
with respect to changes in spread. It is essentially the same concept as duration for 
any bond: The longer the duration of a bond, the greater the price volatility for a given 
change in interest rates/yields.
In addition, investors want to be compensated for the fact that the further one is

from a bond’s maturity (i.e., the longer the bond), the greater the uncertainty about 
an issuer’s future creditworthiness. Based on credit analysis, an investor might be 
confident that an issuer’s risk of default is relatively low in the near term; however, 
looking many years into the future, the investor’s uncertainty grows because of factors 
that are increasingly difficult, if not impossible, to forecast (e.g., poor management 
strategy or execution, technological obsolescence, natural or man-  made disasters, 
corporate leveraging events). This increase in credit risk over time can be seen in 
Exhibit 17. Note that in this Standard & Poor’s study,32 one-  year default rates for the 
2010 issuance pool are 0 percent for all rating categories of B+ or higher. The three-  
year default rates for bonds issued in 2008 are materially higher, and the observed 
defaults include bonds originally rated up to BBB– (i.e., low investment grade). The

10- year default rates for bonds issued in 2001 are appreciably higher than the 3-  year 
default rates, and the defaults include bonds initially rated as high as A+ (i.e., solid 
investment grade). In addition to the risk of default rising over time, the data also 
show quite conclusively that the lower the credit rating, the higher the risk of default. 
Finally, note the very high risk of default for bonds rated CCC or lower over all time 
horizons. This is consistent with Exhibit 7 earlier in the reading, which showed sig -
nificant three-  year ratings variability (“migration”), with much of the migration to 
lower credit ratings (i.e., higher risk of default).
Exhibit 17   Default Rate by Rating Category (%) (Non-  
financials)
Credit 
Rating1 Y ear  
(2010 pool)3 Y ear  
(2008 pool)10 Y ear  
(2001 pool)
   AAA 0.00 0.00 0.00
   AA+ 0.00 0.00 0.00
   AA 0.00 0.00 0.00
   AA– 0.00 0.00 0.00
   A+ 0.00 0.00 1.76
(continued)Exhibit 16   (Continued)

32 From S&P , “2010 Annual Global Corporate Default Study and Ratings Transitions, ” Standard & Poor’s 
report (30 March 2011). Detailed descriptions of the underlying methodology are available in Appendix 
I of the report.

Reading 55 ■ Fundamentals of Credit Analysis 636
Credit 
   A 0.00 0.00 1.70
   A– 0.00 0.00 0.87
   BBB+ 0.00 0.00 5.03
   BBB 0.00 0.00 4.55
   BBB– 0.00 1.04 12.80
   BB+ 0.00 2.12 15.38
   BB 0.00 3.53 19.91
   BB– 0.00 6.14 26.84
   B+ 0.00 12.73 33.69
   B 0.76 22.08 39.02
   B– 2.07 25.23 55.83
   CCC/C 21.99 56.63 65.31
Source:  Based on data from S&P , “2010 Annual Global Corporate Default 
Study and Ratings Transitions, ” Standard & Poor’s report (30 March 2011).
It is also worth noting that bid–ask spreads (in yield terms) translate into higher 
transaction costs for longer-  duration bonds; investors want to be compensated for that 
as well. For these reasons, spread curves (often called credit curves ), like yield curves, 
are typically upward sloping. That is, longer-  maturity bonds of a given issuer typically 
trade at wider spreads than shorter-  maturity bonds to their respective comparable-

maturity government bonds.33 Exhibit 18, using the US telecommunications company 
AT&T as an example, shows the upward-  sloping credit curve by plotting the yields 
of its bonds versus their maturity. (As a large and frequent issuer, AT&T has many 
bonds outstanding across the yield curve.)Exhibit 17   (Continued)
33 There are some exceptions to this—bonds that trade at a high premium price over par due to having 
coupons that are well above the bond’s yield to maturity and bonds that trade at distressed levels due to 
credit concerns. Many investors are averse to paying high premium prices for bonds that have credit risk 
because of the greater potential price decline—towards a recovery price in the event of default—from a 
credit-  adverse event. Thus, high-  coupon intermediate-  maturity bonds can trade at similar or wider spreads 
to longer-  maturity bonds. For distressed credits, the high risk of default causes all bonds for a given issuer

to migrate toward the same expected recovery price. In this case, the shorter-  maturity and shorter-  duration 
bonds will have a higher quoted yield to maturity, and wider spread, than the longer-  maturity and longer-  
duration bonds. This follows from the price impact formulas. The shorter the duration, the higher the yield 
(including spread) must go to bring the price down to a given expected recovery price.

Credit Risk vs. Return: Yields and Spreads 637
Exhibit 18   AT&T Credit Curve vs. US Treasury Curve
Yield to Maturity (%)
6
5
4
3
2
1
0
03 0 5 10 15 20 25
Years to MaturityAT&T
US Treasury
Source:  Based on data from Bloomberg Finance, L.P ., as of 5 October 2011.
EXAMPLE 9   
Price Impact
Calculate the price impact on a 10-  year corporate bond with a 4.75  percent 
coupon priced at 100, with an instantaneous 50 bps widening in spread due 
to the issuer’s announcement that it was adding substantial debt to finance an 
acquisition, resulting in a two-  notch downgrade by the rating agencies. The 
bond has a modified duration of 7.9 and its convexity is 74.9.
Solution:
The impact from the 50 bps spread widening is:
Price impact ≈ –(MDur × ∆Spread) + ½ Cvx × (∆Spread)2
= –(0.0050 × 7.9) + (0.5 × 74.9) × (0.0050)2
= –0.0386, or –3.86 percent
Because yields and bond prices move in opposite directions, the wider spread 
caused the bond price to fall. Using a bond-  pricing calculator, the exact return

is –3.85 percent, so this approximation was very accurate.
In summary, spread changes can have a significant impact on the performance of 
credit-  risky bonds over a given holding period, and the higher the modified duration 
of the bond(s), the greater the price impact from changes in spread. Wider spreads 
hurt bond performance, whereas narrower spreads help bond performance. For bond 
investors who actively manage their portfolios (i.e., don’t just buy bonds and hold 
them to maturity), forecasting spread changes and expected credit losses on both 
individual bonds and their broader portfolios is an important strategy for enhancing 
investment performance.

Reading 55 ■ Fundamentals of Credit Analysis 638
SPECIAL CONSIDERATIONS OF HIGH-  YIELD, 
SOVEREIGN, AND NON-  SOVEREIGN CREDIT ANALYSIS
Thus far, we have focused primarily on basic principles of credit analysis and investing 
with emphasis on higher-  quality, investment-  grade corporate bonds. Although many 
of these principles are applicable to other credit-  risky segments of the bond market, 
there are some differences in credit analysis that need to be considered. This section 
focuses on special considerations in evaluating the credit of debt issuers from the 
following three market segments: high-  yield corporate bonds, sovereign bonds, and 
non-  sovereign government bonds.
7.1 High Yield
Recall that high-  yield, or non-  investment-  grade, corporate bonds are those rated below 
Baa3/BBB– by the major rating agencies. These bonds are sometimes referred to as 
“junk bonds” because of the higher risk inherent in their weak balance sheets and/or 
poor or less-  proven business prospects.

There are many reasons companies are rated below investment grade, including
■■Highly leveraged capital structure
■■Weak or limited operating history
■■Limited or negative free cash flow
■■Highly cyclical business
■■Poor management
■■Risky financial policies
■■Lack of scale and/or competitive advantages
■■Large off-  balance-  sheet liabilities
■■Declining industry (e.g., newspaper publishing)
Companies with weak balance sheets and/or business profiles have lower margin 
for error and greater risk of default relative to higher-  quality investment-  grade names. 
And the higher risk of default means more attention must be paid to recovery analysis 
(or loss severity, in the event of default). Consequently, high-  yield analysis typically 
is more in-  depth than investment-  grade analysis and thus has special considerations. 
This includes the following:
■■Greater focus on issuer liquidity and cash flow
■■Detailed financial projections

■■Detailed understanding and analysis of the debt structure
■■Understanding of an issuer’s corporate structure
■■Equity-  like approach to high yield analysis
Liquidity.  Liquidity—that is, having cash and/or the ability to generate or raise cash—is 
important to all issuers. It is absolutely critical for high-  yield companies. Investment-  
grade companies typically have substantial cash on their balance sheets, generate a 
lot of cash from operations relative to their debt (or else they wouldn’t be investment 
grade!), and/or are presumed to have alternate sources of liquidity, such as bank lines 7

Special Considerations of High-  Yield, Sovereign, and Non-  Sovereign Credit Analysis 639
and commercial paper.34 For these reasons, investment-  grade companies can more 
easily roll over (refinance) maturing debt. On the other hand, high-  yield companies 
may not have those options available. For example, there is no high-  yield commercial 
paper market, and bank credit facilities often carry tighter restrictions for high-  yield 
companies. Both bad company-  specific news and difficult financial market conditions 
can lead to high-  yield companies being unable to access the debt markets. And although 
the vast majority of investment-  grade corporate debt issuers have publicly traded equity 
and can thus use that equity as a financing option, many high-  yield companies are 
privately held and thus don’t have access to public equity markets.
Thus, issuer liquidity is a key focus in high-  yield analysis. Sources of liquidity, from 
strongest to weakest, are the following:

1 Cash on the balance sheet
2 Working capital
3 Operating cash flow
4 Bank credit facilities
5 Equity issuance
6 Asset sales
Cash on the balance sheet is easy to see and self-  evident as a source for repaying 
debt.35 As mentioned earlier in this reading, working capital can be a large source 
or use of liquidity, depending on its amount, its use in a company’s cash-  conversion 
cycle, and its role in a company’s operations. Operating cash flow is a ready source 
of liquidity as sales turn to receivables, which turn to cash over a fairly short time 
period. Bank lines, or credit facilities, can be an important source of liquidity, though 
there may be some covenants relating to the use of the bank lines which are crucial to 
know and will be covered a little later. Equity issuance may not be a reliable source of 
liquidity because an issuer is private or because of poor market conditions if a company

does have publicly traded equity. Asset sales are the least reliable source of liquidity 
because both the potential value and the actual time of closing can be highly uncertain.
The amount of these liquidity sources should be compared with the amount 
and timing of upcoming debt maturities. A large amount of debt coming due in the 
next 6–12 months alongside low sources of liquidity will be a warning flag for bond 
investors and could push an issuer into default because investors may choose not to 
buy new bonds intended to pay off the existing debt. Insufficient liquidity—that is, 
running out of cash or no longer having access to external financing to refinance or 
pay off existing debt—is the principal reason issuers default. Although liquidity is 
important for industrial companies, it is an absolute necessity for financial firms, as 
seen in the case of Lehman Brothers and other troubled firms during the financial

crisis of 2008. Financial institutions are highly levered and often highly dependent on 
funding longer-  term assets with short-  term term liabilities.
Financial Projections.  Because high-  yield companies have less room for error, it’s 
important to forecast, or project, future earnings and cash flow out several years, per -
haps including several scenarios, to assess whether the issuer’s credit profile is stable, 
improving, or declining and thus whether it needs other sources of liquidity or is at 
34 Commercial paper (CP) is short-  term funding—fewer than 270 days—used by many large, investment-  
grade corporations on a daily basis. In practice, issuance of CP requires solid, long-  term, investment-  grade 
ratings, mostly A rated or better, with a much smaller market for BBB rated companies.
35 Note that some cash may be “trapped” in other countries for certain tax, business, or regulatory reasons,

and may not be easily accessible, or repatriation—bringing the money back to the home country—could 
trigger cash tax payments.

Reading 55 ■ Fundamentals of Credit Analysis 640
risk of default. Ongoing capital expenditures and working capital changes should be 
incorporated as well. Special emphasis should be given to realistic “stress” scenarios 
that could expose a borrower’s vulnerabilities.
Debt Structure.  High-  yield companies tend to have many layers of debt in their 
capital structures, with varying levels of seniority and, therefore, different potential 
recovery rates in the event of default. (Recall the historical table of default recovery 
rates based on seniority in Exhibit 2.) A high-  yield issuer will often have at least some 
of the following types of obligations in its debt structure:
■■(Secured) Bank debt36
■■Second lien debt
■■Senior unsecured debt
■■Subordinated debt, which may include convertible bonds37
■■Preferred stock38
The lower the ranking in the debt structure, the lower the credit rating and the 
lower the expected recovery in the event of default. In exchange for these associated

higher risks, investors will normally demand higher yields.
As discussed in Section 5, a standard leverage calculation used by credit analysts 
is debt/EBITDA and is quoted as a multiple (e.g., “5.2x levered”). For an issuer with 
several layers of debt with different expected recovery rates, high-  yield analysts should 
calculate leverage at each level of the debt structure. Example 10 shows calculations of 
gross leverage, as measured by Debt/EBITDA, at each level of the debt structure and 
net leverage for the entire debt structure. Gross leverage calculations do not adjust 
debt for cash on hand. Net leverage adjusts debt by subtracting cash from total debt. 
EXAMPLE 10   
Debt Structure and Leverage
Freescale Semiconductor specializes in semiconductors that are used in autos, 
communication equipment, and industrial machinery, which are cyclical indus -
tries. This high-  yield-  rated company’s debt structure is complicated because of

the many levels of seniority that resulted from the company’s 2006 leveraged 
buyout by a consortium of private equity firms. Exhibit 19 is a simplified depiction 
of the company’s debt structure, as well as some key credit-  related statistics.
Exhibit 19   Freescale Semiconductor Debt and 
Leverage Structure as of Y ear-  End 2010
Financial Information ($ millions)
Cash $1,050
Total debt $7,611
Net debt $6,561
36 Because of the higher risk of default, in most instances bank debt will be secured for high-  yield issuers.
37 Convertible bonds are debt instruments that give holders the option to convert to a fixed number 
of shares of common stock. They can be at any level of the capital structure but are frequently issued as 
senior subordinated debt.
38 Preferred stock has elements of both debt and equity. It typically receives a fixed payment like a bond 
does and has higher priority of claims than common stock. As a type of equity, however, it is subordinated 
to debt.

Special Considerations of High-  Yield, Sovereign, and Non-  Sovereign Credit Analysis 641
Interest expense $590
EBITDA $990
Debt Structure ($ millions)
Secured debt (bank loan and bonds) $4,899
Senior unsecured bonds $1,948
Subordinated bonds $764
TOTAL DEBT $7,611
Source:  Company Filings, Loomis Sayles & Company.
1 Calculate gross leverage, as measured by Debt/EBITDA, through each 
level of debt, including total debt.
2 Calculate the net leverage, as measured by (Debt – Cash)/EBITDA, for 
the total debt structure.
3 Why might Freescale have so much secured debt relative to unsecured 
debt (both senior and subordinated)? (Note: This question draws on con -
cepts from earlier sections.)
Gross 
Leverage  
(Debt/EBITDA)Net Leverage  
(Debt – Cash)/
EBITDA
Secured debt leverage
(Total secured debt/EBITDA)
4899/990 4.9x
Senior leverage
(Secured debt + Senior unsecured 
debt)/EBITDA
(4899 + 1948)/990 6.9x

Total leverage  (includes subordinated)
(Total debt/EBITDA)
7611/990 7.7x
Net leverage  (leverage net of cash for entire debt 
structure)
(Total debt – Cash)/EBITDA 6.6xExhibit 19   (Continued)

Reading 55 ■ Fundamentals of Credit Analysis 642
Freescale might have that much secured debt because (1) it was less expensive 
than issuing additional unsecured debt on which investors would have demanded 
a higher yield and/or (2) given the riskiness of the business (semiconductors that 
are sold into cyclical industries, such as autos), the leverage of the business model, 
and the riskiness of the balance sheet (lots of debt from a leveraged buyout), 
investors would only lend the company money on a secured basis.
High-  yield companies that have a lot of secured debt (typically bank debt) relative 
to unsecured debt are said to have a “top-  heavy” capital structure. With this structure, 
there is less capacity to take on more bank debt in the event of financial stress. Along 
with the often more stringent covenants associated with bank debt and its generally 
shorter maturity compared with other types of debt, this means that these issuers are

more susceptible to default, as well as to lower recovery for the various less secured 
creditors.
Corporate Structure.  Many debt-  issuing corporations, including high-  yield companies, 
utilize a holding company structure with a parent and several operating subsidiaries. 
Knowing where an issuer’s debt resides (parent versus subsidiaries) and how cash can 
move from subsidiary to parent (“upstream”) and vice versa (“downstream”) are critical 
to the analysis of high-  yield issuers.
In a holding company structure, the parent owns stock in its subsidiaries. Typically, 
the parent doesn’t generate much of its own earnings or cash flow but instead receives 
dividends from its subsidiaries. The subsidiaries’ dividends are generally paid out of 
earnings after they satisfy of all their other obligations, such as debt payments. To the 
extent that their earnings and cash flow are weak, subsidiaries may be limited in their

ability to pay dividends to the parent. Moreover, subsidiaries that carry a lot of their 
own debt may have restrictions or limitations on how much cash they can provide to 
the parent via dividends or in another way, such as through an intercompany loan. 
These restrictions and limitations on cash moving between parent and subsidiaries 
can have a major impact on their respective abilities to meet their debt obligations. 
The parent’s reliance on cash flow from its subsidiaries means the parent’s debt is 
structurally subordinated to the subsidiaries’ debt and thus will usually have a lower 
recovery rating in default.
For companies with very complex holding companies, there may also be one or 
more intermediate holding companies, each carrying their own debt, and in some cases, 
they may not own 100 percent of the subsidiaries’ stock. This structure is sometimes 
seen in high-  yield companies that have been put together through many mergers and

acquisitions or that were part of a leveraged buyout.39
Exhibit 20 returns to United Rentals, Inc. (URI), a high-  yield company highlighted 
earlier as an example of the credit rating agency notching process. URI has a capital 
structure consisting of a parent company that has debt—in this case, convertible 
senior notes—as well as subsidiaries with outstanding debt. And in the case of URI’s 
United Rentals North America subsidiary, it has several layers of debt by seniority.
39 For holding companies with complex corporate structures, such as multiple subsidiaries with their own 
capital structures, a default in one subsidiary may not trigger a cross-  default. Astute analysts will look for 
that in indentures and other legal documentation.

Special Considerations of High-  Yield, Sovereign, and Non-  Sovereign Credit Analysis 643
Exhibit 20   URI’s Capital Structure
United Rentals, Inc.
 4% Convertible Sr. Notes Due 2015 $124
Total Debt $124
Consolidated Total Debt $2,858
2010 Consolidated EBITDA $646
2010 Consolidated Leverage 4.4×
United Rentals North America
 $1.36B First Lien Loan Due 2013 $683
 10.875% Sr. Notes Due 2016 $488
 9.25% Sr. Notes Due 2019 $492
 8.375% Sr. Sub Notes Due 2020 $750
 1.875% Convertible Sr. Sub Due 2023 $22
 $325 Accounts Receivable Facility $212
Total Debt $2,647
2010 EBITDA $646
2010 Leverage 4.1×United Rentals Trust
 6.5% Convert $87
Total Debt $87
Sources:  Based on data from company filings and Loomis, Sayles & Company.
Thus, high-  yield investors should analyze and understand an issuer’s corporate 
structure, including the distribution of debt between the parent and its subsidiaries. 
Leverage ratios should be calculated at each of the debt-  issuing entities, as well as on 
a consolidated basis.

Also important is that although the debt of an operating subsidiary may be “closer 
to” and better secured by particular assets of the subsidiary, the credit quality of a 
parent company might still be higher. The parent company could, while being less 
directly secured by any particular assets, still benefit from the diversity and availability 
of all the cash flows in the consolidated system. In short, credit quality is not simply 
an automatic analysis of debt provisions and liens.
Covenant Analysis.  As discussed earlier, analysis of covenants is very important for all 
bonds. It is especially important for high-  yield credits because of their reduced margin 
of safety. Key covenants for high-  yield issuers may include the following:
■■Change of control put
■■Restricted payments
■■Limitations on liens and additional indebtedness
■■Restricted versus unrestricted subsidiaries
Under the change of control put , in the event of an acquisition (a “change of

control”), bondholders have the right to require the issuer to buy back their debt (a 
“put option”), often at par or at some small premium to par value. This covenant is 
intended to protect creditors from being exposed to a weaker, more indebted bor -
rower as a result of acquisition. For investment-  grade issuers, this covenant typically 
has a two-  pronged test: acquisition of the borrower and a consequent downgrade to 
a high-  yield rating.

Reading 55 ■ Fundamentals of Credit Analysis 644
The restricted payments  covenant is meant to protect creditors by limiting how 
much cash can be paid out to shareholders over time. The restricted payments “basket” 
is typically sized relative to an issuer’s cash flow and debt outstanding—or is being 
raised—and is an amount that can grow with retained earnings or cash flow, giving 
management more flexibility to make pay-  outs.
The limitations on liens  covenant is meant to put limits on how much secured 
debt an issuer can have. This covenant is important to unsecured creditors who are 
structurally subordinated to secured creditors; the higher the amount of debt that is 
layered ahead of them, the less they stand to recover in the event of default.
With regard to restricted versus unrestricted subsidiaries , issuers may classify 
certain of their subsidiaries as restricted and others as unrestricted as it pertains to

offering guarantees for their holding company debt. These subsidiary guarantees can 
be very useful to holding company creditors because they put their debt on equal 
standing (pari passu) with debt at the subsidiaries instead of with structurally subor -
dinated debt. Restricted subsidiaries should be thought of as those that are designated 
to help service parent-  level debt, typically through guarantees. They tend to be an 
issuer’s larger subsidiaries and have significant assets, such as plants and other facilities, 
and/or cash flow. There may be tax or legal (e.g., country of domicile) reasons why 
certain subsidiaries are restricted while others are not. Analysts should carefully read 
the definitions of restricted versus unrestricted subsidiaries in the indenture because 
sometimes the language is so loosely written that the company can reclassify subsid -
iaries from one type to another with a simple vote by a board of directors or trustees.

For high-  yield investors, it is also important to know what covenants are in an 
issuer’s bank credit agreements. These agreements are typically filed with the securities 
commission in the country where the loan document was drafted. Bank covenants 
can be more restrictive than bond covenants and may include so-  called maintenance 
covenants , such as leverage tests, whereby the ratio of, say, debt/EBITDA may not 
exceed “x” times. In the event a covenant is breached, the bank is likely to block 
further loans under the agreement until the covenant is cured. If not cured, the bank 
may accelerate full payment of the facility, triggering a default.
Equity-  like approach to high-  yield analysis.  High-  yield bonds are sometimes thought 
of as a “hybrid” between higher-  quality bonds, such as investment-  grade corporate 
debt, and equity securities. Their more volatile price and spread movements are less 
influenced by interest rate changes than are higher-  quality bonds, and they show

greater correlation with movements in equity markets. Indeed, as shown in Exhibit 21, 
historical returns on high-  yield bonds and the standard deviation of those returns fall 
somewhere between investment-  grade bonds and equities.

Special Considerations of High-  Yield, Sovereign, and Non-  Sovereign Credit Analysis 645
Exhibit 21   US Trailing 12-  Month Returns by Asset Class, 31 
December 1988–30 June 2011
Return (%)
80
204060
0
–20
–40
–60
Inv. Gr. Corp High Yield S&P 500
Avg. Return: 7.86% 9.52% 10.44%
Max. Return: 31.07% 64.95% 53.62%
Min. Return: –13.82% –31.23% –43.32%
Avg. Volatility: 4.95% 7.31% 13.71%
Sources:  Based on data from Barclays, Haver Analytics, and Loomis, Sayles & Company.
Consequently, an equity market-  like approach to analyzing a high-  yield issuer can 
be useful. One approach is to calculate an issuer’s enterprise value. Enterprise value 
(EV) is usually calculated by adding equity market capitalization and total debt and 
then subtracting excess cash.40,41 Enterprise value is a measure of what a business is 
worth (before any takeover premium) because an acquirer of the company would have 
to either pay off or assume the debt and it would receive the acquired company’s cash.

Bond investors like using EV because it shows the amount of equity “cushion” 
beneath the debt. It can also give a sense of (1) how much more leverage manage -
ment might attempt to put on a company in an effort to increase equity returns or 
(2) how likely—and how expensive—a credit-  damaging leveraged buyout might be. 
Similar to how stock investors look at equity multiples, bond investors may calculate 
and compare EV/EBITDA and debt/EBITDA across several issuers as part of their 
analysis. Narrow differences between the EV/EBITDA and debt/EBITDA ratios for 
a given issuer indicate a small equity cushion and, therefore, potentially higher risk 
for bond investors.
7.2 Sovereign Debt
Governments around the world issue debt to help finance their general operations, 
including current expenses such as wages for government employees, and investments 
in long-  term assets such as infrastructure and education. Government bonds in devel -

oped countries have traditionally been viewed as the default risk-  free rate off of which 
all other credits are priced. Fiscal challenges in developed countries exacerbated by 
the 2008 crisis, however, have called into question the notion of a “risk-  free rate, ” even 
40 Excess cash takes total cash and subtracts any negative working capital.
41 Unlike the vast majority of investment-  grade companies, many high-  yield issuers do not have publicly 
traded equity. For those issuers, one can use comparable public company equity data to estimate EV.

Reading 55 ■ Fundamentals of Credit Analysis 646
for some of the highest-  quality government borrowers. As their capital markets have 
developed, an increasing number of sovereign governments have been able to issue 
debt in foreign markets (generally denominated in a currency other than that of the 
sovereign government, often the US dollar or euro) as well as debt in the domestic 
market (issued in the sovereign government’s own currency). Generally, sovereign 
governments with weak currencies can only access foreign debt markets by issuing 
bonds in foreign currencies that are viewed to be safer stores of value. Debt issued 
in the domestic market is somewhat easier to service because the debt is typically 
denominated in the country’s own currency, subject to its own laws, and money can 
be printed to service the sovereign government’s domestic debt. Twenty years ago, 
many emerging market countries42 could only issue debt in foreign markets because

a domestic market did not exist. Today, many are able to issue debt domestically and 
have successfully built yield curves of domestic bonds across the maturity spectrum. 
All sovereign governments are best able to service foreign and domestic debt if they 
run “twin surpluses”—that is, a government budget surplus as well as a current 
account surplus. 
Despite ongoing financial globalization and the development of domestic bond 
markets, sovereign government defaults occur. Defaults are often precipitated by such 
events as war, political upheaval, major currency devaluation, a sharp deterioration in 
trade, or dramatic price declines in a country’s key commodity exports. Default risks 
for some developed countries escalated after 2009 as government revenues dropped 
precipitously following the financial crisis of 2008, expenditures surged, and financial 
markets focused on the long-  term sustainability of public finances, given aging popu -

lations and rising social security needs. Some of the weaker and more highly indebted 
members of the eurozone became unable to access the debt markets at economical 
rates and had to seek loans from the International Monetary Fund (IMF) and the 
European Union. These weaker governments had previously been able to borrow at 
much lower rates because of their membership in the European Union and adoption 
of the euro. Intra-  eurozone yield spreads widened and countries were shut out of mar -
kets, however, as the global financial crisis exacted a high toll on their public finances 
and, in some cases, their banking systems, which became contingent liabilities for the 
sovereigns. In Ireland, the government guaranteed most bank liabilities, causing the 
country’s debt burden to increase dramatically.
Like corporate analysis, sovereign credit analysis is based on a combination of 
qualitative and quantitative factors. Ultimately, the two key issues for sovereign anal -

ysis are 1) a government’s ability to pay and 2) its willingness to pay. Willingness to 
pay is important because, due to the principle of sovereign immunity, investors are 
generally unable to force a sovereign to pay its debts. Sovereign immunity prevents 
governments from being sued.
To illustrate the most important considerations in sovereign credit analysis, we 
present a basic framework for evaluating sovereign credit and assigning sovereign 
debt ratings.43 The framework highlights the specific characteristics analysts should 
expect in a high-  quality sovereign credit. Some of these are self-  explanatory (e.g., 
absence of corruption). For others, a brief rationale and/or range of values is included 
to clarify interpretation. Most, but not all, of these items are included in rating agency 
Standard & Poor’s methodology.
42 There is no commonly accepted definition of emerging market countries. The World Bank considers GDP/

Capita to be a useful measure, with below-  average GDP/Capita likely indicating an emerging market. Other 
factors include the degree of openness and maturity of the economy, as well as a country’s political stability.
43 This outline was developed from the detailed exposition of Standard & Poor’s methodology given in 
“Sovereign Government Rating Methodology and Assumptions, ” June 2011.

Special Considerations of High-  Yield, Sovereign, and Non-  Sovereign Credit Analysis 647
Political and economic profile
■■Institutional effectiveness and political risks
■●Effectiveness, stability, and predictability of policy making and institutions
 ■Successful management of past political, economic, and/or financial 
crises
 ■Ability and willingness to implement reforms to address fiscal challenges
 ■Predictable policy framework
 ■Absence of challenges to political institutions
 ■Checks and balances in the system
 ■Absence of corruption
 ■Unbiased law enforcement and respect for rule of law and property 
rights
 ■Independent/ unfettered media and sources of economic data
■●Perceived commitment to honor debts
■■Economic structure and growth prospects
■●Income per capita: More prosperous countries generally have a broader and 
deeper tax base with which to support debt.
■●Trend growth prospects: Trend GDP growth is primarily a reflection of

productivity. Above-  average trend growth indicates greater ability to service 
debt from future revenue and, therefore, greater creditworthiness.
■●Sources and stability of growth: Stable, broad-  based growth and absence of 
excessive private sector credit expansion indicate stronger sovereign credit.
■●Size of the public sector relative to private sector: A smaller, leaner public 
sector is more likely to be able to enact necessary changes because it should 
be less beholden to special interest groups, including public employee 
unions.
■●Growth and age distribution of population: A relatively young and growing 
population contributes to trend GDP growth and an expanding tax base and 
mitigates the burden of social services, health care, and pensions, which are 
disproportionately costly for aging populations.
Flexibility and performance profile
■■External liquidity and international investment position
■●Status of currency: Sovereigns that control a reserve currency or a very

actively traded currency are able to use their own currency in many interna -
tional transactions and are less vulnerable to adverse shifts in global investor 
■●External liquidity: Countries with a substantial supply of foreign currency 
(foreign exchange reserves plus current account receipts) relative to pro -
jected funding needs in foreign currency (current account payments plus 
debt maturities) are less vulnerable to interruption of external liquidity.
■●External debt: Countries with low foreign debt relative to current account 
receipts are better able to service their foreign debt. This is similar to a cov -
erage ratio for a corporation.
■■Fiscal performance, flexibility, and debt burden

Reading 55 ■ Fundamentals of Credit Analysis 648
■●Trend change in general government debt as a percent of GDP: Stable 
or declining debt as a percent of GDP indicates a strong credit; a rising 
ratio is ultimately unsustainable and is, therefore, a sign of diminishing 
■●Perceived willingness and ability to increase revenue or cut expenditure to 
ensure debt service.
■●General government interest expense as a percent of revenue: Less than 
5 percent is good; greater than 15 percent is poor.
■●Net general government debt as a percent of GDP: Less than 30 percent is 
good; more than 100 percent is poor.
■●Contingent liabilities arising from financial sector, public enterprises, and 
guarantees: Less than 30 percent of GDP is good; more than 80 percent is 
very poor.
■■Monetary flexibility
■●Ability to use monetary policy to address domestic economic objectives  (e.g., 
growth)
 ■Exchange rate regime: A freely floating currency allows maximum

effectiveness for monetary policy. A fixed-  rate regime limits effectiveness 
and flexibility. A hard peg, such as a currency board or monetary union, 
affords no independent monetary policy.
■●Credibility of monetary policy
 ■Operationally independent central bank: An independent central bank is 
less likely to “debase the currency” by excessive money creation (e.g., in 
order to fund government deficits).
 ■Clear central bank mandate/objectives
 ■Track record of low and stable inflation
 ■Central government’s ability to issue substantial long-  term, fixed-  rate 
debt in domestic currency: This is a sign of market confidence in the 
currency as a store of value.
■●Effectiveness of monetary policy transmission via domestic capital markets
 ■Well-  developed banking system
 ■Active money market and corporate bond market
 ■Greater reliance on market-  based policy tools (e.g., open market oper -
ations) and limited reliance on blunt, administrative policy tools (e.g., 
reserve requirements)

In light of a sovereign government’s various powers—taxation, regulation, monetary 
policy, and ultimately, the sovereign’s ability to “print money” to repay debt—within its 
own economy, it is virtually always at least as good a credit in its domestic currency 
as it is in foreign currency. Thus, credit rating agencies often distinguish between 
domestic and foreign bonds, with domestic bond ratings as much as two notches 
higher. Of course, if a sovereign government were to rely heavily on printing money 
to repay debt, it would fuel high inflation or hyperinflation and increase default risk 
on domestic debt as well.44
44 According to Reinhart and Rogoff in their book This Time is Different , between 1800 and 2009 there 
have been more than 250 defaults on foreign sovereign debt and at least 68 defaults on domestic debt. 
Reinhart and Rogoff use a broader definition of default that includes very high levels of inflation (more 
than 20 percent).

Special Considerations of High-  Yield, Sovereign, and Non-  Sovereign Credit Analysis 649
EXAMPLE 11   
Sovereign Debt
Exhibit 22 shows several key sovereign statistics for Portugal.
Exhibit 22   Key Sovereign Statistics for Portugal
€ (billions), except where 
noted2005 2006 2007 2008 2009 2010
Nominal GDP 153.7 160.3 169.3 171.2 168.6 172.6
Population (millions) 10.6 10.6 10.6 10.6 10.6 10.6
Unemployment (%) 8.6 8.6 8.9 8.5 10.6 12.0
Exports as share GDP (%) 20.3 22.2 22.6 22.6 18.8 21.3
Current account as share 
GDP (%)–10.3 –10.7 –10.1 –12.6 –10.9 –10.0
Government revenues 61.3 64.8 69.7 70.7 67.0 71.8
Government expenditures 70.4 71.4 75.1 77.1 84.1 88.7
Budget balance (surplus/
deficit)–9.0 –6.5 –5.4 –6.4 –17.1 –16.9
Government interest 
payments3.8 4.2 5.1 5.3 4.9 5.2
Primary balance (surplus/
deficit)–5.3 –2.2 –0.4 –1.1 –12.2 –11.7
Government debt 96.5 102.4 115.6 123.1 139.9 161.3
Interest rate on new debt 
(%)3.4 3.9 4.4 4.5 4.2 5.4

Sources:  Based on data from Haver Analytics, Eurostat, and Instituto Nacional de 
Estatistica (Portugal).
1 Calculate the government debt/GDP ratio for Portugal over the years 
2005–2010.
2 Calculate GDP/Capita for the same period.
3 Based on those calculations, as well as other data from Exhibit 22, what 
can you say about Portugal’s credit trend?
2005 2006 2007 2008 2009 2010
Gross government debt/
GDP63% 64% 68% 72% 83% 93%
GDP/Capita 14,500 15,123 15,972 16,151 15,906 16,283

Reading 55 ■ Fundamentals of Credit Analysis 650
The credit trend is deteriorating. Government debt/GDP is rising rapidly. The 
government is running a budget deficit, and the country is running a sizable 
current account deficit, which means it must attract funding from outside the 
country. Interest payments are generally rising, as is the interest rate on new debt.
7.3 Non-  Sovereign Government Debt
Sovereigns are the largest issuers of government debt but non-  sovereign—sometimes 
called sub-  sovereign or local—governments and the quasi-  government entities that are 
created by governments issue bonds as well. The non-  sovereign or local governments 
include governments of states, provinces, regions and cities. For example, the City of 
Tokyo (Tokyo Metropolitan Government) has debt outstanding, as does the Lombardy 
region in Italy, the City of Buenos Aires in Argentina, and the State of California in

the United States. Local government bonds may be referred to as municipal bonds. 
However, when people talk about municipal bonds, they are usually referring 
to US municipal bonds, which represent one of the largest bond markets. In 3rd 
quarter 2011, the US municipal bond market was approximately $3.7 trillion in size, 
roughly 10 percent of the total US bond market.45 The US municipal bond market is 
composed of both tax-  exempt46 and, to a lesser extent, taxable bonds issued by state 
and city governments and their agencies. Municipal borrowers may also issue bonds 
on behalf of private entities, such as non-  profit colleges or hospitals. Historically, for 
any given rating category, these bonds have much lower default rates than corporate 
bonds with the same ratings. For example, according to Moody’s Investors Service, 
the 10-  year average cumulative default rate from 1970 through 2009 was 0.09 percent 
for municipal bonds, compared with an 11.06 percent 10-  year average cumulative

default rate for all corporate debt.47 
The majority of local government bonds, including municipal bonds, are either 
general obligation bonds or revenue bonds. General obligation (GO) bonds are 
unsecured bonds issued with the full faith and credit of the issuing non-  sovereign 
government. These bonds are supported by the taxing authority of the issuer. Revenue 
bonds are issued for specific project financing (e.g., financing for a new sewer system, 
a toll road, bridge, hospital, a sports arena, etc.).
The credit analysis of GO bonds has some similarities to sovereign debt analysis 
(e.g., the ability to levy and collect taxes and fees to help service debt) but also some 
differences. For example, almost without exception, US municipalities must balance 
their operating budgets (i.e., exclusive of long-  term capital projects) annually. Non-  
sovereign governments are unable to use monetary policy the way many sovereigns can.

The economic analysis of non-  sovereign government GO bonds, including US 
municipal bonds, focuses on employment, per capita income (and changes in it over 
time), per capita debt (and changes in it over time), the tax base (depth, breadth, 
diversification, stability, etc.), demographics, and net population growth, as well as 
an analysis of whether the area represented by the non-  sovereign government has the 
infrastructure and location to attract and support new jobs. Analysis should look at 
the volatility and variability of revenues during times of both economic strength and 
weakness. An overreliance on one or two types of tax revenue—particularly a volatile 
45 Securities Industry and Financial Markets Association (SIFMA), “Outstanding US Bond Market Data, ” 
(Q3 2011).
46 Tax exempt refers to the fact that interest received on these bonds is not subject to US federal income 
taxes and, in many cases, is exempt for in-  state residents from state and city income taxes as well.

47 Moody’s Investors Service, “US Municipal Bond Defaults and Recoveries, 1970–2009, ” Moody’s Special 
Comment (February 2010).

Special Considerations of High-  Yield, Sovereign, and Non-  Sovereign Credit Analysis 651
one, such as capital gains taxes or sales taxes—can signal increased credit risk. Pensions 
and other post-  retirement obligations may not show up directly on the non-  sovereign 
government’s balance sheet, and many of these entities have underfunded pensions that 
need to be addressed. Adding the unfunded pension and post-  retirement obligations 
to the debt reveals a more realistic picture of the issuer’s debt and longer-  term obli -
gations. The relative ease or difficulty in managing the annual budgeting process and 
the government’s ability to operate consistently within its budget are also important 
credit analysis considerations.
Disclosure by non-  sovereign governments varies widely, with some of the smaller 
issuers providing limited financial information. Reporting requirements are incon -
sistent, so the financial reports may not be available for six months or more after the

closing of a reporting period.
Exhibit  23 compares several key debt statistics from two of the largest states 
in the United States: California and Texas. California has one of the lowest credit 
ratings of any of the states, whereas Texas has one of the highest. Note the higher 
debt burden (and ranking) across several measures: Total debt, Debt/Capita, Debt/
Personal income, and debt as a percent of state GDP . What is not shown here is that 
California also has a higher tax burden and greater difficulty balancing its budget on 
an annual basis than Texas.
Exhibit 23   Municipal Debt Comparison: California vs. Texas
California Texas
Ratings:
Moody's Investors Service A1 Aaa
Standard & Poor’s A– AA+
Fitch A– AAA
   
Unemployment rate (%) 12.40 8.20
Personal income per capita ($) 43,641 37,774
Debt burden, net ($/rank):
Total (millions) 94,715 (1) 15,433 (9)
Per capita 2,542 (8) 612 (39)
As a percent of 2009 personal income 6.00 (9) 1.60 (40)
As a percent of 2010 GDP 4.73 (8) 1.05 (41)

Sources:  Based on data from the US Bureau of Labor Statistics (as of 2010), the US Census 
Bureau (as of 2008), and Moody’s Investors Service (as of 2010).
Revenue bonds, which are issued to finance a specific project, have a higher degree 
of risk than GO bonds because they are dependent on a single source of revenue. The 
analysis of these bonds is a combination of an analysis of the project and the finances 
around the particular project. The project analysis focuses on the need and projected 
utilization of the project, as well as on the economic base supporting the project. The 
financial analysis has some similarities to the analysis of a corporate bond in that it is 
focused on operating results, cash flow, liquidity, capital structure, and the ability to 
service and repay the debt. A key credit measure for revenue-  backed non-  sovereign 
government bonds is the debt-  service-  coverage (DSC) ratio, which measures how much

Reading 55 ■ Fundamentals of Credit Analysis 652
revenue is available to cover debt payments (principal and interest) after operating 
expenses. Many revenue bonds have a minimum DSC ratio covenant; the higher the 
DSC ratio, the stronger the creditworthiness.
SUMMARY
In this reading, we introduced readers to the basic principles of credit analysis. We 
described the importance of the credit markets and credit and credit-  related risks. We 
discussed the role and importance of credit ratings and the methodology associated 
with assigning ratings, as well as the risks of relying on credit ratings. The reading 
covered the key components of credit analysis and the financial measure used to help 
assess creditworthiness.
We also discussed risk versus return when investing in credit and how spread 
changes affect holding period returns. In addition, we addressed the special consid -
erations to take into account when doing credit analysis of high-  yield companies,

sovereign borrowers, and non-  sovereign government bonds.
■■Credit risk is the risk of loss resulting from the borrower failing to make full 
and timely payments of interest and/or principal.
■■The key components of credit risk are risk of default and loss severity in the 
event of default. The product of the two is expected loss. Investors in higher-  
quality bonds tend not to focus on loss severity because default risk for those 
securities is low.
■■Loss severity equals (1 – Recovery rate).
■■Credit-  related risks include downgrade risk (also called credit migration risk) 
and market liquidity risk. Either of these can cause yield spreads—yield premi -
ums—to rise and bond prices to fall.
■■Downgrade risk refers to a decline in an issuer’s creditworthiness. Downgrades 
will cause its bonds to trade with wider yield spreads and thus lower prices.
■■Market liquidity risk refers to a widening of the bid–ask spread on an issuer’s

bonds. Lower-  quality bonds tend to have greater market liquidity risk than 
higher-  quality bonds, and during times of market or financial stress, market 
liquidity risk rises.
■■The composition of an issuer’s debt and equity is referred to as its “capital 
structure. ” Debt ranks ahead of all types of equity with respect to priority of 
payment, and within the debt component of the capital structure, there can be 
varying levels of seniority.
■■With respect to priority of claims, secured debt ranks ahead of unsecured debt, 
and within unsecured debt, senior debt ranks ahead of subordinated debt. In 
the typical case, all of an issuer’s bonds have the same probability of default due 
to cross-  default provisions in most indentures. Higher priority of claim implies 
higher recovery rate—lower loss severity—in the event of default.
■■For issuers with more complex corporate structures—for example, a parent 
holding company that has operating subsidiaries—debt at the holding company

is structurally subordinated to the subsidiary debt, although the possibility of 
more diverse assets and earnings streams from other sources could still result in 
the parent having higher effective credit quality than a particular subsidiary.

Summary 653
■■Recovery rates can vary greatly by issuer and industry. They are influenced by 
the composition of an issuer’s capital structure, where in the economic and 
credit cycle the default occurred, and what the market’s view of the future pros -
pects are for the issuer and its industry.
■■The priority of claims in bankruptcy is not always absolute. It can be influ -
enced by several factors, including some leeway accorded to bankruptcy judges, 
government involvement, or a desire on the part of the more senior creditors 
to settle with the more junior creditors and allow the issuer to emerge from 
bankruptcy as a going concern, rather than risking smaller and delayed recovery 
in the event of a liquidation of the borrower.
■■Credit rating agencies, such as Moody’s, Standard & Poor’s, and Fitch, play a 
central role in the credit markets. Nearly every bond issued in the broad debt 
markets carries credit ratings, which are opinions about a bond issue’s credit -

worthiness. Credit ratings enable investors to compare the credit risk of debt 
issues and issuers within a given industry, across industries, and across geo -
graphic markets.
■■Bonds rated Aaa to Baa3 by Moody’s and AAA to BBB– by Standard & Poor’s 
(S&P) and/or Fitch (higher to lower) are referred to as “investment grade. ” 
Bonds rated lower than that—Ba1 or lower by Moody’s and BB+ or lower by 
S&P and/or Fitch—are referred to as “below investment grade” or “speculative 
grade. ” Below-  investment-  grade bonds are also called “high-  yield” or “junk” 
bonds.
■■The rating agencies rate both issuers and issues. Issuer ratings are meant to 
address an issuer’s overall creditworthiness—its risk of default. Ratings for 
issues incorporate such factors as their rankings in the capital structure.
■■The rating agencies will notch issue ratings up or down to account for such fac -
tors as capital structure ranking for secured or subordinated bonds, reflecting

different recovery rates in the event of default. Ratings may also be notched due 
to structural subordination.
■■There are risks in relying too much on credit agency ratings. Creditworthiness 
may change over time, and initial/current ratings do not necessarily reflect 
the creditworthiness of an issuer or bond over an investor’s holding period. 
Valuations often adjust before ratings change, and the notching process may not 
adequately reflect the price decline of a bond that is lower ranked in the capital 
structure. Because ratings primarily reflect the probability of default but not 
necessarily the severity of loss given default, bonds with the same rating may 
have significantly different expected losses (default probability times loss sever -
ity). And like analysts, credit rating agencies may have difficulty forecasting 
certain credit-  negative outcomes, such as adverse litigation, leveraging corpo -
rate transactions, and such low probability/high severity events as earthquakes

and hurricanes.
■■The role of corporate credit analysis is to assess the company’s ability to make 
timely payments of interest and to repay principal at maturity. 
■■Credit analysis is similar to equity analysis. It is important to understand, 
however, that bonds are contracts and that management’s duty to bondholders 
and other creditors is limited to the terms of the contract. In contrast, manage -
ment’s duty to shareholders is to act in their best interest by trying to maximize 
the value of the company—perhaps even at the expense of bondholders at 
times.
■■Credit analysts tend to focus more on the downside risk given the asymmetry 
of risk/return, whereas equity analysts focus more on upside opportunity from 
earnings growth, and so on.

Reading 55 ■ Fundamentals of Credit Analysis 654
■■The “4 Cs” of credit—capacity, collateral, covenants, and character—provide a 
useful framework for evaluating credit risk.
■■Credit analysis focuses on an issuer’s ability to generate cash flow. The analysis 
starts with an industry assessment—structure and fundamentals—and contin -
ues with an analysis of an issuer’s competitive position, management strategy, 
and track record.
■■Credit measures are used to calculate an issuer’s creditworthiness, as well as 
to compare its credit quality with peer companies. Key credit ratios focus on 
leverage and interest coverage and use such measures as EBITDA, free cash 
flow, funds from operations, interest expense and balance sheet debt.
■■An issuer’s ability to access liquidity is also an important consideration in credit 
analysis.
■■The higher the credit risk, the greater the offered/required yield and potential 
return demanded by investors. Over time, bonds with more credit risk offer

higher returns but with greater volatility of return than bonds with lower credit 
risk.
■■The yield on a credit-  risky bond comprises the yield on a default risk–free bond 
with a comparable maturity plus a yield premium, or “spread, ” that comprises 
a credit spread and a liquidity premium. That spread is intended to compen -
sate investors for credit risk—risk of default and loss severity in the event of 
default—and the credit-  related risks that can cause spreads to widen and prices 
to decline—downgrade or credit migration risk and market liquidity risk.
Yield spread = Liquidity premium + Credit spread.
■■In times of financial market stress, the liquidity premium can increase sharply, 
causing spreads to widen on all credit-  risky bonds, with lower-  quality issu -
ers most affected. In times of credit improvement or stability, however, credit 
spreads can narrow sharply as well, providing attractive investment returns.

■■Credit curves—the plot of yield spreads for a given bond issuer across the yield 
curve—are typically upward sloping, with the exception of high premium-  
priced bonds and distressed bonds, where credit curves can be inverted because 
of the fear of default, when all creditors at a given ranking in the capital struc -
ture will receive the same recovery rate without regard to debt maturity.
■■The impact of spread changes on holding period returns for credit-  risky bonds 
are a product of two primary factors: the basis point spread change and the 
sensitivity of price to yield as reflected by (end-  of- period) modified duration 
and convexity. Spread narrowing enhances holding period returns, whereas 
spread widening has a negative impact on holding period returns. Longer-  
duration bonds have greater price and return sensitivity to changes in spread 
than shorter-  duration bonds.

■■For high-  yield bonds, with their greater risk of default, more emphasis should 
be placed on an issuer’s sources of liquidity, as well as on its debt structure and 
corporate structure. Credit risk can vary greatly across an issuer’s debt structure 
depending on the seniority ranking. Many high-  yield companies have complex 
capital structures, resulting in different levels of credit risk depending on where 
the debt resides.

Summary 655
■■Covenant analysis is especially important for high-  yield bonds. Key covenants 
include payment restrictions, limitation on liens, change of control, cover -
age maintenance tests (often limited to bank loans), and any guarantees from 
restricted subsidiaries. Covenant language can be very technical and legalistic, 
so it may help to seek legal or expert assistance.
■■An equity-  like approach to high-  yield analysis can be helpful. Calculating and 
comparing enterprise value with EBITDA and debt/EBITDA can show a level of 
equity “cushion” or support beneath an issuer’s debt.
■■Sovereign credit analysis includes assessing both an issuer’s ability and willing -
ness to pay its debt obligations. Willingness to pay is important because, due to 
sovereign immunity, a sovereign government cannot be forced to pay its debts.
■■In assessing sovereign credit risk, a helpful framework is to focus on five broad 
areas: (1) institutional effectiveness and political risks, (2) economic struc -

ture and growth prospects, (3) external liquidity and international investment 
position, (4) fiscal performance, flexibility, and debt burden, and (5) monetary 
■■Among the characteristics of a high-  quality sovereign credit are the absence 
of corruption and/or challenges to political framework; governmental checks 
and balances; respect for rule of law and property rights; commitment to honor 
debts; high per capita income with stable, broad-  based growth prospects; 
control of a reserve or actively traded currency; currency flexibility; low foreign 
debt and foreign financing needs relative to receipts in foreign currencies; stable 
or declining ratio of debt to GDP; low debt service as a percent of revenue; low 
ratio of net debt to GDP; operationally independent central bank; track record 
of low and stable inflation; and a well-  developed banking system and active 
money market.
■■Non-  sovereign or local government bonds, including municipal bonds, are typi -

cally either general obligation bonds or revenue bonds.
■■General obligation (GO) bonds are backed by the taxing authority of the issuing 
non-  sovereign government. The credit analysis of GO bonds has some similari -
ties to sovereign analysis—debt burden per capita versus income per capita, tax 
burden, demographics, and economic diversity. Underfunded and “off-  balance-  
sheet” liabilities, such as pensions for public employees and retirees, are debt-  
like in nature.
■■Revenue-  backed bonds support specific projects, such as toll roads, bridges, air -
ports, and other infrastructure. The creditworthiness comes from the revenues 
generated by usage fees and tolls levied.

Reading 55 ■ Fundamentals of Credit Analysis 656
1 The risk that a bond’s creditworthiness declines is best described by:
A credit migration risk.
B market liquidity risk.
C spread widening risk.
2 Stedsmart Ltd and Fignermo Ltd are alike with respect to financial and oper -
ating characteristics, except that Stedsmart Ltd has less publicly traded debt 
outstanding than Fignermo Ltd. Stedsmart Ltd is most likely  to have:
A no market liquidity risk.
B lower market liquidity risk.
C higher market liquidity risk.
3 In the event of default, the recovery rate of which of the following bonds would 
most likely  be the highest?
A First mortgage debt
B Senior unsecured debt
C Junior subordinate debt
4 During bankruptcy proceedings of a firm, the priority of claims was not strictly 
adhered to. Which of the following is the least likely  explanation for this 
outcome?
A Senior creditors compromised.
B The value of secured assets was less than the amount of the claims.

C A judge’s order resulted in actual claims not adhering to strict priority of 
claims.
5 A fixed income analyst is least likely  to conduct an independent analysis of 
credit risk because credit rating agencies:
A may at times mis-  rate issues.
B often lag the market in pricing credit risk.
C cannot foresee future debt-  financed acquisitions.
6 If goodwill makes up a large percentage of a company’s total assets, this most 
likely  indicates that:
A the company has low free cash flow before dividends.
B there is a low likelihood that the market price of the company’s common 
stock is below book value.
C a large percentage of the company’s assets are not of high quality.
7 In order to analyze the collateral  of a company a credit analyst should assess 
the:
A cash flows of the company.
B soundness of management’s strategy.
C value of the company’s assets in relation to the level of debt.
8 In order to determine the capacity  of a company, it would be most  appropriate 
to analyze the:

A company’s strategy.

Practice Problems 657
B growth prospects of the industry.
C aggressiveness of the company’s accounting policies.
9 A credit analyst is evaluating the credit worthiness of three companies: a con -
struction company, a travel and tourism company, and a beverage company. 
Both the construction and travel and tourism companies are cyclical, whereas 
the beverage company is non-  cyclical. The construction company has the 
highest debt level of the three companies. The highest credit risk is most likely  
exhibited by the:
A construction company.
B beverage company.
C travel and tourism company.
10 Based on the information provided in Exhibit 1, the EBITDA interest coverage 
ratio of Adidas AG is closest  to:
A 7.91x.
B 10.12x.
C 12.99x.
Exhibit 1   Adidas AG Excerpt from Consolidated Income 
Statement Y ear Ending 31 December 2010 (€ in 
millions)
Gross profit 5,730
Royalty and commission income 100
Other operating income 110
Other operating expenses 5,046
Operating profit 894
Interest income 25

Interest expense 113
Income before taxes 806
Income taxes 238
Net income 568
Additional information:  
Depreciation and amortization: €249 million
Source:  Adidas AG Annual Financial Statements, December 2010
11 The following information is from the annual report of Adidas AG for 
December 2010:
■●Depreciation and amortization: €249 million
■●Total assets: €10,618 million
■●Total debt: €1,613 million
■●Shareholders’ equity: €4,616 million
 The debt/capital ratio of Adidas AG is closest  to:
A 15.19%.
B 25.90%.
C 34.94%.

Reading 55 ■ Fundamentals of Credit Analysis 658
12 Funds from operations (FFO) of Pay Handle Ltd increased in 2011. In 2011 
the total debt of the company remained unchanged, while additional common 
shares were issued. Pay Handle Ltd’s ability to service its debt in 2011, as com -
pared to 2010, most likely :
A improved.
B worsened.
C remained the same.
13 Based on the information in Exhibit 2, Grupa Zywiec SA’s credit risk is most 
likely :
A lower than the industry.
B higher than the industry.
C the same as the industry.
Exhibit 2   European Food, Beverage, and Tobacco Industry and Grupa 
Zywiec SA Selected Financial Ratios for 2010
Total  
debt/Total  
capital  
(%)FFO/Total 
debt  
(%)Return on 
capital  
(%)Total debt/
EBITDA  
(x)EBITDA 
interest 
coverage  
(x)
Grupa Zywiec 
SA47.1 77.5 19.6 1.2 17.7
Industry 
Median42.4 23.6 6.55 2.85 6.45
14 Based on the information in Exhibit 3, the credit rating of Davide Campari-  
Milano S.p.A. is most likely :
A lower than Associated British Foods plc.

B higher than Associated British Foods plc.
C the same as Associated British Foods plc.
Exhibit 3   European Food, Beverage, and Tobacco Industry; Associated 
British Foods plc; and Davide Campari-  Milano S.p.A Selected 
Financial Ratios, 2010
CompanyTotal  
debt/total  
capital  
(%)FFO/total  
debt  
capital  
(%)Total  
debt/EBITDA  
(x)EBITDA 
interest 
coverage  
(x)
Associated British 
Foods plc0.2 84.3 0.1 1.0 13.9
Davide Campari-  
Milano S.p.A.42.9 22.9 8.2 3.2 3.2
European Food, 
Beverage, and 
Tobacco Median42.4 23.6 6.55 2.85 6.45

Practice Problems 659
15 Holding all other factors constant, the most likely  effect of low demand and 
heavy new issue supply on bond yield spreads is that yield spreads will:
A widen.
B tighten.
C not be affected.
16 Credit risk of a corporate bond is best described as the:
A risk that an issuer’s creditworthiness deteriorates.
B probability that the issuer fails to make full and timely payments.  
C risk of loss resulting from the issuer failing to make full and timely 
payments.
17 The risk that the price at which investors can actually transact differs from the 
quoted price in the market is called:
A spread risk.
B credit migration risk.
C market liquidity risk.
18 Loss severity is best described as the:
A default probability multiplied by the loss given default.
B portion of a bond’s value recovered by bondholders in the event of default.
C portion of a bond’s value, including unpaid interest, an investor loses in the 
event of default.

19 The two components of credit risk are default probability and:
B loss severity.
20 For a high-  quality debt issuer with a large amount of publicly traded debt, bond 
investors tend to devote most  effort to assessing the issuer’s:
A default risk. 
B loss severity. 
C market liquidity risk. 
21 The expected loss for a given debt instrument is estimated as the product of 
default probability and:
A (1 + Recovery rate).
B (1 – Recovery rate).
C 1/(1 + Recovery rate).
22 The priority of claims for senior subordinated debt is: 
A lower than for senior unsecured debt.
B the same as for senior unsecured debt. 
C higher than for senior unsecured debt. 
23 A senior unsecured credit instrument holds a higher priority of claims than one 
ranked as:
A mortgage debt.
B second lien loan.
C senior subordinated.
24 In a bankruptcy proceeding, when the absolute priority of claims is enforced: 
A senior subordinated creditors rank above second lien holders.

Reading 55 ■ Fundamentals of Credit Analysis 660
B preferred equity shareholders rank above unsecured creditors. 
C creditors with a secured claim have the first right to the value of that spe -
cific property.
25 In the event of default, which of the following is most likely to have the highest 
recovery rate?
A Second lien
B Senior unsecured
C Senior subordinated
26 The process of moving credit ratings of different issues up or down from the 
issuer rating in response to different payment priorities is best described as:
A notching.
B structural subordination.
C cross-  default provisions. 
27 The factor considered by rating agencies when a corporation has debt at both 
its parent holding company and operating subsidiaries is best referred to as:
B corporate family rating. 
C structural subordination. 
28 Which type of security is most likely  to have the same rating as the issuer?
A Preferred stock 
B Senior secured bond
C Senior unsecured bond

29 Which of the following corporate debt instruments has the highest seniority 
ranking?
30 An issuer credit rating usually applies to a company’s:
A secured debt.
B subordinated debt.
C senior unsecured debt. 
31 The rating agency process whereby the credit ratings on issues are moved up or 
down from the issuer rating best describes:
B pari passu ranking.
32 The notching adjustment for corporate bonds rated Aa2/AA is most likely :
A larger than the notching adjustment for corporate bonds rated B2/B.
B the same as the notching adjustment for corporate bonds rated B2/B.
C smaller than the notching adjustment for corporate bonds rated B2/B.
33 Which of the following statements about credit ratings is most accurate ? 
A Credit ratings can migrate over time.
B Changes in bond credit ratings precede changes in bond prices.

C Credit ratings are focused on expected loss rather than risk of default.

Practice Problems 661
34 Which industry characteristic most likely  has a positive effect on a company’s 
ability to service debt?
A Low barriers to entry in the industry
B High number of suppliers to the industry
C Broadly dispersed market share among large number of companies in the 
industry 
35 When determining the capacity of a borrower to service debt, a credit analyst 
should begin with an examination of:
A industry structure.
B industry fundamentals.
C company fundamentals.
36 Which of the following accounting issues should mostly likely  be considered a 
character warning flag in credit analysis?
A Expensing items immediately
B Changing auditors infrequently
C Significant off-  balance-  sheet financing
37 In credit analysis, capacity is best described as the:
A quality of management.
B ability of the borrower to make its debt payments on time.
C quality and value of the assets supporting an issuer’s indebtedness.
38 Among the Four Cs of credit analysis, the recognition of revenue prematurely

most likely  reflects a company’s:
A character .
B covenants.
C collateral.
Use the following Exhibit for Questions 39 and 40
Exhibit 4   Industrial Comparative Ratio Analysis, Y ear 20XX
EBITDA 
Margin  
(%)Return 
on 
Capital  
(%)EBIT/
Interest 
Expense  
(×)EBITDA/
Interest 
Expense  
(×)Debt/
EBITDA  
(×)Debt/
Capital  
(%)
Company A 25.1 25.0 15.9 19.6 1.6 35.2
Company B 29.6 36.3 58.2 62.4 0.5 15.9
Company C 21.8 16.6 8.9 12.4 2.5 46.3
39 Based on only the leverage ratios in Exhibit 4, the company with the highest 
credit risk is:

Reading 55 ■ Fundamentals of Credit Analysis 662
40 Based on only the coverage ratios in Exhibit 4, the company with the highest 
credit quality is:
Use the following Exhibits for Questions 41 and 
42
Exhibit 5   Consolidated Income Statement (£ millions)
Company X Company Y
Net revenues 50.7 83.7
Operating expenses 49.6 70.4
Operating income 1.1 13.3
Interest income 0.0 0.0
Interest expense 0.6 0.8
Income before income taxes 0.5 12.5
Provision for income taxes –0.2 –3.5
Net income 0.3 9.0
Exhibit 6   Consolidated Balance Sheets (£ millions)
ASSETS
  Current assets 10.3 21.9
  Property, plant, and equipment, net 3.5 20.1
  Goodwill 8.3 85.0
  Other assets 0.9 5.1
Total assets 23.0 132.1
  Accounts payable and accrued expenses 8.4 16.2
  Short-  term debt 0.5 8.7

Total current liabilities 8.9 24.9
  Long-  term debt 11.7 21.1
  Other non-  current liabilities 1.1 22.1
Total liabilities 21.7 68.1
  Total shareholders’ equity 1.3 64.0
Total liabilities and shareholders’ equity 23.0 132.1
Exhibit 7   Consolidated Statements of Cash Flow (£ millions)
ACTIVITIES
  Net income 0.3 9.0
  Depreciation 1.0 3.8
  Goodwill impairment 2.0 1.6
  Changes in working capital 0.0 –0.4
Net cash provided by operating activities 3.3 14.0
CASH FLOWS FROM INVESTING 
  Additions to property and equipment –1.0 –4.0
  Additions to marketable securities –0.1 0.0
equipment0.2 2.9
  Proceeds from sale of marketable securities 0.3 0.0
Net cash used in investing activities –0.6 –1.1
  Repurchase of common stock –1.5 –4.0
  Dividends to shareholders –0.3 –6.1
  Change in short-  term debt 0.0 –3.4

Change in short-  term debt 0.0 –3.4
  Additions to long-  term debt 3.9 3.9
  Reductions in long-  term debt –3.4 –2.5
Net cash – financing activities –1.3 –12.1

Reading 55 ■ Fundamentals of Credit Analysis 664
NET INCREASE IN CASH AND CASH 
EQUIVALENTS1.4 0.8
41 Based on Exhibits 5–7, in comparison to Company X, Company Y has a higher: 
A debt/capital ratio.
B debt/EBITDA ratio.
C free cash flow after dividends/debt ratio.
42 Based on Exhibits 5–7, in comparison to Company Y, Company X has greater: 
B interest coverage. 
C operating profit margin.
43 Credit yield spreads most likely  widen in response to:
A high demand for bonds.
B weak performance of equities.
C strengthening economic conditions.
44 The factor that most likely  results in corporate credit spreads widening is:
A an improving credit cycle.
B weakening economic conditions.
C a period of high demand for bonds.
45 Credit spreads are most likely  to widen:
A in a strengthening economy.
B as the credit cycle improves.
C in periods of heavy new issue supply and low borrower demand.
46 Which of the following factors in credit analysis is more important for general

obligation non-  sovereign government debt than for sovereign debt? 
A Per capita income
B Power to levy and collect taxes
C Requirement to balance an operating budget
47 In contrast to high-  yield credit analysis, investment-  grade analysis is more likely  
to rely on: 
B an assessment of bank credit facilities.
C matching of liquidity sources to upcoming debt maturities.
48 Which of the following factors would best justify a decision to avoid investing in 
a country’s sovereign debt?
A Freely floating currency Exhibit 7   (Continued)

B A population that is not growing
C Suitable checks and balances in policymaking

Reading 55 ■ Fundamentals of Credit Analysis 666
SOLUTIONS
1 A is correct. Credit migration risk or downgrade risk refers to the risk that a 
bond issuer’s creditworthiness may deteriorate or migrate lower. The result is 
that investors view the risk of default to be higher, causing the spread on the 
issuer’s bonds to widen.
2 C is correct. Market liquidity risk refers to the risk that the price at which inves -
tors transact may be different from the price indicated in the market. Market 
liquidity risk is increased by (1) less debt outstanding and/or (2) a lower issue 
credit rating. Because Stedsmart Ltd is comparable to Fignermo Ltd except for 
less publicly traded debt outstanding, it should have higher market liquidity 
risk.
3 A is correct. First mortgage debt is senior secured debt and has the highest 
priority of claims. First mortgage debt also has the highest expected recovery 
rate. First mortgage debt refers to the pledge of specific property. Neither senior

unsecured nor junior subordinate debt has any claims on specific assets.
4 B is correct. Whether or not secured assets are sufficient for the claims against 
them does not influence priority of claims. Any deficiency between pledged 
assets and the claims against them becomes senior unsecured debt and still 
adheres to the guidelines of priority of claims.
5 C is correct. Both analysts and ratings agencies have difficulty foreseeing future 
debt-  financed acquisitions.
6 C is correct. Goodwill is viewed as a lower quality asset compared with tangible 
assets that can be sold and more easily converted into cash.
7 C is correct. The value of assets in relation to the level of debt is important to 
assess the collateral of the company; that is, the quality and value of the assets 
that support the debt levels of the company.
8 B is correct. The growth prospects of the industry provide the analyst insight 
regarding the capacity of the company.

9 A is correct. The construction company is both highly leveraged, which 
increases credit risk, and in a highly cyclical industry, which results in more 
volatile earnings. 
10 B is correct. The interest expense is €113 million and EBITDA = Operating 
profit + Depreciation and amortization = €894 + 249 million = €1,143 million. 
EBITDA interest coverage = EBITDA/Interest expense = 1,143/113 = 10.12 
times.
11 B is correct. Total debt is €1,613 million with Total capital = Total debt + 
Shareholders’ equity = €1,613 + 4,616 = €6,229 million. The Debt/Capital ratio 
= 1,613/6,229 = 25.90%.
12 A is correct. If the debt of the company remained unchanged but FFO 
increased, more cash is available to service debt compared to the previous year. 
Additionally, the debt/capital ratio has improved. It would imply that the ability 
of Pay Handle Ltd to service their debt has improved.
13 A is correct. Based on four of the five credit ratios, Grupa Zywiec SA’s credit

quality is superior to that of the industry.
14 A is correct. Davide Campari-  Milano S.p.A. has more financial leverage and 
less interest coverage than Associated British Foods plc, which implies greater 

15 A is correct. Low demand implies wider yield spreads, while heavy supply will 
widen spreads even further.
16 C is correct. Credit risk is the risk of loss resulting from the borrower failing to 
make full and timely payments of interest and/or principal. 
17 C is correct. Market liquidity risk is the risk that the price at which investors 
can actually transact—buying or selling—may differ from the price indicated in 
the market. 
18 C is correct. Loss severity is the portion of a bond’s value (including unpaid 
interest) an investor loses in the event of default. 
19 B is correct. The two components of credit risk are default probability and loss 
severity. In the event of default, loss severity is the portion of a bond’s value 
(including unpaid interest) an investor loses. A and C are incorrect because 
spread and market liquidity risk are credit-  related risks, not components of 
credit risk. 
20 A is correct. Credit risk has two components: default risk and loss severity.

Because default risk is quite low for most high-  quality debt issuers, bond inves -
tors tend to focus more on this likelihood and less on the potential loss severity.
21 B is correct. The expected loss for a given debt instrument is the default prob -
ability multiplied by the loss severity given default. The loss severity is often 
expressed as (1 – Recovery rate). 
22 A is correct. Senior subordinated debt is ranked lower than senior unsecured 
debt and thus has a lower priority of payment.
23 C is correct. The highest-  ranked unsecured debt is senior unsecured debt. 
Lower-  ranked debt includes senior subordinated debt. A and B are incorrect 
because mortgage debt and second lien loans are secured and higher ranked.
24 C is correct. According to the absolute priority of claims, in the event of bank -
ruptcy, creditors with a secured claim have the right to the value of that specific 
property before any other claim.

25 A is correct. A second lien has a secured interest in the pledged assets. Second 
lien debt ranks higher in priority of payment than senior unsecured and senior 
subordinated debt and thus would most likely have a higher recovery rate.
26 A is correct. Notching is the process for moving ratings up or down relative to 
the issuer rating when rating agencies consider secondary factors, such as prior -
ity of claims in the event of a default and the potential loss severity.
27 C is correct. Structural subordination can arise when a corporation with a 
holding company structure has debt at both its parent holding company and 
operating subsidiaries. Debt at the operating subsidiaries is serviced by the cash 
flow and assets of the subsidiaries before funds are passed to the parent holding 
company.
28 C is correct. The issuer credit rating usually applies to its senior unsecured 
debt.

debt.
29 A is correct. Second lien debt is secured debt, which is senior to unsecured debt 
and to subordinated debt. 
30 C is correct. An issuer credit rating usually applies to its senior unsecured debt. 
31 A is correct. Recognizing different payment priorities, and thus the potential for 
higher (or lower) loss severity in the event of default, the rating agencies have 
adopted a notching process whereby their credit ratings on issues can be moved 
up or down from the issuer rating (senior unsecured).

Reading 55 ■ Fundamentals of Credit Analysis 668
32 C is correct. As a general rule, the higher the senior unsecured rating, the 
smaller the notching adjustment. Thus, for corporate bonds rated Aa2/AA, the 
rating agencies will typically apply smaller rating adjustments, or notches, to 
the related issue. 
33 A is correct. Credit migration is the risk that a bond issuer’s creditworthiness 
deteriorates, or migrates lower. Over time, credit ratings can migrate signifi -
cantly from what they were at the time a bond was issued. An investor should 
not assume that an issuer’s credit rating will remain the same from the time of 
purchase through the entire holding period. 
34 B is correct. An industry with a high number of suppliers reduces the suppliers’ 
negotiating power, thus helping companies control expenses and aiding in the 
servicing of debt.
35 A is correct. Credit analysis starts with industry structure—for example, by

looking at the major forces of competition, followed by an analysis of industry 
fundamentals—and then turns to examination of the specific issuer.
36 C is correct. Credit analysts can make judgments about management’s character 
by evaluating the use of aggressive accounting policies, such as timing reve -
nue recognition. This activity is a potential warning flag for other behaviors or 
actions that may adversely affect an issuer’s creditworthiness.
37 B is correct. Capacity refers to the ability of a borrower to service its debt. 
Capacity is determined through credit analysis of an issuer’s industry and of the 
specific issuer. 
38 A is correct. Credit analysts can make judgments about management’s charac -
ter in a number of ways, including by observing its use of aggressive accounting 
policies and/or tax strategies. An example of this aggressiveness is recognizing 
revenue prematurely. 
39 C is correct. The debt/capital and debt/EBITDA ratios are used to assess a com -

pany’s leverage. Higher leverage ratios indicate more leverage and thus higher 
credit risk. Company C’s debt/capital (46.3%) and debt/EBITDA (2.5×) leverage 
ratios are higher than those for Companies A and B.
40 B is correct. The EBITDA/interest expense and EBIT/interest expense ratios are 
coverage ratios. Coverage ratios measure an issuer’s ability to meet its interest 
payments. A higher ratio indicates better credit quality. Company B’s EBITDA/
interest expense (62.4×) and EBIT/interest expense (58.2×) coverage ratios are 
higher than those for Companies A and C.
41 C is correct because Company Y has a higher ratio of free cash flow after divi -
dends to debt than Company X, not lower, as shown in the following table.
Free cash flow after dividends as a % of debt =  FCF after di vidends
Debt
Cash flow from operations £3.3 £14.0
Less
  Net capital expenditures –0.8 –1.1
  Dividends –0.3 –6.1
Free cash flow after dividends £2.2 £6.8
 
Debt £12.2 £29.8

Free cash flow after dividends as a % of debt (2.2/12.2) × 100 (6.8/29.8) × 100
Free cash flow after dividends as a % of debt 18.0% 22.8%
 A is incorrect. Company Y has a lower debt/capital ratio than Company X, as 
shown in the following table. 
Debt divided by Capital (%) =  Debt
Debt Equity+ ()
   
Capital
  Debt 12.2 29.8
  + Equity 1.3 64.0
Capital £13.5 £93.8
Debt/Capital (%) (12.2/13.5) × 100 (29.8/93.8) × 100
Debt/Capital (%) 90.4% 31.8%
 B is incorrect because Company Y has a lower debt/EBITDA ratio than 
Company Y, not higher, as shown in the following table. 
Operating income £1.1 £13.3
   
EBIT £1.1 £13.3
plus
  Amortization 0.0 0.0
EBITDA £2.1 £17.1
   
Debt/EBITDA 12.2/2.1 29.8/17.1
   
Debt/EBITDA 5.81 1.74
42 A is correct. Compared with Company Y, based on both their debt/capital ratios 
and their ratios of free cash flow after dividends to debt, which are measures of

leverage commonly used in credit analysis, Company X is more highly lever -
aged, as shown in the following table.
Debt £2.2 £29.8

Reading 55 ■ Fundamentals of Credit Analysis 670
Capital
  Debt 2.2 29.8
  + Equity 4.3 64.0
Capital £6.5 £93.8
Debt
Less
43 B is correct. In weak financial markets, including weak markets for equities, 
credit spreads will widen. 
44 B is correct. Weakening economic conditions will push investors to desire a 
greater risk premium and drive overall credit spreads wider.
45 C is correct. In periods of heavy new issue supply, credit spreads will widen if 
demand is insufficient.

demand is insufficient. 
46 C is correct. Non-  sovereign governments typically must balance their operating 
budgets and lack the discretion to use monetary policy as many sovereigns can.
47 A is correct. Most investors in investment-  grade debt focus on spread risk—that 
is, the effect of changes in spreads on prices and returns—while in high-  yield 
analysis, the focus on default risk is relatively greater. 
48 B is correct. Among the most important considerations in sovereign credit 
analysis is growth and age distribution of population. A relatively young and 
growing population contributes to growth in GDP and an expanding tax base 
and relies less on social services, pensions, and health care relative to an older 

Index I-1
A
Abbott Laboratories, 213
abnormal returns, 124
absolute priority rule, 483
ABSs. see asset-backed securities
accelerated book building, 50
accrued interest, 413–417
Acer, 209
active investment strategies
industry analysis in, 188–189
information-acquisition costs for, 
123–124
and market efficiency, 117
active portfolio management
information-motivated trading in, 10
manager performance in, 129
manager selection for, 116
security market indexes in, 94
active returns, 116
activity ratios, in company analysis, 
230–231
ADB. see Asian Developmental Bank
add-on rates, 429–431
Adidas AG, 657–658
adjustable-rate mortgages (ARMs), 487
ADRs. see American depository receipts
ADSs. see American depository shares
ADT Security Services, Inc., 199, 200
Advanced Micro Devices, 209
adverse selection, with insurance, 34
aerospace industry, governmental 
influences on, 225–226
AFDB. see African Developmental Bank
affirmative covenants, 310, 626
Africa, 350, 617. see also  specific 

African Developmental Bank (AFDB), 
372
agency bonds, 372–373
agency problems, with market 
regulation, 61
agency RMBS, 490–491, 503. see 
also collateralized mortgage 
obligations (CMOs); mortgage 
pass-through securities
agents, trustee, 479
aggregate indexes, fixed-income, 99
Agnelli Industries, 484–485
Airbus
governmental influences on, 225–226
in method of comparables, 270–271
strategic analysis with, 207–209, 218
Aircastle Limited, 27
aircraft manufacturing industry, 
strategic analysis of, 207–208, 218
airline industry
asset-based equity valuation for, 278
life-cycle stage and business cycle 
sensitivity, 227–228
Air Products and Chemicals, 209
Alcoa, 276
Allianz SE, 165allocationally efficient financial systems, 
59
allocative efficiency, 116n.2
all-or-nothing orders (AONs), 47
alpha, 94
alternative investments
markets for, 15–16
security market indexes for, 101–104
alternative trading systems (ATSs), 
29–30
Ameren, 255
American calls, 330
American depository receipts (ADRs), 
167–168

167–168
American depository shares (ADSs), 167
American puts, 332n.6
American Stock Exchange (AMEX), 168
American-style contracts, 24
AmeriCredit Automobile Receivable 
Trust 2013–4, 509–511
AmeriGas, 210
AMEX. see American Stock Exchange
Amgen, 209
amortization provisions, 512
amortization schedule, residential 
mortgage loan, 487–488
amortizing bonds, 318–320
amortizing loans, 487, 508
anchor, underwritten offerings, 361
Anglo American, 276
AngloGold Ashanti, 276
Anheuser-Busch InBev, 200
annual coupon rate, 404
annualized convexity, 561–562
annualized yield measures, 420
annual modified duration, 542–544
anomalies, market. see market anomalies
ANZSIC. see Australia and New Zealand 
Standard Industrial Classification
AONs. see all-or-nothing orders
Apollo Group, 210
Applied Materials, 209
approximate modified duration, 543–545
APs. see authorized participants
arbitrage
bounds of, 123
and market efficiency, 123
arbitrageurs, 34–36, 123
ArcelorMittal, 622–623, 625
Argentina

Argentina
inflation-linked bonds, 326, 370
MSCI multi-market index, 96
non-sovereign government debt, 650
Ariane space program, 225
ARMs. see adjustable-rate mortgages
Asia. see also  specific countries and 
regions
capitalization level and contributions 
to global GDP , 151
debt and equity outstanding, 350
Asia 50 ADR Index Fund, 169
Asian Developmental Bank (ADB), 372Asian Financial Crisis (1997-1998), 164
Asian-Pacific Aggregate Bond Index, 357
ask prices, 44
ask sizes, 44
ASML Holdings NV, 200–202
asset allocation, 94
asset-backed securities (ABSs), 473–525
about, 473–474
auto loan, 508–511
collateral backing for, 308
collateralized debt obligations, 
512–515
structure, 513
transaction example, 513–515
commercial mortgage-backed 
securities, 503–508
balloon maturity provisions, 505
call protection, 504–505
credit risk, 504
structure, 504–508
creation of, 31–32
credit card receivable, 511–512
defined, 474
economic benefits of securitization, 
474–476
in global debt, 349, 350

474–476
legal identity of issuers, 306
non-mortgage asset-backed securities, 
508–512
auto loan ABS, 508–511
credit card receivable ABS, 511–512
as pooled investments, 19
practice problems, 519–522
repayment sources for, 307
residential mortgage-backed securities, 
490–503
collateralized mortgage obligations, 
497–503
mortgage pass-through securities, 
491–496
non-agency residential mortgage-
backed securities, 503
residential mortgage loans, 485–490
amortization schedule, 487–488
interest rates, 486–487
lender’s rights in foreclosure, 
488–489
maturity, 486
prepayment options and penalties, 
488
securitization, 474–485
economic and market benefits, 
474–476
parties’ roles in transaction,  
478–480
special purpose entities, 482–485
structure of securitization, 481–482
transaction example, 476–478
solutions to problems, 523–525
as structured financial instruments, 
381
traditional bonds vs., 299

I-2 Index
asset-based equity valuation models, 
276–280
for airline industry, 278
defined, 247
for family-owned laundry, 277
other models vs., 246–248, 279–280
for restaurant, 278
returns by, 644–645
security market indexes as proxies for, 94
assets
and classification of markets, 14–16
as collateral, 626
currencies, 19–20
financial, 14
intangible, 277–278
liquidity and sales of, 639
market efficiency and prices of, 118–120
in markets, 14–20
physical, 14
real, 14, 26–28
securities, 16–19
equities, 17–18
fixed-income, 17
pooled investments, 18–19
securitized, 474
underlying, 20
asset swaps, 443
assumptions, of Gordon growth model, 
259–260
ATSs. see alternative trading systems
AT&T
credit curves for, 636–637
industry classification of, 192
and industry structure, 217
auctions, 54, 360, 362–364
Australia
bonds outstanding, 354, 360
domestic and international debt 
securities, 315
foreign bonds, 313
foreign investment, 164
inflation-linked bonds, 326, 327
residential mortgage loans, 487

returns
on bonds and bills, 152–153
on equities, 152–153
risk tolerance and equity ownership, 154
sovereign bonds, 370
Australia and New Zealand Standard 
Industrial Classification 
(ANZSIC), 196
Australian Bureau of Statistics, 196
Australian dollar, 351
Australian Securities Exchange, 154
Austria, 96
authorized participants (APs), 19
auto loan asset-backed securities, 
508–511
automobile industry, similar companies 
in, 189
average life, mortgage pass-through 
securities, 495
B
Baby Boom, 223, 224
backup lines of credit, 375
Bahrain, 96Baker Hughes, 219–221
balance sheets, cash on, 618, 639
balloon payments, 318
balloon risk, 505
BancoFinansur, 509
Banco Santander, 306
Bangladesh, 323
banker’s acceptances, 430–431
Bank for International Settlements, 476
bank guarantees, 309
bank loans, 349, 350, 373–374
Bank of International Settlement, 161
Bank of New York Mellon, 166
bankruptcy
priority of claims in, 599–600
regulations for bankrupt traders, 63

and special purpose entities, 483–485
banks
benefits of securitization for, 475
as brokers, 29
credit cycle assessments by, 598n.7
depository, 166
as financial intermediaries, 32, 33
short-term funding for, 384–390
repurchase and reverse repurchase 
agreements, 386–389
retail deposits, 385
wholesale funds, 385–386
Barrick Gold, 276
barriers to entry
in credit analysis, 612
in strategic industry analysis, 206–208, 
219
barriers to exit, 208
barriers to success, 207
Basel III global framework for bank 
supervision, 601n.12
base prospectus, 478n.3
BASF, 165
Basic Materials and Processing sector, 
193
basis point, 418
defined, 301
price value of, 558
basis point value (BPV), 558
baskets of listed depository receipts 
(BLDRs), 169
BATS, 30
Baxter-FX, 30
BBA. see British Bankers’ Association
bearer bonds, 314
behavioral biases, 137–139
behavioral finance, 136–139
behind the market (term), 45
Belgium, 96, 153, 369
benchmark issue, 368
benchmark rate, 418, 441–443
benchmarks
PSA prepayment, 493

security market indexes as, 94
spread over, 418
benchmark spread, 442
benchmark yield, 574
benchmark yield curve, 443–445
Berkshire Hathaway, Inc., 160, 176
Bermuda-style calls, 331
Bermuda-style puts, 332
best bid, 44best efforts offering, 51, 360
best offer, 44
beta, security market indexes and, 94
BHP Billiton, 276
biases
behavioral, 137–139
survivorship, 102
bid–ask spread, 44, 365–366
bid–offer spread, 365–366
bid prices, 44, 574
bid sizes, 44
bilateral loans, 373, 374
Biomet, 213
BlackRock, 210
BLDRs. see baskets of listed depository 
receipts
block brokers, 28
Bloomberg Barclays
corporate yields, 629–630
minimum issue size and bond holdings 
in indexes, 98
Bond Index, 100, 103, 357
Bloomberg Barclays US Aggregate Bond 
Index, 99, 491n.9
Bloomberg Fixed Income Electronic 
Trading, 365
Bloomberg Fixed Income Relative Value 
page, 444
Bloomberg risk statistic, 558
Bloomberg Yield and Spread Analysis 
page, 547–548, 558, 560–561
blue-chip companies, 173

blue-chip shares, 121n.7
BME Spanish Exchanges, 152
BMW, 218, 270
BNY Mellon, 209
Boeing
effects of government purchases on, 
226
method of comparables for, 270–271
bond(s). see also  fixed-income securities; 
specific types
credit ratings and prices of, 607–608
credit ratings of issuers vs., 603–605
defined, 298, 304
intrinsic value of, 119
legal form of, 305–306
notes vs., 17
returns on equities and bills vs., 
152–153
securitization vs. issue of, 483
as short positions, 40
bond classes
mezzanine, 513
and tranching, 481–482
bond convexity, 559–567
bond equivalent yield, 431–433
bondholders
negotiation on covenants by, 627
shareholders vs., 610–611
bond indenture, 305–313
collateral backing, 307–308
covenants, 310–311, 626
credit enhancements, 308–310
legal identity of issuer/legal form of 
bond, 305–306
repayment proceeds, 306–307

Index  I-3
bond market. see also  fixed-income 
market
developed, 355
emerging, 355
primary, 359–365
private placements, 360, 364–365
public offerings, 360–364
secondary, 359, 365–367
bond portfolios, duration of, 555–557
bonos del Estado, 368
bonus issue of shares (stock dividend), 
249
book building, 50
book runners, 50
book value
in asset-based valuation models, 247
intrinsic vs., 176–177
and market value, 172
in ROE, 172–173
borrowing
and equilibrium interest rate, 12
as financial system function, 8–9
Boston Scientific, 213
Botswana, 96
bottom-up approach to equity valuation, 
244
BP , 209
BPV. see basis point value
Brady bonds, 357
Brazil
inflation-linked bonds, 326
sovereign bonds, 369, 370
breakeven reinvestment rate, 439
bridge financing, 374
Brightman, Christopher J., 116n.1
Brink’s Home Security, 199–200
British American Tobacco, 209
British Bankers’ Association (BBA),  
353
British Financial Services Authority, 29
British pound, 19, 351

British Telecom, 324, 634–635
broad market equity indexes, 95
broker–dealers, 30
brokered markets, 55, 57
brokers
clearinghouses for, 36
and dealers, 30–31
as financial intermediaries, 28–29
lending by, 33
prime, 33, 49
Brown, George Garvin, 262
Brown-Forman Corporation, 262–264
Buenos Aires, Argentina, 650
Buffett, Warren, 176
Bulgaria, 96
bulldog bonds, 313
bullet bonds, 318–320
bullet loans, 374
bullet mortgages, 488
Bundesanstalt für 
Finanzdienstleistungsaufsicht, 29
Bunds, 300, 367, 368, 630
Burlington Northern, 209
business-cycle sensitivities, 190–191, 
227–228business environment, in industry 
analysis, 188
buyback (share repurchase), 249
buyers, power of, 205, 612
C
Cadbury, 209, 219–221
calendar anomalies, 131–132
California, 650, 651
callable bonds, 330–331, 379, 424
effective convexity of, 567
effective duration of, 545–546
interest rate risk with, 553–554
zero-coupon bonds as, 382
callable common shares, 158–159, 171
callable preference shares, 160, 171, 254
call markets, 54

call money rate, 41
American, 330
Bermuda-style, 331
defined, 24
as embedded options ( see callable 
bonds)
European, 331
make-whole, 330
call premium, 330
call price, 330
call protection period, 330, 424
call provisions, 322
calls. see call options
call schedule, 330
Cameco Corporation, 274–275
Canada
auctions in, 362
credit rating services, 602
income trusts, 225
international investments, 165
NAICS system, 197
residential mortgage loans, 486, 487
retractable term preferred shares, 256
returns
on bonds and bills, 153
on equities, 153
risk tolerance and equity ownership, 
154
securities backed by quasi-government 
entities, 490
Canadian dollar, 351
Canon Inc., 271–272
capacity, 611–625
and company fundamentals, 613–617

and industry fundamentals, 613
and industry structure, 612
and issuer liquidity, 618
in strategic industry analysis, 211–212, 
219
of Watson Pharmaceuticals, Inc., 
618–625capital
cost of, 178
debt/capital ratio, 616
net working, 618
raising equity, 9
requirements, 61–62
ROIC, 204
venture, 15, 162
WACC, 178, 204
working, 618, 639
capital allocation, efficiency of, 13–14
capital asset pricing model (CAPM)
for cost of equity, 178
Fama and French three-factor model 
vs., 133
required rate of return from, 254
security market indexes as proxy, 94
capital budgeting, 178
capital expenditures (capital projects), 
8, 9, 618
capital gains, 316, 533, 569
capital-indexed bonds, 327
capital losses, 316, 533–535, 569
capital markets, 13–15
capital market securities, 300
capital protected instruments, 382
capital structure, 595, 642
capped floating interest rate, 511
caps, floating-rate note, 324
carbon credits, 10
Carrefour Group, 210

carrying value, 247, 533. see also  book 
value
case study, Watson Pharmaceuticals Inc., 
618–625
cash, on balance sheets, 618, 639
cash collateral accounts, 309–310
cash flow from operations (CFO), 252, 
615n.24, 618, 639
cash flows
for collateralized debt obligations, 
514–515
in credit analysis, 615–616, 618
discounting of, 246–247
excess interest, 509
for mortgage pass-through securities, 
491, 493–494
of non-agency RMBSs, 503
operating, 252, 618, 639
for plain vanilla bonds, 302, 318
cash flow structures, 318–329
coupon payment, 323–329
principal repayment, 318–323
cash flow yield, 555
cash market securities, 437
cash reserve funds, 309
cash settlement, 20, 366
Caterpillar Inc., 198, 209, 219
CBOs. see collateralized bond 
CCR. see corporate credit rating
CDOs. see collateralized debt  
central bank funds market, 385
central bank funds rates, 385
central banks, 358, 598n.7

I-4 Index
Central Europe, 350. see also  specific 
countries
century bonds, 377, 442
certificates of deposit (CDs), 386
performance standards of, 61
Standards of Professional Conduct, 
49, 51
CFD. see contracts for difference
CFO. see cash flow from operations
CFR. see corporate family rating
change of control covenant, 626n.26
change of control put option, 643
character, in four Cs framework, 611, 627
Chartered Financial Analyst Program, 61
Chicago Mercantile Exchange, 29, 209
Chile, 96, 326, 370
China
foreign investment in, 164
as growth country, 190n.2
industrialization, 211
market efficiency, 121
in MSCI multi-market index, 96
securitization pilot program, 475
China Mobile Ltd., 192
Chi-X Europe, 30
Cisco Systems, 209
Citibank, 166
Citigroup Commercial Mortgage Trust 
2013-GCJ11, 506–508
clean price, 413
clearinghouses, 22, 36
clearing instructions, 44, 49–50
Clearstream, 366, 380

CLOs. see collateralized loan obligations
closed-end funds, 18–19, 133–134
closing day, 362
Coca-Cola, 176, 209, 211
CoCos. see contingent convertible bonds
Coinstar, Inc., 199
collateral(s)
for bond indenture, 305
default rate for, 503
in four Cs framework, 611, 625–626
and repo margin, 388
and repo rate, 387
collateral backing, 307–308, 379
collateralized bond obligations (CBOs), 
512
collateralized debt obligations (CDOs), 
512–515
as structured financial instruments, 381
collateralized loan obligations (CLOs), 
513
(CMOs), 497–503
defined, 497
with floating-rate tranches, 501mortgage pass-through securities vs., 
497
backed securities vs., 503
with planned amortization class 
tranches, 499–501
with sequential-pay structures, 
497–499

497–499
with support tranches, 499–501
collateral managers, 513
collateral trust bonds, 307
Colombia, 96, 326
combinations, stock, 157
commercial banks, 32, 33
commercial industry classification 
systems, 192–196
example, 194–196
GICS standard, 192
ICB system, 192–193
representative sectors in, 193–194
RGS system, 192
(CMBS), 503–508
commercial paper (CP), 374–377
credit quality, 375–376
issuance of, 639n.34
issuers, 374
US vs. Euro markets, 376–377
committed bank lines, 618
commodities, 14, 21, 25–26
commodity indexes, 101
Commodity Research Bureau (CRB) 
Index, 101
commodity swaps, 24
common shares, 156–159
callable, 158–159, 171
defined, 156
and fixed-income securities, 298
at Ford Motor Company, 157–158
and preference shares, 159–160
preferred vs., 17–18
putable, 159, 171
at Viacom Corporation, 156–157
350
companies

350
companies
as bond issuers, 299
borrowing by, 8
cyclical, 190–191, 221, 613
fundamentals of, 613–617
non-cyclical, 190–191, 613
securitization benefits for, 475
similar, 189–191
value of, 172–178, 204
variability of recovery rates for, 599
companion (support) tranches, 499–501
company analysis, 228–232
defined, 188
elements of, 229–232
and industry analysis, 614–615
spreadsheet modeling in, 232
comparables. see method of comparables
in strategic analysis, 205competitive position, as fundamental, 613
competitive strategy
and capacity, 612
in company analysis, 228
complete markets, 58
compounded yield measures, 420
compounding conversions, 421–422
computer hardware industry, 222–223
concavity, 567
concentration, industry, 208–211, 219
conditional prepayment rate (CPR), 492, 
493
confections industry, 219–221
conforming mortgages, 490
conservatism, 138
conservatorship, 490n.8
consols, 368, 550
constant-yield price trajectory, 410, 411

constituent securities, 78, 91
construction industry, 225
Consumer Discretionary sector, 193
Consumer Price Index for All Urban 
Consumers (CPI-U), 370
Consumer Staples sector, 193
contingency provisions, 298, 329–335
callable bonds, 330–331
convertible bonds, 332–334
with corporate notes/bonds, 379–380
putable bonds, 332
contingent convertible bonds (CoCos), 
334
contingent liabilities, 648
continuous trading markets, 54, 56–57
contraction risk, 492
contract markets, 20–25, 54–58
contracts for difference, 20–21
execution mechanisms, 54–57
forwards, 21–22
futures, 22–23
insurance contracts, 25
market information systems, 58
options, 24–25
swaps, 23–24
trading sessions on, 54
contract rates, mortgage, 486–487
contracts
American- vs. European-style, 24
currency, 39
derivative, 15
insurance, 25
short positions in, 39–41
sides of, 39
spot, 20
contracts for difference (CFD), 20–21
contrarian effect, 91
conventional bonds, 301. see also  plain 
vanilla bonds

conversion premium, 333
conversion price, 333
conversion ratio, 333
conversion value, 333
convertible bonds, 332–334, 379–380
convertible common stock, 157
convertible mortgages, 487
convertible preference shares, 161
convexity, 559–567
annualized, 561–562
of credit risk/return, 633–634

Index  I-5
effective, 566–567
money, 564–565
and return, 530
convexity adjustment, 560–563
convexity effect, 407–409, 567
corporate bonds, 377–380
earnings surprise for, 135n.43
legal issuers of, 306
sources of repayment for, 307
corporate credit rating (CCR), 603
corporate debt, 373–381
bank and syndicated loans, 373–374
commercial paper, 374–377
corporate notes and bonds, 377–380
corporate debt securities, 610–628
corporate family rating (CFR), 603
corporate governance, for private equity 
firms, 163
corporate notes, 377–380
corporate profile, in company analysis, 
229
corporate sector, 349
corporate structure, in high-yield credit 
analysis, 642–643
corporate treasurers, 6
corporations, real assets of, 27
cost of capital, 178
cost of debt, 177
cost of equity, 177–178
costs
fixed, 612
information-acquisition, 123–124
transaction, 9, 123
counterparty risk, 22, 36
coupon effect, 408, 409
coupon payment structures, 323–329
corporate notes/bonds, 378
credit-linked coupon bonds, 324–325
deferred coupon bonds, 325

floating-rate notes, 323–324
index-linked bonds, 325–328
payment-in-kind coupon bonds, 325
step-up coupon bonds, 324
coupon rate, 300–301, 403–405, 
550–551
coupon-type classification for fixed-
income markets, 352–353
Covenant Review, 627
covenants, 310–311
affirmative, 310, 626
in four Cs framework, 611, 626–627
in high-yield credit analysis, 643–644
limitations on liens, 644
maintenance, 644
negative, 310–311, 626
restricted payments, 644
coverage ratios, 617, 651–652
covered bonds, 308
covering, of positions, 40
CPI. see French consumer price index; 
US Consumer Price Index
CPI-U. see Consumer Price Index for All 
Urban Consumers
CPR. see conditional prepayment rate
CRB Index. see Commodity Research 
Bureau Indexcredit analysis, 591–670
capital structure in, 595
for corporate debt securities, 610–628
defined, 592–594
return vs., 628–637
four Cs framework, 610–628

character, 627
collateral, 625–626
covenants, 626–627
Watson Pharmaceuticals Inc. case 
study, 618–625
functions of, 592
high-yield, 638–645
corporate structure in, 642–643
covenant analysis, 643–644
debt structure and leverage in, 
640–642
equity-like approach to, 644–645
financial projections for, 639–640
liquidity in, 638–639
and non-investment grade ratings, 638
for non-sovereign government debt, 
650–652
practice problems, 656–665
by ratings agencies, 601–610
credit ratings, 602–603
issuer vs. issue ratings, 603–605
risks of relying on ratings, 605–608
use of ratings, 601–602
recovery rates in, 597–600
seniority ranking in, 595–597
solutions to problems, 666–670
for sovereign debt, 645–650
flexibility and performance profile, 
647–648
political and economic profile, 647
in Portugal, 649–650
sovereign debt defaults, 645–646
credit card networks, barriers to entry 
for, 206–207
credit card receivable asset-backed 
securities, 511–512
credit crisis (2007-2009), 160, 309

credit curve, 636–637
credit cycle, 598–599, 631
credit default swaps (CDSs), 25, 34
credit duration, 546, 574
credit enhancements
for auto loan ABSs, 509
and bond indenture, 308–310
defined, 305
external, 309–310, 479
internal, 308–309, 479
with non-agency RMBSs, 503
in securitizations, 479
credit-linked notes (CLNs), 382
credit migration risk, 593
credit quality
classifying fixed-income markets by, 
350–351
of commercial paper, 375–376
of sovereign bonds, 368–369
credit ratings
basis for, 602–603
for issuer vs. issue, 603–605non-investment grade, 638
risks of relying on, 605–608
and special purpose entities, 482, 483
use of, 601–602
credit ratings agencies, 601–610
basis for ratings, 602–603
fallibility of, 608
credit risk, 592–594
with commercial mortgage-backed 
securities, 504
with corporate notes/bonds, 379
with fixed-income securities, 299–300, 
574–575

574–575
with floating-rate bonds, 426
with floating-rate notes, 323
with repurchase agreements, 388
and yield-to-maturity, 433
Credit Roundtable, 627
credit services, financial institutions’ , 32
credit spreads
and credit ratings, 607
defined, 482–483
term structure of, 419
Credit Suisse, 210
credit tranching, 308–309, 481
Croatia, 96
cross-default provisions, 604
crossing networks, derivatives pricing 
rule for, 57
cross-sectional pricing anomalies, 130, 
133
cumulative preference shares, 160, 171
cumulative voting, 156
currency(-ies), 14
351
for fixed-income securities, 301–302
in markets, 19–20
for sovereign bonds, 368–369
in sovereign credit analysis, 647
currency contracts, 39
currency option bonds, 302
currency swaps, 24
current yield, 304, 423
curve duration, 538, 545, 548, 562
custodial services, by financial 
intermediaries, 36–37
customers, power of, 612
The Customers’ Afternoon Letter,  78

cyclical companies, 190–191, 221, 613
Czech Republic, 96
D
Daimler, 189, 209, 270
Daimler Chrysler, 168
dark pools, 29
data mining, 130
data snooping, 130
Davide Campari-Milano S.p.A., 658–
659, 667
day-of-the-week effect, 132
day order, 48
DBRS. see Dominion Bond Rating 
Service
DBS Bank, 161

I-6 Index
DBS Group Holdings, 161
DDM. see dividend discount model
dealer markets. see quote-driven markets
dealers
and arbitrageurs, 34–36
and brokers, 30–31
primary, 30, 364
debentures, 307
DeBondt, Werner, 132
debt. see also  collateralized debt 
obligations (CDOs)
amount of debt coming due, 618
corporate, 373–381
cost of, 177
defined, 297
external, 647
FCF after dividends/debt ratio, 617
FFO/debt ratio, 617
fixed-rate, 352
floating-rate, 352
in high-yield credit analysis, 640–642
lien, 596
market value of, 274–275
mortgage, 596
net, 616
non-sovereign government, 650–652
secured, 595, 596
seniority rankings of, 595–597
sovereign, 645–650
credit analysis for, 645–650
647–648
subordinated, 596–597
unsecured, 595, 596
debt/EBITDA ratio, 616
debt instruments, 15

debt markets, credit analysis in, 592
debt securities. see also  fixed-income 
corporate, 610–628
equity vs., 155
debt service coverage ratio (DSCR), 504, 
651–652
declaration date, 249
decline stage (industry life-cycle), 215
deeds, trust, 305, 626
default(s)
loss given, 592
price reaction to, 118–119
recovery rates for, 597–600
sovereign debt, 645–646
strategic, 488
default interest rate, 505
default probability, 592
default rates
for collateral, 503
by credit rating, 605–606
and credit risk/return, 635–636
default risk, 592, 593
defeasance, 505
defensive industries, 190, 191, 221deferred coupon bonds, 325, 378
defined-benefit pension schemes, 
546–547
delivery
in spot market trading, 10
Dell Computer, 209
demand, 230, 352, 631
demographic influences
in industry analysis, 203, 223–224
and industry life-cycle, 217
in strategic analysis, 220
Denmark
domestic and international debt

Denmark
residential mortgage loans, 486–488
returns on bonds, bills, and equities, 
153
depositary receipts (DRs), 18, 166–169
depositories, 19, 37
depositors, in securitization process, 478
depository banks, 166
depository institutions, 32–33
deposits, retail, 385
derivative contracts, 15
derivatives pricing rule, 57
Deutsche Bank, 166
Deutsche Börse, 29, 152, 209, 333
Deutsche Securities, 30
Deutsche Telekom AG, 272–273
developed bond markets, 355
DeVry University, 210
DHL International, 209
Diageo, 209
differentiation strategy, for companies, 
228
direct investing
in non-domestic equity securities, 
165–166
in real assets, 26
Directive for Criminal Sanctions for 
Market Abuse, 122n.11
disclosure
and market efficiency, 122
standards for exchanges, 29
discount bonds, 531, 551
discounted cash flow models, 246–247. 
see also  present value models
discounting, 16, 246–247
discount margin, 426–429
discount rates, 429–430
discounts, 133–134, 403–406

discriminatory pricing rule, 56
disintermediation, 475
displayed orders, 47–48
display size, of orders, 47
divest (term), 8
dividend discount model (DDM)
defined, 246
description, 251–254
dividends and, 248–250
Gordon growth model vs., 260
as present value model for equity 
valuation, 248–264
three-stage, 262
two-stage, 261–264dividend per share (DPS), 279–280
dividend reinvestment plans (DRPs), 52
dividends
calculating, from DDM, 261
and DDM, 248–250
and free cash flow, 616
and Gordon growth model, 257, 260
payments-in-lieu of, 40
on preference shares, 159–160
reinvested, 169–170
at Viacom Corporation, 157
divisor, price return index, 79
DJIA. see Dow Jones Industrial Average
dollar, Australian, 351
dollar, Canadian, 351
dollar, Hong Kong, 351
dollar, US
foreign exchange gains, 169
international bonds outstanding in, 
351
as reserve currency, 19
spot market trading of, 10
dollar duration, 557

domestic bonds, 313, 314, 354
Dominion Bond Rating Service (DBRS), 
602
Dow, Charles H., 78, 83
Dow Jones Average, 78
Dow Jones & Company
company classifications, 192
formulation of Nikkei Stock Average, 
103
ICB development, 192
Dow Jones Industrial Average (DJIA)
creation of, 78
features of, 103
as gauge of market sentiment, 93
price weighting of, 83
Dow Jones Transportation Average, 78
downgrade risk, 593
DPS. see dividend per share
DRAM & Flash Product, 209
Dreyer’s Grand Ice Cream Holdings, 
Inc., 159
DRPs. see dividend reinvestment plans
DRs. see depositary receipts
dry-bulk shipping industry, 211–212
DSCR. see debt service coverage ratio
dual-currency bonds, 301–302
dual listing, of shares, 164–165
Dubai International Financial Exchange, 
167
duration
approximate modified, 543–545
of bond portfolio, 555–557
credit, 546, 574
and credit risk/return, 634–635
curve, 538, 545, 548, 562
defined, 538
dollar, 557
effective
calculating, 545–548
of callable bonds, 553–554

of putable bonds, 554
inflation, 574
key rate, 549
liquidity, 574

Index  I-7
Macaulay
calculating, 538–542
and interest rate risk/investment 
horizon, 569–574
and modified duration, 549–551
of portfolio, 555–557
modified
annual, 542–544
approximate, 543–545
calculating, 542–543
and credit risk/return, 633–635
and effective duration, 547–548
and Macaulay duration, 549–551
money, 557–559, 572
OAS, 548
partial, 549
properties of, 549–554
real rate, 574
yield, 538, 545, 548, 562
DURATION financial function, 541n.2
duration gap, 573
dynamic random access memory, 210
E
EADS. see European Aeronautic Defense 
and Space Company
early amortization provisions, 512
early repayment option, 488
earnings announcements, 134–135
(EBITDA)
in credit analysis, 615
EBITDA/interest expense ratio, 617
enterprise value/EBITDA ratio, 645
in enterprise value multiples, 274
earnings before interest and taxes (EBIT)
EBIT/interest expense ratio, 617

earnings per share (EPS), 279–280
earnings surprises, 134–135
Eastern Europe, 350. see also  specific 
countries
taxes
Echo Boomers, 224
ECNs. see electronic communications 
networks
economic conditions, yield spread and, 
631
economic profits, in strategic analysis, 204
economic structure, in sovereign credit 
analysis, 647
economy, securitization and, 474–476
E C P.  see Eurocommercial paper market
effective annual rate, 420
effective convexity, 566–567
effective duration
of putable bonds, 554efficiency
of capital allocation, 13–14
of financial systems, 58–59
market ( see market efficiency)
efficient market hypothesis, 124, 
128–129
efficient markets
description of, 117–119
intrinsic value in, 119–120
semi-strong-form, 125–128
strong-form, 128

weak-form, 125, 128, 129
Egypt, 96
EIB. see European Investment Bank
electronic communications networks 
(ECNs), 29–30
embedded options, 329, 424. see also  
callable bonds; putable bonds
EMBI Global. see J.P . Morgan Emerging 
Market Bond Index Global
embryonic stage (industry life-cycle), 
214
EMC, 209
emerging bond markets, 355
emerging markets
securitization in, 475
sovereign debt of, 646
technical analysis for, 125
World Bank definition of, 646n.42
Energy sector, 193
Enron, 608
enterprise, NAICS definition, 197
enterprise value (EV), 645
enterprise value multiples, 247
in models for equity valuation, 
274–276
EPRA. see European Real Estate 
equal weighting, of security market 
indexes, 85–86
equilibrium interest rate, 12–13
equipment trust certificates, 307–308
equity. see also  return on equity (ROE)
cost of, 177–178
shareholders’ , 174

equity analysis, of corporate debt 
securities, 610–611
equity capital, raising, 9
equity derivatives, 15
equity indexes, 95–97
equity-like approach to high-yield 
analysis, 644–645
equity-related bonds, 334
equity securities (equities), 17–18, 
149–185
and company value, 172–178
accounting return on equity, 172–177
cost of equity and investors’ required 
rates of return, 177–178
debt securities vs., 155
in global finance markets, 150–155
importance of, 149–150
international ownership comparisons 
for, 154–155
liquidity and issuance of, 639non-domestic, 164–169
depositary receipts, 166–169
direct investing in, 165–166
practice problems, 180–183
private vs. public, 162–164
return characteristics, 169–170
returns on, 152–154
risk characteristics, 170–171
solutions to problems, 184–185
types of, 155–161
preference shares, 159–161
volatility of, 153–154
equity swaps, 24
equity tranche, 504
equity valuation, 243–292
asset-based, 276–280
for airline, 278

estimated value and market price in, 
245–246
multiplier models, 265–276
enterprise values in, 274–276
example, 272–273
fundamentals in, 266–267
method of comparables, 269–272
price multiples in, 266–269
practice problems, 283–288
present value models, 248–264
examples, 253
Gordon growth model, 256–261
multistage, 261–264
preferred stock valuation with, 
254–256
share value for three-year investment 
horizon, 252
purpose, 244
solutions to problems, 289–292
establishment, NAICS definition, 197
estimates
of enterprise value and market value of 
debt, 274–275
of equity value and market price, 
245–246
of intrinsic value, 119
Estonia, 96
ETNs. see exchange-traded notes
Eurex, 29
Euribor. see Euro interbank offered rate
euro, 10, 19, 351
Eurobonds
coupon payment structure for, 323

Eurobonds
defined, 314
foreign and domestic bonds vs., 354
in global bond market, 313
in secondary market, 365–366
settlement of, 380
Euroclear, 366, 380
Eurocommercial paper (ECP) market, 
376–377
Eurocopter, 225
Eurodollar bonds, 314
Eurofighter consortium, 226

I-8 Index
Euro interbank offered rate (Euribor), 
301, 353
regions
corporate notes and bonds, 377
industrial comparative ratio analysis, 
617
maturity of mortgages, 486
residential mortgage loans, 488
152–153
securities ranked lower than 
subordinated debt, 596
use of enterprise value, 274
European Aeronautic Defense and Space 
Company (EADS), 225–226, 271
European calls, 331
European Investment Bank (EIB), 372
European Model Covenant Initiative, 627
European Parliament, 122n.11
European puts, 332
European Real Estate Association 
(EPRA), 101, 102
European-style contracts, 24
insider trading laws in, 122
European Union (EU), 151, 357, 484n.5, 
646
Euroyen bonds, 314
Eurozone, inflation-linked bonds, 370
EV. see enterprise value
event risk, 608
event studies, in semi-strong efficient 
markets, 126
excess interest cash flow, 509
excess spread, 309, 509

excess spread accounts, 309
exchanges, 29
exchange-traded funds (ETFs), 19, 95, 
169
exchange-traded notes (ETNs), 19
ex-dividend date (ex-date), 249
execution instructions, 44–48
execution mechanisms, secondary 
market, 54–57
exercise price, 18
expansion risk, 492
expected loss, credit risk and, 593
expenditures, capital (capital projects), 
8, 9, 618
expenses, interest, 617, 648
experience curve, 203
exposure instructions, for orders, 47
external credit enhancements, 309–310, 
479
external debt, 647
external influences on industry analysis, 
222–228
demographic, 223–224
governmental, 224–226
macroeconomic, 222
social, 226–227
technological, 222–223
external liquidity, in sovereign credit 
extra dividend (special dividend), 248–249
ExxonMobil, 209F
face value. see par value
fairly valued (term), 245
fallibility, of rating agencies, 608
Fama, Eugene, 124, 133
Fama and French three-factor model, 
133
Fannie Mae. see Federal National 
Mortgage Association
FASB. see Financial Accounting

Fastenal, 210
FCFE model. see free-cash-flow-to-
equity model
Federal Home Loan Banks (FHLB), 323, 
372
Federal Home Loan Mortgage 
Corporation (Freddie Mac), 323, 
372, 490, 503
Federal National Mortgage Association 
(Fannie Mae), 323, 372, 490, 503
Federal Reserve
funds and fund rate of, 385
initial margin requirement of, 41
Regulation T, 41
Federal Reserve Bank of New York, 364
FedEx, 209
Fed funds, 385
Fed funds rate, 385
Ferrellgas, 210
FHLB. see Federal Home Loan Banks
Fideicomiso Financiero Autos VI, 509
Fidelity, 210
fill or kill orders, 48
finance charges, 511
(FASB), 61
financial analysts
decisions of, 6
industry analysis by, 202–203
market efficiency and number of, 121
financial assets, 14
353n.3

353n.3
financial corporations, as intermediaries, 
32–33
financial crisis (2008-2009)
bond defaults, 601n.11
and credit enhancement, 503
credit ratings agencies contribution, 
602
liquidity issues, 594, 639
and risk-free rate, 645–646
and securitization, 475, 479
sovereign ratings, 368–369
and yield spread, 631
financial disclosure, market efficiency 
and, 122
financial industry, governmental 
influences on, 225
financial institutions, 32–33financial intermediaries, 28–38
arbitrageurs, 34–36
brokers, exchanges, and alternative 
trading systems, 28–30
dealers, 30–31, 34–36
defined, 6
depository institutions and financial 
corporations, 32–33
insurance companies, 33–34
securitization of real assets by, 26
securitizers, 31–32
for settlement and custodial services, 
36–37
transactions facilitated by, 38
in well-functioning financial systems, 
58–59
financial leverage, 41–44
financial markets. see markets

financial projections, in high-yield credit 
analysis, 639–640
financial ratios, in company analysis, 
230–232
financial reporting, regulations on, 61
Financial Services Authority, 353
Financial Services sector, 193
Financial Stability Board (FSB), 476
financial statistics, in company analysis, 
231–232
financial system
efficiency of, 58–59
functions of, 6–14
capital allocation efficiency, 13–14
determining rates of return, 12–13
for individuals, 7–12
well-functioning, 58–60
Financial Times Stock Exchange (FTSE), 
192
Finland, 96, 153, 487
firearms industry, governmental 
firm commitment offerings. see 
underwritten offerings
first lien debt, 596
first loss piece, 504
first mortgage debt, 596
First Section, in TOPIX, 82
fiscal performance, in sovereign credit 
analysis, 647–648
Fitch Ratings
commercial paper ratings, 375
investment-grade ratings, 299n.2, 350
long-term ratings matrix, 602–603
municipal debt ratings, 651
role in credit markets, 601, 602

sovereign ratings, 368
five forces framework for strategic 
industry analysis, 205–206
fixed costs, capacity and, 612
fixed income analysts, 6
fixed-income derivatives, 15
fixed-income indexes, 98–100, 357–358
fixed-income instruments, 15, 17
fixed-income market, 347–400
classification of, 348–357
function of, 347–348

Index  I-9
indexes, 357–358
investors in, 357–359
non-sovereign bonds, 371–373
practice problems, 393–396
private placements, 364–365
quasi-government bonds, 372–373
secondary, 365–367
short-term funding for banks, 384–390
solutions to problems, 397–400
sovereign bonds, 367–371
credit quality, 368–369
names of, 367–368
types, 369–370
structured financial instruments, 
381–384
leveraged instruments, 383
participation instruments, 382–383
yield enhancement instruments, 382
supranational bonds, 372–373
fixed-income securities, 297–346
with contingency provisions, 298, 
329–335

329–335
coupon rate, 300–301
credit risk with, 299–300, 574–575
currency denomination for, 301–302
interest rate risk with, 537–574
approximate modified duration, 
543–545
duration of bond portfolio, 555–557
effective duration, 545–548
and investment horizon, 569–574
key rate duration, 549
Macaulay duration, 538–542, 
569–574
modified duration, 542–543
money duration, 557–559
price value of a basis point, 558
properties of bond duration, 549–554
yield volatility, 568–569
investing in, 298
issuers of, 299–300
legal and regulatory considerations, 
313–316
liquidity risk with, 574–575
maturity, 300
par value, 300
in portfolio management, 298
practice problems, 339–342return on, 530–537
solutions to problems, 343–346
tax considerations, 316–318
yield measures, 304
fixed-income valuation, 401–471
about, 401–402
flat price, 413–417
full price, 413–417
matrix pricing, 417–420

maturity structure of interest rates, 
433–441
practice problems, 449–457
solutions to problems, 458–471
and time value of money, 402–413
market discount rate, 402–411
spot rates, 411–413
yield to maturity, 406–407
yield measures, 420–433
for fixed-rate bonds, 420–425
for floating-rate notes, 425–429
for money market instruments, 
429–433
yield spreads, 441–445
fixed-rate bonds
sovereign, 369
yield measures for, 420–425
fixed-rate debt, 352
fixed-rate mortgages, 486
Flaherty, James, 225
flexibility, in sovereign debt credit 
float-adjusted market-capitalization 
weighting, 87, 89, 90
floaters. see floating-rate notes (FRNs)
floating interest rates, capped, 511
floating-rate bonds (floaters)
inverse, 383
outstanding, 334
as participation instruments, 382–383
floating-rate debt, 352
floating-rate notes (FRNs)
cash flows from, 323–324
as corporate debt, 378
coupon rate for, 301
inverse, 324
yield measures for, 425–429

floating-rate tranches, 501
floors, floating-rate note, 324
Ford Motor Company
credit ratings, 607
P/S value of, 269
share class arrangements, 157–158
similar companies to, 189
foreclosures, 485, 488–489
foreign bonds, 313–314, 354
forward curves, 438–441
forward markets, 437
forward rates, 436–440
forwards
in commodities, 25
in contract markets, 21–22
futures vs., 23
options vs., 25
swap contracts vs., 24
forward yields, 438four Cs framework for corporate debt 
securities, 610–628
fragile information cascades, 138
franc, Swiss, 19, 351
France
overconfidence and mispricing in 
markets, 137
153
sovereign bonds, 367
Frankfurt Stock Exchange, 165

fraud, 34, 61
Freddie Mac. see Federal Home Loan 
Mortgage Corporation
free cash flow after dividends, 616
free cash flow before dividends, 616
free-cash-flow-to-equity (FCFE) model, 
246, 252–253
616n.25
free float, 165n.23
free-float-adjusted market-
capitalization-weighted indexes, 
87
Freeman Spogli & Co., 163
Freeport-McMoRan Copper & Gold, 276
Freescale Semiconductor, 640–642
French, Kenneth R., 133
French consumer price index (CPI), 370
FRNs. see floating-rate notes
Frontiers of Finance Survey, 136
Frontline, 210
FSB. see Financial Stability Board
FTC. see US Federal Trade Commission
FTSE. see Financial Times Stock 
Exchange
FTSE 100 Index, 82
FTSE EPRA/NAREIT Global Real Estate 
Index Series, 101–103
FTSE Global Bond Index Series, 357
FTSE Global Small Cap Index, 94
Fujifilm, 223
fully amortized bonds, 318–320
fully amortizing loans, 487
fundamental analysis, 128–129
fundamentals
company, 613–617
industry, 613

in multiplier models, 266–267
fundamental value, 119, 244. see also  
intrinsic value
fundamental weighting
in multi-market equity indexes, 96
of security market indexes, 89, 91
funding, short-term. see short-term 
funding
funds from operations (FFO), 615

I-10  Index
futures
in commodities, 25, 26
in contracts market, 22–23
forwards vs., 23
rollover of, 102
G
G-20. see Group of Twenty
gains
capital, 316, 533, 569
foreign exchange, 169
Galileo space program, 225
GDRs. see global depository receipts
GE Capital Bank, 512
GE Capital Corporation, 512
GE Capital Credit Card Master Note 
Trust Series 2013-1, 512
General Dynamics, 209
General Motors, 189, 209, 269
general obligation (GO) bonds, 650
Genomic Solutions, 158–159
Genzyme, 209
geographic classifications for fixed-
income markets, 354–355
geometric average of forward rates, 441
Germany
auctions, 362
fixed-income indexes, 357
investments in BASF, 165
non-sovereign government bonds, 371
153
154

153
154
sovereign bonds, 367–369
Ghana, 96
GICS. see Global Industry Classification 
Standard
Gillette, 176
gilts, 367, 368
Ginnie Mae. see Government National 
in pharmaceutical industry, 189
ROE for, 173–175
strategic analysis, 219–221
global bonds, 314
global debt markets, 349–350
global depository receipts (GDRs), 167
global equity markets, 349–350
global finance markets
and depository receipts, 166–169
direct investing, 165–166
equity securities in, 150–155
integration and growth in, 164–165
Global Industry Classification Standard 
(GICS), 189, 190, 192
Global Investment Performance 
Standards, 61
global registered shares (GRSs), 168GO bonds. see general obligation bonds
gold, forward contracts on, 21–22
Goldcorp, 276
Goldman Sachs
callable preference shares, 160
as dealers, 30
industry concentration and pricing 
power, 209
QUIDS at, 300
good-on-close orders, 48
good-on-open orders, 48
good-till-cancelled orders (GTCs), 48

Gootkind, Christopher L., 608n.21
applying, 258–259
justified value of price multiple from, 
266
with no current dividend, 260–261
governmental debt. see sovereign debt
governmental industry classification 
systems, 196–197
ANZSIC system, 196
ISIC system, 196
NACE system, 196
governmental influences
in industry analysis, 203, 224–226
government and government-related 
sector, 348–349
government equivalent yield, 423
Government National Mortgage 
Association (Ginnie Mae), 490, 
503
government-sponsored enterprises 
(GSEs), 371, 490
Greece, 96, 487
greenfields, constructing, 211
grey market, 361
gross domestic product (GDP)
contributions to global, 150–151
and governmental debt, 648
Group of Twenty (G-20), 476
growth, industry, 613
growth cyclical companies, 191n.3
growth industries, 190, 191, 221
growth stage (industry life-cycle), 
214–215
growth stocks, 97

214–215
GRSs. see global registered shares
Grupa Zywiec SA, 658, 666
GSEs. see government-sponsored 
enterprises
G-spread, 442, 445
GTCs. see good-till-cancelled orders
guarantee certificates, 382
H
haircut, 388
Halliburton, 219–221
Harley-Davidson, Inc., 479–480, 482
Harley-Davidson Credit Corp.,  
479, 480
Harley-Davidson Motorcycle Trust 
2005-2, 479, 480
Harmonized Index of Consumer Prices 
(HICP), 370
HBOS, 324Health Care sector, 193
heavy truck industry, similar companies 
in, 189
hedge fund indexes, 102
hedge funds, 15, 19, 102
hedgers, 9–10, 21, 39
herding behavior, 137
Hershey, 219–221
Hewlett-Packard Company, 200, 209
HFRX Equal Weighted Strategies EUR 
Index, 104
HFRX Global Hedge Fund Index, 104
hhgregg, 162
Hibor. see Hong Kong interbank offered 
rate
HICAP . see Harmonized Index of 
Consumer Prices
hidden orders, 47–48
high yield bonds. see non-investment-
grade bonds
high-yield credit analysis, 638–645
debt structure and leverage in,

640–642
and non-investment grade  
ratings, 638
high-yield indexes, 99
Hillenbrand, Inc., 199
HM Treasury, 306
holder-of-record date, 249
holding companies, 306, 642
holding-period rate of return, 571
holding periods, for private equity 
investments, 163
holiday effect, 132
Home Depot, 208, 216–217
Honda Motor Company, 189, 270
margin requirements of, 41
Hong Kong dollar, 351
Hong Kong interbank offered rate 
(Hibor), 301, 353
Hong Kong Stock Exchange, 152, 167, 
333
horizon yield, 532–536, 571
housing industry, demographic 
influences in, 224
H&R Block, Inc., 199
human-capital based companies, 
collateral of, 626
Hungary, 96
Hurricane Katrina, 212
hybrid mortgages, 487
hybrid securities, 596n.4
Hynix, 209
Hyundai, 189
I
IBM, 443, 444
ICB. see Industry Classification 
Benchmark
iceberg orders, 47

Index  I-11
ICMA. see International Capital Market 
IG Group plc, 30
IKEA, 164
immediate or cancel orders (IOCs), 48
implied forward rates, 438
“in arrears” payment structure, 426
income
interest, 536
net, 172–174
net operating, 504
operating, 276
income per capita measure, 647
income trusts, 224–225
indenture. see bond indenture
indexed-annuity bonds, 327
indexed-referenced ARM, 487
indexes, 78. see also  security market 
indexes
index weighting of security market 
indexes, 83–91
equal weighting, 85–86
fundamental weighting, 89, 91
market-capitalization weighting, 85, 
87–90
price weighting, 83–85
India
coupon payment structures, 323
indirect investing, in real assets, 26
individuals
financial system functions for, 7–12

information-motivated trading by, 
10–12
raising of equity capital by, 9
rationality of markets vs., 137
risk management by, 9–10
savings of, 7–8
spot market trading by, 10
Indonesia, 96, 164, 369
Industrial/Producer Durables sector, 
193
in company analysis, 229–230
defined, 189
describing, 202–203
fundamentals of, 613
ICB definition, 192
peer group vs., 200
performance of, 202–203
recovery rate variation by, 598
statistics on fundamentals for, 613
structure of, 612
industry analysis, 187–242
and company analysis, 228–232
in credit analysis, 614–615
describing industries for, 202–203external influences, 222–228
in airline industry, 227–228
industry classification systems, 
192–202
commercial, 192–196
governmental, 196–197
and peer groups construction, 
198–202
strengths and weakness, 197

198–202
practice problems, 237–240
with similar companies, 189–191
solutions to problems, 241–242
strategic, 204–222
barriers to entry in, 206–208
capacity in, 211–212
example, 219–222
five forces framework, 205–206
industry concentration in, 208–211
industry life-cycle model in, 213–218
market share stability in, 212–213
price competition in, 218–219
uses, 188–189
industry capacity. see capacity
Industry Classification Benchmark 
(ICB), 189–190, 192–193
industry classification systems, 192–202
and peer group construction, 198–202
for Brink’s Home Security, 199–200
for semiconductor industry, 200–202
industry concentration, 208–211, 219
industry life-cycle model, 213–218
airline industry in, 227
example, 217–218
industry classifications based on, 203

limitations of, 217
stages of industry life cycle, 213–216
using, 216–217
inefficient markets, intrinsic value in, 119
inflation duration, 574
inflation-linked bonds (linkers), 
325–328, 370
market anomalies and prior, 135–136
market efficiency and availability of, 122
nonpublic (private), 128
public, 125–128
information-acquisition costs, 123–124
informationally efficient financial 
systems, 58–59
informationally efficient markets, 58–59, 
117. see also  efficient marketsinformation cascades, 138
information-motivated trading, 10–12, 26
initial margin requirements, 22, 41
initial PAC collar (initial PAC band), 499
initial period fixed-rate mortgages, 487
initial public offerings (IPOs)
defined, 50
in markets, 51–52
and pricing anomalies, 135
and venture capital, 162
insider trading, 61, 122
institutional investors, 358, 362
insurance companies
as financial intermediaries, 33–34
monoline, 479
regulation of, 62

intangible assets, in asset-based 
valuation, 277–278
Intel Corporation
power, 209
share price and FTC investigation, 127, 
128n.21
sub-industry classification, 200, 201
technological influences, 223
intellectual-capital based companies, 
interbank funds, 385–386
interbank market, 352, 385–386
interbank money market, 352
Intercontinental Exchange, 209
interest
accrued, 413–417
shifting interest mechanism, 503
in USCP vs. ECP markets, 376–377
interest expenses, 617, 648
interest income, 536
interest-indexed bonds, 327
interest-only mortgages, 487–488
interest-only tranches, structured, 497n.11
interest rate risk, 537–574
543–545
defined, 531
and floating-rate notes, 323
Macaulay duration, 538–542, 569–574

capped floating, 511
default, 505
equilibrium, 12–13
maturity structure of, 433–441
and money duration, 572
net interest pass-through rates, 491
of residential mortgage loans, 486–487
and returns on fixed-income securities, 
531–536
term structure of, 568

I-12  Index
interest rate swaps, 23–24
internal credit enhancements, 308–309, 
479
Board (IASB), 61
International Bank for Reconstruction 
and Development (World Bank)
bonds issued by, 349
definition of emerging markets, 
646n.42
supranational bonds from, 372
use of ISIC system, 196
International Capital Market Association 
(ICMA), 365
Standards (IFRS), 189n.1
disclosure of operating segment, 200
on ROE, 173n.28
International Monetary Fund (IMF), 
196, 372, 646
International Standard Industrial 
Classification of All Economic 
Activities (ISIC), 196
interpolated spread (I-spread), 443
book vs., 176–177
from dividend discount model, 251
in equity valuation, 244
market vs., 119–120
inverse effect, 407, 408
inverse floating-rate bonds (inverse 
floaters), 383
inverse floating-rate notes, 324
inverted yield curve, 434
invest (term), 8
investment banks, 29
investment-grade bonds
and classification of bond market, 
350–351

350–351
credit ratings of, 602, 603
credit risk with, 299–300
yield spreads of, 631–632
investment-grade indexes, 99
investment horizon
for fixed-income securities, 536–537
and interest rate risk, 569–574
share value for three-year, 252
investment pools, 18–19, 32
investor pay model, 601n.13
investors
behavioral biases and decision making 
by, 139
benefits of securitization for, 474–475
in debt vs. equity securities, 155
defined, 8
in fixed-income markets, 357–359
and information-motivated traders, 
10–11
institutional, 358, 362
required rates of return for equities, 
177–178
retail, 358
IOCs. see immediate or cancel orders
Ireland
debt burden, 646
international investments in BASF, 165
MSCI multi-market index, 96residential mortgage loans, 486, 487
153
sovereign bonds, 368
iShares Morningstar ETFs, 104
ISIC. see International Standard 
Industrial Classification of All

Industrial Classification of All 
Economic Activities
I-spread. see interpolated spread
Israel, 96, 326, 370
issuer pay model, 601n.13
issuers
of commercial paper, 374
credit ratings of issues vs., 603–605
of fixed-income securities, 299–300
and classification of market, 348–350
legal identity, 305–306
in securitization process, 478
Italy
153
securitization, 475
J
Jamaica, 96
January effect, 131
Japan
benchmark rate, 442
demographic influences, 224
foreign bonds, 313, 314
government-sponsored enterprises, 490

proxy for market portfolio, 94
153
sovereign bonds, 367, 369
tax considerations with bonds, 316
Japan Airlines Group, 166–167
Japan Bank for International 
Cooperation (JBIC), 372
Japanese Financial Services Agency, 29
Japanese government bonds (JGBs), 367, 
368, 423
Japanese yen
351
as reserve currency, 19Japan Housing Finance Agency (JHF), 
490
JBIC. see Japan Bank for International 
Cooperation
JGBs. see Japanese government bonds
JHF. see Japan Housing Finance Agency
John Deere, 198, 219
Johnson & Johnson
credit ratios, 622, 624–625
market share stability, 213
Jones, Edward D., 78
Jordan, 96
J.P . Morgan Emerging Market Bond 
Index (EMBI) Global, 357
JPMorgan, 166
junk bonds. see non-investment-grade 
bonds
justified values of price multiples,

bonds
justified values of price multiples, 
266–269
K
kangaroo bonds, 313
Kazakhstan, 96
Kenya, 96
kimchi bonds, 313
Knight Securities, 30
Kodak, 223
Komatsu, 209, 219
Koninklijke Philips Electronics, 209
Korea interbank offered rate (Koribor), 
353
krona, Swedish, 351
krone, Norwegian, 351
Kuwait, 96, 351
L
LabCorp, 209
Lam Research Corporation, 200–202
large-denomination negotiable CDs, 386
Latin America, 350, 357. see also  specific 
countries
laundry business, asset-based equity 
valuation, 277
law of one price, 269
lawyers, in securitization process, 
478–479
lead underwriter, 50
learning, personal, 138
Lebanon, 96
legal considerations, with fixed-income 
securities, 313–316
legal form of bonds, 305–306
legal identity, bond issuer, 305–306
legal maturity, mortgage-backed 
security, 495
Lehman Brothers, 386, 639
Lehman Brothers Aggregate Bond Index, 
99
Lehman Brothers Global Aggregate 
Bond Index, 103
lenders’ rights, in foreclosures, 488–489
lending, 8–9, 32–33
Lenovo, 209

letras del Tesoro, 368
letters of credit, 309
Level I ADRs, 168
Level II ADRs, 168

Index  I-13
Level III ADRs, 168
leverage
and debt structure, 640–642
financial, 41–44
operating, 612
leveraged buyouts (LBOs)
covenants for, 626–627
as private equity investments, 162, 163
leveraged positions, in markets, 41–44
leverage ratios, 41–42, 616–617
Lexmark, 209
LG Group, 315–316
liabilities, contingent, 648
Libor. see London interbank offered rate
liens, 596, 644
life-cycle stage
of airline industry, 227
Light Sweet Crude Oil futures contract, 
23
limitations on liens covenant, 644
limited partnerships, 18, 26
limit order book, 45–46
limit orders, 44–49
lines of credit, 375, 618, 639
linkers. see inflation-linked bonds
liquidating dividend, 249n.1
liquidation
absolute priority rule in, 483
priority of preference shares in, 
159n.14
stockholders’ rights in, 157
liquidity
in credit analysis, 618
from dealers, 30
and forward contracts, 22
in high-yield credit analysis, 638–639

and operating cash flow, 639
and secondary bond markets, 365
and securitization, 475
liquidity duration, 574
liquidity enhancement, 375
liquidity ratios, 231
with fixed-income securities, 574–575
market, 593–594
liquid markets
information-motivated trading in, 12
raising capital in, 9
risk management in, 10
secondary, 53
Liquidnet, 30
Lithuania, 96
litigation risk, 608
loans
amortizing, 487, 508
bank, 349, 350, 373–374
bilateral, 373, 374
bullet, 374
margin, 41
mortgage, 485–490
non-amortizing, 508non-recourse, 488
prime, 486
recourse, 488
residential mortgage, 485–490
lender’s rights in foreclosures, 
488–489
488
subprime, 486
syndicated, 364, 374
loan-to-value ratio (LTV), 486, 504
lockout period, 508, 511
Lombardy region, Italy, 650
London interbank offered rate (Libor)

and coupon rate, 301
and I-spread, 443
as reference rate, 352–353, 425
setting, 353
GDRs on, 167
information availability, 122
total market capitalization in,  
151, 152
long positions, 39
long sales, clearing instructions on, 50
loss aversion, 137
losses
capital, 316, 533–535, 569
expected, 593
stop-loss orders, 48–49
tax-loss selling hypothesis, 131
loss given default, 592
loss severity, 592, 593
low-cost strategy, for companies, 228
lower Tier 2 securities, 596n.4
Lowe’s, 208
LT V. see loan-to-value ratio
Lund, Susan, 348n.1
Luxembourg Stock Exchange, 167
M
Macaulay, Frederick, 538
Macaulay duration
McDonalds, 216–217
macroeconomic influences, on industry 
analysis, 203, 222
Maersk Line, 210
maintenance covenants, 644
maintenance margin requirement, 22, 
43–44
make-whole calls, 330
make-whole charge, 505

43–44
making a market, 45, 46, 631
Malaysia, 96
management, book value and, 172
management buyouts (MBOs), 162
management strategy, as company 
fundamental, 613–614
maple bonds, 313
Marathon Oil, 209margin
discount, 426–429
maintenance margin requirements, 22, 
43–44
quoted, 426
repo, 388
required, 426
variation margin payments, 22
margin calls, 43
margin loans, 41
marketable limit orders, 45
Market Abuse Regulation, 122n.11
market anomalies, 129–136
and closed-end investment fund 
discounts, 133–134
cross-sectional, 133
and earnings surprises, 134–135
for initial public offerings, 135
investment strategies using, 136
and predictability of returns, 135–136
time-series, 130–132
market bid–ask spread, 44
market capitalization
of equity markets, 150–152
style indexes based on, 97
total, 87
market-capitalization weighting, of 
indexes, 85, 87–90
market discount rate
bond price and, 407–411
calculating, 402–406
market efficiency, 115–146

and active manager selection, 116
anomalies, 129–136
in behavioral finance, 136–139
contributing factors, 120–123
description of efficient market, 
117–119
forms of, 124–129
and market vs. intrinsic value, 119–120
and portfolio management, 129
practice problems, 142–144
semi-strong-form efficient markets, 
125–128
solutions to problems, 145–146
strong-form efficient markets, 128
and transaction/information-
acquisition costs, 123–124
weak-form efficient markets, 125
market float, securities’ , 87
market liquidity risk, 593–594
market multiple models, 247. see also  
multiplier models for equity 
valuation
market-on-close orders, 48
market orders, 44, 45, 47–48
market participants
fair treatment of, 122

and market efficiency, 120–122

I-14  Index
market price, estimated value and, 
245–246
markets, 5–76. see also  fixed-income 
market
assets in, 14–20
real assets, 26–28
benefits of securitization for, 474–476
call, 54
capital, 13–15
central bank funds, 385
commodities in, 25–26
complete, 58
continuous trading, 54, 56–57
contract, 20–25, 27–28, 54–58
debt, 592
efficient
weak-form, 125
emerging
bonds in, 355
Eurocommercial paper, 376–377
and financial analyst decisions, 6
financial intermediaries, 28–38

36–37
forward, 437
and functions of financial system, 6–14
global debt, 349–350
global equity, 349–350
global finance
inefficient, 119
interbank, 352, 385–386liquid
exchanging assets for immediate 
delivery in, 10
making, 45, 46, 631
orders in, 44–50
over-the-counter, 55, 168, 358, 365
positions in, 38–44
practice problems, 66–72
primary security, 50–53
rationality of individuals vs., 137
regulation of, 60–63

secondary security, 53–58
solutions to problems, 73–76
sustainable securitization, 476
taking, 46
target, for security indexes, 82
US commercial paper, 376–377
58–60
yield spread and performance of, 631
market sentiment, 93
market share
and industry concentration, 208–209
stability of, 212–213, 220
market-to-book ratio, 175
market value
and asset-based valuation, 276, 277
and book value, 172
of debt, 274–275
intrinsic vs., 119–120
total, 175
Market Vectors Vietnam ETF, 95
Markit iBoxx, 98
Markit iBoxx Euro High-Yield Bond 
Indexes, 103
Mars/Wrigley, 209, 219–221
MasterCard, 206, 209
master limited partnerships (MLPs), 26
matador bonds, 313
material adverse change provisions, 375
Mathews International Corporation,  
199
matrioshka bonds, 313
mature stage (industry life-cycle), 215
maturity
351
of corporate notes/bonds, 377–378
of fixed-income securities, 300
legal, 495

legal, 495
of residential mortgage loans, 486
weighted average, 491–494
maturity effect, 408, 409
433–441
maturity value. see par value
Mauritius, 96
MBS. see mortgage-backed securities
MDURATION financial function,  
542n.4
Medical Equipment Trust (MET), 
477–478, 481–483medical industry, governmental 
Mediquip, 476–478, 482–483
medium-term notes (MTNs), 378
Medtronic, 213
mental accounting, 138
Mercedes, 218
Merck & Co.
power of, 209
in strategic analysis, 219–221
MET. see Medical Equipment Trust
method of comparables
and multiplier models for equity 
valuation, 269–272
price multiples in, 266
Mexican Comisión Nacional Bancaria y 
de Valores, 29
Mexican peso, 10
Mexico, 96, 197, 326, 369
mezzanine bond classes, 513
Mibor. see Mumbai interbank offered 
rate
Michelin Group, 68, 74
Middle East, 350, 617. see also  specific 
countries
mid-swaps (term), 442

countries
migration, credit ratings, 606–607
Mikuni & Co., 602
minimum required rate of return, 177
model portfolios, security market 
indexes in, 94–95
modified duration
momentum anomalies, 132
momentum effect, of market-
91
Monetary Authority of Singapore, 161
monetary flexibility, in sovereign credit 
analysis, 648
monetary policy, 648
money, time value of. see time value of 
money
money convexity, 564–565
money duration, 557–559, 572
money market instruments, yield of, 
429–433
money markets, 15, 17
money market securities, 300
Monitronics International, Inc., 199
monoline insurance companies, 479
Moody, John, 601
Moody’s Investors Service
in credit markets, 601, 602

municipal debt ratings, 650, 651
ratings for Ford Motor Company, 607
Moore’s law, 222

Index  I-15
moral hazard, insurance and, 34
Morgan Stanley, 300
Morningstar, 98, 104
Morningstar US Market Index, 104
Morocco, 96
mortgage-backed securities (MBS), 308
commercial, 503–508
coupon frequency, 300–301
effective duration of, 546
overcollateralization with, 309
repayment structure for, 320
residential, 490–503
497–503
mortgage pass-through securities, 31, 
491–496
and securitizers, 31
mortgage debt, 596
mortgage design, 486, 489–490
mortgage loans
defined, 485
residential, 485–490
488–489
488
491–496
cash flow construction, 493–494
characteristics, 491–492
collateralized mortgage obligations vs., 
497
defined, 491

497
prepayment rate measures, 492–493
prepayment risk, 492
weighted average life, 495–496
mortgage pools, 31
mortgage rates, 486–487
mortgages. see residential mortgage 
loans
mortgage sector, 491n.9
MSCI All Country World Index, 103
MSCI Argentina Index, 96n.1
MSCI Barra
multi-market indexes of, 95–96
MSCI Developed Markets Index, 96
MSCI EAFE Index, 96
MSCI Emerging Markets Index, 96
MSCI Frontier Markets Index, 96
MSCI GCC Countries Index, 96n.4
MSCI Jamaica Index, 96n.3
MSCI Pakistan Index, 96n.2
MSCI Trinidad & Tobago Index,  
96n.3
MSCI World Index, 94
MTNs. see medium-term notes
multilateral trading facilities (MTFs), 
29–30multi-market equity indexes, 95–96
multiple-price auctions, 362
multiple put bonds, 332
multiplier models for equity valuation, 
265–276
multistage dividend discount models,

multistage dividend discount models, 
261–264
Mumbai interbank offered rate (Mibor), 
353
municipal bonds (munis), 355
mutual funds
barriers to entry for, 207
performance of, 129
as pooled investments, 18–19
N
NACE. see Statistical Classification 
of Economic Activities in the 
NAICS. see North American Industry 
narrow framing, 138
NASDAQ. see National Association of 
Securities Dealers Automated 
Quotations
NASDAQ OMX, 151, 152
Investment Trusts (NAREIT), 101, 
102
National Association of Securities 
Dealers Automated Quotations 
(NASDAQ), 93, 151n.3, 168
National Highways Authority of India 
(NHAI), 355
Navistar, 189
negative covenants, 310–311, 626
negative pledges, 310
negotiable CDs, 386
Nestlé
justified forward P/E of, 267–269
subsidiary of, 159
net asset value (NAV), 134
net coupon pass-through rate, 491
net debt, 616

153
net income, in ROE, 172–174
net interest pass-through rate, 491
net operating income (NOI), 504
net working capital, in credit analysis, 
618new entrants, in strategic analysis, 
205–208
Newmont Mining, 276
New York Mercantile Exchange 
(NYMEX), 23
ADRs on, 168
delisting of Allianz SE on, 165
information availability of, 122
inflation-linked bonds, 327
returns
on bills and bonds, 152–153
155
NHAI. see National Highways Authority 
of India
Nigeria, 96
Nikkei Stock Average, 103
Nikon Corporation, 223
Nissan Motor Company, 189, 270

no-arbitrage value, 411
Nokia, 217
nominal rate. see coupon rate
Nomura, 30
non-agency residential mortgage-backed 
securities, 490, 491, 503
non-amortizing loans, 508
non-callable, non-convertible perpetual 
preferred shares, 254–255
non-conforming mortgages, 490
non-cumulative preference shares, 160
non-cyclical companies, 190–191, 613
non-domestic equity securities,  
164–169
non-investment-grade bonds (high-yield 
bonds), 603
350–351
credit analysis of, 638, 643–645
non-investment grade credit ratings,  
638
508–512
auto loan ABSs, 508–511
credit card receivable ABSs, 511–512
non-participating preference shares, 160
nonpublic information, 128
non-recourse loans, 488
non-sovereign bonds, 307, 371–373
non-sovereign government debt, 
650–651
non-sovereign governments, 299

650–651
North American Industry Classification 
System (NAICS), 197
Northern Trust, 210
Norway, 96, 153
Norwegian krone, 351
notching, 604
note rates, 486–487

I-16  Index
notes
bonds vs., 17
corporate, 377–380
credit-linked, 382
exchange-traded, 19
floating-rate
medium-term, 378
privately placed, 510
publicly offered, 509
US Treasury, 368, 547–548
variable-rate, 323
power, 209
NYMEX. see New York Mercantile 
Exchange
NYSE-Euronext
as exchange, 29
total market capitalization in, 151, 152
O
OAS. see option-adjusted spread
OAS duration, 548
obligaciones del Estado, 368
obligations assimilables du Trésor 
(OATs), 367, 368
offering day, 362
offerings
best efforts, 51
initial public
public, 50–53, 360–364
rights, 52
seasoned, 50
syndicated, 361
underwritten, 50, 51, 360–362
offer prices, 44, 574
off-the-run securities, 442

oil services industry, strategic analysis 
of, 219–221
Oman, 96
Ontario Securities Commission, 29
on-the-run securities, 368, 442
open-ended funds, 18
open market operations, 358
operating cash flow, 252, 618, 639
operating history, as company 
fundamental, 613
operating income, enterprise value and, 
276
operating leverage, capacity and, 612
Operating Segments  (IFRS 8), 189n.1
operationally efficient financial systems, 
58–59
option-adjusted price, 425
option-adjusted spread (OAS), 445, 631
option-adjusted yield, 425option premiums, 24
options, 329. see also  embedded options
call, 24
in contract markets, 24–25
dealers of, 35
forwards vs., 25
long and short sides of, 39
put, 24, 643
underlying risk exposures of, 39
option writers, 24
order-driven markets, 54–57
Order Machine, 30
order matching rules, 55
order precedence hierarchy, 55
orders, 44–50
clearing instructions for, 44, 49–50
execution instructions for, 44–48
validity instructions for, 44, 48–49

organized exchanges, 365
original issue discount tax provision, 317
orthopedic device industry, market share 
stability in, 212–213
markets
overcapacity, 208
overcollateralization, 309
overconfidence, 137
overnight repo, 387
overreaction anomalies, 132
over-the-counter (OTC) markets, 55, 
168, 358, 365. see also  quote-
driven markets
overvalued (term), 245
P
Paccar, 189
PAC tranches. see planned amortization 
class tranches
Pakistan, 96
panda bonds, 313
Pan-European Aggregate Bond Index, 
357
parallel shift, 556
par curve, 436–437
pari passu ranking, 597, 644
parity value, 333
Parmalat, 608
partial duration, 549
partially amortized bonds, 318–320
partially amortizing loans, 487
participating preference shares, 160
partnerships, limited, 18, 26
par value
and market discount rate, 403–406
passive investment strategies, 117
passive portfolio management, 129
pass-through rate, 491

passthrough securities, on investment 
pools, 32
path dependence, 218n.14
payable date (payment date), 249
payment-in-kind (PIK) coupon bonds, 
325, 378
payments-in-lieu of dividends, 40
payout ratio, 266–269
P/B. see price-to-book ratio
P/CF. see price-to-cash-flow ratioP/E. see price-to-earnings ratio
peer groups, 197–202
constructing, 198–202
defined, 197
penal sum, 309
penalties, prepayment, 488
pension funds, regulation of, 62
Pentax Imaging Company, 223
People’s Bank of China, 475
PepsiCo, Inc., 209, 211
performance
of hedge funds, 102
risk-adjusted, 94
standards for, 61
performance attribution, industry 
analysis in, 189
periodicity, 420–421, 433
periodicity conversions, 421–422
PerkinElmer, 158–159
Pernod Ricard, 209
perpetual bonds, 300
perpetuities, 550
personal learning, 138
Peru, 96
peso, Mexican, 10
Petroleo Brasileiro SA (Petrobras), 
266–267
Peugeot, 269, 270
Pfizer Inc.
pharmaceutical industry

similar companies in, 189
strategic analysis for, 219–221
Philip Morris, 209
Philippines, 96
photographic film industry, 223
physical assets, 14
physical settlement, of contracts, 20
PIK coupon bonds. see payment-in-kind 
coupon bonds
Piotowski, John, 348n.1
PIPEs. see private investments in public 
equity
plain vanilla (conventional) bonds, 301
cash flows for, 302, 318
planned amortization class (PAC) 
Playtech, 51–52
pledges, negative, 310
Poland, 96, 326, 369
political risk, 647
pooled investments, 15, 18–19, 32
Porter, Michael, 205, 228, 612
portfolio management
active
manager performance, 129
manager selection, 116
with fixed-income securities, 298
passive, 129
defined, 38
duration of, 555–557
model, 94–95
Portugal, 96, 487, 649–650

Index  I-17
POSIT, 30, 57
positions, 38–44
leveraged, 41–44
long, 39
short, 39–41
post-trade transparent markets, 58
pound, British, 19, 351
Authority
Praxair, 209
predictability, of returns, 135–136
preemptive rights, stockholders’ , 157
prefabricated housing industry, 215–216
preference shares (preferred shares), 
159–161, 171
callable, 160, 171, 254
common vs., 17–18
convertible, 161
cumulative, 160, 171
non-callable, non-convertible 
perpetual, 254–255
non-cumulative, 160
non-participating, 160
participating, 160
retractable term, 255–256
risk of, 171
preferred stock, valuation of, 254–256
premium bonds
returns on, 531
tax provisions for, 317
premiums, 403–406
call, 330
conversion, 333
option, 24
Pre-Paid Legal Services Inc., 199
prepayment lockouts, 505
prepayment option, residential mortgage 
loan, 488
prepayment penalties, 488
prepayment penalty mortgages, 488
prepayment penalty points, 505
prepayment rate, 492–493
prepayment risk
and contraction/expansion risk, 492

in securitization transactions, 481–482
pre-refunded bonds, 505n.12
present value models for equity 
defined, 246–247
254–256
present value of growth opportunities, 
257n.3
pre-trade transparent markets, 58
price
ask, 44
bid, 44, 574
call, 330
clean, 413
exercise, 18
flat, 413–417
full, 413–417law of one price, 269
and limit vs. market orders, 45–46
market, 245–246
offer, 44, 574
option-adjusted, 425
quoted, 413
repurchase, 387
price competition, in strategic analysis, 
218–220
price-driven markets. see quote-driven 
markets
PRICE financial function, 415n.1
price index. see price return index
price multiples. see also  specific price 
multiples
defined, 265
example valuation based on, 272–273
and method of comparables, 269–272
in multiplier models for equity

in multiplier models for equity 
valuation, 266–269
price priority, in order-driven markets, 
55
price return, 78–81
price return index (price index), 78–81
price-to-book ratio (P/B), 175–176, 265
price-to-cash-flow ratio (P/CF), 265
price-to-earnings ratio (P/E)
for Canon Inc., 271–272
comparing equity valuation models 
with, 279–280
justified value of, 266–269
in method of comparables, 269–272
price-to-sales ratio (P/S), 265, 269–270
price value of a basis point (PVBP), 558
price weighting, 83–85, 91
pricing, 230
pricing day, 362
pricing power, 207–210
primary dealers, 30, 364
primary markets
bond, 359–365
private placements on, 360, 364–365
public offerings on, 360–364
capital, 13–14
securities, 14–15, 50–53
private placements on, 52–53
public offerings on, 50–53
and secondary markets, 53
Prime Bank, 307
prime brokers, 33, 49
prime lending rate, 374
prime loans, 486
prime paper, 375
principal (principal amount; principal 
value), 300
principal business activity, industry

principal business activity, industry 
classification based on, 189
principal repayment structures, 318–323
for bullet bonds, 318–320
for corporate notes/bonds, 378–379
for fully amortized bonds, 318–320
for sinking fund arrangements, 
321–323
principal value. see par value
prior information, 135–136
priority of claims, 595, 599–600
private equity securities, 15, 162–164private information, 128
private investments in public equity 
(PIPEs), 162–163
privately placed notes, 510
private placements
on bond market, 360, 364–365
on securities market, 52–53
private sector, size of, 647
Procter & Gamble, 210
products, of similar companies, 189–190
profit, economic, 204
profitability, in credit analysis, 615–616
profitability ratios, 231
prospectus, 478n.3, 479, 626
Protection One, Inc., 199, 200
353n.3
P/S. see price-to-sales ratio
PSA Peugeot Citroën, 189
PSA prepayment benchmark. see Public 
Securities Association prepayment 
benchmark
public auctions, 362–364

benchmark
public equity securities, 15, 162–164
public information, 125–128
publicly offered notes, 509
public offerings
on bond market, 360–364
initial
on securities market, 50–53
public sector, size of, 647
Public Securities Association (PSA) 
prepayment benchmark, 493
pull to par effect, 410–411
purchase agreements, 478–479
pure discount bonds, 301
PureTrading, 30
putable bonds, 332, 379
interest rate risk with, 554
putable common shares, 159, 171
putable preference shares, 171
American, 332n.6
Bermuda-style, 332
change of control, 643
embedded ( see putable bonds)
European, 332
PVBP . see price value of a basis point
Q
Qatar, 96, 351
qualified institutional investors, 362
quarterly interest bonds (QUIBS), 300
quarterly interest debt securities 
(QUIDS), 300
quasi-government entities, 299
Quest Diagnostics, 209

QUIBS. see quarterly interest bonds
QUIDS. see quarterly interest debt 
quoted margin, 426
quoted price, 413

I-18  Index
quote-driven markets (dealer markets)
defined, 54, 55
execution mechanisms for, 55
and fixed-income indexes, 98
order-driven and brokered markets 
vs., 57
R
random walk hypothesis, 125n.15
rapid amortization provisions, 512
and functions of financial system, 
12–13
holding-period, 571
required, 177–178, 254, 402
rating agencies. see credit ratings 
agencies
ratio analysis, 615–617
rationality, of markets vs. individuals, 137
RBC Bank, 209
RBC Capital Markets, 30
real assets, 14, 26–28
real estate investment trust (REIT) 
indexes, 101–102
real estate investment trusts (REITs), 26
real rate duration, 574
real returns, on equity securities, 152–154
reasonableness testing, for company 
analysis, 232
rebalancing, of indexes, 86, 91
reconstitution, 92–93
recourse loans, 488
recovery rates, 503, 597–600
redemption yield, 304. see also  
yield-to-maturity
reference rates, 352–353, 425–426
Regis Corporation, 199
registered bonds, 314
Regulation FD (SEC), 122
regulations
on financial reporting, 61

for markets, 60–63
for pension funds, 62
Regulation S ADRs, 168
Regulation T (Federal Reserve), 41
regulatory influences
and fixed-income securities, 313–316
of government, 224–226
reinvested dividends, 169–170
reinvestment risk, 322
REIT indexes. see real estate investment 
trust indexes
renminbi, yuan, 351
reorganization, 600
repayment proceeds, bond, 306–307
replication, by arbitrageurs, 35
repo margin, 388
repo rate, 387
“Report on Securitization Incentives” 
(Bank for International 
Settlements), 476
repos. see repurchase agreements
repo to maturity, 387
representativeness bias, 138
representative sectors, for commercial 
industry classifications, 193–194representative security market indexes, 
103–104
repurchase agreements (repos), 17, 
386–389
repurchase date, 387
repurchase price, 387
required margin, 426
required rate of return, 177–178, 254, 402
required yield, 402

required yield spread, 418
reserve accounts, 309
reserve funds, 309, 385–386
(RMBS), 490–503
497–503
planned amortization class tranches, 
499–501
sequential-pay structures, 497–499
support tranches, 499–501
491–496
vs., 497
weighted average life, 495
lender’s rights in foreclosures, 488–489
prepayment options and penalties, 488
residual tranche, 504
restaurants
barriers to entry for, 206
restricted payments covenant, 644
restricted subsidiaries, 644
restrictions
on asset disposals, 310
on debt, 310

on distributions to shareholders, 310
on international investment, 164
on investments, 310
on mergers and acquisitions, 310
on prior claims, 310
retail currency transactions, 20
retail investors, 358
Retail Price Index (RPI), 325, 326, 370
retractable term preferred shares, 
255–256
retraction, 256n.2
return(s)
abnormal, 124
active, 116
for commodities vs. commodity 
indexes, 101
credit risk vs., 628–637
on equity securities, 169–170
Fama and French three-factor model, 133on fixed-income securities, 530–537
industry classifications based on 
correlations in, 191
predictability of, 135–136
price, 78–81
real, 152–154
security market indexes as proxies for, 
94
single-period, 79–81
total
for equity securities, 169–170
for leveraged stock purchase, 42–43
for multiple periods, 81–82
price vs., 78–79
for single period, 80–81
return on equity (ROE), 172–177
and accounting method, 173
and book vs. intrinsic value, 176–177

in company analysis, 232
formulas, 172–173
and justified forward P/E, 268–269
for Pfizer, Novartis AG, and 
GlaxoSmithKline, 173–175
return on invested capital (ROIC), 204
Reuters, 386
revenue, interest expense and, 648
revenue bonds, 651–652
reverse floating-rate notes, 324
reverse repurchase agreements (reverse 
repos), 388
reverse stock split, 249
reviewable ARM, 487
revolving period, 508
RGS classification. see Russell Global 
Sectors classification
rights offerings, 52
Rio Tinto, 209, 276
risk
balloon, 505
Bloomberg’s statistic for, 558
contraction, 492
counterparty, 22, 36
credit, 592–594
with fixed-income securities, 
299–300, 574–575
credit migration, 593
default, 592, 593
downgrade, 593
of equity securities, 170–171
event, 608
expansion, 492
interest rate, 537–574

event, 608
543–545

Index  I-19
569–574
liquidity, 574–575, 593–594
litigation, 608
political, 647
prepayment, 481–482, 492
reinvestment, 322
of relying on credit ratings, 605–608
rollover, 375
shaping, 549
spread, 593
substitution, 612
systematic, 94
systemic, 333
risk-adjusted performance, 94
risk aversion, 137
risk exposures, underlying, 39
risk-free rate, 419, 645–646
risk management, 9–10
risk managers, 6
risk tolerance, 154–155
rivalries, 205, 612
Roche Holding AG, 189
ROIC. see return on invested capital
rollover, of futures, 101
rollover risk, 375
Romania, 96
Roxburgh, Charles, 348n.1
Royal Bank of Scotland PLC, 307, 383
RPI. see Retail Price Index
Rule 10b5-1 (SEC), 122n.10
Rule 10b5-2 (SEC), 122n.10
Rule 144A ADRs, 168
running yield, 304
Russell 2000 Index, 92

Russell 3000 Index
as broad market index, 95
reconstitution of, 92
Russell Global Sectors (RGS) 
classification, 189, 190, 192
Russell Investments, 192
Russia, 96, 313
S
sales
of assets, 639
long and short, 50, 123
price-to-sales ratio, 265, 269–270
Samsung Electronics Co. Ltd., 209, 306
Samurai bonds, 313
Sandoz, 209
Sanofi-aventis S.A., 189
Santander UK plc, 306
Saudi Arabia, 96
saving, 7–8, 12
Schlumberger, 219–221
seasoned offering, 50
seasoned securities, 50
Commissionsecondary markets
bond, 359, 365–367
security, 53–58
and primary markets, 50, 53
secondary precedence rules, 55
second lien debt, 596
sector indexes, 97
sectors
economic sensitivity of, 190–191
representative, 193–194
secured bonds, 307, 483
secured debt, 595, 596
securities. see also  specific types of 
asset-backed, 473–525

512–515
474–476
non-mortgage asset-backed 
securities, 508–512
residential mortgage-backed 
securities, 490–503
securitization process, 474–485
defined, 16–17
in markets, 16–19
for security market indexes, 82
Securities and Futures Commission, 41
Securities Industry and Financial 
Markets Association (SIFMA), 493
for asset-backed securities, 299
defined, 473
economic benefits of, 474–476
and financial markets, 474–476
parties’ roles in, 478–480
of structured financial instruments, 349
structure of, 481–482
securitization markets, sustainable, 476
securitized assets, 474

security lending agreements, 40
security market indexes, 77–114
for alternative investments, 101–104
construction of, 82–91
fixed-income indexes, 98–100, 357
index values over multiple time 
periods, 81–82
management, 91–93
origins of, 78practice problems, 106–111
representative, 103–104
single-period returns for, 79–81
solutions to problems, 112–114
uses of, 93–95
self-regulating organizations (SROs), 62
sellers, in securitization process, 478
semiannual bond basis yield, 421
semiconductor industry, 200–202
125–128
seniority ranking, 307, 595–597
Sensex Index, 82
sensitivity analysis, for justified forward 
P/E, 268–269
sequential-pay tranches, 497–499
Serbia, 96
serial correlation, 125n.16
serial maturity structures, 378
Service Corporation International, 199
servicers, in securitization process, 478
services, of similar companies, 189–190
servicing fee, mortgage pass-through 
security, 491

clearing instructions for, 49–50
of contracts, 20
of corporate notes and bonds, 380
by financial intermediaries, 36–37
in secondary bond markets, 366
settlement date, 413
shakeout stage (industry life-cycle), 215
Shanghai Stock Exchange, 151, 152
Shanghai Stock Exchange Composite 
Index (SSE), 95
shaping risk, 549
shareholders
bondholders vs., 610–611
voting rights of, 156, 157
shareholders’ equity, ROE and, 174
share repurchase (buyback), 249
shares
common, 156–159
dual listing of, 164–165
global registered, 168
preference (preferred), 159–161
small-cap, 121, 133

value of, for three-year investment 

I-20  Index
shelf registration, 52, 362
short positions, 39–41
short rebate rates, 40
short sales, 50, 123
Sibor. see Singapore interbank offered 
rate
SIC system. see Standard Industrial 
Classification system
Siemens AG, 258–259
SIFMA. see Securities Industry and 
Financial Markets Association
similar companies, 189–191
simple yield, 423
Singapore, 96, 368
Singapore interbank offered rate (Sibor), 
301, 353
Singapore Stock Exchange, 29, 167
single monthly mortality (SMM) rate, 
492–494
single-period returns, for security 
market indexes, 79–81
single price auctions, 54
sinking fund arrangements, 321–323, 
378–379
size effect, 133
Slovenia, 96
small-cap shares, 121, 133
small-denomination negotiable CDs, 386
Smith, Donald J., 541n.3, 560n.6
Smith & Nephew, 209, 213
SMM rate. see single monthly mortality 
rate
social influences

rate
in industry analysis, 203, 226–227
solvency ratios, in company analysis, 231
Sony Electronics, 209, 315, 316
Sotheby’s, 199
returns
South America, 475. see also  specific 
international investment, 164
154–155
legal issuers, 305–306names of, 367–368
sources of repayment, 306
sovereign debt, 645–650
647–648
sovereign governments, 299, 475

sovereign wealth funds, 358
S&P . see Standard & Poor’s
number of securities in, 82
as proxy for market portfolio, 94
securities selection for, 82
Spain
153
sovereign bonds, 368, 369
SPCs. see special purpose companies
S&P Developed Ex-US BMI Energy 
Sector Index, 103
SPDRs. see Standard & Poor’s 
Depositary Receipts
SPDR© S&P Energy Sector Exchange-
Traded Fund, 103
special dividend (extra dividend), 
248–249
Specialized Consumer Services sub-
industry, 199
special purpose companies (SPCs), 306, 
477
special purpose entities (SPEs)
and bankruptcy, 483–485
defined, 31, 306, 477
obligations of, 306
as party to securitization, 478
role of, 482–485
as securitizers, 31–32
special purpose vehicles (SPVs)
as financial intermediaries, 31–32
legal obligation of, 306

in securitization transaction, 477
SPEs. see special purpose entities
S&P GSCI Index, 101
split coupon bonds, 325
sponsored depository receipts, 166
spot commodities markets, 25, 26
spot contracts, 20
spot currency transactions, 20
spot curve, 434–435
spot exchange rate, 20
spot markets, 10, 15
spread(s)
benchmark, 442
and benchmark yield, 574–575
bid–ask, 44, 365–366
bid–offer, 365–366
credit, 419, 482–483, 607
excess, 309, 509
G-, 442, 445interpolated, 443
option-adjusted, 445, 631
yield, 441–445
and benchmark rates, 441–443
and benchmark yield curve, 443–445
and credit risk/return, 630–637
required, 418
zero-volatility, 443, 445
spread over the benchmark, 418
spread risk, 593
spreadsheet modeling, 232
Sprint, 217
S&P/TSX Capped Income Trust Index, 
225
SPVs. see special purpose vehicles
Sri Lanka, 96
SROs. see self-regulating organizations
SSE. see Shanghai Stock Exchange 
Composite Index
stable industries, 190, 191
standard deviation, of expected total 
return, 170

Standard Industrial Classification (SIC) 
system, 197
standardized yield measures, 420
Standard & Poor’s (S&P)
company classifications, 192, 201–202
credit ratings, 99
investment-grade, 299n.2, 350
transition rates of, 606–607
for United Rentals, Inc., 604–605
default rates by credit category, 
605–606, 635–636
funds from operations, 615
617
notching guidelines, 604–605
sovereign credit analysis, 646–648
Standard & Poor’s Depositary Receipts 
(SPDRs), 68, 74
Standards of Professional Conduct (CFA 
Institute), 49, 51
standing limit orders, 45–46
Stanley Security Solutions, 199, 200
The Stanley Works, 199, 200
State Street, 209
Statistical Classification of Economic 
Activities in the European 
Community (NACE), 196
statistical similarities, of similar 
companies, 191

Statistics New Zealand, 196
statutory voting, 156
STMicroelectronics, 210
stock. see also  shares
convertible common, 157
growth, 97
preferred, 254–256
subdivisions and combinations of, 157
value, 97, 133
stock analysts, 6
stock dividend (bonus issue of shares), 
249

Index  I-21
stock splits, 83, 85, 157, 249
stop-buy orders, 48, 49
stop orders, 48–49
strategic default, 488
strategic groups, analysis of, 202–203
strategic industry analysis, 204–222
industry capacity in, 211–212
street conversion, 422
strip curve, 434
structural subordination, 604
structured finance CDOs, 513
structured finance sector, 349
structured financial instruments, 381–384
structured interest-only tranches, 
497n.11
structured products, 381–382
structuring process, 497
Stryker, 213
style indexes, 97

subdivisions, of stock, 157
subordinated debt, 596–597
subordination, 308–309, 481, 503
subprime loans, 486
subsidiaries
high-yield credit analysis for, 642–643
of Nestlé, 159
restricted vs. unrestricted, 644
substitute products, 205, 612
substitution risk, 612
superannuation funds, 546
supplementary prospectus, 478n.3
suppliers, power of, 205, 612
supply, 230, 352, 631
supranational organizations, 299
supranationals, 601n.10
surety bond, 309
survivorship bias, 102
sustainable securitization markets, 476
swaps
asset, 443
in contract markets, 23–24
credit default, 25, 34
interest rate, 23–24
long and short side of, 39
Sweden
returns
on equities, 152–153risk tolerance and equity ownership, 
154–155
Swedish krona, 351
Swiss franc, 19, 351
foreign bonds, 314

153
155
Synchrony Bank, 512
syndicated loans, 364, 374
syndicated offerings, 361
synthetic CDOs, 513
systematic risk, 94
systemic risk, 334
T
T + 1 settlement, 366
Tai, Jackson, 161
Taiwan, 96
Taiwan Semiconductor Manufacturing 
Company Ltd., 200, 201
taking a market, 46
target market, for security market 
indexes, 82
Tata Motors, 270
taxes
and fixed-income securities, 316–318
and income trusts in Canada, 225
tax-exempt bonds, 355
T-bonds. see US Treasury bonds
TD Bank, 209
technical analysis, 125, 129
technological influences
in industry analysis, 203, 222–223
on industry life-cycle, 217
in strategic analysis, 221
technology, substitution risk and, 612
Technology sector, 193
telecommunications industry, structure 
of, 217
Telecommunications sector, 193
Telefónica S.A., 192, 272–273
tenor, 300, 438

TEPCO. see Tokyo Electric Power 
Company
terminal stock value (terminal value), 
251, 261
term maturity structures, 378
term of repurchase agreement, 387
term repo, 387
term structure
of credit spreads, 419
of interest rates, 433–441, 568
of risk free rates, 419
of yield volatility, 568–569
Tesco, 362
Tesoro Público, 368
Teva Pharmaceutical Industries, 209
Texas, 651
Texas Instruments, 210Thailand, 96, 164
Thaler, Richard, 132
threat of entry, 205, 612
three-stage dividend discount model, 
262
Tibor. see Tokyo interbank offered rate
TIIS. see Treasury inflation-indexed 
Timber Hill, 30
time frame, for market efficiency, 117
time periods, security index values over 
multiple, 81–82
time-series pricing anomalies, 130–132
time-to-maturity, 551
time tranching, 482
time value of money, 402–413
market discount rate, 402–406, 
407–411
TIPS. see Treasury inflation-protected 
T-notes. see US Treasury notes

tobacco industry, 225, 226
Tokyo, Japan, 650
Tokyo Electric Power Company 
(TEPCO), 608
Tokyo Electron, 209
Tokyo interbank offered rate (Tibor), 353
Tokyo Stock Exchange
and TOPIX, 103
Tokyo Stock Exchange Group, 151, 152
Tokyo Stock Price Index (TOPIX)
top-down approach to equity valuation, 
244
top heavy capital structure, 642
TOPIX. see Tokyo Stock Price Index
total market capitalization, 87
total market value, ROE and, 175
total return
total return index, 78–82
value of, 79–81
Total S. A., 250
“toxic waste, ” 32
Toyota Motor Company, 189, 209, 270
track record, as company fundamental, 
613
trade pricing rules, 56
trading
alternative systems, 29–30

trading
continuous trading markets, 54
on contract/secondary security 
markets, 54
information-motivated, 10–12, 26
insider, 61, 122
multilateral facilities, 29–30
spot market, 10

I-22  Index
trading limits, 123
traditional bonds, ABSs vs., 299
traditional investment markets, 15
tranches
for collateralized debt obligations, 513
for collateralized mortgage obligations, 
497–501
defined, 32
equity, 504
floating-rate, 501
loss severity and credit risk for, 593n.1
planned amortization class, 499–501
residual, 504
sequential-pay, 497–499
structured interest-only, 497n.11
support (companion), 499–501
tranching, 308–309, 481–482
transaction costs, 9, 123
transparency, of markets, 58
Treasury inflation-indexed securities 
(TIIS), 326
Treasury inflation-protected securities 
(TIPS), 326, 328, 329
Trinidad & Tobago, 96
true yield, 422
true yield-to-maturity, 422–423
trust deeds, 305, 626
trustee agents, 479
trustees
bond indenture, 305
in securitization process, 479
trust law, 484
trust preferred securities, 596n.4
trusts, in securitization process, 478
TSX Group, 152
Tunisia, 96
Turkey, 96, 326, 369
turn-of-the-month effect, 132
turn-of-the-year effect, 131
Turquoise, 30
two-stage dividend discount model,

two-stage dividend discount model, 
261–264
Tyco International, Ltd., 199, 200
U
UBS, 209
Ukraine, 96
underlying asset, value of contract and, 20
underlying risk exposures, of options, 39
undervalued (term), 245
underwater mortgages, 488
underwriters, 360, 479
underwritten offerings, 50, 51, 360–362
uniform pricing rule, 56
Unilever, 210
Union Electric Company, 255–256
United Arab Emirates, 96
bankruptcy, 600
commercial paper, 374
covenant-strengthening investor 
groups, 627
securities, 315foreign bonds, 313, 314
inflation-linked bonds, 326, 327, 370
perpetual bonds in, 300
153

153
risk tolerance and equity ownership, 155
sinking fund arrangements, 322
social influences on tobacco industry, 
226
sovereign bonds, 305–306, 367–370
UK Debt Management Office, 306
bonds issued by, 315
United Nations, 196
United Rentals, Inc., 604–605, 642–643
ADRs, 167–168
auctions, 362–364
bond yields and credit risk/return, 
629–630
to global GDP , 150–151
commercial paper in, 374
company activities of government 
industries, 197
development of NAICS system, 197
floating-rate notes, 323
government-sponsored enterprises, 
490
617

617
municipal bonds in, 355
PSA prepayment benchmark, 493
residential mortgage loans, 486–489
returns
by asset class, 644–645
on reinvested dividends, 170
154–155
entities, 490securities ranked lower than 
securitization market, 474
sovereign bonds, 367–370
transition rates of credit ratings, 606
trust law in, 484
US Aggregate Bond Index, 357
US Air Force, 226
US Census Bureau, 197
US commercial paper (USCP) market, 
376–377
US Consumer Price Index (CPI), 325, 
326, 328, 329
US Department of Housing and Urban 
Development, 490
US dollar

US dollar
international bonds outstanding in, 351
US Federal Trade Commission (FTC), 
127
US GAAP
on disclosure of operating segment, 200
US Securities and Exchange Commission 
(SEC), 29
disclosure regulations, 122
prospectuses filed with, 478n.3
registration with, 168
Regulation FD, 122
requirements for sponsored DRs, 166
Rule 10b5-1 and 10b5-2, 122n.10
Rule 144A, 168
US Treasury, public auctions by, 
362–364
characteristics of, 368
discount rate, 429
maturity of, 351
returns on equities and bonds vs., 
152–153
transaction costs with, 123
US Treasury bonds (T-bonds), 368, 
560–561
US Treasury notes (T-notes), 368, 
547–548
units (term), 18
unrealized capital gains and losses, 569
unrestricted subsidiaries, 644
unsecured debt, 595, 596
unsponsored depository receipts, 166
upper Tier 2 securities, 596n.4
UPS, 209
Uranium Energy Corporation, 92–93
USCP market. see US commercial paper 
market

market
Utilities sector, 193
V
Vale, 209
Valero, 209
validity instructions, 44, 48–49
valuation
of equities ( see equity valuation)
of fixed-income securities ( see fixed-
income valuation)

Index  I-23
value. see also  present value models for 
equity valuation
book, 172–173, 176–177, 247
carrying, 247, 533
enterprise, 247, 274–276, 645
estimated, 245–246
fairly valued, 245
fundamental value, 119, 244
of growth opportunities, 257n.3
intrinsic
266–269
market
net asset value, 134
terminal, 251, 261
total market, 175
value effect, 133
Value Line,  262–264
value stocks, 97, 133
value tilt, of indexes, 91
value weighting. see market-
capitalization weighting
variable-rate mortgages, 487
variable-rate notes, 323
variation margin payments, for futures 
contracts, 22
venture capital, 15, 162
Viacom Corporation, 156–157
Vietnam, 96
Visa, 206, 209
in equity markets, 153–154
yield, 568–569
Volkswagen AG, 10, 189, 306
Volvo, 189
vote by proxy, 156
voting rights, shareholders’ , 156, 157
W

W
WAC. see weighted average coupon rate
capital
Waha Capital, 27
Wall Street Journal,  103Wal-Mart Stores Inc.
as bond issuer, 306
bonds issued by, 315, 316
industry life cycle of, 216–217
two-factor analysis of, 210
Walt Disney Company, 377
WAM. see weighted average maturity
warrants, 18, 333, 334
waterfall structures, 308, 481
Watson Pharmaceuticals Inc. case study, 
618–625
weak-form efficient markets, 125, 128, 
129
weekend effect, 132
(WACC), 178, 204
weighted average coupon rate (WAC), 
491–494
weighted average maturity (WAM), 
491–494
Western Europe, 350. see also  specific 
countries
Wilshire 5000 Total Market Index, 95
window dressing, 131
women, in workforce, 226–227
working capital, 618, 639
workout period, 505
World Bank. see International Bank for 
WorldCom, 608
W.W. Grainger, 210
Y
Yahoo!, 40
Yankee bonds, 313

Y
Yahoo!, 40
yen, Japanese
351
yield, 420–433
benchmark, 574
bond equivalent, 431–433
cash flow, 555
and credit risk/return, 629–630
current, 423
of fixed-income securities, 304
of fixed-rate bonds, 420–433
of floating-rate notes, 425–429
forward, 438government equivalent, 423
horizon, 532–536, 571
429–433
redemption, 304 ( see also  
yield-to-maturity)
required, 402
running, 304
simple, 423
true, 422
yield curves
benchmark, 443–445
inverted, 434
yield duration, 538, 545, 548, 562
yield maintenance charges, 505
over benchmark rates, 441–443
over benchmark yield curve, 443–445
based on spot rates, 412–413
for bond vs. money market, 429
building blocks of, 441–442
calculation of, 406–407
defined, 304, 407

differences in, 433–435
and Macaulay duration, 551
and rate of return, 531–532
true, 422–423
yield to redemption, 304
yield-to-worst, 425
YPG Holdings, 256
yuan renminbi, 351
Z
zero-coupon bonds, 301, 378
with call options, 382
convexity adjustment for, 560–563
as deferred coupon bonds, 325
spot curve for, 434
zero-coupon indexed bonds, 327
zero curve, 434
zero rates, 411
zero-volatility spread (Z-spread), 443, 
445
Zimmer, 209, 213

Ethical and Professional 
Standards 
Study Session 1 Ethical and Professional Standards 
The candidate should be able to explain the need for high ethical standards in the 
investment industry and the ethical responsibilities required by the CFA Institute 
Code of Ethics and Standards of Professional Conduct and to demonstrate the appli -
cation of the Code and Standards. The candidate should also be able to demonstrate 
an understanding of the Global Investment Performance Standards.
Trust in the investment profession is achieved only if those practicing within the 
industry adhere to the highest levels of ethical conduct and behavior. The CFA Institute 
Code of Ethics and Standards of Professional Conduct (Code and Standards) serve as 
the ethical foundation for the CFA Institute self-  regulatory program.
The Standards of Practice Handbook provides practical application of the Code

and Standards by explaining the purpose and scope of each standard, presenting rec -
ommended procedures for compliance, and providing examples of each standard in 
practice. 
The Global Investment Performance Standards (GIPS®) establish global standards 
for performance reporting by investment managers. By providing a consistent set of 
standards and methodology, GIPS facilitate the fair and accurate comparison of man -
agers around the world, while minimizing the potential for ambiguous or misleading 
performance reporting practices.

Standards 
This study session introduces ethics, related challenges to ethical behavior, and the 
role played by ethics in the investment profession. A framework to support ethical 
decision-  making is provided to help guide behavior. The CFA Institute Code of 
Ethics and Standards of Professional Conduct (Code and Standards) are examined, 
with attention given to each standard and its application. The session concludes with 
coverage of the Global Investment Performance Standards. 
Reading 1 Ethics and Trust in the Investment Profession  
by Bidhan L. Parmar, PhD, Dorothy C. Kelly, CFA, and 
David B. Stevens, CIMC, CFA
Reading 2 Code of Ethics and Standards of Professional Conduct  
Standards of Practice Handbook , Eleventh Edition
Reading 3 Guidance for Standards I–VII  
Standards of Practice Handbook , Eleventh Edition 
Reading 4 Introduction to the Global Investment Performance 
Standards (GIPS)

Reading 5 Global Investment Performance Standards (GIPS)EThICAL  AN d Pr OFESSIONAL  STAN dArd S 
1

Ethics and Trust in the 
Investment Profession
by Bidhan L. Parmar, PhD, Dorothy C. Kelly, CFA, and 
David B. Stevens, CIMC, CFA
Bidhan L. Parmar, PhD, is at the University of Virginia (USA). Dorothy C. Kelly, CFA, is at 
McIntire School of Commerce, University of Virginia (USA). David B. Stevens, CIMC, CFA, 
is at Wells Fargo Private Bank (USA).
a. explain ethics;
b. describe the role of a code of ethics in defining a profession;
c. identify challenges to ethical behavior;
d. describe the need for high ethical standards in the investment 
industry;
e. distinguish between ethical and legal standards;
f. describe and apply a framework for ethical decision making.
As a candidate in the CFA Program, you are both expected and required to meet 
high ethical standards. This reading introduces ideas and concepts that will help you 
understand the importance of ethical behavior in the investment industry. You will

be introduced to various types of ethical issues within the investment profession and 
learn about the CFA Institute Code of Ethics. Subsequently, you will be introduced 
to a framework as a way to approach ethical decision making.
Imagine that you are employed in the research department of a large financial 
services firm. You and your colleagues spend your days researching, analyzing, and 
valuing the shares of publicly traded companies and sharing your investment recom -
mendations with clients. You love your work and take great satisfaction in knowing 
that your recommendations can help the firm’s investing clients make informed invest -
ment decisions that will help them meet their financial goals and improve their lives.1rEAdING
1

Reading 1 ■ Ethics and Trust in the Investment Profession 6
Several months after starting at the firm, you learn that an analyst at the firm has 
been terminated for writing and publishing research reports that misrepresented the 
fundamental risks of some companies to investors. You learn that the analyst wrote 
the reports with the goal of pleasing the management of the companies that were 
the subjects of the research reports. He hoped that these companies would hire your 
firm’s investment banking division for its services and he would be rewarded with 
large bonuses for helping the firm increase its investment banking fees. Some clients 
bought shares based on the analyst’s reports and suffered losses. They posted stories 
on the internet about their losses and the misleading nature of the reports. When 
the media investigated and published the story, the firm’s reputation for investment 
research suffered. Investors began to question the firm’s motives and the objectivity of

its research recommendations. The firm’s investment clients started to look elsewhere 
for investment advice, and company clients begin to transfer their business to firms 
with untarnished reputations. With business declining, management is forced to trim 
staff. Along with many other hard-  working colleagues, you lose your job—through 
no fault of your own.
Imagine how you would feel in this situation. Most people would feel upset and 
resentful that their hard and honest work was derailed by someone else’s unethical 
behavior. Yet, this type of scenario is not uncommon. Around the world, unsuspecting 
employees at such companies as SAC Capital, Stanford Financial Group, Everbright 
Securities, Enron, Satyam Computer Services, Arthur Andersen, and other large com -
panies have experienced such career setbacks when someone else’s actions destroyed 
trust in their companies and industries.
Businesses and financial markets thrive on trust—defined as a strong belief in

the reliability of a person or institution. In a 2013 study on trust, investors indicated 
that to earn their trust, the top three attributes of an investment manager should be 
that it (1) has transparent and open business practices, (2) takes responsible actions 
to address an issue or crisis, and (3) has ethical business practices.1 Although these 
attributes are valued by customers and clients in any industry, this reading will explore 
why they are of particular importance to the investment industry.
People may think that ethical behavior is simply about following laws, regulations, 
and other rules, but throughout our lives and careers we will encounter situations in 
which there is no definitive rule that specifies how to act, or the rules that exist may be 
unclear or even in conflict with each other. Responsible people, including investment 
professionals, must be willing and able to identify potential ethical issues and create

solutions to them even in the absence of clearly stated rules.
ETHICS
Through our individual actions, each of us can affect the lives of others. Our decisions 
and behavior can harm or benefit a variety of stakeholders —individuals or groups 
of individuals who could be affected either directly or indirectly by a decision and 
thus have an interest, or stake, in the decision. Examples of stakeholders in decisions 
made by investment industry professionals include our colleagues, our clients, our 
employers, the communities in which we live and work, the investment profession, 
and other financial market participants. In some cases, our actions may benefit all of 
these stakeholder groups; in other cases, our actions may benefit only some stakeholder 
groups; and in still other cases, our actions may benefit some stakeholder groups and 2
1 CFA Institute and Edelman, “Investor Trust Study” (2013): http://www.cfapubs.org/doi/pdf/10.2469/
ccb.v2013.n14.1.

Ethics 7
harm others. For example, recall the research analyst in the introduction who wrote 
misleading research reports with the aim of increasing the financial benefit to him -
self and his employer. In the very short term, his conduct seemed to directly benefit 
some stakeholders (certain clients, himself, and his employer) and to harm other 
stakeholders (clients who invested based on his reports). Over a longer time period, 
his conduct resulted in harm to himself and many other stakeholders—his employer, 
his employer’s clients, his colleagues, investors, and through loss of trust when the 
story was published, the larger financial market.
Ethics encompasses a set of moral principles and rules of conduct that provide 
guidance for our behavior. The word “ethics” comes from the Greek word “ethos, ” 
meaning character, used to describe the guiding beliefs or ideals characterizing a 
society or societal group. Beliefs are assumptions or thoughts we hold to be true. A

principle is defined as a belief or fundamental truth that serves as the foundation for 
a system of belief or behavior or a chain of reasoning. Our beliefs form our values—
those things we deem to have worth or merit.
Moral principles  or ethical principles  are beliefs regarding what is good, accept -
able, or obligatory behavior and what is bad, unacceptable, or forbidden behavior. 
Ethical principles may refer to beliefs regarding behavior that an individual expects of 
himself or herself, as well as shared beliefs regarding standards of behavior expected 
or required by a community or societal group.
Another definition of ethics  is the study of moral principles, which can be described 
as the study of good and bad behavior or the study of making good choices as opposed 
to bad choices. The study of ethics examines the role of consequences and personal 
character in defining what is considered good, or ethical, conduct.

Ethical conduct is behavior that follows moral principles and balances self-  interest 
with both the direct and the indirect consequences of the behavior on others. Ethical 
actions are those actions that are perceived as beneficial and conforming to the ethi -
cal expectations of society. An action may be considered beneficial if it improves the 
outcomes or consequences for stakeholders affected by the action. Telling the truth 
about the risks or costs associated with a recommended investment, for example, is 
an ethical action—that is, one that conforms to the ethical expectations of society in 
general and clients in particular. Telling the truth is also beneficial; telling the truth 
builds trust with customers and clients and enables them to make more informed 
decisions, which should lead to better outcomes for them and higher levels of client/
customer satisfaction for you and your employer.
Widely acknowledged ethical principles include honesty, fairness or justice, dili -

gence, and respect for the rights of others. Most societal groups share these fundamen -
tal ethical principles and build on them, establishing a shared set of rules regarding 
how members should behave in certain situations. The principles or rules may take 
different forms depending on the community establishing them.
Governments and related entities, for example, may establish laws and/or regula -
tions to reflect widely shared beliefs about obligatory and forbidden conduct. Laws and 
regulations are rules of conduct specified by a governing body, such as a legislature 
or a regulator, identifying how individuals and entities under its jurisdiction should 
behave in certain situations. Most countries have laws and regulations governing the 
investment industry and the conduct of its participants. Differences in laws may reflect 
differences in beliefs and values.
In some countries, for example, the law requires that an investment adviser act

in the best interests of his or her clients. Other countries require that investment 
professionals recommend investments that are suitable for their clients. Investment 
advisers and portfolio managers who are required by law to act in their clients’ best 
interests must always put their clients’ interests ahead of their own or their employ -
ers’ interests. An investment adviser who is required by law to act in a client’s best 
interest must understand the client’s financial objectives and risk tolerance, research

Reading 1 ■ Ethics and Trust in the Investment Profession 8
and investigate multiple investment opportunities, and recommend the investment 
or investment portfolio that is most  suitable for the client in terms of meeting his 
or her long-  term financial objectives. In addition, the investment adviser would be 
expected to monitor the client’s financial situation and investments to ensure that 
the investments recommended remain the best overall option for meeting the client’s 
long-  term financial objectives. In countries with only a suitability requirement, it is 
legal for investment professionals to recommend a suitable investment to a client even 
if other, similar suitable investments with lower fees are available. These differences 
in laws reflect differences in beliefs and values.
Specific communities or societal groups in which we live and work sometimes cod -
ify their beliefs about obligatory and forbidden conduct in a written set of principles,

often called a code of ethics . Universities, employers, and professional associations 
often adopt a code of ethics to communicate the organization’s values and overall 
expectations regarding member behavior. The code of ethics serves as a general 
guide for how community members should act. Some communities will also expand 
on their codes of ethics and adopt explicit rules or standards that identify specific 
behaviors required of community members. These standards of conduct  serve as 
benchmarks for the minimally acceptable behavior of community members and can 
help clarify the code of ethics. Members can choose behaviors that demonstrate even 
higher standards. By joining the community, members are agreeing to adhere to the 
community’s code of ethics and standards of conduct. To promote their code of ethics 
and reduce the incidence of violations, communities frequently display their codes in 
prominent locations and in written materials. In addition, most communities require

that members commit to their codes in writing on an annual or more frequent basis.
Violations of a community’s established code of ethics and/or standards of con -
duct can harm the community in a variety of ways. Violations have the potential to 
damage the community’s reputation among external stakeholders and the general 
public. Violations can also damage the community’s reputation internally and lead to 
reduced trust among community members and can cause the organization to fracture 
or splinter from within. To protect the reputation of its membership and limit potential 
harm to innocent members, the community may take corrective actions to investigate 
possible violations, repair any damages, and attempt to discipline the violator or, in 
severe cases, revoke the violator’s membership in the community.
CFA Institute is an example of a community with an established code of ethics 
and standards of conduct. Its members and candidates commit to adhere to shared

beliefs about acceptable conduct for individuals participating in the investment indus -
try. These beliefs are presented in the Code of Ethics and Standards of Professional 
Conduct (Code and Standards), which are included in the CFA Institute Standards of 
Practice Handbook . The Code of Ethics communicates the organization’s principles, 
values, and expectations. For example, the Code states that members and candidates 
“place the integrity of the investment profession and the interests of clients above 
their own personal interests. ” The Standards of Professional Conduct outline mini -
mally acceptable behaviors expected of all CFA Institute members and candidates. 
For example, one standard requires that “Members and Candidates must act for the 
benefit of their clients and place their clients’ interests before their employer’s or their 
own interests. ” Another standard requires that “Members and Candidates must make

full and fair disclosure of all matters that could reasonably be expected to impair 
their independence and objectivity or interfere with respective duties to their clients, 
prospective clients, and employer. Members and Candidates must ensure that such 
disclosures are prominent, are delivered in plain language, and communicate the 
relevant information effectively. ”
CFA Institute members and candidates re-  affirm their commitment to adhere to the 
Code and Standards each year. In addition, to protect the reputation of the community, 
members and candidates agree to submit a Professional Conduct Statement each year

Ethics and Professionalism 9
disclosing conduct that may have violated the Code and Standards. To protect mem -
bers and candidates, CFA Institute has an established disciplinary process. Members 
and candidates who violate the Code and Standards are subject to disciplinary action.
EXAMPLE 1   
Ethics
1 Which of the following statements is most  accurate? Ethics can be 
A a commitment to upholding the law.
B an individual’s personal opinion about right and wrong.
C a set of moral principles that provide guidance for our behavior.
2 Which of the following statements is most  accurate? Standards of conduct:
A are a necessary component of any code of ethics.
B serve as a general guide regarding proper conduct by members of a 
group.
C serve as benchmarks for the minimally acceptable behavior required of 
members of a group.
C is correct. Ethics can be described as a set of moral principles that provide

guidance for our behavior; these may be moral principles shared by a community 
or societal group.
C is correct. Standards of conduct serve as benchmarks for the minimally 
acceptable behavior required of members of a group. Some organizations will 
adopt only a code of ethics, which communicates the organization’s values and 
overall expectations regarding member behavior. Others may adopt both a 
code of ethics and standards of conduct. Standards of conduct identify specific 
behavior required of community members and serve as benchmarks for the 
minimally acceptable behavior of community members.
ETHICS AND PROFESSIONALISM
As you progress in your career, you may find that attitudes among your peers vary: 
Some of your peers may be happy to have a job, others may consider themselves fortu -
nate to find a vocation, and some may consider themselves part of a profession. What 
are the differences? A job is very simply the work someone does to earn a living. A

vocation is a job or occupation to which someone is particularly well suited and is very 
dedicated. Often, people will refer to a vocation as a calling: They work in service of a 
cause they consider worthy. A profession is the ultimate evolution of an occupation, 
resulting from the efforts of members practicing the occupation at a high level and 
creating a set of ethics and standards of conduct for the entire group. A profession has 
several characteristics that distinguish it from ordinary occupations. A profession is
1 based on specialized knowledge and skills.3

Reading 1 ■ Ethics and Trust in the Investment Profession 10
2 based on service to others.
3 practiced by members who share and agree to adhere to a common code of 
ethics.
Professionals use their specialized knowledge and skills to serve their clients—with 
whom they have a special relationship and to whom they have a special duty. Clients 
differ from customers. A customer purchases goods or services in a single transaction 
or series of transactions and pays for each transaction or series of transactions. A 
client, in contrast, enters into an ongoing relationship with a professional, hiring the 
professional to use his or her special knowledge for the benefit of the client, usually 
for a fee. The relationship between client and professional is based on trust rather than 
transactions. In exchange for the agreed-  on fee, the professional accepts the duty to 
place the client’s interests first at all times.
In any given profession, the code of ethics communicates the shared principles and

expected behaviors of its members. In addition to providing members with guidance for 
decision making, a code of ethics may generate confidence among not only members 
of the profession but also individuals who are not members of the profession, such as 
clients, prospective clients, and/or the general public. The code of ethics informs and 
provides some assurance to the public that the profession’s members will use their 
specialized skills and knowledge in service of others.
Some codes will be enhanced and clarified by the adoption of standards of conduct 
or specific benchmarks of behavior required of members. These standards may be 
principle based or rule based. The CFA Institute Code and Standards are an example 
of principle-  based standards; they are based on the shared principles of honesty, 
integrity, transparency, diligence, and placing client interests first. Rule-  based stan -
dards are often narrowly defined, applying to specific groups of individuals in specific

circumstances. Principle-  based standards, such as those of CFA Institute, apply to 
all candidates and members at all times regardless of title, position, occupation, geo -
graphic location, or specific situation.
As a CFA Program candidate, you are expected to act in accordance with the 
ethical and professional competency responsibilities of the investment profession as 
expressed in the Code and Standards. The Code and Standards are designed to foster 
and reinforce a culture of responsibility and professionalism. The Code and Standards 
apply to all your professional activities, including but not limited to trading securities 
for yourself and/or others, providing investment advice, conducting research, and 
performing other investment services.
EXAMPLE 2   
Ethics and Professionalism
1 Which of the following statements best describes how professionals use 
their specialized knowledge and skills? Professionals use their specialized 
knowledge and skills:
A in service to others.

B to advance their career.
C for the exclusive benefit of their employers.
2 Which of the following statements is most  accurate? A profession’s code of 
ethics:
A includes standards of conduct or specific benchmarks for behavior.

Challenges to Ethical Conduct 11
B ensures that all members of a profession will act ethically at all times.
C publicly communicates the shared principles and expected behaviors 
of a profession’s members.
A is correct. Professionals use specialized knowledge and skills in service to 
others. Their career and employer may benefit, but those results are not the pri -
mary focus of a professional’s use of his or her specialized knowledge and skills.
C is correct. A profession’s code of ethics publicly communicates the shared 
principles and expected behaviors of a profession’s members. The existence 
of a code of ethics does not ensure that all members will behave in a manner 
consistent with the code and act ethically at all times. A profession will often 
establish a disciplinary process to address alleged violations of the code of eth -
ics. A profession may adopt standards of conduct to enhance and clarify the 
code of ethics.
CHALLENGES TO ETHICAL CONDUCT

Professionals generally aim to be responsible and to adhere to high moral standards, so 
what is the benefit of studying ethics? Throughout our careers, we may find ourselves 
in difficult or at least unfamiliar situations in which an appropriate course of action is 
not immediately clear and/or there may be more than one seemingly acceptable choice; 
studying ethics helps us prepare for such situations. This section addresses challenges 
to engaging in ethical conduct. Failure to acknowledge, understand, or consider these 
challenges can lead to poor decision making, resulting in unintentional consequences, 
such as unethical conduct and potential violations of the Code and Standards.
Several challenges can make adherence to ethical conduct difficult. First, people 
tend to believe that they are ethical people and that their ethical standards are higher 
than average. Of course, everyone cannot be above average. However, surveys show

this belief in above averageness remains. As reported in A Crisis of Culture  (2013), for 
example, 71% of surveyed financial services executives rated their firm’s reputation for 
ethical conduct better than the rest of the industry.2 Among those surveyed, 59% rated 
the industry’s reputation for ethical conduct as positive. In contrast, a survey of global 
consumer sentiment conducted the same year revealed that only 46% of consumers 
surveyed trusted financial service providers to do the right thing.3 In fact, financial 
services was the least trusted of all industries included in the survey.
These survey results illustrate overconfidence, a common behavioral bias that 
can lead to faulty decision making. Studies have shown that our beliefs and emotions 
frequently interfere with our cognitive reasoning and result in behavioral bias, a ten -
dency to behave in a way that is not strictly rational.4 As a result of the overconfidence

bias, we are more likely to overestimate the morality of our own behavior, particularly 
in situations that we have not faced before. The overconfidence bias can result in a 4
2 Economist Intelligence Unit, “ A Crisis of Culture: Valuing Ethics and Knowledge in Financial Services, ” 
Economist Intelligence Unit Report sponsored by CFA Institute (2013).
3 CFA Institute and Edelman, “Investor Trust Study” (2013): http://www.cfapubs.org/doi/pdf/10.2469/
4 Max H. Bazerman and Don A. Moore, Judgment in Managerial Decision Making , 8th ed. (Hoboken, NJ: 
John Wiley & Sons, 2013).

Reading 1 ■ Ethics and Trust in the Investment Profession 12
failure to consider, explicitly or implicitly, important inputs and variables needed to 
form the best decision from an ethical perspective. In general, the overconfidence bias 
leads us to place too much importance on internal traits and intrinsic motivations, 
such as “I’m honest and would not lie, ” even though studies have shown that internal 
traits are generally not the main determinant of whether or not someone will behave 
ethically in a given situation.5
A second challenge is that decision makers often fail to recognize and/or signifi -
cantly underestimate the effect of situational influences, such as what other people 
around them are doing. Situational influences  are external factors, such as environ -
mental or cultural elements, that shape our thinking, decision making, and behavior. 
Social psychologists have studied how much situational influences affect our behavior

and have found that even good people with honorable motives can and often will be 
influenced to do unethical things when put into difficult situations.6 Experiments have 
shown that even people who consider themselves strong, independent, free thinkers 
will conform to social pressures in many situations.7 The bystander effect, for example, 
demonstrates that people are less likely to intervene in an emergency when others 
are present. Fortunately, experiments have also shown that situational influences can 
induce people to act more ethically. For example, people tend to behave more ethically 
when they think someone else is watching or when there is a mirror placed close to 
them.8 The important concept to understand is that situational influences have a very 
powerful and often unrecognized effect on our thinking and behavior. Thus, learning 
to recognize situational influences is critical to making good decisions.

Common situational influences in the investment industry that can shape think -
ing and behavior include money and prestige. One experiment found that simply 
mentioning money can reduce ethical behavior. In the experiment, participants were 
less likely to cooperate when playing a game if the game was called the Wall Street 
Game, rather than the Community Game.9 In the investment industry, large financial 
rewards—including individual salaries, bonuses, and/or investment gains—can induce 
honest and well-  intentioned individuals to act in ways that others might not consider 
ethical. Large financial rewards and/or prestige can motivate individuals to act in their 
own short-  term self-  interests, ignoring possible short-  term risks or consequences to 
themselves and others as well as long-  term risks or consequences for both themselves 
and others. Another extremely powerful situational influence is loyalty. Loyalty to

supervisors or organizations, fellow employees, and other colleagues can tempt indi -
viduals to make compromises and take actions that they would reject under different 
situational influences or judge harshly when taken by others.
Situational influences often blind people to other important considerations. 
Bonuses, promotions, prestige, and loyalty to employer and colleagues are examples 
of situational influences that frequently have a disproportionate weight in our decision 
making. Our brains more easily and quickly identify, recognize, and consider these 
short-  term situational influences than longer-  term considerations, such as a commit -
ment to maintaining our integrity and contributing to the integrity of the financial 
markets. Although absolutely important, these long-  term considerations often have 
5 Lee Ross and Richard E. Nisbett, The Person and the Situation: Perspectives of Social Psychology  (New 
York: McGraw-  Hill, 1991).

6 Stanley Milgram, Obedience to Authority: An Experimental View  (New York: Harper & Row, 1974).
7 Philip G. Zimbardo, The Power and Pathology of Imprisonment: Hearings Before Subcommittee No. 3 of 
the Committee on the Judiciary , 92nd Congress, Corrections: Part II, Prisons, Prison Reform, and Prisoners’ 
Rights Congressional Record (Serial No. 15, 25 October 1971).
8 John M. Darley and C. Daniel Batson, “From Jerusalem to Jericho: A Study of Situational and Dispositional 
Variables in Helping Behavior, ” Journal of Personality and Social Psychology , vol., 27, no. 1 (1973): 100–108.
9 Varda Liberman, Steven M. Samuels, and Lee Ross, “The Name of the Game: Predictive Power of 
Reputations versus Situational Labels in Determining Prisoner’s Dilemma Game Moves, ” Personality and 
Social Psychology Bulletin,  vol. 30, no. 9 (September 2004): 1175–1185.

Challenges to Ethical Conduct 13
less immediate consequences than situational influences, making them less obvious 
as factors to consider in a decision and, therefore, less likely to influence our overall 
decision making. Situational influences shift our brain’s focus from the long term to 
the short or immediate term. When our decision making is too narrowly focused on 
short-  term factors and/or self-  interest, we tend to ignore and/or minimize the longer-  
term risks and/or costs and consequences to ourselves and others, and the likelihood 
of suffering ethical lapses and making poor decisions increases.
The story of Enron Corporation, a US energy company, illustrates the power 
of situational influences. In the late 1990s, with approximately 20,000 employees, 
the company’s culture focused on increasing current revenues and the share price 
without regard for the long-  term sustainability or consequences of such a culture.

Management received significant stock options, which provided strong motivation 
to make decisions and take actions that would increase the share price. The focus on 
share price was inescapable; employees were greeted by the stock ticker in lobbies 
and elevators and on their computer screens. The focus on share price overshadowed 
considerations about stakeholders and the long-  term sustainability of the business 
and its profits. Under these situational influences, some senior managers made poor 
decisions and eventually succumbed to unethical conduct. They devised and adopted 
complex accounting strategies that inflated revenues, obscured the company’s financial 
performance, and hid billions of dollars in debt. In October 2001, the financial press 
revealed what Enron’s accounting practices had previously concealed. Shares of Enron, 
which had reached a high of US$90.75 in mid-  2000, fell to less than US$1 by the end of

November 2001. The company, which had claimed revenues of nearly US$111 billion 
in 2000, secured a place in the record books as one of the largest bankruptcies in US 
history. Dozens of former executives and employees were investigated, and many were 
charged with fraud and/or conspiracy. Sixteen individuals pled guilty, including Chief 
Financial Officer (CFO) Andrew S. Fastow, who pled guilty to conspiracy, forfeited 
nearly US$30 million in cash and property, and was sentenced to six years in prison. 
After a lengthy investigation and trial, former Chief Executive Officer Jeffrey K. 
Skilling was convicted in May 2006 of fraud, conspiracy, insider trading, and making 
false statements. He was sentenced to more than 24 years in prison, a sentence that 
was eventually reduced to 14 years.10
Loyalty to employer and/or colleagues is an extremely powerful situational influence. 
Our colleagues can influence our thinking and behavior in both positive and negative

ways. For example, colleagues may have encouraged you to signal your commitment 
to your career and high ethical standards by enrolling in the CFA Program. If you 
work for or with people who are not bound by the Code and Standards, they might 
encourage you to take actions that are consistent with local law, unaware that the 
recommended conduct falls short of the Code and Standards.
Well-  intentioned firms may adopt or develop strong compliance programs to 
encourage adherence to rules, regulations, and policies. A strong compliance policy 
is a good start to developing an ethical culture, but a focus on adherence to rules 
may not be sufficient. A compliance approach may not encourage decision makers 
to consider the larger picture and can oversimplify decision making. Taken to the 
extreme, a strong compliance culture can become another situational influence that 
blinds employees to other important considerations. In a firm focused primarily on

compliance, employees may adopt a “check the box” mentality rather than an ethical 
decision-  making approach. Employees may ask the question “What can I do?” rather 
than “What should  I do?” At Enron, for example, in compliance with procedures, CFO 
Fastow dutifully disclosed that he was the owner of several partnerships planning to 
10 Chairman Kenneth M. Lay was also convicted of fraud, conspiracy, and making false statements. Lay 
died on 5 July 2006 of heart failure while awaiting sentencing. Because he died before he could appeal the 
verdict, the convictions were subsequently vacated.

Reading 1 ■ Ethics and Trust in the Investment Profession 14
transact business with Enron. With powerful situational influences at work, Fastow 
and board members focused on “What can I do?” rather than “What should  I do?” 
Compliance required that Fastow make the ownership disclosures and request approval 
for the proposed business transactions from Enron’s board of directors, which he did. 
Board members seemed to focus on the compliance requirements to provide board 
approval of the proposed transactions rather than considering their obligations to 
shareholders. In so doing, they neglected to view the issue from a broader perspec -
tive and consider “What should  we do?” Consequently, they failed to recognize that 
the proposed transactions placed Fastow’s interests in direct conflict with those of 
his employer and its shareholders. By focusing on the compliance requirements to 
provide board approval, board members failed to prevent Fastow from engaging in

activity that enriched himself at the expense of his employer and its shareholders. The 
Enron case illustrates both the power of situational influences and the limitations of 
a compliance approach, which can contribute to overconfidence and is insufficient 
for ensuring ethical decision making,
EXAMPLE 3   
Challenges to Ethical Conduct
1 Which of the following will most likely  determine whether an individual 
will behave unethically?
A The person’s character
B The person’s internal traits and intrinsic motivation
C External factors, such as environmental or cultural elements
2 Which of the following statements is most  accurate?
A Large financial rewards, such as bonuses, are the most powerful situa -
tional influences.
B When decision making focuses on short-  term factors, the likelihood of 
ethical conduct increases.
C Situational influences can motivate individuals to act in their short-  
term self-  interests without recognizing the long-  term risks or conse -

quences for themselves and others.
C is correct. Social psychologists have shown that even good people may behave 
unethically in difficult situations. Situational influences, which are external fac -
tors (e.g., environmental or cultural elements), can shape our thinking, decision 
making, and behavior and are more likely to lead to unethical behavior than 
internal traits or character.
C is correct. Situational influences can motivate individuals to act in their short-  
term self-  interests without recognizing the long-  term risks or consequences 
for themselves and others. Large financial rewards are powerful situational 
influences, but in some situations, other situational influences, such as loyalty 
to colleagues, may be even more powerful.

The Importance of Ethical Conduct in the Investment Industry 15
THE IMPORTANCE OF ETHICAL CONDUCT IN THE 
INVESTMENT INDUSTRY
Why are high ethical standards so important for the investment industry and invest -
ment professionals? As the global financial crisis of 2008 demonstrated, isolated and 
seemingly unimportant individual decisions, such as approving loans to individuals 
unable to provide proof of stable income, in aggregate can precipitate a market crisis 
that can lead to economic difficulties and job losses for millions of individuals. In an 
interconnected global economy and marketplace, each market participant must strive 
to understand how his or her decisions and actions, and the products and services he 
or she provides, may affect others not just in the short term but also the long term.
The investment industry serves society by matching those who supply capital, or 
money, with those who seek capital to finance, or fund, their activities. For simplicity,

let us refer to those who supply capital as investors and those who seek capital as 
borrowers. Borrowers may seek capital to achieve long-  term goals, such as building or 
upgrading factories, schools, bridges, highways, airports, railroads, or other facilities. 
They may also seek short-  term capital to fund short-  term goals and/or support their 
daily operations. Borrowers seeking capital to meet short- and long-  term objectives 
include sovereign entities, businesses, schools, hospitals, companies, and other 
organizations that serve others. Some borrowers will turn to banks or other lending 
institutions to finance their activities; others will turn to the financial markets to access 
the funds they need to achieve their goals.
In exchange for supplying capital to fund the borrowers’ endeavors, investors 
expect that their investments will generate returns that compensate them for the use 
of their funds and the risks involved. Before providing capital, diligent and disciplined

investors will evaluate the risks and rewards of providing the capital. Some risks, such 
as a downturn in the economy or a new competitor, could adversely affect the returns 
expected from the investment. To help evaluate the potential risks and rewards of the 
investment, investors conduct research, reading and evaluating the borrower’s finan -
cial statements, management’s business plan, research reports, industry reports, and 
competitive analyses. Responsible investors will not invest their capital unless they 
trust that their capital will be used in the way that has been described and is likely 
to generate the returns they desire. Investors and society benefit when capital flows 
to borrowers that can create the most value from the capital through their products 
Capital flows more efficiently between investors and borrowers when financial 
market participants are confident that all parties will behave ethically. Ethical behavior

builds and fosters trust, which has benefits for individuals, firms, the financial mar -
kets, and society. When people believe that a person or institution is reliable and acts 
in accordance with their expectations, they are more willing to take risks involving 
those people and institutions. For example, when people trust their financial advisers, 
institutions, and the financial markets, they are more likely to invest their money and 
accept the risk of short-  term price fluctuations because they can reasonably believe 
that their investments will provide them with long-  term benefits. Entrepreneurs are 
more likely to accept the risk of expanding their businesses, and hiring additional 
employees, if they believe they will be able to attract investors with the funds needed 
to expand at a reasonable cost. The higher the level of trust in the financial system, the 
more people are willing to participate in the financial markets. Broad participation in

the financial markets enables the flow of capital to fund the growth in goods, services, 
and infrastructure that benefits society with new and often better hospitals, bridges, 
products, services, and jobs. Broad participation in the financial markets also means 5

Reading 1 ■ Ethics and Trust in the Investment Profession 16
that the need and demand for investment professionals increase, resulting in more 
job opportunities for those seeking to use their specialized skills and knowledge of 
the financial markets in service to others.
Ethics always matter, but ethics are of particular importance in the investment 
industry because the investment industry and financial markets are built on trust. Trust 
is important to all business, yet it is especially important in the investment industry for 
several reasons, including the nature of the client relationship, differences in knowl -
edge and access to information, and the nature of investment products and services.
In the client relationship, investors entrust their assets to financial firms for care 
and safekeeping. By doing so, clients charge the firm and its employees with a special 
responsibility; they are putting their faith and trust in the firm and its employees to

protect their assets. If the firm and its employees fail to protect clients’ assets, it could 
have severe consequences for those clients. Without trust in that protection, the firm 
and its employees would not have any business.
Those who work in the investment industry, as well as those who work in other 
professions, have specialized knowledge and sometimes better access to information. 
Having specialized knowledge and better access to information is an advantage in 
any relationship, giving one party more power than the other. Investors trust that the 
professionals they hire will not use their knowledge to take advantage of them. They 
rely on the investment professional to use his or her specialized knowledge to serve 
or benefit their clients’ interests.
Another reason why trust is so important in the investment industry has to do with 
the nature of its products and services. In other industries—such as the transportation

industry, the technology industry, the retail industry, or the food industry—companies 
produce products and/or provide services that are tangible and/or clearly visible. 
We can hold an electronic tablet in our hands and inspect it. We can use software 
programs, shop at retailers, dine at restaurant chains, and watch films. We can judge 
the quality of the product or service based on a variety of factors: How well does it 
perform its intended function? How efficient is it? How durable is it? How appealing 
is it? Is the price reasonable or appropriate for the product or service?
In the investment industry, many investments are intangible and appear only as 
numbers on a page or a screen. Investors cannot hold, inspect, or test their intended 
purchases as they can a smartphone or a television set, each of which often come 
with warranties should they fail to function as advertised. Without tangible products 
to inspect, and with no warranties for protection should the product or service fail

to perform as expected, investors must rely on the information provided about the 
investment—both before and after purchase. When they call their financial adviser 
and ask to see their investments, they receive either an electronic or printed statement 
with a list of holdings. They trust that the information is accurate and complete—a 
fair representation—just as they trust that the investment professionals with whom 
they are dealing will protect their interests. The globalization of finance also means 
that investment professionals are likely to have business opportunities in new or 
unfamiliar places. Without trust, financial transactions, including global transactions, 
are less likely to occur.
Because of these factors, trust is the very foundation of the financial markets. This 
trust is built, fostered, and maintained by the ethical actions of all the individuals who 
work and/or participate in the markets, including those who work for companies,

banks, investment firms, sovereign entities, rating agencies, accounting firms, financial 
advisers and planners, and institutional and retail investors. When market participants 
act ethically, investors and others can trust that the numbers on the screen or the 
page are accurate representations and be confident that investing and participating 
in the financial markets is worthwhile.

Ethical vs. Legal Standards 17
Ethical behavior by all market participants can lead to broader participation in 
the markets, protection of clients’ interests, and more opportunities for investment 
professionals and their firms. Ethical behavior by firms can lead to higher levels of 
success and profitability for the firms as well as their employees. Clients are attracted 
to firms with trustworthy reputations, leading to more business, higher revenues, 
and more profits. Ethical firms may also enjoy lower relative costs than unethical 
firms because regulators are less likely to have cause to initiate costly investigations 
or impose significant fines on firms in which high ethical standards are the norm.
Conversely, unethical behavior erodes and can even destroy trust. When clients 
and investors suspect that they are not receiving accurate information or that the 
market is not a level playing field, they lose trust. Investors with low trust are less

willing to accept risks. They may demand a higher return for the use of their capital, 
choose to invest elsewhere, or choose not to invest at all. Any of these actions would 
increase costs for borrowers seeking capital to finance their activities. Without access 
to capital, borrowers may not be able to meet their goals of building new factories, 
bridges, or hospitals. Decreases in investments can harm society by reducing jobs, 
growth, and innovation. Unethical behavior ultimately harms not only clients, but 
also the firm, its employees, and others.
Diminished trust in financial markets can reduce growth in the investment industry 
and tarnish the reputation of firms and individuals in the industry, even if they did 
not participate in the unethical behavior. Unethical behavior interferes with the ability 
of markets to channel capital to the borrowers that can create the most value from 
the capital, contributing to economic growth. Both markets and society suffer when

unethical behavior destroys trust in financial markets. For you personally, unethical 
behavior can cost you your job, reputation, and professional stature and can lead to 
monetary penalties and possibly time in jail.
EXAMPLE 4   
The Importance of Ethical Conduct in the Investment 
Industry
Which of the following statements is most  accurate? Investment professionals 
have a special responsibility to act ethically because:
A the industry is heavily regulated.
B they are entrusted to protect clients’ assets.
C the profession requires compliance with its code of ethics.
Solution:
B is correct. Investment professionals have a special responsibility because clients 
entrust them to protect the clients’ assets.
ETHICAL VS. LEGAL STANDARDS
Many times, stakeholders have common ethical expectations. Other times, different 
stakeholders will have different perceptions and perspectives and use different criteria 
to decide whether something is beneficial and/or ethical.

Laws and regulations often codify ethical actions that lead to better outcomes for 
society or specific groups of stakeholders. For example, some laws and regulations 
require businesses and their representatives to tell the truth. They require specific 6

Reading 1 ■ Ethics and Trust in the Investment Profession 18
written disclosures in marketing and other materials. Complying with such rules is 
considered an ethical action; it creates a more satisfactory outcome that conforms to 
stakeholders’ ethical expectations. As an example, consider disclosure requirements 
mandated by securities regulators regarding the risks of investing. Complying with 
such rules creates better outcomes for you, your clients, and your employer. First, 
compliance with the rule reduces the risk that clients will invest in securities without 
understanding the risks involved, which, in turn, reduces the risk that clients will file 
complaints and/or take legal action if their investments decline in value. Complying 
with the rules also reduces the risk that regulators will initiate an investigation, file 
charges, or/and discipline or sanction you and/or your employer. Any of these actions

could jeopardize the reputation and future prospects of you and your employer. Conduct 
that reduces these risks (e.g., following disclosure rules) would be considered ethical; 
it leads to better outcomes for you, your clients, and your employer and conforms to 
the ethical expectations of various stakeholders.
Although laws frequently codify ethical actions, legal and ethical conduct are not 
always the same. Think about the diagram in Exhibit 1. Many types of conduct are 
both legal and ethical, but some conduct may be one and not the other. Some legal 
behaviors or activities may be considered unethical, and some behaviors or activi -
ties considered ethical may be deemed illegal in certain jurisdictions. Acts of civil 
disobedience, such as peaceful protests, may be in response to laws that individuals 
consider unethical. The act of civil disobedience may itself be considered ethical, and 
yet it violates existing local laws.

The investment industry has examples of conduct that may be legal but considered 
by some to be unethical. Some countries, for example, do not have laws prohibiting 
trading while in possession of material nonpublic information, but many investment 
professionals and CFA Institute consider such trading unethical.
Another area in which ethics and laws may conflict is the area of “whistleblowing. ” 
Whistleblowing refers to the disclosure by an individual of dishonest, corrupt, or 
illegal activity by an organization or government. Depending on the circumstances, 
a whistleblower may violate organizational policies and even local laws with the dis -
closure; thus, a whistleblower’s actions may be deemed illegal and yet considered by 
some to be ethical.
Exhibit 1   Types of Conduct
LegalLegal
&
EthicalEthical
Some people advocate that increased regulation and monitoring of the behavior

of participants in the investment industry will increase trust in the financial markets. 
Although this approach may work in some circumstances, the law is not always the

Ethical vs. Legal Standards 19
best mechanism to reduce unethical behavior for several reasons. First, laws typically 
follow market practices; regulators may proactively design laws and regulations to 
address existing or anticipated practices that may adversely affect the fairness and 
efficiency of markets or reactively design laws and regulations in response to a crisis 
or an event that resulted in significant monetary losses and loss of confidence/trust 
in the financial system. Regulators’ responses typically take significant time, during 
which the problematic practice may continue or even grow. Once enacted, a new law 
may be vague, conflicting, and/or too narrow in scope. A new law may reduce or even 
eliminate the existing activity while simultaneously creating an opportunity for a dif -
ferent, but similarly problematic, activity. Additionally, laws vary across countries or 
jurisdictions, allowing questionable practices to move to places that lack laws relevant

to the questionable practice. Laws are also subject to interpretation and compliance 
by market participants, who may choose to interpret the law in the most advanta -
geous way possible or delay compliance until a later date. For these reasons, laws and 
regulations are insufficient to ensure the ethical behavior of investment professionals 
and market participants.
Ethical conduct goes beyond what is legally required and encompasses what dif -
ferent societal groups or communities, including professional associations, consider 
to be ethically correct behavior. To act ethically, individuals need to be able to think 
through the facts of the situation and make good choices even in the absence of clear 
laws or rules. In many cases, there is no simple algorithm or formula that will always 
lead to an ethical course of action. Ethics requires judgment—the ability to make 
considered decisions and reach sensible conclusions. Good ethical judgment requires

actively considering the interests of stakeholders and trying to benefit multiple stake -
holders—clients, family, colleagues, employers, market participants, and so forth—and 
minimize risks, including reputational risk.
EXAMPLE 5   
Ethical vs. Legal Standards
1 Which of the following statements is most  accurate?
A All legal behavior is ethical behavior.
B Some ethical behavior may be illegal.
C Legal standards represent the highest standard.
A Increased regulations are the most useful means to reduce unethical 
behavior by market participants.
B Regulators quickly design and implement laws and regulations to 
address practices that adversely affect the fairness and efficiency of 
markets.
C New laws designed to reduce or eliminate conduct that adversely 
affects the markets can create opportunities for different, but similarly 
problematic, conduct.

B is correct. Some ethical behavior may be illegal. Civil disobedience is an exam -
ple of what may be illegal behavior that some consider to be ethical. Legal and 
ethical behavior often coincide but not always. Standards of conduct based on 
ethical principles may represent a higher standard of behavior than the behavior 
required by law.

Reading 1 ■ Ethics and Trust in the Investment Profession 20
C is correct. New laws designed to reduce or eliminate conduct that adversely 
affects the markets can create opportunities for different, but similarly prob -
lematic, conduct.
ETHICAL DECISION-  MAKING FRAMEWORKS
Laws, regulations, professional standards, and codes of ethics can guide ethical behav -
ior, but individual judgment is a critical ingredient in making principled choices and 
engaging in appropriate conduct. One strategy to increase trust in the investment 
industry is to increase the ability and motivation of market participants to act ethically 
and help them minimize the likelihood of unethical actions. By integrating ethics into 
the decision-  making activities of employees, firms can enhance the ability and the 
motivation of employees to act ethically, thereby reducing the likelihood of unethical 
actions. The ability to relate an ethical decision-  making framework to a firm’s or pro -

fession’s code of ethics allows investment professionals to bring the principles of the 
code of ethics to life. An investment professional’s natural desire to “do the right thing” 
can be reinforced by building a culture of integrity in the workplace. Development, 
maintenance, and demonstration of a strong culture of integrity within the firm by 
senior management may be the single most important factor in promoting ethical 
behavior among the firm’s employees.
Adopting a code that clearly lays out the ethical principles that guide the thought 
processes and conduct the firm expects from its employees is a critical first step. But 
a code of ethics, although necessary, is insufficient. Simply nurturing an inclination to 
do right is no match for the multitude of daily decisions that investment profession -
als make. We need to exercise ethical decision-  making skills to develop the muscle 
memory necessary for fundamentally ethical people to make good decisions despite

the reality of conflicts and our natural instinct for self-  preservation. Just as coaching 
and practice transform our natural ability to run across a field into the technique 
and endurance required to run a race, teaching, reinforcing, and practicing ethical 
decision-  making skills prepare us to confront the hard issues effectively. It is good 
for business, individuals, firms, the industry, and the markets, as well as society as a 
whole, to engage in the investment management profession in a highly ethical manner. 
A strong ethical culture that helps honest, ethical people engage in ethical behavior 
will foster the trust of investors, lead to robust global financial markets, and ultimately 
benefit society. That is why ethics matter.
When faced with decisions that can affect multiple stakeholders, investment 
professionals must have a well-  developed set of principles; otherwise, their thought 
processes can lead to, at best, indecision and, at worst, fraudulent conduct and

destruction of the public trust. Establishing an ethical framework to guide your internal 
thought process regarding how to act is a crucial step to engaging in ethical conduct. 
Investment professionals are generally comfortable analyzing and making decisions 
from an economic (profit/loss) perspective. Given the importance of ethical behavior 
in carrying out professional responsibilities, it is also important to analyze decisions 
and their potential consequences from an ethical perspective. Using a framework 
for ethical decision making will help investment professionals to effectively examine 
their choices in the context of conflicting interests common to their professional 
obligations (e.g., researching and gathering information, developing investment 
recommendations, and managing money for others). Such a framework will allow 
investment professionals to analyze and choose options in a way that allows them

to meet high standards of ethical behavior. An ethical decision-  making framework 7

Ethical Decision-  Making Frameworks 21
provides investment professionals with a tool to help them adhere to a code of eth -
ics. By applying the framework and analyzing the particular circumstances of each 
available alternative, investment professionals are able to determine the best course 
of action to fulfill their responsibilities in an ethical manner.
An ethical decision-  making framework will help a decision maker see the situation 
from multiple perspectives and pay attention to aspects of the situation that may be 
less evident with a short-  term, self-  focused perspective. The goal of getting a broader 
picture of a situation is to be able to create a plan of action that is less likely to harm 
stakeholders and more likely to benefit them. If a decision maker does not know or 
understand the effects of his or her actions on stakeholders, the likelihood of making 
a decision and taking action that harms stakeholders is more likely to occur, even if

unintentionally. Finally, an ethical decision-  making framework helps decision makers 
justify their actions to a broader audience of stakeholders.
Ethical decision-  making frameworks are designed to facilitate the decision-  making 
process for all decisions. They help people look at and evaluate a decision from mul -
tiple perspectives, enabling them to identify important issues they might not oth -
erwise consider. Using an ethical decision-  making framework consistently will help 
you develop sound judgment and decision-  making skills and avoid making decisions 
that have unanticipated ethical consequences. Ethical decision-  making frameworks 
come in many forms with varying degrees of detail. A general ethical decision-  making 
framework is shown in Exhibit 2.
Exhibit 2   Ethical Decision-  Making Framework
■■Identify: Relevant facts, stakeholders and duties owed, ethical principles, 
conflicts of interest
■■Consider: Situational influences, additional guidance, alternative actions

■■Decide and act
■■Reflect: Was the outcome as anticipated? Why or why not?
The ethical decision-  making process includes multiple phases, each of which has 
multiple components. The process is often iterative, and you, the decision maker, may 
move between phases in an order different from what is presented. For simplicity, we 
will discuss the phases sequentially. In the initial phase, you will want to identify the 
important facts that you have available to you, as well as information that you may 
not have but would like to have to give yourself a more complete understanding of the 
situation. You will also want to identify the stakeholders—clients, family, colleagues, 
your employer, market participants, and so forth—and the duties you have to each of 
them. You will then want to identify relevant ethical principles and/or legal require -
ments that might apply to the situation. You should also identify any potential conflicts

of interest inherent in the situation or conflicts in the duties you hold to others. For 
example, your duty to your client may conflict with your duty to your employer.
In the second phase of ethical decision making, you will take time to consider 
the situational influences as well as personal behavioral biases that could affect your 
thinking and thus decision making. These situational influences and biases could 
include a desire to please your boss, to be seen as successful by your peers and family, 
to gain acceptance, to earn a large bonus, and so on. During this phase, you may seek 
additional guidance from trusted sources—perhaps a family member, colleague, or 
mentor who can help you think through the situation and help you identify and evaluate 
alternative actions. You may turn to your compliance department for assistance or 
you may even consult outside legal counsel. Seeking additional guidance is a critical

Reading 1 ■ Ethics and Trust in the Investment Profession 22
step in viewing the situation from different perspectives. You should seek guidance 
from someone who is not affected by the same situational influences and behavioral 
biases as you are and can, therefore, provide a fresh perspective. You should also 
seek guidance from your firm’s policies and procedures and the CFA Institute Code 
and Standards . A helpful technique might be to imagine how an ethical peer or role 
model might act in the situation.
The next phase of the framework is to make a decision and act. After you have 
acted on your decision, you should take the time to reflect on and assess your deci -
sion and its outcome. Was the outcome what you anticipated? Why or why not? Had 
you properly identified all the important facts, stakeholders, duties to stakeholders, 
conflicts of interest, and relevant ethical principles? Had you considered the situa -

tional influences? Did you identify personal behavioral biases that might affect your 
thinking? Had you sought sufficient guidance? Had you considered and properly 
evaluated a variety of alternative actions? You may want to reflect on the decision 
multiple times as the immediate and longer-  term consequences of your decision and 
actions become apparent.
The process is often iterative. After identifying the relevant facts and considering 
situational influences, you may, for example, decide that you cannot make a decision 
without more information. You may seek additional guidance on how to obtain the 
information you need. You may also begin considering alternative actions regarding 
how to proceed based on expectations of what the additional information will reveal, 
or you may wait until you have more information, reflect on what you have done and 
learned so far, and start the process over again. Sometimes cases can be complicated

and multiple iterations may reveal that no totally acceptable solution can be created. 
Applying an ethical decision-  making framework can help you evaluate the situation 
so you can make the best possible decision. The next section shows applications of 
the framework shown in Exhibit 2.
7.1 Applying the Framework
To illustrate how the framework could be applied in your career, consider the scenario 
in Example 6.
EXAMPLE 6   
Applying an Ethical Decision-  Making Framework I
You have been hired as a junior analyst with a major investment bank. When 
you join the bank, you receive a copy of the firm’s policies as well as training on 
the policies. Your supervisor is the senior technology analyst for the investment 
bank. As part of your duties, you gather information, draft documents, conduct 
analysis, and perform other support functions for the senior analyst.
Your employer is one of several investment banks working on the initial

public offering (IPO) of a well-  known technology company. The IPO is expected 
to generate significant revenues for the investment banks participating in the 
offering. The IPO has been highly anticipated and is in the news every day.
You are thrilled when your supervisor asks you to work on several research 
projects related to analyzing and valuing the upcoming IPO for investors. You 
eagerly compile information and draft a one-  page outline. You stop to consider 
what other information you could add to improve the report before proceeding. 
You realize that you have two excellent contacts in the technology industry who 
could review your work and provide some additional and potentially valuable 
perspectives. You draft an email to your contacts reading:

Ethical Decision-  Making Frameworks 23
I am working on an analysis and valuation of Big Tech Company for 
investors. My employer is one of the banks participating in the IPO, 
and I want to make sure I have considered everything. I was hoping 
you could give me feedback on the prospects and risks facing Big 
Tech. Please treat all the attached material as confidential.
Before hitting the send button, you stop and think about the ethical decision-  
making framework you have studied. You decide to apply the framework and jot 
down some notes as you work through the process: On the first page, you work 
through the identification phase and make a list of the relevant facts, stakeholders 
to whom you owe a duty, potential conflicts of interest, and ethical principles. 
This list is shown is Exhibit 3.
Exhibit 3   Identification Phase
1 Relevant facts:
■●Working on the deal/IPO of the decade
■●Employer is one of several investment banks working on IPO
■●The IPO is highly anticipated

■●A successful IPO could lead to additional investment banking 
deals and revenues for the firm
■●Supervisor is relying on me
■●Employer has documented policies and procedures
■●Industry is regulated, with many rules and regulations in place
2 Stakeholders and duties owed. I have a duty to the following:
■●Supervisor
■●Employer
■●Employer’s corporate client, the technology company
■●Employer’s asset management and other investing clients
■●Employer’s partners in the IPO
■●Investors and market participants interested in the IPO
■●All capital market participants
3 Conflicts or potential conflicts of interest include the following:
■●Gathering additional research versus maintaining confidentiality
■●Duty to supervisor versus desire to impress
■●Duty to corporate client versus duty to other clients of the firm
■●The firm’s corporate client benefits from a high IPO price whereas 
the firm’s asset management clients would benefit from a low IPO 
price

price
■●Desire to work on more deals/IPOs versus objective analysis of the 
investment potential of this deal
■●My bonus, compensation, and career prospects are tied to my 
supervisor’s and the IPO’s success; duty to employer
4 Ethical principles that are relevant to this situation include the 
■●Duty of loyalty to employer

Reading 1 ■ Ethics and Trust in the Investment Profession 24
■●Client interests come first
■●Maintain confidences and confidentiality of information
On the next page, you write notes relating to the second phase of the frame -
work, considering the various situational factors and the guidance available to 
you before considering alternative actions. These notes are shown in Exhibit 4.
Exhibit 4   Consideration Phase
1 Situational influences:
■●The firm’s written policies
■●The bank will earn big fees from the IPO
■●I want to impress my boss—and potential future bosses
■●My bonus, compensation, and career prospects will be influenced 
by my contribution to this deal and other deals
■●I am one of very few people working on this deal; it is a real 
honor, and others would be impressed that I am working on this 
deal
■●My employer is filled with successful and wealthy people who are 
go- getters; I want to be successful and wealthy like them
2 Additional guidance. I could seek guidance from the following:

■●The firm’s code of ethics
■●A peer in my firm
■●My supervisor, the senior analyst
■●The compliance department
■●A mentor either at the firm or perhaps from university
■●The CFA Institute Code and Standards
3 Alternative actions. I could consider the following:
■●Asking contacts what they have heard
■●Submitting the report as a draft and suggesting that contacts in 
the industry might be able to provide more perspective
■●Sending a survey to various technology industry veterans soliciting 
their viewpoints on developments
After completing these steps, you decide to check the firm’s policies. Under 
a section entitled “Research Analyst Role in Securities Offerings, ” the manual 
states, “You may not distribute any written (which include email, fax, electronic, 
and other means) material related to companies and/or their offerings . . . during 
the course of any offering and the related quiet period. ”
You read further and note a section entitled “Wall Crossing Policy and

Procedures” that states that “employees with confidential information may not 
communicate the information to anyone who does not have a valid need to know” 
without first obtaining clearance from the legal and compliance department.Exhibit 3   (Continued)

Ethical Decision-  Making Frameworks 25
You decide that your contacts do not have a “valid need to know” and that it 
is unlikely the firm’s legal and compliance professionals would approve sharing 
the information. You then decide to mention your contacts to the senior research 
analyst. He suggests that they may have some useful perspective and that you 
might talk to them to hear their perspective and cautions you not to disclose 
any information about any of the firm’s clients, pending deals, or research. You 
return to your desk, delete the email, and following the senior research analyst’s 
advice, call your contacts on the telephone to discuss the technology sector, its 
prospects, and its challenges. During the calls, you take care not to reveal any 
details about Big Tech Company or its offering.
Whatever action you take, you should take time afterward to reflect on the 
decision and the outcome. Was the outcome as anticipated? Why or why not?

The initial facts presented in the example are based on the real-  life experience of 
a young junior analyst working on a highly anticipated IPO. The junior analyst may 
or may not have used an ethical decision-  making framework to evaluate his situation. 
Without seeking additional guidance, the junior analyst sent an email similar to the 
one in the example with an attachment that included confidential, proprietary infor -
mation, including the senior analyst’s analysis and forecasts. Months later, long after 
the IPO offering, the junior analyst’s email was discovered by his employer. When 
questioned, he admitted that he had received training regarding the firm’s policies 
and that he did not discuss or seek approval from anyone before sending the email. 
Two days later, the firm terminated the junior analyst’s employment and reported to 
regulatory authorities that he had been terminated for distributing written materials,

by email, during a securities offering in violation of firm policies that prohibit the 
dissemination of any written materials during the course of a securities offering and 
related periods. The junior analyst’s supervisor also lost his job for failing to properly 
supervise the analyst. Multiple regulators investigated the matter, and the firm was 
fined millions of dollars for failing to supervise its employees properly. The information 
regarding the junior analyst’s termination was posted and remains available on the 
regulator’s website for all to see. Future employers conducting routine background 
checks will know that the analyst was terminated for violating firm policies relating 
to a securities offering.
The example presented is similar to situations faced by many analysts. Using an 
ethical decision-  making framework will help you evaluate situations from multiple 
perspectives, avoid poor decision making, and avoid the consequences that can result

from taking an ill-  conceived course of action. Using an ethical decision-  making 
framework is no guarantee of a positive outcome but may help you avoid making 
unethical decisions.
EXAMPLE 7   
Applying an Ethical Decision-  Making Framework II
A financial adviser has been saving a portion of his salary to purchase a new 
vehicle. He is on track to have enough saved within the next three months. His 
employer has offered a special bonus for this quarter, which will go to the team 
that attracts the most new investors into the firm’s investment funds. In addi -
tion to the potential bonus, the firm pays a 5% commission to employees who 
sell shares in the firm’s investment funds. Several of the funds are highly rated, 
including one designed to provide steady income to investors.

Reading 1 ■ Ethics and Trust in the Investment Profession 26
The financial adviser has added only a few new investors to the firm’s funds, 
but his teammates have been very successful in their efforts. The end of the 
quarter is one week away, and his team is competing closely with another team 
for the bonus. One of his teammates informs the financial adviser that he really 
needs the bonus so his elderly mother can receive medical treatment.
Later that day, the financial adviser meets with an elderly client on a limited 
income who is seeking more income from his investment portfolio. The client 
is 89 years old and in poor health. According to the client’s will, the client’s 
investment portfolio will go to his favorite charity upon his death.
1 Which of the following situational influences is likely to have the most  
effect on the financial adviser’s efforts to get new clients to invest in the 
funds? His relationship with his:
A client.
B employer.
C teammates.

A client.
2 Which of the following statements is most  accurate? An ethical decision-  
making framework:
A is only beneficial when a firm lacks a code of ethics.
B is used to improve compliance with laws and regulations.
C is a tool for analyzing the potential alternative actions and conse -
quences of a decision.
3 Which of the following is most  accurate? Ethical decision-  making 
frameworks:
A raise awareness of different perspectives.
B focus attention on short-  term consequences.
C allocate more weight to those who will directly benefit from the 
decision.
4 Which of the following is most  accurate? Ethical decision-  making 
A are not needed if behavior is legal.
B identify who gains the most from a decision.
C can help reduce unanticipated ethical lapses and unexpected 
consequences.
5 Using an ethical decision-  making framework, which of the following 
duties would most likely  take precedence in the scenario described? The 
financial adviser’s duty to his:

A client.
C colleagues.
6 Using an ethical decision-  making framework, the financial adviser would 
A recommend that the elderly client invest at least some of his assets in 
the highly rated fund.
B research other investments that can provide steady income before 
making a recommendation to his elderly client.
C disclose the commission he would earn before recommending that the 
elderly client invest at least some of his assets in the highly rated fund.

Conclusion 27
C is correct. The financial adviser’s relationship with his teammates is likely to 
have the most effect on the financial adviser’s efforts.
C is correct. An ethical decision-  making framework is a tool for analyzing the 
potential alternative actions and consequences of a decision.
A is correct. Ethical decision-  making frameworks raise awareness of different 
perspectives.
C is correct. Ethical decision-  making frameworks can help avoid unanticipated 
ethical consequences.
A is correct. Using an ethical decision-  making framework, the financial adviser’s 
relationship with his client would most likely take precedence in this scenario. 
The adviser should put his client’s interests first. The exception to client inter -
ests taking precedence occurs when market integrity effects take precedence.
B is correct. Using an ethical decision-  making framework, the financial adviser

would identify the relevant facts, stakeholders, duties owed, and potential con -
flicts. In this scenario, the financial adviser owes a duty to his client as well as 
his employer. His client’s interests take precedence over all other interests. The 
bonus and his colleague’s desire to help his mother are situational influences. To 
navigate this situation, the financial adviser should seek additional information; 
he should research the risk and return parameters and fee structures of other 
investments that can provide steady income before making a recommendation 
to his client.
This reading introduced ideas and concepts that will help you understand the impor -
tance of ethical behavior in the investment industry as well as the challenges to adhering 
to high ethical standards. A code of ethics will communicate an organization’s values 
and the expected behavior of its members as well as provide guidance for decision

making. A code of ethics may be further enhanced and clarified by the adoption of 
standards of conduct. An ethical decision-  making framework combined with a code 
of ethics may help investment professionals analyze their decisions in a way that 
identifies potential conflicts and negative consequences.
Knowing the rules to apply in a particular situation, although important, may not 
be sufficient to ensure ethical conduct if used alone. Responsible professionals in the 
investment industry must be able both to recognize areas that are prone to ethical 
pitfalls and to identify and process those circumstances and influences that can impair 
judgment and lead to ethical lapses.8

Reading 1 ■ Ethics and Trust in the Investment Profession 28
SUMMARY
■■Ethics refers to the study of making good choices. Ethics encompasses a set of 
moral principles and rules of conduct that provide guidance for our behavior.
■■Situational influences are external factors that may shape our behavior.
■■Challenges to ethical behavior include being overconfident in our own morality, 
underestimating the effect of situational influences, and focusing on the imme -
diate rather than long-  term outcomes or consequences of a decision.
■■In any given profession, the code of ethics publicly communicates the estab -
lished principles and expected behavior of its members.
■■Members of a profession use specialized knowledge and skills to serve others; 
they share and agree to adhere to a common code of ethics to serve others and 
advance the profession.
■■A code of ethics helps foster public confidence that members of the profession

will use their specialized skills and knowledge to serve their clients and others.
■■High ethical standards always matter and are of particular importance in the 
investment industry, which is based almost entirely on trust. Clients trust 
investment professionals to use their specialized skills and knowledge to serve 
clients and protect client assets. All stakeholders gain long-  term benefits when 
investment professionals adhere to high ethical standards.
■■Rules and laws often codify ethical actions that lead to better outcomes for soci -
ety or specific groups of stakeholders.
■■Organizations and individuals generally adhere to legal standards, but legal 
standards are often created to address past ethical failings and do not provide 
guidance for an evolving and increasingly complex world.
■■Legal standards are often rule based. Ethical conduct goes beyond legal stan -
dards, balancing self-  interest with the direct and indirect consequences of 
behavior on others.

■■A framework for ethical decision making can help people look at and evaluate a 
decision from different perspectives, enabling them to identify important issues, 
make wise decisions, and limit unintended consequences.

Practice Problems 29
PRACTICE  PROBLEMS
1 Benchmarks for minimally acceptable behaviors of community members are:
A a code of ethics.
B laws and regulations.
C standards of conduct.
2 Specialized knowledge and skills, a commitment to serve others, and a shared 
code of ethics best characterize a(n):
A vocation.
B profession.
C occupation.
3 Which of the following best identifies an internal trait that may lead to poor 
ethical decision making?
A Overconfidence
B Loyalty to employer
C Promise of money or prestige
4 Situational influences in decision making will most  likely  be minimized if:
A strong compliance programs are in place.
B longer-  term consequences are considered.
C individuals believe they are truthful and honest.
5 Decision makers who use a compliance approach are most  likely  to:
A avoid situational influences.
B oversimplify decision making.
C consider more factors than when using an ethical decision-  making 
approach.

approach.
6 When unethical behavior erodes trust in an investment firm, that firm is more  
likely  to experience:
A lower revenues only.
B higher expenses only.
C lower revenues and higher expenses.
7 Which is an example of an activity that may be legal but that CFA Institute 
considers unethical?
A Making legally required disclosures in marketing materials
B Trading while in possession of material nonpublic information
C Disclosure by an employee of his or her own company’s dishonest activity
8 An ethical decision-  making framework will most  likely :
A include a pre-  determined, uniform sequence.
B focus exclusively on confirmable facts and relationships.
C help avoid a decision that has unanticipated ethical consequences.

Reading 1 ■ Ethics and Trust in the Investment Profession 30
SOLUTIONS
1 C is correct. Standards of conduct are applied to specific communities or soci -
etal groups and identify specific behaviors required of community members. 
These standards of conduct serve as benchmarks for the minimally acceptable 
behavior of community members. Codes of ethics serve as a general guide for 
how community members should act; they communicate the organization’s 
values and overall expectations regarding member behavior, but they do not 
identify specific behaviors required of community members. Laws and regu -
lations are rules of conduct defined by governments and related entities about 
obligatory and forbidden conduct broadly applicable for individuals and entities 
under their jurisdiction.
2 B is correct. A profession has several characteristics that distinguish it from 
an occupation or vocation, such as specialized knowledge and skills, service to

others, and a code of ethics shared by its members. A profession is the ultimate 
evolution of an occupation, resulting from excellence in practice and expected 
adherence to a code of ethics and standards of practice.
3 A is correct. An overconfidence bias can lead individuals to put too much 
importance on internal traits and intrinsic motivations, such as their own per -
ceptions of personal honesty, that can lead to faulty decision making. Loyalty 
to an employer and promise of money or prestige are situational influences that 
can lead to faulty decision making.
4 B is correct. Consciously considering long-  term consequences will help off -
set situational influences. We more easily recognize and consider short-  term 
situational influences than longer-  term considerations because longer-  term 
considerations have fewer immediate consequences than situational influences 
do. When decision making is too narrowly focused on short-  term factors, we

tend to ignore longer-  term risks and consequences, and the likelihood of poor 
ethical decision making increases. A strong compliance policy is a good first 
step toward developing an ethical culture; a focus on rules adherence may not 
be sufficient. Emphasis on compliance may not encourage decision makers to 
consider the larger picture and can oversimplify decision making. Taken to the 
extreme, a strong compliance culture can become another situational influence 
that blinds employees to other important considerations. An overconfidence 
bias can place too much importance on internal traits and intrinsic motivations, 
such as “I’m honest and would not lie, ” even though studies have shown that 
internal traits are generally not the main determinant of whether or not some -
one will behave ethically in a given situation.
5 B is correct. A compliance approach can oversimplify decision making and may 
not encourage decision makers to consider the larger picture. A strong com -

pliance culture may be a good start in developing an ethical culture but can 
become another situational influence that may result in employees failing to 
consider other important factors.
6 C is correct. Unethical behavior ultimately harms investment firms. Clients are 
not attracted if they suspect unethical behavior, leading to less business and 
lower revenues. Investment firms may also experience higher relative costs 
because regulators are more likely to have cause to initiate costly investigations.

Solutions 31
7 B is correct. The investment industry has examples of conduct that may be 
legal but that CFA Institute considers unethical. Trading while in possession 
of material nonpublic information is not prohibited by law worldwide and can, 
therefore, be legal, but CFA Institute considers such trading unethical.
8 C is correct. Using an ethical decision-  making framework consistently will help 
you develop sound judgment and decision-  making skills and avoid making 
decisions that have unanticipated ethical consequences. The decision-  making 
process is often iterative, and the decision maker may move between phases of 
the framework. A decision maker should consider more than confirmable facts 
and relationships; for example, the decision maker should consider situational 
influences and personal biases.

Code of Ethics and Standards 
of Professional Conduct
a. describe the structure of the CFA Institute Professional Conduct 
Program and the process for the enforcement of the Code and 
Standards;
b. state the six components of the Code of Ethics and the seven 
Standards of Professional Conduct;
c. explain the ethical responsibilities required by the Code and 
Standards, including the sub-  sections of each Standard.
PREFACE
The Standards of Practice Handbook  (Handbook ) provides guidance to the people 
who grapple with real ethical dilemmas in the investment profession on a daily basis; 
the Handbook  addresses the professional intersection where theory meets practice 
and where the concept of ethical behavior crosses from the abstract to the concrete. 
The Handbook  is intended for a diverse and global audience: CFA Institute members 
navigating ambiguous ethical situations; supervisors and direct/indirect reports

determining the nature of their responsibilities to each other, to existing and poten -
tial clients, and to the broader financial markets; and candidates preparing for the 
Chartered Financial Analyst (CFA) examinations.
Recent events in the global financial markets have tested the ethical mettle of 
financial market participants, including CFA Institute members. The standards taught 
in the CFA Program and by which CFA Institute members and candidates must abide 
represent timeless ethical principles and professional conduct for all market conditions. 
Through adherence to these standards, which continue to serve as the model for ethi -
cal behavior in the investment professional globally, each market participant does his 
or her part to improve the integrity and efficient operations of the financial markets.
The Handbook  provides guidance in understanding the interconnectedness of 
the aspirational and practical principles and provisions of the Code of Ethics and

Standards of Professional Conduct (Code and Standards). The Code contains high-  
level aspirational ethical principles that drive members and candidates to create a rEAdING
2

Reading 2 ■ Code of Ethics and Standards of Professional Conduct 34
positive and reputable investment profession. The Standards contain practical ethical 
principles of conduct that members and candidates must follow to achieve the broader 
industry expectations. However, applying the principles individually may not capture 
the complexity of ethical requirements related to the investment industry. The Code 
and Standards should be viewed and interpreted as an interwoven tapestry of ethical 
requirements. Through members’ and candidates’ adherence to these principles as a 
whole, the integrity of and trust in the capital markets are improved.
Evolution of the CFA Institute Code of Ethics and Standards of 
Professional Conduct
Generally, changes to the Code and Standards over the years have been minor. CFA 
Institute has revised the language of the Code and Standards and occasionally added 
a new standard to address a prominent issue of the day. For instance, in 1992, CFA

Institute added the standard addressing performance presentation to the existing list 
of standards.
Major changes came in 2005 with the ninth edition of the Handbook . CFA Institute 
adopted new standards, revised some existing standards, and reorganized the standards. 
The revisions were intended to clarify the requirements of the Code and Standards 
and effectively convey to its global membership what constitutes “best practice” in a 
number of areas relating to the investment profession.
The Code and Standards must be regularly reviewed and updated if they are to 
remain effective and continue to represent the highest ethical standards in the global 
investment industry. CFA Institute strongly believes that revisions of the Code and 
Standards are not undertaken for cosmetic purposes but to add value by addressing 
legitimate concerns and improving comprehension.
Changes to the Code and Standards have far-  reaching implications for the CFA

Institute membership, the CFA Program, and the investment industry as a whole. CFA 
Institute members and candidates are required  to adhere to the Code and Standards. In 
addition, the Code and Standards are increasingly being adopted, in whole or in part, 
by firms and regulatory authorities. Their relevance goes well beyond CFA Institute 
members and candidates.
Standards of Practice Handbook
The periodic revisions of the Code and Standards have come in conjunction with 
updates of the Standards of Practice Handbook . The Handbook  is the fundamental 
element of the ethics education effort of CFA Institute and the primary resource for 
guidance in interpreting and implementing the Code and Standards. The Handbook  
seeks to educate members and candidates on how to apply the Code and Standards to 
their professional lives and thereby benefit their clients, employers, and the investing 
public in general. The Handbook  explains the purpose of the Code and Standards

and how they apply in a variety of situations. The sections discuss and amplify each 
standard and suggest procedures to prevent violations.
Examples in the “ Application of the Standard” sections are meant to illustrate how 
the standard applies to hypothetical but factual situations. The names contained in 
the examples are fictional and are not meant to refer to any actual person or entity. 
Unless otherwise stated (e.g., one or more people specifically identified), individuals in 
each example are CFA Institute members and holders of the CFA designation. Because 
factual circumstances vary so widely and often involve gray areas, the explanatory 
material and examples are not intended to be all inclusive. Many examples set forth 
in the application sections involve standards that have legal counterparts; members

Preface 35
are strongly urged to discuss with their supervisors and legal and compliance 
departments the content of the Code and Standards and the members’ general 
obligations under the Code and Standards .
CFA Institute recognizes that the presence of any set of ethical standards may 
create a false sense of security unless the documents are fully understood, enforced, 
and made a meaningful part of everyday professional activities. The Handbook  is 
intended to provide a useful frame of reference that suggests ethical  professional 
behavior in the investment decision-  making process. This book cannot cover every 
contingency or circumstance, however, and it does not attempt to do so. The develop -
ment and interpretation of the Code and Standards are evolving processes; the Code 
and Standards will be subject to continuing refinement.
Summary of Changes in the Eleventh Edition
The comprehensive review of the Code and Standards in 2005 resulted in principle

requirements that remain applicable today. The review carried out for the eleventh 
edition focused on market practices that have evolved since the tenth edition. Along 
with updates to the guidance and examples within the Handbook , the eleventh edi -
tion includes an update to the Code of Ethics that embraces the members’ role of 
maintaining the social contract between the industry and investors. Additionally, 
there are three changes to the Standards of Professional Conduct, which recognize 
the importance of proper supervision, clear communications with clients, and the 
expanding educational programs of CFA Institute. 
Inclusion of Updated CFA Institute Mission
The CFA Institute Board of Governors approved an updated mission for the organi -
zation that is included in the Preamble to the Code and Standards. The new mission 
conveys the organization’s conviction in the investment industry’s role in the better -
ment of society at large. 
Mission:

Mission:
To lead the investment profession globally by promoting the highest stan -
dards of ethics, education, and professional excellence for the ultimate 
benefit of society.
Updated Code of Ethics Principle
One of the bullets in the Code of Ethics was updated to reflect the role that the capital 
markets have in the greater society. As members work to promote and maintain the 
integrity of the markets, their actions should also help maintain the social contract 
with investors. 
Old:
Promote the integrity of and uphold the rules governing capital markets.
New:
Promote the integrity and viability of the global capital markets for the 
ultimate benefit of society.

Reading 2 ■ Code of Ethics and Standards of Professional Conduct 36
New Standard Regarding Responsibilities of Supervisors [IV(C)]
The standard for members and candidates with supervision or authority over others 
within their firms was updated to bring about improvements in preventing illegal 
and unethical actions from occurring. The prior version of Standard IV(C) focused 
on the detection and prevention of violations. The updated version stresses broader 
compliance expectations, which include the detection and prevention aspects of the 
original version. 
Old:
Members and Candidates must make reasonable efforts to detect and 
prevent violations of applicable laws, rules, regulations, and the Code and 
Standards by anyone subject to their supervision or authority. 
New:
Members and Candidates must make reasonable efforts to ensure that 
anyone subject to their supervision or authority complies with applicable 
laws, rules, regulations, and the Code and Standards.

Additional Requirement under the Standard for Communication with Clients and 
Prospective Clients [V(B)]
Given the constant development of new and exotic financial instruments and strat -
egies, the standard regarding communicating with clients now includes an implicit 
requirement to discuss the risks and limitations of recommendations being made to 
clients. The new principle and related guidance take into account the fact that levels of 
disclosure will differ between products and services. Members and candidates, along 
with their firms, must determine the specific disclosures their clients should receive 
while ensuring appropriate transparency of the individual firms’ investment processes. 
Addition:
Disclose to clients and prospective clients significant limitations and risks 
associated with the investment process.
Modification to Standard VII(A) 
Since this standard was developed, CFA Institute has launched additional educational

programs. The updated standard not only maintains the integrity of the CFA Program 
but also expands the same ethical considerations when members or candidates par -
ticipate in such programs as the CIPM Program and the CFA Institute Investment 
Foundations certificate program. Whether participating as a member assisting with the 
curriculum or an examination or as a sitting candidate within a program, we expect 
them to engage in these programs as they would participate in the CFA Program.
Old:
Conduct as Members and Candidates in the CFA Program 
Members and Candidates must not engage in any conduct that compro -
mises the reputation or integrity of CFA Institute or the CFA designation 
or the integrity, validity, or security of the CFA examinations.

Preface 37
New:
Conduct as Participants in CFA Institute Programs 
or the integrity, validity, or security of CFA Institute programs.
General Guidance and Example Revision
The guidance and examples were updated to reflect practices and scenarios applicable 
to today’s investment industry. Two concepts that appear frequently in the updates in 
this edition relate to the increased use of social media for business communications 
and the use of and reliance on the output of quantitative models. The use of social 
media platforms has increased significantly since the publication of the tenth edition. 
And although financial modeling is not new to the industry, this update reflects upon 
actions that are viewed as possible contributing factors to the financial crises of the 
past decade.
CFA Institute Professional Conduct Program

All CFA Institute members and candidates enrolled in the CFA Program are required 
to comply with the Code and Standards. The CFA Institute Board of Governors main -
tains oversight and responsibility for the Professional Conduct Program (PCP), which, 
in conjunction with the Disciplinary Review Committee (DRC), is responsible for 
enforcement of the Code and Standards. The DRC is a volunteer committee of CFA 
charterholders who serve on panels to review conduct and partner with Professional 
Conduct staff to establish and review professional conduct policies. The CFA Institute 
Bylaws and Rules of Procedure for Professional Conduct (Rules of Procedure) form 
the basic structure for enforcing the Code and Standards. The Professional Conduct 
division is also responsible for enforcing testing policies of other CFA Institute 
education programs as well as the professional conduct of Certificate in Investment 
Performance Measurement (CIPM) certificants.

Performance Measurement (CIPM) certificants. 
Professional Conduct inquiries come from a number of sources. First, members 
and candidates must self-  disclose on the annual Professional Conduct Statement all 
matters that question their professional conduct, such as involvement in civil litigation 
or a criminal investigation or being the subject of a written complaint. Second, written 
complaints received by Professional Conduct staff can bring about an investigation. 
Third, CFA Institute staff may become aware of questionable conduct by a member 
or candidate through the media, regulatory notices, or another public source. Fourth, 
candidate conduct is monitored by proctors who complete reports on candidates 
suspected to have violated testing rules on exam day. Lastly, CFA Institute may also 
conduct analyses of scores and exam materials after the exam, as well as monitor online 
and social media to detect disclosure of confidential exam information.

When an inquiry is initiated, the Professional Conduct staff conducts an investiga -
tion that may include requesting a written explanation from the member or candidate; 
interviewing the member or candidate, complaining parties, and third parties; and 
collecting documents and records relevant to the investigation. Upon reviewing the 
material obtained during the investigation, the Professional Conduct staff may con -
clude the inquiry with no disciplinary sanction, issue a cautionary letter, or continue 
proceedings to discipline the member or candidate. If the Professional Conduct staff  
believes a violation of the Code and Standards or testing policies has occurred, the 
member or candidate has the opportunity to reject or accept any charges and the 
proposed sanctions.

Reading 2 ■ Code of Ethics and Standards of Professional Conduct 38
If the member or candidate does not accept the charges and proposed sanction, 
the matter is referred to a panel composed of DRC members. Panels review materials 
and presentations from Professional Conduct staff and from the member or candidate. 
The panel’s task is to determine whether a violation of the Code and Standards or 
testing policies occurred and, if so, what sanction should be imposed.
Sanctions imposed by CFA Institute may have significant consequences; they 
include public censure, suspension of membership and use of the CFA designation, 
and revocation of the CFA charter. Candidates enrolled in the CFA Program who have 
violated the Code and Standards or testing policies may be suspended or prohibited 
from further participation in the CFA Program.
Adoption of the Code and Standards
The Code and Standards apply to individual members of CFA Institute and candi -

dates in the CFA Program. CFA Institute does encourage firms to adopt the Code 
and Standards, however, as part of their code of ethics. Those who claim compliance 
should fully understand the requirements of each of the principles of the Code and 
Standards.
Once a party—nonmember or firm—ensures its code of ethics meets the principles 
of the Code and Standards, that party should make the following statement whenever 
claiming compliance:
“[Insert name of party] claims compliance with the CFA Institute Code 
of Ethics and Standards of Professional Conduct. This claim has not been 
verified by CFA Institute. ”
CFA Institute welcomes public acknowledgement, when appropriate, that firms 
are complying with the CFA Institute Code of Ethics and Standards of Professional 
Conduct and encourages firms to notify us of the adoption plans. For firms that would 
like to distribute the Code and Standards to clients and potential clients, attractive

one-  page copies of the Code and Standards, including translations, are available on 
the CFA Institute website (www.cfainstitute.org). 
CFA Institute has also published the Asset Manager Code of Professional Conduct, 
which is designed, in part, to help asset managers comply with the regulations man -
dating codes of ethics for investment advisers. Whereas the Code and Standards are 
aimed at individual investment professionals who are members of CFA Institute or 
candidates in the CFA Program, the Asset Manager Code was drafted specifically 
for firms. The Asset Manager Code provides specific, practical guidelines for asset 
managers in six areas: loyalty to clients, the investment process, trading, compliance, 
performance evaluation, and disclosure. The Asset Manager Code and the appropri -
ate steps to acknowledge adoption or compliance can be found on the CFA Institute 
website (www.cfainstitute.org).
Acknowledgments

CFA Institute is a not-  for- profit organization that is heavily dependent on the exper -
tise and intellectual contributions of member volunteers. Members devote their time 
because they share a mutual interest in the organization’s mission to promote and 
achieve ethical practice in the investment profession. CFA Institute owes much to the 
volunteers’ abundant generosity and energy in extending ethical integrity.
The CFA Institute Standards of Practice Council (SPC), a group consisting of CFA 
charterholder volunteers from many different countries, is charged with maintaining 
and interpreting the Code and Standards and ensuring that they are effective. The 
SPC draws its membership from a broad spectrum of organizations in the securities

Ethics and the Investment Industry 39
field, including brokers, investment advisers, banks, and insurance companies. In 
most instances, the SPC members have important supervisory responsibilities within 
their firms.
The SPC continually evaluates the Code and Standards, as well as the guidance in 
the Handbook , to ensure that they are
■■representative of high standards of professional conduct,
■■relevant to the changing nature of the investment profession,
■■globally applicable,
■■sufficiently comprehensive, practical, and specific,
■■enforceable, and
■■testable for the CFA Program.
The SPC has spent countless hours reviewing and discussing revisions to the Code 
and Standards and updates to the guidance that make up the eleventh  edition of the 
Handbook . Following is a list of the current and former members of the SPC who 
generously donated their time and energy to this effort.
James E. Hollis III, CFA, Chair Christopher C. Loop, CFA, 
Rik Albrecht, CFA James M. Meeth, CFA

Terence E. Burns, CFA Guy G. Rutherfurd, Jr., CFA
Laura Dagan, CFA Edouard Senechal, CFA
Samuel B. Jones, Jr., CFA Wenliang (Richard) Wang, CFA
Ulrike Kaiser-  Boeing, CFA Peng Lian Wee, CFA
Jinliang (Jack) Li, CFA
ETHICS AND THE INVESTMENT INDUSTRY
Society ultimately benefits from efficient markets where capital can freely flow to 
the most productive or innovative destination. Well-  functioning capital markets 
efficiently match those needing capital with those seeking to invest their assets in 
revenue-  generating ventures. In order for capital markets to be efficient, investors 
must be able to trust that the markets are fair and transparent and offer them the 
opportunity to be rewarded for the risk they choose to take. Laws, regulations, and 
enforcement play a vital role but are insufficient alone to guarantee fair and trans -
parent markets. The markets depend on an ethical foundation to guide participants’

judgment and behavior. CFA Institute maintains and promotes the Code of Ethics 
and Standards of Professional Conduct in order to create a culture of ethics for the 
ultimate benefit of society. 
Why Ethics Matters
Ethics can be defined as a set of moral principles or rules of conduct that provide 
guidance for our behavior when it affects others. Widely acknowledged fundamental 
ethical principles include honesty, fairness, diligence, and care and respect for others. 
Ethical conduct follows those principles and balances self-  interest with both the direct 
and the indirect consequences of that behavior for other people. 
Not only does unethical behavior by individuals have serious personal conse -
quences—ranging from job loss and reputational damage to fines and even jail—but 
unethical conduct from market participants, investment professionals, and those who 
service investors can damage investor trust and thereby impair the sustainability of

Reading 2 ■ Code of Ethics and Standards of Professional Conduct 40
the global capital markets as a whole. Unfortunately, there seems to be an unending 
parade of stories bringing to light accounting frauds and manipulations, Ponzi schemes, 
insider-  trading scandals, and other misdeeds. Not surprisingly, this has led to erosion 
in public confidence in investment professionals. Empirical evidence from numerous 
surveys documents the low standing in the eyes of the investing public of banks and 
financial services firms—the very institutions that are entrusted with the economic 
well-  being and retirement security of society. 
Governments and regulators have historically tried to combat misconduct in the 
industry through regulatory reform, with various levels of success. Global capital 
markets are highly regulated to protect investors and other market participants. 
However, compliance with regulation alone is insufficient to fully earn investor trust.

Individuals and firms must develop a “culture of integrity” that permeates all levels 
of operations and promotes the ethical principles of stewardship of investor assets 
and working in the best interests of clients, above and beyond strict compliance with 
the law. A strong ethical culture that helps honest, ethical people engage in ethical 
behavior will foster the trust of investors, lead to robust global capital markets, and 
ultimately benefit society. That is why ethics matters. 
Ethics, Society, and the Capital Markets
CFA Institute recently added the concept “for the ultimate benefit of society” to its 
mission. The premise is that we want to live in a socially, politically, and financially 
stable society that fosters individual well-  being and welfare of the public. A key 
ingredient for this goal is global capital markets that facilitate the efficient allocation 
of resources so that the available capital finds its way to places where it most benefits

that society. These investments are then used to produce goods and services, to fund 
innovation and jobs, and to promote improvements in standards of living. Indeed, 
such a function serves the interests of the society. Efficient capital markets, in turn, 
provide a host of benefits to those providing the investment capital. Investors are 
provided the opportunity to transfer and transform risk because the capital markets 
serve as an information exchange, create investment products, provide liquidity, and 
limit transaction costs. 
However, a well-  functioning and efficient capital market system is dependent on 
trust of the participants. If investors believe that capital market participants—invest -
ment professionals and firms—cannot be trusted with their financial assets or that 
the capital markets are unfair such that only insiders can be successful, they will be 
unlikely to invest or, at the very least, will require a higher risk premium. Decreased

investment capital can reduce innovation and job creation and hurt the economy and 
society as a whole. Reduced trust in capital markets can also result in a less vibrant, 
if not smaller, investment industry. 
Ethics for a global investment industry should be universal and ultimately support 
trust and integrity above acceptable local or regional customs and culture. Universal 
ethics for a global industry strongly supports the efficiency, values, and mission of 
the industry as a whole. Different countries may be at different stages of development 
in establishing standards of practice, but the end goal must be to achieve rules, reg -
ulations, and standards that support and promote fundamental ethical principles on 
a global basis.
Capital Market Sustainability and the Actions of One
Individuals and firms also have to look at the indirect impacts of their actions on the 
broader investment community. The increasingly interconnected nature of global

finance brings to the fore an added consideration of market sustainability that was, 
perhaps, less appreciated in years past. In addition to committing to the highest lev -
els of ethical behavior, today’s investment professionals and their employers should 
consider the long-  term health of the market as a whole.

Ethics and the Investment Industry 41
As recent events have demonstrated, apparently isolated and unrelated decisions, 
however innocuous when considered on an individual basis, in aggregate can pre -
cipitate a market crisis. In an interconnected global economy and marketplace, each 
participant should strive to be aware of how his or her actions or the products he or 
she distributes may have an impact on capital market participants in other regions 
or countries. 
Investment professionals should consider how their investment decision-  making 
processes affect the global financial markets in the broader context of how they apply 
their ethical and professional obligations. Those in positions of authority have a spe -
cial responsibility to consider the broader context of market sustainability in their 
development and approval of corporate policies, particularly those involving risk 
management and product development. In addition, corporate compensation strategies

should not encourage otherwise ethically sound individuals to engage in unethical or 
questionable conduct for financial gain. Ethics, sustainability, and properly functioning 
capital markets are components of the same concept of protecting the best interests 
of all. To always place the interests of clients ahead of both investment professionals’ 
own interests and those of their employer remains a key ethos.
The Relationship between Ethics and Regulations
Some equate ethical behavior with legal behavior: If you are following the law, you 
must be acting appropriately. Ethical principles, like laws and regulations, prescribe 
appropriate constraints on our natural tendency to pursue self-  interest that could harm 
the interests of others. Laws and regulations often attempt to guide people toward 
ethical behavior, but they do not cover all unethical behavior. Ethical behavior is often 
distinguished from legal conduct by describing legal behavior as what is required and

ethical behavior as conduct that is morally correct. Ethical principles go beyond that 
which is legally sufficient and encompass what is the right thing to do. 
Given many regulators’ lack of sufficient resources to enforce well-  conceived rules 
and regulations, relying on a regulatory framework to lead the charge in establishing 
ethical behavior has its challenges. Therefore, reliance on compliance with laws and 
regulation alone is insufficient to ensure ethical behavior of investment professionals 
or to create a truly ethical culture in the industry. 
The recent past has shown us that some individuals will succeed at circumventing 
the regulatory rules for their personal gain. Only the application of strong ethical 
principles, at both the individual level and the firm level, will limit abuses. Knowing 
the rules or regulations to apply in a particular situation, although important, may 
not be sufficient to ensure ethical conduct. Individuals must be able both to recognize

areas that are prone to ethical pitfalls and to identify and process those circumstances 
and influences that can impair ethical judgment.
Applying an Ethical Framework 
engaging in appropriate conduct. When faced with an ethical dilemma, individuals 
must have a well-  developed set of principles; otherwise, their thought processes can 
lead to, at best, equivocation and indecision and, at worst, fraudulent conduct and 
destruction of the public trust. Establishing an ethical framework for an internal 
thought process prior to deciding to act is a crucial step in engaging in ethical conduct. 
Most investment professionals are used to making decisions from a business 
(profit/loss) outlook. But given the importance of ethical behavior in carrying out

professional responsibilities, it is critical to also analyze decisions and potential con -
duct from an ethical perspective. Utilizing a framework for ethical decision making 
will help investment professionals effectively examine their conduct in the context 
of conflicting interests common to their professional obligations (e.g., researching

Reading 2 ■ Code of Ethics and Standards of Professional Conduct 42
and gathering information, developing investment recommendations, and managing 
money for others). Such a framework will allow investment professionals to analyze 
their conduct in a way that meets high standards of ethical behavior. 
An ethical decision-  making framework can come in many forms but should provide 
investment professionals with a tool for following the principles of the firm’s code of 
ethics. Through analyzing the particular circumstances of each decision, investment 
professionals are able to determine the best course of action to fulfill their responsi -
bilities in an ethical manner.
Commitment to Ethics by Firms
A firm’s code of ethics risks becoming a largely ignored, dusty compilation if it is not 
truly integrated into the fabric of the business. The ability to relate an ethical decision-  
making framework to a firm’s code of ethics allows investment professionals to bring

the aspirations and principles of the code of ethics to life—transforming it from a 
compliance exercise to something that is at the heart of a firm’s culture. 
An investment professional’s natural desire to “do the right thing” must be reinforced 
by building a culture of integrity in the workplace. Development, maintenance, and 
demonstration of a strong culture of integrity within the firm by senior management 
may be the single most important factor in promoting ethical behavior among the 
firm’s employees. Adopting a code that clearly lays out the ethical principles that guide 
the thought processes and conduct the firm expects from its employees is a critical 
first step. But a code of ethics, while necessary, is insufficient. 
Simply nurturing an inclination to do right is no match for the multitude of daily 
decisions that investment managers make. We need to exercise ethical decision-  making 
skills to develop the muscle memory necessary for fundamentally ethical people to

make good decisions despite the reality of agent conflicts. Just as coaching and practice 
transform our natural ability to run across a field into the technique and endurance 
required to run a race, teaching, reinforcing, and practicing ethical decision-  making 
skills prepare us to confront the hard issues effectively. It is good for business, indi -
viduals, firms, the industry, and the markets, as well as society as a whole, to engage 
in the investment management profession in a highly ethical manner.
Ethical Commitment of CFA Institute
An important goal of CFA Institute is to ensure that the organization and its mem -
bers and candidates develop, promote, and follow the highest ethical standards in 
the investment industry. The CFA Institute Code of Ethics (Code) and Standards of 
Professional Conduct (Standards) are the foundation supporting the organization’s quest 
to uphold the industry’s highest standards of individual and corporate practice and to

help serve the greater good. The Code is a set of principles that define the overarching 
conduct CFA Institute expects from its members and CFA Program candidates. The 
Code  works in tandem with the Standards, which outline professional conduct that 
constitutes fair and ethical business practices.
For more than 50 years, CFA Institute members and candidates have been required 
to abide by the organization’s Code and Standards. Periodically, CFA Institute has 
revised and updated its Code and Standards to ensure that they remain relevant to 
the changing nature of the investment profession and representative of the highest 
standard of professional conduct. Within this Handbook , CFA Institute addresses 
ethical principles for the profession, including individual professionalism; respon -
sibilities to capital markets, clients, and employers; ethics involved in investment 
analysis, recommendations, and actions; and possible conflicts of interest. Although

the investment world has become a far more complex place since the first publication 
of the Standard of Practice Handbook , distinguishing right from wrong remains the 
paramount principle of the Code and Standards.

CFA Institute Code of Ethics and Standards of Professional Conduct 43
New challenges will continually arise for members and candidates in applying the 
Code and Standards because many decisions are not unambiguously right or wrong. 
The dilemma exists because the choice between right and wrong is not always clear. 
Even well-  intentioned investment professionals can find themselves in circumstances 
that may tempt them to cut corners. Situational influences can overpower the best 
of intentions.
CFA Institute has made a significant commitment to providing members and 
candidates with the resources to extend and deepen their understanding of how to 
appropriately apply the principles of the Code and Standards. The product offerings 
from CFA Institute offer a wealth of material. Through publications, conferences, 
webcasts, and podcasts, the ethical challenges of investment professionals are brought 
to light. Archived issues of these items are available on the CFA Institute website

(www.cfainstitute.org).
By reviewing these resources and discussing with their peers, market participants 
can further enhance their abilities to apply an effective ethical decision-  making frame -
work. In time, this should help restore some of the trust recently lost by investors.
Markets function to an important extent on trust. Recent events have shown the 
fragility of this foundation and the devastating consequences that can ensue when it 
is fundamentally questioned. Investment professionals should remain mindful of the 
long-  term health of financial markets and incorporate this concern for the market’s 
sustainability in their investment decision making. CFA Institute and the Standards of 
Practice Council hope this edition of the Handbook  will assist and guide investment 
professionals in meeting the ethical demands of the highly interconnected global 
capital markets for the ultimate benefit of society.
CFA INSTITUTE CODE OF ETHICS AND STANDARDS 
OF PROFESSIONAL CONDUCT
Preamble

Preamble
The CFA Institute Code of Ethics and Standards of Professional Conduct are funda -
mental to the values of CFA Institute and essential to achieving its mission to lead the 
investment profession globally by promoting the highest standards of ethics, education, 
and professional excellence for the ultimate benefit of society. High ethical standards 
are critical to maintaining the public’s trust in financial markets and in the investment 
profession. Since their creation in the 1960s, the Code and Standards have promoted 
the integrity of CFA Institute members and served as a model for measuring the ethics 
of investment professionals globally, regardless of job function, cultural differences, 
or local laws and regulations. All CFA Institute members (including holders of the 
Chartered Financial Analyst [CFA] designation) and CFA candidates have the personal 
responsibility to embrace and uphold the provisions of the Code and Standards and

are encouraged to notify their employer of this responsibility. Violations may result 
in disciplinary sanctions by CFA Institute. Sanctions can include revocation of mem -
bership, revocation of candidacy in the CFA Program, and revocation of the right to 
use the CFA designation.

Reading 2 ■ Code of Ethics and Standards of Professional Conduct 44
The Code of Ethics
Members of CFA Institute (including CFA charterholders) and candidates for the CFA 
designation (“Members and Candidates”) must:
■■Act with integrity, competence, diligence, and respect and in an ethical manner 
with the public, clients, prospective clients, employers, employees, colleagues in 
the investment profession, and other participants in the global capital markets.
■■Place the integrity of the investment profession and the interests of clients 
above their own personal interests.
■■Use reasonable care and exercise independent professional judgment when 
conducting investment analysis, making investment recommendations, taking 
investment actions, and engaging in other professional activities.
■■Practice and encourage others to practice in a professional and ethical manner 
that will reflect credit on themselves and the profession.

■■Promote the integrity and viability of the global capital markets for the ultimate 
■■Maintain and improve their professional competence and strive to maintain and 
improve the competence of other investment professionals.
Standards of Professional Conduct
 I. PROFESSIONALISM
A Knowledge of the Law
 Members and Candidates must understand and comply with all applicable 
laws, rules, and regulations (including the CFA Institute Code of Ethics 
and Standards of Professional Conduct) of any government, regulatory 
organization, licensing agency, or professional association governing their 
professional activities. In the event of conflict, Members and Candidates 
must comply with the more strict law, rule, or regulation. Members and 
Candidates must not knowingly participate or assist in and must dissociate 
from any violation of such laws, rules, or regulations.
B Independence and Objectivity
 Members and Candidates must use reasonable care and judgment to achieve

and maintain independence and objectivity in their professional activities. 
Members and Candidates must not offer, solicit, or accept any gift, benefit, 
compensation, or consideration that reasonably could be expected to com -
promise their own or another’s independence and objectivity.
C Misrepresentation
 Members and Candidates must not knowingly make any misrepresentations 
relating to investment analysis, recommendations, actions, or other profes -
sional activities.
D Misconduct
 Members and Candidates must not engage in any professional conduct 
involving dishonesty, fraud, or deceit or commit any act that reflects 
adversely on their professional reputation, integrity, or competence.
 II. INTEGRITY OF CAPITAL MARKETS
A Material Nonpublic Information

CFA Institute Code of Ethics and Standards of Professional Conduct 45
 Members and Candidates who possess material nonpublic information that 
could affect the value of an investment must not act or cause others to act 
on the information. 
B Market Manipulation
 Members and Candidates must not engage in practices that distort prices 
or artificially inflate trading volume with the intent to mislead market 
participants.
 III. DUTIES TO CLIENTS
A Loyalty, Prudence, and Care
 Members and Candidates have a duty of loyalty to their clients and must 
act with reasonable care and exercise prudent judgment. Members and 
Candidates must act for the benefit of their clients and place their clients’ 
interests before their employer’s or their own interests.
B Fair Dealing
 Members and Candidates must deal fairly and objectively with all clients 
when providing investment analysis, making investment recommendations, 
taking investment action, or engaging in other professional activities.
C Suitability

1 When Members and Candidates are in an advisory relationship with a 
client, they must:
a Make a reasonable inquiry into a client’s or prospective client’s 
investment experience, risk and return objectives, and financial con -
straints prior to making any investment recommendation or taking 
investment action and must reassess and update this information 
regularly.
b Determine that an investment is suitable to the client’s financial sit -
uation and consistent with the client’s written objectives, mandates, 
and constraints before making an investment recommendation or 
taking investment action.
c Judge the suitability of investments in the context of the client’s total 
2 When Members and Candidates are responsible for managing a portfolio 
to a specific mandate, strategy, or style, they must make only investment 
recommendations or take only investment actions that are consistent 
with the stated objectives and constraints of the portfolio.
D Performance Presentation

 When communicating investment performance information, Members and 
Candidates must make reasonable efforts to ensure that it is fair, accurate, 
and complete.
E Preservation of Confidentiality
 Members and Candidates must keep information about current, former, and 
prospective clients confidential unless:
1 The information concerns illegal activities on the part of the client or 
prospective client,
2 Disclosure is required by law, or
3 The client or prospective client permits disclosure of the information.
 IV. DUTIES TO EMPLOYERS
A Loyalty

Reading 2 ■ Code of Ethics and Standards of Professional Conduct 46
 In matters related to their employment, Members and Candidates must 
act for the benefit of their employer and not deprive their employer of the 
advantage of their skills and abilities, divulge confidential information, or 
otherwise cause harm to their employer.
B Additional Compensation Arrangements
 Members and Candidates must not accept gifts, benefits, compensation, or 
consideration that competes with or might reasonably be expected to create 
a conflict of interest  with their employer’s interest unless they obtain written 
consent from all parties involved.
C Responsibilities of Supervisors
 Members and Candidates must make reasonable efforts to ensure that any -
one subject to their supervision or authority complies with applicable laws, 
rules, regulations, and the Code and Standards.
 V. INVESTMENT ANALYSIS, RECOMMENDATIONS, AND ACTIONS
A Diligence and Reasonable Basis
 Members and Candidates must:

Members and Candidates must:
1 Exercise diligence, independence, and thoroughness in analyzing invest -
ments, making investment recommendations, and taking investment 
actions.
2 Have a reasonable and adequate basis, supported by appropriate 
research and investigation, for any investment analysis, recommenda -
tion, or action.
B Communication with Clients and Prospective Clients
1 Disclose to clients and prospective clients the basic format and general 
principles of the investment processes they use to analyze investments, 
select securities, and construct portfolios and must promptly disclose 
any changes that might materially affect those processes.
2 Disclose to clients and prospective clients significant limitations and 
risks associated with the investment process.
3 Use reasonable judgment in identifying which factors are important to 
their investment analyses, recommendations, or actions and include

those factors in communications with clients and prospective clients.
4 Distinguish between fact and opinion in the presentation of investment 
analysis and recommendations.
C Record Retention
 Members and Candidates must develop and maintain appropriate records 
to support their investment analyses, recommendations, actions, and other 
investment-  related communications with clients and prospective clients.
 VI. CONFLICTS OF INTEREST
A Disclosure of Conflicts
 Members and Candidates must make full and fair disclosure of all matters 
that could reasonably be expected to impair their independence and objec -
tivity or interfere with respective duties to their clients, prospective clients, 
and employer. Members and Candidates must ensure that such disclosures 
are prominent, are delivered in plain language, and communicate the rele -
vant information effectively.
B Priority of Transactions

CFA Institute Code of Ethics and Standards of Professional Conduct 47
 Investment transactions for clients and employers must have priority over 
investment transactions in which a Member or Candidate is the beneficial 
owner.
C Referral Fees
 Members and Candidates must disclose to their employer, clients, and pro -
spective clients, as appropriate, any compensation, consideration, or benefit 
received from or paid to others for  the recommendation of products or 
services .
 VII. RESPONSIBILITIES AS A CFA INSTITUTE MEMBER OR CFA CANDIDATE
A Conduct as Participants in CFA Institute Programs
 Members and Candidates must not engage in any conduct that compro -
mises the reputation or integrity of CFA Institute or the CFA designation or 
the integrity, validity, or security of CFA Institute programs.
B Reference to CFA Institute, the CFA Designation, and the CFA Program
 When referring to CFA Institute, CFA Institute membership, the CFA des -

ignation, or candidacy in the CFA Program, Members and Candidates must 
not misrepresent or exaggerate the meaning or implications of membership 
in CFA Institute, holding the CFA designation, or candidacy in the CFA 
Program.

Guidance for Standards I–VII
a. demonstrate the application of the Code of Ethics and Standards 
of Professional Conduct to situations involving issues of 
professional integrity;
b. distinguish between conduct that conforms to the Code and 
Standards and conduct that violates the Code and Standards;
c. recommend practices and procedures designed to prevent 
violations of the Code of Ethics and Standards of Professional 
Conduct.
STANDARD I: PROFESSIONALISM
Standard I(A) Knowledge of the Law
Members and Candidates must understand and comply with all applicable laws, rules, 
and regulations (including the CFA Institute Code of Ethics and Standards of Professional 
Conduct) of any government, regulatory organization, licensing agency, or professional 
association governing their professional activities. In the event of conflict, Members 
and Candidates must comply with the more strict law, rule, or regulation. Members and

Candidates must not knowingly participate or assist in and must dissociate from any 
violation of such laws, rules, or regulations. 
Guidance
Highlights:
■■Relationship between the Code and Standards and Applicable Law
■■Participation in or Association with Violations by Others
■■Investment Products and Applicable LawsrEAdING
3

Reading 3 ■ Guidance for Standards I–VII 50
Members and candidates must understand the applicable laws and regulations of 
the countries and jurisdictions where they engage in professional activities. These 
activities may include, but are not limited to, trading of securities or other financial 
instruments, providing investment advice, conducting research, or performing other 
investment services. On the basis of their reasonable and good faith understanding, 
members and candidates must comply with the laws and regulations that directly 
govern their professional activities and resulting outcomes and that protect the 
interests of the clients. 
When questions arise, members and candidates should know their firm’s policies 
and procedures for accessing compliance guidance. This standard does not require 
members and candidates to become experts, however, in compliance. Additionally, 
members and candidates are not required to have detailed knowledge of or be experts

on all the laws that could potentially govern their activities.
During times of changing regulations, members and candidates must remain vigilant 
in maintaining their knowledge of the requirements for their professional activities. 
New financial products and processes, along with uncovered ethical missteps, create an 
environment for recurring and potentially wide-  ranging regulatory changes. Members 
and candidates are also continually provided improved and enhanced methods of 
communicating with both clients and potential clients, such as mobile applications 
and web-  based social networking platforms. As new local, regional, and global 
requirements are updated to address these and other changes, members, candidates, 
and their firms must adjust their procedures and practices to remain in compliance.
Relationship between the Code and Standards and Applicable Law
Some members or candidates may live, work, or provide investment services to clients

living in a country that has no law or regulation governing a particular action or that 
has laws or regulations that differ from the requirements of the Code and Standards. 
When applicable law and the Code and Standards require different conduct, mem -
bers and candidates must follow the more strict of the applicable law or the Code 
and Standards.
“ Applicable law” is the law that governs the member’s or candidate’s conduct. 
Which law applies will depend on the particular facts and circumstances of each 
case. The “more strict” law or regulation is the law or regulation that imposes greater 
restrictions on the action of the member or candidate or calls for the member or 
candidate to exert a greater degree of action that protects the interests of investors. 
For example, applicable law or regulation may not require members and candidates 
to disclose referral fees received from or paid to others for the recommendation of

investment products or services. Because the Code and Standards impose this obli -
gation, however, members and candidates must disclose the existence of such fees.
Members and candidates must adhere to the following principles:
■■Members and candidates must comply with applicable laws or regulations 
related to their professional activities. 
■■Members and candidates must not engage in conduct that constitutes a viola -
tion of the Code and Standards, even though it may otherwise be legal.
■■In the absence of any applicable law or regulation or when the Code and 
Standards impose a higher degree of responsibility than applicable laws and 
regulations, members and candidates must adhere to the Code and Standards. 
Applications of these principles are outlined in Exhibit 1.
The applicable laws governing the responsibilities of a member or candidate should 
be viewed as the minimal threshold of acceptable actions. When members and can -

didates take actions that exceed the minimal requirements, they further support the 
conduct required of Standard I(A).

Standard I: Professionalism 51
CFA Institute members are obligated to abide by the CFA Institute Articles of 
Incorporation, Bylaws, Code of Ethics, Standards of Professional Conduct, Rules of 
Procedure, Membership Agreement, and other applicable rules promulgated by CFA 
Institute, all as amended periodically. CFA candidates who are not members must also 
abide by these documents (except for the Membership Agreement) as well as rules 
and regulations related to the administration of the CFA examination, the Candidate 
Responsibility Statement, and the Candidate Pledge.
Participation in or Association with Violations by Others
Members and candidates are responsible for violations in which they knowingly  par-
ticipate or assist. Although members and candidates are presumed to have knowledge 
of all applicable laws, rules, and regulations, CFA Institute acknowledges that mem -
bers may not recognize violations if they are not aware of all the facts giving rise to

the violations. Standard I(A) applies when members and candidates know or should 
know that their conduct may contribute to a violation of applicable laws, rules, or 
regulations or the Code and Standards.
If a member or candidate has reasonable grounds to believe that imminent or 
ongoing client or employer activities are illegal or unethical, the member or candi -
date must dissociate, or separate, from the activity. In extreme cases, dissociation 
may require a member or candidate to leave his or her employment. Members and 
candidates may take the following intermediate steps to dissociate from ethical vio -
lations of others when direct discussions with the person or persons committing the 
violation are unsuccessful. The first step should be to attempt to stop the behavior by 
bringing it to the attention of the employer through a supervisor or the firm’s compli -
ance department. If this attempt is unsuccessful, then members and candidates have

a responsibility to step away and dissociate from the activity. Dissociation practices 
will differ on the basis of the member’s or candidate’s role in the investment industry. 
It may include removing one’s name from written reports or recommendations, asking 
for a different assignment, or refusing to accept a new client or continue to advise a 
current client. Inaction combined with continuing association with those involved 
in illegal or unethical conduct may be construed as participation or assistance in the 
illegal or unethical conduct.
CFA Institute strongly encourages members and candidates to report potential 
violations of the Code and Standards committed by fellow members and candidates. 
Although a failure to report is less likely to be construed as a violation than a failure to 
dissociate from unethical conduct, the impact of inactivity on the integrity of capital 
markets can be significant. Although the Code and Standards do not compel members

and candidates to report violations to their governmental or regulatory organizations 
unless such disclosure is mandatory under applicable law (voluntary reporting is 
often referred to as whistleblowing), such disclosure may be prudent under certain 
circumstances. Members and candidates should consult their legal and compliance 
advisers for guidance.
Additionally, CFA Institute encourages members, nonmembers, clients, and the 
investing public to report violations of the Code and Standards by CFA Institute 
members or CFA candidates by submitting a complaint in writing to the CFA Institute 
Professional Conduct Program via e-  mail (pcprogram@cfainstitute.org) or the CFA 
Institute website (www.cfainstitute.org).
Investment Products and Applicable Laws
Members and candidates involved in creating or maintaining investment services or 
investment products or packages of securities and/or derivatives should be mindful

of where these products or packages will be sold as well as their places of origina -
tion. The applicable laws and regulations of the countries or regions of origination 
and expected sale should be understood by those responsible for the supervision of

Reading 3 ■ Guidance for Standards I–VII 52
the services or creation and maintenance of the products or packages. Members or 
candidates should make reasonable efforts to review whether associated firms that 
are distributing products or services developed by their employing firm also abide by 
the laws and regulations of the countries and regions of distribution. Members and 
candidates should undertake the necessary due diligence when transacting cross-  
border business to understand the multiple applicable laws and regulations in order 
to protect the reputation of their firm and themselves.
Given the complexity that can arise with business transactions in today’s market, 
there may be some uncertainty surrounding which laws or regulations are considered 
applicable when activities are being conducted in multiple jurisdictions. Members 
and candidates should seek the appropriate guidance, potentially including the firm’s

compliance or legal departments and legal counsel outside the organization, to gain 
a reasonable understanding of their responsibilities and how to implement them 
appropriately.
Exhibit 1   Global Application of the Code and Standards
Members and candidates who practice in multiple jurisdictions may be subject 
to varied securities laws and regulations. If applicable law is stricter than the 
requirements of the Code and Standards, members and candidates must adhere 
to applicable law; otherwise, they must adhere to the Code and Standards. The 
following chart provides illustrations involving a member who may be subject 
to the securities laws and regulations of three different types of countries:
NS: country with no securities laws or regulations 
LS: country with less strict securities laws and regulations than the Code and 
Standards
MS: country with more  strict securities laws and regulations than the Code and 
Standards
Applicable Law Duties Explanation
Member resides in NS

Member resides in NS 
country, does business in 
LS country; LS law applies.Member must adhere to 
the Code and Standards.Because applicable law is 
less strict than the Code 
and Standards, the member 
must adhere to the Code 
country, does business 
in MS country; MS law 
applies.Member must adhere to 
the law of MS country.Because applicable law is 
stricter than the Code and 
Standards, member must 
adhere to the more strict 
applicable law.
Member resides in LS 
NS country; LS law applies.Member must adhere to 
and Standards, member 
the law of MS country. Because applicable law is 

Standard I: Professionalism 53
NS country; LS law applies, 
but it states that law of 
locality where business is 
conducted governs.Member must adhere to 
the Code and Standards.Because applicable law 
states that the law of the 
locality where the business 
is conducted governs and 
there is no local law, the 
member must adhere to the 
Code and Standards.
MS country; LS law applies, 
the law of MS country.Because applicable law 
of the locality where the 
business is conducted 
governs and local law is 
Member resides in MS 
LS country; MS law applies.Member must adhere to 
stricter than the Code and

LS country; MS law applies, 
local law is less strict than 
the Code and Standards, 
LS country with a client 
who is a citizen of LS 
country; MS law applies, 
but it states that the law of 
the client’s home country 
governs.Member must adhere to 
client’s home country 
governs (which is less 
strict than the Code and 
Standards), member must 
adhere to the Code and 
who is a citizen of MS

who is a citizen of MS 
governs and the law of the 
client’s home country is 
Standards, the member 
must adhere to the more 
strict applicable law.Exhibit 1   (Continued)

Reading 3 ■ Guidance for Standards I–VII 54
Recommended Procedures for Compliance
Members and Candidates
Suggested methods by which members and candidates can acquire and maintain 
understanding of applicable laws, rules, and regulations include the following:
■■Stay informed : Members and candidates should establish or encourage their 
employers to establish a procedure by which employees are regularly informed 
about changes in applicable laws, rules, regulations, and case law. In many 
instances, the employer’s compliance department or legal counsel can provide 
such information in the form of memorandums distributed to employees in the 
organization. Also, participation in an internal or external continuing education 
program is a practical method of staying current.
■■Review procedures : Members and candidates should review, or encourage their 
employers to review, the firm’s written compliance procedures on a regular

basis to ensure that the procedures reflect current law and provide adequate 
guidance to employees about what is permissible conduct under the law and/
or the Code and Standards. Recommended compliance procedures for spe -
cific items of the Code and Standards are discussed in this Handbook  in the 
“Guidance” sections associated with each standard.
■■Maintain current files : Members and candidates should maintain or encourage 
their employers to maintain readily accessible current reference copies of appli -
cable statutes, rules, regulations, and important cases.
Distribution Area Laws
Members and candidates should make reasonable efforts to understand the applicable 
laws—both country and regional—for the countries and regions where their investment 
products are developed and are most likely to be distributed to clients.
Legal Counsel
When in doubt about the appropriate action to undertake, it is recommended that 
a member or candidate seek the advice of compliance personnel or legal counsel

concerning legal requirements. If a potential violation is being committed by a fellow 
employee, it may also be prudent for the member or candidate to seek the advice of 
the firm’s compliance department or legal counsel.
Dissociation
When dissociating from an activity that violates the Code and Standards, members 
and candidates should document the violation and urge their firms to attempt to 
persuade the perpetrator(s) to cease such conduct. To dissociate from the conduct, a 
member or candidate may have to resign his or her employment.
Firms
The formality and complexity of compliance procedures for firms depend on the nature 
and size of the organization and the nature of its investment operations. Members 
and candidates should encourage their firms to consider the following policies and 
procedures to support the principles of Standard I(A):
■■Develop and/or adopt a code of ethics : The ethical culture of an organization

starts at the top. Members and candidates should encourage their super -
visors or managers to adopt a code of ethics. Adhering to a code of ethics 
facilitates solutions when people face ethical dilemmas and can prevent the 
need for employees to resort to a “whistleblowing” solution publicly alleging

Standard I: Professionalism 55
concealed misconduct. CFA Institute has published the Asset Manager Code of 
Professional Conduct , which firms may adopt or use as the basis for their codes 
(visit www.cfainstitute.org).
■■Provide information on applicable laws : Pertinent information that highlights 
applicable laws and regulations might be distributed to employees or made 
available in a central location. Information sources might include primary 
information developed by the relevant government, governmental agencies, 
regulatory organizations, licensing agencies, and professional associations (e.g., 
from their websites); law firm memorandums or newsletters; and association 
memorandums or publications (e.g., CFA Institute Magazine ).
■■Establish procedures for reporting violations : Firms might provide written proto -
cols for reporting suspected violations of laws, regulations, or company policies.
Application of the Standard
Example 1 (Notification of Known Violations):

Michael Allen works for a brokerage firm and is responsible for an underwriting of 
securities. A company official gives Allen information indicating that the financial 
statements Allen filed with the regulator overstate the issuer’s earnings. Allen seeks 
the advice of the brokerage firm’s general counsel, who states that it would be difficult 
for the regulator to prove that Allen has been involved in any wrongdoing.
Comment : Although it is recommended that members and candidates seek 
the advice of legal counsel, the reliance on such advice does not absolve 
a member or candidate from the requirement to comply with the law or 
regulation. Allen should report this situation to his supervisor, seek an 
independent legal opinion, and determine whether the regulator should 
be notified of the error.
Example 2 (Dissociating from a Violation):
Lawrence Brown’s employer, an investment banking firm, is the principal underwriter

for an issue of convertible debentures by the Courtney Company. Brown discovers 
that the Courtney Company has concealed severe third-  quarter losses in its foreign 
operations. The preliminary prospectus has already been distributed.
Comment : Knowing that the preliminary prospectus is misleading, Brown 
should report his findings to the appropriate supervisory persons in his 
firm. If the matter is not remedied and Brown’s employer does not dissociate 
from the underwriting, Brown should sever all his connections with the 
underwriting. Brown should also seek legal advice to determine whether 
additional reporting or other action should be taken.
Example 3 (Dissociating from a Violation):
Kamisha Washington’s firm advertises its past performance record by showing the 
10- year return of a composite of its client accounts. Washington discovers, however, 
that the composite omits the performance of accounts that have left the firm during

the 10-  year period, whereas the description of the composite indicates the inclusion of 
all firm accounts. This omission has led to an inflated performance figure. Washington 
is asked to use promotional material that includes the erroneous performance number 
when soliciting business for the firm.

Reading 3 ■ Guidance for Standards I–VII 56
Comment : Misrepresenting performance is a violation of the Code and 
Standards. Although she did not calculate the performance herself, 
Washington would be assisting in violating Standard I(A) if she were to 
use the inflated performance number when soliciting clients. She must 
dissociate herself from the activity. If discussing the misleading number 
with the person responsible is not an option for correcting the problem, she 
can bring the situation to the attention of her supervisor or the compliance 
department at her firm. If her firm is unwilling to recalculate performance, 
she must refrain from using the misleading promotional material and should 
notify the firm of her reasons. If the firm insists that she use the material, 
she should consider whether her obligation to dissociate from the activity 
requires her to seek other employment.
Example 4 (Following the Highest Requirements):

James Collins is an investment analyst for a major Wall Street brokerage firm. He 
works in a developing country with a rapidly modernizing economy and a growing 
capital market. Local securities laws are minimal—in form and content—and include 
no punitive prohibitions against insider trading.
Comment : Collins must abide by the requirements of the Code and 
Standards, which might be more strict than the rules of the developing 
country. He should be aware of the risks that a small market and the absence 
of a fairly regulated flow of information to the market represent to his ability 
to obtain information and make timely judgments. He should include this 
factor in formulating his advice to clients. In handling material nonpublic 
information that accidentally comes into his possession, he must follow 
Standard II(A)–Material Nonpublic Information.
Example 5 (Following the Highest Requirements):

Laura Jameson works for a multinational investment adviser based in the United 
States. Jameson lives and works as a registered investment adviser in the tiny, but 
wealthy, island nation of Karramba. Karramba’s securities laws state that no invest -
ment adviser registered and working in that country can participate in initial public 
offerings (IPOs) for the adviser’s personal account. Jameson, believing that, as a US 
citizen working for a US-  based company, she should comply only with US law, has 
ignored this Karrambian law. In addition, Jameson believes that as a charterholder, 
as long as she adheres to the Code and Standards requirement that she disclose her 
participation in any IPO to her employer and clients when such ownership creates a 
conflict of interest, she is meeting the highest ethical requirements.
Comment : Jameson is in violation of Standard I(A). As a registered invest -

ment adviser in Karramba, Jameson is prevented by Karrambian securities 
law from participating in IPOs regardless of the law of her home country. 
In addition, because the law of the country where she is working is stricter 
than the Code and Standards, she must follow the stricter requirements 
of the local law rather than the requirements of the Code and Standards.
Example 6 (Laws and Regulations Based on Religious Tenets):
Amanda Janney is employed as a fixed-  income portfolio manager for a large interna -
tional firm. She is on a team within her firm that is responsible for creating and man -
aging a fixed-  income hedge fund to be sold throughout the firm’s distribution centers 
to high-  net- worth clients. Her firm receives expressions of interest from potential 
clients from the Middle East who are seeking investments that comply with Islamic

Standard I: Professionalism 57
law. The marketing and promotional materials for the fixed-  income hedge fund do 
not specify whether or not the fund is a suitable investment for an investor seeking 
compliance with Islamic law. Because the fund is being distributed globally, Janney 
is concerned about the reputation of the fund and the firm and believes disclosure 
of whether or not the fund complies with Islamic law could help minimize potential 
mistakes with placing this investment.
Comment : As the financial market continues to become globalized, members 
and candidates will need to be aware of the differences between cultural 
and religious laws and requirements as well as the different governmental 
laws and regulations. Janney and the firm could be proactive in their efforts 
to acknowledge areas where the new fund may not be suitable for clients.
Example 7 (Reporting Potential Unethical Actions):
Krista Blume is a junior portfolio manager for high-  net- worth portfolios at a large

global investment manager. She observes a number of new portfolios and relationships 
coming from a country in Europe where the firm did not have previous business and 
is told that a broker in that country is responsible for this new business. At a meeting 
on allocation of research resources to third-  party research firms, Blume notes that this 
broker has been added to the list and is allocated payments for research. However, she 
knows the portfolios do not invest in securities in the broker’s country, and she has 
not seen any research come from this broker. Blume asks her supervisor about the 
name being on the list and is told that someone in marketing is receiving the research 
and that the name being on the list is OK. She believes that what may be going on 
is that the broker is being paid for new business through the inappropriate research 
payments, and she wishes to dissociate from the misconduct.
Comment : Blume should follow the firm’s policies and procedures for

reporting potential unethical activity, which may include discussions with 
her supervisor or someone in a designated compliance department. She 
should communicate her concerns appropriately while advocating for dis -
closure between the new broker relationship and the research payments.
Example 8 (Failure to Maintain Knowledge of the Law):
Colleen White is excited to use new technology to communicate with clients and 
potential clients. She recently began posting investment information, including per -
formance reports and investment opinions and recommendations, to her Facebook 
page. In addition, she sends out brief announcements, opinions, and thoughts via her 
Twitter account (for example, “Prospects for future growth of XYZ company look 
good! #makingmoney4U”). Prior to White’s use of these social media platforms, the 
local regulator had issued new requirements and guidance governing online elec -
tronic communication. White’s communications appear to conflict with the recent

regulatory announcements. 
Comment : White is in violation of Standard I(A) because her communica -
tions do not comply with the existing guidance and regulation governing 
use of social media. White must be aware of the evolving legal requirements 
pertaining to new and dynamic areas of the financial services industry that 
are applicable to her. She should seek guidance from appropriate, knowl -
edgeable, and reliable sources, such as her firm’s compliance department, 
external service providers, or outside counsel, unless she diligently follows 
legal and regulatory trends affecting her professional responsibilities.

Reading 3 ■ Guidance for Standards I–VII 58
Standard I(B) Independence and Objectivity
Members and Candidates must use reasonable care and judgment to achieve and maintain 
independence and objectivity in their professional activities. Members and Candidates 
must not offer, solicit, or accept any gift, benefit, compensation, or consideration that 
reasonably could be expected to compromise their own or another’s independence 
and objectivity. 
Guidance
■■Buy-  Side Clients
■■Fund Manager and Custodial Relationships
■■Investment Banking Relationships
■■Performance Measurement and Attribution
■■Public Companies
■■Credit Rating Agency Opinions
■■Influence during the Manager Selection/Procurement Process
■■Issuer-  Paid Research
■■Travel Funding
Standard I(B) states the responsibility of CFA Institute members and candidates in 
the CFA Program to maintain independence and objectivity so that their clients will 
have the benefit of their work and opinions unaffected by any potential conflict of

interest or other circumstance adversely affecting their judgment. Every member and 
candidate should endeavor to avoid situations that could cause or be perceived to 
cause a loss of independence or objectivity in recommending investments or taking 
investment action.
External sources may try to influence the investment process by offering analysts 
and portfolio managers a variety of benefits. Corporations may seek expanded research 
coverage, issuers and underwriters may wish to promote new securities offerings, 
brokers may want to increase commission business, and independent rating agencies 
may be influenced by the company requesting the rating. Benefits may include gifts, 
invitations to lavish functions, tickets, favors, or job referrals. One type of benefit 
is the allocation of shares in oversubscribed IPOs to investment managers for their 
personal accounts. This practice affords managers the opportunity to make quick

profits that may not be available to their clients. Such a practice is prohibited under 
Standard I(B). Modest gifts and entertainment are acceptable, but special care must 
be taken by members and candidates to resist subtle and not-  so- subtle pressures to 
act in conflict with the interests of their clients. Best practice dictates that members 
and candidates reject any offer of gift or entertainment that could be expected to 
threaten their independence and objectivity.
Receiving a gift, benefit, or consideration from a client  can be distinguished from 
gifts given by entities seeking to influence a member or candidate to the detriment 
of other clients. In a client relationship, the client has already entered some type of 
compensation arrangement with the member, candidate, or his or her firm. A gift 
from a client could be considered supplementary compensation. The potential for 
obtaining influence to the detriment of other clients, although present, is not as great

Standard I: Professionalism 59
as in situations where no compensation arrangement exists. When possible, prior to 
accepting “bonuses” or gifts from clients, members and candidates should disclose to 
their employers such benefits offered by clients. If notification is not possible prior to 
acceptance, members and candidates must disclose to their employer benefits previ -
ously accepted from clients. Disclosure allows the employer of a member or candidate 
to make an independent determination about the extent to which the gift may affect 
the member’s or candidate’s independence and objectivity.
Members and candidates may also come under pressure from their own firms to, for 
example, issue favorable research reports or recommendations for certain companies 
with potential or continuing business relationships with the firm. The situation may be 
aggravated if an executive of the company sits on the bank or investment firm’s board

and attempts to interfere in investment decision making. Members and candidates 
acting in a sales or marketing capacity must be especially mindful of their objectivity 
in promoting appropriate investments for their clients.
Left unmanaged, pressures that threaten independence place research analysts in a 
difficult position and may jeopardize their ability to act independently and objectively. 
One of the ways that research analysts have coped with these pressures in the past 
is to use subtle and ambiguous language in their recommendations or to temper the 
tone of their research reports. Such subtleties are lost on some investors, however, 
who reasonably expect research reports and recommendations to be straightforward 
and transparent and to communicate clearly an analyst’s views based on unbiased 
analysis and independent judgment.
Members and candidates are personally responsible for maintaining independence

and objectivity when preparing research reports, making investment recommendations, 
and taking investment action on behalf of clients. Recommendations must convey the 
member’s or candidate’s true opinions, free of bias from internal or external pressures, 
and be stated in clear and unambiguous language.
Members and candidates also should be aware that some of their professional or 
social activities within CFA Institute or its member societies may subtly threaten their 
independence or objectivity. When seeking corporate financial support for conventions, 
seminars, or even weekly society luncheons, the members or candidates responsible 
for the activities should evaluate both the actual effect of such solicitations on their 
independence and whether their objectivity might be perceived to be compromised 
in the eyes of their clients.
Buy-  Side Clients
One source of pressure on sell-  side analysts is buy-  side clients. Institutional clients

are traditionally the primary users of sell-  side research, either directly or with soft 
dollar brokerage. Portfolio managers may have significant positions in the security 
of a company under review. A rating downgrade may adversely affect the portfolio’s 
performance, particularly in the short term, because the sensitivity of stock prices 
to ratings changes has increased in recent years. A downgrade may also affect the 
manager’s compensation, which is usually tied to portfolio performance. Moreover, 
portfolio performance is subject to media and public scrutiny, which may affect the 
manager’s professional reputation. Consequently, some portfolio managers implicitly 
or explicitly support sell-  side ratings inflation.
Portfolio managers have a responsibility to respect and foster the intellectual hon -
esty of sell-  side research. Therefore, it is improper for portfolio managers to threaten 
or engage in retaliatory practices, such as reporting sell-  side analysts to the covered

company in order to instigate negative corporate reactions. Although most portfolio 
managers do not engage in such practices, the perception by the research analyst 
that a reprisal is possible may cause concern and make it difficult for the analyst to 
maintain independence and objectivity.

Reading 3 ■ Guidance for Standards I–VII 60
Fund Manager and Custodial Relationships
Research analysts are not the only people who must be concerned with maintaining 
their independence. Members and candidates who are responsible for hiring and 
retaining outside managers and third-  party custodians should not accepts gifts, 
entertainment, or travel funding that may be perceived as impairing their decisions. 
The use of secondary fund managers has evolved into a common practice to manage 
specific asset allocations. The use of third-  party custodians is common practice for 
independent investment advisory firms and helps them with trading capabilities and 
reporting requirements. Primary and secondary fund managers, as well as third-  party 
custodians, often arrange educational and marketing events to inform others about 
their business strategies, investment process, or custodial services. Members and 
candidates must review the merits of each offer individually in determining whether

they may attend yet maintain their independence.
Investment Banking Relationships
Some sell-  side firms may exert pressure on their analysts to issue favorable research 
reports on current or prospective investment banking clients. For many of these firms, 
income from investment banking has become increasingly important to overall firm 
profitability because brokerage income has declined as a result of price competition. 
Consequently, firms offering investment banking services work hard to develop and 
maintain relationships with investment banking clients and prospects. These compa -
nies are often covered by the firm’s research analysts because companies often select 
their investment banks on the basis of the reputation of their research analysts, the 
quality of their work, and their standing in the industry.
In some countries, research analysts frequently work closely with their investment 
banking colleagues to help evaluate prospective investment banking clients. In other

countries, because of past abuses in managing the obvious conflicts of interest, regula -
tors have established clear rules prohibiting the interaction of these groups. Although 
collaboration between research analysts and investment banking colleagues may 
benefit the firm and enhance market efficiency (e.g., by allowing firms to assess risks 
more accurately and make better pricing assumptions), it requires firms to carefully 
balance the conflicts of interest inherent in the collaboration. Having analysts work 
with investment bankers is appropriate only when the conflicts are adequately and 
effectively managed and disclosed. Firm managers have a responsibility to provide an 
environment in which analysts are neither coerced nor enticed into issuing research 
that does not reflect their true opinions. Firms should require public disclosure of 
actual conflicts of interest to investors.
Members, candidates, and their firms must adopt and follow perceived best

practices in maintaining independence and objectivity in the corporate culture and 
protecting analysts from undue pressure by their investment banking colleagues. The 
“firewalls” traditionally built between these two functions must be managed to minimize 
conflicts of interest; indeed, enhanced firewall policies may go as far as prohibiting 
all communications between these groups. A key element of an enhanced firewall 
is separate reporting structures for personnel on the research side and personnel 
on the investment banking side. For example, investment banking personnel should 
not have any authority to approve, disapprove, or make changes to research reports 
or recommendations. Another element should be a compensation arrangement that 
minimizes the pressures on research analysts and rewards objectivity and accuracy. 
Compensation arrangements should not link analyst remuneration directly to invest -
ment banking assignments in which the analyst may participate as a team member.

Firms should also regularly review their policies and procedures to determine whether

Standard I: Professionalism 61
analysts are adequately safeguarded and to improve the transparency of disclosures 
relating to conflicts of interest. The highest level of transparency is achieved when 
disclosures are prominent and specific rather than marginalized and generic.
Performance Measurement and Attribution
Members and candidates working within a firm’s investment performance measurement 
department may also be presented with situations that challenge their independence 
and objectivity. As performance analysts, their analyses may reveal instances where 
managers may appear to have strayed from their mandate. Additionally, the perfor -
mance analyst may receive requests to alter the construction of composite indexes 
owing to negative results for a selected account or fund. The member or candidate 
must not allow internal or external influences to affect their independence and objec -
tivity as they faithfully complete their performance calculation and analysis-  related

responsibilities.
Public Companies
Analysts may be pressured to issue favorable reports and recommendations by the 
companies they follow. Not every stock is a “buy, ” and not every research report is 
favorable—for many reasons, including the cyclical nature of many business activities 
and market fluctuations. For instance, a “good company” does not always translate into 
a “good stock” rating if the current stock price is fully valued. In making an invest -
ment recommendation, the analyst is responsible for anticipating, interpreting, and 
assessing a company’s prospects and stock price performance in a factual manner. 
Many company managers, however, believe that their company’s stock is underval -
ued, and these managers may find it difficult to accept critical research reports or 
ratings downgrades. Company managers’ compensation may also be dependent on 
stock performance.
Due diligence in financial research and analysis involves gathering information

from a wide variety of sources, including public disclosure documents (such as proxy 
statements, annual reports, and other regulatory filings) and also company manage -
ment and investor-  relations personnel, suppliers, customers, competitors, and other 
relevant sources. Research analysts may justifiably fear that companies will limit 
their ability to conduct thorough research by denying analysts who have “negative” 
views direct access to company managers and/or barring them from conference calls 
and other communication venues. Retaliatory practices include companies bringing 
legal action against analysts personally and/or their firms to seek monetary damages 
for the economic effects of negative reports and recommendations. Although few 
companies engage in such behavior, the perception that a reprisal is possible is a rea -
sonable concern for analysts. This concern may make it difficult for them to conduct

the comprehensive research needed to make objective recommendations. For further 
information and guidance, members and candidates should refer to the CFA Institute 
publication Best Practice Guidelines Governing Analyst/Corporate Issuer Relations 
(www.cfainstitute.org) .
Credit Rating Agency Opinions
Credit rating agencies provide a service by grading the fixed-  income products offered 
by companies. Analysts face challenges related to incentives and compensation 
schemes that may be tied to the final rating and successful placement of the product. 
Members and candidates employed at rating agencies should ensure that procedures 
and processes at the agencies prevent undue influences from a sponsoring company 
during the analysis. Members and candidates should abide by their agencies’ and the 
industry’s standards of conduct regarding the analytical process and the distribution 
of their reports.

Reading 3 ■ Guidance for Standards I–VII 62
The work of credit rating agencies also raises concerns similar to those inherent 
in investment banking relationships. Analysts may face pressure to issue ratings at a 
specific level because of other services the agency offers companies—namely, advis -
ing on the development of structured products. The rating agencies need to develop 
the necessary firewalls and protections to allow the independent operations of their 
different business lines.
When using information provided by credit rating agencies, members and can -
didates should be mindful of the potential conflicts of interest. And because of the 
potential conflicts, members and candidates may need to independently validate the 
rating granted.
Influence during the Manager Selection/Procurement Process
Members and candidates may find themselves on either side of the manager selection 
process. An individual may be on the hiring side as a representative of a pension

organization or an investment committee member of an endowment or a charitable 
organization. Additionally, other members may be representing their organizations in 
attempts to earn new investment allocation mandates. The responsibility of members 
and candidates to maintain their independence and objectivity extends to the hiring 
or firing of those who provide business services beyond investment management. 
When serving in a hiring capacity, members and candidates should not solicit 
gifts, contributions, or other compensation that may affect their independence and 
objectivity. Solicitations do not have to benefit members and candidates personally to 
conflict with Standard I(B). Requesting contributions to a favorite charity or political 
organization may also be perceived as an attempt to influence the decision-  making 
process. Additionally, members and candidates serving in a hiring capacity should 
refuse gifts, donations, and other offered compensation that may be perceived to

influence their decision-  making process. 
When working to earn a new investment allocation, members and candidates 
should not offer gifts, contributions, or other compensation to influence the decision 
of the hiring representative. The offering of these items with the intent to impair the 
independence and objectivity of another person would not comply with Standard I(B). 
Such prohibited actions may include offering donations to a charitable organization 
or political candidate referred by the hiring representative. 
A clear example of improperly influencing hiring representatives was displayed 
in the “pay-  to- play” scandal involving government-  sponsored pension funds in the 
United States. Managers looking to gain lucrative allocations from the large funds 
made requested donations to the political campaigns of individuals directly respon -
sible for the hiring decisions. This scandal and other similar events have led to new

laws requiring additional reporting concerning political contributions and bans on 
hiring—or hiring delays for—managers that made campaign contributions to repre -
sentatives associated with the decision-  making process. 
Issuer-  Paid Research
In light of the recent reduction of sell-  side research coverage, many companies, seeking 
to increase visibility both in the financial markets and with potential investors, have 
hired analysts to produce research reports analyzing their companies. These reports 
bridge the gap created by the lack of coverage and can be an effective method of 
communicating with investors.
Issuer-  paid research conducted by independent analysts, however, is fraught with 
potential conflicts. Depending on how the research is written and distributed, investors 
may be misled into believing that the research is from an independent source when, 
in reality, it has been paid for by the subject company.

Standard I: Professionalism 63
Members and candidates must adhere to strict standards of conduct that govern 
how the research is to be conducted and what disclosures must be made in the report. 
Analysts must engage in thorough, independent, and unbiased analysis and must fully 
disclose potential conflicts of interest, including the nature of their compensation. 
Otherwise, analysts risk misleading investors.
Investors need clear, credible, and thorough information about companies, and 
they need research based on independent thought. At a minimum, issuer-  paid  research 
should include a thorough analysis of the company’s financial statements based on 
publicly disclosed information, benchmarking within a peer group, and industry anal -
ysis. Analysts must exercise diligence, independence, and thoroughness in conducting 
their research in an objective manner. Analysts must distinguish between fact and 
opinion in their reports. Conclusions must have a reasonable and adequate basis and

must be supported by appropriate research.
Independent analysts must also strictly limit the type of compensation that they 
accept for conducting issuer-  paid research. Otherwise, the content and conclusions 
of the reports could reasonably be expected to be determined or affected by com -
pensation from the sponsoring companies. Compensation that might influence the 
research report could be direct, such as payment based on the conclusions of the 
report, or indirect, such as stock warrants or other equity instruments that could 
increase in value on the basis of positive coverage in the report. In such instances, 
the independent analyst has an incentive to avoid including negative information 
or making negative conclusions. Best practice is for independent analysts, prior to 
writing their reports, to negotiate only a flat fee for their work that is not linked to 
their conclusions or recommendations.
Travel Funding

The benefits related to accepting paid travel extend beyond the cost savings to the 
member or candidate and his firm, such as the chance to talk exclusively with the 
executives of a company or learning more about the investment options provided 
by an investment organization. Acceptance also comes with potential concerns; for 
example, members and candidates may be influenced by these discussions when fly -
ing on a corporate or chartered jet or attending sponsored conferences where many 
expenses, including airfare and lodging, are covered. To avoid the appearance of com -
promising their independence and objectivity, best practice dictates that members and 
candidates always use commercial transportation at their expense or at the expense 
of their firm rather than accept paid travel arrangements from an outside company. 
Should commercial transportation be unavailable, members and candidates may

accept modestly arranged travel to participate in appropriate information-  gathering 
events, such as a property tour.
Members and candidates should adhere to the following practices and should encourage 
their firms to establish procedures to avoid violations of Standard I(B):
■■Protect the integrity of opinions : Members, candidates, and their firms should 
establish policies stating that every research report concerning the securities 
of a corporate client should reflect the unbiased opinion of the analyst. Firms 
should also design compensation systems that protect the integrity of the 
investment decision process by maintaining the independence and objectivity of 
analysts.

Reading 3 ■ Guidance for Standards I–VII 64
■■Create a restricted list : If the firm is unwilling to permit dissemination of 
adverse opinions about a corporate client, members and candidates should 
encourage the firm to remove the controversial company from the research 
universe and put it on a restricted list so that the firm disseminates only factual 
information about the company.
■■Restrict special cost arrangements : When attending meetings at an issuer’s 
headquarters, members and candidates should pay for commercial transpor -
tation and hotel charges. No corporate issuer should reimburse members or 
candidates for air transportation. Members and candidates should encourage 
issuers to limit the use of corporate aircraft to situations in which commercial 
transportation is not available or in which efficient movement could not oth -
erwise be arranged. Members and candidates should take particular care that 
when frequent meetings are held between an individual issuer and an individ -

ual member or candidate, the issuer should not always host the member or 
candidate.
■■Limit gifts : Members and candidates must limit the acceptance of gratuities 
and/or gifts to token items. Standard I(B) does not preclude customary, ordi -
nary business-  related entertainment as long as its purpose is not to influence 
or reward members or candidates. Firms should consider a strict value limit 
for acceptable gifts that is based on the local or regional customs and should 
address whether the limit is per gift or an aggregate annual value.
■■Restrict investments : Members and candidates should encourage their invest -
ment firms to develop formal policies related to employee purchases of equity 
or equity-  related IPOs. Firms should require prior approval for employee 
participation in IPOs, with prompt disclosure of investment actions taken 
following the offering. Strict limits should be imposed on investment personnel 
acquiring securities in private placements.

■■Review procedures : Members and candidates should encourage their firms to 
implement effective supervisory and review procedures to ensure that analysts 
and portfolio managers comply with policies relating to their personal invest -
ment activities.
■■Independence policy : Members, candidates, and their firms should establish 
a formal written policy on the independence and objectivity of research and 
implement reporting structures and review procedures to ensure that research 
analysts do not report to and are not supervised or controlled by any depart -
ment of the firm that could compromise the independence of the analyst. 
More detailed recommendations related to a firm’s policies regarding research 
objectivity are set forth in the CFA Institute statement Research Objectivity 
Standards  (www.cfainstitute.org).
■■Appointed officer : Firms should appoint a senior officer with oversight responsi -

bilities for compliance with the firm’s code of ethics and all regulations concern -
ing its business. Firms should provide every employee with the procedures and 
policies for reporting potentially unethical behavior, violations of regulations, or 
other activities that may harm the firm’s reputation.
Example 1 (Travel Expenses):
Steven Taylor, a mining analyst with Bronson Brokers, is invited by Precision Metals 
to join a group of his peers in a tour of mining facilities in several western US states. 
The company arranges for chartered group flights from site to site and for accom -
modations in Spartan Motels, the only chain with accommodations near the mines,

Standard I: Professionalism 65
for three nights. Taylor allows Precision Metals to pick up his tab, as do the other 
analysts, with one exception—John Adams, an employee of a large trust company 
who insists on following his company’s policy and paying for his hotel room himself.
Comment : The policy of the company where Adams works complies 
closely with Standard I(B) by avoiding even the appearance of a conflict of 
interest, but Taylor and the other analysts were not necessarily violating 
Standard I(B). In general, when allowing companies to pay for travel and/
or accommodations in these circumstances, members and candidates must 
use their judgment. They must be on guard that such arrangements not 
impinge on a member’s or candidate’s independence and objectivity. In this 
example, the trip was strictly for business and Taylor was not accepting 
irrelevant or lavish hospitality. The itinerary required chartered flights, for

which analysts were not expected to pay. The accommodations were modest. 
These arrangements are not unusual and did not violate Standard I(B) as 
long as Taylor’s independence and objectivity were not compromised. In 
the final analysis, members and candidates should consider both whether 
they can remain objective and whether their integrity might be perceived 
by their clients to have been compromised.
Example 2 (Research Independence):
Susan Dillon, an analyst in the corporate finance department of an investment ser -
vices firm, is making a presentation to a potential new business client that includes 
the promise that her firm will provide full research coverage of the potential client.
Comment : Dillon may agree to provide research coverage, but she must 
not commit her firm’s research department to providing a favorable recom -
mendation. The firm’s recommendation (favorable, neutral, or unfavorable) 
must be based on an independent and objective investigation and analysis

of the company and its securities.
Example 3 (Research Independence and Intrafirm Pressure):
Walter Fritz is an equity analyst with Hilton Brokerage who covers the mining industry. 
He has concluded that the stock of Metals & Mining is overpriced at its current level, 
but he is concerned that a negative research report will hurt the good relationship 
between Metals & Mining and the investment banking division of his firm. In fact, a 
senior manager of Hilton Brokerage has just sent him a copy of a proposal his firm 
has made to Metals & Mining to underwrite a debt offering. Fritz needs to produce a 
report right away and is concerned about issuing a less-  than-  favorable rating.
Comment : Fritz’s analysis of Metals & Mining must be objective and based 
solely on consideration of company fundamentals. Any pressure from 
other divisions of his firm is inappropriate. This conflict could have been 
eliminated if, in anticipation of the offering, Hilton Brokerage had placed

Metals & Mining on a restricted list for its sales force.
Example 4 (Research Independence and Issuer Relationship Pressure):
As in Example 3, Walter Fritz has concluded that Metals & Mining stock is overvalued 
at its current level, but he is concerned that a negative research report might jeop -
ardize a close rapport that he has nurtured over the years with Metals & Mining’s 
CEO, chief finance officer, and investment relations officer.  Fritz is concerned that a 
negative report might result also in management retaliation—for instance, cutting him 
off from participating in conference calls when a quarterly earnings release is made,

Reading 3 ■ Guidance for Standards I–VII 66
denying him the ability to ask questions on such calls, and/or denying him access to 
top management for arranging group meetings between Hilton Brokerage clients and 
top Metals & Mining managers.
Comment : As in Example 3, Fritz’s analysis must be objective and based 
Metals & Mining is inappropriate. Fritz should reinforce the integrity of 
his conclusions by stressing that his investment recommendation is based 
on relative valuation, which may include qualitative issues with respect to 
Metals & Mining’s management.
Example 5 (Research Independence and Sales Pressure):
As support for the sales effort of her corporate bond department, Lindsey Warner 
offers credit guidance to purchasers of fixed-  income securities. Her compensation is 
closely linked to the performance of the corporate bond department. Near the quarter’s

end, Warner’s firm has a large inventory position in the bonds of Milton, Ltd., and has 
been unable to sell the bonds because of Milton’s recent announcement of an oper -
ating problem. Salespeople have asked her to contact large clients to push the bonds.
Comment : Unethical sales practices create significant potential violations 
of the Code and Standards. Warner’s opinion of the Milton bonds must 
not be affected by internal pressure or compensation. In this case, Warner 
must refuse to push the Milton bonds unless she is able to justify that the 
market price has already adjusted for the operating problem.
Example 6 (Research Independence and Prior Coverage):
Jill Jorund is a securities analyst following airline stocks and a rising star at her firm. 
Her boss has been carrying a “buy” recommendation on International Airlines and 
asks Jorund to take over coverage of that airline. He tells Jorund that under no cir -
cumstances should the prevailing buy recommendation be changed.

Comment : Jorund must be independent and objective in her analysis of 
International Airlines. If she believes that her boss’s instructions have 
compromised her, she has two options: She can tell her boss that she 
cannot cover the company under these constraints, or she can take over 
coverage of the company, reach her own independent conclusions, and if 
they conflict with her boss’s opinion, share the conclusions with her boss 
or other supervisors in the firm so that they can make appropriate rec -
ommendations. Jorund must issue only recommendations that reflect her 
independent and objective opinion.
Example 7 (Gifts and Entertainment from Related Party):
Edward Grant directs a large amount of his commission business to a New York–based 
brokerage house. In appreciation for all the business, the brokerage house gives Grant 
two tickets to the World Cup in South Africa, two nights at a nearby resort, several

meals, and transportation via limousine to the game. Grant fails to disclose receiving 
this package to his supervisor.
Comment : Grant has violated Standard I(B) because accepting these sub -
stantial gifts may impede his independence and objectivity. Every member 
and candidate should endeavor to avoid situations that might cause or be 
perceived to cause a loss of independence or objectivity in recommending

Standard I: Professionalism 67
investments or taking investment action. By accepting the trip, Grant has 
opened himself up to the accusation that he may give the broker favored 
treatment in return.
Example 8 (Gifts and Entertainment from Client):
Theresa Green manages the portfolio of Ian Knowlden, a client of Tisbury Investments. 
Green achieves an annual return for Knowlden that is consistently better than that of 
the benchmark she and the client previously agreed to. As a reward, Knowlden offers 
Green two tickets to Wimbledon and the use of Knowlden’s flat in London for a week. 
Green discloses this gift to her supervisor at Tisbury.
Comment : Green is in compliance with Standard I(B) because she disclosed 
the gift from one of her clients in accordance with the firm’s policies. 
Members and candidates may accept bonuses or gifts from clients as long 
as they disclose them to their employer because gifts in a client relation -

ship are deemed less likely to affect a member’s or candidate’s objectivity 
and independence than gifts in other situations. Disclosure is required, 
however, so that supervisors can monitor such situations to guard against 
employees favoring a gift-  giving client to the detriment of other fee-  paying 
clients (such as by allocating a greater proportion of IPO stock to the gift-  
giving client’s portfolio).
Best practices for monitoring include comparing the transaction costs 
of the Knowlden account with the costs of other accounts managed by 
Green and other similar accounts within Tisbury. The supervisor could also 
compare the performance returns with the returns of other clients with 
the same mandate. This comparison will assist in determining whether a 
pattern of favoritism by Green is disadvantaging other Tisbury clients or 
the possibility that this favoritism could affect her future behavior.
Example 9 (Travel Expenses from External Manager):

Tom Wayne is the investment manager of the Franklin City Employees Pension Plan. 
He recently completed a successful search for a firm to manage the foreign equity 
allocation of the plan’s diversified portfolio. He followed the plan’s standard proce -
dure of seeking presentations from a number of qualified firms and recommended 
that his board select Penguin Advisors because of its experience, well-  defined invest -
ment strategy, and performance record. The firm claims compliance with the Global 
Investment Performance Standards (GIPS) and has been verified. Following the selec -
tion of Penguin, a reporter from the Franklin City Record  calls to ask if there was any 
connection between this action and the fact that Penguin was one of the sponsors 
of an “investment fact-  finding trip to Asia” that Wayne made earlier in the year. The 
trip was one of several conducted by the Pension Investment Academy, which had

arranged the itinerary of meetings with economic, government, and corporate officials 
in major cities in several Asian countries. The Pension Investment Academy obtains 
support for the cost of these trips from a number of investment managers, including 
Penguin Advisors; the Academy then pays the travel expenses of the various pension 
plan managers on the trip and provides all meals and accommodations. The president 
of Penguin Advisors was also one of the travelers on the trip.
Comment : Although Wayne can probably put to good use the knowledge he 
gained from the trip in selecting portfolio managers and in other areas of 
managing the pension plan, his recommendation of Penguin Advisors may 
be tainted by the possible conflict incurred when he participated in a trip 
partly paid for by Penguin Advisors and when he was in the daily company 
of the president of Penguin Advisors. To avoid violating Standard  I(B),

Reading 3 ■ Guidance for Standards I–VII 68
Wayne’s basic expenses for travel and accommodations should have been 
paid by his employer or the pension plan; contact with the president of 
Penguin Advisors should have been limited to informational or educational 
events only; and the trip, the organizer, and the sponsor should have been 
made a matter of public record. Even if his actions were not in violation of 
Standard I(B), Wayne should have been sensitive to the public perception 
of the trip when reported in the newspaper and the extent to which the 
subjective elements of his decision might have been affected by the famil -
iarity that the daily contact of such a trip would encourage. This advantage 
would probably not be shared by firms competing with Penguin Advisors.
Example 10 (Research Independence and Compensation Arrangements):
Javier Herrero recently left his job as a research analyst for a large investment adviser.

While looking for a new position, he was hired by an investor-  relations firm to write 
a research report on one of its clients, a small educational software company. The 
investor-  relations firm hopes to generate investor interest in the technology company. 
The firm will pay Herrero a flat fee plus a bonus if any new investors buy stock in the 
company as a result of Herrero’s report.
Comment : If Herrero accepts this payment arrangement, he will be in 
violation of Standard  I(B) because the compensation arrangement can 
reasonably be expected to compromise his independence and objectivity. 
Herrero will receive a bonus for attracting investors, which provides an 
incentive to draft a positive report regardless of the facts and to ignore or 
play down any negative information about the company. Herrero should 
accept only a flat fee that is not tied to the conclusions or recommendations 
of the report. Issuer-  paid research that is objective and unbiased can be

done under the right circumstances as long as the analyst takes steps to 
maintain his or her objectivity and includes in the report proper disclosures 
regarding potential conflicts of interest.
Example 11 (Recommendation Objectivity and Service Fees):
Two years ago, Bob Wade, trust manager for Central Midas Bank, was approached 
by Western Funds about promoting its family of funds, with special interest in the 
service-  fee class of funds. To entice Central to promote this class, Western Funds 
offered to pay the bank a service fee of 0.25%. Without disclosing the fee being offered 
to the bank, Wade asked one of the investment managers to review Western’s funds 
to determine whether they were suitable for clients of Central Midas Bank. The man -
ager completed the normal due diligence review and determined that the new funds 
were fairly valued in the market with fee structures on a par with competitors. Wade 
decided to accept Western’s offer and instructed the team of portfolio managers to

exclusively  promote these funds and the service-  fee class to clients  seeking to invest 
new funds or transfer from their current investments.
Now, two years later, the funds managed by Western begin to underperform their 
peers. Wade is counting on the fees to reach his profitability targets and continues to 
push these funds as acceptable investments for Central’s clients.
Comment : Wade is violating Standard I(B)  because the fee arrangement 
has affected the objectivity of his recommendations. Wade is relying on 
the fee as a component of the department’s profitability and is unwilling 
to offer other products that may affect the fees received.
See also Standard VI(A)–Disclosure of Conflicts.

Standard I: Professionalism 69
Example 12 (Recommendation Objectivity):
Bob Thompson has been doing research for the portfolio manager of the fixed-  income 
department. His assignment is to do sensitivity analysis on securitized subprime 
mortgages. He has discussed with the manager possible scenarios to use to calculate 
expected returns. A key assumption in such calculations is housing price appreciation 
(HPA) because it drives “prepays”  (prepayments of mortgages) and losses. Thompson 
is concerned with the significant appreciation experienced over the previous five years 
as a result of the increased availability of funds from subprime mortgages. Thompson 
insists that the analysis should include a scenario run with –10% for Year 1, –5% for 
Year 2, and then (to project a worst-  case scenario) 0% for Years 3 through 5. The 
manager replies that these assumptions are too dire because there has never been a 
time in their available database when HPA was negative.

Thompson conducts his research to better understand the risks inherent in these 
securities and evaluates these securities in the worst-  case scenario, an unlikely but 
possible environment. Based on the results of the enhanced scenarios, Thompson 
does not recommend the purchase of the securitization. Against the general market 
trends, the manager follows Thompson’s recommendation and does not invest. The 
following year, the housing market collapses. In avoiding the subprime investments, 
the manager’s portfolio outperforms its peer group that year.
Comment : Thompson’s actions in running the worst-  case scenario against 
the protests of the portfolio manager are in alignment with the principles 
of Standard  I(B). Thompson did not allow his research to be pressured 
by the general trends of the market or the manager’s desire to limit the 
research to historical norms.
See also Standard V(A)–Diligence and Reasonable Basis.
Example 13 (Influencing Manager Selection Decisions):

Adrian Mandel, CFA, is a senior portfolio manager for ZZYY Capital Management 
who oversees a team of investment professionals who manage labor union pension 
funds. A few years ago, ZZYY sought to win a competitive asset manager search to 
manage a significant allocation of the pension fund of the United Doughnut and Pretzel 
Bakers Union (UDPBU). UDPBU’s investment board is chaired by a recognized key 
decision maker and long-  time leader of the union, Ernesto Gomez. To improve ZZYY’s 
chances of winning the competition, Mandel made significant monetary contributions 
to Gomez’s union reelection campaign fund. Even after ZZYY was hired as a primary 
manager of the pension, Mandel believed that his firm’s position was not secure. Mandel 
continued to contribute to Gomez’s reelection campaign chest as well as to entertain 
lavishly the union leader and his family at top restaurants on a regular basis. All of 
Mandel’s outlays were routinely handled as marketing expenses reimbursed by ZZYY’s

expense accounts and were disclosed to his senior management as being instrumental 
in maintaining a strong close relationship with an important client.
Comment : Mandel not only offered but actually gave monetary gifts, benefits, 
and other considerations that reasonably could be expected to compromise 
Gomez’s objectivity. Therefore, Mandel was in violation of Standard I(B).
Example 14 (Influencing Manager Selection Decisions):
Adrian Mandel, CFA, had heard about the manager search competition for the 
UDPBU Pension Fund through a broker/dealer contact. The contact told him that a 
well-  known retired professional golfer, Bobby “The Bear” Finlay, who had become a 
licensed broker/dealer serving as a pension consultant, was orchestrating the UDPBU 
manager search. Finlay had gained celebrity status with several labor union pension

Reading 3 ■ Guidance for Standards I–VII 70
fund boards by entertaining their respective board members and regaling them with 
colorful stories of fellow pro golfers’ antics in clubhouses around the world. Mandel 
decided to improve ZZYY’s chances of being invited to participate in the search compe -
tition by befriending Finlay to curry his favor. Knowing Finlay’s love of entertainment, 
Mandel wined and dined Finlay at high-  profile bistros where Finlay could glow in the 
fan recognition lavished on him by all the other patrons. Mandel’s endeavors paid off  
handsomely when Finlay recommended to the UDPBU board that ZZYY be entered 
as one of three finalist asset management firms in its search.
Comment : Similar to Example 13, Mandel lavished gifts, benefits, and other 
considerations in the form of expensive entertainment that could reasonably 
be expected to influence the consultant to recommend the hiring of his 
firm. Therefore, Mandel was in violation of Standard I(B).

Example 15 (Fund Manager Relationships):
Amie Scott is a performance analyst within her firm with responsibilities for analyz -
ing the performance of external managers. While completing her quarterly analysis, 
Scott notices a change in one manager’s reported composite construction. The change 
concealed the bad performance of a particularly large account by placing that account 
into a new residual composite. This change allowed the manager to remain at the top 
of the list of manager performance. Scott knows her firm has a large allocation to this 
manager, and the fund’s manager is a close personal friend of the CEO. She needs 
to deliver her final report but is concerned with pointing out the composite change.
Comment : Scott would be in violation of Standard I(B) if she did not disclose 
the change in her final report. The analysis of managers’ performance should 
not be influenced by personal relationships or the size of the allocation to

the outside managers. By not including the change, Scott would not be 
providing an independent analysis of the performance metrics for her firm.
Example 16 (Intrafirm Pressure):
Jill Stein is head of performance measurement for her firm. During the last quarter, 
many members of the organization’s research department were removed because of 
the poor quality of their recommendations. The subpar research caused one larger 
account holder to experience significant underperformance, which resulted in the 
client withdrawing his money after the end of the quarter. The head of sales requests 
that Stein remove this account from the firm’s performance composite because the 
performance decline can be attributed to the departed research team and not the 
client’s adviser.
Comment : Pressure from other internal departments can create situations 
that cause a member or candidate to violate the Code and Standards. Stein 
must maintain her independence and objectivity and refuse to exclude

specific accounts from the firm’s performance composites to which they 
belong. As long as the client invested under a strategy similar to that of 
the defined composite, it cannot be excluded because of the poor stock 
selections that led to the underperformance and asset withdrawal.

Standard I: Professionalism 71
Standard I(C) Misrepresentation
Members and Candidates must not knowingly make any misrepresentations relating to 
investment analysis, recommendations, actions, or other professional activities. 
Guidance
■■Impact on Investment Practice
■■Performance Reporting
■■Social Media
■■Omissions
■■Plagiarism
■■Work Completed for Employer
Trust is the foundation of the investment profession. Investors must be able to rely on 
the statements and information provided to them by those with whom the investors 
have trusted their financial well-  being. Investment professionals who make false or 
misleading statements not only harm investors but also reduce the level of investor 
confidence in the investment profession and threaten the integrity of capital markets 
as a whole.
A misrepresentation is any untrue statement or omission of a fact or any statement 
that is otherwise false or misleading. A member or candidate must not knowingly

omit or misrepresent information or give a false impression of a firm, organization, 
or security in the member’s or candidate’s oral representations, advertising (whether 
in the press or through brochures), electronic communications, or written materials 
(whether publicly disseminated or not). In this context, “knowingly” means that the 
member or candidate either knows or should have known that the misrepresentation 
was being made or that omitted information could alter the investment decision-  
making process.
Written materials include, but are not limited to, research reports, underwriting 
documents, company financial reports, market letters, newspaper columns, and books. 
Electronic communications include, but are not limited to, internet communications, 
webpages, mobile applications, and e-  mails. Members and candidates who use webpages 
should regularly monitor materials posted on these sites to ensure that they contain

current information. Members and candidates should also ensure that all reasonable 
precautions have been taken to protect the site’s integrity and security and that the 
site does not misrepresent any information and does provide full disclosure.
Standard I(C) prohibits members and candidates from guaranteeing clients any 
specific return on volatile investments. Most investments contain some element of 
risk that makes their return inherently unpredictable. For such investments, guaran -
teeing either a particular rate of return or a guaranteed preservation of investment 
capital (e.g., “I can guarantee that you will earn 8% on equities this year” or “I can 
guarantee that you will not lose money on this investment”) is misleading to investors. 
Standard I(C) does not prohibit members and candidates from providing clients with 
information on investment products that have guarantees built into the structure of 
the products themselves or for which an institution has agreed to cover any losses.

Reading 3 ■ Guidance for Standards I–VII 72
Impact on Investment Practice
Members and candidates must not misrepresent any aspect of their practice, including 
(but not limited to) their qualifications or credentials, the qualifications or services 
provided by their firm, their performance record and the record of their firm, and 
the characteristics of an investment. Any misrepresentation made by a member or 
candidate relating to the member’s or candidate’s professional activities is a breach 
of this standard.
Members and candidates should exercise care and diligence when incorporating 
third-  party information. Misrepresentations resulting from the use of the credit 
ratings, research, testimonials, or marketing materials of outside parties become 
the responsibility of the investment professional when it affects that professional’s 
business practices.
Investing through outside managers continues to expand as an acceptable method

of investing in areas outside a firm’s core competencies. Members and candidates must 
disclose their intended use of external managers and must not represent those man -
agers’ investment practices as their own. Although the level of involvement of outside 
managers may change over time, appropriate disclosures by members and candidates 
are important in avoiding misrepresentations, especially if the primary activity is to 
invest directly with a single external manager. Standard V(B)–Communication with 
Clients and Prospective Clients discusses in further detail communicating the firm’s 
investment practices.
Performance Reporting
The performance benchmark selection process is another area where misrepresen -
tations may occur. Members and candidates may misrepresent the success of their 
performance record through presenting benchmarks that are not comparable to their 
strategies. Further, clients can be misled if the benchmark’s results are not reported on

a basis comparable to that of the fund’s or client’s results. Best practice is selecting the 
most appropriate available benchmark from a universe of available options. The trans -
parent presentation of appropriate performance benchmarks is an important aspect 
in providing clients with information that is useful in making investment decisions. 
However, Standard I(C) does not require that a benchmark always be provided in 
order to comply. Some investment strategies may not lend themselves to displaying 
an appropriate benchmark because of the complexity or diversity of the investments 
included. Furthermore, some investment strategies may use reference indexes that 
do not reflect the opportunity set of the invested assets—for example, a hedge fund 
comparing its performance with a “cash plus” basis. When such a benchmark is used, 
members and candidates should make reasonable efforts to ensure that they disclose

the reasons behind the use of this reference index to avoid misrepresentations of their 
performance. Members and candidates should discuss with clients on a continuous 
basis the appropriate benchmark to be used for performance evaluations and related 
fee calculations.
Reporting misrepresentations may also occur when valuations for illiquid or non-  
traded securities are available from more than one source. When different options 
are available, members and candidates may be tempted to switch providers to obtain 
higher security valuations. The process of shopping for values may misrepresent a 
security’s worth, lead to misinformed decisions to sell or hold an investment, and 
result in overcharging clients advisory fees. 
Members and candidates should take reasonable steps to provide accurate and 
reliable security pricing information to clients on a consistent basis. Changing pric -
ing providers should not be based solely on the justification that the new provider

reports a higher current value of a security. Consistency in the reported information

Standard I: Professionalism 73
will improve the perception of the valuation process for illiquid securities. Clients will 
likely have additional confidence that they were able to make an informed decision 
about continuing to hold these securities in their portfolios.
Social Media
The advancement of online discussion forums and communication platforms, com -
monly referred to as “social media, ” is placing additional responsibilities on members 
and candidates. When communicating through social media channels, members and 
candidates should provide only the same information they are allowed to distribute to 
clients and potential clients through other traditional forms of communication. The 
online or interactive aspects of social media do not remove the need to be open and 
honest about the information being distributed.
Along with understanding and following existing and newly developing rules and 
regulations regarding the allowed use of social media, members and candidates should

also ensure that all communications in this format adhere to the requirements of the 
Code and Standards. The perceived anonymity granted through these platforms may 
entice individuals to misrepresent their qualifications or abilities or those of their 
employer. Actions undertaken through social media that knowingly misrepresent 
investment recommendations or professional activities are considered a violation of 
Standard I(C). 
Omissions
The omission of a fact or outcome can be misleading, especially given the growing 
use of models and technical analysis processes. Many members and candidates rely 
on such models and processes to scan for new investment opportunities, to develop 
investment vehicles, and to produce investment recommendations and ratings. 
When inputs are knowingly omitted, the resulting outcomes may provide misleading 
information to those who rely on it for making investment decisions. Additionally,

the outcomes from models shall not be presented as fact because they represent the 
expected results based on the inputs and analysis process incorporated. 
Omissions in the performance measurement and attribution process can also 
misrepresent a manager’s performance and skill. Members and candidates should 
encourage their firms to develop strict policies for composite development to prevent 
cherry picking—situations in which selected accounts are presented as representa -
tive of the firm’s abilities. The omission of any accounts appropriate for the defined 
composite may misrepresent to clients the success of the manager’s implementation 
of its strategy.
Plagiarism
Standard I(C) also prohibits plagiarism in the preparation of material for distribution to 
employers, associates, clients, prospects, or the general public. Plagiarism is defined as 
copying or using in substantially the same form materials prepared by others without

acknowledging the source of the material or identifying the author and publisher of 
such material. Members and candidates must not copy (or represent as their own) 
original ideas or material without permission and must acknowledge and identify the 
source of ideas or material that is not their own.
The investment profession uses a myriad of financial, economic, and statistical 
data in the investment decision-  making process. Through various publications and 
presentations, the investment professional is constantly exposed to the work of others 
and to the temptation to use that work without proper acknowledgment.
Misrepresentation through plagiarism in investment management can take various 
forms. The simplest and most flagrant example is to take a research report or study 
done by another firm or person, change the names, and release the material as one’s

Reading 3 ■ Guidance for Standards I–VII 74
own original analysis. This action is a clear violation of Standard I(C). Other practices 
include (1) using excerpts from articles or reports prepared by others either verbatim 
or with only slight changes in wording without acknowledgment, (2) citing specific 
quotations as attributable to “leading analysts” and “investment experts” without nam -
ing the specific references, (3) presenting statistical estimates of forecasts prepared 
by others and identifying the sources but without including the qualifying statements 
or caveats that may have been used, (4) using charts and graphs without stating their 
sources, and (5) copying proprietary computerized spreadsheets or algorithms without 
seeking the cooperation or authorization of their creators.
In the case of distributing third-  party, outsourced research, members and candi -
dates may use and distribute such reports as long as they do not represent themselves

as the report’s authors. Indeed, the member or candidate may add value for the client 
by sifting through research and repackaging it for clients. In such cases, clients should 
be fully informed that they are paying for the ability of the member or candidate to 
find the best research from a wide variety of sources. Members and candidates must 
not misrepresent their abilities, the extent of their expertise, or the extent of their 
work in a way that would mislead their clients or prospective clients. Members and 
candidates should disclose whether the research being presented to clients comes 
from another source—from either within or outside the member’s or candidate’s firm. 
This allows clients to understand who has the expertise behind the report or whether 
the work is being done by the analyst, other members of the firm, or an outside party.
Standard I(C) also applies to plagiarism in oral communications, such as through

group meetings; visits with associates, clients, and customers; use of audio/video 
media (which is rapidly increasing); and telecommunications, including electronic 
data transfer and the outright copying of electronic media.
One of the most egregious practices in violation of this standard is the preparation 
of research reports based on multiple sources of information without acknowledging 
the sources. Examples of information from such sources include ideas, statistical com -
pilations, and forecasts combined to give the appearance of original work. Although 
there is no monopoly on ideas, members and candidates must give credit where it is 
clearly due. Analysts should not use undocumented forecasts, earnings projections, 
asset values, and so on. Sources must be revealed to bring the responsibility directly 
back to the author of the report or the firm involved.
Work Completed for Employer
The preceding paragraphs address actions that would constitute a violation of

Standard I(C). In some situations, however, members or candidates may use research 
conducted or models developed by others within the same firm without committing a 
violation. The most common example relates to the situation in which one (or more) 
of the original analysts is no longer with the firm. Research and models developed 
while employed by a firm are the property of the firm. The firm retains the right to 
continue using the work completed after a member or candidate has left the organi -
zation. The firm may issue future reports without providing attribution to the prior 
analysts. A member or candidate cannot, however, reissue a previously released report 
solely under his or her name.
Factual Presentations
Members and candidates can prevent unintentional misrepresentations of their qual -
ifications or the services they or their firms provide if each member and candidate

understands the limit of the firm’s or individual’s capabilities and the need to be accurate 
and complete in presentations. Firms can provide guidance for employees who make

Standard I: Professionalism 75
written or oral presentations to clients or potential clients by providing a written list 
of the firm’s available services and a description of the firm’s qualifications. This list 
should suggest ways of describing the firm’s services, qualifications, and compensation 
that are both accurate and suitable for client or customer presentations. Firms can 
also help prevent misrepresentation by specifically designating which employees are 
authorized to speak on behalf of the firm. Regardless of whether the firm provides 
guidance, members and candidates should make certain that they understand the 
services the firm can perform and its qualifications.
Qualification Summary
In addition, to ensure accurate presentations to clients, each member and candidate 
should prepare a summary of his or her own qualifications and experience and a list 
of the services the member or candidate is capable of performing. Firms can assist

member and candidate compliance by periodically reviewing employee correspon -
dence and documents that contain representations of individual or firm qualifications.
Verify Outside Information
When providing information to clients from a third party, members and candidates 
share a responsibility for the accuracy of the marketing and distribution materials that 
pertain to the third party’s capabilities, services, and products. Misrepresentation by 
third parties can damage the member’s or candidate’s reputation, the reputation of 
the firm, and the integrity of the capital markets. Members and candidates should 
encourage their employers to develop procedures for verifying information of third-  
party firms.
Maintain Webpages
Members and candidates who publish a webpage should regularly monitor materials 
posted on the site to ensure that the site contains current information. Members 
and candidates should also ensure that all reasonable precautions have been taken

to protect the site’s integrity, confidentiality, and security and that the site does not 
misrepresent any information and provides full disclosure.
Plagiarism Policy
To avoid plagiarism in preparing research reports or conclusions of analysis, members 
and candidates should take the following steps:
■■Maintain copies : Keep copies of all research reports, articles containing 
research ideas, material with new statistical methodologies, and other materials 
that were relied on in preparing the research report.
■■Attribute quotations : Attribute to their sources any direct quotations, including 
projections, tables, statistics, model/product ideas, and new methodologies 
prepared by persons other than recognized financial and statistical reporting 
services or similar sources.
■■Attribute summaries : Attribute to their sources any paraphrases or summaries 
of material prepared by others. For example, to support his analysis of Brown

Company’s competitive position, the author of a research report on Brown 
might summarize another analyst’s report on Brown’s chief competitor, but the 
author of the Brown report must acknowledge in his own report the reliance on 
the other analyst’s report.

Reading 3 ■ Guidance for Standards I–VII 76
Example 1 (Disclosure of Issuer-  Paid Research):
Anthony McGuire is an issuer-  paid analyst hired by publicly traded companies to 
electronically promote their stocks. McGuire creates a website that promotes his 
research efforts as a seemingly independent analyst. McGuire posts a profile and a 
strong buy recommendation for each company on the website indicating that the stock 
is expected to increase in value. He does not disclose the contractual relationships 
with the companies he covers on his website, in the research reports he issues, or in 
the statements he makes about the companies in internet chat rooms.
Comment : McGuire has violated Standard  I(C) because the website is 
misleading to potential investors. Even if the recommendations are valid 
and supported with thorough research, his omissions regarding the true 
relationship between himself and the companies he covers constitute a

misrepresentation. McGuire has also violated Standard VI(A)–Disclosure 
of Conflicts by not disclosing the existence of an arrangement with the 
companies through which he receives compensation in exchange for his 
services.
Example 2 (Correction of Unintentional Errors):
Hijan Yao is responsible for the creation and distribution of the marketing materials 
for his firm, which claims compliance with the GIPS standards. Yao creates and dis -
tributes a presentation of performance by the firm’s Asian equity composite that states 
the composite has ¥350 billion in assets. In fact, the composite has only ¥35 billion in 
assets, and the higher figure on the presentation is a result of a typographical error. 
Nevertheless, the erroneous material is distributed to a number of clients before Yao 
catches the mistake.
Comment : Once the error is discovered, Yao must take steps to cease 
distribution of the incorrect material and correct the error by informing

those who have received the erroneous information. Because Yao did 
not knowingly make the misrepresentation, however, he did not violate 
Standard I(C). Because his firm claims compliance with the GIPS standards, 
it must also comply with the GIPS Guidance Statement on Error Correction 
in relation to the error.
Example 3 (Noncorrection of Known Errors):
Syed Muhammad is the president of an investment management firm. The promo -
tional material for the firm, created by the firm’s marketing department, incorrectly 
claims that Muhammad has an advanced degree in finance from a prestigious business 
school in addition to the CFA designation. Although Muhammad attended the school 
for a short period of time, he did not receive a degree. Over the years, Muhammad 
and others in the firm have distributed this material to numerous prospective clients 
and consultants.
Comment : Even though Muhammad may not have been directly respon -

sible for the misrepresentation of his credentials in the firm’s promotional 
material, he used this material numerous times over an extended period 
and should have known of the misrepresentation. Thus, Muhammad has 
violated Standard I(C).

Standard I: Professionalism 77
Example 4 (Plagiarism):
Cindy Grant, a research analyst for a Canadian brokerage firm, has specialized in the 
Canadian mining industry for the past 10 years. She recently read an extensive research 
report on Jefferson Mining, Ltd., by Jeremy Barton, another analyst. Barton provided 
extensive statistics on the mineral reserves, production capacity, selling rates, and 
marketing factors affecting Jefferson’s operations. He also noted that initial drilling 
results on a new ore body, which had not been made public, might show the existence 
of mineral zones that could increase the life of Jefferson’s main mines, but Barton cited 
no specific data as to the initial drilling results. Grant called an officer of Jefferson, 
who gave her the initial drilling results over the telephone. The data indicated that 
the expected life of the main mines would be tripled. Grant added these statistics to 
Barton’s report and circulated it within her firm as her own report.

Comment : Grant plagiarized Barton’s report by reproducing large parts of 
it in her own report without acknowledgment.
Example 5 (Misrepresentation of Information):
When Ricki Marks sells mortgage-  backed derivatives called “interest-  only strips” (IOs) 
to public pension plan clients, she describes them as “guaranteed by the US govern -
ment. ” Purchasers of the IOs are entitled only to the interest stream generated by the 
mortgages, however, not the notional principal itself. One particular municipality’s 
investment policies and local law require that securities purchased by its public pen -
sion plans be guaranteed by the US government. Although the underlying mortgages 
are guaranteed, neither the investor’s investment nor the interest stream on the IOs 
is guaranteed. When interest rates decline, causing an increase in prepayment of 
mortgages, interest payments to the IOs’ investors decline, and these investors lose 
a portion of their investment.

Comment : Marks violated Standard I(C) by misrepresenting the terms and 
character of the investment.
Example 6 (Potential Information Misrepresentation):
Khalouck Abdrabbo manages the investments of several high-  net- worth individuals in 
the United States who are approaching retirement. Abdrabbo advises these individuals 
that a portion of their investments be moved from equity to bank-  sponsored certificates 
of deposit and money market accounts so that the principal will be “guaranteed” up 
to a certain amount. The interest is not guaranteed.
Comment : Although there is risk that the institution offering the certifi -
cates of deposits and money market accounts could go bankrupt, in the 
United States, these accounts are insured by the US government through 
the Federal Deposit Insurance Corporation. Therefore, using the term 
“guaranteed” in this context is not inappropriate as long as the amount is

within the government-  insured limit. Abdrabbo should explain these facts 
to the clients.
Example 7 (Plagiarism):
Steve Swanson is a senior analyst in the investment research department of Ballard 
and Company. Apex Corporation has asked Ballard to assist in acquiring the majority 
ownership of stock in the Campbell Company, a financial consulting firm, and to pre -
pare a report recommending that stockholders of Campbell agree to the acquisition. 
Another investment firm, Davis and Company, had already prepared a report for Apex 
analyzing both Apex and Campbell and recommending an exchange ratio. Apex has

Reading 3 ■ Guidance for Standards I–VII 78
given the Davis report to Ballard officers, who have passed it on to Swanson. Swanson 
reviews the Davis report and other available material on Apex and Campbell. From 
his analysis, he concludes that the common stocks of Campbell and Apex represent 
good value at their current prices; he believes, however, that the Davis report does 
not consider all the factors a Campbell stockholder would need to know to make a 
decision. Swanson reports his conclusions to the partner in charge, who tells him to 
“use the Davis report, change a few words, sign your name, and get it out. ”
Comment : If Swanson does as requested, he will violate Standard  I(C). 
He could refer to those portions of the Davis report that he agrees with if 
he identifies Davis as the source; he could then add his own analysis and 
conclusions to the report before signing and distributing it.
Example 8 (Plagiarism):

Claude Browning, a quantitative analyst for Double Alpha, Inc., returns from a seminar 
in great excitement. At that seminar, Jack Jorrely, a well-  known quantitative analyst 
at a national brokerage firm, discussed one of his new models in great detail, and 
Browning is intrigued by the new concepts. He proceeds to test the model, making 
some minor mechanical changes but retaining the concepts, until he produces some 
very positive results. Browning quickly announces to his supervisors at Double Alpha 
that he has discovered a new model and that clients and prospective clients should 
be informed of this positive finding as ongoing proof of Double Alpha’s continuing 
innovation and ability to add value.
Comment : Although Browning tested Jorrely’s model on his own and even 
slightly modified it, he must still acknowledge the original source of the 
idea. Browning can certainly take credit for the final, practical results;

he can also support his conclusions with his own test. The credit for the 
innovative thinking, however, must be awarded to Jorrely.
Example 9 (Plagiarism):
Fernando Zubia would like to include in his firm’s marketing materials some “plain-  
language” descriptions of various concepts, such as the price-  to- earnings (P/E) multiple 
and why standard deviation is used as a measure of risk. The descriptions come from 
other sources, but Zubia wishes to use them without reference to the original authors. 
Would this use of material be a violation of Standard I(C)?
Comment : Copying verbatim any material without acknowledgement, 
including plain-  language descriptions of the P/E multiple and standard 
deviation, violates Standard I(C). Even though these concepts are general, 
best practice would be for Zubia to describe them in his own words or 
cite the sources from which the descriptions are quoted. Members and 
candidates would be violating Standard I(C) if they either were responsi -

ble for creating marketing materials without attribution or knowingly use 
plagiarized materials.
Example 10 (Plagiarism):
Through a mainstream media outlet, Erika Schneider learns about a study that she 
would like to cite in her research. Should she cite both the mainstream intermediary 
source as well as the author of the study itself when using that information?
Comment : In all instances, a member or candidate must cite the actual 
source of the information. Best practice for Schneider would be to obtain 
the information directly from the author and review it before citing it in

Standard I: Professionalism 79
a report. In that case, Schneider would not need to report how she found 
out about the information. For example, suppose Schneider read in the 
Financial Times  about a study issued by CFA Institute; best practice for 
Schneider would be to obtain a copy of the study from CFA Institute, review 
it, and then cite it in her report. If she does not use any interpretation of 
the report from the Financial Times  and the newspaper does not add value 
to the report itself, the newspaper is merely a conduit of the original infor -
mation and does not need to be cited. If she does not obtain the report and 
review the information, Schneider runs the risk of relying on second-  hand 
information that may misstate facts. If, for example, the Financial Times  
erroneously reported some information from the original CFA Institute 
study and Schneider copied that erroneous information without acknowl -
edging CFA Institute, she could be the object of complaints. Best practice

would be either to obtain the complete study from its original author and 
cite only that author or to use the information provided by the intermediary 
and cite both sources.
Example 11 (Misrepresentation of Information):
Paul  Ostrowski runs a two-  person investment management firm. Ostrowski’s firm 
subscribes to a service from a large investment research firm that provides research 
reports that can be repackaged by smaller firms for those firms’ clients. Ostrowski’s 
firm distributes these reports to clients as its own work.
Comment : Ostrowski can rely on third-  party research that has a reason -
able and adequate basis, but he cannot imply that he is the author of such 
research. If he does, Ostrowski is misrepresenting the extent of his work 
in a way that misleads the firm’s clients or prospective clients.
Example 12 (Misrepresentation of Information):
Tom Stafford is part of a team within Appleton Investment Management responsible

for managing a pool of assets for Open Air Bank, which distributes structured securi -
ties to offshore clients. He becomes aware that Open Air is promoting the structured 
securities as a much less risky investment than the investment management policy 
followed by him and the team to manage the original pool of assets. Also, Open Air 
has procured an independent rating for the pool that significantly overstates the 
quality of the investments. Stafford communicates his concerns to his supervisor, 
who responds that Open Air owns the product and is responsible for all marketing 
and distribution. Stafford’s supervisor goes on to say that the product is outside of 
the US regulatory regime that Appleton follows and that all risks of the product are 
disclosed at the bottom of page 184 of the prospectus.
Comment : As a member of the investment team, Stafford is qualified to 
recognize the degree of accuracy of the materials that characterize the

portfolio,  and he is correct to be worried about Appleton’s responsibility 
for a misrepresentation of the risks. Thus, he should continue to pursue 
the issue of Open Air’s inaccurate promotion of the portfolio according to 
the firm’s policies and procedures.
The Code and Standards stress protecting the reputation of the firm and 
the sustainability and integrity of the capital markets. Misrepresenting the 
quality and risks associated with the investment pool may lead to negative 
consequences for others well beyond the direct investors.

Reading 3 ■ Guidance for Standards I–VII 80
Example 13 (Avoiding a Misrepresentation):
Trina Smith is a fixed-  income portfolio manager at a pension fund. She has observed 
that the market for highly structured mortgages is the focus of salespeople she meets 
and that these products represent a significant number of trading opportunities. In 
discussions about this topic with her team, Smith learns that calculating yields on 
changing cash flows within the deal structure requires very specialized vendor software. 
After more research, they find out that each deal is unique and that deals can have 
more than a dozen layers and changing cash flow priorities. Smith comes to the con -
clusion that, because of the complexity of these securities, the team cannot effectively 
distinguish between potentially good and bad investment options. To avoid misrep -
resenting their understanding, the team decides that the highly structured mortgage

segment of the securitized market should not become part of the core of the fund’s 
portfolio; they will allow some of the less complex securities to be part of the core.
Comment : Smith is in compliance with Standard I(C) by not investing in 
securities that she and her team cannot effectively understand. Because 
she is not able to describe the risk and return profile of the securities to 
the pension fund beneficiaries and trustees, she appropriately limits the 
fund’s exposure to this sector.
Example 14 (Misrepresenting Composite Construction):
Robert Palmer is head of performance for a fund manager. When asked to provide 
performance numbers to fund rating agencies, he avoids mentioning that the fund 
manager is quite liberal in composite construction. The reason accounts are included/
excluded is not fully explained. The performance values reported to the rating agencies 
for the composites, although accurate for the accounts shown each period, may not

present a true representation of the fund manager’s ability.
Comment : “Cherry picking” accounts to include in either published reports 
or information provided to rating agencies conflicts with Standard I(C). 
Moving accounts into or out of a composite to influence the overall per -
formance results materially misrepresents the reported values over time. 
Palmer should work with his firm to strengthen its reporting practices 
concerning composite construction to avoid misrepresenting the firm’s 
track record or the quality of the information being provided.
Example 15 (Presenting Out-  of- Date Information):
David Finch is a sales director at a commercial bank, where he directs the bank’s client 
advisers in the sale of third-  party mutual funds. Each quarter, he holds a division-  wide 
training session where he provides fact sheets on investment funds the bank is allowed 
to offer to clients. These fact sheets, which can be redistributed to potential clients,

are created by the fund firms and contain information about the funds, including 
investment strategy and target distribution rates.
Finch knows that some of the fact sheets are out of date; for example, one long-  
only fund approved the use of significant leverage last quarter as a method to enhance 
returns. He continues to provide the sheets to the sales team without updates because 
the bank has no control over the marketing material released by the mutual fund firms.
Comment : Finch is violating Standard I(C) by providing information that 
misrepresents aspects of the funds. By not providing the sales team and, 
ultimately, the clients with the updated information, he is misrepresenting 
the potential risks associated with the funds with outdated fact sheets. Finch

Standard I: Professionalism 81
can instruct the sales team to clarify the deficiencies in the fact sheets with 
clients and ensure they have the most recent fund prospectus document 
before accepting orders for investing in any fund.
Example 16 (Overemphasis of Firm Results):
Bob Anderson is chief compliance officer for Optima Asset Management Company, 
a firm currently offering eight funds to clients. Seven of the eight had 10-  year returns 
below the median for their respective sectors. Anderson approves a recent advertise -
ment, which includes this statement: “Optima Asset Management is achieving excellent 
returns for its investors. The Optima Emerging Markets Equity fund, for example, has 
10- year returns that exceed the sector median by more than 10%. ” 
Comment : From the information provided it is difficult to determine whether 
a violation has occurred as long as the sector outperformance is correct. 
Anderson may be attempting to mislead potential clients by citing the

performance of the sole fund that achieved such results. Past performance 
is often used to demonstrate a firm’s skill and abilities in comparison to 
funds in the same sectors.
However, if all the funds outperformed their respective benchmarks, 
then Anderson’s assertion that the company “is achieving excellent returns” 
may be factual. Funds may exhibit positive returns for investors, exceed 
benchmarks, and yet have returns below the median in their sectors. 
Members and candidates need to ensure that their marketing efforts 
do not include statements that misrepresent their skills and abilities to 
remain compliant with Standard I(C). Unless the returns of a single fund 
reflect the performance of a firm as a whole, the use of a singular fund for 
performance comparisons should be avoided.
Standard I(D) Misconduct
Members and Candidates must not engage in any professional conduct involving dis -
honesty, fraud, or deceit or commit any act that reflects adversely on their professional

reputation, integrity, or competence. 
Guidance
Whereas Standard I(A) addresses the obligation of members and candidates to comply 
with applicable law that governs their professional activities, Standard I(D) addresses 
all conduct that reflects poorly on the professional integrity, good reputation, or 
competence of members and candidates. Any act that involves lying, cheating, steal -
ing, or other dishonest conduct is a violation of this standard if the offense reflects 
adversely on a member’s or candidate’s professional activities. Although CFA Institute 
discourages any sort of unethical behavior by members and candidates, the Code 
and Standards are primarily aimed at conduct and actions related to a member’s or 
candidate’s professional life.
Conduct that damages trustworthiness or competence may include behavior that, 
although not illegal, nevertheless negatively affects a member’s or candidate’s ability to

perform his or her responsibilities. For example, abusing alcohol during business hours 
might constitute  a violation of this standard because it could have a detrimental effect

Reading 3 ■ Guidance for Standards I–VII 82
on the member’s or candidate’s ability to fulfill his or her professional responsibilities. 
Personal bankruptcy may not reflect on the integrity or trustworthiness of the person 
declaring bankruptcy, but if the circumstances of the bankruptcy involve fraudulent 
or deceitful business conduct, the bankruptcy may be a violation of this standard.
In some cases, the absence of appropriate conduct or the lack of sufficient effort 
may be a violation of Standard I(D). The integrity of the investment profession is built 
on trust. A member or candidate—whether an investment banker, rating or research 
analyst, or portfolio manager—is expected to conduct the necessary due diligence to 
properly understand the nature and risks of an investment before making an investment 
recommendation. By not taking these steps and, instead, relying on someone else in 
the process to perform them, members or candidates may violate the trust their clients

have placed in them. This loss of trust may have a significant impact on the reputation 
of the member or candidate and the operations of the financial market as a whole.
Individuals may attempt to abuse the CFA Institute Professional Conduct Program 
by actively seeking CFA Institute enforcement of the Code and Standards, and 
Standard I(D) in particular, as a method of settling personal, political, or other disputes 
unrelated to professional ethics. CFA Institute is aware of this issue, and appropriate 
disciplinary policies, procedures, and enforcement mechanisms are in place to address 
misuse of the Code and Standards and the Professional Conduct Program in this way.
In addition to ensuring that their own behavior is consistent with Standard I(D), to 
prevent general misconduct, members and candidates should encourage their firms to 
adopt the following policies and procedures to support the principles of Standard I(D):

■■Code of ethics : Develop and/or adopt a code of ethics to which every employee 
must subscribe, and make clear that any personal behavior that reflects poorly 
on the individual involved, the institution as a whole, or the investment indus -
try will not be tolerated.
■■List of violations : Disseminate to all employees a list of potential violations and 
associated disciplinary sanctions, up to and including dismissal from the firm.
■■Employee references : Check references of potential employees to ensure that 
they are of good character and not ineligible to work in the investment industry 
because of past infractions of the law.
Example 1 (Professionalism and Competence):
Simon Sasserman is a trust investment officer at a bank in a small affluent town. He 
enjoys lunching every day with friends at the country club, where his clients have 
observed him having numerous drinks. Back at work after lunch, he clearly is intoxi -

cated while making investment decisions. His colleagues make a point of handling any 
business with Sasserman in the morning because they distrust his judgment after lunch.
Comment : Sasserman’s excessive drinking at lunch and subsequent intoxi -
cation at work constitute a violation of Standard I(D) because this conduct 
has raised questions about his professionalism and competence. His behavior 
reflects poorly on him, his employer, and the investment industry.

Standard I: Professionalism 83
Example 2 (Fraud and Deceit):
Howard Hoffman, a security analyst at ATZ Brothers, Inc., a large brokerage house, 
submits reimbursement forms over a two-  year period to ATZ’s self-  funded health 
insurance program for more than two dozen bills, most of which have been altered 
to increase the amount due. An investigation by the firm’s director of employee ben -
efits uncovers the inappropriate conduct. ATZ subsequently terminates Hoffman’s 
employment and notifies CFA Institute.
Comment : Hoffman violated Standard I(D) because he engaged in inten -
tional conduct involving fraud and deceit in the workplace that adversely 
reflected on his integrity.
Example 3 (Fraud and Deceit):
Jody Brink, an analyst covering the automotive industry, volunteers much of her 
spare time to local charities. The board of one of the charitable institutions decides 
to buy five new vans to deliver hot lunches to low-  income elderly people. Brink offers

to donate her time to handle purchasing agreements. To pay a long-  standing debt to 
a friend who operates an automobile dealership—and to compensate herself for her 
trouble—she agrees to a price 20% higher than normal and splits the surcharge with 
her friend. The director of the charity ultimately discovers the scheme and tells Brink 
that her services, donated or otherwise, are no longer required.
Comment : Brink engaged in conduct involving dishonesty, fraud, and mis -
representation and has violated Standard I(D).
Example 4 (Personal Actions and Integrity):
Carmen Garcia manages a mutual fund dedicated to socially responsible investing. 
She is also an environmental activist. As the result of her participation in nonviolent 
protests, Garcia has been arrested on numerous occasions for trespassing on the 
property of a large petrochemical plant that is accused of damaging the environment.
Comment : Generally, Standard I(D) is not meant to cover legal transgres -

sions resulting from acts of civil disobedience in support of personal beliefs 
because such conduct does not reflect poorly on the member’s or candidate’s 
professional reputation, integrity, or competence.
Example 5 (Professional Misconduct):
Meredith Rasmussen works on a buy-  side trading desk of an investment management 
firm and concentrates on in-  house trades for a hedge fund subsidiary managed by a 
team at the investment management firm. The hedge fund has been very successful 
and is marketed globally by the firm. From her experience as the trader for much of 
the activity of the fund, Rasmussen has become quite knowledgeable about the hedge 
fund’s strategy, tactics, and performance. When a distinct break in the market occurs 
and many of the securities involved in the hedge fund’s strategy decline markedly in 
value, Rasmussen observes that the reported performance of the hedge fund does not 
reflect this decline. In her experience, the lack of effect is a very unlikely occurrence.

She approaches the head of trading about her concern and is told that she should not 
ask any questions and that the fund is big and successful and is not her concern. She 
is fairly sure something is not right, so she contacts the compliance officer, who also 
tells her to stay away from the issue of the hedge fund’s reporting.
Comment : Rasmussen has clearly come across an error in policies, proce -
dures, and compliance practices within the firm’s operations. According 
to the firm’s procedures for reporting potentially unethical activity, she

Reading 3 ■ Guidance for Standards I–VII 84
should pursue the issue by gathering some proof of her reason for doubt. 
Should all internal communications within the firm not satisfy her concerns, 
Rasmussen should consider reporting the potential unethical activity to 
the appropriate regulator.
See also Standard  IV(A) for guidance on whistleblowing and 
Standard IV(C) for the duties of a supervisor.
STANDARD II: INTEGRITY OF CAPITAL MARKETS
Standard II(A) Material Nonpublic Information
Members and Candidates who possess material nonpublic information that could affect 
the value of an investment must not act or cause others to act on the information. 
Guidance
■■What Is “Material” Information?
■■What Constitutes “Nonpublic” Information?
■■Mosaic Theory
■■Using Industry Experts 
■■Investment Research Reports
Trading or inducing others to trade on material nonpublic information erodes confi -
dence in capital markets, institutions, and investment professionals by supporting the

idea that those with inside information and special access can take unfair advantage 
of the general investing public. Although trading on inside information may lead to 
short-  term profits, in the long run, individuals and the profession as a whole suffer 
from such trading. These actions have caused and will continue to cause investors 
to avoid capital markets because the markets are perceived to be “rigged” in favor 
of the knowledgeable insider. When the investing public avoids capital markets, the 
markets and capital allocation become less efficient and less supportive of strong and 
vibrant economies. Standard II(A) promotes and maintains a high level of confidence 
in market integrity, which is one of the foundations of the investment profession.
The prohibition on using this information goes beyond the direct buying and sell -
ing of individual securities or bonds. Members and candidates must not use material

nonpublic information to influence their investment actions related to derivatives (e.g., 
swaps or option contracts), mutual funds, or other alternative investments. Any trading 
based on material nonpublic information constitutes a violation of Standard II(A). 
The expansion of financial products and the increasing interconnectivity of financial 
markets globally have resulted in new potential opportunities  for trading on material 
nonpublic information.

Standard II: Integrity of Capital Markets 85
What Is “Material” Information?
Information is “material” if its disclosure would probably have an impact on the price 
of a security or if reasonable investors would want to know the information before 
making an investment decision. In other words, information is material if it would 
significantly alter the total mix of information currently available about a security in 
such a way that the price of the security would be affected.
The specificity of the information, the extent of its difference from public informa -
tion, its nature, and its reliability are key factors in determining whether a particular 
piece of information fits the definition of material. For example, material information 
may include, but is not limited to, information on the following:
■■earnings;
■■mergers, acquisitions, tender offers, or joint ventures;
■■changes in assets or asset quality;
■■innovative products, processes, or discoveries (e.g., new product trials or

research efforts);
■■new licenses, patents, registered trademarks, or regulatory approval/rejection of 
a product;
■■developments regarding customers or suppliers (e.g., the acquisition or loss of a 
contract);
■■changes in management;
■■change in auditor notification or the fact that the issuer may no longer rely on 
an auditor’s report or qualified opinion;
■■events regarding the issuer’s securities (e.g., defaults on senior securities, calls 
of securities for redemption, repurchase plans, stock splits, changes in divi -
dends, changes to the rights of security holders, and public or private sales of 
additional securities);
■■bankruptcies;
■■significant legal disputes;
■■government reports of economic trends (employment, housing starts, currency 
information, etc.);
■■orders for large trades before they are executed; and
■■new or changing equity or debt ratings issued by a third party (e.g., sell-  side 
recommendations and credit ratings).

In addition to the substance and specificity of the information, the source or 
relative reliability of the information also determines materiality. The less reliable a 
source, the less likely the information provided would be considered material. For 
example, factual information from a corporate insider regarding a significant new 
contract for a company is likely to be material, whereas an assumption based on 
speculation by a competitor about the same contract is likely to be less reliable and, 
therefore, not material. Additionally, information about trials of a new drug, product, 
or service under development from qualified personnel involved in the trials is likely 
to be material, whereas educated conjecture by subject experts not connected to the 
trials is unlikely to be material.
Also, the more ambiguous the effect of the information on price, the less material

that information is considered. If it is unclear whether and to what extent the informa -
tion will affect the price of a security, the information may not be considered material. 
The passage of time may also render information that was once important immaterial.

Reading 3 ■ Guidance for Standards I–VII 86
What Constitutes “Nonpublic” Information?
Information is “nonpublic” until it has been disseminated or is available to the mar -
ketplace in general (as opposed to a select group of investors). “Disseminated” can be 
defined as “made known. ” For example, a company report of profits that is posted on 
the internet and distributed widely through a press release or accompanied by a filing 
has been effectively disseminated to the marketplace. Members and candidates must 
have a reasonable expectation that people have received the information before it can 
be considered public. It is not necessary, however, to wait for the slowest method of 
delivery. Once the information is disseminated to the market, it is public information 
that is no longer covered by this standard.
Members and candidates must be particularly aware of information that is selec -
tively disclosed by corporations to a small group of investors, analysts, or other market

participants. Information that is made available to analysts remains nonpublic until it 
is made available to investors in general. Corporations that disclose information on 
a limited basis create the potential for insider-  trading violations.
Issues of selective disclosure often arise when a corporate insider provides mate -
rial information to analysts in a briefing or conference call before that information is 
released to the public. Analysts must be aware that a disclosure made to a room full of 
analysts does not necessarily make the disclosed information “public. ” Analysts should 
also be alert to the possibility that they are selectively receiving material nonpublic 
information when a company provides them with guidance or interpretation of such 
publicly available information as financial statements or regulatory filings.
A member or candidate may use insider information provided legitimately by 
the source company for the specific purpose of conducting due diligence according

to the business agreement between the parties for such activities as mergers, loan 
underwriting, credit ratings, and offering engagements. In such instances, the invest -
ment professional would not be considered in violation of Standard II(A) by using 
the material information. However, the use of insider information provided by the 
source company for other purposes, especially to trade or entice others to trade the 
securities of the firm, conflicts with this standard.
Mosaic Theory
A financial analyst gathers and interprets large quantities of information from many 
sources. The analyst may use significant conclusions derived from the analysis of public 
and nonmaterial nonpublic information as the basis for investment recommendations 
and decisions even if those conclusions would have been material inside information 
had they been communicated directly to the analyst by a company. Under the “mosaic 
theory, ” financial analysts are free to act on this collection, or mosaic, of information

without risking violation.
The practice of financial analysis depends on the free flow of information. For 
the fair and efficient operation of the capital markets, analysts and investors must 
have the greatest amount of information possible to facilitate making well-  informed 
investment decisions about how and where to invest capital. Accurate, timely, and 
intelligible communication is essential if analysts and investors are to obtain the data 
needed to make informed decisions about how and where to invest capital. These 
disclosures must go beyond the information mandated by the reporting requirements 
of the securities laws and should include specific business information about items 
used to guide a company’s future growth, such as new products, capital projects, and 
the competitive environment. Analysts seek and use such information to compare and 
contrast investment alternatives.
Much of the information used by analysts comes directly from companies. Analysts

often receive such information through contacts with corporate insiders, especially 
investor-  relations staff and financial officers. Information may be disseminated in the

Standard II: Integrity of Capital Markets 87
form of press releases, through oral presentations by company executives in analysts’ 
meetings or conference calls, or during analysts’ visits to company premises. In seeking 
to develop the most accurate and complete picture of a company, analysts should also 
reach beyond contacts with companies themselves and collect information from other 
sources, such as customers, contractors, suppliers, and the companies’ competitors. 
Analysts are in the business of formulating opinions and insights that are not 
obvious to the general investing public about the attractiveness of particular securi -
ties. In the course of their work, analysts actively seek out corporate information not 
generally known to the market for the express purpose of analyzing that informa -
tion, forming an opinion on its significance, and informing their clients, who can be 
expected to trade on the basis of the recommendation. Analysts’ initiatives to discover

and analyze information and communicate their findings to their clients significantly 
enhance market efficiency, thus benefiting all investors (see Dirks v. Securities and 
Exchange Commission ). Accordingly, violations of Standard II(A) will not result when 
a perceptive analyst reaches a conclusion about a corporate action or event through 
an analysis of public information and items of nonmaterial nonpublic information.
Investment professionals should note, however, that although analysts are free to use 
mosaic information in their research reports, they should save and document all their 
research [see Standard V(C)–Record Retention]. Evidence of the analyst’s knowledge 
of public and nonmaterial nonpublic information about a corporation strengthens the 
assertion that the analyst reached his or her conclusions solely through appropriate 
methods rather than through the use of material nonpublic information.

The continuing advancement in technology allows members, candidates, and the 
industry at large to exchange information at rates not previously available. It is import -
ant for investment professionals to understand the implications of using information 
from the internet and social media platforms because all such information may not 
actually be considered public.
Some social media platforms require membership in specific groups in order to 
access the published content. Members and candidates participating in groups with 
membership limitations should verify that material information obtained from these 
sources can also be accessed from a source that would be considered available to the 
public (e.g., company filings, webpages, and press releases). 
Members and candidates may use social media platforms to communicate with 
clients or investors without conflicting with this standard. As long as the information

reaches all clients or is open to the investing public, the use of these platforms would 
be comparable with other traditional forms of communications, such as e-  mails and 
press releases. Members and candidates, as required by Standard I(A), should also 
complete all appropriate regulatory filings related to information distributed through 
social media platforms. 
Using Industry Experts 
The increased demand for insights for understanding the complexities of some 
industries has led to an expansion of engagement with outside experts. As the level 
of engagement increased, new businesses formed to connect analysts and investors 
with individuals who have specialized knowledge of their industry (e.g., technology or 
pharmaceuticals). These networks offer investors the opportunity to reach beyond their 
usual business circles to speak with experts regarding economic conditions, industry 
trends, and technical issues relating to specific products and services.

Members and candidates may provide compensation to individuals for their insights 
without violating this standard. However, members and candidates are ultimately 
responsible for ensuring that they are not requesting or acting on confidential infor -
mation received from external experts, which is in violation of security regulations

Reading 3 ■ Guidance for Standards I–VII 88
and laws or duties to others. As the recent string of insider-  trading cases displayed, 
some experts are willing to provide confidential and protected information for the 
right incentive. 
Firms connecting experts with members or candidates often require both parties 
to sign agreements concerning the disclosure of material nonpublic information. Even 
with the protections from such compliance practices, if an expert provides material 
nonpublic information, members and candidates would be prohibited from taking 
investment actions on the associated firm until the information became publicly 
known to the market.
Investment Research Reports
When a particularly well-  known or respected analyst issues a report or makes changes 
to his or her recommendation, that information alone may have an effect on the market 
and thus may be considered material. Theoretically, under Standard II(A), such a report

would have to be made public at the time it was distributed to clients. The analyst 
is not a company insider, however, and does not have access to inside information. 
Presumably, the analyst created the report from information available to the public 
(mosaic theory) and by using his or her expertise to interpret the information. The 
analyst’s hard work, paid for by the client, generated the conclusions. 
Simply because the public in general would find the conclusions material does not 
require that the analyst make his or her work public. Investors who are not clients 
of the analyst can either do the work themselves or become clients of the analyst to 
gain access to the analyst’s expertise.
Achieve Public Dissemination
If a member or candidate determines that information is material, the member or 
candidate should make reasonable efforts to achieve public dissemination of the

information. These efforts usually entail encouraging the issuing company to make the 
information public. If public dissemination is not possible, the member or candidate 
must communicate the information only to the designated supervisory and compli -
ance personnel within the member’s or candidate’s firm and must not take investment 
action or alter current investment recommendations on the basis of the information. 
Moreover, members and candidates must not knowingly engage in any conduct that 
may induce company insiders to privately disclose material nonpublic information.
Adopt Compliance Procedures
Members and candidates should encourage their firms to adopt compliance procedures 
to prevent the misuse of material nonpublic information. Particularly important is 
improving compliance in such areas as the review of employee and proprietary trad -
ing, the review of investment recommendations, documentation of firm procedures,

and the supervision of interdepartmental communications in multiservice firms. 
Compliance procedures should suit the particular characteristics of a firm, including 
its size and the nature of its business. 
Members and candidates are encouraged to inform their supervisor and compliance 
personnel of suspected inappropriate use of material nonpublic information as the 
basis for security trading activities or recommendations being made within their firm.
Adopt Disclosure Procedures
Members and candidates should encourage their firms to develop and follow disclo -
sure policies designed to ensure that information is disseminated to the marketplace 
in an equitable manner. For example, analysts from small firms should receive the

Standard II: Integrity of Capital Markets 89
same information and attention from a company as analysts from large firms receive. 
Similarly, companies should not provide certain information to buy-  side analysts but 
not to sell-  side analysts, or vice versa. Furthermore, a company should not discriminate 
among analysts in the provision of information or “blackball” particular analysts who 
have given negative reports on the company in the past.
Within investment and research firms, members and candidates should encourage 
the development of and compliance with procedures for distributing new and updated 
investment opinions to clients. Recommendations of this nature may represent mate -
rial market-  moving information that needs to be communicated to all clients fairly. 
Issue Press Releases
Companies should consider issuing press releases prior to analyst meetings and 
conference calls and scripting those meetings and calls to decrease the chance that

further information will be disclosed. If material nonpublic information is disclosed 
for the first time in an analyst meeting or call, the company should promptly issue a 
press release or otherwise make the information publicly available.
Firewall Elements
An information barrier commonly referred to as a “firewall” is the most widely used 
approach for preventing the communication of material nonpublic information within 
firms. It restricts the flow of confidential information to those who need to know the 
information to perform their jobs effectively. The minimum elements of such a system 
include, but are not limited to, the following:
■■substantial control of relevant interdepartmental communications, prefera -
bly through a clearance area within the firm in either the compliance or legal 
department;
■■review of employee trading through the maintenance of “watch, ” “restricted, ” 
and “rumor” lists;
■■documentation of the procedures designed to limit the flow of information

between departments and of the actions taken to enforce those procedures; and
■■heightened review or restriction of proprietary trading while a firm is in posses -
sion of material nonpublic information.
Appropriate Interdepartmental Communications
Although documentation requirements must, for practical reasons, take into account 
the differences between the activities of small firms and those of large, multiservice 
firms, firms of all sizes and types benefit by improving the documentation of their 
internal enforcement of firewall procedures. Therefore, even at small firms, procedures 
concerning interdepartmental communication, the review of trading activity, and the 
investigation of possible violations should be compiled and formalized.
Physical Separation of Departments
As a practical matter, to the greatest extent possible, firms should consider the phys -
ical separation of departments and files to prevent the communication of sensitive

information that should not be shared. For example, the investment banking and 
corporate finance areas of a brokerage firm should be separated from the sales and 
research departments, and a bank’s commercial lending department should be seg -
regated from its trust and research departments.

Reading 3 ■ Guidance for Standards I–VII 90
Prevention of Personnel Overlap
There should be no overlap of personnel between the investment banking and corporate 
finance areas of a brokerage firm and the sales and research departments or between 
a bank’s commercial lending department and its trust and research departments. For 
a firewall to be effective in a multiservice firm, an employee should be on only one 
side of the firewall at any time. Inside knowledge may not be limited to information 
about a specific offering or the current financial condition of a company. Analysts 
may be exposed to much information about the company, including new product 
developments or future budget projections that clearly constitute inside knowledge 
and thus preclude the analyst from returning to his or her research function. For 
example, an analyst who follows a particular company may provide limited assistance 
to the investment bankers under carefully controlled circumstances when the firm’s

investment banking department is involved in a deal with the company. That analyst 
must then be treated as though he or she were an investment banker; the analyst must 
remain on the investment banking side of the wall until any information he or she 
learns is publicly disclosed. In short, the analyst cannot use any information learned 
in the course of the project for research purposes and cannot share that information 
with colleagues in the research department.
A Reporting System
A primary objective of an effective firewall procedure is to establish a reporting 
system in which authorized people review and approve communications between 
departments. If an employee behind a firewall believes that he or she needs to share 
confidential information with someone on the other side of the wall, the employee 
should consult a designated compliance officer to determine whether sharing the 
information is necessary and how much information should be shared. If the sharing

is necessary, the compliance officer should coordinate the process of “looking over 
the wall” so that the necessary information will be shared and the integrity of the 
procedure will be maintained.
A single supervisor or compliance officer should have the specific authority and 
responsibility of deciding whether information is material and whether it is sufficiently 
public to be used as the basis for investment decisions. Ideally, the supervisor or 
compliance officer responsible for communicating information to a firm’s research 
or brokerage area would not be a member of that area.
Personal Trading Limitations
Firms should consider restrictions or prohibitions on personal trading by employ -
ees and should carefully monitor both proprietary trading and personal trading by 
employees. Firms should require employees to make periodic reports (to the extent 
that such reporting is not already required by securities laws) of their own transactions

and transactions made for the benefit of family members. Securities should be placed 
on a restricted list when a firm has or may have material nonpublic information. The 
broad distribution of a restricted list often triggers the sort of trading the list was 
developed to avoid. Therefore, a watch list shown to only the few people responsible 
for compliance should be used to monitor transactions in specified securities. The use 
of a watch list in combination with a restricted list is an increasingly common means 
of ensuring effective control of personal trading.
Record Maintenance
Multiservice firms should maintain written records of the communications between 
various departments. Firms should place a high priority on training and should 
consider instituting comprehensive training programs, particularly for employees in 
sensitive areas.

Standard II: Integrity of Capital Markets 91
Proprietary Trading Procedures
Procedures concerning the restriction or review of a firm’s proprietary trading 
while the firm possesses material nonpublic information will necessarily depend 
on the types of proprietary trading in which the firm may engage. A prohibition 
on all types of proprietary activity when a firm comes into possession of material 
nonpublic information is not appropriate. For example, when a firm acts as a market 
maker, a prohibition on proprietary trading may be counterproductive to the goals 
of maintaining the confidentiality of information and market liquidity. This concern 
is particularly important in the relationships between small, regional broker/dealers 
and small issuers. In many situations, a firm will take a small issuer public with the 
understanding that the firm will continue to be a market maker in the stock. In such 
instances, a withdrawal by the firm from market-  making activities would be a clear

tip to outsiders. Firms that continue market-  making activity while in the possession 
of material nonpublic information should, however, instruct their market makers to 
remain passive with respect to the market—that is, to take only the contra side of 
unsolicited customer trades.
In risk-  arbitrage trading, the case for a trading prohibition is more compelling 
than it is in the case of market making. The impetus for arbitrage trading is neither 
passive nor reactive, and the potential for illegal profits is greater than in market 
making. The most prudent course for firms is to suspend arbitrage activity when a 
security is placed on the watch list. Those firms that continue arbitrage activity face 
a high hurdle in proving the adequacy of their internal procedures for preventing 
trading on material nonpublic information and must demonstrate a stringent review 
and documentation of firm trades.
Communication to All Employees

Members and candidates should encourage their employers to circulate written com -
pliance policies and guidelines to all employees. Policies and guidelines should be 
used in conjunction with training programs aimed at enabling employees to recognize 
material nonpublic information. Such information is not always clearly identifiable. 
Employees must be given sufficient training to either make an informed decision 
or to realize they need to consult a supervisor or compliance officer before engag -
ing in questionable transactions. Appropriate policies reinforce that using material 
nonpublic information is illegal in many countries. Such trading activities based on 
material nonpublic information undermine the integrity of the individual, the firm, 
and the capital markets.
Example 1 (Acting on Nonpublic Information):
Frank Barnes, the president and controlling shareholder of the SmartTown clothing

chain, decides to accept a tender offer and sell the family business at a price almost dou -
ble the market price of its shares. He describes this decision to his sister (SmartTown’s 
treasurer), who conveys it to her daughter (who owns no stock in the family company 
at present), who tells her husband, Staple. Staple, however, tells his stockbroker, Alex 
Halsey, who immediately buys SmartTown stock for himself.
Comment : The information regarding the pending sale is both material and 
nonpublic. Staple has violated Standard II(A) by communicating the inside 
information to his broker. Halsey also has violated the standard by buying 
the shares on the basis of material nonpublic information.

Reading 3 ■ Guidance for Standards I–VII 92
Example 2 (Controlling Nonpublic Information):
Samuel Peter, an analyst with Scotland and Pierce Incorporated, is assisting his firm 
with a secondary offering for Bright Ideas Lamp Company. Peter participates, via 
telephone conference call, in a meeting with Scotland and Pierce investment bank -
ing employees and Bright Ideas’ CEO. Peter is advised that the company’s earnings 
projections for the next year have significantly dropped. Throughout the telephone 
conference call, several Scotland and Pierce salespeople and portfolio managers walk 
in and out of Peter’s office, where the telephone call is taking place. As a result, they 
are aware of the drop in projected earnings for Bright Ideas. Before the conference call 
is concluded, the salespeople trade the stock of the company on behalf of the firm’s 
clients and other firm personnel trade the stock in a firm proprietary account and in 
employees’ personal accounts.

Comment : Peter has violated Standard II(A) because he failed to prevent 
the transfer and misuse of material nonpublic information to others in his 
firm. Peter’s firm should have adopted information barriers to prevent the 
communication of nonpublic information between departments of the firm. 
The salespeople and portfolio managers who traded on the information have 
also violated Standard II(A) by trading on inside information.
Example 3 (Selective Disclosure of Material Information):
Elizabeth Levenson is based in Taipei and covers the Taiwanese market for her firm, 
which is based in Singapore. She is invited, together with the other 10 largest share -
holders of a manufacturing company, to meet the finance director of that company. 
During the meeting, the finance director states that the company expects its workforce 
to strike next Friday, which will cripple productivity and distribution. Can Levenson use

this information as a basis to change her rating on the company from “buy” to “sell”?
Comment : Levenson must first determine whether the material information 
is public. According to Standard II(A), if the company has not made this 
information public (a small group forum does not qualify as a method of 
public dissemination), she cannot use the information.
Example 4 (Determining Materiality):
Leah Fechtman is trying to decide whether to hold or sell shares of an oil-  and-  gas 
exploration company that she owns in several of the funds she manages. Although 
the company has underperformed the index for some time already, the trends in the 
industry sector signal that companies of this type might become takeover targets. 
While she is considering her decision, her doctor, who casually follows the markets, 
mentions that she thinks that the company in question will soon be bought out by a 
large multinational conglomerate and that it would be a good idea to buy the stock

right now. After talking to various investment professionals and checking their opin -
ions on the company as well as checking industry trends, Fechtman decides the next 
day to accumulate more stock in the oil-  and-  gas exploration company.
Comment : Although information on an expected takeover bid may be of 
the type that is generally material and nonpublic, in this case, the source of 
information is unreliable, so the information cannot be considered material. 
Therefore, Fechtman is not prohibited from trading the stock on the basis 
of this information.

Standard II: Integrity of Capital Markets 93
Example 5 (Applying the Mosaic Theory):
Jagdish Teja is a buy-  side analyst covering the furniture industry. Looking for an attrac -
tive company to recommend as a buy, he analyzes several furniture makers by studying 
their financial reports and visiting their operations. He also talks to some designers 
and retailers to find out which furniture styles are trendy and popular. Although none 
of the companies that he analyzes are a clear buy, he discovers that one of them, Swan 
Furniture Company (SFC), may be in financial trouble. SFC’s extravagant new designs 
have been introduced at substantial cost. Even though these designs initially attracted 
attention, the public is now buying more conservative furniture from other makers. 
Based on this information and on a profit-  and-  loss analysis, Teja believes that SFC’s 
next quarter earnings will drop substantially. He issues a sell recommendation for

SFC. Immediately after receiving that recommendation, investment managers start 
reducing the SFC stock in their portfolios.
Comment : Information on quarterly earnings data is material and nonpub -
lic. Teja arrived at his conclusion about the earnings drop on the basis of 
public information and on pieces of nonmaterial nonpublic information 
(such as opinions of designers and retailers). Therefore, trading based on 
Teja’s correct conclusion is not prohibited by Standard II(A).
Example 6 (Applying the Mosaic Theory):
Roger Clement is a senior financial analyst who specializes in the European automobile 
sector at Rivoli Capital. Because he has been repeatedly nominated by many leading 
industry magazines and newsletters as a “best analyst” for the automobile industry, he 
is widely regarded as an authority on the sector. After speaking with representatives 
of Turgot Chariots—a European auto manufacturer with sales primarily in South

Korea—and after conducting interviews with salespeople, labor leaders, his firm’s 
Korean currency analysts, and banking officials, Clement analyzed Turgot Chariots 
and concluded that (1) its newly introduced model will probably not meet sales expec -
tations, (2) its corporate restructuring strategy may well face serious opposition from 
unions, (3) the depreciation of the Korean won should lead to pressure on margins for 
the industry in general and Turgot’s market segment in particular, and (4) banks could 
take a tougher-  than-  expected stance in the upcoming round of credit renegotiations 
with the company. For these reasons, he changes his conclusion about the company 
from “market outperform” to “market underperform. ” Clement retains the support 
material used to reach his conclusion in case questions later arise.
Comment : To reach a conclusion about the value of the company, Clement 
has pieced together a number of nonmaterial or public bits of information

that affect Turgot Chariots. Therefore, under the mosaic theory, Clement 
has not violated Standard II(A) in drafting the report.
Example 7 (Analyst Recommendations as Material Nonpublic Information):
The next day, Clement is preparing to be interviewed on a global financial news 
television program where he will discuss his changed recommendation on Turgot 
Chariots for the first time in public. While preparing for the program, he mentions 
to the show’s producers and Mary Zito, the journalist who will be interviewing him, 
the information he will be discussing. Just prior to going on the air, Zito sells her 
holdings in Turgot Chariots. She also phones her father with the information because 
she knows that he and other family members have investments in Turgot Chariots.
Comment : When Zito receives advance notice of Clement’s change of opin -
ion, she knows it will have a material impact on the stock price, even if she

is not totally aware of Clement’s underlying reasoning. She is not a client

Reading 3 ■ Guidance for Standards I–VII 94
of Clement but obtains early access to the material nonpublic information 
prior to publication. Her trades are thus based on material nonpublic 
information and violate Standard II(A).
Zito further violates the Standard by relaying the information to her 
father. It would not matter if he or any other family member traded; the 
act of providing the information violates Standard II(A). The fact that the 
information is provided to a family member does not absolve someone of 
the prohibition of using or communicating material nonpublic information.
Example 8 (Acting on Nonpublic Information):
Ashton Kellogg is a retired investment professional who manages his own portfolio. 
He owns shares in National Savings, a large local bank. A close friend and golfing 
buddy, John Mayfield, is a senior executive at National. National has seen its stock 
price drop considerably, and the news and outlook are not good. In a conversation

about the economy and the banking industry on the golf course, Mayfield relays the 
information that National will surprise the investment community in a few days when 
it announces excellent earnings for the quarter. Kellogg is pleasantly surprised by this 
information, and thinking that Mayfield, as a senior executive, knows the law and would 
not disclose inside information, he doubles his position in the bank. Subsequently, 
National announces that it had good operating earnings but had to set aside reserves 
for anticipated significant losses on its loan portfolio. The combined news causes the 
stock to go down 60%.
Comment : Even though Kellogg believes that Mayfield would not break the 
law by disclosing inside information and money was lost on the purchase, 
Kellogg should not have purchased additional shares of National. It is the 
member’s or candidate’s responsibility to make sure, before executing 
investment actions, that comments about earnings are not material non -

public information. Kellogg has violated Standard II(A).
Example 9 (Mosaic Theory): 
John Doll is a research analyst for a hedge fund that also sells its research to a select 
group of paying client investment firms. Doll’s focus is medical technology companies 
and products, and he has been in the business long enough and has been successful 
enough to build up a very credible network of friends and experts in the business. Doll 
has been working on a major research report recommending Boyce Health, a medical 
device manufacturer. He recently ran into an old acquaintance at a wedding who is 
a senior executive at Boyce, and Doll asked about the business. Doll was drawn to a 
statement that the executive, who has responsibilities in the new products area, made 
about a product: “I would not get too excited about the medium-  term prospects; we 
have a lot of work to do first. ” Doll incorporated this and other information about the 
new Boyce product in his long-  term recommendation of Boyce.

Comment : Doll’s conversation with the senior executive is part of the mosaic 
of information used in recommending Boyce. When holding discussions 
with a firm executive, Doll would need to guard against soliciting or obtain -
ing material nonpublic information. Before issuing the report, the executive’s 
statement about the continuing development of the product would need 
to be weighed against the other known public facts to determine whether 
it would be considered material.

Standard II: Integrity of Capital Markets 95
Example 10 (Materiality Determination):
Larry Nadler, a trader for a mutual fund, gets a text message from another firm’s trader, 
whom he has known for years. The message indicates a software company is going 
to report strong earnings when the firm publicly announces in two days. Nadler has 
a buy order from a portfolio manager within his firm to purchase several hundred 
thousand shares of the stock. Nadler is aggressive in placing the portfolio manager’s 
order and completes the purchases by the following morning, a day ahead of the firm’s 
planned earnings announcement.
Comment : There are often rumors and whisper numbers before a release 
of any kind. The text message from the other trader would most likely be 
considered market noise. Unless Nadler knew that the trader had an ongoing 
business relationship with the public firm, he had no reason to suspect he 
was receiving material nonpublic information that would prevent him from

completing the trading request of the portfolio manager. 
Example 11 (Using an Expert Network):
Mary McCoy is the senior drug analyst at a mutual fund. Her firm hires a service 
that connects her to experts in the treatment of cancer. Through various phone con -
versations, McCoy enhances her understanding of the latest therapies for successful 
treatment. This information is critical to Mary making informed recommendations 
of the companies producing these drugs. 
Comment : McCoy is appropriately using the expert networks to enhance 
her evaluation process. She has neither asked for nor received information 
that may be considered material and nonpublic, such as preliminary trial 
results. McCoy is allowed to seek advice from professionals within the 
industry that she follows.
Example 12 (Using an Expert Network):
Tom Watson is a research analyst working for a hedge fund. To stay informed, 
Watson relies on outside experts for information on such industries as technology

and pharmaceuticals, where new advancements occur frequently. The meetings with 
the industry experts often are arranged through networks or placement agents that 
have specific policies and procedures in place to deter the exchange of material non -
public information. 
Watson arranges a call to discuss future prospects for one of the fund’s existing 
technology company holdings, a company that was testing a new semiconductor 
product. The scientist leading the tests indicates his disappointment with the per -
formance of the new semiconductor. Following the call, Watson relays the insights 
he received to others at the fund. The fund sells its current position in the company 
and buys many put options because the market is anticipating the success of the new 
semiconductor and the share price reflects the market’s optimism.
Comment : Watson has violated Standard II(A) by passing along material 
nonpublic information concerning the ongoing product tests, which the fund

used to trade in the securities and options of the related company. Watson 
cannot simply rely on the agreements signed by individuals who participate 
in expert networks that state that he has not received information that 
would prohibit his trading activity. He must make his own determination 
whether information he received through these arrangements reaches a 
materiality threshold that would affect his trading abilities.

Reading 3 ■ Guidance for Standards I–VII 96
Standard II(B) Market Manipulation
Members and Candidates must not engage in practices that distort prices or artificially 
inflate trading volume with the intent to mislead market participants. 
Guidance
■■Information-  Based Manipulation
■■Transaction-  Based Manipulation
Standard  II(B) requires that members and candidates uphold market integrity by 
prohibiting market manipulation. Market manipulation includes practices that distort 
security prices or trading volume with the intent to deceive people or entities that 
rely on information in the market. Market manipulation damages the interests of all 
investors by disrupting the smooth functioning of financial markets and lowering 
investor confidence.
Market manipulation may lead to a lack of trust in the fairness of the capital 
markets, resulting in higher risk premiums and reduced investor participation. A

reduction in the efficiency of a local capital market may negatively affect the growth 
and economic health of the country and may also influence the operations of the 
globally interconnected capital markets. Although market manipulation may be less 
likely to occur in mature financial markets than in emerging markets, cross-  border 
investing increasingly exposes all global investors to the potential for such practices.
Market manipulation includes (1) the dissemination of false or misleading informa -
tion and (2) transactions that deceive or would be likely to mislead market participants 
by distorting the price-  setting mechanism of financial instruments. The development 
of new products and technologies increases the incentives, means, and opportunities 
for market manipulation. Additionally, the increasing complexity and sophistication 
of the technologies used for communicating with market participants have created 
new avenues for manipulation.
Information-  Based Manipulation

Information-  based manipulation includes, but is not limited to, spreading false rumors 
to induce trading by others. For example, members and candidates must refrain from 
“pumping up” the price of an investment by issuing misleading positive information 
or overly optimistic projections of a security’s worth only to later “dump” the invest -
ment (i.e., sell it) once the price, fueled by the misleading information’s effect on other 
market participants, reaches an artificially high level.

Standard II: Integrity of Capital Markets 97
Transaction-  Based Manipulation
Transaction-  based manipulation involves instances where a member or candidate knew 
or should have known that his or her actions could affect the pricing of a security. 
This type of manipulation includes, but is not limited to, the following:
■■transactions that artificially affect prices or volume to give the impression of 
activity or price movement in a financial instrument, which represent a diver -
sion from the expectations of a fair and efficient market, and
■■securing a controlling, dominant position in a financial instrument to exploit 
and manipulate the price of a related derivative and/or the underlying asset.
Standard II(B) is not intended to preclude transactions undertaken on legitimate 
trading strategies based on perceived market inefficiencies. The intent of the action 
is critical to determining whether it is a violation of this standard.

Example 1 (Independent Analysis and Company Promotion):
The principal owner of Financial Information Services (FIS) entered into an agreement 
with two microcap companies to promote the companies’ stock in exchange for stock 
and cash compensation. The principal owner caused FIS to disseminate e-  mails, design 
and maintain several websites, and distribute an online investment newsletter—all of 
which recommended investment in the two companies. The systematic publication of 
purportedly independent analyses and recommendations containing inaccurate and 
highly promotional and speculative statements increased public investment in the 
companies and led to dramatically higher stock prices.
Comment : The principal owner of FIS violated Standard  II(B) by using 
inaccurate reporting and misleading information under the guise of inde -
pendent analysis to artificially increase the stock price of the companies.

Furthermore, the principal owner violated Standard V(A)–Diligence and 
Reasonable Basis by not having a reasonable and adequate basis for rec -
ommending the two companies and violated Standard VI(A)–Disclosure 
of Conflicts by not disclosing to investors the compensation agreements 
(which constituted a conflict of interest).
Example 2 (Personal Trading Practices and Price):
John Gray is a private investor in Belgium who bought a large position several years ago 
in Fame Pharmaceuticals, a German small-  cap security with limited average trading 
volume. He has now decided to significantly reduce his holdings owing to the poor 
price performance. Gray is worried that the low trading volume for the stock may 
cause the price to decline further as he attempts to sell his large position.
Gray devises a plan to divide his holdings into multiple accounts in different bro -
kerage firms and private banks in the names of family members, friends, and even a

private religious institution. He then creates a rumor campaign on various blogs and 
social media outlets promoting the company. 
Gray begins to buy and sell the stock using the accounts in hopes of raising the 
trading volume and the price. He conducts the trades through multiple brokers, 
selling slightly larger positions than he bought on a tactical schedule, and over time, 
he is able to reduce his holding as desired without negatively affecting the sale price.
Comment : John violated Standard II(B) by fraudulently creating the appear -
ance that there was a greater investor interest in the stock through the 
online rumors. Additionally, through his trading strategy, he created the

Reading 3 ■ Guidance for Standards I–VII 98
appearance that there was greater liquidity in the stock than actually 
existed. He was able to manipulate the price through both misinformation 
and trading practices.
Example 3 (Creating Artificial Price Volatility):
Matthew Murphy is an analyst at Divisadero Securities & Co., which has a significant 
number of hedge funds among its most important brokerage clients. Some of the hedge 
funds hold short positions on Wirewolf Semiconductor. Two trading days before the 
publication of a quarter-  end report, Murphy alerts his sales force that he is about to 
issue a research report on Wirewolf that will include the following opinions:
■■quarterly revenues are likely to fall short of management’s guidance,
■■earnings will be as much as 5 cents per share (or more than 10%) below consen -
sus, and
■■Wirewolf’s highly respected chief financial officer may be about to join another 
company.

company.
Knowing that Wirewolf has already entered its declared quarter-  end “quiet period” 
before reporting earnings (and thus would be reluctant to respond to rumors), 
Murphy times the release of his research report specifically to sensationalize the 
negative aspects of the message in order to create significant downward pressure on 
Wirewolf’s stock—to the distinct advantage of Divisadero’s hedge fund clients. The 
report’s conclusions are based on speculation, not on fact. The next day, the research 
report is broadcast to all of Divisadero’s clients and to the usual newswire services.
Before Wirewolf’s investor-  relations department can assess the damage on the final 
trading day of the quarter and refute Murphy’s report, its stock opens trading sharply 
lower, allowing Divisadero’s clients to cover their short positions at substantial gains.
Comment : Murphy violated Standard II(B) by aiming to create artificial price

volatility designed to have a material impact on the price of an issuer’s stock. 
Moreover, by lacking an adequate basis for the recommendation, Murphy 
also violated Standard V(A)–Diligence and Reasonable Basis.
Example 4 (Personal Trading and Volume):
Rajesh Sekar manages two funds—an equity fund and a balanced fund—whose 
equity components are supposed to be managed in accordance with the same model. 
According to that model, the funds’ holdings in stock of Digital Design Inc. (DD) are 
excessive. Reduction of the DD holdings would not be easy, however, because the stock 
has low liquidity in the stock market. Sekar decides to start trading larger portions of 
DD stock back and forth between his two funds to slowly increase the price; he believes 
market participants will see growing volume and increasing price and become inter -
ested in the stock. If other investors are willing to buy the DD stock because of such

interest, then Sekar will be able to get rid of at least some of his overweight position 
without inducing price decreases. In this way, the whole transaction will be for the 
benefit of fund participants, even if additional brokers’ commissions are incurred.
Comment : Sekar’s plan would be beneficial for his funds’ participants but 
is based on artificial distortion of both trading volume and the price of the 
DD stock and thus constitutes a violation of Standard II(B).

Standard II: Integrity of Capital Markets 99
Example 5 (“Pump-  Priming” Strategy):
ACME Futures Exchange is launching a new bond futures contract. To convince 
investors, traders, arbitrageurs, hedgers, and so on, to use its contract, the exchange 
attempts to demonstrate that it has the best liquidity. To do so, it enters into agree -
ments with members in which they commit to a substantial minimum trading volume 
on the new contract over a specific period in exchange for substantial reductions of 
their regular commissions.
Comment : The formal liquidity of a market is determined by the obligations 
set on market makers, but the actual liquidity of a market is better estimated 
by the actual trading volume and bid–ask spreads. Attempts to mislead 
participants about the actual liquidity of the market constitute a violation 
of Standard II(B). In this example, investors have been intentionally misled 
to believe they chose the most liquid instrument for some specific purpose,

but they could eventually see the actual liquidity of the contract significantly 
reduced after the term of the agreement expires. If the ACME Futures 
Exchange fully discloses its agreement with members to boost transactions 
over some initial launch period, it will not violate Standard II(B). ACME’s 
intent is not to harm investors but, on the contrary, to give them a better 
service. For that purpose, it may engage in a liquidity-  pumping strategy, 
but the strategy must be disclosed.
Example 6 (Creating Artificial Price Volatility):
Emily Gordon, an analyst of household products companies, is employed by a research 
boutique, Picador & Co. Based on information that she has gathered during a trip 
through Latin America, she believes that Hygene, Inc., a major marketer of personal 
care products, has generated better-  than-  expected sales from its new product initia -
tives in South America. After modestly boosting her projections for revenue and for

gross profit margin in her worksheet models for Hygene, Gordon estimates that her 
earnings projection of US$2.00 per diluted share for the current year may be as much 
as 5% too low. She contacts the chief financial officer (CFO) of Hygene to try to gain 
confirmation of her findings from her trip and to get some feedback regarding her 
revised models. The CFO declines to comment and reiterates management’s most 
recent guidance of US$1.95–US$2.05 for the year.
Gordon decides to try to force a comment from the company by telling Picador 
& Co. clients who follow a momentum investment style that consensus earnings 
projections for Hygene are much too low; she explains that she is considering raising 
her published estimate by an ambitious US$0.15 to US$2.15 per share. She believes 
that when word of an unrealistically high earnings projection filters back to Hygene’s 
investor-  relations department, the company will feel compelled to update its earnings

guidance. Meanwhile, Gordon hopes that she is at least correct with respect to the 
earnings direction and that she will help clients who act on her insights to profit from 
a quick gain by trading on her advice.
Comment : By exaggerating her earnings projections in order to try to fuel a 
quick gain in Hygene’s stock price, Gordon is in violation of Standard II(B). 
Furthermore, by virtue of previewing her intentions of revising upward her 
earnings projections to only a select group of clients, she is in violation of 
Standard III(B)–Fair Dealing. However, it would have been acceptable for 
Gordon to write a report that
■■framed her earnings projection in a range of possible outcomes,

Reading 3 ■ Guidance for Standards I–VII 100
■■outlined clearly the assumptions used in her Hygene models that 
took into consideration the findings from her trip through Latin 
America, and
■■was distributed to all Picador & Co. clients in an equitable 
manner.
Example 7 (Pump and Dump Strategy):
In an effort to pump up the price of his holdings in Moosehead & Belfast Railroad 
Company, Steve Weinberg logs on to several investor chat rooms on the internet to 
start rumors that the company is about to expand its rail network in anticipation of 
receiving a large contract for shipping lumber.
Comment : Weinberg has violated Standard  II(B) by disseminating false 
information about Moosehead & Belfast with the intent to mislead market 
Example 8 (Manipulating Model Inputs):
Bill Mandeville supervises a structured financing team for Superior Investment Bank. 
His responsibilities include packaging new structured investment products and man -

aging Superior’s relationship with relevant rating agencies. To achieve the best rating 
possible, Mandeville uses mostly positive scenarios as model inputs—scenarios that 
reflect minimal downside risk in the assets underlying the structured products. The 
resulting output statistics in the rating request and underwriting prospectus support 
the idea that the new structured products have minimal potential downside risk. 
Additionally, Mandeville’s compensation from Superior is partially based on both 
the level of the rating assigned and the successful sale of new structured investment 
products but does not have a link to the long-  term performance of the instruments.
Mandeville is extremely successful and leads Superior as the top originator of 
structured investment products for the next two years. In the third year, the economy 
experiences difficulties and the values of the assets underlying structured products sig -

nificantly decline. The subsequent defaults lead to major turmoil in the capital markets, 
the demise of Superior Investment Bank, and the loss of Mandeville’s employment.
Comment : Mandeville manipulates the inputs of a model to minimize 
associated risk to achieve higher ratings. His understanding of structured 
products allows him to skillfully decide which inputs to include in support of 
the desired rating and price. This information manipulation for short-  term 
gain, which is in violation of Standard II(B), ultimately causes significant 
damage to many parties and the capital markets as a whole. Mandeville 
should have realized that promoting a rating and price with inaccurate 
information could cause not only a loss of price confidence in the particular 
structured product but also a loss of investor trust in the system. Such loss 
of confidence affects the ability of the capital markets to operate efficiently.
Example 9 (Information Manipulation):

Allen King is a performance analyst for Torrey Investment Funds. King believes that 
the portfolio manager for the firm’s small- and microcap equity fund dislikes him 
because the manager never offers him tickets to the local baseball team’s games but 
does offer tickets to other employees. To incite a potential regulatory review of the 
manager, King creates user profiles on several online forums under the portfolio 
manager’s name and starts rumors about potential mergers for several of the smaller

Standard III: Duties to Clients 101
companies in the portfolio. As the prices of these companies’ stocks increase, the 
portfolio manager sells the position, which leads to an investigation by the regulator 
as King desired.
Comment : King has violated Standard II(B) even though he did not per -
sonally profit from the market’s reaction to the rumor. In posting the false 
information, King misleads others into believing the companies were likely 
to be acquired. Although his intent was to create trouble for the portfolio 
manager, his actions clearly manipulated the factual information that was 
available to the market.
STANDARD III: DUTIES TO CLIENTS
Standard III(A) Loyalty, Prudence, and Care
Members and Candidates have a duty of loyalty to their clients and must act with rea -
sonable care and exercise prudent judgment. Members and Candidates must act for 
the benefit of their clients and place their clients’ interests before their employer’s or 
their own interests. 
Guidance

Guidance
■■Understanding the Application of Loyalty, Prudence, and Care
■■Identifying the Actual Investment Client
■■Developing the Client’s Portfolio
■■Soft Commission Policies
■■Proxy Voting Policies
Standard III(A) clarifies that client interests are paramount. A member’s or candidate’s 
responsibility to a client includes a duty of loyalty and a duty to exercise reasonable 
care. Investment actions must be carried out for the sole benefit of the client and in a 
manner the member or candidate believes, given the known facts and circumstances, 
to be in the best interest of the client. Members and candidates must exercise the same 
level of prudence, judgment, and care that they would apply in the management and 
disposition of their own interests in similar circumstances.
Prudence requires caution and discretion. The exercise of prudence by invest -
ment professionals requires that they act with the care, skill, and diligence that a

reasonable person acting in a like capacity and familiar with such matters would 
use. In the context of managing a client’s portfolio, prudence requires following the 
investment parameters set forth by the client and balancing risk and return. Acting 
with care requires members and candidates to act in a prudent and judicious manner 
in avoiding harm to clients.
Standard III(A) sets minimum expectations for members and candidates when 
fulfilling their responsibilities to their clients. Regulatory and legal requirements for 
such duties can vary across the investment industry depending on a variety of factors,

Reading 3 ■ Guidance for Standards I–VII 102
including job function of the investment professional, the existence of an adviser/client 
relationship, and the nature of the recommendations being offered. From the perspec -
tive of the end user of financial services, these different standards can be arcane and 
confusing, leaving investors unsure of what level of service to expect from investment 
professionals they employ. The single standard of conduct described in Standard III(A) 
benefits investors by establishing a benchmark for the duties of loyalty, prudence, and 
care and clarifies that all CFA Institute members and candidates, regardless of job 
title, local laws, or cultural differences, are required to comply with these fundamental 
responsibilities. Investors hiring members or candidates who must adhere to the duty 
of loyalty, prudence, and care set forth in this standard can be confident that these

responsibilities are a requirement regardless of any legally imposed fiduciary duties.
Standard III(A), however, is not a substitute for a member’s or candidate’s legal 
or regulatory obligations. As stated in Standard I(A), members and candidates must 
abide by the most strict requirements imposed on them by regulators or the Code and 
Standards, including any legally imposed fiduciary duty. Members and candidates must 
also be aware of whether they have “custody” or effective control of client assets. If so, 
a heightened level of responsibility arises. Members and candidates are considered to 
have custody if they have any direct or indirect access to client funds. Members and 
candidates must manage any pool of assets in their control in accordance with the 
terms of the governing documents (such as trust documents and investment man -
agement agreements), which are the primary determinant of the manager’s powers

and duties. Whenever their actions are contrary to provisions of those instruments 
or applicable law, members and candidates are at risk of violating Standard III(A).
Understanding the Application of Loyalty, Prudence, and Care 
Standard III(A) establishes a minimum benchmark for the duties of loyalty, prudence, 
and care that are required of all members and candidates regardless of whether a legal 
fiduciary duty applies. Although fiduciary duty often encompasses the principles of 
loyalty, prudence, and care, Standard III(A) does not render all members and candidates 
fiduciaries. The responsibilities of members and candidates for fulfilling their obligations 
under this standard depend greatly on the nature of their professional responsibilities 
and the relationships they have with clients. The conduct of members and candidates 
may or may not rise to the level of being a fiduciary, depending on the type of client,

whether the member or candidate is giving investment advice, and the many facts and 
circumstances surrounding a particular transaction or client relationship.  
Fiduciary duties are often imposed by law or regulation when an individual or 
institution is charged with the duty of acting for the benefit of another party, such 
as managing investment assets. The duty required in fiduciary relationships exceeds 
what is acceptable in many other business relationships because a fiduciary is in an 
enhanced position of trust. Although members and candidates must comply with any 
legally imposed fiduciary duty, the Code and Standards neither impose such a legal 
responsibility nor require all members or candidates to act as fiduciaries. However, 
Standard III(A) requires members and candidates to work in the client’s best interest 
no matter what the job function. 
A member or candidate who does not provide advisory services to a client but who

acts only as a trade execution professional must prudently work in the client’s interest 
when completing requested trades. Acting in the client’s best interest requires these 
professionals to use their skills and diligence to execute trades in the most favorable 
terms that can be achieved. Members and candidates operating in such positions 
must use care to operate within the parameters set by the client’s trading instructions.
Members and candidates may also operate in a blended environment where they 
execute client trades and offer advice on a limited set of investment options. The extent 
of the advisory arrangement and limitations should be outlined in the agreement with 
the client at the outset of the relationship. For instance, members and candidates should

Standard III: Duties to Clients 103
inform clients that the advice provided will be limited to the propriety products of 
the firm and not include other products available on the market. Clients who want 
access to a wider range of investment products would have the information necessary 
to decide not to engage with members or candidates working under these restrictions.
Members and candidates operating in this blended context would comply with 
their obligations by recommending the allowable products that are consistent with 
the client’s objectives and risk tolerance. They would exercise care through diligently 
aligning the client’s needs with the attributes of the products being recommended. 
Members and candidates should place the client’s interests first by disregarding any 
firm or personal interest in motivating a recommended transaction.
There is a large variety of professional relationships that members and candidates

have with their clients. Standard III(A) requires them to fulfill the obligations outlined 
explicitly or implicitly in the client agreements to the best of their abilities and with 
loyalty, prudence, and care. Whether a member or candidate is structuring a new secu -
ritization transaction, completing a credit rating analysis, or leading a public company, 
he or she must work with prudence and care in delivering the agreed-  on services. 
Identifying the Actual Investment Client
The first step for members and candidates in fulfilling their duty of loyalty to clients 
is to determine the identity of the “client” to whom the duty of loyalty is owed. In 
the context of an investment manager managing the personal assets of an individual, 
the client is easily identified. When the manager is responsible for the portfolios of 
pension plans or trusts, however, the client is not the person or entity who hires the

manager but, rather, the beneficiaries of the plan or trust. The duty of loyalty is owed 
to the ultimate beneficiaries.
In some situations, an actual client or group of beneficiaries may not exist. Members 
and candidates managing a fund to an index or an expected mandate owe the duty of 
loyalty, prudence, and care to invest in a manner consistent with the stated mandate. 
The decisions of a fund’s manager, although benefiting all fund investors, do not have 
to be based on an individual investor’s requirements and risk profile. Client loyalty and 
care for those investing in the fund are the responsibility of members and candidates 
who have an advisory relationship with those individuals.
Situations involving potential conflicts of interest with respect to responsibilities 
to clients may be extremely complex because they may involve a number of competing 
interests. The duty of loyalty, prudence, and care applies to a large number of per -

sons in varying capacities, but the exact duties may differ in many respects in accord 
with the relationship with each client or each type of account in which the assets are 
managed. Members and candidates must not only put their obligations to clients first 
in all dealings but also endeavor to avoid all real or potential conflicts of interest.
Members and candidates with positions whose responsibilities do not include 
direct investment management also have “clients” that must be considered. Just as 
there are various types of advisory relationships, members and candidates must look 
at their roles and responsibilities when making a determination of who their clients 
are. Sometimes the client is easily identifiable; such is the case in the relationship 
between a company executive and the firm’s public shareholders. At other times, the 
client may be the investing public as a whole, in which case the goals of independence

and objectivity of research surpass the goal of loyalty to a single organization.
Developing the Client’s Portfolio
The duty of loyalty, prudence, and care owed to the individual client is especially 
important because the professional investment manager typically possesses greater 
knowledge in the investment arena than the client does. This disparity places the indi -
vidual client in a vulnerable position; the client must trust the manager. The manager 
in these situations should ensure that the client’s objectives and expectations for the

Reading 3 ■ Guidance for Standards I–VII 104
performance of the account are realistic and suitable to the client’s circumstances 
and that the risks involved are appropriate. In most circumstances, recommended 
investment strategies should relate to the long-  term objectives and circumstances 
of the client. 
Particular care must be taken to detect whether the goals of the investment 
manager or the firm in conducting business, selling products, and executing security 
transactions potentially conflict with the best interests and objectives of the client. 
When members and candidates cannot avoid potential conflicts between their firm 
and clients’ interests, they must provide clear and factual disclosures of the circum -
stances to the clients.
Members and candidates must follow any guidelines set by their clients for the 
management of their assets. Some clients, such as charitable organizations and pension 
plans, have strict investment policies that limit investment options to certain types

or classes of investment or prohibit investment in certain securities. Other organiza -
tions have aggressive policies that do not prohibit investments by type but, instead, 
set criteria on the basis of the portfolio’s total risk and return.
Investment decisions must be judged in the context of the total portfolio rather 
than by individual investment within the portfolio. The member’s or candidate’s duty 
is satisfied with respect to a particular investment if the individual has thoroughly 
considered the investment’s place in the overall portfolio, the risk of loss and oppor -
tunity for gains, tax implications, and the diversification, liquidity, cash flow, and 
overall return requirements of the assets or the portion of the assets for which the 
manager is responsible.
Soft Commission Policies
An investment manager often has discretion over the selection of brokers executing 
transactions. Conflicts may arise when an investment manager uses client brokerage

to purchase research services, a practice commonly called “soft dollars” or “soft com -
missions. ” A member or candidate who pays a higher brokerage commission than he 
or she would normally pay to allow for the purchase of goods or services, without 
corresponding benefit to the client, violates the duty of loyalty to the client.
From time to time, a client will direct a manager to use the client’s brokerage to 
purchase goods or services for the client, a practice that is commonly called “directed 
brokerage. ” Because brokerage commission is an asset of the client and is used to 
benefit that client, not the manager, such a practice does not violate any duty of 
loyalty. However, a member or candidate is obligated to seek “best price” and “best 
execution” and be assured by the client that the goods or services purchased from the 
brokerage will benefit the account beneficiaries. “Best execution” refers to a trading

process that seeks to maximize the value of the client’s portfolio within the client’s 
stated investment objectives and constraints. In addition, the member or candidate 
should disclose to the client that the client may not be getting best execution from 
the directed brokerage.
Proxy Voting Policies
The duty of loyalty, prudence, and care may apply in a number of situations facing the 
investment professional besides those related directly to investing assets.
Part of a member’s or candidate’s duty of loyalty includes voting proxies in an 
informed and responsible manner. Proxies have economic value to a client, and 
members and candidates must ensure that they properly safeguard and maximize this 
value. An investment manager who fails to vote, casts a vote without considering the 
impact of the question, or votes blindly with management on nonroutine governance 
issues (e.g., a change in company capitalization) may violate this standard. Voting of

Standard III: Duties to Clients 105
A cost–benefit analysis may show that voting all proxies may not benefit the cli -
ent, so voting proxies may not be necessary in all instances. Members and candidates 
should disclose to clients their proxy voting policies.
Regular Account Information
Members and candidates with control of client assets (1) should submit to each cli -
ent, at least quarterly, an itemized statement showing the funds and securities in the 
custody or possession of the member or candidate plus all debits, credits, and trans -
actions that occurred during the period, (2) should disclose to the client where the 
assets are to be maintained, as well as where or when they are moved, and (3) should 
separate the client’s assets from any other party’s assets, including the member’s or 
candidate’s own assets.
Client Approval
If a member or candidate is uncertain about the appropriate course of action with

respect to a client, the member or candidate should consider what he or she would 
expect or demand if the member or candidate were the client. If in doubt, a member 
or candidate should disclose the questionable matter in writing to the client and 
obtain client approval.
Firm Policies
Members and candidates should address and encourage their firms to address the 
following topics when drafting the statements or manuals containing their policies 
and procedures regarding responsibilities to clients:
■■Follow all applicable rules and laws : Members and candidates must follow all 
legal requirements and applicable provisions of the Code and Standards.
■■Establish the investment objectives of the client : Make a reasonable inquiry 
into a client’s investment experience, risk and return objectives, and financial 
constraints prior to making investment recommendations or taking investment 
actions.
■■Consider all the information when taking actions : When taking investment

actions, members and candidates must consider the appropriateness and suit -
ability of the investment relative to (1) the client’s needs and circumstances, (2) 
the investment’s basic characteristics, and (3) the basic characteristics of the 
total portfolio.
■■Diversify : Members and candidates should diversify investments to reduce the 
risk of loss, unless diversification is not consistent with plan guidelines or is 
contrary to the account objectives.
■■Carry out regular reviews : Members and candidates should establish regular 
review schedules to ensure that the investments held in the account adhere to 
the terms of the governing documents.
■■Deal fairly with all clients with respect to investment actions : Members and can -
didates must not favor some clients over others and should establish policies for 
allocating trades and disseminating investment recommendations.
■■Disclose conflicts of interest : Members and candidates must disclose all actual

and potential conflicts of interest so that clients can evaluate those conflicts.
■■Disclose compensation arrangements : Members and candidates should make 
their clients aware of all forms of manager compensation.

Reading 3 ■ Guidance for Standards I–VII 106
■■Vote proxies : In most cases,  members and candidates should determine who is 
authorized to vote shares and vote proxies in the best interests of the clients 
and ultimate beneficiaries.
■■Maintain confidentiality : Members and candidates must preserve the confiden -
tiality of client information.
■■Seek best execution : Unless directed by the client as ultimate beneficiary, mem -
bers and candidates must seek best execution for their clients. (Best execution 
is defined in the preceding text.)
■■Place client interests first : Members and candidates must serve the best interests 
of clients.
Example 1 (Identifying the Client—Plan Participants):
First Country Bank serves as trustee for the Miller Company’s pension plan. Miller 
is the target of a hostile takeover attempt by Newton, Inc. In attempting to ward off  
Newton, Miller’s managers persuade Julian Wiley, an investment manager at First

Country Bank, to purchase Miller common stock in the open market for the employee 
pension plan. Miller’s officials indicate that such action would be favorably received 
and would probably result in other accounts being placed with the bank. Although 
Wiley believes the stock is overvalued and would not ordinarily buy it, he purchases 
the stock to support Miller’s managers, to maintain Miller’s good favor toward the 
bank, and to realize additional new business. The heavy stock purchases cause Miller’s 
market price to rise to such a level that Newton retracts its takeover bid.
Comment : Standard III(A) requires that a member or candidate, in evaluating 
a takeover bid, act prudently and solely in the interests of plan participants 
and beneficiaries. To meet this requirement, a member or candidate must 
carefully evaluate the long-  term prospects of the company against the 
short-  term prospects presented by the takeover offer and by the ability to

invest elsewhere. In this instance, Wiley, acting on behalf of his employer, 
which was the trustee for a pension plan, clearly violated Standard III(A). 
He used the pension plan to perpetuate existing management, perhaps to 
the detriment of plan participants and the company’s shareholders, and 
to benefit himself. Wiley’s responsibilities to the plan participants and 
beneficiaries should have taken precedence over any ties of his bank to 
corporate managers and over his self-  interest. Wiley had a duty to examine 
the takeover offer on its own merits and to make an independent decision. 
The guiding principle is the appropriateness of the investment decision to 
the pension plan, not whether the decision benefited Wiley or the company 
that hired him.
Example 2 (Client Commission Practices):
JNI, a successful investment counseling firm, serves as investment manager for the 
pension plans of several large regionally based companies. Its trading activities gener -

ate a significant amount of commission-  related business. JNI uses the brokerage and 
research services of many firms, but most of its trading activity is handled through 
a large brokerage company, Thompson, Inc., because the executives of the two firms 
have a close friendship. Thompson’s commission structure is high in comparison with 
charges for similar brokerage services from other firms. JNI considers Thompson’s

Standard III: Duties to Clients 107
research services and execution capabilities average. In exchange for JNI directing 
its brokerage to Thompson, Thompson absorbs a number of JNI overhead expenses, 
including those for rent.
Comment : JNI executives are breaching their responsibilities by using client 
brokerage for services that do not benefit JNI clients and by not obtaining 
best price and best execution for their clients. Because JNI executives are 
not upholding their duty of loyalty, they are violating Standard III(A).
Example 3 (Brokerage Arrangements):
Charlotte Everett, a struggling independent investment adviser, serves as investment 
manager for the pension plans of several companies. One of her brokers, Scott 
Company, is close to consummating management agreements with prospective new 
clients whereby Everett would manage the new client accounts and trade the accounts 
exclusively through Scott. One of Everett’s existing clients, Crayton Corporation, has

directed Everett to place securities transactions for Crayton’s account exclusively 
through Scott. But to induce Scott to exert efforts to send more new accounts to her, 
Everett also directs transactions to Scott from other clients without their knowledge.
Comment : Everett has an obligation at all times to seek best price and best 
execution on all trades. Everett may direct new client trades exclusively 
through Scott Company as long as Everett receives best price and execution 
on the trades or receives a written statement from new clients that she is not 
to seek best price and execution and that they are aware of the consequence 
for their accounts. Everett may trade other accounts through Scott as a 
reward for directing clients to Everett only if the accounts receive best price 
and execution and the practice is disclosed to the accounts. Because Everett 
does not disclose the directed trading, Everett has violated Standard III(A).
Example 4 (Brokerage Arrangements):

Emilie Rome is a trust officer for Paget Trust Company. Rome’s supervisor is responsible 
for reviewing Rome’s trust account transactions and her monthly reports of personal 
stock transactions. Rome has been using Nathan Gray, a broker, almost exclusively for 
trust account brokerage transactions. When Gray makes a market in stocks, he has 
been giving Rome a lower price for personal purchases and a higher price for sales 
than he gives to Rome’s trust accounts and other investors.
Comment : Rome is violating her duty of loyalty to the bank’s trust accounts 
by using Gray for brokerage transactions simply because Gray trades Rome’s 
personal account on favorable terms. Rome is placing her own interests 
before those of her clients.
Example 5 (Client Commission Practices):
Lauren Parker, an analyst with Provo Advisors, covers South American equities for 
her firm. She likes to travel to the markets for which she is responsible and decides to

go on a trip to Chile, Argentina, and Brazil. The trip is sponsored by SouthAM, Inc., 
a research firm with a small broker/dealer affiliate that uses the clearing facilities of a 
larger New York brokerage house. SouthAM specializes in arranging South American 
trips for analysts during which they can meet with central bank officials, government 
ministers, local economists, and senior executives of corporations. SouthAM accepts 
commission dollars at a ratio of 2 to 1 against the hard-  dollar costs of the research 
fee for the trip. Parker is not sure that SouthAM’s execution is competitive, but 
without informing her supervisor, she directs the trading desk at Provo to start giving

Reading 3 ■ Guidance for Standards I–VII 108
commission business to SouthAM so she can take the trip. SouthAM has conveniently 
timed the briefing trip to coincide with the beginning of Carnival season, so Parker 
also decides to spend five days of vacation in Rio de Janeiro at the end of the trip. 
Parker uses commission dollars to pay for the five days of hotel expenses.
Comment : Parker is violating Standard III(A) by not exercising her duty of 
loyalty to her clients. She should have determined whether the commis -
sions charged by SouthAM are reasonable in relation to the benefit of the 
research provided by the trip. She also should have determined whether 
best execution and prices could be received from SouthAM. In addition, 
the five extra days are not part of the research effort because they do not 
assist in the investment decision making. Thus, the hotel expenses for the 
five days should not be paid for with client assets.
Example 6 (Excessive Trading):

Vida Knauss manages the portfolios of a number of high-  net- worth individuals. A 
major part of her investment management fee is based on trading commissions. 
Knauss engages in extensive trading for each of her clients to ensure that she attains 
the minimum commission level set by her firm. Although the securities purchased 
and sold for the clients are appropriate and fall within the acceptable asset classes 
for the clients, the amount of trading for each account exceeds what is necessary to 
accomplish the client’s investment objectives.
Comment : Knauss has violated Standard III(A) because she is using the 
assets of her clients to benefit her firm and herself.
Example 7 (Managing Family Accounts):
Adam Dill recently joined New Investments Asset Managers. To assist Dill in building 
a book of clients, both his father and brother opened new fee-  paying accounts. Dill 
followed all the firm’s procedures in noting his relationships with these clients and in

developing their investment policy statements.
After several years, the number of Dill’s clients has grown, but he still manages 
the original accounts of his family members. An IPO is coming to market that is a 
suitable investment for many of his clients, including his brother. Dill does not receive 
the amount of stock he requested, so to avoid any appearance of a conflict of interest, 
he does not allocate any shares to his brother’s account.
Comment : Dill has violated Standard III(A) because he is not acting for the 
benefit of his brother’s account as well as his other accounts. The brother’s 
account is a regular fee-  paying account comparable to the accounts of 
his other clients. By not allocating the shares proportionately across all 
accounts for which he thought the IPO was suitable, Dill is disadvantaging 
specific clients.
Dill would have been correct in not allocating shares to his brother’s 
account if that account was being managed outside the normal fee struc -
ture of the firm.

Example 8 (Identifying the Client):
Donna Hensley has been hired by a law firm to testify as an expert witness. Although 
the testimony is intended to represent impartial advice, she is concerned that her work 
may have negative consequences for the law firm. If the law firm is Hensley’s client, 
how does she ensure that her testimony will not violate the required duty of loyalty, 
prudence, and care to one’s client?

Standard III: Duties to Clients 109
Comment : In this situation, the law firm represents Hensley’s employer 
and the aspect of “who is the client” is not well defined. When acting as 
an expert witness, Hensley is bound by the standard of independence and 
objectivity in the same manner as an independent research analyst would 
be bound. Hensley must not let the law firm influence the testimony she 
provides in the legal proceedings.
Example 9 (Identifying the Client):
Jon Miller is a mutual fund portfolio manager. The fund is focused on the global 
financial services sector. Wanda Spears is a private wealth manager in the same city 
as Miller and is a friend of Miller. At a local CFA Institute society meeting, Spears 
mentions to Miller that her new client is an investor in Miller’s fund. She states that 
the two of them now share a responsibility to this client.
Comment : Spears’ statement is not totally correct. Because she provides

the advisory services to her new client, she alone is bound by the duty of 
loyalty to this client. Miller’s responsibility is to manage the fund according 
to the investment policy statement of the fund. His actions should not be 
influenced by the needs of any particular fund investor.
Example 10 (Client Loyalty):
After providing client account investment performance to the external-  facing depart -
ments but prior to it being finalized for release to clients, Teresa Nguyen, an invest -
ment performance analyst, notices the reporting system missed a trade. Correcting 
the omission resulted in a large loss for a client that had previously placed the firm 
on “watch” for potential termination owing to underperformance in prior periods. 
Nguyen knows this news is unpleasant but informs the appropriate individuals that 
the report needs to be updated before releasing it to the client.
Comment : Nguyen’s actions align with the requirements of Standard III(A).

Even though the correction may lead to the firm’s termination by the cli -
ent, withholding information on errors would not be in the best interest 
Example 11 (Execution-  Only Responsibilities):
Baftija Sulejman recently became a candidate in the CFA Program. He is a broker who 
executes client-  directed trades for several high-  net- worth individuals. Sulejman does 
not provide any investment advice and only executes the trading decisions made by 
clients. He is concerned that the Code and Standards impose a fiduciary duty on him 
in his dealing with clients and sends an e-  mail to the CFA Ethics Helpdesk (ethics@
cfainstitute.org) to seek guidance on this issue.
Comment : In this instance, Sulejman serves in an execution-  only capacity 
and his duty of loyalty, prudence, and care is centered on the skill and 
diligence used when executing trades—namely, by seeking best execution 
and making trades within the parameters set by the clients (instructions

on quantity, price, timing, etc.). Acting in the best interests of the client 
dictates that trades are executed on the most favorable terms that can be 
achieved for the client. Given this job function, the requirements of the 
Code and Standards for loyalty, prudence, and care clearly do not impose 
a fiduciary duty.

Reading 3 ■ Guidance for Standards I–VII 110
Standard III(B) Fair Dealing
Members and Candidates must deal fairly and objectively with all clients when providing 
investment analysis, making investment recommendations, taking investment action, 
or engaging in other professional activities. 
Guidance
■■Investment Recommendations
■■Investment Action
Standard  III(B)  requires members and candidates to treat all clients fairly when 
disseminating investment recommendations or making material changes to prior 
investment recommendations or when taking investment action with regard to gen -
eral purchases, new issues, or secondary offerings. Only through the fair treatment 
of all parties can the investment management profession maintain the confidence of 
the investing public.
When an investment adviser has multiple clients, the potential exists for the adviser 
to favor one client over another. This favoritism may take various forms—from the

quality and timing of services provided to the allocation of investment opportunities.
The term “fairly” implies that the member or candidate must take care not to 
discriminate against any clients when disseminating investment recommendations or 
taking investment action. Standard III(B) does not state “equally” because members 
and candidates could not possibly reach all clients at exactly the same time—whether 
by printed mail, telephone (including text messaging), computer (including internet 
updates and e-  mail distribution), facsimile (fax), or wire. Each client has unique needs, 
investment criteria, and investment objectives, so not all investment opportunities 
are suitable for all clients. In addition, members and candidates may provide more 
personal, specialized, or in-  depth service to clients who are willing to pay for premium 
services through higher management fees or higher levels of brokerage. Members and

candidates may differentiate their services to clients, but different levels of service 
must not disadvantage or negatively affect clients. In addition, the different service 
levels should be disclosed to clients and prospective clients and should be available 
to everyone (i.e., different service levels should not be offered selectively).
Standard  III(B) covers conduct in two broadly defined categories—investment 
recommendations and investment action.
Investment Recommendations
The first category of conduct involves members and candidates whose primary func -
tion is the preparation of investment recommendations to be disseminated either to 
the public or within a firm for the use of others in making investment decisions. This 
group includes members and candidates employed by investment counseling, advisory, 
or consulting firms as well as banks, brokerage firms, and insurance companies. The 
criterion is that the member’s or candidate’s primary responsibility is the preparation

of recommendations to be acted on by others, including those in the member’s or 
candidate’s organization.

Standard III: Duties to Clients 111
An investment recommendation is any opinion expressed by a member or candi -
date in regard to purchasing, selling, or holding a given security or other investment. 
The opinion may be disseminated to customers or clients through an initial detailed 
research report, through a brief update report, by addition to or deletion from a list 
of recommended securities, or simply by oral communication. A recommendation 
that is distributed to anyone outside the organization is considered a communication 
for general distribution under Standard III(B).
Standard III(B) addresses the manner in which investment recommendations or 
changes in prior recommendations are disseminated to clients. Each member or can -
didate is obligated to ensure that information is disseminated in such a manner that 
all clients have a fair opportunity to act on every recommendation. Communicating 
with all clients on a uniform basis presents practical problems for members and can -

didates because of differences in timing and methods of communication with various 
types of customers and clients. Members and candidates should encourage their firms 
to design an equitable system to prevent selective or discriminatory disclosure and 
should inform clients about what kind of communications they will receive.
The duty to clients imposed by Standard III(B) may be more critical when mem -
bers or candidates change their recommendations than when they make initial 
recommendations. Material changes in a member’s or candidate’s prior investment 
recommendations because of subsequent research should be communicated to all 
current clients; particular care should be taken that the information reaches those 
clients who the member or candidate knows have acted on or been affected by the 
earlier advice. Clients who do not know that the member or candidate has changed a 
recommendation and who, therefore, place orders contrary to a current recommenda -

tion should be advised of the changed recommendation before the order is accepted.
Investment Action
The second category of conduct includes those members and candidates whose pri -
mary function is taking investment action (portfolio management) on the basis of 
recommendations prepared internally or received from external sources. Investment 
action, like investment recommendations, can affect market value. Consequently, 
Standard III(B) requires that members or candidates treat all clients fairly in light of 
their investment objectives and circumstances. For example, when making invest -
ments in new offerings or in secondary financings, members and candidates should 
distribute the issues to all customers for whom the investments are appropriate in a 
manner consistent with the policies of the firm for allocating blocks of stock. If the 
issue is oversubscribed, then the issue should be prorated to all subscribers. This action

should be taken on a round-  lot basis to avoid odd-  lot distributions. In addition, if 
the issue is oversubscribed, members and candidates should forgo any sales to them -
selves or their immediate families in order to free up additional shares for clients. If 
the investment professional’s family-  member accounts are managed similarly to the 
accounts of other clients of the firm, however, the family-  member accounts should 
not be excluded from buying such shares.
Members and candidates must make every effort to treat all individual and insti -
tutional clients in a fair and impartial manner. A member or candidate may have 
multiple relationships with an institution; for example, the member or candidate 
may be a corporate trustee, pension fund manager, manager of funds for individuals 
employed by the customer, loan originator, or creditor. A member or candidate must 
exercise care to treat all clients fairly.
Members and candidates should disclose to clients and prospective clients the

documented allocation procedures they or their firms have in place and how the 
procedures would affect the client or prospect. The disclosure should be clear and 
complete so that the client can make an informed investment decision. Even when

Reading 3 ■ Guidance for Standards I–VII 112
complete disclosure is made, however, members and candidates must put client interests 
ahead of their own. A member’s or candidate’s duty of fairness and loyalty to clients 
can never be overridden by client consent to patently unfair allocation procedures.
Treating clients fairly also means that members and candidates should not take 
advantage of their position in the industry to the detriment of clients. For instance, in 
the context of IPOs, members and candidates must make bona fide public distributions 
of “hot issue” securities (defined as securities of a public offering that are trading at 
a premium in the secondary market whenever such trading commences because of 
the great demand for the securities). Members and candidates are prohibited from 
withholding such securities for their own benefit and must not use such securities as 
a reward or incentive to gain benefit.
Develop Firm Policies

Although Standard III(B) refers to a member’s or candidate’s responsibility to deal 
fairly and objectively with clients, members and candidates should also encourage 
their firms to establish compliance procedures requiring all employees who dissemi -
nate investment recommendations or take investment actions to treat customers and 
clients fairly. At the very least, a member or candidate should recommend appropriate 
procedures to management if none are in place. And the member or candidate should 
make management aware of possible violations of fair-  dealing practices within the 
firm when they come to the attention of the member or candidate.
The extent of the formality and complexity of such compliance procedures depends 
on the nature and size of the organization and the type of securities involved. An 
investment adviser who is a sole proprietor and handles only discretionary accounts 
might not disseminate recommendations to the public, but that adviser should have

formal written procedures to ensure that all clients receive fair investment action.
Good business practice dictates that initial recommendations be made available 
to all customers who indicate an interest. Although a member or candidate need not 
communicate a recommendation to all customers, the selection process by which 
customers receive information should be based on suitability and known interest, 
not on any preferred or favored status. A common practice to assure fair dealing is 
to communicate recommendations simultaneously within the firm and to customers.
Members and candidates should consider the following points when establishing 
fair-  dealing compliance procedures:
■■Limit the number of people involved : Members and candidates should make 
reasonable efforts to limit the number of people who are privy to the fact that a 
recommendation is going to be disseminated.
■■Shorten the time frame between decision and dissemination : Members and can -

didates should make reasonable efforts to limit the amount of time that elapses 
between the decision to make an investment recommendation and the time the 
actual recommendation is disseminated. If a detailed institutional recommen -
dation that might take two or three weeks to publish is in preparation, a short 
summary report including the conclusion might be published in advance. In an 
organization where both a research committee and an investment policy com -
mittee must approve a recommendation, the meetings should be held on the 
same day if possible. The process of reviewing reports and printing and mail -
ing them, faxing them, or distributing them by e-  mail necessarily involves the 
passage of time, sometimes long periods of time. In large firms with extensive 
review processes, the time factor is usually not within the control of the analyst 
who prepares the report. Thus, many firms and their analysts communicate

Standard III: Duties to Clients 113
to customers and firm personnel the new or changed recommendations by an 
update or “flash” report. The communication technique might be fax, e-  mail, 
wire, or short written report.
■■Publish guidelines for pre-  dissemination behavior : Members and candidates 
should encourage firms to develop guidelines that prohibit personnel who have 
prior knowledge of an investment recommendation from discussing or taking 
any action on the pending recommendation.
■■Simultaneous dissemination : Members and candidates should establish pro -
cedures for the timing of  dissemination of investment recommendations so 
that all clients are treated fairly—that is, are informed at approximately the 
same time. For example, if a firm is going to announce a new recommenda -
tion, supervisory personnel should time the announcement to avoid placing 
any client or group of clients at an unfair advantage relative to other clients. A

communication to all branch offices should be sent at the time of the general 
announcement. (When appropriate, the firm should accompany the announce -
ment of a new recommendation with a statement that trading restrictions for 
the firm’s employees are now in effect. The trading restrictions should stay in 
effect until the recommendation is widely distributed to all relevant clients.) 
Once this distribution has occurred, the member or candidate may follow up 
separately with individual clients, but members and candidates should not give 
favored clients advance information when such advance notification may disad -
vantage other clients.
■■Maintain a list of clients and their holdings : Members and candidates should 
maintain a list of all clients and the securities or other investments each client 
holds in order to facilitate notification of customers or clients of a change in an 
investment recommendation. If a particular security or other investment is to

be sold, such a list can be used to ensure that all holders are treated fairly in the 
liquidation of that particular investment.
■■Develop and document trade allocation procedures : When formulating proce -
dures for allocating trades, members and candidates should develop a set of 
guiding principles that ensure
■●fairness to advisory clients, both in priority of execution of orders and in the 
allocation of the price obtained in execution of block orders or trades,
■●timeliness and efficiency in the execution of orders, and
■●accuracy of the member’s or candidate’s records as to trade orders and client 
account positions.
With these principles in mind, members and candidates should develop or encour -
age their firm to develop written allocation procedures, with particular attention to 
procedures for block trades and new issues. Procedures to consider are as follows:
■■requiring orders and modifications or cancellations of orders to be documented 
and time stamped;

■■processing and executing orders on a first-  in, first-  out basis with consider -
ation of bundling orders for efficiency  as appropriate for the asset class or the 
security;
■■developing a policy to address such issues as calculating execution prices and 
“partial fills” when trades are grouped, or in a block, for efficiency;
■■giving all client accounts participating in a block trade the same execution price 
and charging the same commission;

Reading 3 ■ Guidance for Standards I–VII 114
■■when the full amount of the block order is not executed, allocating partially 
executed orders among the participating client accounts pro rata on the basis 
of order size while not going below an established minimum lot size for some 
securities (e.g., bonds); and
■■when allocating trades for new issues, obtaining advance indications of interest, 
allocating securities by client (rather than portfolio manager), and providing a 
method for calculating allocations.
Disclose Trade Allocation Procedures
Members and candidates should disclose to clients and prospective clients how they 
select accounts to participate in an order and how they determine the amount of 
securities each account will buy or sell. Trade allocation procedures must be fair 
and equitable, and disclosure of inequitable allocation methods does not relieve the 
member or candidate of this obligation.
Establish Systematic Account Review

Member and candidate supervisors should review each account on a regular basis to 
ensure that no client or customer is being given preferential treatment and that the 
investment actions taken for each account are suitable for each account’s objectives. 
Because investments should be based on individual needs and circumstances, an 
investment manager may have good reasons for placing a given security or other 
investment in one account while selling it from another account and should fully 
document the reasons behind both sides of the transaction. Members and candidates 
should encourage firms to establish review procedures, however, to detect whether 
trading in one account is being used to benefit a favored client.
Disclose Levels of Service
Members and candidates should disclose to all clients whether the organization offers 
different levels of service to clients for the same fee or different fees. Different levels

of service should not be offered to clients selectively.
Example 1 (Selective Disclosure):
Bradley Ames, a well-  known and respected analyst, follows the computer industry. In 
the course of his research, he finds that a small, relatively unknown company whose 
shares are traded over the counter has just signed significant contracts with some 
of the companies he follows. After a considerable amount of investigation, Ames 
decides to write a research report on the small company and recommend purchase 
of its shares. While the report is being reviewed by the company for factual accuracy, 
Ames schedules a luncheon with several of his best clients to discuss the company. At 
the luncheon, he mentions the purchase recommendation scheduled to be sent early 
the following week to all the firm’s clients.
Comment : Ames has violated Standard III(B) by disseminating the purchase 
recommendation to the clients with whom he has lunch a week before the

recommendation is sent to all clients.
Example 2 (Fair Dealing between Funds):
Spencer Rivers, president of XYZ Corporation, moves his company’s growth-  oriented 
pension fund to a particular bank primarily because of the excellent investment 
performance achieved by the bank’s commingled fund for the prior five-  year period.

Standard III: Duties to Clients 115
Later, Rivers compares the results of his pension fund with those of the bank’s com -
mingled fund. He is startled to learn that, even though the two accounts have the 
same investment objectives and similar portfolios, his company’s pension fund has 
significantly underperformed the bank’s commingled fund. Questioning this result at 
his next meeting with the pension fund’s manager, Rivers is told that, as a matter of 
policy, when a new security is placed on the recommended list, Morgan Jackson, the 
pension fund manager, first purchases the security for the commingled account and 
then purchases it on a pro rata basis for all other pension fund accounts. Similarly, 
when a sale is recommended, the security is sold first from the commingled account 
and then sold on a pro rata basis from all other accounts. Rivers also learns that if 
the bank cannot get enough shares (especially of hot issues) to be meaningful to all

the accounts, its policy is to place the new issues only in the commingled account.
Seeing that Rivers is neither satisfied nor pleased by the explanation, Jackson 
quickly adds that nondiscretionary pension accounts and personal trust accounts have 
a lower priority on purchase and sale recommendations than discretionary pension 
fund accounts. Furthermore, Jackson states, the company’s pension fund had the 
opportunity to invest up to 5% in the commingled fund.
Comment : The bank’s policy does not treat all customers fairly, and Jackson 
has violated her duty to her clients by giving priority to the growth-  oriented 
commingled fund over all other funds and to discretionary accounts over 
nondiscretionary accounts. Jackson must execute orders on a systematic 
basis that is fair to all clients. In addition, trade allocation procedures 
should be disclosed to all clients when they become clients. Of course, in 
this case, disclosure of the bank’s policy would not change the fact that

the policy is unfair.
Example 3 (Fair Dealing and IPO Distribution):
Dominic Morris works for a small regional securities firm. His work consists of corpo -
rate finance activities and investing for institutional clients. Arena, Ltd., is planning to 
go public. The partners have secured rights to buy an arena football league franchise 
and are planning to use the funds from the issue to complete the purchase. Because 
arena football is the current rage, Morris believes he has a hot issue on his hands. 
He has quietly negotiated some options for himself for helping convince Arena to do 
the financing through his securities firm.  When he seeks expressions of interest, the 
institutional buyers oversubscribe the issue. Morris, assuming that the institutions 
have the financial clout to drive the stock up, then fills all orders (including his own) 
and decreases the institutional blocks.
Comment : Morris has violated Standard III(B) by not treating all custom -

ers fairly. He should not have taken any shares himself and should have 
prorated the shares offered among all clients. In addition, he should have 
disclosed to his firm and to his clients that he received options as part of 
the deal [see Standard VI(A)–Disclosure of Conflicts].
Example 4 (Fair Dealing and Transaction Allocation):
Eleanor Preston, the chief investment officer of Porter Williams Investments (PWI), 
a medium-  size money management firm, has been trying to retain a client, Colby 
Company. Management at Colby, which accounts for almost half of PWI’s revenues, 
recently told Preston that if the performance of its account did not improve, it would 
find a new money manager. Shortly after this threat, Preston purchases mortgage-  
backed securities (MBSs) for several accounts, including Colby’s. Preston is busy with 
a number of transactions that day, so she fails to allocate the trades immediately or

write up the trade tickets. A few days later, when Preston is allocating trades, she notes

Reading 3 ■ Guidance for Standards I–VII 116
that some of the MBSs have significantly increased in price and some have dropped. 
Preston decides to allocate the profitable trades to Colby and spread the losing trades 
among several other PWI accounts.
Comment : Preston has violated Standard III(B) by failing to deal fairly with 
her clients in taking these investment actions. Preston should have allocated 
the trades prior to executing the orders, or she should have had a systematic 
approach to allocating the trades, such as pro rata, as soon as practical 
after they were executed. Among other things, Preston must disclose to 
the client that the adviser may act as broker for, receive commissions from, 
and have a potential conflict of interest regarding both parties in agency 
cross-  transactions. After the disclosure, she should obtain from the client 
consent authorizing such transactions in advance.
Example 5 (Selective Disclosure):

Saunders Industrial Waste Management (SIWM) publicly indicates to analysts that 
it is comfortable with the somewhat disappointing earnings-  per-  share projection 
of US$1.16 for the quarter. Bernard Roberts, an analyst at Coffey Investments, is 
confident that SIWM management has understated the forecasted earnings so that 
the real announcement will cause an “upside surprise” and boost the price of SIWM 
stock. The “whisper number” (rumored) estimate based on extensive research and 
discussed among knowledgeable analysts is higher than US$1.16. Roberts repeats the 
US$1.16 figure in his research report to all Coffey clients but informally tells his large 
clients that he expects the earnings per share to be higher, making SIWM a good buy.
Comment : By not sharing his opinion regarding the potential for a significant 
upside earnings surprise with all clients, Roberts is not treating all clients 
fairly and has violated Standard III(B).

Example 6 (Additional Services for Select Clients):
Jenpin Weng uses e-  mail to issue a new recommendation to all his clients. He then 
calls his three largest institutional clients to discuss the recommendation in detail.
Comment : Weng has not violated Standard III(B) because he widely dissem -
inated the recommendation and provided the information to all his clients 
prior to discussing it with a select few. Weng’s largest clients received addi -
tional personal service because they presumably pay higher fees or because 
they have a large amount of assets under Weng’s management. If Weng had 
discussed the report with a select group of clients prior to distributing it 
to all his clients, he would have violated Standard III(B).
Example 7 (Minimum Lot Allocations):
Lynn Hampton is a well-  respected private wealth manager in her community with 
a diversified client base. She determines that a new 10-  year bond being offered by

Healthy Pharmaceuticals is appropriate for five of her clients. Three clients request 
to purchase US$10,000 each, and the other two request US$50,000 each. The mini -
mum lot size is established at US$5,000, and the issue is oversubscribed at the time 
of placement. Her firm’s policy is that odd-  lot allocations, especially those below the 
minimum, should be avoided because they may affect the liquidity of the security at 

Standard III: Duties to Clients 117
Hampton is informed she will receive only US$55,000 of the offering for all 
accounts. Hampton distributes the bond investments as follows: The three accounts 
that requested US$10,000 are allocated US$5,000 each, and the two accounts that 
requested US$50,000 are allocated US$20,000 each.
Comment : Hampton has not violated Standard  III(B), even though the 
distribution is not on a completely pro rata basis because of the required 
minimum lot size. With the total allocation being significantly below the 
amount requested, Hampton ensured that each client received at least the 
minimum lot size of the issue. This approach allowed the clients to efficiently 
sell the bond later if necessary.
Example 8 (Excessive Trading):
Ling Chan manages the accounts for many pension plans, including the plan of his 
father’s employer. Chan developed similar but not identical investment policies for

each client, so the investment portfolios are rarely the same. To minimize the cost to 
his father’s pension plan, he intentionally trades more frequently in the accounts of 
other clients to ensure the required brokerage is incurred to continue receiving free 
research for use by all the pensions.
Comment : Chan is violating Standard III(B) because his trading actions are 
disadvantaging his clients to enhance a relationship with a preferred client. 
All clients are benefiting from the research being provided and should incur 
their fair portion of the costs. This does not mean that additional trading 
should occur if a client has not paid an equal portion of the commission; 
trading should occur only as required by the strategy.
Example 9 (Limited Social Media Disclosures):
Mary Burdette was recently hired by Fundamental Investment Management (FIM) as a 
junior auto industry analyst. Burdette is expected to expand the social media presence

of the firm because she is active with various networks, including Facebook, LinkedIn, 
and Twitter. Although Burdette’s supervisor, Joe Graf, has never used social media, he 
encourages Burdette to explore opportunities to increase FIM’s online presence and 
ability to share content, communicate, and broadcast information to clients. In response 
to Graf’s encouragement, Burdette is working on a proposal detailing the advantages 
of getting FIM onto Twitter in addition to launching a company Facebook page.
As part of her auto industry research for FIM, Burdette is completing a report on 
the financial impact of Sun Drive Auto Ltd. ’s new solar technology for compact auto -
mobiles. This research report will be her first for FIM, and she believes Sun Drive’s 
technology could revolutionize the auto industry. In her excitement, Burdette sends 
a quick tweet to FIM Twitter followers summarizing her “buy” recommendation for 
Sun Drive Auto stock.

Sun Drive Auto stock. 
Comment : Burdette has violated Standard III(B) by sending an investment 
recommendation to a select group of contacts prior to distributing it to all 
clients. Burdette must make sure she has received the appropriate training 
about FIM’s policies and procedures, including the appropriate business 
use of personal social media networks before engaging in such activities. 
See Standard IV(C) for guidance related to the duties of the supervisor.

Reading 3 ■ Guidance for Standards I–VII 118
Example 10 (Fair Dealing between Clients):
Paul Rove, performance analyst for Alpha-  Beta Investment Management, is describing 
to the firm’s chief investment officer (CIO) two new reports he would like to develop 
to assist the firm in meeting its obligations to treat clients fairly. Because many of the 
firm’s clients have similar investment objectives and portfolios, Rove suggests a report 
detailing securities owned across several clients and the percentage of the portfolio the 
security represents. The second report would compare the monthly performance of 
portfolios with similar strategies. The outliers within each report would be submitted 
to the CIO for review.
Comment : As a performance analyst, Rove likely has little direct contact 
with clients and thus has limited opportunity to treat clients differently. 
The recommended reports comply with Standard III(B) while helping the

firm conduct after-  the- fact reviews of how effectively the firm’s advisers 
are dealing with their clients’ portfolios. Reports that monitor the fair 
treatment of clients are an important oversight tool to ensure that clients 
are treated fairly.
Standard III(C) Suitability
1 When Members and Candidates are in an advisory relationship with a client, they 
must:
a Make a reasonable inquiry into a client’s or prospective client’s investment 
experience, risk and return objectives, and financial constraints prior to mak -
ing any investment recommendation or taking investment action and must 
reassess and update this information regularly.
b d etermine that an investment is suitable to the client’s financial situation 
and consistent with the client’s written objectives, mandates, and constraints 
before making an investment recommendation or taking investment action.

2 When Members and Candidates are responsible for managing a portfolio to a spe -
cific mandate, strategy, or style, they must make only investment recommenda -
tions or take only investment actions that are consistent with the stated objectives 
and constraints of the portfolio.
Guidance
■■Developing an Investment Policy
■■Understanding the Client’s Risk Profile
■■Updating an Investment Policy
■■The Need for Diversification
■■Addressing Unsolicited Trading Requests
■■Managing to an Index or Mandate

Standard III: Duties to Clients 119
Standard  III(C) requires that members and candidates who are in an investment 
advisory relationship with clients consider carefully the needs, circumstances, and 
objectives of the clients when determining the appropriateness and suitability of a given 
investment or course of investment action. An appropriate suitability determination 
will not, however, prevent some investments or investment actions from losing value.
In judging the suitability of a potential investment, the member or candidate 
should review many aspects of the client’s knowledge, experience related to investing, 
and financial situation. These aspects include, but are not limited to, the risk profile 
of the investment as compared with the constraints of the client, the impact of the 
investment on the diversity of the portfolio, and whether the client has the means or 
net worth to assume the associated risk. The investment professional’s determination

of suitability should reflect only the investment recommendations or actions that a 
prudent person would be willing to undertake. Not every investment opportunity 
will be suitable for every portfolio, regardless of the potential return being offered.
The responsibilities of members and candidates to gather information and make 
a suitability analysis prior to making a recommendation or taking investment action 
fall on those members and candidates who provide investment advice in the course of 
an advisory relationship with a client. Other members and candidates may be simply 
executing specific instructions for retail clients when buying or selling securities, such 
as shares in mutual funds. These members and candidates and some others, such as 
sell- side analysts, may not have the opportunity to judge the suitability of a particular 
investment for the ultimate client. 
Developing an Investment Policy
When an advisory relationship exists, members and candidates must gather client

information at the inception of the relationship. Such information includes the cli -
ent’s financial circumstances, personal data (such as age and occupation) that are 
relevant to investment decisions, attitudes toward risk, and objectives in investing. 
This information should be incorporated into a written investment policy statement 
(IPS) that addresses the client’s risk tolerance, return requirements, and all investment 
constraints (including time horizon, liquidity needs, tax concerns, legal and regulatory 
factors, and unique circumstances). Without identifying such client factors, members 
and candidates cannot judge whether a particular investment or strategy is suitable 
for a particular client. The IPS also should identify and describe the roles and respon -
sibilities of the parties to the advisory relationship and investment process, as well as 
schedules for review and evaluation of the IPS. After formulating long-  term capital

market expectations, members and candidates can assist in developing an appropriate 
strategic asset allocation and investment program for the client, whether these are 
presented in separate documents or incorporated in the IPS or in appendices to the IPS.
Understanding the Client’s Risk Profile
One of the most important factors to be considered in matching appropriateness and 
suitability of an investment with a client’s needs and circumstances is measuring that 
client’s tolerance for risk. The investment professional must consider the possibilities 
of rapidly changing investment environments and their likely impact on a client’s 
holdings, both individual securities and the collective portfolio. The risk of many 
investment strategies can and should be analyzed and quantified in advance.
The use of synthetic investment vehicles and derivative investment products has 
introduced particular issues of risk. Members and candidates should pay careful

attention to the leverage inherent in many of these vehicles or products when con -
sidering them for use in a client’s investment program. Such leverage and limited 
liquidity, depending on the degree to which they are hedged, bear directly on the 
issue of suitability for the client.

Reading 3 ■ Guidance for Standards I–VII 120
Updating an Investment Policy
Updating the IPS should be repeated at least annually and also prior to material 
changes to any specific investment recommendations or decisions on behalf of the 
client. The effort to determine the needs and circumstances of each client is not a 
one-  time occurrence. Investment recommendations or decisions are usually part of an 
ongoing process that takes into account the diversity and changing nature of portfolio 
and client characteristics. The passage of time is bound to produce changes that are 
important with respect to investment objectives.
For an individual client, important changes might include the number of depen -
dents, personal tax status, health, liquidity needs, risk tolerance, amount of wealth 
beyond that represented in the portfolio, and extent to which compensation and other 
income provide for current income needs. With respect to an institutional client, such

changes might relate to the magnitude of unfunded liabilities in a pension fund, the 
withdrawal privileges in an employee savings plan, or the distribution requirements 
of a charitable foundation. Without efforts to update information concerning client 
factors, one or more factors could change without the investment manager’s knowledge.
Suitability review can be done most effectively when the client fully discloses his 
or her complete financial portfolio, including those portions not managed by the 
member or candidate. If clients withhold information about their financial portfolios, 
the suitability analysis conducted by members and candidates cannot be expected to 
be complete; it must be based on the information provided.
The Need for Diversification
The investment profession has long recognized that combining several different 
investments is likely to provide a more acceptable level of risk exposure than having

all assets in a single investment. The unique characteristics (or risks) of an individual 
investment may become partially or entirely neutralized when it is combined with 
other individual investments within a portfolio. Some reasonable amount of diversifi -
cation is thus the norm for many portfolios, especially those managed by individuals 
or institutions that have some degree of legal fiduciary responsibility.
An investment with high relative risk on its own may be a suitable investment in 
the context of the entire portfolio or when the client’s stated objectives contemplate 
speculative or risky investments. The manager may be responsible for only a portion of 
the client’s total portfolio, or the client may not have provided a full financial picture. 
Members and candidates can be responsible for assessing the suitability of an invest -
ment only on the basis of the information and criteria actually provided by the client.
Addressing Unsolicited Trading Requests

Members and candidates may receive requests from a client for trades that do not 
properly align with the risk and return objectives outlined in the client’s investment 
policy statement. These transaction requests may be based on the client’s individual 
biases or professional experience. Members and candidates will need to make rea -
sonable efforts to balance their clients’ trading requests with their responsibilities to 
follow the agreed-  on investment policy statement.
In cases of unsolicited trade requests that a member or candidate knows are unsuit -
able for a client, the member or candidate should refrain from making the trade until 
he or she discusses the concerns with the client. The discussions and resulting actions 
may encompass a variety of scenarios depending on how the requested unsuitable 
investment relates to the client’s full portfolio.
Many times, an unsolicited request may be expected to have only a minimum impact

on the entire portfolio because the size of the requested trade is small or the trade 
would result in a limited change to the portfolio’s risk profile. In discussing the trade, 
the member or candidate should focus on educating the investor on how the request

Standard III: Duties to Clients 121
deviates from the current policy statement. Following the discussion, the member or 
candidate may follow his or her firm’s policies regarding the necessary client approval 
for executing unsuitable trades. At a minimum, the client should acknowledge the 
discussion and accept the conditions that make the recommendation unsuitable.
Should the unsolicited request be expected to have a material impact on the port -
folio, the member or candidate should use this opportunity to update the investment 
policy statement. Doing so would allow the client to fully understand the potential 
effect of the requested trade on his or her current goals or risk levels. 
Members and candidates may have some clients who decline to modify their 
policy statements while insisting an unsolicited trade be made. In such instances, 
members or candidates will need to evaluate the effectiveness of their services to the

client. The options available to the members or candidates will depend on the services 
provided by their employer. Some firms may allow for the trade to be executed in a 
new unmanaged account. If alternative options are not available, members and can -
didates ultimately will need to determine whether they should continue the advisory 
arrangement with the client. 
Managing to an Index or Mandate
Some members and candidates do not manage money for individuals but are respon -
sible for managing a fund to an index or an expected mandate. The responsibility of 
these members and candidates is to invest in a manner consistent with the stated 
mandate. For example, a member or candidate who serves as the fund manager for a 
large-  cap income fund would not be following the fund mandate by investing heavily 
in small-  cap or start-  up companies whose stock is speculative in nature. Members 
and candidates who manage pooled assets to a specific mandate are not responsible

for determining the suitability of the fund  as an investment for investors who may be 
purchasing shares in the fund. The responsibility for determining the suitability of an 
investment for clients can be conferred only on members and candidates who have 
an advisory relationship with clients.
Investment Policy Statement
To fulfill the basic provisions of Standard III(C), a member or candidate should put 
the needs and circumstances of each client and the client’s investment objectives into 
a written investment policy statement. In formulating an investment policy for the 
client, the member or candidate should take the following into consideration:
■■client identification—(1) type and nature of client, (2) the existence of separate 
beneficiaries, and (3) approximate portion of total client assets that the member 
or candidate is managing;
■■investor objectives—(1) return objectives (income, growth in principal, main -

tenance of purchasing power) and (2) risk tolerance (suitability, stability of 
values);
■■investor constraints—(1) liquidity needs, (2) expected cash flows (patterns of 
additions and/or withdrawals), (3) investable funds (assets and liabilities or 
other commitments), (4) time horizon, (5) tax considerations, (6) regulatory and 
legal circumstances, (7) investor preferences, prohibitions, circumstances, and 
unique needs, and (8) proxy voting responsibilities and guidance; and
■■performance measurement benchmarks.

Reading 3 ■ Guidance for Standards I–VII 122
Regular Updates
The investor’s objectives and constraints should be maintained and reviewed period -
ically to reflect any changes in the client’s circumstances. Members and candidates 
should regularly compare client constraints with capital market expectations to arrive 
at an appropriate asset allocation. Changes in either factor may result in a fundamen -
tal change in asset allocation. Annual review is reasonable unless business or other 
reasons, such as a major change in market conditions, dictate more frequent review. 
Members and candidates should document attempts to carry out such a review if 
circumstances prevent it.
Suitability Test Policies
With the increase in regulatory required suitability tests, members and candidates 
should encourage their firms to develop related policies and procedures. The proce -
dures will differ according to the size of the firm and the scope of the services offered 
to its clients.

The test procedures should require the investment professional to look beyond 
the potential return of the investment and include the following:
■■an analysis of the impact on the portfolio’s diversification,
■■a comparison of the investment risks with the client’s assessed risk tolerance, 
and
■■the fit of the investment with the required investment strategy.
Example 1 (Investment Suitability—Risk Profile):
Caleb Smith, an investment adviser, has two clients: Larry Robertson, 60 years old, and 
Gabriel Lanai, 40 years old. Both clients earn roughly the same salary, but Robertson 
has a much higher risk tolerance because he has a large asset base. Robertson is willing 
to invest part of his assets very aggressively; Lanai wants only to achieve a steady rate 
of return with low volatility to pay for his children’s education. Smith recommends 
investing 20% of both portfolios in zero-  yield, small-  cap, high-  technology equity issues.

Comment : In Robertson’s case, the investment may be appropriate because 
of his financial circumstances and aggressive investment position, but this 
investment is not suitable for Lanai. Smith is violating Standard III(C) by 
applying Robertson’s investment strategy to Lanai because the two clients’ 
financial circumstances and objectives differ.
Example 2 (Investment Suitability—Entire Portfolio):
Jessica McDowell, an investment adviser, suggests to Brian Crosby, a risk-  averse 
client, that covered call options be used in his equity portfolio. The purpose would 
be to enhance Crosby’s income and partially offset any untimely depreciation in the 
portfolio’s value should the stock market or other circumstances affect his holdings 
unfavorably. McDowell educates Crosby about all possible outcomes, including the 
risk of incurring an added tax liability if a stock rises in price and is called away and, 
conversely, the risk of his holdings losing protection on the downside if prices drop

sharply.
Comment : When determining suitability of an investment, the primary 
focus should be the characteristics of the client’s entire portfolio, not the 
characteristics of single securities on an issue-  by- issue basis. The basic char -
acteristics of the entire portfolio will largely determine whether investment

Standard III: Duties to Clients 123
recommendations are taking client factors into account. Therefore, the most 
important aspects of a particular investment are those that will affect the 
characteristics of the total portfolio. In this case, McDowell properly con -
siders the investment in the context of the entire portfolio and thoroughly 
explains the investment to the client.
Example 3 (IPS Updating):
In a regular meeting with client Seth Jones, the portfolio managers at Blue Chip 
Investment Advisors are careful to allow some time to review his current needs and 
circumstances. In doing so, they learn that some significant changes have recently 
taken place in his life. A wealthy uncle left Jones an inheritance that increased his net 
worth fourfold, to US$1 million.
Comment : The inheritance has significantly increased Jones’s ability (and 
possibly his willingness) to assume risk and has diminished the average 
yield required to meet his current income needs. Jones’s financial circum -

stances have definitely changed, so Blue Chip managers must update Jones’s 
investment policy statement to reflect how his investment objectives have 
changed. Accordingly, the Blue Chip portfolio managers should consider 
a somewhat higher equity ratio for his portfolio than was called for by the 
previous circumstances, and the managers’ specific common stock recom -
mendations might be heavily tilted toward low-  yield, growth-  oriented issues.
Example 4 (Following an Investment Mandate):
Louis Perkowski manages a high-  income mutual fund. He purchases zero-  dividend 
stock in a financial services company because he believes the stock is undervalued 
and is in a potential growth industry, which makes it an attractive investment.
Comment : A zero-  dividend stock does not seem to fit the mandate of the 
fund that Perkowski is managing. Unless Perkowski’s investment fits within 
the mandate or is within the realm of allowable investments the fund has

made clear in its disclosures, Perkowski has violated Standard III(C).
Example 5 (IPS Requirements and Limitations):
Max Gubler, chief investment officer of a property/casualty insurance subsidiary of a 
large financial conglomerate, wants to improve the diversification of the subsidiary’s 
investment portfolio and increase its returns. The subsidiary’s investment policy state -
ment provides for highly liquid investments, such as large-  cap equities and government, 
supranational, and corporate bonds with a minimum credit rating of AA and maturity 
of no more than five years. In a recent presentation, a venture capital group offered 
very attractive prospective returns on some of its private equity funds that provide seed 
capital to ventures. An exit strategy was already contemplated, but investors would 
have to observe a minimum three-  year lockup period and a subsequent laddered exit 
option for a maximum of one-  third of their shares per year. Gubler does not want to

miss this opportunity. After extensive analysis, with the intent to optimize the return 
on the equity assets within the subsidiary’s current portfolio, he invests 4% in this 
seed fund, leaving the portfolio’s total equity exposure still well below its upper limit.
Comment : Gubler is violating Standard  III(A)–Loyalty, Prudence, and 
Care as well as Standard III(C). His new investment locks up part of the 
subsidiary’s assets for at least three years and up to as many as five years 
and possibly beyond. The IPS requires investments in highly liquid invest -
ments and describes accepted asset classes; private equity investments with

Reading 3 ■ Guidance for Standards I–VII 124
a lockup period certainly do not qualify. Even without a lockup period, 
an asset class with only an occasional, and thus implicitly illiquid, market 
may not be suitable for the portfolio. Although an IPS typically describes 
objectives and constraints in great detail, the manager must also make 
every effort to understand the client’s business and circumstances. Doing 
so should enable the manager to recognize, understand, and discuss with 
the client other factors that may be or may become material in the invest -
ment management process.
Example 6 (Submanager and IPS Reviews):
Paul  Ostrowski’s investment management  business has grown significantly over the 
past couple of years, and some clients want to diversify internationally. Ostrowski 
decides to find a submanager to handle the expected international investments. Because 
this will be his first subadviser, Ostrowski uses the CFA Institute model “request for

proposal” to design a questionnaire for his search. By his deadline, he receives seven 
completed questionnaires from a variety of domestic and international firms trying 
to gain his business. Ostrowski reviews all the applications in detail and decides to 
select the firm that charges the lowest fees because doing so will have the least impact 
on his firm’s bottom line.
Comment : When selecting an external manager or subadviser, Ostrowski 
needs to ensure that the new manager’s services are appropriate for his 
clients. This due diligence includes comparing the risk profile of the clients 
with the investment strategy of the manager. In basing the decision on the 
fee structure alone, Ostrowski may be violating Standard III(C).
When clients ask to diversify into international products, it is an 
appropriate time to review and update the clients’ IPSs. Ostrowski’s review 
may determine that the risk of international investments modifies the risk

profiles of the clients or does not represent an appropriate investment.
See also Standard V(A)–Diligence and Reasonable Basis for further dis -
cussion of the review process needed in selecting appropriate submanagers.
Example 7 (Investment Suitability—Risk Profile):
Samantha Snead, a portfolio manager for Thomas Investment Counsel, Inc., special -
izes in managing public retirement funds and defined benefit pension plan accounts, 
all of which have long-  term investment objectives. A year ago, Snead’s employer, in 
an attempt to motivate and retain key investment professionals, introduced a bonus 
compensation system that rewards portfolio managers on the basis of quarterly per -
formance relative to their peers and to certain benchmark indexes. In an attempt to 
improve the short-  term performance of her accounts, Snead changes her investment 
strategy and purchases several high-  beta stocks for client portfolios. These purchases

are seemingly contrary to the clients’ investment policy statements. Following their 
purchase, an officer of Griffin Corporation, one of Snead’s pension fund clients, asks 
why Griffin Corporation’s portfolio seems to be dominated by high-  beta stocks of 
companies that often appear among the most actively traded issues. No change in 
objective or strategy has been recommended by Snead during the year.
Comment : Snead violated Standard III(C) by investing the clients’ assets 
in high-  beta stocks. These high-  risk investments are contrary to the long-  
term risk profile established in the clients’ IPSs. Snead has changed the 
investment strategy of the clients in an attempt to reap short-  term rewards 
offered by her firm’s new compensation arrangement, not in response to 
changes in clients’ investment policy statements.

Standard III: Duties to Clients 125
Example 8 (Investment Suitability):
Andre Shrub owns and operates Conduit, an investment advisory firm. Prior to opening 
Conduit, Shrub was an account manager with Elite Investment, a hedge fund man -
aged by his good friend Adam Reed. To attract clients to a new Conduit fund, Shrub 
offers lower-  than-  normal management fees. He can do so because the fund consists 
of two top-  performing funds managed by Reed. Given his personal friendship with 
Reed and the prior performance record of these two funds, Shrub believes this new 
fund is a winning combination for all parties. Clients quickly invest with Conduit to 
gain access to the Elite funds. No one is turned away because Conduit is seeking to 
expand its assets under management.
Comment : Shrub has violated Standard  III(C) because the risk profile 
of the new fund may not be suitable for every client. As an investment 
adviser, Shrub needs to establish an investment policy statement for each

client and recommend only investments that match each client’s risk and 
return profile in the IPS. Shrub is required to act as more than a simple 
sales agent for Elite. 
Although Shrub cannot disobey the direct request of a client to purchase 
a specific security, he should fully discuss the risks of a planned purchase 
and provide reasons why it might not be suitable for a client. This require -
ment may lead members and candidates to decline new customers if those 
customers’ requested investment decisions are significantly out of line with 
their stated requirements.
Standard III(D) Performance Presentation
When communicating investment performance information, Members and Candidates 
must make reasonable efforts to ensure that it is fair, accurate, and complete.
Guidance
Standard III(D) requires members and candidates to provide credible performance 
information to clients and prospective clients and to avoid misstating performance

or misleading clients and prospective clients about the investment performance of 
members or candidates or their firms. This standard encourages full disclosure of 
investment performance data to clients and prospective clients.
Standard III(D) covers any practice that would lead to misrepresentation of a mem -
ber’s or candidate’s performance record, whether the practice involves performance 
presentation or performance measurement. This standard prohibits misrepresentations 
of past performance or reasonably expected performance. A member or candidate 
must give a fair and complete presentation of performance information whenever 
communicating data with respect to the performance history of individual accounts, 
composites or groups of accounts, or composites of an analyst’s or firm’s performance 
results. Furthermore, members and candidates should not state or imply that clients 
will obtain or benefit from a rate of return that was generated in the past.

Reading 3 ■ Guidance for Standards I–VII 126
The requirements of this standard are not limited to members and candidates 
managing separate accounts. Whenever a member or candidate provides performance 
information for which the manager is claiming responsibility, such as for pooled funds, 
the history must be accurate. Research analysts promoting the success or accuracy of 
their recommendations must ensure that their claims are fair, accurate, and complete.
If the presentation is brief, the member or candidate must make available to clients 
and prospects, on request, the detailed information supporting that communication. 
Best practice dictates that brief presentations include a reference to the limited nature 
of the information provided.
Apply the GIPS Standards 
For members and candidates who are showing the performance history of the assets 
they manage, compliance with the GIPS standards is the best method to meet their

obligations under Standard III(D). Members and candidates should encourage their 
firms to comply with the GIPS standards.
Compliance without Applying GIPS Standards
Members and candidates can also meet their obligations under Standard III(D) by
■■considering the knowledge and sophistication of the audience to whom a per -
formance presentation is addressed,
■■presenting the performance of the weighted composite of similar portfolios 
rather than using a single representative account,
■■including terminated accounts as part of performance history with a clear indi -
cation of when the accounts were terminated,
■■including disclosures that fully explain the performance results being reported 
(for example, stating, when appropriate, that results are simulated when model 
results are used, clearly indicating when the performance record is that of a 
prior entity, or disclosing whether the performance is gross of fees, net of fees, 
or after tax), and

■■maintaining the data and records used to calculate the performance being 
presented.
Example 1 (Performance Calculation and Length of Time):
Kyle Taylor of Taylor Trust Company, noting the performance of Taylor’s common 
trust fund for the past two years, states in a brochure sent to his potential clients, 
“You can expect steady 25% annual compound growth of the value of your investments 
over the year. ” Taylor Trust’s common trust fund did increase at the rate of 25% per 
year for the past year, which mirrored the increase of the entire market. The fund has 
never averaged that growth for more than one year, however, and the average rate of 
growth of all of its trust accounts for five years is 5% per year.
Comment : Taylor’s brochure is in violation of Standard  III(D). Taylor 
should have disclosed that the 25% growth occurred only in one year. 
Additionally, Taylor did not include client accounts other than those in

the firm’s common trust fund. A general claim of firm performance should 
take into account the performance of all categories of accounts. Finally, by

Standard III: Duties to Clients 127
stating that clients can expect a steady 25% annual compound growth rate, 
Taylor is also violating Standard I(C)–Misrepresentation, which prohibits 
assurances or guarantees regarding an investment.
Example 2 (Performance Calculation and Asset Weighting):
Anna Judd, a senior partner of Alexander Capital Management, circulates a perfor -
mance report for the capital appreciation accounts for the years 1988 through 2004. 
The firm claims compliance with the GIPS standards. Returns are not calculated in 
accordance with the requirements of the GIPS standards, however, because the com -
posites are not asset weighted.
Comment : Judd is in violation of Standard III(D). When claiming compli -
ance with the GIPS standards, firms must meet all of the requirements, 
make mandatory disclosures, and meet any other requirements that apply 
to that firm’s specific situation. Judd’s violation is not from any misuse of 
the data but from a false claim of GIPS compliance.

Example 3 (Performance Presentation and Prior Fund/Employer):
Aaron McCoy is vice president and managing partner of the equity investment group 
of Mastermind Financial Advisors, a new business. Mastermind recruited McCoy 
because he had a proven six-  year track record with G&P Financial. In developing 
Mastermind’s advertising and marketing campaign, McCoy prepares an advertisement 
that includes the equity investment performance he achieved at G&P Financial. The 
advertisement for Mastermind does not identify the equity performance as being 
earned while at G&P . The advertisement is distributed to existing clients and pro -
spective clients of Mastermind.
Comment : McCoy has violated Standard III(D) by distributing an adver -
tisement that contains material misrepresentations about the historical 
performance of Mastermind. Standard III(D) requires that members and 
candidates make every reasonable effort to ensure that performance infor -

mation is a fair, accurate, and complete representation of an individual’s 
or firm’s performance. As a general matter, this standard does not prohibit 
showing past performance of funds managed at a prior firm as part of a 
performance track record as long as showing that record is accompanied 
by appropriate disclosures about where the performance took place and 
the person’s specific role in achieving that performance. If McCoy chooses 
to use his past performance from G&P in Mastermind’s advertising, he 
should make full disclosure of the source of the historical performance.
Example 4 (Performance Presentation and Simulated Results):
Jed Davis has developed a mutual fund selection product based on historical informa -
tion from the 1990–95 period. Davis tested his methodology by applying it retroactively 
to data from the 1996–2003 period, thus producing simulated performance results for 
those years. In January 2004, Davis’s employer decided to offer the product and Davis

began promoting it through trade journal advertisements and direct dissemination 
to clients. The advertisements included the performance results for the 1996–2003 
period but did not indicate that the results were simulated.
Comment : Davis violated Standard  III(D) by failing to clearly identify 
simulated performance results. Standard  III(D) prohibits members and 
candidates from making any statements that misrepresent the performance 
achieved by them or their firms and requires members and candidates

Reading 3 ■ Guidance for Standards I–VII 128
to make every reasonable effort to ensure that performance information 
presented to clients is fair, accurate, and complete. Use of simulated results 
should be accompanied by full disclosure as to the source of the performance 
data, including the fact that the results from 1995 through 2003 were the 
result of applying the model retroactively to that time period.
Example 5 (Performance Calculation and Selected Accounts Only):
In a presentation prepared for prospective clients, William Kilmer shows the rates 
of return realized over a five-  year period by a “composite” of his firm’s discretionary 
accounts that have a “balanced” objective. This composite, however, consisted of only a 
few of the accounts that met the balanced criterion set by the firm, excluded accounts 
under a certain asset level without disclosing the fact of their exclusion, and included 
accounts that did not have the balanced mandate because those accounts would boost

the investment results. In addition, to achieve better results, Kilmer manipulated the 
narrow range of accounts included in the composite by changing the accounts that 
made up the composite over time.
Comment : Kilmer violated Standard III(D) by misrepresenting the facts in 
the promotional material sent to prospective clients, distorting his firm’s 
performance record, and failing to include disclosures that would have 
clarified the presentation.
Example 6 (Performance Attribution Changes):
Art Purell is reviewing the quarterly performance attribution reports for distribu -
tion to clients. Purell works for an investment management firm with a bottom-  up, 
fundamentals-  driven investment process that seeks to add value through stock selec -
tion. The attribution methodology currently compares each stock with its sector. The 
attribution report indicates that the value added this quarter came from asset allocation 
and that stock selection contributed negatively to the calculated return.

Through running several different scenarios, Purell discovers that calculating 
attribution by comparing each stock with its industry and then rolling the effect to 
the sector level improves the appearance of the manager’s stock selection activities. 
Because the firm defines the attribution terms and the results better reflect the stated 
strategy, Purell recommends that  the client reports should use the revised methodology.
Comment : Modifying the attribution methodology without proper notifi -
cations to clients would fail to meet the requirements of Standard III(D). 
Purrell’s recommendation is being done solely for the interest of the firm 
to improve its perceived ability to meet the stated investment strategy. 
Such changes are unfair to clients and obscure the facts regarding the 
firm’s abilities.
Had Purell believed the new methodology offered improvements to the 
original model, then he would have needed to report the results of both

calculations to the client. The report should also include the reasons why 
the new methodology is preferred, which would allow the client to make a 
meaningful comparison to prior results and provide a basis for comparing 
future attributions.
Example 7 (Performance Calculation Methodology Disclosure):
While developing a new reporting package for existing clients, Alisha Singh, a perfor -
mance analyst, discovers that her company’s new system automatically calculates both 
time-  weighted and money-  weighted returns. She asks the head of client services and 
retention which value would be preferred given that the firm has various investment

Standard III: Duties to Clients 129
strategies that include bonds, equities, securities without leverage, and alternatives. 
Singh is told not to label the return value so that the firm may show whichever value 
is greatest for the period.
Comment : Following these instructions would lead to Singh violating 
Standard III(D). In reporting inconsistent return values, Singh would not 
be providing complete information to the firm’s clients. Full information is 
provided when clients have sufficient information to judge the performance 
generated by the firm. 
Example 8 (Performance Calculation Methodology Disclosure):
Richmond Equity Investors manages a long–short equity fund in which clients can trade 
once a week (on Fridays). For transparency reasons, a daily net asset value of the fund 
is calculated by Richmond. The monthly fact sheets of the fund report month-  to- date 
and year-  to- date performance. Richmond publishes the performance based on the

higher of the last trading day of the month (typically, not the last business day) or the 
last business day of the month as determined by Richmond. The fact sheet mentions 
only that the data are as of the end of the month, without giving the exact date. Maggie 
Clark, the investment performance analyst in charge of the calculations, is concerned 
about the frequent changes and asks her supervisor whether they are appropriate.
Comment : Clark’s actions in questioning the changing performance metric 
comply with Standard III(D). She has shown concern that these changes 
are not presenting an accurate and complete picture of the performance 
generated.
Standard III(E) Preservation of Confidentiality
Members and Candidates must keep information about current, former, and prospective 
clients confidential unless:
1 The information concerns illegal activities on the part of the client;
2 d isclosure is required by law; or
Guidance

Guidance
■■Status of Client
■■Compliance with Laws
■■Electronic Information and Security
■■Professional Conduct Investigations by CFA Institute
Standard III(E) requires that members and candidates preserve the confidentiality of 
information communicated to them by their clients, prospective clients, and former 
clients. This standard is applicable when (1) the member or candidate receives infor -
mation because of his or her special ability to conduct a portion of the client’s business 
or personal affairs and (2) the member or candidate receives information that arises

Reading 3 ■ Guidance for Standards I–VII 130
from or is relevant to that portion of the client’s business that is the subject of the 
special or confidential relationship. If disclosure of the information is required by law 
or the information concerns illegal activities by the client, however, the member or 
candidate may have an obligation to report the activities to the appropriate authorities.
Status of Client
This standard protects the confidentiality of client information even if the person 
or entity is no longer a client of the member or candidate. Therefore, members and 
candidates must continue to maintain the confidentiality of client records even after 
the client relationship has ended. If a client or former client expressly authorizes the 
member or candidate to disclose information, however, the member or candidate may 
follow the terms of the authorization and provide the information.
Compliance with Laws

As a general matter, members and candidates must comply with applicable law. If appli -
cable law requires disclosure of client information in certain circumstances, members 
and candidates must comply with the law. Similarly, if applicable law requires members 
and candidates to maintain confidentiality, even if the information concerns illegal 
activities on the part of the client, members and candidates should not disclose such 
information. Additionally, applicable laws, such as inter-  departmental communication 
restrictions within financial institutions, can impose limitations on information flow 
about a client within an entity that may lead to a violation of confidentiality. When 
in doubt, members and candidates should consult with their employer’s compliance 
personnel or legal counsel before disclosing confidential information about clients.
Electronic Information and Security
Because of the ever-  increasing volume of electronically stored information, members

and candidates need to be particularly aware of possible accidental disclosures. Many 
employers have strict policies about how to electronically communicate sensitive 
client information and store client information on personal laptops, mobile devices, 
or portable disk/flash drives. In recent years, regulatory authorities have imposed 
stricter data security laws applying to the use of mobile remote digital communication, 
including the use of social media, that must be considered. Standard III(E) does not 
require members or candidates to become experts in information security technology, 
but they should have a thorough understanding of the policies of their employer. The 
size and operations of the firm will lead to differing policies for ensuring the security of 
confidential information maintained within the firm. Members and candidates should 
encourage their firm to conduct regular periodic training on confidentiality proce -

dures for all firm personnel, including portfolio associates, receptionists, and other 
non-  investment staff who have routine direct contact with clients and their records.
Professional Conduct Investigations by CFA Institute
The requirements of Standard III(E) are not intended to prevent members and can -
didates from cooperating with an investigation by the CFA Institute Professional 
Conduct Program (PCP). When permissible under applicable law, members and 
candidates shall consider the PCP an extension of themselves when requested to 
provide information about a client in support of a PCP investigation into their own 
conduct. Members and candidates are encouraged to cooperate with investigations 
into the conduct of others. Any information turned over to the PCP is kept in the 
strictest confidence. Members and candidates will not be considered in violation of 
this standard by forwarding confidential information to the PCP .

Standard III: Duties to Clients 131
The simplest, most conservative, and most effective way to comply with Standard III(E) 
is to avoid disclosing any information received from a client except to authorized 
fellow employees who are also working for the client. In some instances, however, a 
member or candidate may want to disclose information received from clients that is 
outside the scope of the confidential relationship and does not involve illegal activities. 
Before making such a disclosure, a member or candidate should ask the following:
■■In what context was the information disclosed? If disclosed in a discussion of 
work being performed for the client, is the information relevant to the work?
■■Is the information background material that, if disclosed, will enable the mem -
ber or candidate to improve service to the client?
Members and candidates need to understand and follow their firm’s electronic infor -

mation communication and storage procedures. If the firm does not have procedures 
in place, members and candidates should encourage the development of procedures 
that appropriately reflect the firm’s size and business operations.
Communicating with Clients 
Technological changes are constantly enhancing the methods that are used to com -
municate with clients and prospective clients. Members and candidates should make 
reasonable efforts to ensure that firm-  supported communication methods and com -
pliance procedures follow practices designed for preventing accidental distribution 
of confidential information. Given the rate at which technology changes, a regular 
review of privacy protection measures is encouraged.
Members and candidates should be diligent in discussing with clients the appro -
priate methods for providing confidential information. It is important to convey to cli -
ents that not all firm-  sponsored resources may be appropriate for such communications.

Example 1 (Possessing Confidential Information):
Sarah Connor, a financial analyst employed by Johnson Investment Counselors, Inc., 
provides investment advice to the trustees of City Medical Center. The trustees have 
given her a number of internal reports concerning City Medical’s needs for physical 
plant renovation and expansion. They have asked Connor to recommend investments 
that would generate capital appreciation in endowment funds to meet projected capital 
expenditures. Connor is approached by a local businessman, Thomas Kasey, who is 
considering a substantial contribution either to City Medical Center or to another 
local hospital. Kasey wants to find out the building plans of both institutions before 
making a decision, but he does not want to speak to the trustees.
Comment : The trustees gave Connor the internal reports so she could 
advise them on how to manage their endowment funds. Because the infor -

mation in the reports is clearly both confidential and within the scope of 
the confidential relationship, Standard III(E) requires that Connor refuse 
to divulge information to Kasey.
Example 2 (Disclosing Confidential Information):
Lynn Moody is an investment officer at the Lester Trust Company. She has an advisory 
customer who has talked to her about giving approximately US$50,000 to charity to 
reduce her income taxes. Moody is also treasurer of the Home for Indigent Widows 
(HIW), which is planning its annual giving campaign. HIW hopes to expand its list

Reading 3 ■ Guidance for Standards I–VII 132
of prospects, particularly those capable of substantial gifts. Moody recommends that 
HIW’s vice president for corporate gifts call on her customer and ask for a donation 
in the US$50,000 range.
Comment : Even though the attempt to help the Home for Indigent Widows 
was well intended, Moody violated Standard III(E) by revealing confidential 
information about her client.
Example 3 (Disclosing Possible Illegal Activity):
Government officials approach Casey Samuel, the portfolio manager for Garcia 
Company’s pension plan, to examine pension fund records. They tell her that Garcia’s 
corporate tax returns are being audited and the pension fund is being reviewed. Two 
days earlier, Samuel had learned in a regular investment review with Garcia officers 
that potentially excessive and improper charges were being made to the pension plan 
by Garcia. Samuel consults her employer’s general counsel and is advised that Garcia

has probably violated tax and fiduciary regulations and laws.
Comment : Samuel should inform her supervisor of these activities, and her 
employer should take steps, with Garcia, to remedy the violations. If that 
approach is not successful, Samuel and her employer should seek advice of 
legal counsel to determine the appropriate steps to be taken. Samuel may 
well have a duty to disclose the evidence she has of the continuing legal 
violations and to resign as asset manager for Garcia.
Example 4 (Disclosing Possible Illegal Activity):
David Bradford manages money for a family-  owned real estate development corpora -
tion. He also manages the individual portfolios of several of the family members and 
officers of the corporation, including the chief financial officer (CFO). Based on the 
financial records of the corporation and some questionable practices of the CFO that 
Bradford has observed, Bradford believes that the CFO is embezzling money from

the corporation and putting it into his personal investment account.
Comment : Bradford should check with his firm’s compliance department 
or appropriate legal counsel to determine whether applicable securities 
regulations require reporting the CFO’s financial records.
Example 5 (Accidental Disclosure of Confidential Information):
Lynn Moody is an investment officer at the Lester Trust Company (LTC). She has 
stewardship of a significant number of individually managed taxable accounts. In 
addition to receiving quarterly written reports, about a dozen high-  net- worth individ -
uals have indicated to Moody a willingness to receive communications about overall 
economic and financial market outlooks directly from her by way of a social media 
platform. Under the direction of her firm’s technology and compliance departments, 
she established a new group page on an existing social media platform specifically 
for her clients. In the instructions provided to clients, Moody asked them to “join”

the group so they may be granted access to the posted content. The instructions also 
advised clients that all comments posted would be available to the public and thus the 
platform was not an appropriate method for communicating personal or confidential 

Standard IV: Duties to Employers 133
Six months later, in early January, Moody posted LTC’s year-  end “Market Outlook. ” 
The report outlined a new asset allocation strategy that the firm is adding to its recom -
mendations in the new year. Moody introduced the publication with a note informing 
her clients that she would be discussing the changes with them individually in their 
upcoming meetings.
One of Moody’s clients responded directly on the group page that his family 
recently experienced a major change in their financial profile. The client described 
highly personal and confidential details of the event. Unfortunately, all clients that 
were part of the group were also able to read the detailed posting until Moody was 
able to have the comment removed. 
Comment : Moody has taken reasonable steps for protecting the confiden -
tiality of client information while using the social media platform. She 
provided instructions clarifying that all information posted to the site would

be publically viewable to all group members and warned against using this 
method for communicating confidential information. The accidental disclo -
sure of confidential information by a client is not under Moody’s control. 
Her actions to remove the information promptly once she became aware 
further align with Standard III(E). 
In understanding the potential sensitivity clients express surrounding 
the confidentiality of personal information, this event highlights a need 
for further training. Moody might advocate for additional warnings or 
controls for clients when they consider using social media platforms for 
two-  way communications.
STANDARD IV: DUTIES TO EMPLOYERS
Standard IV(A) Loyalty
In matters related to their employment, Members and Candidates must act for the benefit 
of their employer and not deprive their employer of the advantage of their skills and 
abilities, divulge confidential information, or otherwise cause harm to their employer.
Guidance

Guidance
■■Employer Responsibilities
■■Independent Practice
■■Leaving an Employer
■■Use of  Social Media
■■Whistleblowing
■■Nature of Employment
Standard  IV(A) requires members and candidates to protect the interests of their 
firm by refraining from any conduct that would injure the firm, deprive it of profit, or 
deprive it of the member’s or candidate’s skills and ability. Members and candidates

Reading 3 ■ Guidance for Standards I–VII 134
must always place the interests of clients above the interests of their employer but 
should also consider the effects of their conduct on the sustainability and integrity of 
the employer firm. In matters related to their employment, members and candidates 
must not engage in conduct that harms the interests of their employer. Implicit in 
this standard is the obligation of members and candidates to comply with the policies 
and procedures established by their employers that govern the employer–employee 
relationship—to the extent that such policies and procedures do not conflict with 
applicable laws, rules, or regulations or the Code and Standards.
This standard is not meant to be a blanket requirement to place employer interests 
ahead of personal interests in all matters. The standard does not require members and 
candidates to subordinate important personal and family obligations to their work.

Members and candidates should enter into a dialogue with their employer about 
balancing personal and employment obligations when personal matters may interfere 
with their work on a regular or significant basis.
Employer Responsibilities
The employer–employee relationship imposes duties and responsibilities on both 
parties. Employers must recognize the duties and responsibilities that they owe to 
their employees if they expect to have content and productive employees.
Members and candidates are encouraged to provide their employer with a copy 
of the Code and Standards. These materials will inform the employer of the respon -
sibilities of a CFA Institute member or a candidate in the CFA Program. The Code 
and Standards also serve as a basis for questioning employer policies and practices 
that conflict with these responsibilities.
Employers are not obligated to adhere to the Code and Standards. In expecting 
to retain competent employees who are members and candidates, however, they

should not develop conflicting policies and procedures. The employer is responsible 
for a positive working environment, which includes an ethical workplace. Senior 
management has the additional responsibility to devise compensation structures and 
incentive arrangements that do not encourage unethical behavior.
Independent Practice 
Included in Standard IV(A) is the requirement that members and candidates abstain 
from independent competitive activity that could conflict with the interests of their 
employer. Although Standard IV(A) does not preclude members or candidates from 
entering into an independent business while still employed, members and candidates 
who plan to engage in independent practice for compensation must notify their 
employer and describe the types of services they will render to prospective independent 
clients, the expected duration of the services, and the compensation for the services. 
Members and candidates should not render services until they receive consent from

their employer to all of the terms of the arrangement. “Practice” means any service that 
the employer currently makes available for remuneration. “Undertaking independent 
practice” means engaging in competitive business, as opposed to making preparations 
to begin such practice.
Leaving an Employer
When members and candidates are planning to leave their current employer, they 
must continue to act in the employer’s best interest. They must not engage in any 
activities that would conflict with this duty until their resignation becomes effective. 
It is difficult to define specific guidelines for those members and candidates who are 
planning to compete with their employer as part of a new venture. The circumstances

Standard IV: Duties to Employers 135
of each situation must be reviewed to distinguish permissible preparations from vio -
lations of duty. Activities that might constitute a violation, especially in combination, 
■■misappropriation of trade secrets,
■■misuse of confidential information,
■■solicitation of the employer’s clients prior to cessation of employment,
■■self-  dealing (appropriating for one’s own property a business opportunity or 
information belonging to one’s employer), and
■■misappropriation of clients or client lists.
A departing employee is generally free to make arrangements or preparations to 
go into a competitive business before terminating the relationship with his or her 
employer as long as such preparations do not breach the employee’s duty of loyalty. 
A member or candidate who is contemplating seeking other employment must not 
contact existing clients or potential clients prior to leaving his or her employer for

purposes of soliciting their business for the new employer. Once notice is provided 
to the employer of the intent to resign, the member or candidate must follow the 
employer’s policies and procedures related to notifying clients of his or her planned 
departure. In addition, the member or candidate must not take records or files to a 
new employer without the written permission of the previous employer.
Once an employee has left the firm, the skills and experience that an employee 
obtained while employed are not “confidential” or “privileged” information. Similarly, 
simple knowledge of the names and existence of former clients is generally not confi -
dential information unless deemed such by an agreement or by law. Standard IV(A) 
does not prohibit experience or knowledge gained at one employer from being used 
at another employer. Firm records or work performed on behalf of the firm that is 
stored in paper copy or electronically for the member’s or candidate’s convenience

while employed, however, should be erased or returned to the employer unless the 
firm gives permission to keep those records after employment ends.
The standard does not prohibit former employees from contacting clients of their 
previous firm as long as the contact information does not come from the records of 
the former employer or violate an applicable “noncompete agreement. ” Members and 
candidates are free to use public information after departing to contact former clients 
without violating Standard IV(A) as long as there is no specific agreement not to do so. 
Employers often require employees to sign noncompete agreements that preclude a 
departing employee from engaging in certain conduct. Members and candidates should 
take care to review the terms of any such agreement when leaving their employer to 
determine what, if any, conduct those agreements may prohibit.
In some markets, there are agreements between employers within an industry that

outline information that departing employees are permitted to take upon resignation, 
such as the “Protocol for Broker Recruiting” in the United States. These agreements 
ease individuals’ transition between firms that have agreed to follow the outlined 
procedures. Members and candidates who move between firms that sign such agree -
ments may rely on the protections provided as long as they faithfully adhere to all 
the procedures outlined. 
For example, under the agreement between many US brokers, individuals are 
allowed to take some general client contact information when departing. To be pro -
tected, a copy of the information the individual is taking must be provided to the 
local management team for review. Additionally, the specific client information may 
only be used by the departing employee and not others employed by the new firm.

Reading 3 ■ Guidance for Standards I–VII 136
Use of Social Media
The growth in various online networking platforms, such as LinkedIn, Twitter, and 
Facebook (commonly referred to as social media platforms), is providing new oppor -
tunities and challenges for businesses. Members and candidates should understand 
and abide by all applicable firm policies and regulations as to the acceptable use of 
social media platforms to interact with clients and prospective clients. This is especially 
important when a member or candidate is planning to leave an employer.
Social media use makes determining how and when departure notification is deliv -
ered to clients more complex. Members and candidates may have developed profiles 
on these platforms that include connections with individuals who are clients of the 
firm, as well as individuals unrelated to their employer. Communications through 
social media platforms that potentially reach current clients should adhere to the

employer’s policies and procedures regarding notification of departing employees.
Social media connections with clients are also raising questions concerning the 
differences between public information and firm property. Specific accounts and user 
profiles of members and candidates may be created for solely professional reasons, 
including firm-  approved accounts for client engagements. Such firm-  approved business-  
related accounts would be considered part of the firm’s assets, thus requiring members 
and candidates to transfer or delete the accounts as directed by their firm’s policies 
and procedures. Best practice for members and candidates is to maintain separate 
accounts for their personal and professional social media activities. Members and 
candidates should discuss with their employers how profiles should be treated when 
a single account includes personal connections and also is used to conduct aspects 
of their professional activities.
Whistleblowing

A member’s or candidate’s personal interests, as well as the interests of his or her 
employer, are secondary to protecting the integrity of capital markets and the interests 
of clients. Therefore, circumstances may arise (e.g., when an employer is engaged in 
illegal or unethical activity) in which members and candidates must act contrary to 
their employer’s interests in order to comply with their duties to the market and clients. 
In such instances, activities that would normally violate a member’s or candidate’s 
duty to his or her employer (such as contradicting employer instructions, violating 
certain policies and procedures, or preserving a record by copying employer records) 
may be justified. Such action would be permitted only if the intent is clearly aimed at 
protecting clients or the integrity of the market, not for personal gain.
Nature of Employment
A wide variety of business relationships exists within the investment industry. For

instance, a member or candidate may be an employee or an independent contractor. 
Members and candidates must determine whether they are employees or independent 
contractors in order to determine the applicability of Standard IV(A). This issue will 
be decided largely by the degree of control exercised by the employing entity over the 
member or candidate. Factors determining control include whether the member’s or 
candidate’s hours, work location, and other parameters of the job are set; whether 
facilities are provided to the member or candidate; whether the member’s or candidate’s 
expenses are reimbursed; whether the member or candidate seeks work from other 
employers; and the number of clients or employers the member or candidate works for.
A member’s or candidate’s duties within an independent contractor relation -
ship are governed by the oral or written agreement between the member and the 
client. Members and candidates should take care to define clearly the scope of their

Standard IV: Duties to Employers 137
responsibilities and the expectations of each client within the context of each rela -
tionship. Once a member or candidate establishes a relationship with a client, the 
member or candidate has a duty to abide by the terms of the agreement.
Employers may establish codes of conduct and operating procedures for their employees 
to follow. Members and candidates should fully understand the policies to ensure that 
they are not in conflict with the Code and Standards. The following topics identify 
policies that members and candidates should encourage their firms to adopt if the 
policies are not currently in place.
Competition Policy
A member or candidate must understand any restrictions placed by the employer 
on offering similar services outside the firm while employed by the firm. The policy 
may outline the procedures for requesting approval to undertake the outside service

or may be a strict prohibition of such service. If a member’s or candidate’s employer 
elects to have its employees sign a noncompete agreement as part of the employment 
agreement, the member or candidate should ensure that the details are clear and fully 
explained prior to signing the agreement.
Termination Policy
Members and candidates should clearly understand the termination policies of their 
employer. Termination policies should establish clear procedures regarding the 
resignation process, including addressing how the termination will be disclosed to 
clients and staff and whether updates posted through social media platforms will be 
allowed. The firm’s policy may also outline the procedures for transferring ongoing 
research and account management responsibilities. Finally, the procedures should 
address agreements that allow departing employees to remove specific client-  related 
information upon resignation.
Incident-  Reporting Procedures

Members and candidates should be aware of their firm’s policies related to whis -
tleblowing and encourage their firm to adopt industry best practices in this area. Many 
firms are required by regulatory mandates to establish confidential and anonymous 
reporting procedures that allow employees to report potentially unethical and illegal 
activities in the firm.
Employee Classification
Members and candidates should understand their status within their employer firm. 
Firms are encouraged to adopt a standardized classification structure (e.g., part time, 
full time, outside contractor) for their employees and indicate how each of the firm’s 
policies applies to each employee class.
Example 1 (Soliciting Former Clients):
Samuel Magee manages pension accounts for Trust Assets, Inc., but has become frus -
trated with the working environment and has been offered a position with Fiduciary

Management. Before resigning from Trust Assets, Magee asks four big accounts to

Reading 3 ■ Guidance for Standards I–VII 138
leave that firm and open accounts with Fiduciary. Magee also persuades several pro -
spective clients to sign agreements with Fiduciary Management. Magee had previously 
made presentations to these prospects on behalf of Trust Assets.
Comment : Magee violated the employee–employer principle requiring 
him to act solely for his employer’s benefit. Magee’s duty is to Trust Assets 
as long as he is employed there. The solicitation of Trust Assets’ current 
clients and prospective clients is unethical and violates Standard IV(A).
Example 2 (Former Employer’s Documents and Files):
James Hightower has been employed by Jason Investment Management Corporation 
for 15 years. He began as an analyst but assumed increasing responsibilities and is 
now a senior portfolio manager and a member of the firm’s investment policy com -
mittee. Hightower has decided to leave Jason Investment and start his own investment

management business. He has been careful not to tell any of Jason’s clients that he is 
leaving; he does not want to be accused of breaching his duty to Jason by soliciting 
Jason’s clients before his departure. Hightower is planning to copy and take with him 
the following documents and information he developed or worked on while at Jason: 
(1) the client list, with addresses, telephone numbers, and other pertinent client 
information; (2) client account statements; (3) sample marketing presentations to 
prospective clients containing Jason’s performance record; (4) Jason’s recommended 
list of securities; (5) computer models to determine asset allocations for accounts 
with various objectives; (6) computer models for stock selection; and (7) personal 
computer spreadsheets for Hightower’s major corporate recommendations, which 
he developed when he was an analyst.
Comment : Except with the consent of their employer, departing mem -

bers and candidates may not take employer property, which includes 
books, records, reports, and other materials, because taking such materials 
may interfere with their employer’s business opportunities. Taking any 
employer records, even those the member or candidate prepared, violates 
Standard IV(A). Employer records include items stored in hard copy or any 
other medium (e.g., home computers, portable storage devices, cell phones).
Example 3 (Addressing Rumors):
Reuben Winston manages all-  equity portfolios at Target Asset Management (TAM), 
a large, established investment counselor. Ten years previously, Philpott & Company, 
which manages a family of global bond mutual funds, acquired TAM in a diversifica -
tion move. After the merger, the combined operations prospered in the fixed-  income 
business but the equity management business at TAM languished. Lately, a few of the 
equity pension accounts that had been with TAM before the merger have terminated

their relationships with TAM. One day, Winston finds on his voice mail the following 
message from a concerned client: “Hey! I just heard that Philpott is close to announc -
ing the sale of your firm’s equity management business to Rugged Life. What is going 
on?” Not being aware of any such deal, Winston and his associates are stunned. Their 
internal inquiries are met with denials from Philpott management, but the rumors 
persist. Feeling left in the dark, Winston contemplates leading an employee buyout 
of TAM’s equity management business.
Comment : An employee-  led buyout of TAM’s equity asset management 
business would be consistent with Standard IV(A) because it would rest 
on the permission of the employer and, ultimately, the clients. In this case,

Standard IV: Duties to Employers 139
however, in which employees suspect the senior managers or principals 
are not truthful or forthcoming, Winston should consult legal counsel to 
determine appropriate action.
Example 4 (Ownership of Completed Prior Work):
Laura Clay, who is unemployed, wants part-  time consulting work while seeking a full-  
time analyst position. During an interview at Bradley Associates, a large institutional 
asset manager, Clay is told that the firm has no immediate research openings but would 
be willing to pay her a flat fee to complete a study of the wireless communications indus -
try within a given period of time. Clay would be allowed unlimited access to Bradley’s 
research files and would be welcome to come to the offices and use whatever support 
facilities are available during normal working hours. Bradley’s research director does 
not seek any exclusivity for Clay’s output, and the two agree to the arrangement on a

handshake. As Clay nears completion of the study, she is offered an analyst job in the 
research department of Winston & Company, a brokerage firm, and she is pondering 
submitting the draft of her wireless study for publication by Winston.
Comment : Although she is under no written contractual obligation to 
Bradley, Clay has an obligation to let Bradley act on the output of her study 
before Winston & Company or Clay uses the information to their advantage. 
That is, unless Bradley gives permission to Clay and waives its rights to her 
wireless report, Clay would be in violation of Standard IV(A) if she were to 
immediately recommend to Winston the same transactions recommended 
in the report to Bradley. Furthermore, Clay must not take from Bradley any 
research file material or other property that she may have used.
Example 5 (Ownership of Completed Prior Work):
Emma Madeline, a recent college graduate and a candidate in the CFA Program,

spends her summer as an unpaid intern at Murdoch and Lowell. The senior managers 
at Murdoch are attempting to bring the firm into compliance with the GIPS standards, 
and Madeline is assigned to assist in its efforts. Two months into her internship, 
Madeline applies for a job at McMillan & Company, which has plans to become GIPS 
compliant. Madeline accepts the job with McMillan. Before leaving Murdoch, she 
copies the firm’s software that she helped develop because she believes this software 
will assist her in her new position.
Comment : Even though Madeline does not receive monetary compensation 
for her services at Murdoch, she has used firm resources in creating the 
software and is considered an employee because she receives compensation 
and benefits in the form of work experience and knowledge. By copying the 
software, Madeline violated Standard IV(A) because she misappropriated 
Murdoch’s property without permission.
Example 6 (Soliciting Former Clients):

Dennis Elliot has hired Sam Chisolm, who previously worked for a competing firm. 
Chisolm left his former firm after 18 years of employment. When Chisolm begins 
working for Elliot, he wants to contact his former clients because he knows them well 
and is certain that many will follow him to his new employer. Is Chisolm in violation 
of Standard IV(A) if he contacts his former clients?
Comment : Because client records are the property of the firm, contact -
ing former clients for any reason through the use of client lists or other 
information taken from a former employer without permission would be a

Reading 3 ■ Guidance for Standards I–VII 140
violation of Standard IV(A). In addition, the nature and extent of the con -
tact with former clients may be governed by the terms of any noncompete 
agreement signed by the employee and the former employer that covers 
contact with former clients after employment.
Simple knowledge of the names and existence of former clients is not 
confidential information, just as skills or experience that an employee 
obtains while employed are not “confidential” or “privileged” information. 
The Code and Standards do not impose a prohibition on the use of expe -
rience or knowledge gained at one employer from being used at another 
employer. The Code and Standards also do not prohibit former employees 
from contacting clients of their previous firm, in the absence of a noncom -
pete agreement. Members and candidates are free to use public information 
about their former firm after departing to contact former clients without 
violating Standard IV(A).

In the absence of a noncompete agreement, as long as Chisolm main -
tains his duty of loyalty to his employer before joining Elliot’s firm, does 
not take steps to solicit clients until he has left his former firm, and does 
not use material from his former employer without its permission after he 
has left, he is not in violation of the Code and Standards.
Example 7 (Starting a New Firm):
Geraldine Allen currently works at a registered investment company as an equity 
analyst. Without notice to her employer, she registers with government authorities to 
start an investment company that will compete with her employer, but she does not 
actively seek clients. Does registration of this competing company with the appropriate 
regulatory authorities constitute a violation of Standard IV(A)?
Comment : Allen’s preparation for the new business by registering with the 
regulatory authorities does not conflict with the work for her employer if

the preparations have been done on Allen’s own time outside the office and 
if Allen will not be soliciting clients for the business or otherwise operating 
the new company until she has left her current employer.
Example 8 (Competing with Current Employer):
Several employees are planning to depart their current employer within a few weeks 
and have been careful to not engage in any activities that would conflict with their 
duty to their current employer. They have just learned that one of their employer’s 
clients has undertaken a request for proposal (RFP) to review and possibly hire a new 
investment consultant. The RFP has been sent to the employer and all of its com -
petitors. The group believes that the new entity to be formed would be qualified to 
respond to the RFP and be eligible for the business. The RFP submission period is likely 
to conclude before the employees’ resignations are effective. Is it permissible for the

group of departing employees to respond to the RFP for their anticipated new firm?
Comment : A group of employees responding to an RFP that their employer is 
also responding to would lead to direct competition between the employees 
and the employer. Such conduct violates Standard IV(A) unless the group 
of employees receives permission from their employer as well as the entity 
sending out the RFP .

Standard IV: Duties to Employers 141
Example 9 (Externally Compensated Assignments):
Alfonso Mota is a research analyst with Tyson Investments. He works part time as a 
mayor for his hometown, a position for which he receives compensation. Must Mota 
seek permission from Tyson to serve as mayor?
Comment : If Mota’s mayoral duties are so extensive and time-  consuming 
that they might detract from his ability to fulfill his responsibilities at Tyson, 
he should discuss his outside activities with his employer and come to a 
mutual agreement regarding how to manage his personal commitments 
with his responsibilities to his employer.
Example 10 (Soliciting Former Clients):
After leaving her employer, Shawna McQuillen establishes her own money management 
business. While with her former employer, she did not sign a noncompete agreement 
that would have prevented her from soliciting former clients. Upon her departure, she

does not take any of her client lists or contact information and she clears her personal 
computer of any employer records, including client contact information. She obtains 
the phone numbers of her former clients through public records and contacts them 
to solicit their business.
Comment : McQuillen is not in violation of Standard IV(A) because she 
has not used information or records from her former employer and is not 
prevented by an agreement with her former employer from soliciting her 
former clients.
Example 11 (Whistleblowing Actions):
Meredith Rasmussen works on a buy-  side trading desk and concentrates on in-  house 
trades for a hedge fund subsidiary managed by a team at the investment management 
firm. The hedge fund has been very successful and is marketed globally by the firm. 
From her experience as the trader for much of the activity of the fund, Rasmussen has 
become quite knowledgeable about the hedge fund’s strategy, tactics, and performance.

When a distinct break in the market occurs, however, and many of the securities 
involved in the hedge fund’s strategy decline markedly in value, Rasmussen observes 
that the reported performance of the hedge fund does not reflect this decline. In her 
experience, the lack of any effect is a very unlikely occurrence. She approaches the head 
of trading about her concern and is told that she should not ask any questions and that 
the fund is big and successful and is not her concern. She is fairly sure something is 
not right, so she contacts the compliance officer, who also tells her to stay away from 
the issue of this hedge fund’s reporting.
Comment : Rasmussen has clearly come upon an error in policies, pro -
cedures, and compliance practices in the firm’s operations. Having been 
unsuccessful in finding a resolution with her supervisor and the compli -
ance officer, Rasmussen should consult the firm’s whistleblowing policy to

determine the appropriate next step toward informing management of her 
concerns. The potentially unethical actions of the investment management 
division are appropriate grounds for further disclosure, so Rasmussen’s 
whistleblowing would not represent a violation of Standard IV(A).
See also Standard I(D)–Misconduct and Standard IV(C)–Responsibilities 
of Supervisors.

Reading 3 ■ Guidance for Standards I–VII 142
Example 12 (Soliciting Former Clients):
Angel Crome has been a private banker for YBSafe Bank for the past eight years. She 
has been very successful and built a considerable client portfolio during that time 
but is extremely frustrated by the recent loss of reputation by her current employer 
and subsequent client insecurity. A locally renowned headhunter contacted Crome a 
few days ago and offered her an interesting job with a competing private bank. This 
bank offers a substantial signing bonus for advisers with their own client portfolios. 
Crome figures that she can solicit at least 70% of her clients to follow her and gladly 
enters into the new employment contract.
Comment : Crome may contact former clients upon termination of her 
employment with YBSafe Bank, but she is prohibited from using client 
records built by and kept with her in her capacity as an employee of YBSafe

Bank. Client lists are proprietary information of her former employer and 
must not be used for her or her new employer’s benefit. The use of writ -
ten, electronic, or any other form of records other than publicly available 
information to contact her former clients at YBSafe Bank will be a violation 
of Standard IV(A).
Example 13 (Notification of Code and Standards):
Krista Smith is a relatively new assistant trader for the fixed-  income desk of a major 
investment bank. She is on a team responsible for structuring collateralized debt 
obligations (CDOs) made up of securities in the inventory of the trading desk. At a 
meeting of the team, senior executives explain the opportunity to eventually separate 
the CDO into various risk-  rated tranches to be sold to the clients of the firm. After the 
senior executives leave the meeting, the head trader announces various responsibilities 
of each member of the team and then says, “This is a good time to unload some of

the junk we have been stuck with for a while and disguise it with ratings and a thick, 
unreadable prospectus, so don’t be shy in putting this CDO together. Just kidding. ” 
Smith is worried by this remark and asks some of her colleagues what the head trader 
meant. They all respond that he was just kidding but that there is some truth in the 
remark because the CDO is seen by management as an opportunity to improve the 
quality of the securities in the firm’s inventory.
Concerned about the ethical environment of the workplace, Smith decides to 
talk to her supervisor about her concerns and provides the head trader with a copy 
of the Code and Standards. Smith discusses the principle of placing the client above 
the interest of the firm and the possibility that the development of the new CDO will 
not adhere to this responsibility. The head trader assures Smith that the appropriate 
analysis will be conducted when determining the appropriate securities for collateral.

Furthermore, the ratings are assigned by an independent firm and the prospectus will 
include full and factual disclosures. Smith is reassured by the meeting, but she also 
reviews the company’s procedures and requirements for reporting potential violations 
of company policy and securities laws.
Comment : Smith’s review of the company policies and procedures for report -
ing violations  allows her to be prepared to report through the appropriate 
whistleblower process if she decides that the CDO development process 
involves unethical actions by others. Smith’s actions comply with the Code 
and Standards principles of placing the client’s interests first and being 
loyal to her employer. In providing her supervisor with a copy of the Code 
and Standards, Smith is highlighting the high level of ethical conduct she 
is required to adhere to in her professional activities.

Standard IV: Duties to Employers 143
Example 14 (Leaving an Employer):
Laura Webb just left her position as portfolio analyst at Research Systems, Inc. (RSI). 
Her employment contract included a non-  solicitation agreement that requires her to 
wait two years before soliciting RSI clients for any investment-  related services. Upon 
leaving, Webb was informed that RSI would contact clients immediately about her 
departure and introduce her replacement. 
While working at RSI, Webb connected with clients, other industry associates, 
and friends through her LinkedIn network. Her business and personal relationships 
were intermingled because she considered many of her clients to be personal friends. 
Realizing that her LinkedIn network would be a valuable resource for new employment 
opportunities, she updated her profile several days following her departure from RSI. 
LinkedIn automatically sent a notification to Webb’s entire network that her employ -
ment status had been changed in her profile.

Comment : Prior to her departure, Webb should have discussed any client 
information contained in her social media networks. By updating her 
LinkedIn profile after RSI notified clients and after her employment ended, 
she has appropriately placed her employer’s interests ahead of her own 
personal interests. In addition, she has not violated the non-  solicitation 
agreement with RSI, unless it prohibited any contact with clients during 
the two-  year period.
Example 15 (Confidential Firm Information):
Sanjay Gupta is a research analyst at Naram Investment Management (NIM). NIM 
uses a team-  based research process to develop recommendations on investment 
opportunities covered by the team members. Gupta, like others, provides commen -
tary for NIM’s clients through the company blog, which is posted weekly on the NIM 
password-  protected website. According to NIM’s policy, every contribution to the

website must be approved by the company’s compliance department before posting. 
Any opinions expressed on the website are disclosed as representing the perspective 
of NIM.
Gupta also writes a personal blog to share his experiences with friends and family. 
As with most blogs, Gupta’s personal blog is widely available to interested readers 
through various internet search engines. Occasionally, when he disagrees with the 
team-  based research opinions of NIM, Gupta uses his personal blog to express his 
own opinions as a counterpoint to the commentary posted on the NIM website. 
Gupta believes this provides his readers with a more complete perspective on these 
investment opportunities. 
Comment : Gupta is in violation of Standard IV(A) for disclosing confidential 
firm information through his personal blog. The recommendations on the 
firm’s blog to clients are not freely available across the internet, but his 
personal blog post indirectly provides the firm’s recommendations.

Additionally, by posting research commentary on his personal blog, 
Gupta is using firm resources for his personal advantage. To comply with 
Standard IV(A), members and candidates must receive consent from their 
employer prior to using company resources.

Reading 3 ■ Guidance for Standards I–VII 144
Standard IV(B) Additional Compensation Arrangements
Members and Candidates must not accept gifts, benefits, compensation, or consideration 
that competes with or might reasonably be expected to create a conflict of interest with 
their employer’s interest unless they obtain written consent from all parties involved.
Guidance
Standard IV(B) requires members and candidates to obtain permission from their 
employer before accepting compensation or other benefits from third parties for the 
services rendered to the employer or for any services that might create a conflict with 
their employer’s interest. Compensation and benefits include direct compensation by 
the client and any indirect compensation or other benefits received from third parties. 
“Written consent” includes any form of communication that can be documented (for 
example, communication via e-  mail that can be retrieved and documented).

Members and candidates must obtain permission for additional compensation/
benefits because such arrangements may affect loyalties and objectivity and create 
potential conflicts of interest. Disclosure allows an employer to consider the outside 
arrangements when evaluating the actions and motivations of members and candi -
dates. Moreover, the employer is entitled to have full knowledge of all compensation/
benefit arrangements so as to be able to assess the true cost of the services members 
or candidates are providing.
There may be instances in which a member or candidate is hired by an employer 
on a “part-  time” basis. “Part-  time” status applies to employees who do not commit 
the full number of hours required for a normal work week. Members and candidates 
should discuss possible limitations to their abilities to provide services that may be 
competitive with their employer during the negotiation and hiring process. The require -

ments of Standard IV(B) would be applicable to limitations identified at that time.
Members and candidates should make an immediate written report to their supervisor 
and compliance officer specifying any compensation they propose to receive for services 
in addition to the compensation or benefits received from their employer. The details 
of the report should be confirmed by the party offering the additional compensation, 
including performance incentives offered by clients. This written report should state 
the terms of any agreement under which a member or candidate will receive addi -
tional compensation; “terms” include the nature of the compensation, the approximate 
amount of compensation, and the duration of the agreement.
Example 1 (Notification of Client Bonus Compensation):
Geoff Whitman, a portfolio analyst for Adams Trust Company, manages the account

of Carol Cochran, a client. Whitman is paid a salary by his employer, and Cochran 
pays the trust company a standard fee based on the market value of assets in her 
portfolio. Cochran proposes to Whitman that “any year that my portfolio achieves at 
least a 15% return before taxes, you and your wife can fly to Monaco at my expense

Standard IV: Duties to Employers 145
and use my condominium during the third week of January. ” Whitman does not inform 
his employer of the arrangement and vacations in Monaco the following January as 
Cochran’s guest.
Comment : Whitman violated Standard  IV(B) by failing to inform his 
employer in writing of this supplemental, contingent compensation arrange -
ment. The nature of the arrangement could have resulted in partiality to 
Cochran’s account, which could have detracted from Whitman’s perfor -
mance with respect to other accounts he handles for Adams Trust. Whitman 
must obtain the consent of his employer to accept such a supplemental 
benefit.
Example 2 (Notification of Outside Compensation):
Terry Jones sits on the board of directors of Exercise Unlimited, Inc. In return for his 
services on the board, Jones receives unlimited membership privileges for his family 
at all Exercise Unlimited facilities. Jones purchases Exercise Unlimited stock for the

client accounts for which it is appropriate. Jones does not disclose this arrangement 
to his employer because he does not receive monetary compensation for his services 
to the board.
Comment : Jones has violated Standard IV(B) by failing to disclose to his 
employer benefits received in exchange for his services on the board of 
directors. The nonmonetary compensation may create a conflict of interest 
in the same manner as being paid to serve as a director.
Example 3 (Prior Approval for Outside Compensation):
Jonathan Hollis is an analyst of oil-  and-  gas companies for Specialty Investment 
Management. He is currently recommending the purchase of ABC Oil Company 
shares and has published a long, well-  thought-  out research report to substantiate 
his recommendation. Several weeks after publishing the report, Hollis receives a call 
from the investor-  relations office of ABC Oil saying that Thomas Andrews, CEO of

the company, saw the report and really liked the analyst’s grasp of the business and his 
company. The investor-  relations officer invites Hollis to visit ABC Oil to discuss the 
industry further. ABC Oil offers to send a company plane to pick Hollis up and arrange 
for his accommodations while visiting. Hollis, after gaining the appropriate approvals, 
accepts the meeting with the CEO but declines the offered travel arrangements.
Several weeks later, Andrews and Hollis meet to discuss the oil business and Hollis’s 
report. Following the meeting, Hollis joins Andrews and the investment relations 
officer for dinner at an upscale restaurant near ABC Oil’s headquarters.
Upon returning to Specialty Investment Management, Hollis provides a full review 
of the meeting to the director of research, including a disclosure of the dinner attended.
Comment : Hollis’s actions did not violate Standard IV(B). Through gaining 
approval before accepting the meeting and declining the offered travel

arrangements, Hollis sought to avoid any potential conflicts of interest 
between his company and ABC Oil. Because the location of the dinner was 
not available prior to arrival and Hollis notified his company of the dinner 
upon his return, accepting the dinner should not impair his objectivity. By 
disclosing the dinner, Hollis has enabled Specialty Investment Management 
to assess whether it has any impact on future reports and recommendations 
by Hollis related to ABC Oil.

Reading 3 ■ Guidance for Standards I–VII 146
Standard IV(C) Responsibilities of Supervisors
Members and Candidates must make reasonable efforts to ensure that anyone subject 
to their supervision or authority complies with applicable laws, rules, regulations, and 
the Code and Standards.
Guidance
■■System for Supervision
■■Supervision Includes Detection
Standard  IV(C) states that members and candidates must promote actions by all 
employees under their supervision and authority to comply with applicable laws, 
rules, regulations, and firm policies and the Code and Standards.
Any investment professional who has employees subject to her or his control or 
influence—whether or not the employees are CFA Institute members, CFA charter -
holders, or candidates in the CFA Program—exercises supervisory responsibility. 
Members and candidates acting as supervisors must also have in-  depth knowledge 
of the Code and Standards so that they can apply this knowledge in discharging their

supervisory responsibilities.
The conduct that constitutes reasonable supervision in a particular case depends 
on the number of employees supervised and the work performed by those employees. 
Members and candidates with oversight responsibilities for large numbers of employees 
may not be able to personally evaluate the conduct of these employees on a continuing 
basis. These members and candidates may delegate supervisory duties to subordinates 
who directly oversee the other employees. A member’s or candidate’s responsibilities 
under Standard IV(C) include instructing those subordinates to whom supervision is 
delegated about methods to promote compliance, including preventing and detecting 
violations of laws, rules, regulations, firm policies, and the Code and Standards.
At a minimum, Standard  IV(C) requires that members and candidates with 
supervisory responsibility make reasonable efforts to prevent and detect violations

by ensuring the establishment of effective compliance systems. However, an effective 
compliance system goes beyond enacting a code of ethics, establishing policies and 
procedures to achieve compliance with the code and applicable law, and reviewing 
employee actions to determine whether they are following the rules. 
To be effective supervisors, members and candidates should implement educa -
tion and training programs on a recurring or regular basis for employees under their 
supervision. Such programs will assist the employees with meeting their professional 
obligations to practice in an ethical manner within the applicable legal system. Further, 
establishing incentives—monetary or otherwise—for employees not only to meet 
business goals but also to reward ethical behavior offers supervisors another way to 
assist employees in complying with their legal and ethical obligations. 
Often, especially in large organizations, members and candidates may have super -

visory responsibility but not the authority to establish or modify firm-  wide compliance 
policies and procedures or incentive structures. Such limitations should not prevent

Standard IV: Duties to Employers 147
a member or candidate from working with his or her own superiors and within the 
firm structure to develop and implement effective compliance tools, including but 
not limited to:
■■a code of ethics, 
■■compliance policies and procedures, 
■■education and training programs, 
■■an incentive structure that rewards ethical conduct, and 
■■adoption of firm-  wide best practice standards (e.g., the GIPS standards, the 
CFA Institute Asset Manager Code of Professional Conduct). 
A member or candidate with supervisory responsibility should bring an inadequate 
compliance system to the attention of the firm’s senior managers and recommend 
corrective action. If the member or candidate clearly cannot discharge supervisory 
responsibilities because of the absence of a compliance system or because of an 
inadequate compliance system, the member or candidate should decline in writing 
to accept supervisory responsibility until the firm adopts reasonable procedures to

allow adequate exercise of supervisory responsibility.
System for Supervision 
Members and candidates with supervisory responsibility must understand what 
constitutes an adequate compliance system for their firms and make reasonable 
efforts to see that appropriate compliance procedures are established, documented, 
communicated to covered personnel, and followed. “ Adequate” procedures are those 
designed to meet industry standards, regulatory requirements, the requirements of the 
Code and Standards, and the circumstances of the firm. Once compliance procedures 
are established, the supervisor must also make reasonable efforts to ensure that the 
procedures are monitored and enforced.
To be effective, compliance procedures must be in place prior to the occurrence 
of a violation of the law or the Code and Standards. Although compliance procedures 
cannot be designed to anticipate every potential violation, they should be designed to

anticipate the activities most likely to result in misconduct. Compliance programs must 
be appropriate for the size and nature of the organization. The member or candidate 
should review model compliance procedures or other industry programs to ensure 
that the firm’s procedures meet the minimum industry standards.
Once a supervisor learns that an employee has violated or may have violated the 
law or the Code and Standards, the supervisor must promptly initiate an assessment 
to determine the extent of the wrongdoing. Relying on an employee’s statements 
about the extent of the violation or assurances that the wrongdoing will not reoccur 
is not enough. Reporting the misconduct up the chain of command and warning 
the employee to cease the activity are also not enough. Pending the outcome of the 
investigation, a supervisor should take steps to ensure that the violation will not be 
repeated, such as placing limits on the employee’s activities or increasing the moni -

toring of the employee’s activities.
Supervision Includes Detection
Members and candidates with supervisory responsibility must also make reasonable 
efforts to detect violations of laws, rules, regulations, firm policies, and the Code 
and Standards. The supervisors exercise reasonable supervision by establishing and 
implementing written compliance procedures and ensuring that those procedures are 
followed through periodic review. If a member or candidate has adopted reasonable 
procedures and taken steps to institute an effective compliance program, then the 
member or candidate may not be in violation of Standard IV(C) if he or she does not 
detect violations that occur despite these efforts. The fact that violations do occur may

Reading 3 ■ Guidance for Standards I–VII 148
indicate, however, that the compliance procedures are inadequate. In addition, in some 
cases, merely enacting such procedures may not be sufficient to fulfill the duty required 
by Standard IV(C). A member or candidate may be in violation of Standard IV(C) if 
he or she knows or should know that the procedures designed to promote compliance, 
including detecting and preventing violations, are not being followed.
Codes of Ethics or Compliance Procedures
Members and candidates are encouraged to recommend that their employers adopt a 
code of ethics. Adoption of a code of ethics is critical to establishing a strong ethical 
foundation for investment advisory firms and their employees. Codes of ethics for -
mally emphasize and reinforce the client loyalty responsibilities of investment firm 
personnel, protect investing clients by deterring misconduct, and protect the firm’s 
reputation for integrity.

There is a distinction, however, between codes of ethics and the specific policies 
and procedures needed to ensure compliance with the codes and with securities laws 
and regulations. Although both are important, codes of ethics should consist of fun -
damental, principle-  based ethical and fiduciary concepts that are applicable to all of 
the firm’s employees. In this way, firms can best convey to employees and clients the 
ethical ideals that investment advisers strive to achieve. These concepts need to be 
implemented, however, by detailed, firm-  wide compliance policies and procedures. 
Compliance procedures assist the firm’s personnel in fulfilling the responsibilities 
enumerated in the code of ethics and make probable  that the ideals expressed in the 
code of ethics will be adhered to in the day-  to- day operation of the firm.
Stand-  alone codes of ethics should be written in plain language and should address

general fiduciary concepts. They should be unencumbered by numerous detailed pro -
cedures. Codes presented in this way are the most effective in stressing to employees 
that they are in positions of trust and must act with integrity at all times. Mingling 
compliance procedures in the firm’s code of ethics goes against the goal of reinforcing 
the ethical obligations of employees.
Separating the code of ethics from compliance procedures will also reduce, if not 
eliminate, the legal terminology and “boilerplate” language that can make the under -
lying ethical principles incomprehensible to the average person. Above all, to ensure 
the creation of a culture of ethics and integrity rather than one that merely focuses 
on following the rules, the principles in the code of ethics must be stated in a way 
that is accessible and understandable to everyone in the firm.
Members and candidates should encourage their employers to provide their codes

of ethics to clients. In this case also, a simple, straightforward code of ethics will be 
best understood by clients. Unencumbered by the compliance procedures, the code of 
ethics will be effective in conveying that the firm is committed to conducting business 
in an ethical manner and in the best interests of the clients.
Adequate Compliance Procedures
A supervisor complies with Standard IV(C) by identifying situations in which legal 
violations or violations of the Code and Standards are likely to occur and by estab -
lishing and enforcing compliance procedures to prevent such violations. Adequate 
compliance procedures should
■■be contained in a clearly written and accessible manual that is tailored to the 
firm’s operations,
■■be drafted so that the procedures are easy to understand,

Standard IV: Duties to Employers 149
■■designate a compliance officer whose authority and responsibility are clearly 
defined and who has the necessary resources and authority to implement the 
firm’s compliance procedures,
■■describe the hierarchy of supervision and assign duties among supervisors,
■■implement a system of checks and balances,
■■outline the scope of the procedures,
■■outline procedures to document the monitoring and testing of compliance 
procedures,
■■outline permissible conduct, and
■■delineate procedures for reporting violations and sanctions.
Once a compliance program is in place, a supervisor should
■■disseminate the contents of the program to appropriate personnel,
■■periodically update procedures to ensure that the measures are adequate under 
the law,
■■continually educate personnel regarding the compliance procedures,
■■issue periodic reminders of the procedures to appropriate personnel,
■■incorporate a professional conduct evaluation as part of an employee’s perfor -

mance review,
■■review the actions of employees to ensure compliance and identify violators, 
and
■■take the necessary steps to enforce the procedures once a violation has 
occurred.
Once a violation is discovered, a supervisor should
■■respond promptly,
■■conduct a thorough investigation of the activities to determine the scope of the 
wrongdoing,
■■increase supervision or place appropriate limitations on the wrongdoer pending 
the outcome of the investigation, and
■■review procedures for potential changes necessary to prevent future violations 
from occurring.
Implementation of Compliance Education and Training
No amount of ethics education and awareness will deter someone determined to com -
mit fraud for personal enrichment. But the vast majority of investment professionals 
strive to achieve personal success with dedicated service to their clients and employers. 
Regular ethics and compliance training, in conjunction with adoption of a code

of ethics, is critical to investment firms seeking to establish a strong culture of integ -
rity and to provide an environment in which employees routinely engage in ethical 
conduct in compliance with the law. Training and education assist individuals in both 
recognizing areas that are prone to ethical and legal pitfalls and identifying those 
circumstances and influences that can impair ethical judgment. 
By implementing educational programs, supervisors can train their subordinates 
to put into practice what the firm’s code of ethics requires. Education helps employees 
make the link between legal and ethical conduct and the long-  term success of the 
business; a strong culture of compliance signals to clients and potential clients that 
the firm has truly embraced ethical conduct as fundamental to the firm’s mission to 
serve its clients.

Reading 3 ■ Guidance for Standards I–VII 150
Establish an Appropriate Incentive Structure
Even if individuals want to make the right choices and follow an ethical course of 
conduct and are aware of the obstacles that may trip them up, they can still be influ -
enced to act improperly by a corporate culture that embraces a “succeed at all costs” 
mentality, stresses results regardless of the methods used to achieve those results, and 
does not reward ethical behavior. Supervisors can reinforce an individual’s natural 
desire to “do the right thing” by building a culture of integrity in the workplace. 
Supervisors and firms must look closely at their incentive structure to determine 
whether the structure encourages profits and returns at the expense of ethically appro -
priate conduct. Reward structures may turn a blind eye to how desired outcomes are 
achieved and encourage dysfunctional or counterproductive behavior. Only when

compensation and incentives are firmly tied to client interests and how outcomes 
are achieved, rather than how much  is generated for the firm, will employees work to 
achieve a culture of integrity.
Example 1 (Supervising Research Activities):
Jane Mattock, senior vice president and head of the research department of H&V, Inc., 
a regional brokerage firm, has decided to change her recommendation for Timber 
Products from buy to sell. In line with H&V’s procedures, she orally advises certain 
other H&V executives of her proposed actions before the report is prepared for pub -
lication. As a result of Mattock’s conversation with Dieter Frampton, one of the H&V 
executives accountable to Mattock, Frampton immediately sells Timber’s stock from 
his own account and from certain discretionary client accounts. In addition, other 
personnel inform certain institutional customers of the changed recommendation

before it is printed and disseminated to all H&V customers who have received pre -
vious Timber reports.
Comment : Mattock has violated Standard IV(C) by failing to reasonably 
and adequately supervise the actions of those accountable to her. She 
did not prevent or establish reasonable procedures designed to prevent 
dissemination of or trading on the information by those who knew of her 
changed recommendation. She must ensure that her firm has procedures 
for reviewing or recording any trading in the stock of a corporation that has 
been the subject of an unpublished change in recommendation. Adequate 
procedures would have informed the subordinates of their duties and 
detected sales by Frampton and selected customers.
Example 2 (Supervising Research Activities):
Deion Miller is the research director for Jamestown Investment Programs. The portfolio 
managers have become critical of Miller and his staff because the Jamestown portfolios

do not include any stock that has been the subject of a merger or tender offer. Georgia 
Ginn, a member of Miller’s staff, tells Miller that she has been studying a local company, 
Excelsior, Inc., and recommends its purchase. Ginn adds that the company has been 
widely rumored to be the subject of a merger study by a well-  known conglomerate and 
discussions between them are under way. At Miller’s request, Ginn prepares a memo 
recommending the stock. Miller passes along Ginn’s memo to the portfolio managers 
prior to leaving for vacation, and he notes that he has not reviewed the memo. As 
a result of the memo, the portfolio managers buy Excelsior stock immediately. The 
day Miller returns to the office, he learns that Ginn’s only sources for the report were 
her brother, who is an acquisitions analyst with Acme Industries, the “well-  known 
conglomerate, ” and that the merger discussions were planned but not held.

Standard IV: Duties to Employers 151
Comment : Miller violated Standard  IV(C) by not exercising reasonable 
supervision when he disseminated the memo without checking to ensure 
that Ginn had a reasonable and adequate basis for her recommendations 
and that Ginn was not relying on material nonpublic information.
Example 3 (Supervising Trading Activities):
David Edwards, a trainee trader at Wheeler & Company, a major national brokerage 
firm, assists a customer in paying for the securities of Highland, Inc., by using antic -
ipated profits from the immediate sale of the same securities. Despite the fact that 
Highland is not on Wheeler’s recommended list, a large volume of its stock is traded 
through Wheeler in this manner. Roberta Ann Mason is a Wheeler vice president 
responsible for supervising compliance with the securities laws in the trading depart -
ment. Part of her compensation from Wheeler is based on commission revenues from

the trading department. Although she notices the increased trading activity, she does 
nothing to investigate or halt it.
Comment : Mason’s failure to adequately review and investigate purchase 
orders in Highland stock executed by Edwards and her failure to super -
vise the trainee’s activities violate Standard IV(C). Supervisors should be 
especially sensitive to actual or potential conflicts between their own self-  
interests and their supervisory responsibilities.
Example 4 (Supervising Trading Activities and Record Keeping):
Samantha Tabbing is senior vice president and portfolio manager for Crozet, Inc., a 
registered investment advisory and registered broker/dealer firm. She reports to Charles 
Henry, the president of Crozet. Crozet serves as the investment adviser and principal 
underwriter for ABC and XYZ public mutual funds. The two funds’ prospectuses allow 
Crozet to trade financial futures for the funds for the limited purpose of hedging against

market risks. Henry, extremely impressed by Tabbing’s performance in the past two 
years, directs Tabbing to act as portfolio manager for the funds. For the benefit of its 
employees, Crozet has also organized the Crozet Employee Profit-  Sharing Plan (CEPSP), 
a defined contribution retirement plan. Henry assigns Tabbing to manage 20% of the 
assets of CEPSP . Tabbing’s investment objective for her portion of CEPSP’s assets is 
aggressive growth. Unbeknownst to Henry, Tabbing frequently places S&P 500 Index 
purchase and sale orders for the funds and the CEPSP without providing the futures 
commission merchants (FCMs) who take the orders with any prior or simultaneous 
designation of the account for which the trade has been placed. Frequently, neither 
Tabbing nor anyone else at Crozet completes an internal trade ticket to record the 
time an order was placed or the specific account for which the order was intended.

FCMs often designate a specific account only after the trade, when Tabbing provides 
such designation. Crozet has no written operating procedures or compliance manual 
concerning its futures trading, and its compliance department does not review such 
trading. After observing the market’s movement, Tabbing assigns to CEPSP the S&P 
500 positions with more favorable execution prices and assigns positions with less 
favorable execution prices to the funds.
Comment : Henry violated Standard IV(C) by failing to adequately super -
vise Tabbing with respect to her S&P 500 trading. Henry further violated 
Standard IV(C) by failing to establish record-  keeping and reporting pro -
cedures to prevent or detect Tabbing’s violations. Henry must make a rea -
sonable effort to determine that adequate compliance procedures covering 
all employee trading activity are established, documented, communicated, 
and followed.

Reading 3 ■ Guidance for Standards I–VII 152
Example 5 (Accepting Responsibility):
become quite knowledgeable about the hedge fund’s strategy, tactics, and performance. 
When a distinct break in the market occurs and many of the securities involved in the 
hedge fund’s strategy decline markedly in value, however, Rasmussen observes that 
the reported performance of the hedge fund does not at all reflect this decline. From 
her experience, this lack of an effect is a very unlikely occurrence. She approaches the 
head of trading about her concern and is told that she should not ask any questions

and that the fund is too big and successful and is not her concern. She is fairly sure 
something is not right, so she contacts the compliance officer and is again told to stay 
away from the hedge fund reporting issue.
Comment : Rasmussen has clearly come upon an error in policies, proce -
dures, and compliance practices within the firm’s operations. According to 
Standard IV(C), the supervisor and the compliance officer have the respon -
sibility to review the concerns brought forth by Rasmussen. Supervisors 
have the responsibility of establishing and encouraging an ethical culture 
in the firm. The dismissal of Rasmussen’s question violates Standard IV(C) 
and undermines the firm’s ethical operations.
See also Standard I(D)–Misconduct and, for guidance on whistleblowing, 
Standard IV(A)–Loyalty.
Example 6 (Inadequate Procedures):
Brendan Witt, a former junior sell-  side technology analyst, decided to return to 
school to earn an MBA. To keep his research skills and industry knowledge sharp,

Witt accepted a position with On-  line and Informed, an independent internet-  based 
research company. The position requires the publication of a recommendation and 
report on a different company every month. Initially, Witt is a regular contributor 
of new research and a participant in the associated discussion boards that generally 
have positive comments on the technology sector. Over time, his ability to manage 
his educational requirements and his work requirements begin to conflict with one 
another. Knowing a recommendation is due the next day for On-  line, Witt creates a 
report based on a few news articles and what the conventional wisdom of the markets 
has deemed the “hot” security of the day.
Comment : Allowing the report submitted by Witt to be posted highlights a 
lack of compliance procedures by the research firm. Witt’s supervisor needs 
to work with the management of On-  line to develop an appropriate review

process to ensure that all contracted analysts comply with the requirements.
See also Standard  V(A)–Diligence and Reasonable Basis because it 
relates to Witt’s responsibility for substantiating a recommendation.
Example 7 (Inadequate Supervision):
Michael Papis is the chief investment officer of his state’s retirement fund. The fund 
has always used outside advisers for the real estate allocation, and this information is 
clearly presented in all fund communications. Thomas Nagle, a recognized sell-  side 
research analyst and Papis’s business school classmate, recently left the investment 
bank he worked for to start his own asset management firm, Accessible Real Estate. 
Nagle is trying to build his assets under management and contacts Papis about gaining 
some of the retirement fund’s allocation. In the previous few years, the performance

Standard IV: Duties to Employers 153
of the retirement fund’s real estate investments was in line with the fund’s benchmark 
but was not extraordinary. Papis decides to help out his old friend and also to seek 
better returns by moving the real estate allocation to Accessible. The only notice of the 
change in adviser appears in the next annual report in the listing of associated advisers.
Comment : Papis’s actions highlight the need for supervision and review at 
all levels in an organization. His responsibilities may include the selection 
of external advisers, but the decision to change advisers appears arbitrary. 
Members and candidates should ensure that their firm has appropriate 
policies and procedures in place to detect inappropriate actions, such as 
the action taken by Papis.
See also Standard V(A)–Diligence and Reasonable Basis, Standard V(B)–
Communication with Clients and Prospective Clients, and Standard VI(A)–
Disclosure of Conflicts.
Example 8 (Supervising Research Activities):

junior auto industry analyst. Burdette is expected to expand the social media presence 
mobiles. This research report will be her first for FIM, and she believes Sun Drive’s

Comment : Graf has violated Standard IV(C) by failing to reasonably super -
vise Burdette with respect to the contents of her tweet. He did not estab -
lish reasonable procedures to prevent the unauthorized dissemination of 
company research through social media networks. Graf must make sure 
all employees receive regular training about FIM’s policies and procedures, 
including the appropriate business use of personal social media networks. 
See Standard III(B) for additional guidance.
Example 9 (Supervising Research Activities):
Chen Wang leads the research department at YYRA Retirement Planning Specialists. 
Chen supervises a team of 10 analysts in a fast-  paced and understaffed organization. 
He is responsible for coordinating the firm’s approved process to review all reports

before they are provided to the portfolio management team for use in rebalancing 
client portfolios.
One of Chen’s direct reports, Huang Mei, covers the banking industry. Chen must 
submit the latest updates to the portfolio management team tomorrow morning. Huang 
has yet to submit her research report on ZYX Bank because she is uncomfortable pro -
viding a “buy” or “sell” opinion of ZYX on the basis of the completed analysis. Pressed 
for time and concerned that Chen will reject a “hold” recommendation, she researches 
various websites and blogs on the banking sector for whatever she can find on ZYX. 
One independent blogger provides a new interpretation of the recently reported data 
Huang has analyzed and concludes with a strong “sell” recommendation for ZYX. She 
is impressed by the originality and resourcefulness of this blogger’s report.

Reading 3 ■ Guidance for Standards I–VII 154
Very late in the evening, Huang submits her report and “sell” recommendation to 
Chen without any reference to the independent blogger’s report. Given the late time 
of the submission and the competence of Huang’s prior work, Chen compiles this 
report with the recommendations from each of the other analysts and meets with 
the portfolio managers to discuss implementation. 
Comment : Chen has violated Standard IV(C) by neglecting to reasonably 
and adequately follow the firm’s approved review process for Huang’s 
research report. The delayed submission and the quality of prior work do 
not remove Chen’s requirement to uphold the designated review process. A 
member or candidate with supervisory responsibility must make reasonable 
efforts to see that appropriate procedures are established, documented, 
communicated to covered personnel, and followed. 
STANDARD V: INVESTMENT ANALYSIS, 
RECOMMENDATIONS, AND ACTIONS

Standard V(A) Diligence and Reasonable Basis
1 Exercise diligence, independence, and thoroughness in analyzing investments, 
making investment recommendations, and taking investment actions.
2 h ave a reasonable and adequate basis, supported by appropriate research and 
investigation, for any investment analysis, recommendation, or action.
Guidance
■■Defining Diligence and Reasonable Basis
■■Using Secondary or Third-  Party Research
■■Using  Quantitatively Oriented Research
■■Developing  Quantitatively Oriented Techniques
■■Selecting External Advisers and Subadvisers
■■Group Research and Decision Making
The application of Standard V(A) depends on the investment philosophy the member, 
candidate, or firm is following, the role of the member or candidate in the investment 
decision-  making process, and the support and resources provided by the member’s

or candidate’s employer. These factors will dictate the nature of the diligence and 
thoroughness of the research and the level of investigation required by Standard V(A).
The requirements for issuing conclusions based on research will vary in relation 
to the member’s or candidate’s role in the investment decision-  making process, but 
the member or candidate must make reasonable efforts to cover all pertinent issues

Standard V: Investment Analysis, Recommendations, and Actions 155
when arriving at a recommendation. Members and candidates enhance transparency 
by providing or offering to provide supporting information to clients when recom -
mending a purchase or sale or when changing a recommendation.
Defining Diligence and Reasonable Basis
Every investment decision is based on a set of facts known and understood at the time. 
Clients turn to members and candidates for advice and expect these advisers to have 
more information and knowledge than they do. This information and knowledge is 
the basis from which members and candidates apply their professional judgment in 
taking investment actions and making recommendations.
At a basic level, clients want assurance that members and candidates are put -
ting forth the necessary effort to support the recommendations they are making. 
Communicating the level and thoroughness of the information reviewed before the

member or candidate makes a judgment allows clients to understand the reasonable -
ness of the recommended investment actions.
As with determining the suitability of an investment for the client, the necessary 
level of research and analysis will differ with the product, security, or service being 
offered. In providing an investment service, members and candidates typically use 
a variety of resources, including company reports, third-  party research, and results 
from quantitative models. A reasonable basis is formed through a balance of these 
resources appropriate for the security or decision being analyzed.
The following list provides some, but definitely not all, examples of attributes to 
consider while forming the basis for a recommendation:
■■global, regional, and country macroeconomic conditions,
■■a company’s operating and financial history,
■■the industry’s and sector’s current conditions and the stage of the business 
cycle,
■■a mutual fund’s fee structure and management history,

■■the output and potential limitations of quantitative models,
■■the quality of the assets included in a securitization, and
■■the appropriateness of selected peer-  group comparisons.
Even though an investment recommendation may be well informed, downside 
risk remains for any investment. Members and candidates can base their decisions 
only on the information available at the time decisions are made. The steps taken in 
developing a diligent and reasonable recommendation should minimize unexpected 
downside events.
Using Secondary or Third-  Party Research
If members and candidates rely on secondary or third-  party research, they must 
make reasonable and diligent efforts to determine whether such research is sound. 
Secondary research is defined as research conducted by someone else in the member’s 
or candidate’s firm. Third-  party research is research conducted by entities outside 
the member’s or candidate’s firm, such as a brokerage firm, bank, or research firm.

If a member or candidate has reason to suspect that either secondary or third-  party 
research or information comes from a source that lacks a sound basis, the member 
or candidate must not rely on that information. 
Members and candidates should make reasonable enquiries into the source and 
accuracy of all data used in completing their investment analysis and recommenda -
tions. The sources of the information and data will influence the level of the review 
a member or candidate must undertake. Information and data taken from internet

Reading 3 ■ Guidance for Standards I–VII 156
sources, such as personal blogs, independent research aggregation websites, or social 
media websites, likely require a greater level of review than information from more 
established research organizations.
Criteria that a member or candidate can use in forming an opinion on whether 
research is sound include the following:
■■assumptions used,
■■rigor of the analysis performed,
■■date/timeliness of the research, and
■■evaluation of the objectivity and independence of the recommendations.
A member or candidate may rely on others in his or her firm to determine whether 
secondary or third-  party research is sound and use the information in good faith 
unless the member or candidate has reason to question its validity or the processes 
and procedures used by those responsible for the research. For example, a portfolio 
manager may not have a choice of a data source because the firm’s senior managers

conducted due diligence to determine which vendor would provide services; the mem -
ber or candidate can use the information in good faith assuming the due diligence 
process was deemed adequate.
A member or candidate should verify that the firm has a policy about the timely 
and consistent review of approved research providers to ensure that the quality of the 
research continues to meet the necessary standards. If such a policy is not in place at 
the firm, the member or candidate should encourage the development and adoption 
of a formal review practice.
Using Quantitatively Oriented Research
Standard V(A) applies to the rapidly expanding use of quantitatively oriented research 
models and processes, such as computer-  generated modeling, screening, and rank -
ing of investment securities; the creation or valuation of derivative instruments; and 
quantitative portfolio construction techniques. These models and processes are being

used for much more than the back testing of investment strategies, especially with 
continually advancing technology and techniques. The continued broad development of 
quantitative methods and models is an important part of capital market developments.
Members and candidates need to have an understanding of the parameters used 
in models and quantitative research that are incorporated into their investment rec -
ommendations. Although they are not required to become experts in every technical 
aspect of the models, they must understand the assumptions and limitations inherent 
in any model and how the results were used in the decision-  making process.
The reliance on and potential limitations of financial models became clear through 
the investment crisis that unfolded in 2007 and 2008. In some cases, the financial 
models used to value specific securities and related derivative products did not ade -
quately demonstrate the level of associated risks. Members and candidates should make

reasonable efforts to test the output of investment models and other pre-  programed 
analytical tools they use. Such validation should occur before incorporating the process 
into their methods, models, or analyses.
Although not every model can test for every factor or outcome, members and 
candidates should ensure that their analyses incorporate a broad range of assumptions 
sufficient to capture the underlying characteristics of investments. The omission from 
the analysis of potentially negative outcomes or of levels of risk outside the norm  may 
misrepresent the true economic value of an investment. The possible scenarios for 
analysis should include factors that are likely to have a substantial influence on the 
investment value and may include extremely positive and negative scenarios.

Standard V: Investment Analysis, Recommendations, and Actions 157
Developing Quantitatively Oriented Techniques 
Individuals who create new quantitative models and services must exhibit a higher 
level of diligence in reviewing new products than the individuals who ultimately use 
the analytical output. Members and candidates involved in the development and 
oversight of quantitatively oriented models, methods, and algorithms must understand 
the technical aspects of the products they provide to clients. A thorough testing of 
the model and resulting analysis should be completed prior to product distribution.
Members and candidates need to consider the source and time horizon of the data 
used as inputs in financial models. The information from many commercially available 
databases may not effectively incorporate both positive and negative market cycles. 
In the development of a recommendation, the member or candidate may need to test

the models by using volatility and performance expectations that represent scenarios 
outside the observable databases. In reviewing the computer models or the resulting 
output, members and candidates need to pay particular attention to the assumptions 
used in the analysis and the rigor of the analysis to ensure that the model incorporates 
a wide range of possible input expectations, including negative market events.
Selecting External Advisers and Subadvisers
Financial instruments and asset allocation techniques continue to develop and evolve. 
This progression has led to the use of specialized managers to invest in specific asset 
classes or diversification strategies that complement a firm’s in-  house expertise. 
Standard V(A) applies to the level of review necessary in selecting an external adviser 
or subadviser to manage a specifically mandated allocation. Members and candidates 
must review managers as diligently as they review individual funds and securities.

Members and candidates who are directly involved with the use of external advisers 
need to ensure that their firms have standardized criteria for reviewing these selected 
external advisers and managers. Such criteria would include, but would not be limited 
to, the following:
■■reviewing the adviser’s established code of ethics,
■■understanding the adviser’s compliance and internal control procedures,
■■assessing the quality of the published return information, and
■■reviewing the adviser’s investment process and adherence to its stated strategy.
Codes, standards, and guides to best practice published by CFA Institute provide 
members and candidates with examples of acceptable practices for external advisers 
and advice in selecting a new adviser. The following guides are available at the CFA 
Institute website (www.cfainstitute.org): Asset Manager Code of Professional Conduct, 
Global Investment Performance Standards, and Model Request for Proposal  (for equity,

credit, or real estate managers).
Group Research and Decision Making
Commonly, members and candidates are part of a group or team that is collectively 
responsible for producing investment analysis or research. The conclusions or rec -
ommendations of the group report represent the consensus of the group and are not 
necessarily the views of the member or candidate, even though the name of the member 
or candidate is included on the report. In some instances, a member or candidate will 
not agree with the view of the group. If, however, the member or candidate believes 
that the consensus opinion has a reasonable and adequate basis and is independent and 
objective, the member or candidate need not decline to be identified with the report. 
If the member or candidate is confident in the process, the member or candidate does 
not need to dissociate from the report even if it does not reflect his or her opinion.

Reading 3 ■ Guidance for Standards I–VII 158
Members and candidates should encourage their firms to consider the following 
policies and procedures to support the principles of Standard V(A):
■■Establish a policy requiring that research reports, credit ratings, and investment 
recommendations have a basis that can be substantiated as reasonable and 
adequate. An individual employee (a supervisory analyst) or a group of employ -
ees (a review committee) should be appointed to review and approve such items 
prior to external circulation to determine whether the criteria established in the 
policy have been met.
■■Develop detailed, written guidance for analysts (research, investment, or credit), 
supervisory analysts, and review committees that establishes the due diligence 
procedures for judging whether a particular recommendation has a reasonable 
and adequate basis.
■■Develop measurable criteria for assessing the quality of research, the reason -

ableness and adequacy of the basis for any recommendation or rating, and the 
accuracy of recommendations over time. In some cases, firms may consider 
implementing compensation arrangements that depend on these measurable 
criteria and that are applied consistently to all related analysts.
■■Develop detailed, written guidance that establishes minimum levels of scenario 
testing of all computer-  based models used in developing, rating, and evaluating 
financial instruments. The policy should contain criteria related to the breadth 
of the scenarios tested, the accuracy of the output over time, and the analysis of 
cash flow sensitivity to inputs.
■■Develop measurable criteria for assessing outside providers, including the 
quality of information being provided, the reasonableness and adequacy of the 
provider’s collection practices, and the accuracy of the information over time. 
The established policy should outline how often the provider’s products are 
reviewed.

reviewed.
■■Adopt a standardized set of criteria for evaluating the adequacy of external 
advisers. The policy should include how often and on what basis the allocation 
of funds to the adviser will be reviewed.
Example 1 (Sufficient Due Diligence):
Helen Hawke manages the corporate finance department of Sarkozi Securities, Ltd. 
The firm is anticipating that the government will soon close a tax loophole that cur -
rently allows oil-  and-  gas exploration companies to pass on drilling expenses to holders 
of a certain class of shares. Because market demand for this tax-  advantaged class of 
stock is currently high, Sarkozi convinces several companies to undertake new equity 
financings at once, before the loophole closes. Time is of the essence, but Sarkozi 
lacks sufficient resources to conduct adequate research on all the prospective issuing 
companies. Hawke decides to estimate the IPO prices on the basis of the relative size

of each company and to justify the pricing later when her staff has time.
Comment : Sarkozi should have taken on only the work that it could ade -
quately handle. By categorizing the issuers by general size, Hawke has 
bypassed researching all the other relevant aspects that should be consid -
ered when pricing new issues and thus has not performed sufficient due 
diligence. Such an omission can result in investors purchasing shares at 
prices that have no actual basis. Hawke has violated Standard V(A).

Standard V: Investment Analysis, Recommendations, and Actions 159
Example 2 (Sufficient Scenario Testing):
Babu Dhaliwal works for Heinrich Brokerage in the corporate finance group. He has 
just persuaded Feggans Resources, Ltd., to allow his firm to do a secondary equity 
financing at Feggans Resources’ current stock price. Because the stock has been trad -
ing at higher multiples than similar companies with equivalent production, Dhaliwal 
presses the Feggans Resources managers to project what would be the maximum 
production they could achieve in an optimal scenario. Based on these numbers, he is 
able to justify the price his firm will be asking for the secondary issue. During a sales 
pitch to the brokers, Dhaliwal then uses these numbers as the base-  case production 
levels that Feggans Resources will achieve.
Comment : When presenting information to the brokers, Dhaliwal should 
have given a range of production scenarios and the probability of Feggans

Resources achieving each level. By giving the maximum production level 
as the likely level of production, he has misrepresented the chances of 
achieving that production level and seriously misled the brokers. Dhaliwal 
has violated Standard V(A).
Example 3 (Developing a Reasonable Basis):
school to earn an MBA. To keep his research skills and industry knowledge sharp, 
his educational requirements and his work requirements begin to conflict with one

Comment : Witt’s knowledge of and exuberance for technology stocks, a 
few news articles, and the conventional wisdom of the markets do not 
constitute, without more information, a reasonable and adequate basis for 
a stock recommendation that is supported by appropriate research and 
investigation. Therefore, Witt has violated Standard V(A).
See also Standard  IV(C)–Responsibilities of Supervisors because it 
relates to the firm’s inadequate procedures.
Example 4 (Timely Client Updates):
Kristen Chandler is an investment consultant in the London office of Dalton Securities, 
a major global investment consultant firm. One of her UK pension funds has decided 
to appoint a specialist US equity manager. Dalton’s global manager of research relies

on local consultants to cover managers within their regions and, after conducting 
thorough due diligence, puts their views and ratings in Dalton’s manager database. 
Chandler accesses Dalton’s global manager research database and conducts a screen 
of all US equity managers on the basis of a match with the client’s desired philoso -
phy/style, performance, and tracking-  error targets. She selects the five managers that 
meet these criteria and puts them in a briefing report that is delivered to the client 
10 days later. Between the time of Chandler’s database search and the delivery of the 
report to the client, Chandler is told that Dalton has updated the database with the 
information that one of the firms that Chandler has recommended for consideration

Reading 3 ■ Guidance for Standards I–VII 160
lost its chief investment officer, the head of its US equity research, and the majority 
of its portfolio managers on the US equity product—all of whom have left to establish 
their own firm. Chandler does not revise her report with this updated information.
Comment : Chandler has failed to satisfy the requirement of Standard V(A). 
Although Dalton updated the manager ratings to reflect the personnel 
turnover at one of the firms, Chandler did not update her report to reflect 
the new information.
Example 5 (Group Research Opinions):
Evelyn Mastakis is a junior analyst who has been asked by her firm to write a research 
report predicting the expected interest rate for residential mortgages over the next 
six months. Mastakis submits her report to the fixed-  income investment committee 
of her firm for review, as required by firm procedures. Although some committee 
members support Mastakis’s conclusion, the majority of the committee disagrees with

her conclusion, and the report is significantly changed to indicate that interest rates 
are likely to increase more than originally predicted by Mastakis. Should Mastakis 
ask that her name be taken off the report when it is disseminated?
Comment : The results of research are not always clear, and different people 
may have different opinions based on the same factual evidence. In this case, 
the committee may have valid reasons for issuing a report that differs from 
the analyst’s original research. The firm can issue a report that is different 
from the original report of an analyst as long as there is a reasonable and 
adequate basis for its conclusions.
Generally, analysts must write research reports that reflect their own 
opinion and can ask the firm not to put their name on reports that ultimately 
differ from that opinion. When the work is a group effort, however, not all 
members of the team may agree with all aspects of the report. Ultimately,

members and candidates can ask to have their names removed from the 
report, but if they are satisfied that the process has produced results or 
conclusions that have a reasonable and adequate basis, members and can -
didates do not have to dissociate from the report even when they do not 
agree with its contents. If Mastakis is confident in the process, she does not 
need to dissociate from the report even if it does not reflect her opinion.
Example 6 (Reliance on Third-  Party Research):
Gary McDermott runs a two-  person investment management firm. McDermott’s firm 
reports. McDermott’s firm makes investment recommendations on the basis of these 
reports.
Comment : Members and candidates can rely on third-  party research but 
must make reasonable and diligent efforts to determine that such research 
is sound. If McDermott undertakes due diligence efforts on a regular basis

to ensure that the research produced by the large firm is objective and 
reasonably based, McDermott can rely on that research when making 
investment recommendations to clients.
Example 7 (Due Diligence in Submanager Selection):
Paul Ostrowski’s business has grown significantly over the past couple of years, 
and some clients want to diversify internationally. Ostrowski decides to find a sub -
manager to handle the expected international investments. Because this will be his

Standard V: Investment Analysis, Recommendations, and Actions 161
first subadviser, Ostrowski uses the CFA Institute model “request for proposal” to 
design a questionnaire for his search. By his deadline, he receives seven completed 
questionnaires from a variety of domestic and international firms trying to gain his 
business. Ostrowski reviews all the applications in detail and decides to select the 
firm that charges the lowest fees because doing so will have the least impact on his 
firm’s bottom line.
Comment : The selection of an external adviser or subadviser should be 
based on a full and complete review of the adviser’s services, performance 
history, and cost structure. In basing the decision on the fee structure alone, 
Ostrowski may be violating Standard V(A).
See also Standard III(C)–Suitability because it relates to the ability of 
the selected adviser to meet the needs of the clients.
Example 8 (Sufficient Due Diligence):

some of the retirement fund’s allocation. In the previous few years, the performance 

Comment : Papis violated Standard V(A). His responsibilities may include 
the selection of the external advisers, but the decision to change advisers 
appears to have been arbitrary. If Papis was dissatisfied with the current 
real estate adviser, he should have conducted a proper solicitation to select 
the most appropriate adviser.
See also Standard IV(C)–Responsibilities of Supervisors, Standard V(B)–
Example 9 (Sufficient Due Diligence):
of two top-  performing funds managed by Reed. Given his personal friendship with

Comment : Shrub violated Standard  V(A) by not conducting a thorough 
analysis of the funds managed by Reed before developing the new Conduit 
fund. Shrub’s reliance on his personal relationship with Reed and his prior 
knowledge of Elite are insufficient justification for the investments. The 
funds may be appropriately considered, but a full review of their operating 
procedures, reporting practices, and transparency are some elements of 
the necessary due diligence.

Reading 3 ■ Guidance for Standards I–VII 162
See also Standard III(C)–Suitability.
Example 10 (Sufficient Due Diligence):
manager replies that these assumptions are too dire because there has never been a

securities and evaluates these securities in the worst-  case scenario, a less likely but 
Comment : Thompson’s actions in running the scenario test with inputs 
beyond the historical trends available in the firm’s databases adhere to the 
principles of Standard  V(A). His concerns over recent trends provide a 
sound basis for further analysis. Thompson understands the limitations of 
his model, when combined with the limited available historical information,

to accurately predict the performance of the funds if market conditions 
change negatively.
See also Standard I(B)–Independence and Objectivity.
Example 11 (Use of Quantitatively Oriented Models):
Espacia Liakos works in sales for Hellenica Securities, a firm specializing in developing 
intricate derivative strategies to profit from particular views on market expectations. 
One of her clients is Eugenie Carapalis, who has become convinced that commodity 
prices will become more volatile over the coming months. Carapalis asks Liakos to 
quickly engineer a strategy that will benefit from this expectation. Liakos turns to 
Hellenica’s modeling group to fulfill this request. Because of the tight deadline, the 
modeling group outsources parts of the work to several trusted third parties. Liakos 
implements the disparate components of the strategy as the firms complete them.
Within a month, Carapalis is proven correct: Volatility across a range of commod -

ities increases sharply. But her derivatives position with Hellenica returns huge losses, 
and the losses increase daily. Liakos investigates and realizes that although each of the 
various components of the strategy had been validated, they had never been evalu -
ated as an integrated whole. In extreme conditions, portions of the model worked at 
cross-  purposes with other portions, causing the overall strategy to fail dramatically.
Comment : Liakos violated Standard V(A). Members and candidates must 
understand the statistical significance of the results of the models they 
recommend and must be able to explain them to clients. Liakos did not 
take adequate care to ensure a thorough review of the whole model; its 
components were evaluated only individually. Because Carapalis clearly

Standard V: Investment Analysis, Recommendations, and Actions 163
intended to implement the strategy as a whole rather than as separate parts, 
Liakos should have tested how the components of the strategy interacted 
as well as how they performed individually.
Example 12 (Successful Due Diligence/Failed Investment):
Alton Newbury is an investment adviser to high-  net- worth clients. A client with an 
aggressive risk profile in his investment policy statement asks about investing in the 
Top Shelf hedge fund. This fund, based in Calgary, Alberta, Canada,  has reported 20% 
returns for the first three years. The fund prospectus states that its strategy involves 
long and short positions in the energy sector and extensive leverage. Based on his 
analysis of the fund’s track record, the principals involved in managing the fund, the 
fees charged, and the fund’s risk profile, Newbury recommends the fund to the client

and secures a position in it. The next week, the fund announces that it has suffered 
a loss of 60% of its value and is suspending operations and redemptions until after a 
regulatory review. Newbury’s client calls him in a panic and asks for an explanation.
Comment : Newbury’s actions were consistent with Standard V(A). Analysis 
of an investment that results in a reasonable basis for recommendation does 
not guarantee that the investment has no downside risk. Newbury should 
discuss the analysis process with the client while reminding him or her that 
past performance does not lead to guaranteed future gains and that losses 
in an aggressive  investment portfolio should be expected.
Example 13 (Quantitative Model Diligence):
Barry Cannon is the lead quantitative analyst at CityCenter Hedge Fund. He is 
responsible for the development, maintenance, and enhancement of the proprietary 
models the fund uses to manage its investors’ assets. Cannon reads several high-  level

mathematical publications and blogs to stay informed of current developments. One 
blog, run by Expert CFA, presents some intriguing research that may benefit one 
of CityCenter’s current models. Cannon is under pressure from firm executives to 
improve the model’s predictive abilities, and he incorporates the factors discussed in 
the online research. The updated output recommends several new investments to the 
fund’s portfolio managers. 
Comment : Cannon has violated Standard V(A) by failing to have a reasonable 
basis for the new recommendations made to the portfolio managers. He 
needed to diligently research the effect of incorporating the new factors 
before offering the output recommendations. Cannon may use the blog 
for ideas, but it is his responsibility to determine the effect on the firm’s 
proprietary models.
See Standard VII(B) regarding the violation by “Expert CFA” in the use 
of the CFA designation.
Example 14 (Selecting a Service Provider):

Ellen Smith is a performance analyst at Artic Global Advisors, a firm that manages 
global equity mandates for institutional clients. She was asked by her supervisor to 
review five new performance attribution systems and recommend one that would more 
appropriately explain the firm’s investment strategy to clients. On the list was a system 
she recalled learning about when visiting an exhibitor booth at a recent conference. 
The system is highly quantitative and something of a “black box” in how it calculates 
the attribution values. Smith recommended this option without researching the others 
because the sheer complexity of the process was sure to impress the clients.

Reading 3 ■ Guidance for Standards I–VII 164
Comment : Smith’s actions do not demonstrate a sufficient level of dili -
gence in reviewing this product to make a recommendation for selecting 
the service. Besides not reviewing or considering the other four potential 
systems, she did not determine whether the “black box” attribution process 
aligns with the investment practices of the firm, including its investments 
in different countries and currencies. Smith must review and understand 
the process of any software or system before recommending its use as the 
firm’s attribution system.
Example 15 (Subadviser Selection):
Craig Jackson is working for Adams Partners, Inc., and has been assigned to select a 
hedge fund subadviser to improve the diversification of the firm’s large fund-  of- funds 
product. The allocation must be in place before the start of the next quarter. Jackson 
uses a consultant database to find a list of suitable firms that claim compliance with

the GIPS standards. He calls more than 20 firms on the list to confirm their potential 
interest and to determine their most recent quarterly and annual total return values. 
Because of the short turnaround, Jackson recommends the firm with the greatest total 
return values for selection.
Comment : By considering only performance and GIPS compliance, Jackson 
has not conducted sufficient review of potential firms to satisfy the require -
ments of Standard V(A). A thorough investigation of the firms and their 
operations should be conducted to ensure that their addition would increase 
the diversity of clients’ portfolios and that they are suitable for the fund-  
of- funds product.
Example 16 (Manager Selection):
Timothy Green works for Peach Asset Management, where he creates proprietary 
models that analyze data from the firm request for proposal questionnaires to iden -
tify managers for possible inclusion in the firm’s fund-  of- funds investment platform.

Various criteria must be met to be accepted to the platform. Because of the number 
of respondents to the questionnaires, Green uses only the data submitted to make a 
recommendation for adding a new manager.
Comment : By failing to conduct any additional outside review of the infor -
mation to verify what was submitted through the request for proposal, Green 
has likely not satisfied the requirements of Standard V(A). The amount of 
information requested from outside managers varies among firms. Although 
the requested information may be comprehensive, Green should ensure 
sufficient effort is undertaken to verify the submitted information before 
recommending a firm for inclusion. This requires that he go beyond the 
information provided by the manager on the request for proposal ques -
tionnaire and may include interviews with interested managers, reviews of 
regulatory filings, and discussions with the managers’ custodian or auditor.
Example 17 (Technical Model Requirements):

Jérôme Dupont works for the credit research group of XYZ Asset Management, where 
he is in charge of developing and updating credit risk models. In order to perform 
accurately, his models need to be regularly updated with the latest market data.

Standard V: Investment Analysis, Recommendations, and Actions 165
Dupont does not interact with or manage money for any of the firm’s clients. He is 
in contact with the firm’s US corporate bond fund manager, John Smith, who has only 
very superficial knowledge of the model and who from time to time asks very basic 
questions regarding the output recommendations. Smith does not consult Dupont 
with respect to finalizing his clients’ investment strategies. 
Dupont’s recently assigned objective is to develop a new emerging market corpo -
rate credit risk model. The firm is planning to expand into emerging credit, and the 
development of such a model is a critical step in this process. Because Smith seems 
to follow the model’s recommendations without much concern for its quality as he 
develops his clients’ investment strategies, Dupont decides to focus his time on the 
development of the new emerging market model and neglects to update the US model.

After several months without regular updates, Dupont’s diagnostic statistics start 
to show alarming signs with respect to the quality of the US credit model. Instead 
of conducting the long and complicated data update, Dupont introduces new codes 
into his model with some limited new data as a quick “fix. ” He thinks this change will 
address the issue without needing to complete the full data update, so he continues 
working on the new emerging market model. 
Several months following the quick “fix, ” another set of diagnostic statistics reveals 
nonsensical results and Dupont realizes that his earlier change contained an error. He 
quickly corrects the error and alerts Smith. Smith realizes that some of the prior trades 
he performed were due to erroneous model results. Smith rebalances the portfolio 
to remove the securities purchased on the basis of the questionable results without 
reporting the issue to anyone else.

reporting the issue to anyone else.    
Comment : Smith violated standard V(A) because exercising “diligence, inde -
pendence, and thoroughness in analyzing investments, making investment 
recommendations, and taking investment actions” means that members 
and candidates must understand the technical aspects of the products they 
provide to clients. Smith does not understand the model he is relying on 
to manage money. Members and candidates should also make reasonable 
enquiries into the source and accuracy of all data used in completing their 
investment analysis and recommendations.
Dupont violated V(A) even if he does not trade securities or make invest -
ment decisions. Dupont’s models give investment recommendations, and 
Dupont is accountable for the quality of those recommendations. Members 
and candidates should make reasonable efforts to test the output of pre-  
programed analytical tools they use. Such validation should occur before

incorporating the tools into their decision-  making process.  
See also Standard V(B)–Communication with Clients and Prospective 
Clients.
Standard V(B) Communication with Clients and Prospective 
Clients
1 d isclose to clients and prospective clients the basic format and general principles 
of the investment processes they use to analyze investments, select securities, and 
construct portfolios and must promptly disclose any changes that might materi -
ally affect those processes.

Reading 3 ■ Guidance for Standards I–VII 166
2 d isclose to clients and prospective clients significant limitations and risks associ -
ated with the investment process.
3 Use reasonable judgment in identifying which factors are important to their 
investment analyses, recommendations, or actions and include those factors in 
communications with clients and prospective clients.
4 d istinguish between fact and opinion in the presentation of investment analyses 
and recommendations.
Guidance
■■Informing Clients of the Investment Process
■■Different Forms of Communication
■■Identifying Risk and Limitations 
■■Report Presentation
■■Distinction between Facts and Opinions in Reports
Standard V(B) addresses member and candidate conduct with respect to commu -
nicating with clients. Developing and maintaining clear, frequent, and thorough 
communication practices is critical to providing high-  quality financial services to

clients. When clients understand the information communicated to them, they also 
can understand exactly how members and candidates are acting on their behalf, which 
gives clients the opportunity to make well-  informed decisions about their investments. 
Such understanding can be accomplished only through clear communication.
Standard V(B) states that members and candidates should communicate in a rec -
ommendation the factors that were instrumental in making the investment recommen -
dation. A critical part of this requirement is to distinguish clearly between opinions 
and facts. In preparing a research report, the member or candidate must present the 
basic characteristics of the security(ies) being analyzed, which will allow the reader 
to evaluate the report and incorporate information the reader deems relevant to his 
or her investment decision-  making process.
Similarly, in preparing a recommendation about, for example, an asset allocation

strategy, alternative investment vehicle, or structured investment product, the member 
or candidate should include factors that are relevant to the asset classes that are being 
discussed. Follow-  up communication of significant changes in the risk characteristics 
of a security or asset strategy is required. Providing regular updates to any changes 
in the risk characteristics is recommended.
Informing Clients of the Investment Process
Members and candidates must adequately describe to clients and prospective clients 
the manner in which they conduct the investment decision-  making process. Such 
disclosure should address factors that have positive and negative influences on the 
recommendations, including significant risks and limitations of the investment pro -
cess used. The member or candidate must keep clients and other interested parties 
informed on an ongoing basis about changes to the investment process, especially

newly identified significant risks and limitations. Only by thoroughly understanding 
the nature of the investment product or service can a client determine whether changes 
to that product or service could materially affect his or her investment objectives.
Understanding the basic characteristics of an investment is of great importance 
in judging the suitability of that investment on a standalone basis, but it is especially 
important in determining the impact each investment will have on the characteristics

Standard V: Investment Analysis, Recommendations, and Actions 167
of a portfolio. Although the risk and return characteristics of a common stock might 
seem to be essentially the same for any investor when the stock is viewed in isolation, 
the effects of those characteristics greatly depend on the other investments held. For 
instance, if the particular stock will represent 90% of an individual’s investments, 
the stock’s importance in the portfolio is vastly different from what it would be to 
an investor with a highly diversified portfolio for whom the stock will represent only 
2% of the holdings.
A firm’s investment policy may include the use of outside advisers to manage var -
ious portions of clients’ assets under management. Members and candidates should 
inform the clients about the specialization or diversification expertise provided by 
the external adviser(s). This information allows clients to understand the full mix of

products and strategies being applied that may affect their investment objectives.
Different Forms of Communication
For purposes of Standard V(B), communication is not confined to a written report 
of the type traditionally generated by an analyst researching a security, company, or 
industry. A presentation of information can be made via any means of communication, 
including in-  person recommendation or description, telephone conversation, media 
broadcast, or transmission by computer (e.g., on the internet). 
Computer and mobile device communications have rapidly evolved over the past 
few years. Members and candidates using any social media service to communicate 
business information must be diligent in their efforts to avoid unintended problems 
because these services may not be available to all clients. When providing information 
to clients through new technologies, members and candidates should take reasonable

steps to ensure that such delivery would treat all clients fairly and, if necessary, be 
considered publicly disseminated.
The nature of client communications is highly diverse—from one word (“buy” or 
“sell”) to in-  depth reports of more than 100 pages. A communication may contain a 
general recommendation about the market, asset allocations, or classes of investments 
(e.g., stocks, bonds, real estate) or may relate to a specific security. If recommenda -
tions are contained in capsule form (such as a recommended stock list), members and 
candidates should notify clients that additional information and analyses are available 
from the producer of the report.
Identifying Risks and Limitations 
Members and candidates must outline to clients and prospective clients significant 
risks and limitations of the analysis contained in their investment products or recom -
mendations. The type and nature of significant risks will depend on the investment

process that members and candidates are following and on the personal circumstances 
of the client. In general, the use of leverage constitutes a significant risk and should 
be disclosed. 
Members and candidates must adequately disclose the general market-  related 
risks and the risks associated with the use of complex financial instruments that are 
deemed significant. Other types of risks that members and candidates may consider 
disclosing include, but are not limited to, counterparty risk, country risk, sector or 
industry risk, security-  specific risk, and credit risk.
Investment securities and vehicles may have limiting factors that influence a client’s 
or potential client’s investment decision. Members and candidates must report to 
clients and prospective clients the existence of limitations significant to the decision-  
making process. Examples of such factors and attributes include, but are not limited

to, investment liquidity and capacity. Liquidity is the ability to liquidate an investment 
on a timely basis at a reasonable cost. Capacity is the investment amount beyond 
which returns will be negatively affected by new investments.

Reading 3 ■ Guidance for Standards I–VII 168
The appropriateness of risk disclosure should be assessed on the basis of what was 
known at the time the investment action was taken (often called an ex ante  basis). 
Members and candidates must disclose significant risks known to them at the time 
of the disclosure. Members and candidates cannot be expected to disclose risks they 
are unaware of at the time recommendations or investment actions are made. In 
assessing compliance with Standard V(B), it is important to establish knowledge of a 
purported significant risk or limitation. A one-  time investment loss that occurs after 
the disclosure does not constitute a pertinent factor in assessing whether significant 
risks and limitations were properly disclosed. Having no knowledge of a risk or lim -
itation that subsequently triggers a loss may reveal a deficiency in the diligence and 
reasonable basis of the research of the member or candidate but may not reveal a 
breach of Standard V(B).

Report Presentation
Once the analytical process has been completed, the member or candidate who prepares 
the report must include those elements that are important to the analysis and conclu -
sions of the report so that the reader can follow and challenge the report’s reasoning. 
A report writer who has done adequate investigation may emphasize certain areas, 
touch briefly on others, and omit certain aspects deemed unimportant. For instance, 
a report may dwell on a quarterly earnings release or new-  product introduction and 
omit other matters as long as the analyst clearly stipulates the limits to the scope of 
the report.
Investment advice based on quantitative research and analysis must be supported 
by readily available reference material and should be applied in a manner consistent 
with previously applied methodology. If changes in methodology are made, they 
should be highlighted.
Distinction between Facts and Opinions in Reports

Standard V(B) requires that opinion be separated from fact. Violations often occur 
when reports fail to separate the past from the future by not indicating that earnings 
estimates, changes in the outlook for dividends, or future market price information 
are opinions  subject to future circumstances. 
In the case of complex quantitative analyses, members and candidates must clearly 
separate fact from statistical conjecture and should identify the known limitations of 
an analysis. Members and candidates may violate Standard V(B) by failing to identify 
the limits of statistically developed projections because such omission leaves readers 
unaware of the limits of the published projections.
Members and candidates should explicitly discuss with clients and prospective 
clients the assumptions used in the investment models and processes to generate the 
analysis. Caution should be used in promoting the perceived accuracy of any model or

process to clients because the ultimate output is merely an estimate of future results 
and not a certainty.
Because the selection of relevant factors is an analytical skill, determination of whether 
a member or candidate has used reasonable judgment in excluding and including 
information in research reports depends heavily on case-  by- case review rather than 
a specific checklist. 
Members and candidates should encourage their firms to have a rigorous methodol -
ogy for reviewing research that is created for publication and dissemination to clients.

Standard V: Investment Analysis, Recommendations, and Actions 169
To assist in the after-  the- fact review of a report, the member or candidate must 
maintain records indicating the nature of the research and should, if asked, be able to 
supply additional information to the client (or any user of the report) covering factors 
not included in the report.
Example 1 (Sufficient Disclosure of Investment System):
Sarah Williamson, director of marketing for Country Technicians, Inc., is convinced 
that she has found the perfect formula for increasing Country Technicians’ income 
and diversifying its product base. Williamson plans to build on Country Technicians’ 
reputation as a leading money manager by marketing an exclusive and expensive 
investment advice letter to high-  net- worth individuals. One hitch in the plan is the 
complexity of Country Technicians’ investment system—a combination of technical

trading rules (based on historical price and volume fluctuations) and portfolio con -
struction rules designed to minimize risk. To simplify the newsletter, she decides to 
include only each week’s top five “buy” and “sell” recommendations and to leave out 
details of the valuation models and the portfolio structuring scheme.
Comment : Williamson’s plans for the newsletter violate Standard  V(B). 
Williamson need not describe the investment system in detail in order to 
implement the advice effectively, but she must inform clients of Country 
Technicians’ basic process and logic. Without understanding the basis for 
a recommendation, clients cannot possibly understand its limitations or 
its inherent risks.
Example 2 (Providing Opinions as Facts):
Richard Dox is a mining analyst for East Bank Securities. He has just finished his report 
on Boisy Bay Minerals. Included in his report is his own assessment of the geological

extent of mineral reserves likely to be found on the company’s land. Dox completed 
this calculation on the basis of the core samples from the company’s latest drilling. 
According to Dox’s calculations, the company has more than 500,000 ounces of gold 
on the property. Dox concludes his research report as follows: “Based on the fact that 
the company has 500,000 ounces of gold to be mined, I recommend a strong BUY. ”
Comment : If Dox issues the report as written, he will violate Standard V(B). 
His calculation of the total gold reserves for the property based on the com -
pany’s recent sample drilling is a quantitative opinion, not a fact. Opinion 
must be distinguished from fact in research reports.
Example 3 (Proper Description of a Security):
Olivia Thomas, an analyst at Government Brokers, Inc., which is a brokerage firm 
specializing in government bond trading, has produced a report that describes an 
investment strategy designed to benefit from an expected decline in US interest rates.

The firm’s derivative products group has designed a structured product that will allow 
the firm’s clients to benefit from this strategy. Thomas’s report describing the strategy 
indicates that high returns are possible if various scenarios for declining interest rates 
are assumed. Citing the proprietary nature of the structured product underlying the 
strategy, the report does not describe in detail how the firm is able to offer such returns 
or the related risks in the scenarios, nor does the report address the likely returns of 
the strategy if, contrary to expectations, interest rates rise.

Reading 3 ■ Guidance for Standards I–VII 170
Comment : Thomas has violated Standard V(B) because her report fails to 
describe properly the basic characteristics of the actual and implied risks 
of the investment strategy, including how the structure was created and 
the degree to which leverage was embedded in the structure. The report 
should include a balanced discussion of how the strategy would perform in 
the case of rising as well as falling interest rates, preferably illustrating how 
the strategies might be expected to perform in the event of a reasonable 
variety of interest rate and credit risk–spread scenarios. If liquidity issues 
are relevant with regard to the valuation of either the derivatives or the 
underlying securities, provisions the firm has made to address those risks 
should also be disclosed.
Example 4 (Notification of Fund Mandate Change):
May & Associates is an aggressive growth manager that has represented itself since

its inception as a specialist at investing in small-  cap US stocks. One of May’s selection 
criteria is a maximum capitalization of US$250 million for any given company. After 
a string of successful years of superior performance relative to its peers, May has 
expanded its client base significantly, to the point at which assets under management 
now exceed US$3 billion. For liquidity purposes, May’s chief investment officer (CIO) 
decides to lift the maximum permissible market-  cap ceiling to US$500 million and 
change the firm’s sales and marketing literature accordingly to inform prospective 
clients and third-  party consultants.
Comment : Although May’s CIO is correct about informing potentially 
interested parties as to the change in investment process, he must also 
notify May’s existing clients. Among the latter group might be a number of 
clients who not only retained May as a small-  cap manager but also retained

mid-  cap and large-  cap specialists in a multiple-  manager approach. Such 
clients could regard May’s change of criteria as a style change that distorts 
their overall asset allocations.
Example 5 (Notification of Fund Mandate Change):
Rather than lifting the ceiling for its universe from US$250 million to US$500 million, 
May & Associates extends its small-  cap universe to include a number of non-  US 
Comment : Standard V(B) requires that May’s CIO advise May’s clients of 
this change because the firm may have been retained by some clients spe -
cifically for its prowess at investing in US small-  cap stocks. Other changes 
that require client notification are introducing derivatives to emulate a 
certain market sector or relaxing various other constraints, such as portfolio 
beta. In all such cases, members and candidates must disclose changes to 
all interested parties.
Example 6 (Notification of Changes to the Investment Process):

RJZ Capital Management is an active value-  style equity manager that selects stocks by 
using a combination of four multifactor models. The firm has found favorable results 
when back testing the most recent 10 years of available market data in a new dividend 
discount model (DDM) designed by the firm. This model is based on projected inflation 
rates, earnings growth rates, and interest rates. The president of RJZ decides to replace 
its simple model that uses price to trailing 12-  month earnings with the new DDM.

Standard V: Investment Analysis, Recommendations, and Actions 171
Comment : Because the introduction of a new and different valuation model 
represents a material change in the investment process, RJZ’s president 
must communicate the change to the firm’s clients. RJZ is moving away 
from a model based on hard data toward a new model that is at least partly 
dependent on the firm’s forecasting skills. Clients would likely view such a 
model as a significant change rather than a mere refinement of RJZ’s process.
Example 7 (Notification of Changes to the Investment Process):
RJZ Capital Management loses the chief architect of its multifactor valuation system. 
Without informing its clients, the president of RJZ decides to redirect the firm’s tal -
ents and resources toward developing a product for passive equity management—a 
product that will emulate the performance of a major market index.
Comment : By failing to disclose to clients a substantial change to its invest -

ment process, the president of RJZ has violated Standard V(B).
Example 8 (Notification of Changes to the Investment Process):
At Fundamental Asset Management, Inc., the responsibility for selecting stocks for 
addition to the firm’s “approved” list has just shifted from individual security analysts 
to a committee consisting of the research director and three senior portfolio managers. 
Eleanor Morales, a portfolio manager with Fundamental Asset Management, thinks 
this change is not important enough to communicate to her clients.
Comment : Morales must disclose the process change to all her clients. 
Some of Fundamental’s clients might be concerned about the morale and 
motivation among the firm’s best research analysts after such a change. 
Moreover, clients might challenge the stock-  picking track record of the 
portfolio managers and might even want to monitor the situation closely.
Example 9 (Sufficient Disclosure of Investment System):

Amanda Chinn is the investment director for Diversified Asset Management, which 
manages the endowment of a charitable organization. Because of recent staff departures, 
Diversified has decided to limit its direct investment focus to large-  cap securities and 
supplement the needs for small-  cap and mid-  cap management by hiring outside fund 
managers. In describing the planned strategy change to the charity, Chinn’s update 
letter states, “ As investment director, I will directly oversee the investment team man -
aging the endowment’s large-  capitalization allocation. I will coordinate the selection 
and ongoing review of external managers responsible for allocations to other classes. ” 
The letter also describes the reasons for the change and the characteristics external 
managers must have to be considered.
Comment : Standard V(B) requires the disclosure of the investment pro -
cess used to construct the portfolio of the fund. Changing the investment

process from managing all classes of investments within the firm to the 
use of external managers is one example of information that needs to be 
communicated to clients. Chinn and her firm have embraced the principles 
of Standard V(B) by providing their client with relevant information. The 
charity can now make a reasonable decision about whether Diversified 
Asset Management remains the appropriate manager for its fund.

Reading 3 ■ Guidance for Standards I–VII 172
Example 10 (Notification of Changes to the Investment Process):
better returns by moving the real estate allocation to Accessible. The only notice of the

Comment : Papis has violated Standard V(B). He attempted to hide the nature 
of his decision to change external managers by making only a limited dis -
closure. The plan recipients and the fund’s trustees need to be aware when 
changes are made to ensure that operational procedures are being followed.
See also Standard IV(C)–Responsibilities of Supervisors, Standard V(A)–
Diligence and Reasonable Basis, and Standard VI(A)–Disclosure of Conflicts.
Example 11 (Notification of Errors):
accurately, his models need to be regularly updated with the latest market data. 
in contact with the firm’s US corporate bond fund manager, John Smith, who has only

development of the new emerging market model and neglects to update the US model.    
of conducting the long and complicated data update, Dupont introduces new codes

Comment : Smith violated V(B) by not disclosing a material error in the 
investment process. Clients should have been informed about the error 
and the corrective actions the firm was undertaking on their behalf.

Standard V: Investment Analysis, Recommendations, and Actions 173
Example 12 (Notification of Risks and Limitations):
Quantitative analyst Yuri Yakovlev has developed an investment strategy that selects 
small-  cap stocks on the basis of quantitative signals. Yakovlev’s strategy typically 
identifies only a small number of stocks (10–20) that tend to be illiquid, but according 
to his backtests, the strategy generates significant risk-  adjusted returns. The partners 
at Yakovlev’s firm, QSC Capital, are impressed by these results. After a thorough 
examination of the strategy’s risks, stress testing, historical back testing, and scenario 
analysis, QSC decides to seed the strategy with US$10 million of internal capital in 
order for Yakovlev to create a track record for the strategy. 
After two years, the strategy has generated performance returns greater than the 
appropriate benchmark and the Sharpe ratio of the fund is close to 1.0. On the basis of

these results, QSC decides to actively market the fund to large institutional investors. 
While creating the offering materials, Yakovlev informs the marketing team that the 
capacity of the strategy is limited. The extent of the limitation is difficult to ascertain 
with precision; it depends on market liquidity and other factors in his model that 
can evolve over time. Yakovlev indicates that given the current market conditions, 
investments in the fund beyond US$100 million of capital could become more difficult 
and negatively affect expected fund returns. 
Alan Wellard, the manager of the marketing team, is a partner with 30 years of 
marketing experience and explains to Yakovlev that these are complex technical issues 
that will muddy the marketing message. According to Wellard, the offering material 
should focus solely on the great track record of the fund. Yakovlev does not object 
because the fund has only US$12 million of capital, very far from the US$100 million 
threshold.

threshold. 
Comment : Yakovlev and Wellard have not appropriately disclosed a signif -
icant limitation associated with the investment product. Yakovlev believes 
this limitation, once reached, will materially affect the returns of the fund. 
Although the fund is currently far from the US$100 million mark, current 
and prospective investors must be made aware of this capacity issue. If 
significant limitations are complicated to grasp and clients do not have the 
technical background required to understand them, Yakovlev and Wellard 
should either educate the clients or ascertain whether the fund is suitable 
for each client. 
Example 13 (Notification of Risks and Limitations):
Brickell Advisers offers investment advisory services mainly to South American clients. 
Julietta Ramon, a risk analyst at Brickell, describes to clients how the firm uses value at 
risk (VaR) analysis to track the risk of its strategies. Ramon assures clients that calcu -

lating a VaR at a 99% confidence level, using a 20-  day holding period, and applying a 
methodology based on an ex ante  Monte Carlo simulation is extremely effective. The 
firm has never had losses greater than those predicted by this VaR analysis.
Comment : Ramon has not sufficiently communicated the risks associated 
with the investment process to satisfy the requirements of Standard V(B). 
The losses predicted by a VaR analysis depend greatly on the inputs used 
in the model. The size and probability of losses can differ significantly from 
what an individual model predicts. Ramon must disclose how the inputs 
were selected and the potential limitations and risks associated with the 
investment strategy.

Reading 3 ■ Guidance for Standards I–VII 174
Example 14 (Notification of Risks and Limitations):
Lily Smith attended an industry conference and noticed that John Baker, an invest -
ment manager with Baker Associates, attracted a great deal of attention from the 
conference participants. On the basis of her knowledge of Baker’s reputation and the 
interest he received at the conference, Smith recommends adding Baker Associates 
to the approved manager platform. Her recommendation to the approval committee 
included the statement “John Baker is well respected in the industry, and his insights 
are consistently sought after by investors. Our clients are sure to benefit from investing 
with Baker Associates. ”
Comment : Smith is not appropriately separating facts from opinions in her 
recommendation to include the manager within the platform. Her actions 
conflict with the requirements of Standard V(B). Smith is relying on her 
opinions about Baker’s reputation and the fact that many attendees were

talking with him at the conference. Smith should also review the require -
ments of Standard V(A) regarding reasonable basis to determine the level 
of review necessary to recommend Baker Associates.
Standard V(C) Record Retention
Members and Candidates must develop and maintain appropriate records to support 
their investment analyses, recommendations, actions, and other investment-  related 
Guidance
■■New Media Records
■■Records Are Property of the Firm
■■Local Requirements
Members and candidates must retain records that substantiate the scope of their 
research and reasons for their actions or conclusions. The retention requirement 
applies to decisions to buy or sell a security as well as reviews undertaken that do 
not lead to a change in position. Which records are required to support recommen -
dations or investment actions depends on the role of the member or candidate in the

investment decision-  making process. Records may be maintained either in hard copy 
or electronic form.
Some examples of supporting documentation that assists the member or candidate 
in meeting the requirements for retention are as follows:
■■personal notes from meetings with the covered company,
■■press releases or presentations issued by the covered company,
■■computer-  based model outputs and analyses,
■■computer-  based model input parameters,
■■risk analyses of securities’ impacts on a portfolio,
■■selection criteria for external advisers,

Standard V: Investment Analysis, Recommendations, and Actions 175
■■notes from clients from meetings to review investment policy statements, and
■■outside research reports.
New Media Records
The increased use of new and evolving technological formats (e.g., social media) for 
gathering and sharing information creates new challenges in maintaining the appro -
priate records and files. The nature or format of the information does not remove a 
member’s or candidate’s responsibility to maintain a record of information used in 
his or her analysis or communicated to clients.
Members and candidates should understand that although employers and local 
regulators are developing digital media retention policies, these policies may lag behind 
the advent of new communication channels. Such lag places greater responsibility on 
the individual for ensuring that all relevant information is retained. Examples of non-  
print media formats that should be retained include, but are not limited to,
■■e- mails,

■■text messages,
■■blog posts, and
■■Twitter posts.
Records Are Property of the Firm
As a general matter, records created as part of a member’s or candidate’s professional 
activity on behalf of his or her employer are the property of the firm. When a mem -
ber or candidate leaves a firm to seek other employment, the member or candidate 
cannot take the property of the firm, including original forms or copies of supporting 
records of the member’s or candidate’s work, to the new employer without the express 
consent of the previous employer. The member or candidate cannot use historical 
recommendations or research reports created at the previous firm because the sup -
porting documentation is unavailable. For future use, the member or candidate must 
re- create the supporting records at the new firm with information gathered through 
public sources or directly from the covered company and not from memory or sources 
obtained at the previous employer.
Local Requirements

Local regulators often impose requirements on members, candidates, and their firms 
related to record retention that must be followed. Firms may also implement policies 
detailing the applicable time frame for retaining research and client communication 
records. Fulfilling such regulatory and firm requirements satisfies the requirements of 
Standard V(C). In the absence of regulatory guidance or firm policies, CFA Institute 
recommends maintaining records for at least seven years.
The responsibility to maintain records that support investment action generally falls 
with the firm rather than individuals. Members and candidates must, however, archive 
research notes and other documents, either electronically or in hard copy, that support 
their current investment-  related communications. Doing so will assist their firms in 
complying with requirements for preservation of internal or external records.

Reading 3 ■ Guidance for Standards I–VII 176
Example 1 (Record Retention and IPS Objectives and Recommendations):
One of Nikolas Lindstrom’s clients is upset by the negative investment returns of his 
equity portfolio. The investment policy statement for the client requires that the port -
folio manager follow a benchmark-  oriented approach. The benchmark for the client 
includes a 35% investment allocation in the technology sector. The client acknowl -
edges that this allocation was appropriate, but over the past three years, technology 
stocks have suffered severe losses. The client complains to the investment manager 
for allocating so much money to this sector.
Comment : For Lindstrom, having appropriate records is important to 
show that over the past three years, the portion of technology stocks in 
the benchmark index was 35%, as called for in the IPS. Lindstrom should 
also have the client’s IPS stating that the benchmark was appropriate for

the client’s investment objectives. He should also have records indicating 
that the investment has been explained appropriately to the client and that 
the IPS was updated on a regular basis. Taking these actions, Lindstrom 
would be in compliance with Standard V(C).
Example 2 (Record Retention and Research Process):
Malcolm Young is a research analyst who writes numerous reports rating companies 
in the luxury retail industry. His reports are based on a variety of sources, including 
interviews with company managers, manufacturers, and economists; on-  site com -
pany visits; customer surveys; and secondary research from analysts covering related 
Comment : Young must carefully document and keep copies of all the infor -
mation that goes into his reports, including the secondary or third-  party 
research of other analysts. Failure to maintain such files would violate 
Standard V(C).
Example 3 (Records as Firm, Not Employee, Property):

Martin Blank develops an analytical model while he is employed by Green Partners 
Investment Management, LLP (GPIM). While at the firm, he systematically docu -
ments the assumptions that make up the model as well as his reasoning behind the 
assumptions. As a result of the success of his model, Blank is hired to be the head 
of the research department of one of GPIM’s competitors. Blank takes copies of the 
records supporting his model to his new firm.
Comment : The records created by Blank supporting the research model he 
developed at GPIM are the records of GPIM. Taking the documents with 
him to his new employer without GPIM’s permission violates Standard V(C). 
To use the model in the future, Blank must re-  create the records supporting 
his model at the new firm.

Standard VI: Conflicts of Interest 177
STANDARD VI: CONFLICTS OF INTEREST
Standard VI(A) Disclosure of Conflicts
Members and Candidates must make full and fair disclosure of all matters that could 
reasonably be expected to impair their independence and objectivity or interfere with 
respective duties to their clients, prospective clients, and employer. Members and 
Candidates must ensure that such disclosures are prominent, are delivered in plain 
language, and communicate the relevant information effectively.
Guidance
■■Disclosure of Conflicts to Employers
■■Disclosure to Clients
■■Cross-  Departmental Conflicts
■■Conflicts with Stock Ownership
■■Conflicts as a Director
Best practice is to avoid actual conflicts or the appearance of conflicts of interest when 
possible. Conflicts of interest often arise in the investment profession. Conflicts can 
occur between the interests of clients, the interests of employers, and the member’s

or candidate’s own personal interests. Common sources for conflict are compensation 
structures, especially incentive and bonus structures that provide immediate returns 
for members and candidates with little or no consideration of long-  term value creation.
Identifying and managing these conflicts is a critical part of working in the invest -
ment industry and can take many forms. When conflicts cannot be reasonably avoided, 
clear and complete disclosure of their existence is necessary.
Standard  VI(A) protects investors and employers by requiring members and 
candidates to fully disclose to clients, potential clients, and employers all actual and 
potential conflicts of interest. Once a member or candidate has made full disclosure, 
the member’s or candidate’s employer, clients, and prospective clients will have the 
information needed to evaluate the objectivity of the investment advice or action 
taken on their behalf.

To be effective, disclosures must be prominent and must be made in plain language 
and in a manner designed to effectively communicate the information. Members and 
candidates have the responsibility of determining how often, in what manner, and in 
what particular circumstances the disclosure of conflicts must be made. Best prac -
tices dictate updating disclosures when the nature of a conflict of interest changes 
materially—for example, if the nature of a conflict of interest worsens through the 
introduction of bonuses based on each quarter’s profits as to opposed annual profits. 
In making and updating disclosures of conflicts of interest, members and candidates 
should err on the side of caution to ensure that conflicts are effectively communicated.

Reading 3 ■ Guidance for Standards I–VII 178
Disclosure of Conflicts to Employers
Disclosure of conflicts to employers may be appropriate in many instances. When 
reporting conflicts of interest to employers, members and candidates must give their 
employers enough information to assess the impact of the conflict. By complying 
with employer guidelines, members and candidates allow their employers to avoid 
potentially embarrassing and costly ethical or regulatory violations.
Reportable situations include conflicts that would interfere with rendering unbiased 
investment advice and conflicts that would cause a member or candidate to act not 
in the employer’s best interest. The same circumstances that generate conflicts to be 
reported to clients and prospective clients also would dictate reporting to employers. 
Ownership of stocks analyzed or recommended, participation on outside boards, 
and financial or other pressures that could influence a decision are to be promptly

reported to the employer so that their impact can be assessed and a decision on how 
to resolve the conflict can be made.
The mere appearance of a conflict of interest may create problems for members, 
candidates, and their employers. Therefore, many of the conflicts previously mentioned 
could be explicitly prohibited by an employer. For example, many employers restrict 
personal trading, outside board membership, and related activities to prevent situa -
tions that might not normally be considered problematic from a conflict-  of- interest 
point of view but that could give the appearance of a conflict of interest. Members 
and candidates must comply with these restrictions. Members and candidates must 
take reasonable steps to avoid conflicts and, if they occur inadvertently, must report 
them promptly so that the employer and the member or candidate can resolve them 
as quickly and effectively as possible.
Standard  VI(A) also deals with a member’s or candidate’s conflicts of interest

that might be detrimental to the employer’s business. Any potential conflict situation 
that could prevent clear judgment about or full commitment to the execution of a 
member’s or candidate’s duties to the employer should be reported to the member’s 
or candidate’s employer and promptly resolved.
Disclosure to Clients
Members and candidates must maintain their objectivity when rendering investment 
advice or taking investment action. Investment advice or actions may be perceived to 
be tainted in numerous situations. Can a member or candidate remain objective if, 
on behalf of the firm, the member or candidate obtains or assists in obtaining fees for 
services? Can a member or candidate give objective advice if he or she owns stock in 
the company that is the subject of an investment recommendation or if the member 
or candidate has a close personal relationship with the company managers? Requiring 
members and candidates to disclose all matters that reasonably could be expected to

impair the member’s or candidate’s objectivity allows clients and prospective clients 
to judge motives and possible biases for themselves.
Often in the investment industry, a conflict, or the perception of a conflict, 
cannot be avoided. The most obvious conflicts of interest, which should always be 
disclosed, are relationships between an issuer and the member, the candidate, or his 
or her firm (such as a directorship or consultancy by a member; investment banking, 
underwriting, and financial relationships; broker/dealer market-  making activities; and 
material beneficial ownership of stock). For the purposes of Standard VI(A), members 
and candidates beneficially own securities or other investments if they have a direct 
or indirect pecuniary interest in the securities, have the power to vote or direct the 
voting of the shares of the securities or investments, or have the power to dispose or 
direct the disposition of the security or investment.

Standard VI: Conflicts of Interest 179
A member or candidate must take reasonable steps to determine whether a con -
flict of interest exists and disclose to clients any known conflicts of the member’s or 
candidate’s firm. Disclosure of broker/dealer market-  making activities alerts clients 
that a purchase or sale might be made from or to the firm’s principal account and that 
the firm has a special interest in the price of the stock.
Additionally, disclosures should be made to clients regarding fee arrangements, 
subadvisory agreements, or other situations involving nonstandard fee structures. 
Equally important is the disclosure of arrangements in which the firm benefits directly 
from investment recommendations. An obvious conflict of interest is the rebate of a 
portion of the service fee some classes of mutual funds charge to investors. Members 
and candidates should ensure that their firms disclose such relationships so clients

can fully understand the costs of their investments and the benefits received by their 
investment manager’s employer.
Cross-  Departmental Conflicts
Other circumstances can give rise to actual or potential conflicts of interest. For 
instance, a sell-  side analyst working for a broker/dealer may be encouraged, not only by 
members of her or his own firm but by corporate issuers themselves, to write research 
reports about particular companies. The buy-  side analyst is likely to be faced with 
similar conflicts as banks exercise their underwriting and security-  dealing powers. The 
marketing division may ask an analyst to recommend the stock of a certain company 
in order to obtain business from that company.
The potential for conflicts of interest also exists with broker-  sponsored limited 
partnerships formed to invest venture capital. Increasingly, members and candidates 
are expected not only to follow issues from these partnerships once they are offered

to the public but also to promote the issues in the secondary market after public 
offerings. Members, candidates, and their firms should attempt to resolve situations 
presenting potential conflicts of interest or disclose them in accordance with the 
principles set forth in Standard VI(A).
Conflicts with Stock Ownership
The most prevalent conflict requiring disclosure under Standard VI(A) is a member’s 
or candidate’s ownership of stock in companies that he or she recommends to clients 
or that clients hold. Clearly, the easiest method for preventing a conflict is to prohibit 
members and candidates from owning any such securities, but this approach is overly 
burdensome and discriminates against members and candidates.
Therefore, sell-  side members and candidates should disclose any materially benefi -
cial ownership interest in a security or other investment that the member or candidate 
is recommending. Buy-  side members and candidates should disclose their procedures

for reporting requirements for personal transactions. Conflicts arising from personal 
investing are discussed more fully in the guidance for Standard VI(B).
Conflicts as a Director
Service as a director poses three basic conflicts of interest. First, a conflict may exist 
between the duties owed to clients and the duties owed to shareholders of the com -
pany. Second, investment personnel who serve as directors may receive the securities 
or options to purchase securities of the company as compensation for serving on the 
board, which could raise questions about trading actions that might increase the value 
of those securities. Third, board service creates the opportunity to receive material 
nonpublic information involving the company. Even though the information is confi -
dential, the perception could be that information not available to the public is being 
communicated to a director’s firm—whether a broker, investment adviser, or other

Reading 3 ■ Guidance for Standards I–VII 180
type of organization. When members or candidates providing investment services also 
serve as directors, they should be isolated from those making investment decisions 
by the use of firewalls or similar restrictions.
Members or candidates should disclose special compensation arrangements with the 
employer that might conflict with client interests, such as bonuses based on short-  term 
performance criteria, commissions, incentive fees, performance fees, and referral fees. 
If the member’s or candidate’s firm does not permit such disclosure, the member or 
candidate should document the request and may consider dissociating from the activity.
Members’ and candidates’ firms are encouraged to include information on compen -
sation packages in firms’ promotional literature. If a member or candidate manages a 
portfolio for which the fee is based on capital gains or capital appreciation (a perfor -

mance fee), this information should be disclosed to clients. If a member, a candidate, 
or a member’s or candidate’s firm has outstanding agent options to buy stock as part 
of the compensation package for corporate financing activities, the amount and expi -
ration date of these options should be disclosed as a footnote to any research report 
published by the member’s or candidate’s firm.
Example 1 (Conflict of Interest and Business Relationships):
Hunter Weiss is a research analyst with Farmington Company, a broker and invest -
ment banking firm. Farmington’s merger and acquisition department has represented 
Vimco, a conglomerate, in all of Vimco’s acquisitions for 20 years. From time to time, 
Farmington officers sit on the boards of directors of various Vimco subsidiaries. Weiss 
is writing a research report on Vimco.
Comment : Weiss must disclose in his research report Farmington’s special 
relationship with Vimco. Broker/dealer management of and participation

in public offerings must be disclosed in research reports. Because the 
position of underwriter to a company entails a special past and potential 
future relationship with a company that is the subject of investment advice, 
it threatens the independence and objectivity of the report writer and must 
be disclosed.
Example 2 (Conflict of Interest and Business Stock Ownership):
The investment management firm of Dover & Roe sells a 25% interest in its partnership 
to a multinational bank holding company, First of New York. Immediately after the 
sale, Margaret Hobbs, president of Dover & Roe, changes her recommendation for 
First of New York’s common stock from “sell” to “buy” and adds First of New York’s 
commercial paper to Dover & Roe’s approved list for purchase.
Comment : Hobbs must disclose the new relationship with First of New 
York to all Dover & Roe clients. This relationship must also be disclosed to 
clients by the firm’s portfolio managers when they make specific investment

recommendations or take investment actions with respect to First of New 
York’s securities.

Standard VI: Conflicts of Interest 181
Example 3 (Conflict of Interest and Personal Stock Ownership):
Carl Fargmon, a research analyst who follows firms producing office equipment, has 
been recommending purchase of Kincaid Printing because of its innovative new line 
of copiers. After his initial report on the company, Fargmon’s wife inherits from a 
distant relative US$3 million of Kincaid stock. He has been asked to write a follow-  up 
report on Kincaid .
Comment : Fargmon must disclose his wife’s ownership of the Kincaid 
stock to his employer and in his follow-  up report. Best practice would be 
to avoid the conflict by asking his employer to assign another analyst to 
draft the follow-  up report.
Example 4 (Conflict of Interest and Personal Stock Ownership):
Betty Roberts is speculating in penny stocks for her own account and purchases 
100,000 shares of Drew Mining, Inc., for US$0.30 a share. She intends to sell these

shares at the sign of any substantial upward price movement of the stock. A week 
later, her employer asks her to write a report on penny stocks in the mining industry 
to be published in two weeks. Even without owning the Drew stock, Roberts would 
recommend it in her report as a “buy. ” A surge in the price of the stock to the US$2 
range is likely to result once the report is issued.
Comment : Although this holding may not be material, Roberts must dis -
close it in the report and to her employer before writing the report because 
the gain for her will be substantial if the market responds strongly to her 
recommendation. The fact that she has only recently purchased the stock 
adds to the appearance that she is not entirely objective.
Example 5 (Conflict of Interest and Compensation Arrangements):
izes in managing public retirement funds and defined benefit pension plan accounts,

strategy and purchases several high-  beta stocks for client portfolios. These purchases 
Comment : Snead has violated Standard VI(A) by failing to inform her clients

of the changes in her compensation arrangement with her employer, which 
created a conflict of interest between her compensation and her clients’ 
IPSs. Firms may pay employees on the basis of performance, but pressure 
by Thomas Investment Counsel to achieve short-  term performance goals 
is in basic conflict with the objectives of Snead’s accounts.

Reading 3 ■ Guidance for Standards I–VII 182
Example 6 (Conflict of Interest, Options, and Compensation Arrangements):
Wayland Securities works with small companies doing IPOs or secondary offerings. 
Typically, these deals are in the US$10 million to US$50 million range, and as a result, 
the corporate finance fees are quite small. To compensate for the small fees, Wayland 
Securities usually takes “agent options”—that is, rights (exercisable within a two-  year 
time frame) to acquire up to an additional 10% of the current offering. Following an 
IPO performed by Wayland for Falk Resources, Ltd., Darcy Hunter, the head of cor -
porate finance at Wayland, is concerned about receiving value for her Falk Resources 
options. The options are due to expire in one month, and the stock is not doing well. 
She contacts John Fitzpatrick in the research department of Wayland Securities, 
reminds him that he is eligible for 30% of these options, and indicates that now would

be a good time to give some additional coverage to Falk Resources. Fitzpatrick agrees 
and immediately issues a favorable report.
Comment : For Fitzpatrick to avoid being in violation of Standard VI(A), he 
must indicate in the report the volume and expiration date of agent options 
outstanding. Furthermore, because he is personally eligible for some of 
the options, Fitzpatrick must disclose the extent of this compensation. He 
also must be careful to not violate his duty of independence and objectivity 
under Standard I(B).
Example 7 (Conflict of Interest and Compensation Arrangements):
Gary Carter is a representative with Bengal International, a registered broker/dealer. 
Carter is approached by a stock promoter for Badger Company, who offers to pay 
Carter additional compensation for sales of Badger Company’s stock to Carter’s clients. 
Carter accepts the stock promoter’s offer but does not disclose the arrangements to

his clients or to his employer. Carter sells shares of the stock to his clients.
Comment : Carter has violated Standard VI(A) by failing to disclose to clients 
that he is receiving additional compensation for recommending and selling 
Badger stock. Because he did not disclose the arrangement with Badger to 
his clients, the clients were unable to evaluate whether Carter’s recommen -
dations to buy Badger were affected by this arrangement. Carter’s conduct 
also violated Standard VI(A) by failing to disclose to his employer monetary 
compensation received in addition to the compensation and benefits con -
ferred by his employer. Carter was required by Standard VI(A) to disclose 
the arrangement with Badger to his employer so that his employer could 
evaluate whether the arrangement affected Carter’s objectivity and loyalty.
Example 8 (Conflict of Interest and Directorship):
Carol Corky, a senior portfolio manager for Universal Management, recently became

involved as a trustee with the Chelsea Foundation, a large not-  for- profit foundation in 
her hometown. Universal is a small money manager (with assets under management 
of approximately US$100  million) that caters to individual investors. Chelsea has 
assets in excess of US$2 billion. Corky does not believe informing Universal of her 
involvement with Chelsea is necessary.
Comment : By failing to inform Universal of her involvement with Chelsea, 
Corky violated Standard VI(A). Given the large size of the endowment at 
Chelsea, Corky’s new role as a trustee can reasonably be expected to be 
time consuming, to the possible detriment of Corky’s portfolio responsi -
bilities with Universal. Also, as a trustee, Corky may become involved in 
the investment decisions at Chelsea. Therefore, Standard VI(A) obligates 
Corky to discuss becoming a trustee at Chelsea with her compliance officer

Standard VI: Conflicts of Interest 183
or supervisor at Universal before accepting the position, and she should 
have disclosed the degree to which she would be involved in investment 
decisions at Chelsea.
Example 9 (Conflict of Interest and Personal Trading):
Bruce Smith covers eastern European equities for Marlborough Investments, an 
investment management firm with a strong presence in emerging markets. While 
on a business trip to Russia, Smith learns that investing in Russian equities directly 
is difficult but that equity-  linked notes that replicate the performance of underlying 
Russian equities can be purchased from a New York–based investment bank. Believing 
that his firm would not be interested in such a security, Smith purchases a note linked 
to a Russian telecommunications company for his own account without informing 
Marlborough. A month later, Smith decides that the firm should consider investing

in Russian equities by way of the equity-  linked notes. He prepares a write-  up on the 
market that concludes with a recommendation to purchase several of the notes. One 
note he recommends is linked to the same Russian telecom company that Smith holds 
in his personal account.
Comment : Smith has violated Standard VI(A) by failing to disclose his pur -
chase and ownership of the note linked to the Russian telecom company. 
Smith is required by the standard to disclose the investment opportunity 
to his employer and look to his company’s policies on personal trading to 
determine whether it was proper for him to purchase the note for his own 
account. By purchasing the note, Smith may or may not have impaired his 
ability to make an unbiased and objective assessment of the appropriate -
ness of the derivative instrument for his firm, but Smith’s failure to disclose 
the purchase to his employer impaired his employer’s ability to decide

whether his ownership of the security is a conflict of interest that might 
affect Smith’s future recommendations. Then, when he recommended the 
particular telecom notes to his firm, Smith compounded his problems by 
not disclosing that he owned the notes in his personal account—a clear 
conflict of interest.
Example 10 (Conflict of Interest and Requested Favors):

Comment : Papis has violated Standard  VI(A) by not disclosing to his 
employer his personal relationship with Nagle. Disclosure of his past his -
tory with Nagle would allow his firm to determine whether the conflict 
may have impaired Papis’s independence in deciding to change managers.
Diligence and Reasonable Basis, and Standard V(B)–Communication with 
Clients and Prospective Clients.

Reading 3 ■ Guidance for Standards I–VII 184
Example 11 (Conflict of Interest and Business Relationships):
Bob Wade, trust manager for Central Midas Bank, was approached by Western Funds 
about promoting its family of funds, with special interest in the service-  fee class. To 
entice Central to promote this class, Western Funds offered to pay the bank a service 
fee of 0.25%. Without disclosing the fee being offered to the bank, Wade asked one of 
the investment managers to review the Western Funds family of funds to determine 
whether they were suitable for clients of Central. The manager completed the normal 
due diligence review and determined that the funds were fairly valued in the market 
with fee structures on a par with their competitors. Wade decided to accept Western’s 
offer and instructed the team of portfolio managers to exclusively promote these funds 
and the service-  fee class to clients seeking to invest new funds or transfer from their

current investments. So as to not influence the investment managers, Wade did not 
disclose the fee offer and allowed that income to flow directly to the bank.
Comment : Wade is violating Standard VI(A) by not disclosing the portion 
of the service fee being paid to Central. Although the investment manag -
ers may not be influenced by the fee, neither they nor the client have the 
proper information about Wade’s decision to exclusively market this fund 
family and class of investments. Central may come to rely on the new fee as 
a component of the firm’s profitability and may be unwilling to offer other 
products in the future that could affect the fees received.
Example 12 (Disclosure of Conflicts to Employers):
Yehudit Dagan is a portfolio manager for Risk Management Bank (RMB), whose cli -
ents include retirement plans and corporations. RMB provides a defined contribution

retirement plan for its employees that offers 20 large diversified mutual fund invest -
ment options, including a mutual fund managed by Dagan’s RMB colleagues. After 
being employed for six months, Dagan became eligible to participate in the retirement 
plan, and she intends to allocate her retirement plan assets in six of the investment 
options, including the fund managed by her RMB colleagues. Dagan is concerned 
that joining the plan will lead to a potentially significant amount of paperwork for 
her (e.g., disclosure of her retirement account holdings and needing preclearance for 
her transactions), especially with her investing in the in-  house fund. 
Comment : Standard VI(A) would not require Dagan to disclosure her per -
sonal or retirement investments in large diversified mutual funds, unless 
specifically required by her employer. For practical reasons, the standard 
does not require Dagan to gain preclearance for ongoing payroll deduction

contributions to retirement plan account investment options. 
Dagan should ensure that her firm does not have a specific policy 
regarding investment—whether personal or in the retirement account—for 
funds managed by the company’s employees. These mutual funds may be 
subject to the company’s disclosure, preclearance, and trading restriction 
procedures to identify possible conflicts prior to the execution of trades.

Standard VI: Conflicts of Interest 185
Standard VI(B) Priority of Transactions
Investment transactions for clients and employers must have priority over investment 
transactions in which a Member or Candidate is the beneficial owner.
Guidance
■■Avoiding Potential Conflicts
■■Personal Trading Secondary to Trading for Clients
■■Standards for Nonpublic Information
■■Impact on All Accounts with Beneficial Ownership
Standard VI(B) reinforces the responsibility of members and candidates to give the 
interests of their clients and employers priority over their personal financial interests. 
This standard is designed to prevent any potential conflict of interest or the appearance 
of a conflict of interest with respect to personal transactions. Client interests have 
priority. Client transactions must take precedence over transactions made on behalf 
of the member’s or candidate’s firm or personal transactions.
Avoiding Potential Conflicts

Conflicts between the client’s interest and an investment professional’s personal 
interest may occur. Although conflicts of interest exist, nothing is inherently unethical 
about individual managers, advisers, or mutual fund employees making money from 
personal investments as long as (1) the client is not disadvantaged by the trade, (2) the 
investment professional does not benefit personally from trades undertaken for clients, 
and (3) the investment professional complies with applicable regulatory requirements.
Some situations occur where a member or candidate may need to enter a personal 
transaction that runs counter to current recommendations or what the portfolio 
manager is doing for client portfolios. For example, a member or candidate may be 
required at some point to sell an asset to make a college tuition payment or a down 
payment on a home, to meet a margin call, or so on. The sale may be contrary to the

long-  term advice the member or candidate is currently providing to clients.  In these 
situations, the same three criteria given in the preceding paragraph should be applied 
in the transaction so as to not violate Standard VI(B).
Personal Trading Secondary to Trading for Clients
Standard VI(B) states that transactions for clients and employers must have priority 
over transactions in securities or other investments for which a member or candidate 
is the beneficial owner. The objective of the standard is to prevent personal trans -
actions from adversely affecting the interests of clients or employers. A member or 
candidate having the same investment positions or being co-  invested with clients 
does not always create a conflict. Some clients in certain investment situations require 
members or candidates to have aligned interests. Personal investment positions or 
transactions of members or candidates or their firm should never, however, adversely 
affect client investments.

Reading 3 ■ Guidance for Standards I–VII 186
Standards for Nonpublic Information
Standard VI(B) covers the activities of members and candidates who have knowledge 
of pending transactions that may be made on behalf of their clients or employers, 
who have access to nonpublic information during the normal preparation of research 
recommendations, or who take investment actions. Members and candidates are 
prohibited from conveying nonpublic information to any person whose relationship 
to the member or candidate makes the member or candidate a beneficial owner of 
the person’s securities. Members and candidates must not convey this information to 
any other person if the nonpublic information can be deemed material.
Impact on All Accounts with Beneficial Ownership
Members or candidates may undertake transactions in accounts for which they are a 
beneficial owner only after their clients and employers have had adequate opportu -

nity to act on a recommendation. Personal transactions include those made for the 
member’s or candidate’s own account, for family (including spouse, children, and 
other immediate family members) accounts, and for accounts in which the member 
or candidate has a direct or indirect pecuniary interest, such as a trust or retirement 
account. Family accounts that are client accounts should be treated like any other firm 
account and should neither be given special treatment nor be disadvantaged because 
of the family relationship. If a member or candidate has a beneficial ownership in 
the account, however, the member or candidate may be subject to preclearance or 
reporting requirements of the employer or applicable law.
Policies and procedures designed to prevent potential conflicts of interest, and even the 
appearance of a conflict of interest, with respect to personal transactions are critical

to establishing investor confidence in the securities industry. Therefore, members and 
candidates should urge their firms to establish such policies and procedures. Because 
investment firms vary greatly in assets under management, types of clients, number 
of employees, and so on, each firm should have policies regarding personal investing 
that are best suited to the firm. Members and candidates should then prominently 
disclose these policies to clients and prospective clients.
The specific provisions of each firm’s standards will vary, but all firms should adopt 
certain basic procedures to address the conflict areas created by personal investing. 
These procedures include the following:
■■Limited participation in equity IPOs : Some eagerly awaited IPOs rise signifi -
cantly in value shortly after the issue is brought to market. Because the new 
issue may be highly attractive and sought after, the opportunity to participate in

the IPO may be limited. Therefore, purchases of IPOs by investment personnel 
create conflicts of interest in two principal ways. First, participation in an IPO 
may have the appearance of taking away an attractive investment opportunity 
from clients for personal gain—a clear breach of the duty of loyalty to clients. 
Second, personal purchases in IPOs may have the appearance that the invest -
ment opportunity is being bestowed as an incentive to make future investment 
decisions for the benefit of the party providing the opportunity. Members and 
candidates can avoid these conflicts or appearances of conflicts of interest by 
not participating in IPOs.
Reliable and systematic review procedures should be established to ensure 
that conflicts relating to IPOs are identified and appropriately dealt with by 
supervisors. Members and candidates should preclear their participation in 
IPOs, even in situations without any conflict of interest between a member’s

or candidate’s participation in an IPO and the client’s interests. Members and

Standard VI: Conflicts of Interest 187
candidates should not benefit from the position that their clients occupy in the 
marketplace—through preferred trading, the allocation of limited offerings, or 
oversubscription.
■■Restrictions on private placements : Strict limits should be placed on investment 
personnel acquiring securities in private placements, and appropriate supervi -
sory and review procedures should be established to prevent noncompliance.
Firms do not routinely use private placements for clients (e.g., venture capital 
deals) because of the high risk associated with them. Conflicts related to private 
placements are more significant to members and candidates who manage large 
pools of assets or act as plan sponsors because these managers may be offered 
special opportunities, such as private placements, as a reward or an enticement 
for continuing to do business with a particular broker.
Participation in private placements raises conflict-  of- interest issues that are

similar to issues surrounding IPOs. Investment personnel should not be 
involved in transactions, including (but not limited to) private placements, that 
could be perceived as favors or gifts that seem designed to influence future 
judgment or to reward past business deals.
Whether the venture eventually proves to be good or bad, managers have an 
immediate conflict concerning private placement opportunities. If and when 
the investments go public, participants in private placements have an incentive 
to recommend the investments to clients regardless of the suitability of the 
investments for their clients. Doing so increases the value of the participants’ 
personal portfolios.
■■Establish blackout/restricted periods : Investment personnel involved in the 
investment decision-  making process should establish blackout periods prior to 
trades for clients so that managers cannot take advantage of their knowledge 
of client activity by “front-  running” client trades (trading for one’s personal

account before trading for client accounts).
Individual firms must decide who within the firm should be required to comply 
with the trading restrictions. At a minimum, all individuals who are involved 
in the investment decision-  making process should be subject to the same 
restricted period. Each firm must determine specific requirements related to 
blackout and restricted periods that are most relevant to the firm while ensur -
ing that the procedures are governed by the guiding principles set forth in the 
Code and Standards. Size of firm and type of securities purchased are relevant 
factors. For example, in a large firm, a blackout requirement is, in effect, a total 
trading ban because the firm is continually trading in most securities. In a small 
firm, the blackout period is more likely to prevent the investment manager from 
front-  running.
■■Reporting requirements : Supervisors should establish reporting procedures

for investment personnel, including disclosure of personal holdings/beneficial 
ownerships, confirmations of trades to the firm and the employee, and preclear -
ance procedures. Once trading restrictions are in place, they must be enforced. 
The best method for monitoring and enforcing procedures to eliminate conflicts 
of interest in personal trading is through reporting requirements, including the 
■●Disclosure of holdings in which the employee has a beneficial interest . 
Disclosure by investment personnel to the firm should be made upon com -
mencement of the employment relationship and at least annually thereafter. 
To address privacy considerations, disclosure of personal holdings should be 
handled in a confidential manner by the firm.

Reading 3 ■ Guidance for Standards I–VII 188
■●Providing duplicate confirmations of transactions . Investment personnel 
should be required to direct their brokers to supply to firms duplicate copies 
or confirmations of all their personal securities transactions and copies of 
periodic statements for all securities accounts. The duplicate confirmation 
requirement has two purposes: (1) The requirement sends a message that 
there is independent verification, which reduces the likelihood of unethi -
cal behavior, and (2) it enables verification of the accounting of the flow of 
personal investments that cannot be determined from merely looking at 
holdings.
■●Preclearance procedures . Investment personnel should examine all 
planned personal trades to identify possible conflicts prior to the execution 
of the trades. Preclearance procedures are designed to identify possible con -
flicts before a problem arises.
■■Disclosure of policies : Members and candidates should fully disclose to inves -

tors their firm’s policies regarding personal investing. The information about 
employees’ personal investment activities and policies will foster an atmosphere 
of full and complete disclosure and calm the public’s legitimate concerns about 
the conflicts of interest posed by investment personnel’s personal trading. The 
disclosure must provide helpful information to investors; it should not be sim -
ply boilerplate language, such as “investment personnel are subject to policies 
and procedures regarding their personal trading. ”
Example 1 (Personal Trading):
Research analyst Marlon Long does not recommend purchase of a common stock for 
his employer’s account because he wants to purchase the stock personally and does 
not want to wait until the recommendation is approved and the stock is purchased 
by his employer.
Comment : Long has violated Standard  VI(B) by taking advantage of his 
knowledge of the stock’s value before allowing his employer to benefit

from that information.
Example 2 (Trading for Family Member Account):
Carol Baker, the portfolio manager of an aggressive growth mutual fund, maintains 
an account in her husband’s name at several brokerage firms with which the fund 
and a number of Baker’s other individual clients do a substantial amount of business. 
Whenever a hot issue becomes available, she instructs the brokers to buy it for her 
husband’s account. Because such issues normally are scarce, Baker often acquires 
shares in hot issues but her clients are not able to participate in them.
Comment : To avoid violating Standard VI(B), Baker must acquire shares 
for her mutual fund first and acquire them for her husband’s account only 
after doing so, even though she might miss out on participating in new 
issues via her husband’s account. She also must disclose the trading for her 
husband’s account to her employer because this activity creates a conflict 
between her personal interests and her employer’s interests.

Standard VI: Conflicts of Interest 189
Example 3 (Family Accounts as Equals):
Erin Toffler, a portfolio manager at Esposito Investments, manages the retirement 
account established with the firm by her parents. Whenever IPOs become available, 
she first allocates shares to all her other clients for whom the investment is appropriate; 
only then does she place any remaining portion in her parents’ account, if the issue 
is appropriate for them. She has adopted this procedure so that no one can accuse 
her of favoring her parents.
Comment : Toffler has violated Standard VI(B) by breaching her duty to her 
parents by treating them differently from her other accounts simply because 
of the family relationship. As fee-  paying clients of Esposito Investments, 
Toffler’s parents are entitled to the same treatment as any other client of 
the firm. If Toffler has beneficial ownership in the account, however, and 
Esposito Investments has preclearance and reporting requirements for

personal transactions, she may have to preclear the trades and report the 
transactions to Esposito.
Example 4 (Personal Trading and Disclosure):
Gary Michaels is an entry-  level employee who holds a low-  paying job serving both 
the research department and the investment management department of an active 
investment management firm. He purchases a sports car and begins to wear expensive 
clothes after only a year of employment with the firm. The director of the investment 
management department, who has responsibility for monitoring the personal stock 
transactions of all employees, investigates and discovers that Michaels has made sub -
stantial investment gains by purchasing stocks just before they were put on the firm’s 
recommended “buy” list. Michaels was regularly given the firm’s quarterly personal 
transaction form but declined to complete it.
Comment : Michaels violated Standard  VI(B) by placing personal trans -

actions ahead of client transactions. In addition, his supervisor violated 
Standard IV(C)–Responsibilities of Supervisors  by permitting Michaels to 
continue to perform his assigned tasks without having signed the quarterly 
personal transaction form. Note also that if Michaels had communicated 
information about the firm’s recommendations to a person who traded the 
security, that action would be a misappropriation of the information and a 
violation of Standard II(A)–Material Nonpublic Information.
Example 5 (Trading Prior to Report Dissemination):
A brokerage’s insurance analyst, Denise Wilson, makes a closed-  circuit TV report to 
her firm’s branches around the country. During the broadcast, she includes negative 
comments about a major company in the insurance industry. The following day, Wilson’s 
report is printed and distributed to the sales force and public customers. The report 
recommends that both short-  term traders and intermediate investors take profits by

selling that insurance company’s stock. Seven minutes after the broadcast, however, 
Ellen Riley, head of the firm’s trading department, had closed out a long “call” posi -
tion in the stock. Shortly thereafter, Riley established a sizable “put” position in the 
stock. When asked about her activities, Riley claimed she took the actions to facilitate 
anticipated sales by institutional clients.
Comment : Riley did not give customers an opportunity to buy or sell in the 
options market before the firm itself did. By taking action before the report 
was disseminated, Riley’s firm may have depressed the price of the calls 
and increased the price of the puts. The firm could have avoided a conflict

Reading 3 ■ Guidance for Standards I–VII 190
of interest if it had waited to trade for its own account until its clients had 
an opportunity to receive and assimilate Wilson’s recommendations. As it 
is, Riley’s actions violated Standard VI(B).
Standard VI(C) Referral Fees
Members and Candidates must disclose to their employer, clients, and prospective cli -
ents, as appropriate, any compensation, consideration, or benefit received from or paid 
to others for the recommendation of products or services.
Guidance
Standard VI(C) states the responsibility of members and candidates to inform their 
employer, clients, and prospective clients of any benefit received for referrals of cus -
tomers and clients. Such disclosures allow clients or employers to evaluate (1) any 
partiality shown in any recommendation of services and (2) the full cost of the services. 
Members and candidates must disclose when they pay a fee or provide compensation

to others who have referred prospective clients to the member or candidate.
Appropriate disclosure means that members and candidates must advise the 
client or prospective client, before entry into any formal agreement for services, of 
any benefit given or received for the recommendation of any services provided by the 
member or candidate. In addition, the member or candidate must disclose the nature 
of the consideration or benefit—for example, flat fee or percentage basis, one-  time or 
continuing benefit, based on performance, benefit in the form of provision of research 
or other noncash benefit—together with the estimated dollar value. Consideration 
includes all fees, whether paid in cash, in soft dollars, or in kind.
Members and candidates should encourage their employers to develop procedures 
related to referral fees. The firm may completely restrict such fees. If the firm does not

adopt a strict prohibition of such fees, the procedures should indicate the appropriate 
steps for requesting approval.
Employers should have investment professionals provide to the clients  notification 
of approved referral fee programs and provide the employer regular (at least quarterly) 
updates on the amount and nature of compensation received.
Example 1 (Disclosure of Referral Arrangements and Outside Parties):
Brady Securities, Inc., a broker/dealer, has established a referral arrangement with Lewis 
Brothers, Ltd., an investment counseling firm. In this arrangement, Brady Securities 
refers all prospective tax-  exempt accounts, including pension, profit-  sharing, and 
endowment accounts, to Lewis Brothers. In return, Lewis Brothers makes available 
to Brady Securities on a regular basis the security recommendations and reports of 
its research staff, which registered representatives of Brady Securities use in serving

customers. In addition, Lewis Brothers conducts monthly economic and market reviews 
for Brady Securities personnel and directs all stock commission business generated 
by referral accounts to Brady Securities.

Standard VI: Conflicts of Interest 191
Willard White, a partner in Lewis Brothers, calculates that the incremental costs 
involved in functioning as the research department of Brady Securities are US$20,000 
annually.
Referrals from Brady Securities last year resulted in fee income of US$200,000 
for Lewis Brothers, and directing all stock trades through Brady Securities resulted 
in additional costs to Lewis Brothers’ clients of US$10,000.
Diane Branch, the chief financial officer of Maxwell Inc., contacts White and says 
that she is seeking an investment manager for Maxwell’s profit-  sharing plan. She adds, 
“My friend Harold Hill at Brady Securities recommended your firm without qualifi -
cation, and that’s good enough for me. Do we have a deal?” White accepts the new 
account but does not disclose his firm’s referral arrangement with Brady Securities.
Comment : White has violated Standard VI(C) by failing to inform the pro -

spective customer of the referral fee payable in services and commissions 
for an indefinite period to Brady Securities. Such disclosure could have 
caused Branch to reassess Hill’s recommendation and make a more critical 
evaluation of Lewis Brothers’ services.
Example 2 (Disclosure of Interdepartmental Referral Arrangements):
James Handley works for the trust department of Central Trust Bank. He receives 
compensation for each referral he makes to Central Trust’s brokerage department and 
personal financial management department that results in a sale. He refers several of 
his clients to the personal financial management department but does not disclose 
the arrangement within Central Trust to his clients.
Comment : Handley has violated Standard  VI(C) by not disclosing the 
referral arrangement at Central Trust Bank to his clients. Standard VI(C) 
does not distinguish between referral payments paid by a third party for

referring clients to the third party and internal payments paid within the 
firm to attract new business to a subsidiary. Members and candidates must 
disclose all such referral fees. Therefore, Handley is required to disclose, 
at the time of referral, any referral fee agreement in place among Central 
Trust Bank’s departments. The disclosure should include the nature and 
the value of the benefit and should be made in writing.
Example 3 (Disclosure of Referral Arrangements and Informing Firm):
Katherine Roberts is a portfolio manager at Katama Investments, an advisory firm 
specializing in managing assets for high-  net- worth individuals. Katama’s trading desk 
uses a variety of brokerage houses to execute trades on behalf of its clients. Roberts 
asks the trading desk to direct a large portion of its commissions to Naushon, Inc., a 
small broker/dealer run by one of Roberts’ business school classmates. Katama’s traders

have found that Naushon is not very competitive on pricing, and although Naushon 
generates some research for its trading clients, Katama’s other analysts have found 
most of Naushon’s research to be not especially useful. Nevertheless, the traders do as 
Roberts asks, and in return for receiving a large portion of Katama’s business, Naushon 
recommends the investment services of Roberts and Katama to its wealthiest clients. 
This arrangement is not disclosed to either Katama or the clients referred by Naushon.
Comment : Roberts is violating Standard  VI(C) by failing to inform her 
employer of the referral arrangement.

Reading 3 ■ Guidance for Standards I–VII 192
Example 4 (Disclosure of Referral Arrangements and Outside Organizations):
Alex Burl is a portfolio manager at Helpful Investments, a local investment advisory 
firm. Burl is on the advisory board of his child’s school, which is looking for ways to 
raise money to purchase new playground equipment for the school. Burl discusses a 
plan with his supervisor in which he will donate to the school a portion of his service 
fee from new clients referred by the parents of students at the school. Upon getting 
the approval from Helpful, Burl presents the idea to the school’s advisory board and 
directors. The school agrees to announce the program at the next parent event and 
asks Burl to provide the appropriate written materials to be distributed. A week fol -
lowing the distribution of the flyers, Burl receives the first school-  related referral. In 
establishing the client’s investment policy statement, Burl clearly discusses the school’s

referral and outlines the plans for distributing the donation back to the school.
Comment : Burl has not violated Standard VI(C) because he secured the 
permission of his employer, Helpful Investments, and the school prior to 
beginning the program and because he discussed the arrangement with the 
client at the time the investment policy statement was designed.
Example 5 (Disclosure of Referral Arrangements and Outside Parties):
The sponsor of a state employee pension is seeking to hire a firm to manage the pen -
sion plan’s emerging market allocation. To assist in the review process, the sponsor 
has hired Thomas Arrow as a consultant to solicit proposals from various advisers. 
Arrow is contracted by the sponsor to represent its best interest in selecting the most 
appropriate new manager. The process runs smoothly, and Overseas Investments is 
selected as the new manager.
The following year, news breaks that Arrow is under investigation by the local

regulator for accepting kickbacks from investment managers after they are awarded 
new pension allocations. Overseas Investments is included in the list of firms allegedly 
making these payments. Although the sponsor is happy with the performance of 
Overseas since it has been managing the pension plan’s emerging market funds, the 
sponsor still decides to have an independent review of the proposals and the selection 
process to ensure that Overseas was the appropriate firm for its needs. This review 
confirms that, even though Arrow was being paid by both parties, the recommendation 
of Overseas appeared to be objective and appropriate.
Comment : Arrow has violated Standard VI(C) because he did not disclose 
the fee being paid by Overseas. Withholding this information raises the 
question of a potential lack of objectivity in the recommendation of Overseas 
by Arrow; this aspect is in addition to questions about the legality of having 
firms pay to be considered for an allocation.

Regulators and governmental agencies may adopt requirements con -
cerning allowable consultant activities. Local regulations sometimes include 
having a consultant register with the regulatory agency’s ethics board. 
Regulator policies may include a prohibition on acceptance of payments 
from investment managers receiving allocations and require regular report -
ing of contributions made to political organizations and candidates. Arrow 
would have to adhere to these requirements as well as the Code and 

Standard VII: Responsibilities as a CFA Institute Member or CFA Candidate 193
STANDARD VII: RESPONSIBILITIES AS A CFA 
INSTITUTE MEMBER OR CFA CANDIDATE
Standard VII(A) Conduct as Participants in CFA Institute 
Programs 
Members and Candidates must not engage in any conduct that compromises the rep -
utation or integrity of CFA Institute or the CFA designation or the integrity, validity, or 
security of CFA Institute programs. 
Guidance
■■Confidential Program Information
■■Additional CFA Program Restrictions
■■Expressing an Opinion
Standard VII(A) covers the conduct of CFA Institute members and candidates involved 
with the CFA Program and prohibits any conduct that undermines the public’s con -
fidence that the CFA charter represents a level of achievement based on merit and 
ethical conduct. There is an array of CFA Institute programs beyond the CFA Program 
that provide additional educational and credentialing opportunities, including the

Certificate in Investment Performance Measurement (CIPM) Program and the CFA 
Institute Investment Foundations™ Program. The standard’s function is to hold members 
and candidates to a high ethical criterion while they are participating in or involved 
with any CFA Institute program. Conduct covered includes but is not limited to
■■giving or receiving assistance (cheating) on any CFA Institute examinations;
■■violating the rules, regulations, and testing policies of CFA Institute programs;
■■providing confidential program or exam information to candidates or the 
public;
■■disregarding or attempting to circumvent security measures established for any 
CFA Institute examinations;
■■improperly using an association with CFA Institute to further personal or pro -
fessional goals; and
■■misrepresenting information on the Professional Conduct Statement or in the 
CFA Institute Continuing Education Program.
Confidential Program Information

CFA Institute is vigilant about protecting the integrity of CFA Institute programs’ 
content and examination processes. CFA Institute program rules, regulations, and 
policies prohibit candidates from disclosing confidential material gained during the 
exam process.

Reading 3 ■ Guidance for Standards I–VII 194
Examples of information that cannot be disclosed by candidates sitting for an 
exam include but are not limited to
■■specific details of questions appearing on the exam and
■■broad topical areas and formulas tested or not tested  on the exam.
All aspects of the exam, including questions, broad topical areas, and formulas, 
tested or not tested, are considered confidential until such time as CFA Institute elects 
to release them publicly. This confidentiality requirement allows CFA Institute to 
maintain the integrity and rigor of exams for future candidates. Standard VII(A) does 
not prohibit candidates from discussing nonconfidential information or curriculum 
material with others or in study groups in preparation for the exam.
Candidates increasingly use online forums and new technology as part of their 
exam preparations. CFA Institute actively polices blogs, forums, and related social net -

working groups for information considered confidential. The organization works with 
both individual candidates and the sponsors of online or offline services to promptly 
remove any and all violations. As noted in the discussion of Standard I(A)–Knowledge 
of the Law, candidates, members, and the public are encouraged to report suspected 
violations to CFA Institute.
Additional CFA Program Restrictions
The CFA Program rules, regulations, and policies define additional allowed and dis -
allowed actions concerning the exams. Violating any of the testing policies, such as 
the calculator policy, personal belongings policy, or the Candidate Pledge, constitutes 
a violation of Standard VII(A). Candidates will find all of these policies on the CFA 
Program portion of the CFA Institute website (www.cfainstitute.org). Exhibit 2 pro -
vides the Candidate Pledge, which highlights the respect candidates must have for 
the integrity, validity, and security of the CFA exam.

Members may participate as volunteers  in various aspects of the CFA Program. 
Standard  VII(A) prohibits members from disclosing and/or soliciting confidential 
material gained prior to or during the exam and grading processes with those outside 
the CFA exam development process.
Examples of information that cannot be shared by members involved in developing, 
administering, or grading the exams include but are not limited to
■■questions appearing on the exam or under consideration,
■■deliberation related to the exam process, and
■■information related to the scoring of questions.
Members may also be asked to offer assistance with other CFA Institute pro -
grams, including but not limited to the CIPM and Investment Foundations programs. 
Members participating in any CFA Institute program should do so with the same level 
of integrity and confidentiality as is required of participation in the CFA Program.
Expressing an Opinion

Standard  VII(A) does not cover expressing opinions regarding CFA Institute, the 
CFA Program, or other CFA Institute programs. Members and candidates are free 
to disagree and express their disagreement with CFA Institute on its policies, its 
procedures, or any advocacy positions taken by the organization. When expressing 
a personal opinion, a candidate is prohibited from disclosing content-  specific infor -
mation, including any actual exam question and the information as to subject matter 
covered or not covered in the exam.

Standard VII: Responsibilities as a CFA Institute Member or CFA Candidate 195
Exhibit 2   Sample of CFA Program Testing Policies
Candidate  
PledgeAs a candidate in the CFA Program, I am obligated to follow 
Standard VII(A) of the CFA Institute Standards of Professional 
Conduct, which states that members and candidates must not 
engage in any conduct that compromises the reputation or 
integrity of CFA Institute or the CFA designation or the integrity, 
validity, or security of the CFA exam. 
■■Prior to this exam, I have not given or received information 
regarding the content of this exam. During this exam, I will not 
give or receive any information regarding the content of this 
exam.
■■After this exam, I will not disclose ANY  portion of this exam 
and I will not remove ANY  exam materials from the testing 
room in original or copied form. I understand that all exam 
materials, including my answers, are the property of CFA 
Institute and will not be returned to me in any form.

■■I will follow ALL  rules of the CFA Program as stated on the 
CFA Institute website and the back cover of the exam book. My 
violation of any rules of the CFA Program will result in CFA 
Institute voiding my exam results and may lead to suspension or 
termination of my candidacy in the CFA Program.
Example 1 (Sharing Exam Questions):
Travis Nero serves as a proctor for the administration of the CFA examination in his 
city. In the course of his service, he reviews a copy of the Level II exam on the evening 
prior to the exam’s administration and provides information concerning the exam 
questions to two candidates who use it to prepare for the exam.
Comment : Nero and the two candidates have violated Standard  VII(A). 
By giving information about the exam questions to two candidates, Nero 
provided an unfair advantage to the two candidates and undermined the 
integrity and validity of the Level II exam as an accurate measure of the

knowledge, skills, and abilities necessary to earn the right to use the CFA 
designation. By accepting the information, the candidates also compromised 
the integrity and validity of the Level II exam and undermined the ethical 
framework that is a key part of the designation.
Example 2 (Bringing Written Material into Exam Room):
Loren Sullivan is enrolled to take the Level II CFA examination. He has been having 
difficulty remembering a particular formula, so prior to entering the exam room, he 
writes the formula on the palm of his hand. During the afternoon section of the exam, 
a proctor notices Sullivan looking at the palm of his hand. She asks to see his hand 
and finds the formula.
Comment : Because Sullivan wrote down information from the Candidate 
Body of Knowledge (CBOK) and took that written information into the exam 
room, his conduct compromised the validity of his exam performance and 
violated Standard VII(A). Sullivan’s conduct was also in direct contradiction

with the rules and regulations of the CFA Program, the Candidate Pledge, 
and the CFA Institute Code and Standards.

Reading 3 ■ Guidance for Standards I–VII 196
Example 3 (Writing after Exam Period End):
At the conclusion of the morning section of the Level I CFA examination, the proctors 
announce, “Stop writing now. ” John Davis has not completed the exam, so he continues 
to randomly fill in ovals on his answer sheet. A proctor approaches Davis’s desk and 
reminds him that he should stop writing immediately. Davis, however, continues to 
complete the answer sheet. After the proctor asks him to stop writing two additional 
times, Davis finally puts down his pencil.
Comment : By continuing to complete his exam after time was called, Davis 
has violated Standard VII(A). By continuing to write, Davis took an unfair 
advantage over other candidates, and his conduct compromised the validity 
of his exam performance. Additionally, by not heeding the proctor’s repeated 
instructions, Davis violated the rules and regulations of the CFA Program.
Example 4 (Sharing Exam Content):

After completing Level II of the CFA exam, Annabelle Rossi posts on her blog about 
her experience. She posts the following: “Level II is complete! I think I did fairly well on 
the exam. It was really difficult, but fair. I think I did especially well on the derivatives 
questions. And there were tons of them! I think I counted 18! The ethics questions 
were really hard. I’m glad I spent so much time on the Code and Standards. I was 
surprised to see there were no questions at all about IPO allocations. I expected there 
to be a couple. Well, off to celebrate getting through it. See you tonight?”
Comment : Rossi did not violate Standard VII(A) when she wrote about how 
difficult she found the exam or how well she thinks she may have done. By 
revealing portions of the CBOK covered on the exam and areas not cov -
ered, however, she did violate Standard VII(A) and the Candidate Pledge. 
Depending on the time frame in which the comments were posted, Rossi

not only may have assisted future candidates but also may have provided 
an unfair advantage to candidates yet to sit for the same exam, thereby 
undermining the integrity and validity of the Level II exam.
Example 5 (Sharing Exam Content):
Level I candidate Etienne Gagne has been a frequent visitor to an internet forum 
designed specifically for CFA Program candidates. The week after completing the 
Level I examination, Gagne and several others begin a discussion thread on the forum 
about the most challenging questions and attempt to determine the correct answers.
Comment : Gagne has violated Standard VII(A) by providing and soliciting 
confidential exam information, which compromises the integrity of the exam 
process and violates the Candidate Pledge. In trying to determine correct 
answers to specific questions, the group’s discussion included question-  
specific details considered to be confidential to the CFA Program. 
Example 6 (Sharing Exam Content):

CFA4Sure is a company that produces test-  preparation materials for CFA Program 
candidates. Many candidates register for and use the company’s products. The day after 
the CFA examination, CFA4Sure sends an e-  mail to all its customers asking them to 
share with the company the hardest questions from the exam so that CFA4Sure can 
better prepare its customers for the next exam administration. Marisol Pena e-  mails 
a summary of the questions she found most difficult on the exam.

Standard VII: Responsibilities as a CFA Institute Member or CFA Candidate 197
Comment : Pena has violated Standard VII(A) by disclosing a portion of the 
exam questions. The information provided is considered confidential until 
publicly released by CFA Institute. CFA4Sure is likely to use such feedback 
to refine its review materials for future candidates. Pena’s sharing of the 
specific questions undermines the integrity of the exam while potentially 
making the exam easier for future candidates.
If the CFA4Sure employees who participated in the solicitation of 
confidential CFA Program information are CFA Institute members or 
candidates, they also have violated Standard VII(A).
Example 7 (Discussion of Exam Grading Guidelines and Results):
Prior to participating in grading CFA examinations, Wesley Whitcomb is required to 
sign a CFA Institute Grader Agreement. As part of the Grader Agreement, Whitcomb 
agrees not to reveal or discuss the exam materials with anyone except CFA Institute

staff or other graders. Several weeks after the conclusion of the CFA exam grading, 
Whitcomb tells several colleagues who are candidates in the CFA Program which 
question he graded. He also discusses the guideline answer and adds that few candi -
dates scored well on the question.
Comment : Whitcomb violated Standard  VII(A) by breaking the Grader 
Agreement and disclosing information related to a specific question on the 
exam, which compromised the integrity of the exam process.
Example 8 (Compromising CFA Institute Integrity as a Volunteer):
Jose Ramirez is an investor-  relations consultant for several small companies that 
are seeking greater exposure to investors. He is also the program chair for the CFA 
Institute society in the city where he works. Ramirez schedules only companies that 
are his clients to make presentations to the society and excludes other companies.
Comment : Ramirez, by using his volunteer position at CFA Institute to

benefit himself and his clients, compromises the reputation and integrity 
of CFA Institute and thus violates Standard VII(A).
Example 9 (Compromising CFA Institute Integrity as a Volunteer):
Marguerite Warrenski is a member of the CFA Institute GIPS Executive Committee, 
which oversees the creation, implementation, and revision of the GIPS standards. As 
a member of the Executive Committee, she has advance knowledge of confidential 
information regarding the GIPS standards, including any new or revised standards 
the committee is considering. She tells her clients that her Executive Committee 
membership will allow her to better assist her clients in keeping up with changes to 
the Standards and facilitating their compliance with the changes.
Comment : Warrenski is using her association with the GIPS Executive 
Committee to promote her firm’s services to clients and potential clients. 
In defining her volunteer position at CFA Institute as a strategic business

advantage over competing firms and implying to clients that she would 
use confidential information to further their interests, Warrenski is com -
promising the reputation and integrity of CFA Institute and thus violating 
Standard VII(A). She may factually state her involvement with the Executive 
Committee but cannot infer any special advantage to her clients from such 
participation.

Reading 3 ■ Guidance for Standards I–VII 198
Standard VII(B) Reference to CFA Institute, the CFA Designation, 
and the CFA Program
When referring to CFA Institute, CFA Institute membership, the CFA designation, or 
candidacy in the CFA Program, Members and Candidates must not misrepresent or 
exaggerate the meaning or implications of membership in CFA Institute, holding the 
CFA designation, or candidacy in the CFA Program.
Guidance
■■CFA Institute Membership
■■Using the CFA Designation
■■Referring to Candidacy in the CFA Program
Standard VII(B) is intended to prevent promotional efforts that make promises or 
guarantees that are tied to the CFA designation. Individuals must not exaggerate the 
meaning or implications of membership in CFA Institute, holding the CFA designation, 
or candidacy in the CFA Program.
Standard VII(B) is not intended to prohibit factual statements related to the pos -
itive benefit of earning the CFA designation. However, statements referring to CFA

Institute, the CFA designation, or the CFA Program that overstate the competency of 
an individual or imply, either directly or indirectly, that superior performance can be 
expected from someone with the CFA designation are not allowed under the standard.
Statements that highlight or emphasize the commitment of CFA Institute mem -
bers, CFA charterholders, and CFA candidates to ethical and professional conduct or 
mention the thoroughness and rigor of the CFA Program are appropriate. Members 
and candidates may make claims about the relative merits of CFA Institute, the CFA 
Program, or the Code and Standards as long as those statements are implicitly or 
explicitly stated as the opinion of the speaker. Statements that do not express opinions 
have to be supported by facts.
Standard VII(B) applies to any form of communication, including but not limited 
to communications made in electronic or written form (such as on firm letterhead,

business cards, professional biographies, directory listings, printed advertising, firm 
brochures, or personal resumes) and oral statements made to the public, clients, or 
prospects.
CFA Institute Membership
The term “CFA Institute member” refers to “regular” and “affiliate” members of CFA 
Institute who have met the membership requirements as defined in the CFA Institute 
Bylaws. Once accepted as a CFA Institute member, the member must satisfy the fol -
lowing requirements to maintain his or her status:
■■remit annually to CFA Institute a completed Professional Conduct Statement, 
which renews the commitment to abide by the requirements of the Code and 
Standards and the CFA Institute Professional Conduct Program, and
■■pay applicable CFA Institute membership dues on an annual basis.

Standard VII: Responsibilities as a CFA Institute Member or CFA Candidate 199
If a CFA Institute member fails to meet any of these requirements, the individual is 
no longer considered an active member. Until membership is reactivated, individuals 
must not present themselves to others as active members. They may state, however, 
that they were CFA Institute members in the past or refer to the years when their 
membership was active.
Using the CFA Designation
Those who have earned the right to use the Chartered Financial Analyst designation 
are encouraged to do so but only in a manner that does not misrepresent or exaggerate 
the meaning or implications of the designation. The use of the designation may be 
accompanied by an accurate explanation of the requirements that have been met to 
earn the right to use the designation.
“CFA charterholders” are those individuals who have earned the right to use the 
CFA designation granted by CFA Institute. These people have satisfied certain require -

ments, including completion of the CFA Program and required years of acceptable 
work experience. Once granted the right to use the designation, individuals must also 
satisfy the CFA Institute membership requirements (see above) to maintain their right 
to use the designation.
If a CFA charterholder fails to meet any of the membership requirements, he or 
she forfeits the right to use the CFA designation. Until membership is reactivated, 
individuals must not present themselves to others as CFA charterholders. They may 
state, however, that they were charterholders in the past.
Given the growing popularity of social media, where individuals may anonymously 
express their opinions, pseudonyms or online profile names created to hide a member’s 
identity should not be tagged with the CFA designation.
Use of the CFA designation by a CFA charterholder is governed by the terms and 
conditions of the annual Professional Conduct Statement Agreement, entered into

between CFA Institute and its membership prior to commencement of use of the CFA 
designation and reaffirmed annually.
Referring to Candidacy in the CFA Program
Candidates in the CFA Program may refer to their participation in the CFA Program, 
but such references must clearly state that an individual is a candidate  in the CFA 
Program and must not imply that the candidate has achieved any type of partial des -
ignation. A person is a candidate in the CFA Program if
■■the person’s application for registration in the CFA Program has been accepted 
by CFA Institute, as evidenced by issuance of a notice of acceptance, and the 
person is enrolled to sit for a specified examination or
■■the registered person has sat for a specified examination but exam results have 
not yet been received.
If an individual is registered for the CFA Program but declines to sit for an exam 
or otherwise does not meet the definition of a candidate as described in the CFA

Institute Bylaws, then that individual is no longer considered an active candidate. 
Once the person is enrolled to sit for a future examination, his or her CFA Program 
candidacy resumes.
CFA Program candidates must never state or imply that they have a partial des -
ignation as a result of passing one or more levels or cite an expected completion date 
of any level of the CFA Program. Final award of the charter is subject to meeting the 
CFA Program requirements and approval by the CFA Institute Board of Governors.

Reading 3 ■ Guidance for Standards I–VII 200
If a candidate passes each level of the exam in consecutive years and wants to state 
that he or she did so, that is not a violation of Standard VII(B) because it is a statement 
of fact. If the candidate then goes on to claim or imply superior ability by obtaining the 
designation in only three years, however, he or she is in violation of Standard VII(B).
Exhibit  3 provides examples of proper and improper references to the CFA 
designation.
Exhibit 3   Proper and Improper References to the CFA Designation
Proper References Improper References
“Completion of the CFA Program has 
enhanced my portfolio management 
skills. ”“CFA charterholders achieve better per -
formance results. ”
“John Smith passed all three CFA 
Program examinations in three consecu -
tive years. ”“John Smith is among the elite, having 
passed all three CFA examinations in 
three consecutive attempts. ”
“The CFA designation is globally rec -
ognized and attests to a charterholder’s

ognized and attests to a charterholder’s 
success in a rigorous and comprehensive 
study program in the field of investment 
management and research analysis. ”“ As a CFA charterholder, I am the most 
qualified to manage client investments. ”
“The credibility that the CFA designation 
affords and the skills the CFA Program 
cultivates are key assets for my future 
career development. ”“ As a CFA charterholder, Jane White pro -
vides the best value in trade execution. ”
“I enrolled in the CFA Program to obtain 
the highest set of credentials in the global 
investment management industry. ”“Enrolling as a candidate in the CFA 
Program ensures one of becoming better 
at valuing debt securities. ”
“I passed Level I of the CFA Program. ” “CFA, Level II”
“I am a 2010 Level III candidate in the 
CFA Program. ”“CFA, Expected 2011”
“I passed all three levels of the CFA 
Program and may be eligible for the CFA 
charter upon completion of the required 
work experience. ”“CFA, Expected 2011”

work experience. ”“CFA, Expected 2011”  
“John Smith, Charter Pending”
Misuse of a member’s CFA designation or CFA candidacy or improper reference to it 
is common by those in a member’s or candidate’s firm who do not possess knowledge 
of the requirements of Standard VII(B). As an appropriate step to reduce this risk, 
members and candidates should disseminate written information about Standard VII(B) 
and the accompanying guidance to their firm’s legal, compliance, public relations, and 
marketing departments (see www.cfainstitute.org).
For materials that refer to employees’ affiliation with CFA Institute, members 
and candidates should encourage their firms to create templates that are approved 
by a central authority (such as the compliance department) as being consistent with 
Standard  VII(B). This practice promotes consistency and accuracy in the firm of 
references to CFA Institute membership, the CFA designation, and CFA candidacy.

Standard VII: Responsibilities as a CFA Institute Member or CFA Candidate 201
Example 1 (Passing Exams in Consecutive Years):
An advertisement for AZ Investment Advisors states that all the firm’s principals are 
CFA charterholders and all passed the three examinations on their first attempt. The 
advertisement prominently links this fact to the notion that AZ’s mutual funds have 
achieved superior performance.
Comment : AZ may state that all principals passed the three examinations 
on the first try as long as this statement is true, but it must not be linked 
to performance or imply superior ability. Implying that (1) CFA charter -
holders achieve better investment results and (2) those who pass the exams 
on the first try may be more successful than those who do not violates 
Standard VII(B).
Example 2 (Right to Use CFA Designation):
Five years after receiving his CFA charter, Louis Vasseur resigns his position as an

investment analyst and spends the next two years traveling abroad. Because he is not 
actively engaged in the investment profession, he does not file a completed Professional 
Conduct Statement with CFA Institute and does not pay his CFA Institute member -
ship dues. At the conclusion of his travels, Vasseur becomes a self-  employed analyst 
accepting assignments as an independent contractor. Without reinstating his CFA 
Institute membership by filing his Professional Conduct Statement and paying his 
dues, he prints business cards that display “CFA” after his name.
Comment : Vasseur has violated Standard VII(B) because his right to use 
the CFA designation was suspended when he failed to file his Professional 
Conduct Statement and stopped paying dues. Therefore, he no longer is able 
to state or imply that he is an active CFA charterholder. When Vasseur files 
his Professional Conduct Statement, resumes paying CFA Institute dues to

activate his membership, and completes the CFA Institute reinstatement 
procedures, he will be eligible to use the CFA designation.
Example 3 (“Retired” CFA Institute Membership Status):
After a 25-  year career, James Simpson retires from his firm. Because he is not actively 
engaged in the investment profession, he does not file a completed Professional 
Conduct Statement with CFA Institute and does not pay his CFA Institute membership 
dues. Simpson designs a plain business card (without a corporate logo) to hand out 
to friends with his new contact details, and he continues to put “CFA” after his name.
Comment : Simpson has violated Standard VII(B). Because he failed to file his 
Professional Conduct Statement and ceased paying dues, his membership 
has been suspended and he has given up the right to use the CFA desig -
nation. CFA Institute has procedures, however, for reclassifying a member 
and charterholder as “retired” and reducing the annual dues. If he wants

to obtain retired status, he needs to file the appropriate paperwork with 
CFA Institute. When Simpson receives his notification from CFA Institute 
that his membership has been reclassified as retired and he resumes paying 
reduced dues, his membership will be reactivated and his right to use the 
CFA designation will be reinstated.

Reading 3 ■ Guidance for Standards I–VII 202
Example 4 (Stating Facts about CFA Designation and Program):
Rhonda Reese has been a CFA charterholder since 2000. In a conversation with a friend 
who is considering enrolling in the CFA Program, she states that she has learned a 
great deal from the CFA Program and that many firms require their employees to be 
CFA charterholders. She would recommend the CFA Program to anyone pursuing a 
career in investment management.
Comment : Reese’s comments comply with Standard VII(B). Her statements 
refer to facts: The CFA Program enhanced her knowledge, and many firms 
require the CFA designation for their investment professionals.
Example 5 (Order of Professional and Academic Designations):
Tatiana Prittima has earned both her CFA designation and a PhD in finance. She 
would like to cite both her accomplishments on her business card but is unsure of 
the proper method for doing so.
Comment : The order of designations cited on such items as resumes and

business cards is a matter of personal preference. Prittima is free to cite the 
CFA designation either before or after citing her PhD. Multiple designations 
must be separated by a comma.
Example 6 (Use of Fictitious Name):
Barry Glass is the lead quantitative analyst at CityCenter Hedge Fund. Glass is 
models the fund uses to manage its investors’ assets. Glass reads several high-  level 
mathematical publications and blogs to stay informed on current developments. 
One blog, run by Expert CFA, presents some intriguing research that may benefit 
one of CityCenter’s current models. Glass is under pressure from firm executives to 
Comment : “Expert CFA” has violated Standard VII(B) by using the CFA

designation inappropriately. As with any research report, authorship of 
online comments must include the charterholder’s full name along with 
any reference to the CFA designation.
See also Standard V(A), which Glass has violated for guidance on dil -
igence and reasonable basis.

Practice Problems 203
Unless otherwise stated in the question, all individuals in the following questions are 
CFA Institute members or candidates in the CFA Program and, therefore, are subject 
to the CFA Institute Code of Ethics and Standards of Professional Conduct.
1 Smith, a research analyst with a brokerage firm, decides to change his recom -
mendation for the common stock of Green Company, Inc., from a “buy” to 
a “sell. ” He mails this change in investment advice to all the firm’s clients on 
Wednesday. The day after the mailing, a client calls with a buy order for 500 
shares of Green Company. In this circumstance, Smith should:
A Accept the order.
B Advise the customer of the change in recommendation before accepting the 
order.
C Not accept the order because it is contrary to the firm’s recommendation.
2 Which statement about a manager’s use of client brokerage commissions vio -
lates the Code and Standards?

A A client may direct a manager to use that client’s brokerage commissions to 
purchase goods and services for that client.
B Client brokerage commissions should be used to benefit the client and 
should be commensurate with the value of the brokerage and research ser -
vices received.
C Client brokerage commissions may be directed to pay for the investment 
manager’s operating expenses.
3 Jamison is a junior research analyst with Howard & Howard, a brokerage and 
investment banking firm. Howard & Howard’s mergers and acquisitions depart -
ment has represented the Britland Company in all of its acquisitions for the past 
20 years. Two of Howard & Howard’s senior officers are directors of various 
Britland subsidiaries. Jamison has been asked to write a research report on 
Britland. What is the best course of action for her to follow?
A Jamison may write the report but must refrain from expressing any opinions

because of the special relationships between the two companies.
B Jamison should not write the report because the two Howard & Howard 
officers serve as directors for subsidiaries of Britland.
C Jamison may write the report if she discloses the special relationships with 
the company in the report.
4 Which of the following statements clearly conflicts  with the recommended 
procedures for compliance presented in the CFA Institute Standards of Practice 
Handbook ?
A Firms should disclose to clients the personal investing policies and proce -
dures established for their employees.
B Prior approval must be obtained for the personal investment transactions of 
all employees.
C For confidentiality reasons, personal transactions and holdings should not 
be reported to employers unless mandated by regulatory organizations.
5 Bronson provides investment advice to the board of trustees of a private uni -
versity endowment fund. The trustees have provided Bronson with the fund’s

financial information, including planned expenditures. Bronson receives a 

Reading 3 ■ Guidance for Standards I–VII 204
phone call on Friday afternoon from Murdock, a prominent alumnus, request -
ing that Bronson fax him comprehensive financial information about the fund. 
According to Murdock, he has a potential contributor but needs the informa -
tion that day to close the deal and cannot contact any of the trustees. Based on 
the CFA Institute Standards, Bronson should:
A Send Murdock the information because disclosure would benefit the client.
B Not send Murdock the information to preserve confidentiality.
C Send Murdock the information, provided Bronson promptly notifies the 
trustees.
6 Miller heads the research department of a large brokerage firm. The firm has 
many analysts, some of whom are subject to the Code and Standards. If Miller 
delegates some supervisory duties, which statement best describes her respon -
sibilities under the Code and Standards?
A Miller’s supervisory responsibilities do not apply to those subordinates who

are not subject to the Code and Standards.
B Miller no longer has supervisory responsibility for those duties delegated to 
her subordinates.
C Miller retains supervisory responsibility for all subordinates despite her 
delegation of some duties.
7 Willier is the research analyst responsible for following Company X. All the 
information he has accumulated and documented suggests that the outlook for 
the company’s new products is poor, so the stock should be rated a weak “hold. ” 
During lunch, however, Willier overhears a financial analyst from another 
firm whom he respects offer opinions that conflict with Willier’s forecasts and 
expectations. Upon returning to his office, Willier releases a strong “buy” rec -
ommendation to the public. Willier:
A Violated the Standards by failing to distinguish between facts and opinions 
in his recommendation.
B Violated the Standards because he did not have a reasonable and adequate 
basis for his recommendation.
C Was in full compliance with the Standards.

8 An investment management firm has been hired by ETV Corporation to work 
on an additional public offering for the company. The firm’s brokerage unit now 
has a “sell” recommendation on ETV, but the head of the investment banking 
department has asked the head of the brokerage unit to change the recommen -
dation from “sell” to “buy. ” According to the Standards, the head of the broker -
age unit would be permitted to:
A Increase the recommendation by no more than one increment (in this case, 
to a “hold” recommendation).
B Place the company on a restricted list and give only factual information 
about the company.
C Assign a new analyst to decide if the stock deserves a higher rating.
9 Albert and Tye, who recently started their own investment advisory business, 
have registered to take the Level III CFA examination. Albert’s business card 
reads, “Judy Albert, CFA Level II. ” Tye has not put anything about the CFA

designation on his business card, but promotional material that he designed 
for the business describes the CFA requirements and indicates that Tye partic -
ipates in the CFA Program and has completed Levels I and II. According to the 
Standards:
A Albert has violated the Standards, but Tye has not.

Practice Problems 205
B Tye has violated the Standards, but Albert has not.
C Both Albert and Tye have violated the Standards.
10 Scott works for a regional brokerage firm. He estimates that Walkton Industries 
will increase its dividend by US$1.50 a share during the next year. He realizes 
that this increase is contingent on pending legislation that would, if enacted, 
give Walkton a substantial tax break. The US representative for Walkton’s 
home district has told Scott that, although she is lobbying hard for the bill and 
prospects for its passage are favorable, concern of the US Congress over the 
federal deficit could cause the tax bill to be voted down. Walkton Industries has 
not made any statements about a change in dividend policy. Scott writes in his 
research report, “We expect Walkton’s stock price to rise by at least US$8.00 
a share by the end of the year because the dividend will increase by US$1.50 a 
share. Investors buying the stock at the current time should expect to realize a

total return of at least 15% on the stock. ” According to the Standards:
A Scott violated the Standards because he used material inside information.
B Scott violated the Standards because he failed to separate opinion from fact.
C Scott violated the Standards by basing his research on uncertain predictions 
of future government action.
11 Which one of the following actions will help to ensure the fair treatment of 
brokerage firm clients when a new investment recommendation is made?
A Informing all people in the firm in advance that a recommendation is to be 
disseminated.
B Distributing recommendations to institutional clients prior to individual 
accounts.
C Minimizing the time between the decision and the dissemination of a 
recommendation.
12 The mosaic theory holds that an analyst:
A Violates the Code and Standards if the analyst fails to have knowledge of 
and comply with applicable laws.
B Can use material public information and nonmaterial nonpublic information 
in the analyst’s analysis.

C Should use all available and relevant information in support of an invest -
ment recommendation.
13 Jurgen is a portfolio manager. One of her firm’s clients has told Jurgen that he 
will compensate her beyond the compensation provided by her firm on the 
basis of the capital appreciation of his portfolio each year. Jurgen should:
A Turn down the additional compensation because it will result in conflicts 
with the interests of other clients’ accounts.
B Turn down the additional compensation because it will create undue pres -
sure on her to achieve strong short-  term performance.
C Obtain permission from her employer prior to accepting the compensation 
arrangement.
14 One of the discretionary accounts managed by Farnsworth is the Jones 
Corporation employee profit-  sharing plan. Jones, the company president, 
recently asked Farnsworth to vote the shares in the profit-  sharing plan in favor

of the slate of directors nominated by Jones Corporation and against the direc -
tors sponsored by a dissident stockholder group. Farnsworth does not want to 
lose this account because he directs all the account’s trades to a brokerage firm 
that provides Farnsworth with useful information about tax-  free investments. 
Although this information is not of value in managing the Jones Corporation

Reading 3 ■ Guidance for Standards I–VII 206
account, it does help in managing several other accounts. The brokerage firm 
providing this information also offers the lowest commissions for trades and 
provides best execution. Farnsworth investigates the director issue, concludes 
that the management-  nominated slate is better for the long-  run performance of 
the company than the dissident group’s slate, and votes accordingly. Farnsworth:
A Violated the Standards in voting the shares in the manner requested by 
Jones but not in directing trades to the brokerage firm.
B Did not violate the Standards in voting the shares in the manner requested 
by Jones or in directing trades to the brokerage firm.
C Violated the Standards in directing trades to the brokerage firm but not in 
voting the shares as requested by Jones.
15 Brown works for an investment counseling firm. Green, a new client of the firm, 
is meeting with Brown for the first time. Green used another counseling firm

for financial advice for years, but she has switched her account to Brown’s firm. 
After spending a few minutes getting acquainted, Brown explains to Green that 
she has discovered a highly undervalued stock that offers large potential gains. 
She recommends that Green purchase the stock. Brown has committed a viola -
tion of the Standards. What should she have done differently?
A Brown should have determined Green’s needs, objectives, and tolerance for 
risk before making a recommendation of any type of security.
B Brown should have thoroughly explained the characteristics of the company 
to Green, including the characteristics of the industry in which the company 
operates.
C Brown should have explained her qualifications, including her education, 
training, and experience and the meaning of the CFA designation.
16 Grey recommends the purchase of a mutual fund that invests solely in long-  
term US Treasury bonds. He makes the following statements to his clients:

I. “The payment of the bonds is guaranteed by the US government; therefore, 
the default risk of the bonds is virtually zero. ”
 II. “If you invest in the mutual fund, you will earn a 10% rate of return each 
year for the next several years based on historical performance of the 
market. ”
 Did Grey’s statements violate the CFA Institute Code and Standards?
A Neither statement violated the Code and Standards.
B Only statement I violated the Code and Standards.
C Only statement II violated the Code and Standards.
17 Anderb, a portfolio manager for XYZ Investment Management Company—a 
registered investment organization that advises investment firms and private 
accounts—was promoted to that position three years ago. Bates, her supervi -
sor, is responsible for reviewing Anderb’s portfolio account transactions and 
her required monthly reports of personal stock transactions. Anderb has been 
using Jonelli, a broker, almost exclusively for brokerage transactions for the

portfolio account. For securities in which Jonelli’s firm makes a market, Jonelli 
has been giving Anderb lower prices for personal purchases and higher prices 
for personal sales than Jonelli gives to Anderb’s portfolio accounts and other 
investors. Anderb has been filing monthly reports with Bates only for those 
months in which she has no personal transactions, which is about every fourth 
month. Which of the following is most likely  to be a violation of the Code and 
Standards?
A Anderb failed to disclose to her employer her personal transactions.

Practice Problems 207
B Anderb owned the same securities as those of her clients.
C Bates allowed Anderb to use Jonelli as her broker for personal trades.
18 Which of the following is a correct statement of a member’s or candidate’s duty 
under the Code and Standards?
A In the absence of specific applicable law or other regulatory requirements, 
the Code and Standards govern the member’s or candidate’s actions.
B A member or candidate is required to comply only with applicable local 
laws, rules, regulations, or customs, even though the Code and Standards 
may impose a higher degree of responsibility or a higher duty on the mem -
ber or candidate.
C A member or candidate who trades securities in a securities market where 
no applicable local laws or stock exchange rules regulate the use of material 
nonpublic information may take investment action based on material non -
public information.
19 Ward is scheduled to visit the corporate headquarters of Evans Industries. Ward

expects to use the information he obtains there to complete his research report 
on Evans stock. Ward learns that Evans plans to pay all of Ward’s expenses for 
the trip, including costs of meals, hotel room, and air transportation. Which of 
the following actions would be the best course for Ward to take under the Code 
and Standards?
A Accept the expense-  paid trip and write an objective report.
B Pay for all travel expenses, including costs of meals and incidental items.
C Accept the expense-  paid trip but disclose the value of the services accepted 
in the report.
20 Which of the following statements is correct  under the Code and Standards?
A CFA Institute members and candidates are prohibited from undertaking 
independent practice in competition with their employer.
B Written consent from the employer is necessary to permit independent 
practice that could result in compensation or other benefits in competition 
with a member’s or candidate’s employer.

C Members and candidates are prohibited from making arrangements or 
preparations to go into a competitive business before terminating their rela -
tionship with their employer.
21 Smith is a financial analyst with XYZ Brokerage Firm. She is preparing a pur -
chase recommendation on JNI Corporation. Which of the following situations 
is most likely  to represent a conflict of interest for Smith that would have to be 
disclosed?
A Smith frequently purchases items produced by JNI.
B XYZ holds for its own account a substantial common stock position in JNI.
C Smith’s brother-  in- law is a supplier to JNI.
22 Michelieu tells a prospective client, “I may not have a long-  term track record 
yet, but I’m sure that you’ll be very pleased with my recommendations and ser -
vice. In the three years that I’ve been in the business, my equity-  oriented clients 
have averaged a total return of more than 26% a year. ” The statement is true, but

Michelieu only has a few clients, and one of his clients took a large position in 
a penny stock (against Michelieu’s advice) and realized a huge gain. This large 
return caused the average of all of Michelieu’s clients to exceed 26% a year. 
Without this one investment, the average gain would have been 8% a year. Has 
Michelieu violated the Standards?

Reading 3 ■ Guidance for Standards I–VII 208
A No, because Michelieu is not promising that he can earn a 26% return in the 
future.
B No, because the statement is a true and accurate description of Michelieu’s 
track record.
C Yes, because the statement misrepresents Michelieu’s track record.
23 An investment banking department of a brokerage firm often receives material 
nonpublic information that could have considerable value if used in advising the 
firm’s brokerage clients. In order to conform to the Code and Standards, which 
one of the following is the best policy for the brokerage firm?
A Permanently prohibit both “buy” and “sell” recommendations of the stocks 
of clients of the investment banking department.
B Establish physical and informational barriers within the firm to prevent the 
exchange of information between the investment banking and brokerage 
C Monitor the exchange of information between the investment banking 
department and the brokerage operation.

24 Stewart has been hired by Goodner Industries, Inc., to manage its pension fund. 
Stewart’s duty of loyalty, prudence, and care is owed to:
A The management of Goodner.
B The participants and beneficiaries of Goodner’s pension plan.
C The shareholders of Goodner.
25 Which of the following statements is a stated purpose of disclosure in 
Standard VI(C)–Referral Fees?
A Disclosure will allow the client to request discounted service fees.
B Disclosure will help the client evaluate any possible partiality shown in the 
recommendation of services.
C Disclosure means advising a prospective client about the referral arrange -
ment once a formal client relationship has been established.
26 Rose, a portfolio manager for a local investment advisory firm, is planning 
to sell a portion of his personal investment portfolio to cover the costs of 
his child’s academic tuition. Rose wants to sell a portion of his holdings in

Household Products, but his firm recently upgraded the stock to “strong buy. ” 
Which of the following describes Rose’s options under the Code and Standards?
A Based on his firm’s “buy” recommendation, Rose cannot sell the 
shares because he would be improperly prospering from the inflated 
B Rose is free to sell his personal holdings once his firm is properly informed 
of his intentions.
C Rose can sell his personal holdings but only when a client of the firm places 
an order to buy shares of Household.
27 A former hedge fund manager, Jackman, has decided to launch a new private 
wealth management firm. From his prior experiences, he believes the new firm 
needs to achieve US$1 million in assets under management in the first year. 
Jackman offers a $10,000 incentive to any adviser who joins his firm with the 
minimum of $200,000 in committed investments. Jackman places notice of the 
opening on several industry web portals and career search sites. Which of the

A A member or candidate is eligible for the new position and incentive if he or 
she can arrange for enough current clients to switch to the new firm and if 
the member or candidate discloses the incentive fee.
B A member or candidate may not accept employment with the new firm 
because Jackman’s incentive offer violates the Code and Standards.
C A member or candidate is not eligible for the new position unless he or she 
is currently unemployed because soliciting the clients of the member’s or 
candidate’s current employer is prohibited.
28 Carter works for Invest Today, a local asset management firm. A broker that 
provides Carter with proprietary research through client brokerage arrange -
ments is offering a new trading service. The broker is offering low-  fee, 
execution-  only trades to complement its traditional full-  service, execution-  and-  
research trades. To entice Carter and other asset managers to send additional

business its way, the broker will apply the commissions paid on the new service 
toward satisfying the brokerage commitment of the prior full-  service arrange -
ments. Carter has always been satisfied with the execution provided on the full-  
service trades, and the new low-  fee trades are comparable to the fees of other 
brokers currently used for the accounts that prohibit soft dollar arrangements.
A Carter can trade for his accounts that prohibit soft dollar arrangements 
under the new low-  fee trading scheme.
B Carter cannot use the new trading scheme because the commissions are 
prohibited by the soft dollar restrictions of the accounts.
C Carter should trade only through the new low-  fee scheme and should 
increase his trading volume to meet his required commission commitment.
29 Rule has worked as a portfolio manager for a large investment management 
firm for the past 10 years. Rule earned his CFA charter last year and has

decided to open his own investment management firm. After leaving his cur -
rent employer, Rule creates some marketing material for his new firm. He states 
in the material, “In earning the CFA charter, a highly regarded credential in the 
investment management industry, I further enhanced the portfolio management 
skills learned during my professional career. While completing the examina -
tion process in three consecutive years, I consistently received the highest 
possible scores on the topics of Ethics, Alternative Investments, and Portfolio 
Management. ” Has Rule violated Standard VII(B)–Reference to CFA Institute, 
the CFA Designation, and the CFA Program in his marketing material?
A Rule violated Standard VII(B) in stating that he completed the exams in 
three consecutive years.
B Rule violated Standard VII(B) in stating that he received the highest scores 
in the topics of Ethics, Alternative Investments, and Portfolio Management.
C Rule did not violate Standard VII(B).

30 Stafford is a portfolio manager for a specialized real estate mutual fund. Her 
firm clearly describes in the fund’s prospectus its soft dollar policies. Stafford 
decides that entering the CFA Program will enhance her investment decision-  
making skill and decides to use the fund’s soft dollar account to pay the regis -
tration and exam fees for the CFA Program. Which of the following statements 
is most likely  correct?
A Stafford did not violate the Code and Standards because the prospectus 
informed investors of the fund’s soft dollar policies.
B Stafford violated the Code and Standards because improving her investment 
skills is not a reasonable use of the soft dollar account.

Reading 3 ■ Guidance for Standards I–VII 210
C Stafford violated the Code and Standards because the CFA Program does 
not meet the definition of research allowed to be purchased with brokerage 
commissions.
31 Long has been asked to be the keynote speaker at an upcoming investment 
conference. The event is being hosted by one of the third-  party investment 
managers currently used by his pension fund. The manager offers to cover all 
conference and travel costs for Long and make the conference registrations 
free for three additional members of his investment management team. To 
ensure that the conference obtains the best speakers, the host firm has arranged 
for an exclusive golf outing for the day following the conference on a local 
championship-  caliber course. Which of the following is least likely  to violate 
Standard I(B)?
A Long may accept only the offer to have his conference-  related expenses paid 
by the host firm.

B Long may accept the offer to have his conference-  related expenses paid and 
may attend the exclusive golf outing at the expense of the hosting firm.
C Long may accept the entire package of incentives offered to speak at this 
conference.
32 Andrews, a private wealth manager, is conducting interviews for a new research 
analyst for his firm. One of the candidates is Wright, an analyst with a local 
investment bank. During the interview, while Wright is describing his analytical 
skills, he mentions a current merger in which his firm is acting as the adviser. 
Andrews has heard rumors of a possible merger between the two companies, 
but no releases have been made by the companies concerned. Which of the fol -
lowing actions by Andrews is least likely  a violation of the Code and Standards?
A Waiting until the next day before trading on the information to allow time 
for it to become public.
B Notifying all investment managers in his firm of the new information so

none of their clients are disadvantaged.
C Placing the securities mentioned as part of the merger on the firm’s 
restricted trading list.
33 Pietro, president of Local Bank, has hired the bank’s market maker, Vogt, to 
seek a merger partner. Local is currently not listed on a stock exchange and 
has not reported that it is seeking strategic alternatives. Vogt has discussed the 
possibility of a merger with several firms, but they have all decided to wait until 
after the next period’s financial data are available. The potential buyers believe 
the results will be worse than the results of prior periods and will allow them to 
pay less for Local Bank.
 Pietro wants to increase the likelihood of structuring a merger deal quickly. 
Which of the following actions would most likely  be a violation of the Code and 
A Pietro could instruct Local Bank to issue a press release announcing that it 
has retained Vogt to find a merger partner.

B Pietro could place a buy order for 2,000 shares (or four times the average 
weekly volume) through Vogt for his personal account.
C After confirming with Local’s chief financial officer, Pietro could instruct 
Local to issue a press release reaffirming the firm’s prior announced earn -
ings guidance for the full fiscal year.
34 ABC Investment Management acquires a new, very large account with two 
concentrated positions. The firm’s current policy is to add new accounts for the 
purpose of performance calculation after the first full month of management.

Cupp is responsible for calculating the firm’s performance returns. Before the 
end of the initial month, Cupp notices that one of the significant holdings of the 
new accounts is acquired by another company, causing the value of the invest -
ment to double. Because of this holding, Cupp decides to account for the new 
portfolio as of the date of transfer, thereby allowing ABC Investment to reap the 
positive impact of that month’s portfolio return.
A Cupp did not violate the Code and Standards because the GIPS standards 
allow composites to be updated on the date of large external cash flows.
B Cupp did not violate the Code and Standards because companies are 
allowed to determine when to incorporate new accounts into their compos -
ite calculation.
C Cupp violated the Code and Standards because the inclusion of the new 
account produces an inaccurate calculation of the monthly results according 
to the firm’s stated policies.

35 Cannan has been working from home on weekends and occasionally saves cor -
respondence with clients and completed work on her home computer. Because 
of worsening market conditions, Cannan is one of several employees released 
by her firm. While Cannan is looking for a new job, she uses the files she saved 
at home to request letters of recommendation from former clients. She also 
provides to prospective clients some of the reports as examples of her abilities.
A Cannan violated the Code and Standards because she did not receive per -
mission from her former employer to keep or use the files after her employ -
ment ended.
B Cannan did not violate the Code and Standards because the files were cre -
ated and saved on her own time and computer.
C Cannan violated the Code and Standards because she is prohibited from 
saving files on her home computer.
36 Quinn sat for the Level III CFA exam this past weekend. He updates his resume

with the following statement: “In finishing the CFA Program, I improved my 
skills related to researching investments and managing portfolios. I will be eligi -
ble for the CFA charter upon completion of the required work experience. ”
A Quinn violated the Code and Standards by claiming he improved his skills 
through the CFA Program.
B Quinn violated the Code and Standards by incorrectly stating that he is 
eligible for the CFA charter.
C Quinn did not violate the Code and Standards with his resume update.
37 During a round of golf, Rodriguez, chief financial officer of Mega Retail, men -
tions to Hart, a local investment adviser and long-  time personal friend, that 
Mega is having an exceptional sales quarter. Rodriguez expects the results to be 
almost 10% above the current estimates. The next day, Hart initiates the pur -
chase of a large stake in the local exchange-  traded retail fund for her personal 
account.
A Hart violated the Code and Standards by investing in the exchange-  traded

fund that included Mega Retail.
B Hart did not violate the Code and Standards because she did not invest 
directly in securities of Mega Retail.
C Rodriguez did not violate the Code and Standards because the comments 
made to Hart were not intended to solicit an investment in Mega Retail.

Reading 3 ■ Guidance for Standards I–VII 212
38 Park is very frustrated after taking her Level II exam. While she was studying 
for the exam, to supplement the curriculum provided, she ordered and used 
study material from a third-  party provider. Park believes the additional material 
focused her attention on specific topic areas that were not tested while ignor -
ing other areas. She posts the following statement on the provider’s discussion 
board: “I am very dissatisfied with your firm’s CFA Program Level II material. I 
found the exam extremely difficult and myself unprepared for specific questions 
after using your product. How could your service provide such limited instruc -
tional resources on the analysis of inventories and taxes when the exam had 
multiple questions about them? I will not recommend your products to other 
candidates. ”
A Park violated the Code and Standards by purchasing third-  party review 
material.

material.
B Park violated the Code and Standards by providing her opinion on the diffi -
culty of the exam.
C Park violated the Code and Standards by providing specific information on 
topics tested on the exam.
39 Paper was recently terminated as one of a team of five managers of an equity 
fund. The fund had two value-  focused managers and terminated one of them 
to reduce costs. In a letter sent to prospective employers, Paper presents, with 
written permission of the firm, the performance history of the fund to demon -
strate his past success.
A Paper did not violate the Code and Standards.
B Paper violated the Code and Standards by claiming the performance of the 
entire fund as his own.
C Paper violated the Code and Standards by including the historical results of 
his prior employer.
40 Townsend was recently appointed to the board of directors of a youth golf 
program that is the local chapter of a national not-  for- profit organization. The

program is beginning a new fund-  raising campaign to expand the number of 
annual scholarships it provides. Townsend believes many of her clients make 
annual donations to charity. The next week in her regular newsletter to all cli -
ents, she includes a small section discussing the fund-  raising campaign and her 
position on the organization’s board.
A Townsend did not violate the Code and Standards.
B Townsend violated the Code and Standards by soliciting donations from her 
clients through the newsletter.
C Townsend violated the Code and Standards by not getting approval of the 
organization before soliciting her clients.

Solutions 213
SOLUTIONS
1 The correct answer is B. This question involves Standard III(B)–Fair Dealing. 
Smith disseminated a change in the stock recommendation to his clients but 
then received a request contrary to that recommendation from a client who 
probably had not yet received the recommendation. Prior to executing the 
order, Smith should take additional steps to ensure that the customer has 
received the change of recommendation. Answer A is incorrect because the cli -
ent placed the order prior to receiving the recommendation and, therefore, does 
not have the benefit of Smith’s most recent recommendation. Answer C  is also 
incorrect; simply because the client request is contrary to the firm’s recommen -
dation does not mean a member can override a direct request by a client. After 
Smith contacts the client to ensure that the client has received the changed rec -
ommendation, if the client still wants to place a buy order for the shares, Smith

is obligated to comply with the client’s directive.
2 The correct answer is C. This question involves Standard III(A)–Loyalty, 
Prudence, and Care and the specific topic of soft dollars or soft commissions. 
Answer C is the correct choice because client brokerage commissions may not 
be directed to pay for the investment manager’s operating expenses. Answer B 
describes how members and candidates should determine how to use brokerage 
commissions—that is, if the use is in the best interests of clients and is com -
mensurate with the value of the services provided. Answer A describes a prac -
tice that is commonly referred to as “directed brokerage. ” Because brokerage 
is an asset of the client and is used to benefit the client, not the manager, such 
practice does not violate a duty of loyalty to the client. Members and candidates 
are obligated in all situations to disclose to clients their practices in the use of 
client brokerage commissions.

3 The correct answer is C. This question involves Standard VI(A)–Disclosure of 
Conflicts. The question establishes a conflict of interest in which an analyst, 
Jamison, is asked to write a research report on a company that is a client of the 
analyst’s employer. In addition, two directors of the company are senior officers 
of Jamison’s employer. Both facts establish that there are conflicts of interest 
that must be disclosed by Jamison in her research report. Answer B is incor -
rect because an analyst is not prevented from writing a report simply because 
of the special relationship the analyst’s employer has with the company as long 
as that relationship is disclosed. Answer A is incorrect because whether or not 
Jamison expresses any opinions in the report is irrelevant to her duty to disclose 
a conflict of interest. Not expressing opinions does not relieve the analyst of the 
responsibility to disclose the special relationships between the two companies.

4 The correct answer is C. This question asks about compliance procedures 
relating to personal investments of members and candidates. The statement in 
answer C clearly conflicts with the recommended procedures in the Standards 
of Practice  Handbook . Employers should compare personal transactions of 
employees with those of clients on a regular basis regardless of the existence of 
a requirement by any regulatory organization. Such comparisons ensure that 
employees’ personal trades do not conflict with their duty to their clients, and 
the comparisons can be conducted in a confidential manner. The statement in 
answer A does not conflict with the procedures in the Handbook . Disclosure of 
such policies will give full information to clients regarding potential conflicts 
of interest on the part of those entrusted to manage their money. Answer B is 
incorrect because firms are encouraged to establish policies whereby employees

clear their personal holdings and transactions with their employers.

Reading 3 ■ Guidance for Standards I–VII 214
5 The correct answer is B. This question relates to Standard III(A)–Loyalty, 
Prudence, and Care and Standard III(E)–Preservation of Confidentiality. In 
this case, the member manages funds of a private endowment. Clients, who 
are, in this case, the trustees of the fund, must place some trust in members 
and candidates. Bronson cannot disclose confidential financial information to 
anyone without the permission of the fund, regardless of whether the disclosure 
may benefit the fund. Therefore, answer A is incorrect. Answer C  is incorrect 
because Bronson must notify the fund and obtain the fund’s permission before 
publicizing the information.
6 The correct answer is C. Under Standard IV(C)–Responsibilities of Supervisors, 
members and candidates may delegate supervisory duties to subordinates but 
such delegation does not relieve members or candidates of their supervisory

responsibilities. As a result, answer B is incorrect. Moreover, whether or not 
Miller’s subordinates are subject to the Code and Standards is irrelevant to her 
supervisory responsibilities. Therefore, answer A  is incorrect.
7 The correct answer is B. This question relates to Standard V(A)–Diligence and 
Reasonable Basis. The opinion of another financial analyst is not an adequate 
basis for Willier’s action in changing the recommendation. Answer C is thus 
incorrect. So is answer A because, although it is true that members and can -
didates must distinguish between facts and opinions in recommendations, the 
question does not illustrate a violation of that nature. If the opinion overheard 
by Willier had sparked him to conduct additional research and investigation 
that justified a change of opinion, then a changed recommendation would be 
appropriate.
8 The correct answer is B. This question relates to Standard I(B)–Independence

and Objectivity. When asked to change a recommendation on a company stock 
to gain business for the firm, the head of the brokerage unit must refuse in 
order to maintain his independence and objectivity in making recommenda -
tions. He must not yield to pressure by the firm’s investment banking depart -
ment. To avoid the appearance of a conflict of interest, the firm should dis -
continue issuing recommendations about the company. Answer A is incorrect; 
changing the recommendation in any manner that is contrary to the analyst’s 
opinion violates the duty to maintain independence and objectivity. Answer C 
is incorrect because merely assigning a new analyst to decide whether the stock 
deserves a higher rating will not address the conflict of interest.
9 The correct answer is A. Standard VII(B)–Reference to CFA Institute, the CFA 
Designation, and the CFA Program is the subject of this question. The reference 
on Albert’s business card implies that there is a “CFA Level II” designation;

Tye merely indicates in promotional material that he is participating in the 
CFA Program and has completed Levels I and II. Candidates may not imply 
that there is some sort of partial designation earned after passing a level of the 
CFA exam. Therefore, Albert has violated Standard VII(B). Candidates may 
communicate that they are participating in the CFA Program, however, and 
may state the levels that they have completed. Therefore, Tye has not violated 
10 The correct answer is B. This question relates to Standard V(B)–
Communication with Clients and Prospective Clients. Scott has issued a 
research report stating that he expects the price of Walkton Industries stock to 
rise by US$8 a share “because the dividend will increase” by US$1.50 per share. 
He has made this statement knowing that the dividend will increase only if 
Congress enacts certain legislation, an uncertain prospect. By stating that the 
dividend will increase, Scott failed to separate fact from opinion.

 The information regarding passage of legislation is not material nonpublic 
information because it is conjecture, and the question does not state whether 
the US representative gave Scott her opinion on the passage of the legislation 
in confidence. She could have been offering this opinion to anyone who asked. 
Therefore, statement A is incorrect. It may be acceptable to base a recommen -
dation, in part, on an expectation of future events, even though they may be 
uncertain. Therefore, answer C is incorrect.
11 The correct answer is C. This question, which relates to Standard III(B)–Fair 
Dealing, tests the knowledge of the procedures that will assist members and 
candidates in treating clients fairly when making investment recommenda -
tions. The step listed in C will help ensure the fair treatment of clients. Answer 
A may have negative effects on the fair treatment of clients. The more people 
who know about a pending change, the greater the chance that someone will

inform some clients before the information’s release. The firm should establish 
policies that limit the number of people who are aware in advance that a recom -
mendation is to be disseminated. Answer B, distributing recommendations to 
institutional clients before distributing them to individual accounts, discrimi -
nates among clients on the basis of size and class of assets and is a violation of 
Standard III(B).
12 The correct answer is B. This question deals with Standard II(A)–Material 
Nonpublic Information. The mosaic theory states that an analyst may use 
material public information and nonmaterial nonpublic information in cre -
ating a larger picture than shown by any individual piece of information and 
the conclusions the analyst reaches become material only after the pieces are 
assembled. Answers A and C are accurate statements relating to the Code and 
Standards but do not describe the mosaic theory.
13 The correct answer is C. This question involves Standard IV(B)–Additional

Compensation Arrangements. The arrangement described in the question—
whereby Jurgen would be compensated beyond the compensation provided 
by her firm, on the basis of an account’s performance—is not a violation of 
the Standards as long as Jurgen discloses the arrangement in writing to her 
employer and obtains permission from her employer prior to entering into 
the arrangement. Answers A  and B  are incorrect; although the private com -
pensation arrangement could conflict with the interests of other clients and 
lead to short-  term performance pressures, members and candidates may enter 
into such agreements as long as they have disclosed the arrangements to their 
employer and obtained permission for the arrangement from their employer.
14 The correct answer is B. This question relates to Standard III(A)–Loyalty, 
Prudence, and Care—specifically, a member’s or candidate’s responsibility for 
voting proxies and the use of client brokerage. According to the facts stated in

the question, Farnsworth did not violate Standard III(A). Although the company 
president asked Farnsworth to vote the shares of the Jones Corporation profit-  
sharing plan a certain way, Farnsworth investigated the issue and concluded, 
independently, the best way to vote. Therefore, even though his decision coin -
cided with the wishes of the company president, Farnsworth is not in violation 
of his responsibility to be loyal and to provide care to his clients. In this case, 
the participants and the beneficiaries of the profit-  sharing plan are the clients, 
not the company’s management. Had Farnsworth not investigated the issue or 
had he yielded to the president’s wishes and voted for a slate of directors that he 
had determined was not in the best interest of the company, Farnsworth would 
have violated his responsibilities to the beneficiaries of the plan. In addition, 
because the brokerage firm provides the lowest commissions and best execu -

tion for securities transactions, Farnsworth has met his obligations to the client

Reading 3 ■ Guidance for Standards I–VII 216
in using this brokerage firm. It does not matter that the brokerage firm also 
provides research information that is not useful for the account generating the 
commission because Farnsworth is not paying extra money of the client’s for 
that information.
15 The correct answer is A. In this question, Brown is providing investment 
recommendations before making inquiries about the client’s financial situa -
tion, investment experience, or investment objectives. Brown is thus violating 
Standard III(C)–Suitability. Answers B and C provide examples of information 
members and candidates should discuss with their clients at the outset of the 
relationship, but these answers do not constitute a complete list of those fac -
tors. Answer A is the best answer.
16 The correct answer i s C. This question involves Standard I(C)–
Misrepresentation. Statement I is a factual statement that discloses to clients

and prospects accurate information about the terms of the investment instru -
ment. Statement II, which guarantees a specific rate of return for a mutual fund, 
is an opinion stated as a fact and, therefore, violates Standard I(C). If statement 
II were rephrased to include a qualifying statement, such as “in my opinion, 
investors may earn . . . , ” it would  not be in violation of the Standards.
17 The correct answer is  A. This question involves three of the Standards. Anderb, 
the portfolio manager, has been obtaining more favorable prices for her per -
sonal securities transactions than she gets for her clients, which is a breach 
of Standard III(A)–Loyalty, Prudence, and Care. In addition, she violated 
Standard I(D)–Misconduct by failing to adhere to company policy and by 
hiding her personal transactions from her firm. Anderb’s supervisor, Bates, 
violated Standard IV(C)–Responsibilities of Supervisors; although the company

had requirements for reporting personal trading, Bates failed to adequately 
enforce those requirements. Answer B  does not represent a violation because 
Standard VI(B)–Priority of Transactions requires that personal trading in 
a security be conducted after the trading in that security of clients and the 
employer. The Code and Standards do not prohibit owning such investments, 
although firms may establish policies that limit the investment opportunities of 
members and candidates. Answer C  does not represent a violation because the 
Code and Standards do not contain a prohibition against employees using the 
same broker for their personal accounts that they use for their client accounts. 
This arrangement should be disclosed to the employer so that the employer may 
determine whether a conflict of interest exists.
18 The correct answer is A because this question relates to Standard I(A)–
Knowledge of the Law—specifically, global application of the Code and

Standards. Members and candidates who practice in multiple jurisdictions may 
be subject to various securities laws and regulations. If applicable law is more 
strict than the requirements of the Code and Standards, members and candi -
dates must adhere to applicable law; otherwise, members and candidates must 
adhere to the Code and Standards. Therefore, answer A is correct. Answer B is 
incorrect because members and candidates must adhere to the higher standard 
set by the Code and Standards if local applicable law is less strict. Answer C is 
incorrect because when no applicable law exists, members and candidates are 
required to adhere to the Code and Standards, and the Code and Standards 
prohibit the use of material nonpublic information.
19 The correct answer is B. The best course of action under Standard I(B)–
Independence and Objectivity is to avoid a conflict of interest whenever 
possible. Therefore, for Ward to pay for all his expenses is the correct answer.

Answer C  details a course of action in which the conflict would be disclosed, 
but the solution is not as appropriate as avoiding the conflict of interest.

Solutions 217
Answer A  would not be the best course because it would not remove the 
appearance of a conflict of interest; even though the report would not be 
affected by the reimbursement of expenses, it could appear to be.
20 The correct answer is B. Under Standard IV(A)–Loyalty, members and candi -
dates may undertake independent practice that may result in compensation or 
other benefit in competition with their employer as long as they obtain consent 
from their employer. Answer C  is not consistent with the Standards because 
the Standards allow members and candidates to make arrangements or prepa -
rations to go into competitive business as long as those arrangements do not 
interfere with their duty to their current employer. Answer A is not consistent 
with the Standards because the Standards do not include a complete prohibi -
tion against undertaking independent practice.
21 The correct answer is B. This question involves Standard VI(A)–Disclosure of

Conflicts—specifically, the holdings of an analyst’s employer in company stock. 
Answers A and C do not describe conflicts of interest that Smith would have to 
disclose. Answer A  describes the use of a firm’s products, which would not be a 
required disclosure. In answer C, the relationship between the analyst and the 
company through a relative is so tangential that it does not create a conflict of 
interest necessitating disclosure.
22 The correct answer is C. This question relates to Standard I(C)–
Misrepresentation. Although Michelieu’s statement about the total return of his 
clients’ accounts on average may be technically true, it is misleading because 
the majority of the gain resulted from one client’s large position taken against 
Michelieu’s advice. Therefore, this statement misrepresents the investment 
performance the member is responsible for. He has not taken steps to present 
a fair, accurate, and complete presentation of performance. Answer B is thus

incorrect. Answer A is incorrect because although Michelieu is not guarantee -
ing future results, his words are still a misrepresentation of his performance 
history.
23 The correct answer is B. The best policy to prevent violation of Standard II(A)–
Material Nonpublic Information is the establishment of firewalls in a firm to 
prevent exchange of insider information. The physical and informational barrier 
of a firewall between the investment banking department and the brokerage 
operation prevents the investment banking department from providing infor -
mation to analysts on the brokerage side who may be writing recommendations 
on a company stock. Prohibiting recommendations of the stock of companies 
that are clients of the investment banking department is an alternative, but 
answer A states that this prohibition would be permanent, which is not the best 
answer. Once an offering is complete and the material nonpublic information

obtained by the investment banking department becomes public, resuming 
publishing recommendations on the stock is not a violation of the Code and 
Standards because the information of the investment banking department no 
longer gives the brokerage operation an advantage in writing the report. Answer 
C is incorrect because no exchange of information should be occurring between 
the investment banking department and the brokerage operation, so monitoring 
of such exchanges is not an effective compliance procedure for preventing the 
use of material nonpublic information.
24 The correct answer is B. Under Standard III(A)–Loyalty, Prudence, and Care, 
members and candidates who manage a company’s pension fund owe these 
duties to the participants and beneficiaries of the pension plan, not the manage -
ment of the company or the company’s shareholders.

Reading 3 ■ Guidance for Standards I–VII 218
25 The correct answer is B. Answer B gives one of the two primary reasons listed 
in the Handbook  for disclosing referral fees to clients under Standard VI(C)–
Referral Fees. (The other is to allow clients and employers to evaluate the full 
cost of the services.) Answer A  is incorrect because Standard VI(C) does not 
require members or candidates to discount their fees when they receive referral 
fees. Answer C is inconsistent with Standard VI(C) because disclosure of refer -
ral fees, to be effective, should be made to prospective clients before entering 
into a formal client relationship with them.
26 The correct answer is B. Standard VI(B)–Priority of Transactions does not limit 
transactions of company employees that differ from current recommendations 
as long as the sale does not disadvantage current clients. Thus, answer A is 
incorrect. Answer C is incorrect because the Standard does not require the 
matching of personal and client trades.

27 Answer C is correct. Standard IV(A)–Loyalty discusses activities permissible to 
members and candidates when they are leaving their current employer; solicit -
ing clients is strictly prohibited. Thus, answer A is inconsistent with the Code 
and Standards even with the required disclosure. Answer B is incorrect because 
the offer does not directly violate the Code and Standards. There may be out-  
of- work members and candidates who can arrange the necessary commitments 
without violating the Code and Standards.
28 Answer A  is correct. The question relates to Standard III(A)–Loyalty, Prudence, 
and Care. Carter believes the broker offers effective execution at a fee that is 
comparable with those of other brokers, so he is free to use the broker for all 
accounts. Answer B  is incorrect because the accounts that prohibit soft dollar 
arrangements do not want to fund the purchase of research by Carter. The new

trading scheme does not incur additional commissions from clients, so it would 
not go against the prohibitions. Answer C is incorrect because Carter should 
not incur unnecessary or excessive “churning” of the portfolios (excessive 
trading) for the purpose of meeting the brokerage commitments of soft dollar 
arrangements.
29 Answer B is correct according to Standard VII(B)–Reference to CFA Institute, 
the CFA Designation, and the CFA Program. CFA Program candidates do not 
receive their actual scores on the exam. Topic and subtopic results are grouped 
into three broad categories, and the exam is graded only as “pass” or “fail. ” 
Although a candidate may have achieved a topical score of “above 70%, ” she 
or he cannot factually state that she or he received the highest possible score 
because that information is not reported. Thus, answer C is incorrect. Answer 
A is incorrect as long as the member or candidate actually completed the exams

consecutively. Standard VII(B) does not prohibit the communication of factual 
information about completing the CFA Program in three consecutive years.
30 Answer C is correct. According to Standard III(A)–Loyalty, Prudence, and Care,  
the CFA Program would be considered a personal or firm expense and should 
not be paid for with the fund’s brokerage commissions. Soft dollar accounts 
should be used only to purchase research services that directly assist the invest -
ment manager in the investment decision-  making process, not to assist the 
management of the firm or to further education. Thus, answer A is incorrect. 
Answer B is incorrect because the reasonableness of how the money is used is 
not an issue; the issue is that educational expense is not research.
31 Answer A  is correct. Standard I(B)–Independence and Objectivity emphasizes 
the need for members and candidates to maintain their independence and 
objectivity. Best practices dictate that firms adopt a strict policy not to accept

compensation for travel arrangements. At times, however, accepting paid

Solutions 219
travel would not compromise one’s independence and objectivity. Answers B  
and C are incorrect because the added benefits—free conference admission 
for additional staff members and an exclusive golf retreat for the speaker—
could be viewed as inducements related to the firm’s working arrangements 
and not solely related to the speaking engagement. Should Long wish to bring 
other team members or participate in the golf outing, he or his firm should be 
responsible for the associated fees.
32 Answer C is correct. The guidance to Standard II(A)–Material Nonpublic 
Information recommends adding securities to the firm’s restricted list when the 
firm has or may have material nonpublic information. By adding these securities 
to this list, Andrews would uphold this standard. Because waiting until the next 
day will not ensure that news of the merger is made public, answer A is incor -
rect. Negotiations may take much longer between the two companies, and the

merger may never happen. Andrews must wait until the information is dissemi -
nated to the market before he trades on that information. Answer B is incorrect 
because Andrews should not disclose the information to other managers; no 
trading is allowed on material nonpublic information.
33 Answer B is correct. Through placing a personal purchase order that is signifi -
cantly greater than the average volume, Pietro is violating Standard IIB–Market 
Manipulation. He is attempting to manipulate an increase in the share price 
and thus bring a buyer to the negotiating table. The news of a possible merger 
and confirmation of the firm’s earnings guidance may also have positive effects 
on the price of Local Bank, but Pietro’s actions in instructing the release of 
the information does not represent a violation through market manipulation. 
Announcements of this nature are common and practical to keep investors 
informed. Thus, answers A and C are incorrect.

34 Answer  C is correct. Cupp violated Standard III(D)–Performance Presentations 
when he deviated from the firm’s stated policies solely to capture the gain from 
the holding being acquired. Answer A is incorrect because the firm does not 
claim GIPS compliance and the GIPS standards require external cash flows to 
be treated in a consistent manner with the firm’s documented policies. Answer 
B is incorrect because the firm does not state that it is updating its composite 
policies. If such a change were to occur, all cash flows for the month would have 
to be reviewed to ensure their consistent treatment under the new policy.
35 Answer A is correct. According to Standard V(C) –Record Retention, Cannan 
needed the permission of her employer to maintain the files at home after her 
employment ended. Without that permission, she should have deleted the files. 
All files created as part of a member’s or candidate’s professional activity are

the property of the firm, even those created outside normal work hours. Thus, 
answer B is incorrect. Answer C is incorrect because the Code and Standards 
do not prohibit using one’s personal computer to complete work for one’s 
employer.
36 Answer B is correct. According to Standard VII(B)–Reference to CFA Institute, 
the CFA Designation, and the CFA Program, Quinn cannot claim to have 
finished the CFA Program or be eligible for the CFA charter until he officially 
learns that he has passed the Level III exam. Until the results for the most 
recent exam are released, those who sat for the exam should continue to refer to 
themselves as “candidates. ” Thus, answer C is incorrect. Answer A is incorrect 
because members and candidates may discuss areas of practice in which they 
believe the CFA Program improved their personal skills.

Reading 3 ■ Guidance for Standards I–VII 220
37 Answer A is correct. Hart’s decision to invest in the retail fund appears directly 
correlated with Rodriguez’s statement about the successful quarter of Mega 
Retail and thus violates Standard II(A)–Material Nonpublic Information. 
Rodriguez’s information would be considered material because it would influ -
ence the share price of Mega Retail and probably influence the price of the 
entire exchange-  traded retail fund. Thus, answer B is incorrect. Answer C is 
also incorrect because Rodriguez shared information that was both material 
and nonpublic. Company officers regularly have such knowledge about their 
firms, which is not a violation. The sharing of such information, however, even 
in a conversation between friends, does violate Standard II(A).
38 Answer C is correct. Standard VII(A)–Conduct as Members and Candidates in 
the CFA Program prohibits providing information to candidates or the public

that is considered confidential to the CFA Program. In revealing that questions 
related to the analysis of inventories and analysis of taxes were on the exam, 
Park has violated this standard. Answer B is incorrect because the guidance for 
the standard explicitly acknowledges that members and candidates are allowed 
to offer their opinions about the CFA Program. Answer A is incorrect because 
candidates are not prohibited from using outside resources.
39 Answer B is correct. Paper has violated Standard III(D)–Performance 
Presentation by not disclosing that he was part of a team of managers that 
achieved the results shown. If he had also included the return of the portion 
he directly managed, he would not have violated the standard. Thus, answer A 
is incorrect. Answer C is incorrect because Paper received written permission 
from his prior employer to include the results.
40 Answer A is correct. Townsend has not provided any information about her

clients to the leaders or managers of the golf program; thus, she has not violated 
Standard III(E)–Preservation of Confidentiality. Providing contact information 
about her clients for a direct-  mail solicitation would have been a violation. 
Answer B is incorrect because the notice in the newsletter does not violate 
Standard III(E). Answer C is incorrect because the golf program’s fund-  raising 
campaign had already begun, so discussing the opportunity to donate was 

Introduction to the Global Investment 
Performance Standards (GIPS)
a. explain why the GIPS standards were created, what parties the 
GIPS standards apply to, and who is served by the standards;
b. explain the construction and purpose of composites in 
performance reporting;
c. explain the requirements for verification.
The objective of this reading is to orient the Level I candidate approaching the assigned 
sections of the GIPS standards. It explains why the GIPS standards were created, who 
can claim compliance, and who benefits from compliance. It also introduces the key 
notion of composites, states the purpose of verification, and previews the structure 
of the Standards.
WHY WERE THE GIPS STANDARDS CREATED?
Institutions and individuals are constantly scrutinizing past investment performance 
returns in search of the best manager to achieve their investment objectives.

In the past, the investment community had great difficulty making meaningful 
comparisons on the basis of accurate investment performance data. Several perfor -
mance measurement practices hindered the comparability of performance returns from 
one firm to another, while others called into question the accuracy and credibility of 
performance reporting overall. Misleading practices included:
■■Representative Accounts : Selecting a top-  performing portfolio to represent the 
firm’s overall investment results for a specific mandate.I.rEAdING
4

Reading 4 ■ Introduction to the Global Investment Performance Standards (GIPS) 222
■■Survivorship Bias : Presenting an “average” performance history that excludes  
portfolios whose poor performance was weak enough to result in termination of 
the firm.
■■Varying Time Periods : Presenting performance for a selected time period 
during which the mandate produced excellent returns or out-  performed 
its benchmark—making comparison with other firms’ results difficult or 
impossible.
Making a valid comparison of investment performance among even the most ethical 
investment management firms was problematic. For example, a pension fund seeking 
to hire an investment management firm might receive proposals from several firms, 
all using different methodologies for calculating their results.
The GIPS standards are a practitioner-  driven set of ethical principles that establish 
a standardized, industry-  wide approach for investment firms to follow in calculating

and presenting their historical investment results to prospective clients. The GIPS 
standards ensure fair representation and full disclosure of investment performance. 
In other words, the GIPS standards lead investment management firms to avoid 
misrepresentations of performance and to communicate all relevant information that 
prospective clients should know in order to evaluate past results.
WHO CAN CLAIM COMPLIANCE?
First, any investment management firm may choose to comply with the GIPS stan -
dards. Complying with the GIPS standards is voluntary. Compliance with the GIPS 
standards is not typically required by legal or regulatory authorities.
Second, only investment management firms that actually manage  assets can 
claim compliance with the Standards. Plan sponsors and consultants cannot make 
a claim of compliance unless they actually manage assets for which they are making 
a claim of compliance. They can claim to endorse the Standards and/or require that

their investment managers comply with the Standards. Similarly, software (and the 
vendors who supply software) cannot be “compliant. ” Software can assist firms in 
achieving compliance with the GIPS standards (e.g., by calculating performance in a 
manner consistent with the calculation requirements of the Standards) but only an 
investment management firm can claim compliance once the firm has satisfied all 
requirements of the Standards.
Third, compliance is a firm-  wide process that cannot be achieved on a single 
product or composite. A firm has only two options with regard to compliance with 
the GIPS standards: fully comply with all requirements of the GIPS standards and 
claim compliance through the use of the GIPS Compliance Statement; or not comply 
with all requirements of the GIPS standards and not claim compliance with, or make 
any reference to, the GIPS standards.
WHO BENEFITS FROM COMPLIANCE?
The GIPS standards benefit two main groups: investment management firms and

prospective clients.
■■By choosing to comply with the GIPS standards, investment management firms 
assure prospective clients that the historical “track record” they report is both 
complete and fairly presented. Compliance enables the GIPS-  compliant firm to II.
III.

Verification 223
participate in competitive bids against other compliant firms throughout the 
world. Achieving and maintaining compliance may also strengthen the firm’s 
internal controls over performance-  related processes and procedures.
■■Investors have a greater level of confidence in the integrity of performance pre -
sentations of a GIPS-  compliant firm and can more easily compare performance 
presentations from different investment management firms. While the GIPS 
standards certainly do not eliminate the need for in-  depth due diligence on the 
part of the investor, compliance with the Standards enhances the credibility of 
investment management firms that have chosen to undertake this responsibility.
COMPOSITES
One of the key concepts of the Standards is the required use of composites. A com -
posite is an aggregation of one or more portfolios managed according to a similar 
investment mandate, objective, or strategy. A composite must include all actual, fee-

paying, discretionary portfolios managed in accordance with the same investment 
mandate, objective, or strategy. For example, if a GIPS-  compliant firm presents its 
track record for a Global Equity Composite (the Composite), the Composite must 
include all portfolios that are managed, or have historically been managed, in the 
firm’s Global Equity strategy. The firm may not subjectively select which Global Equity 
portfolios will be included in or excluded from the calculation and presentation of 
the Global Equity Composite. The determination of which portfolios to include in the 
Composite should be done according to pre-  established criteria (i.e., on an ex-  ante 
basis), not after the fact. This prevents a firm from including only their best-  performing 
portfolios in the Composite.
VERIFICATION
Firms that claim compliance with the GIPS standards are responsible for their claim 
of compliance and for maintaining that compliance. That is, firms self-  regulate their

claim of compliance. Once a firm claims compliance with the Standards, they may 
voluntarily hire an independent third party to perform a verification in order to 
increase confidence in the firm’s claim of compliance. Verification may also increase 
the knowledge of the firm’s performance measurement team and improve the con -
sistency and quality of the firm’s compliant presentations.
Verification is performed with respect to an entire firm, not on specific compos -
ites. Verification does not ensure the accuracy of any specific composite presentation. 
Verification tests:
■■whether the investment firm has complied with all the composite construction 
requirements of the GIPS standards on a firm-  wide basis, and
■■whether the firm’s policies and procedures are designed to calculate and present 
performance in compliance with the GIPS standards.
Verification must be performed by an independent third party. A firm cannot perform 
its own verification.IV.
V.

Reading 4 ■ Introduction to the Global Investment Performance Standards (GIPS) 224
Third-  party verification brings additional credibility to a firm’s claim of compliance. 
A verified firm may provide existing and prospective clients with greater assurance 
about its claim of compliance with the GIPS standards. Verification may also provide 
improved internal processes and procedures as well as marketing advantages to the firm.
THE STRUCTURE OF THE GIPS STANDARDS
The provisions within the 2010 edition of the GIPS standards are divided into nine sec -
tions: Fundamentals of Compliance, Input Data, Calculation Methodology, Composite 
Construction, Disclosure, Presentation and Reporting, Real Estate, Private Equity, and 
Wrap Fee/Separately Managed Account (SMA) Portfolios. The provisions are further 
categorized into requirements and recommendations.VI.

a. describe the key features of the GIPS standards and the 
fundamentals of compliance; 
b. describe the scope of the GIPS standards with respect to an 
investment firm’s definition and historical performance record;
c. explain how the GIPS standards are implemented in countries 
with existing standards for performance reporting and describe 
the appropriate response when the GIPS standards and local 
regulations conflict;
d. describe the nine major sections of the GIPS standards.
PREFACE
CFA Institute is a global not-  for- profit association of investment professionals with the 
mission of leading the investment profession globally by setting the highest standards 
of ethics, education, and professional excellence. CFA Institute has a long-  standing 
history of and commitment to establishing a broadly accepted ethical standard for

calculating and presenting investment performance based on the principles of fair 
representation and full disclosure. The goals in developing and evolving the Global 
Investment Performance Standards (GIPS®) are to establish them as the recognized 
standard for calculating and presenting investment performance around the world 
and for the GIPS standards to become a firm’s “passport” to market investment 
management services globally. As of January 2010, CFA Institute has partnered with 
organizations in 32 countries that contribute to the development and promotion of 
the GIPS standards.OPTIONAL 
SEGMENTrEAdING
5

Reading 5 ■ Global Investment Performance Standards (GIPS) 226
History
In 1995, CFA Institute, formerly known as the Association for Investment Management 
and Research (AIMR), sponsored and funded the Global Investment Performance 
Standards Committee to develop global standards for calculating and presenting 
investment performance, based on the existing AIMR Performance Presentation 
Standards (AIMR-  PPS®).
In 1998, the proposed GIPS standards were posted on the CFA Institute website 
and circulated for comment to more than 4,000 individuals who had expressed inter -
est. The result was the first Global Investment Performance Standards, published in 
April 1999.
The initial edition of the GIPS standards was designed to create a minimum global 
investment performance standard that would:
■■Permit and facilitate acceptance and adoption in developing markets;
■■Give the global investment management industry one commonly accepted 
approach for calculating and presenting performance; and

■■Address liquid asset classes (equity, fixed income, and cash).
In 1999, the Global Investment Performance Standards Committee was replaced by 
the Investment Performance Council (IPC) to further develop and promote the GIPS 
standards. The development of the GIPS standards was a global industry initiative 
with participation from individuals and organizations from more than 15 countries.
The IPC was charged with developing provisions for other asset classes (e.g., 
real estate, private equity) and addressing other performance-  related issues (e.g., 
fees, advertising) to broaden the scope and applicability of the GIPS standards. This 
was accomplished when the second edition of the GIPS standards was published in 
February 2005.
With the release of the 2005 edition of the GIPS standards and growing adoption 
and expansion of the GIPS standards, the IPC decided to move to a single global 
investment performance standard and eliminate the need for local variations of the

GIPS standards. All country-  specific performance standards converged with the 
GIPS standards, resulting in 25 countries adopting a single, global standard for the 
calculation and presentation of investment performance.
In 2005, with the convergence of country-  specific versions to the GIPS standards 
and the need to reorganize the governance structure to facilitate involvement from GIPS 
sponsors, CFA Institute dissolved the IPC and created the GIPS Executive Committee 
and the GIPS Council. The GIPS Executive Committee serves as the decision-  making 
authority for the GIPS standards, and the GIPS Council facilitates the involvement 
of all sponsors in the ongoing development and promotion of the GIPS standards.
To maintain global relevance, and in recognition of the dynamic nature of the 
investment industry, the GIPS standards must be continually updated through inter -
pretations, guidance, and new provisions. In 2008, the GIPS Executive Committee

began its review of the GIPS standards in an effort to further refine the provisions as 
well as eliminate provisions that are no longer necessary and add new requirements 
and recommendations that promote best practice. The GIPS Executive Committee 
worked in close collaboration with its technical subcommittees, specially formed 
working groups, and GIPS sponsors. These groups reviewed the existing provisions 
and guidance and conducted surveys and other research as part of the efforts to pro -
duce the 2010 edition of the GIPS standards.END OPTIONAL 
SEGMENT

Introduction 227
Preamble—Why Is a Global Investment Performance Standard 
Needed?
Standardized Investment Performance 
Financial markets and the investment management industry have become increas -
ingly global in nature. The growth in the types and number of financial entities, 
the globalization of the investment process, and the increased competition among 
investment management firms demonstrate the need to standardize the calculation 
and presentation of investment performance.
Global Passport 
Asset managers and both existing and prospective clients benefit from an established 
global standard for calculating and presenting investment performance. Investment 
practices, regulation, performance measurement, and reporting of performance 
vary considerably from country to country. By adhering to a global standard, firms 
in countries with minimal or no investment performance standards will be able 
to compete for business on an equal footing with firms from countries with more

developed standards. Firms from countries with established practices will have more 
confidence in being fairly compared with local firms when competing for business 
in countries that have not previously adopted performance standards. Performance 
standards that are accepted globally enable investment firms to measure and present 
their investment performance so that investors can readily compare investment per -
formance among firms.
Investor Confidence 
Investment managers that adhere to investment performance standards help assure 
investors that the firm’s investment performance is complete and fairly presented. Both 
prospective and existing clients of investment firms benefit from a global investment 
performance standard by having a greater degree of confidence in the performance 
information presented to them.
Objectives
The establishment of a voluntary global investment performance standard leads to an 
accepted set of best practices for calculating and presenting investment performance

that is readily comparable among investment firms, regardless of geographic location. 
These standards also facilitate a dialogue between investment firms and their existing 
and prospective clients regarding investment performance.
The goals of the GIPS Executive Committee are:
■■To establish investment industry best practices for calculating and presenting 
investment performance that promote investor interests and instill investor 
confidence;
■■To obtain worldwide acceptance of a single standard for the calculation and 
presentation of investment performance based on the principles of fair repre -
sentation and full disclosure;
■■To promote the use of accurate and consistent investment performance data;
■■To encourage fair, global competition among investment firms without creating 
barriers to entry; and
■■To foster the notion of industry “self-  regulation” on a global basis.

Reading 5 ■ Global Investment Performance Standards (GIPS) 228
Overview
Key features of the GIPS standards include the following:
■■The GIPS standards are ethical standards for investment performance presen -
tation to ensure fair representation and full disclosure of investment perfor -
mance. In order to claim compliance, firms must adhere to the requirements 
included in the GIPS standards.
■■Meeting the objectives of fair representation and full disclosure is likely to 
require more than simply adhering to the minimum requirements of the GIPS 
standards. Firms should also adhere to the recommendations to achieve best 
practice in the calculation and presentation of performance.
■■The GIPS standards require firms to include all actual, discretionary, fee-  
paying portfolios in at least one composite defined by investment mandate, 
objective, or strategy in order to prevent firms from cherry-  picking their best 

■■The GIPS standards rely on the integrity of input data. The accuracy of input 
data is critical to the accuracy of the performance presentation. The underlying 
valuations of portfolio holdings drive the portfolio’s performance. It is essential 
for these and other inputs to be accurate. The GIPS standards require firms to 
adhere to certain calculation methodologies and to make specific disclosures 
along with the firm’s performance.
■■Firms must comply with all requirements of the GIPS standards, including 
any updates, Guidance Statements, interpretations, Questions & Answers 
(Q&As), and clarifications published by CFA Institute and the GIPS Executive 
Committee, which are available on the GIPS website (www.gipsstandards.org) 
as well as in the GIPS Handbook .
The GIPS standards do not address every aspect of performance measurement or 
cover unique characteristics of each asset class. The GIPS standards will continue to

evolve over time to address additional areas of investment performance. Understanding 
and interpreting investment performance requires consideration of both risk and 
return. Historically, the GIPS standards focused primarily on returns. In the spirit of 
fair representation and full disclosure, and in order to provide investors with a more 
comprehensive view of a firm’s performance, the 2010 edition of the GIPS standards 
includes new provisions related to risk.
Historical Performance Record
■■A firm is required to initially present, at a minimum, five years of annual invest -
ment performance that is compliant with the GIPS standards. If the firm or 
the composite has been in existence less than five years, the firm must present 
performance since the firm’s inception or the composite inception date.
■■After a firm presents a minimum of five years of GIPS-  compliant performance 
(or for the period since the firm’s inception or the composite inception date if

the firm or the composite has been in existence less than five years), the firm 
must present an additional year of performance each year, building up to a min -
imum of 10 years of GIPS-  compliant performance.
■■Firms may link non-  GIPS-  compliant performance to their GIPS-  compliant 
performance provided that only GIPS-  compliant performance is presented 
for periods after 1 January 2000 and the firm discloses the periods of non-  
compliance. Firms must not link non-  GIPS-  compliant performance for periods 
beginning on or after 1 January 2000 to their GIPS-  compliant performance.

Introduction 229
Firms that manage private equity, real estate, and/or wrap fee/separately man -
aged account (SMA) portfolios must also comply with Sections 6, 7, and 8, 
respectively, of the Provisions of the GIPS standards that became effective as of 
1 January 2006.
Compliance
Firms must take all steps necessary to ensure that they have satisfied all the require -
ments of the GIPS standards before claiming compliance. Firms are strongly encour -
aged to perform periodic internal compliance checks. Implementing adequate internal 
controls during all stages of the investment performance process—from data input 
to preparing performance presentations—will instill confidence in the validity of 
performance presented as well as in the claim of compliance.
Firms may choose to have an independent third-  party verification that tests the 
construction of the firm’s composites as well as the firm’s policies and procedures as

they relate to compliance with the GIPS standards. The value of verification is widely 
recognized, and being verified is considered to be best practice. The GIPS Executive 
Committee strongly recommends that firms be verified. In addition to verification, 
firms may also choose to have specifically focused composite testing (performance 
examination) performed by an independent third-  party verifier to provide additional 
assurance regarding a particular composite.
Effective Date
The effective date for the 2010 edition of the GIPS standards is 1 January  2011. 
Compliant presentations that include performance for periods that begin on or after 
1 January 2011 must be prepared in accordance with the 2010 edition of the GIPS 
standards. Prior editions of the GIPS standards may be found on the GIPS website 
(www.gipsstandards.org).
Implementing a Global Standard
The presence of a local sponsoring organization for investment performance standards

is essential for effective implementation and ongoing support of the GIPS standards 
within a jurisdiction. Such sponsors also provide an important link between the GIPS 
Executive Committee, the governing body for the GIPS standards, and the local mar -
kets in which investment managers operate.
The sponsor, by actively supporting the GIPS standards and the work of the GIPS 
Executive Committee, ensures that the jurisdiction’s interests are taken into account 
as the GIPS standards are developed. Compliance with the GIPS standards is volun -
tary, and support from the local market sponsor helps to drive the adoption of the 
GIPS standards.
The GIPS Executive Committee strongly encourages countries without an invest -
ment performance standard to promote the GIPS standards as the local standard and 
translate them into the local language when necessary. Although the GIPS standards 
may be translated into many languages, if a discrepancy arises, the English version of

the GIPS standards is the official governing version.
The GIPS Executive Committee will continue to promote the principles of fair rep -
resentation and full disclosure and develop the GIPS standards so that they maintain 
their relevance within the changing investment management industry.

Reading 5 ■ Global Investment Performance Standards (GIPS) 230
The self-  regulatory nature of the GIPS standards necessitates a strong commitment 
to ethical integrity. Self-  regulation also assists regulators in exercising their respon -
sibility for ensuring the fair disclosure of information within financial markets. The 
GIPS Executive Committee encourages regulators to:
■■Recognize the benefit of voluntary compliance with standards that represent 
global best practices;
■■Give consideration to taking enforcement actions against firms that falsely claim 
compliance with the GIPS standards; and
■■Recognize and encourage independent third-  party verification.
Where existing laws, regulations, or industry standards already impose require -
ments related to the calculation and presentation of investment performance, firms 
are strongly encouraged to comply with the GIPS standards in addition to applicable 
regulatory requirements. Compliance with applicable law and/or regulation does not

necessarily lead to compliance with the GIPS standards. In cases in which laws and/or 
regulations conflict with the GIPS standards, firms are required to comply with the laws 
and regulations and make full disclosure of the conflict in the compliant presentation.
Sponsors
The presence of a local sponsoring organization for investment performance standards, 
known as a “sponsor, ” is essential for effective implementation of the GIPS standards 
and ongoing support within a local market. Sponsors collectively form the GIPS 
Council, which provides a formal role in the ongoing development and oversight of 
the GIPS standards. Sponsors:
■■Promote the GIPS standards locally;
■■Provide local market support and input for the GIPS standards;
■■Present local market–specific issues to the GIPS Executive Committee; and
■■Participate in the governance of the GIPS standards via membership in the 
GIPS Council and Regional Investment Performance Subcommittees.

Each organization undergoes a formal review before being endorsed as a spon -
sor. Additional information and a current list of sponsors can be found on the GIPS 
website (www.gipsstandards.org).
Endorsed GIPS Sponsors (as of 1 January 2010)
Australia Investment and Financial Services Association Limited—
Performance Analyst Group 
Austria 1) Österreichische Vereinigung für Finanzanalyse und Asset 
Management and  
2) Vereinigung Österreichischer Investmentgesellschaften
Belgium Belgian Asset Managers Association
Canada Canadian Investment Performance Committee
Denmark The Danish Society of Financial Analysts and CFA Denmark
France 1) Société Française des Analystes Financiers and  
2) Association Française de la Gestion FinancièreOPTIONAL 
SEGMENT

Provisions of the Global Investment Performance Standards 231
Germany German Asset Management Standards Committee:  
1) Bundesverband Investment und Asset Management e.V., 2) 
Deutsche Vereinigung für Finanzanalyse und Asset Management, 
and 3) German CFA Society
Greece Hellenic CFA Society
Hong Kong Local Sponsor: The Hong Kong Society of Financial Analysts
Hungary 1) CFA Society of Hungary and 2) the Association of Hungarian 
Investment Fund and Asset Management Companies
Ireland Irish Association of Investment Managers
Italy Italian Investment Performance Committee:  
1) L’Associazione Bancaria Italiana, 2) L’Associazione Italiana degli 
Analisti Finanziari, 3) Assogestioni, 4) Sviluppo Mercato Fondi 
Pensione, 5) Assirevi, and  
6) Italian CFA Society
Japan The Security Analysts Association of Japan
Kazakhstan Kazakhstan Association of Financial and Investment Analysts
Liechtenstein Liechtenstein Bankers' Association
Micronesia Asia Pacific Association for Fiduciary Studies
The

The 
Netherlands The Netherlands Beroepsvereniging van Beleggingsprofessionals
New Zealand CFA Society of New Zealand
Norway The Norwegian Society of Financial Analysts
Pakistan CFA Association of Pakistan
Portugal Associação Portuguesa de Analista Financeiros
Russia National League of Management Companies
Singapore Investment Management Association of Singapore
South Africa Association for Savings and Investment, South Africa
South Korea Korea GIPS Committee
Spain Asociación Española de Presentación de Resultados de Gestión
Sri Lanka CFA Sri Lanka
Sweden Swedish Society of Financial Analysts
Switzerland Swiss Bankers Association
Ukraine The Ukrainian Association of Investment Business
United 
Kingdom UK Investment Performance Committee:  
1) Association of British Insurers, 2) Investment Management 
Association, and  
3) National Association of Pension Funds
United States CFA Institute—US Investment Performance Committee
PROVISIONS OF THE GLOBAL INVESTMENT 
PERFORMANCE STANDARDS

The provisions within the GIPS standards are divided into the following nine sections: 
Fundamentals of Compliance, Input Data, Calculation Methodology, Composite 
Construction, Disclosure, Presentation and Reporting, Real Estate, Private Equity, 
and Wrap Fee/Separately Managed Account ( SMA ) Portfolios.END OPTIONAL 
SEGMENT
I.

Reading 5 ■ Global Investment Performance Standards (GIPS) 232
The provisions for each section are categorized into requirements and recommen -
dations. Firms must meet all the requirements to claim compliance with the GIPS 
standards. Firms are encouraged to implement as many of the recommendations as 
possible. These recommended provisions are considered to be industry best practice 
and assist firms in fully adhering to the spirit and intent of the GIPS standards.
0 Fundamentals of Compliance:  Several core principles create the foundation 
for the GIPS standards, including properly defining the firm, providing com -
pliant presentations to all prospective clients, adhering to applicable laws and 
regulations, and ensuring that information presented is not false or misleading. 
Two important issues that a firm must consider when becoming compliant with 
the GIPS standards are the definition of the firm and the firm’s definition of

discretion. The definition of the firm is the foundation for firm-  wide compliance 
and creates defined boundaries whereby total firm assets can be determined. 
The firm’s definition of discretion establishes criteria to judge which portfolios 
must be included in a composite and is based on the firm’s ability to implement 
its investment strategy.
1 Input Data:  Consistency of input data used to calculate performance is critical 
to effective compliance with the GIPS standards and establishes the foundation 
for full, fair, and comparable investment performance presentations. For periods 
beginning on or after 1 January 2011, all portfolios must be valued in accor -
dance with the definition of fair value and the GIPS Valuation Principles.
2 Calculation Methodology:  Achieving comparability among investment man -
agement firms’ performance presentations requires uniformity in methods used 
to calculate returns. The GIPS standards mandate the use of certain calculation

methodologies to facilitate comparability.
3 Composite Construction:  A composite is an aggregation of one or more 
portfolios managed according to a similar investment mandate, objective, or 
strategy. The composite return is the asset-  weighted average of the performance 
of all portfolios in the composite. Creating meaningful composites is essential 
to the fair presentation, consistency, and comparability of performance over 
time and among firms.
4 Disclosure:  Disclosures allow firms to elaborate on the data provided in the 
presentation and give the reader the proper context in which to understand the 
performance. To comply with the GIPS standards, firms must disclose certain 
information in all compliant presentations regarding their performance and 
the policies adopted by the firm. Although some disclosures are required for all 
firms, others are specific to certain circumstances and may not be applicable in

all situations. One of the essential disclosures for every firm is the claim of com -
pliance. Once a firm meets all the requirements of the GIPS standards, it must 
appropriately use the claim of compliance to indicate compliance with the GIPS 
standards. The 2010 edition of the GIPS standards includes a revised compli -
ance statement that indicates if the firm has or has not been verified.
5 Presentation and Reporting:  After constructing the composites, gathering the 
input data, calculating returns, and determining the necessary disclosures, the 
firm must incorporate this information in presentations based on the require -
ments in the GIPS standards for presenting investment performance. No finite 
set of requirements can cover all potential situations or anticipate future devel -
opments in investment industry structure, technology, products, or practices. 
When appropriate, firms have the responsibility to include in GIPS-  compliant

Provisions of the Global Investment Performance Standards 233
6 Real Estate:  Unless otherwise noted, this section supplements all of the 
required and recommended provisions in Sections 0–5. Real estate provisions 
were first included in the 2005 edition of the GIPS standards and became effec -
tive 1 January 2006. The 2010 edition of the GIPS standards includes new provi -
sions for closed-  end real estate funds. Firms should note that certain provisions 
of Sections 0–5 do not apply to real estate investments or are superseded by 
provisions within Section 6. The provisions that do not apply have been noted 
within Section 6.
7 Private Equity:  Unless otherwise noted, this section supplements all of the 
required and recommended provisions in Sections 0–5. Private equity provi -
sions were first included in the 2005 edition of the GIPS standards and became 
effective 1 January 2006. Firms should note that certain provisions in Sections

0–5 do not apply to private equity investments or are superseded by provisions 
within Section 7. The provisions that do not apply have been noted within 
Section 7.
8 Wrap Fee/Separately Managed Account (SMA) Portfolios:  Unless otherwise 
noted, this section supplements all of the required and recommended provi -
sions in Sections 0–5. Firms should note that certain provisions in Sections 0–5 
of the GIPS standards do not apply to wrap fee/ SMA  portfolios or are super -
seded by provisions within Section 8. The provisions that do not apply have 
been noted within Section 8.
Defined Terms:  Words appearing in small capital letters in the GIPS standards are 
defined in the GIPS Glossary , which is located at the end of this reading.
0 Fundamentals of Compliance
Fundamentals of Compliance—Requirements
0.A.1  Firms  must  comply with all the requirements  of the GIPS standards, 
including any updates, Guidance Statements, interpretations, Questions &

Answers (Q&As), and clarifications published by CFA Institute and the GIPS 
Executive Committee, which are available on the GIPS standards website 
(www.gipsstandards.org) as well as in the GIPS Handbook.
0.A.2  Firms  must  comply with all applicable laws and regulations regarding the 
calculation and presentation of performance.
0.A.3  Firms  must not  present performance or performance-  related information 
that is false or misleading.
0.A.4  The GIPS standards must  be applied on a firm -wide basis.
0.A.5  Firms  must  document their policies and procedures used in establishing 
and maintaining compliance with the GIPS standards, including ensuring the 
existence and ownership of client assets, and must  apply them consistently.
0.A.6  If the firm  does not meet all the requirements  of the GIPS standards, the 
firm  must not  represent or state that it is “in compliance with the Global 
Investment Performance Standards except for . . . ” or make any other state -

ments that may indicate partial compliance with the GIPS standards.
0.A.7  Statements referring to the calculation methodology as being “in accordance, ” 
“in compliance, ” or “consistent” with the Global Investment Performance 
Standards, or similar statements, are prohibited.

Reading 5 ■ Global Investment Performance Standards (GIPS) 234
0.A.8  Statements referring to the performance of a single, existing client portfolio  
as being “calculated in accordance with the Global Investment Performance 
Standards” are prohibited, except when a GIPS-  compliant firm  reports the 
performance of an individual client’s portfolio  to that client.
0.A.9  Firms  must  make every reasonable effort to provide a compliant presen -
tation  to all prospective clients . Firms  must not  choose to whom they 
present a compliant presentation . As long as a prospective client  has 
received a compliant presentation  within the previous 12 months, the 
firm  has met this requirement .
0.A.10  Firms  must  provide a complete list of composite descriptions  to any 
prospective client  that makes such a request. Firms  must  include ter -
minated composites  on the firm’s  list of composite descriptions  for at 
least five years after the composite termination date .

0.A.11  Firms  must  provide a compliant presentation  for any composite  listed 
on the firm’s  list of composite descriptions  to any prospective client  
that makes such a request.
0.A.12  Firms  must  be defined as an investment firm, subsidiary, or division held 
out to clients or prospective clients  as a distinct business entity .
0.A.13  For periods beginning on or after 1 January 2011, total firm assets  must  
be the aggregate fair value  of all discretionary and non-  discretionary assets 
managed by the firm . This includes both fee-  paying and non-  fee- paying 
portfolios .1
0.A.14  Total firm assets  must  include assets assigned to a sub-  advisor  provided 
the firm  has discretion over the selection of the sub-  advisor .
0.A.15  Changes in a firm’s  organization must not  lead to alteration of historical 
composite  performance.
0.A.16  When the firm  jointly markets with other firms, the firm  claiming com -

pliance with the GIPS standards must  be sure that it is clearly defined and 
separate relative to other firms being marketed, and that it is clear which 
firm  is claiming compliance.
Fundamentals of Compliance—Recommendations
0.B.1  Firms  should  comply with the recommendations  of the GIPS standards, 
including recommendations  in any updates, Guidance Statements, inter -
pretations, Questions & Answers (Q&As), and clarifications published by CFA 
Institute and the GIPS Executive Committee, which will be made available on 
the GIPS website (www.gipsstandards.org) as well as in the GIPS Handbook.
0.B.2  Firms  should  be verified.
0.B.3  Firms  should  adopt the broadest, most meaningful definition of the firm . 
The scope of this definition should  include all geographical (country, regional, 
etc.) offices operating under the same brand name regardless of the actual 
name of the individual investment management company.

0.B.4  Firms  should  provide to each existing client, on an annual basis, a com -
pliant presentation  of the composite  in which the client’s portfolio  
is included.
1 For periods prior to 1 January 2011, total firm assets  must  be the aggregate of the market value  
of all discretionary and non-  discretionary assets under management within the defined firm .

Provisions of the Global Investment Performance Standards 235
1 Input Data
Input Data—Requirements
1.A.1  All data and information necessary to support all items included in a com -
pliant presentation  must  be captured and maintained.
1.A.2  For periods beginning on or after 1 January 2011, portfolios  must  be val -
ued in accordance with the definition of fair value  and the GIPS Valuation 
Principles.2
1.A.3  Firms  must  value portfolios  in accordance with the composite -specific 
valuation policy. Portfolios  must  be valued:
a For periods beginning on or after 1 January 2001, at least monthly.3
b For periods beginning on or after 1 January 2010, on the date of all large 
cash flows . Firms  must  define large cash flow  for each composite  
to determine when portfolios  in that composite  must  be valued.
c No more frequently than required by the valuation policy.
1.A.4  For periods beginning on or after 1 January 2010, firms  must  value port -

folios  as of the calendar month end or the last business day of the month.
1.A.5  For periods beginning on or after 1 January 2005, firms  must  use trade 
date accounting .
1.A.6  Accrual accounting  must  be used for fixed-  income securities and all other 
investments that earn interest income. The value of fixed-  income securities 
must  include accrued income.
1.A.7  For periods beginning on or after 1 January 2006, composites  must  have 
consistent beginning and ending annual valuation dates. Unless the com -
posite  is reported on a non-  calendar fiscal year, the beginning and ending 
valuation dates must  be at calendar year end or on the last business day of 
the year.
Input Data—Recommendations
1.B.1  Firms  should  value portfolios  on the date of all external cash flows .
1.B.2  Valuations should  be obtained from a qualified independent third party.
1.B.3  Accrual accounting  should  be used for dividends (as of the ex-  dividend 
date).

date).
1.B.4  Firms  should  accrue investment management fees .
2 Calculation Methodology
Calculation Methodology—Requirements
2.A.1  Total returns  must  be used.
2.A.2  Firms  must  calculate time-  weighted rates of return  that adjust for 
external cash flows . Both periodic and sub-  period returns must  be 
geometrically linked . External cash flows  must  be treated according 
to the firm’s  composite -specific policy. At a minimum:OPTIONAL 
SEGMENT
2 For periods prior to 1 January 2011, portfolio  valuations must  be based on market values  (not 
cost basis or book values).
3 For periods prior to 1 January 2001, portfolios  must  be valued at least quarterly.

Reading 5 ■ Global Investment Performance Standards (GIPS) 236
a For periods beginning on or after 1 January 2001, firms  must  calculate 
portfolio  returns at least monthly.
b For periods beginning on or after 1 January 2005, firms  must  calculate 
portfolio  returns that adjust for daily-  weighted external cash flows .
2.A.3  Returns from cash and cash equivalents held in portfolios  must  be included 
in all return calculations.
2.A.4  All returns must  be calculated after the deduction of the actual trading 
expenses  incurred during the period. Firms  must not  use estimated trad -
ing expenses .
2.A.5  If the actual trading expenses  cannot be identified and segregated from a 
bundled fee :
a When calculating gross-  of- fees  returns, returns must  be reduced by 
the entire bundled fee  or the portion of the bundled fee  that includes 
the trading expenses . Firms  must not  use estimated trading 
expenses .
b When calculating net-  of- fees  returns, returns must  be reduced by the

entire bundled fee  or the portion of the bundled fee  that includes 
the trading expenses  and the investment management fee . Firms  
must not  use estimated trading expenses .
2.A.6  Composite  returns must  be calculated by asset-  weighting the individual 
portfolio  returns using beginning-  of- period values or a method that reflects 
both beginning-  of- period values and external cash flows .
2.A.7  Composite  returns must  be calculated:
a For periods beginning on or after 1 January 2006, by asset-  weighting the 
individual portfolio  returns at least quarterly.
b For periods beginning on or after 1 January 2010, by asset-  weighting the 
individual portfolio  returns at least monthly.
Calculation Methodology—Recommendations
2.B.1  Returns should  be calculated net of non-  reclaimable withholding taxes on 
dividends, interest, and capital gains. Reclaimable withholding taxes should  
be accrued.
2.B.2  For periods prior to 1 January 2010, firms  should  calculate composite

returns by asset-  weighting the individual portfolio  returns at least monthly.
3 Composite Construction
Composite Construction—Requirements
3.A.1  All actual, fee-  paying, discretionary portfolios  must  be included in at least 
one composite . Although non-  fee- paying discretionary portfolios  may 
be included in a composite  (with appropriate disclosure), non-  discretionary 
portfolios  must not  be included in a firm’s  composites .
3.A.2  Composites  must  include only actual assets managed by the firm .
3.A.3  Firms  must not  link  performance of simulated or model portfolios  with 
actual performance.

Provisions of the Global Investment Performance Standards 237
3.A.4  Composites  must  be defined according to investment mandate, objective, 
or strategy. Composites  must  include all portfolios  that meet the com -
posite definition . Any change to a composite definition  must not  be 
applied retroactively. The composite definition  must  be made available 
upon request.
3.A.5  Composites  must  include new portfolios  on a timely and consistent basis 
after each portfolio  comes under management.
3.A.6  Terminated portfolios  must  be included in the historical performance of 
the composite  up to the last full measurement period that each portfolio  
was under management.
3.A.7  Portfolios  must not  be switched from one composite  to another unless 
documented changes to a portfolio’s  investment mandate, objective, or 
strategy or the redefinition of the composite  makes it appropriate. The 
historical performance of the portfolio  must  remain with the original 
composite .

3.A.8  For periods beginning on or after 1 January 2010, a carve-  out  must not  
be included in a composite  unless the carve-  out  is managed separately 
with its own cash balance.4
3.A.9  If the firm  sets a minimum asset level for portfolios  to be included in a 
composite , the firm  must not  include portfolios  below the minimum 
asset level in that composite . Any changes to a composite -specific mini -
mum asset level must not  be applied retroactively.
3.A.10  Firms  that wish to remove portfolios  from composites  in cases of 
significant cash flows  must  define “significant” on an ex- ante , com -
posite -specific basis and must  consistently follow the composite -specific 
policy.
Composite Construction—Recommendations
3.B.1  If the firm  sets a minimum asset level for portfolios  to be included in a 
composite , the firm  should not  present a compliant presentation  
of the composite  to a prospective client  known not to meet the com -
posite’s  minimum asset level.

3.B.2  To remove the effect of a significant cash flow , the firm  should  use a 
temporary new account .
4 Disclosure
Disclosure—Requirements
4.A.1  Once a firm  has met all the requirements  of the GIPS standards, the firm  
must  disclose its compliance with the GIPS standards using one of the fol -
lowing compliance statements. The claim of compliance must  only be used 
in a compliant presentation .
 For firms  that are verified:
“[Insert name of firm ] claims compliance with the Global 
Investment Performance Standards (GIPS®) and has prepared 
and presented this report in compliance with the GIPS standards. 
4 For periods prior to 1 January 2010, if carve-  outs  were included in a composite , cash must  have 
been allocated to the carve-  out  in a timely and consistent manner.

Reading 5 ■ Global Investment Performance Standards (GIPS) 238
[Insert name of firm ] has been independently verified for the 
periods [insert dates]. The verification report(s) is/are available 
Verification assesses whether (1) the firm has complied with all 
the composite construction requirements of the GIPS standards 
on a firm-  wide basis and (2) the firm’s policies and procedures are 
designed to calculate and present performance in compliance with 
the GIPS standards. Verification does not ensure the accuracy of 
any specific composite presentation. ”
 For composites  of a verified firm  that have also had a performance 
examination :
periods [insert dates].
Verification assesses whether (1) the firm has complied with all

the GIPS standards. The [insert name of composite ] composite 
has been examined for the periods [insert dates]. The verification 
and performance examination reports are available upon request. ”
 For firms  that have not been verified:
[Insert name of firm ] has not been independently verified. ”
4.A.2  Firms  must  disclose the definition of the firm  used to determine total 
firm assets  and firm -wide compliance.
4.A.3  Firms  must  disclose the composite description .
4.A.4  Firms  must  disclose the benchmark description .
4.A.5  When presenting gross-  of- fees  returns, firms  must  disclose if any other

fees are deducted in addition to the trading expenses .
4.A.6  When presenting net-  of- fees  returns, firms  must  disclose:
a If any other fees are deducted in addition to the investment manage -
ment fees  and trading expenses ;
b If model or actual investment management fees  are used; and
c If returns are net of any performance-  based fees .
4.A.7  Firms  must  disclose the currency used to express performance.
4.A.8  Firms  must  disclose which measure of internal dispersion  is presented.
4.A.9  Firms  must  disclose the fee schedule  appropriate to the compliant 
presentation .
4.A.10  Firms  must  disclose the composite creation date .
4.A.11  Firms  must  disclose that the firm’s  list of composite descriptions  is 
available upon request.
4.A.12  Firms  must  disclose that policies for valuing portfolios , calculating per -
formance, and preparing compliant presentations  are available upon 
request.

Provisions of the Global Investment Performance Standards 239
4.A.13  Firms  must  disclose the presence, use, and extent of leverage, derivatives, 
and short positions, if material, including a description of the frequency of 
use and characteristics of the instruments sufficient to identify risks.
4.A.14  Firms  must  disclose all significant events that would help a prospective 
client  interpret the compliant presentation .
4.A.15  For any performance presented for periods prior to 1 January 2000 that does 
not comply with the GIPS standards, firms  must  disclose the periods of 
non-  compliance.
4.A.16  If the firm  is redefined, the firm  must  disclose the date of, description of, 
and reason for the redefinition.
4.A.17  If a composite  is redefined, the firm  must  disclose the date of, description 
of, and reason for the redefinition.
4.A.18  Firms  must  disclose changes to the name of a composite .
4.A.19  Firms  must  disclose the minimum asset level, if any, below which portfolios

are not included in a composite . Firms  must  also disclose any changes to 
the minimum asset level.
4.A.20  Firms  must  disclose relevant details of the treatment of withholding taxes 
on dividends, interest income, and capital gains, if material. Firms  must  also 
disclose if benchmark  returns are net of withholding taxes if this information 
is available.
4.A.21  For periods beginning on or after 1 January  2011, firms  must  disclose 
and describe any known material differences in exchange rates or valuation 
sources used among the portfolios  within a composite , and between the 
composite  and the benchmark .5
4.A.22  If the compliant presentation  conforms with laws and/or regulations 
that conflict with the requirements  of the GIPS standards, firms  must  
disclose this fact and disclose the manner in which the laws and/or regulations 
conflict with the GIPS standards.
4.A.23  For periods prior to 1 January 2010, if carve-  outs  are included in a com -

posite , firms  must  disclose the policy used to allocate cash to carve-  outs .
4.A.24  If a composite  contains portfolios  with bundled fees , firms  must  
disclose the types of fees that are included in the bundled fee .
4.A.25  For periods beginning on or after 1 January 2006, firms  must  disclose the 
use of a sub-  advisor  and the periods a sub-  advisor  was used.
4.A.26  For periods prior to 1 January 2010, firms  must  disclose if any portfolios  
were not valued at calendar month end or on the last business day of the 
month.
4.A.27  For periods beginning on or after 1 January 2011, firms  must  disclose the 
use of subjective unobservable inputs for valuing portfolio  investments (as 
described in the GIPS Valuation Principles) if the portfolio  investments 
valued using subjective unobservable inputs are material to the composite .
4.A.28  For periods beginning on or after 1 January 2011, firms  must  disclose if the

composite’s  valuation hierarchy materially differs from the recommended  
hierarchy in the GIPS Valuation Principles.
4.A.29  If the firm  determines no appropriate benchmark  for the composite  exists, 
the firm  must  disclose why no benchmark  is presented.
5 For periods prior to 1 January 2011, firms  must  disclose and describe any known inconsistencies in 
the exchange rates used among the portfolios  within a composite  and between the composite  and 
the benchmark .

Reading 5 ■ Global Investment Performance Standards (GIPS) 240
4.A.30  If the firm  changes the benchmark , the firm  must  disclose the date of, 
description of, and reason for the change.
4.A.31  If a custom benchmark  or combination of multiple benchmarks  is used, the 
firm  must  disclose the benchmark  components, weights, and rebalancing 
process.
4.A.32  If the firm  has adopted a significant cash flow  policy for a specific 
composite , the firm  must  disclose how the firm  defines a significant 
cash flow  for that composite  and for which periods.
4.A.33  Firms  must  disclose if the three-  year annualized ex- post  standard devi -
ation  of the composite  and/or benchmark  is not presented because 36 
monthly returns are not available.
4.A.34  If the firm  determines that the three-  year annualized ex- post  standard 
deviation  is not relevant or appropriate, the firm  must :
a Describe why ex- post  standard deviation  is not relevant or appro -
priate; and

b Describe the additional risk measure presented and why it was selected.
4.A.35  Firms  must  disclose if the performance from a past firm or affiliation is 
linked  to the performance of the firm .
Disclosure—Recommendations
4.B.1  Firms  should  disclose material changes to valuation policies and/or 
methodologies.
4.B.2  Firms  should  disclose material changes to calculation policies and/or 
4.B.3  Firms  should  disclose material differences between the benchmark  and 
the composite’s  investment mandate, objective, or strategy.
4.B.4  Firms  should  disclose the key assumptions used to value portfolio  
4.B.5  If a parent company contains multiple firms, each firm  within the parent 
company should  disclose a list of the other firms contained within the parent 
company.
4.B.6  For periods prior to 1 January 2011, firms  should  disclose the use of sub -
jective unobservable inputs for valuing portfolio  investments (as described

in the GIPS Valuation Principles) if the portfolio  investments valued using 
subjective unobservable inputs are material to the composite .
4.B.7  For periods prior to 1 January  2006, firms  should  disclose the use of a 
sub-  advisor  and the periods a sub-  advisor  was used.
4.B.8  Firms  should  disclose if a composite  contains proprietary assets .
5 Presentation and Reporting
Presentation and Reporting—Requirements
5.A.1  The following items must  be presented in each compliant presentation :
a At least five years of performance (or for the period since the firm’s  incep -
tion or the composite inception date  if the firm  or the composite  
has been in existence less than five years) that meets the requirements  
of the GIPS standards. After a firm  presents a minimum of five years of 
GIPS-  compliant performance (or for the period since the firm’s  inception

Provisions of the Global Investment Performance Standards 241
or the composite inception date  if the firm  or the composite  has 
been in existence less than five years), the firm  must  present an addi -
tional year of performance each year, building up to a minimum of 10 
years of GIPS-  compliant performance.
b Composite  returns for each annual period. Composite  returns must  
be clearly identified as gross-  of- fees  or net-  of- fees .
c For composites  with a composite inception date  of 1 January 2011 
or later, when the initial period is less than a full year, returns from the 
composite inception date  through the initial annual period end.
d For composites  with a composite termination date  of 1 January 2011 
or later, returns from the last annual period end through the composite 
termination date .
e The total return  for the benchmark  for each annual period. The 
benchmark  must  reflect the investment mandate, objective, or strategy 
of the composite .

f The number of portfolios  in the composite  as of each annual period 
end. If the composite  contains five or fewer portfolios  at period end, 
the number of portfolios  is not required .
g Composite  assets as of each annual period end.
h Either total firm assets  or composite  assets as a percentage of total 
firm assets , as of each annual period end.
i A measure of internal dispersion  of individual portfolio  returns for 
each annual period. If the composite  contains five or fewer portfolios  
for the full year, a measure of internal dispersion  is not required .
5.A.2  For periods ending on or after 1 January 2011, firms  must  present, as of 
each annual period end:
a The three-  year annualized ex- post  standard deviation  (using monthly 
returns) of both the composite  and the benchmark ; and
b An additional three-  year ex- post  risk measure for the benchmark  (if 
available and appropriate) and the composite , if the firm  determines that

the three-  year annualized ex- post  standard deviation  is not relevant 
or appropriate. The periodicity  of the composite  and the benchmark  
must  be identical when calculating the ex- post  risk measure.
5.A.3  Firms  must not  link  non-  GIPS-  compliant performance for periods begin -
ning on or after 1 January 2000 to their GIPS-  compliant performance. Firms  
may link  non-  GIPS-  compliant performance to GIPS-  compliant performance 
provided that only GIPS-  compliant performance is presented for periods 
beginning on or after 1 January 2000.
5.A.4  Returns for periods of less than one year must not  be annualized.
5.A.5  For periods beginning on or after 1 January  2006 and ending prior to 1 
January 2011, if a composite  includes carve-  outs , the firm  must  present 
the percentage of composite  assets represented by carve-  outs  as of each 
annual period end.
5.A.6  If a composite  includes non-  fee- paying portfolios , the firm  must  present

the percentage of composite  assets represented by non-  fee- paying port -
folios  as of each annual period end.
5.A.7  If a composite  includes portfolios  with bundled fees , the firm  must  
present the percentage of composite  assets represented by portfolios  
with bundled fees  as of each annual period end.

Reading 5 ■ Global Investment Performance Standards (GIPS) 242
5.A.8  a Performance of a past firm or affiliation must  be linked  to or used to 
represent the historical performance of a new or acquiring firm  if, on a 
composite -specific basis:
 i. Substantially all of the investment decision makers are employed by 
the new or acquiring firm  (e.g., research department staff, portfolio 
managers, and other relevant staff);
 ii. The decision-  making process remains substantially intact and 
independent within the new or acquiring firm ; and
 iii. The new or acquiring firm  has records that document and support 
the performance.
b If a firm  acquires another firm or affiliation, the firm  has one year to 
bring any non-  compliant assets into compliance.
Presentation and Reporting—Recommendations
5.B.1  Firms  should  present gross-  of- fees  returns.
5.B.2  Firms  should  present the following items:
a Cumulative returns of the composite  and the benchmark  for all periods;

b Equal-  weighted mean and median composite  returns;
c Quarterly and/or monthly returns; and
d Annualized composite  and benchmark  returns for periods longer than 
12 months.
5.B.3  For periods prior to 1 January 2011, firms  should  present the three-  year 
annualized ex- post  standard deviation  (using monthly returns) of the 
composite  and the benchmark  as of each annual period end.
5.B.4  For each period for which an annualized ex- post  standard deviation  
of the composite  and the benchmark  are presented, the corresponding 
annualized return of the composite  and the benchmark  should  also be 
5.B.5  For each period for which an annualized return of the composite  and the 
benchmark  are presented, the corresponding annualized ex- post  standard 
deviation  (using monthly returns) of the composite  and the benchmark  
should  also be presented.
5.B.6  Firms  should  present additional relevant composite -level ex- post  risk 
measures.

measures.
5.B.7  Firms  should  present more than 10 years of annual performance in the 
compliant presentation .
5.B.8  Firms  should  comply with the GIPS standards for all historical periods.
5.B.9  Firms  should  update compliant presentations  quarterly.
6 Real Estate
Unless otherwise noted, the following real estate  provisions supplement the 
required  and recommended  provisions of the GIPS standards in Sections 0–5.
Real estate  provisions were first included in the GIPS standards in 2005 and 
became effective 1 January  2006. All compliant presentations  that included 
real estate  performance for periods beginning on or after 1 January  2006 were 
required  to meet all the requirements  of the real estate  provisions of the 2005 
edition of the GIPS standards. The following real estate  provisions are effective 1

Provisions of the Global Investment Performance Standards 243
January 2011. All real estate  composites  that include performance for periods 
beginning on or after 1 January 2011 must  comply with all the requirements  and 
should  adhere to the recommendations  of the following real estate  provisions.
The following investment types are not considered real estate  and, therefore, 
must  follow Sections 0–5 of the Global Investment Performance Standards:
■■Publicly traded real estate  securities;
■■Commercial mortgage-  backed securities (CMBS); and
■■Private debt investments, including commercial and residential loans where the 
expected return is solely related to contractual interest rates without any partic -
ipation in the economic performance of the underlying real estate .
Real Estate—Requirements
Input Data—Requirements (the following provisions do not apply: 1.A.3.a, 1.A.3.b, 
and 1.A.4)
6.A.1  For periods beginning on or after 1 January 2011, real estate  investments

must  be valued in accordance with the definition of fair value  and the 
GIPS Valuation Principles in Chapter II.6
6.A.2  For periods beginning on or after 1 January 2008, real estate  investments 
must  be valued at least quarterly.7
6.A.3  For periods beginning on or after 1 January 2010, firms  must  value port -
folios  as of each quarter end or the last business day of each quarter.
6.A.4  Real estate  investments must  have an external valuation :
a For periods prior to 1 January 2012, at least once every 36 months.
b For periods beginning on or after 1 January 2012, at least once every 
12 months unless client agreements stipulate otherwise, in which case 
real estate  investments must  have an external valuation  at least 
once every 36 months or per the client agreement if the client agreement 
requires external valuations  more frequently than every 36 months.
6.A.5  External valuations  must be performed by an independent external

professionally designated, certified, or licensed commercial 
property valuer/appraiser . In markets where these professionals are 
not available, the firm  must  take the necessary steps to ensure that only 
well-  qualified independent property valuers or appraisers are used.
Calculation Methodology—Requirements (the following provisions do not apply: 
2.A.2.a, 2.A.4, and 2.A.7)
6.A.6  Firms  must  calculate portfolio  returns at least quarterly.
6.A.7  All returns must  be calculated after the deduction of actual transaction 
expenses  incurred during the period.
6 For periods prior to 1 January 2011, real estate  investments must  be valued at market value  (as 
previously defined for real estate  in the 2005 edition of the GIPS standards).
7 For periods prior to 1 January 2008, real estate  investments must  be valued at least once every 12 
months.

Reading 5 ■ Global Investment Performance Standards (GIPS) 244
6.A.8  For periods beginning on or after 1 January  2011, income returns  and 
capital returns  (component returns) must  be calculated separately using 
geometrically linked  time-  weighted rates of return .
6.A.9  Composite  time-  weighted rates of return , including component 
returns, must  be calculated by asset-  weighting the individual portfolio  
returns at least quarterly.
Disclosure—Requirements (the following provisions do not apply: 4.A.5, 4.A.6.a, 
4.A.15, 4.A.26, 4.A.33, and 4.A.34)
6.A.10  The following items must  be disclosed in each compliant presentation :
a The firm’s  description of discretion;
b The internal valuation  methodologies used to value real estate  
investments for the most recent period;
c For periods beginning on or after 1 January 2011, material changes to 
valuation policies and/or methodologies;
d For periods beginning on or after 1 January 2011, material differences

between an external valuation  and the valuation used in performance 
reporting and the reason for the differences;
e The frequency real estate  investments are valued by an independent 
external professionally designated, certified, or licensed com -
mercial property valuer/appraiser ;
f When component returns are calculated separately using geometrically 
linked  time-  weighted rates of return ; and
g For periods prior to 1 January 2011, if component returns are adjusted 
such that the sum of the income return  and the capital return  
equals the total return .
6.A.11  For any performance presented for periods prior to 1 January 2006 that does 
6.A.12  When presenting gross-  of- fees  returns, firms  must  disclose if any other 
fees are deducted in addition to the transaction expenses .
6.A.13  When presenting net-  of- fees  returns, firms  must  disclose if any other

fees are deducted in addition to the investment management fees  and 
transaction expenses .
Presentation and Reporting—Requirements (the following provisions do not apply: 
5.A.1.i, 5.A.2, and 5.A.3)
6.A.14  Firms  must  present component returns in addition to total returns . 
Composite  component returns must  be clearly identified as gross-  of- fees  
or net-  of- fees .
6.A.15  Firms  must not  link  non-  GIPS-  compliant performance for periods begin -
ning on or after 1 January 2006 to their GIPS-  compliant performance. Firms  
may link  non-  GIPS-  compliant performance to their GIPS-  compliant per -
formance provided that only GIPS-  compliant performance is presented for 
periods beginning on or after 1 January 2006.
6.A.16  The following items must  be presented in each compliant presentation :

Provisions of the Global Investment Performance Standards 245
a As a measure of internal dispersion , high and low annual time-  
weighted rates of return  for the individual portfolios  in the 
composite . If the composite  contains five or fewer portfolios  for 
the full year, a measure of internal dispersion  is not required .
b As of each annual period end, the percentage of composite  assets valued 
using an external valuation  during the annual period.
The following provisions are additional requirements  for real  estate  closed - end fund  
composites : 
6.A.17  Firms  must  calculate annualized since inception  internal rates of 
return (SI-  IRR) .
6.A.18  The SI- IRR must  be calculated using quarterly cash flows at a minimum.
6.A.19  Composites  must  be defined by vintage year  and investment mandate, 
objective, or strategy. The composite definition  must  remain consistent 
throughout the life of the composite .

6.A.20  Firms  must  disclose the final liquidation date  for liquidated composites .
6.A.21  Firms  must  disclose the frequency of cash flows used in the SI- IRR calculation.
6.A.22  Firms  must  disclose the vintage year  of the composite  and how the 
vintage year  is defined.
6.A.23  The following items must  be presented in each compliant presentation :
a Firms  must  present the net-  of- fees  SI- IRR of the composite  through 
each annual period end. firms  must  initially present at least five years 
of performance (or for the period since the firm’s  inception or the 
composite inception date  if the firm  or the composite  has been in 
existence less than five years) that meets the requirements  of the GIPS 
standards. Each subsequent year, firms  must  present an additional year 
of performance.
b For periods beginning on or after 1 January 2011, when the initial period

is less than a full year, firms  must  present the non-  annualized net-  of- 
fees  SI- IRR through the initial annual period end.
c For periods ending on or after 1 January 2011, firms  must  present the 
net-  of- fees  SI- IRR through the composite  final liquidation date .
6.A.24  If the gross-  of- fees  SI- IRR of the composite  is presented in the compli -
ant presentation , firms  must  present the gross-  of- fees  SI- IRR of the 
composite  for the same periods as the net-  of- fees  SI- IRR is presented.
6.A.25  Firms  must  present, as of each annual period end:
a Composite  since inception  paid-  in capital ;
b Composite  since inception  distributions ;
c Composite  cumulative committed capital ;
d Total value  to since inception  paid-  in capital  (investment 
multiple  or TVPI );

Reading 5 ■ Global Investment Performance Standards (GIPS) 246
e Since inception  distributions  to since inception  paid-  in capital  
(realization multiple  or DPI);
f Since inception  paid-  in capital  to cumulative committed capital  
(PIC multiple ); and
g Residual value  to since inception  paid-  in capital  (unrealized 
multiple  or RVPI ).
6.A.26  Firms  must  present the SI- IRR of the benchmark  through each annual 
period end. The benchmark  must :
a Reflect the investment mandate, objective, or strategy of the composite ;
b Be presented for the same time period as presented for the composite ; 
and
c Be the same vintage year  as the composite .
Real Estate—Recommendations
Input Data—Recommendations (the following provision does not apply: 1.B.1)
6.B.1  For periods prior to 1 January 2012, real estate  investments should  be 
valued by an independent external professionally designated, certified, 
or licensed commercial property valuer/appraiser  at least once every 
12 months.

12 months.
6.B.2  Real estate  investments should  be valued as of the annual period end 
by an independent external professionally designated, certified, or 
licensed commercial property valuer/appraiser .
6.B.3  Firms  should  disclose the basis of accounting for the portfolios  in the 
composite  (e.g., US GAAP , IFRS).
6.B.4  Firms  should  explain and disclose material differences between the valuation 
used in performance reporting and the valuation used in financial reporting 
as of each annual period end.
6.B.5  For periods prior to 1 January 2011, firms  should  disclose material changes 
to valuation policies and/or methodologies.
Presentation and Reporting—Recommendations (the following provisions do not 
apply: 5.B.3, 5.B.4, and 5.B.5)
6.B.6  Firms  should  present both gross-  of- fees  and net-  of- fees  returns.
6.B.7  Firms  should  present the percentage of the total value of composite  assets 
that are not real estate  as of each annual period end.

6.B.8  Firms  should  present the component returns of the benchmark , if available.
The following provision is an additional recommendation  for real estate  closed - end fund  
6.B.9  The SI- IRR should  be calculated using daily cash flows.

Provisions of the Global Investment Performance Standards 247
7 Private Equity
Unless otherwise noted, the following private equity  provisions supplement the 
Private equity  provisions were first included in the GIPS standards in 2005 
and became effective 1 January 2006. All compliant presentations  that included 
private equity  performance for periods ending on or after 1 January 2006 were 
required  to meet all the requirements  of the private equity  provisions of the 
2005 edition of the GIPS standards. The following private equity  provisions are 
effective 1 January 2011. All private equity  composites  that include performance 
for periods ending on or after 1 January 2011 must  comply with all the require -
ments  and should  comply with the recommendations  of the following private 
equity  provisions.
The following are provisions that apply to the calculation and presentation of

private equity  investments made by fixed life, fixed commitment private equity  
investment vehicles including primary funds  and funds of funds . These provi -
sions also apply to fixed life, fixed commitment secondary funds , which must  
apply either the provisions applicable to primary funds  or the provisions applicable 
to funds of funds,  depending on which form the secondary fund  uses to make 
investments. Private equity  open-  end and evergreen funds  must  follow Sections 
0–5 in the Provisions of the Global Investment Performance Standards. Real estate  
closed-  end funds  must  follow Section 6 in the Provisions of the Global Investment 
Performance Standards.
Private Equity—Requirements
and 1.A.4)
7.A.1  For periods ending on or after 1 January 2011, private equity  investments 
GIPS Valuation Principles in Chapter II.8

7.A.2  Private equity  investments must  be valued at least annually.
2.A.2, 2.A.4, 2.A.6, and 2.A.7)
7.A.3  Firms  must  calculate annualized since inception  internal rates of 
7.A.4  For periods ending on or after 1 January 2011, the SI- IRR must  be calculated 
using daily cash flows. Stock distributions  must  be included as cash flows 
and must  be valued at the time of distribution .9
7.A.5  All returns must  be calculated after the deduction of actual transaction 
7.A.6  Net-  of- fees  returns must  be net of actual investment management 
fees  (including carried interest ).
7.A.7  For funds of funds , all returns must  be net of all underlying partnership 
and/or fund fees and expenses, including carried interest .

8 For periods ending prior to 1 January 2011, private equity  investments must  be valued according to 
either the GIPS Private Equity Valuation Principles in Appendix D of the 2005 edition of the GIPS standards 
or the GIPS Valuation Principles in the 2010 edition of the GIPS standards. 
9 For periods ending prior to 1 January 2011, the si- irr must  be calculated using either daily or monthly 

Reading 5 ■ Global Investment Performance Standards (GIPS) 248
Composite Construction—Requirements (the following provision does not apply: 
3.A.10)
7.A.8  Composite definitions  must  remain consistent throughout the life of the 
7.A.9  Primary funds  must  be included in at least one composite  defined by 
vintage year  and investment mandate, objective, or strategy.
7.A.10  Funds of funds  must  be included in at least one composite  defined by 
vintage year  of the fund of funds  and/or investment mandate, objective, 
or strategy.
4.A.6.b, 4.A.8, 4.A.15, 4.A.26, 4.A.32, 4.A.33, and 4.A.34)
7.A.11  Firms  must  disclose the vintage year  of the composite  and how the 
7.A.12  Firms  must  disclose the final liquidation date  for liquidated composites .
7.A.13  Firms  must  disclose the valuation methodologies used to value private 
equity  investments for the most recent period.

7.A.14  For periods ending on or after 1 January 2011, firms  must  disclose material 
changes to valuation policies and/or methodologies.
7.A.15  If the firm  adheres to any industry valuation guidelines in addition to the 
GIPS Valuation Principles, the firm  must  disclose which guidelines have 
been applied.
7.A.16  Firms  must  disclose the calculation methodology used for the benchmark . 
If firms  present the public market equivalent  of a composite  as a 
benchmark , firms  must  disclose the index used to calculate the public 
market equivalent .
7.A.17  Firms  must  disclose the frequency of cash flows used in the SI- IRR calcu -
lation if daily cash flows are not used for periods prior to 1 January 2011.
7.A.18  For gross-  of- fees  returns, firms  must  disclose if any other fees are deducted 
in addition to the transaction expenses .
7.A.19  For net-  of- fees  returns, firms  must  disclose if any other fees are deducted

in addition to the investment management fees  and transaction 
expenses .
7.A.20  For any performance presented for periods ending prior to 1 January 2006 
that does not comply with the GIPS standards, firms  must  disclose the 
periods of non-  compliance.
5.A.1.a, 5.A.1.b, 5.A.1.c, 5.A.1.d, 5.A.1.e, 5.A.1.i, 5.A.2, and 5.A.3)
7.A.21  The following items must  be presented in each compliant presentation :
a Firms  must  present both the net-  of- fees  and gross-  of- fees  SI- IRR 
of the composite  through each annual period end. firms  must  initially 
present at least five years of performance (or for the period since the 
firm’s  inception or the composite inception date  if the firm  or the 
composite  has been in existence less than five years) that meets the 
requirements  of the GIPS standards. Each subsequent year, firms  
must  present an additional year of performance. Composite  returns

must  be clearly identified as gross-  of- fees  or net-  of- fees .

Provisions of the Global Investment Performance Standards 249
b For periods beginning on or after 1 January 2011, when the initial period 
fees  and gross-  of- fees  SI- IRR through the initial annual period end.
net-  of- fees  and gross-  of- fees  SI- IRR through the composite  final 
liquidation date .
7.A.22  For periods ending on or after 1 January 2011, for fund of funds  compos -
ites , if the composite  is defined only by investment mandate, objective, or 
strategy, firms  must  also present the SI- IRR of the underlying investments 
aggregated by vintage year  as well as other measures as required  in 
7.A.23. These measures must  be presented gross of the fund of funds  
investment management fees  and must  be presented as of the most 
recent annual period end.
7.A.23  Firms  must  present as of each annual period end:

7.A.24  Firms  must  present the SI- IRR for the benchmark  through each annual 
b Be presented for the same time periods as presented for the composite ; 
and
7.A.25  For fund of funds  composites , if the composite  is defined only by invest -
ment mandate, objective, or strategy and a benchmark  is presented for the

underlying investments, the benchmark  must  be the same vintage year  
and investment mandate, objective, or strategy as the underlying investments.
7.A.26  For periods ending  on or after 1 January 2011, for fund of funds  compos -
ites , firms  must  present the percentage, if any, of composite  assets that is 
invested in direct investments  (rather than in fund investment vehicles) 
7.A.27  For periods ending on or after 1 January 2011, for primary fund  compos -
invested in fund investment vehicles (rather than in direct investments ) 
7.A.28  Firms  must not  present non-  GIPS-  compliant performance for periods 
ending on or after 1 January 2006. For periods ending prior to 1 January 2006, 
firms  may present non-  GIPS-  compliant performance.

Reading 5 ■ Global Investment Performance Standards (GIPS) 250
Private Equity—Recommendations
7.B.1  Private equity  investments should  be valued at least quarterly.
Calculation Methodology—Recommendations (the following provision does not 
apply: 2.B.2)
7.B.2  For periods ending prior to 1 January 2011, the SI- IRR should  be calculated 
using daily cash flows.
Composite Construction—Recommendations (the following provision does not 
apply: 3.B.2)  
7.B.3  Firms  should  explain and disclose material differences between the val -
uations used in performance reporting and the valuations used in financial 
reporting as of each annual period end.
7.B.4  For periods prior to 1 January 2011, firms  should  disclose material changes 
apply: 5.B.2, 5.B.3, 5.B.4, and 5.B.5)

7.B.5  For periods ending on or after 1 January 2011, for fund of funds  compos -
ites , if the composite  is defined only by vintage year  of the fund of 
funds , firms  should  also present the SI- IRR of the underlying investments 
aggregated by investment mandate, objective, or strategy and other measures 
as listed in 7.A.23. These measures should  be presented gross of the fund 
of funds  investment management fees .
7.B.6  For periods ending prior to 1 January 2011, for fund of funds  composites , 
firms  should  present the percentage, if any, of composite  assets that is 
7.B.7  For periods ending prior to 1 January 2011, for primary fund  composites , 

8 Wrap Fee/Separately Managed Account (SMA) Portfolios
The following provisions apply to the calculation and presentation of performance 
when presenting a compliant presentation  to a wrap fee /SMA  prospective 
client  (which includes prospective wrap fee /SMA  sponsors, prospective wrap 
fee/SMA  clients, and existing wrap fee /SMA  sponsors). Unless otherwise noted, 
the following wrap fee /SMA  provisions supplement all the required  and recom -
mended  provisions of the GIPS standards in Sections 0–5.
Although there are different types of wrap fee /SMA  structures, these provisions 
apply to all wrap fee /SMA  portfolios  where there are bundled fees  and the wrap 
fee/SMA  sponsor serves as an intermediary between the firm  and the end user of 
the investment services. These provisions are not applicable to portfolios  defined 
as other types of bundled fee  portfolios . These provisions are also not applicable

to model portfolios  that are provided by a firm  to a wrap fee /SMA  sponsor if

Provisions of the Global Investment Performance Standards 251
the firm  does not have discretionary portfolio  management responsibility for the 
individual wrap fee /SMA  portfolios . Similarly, a firm  or overlay manager in a 
Multiple Strategy Portfolio (MSP) or similar program is also excluded from applying 
these provisions to such portfolios  if they do not have discretion.
All wrap fee /SMA  compliant presentations  that include performance results 
for periods beginning on or after 1 January 2006 must  meet all the requirements  
of the following wrap fee /SMA  provisions.
Wrap Fee/SMA Requirements
8.A.1  Firms  must  include the performance record of actual wrap fee /SMA  
portfolios  in appropriate composites  in accordance with the firm’s  estab -
lished portfolio  inclusion policies. Once established, these composites  
(containing actual wrap fee /SMA  portfolios ) must  be used in the firm’s

compliant presentations  presented to wrap fee /SMA  prospective 
clients .
Disclosure—Requirements (the following provision does not apply: 4.A.15)
8.A.2  For all wrap fee /SMA  compliant presentations  that include periods prior 
to the inclusion of an actual wrap fee /SMA  portfolio  in the composite , 
the firm  must  disclose, for each period presented, that the composite  does 
not contain actual wrap fee /SMA  portfolios .
8.A.3  For any performance presented for periods prior to 1 January 2006 that does 
8.A.4  When firms  present composite  performance to an existing wrap fee /
SMA  sponsor that includes only that sponsor’s wrap fee /SMA  portfolios  
(resulting in a “sponsor-  specific composite ”):
a Firms  must  disclose the name of the wrap fee /SMA  sponsor repre -
sented by the sponsor-  specific composite ; and
b If the sponsor-  specific composite  compliant presentation  is

intended for the purpose of generating wrap fee /SMA  business and 
does not include performance net of the entire wrap fee , the com -
pliant presentation  must  disclose that the named sponsor-  specific 
compliant presentation  is only for the use of the named wrap fee /
SMA  sponsor.

Reading 5 ■ Global Investment Performance Standards (GIPS) 252
Presentation and Reporting—Requirements (the following provision does not 
apply: 5.A.3)
8.A.5  When firms  present performance to a wrap fee /SMA  prospective cli -
ent, the composite  presented must  include the performance of all actual 
wrap fee /SMA  portfolios , if any, managed according to the composite  
investment mandate, objective, or strategy, regardless of the wrap fee /SMA  
sponsor (resulting in a “style-  defined composite ”).
8.A.6  When firms  present performance to a wrap fee /SMA  prospective client , 
performance must  be presented net of the entire wrap fee .
8.A.7  Firms  must not  link  non-  GIPS-  compliant performance for periods begin -
ning on or after 1 January 2006 to their GIPS-  compliant performance. firms  

GIPS VALUATION PRINCIPLES
The GIPS standards are based on the ethical principles of fair representation and full 
disclosure. In order for the performance calculations to be meaningful, the valuations 
of portfolio  investments must have integrity and fairly reflect their value. Effective 
1 January 2011, the GIPS standards require  firms  to apply a fair value  method -
ology following the definition and requirements  listed below. The GIPS Valuation 
Principles, including the definition of fair value , were developed with consideration 
of the work done by the International Accounting Standards Board (IASB) and the 
Financial Accounting Standards Board (FASB) as well as other organizations.
The shift to a broader fair value  requirement  has implications for all firms  
claiming compliance with the GIPS standards. For liquid securities in active markets, 
the change to fair value  from market value  will typically not result in a change

to valuations. Firms  must  use the objective, observable, unadjusted quoted market 
prices for identical investments on the measurement date, if available.
Markets are not always liquid and investment prices are not always objective and/
or observable. For illiquid or hard to value investments, or for investments where no 
observable market value  or market price is available, additional steps are neces -
sary. A firm’s  valuation policies and procedures must  address situations where the 
market prices may be available for similar but not identical investments, inputs to 
valuations are subjective rather than objective, and/or markets are inactive instead 
of active. There is a recommended  valuation hierarchy in Section C below. Firms  
must  disclose if the composite’s  valuation hierarchy materially differs from the 
recommended  valuation hierarchy.
Although a firm  may use external third parties to value investments, the firm

still retains responsibility for compliance with the GIPS standards, including the GIPS 
Valuation Principles.
Firms  claiming compliance with the GIPS standards must  adhere to all the 
requirements  and should  comply with the recommendations  below.
Fair Value Definition
Fair value  is defined as the amount at which an investment could be exchanged in a 
current arm’s length transaction between willing parties in which the parties each act 
knowledgeably and prudently. The valuation must  be determined using the objective, II.

GIPS Valuation Principles 253
observable, unadjusted quoted market price for an identical investment in an active 
market on the measurement date, if available. In the absence of an objective, observ -
able, unadjusted quoted market price for an identical investment in an active market 
on the measurement date, the valuation must  represent the firm’s  best estimate of 
the market value . Fair value  must  include accrued income.
Valuation Requirements
Firms  must  comply with the following valuation requirements :
1 For periods beginning on or after 1 January 2011, portfolios  must  be val -
Principles (Provision 1.A.2) Chapter II.
2 Firms  must  value investments using objective, observable, unadjusted quoted 
market prices for identical investments in active markets on the measurement 
date, if available.
3 Firms  must  comply with all applicable laws and regulations regarding the cal -

culation and presentation of performance (Provision 0.A.2). Accordingly, firms  
must  comply with applicable laws and regulations relating to valuation.
4 If the compliant presentation  conforms with laws and/or regulations that 
conflict with the requirements  of the GIPS standards, firms  must  disclose 
this fact and disclose the manner in which the laws and/or regulations conflict 
with the GIPS standards (Provision 4.A.22). This includes any conflicts between 
laws and/or regulations and the GIPS Valuation Principles.
5 Firms  must  document their policies and procedures used in establishing 
existence and ownership of client assets, and must  apply them consistently 
(Provision 0.A.5). Accordingly, firms  must  document their valuation policies, 
procedures, methodologies, and hierarchy, including any changes, and must  
apply them consistently.

6 Firms  must  disclose that policies for valuing portfolios , calculating perfor -
mance, and preparing compliant presentations  are available upon request 
(Provision 4.A.12).
7 For periods beginning on or after 1 January 2011, firms  must  disclose the 
valued using subjective unobservable inputs are material to the composite  
(Provision 4.A.27).
8 For periods beginning on or after 1 January 2011, firms  must  disclose if the 
hierarchy in the GIPS Valuation Principles (Provision 4.A.28).
Additional Real Estate Valuation Requirements
9 Real estate  investments must  have an external valuation  (Provision 
6.A.4). 
10 The external valuation  process must  adhere to practices of the relevant 
valuation governing and standard setting body.

11 The firm  must not  use external valuations  where the valuer’s or apprais -
er’s fee is contingent upon the investment’s appraised value.

Reading 5 ■ Global Investment Performance Standards (GIPS) 254
12 External valuations  must be performed by an independent external pro-
fessionally designated, certified, or licensed commercial property 
valuer/appraiser . In markets where these professionals are not available, the 
firm  must  take necessary steps to ensure that only well-  qualified independent 
property valuers or appraisers are used (Provision 6.A.5).
13 Firms  must  disclose the internal valuation  methodologies used to value 
real estate  investments for the most recent period (Provision 6.A.10.b).
14 For periods beginning on or after 1 January 2011, firms  must  disclose material 
changes to valuation policies and/or methodologies (Provision 6.A.10.c).
15 For periods beginning on or after 1 January 2011, firms  must  disclose mate -
rial differences between an external valuation  and the valuation used in 
performance reporting and the reason for the differences (Provision 6.A.10.d).

16 Firms  must  present, as of each annual period end, the percentage of compos -
ite assets valued using an external valuation  during the annual period 
(Provision 6.A.16.b).
Additional Private Equity Valuation Requirements
17 The valuation methodology selected must  be the most appropriate for a 
particular investment based on the nature, facts, and circumstances of the 
investment. 
18 Firms  must  disclose the valuation methodologies used to value private 
equity  investments for the most recent period (Provision 7.A.13).
19 For periods ending on or after 1 January 2011, firms  must  disclose material 
changes to valuation policies and/or methodologies (Provision 7.A.14).
20 If the firm  adheres to any industry valuation guidelines in addition to the 
GIPS Valuation Principles, the firm  must  disclose which guidelines have been 
applied (Provision 7.A.15).
Valuation Recommendations
Firms  should  comply with the following valuation recommendations :

1 Valuation Hierarchy : firms  should  incorporate the following hierarchy into 
the policies and procedures for determining fair value  for portfolio  invest -
ments on a composite -specific basis.
a Investments must  be valued using objective, observable, unadjusted quoted 
market prices for identical investments in active markets on the measure -
ment date, if available. If not available, then investments should  be valued 
using;
b Objective, observable quoted market prices for similar investments in active 
markets. If not available or appropriate, then investments should  be valued 
using;
c Quoted prices for identical or similar investments in markets that are not 
active (markets in which there are few transactions for the investment, the 
prices are not current, or price quotations vary substantially over time and/
or between market makers). If not available or appropriate, then invest -
ments should  be valued based on;

d Market-  based inputs, other than quoted prices, that are observable for the 
investment. If not available or appropriate, then investments should  be val -
ued based on;

GIPS Valuation Principles 255
e Subjective unobservable inputs for the investment where markets are not 
active at the measurement date. Unobservable inputs should  only be used 
to measure fair value  to the extent that observable inputs and prices are 
not available or appropriate. Unobservable inputs reflect the firm’s  own 
assumptions about the assumptions that market participants would use in 
pricing the investment and should  be developed based on the best infor -
mation available under the circumstances.
2 Firms  should  disclose material changes to valuation policies and/or method -
ologies (Provision 4.B.1).
3 Firms  should  disclose the key assumptions used to value portfolio  invest -
ments (Provision 4.B.4).
4 For periods prior to 1 January 2011, firms  should  disclose the use of sub -
jective unobservable inputs for valuing portfolio  investments (as described 
in the GIPS Valuation Principles in Chapter II) if the portfolio  investments

(Provision 4.B.6).
5 Valuations should  be obtained from a qualified independent third party 
(Provision 1.B.2).
Additional Real Estate Valuation Recommendations
6 Although appraisal standards may allow for a range of estimated values, it is 
recommended  that a single value be obtained from external valuers or apprais -
ers because only one value is used in performance reporting. 
7 It is recommended  that the external appraisal firm be rotated every three to 
five years.
8 Firms  should  explain and disclose material differences between the valuation 
used in performance reporting and the valuation used in financial reporting as 
of each annual period end (Provision 6.B.4).
9 For periods prior to 1 January 2011, firms  should  disclose material changes to 
valuation policies and/or methodologies (Provision 6.B.5).
Additional Private Equity Valuation Recommendations

10 Firms  should  explain and disclose material differences between the valuations 
used in performance reporting and the valuations used in financial reporting as 
of each annual period end (Provision 7.B.3). 
11 For periods prior to 1 January 2011, firms  should  disclose material changes to 
valuation policies and/or methodologies (Provision 7.B.4).
12 The following considerations should  be incorporated into the valuation 
process:
a The quality and reliability of the data used in each methodology;
b The comparability of enterprise or transaction data;
c The stage of development of the enterprise; and
d Any additional considerations unique to the enterprise.

Reading 5 ■ Global Investment Performance Standards (GIPS) 256
GIPS ADVERTISING GUIDELINES
Purpose of the GIPS Advertising Guidelines
The GIPS Advertising Guidelines provide firms  with options for advertising per -
formance when mentioning the firm’s  claim of compliance. The GIPS Advertising 
Guidelines do not replace the GIPS standards, nor do they absolve firms  from pre -
senting a compliant presentation  as required  by the GIPS standards. These 
guidelines only apply to firms  that already satisfy all the requirements  of the GIPS 
standards on a firm -wide basis and claim compliance with the GIPS standards in an 
advertisement. Firms  that choose to claim compliance in an advertisement must  
follow the GIPS Advertising Guidelines or include a compliant presentation  in 
the advertisement.
Definition of Advertisement
For the purposes of these guidelines, an advertisement includes any materials that are 
distributed to or designed for use in newspapers, magazines, firm  brochures, letters,

media, websites, or any other written or electronic material addressed to more than 
one prospective client . Any written material, other than one-  on- one presentations 
and individual client reporting, distributed to maintain existing clients or solicit new 
clients for a firm  is considered an advertisement.
Relationship of GIPS Advertising Guidelines to Regulatory Requirements
Firms  advertising performance must  adhere to all applicable laws and regulations 
governing advertisements. Firms  are encouraged to seek legal or regulatory counsel 
because additional disclosures may be required . In cases where applicable laws and/
or regulations conflict with the requirements  of the GIPS standards and/or the GIPS 
Advertising Guidelines, firms  are required  to comply with the law or regulation.
The calculation and advertisement of pooled unitized investment vehicles, such as 
mutual funds and open-  ended investment companies, are regulated in most markets.

The GIPS Advertising Guidelines are not intended to replace applicable laws and/
or regulations when a firm  is advertising performance solely for a pooled unitized 
investment vehicle.
Other Information
The advertisement may include other information beyond what is required  under 
the GIPS Advertising Guidelines provided the information is shown with equal or 
lesser prominence relative to the information required  by the GIPS Advertising 
Guidelines and the information does not conflict with the requirements  of the 
GIPS standards and/or the GIPS Advertising Guidelines. Firms  must  adhere to the 
principles of fair representation and full disclosure when advertising and must not  
present performance or performance-  related information that is false or misleading.
Requirements of the GIPS Advertising Guidelines
All advertisements that include a claim of compliance with the GIPS standards by 
following the GIPS Advertising Guidelines must  disclose the following:
1 The definition of the firm .

2 How a prospective client  can obtain a compliant presentation  and/or 
the firm’s  list of composite descriptions .
3 The GIPS compliance statement for advertisements: III.

GIPS Advertising Guidelines 257
Investment Performance Standards (GIPS®). ”
 All advertisements that include a claim of compliance with the GIPS standards 
by following the GIPS Advertising Guidelines and that present performance 
must  also disclose the following information, which must  be taken or derived 
from a compliant presentation :
4 The composite description . 
5 Composite  total returns  according to one of the following:
a One-, three-, and five-  year annualized composite  returns through the most 
recent period with the period-  end date clearly identified. If the composite  
has been in existence for less than five years, firms  must  also present the 
annualized returns since the composite inception date . (For example, 
if a composite  has been in existence for four years, firms  must  present 
one-, three-, and four-  year annualized returns through the most recent

period.) Returns for periods of less than one year must not  be annualized.
b Period-  to- date composite  returns in addition to one-, three-, and five-  year 
annualized composite  returns through the same period of time as pre -
sented in the corresponding compliant presentation  with the period 
end date clearly identified. If the composite  has been in existence for less 
than five years, firms  must  also present the annualized returns since the 
composite inception date  (For example, if a composite  has been in 
existence for four years, firms  must  present one-, three-, and four-  year 
annualized returns in addition to the period-  to- date composite  return.) 
Returns for periods of less than one year must not  be annualized.
c Period-  to- date composite  returns in addition to five years of annual com -
posite  returns (or for each annual period since the composite inception 
date  if the composite  has been in existence for less than five years) with

the period end date clearly identified. The annual returns must  be calcu -
lated through the same period of time as presented in the corresponding 
6 Whether returns are presented gross-  of- fees  and/or net-  of- fees .
7 The total return  for the benchmark  for the same periods for which 
the composite  return is presented. Firms  must  present total returns  
for the same benchmark  as presented in the corresponding compliant 
8 The benchmark description .
9 If the firm  determines no appropriate benchmark  for the composite  exists, 
10 The currency used to express performance.
11 The presence, use, and extent of leverage, derivatives, and short positions, if 
material, including a description of the frequency of use and characteristics of 
the instruments sufficient to identify risks.
12 For any performance presented in an advertisement for periods prior to 1

January 2000 that does not comply with the GIPS standards, firms  must  dis-
close the periods of non-  compliance.
13 If the advertisement conforms with laws and/or regulations that conflict 
with the requirements  of the GIPS standards and/or the GIPS Advertising 
Guidelines, firms  must  disclose this fact and disclose the manner in which 
the laws and/or regulations conflict with the GIPS standards and/or the GIPS 
Advertising Guidelines.

Reading 5 ■ Global Investment Performance Standards (GIPS) 258
Verification  is intended to provide a firm  and its existing clients and prospec -
tive clients  additional confidence in the firm’s  claim of compliance with the GIPS 
standards. Verification  may increase the knowledge of the firm’s  performance 
measurement team and improve the consistency and quality of the firm’s  compliant 
presentations . Verification  may also provide improved internal processes and 
procedures as well as marketing advantages to the firm . Verification does not ensure 
the accuracy of any specific composite  presentation.
The GIPS standards recommend  that firms  be verified. Verification  brings 
additional credibility to the claim of compliance and supports the overall guiding prin -
ciples of fair representation and full disclosure of a firm’s  investment performance.
The verification  procedures attempt to strike a balance between ensuring the

quality, accuracy, and relevance of performance presentations and minimizing the 
cost to firms .
Scope and Purpose of Verification
1 Verification  must  be performed by a qualified independent third party.
2 Verification  assesses whether:
a The firm  has complied with all the composite  construction require -
ments  of the GIPS standards on a firm -wide basis and
b The firm’s  policies and procedures are designed to calculate and present 
3 A single verification report  is issued with respect to the whole firm . 
Verification  cannot be carried out on a composite  and, accordingly, does 
not provide assurance about the performance of any specific composite . Firms  
must not  state that a particular composite  has been “verified” or make any 
claim to that effect.
4 The initial minimum period for which verification  can be performed is one 
year (or from firm  inception date through period end if less than one year) of a

firm’s  presented performance. The recommended  period over which verifi -
cation  is performed is that part of the firm’s  performance for which compli -
ance with the GIPS standards is claimed.
5 A verification report  must  opine that:
ments  of the GIPS standards on a firm -wide basis, and
 The firm  must not  state that it has been verified unless a verification 
report  has been issued.
6 A principal verifier may accept the work of another verifier as part of the basis 
for the principal verifier’s opinion. A principal verifier may also choose to rely 
on the audit and/or internal control work of a qualified and reputable indepen -
dent third party. In addition, a principal verifier may choose to rely on the other 
audit and/or internal control work performed by the verification  firm. If

reliance on another party’s work is planned, the scope of work, including time 
period covered, results of procedures performed, qualifications, competency, 
objectivity, and reputation of the other party, must  be assessed by the principal 
verifier when making the determination as to whether to place any reliance on IV.

Verification 259
such work. Reliance considerations and conclusions must  be documented by 
the principal verifier. The principal verifier must  use professional skepticism 
when deciding whether to place reliance on work performed by another inde -
pendent third party.
7 Sample portfolio  Selection: Verifiers must  subject the entire firm  to testing 
when performing verification  procedures unless reliance is placed on work 
performed by a qualified and reputable independent third party or appropriate 
alternative control procedures have been performed by the verifier. Verifiers 
may use a sampling methodology when performing such procedures. Verifiers 
must  consider the following criteria when selecting samples:
a Number of composites  at the firm ;
b Number of portfolios  in each composite ;
c Type of composite ;
d Total firm assets ;
e Internal control structure at the firm  (system of checks and balances in 
place);
f Number of years being verified; and

place);
g Computer applications, software used in the construction and maintenance 
of composites , the use of external performance measurers, and the method 
of calculating performance.
 This list is not all-  inclusive and contains only the minimum criteria that must  
be considered in the selection and evaluation of a sample. For example, one 
potentially useful approach would be to include in the sample a portfolio  
that has the largest impact on composite  performance because of its size or 
because of extremely good or bad performance. Missing or incomplete docu -
ments, or the presence of errors, would normally be expected to warrant select -
ing a larger sample or applying additional verification  procedures.
8 After performing the verification , the verifier may conclude that the firm  
is not in compliance with the GIPS standards or that the records of the firm  
cannot support a verification . In such situations, the verifier must  issue a

statement to the firm  clarifying why a verification report  could not be 
issued. A verification report  must not  be issued when the verifier knows 
that the firm  is not in compliance with the GIPS standards or the records of 
the firm  cannot support a verification .
9 The minimum verification  procedures are described below in Section B. The 
verification report  must  state that the verification  has been conducted 
in accordance with these verification  procedures.
Required Verification Procedures
The following are the minimum procedures that verifiers must  follow when conduct -
ing a verification . Verifiers must  complete the verification  in accordance with 
these procedures prior to issuing a verification report  to the firm :
1 Pre- verification  Procedures:
a Knowledge of the GIPS Standards: Verifiers must  understand all the 
requirements  and recommendations  of the GIPS standards, including 
any updates, Guidance Statements, interpretations, Questions & Answers

(Q&As), and clarifications published by CFA Institute and the GIPS 
(www.gipsstandards.org) as well as in the GIPS Handbook .

Reading 5 ■ Global Investment Performance Standards (GIPS) 260
b Knowledge of Regulations: Verifiers must  be knowledgeable of applicable 
laws and regulations regarding the calculation and presentation of perfor -
mance and must  consider any differences between these laws and regula -
tions and the GIPS standards.
c Knowledge of the firm : Verifiers must  gain an understanding of the firm , 
including the corporate structure of the firm  and how it operates.
d Knowledge of the firm’s  Policies and Procedures: Verifiers must  under -
stand the firm’s  policies and procedures for establishing and maintaining 
compliance with all the applicable requirements  and adopted recom -
mendations  of the GIPS standards. The verifier must  obtain a copy of 
the firm’s  policies and procedures used in establishing and maintaining 
compliance with the GIPS standards and ensure that all applicable policies 
and procedures are properly included and adequately documented.

e Knowledge of Valuation Basis and Performance Calculations: Verifiers 
must  understand the policies, procedures, and methodologies used to value 
portfolios  and compute investment performance.
2 Verification  Procedures:
a Fundamentals of Compliance: Verifiers must  perform sufficient procedures 
to determine that:
 i. The firm  is, and has been, appropriately defined;
 ii. The firm  has defined and maintained composites  in compliance with 
the GIPS standards;
 iii. All the firm’s  actual, fee-  paying, discretionary portfolios  are included 
in at least one composite ;
 iv. The firm’s  definition of discretion has been consistently applied over 
time;
 v. At all times, all portfolios  are included in their respective compos -
ites  and no portfolios  that belong in a particular composite  have 
been excluded;
 vi. The firm’s  policies and procedures for ensuring the existence and 
ownership of client assets are appropriate and have been consistently 
applied;

applied;
 vii. The composite  benchmark  reflects the investment mandate, objective, 
or strategy of the composite ;
 viii. The firm’s  policies and procedures for creating and maintaining com -
posites  have been consistently applied;
 ix. The firm’s  list of composite descriptions  is complete; and
 x. Total firm assets  are appropriately calculated and disclosed.
b Determination of Discretionary Status of portfolios : Verifiers must  
obtain a list of all portfolios . Verifiers must  select portfolios  from this 
list and perform sufficient procedures to determine that the firm’s  classi -
fication of the portfolios  as discretionary or non-  discretionary is appro -
priate by referring to the portfolio’s  investment management agreement 
and/or investment guidelines and the firm’s  policies and procedures for 
determining investment discretion.
c Allocation of portfolios  to composites : Verifiers must  obtain lists of all 
open (both new and existing) and closed portfolios  for all composites

for the periods being verified. Verifiers must  select portfolios  from these 
lists and perform sufficient procedures to determine that:

Verification 261
 i. The timing of inclusion in the composite  is in accordance with policies 
and procedures of the firm .
 ii. The timing of exclusion from the composite  is in accordance with poli -
cies and procedures of the firm .
 iii. The portfolio’s  investment mandate, objective, or strategy, as indi -
cated by the portfolio’s  investment management agreement, invest -
ment guidelines, portfolio  summary, and/or other appropriate docu -
mentation, is consistent with the composite definition .
 iv. Portfolios  are completely and accurately included in composites  by 
tracing selected portfolios  from:
a The portfolio’s  investment management agreement and/or invest -
ment management guidelines to the composite(s) ; and
b The composite(s)  to the portfolio’s  investment management 
agreement and/or investment guidelines.
 v. Portfolios  sharing the same investment mandate, objective, or strat -
egy are included in the same composite .

 vi. Movements from one composite  to another are appropriate and con -
sistent with documented changes to a portfolio’s  investment mandate, 
objective, or strategy or the redefinition of the composite .
d Data Review: For selected portfolios , verifiers must  perform sufficient 
procedures to determine that the treatment of the following items is consis -
tent with the firm’s  policy:
 i. Classification of portfolio  flows (e.g., receipts, disbursements, divi -
dends, interest, fees, and taxes);
 ii. Accounting treatment of income, interest, and dividend accruals and 
receipts;
 iii. Accounting treatment of taxes, tax reclaims, and tax accruals;
 iv. Accounting treatment of purchases, sales, and the opening and closing 
of other positions; and
 v. Accounting treatment and valuation methodologies for investments, 
including derivatives.
e Performance Measurement Calculation: Recognizing that verification

does not provide assurance that specific composite  returns are correctly 
calculated and presented, verifiers must  determine that the firm  has calcu -
lated and presented performance in accordance with the firm’s  policies and 
procedures. Verifiers must  perform the following procedures:
 i. Recalculate rates of return for a sample of portfolios , determine that 
an acceptable return formula as required  by the GIPS standards is 
used, and determine that the firm’s  calculations are in accordance with 
the firm’s  policies and procedures. The verifier must  also determine 
that any fees and expenses are treated in accordance with the GIPS stan -
dards and the firm’s  policies and procedures.
 ii. Take a sample of composite  and benchmark  calculations to determine 
the accuracy of all required numerical data (e.g., risk measures, inter -
nal dispersion ).
 iii. If a custom benchmark  or combination of multiple benchmarks  is

used, take a sample of the benchmark  data used by the firm  to deter -
mine that the calculation methodology has been correctly applied and 
the data used are consistent with the benchmark  disclosure in the 

Reading 5 ■ Global Investment Performance Standards (GIPS) 262
f Compliant presentations : Verifiers must  perform sufficient procedures 
on a sample of compliant presentations  to determine that the presen -
tations include all the information and disclosures required  by the GIPS 
standards. The information and disclosures must  be consistent with the 
firm’s  records, the firm’s  documented policies and procedures, and the 
results of the verifier’s procedures.
g Maintenance of Records: The verifier must  maintain sufficient documen -
tation to support all procedures performed supporting the issuance of the 
verification report , including all significant judgments and conclusions 
made by the verifier.
h Representation Letter: The verifier must  obtain a representation letter 
from the firm  confirming that policies and procedures used in establishing 
and maintaining compliance with the GIPS standards are as described in

the firm’s  policies and procedures documents and have been consistently 
applied throughout the periods being verified. The representation letter 
must  confirm that the firm  complies with the GIPS standards for the 
period being verified. The representation letter must  also contain any other 
specific representations made to the verifier during the verification .
Performance Examinations
In addition to a verification , a firm  may choose to have a specifically focused per-
formance examination  of a particular composite  compliant presentation . 
However, a performance examination report  must not  be issued unless a 
verification report  has also been issued. The performance examination  may 
be performed concurrently with the verification .
A performance examination  is not required  for a firm  to be verified. The 
firm  must not  state that a composite  has been examined unless the performance 
examination report  has been issued for the specific composite .

Please see the Guidance Statement on performance examinations  for addi -
tional guidance.
GIPS GLOSSARY
Accrual accounting The recording of financial transactions as they 
come into existence rather than when they are 
paid or settled.
Additional information Information that is required  or recommended  
under the GIPS standards and is not considered 
supplemental information .
Administrative fee All fees other than trading expenses  
and the investment management fee . 
Administrative fees  include custody fees , 
accounting fees, auditing fees, consulting fees, 
legal fees, performance measurement fees, and 
other related fees. (See “ bundled fee ”)END OPTIONAL 
SEGMENT
V.

GIPS Glossary 263
All-  in fee A type of bundled fee  that can include any 
combination of investment management fees , 
trading expenses , custody fees , and admin -
istrative fees . All-  in- fees  are client specific 
and typically offered in certain jurisdictions where 
asset management, brokerage, and custody ser -
vices are offered by the same company.
Benchmark A point of reference against which the compos -
ite’s  performance and/or risk is compared.
Benchmark description General information regarding the investments, 
structure, and/or characteristics of the bench -
mark . The description must  include the key 
features of the benchmark  or the name of the 
benchmark  for a readily recognized index or 
other point of reference.
Bundled fee A fee that combines multiple fees into one total 
or “bundled” fee. Bundled fees  can include 
any combination of investment management 
fees , trading expenses , custody fees , and/or 
administrative fees . Two examples of bun -

dled fees  are wrap fees  and all-  in- fees .
Capital employed   
(real estate)The denominator of the return calculations 
and is defined as the “weighted-  average equity” 
(weighted-  average capital) during the measure -
ment period. Capital employed  does not 
include any income return  or capital return  
earned during the measurement period. Beginning 
capital is adjusted by weighting the external 
cash flows  that occurred during the period. 
Capital return  
(real estate)The change in value of the real estate  invest -
ments and cash and/or cash equivalent assets held 
throughout the measurement period, adjusted for 
all capital expenditures (subtracted) and net pro -
ceeds from sales (added). The capital return  
is computed as a percentage of the capital 
employed . Also known as “capital appreciation 
return” or “appreciation return. ”
Carried interest  
(real estate and private equity)The profits that general partners  are allocated

from the profits on the investments made by the 
investment vehicle. Also known as “carry” or 
“promote. ”
Carve-  out A portion of a portfolio  that is by itself repre -
sentative of a distinct investment strategy. It is 
used to create a track record for a narrower man -
date from a multiple-  strategy portfolio  man -
aged to a broader mandate. For periods beginning 
on or after 1 January 2010, a carve-  out  must  be 
managed separately with its own cash balance.
Closed-  end fund  
(real estate and private equity)A type of investment vehicle where the number 
of investors, total committed capital , and life 
are fixed and not open for subscriptions and/or 
redemptions. Closed-  end funds  have a capital 
call (drawdown) process in place that is controlled 
by the general partner .

Reading 5 ■ Global Investment Performance Standards (GIPS) 264
Committed capital  
(real estate and private equity)Pledges of capital to an investment vehicle by 
investors ( limited partners  and the general 
partner ) or by the firm . committed capital  
is typically not drawn down at once but drawn 
down over a period of time. Also known as 
“commitments. ”
Compliant presentation A presentation for a composite  that contains all 
the information required  by the GIPS standards 
and may also include additional information  
or supplemental information . (See Sample 
compliant presentations  in Appendix A)
Composite An aggregation of one or more portfolios  man -
aged according to a similar investment mandate, 
objective, or strategy. 
Composite creation date The date when the firm  first groups one or more 
portfolios  to create a composite . The com -
posite creation date  is not necessarily the 
same as the composite inception date .

Composite definition Detailed criteria that determine the assignment of 
portfolios  to composites . Criteria may include 
investment mandate, style or strategy, asset class, 
the use of derivatives, leverage and/or hedging, 
targeted risk metrics, investment constraints or 
restrictions, and/or portfolio  type (e.g., segre -
gated or pooled, taxable versus tax exempt.) 
Composite description General information regarding the investment 
mandate, objective, or strategy of the compos -
ite. The composite description  may be more 
abbreviated than the composite definition  but 
must  include all key features of the composite  
and must  include enough information to allow 
a prospective client  to understand the key 
characteristics of the composite’s  investment 
mandate, objective, or strategy. (See the Sample 
List of Composite Descriptions in Appendix C)
Composite inception date The initial date of the composite’s  performance

record. The composite inception date  is not 
necessarily the same as the composite creation 
date .
Composite termination 
dateThe date that the last portfolio  exits a 
Custody fee The fees payable to the custodian for the safe -
keeping of portfolio  assets. Custody fees  
are considered to be administrative fees  and 
typically contain an asset-  based portion and a 
transaction-  based portion. The custody fee  
may also include charges for additional services, 
including accounting, securities lending, and/or 
performance measurement. Custodial fees that 
are charged per transaction should  be included 
in the custody fee  and not included as part of 
trading expenses .
Direct investments  
(private equity)Investments made directly in private equity  
investments rather than investments made in 
fund investment vehicles or cash and/or cash 
equivalents.

GIPS Glossary 265
Distinct business entity A unit, division, department, or office that is 
organizationally and functionally segregated from 
other units, divisions, departments, or offices and 
that retains discretion over the assets it manages 
and that should have autonomy over the invest -
ment decision-  making process. Possible criteria 
that can be used to determine this include: 
■■being a legal entity,
■■having a distinct market or client type (e.g., 
institutional, retail, private client, etc.), and
■■using a separate and distinct investment 
process. 
Distribution  
(real estate and private equity)Cash or stock distributed to limited part -
ners  (or investors) from an investment vehicle. 
Distributions  are typically at the discre -
tion of the general partner  (or the firm ). 
Distributions  include both recallable and non-  
recallable distributions .
DPI  
(real estate and private equity)Since inception  distributions  divided by 
since inception  paid-  in capital . (See “ reali -

zation multiple ”)
Evergreen fund  
(private equity)An open-  end fund  that allows for on-  going sub -
scriptions and/or redemptions by investors. 
Ex- ante Before the fact. 
Ex- post After the fact. 
External cash flow Capital (cash or investments) that enters or exits a 
portfolio .
External valuation  
(real estate)An assessment of value performed by an inde -
pendent external third party who is a qualified, 
professionally designated, certified, or 
licensed commercial property valuer/
appraiser .
Fair value The amount at which an investment could be 
exchanged in a current arm’s length transaction 
between willing parties in which the parties each 
act knowledgeably and prudently. The valua -
tion must  be determined using the objective, 
observable, unadjusted quoted market price for 
an identical investment in an active market on 
the measurement date, if available. In the absence 
of an objective, observable, unadjusted quoted 
market price for an identical investment in an

market price for an identical investment in an 
active market on the measurement date, the 
valuation must  represent the firm’s  best estimate 
of the market value . Fair value  must  include 
accrued income.
Fee schedule The firm’s  current schedule of investment 
management fees  or bundled fees  relevant to 
the particular compliant presentation .
Final liquidation date  
(real estate and private equity)The date when the last portfolio  in a compos -
ite is fully distributed.
Firm The entity defined for compliance with the GIPS 
standards. (See “ distinct business entity ”)

Reading 5 ■ Global Investment Performance Standards (GIPS) 266
Fund of funds  
(private equity)An investment vehicle that invests in underlying 
investment vehicles. private equity  funds 
of funds  predominately invest in closed-  end 
funds  and may make opportunistic direct 
investments .
General partner  
(real estate and private equity)A class of partner in a limited partnership . The 
general partner  (GP) retains liability for the 
actions of the limited partnership . The gen -
eral partner  is typically the fund manager, and 
the limited partners  (LPs) are the other inves -
tors in the limited partnership . The general 
partner  earns an investment management 
fee that typically includes a percentage of the 
limited partnership’s  profits. (See “ carried 
interest ”)
Gross-  of- fees The return on investments reduced by any trad -
ing expenses  incurred during the period. 
Gross-  of- fees  
(real estate and private equity)The return on investments reduced by any trans -

action expenses  incurred during the period.
Income return  
(real estate)The investment income earned on all investments 
(including cash and cash equivalents) during the 
measurement period net of all non-  recoverable 
expenditures, interest expense on debt, and prop -
erty taxes. The income return  is computed as a 
percentage of the capital employed .
Internal dispersion A measure of the spread of the annual returns 
of individual portfolios  within a compos -
ite. Measures may include, but are not limited 
to, high/low, range, or standard deviation  
(asset weighted or equal weighted) of portfolio  
returns.
Internal valuation  
(real estate)A firm’s  best estimate of value based on the 
most current and accurate information available 
under the circumstances. Internal valuation  
methodologies include applying a discounted cash 
flow model, using a sales comparison or replace -
ment cost approach, or conducting a review of all 
significant events (both general market and asset

significant events (both general market and asset 
specific) that could have a material impact on the 
Investment management 
feeA fee payable to the firm  for the management of a 
portfolio . Investment management fees  are 
typically asset based (percentage of assets), per -
formance based (see “ performance-  based fee ”), 
or a combination of the two but may take different 
forms as well. Investment management fees  
also include carried interest .
Investment multiple (TVPI)  
(real estate and private equity) Total value  divided by since inception  
paid-  in capital . 
Large cash flow The level at which the firm  determines that an 
external cash flow  may distort performance if 
the portfolio  is not valued. Firms  must  define 
the amount in terms of the value of cash/asset 
flow or in terms of a percentage of the portfolio  
assets or the composite  assets.

GIPS Glossary 267
Limited partner  
(real estate and private equity)An investor in a limited partnership . The gen -
eral partner  is liable for the actions of the lim-
ited partnership , and the limited partners  
are generally protected from legal actions and any 
losses beyond their committed capital . 
Limited partnership  
(real estate and private equity)The legal structure used by most private equity  
and real estate  closed-  end funds . Limited 
partnerships  are usually fixed life investment 
vehicles. The general partner  manages the 
limited partnership  pursuant to the partner -
ship agreement.
Link 1 Mathematical Linking : The method by which 
sub-  period returns are geometrically combined 
to calculate the period return using the follow -
ing formula:
Period return = [(1 + R1) × (1 + R2) … (1 + 
Rn)] – 1,
 where R1, R2…Rn are the sub-  period returns 
for sub-  period 1 through n, respectively.
2 Presentational Linking : To be visually con -
nected or otherwise associated within a com -

pliant presentation  (e.g., two pieces of 
information are linked  by placing them next 
to each other).
Market value The price at which investors can buy or sell an 
investment at a given time multiplied by the quan -
tity held plus any accrued income.
Must A provision, task, or action that is mandatory 
or required  to be followed or performed. (See 
“require/requirement ”)
Must not A task or action that is forbidden or prohibited. 
Net-  of- fees The gross-  of- fees  return reduced by 
investment management fees  (includ -
ing performance-  based fees  and carried 
interest ).
Open-  end fund  
of investors and the total committed capital  
is not fixed and is open for subscriptions and/or 
redemptions. (See “ evergreen fund ”)
Paid-  in capital  
(real estate and private equity)Capital inflows to an investment vehicle. 
Committed capital  is typically drawn down

Committed capital  is typically drawn down 
from limited partners  (or investors) over a 
period of time through a series of capital calls, 
which are at the discretion of the general part -
ner or firm . Paid-  in capital  is equal to the 
amount of committed capital  that has been 
drawn down since inception . Paid-  in capital  
includes distributions  that are subsequently 
recalled by the general partner  or firm  and 
reinvested into the investment vehicle.
Performance-  based fee A type of investment management fee  that 
is typically based on the performance of the 
portfolio  on an absolute basis or relative to a 
benchmark .(continued)

Reading 5 ■ Global Investment Performance Standards (GIPS) 268
Performance examination A detailed examination of a specific composite’s  
compliant presentation  by an independent 
verifier.
Performance examination 
reportA performance examination report  is issued 
after a performance examination  has been 
performed and opines that a particular com -
posite’s  compliant presentation  has been 
prepared and presented in compliance with the 
GIPS standards. 
Periodicity The length of the time period over which a vari -
able is measured (e.g., a variable that is measured 
at a monthly periodicity  consists of observations 
for each month).
Pic multiple  
(real estate and private equity)Since inception  paid-  in capital  divided by 
cumulative committed capital . 
Portfolio An individually managed group of investments. A 
portfolio  may be an account or pooled invest -
ment vehicle.
Primary fund  
(private equity)An investment vehicle that makes direct invest -

ments  rather than investing in other investment 
vehicles.
Private equity Investment strategies include, but are not limited 
to, venture capital, leveraged buyouts, consolida -
tions, mezzanine and distressed debt investments, 
and a variety of hybrids, such as venture leasing 
and venture factoring.
Professionally designated, 
certified, or licensed com -
mercial property valuer/
appraiser  
(real estate)In Europe, Canada, and parts of Southeast Asia, 
the predominant professional designation is that 
of the Royal Institution of Chartered Surveyors 
(RICS). In the United States, the professional 
designation is Member [of the] Appraisal Institute 
(MAI). In addition, each state regulates real 
estate  appraisers and registers, licenses, or 
certifies them based on their experience and test 
results.
Proprietary assets Investments owned by the firm , the firm’s  man -
agement, and/or the firm’s  parent company that 
are managed by the firm .

Prospective client Any person or entity that has expressed interest 
in one of the firm’s  composite  strategies and 
qualifies to invest in the composite . Existing 
clients may also qualify as prospective clients  
for any strategy that is different from their current 
investment strategy. Investment consultants and 
other third parties are included as prospective 
clients  if they represent investors that qualify as 
prospective clients .
Public market equivalent 
(pme)  
(private equity)The performance of a public market index 
expressed in terms of an internal rate of return 
(IRR), using the same cash flows and timing as 
those of the composite  over the same time 
period. A PME can be used as a benchmark  by 
comparing the IRR of a private equity  compos -
ite with the PME of a public market index.

GIPS Glossary 269
Real estate Investments in: 
■■wholly owned or partially owned properties;
■■commingled funds, property unit trusts, and 
insurance company separate accounts;
■■unlisted, private placement securities issued 
by private real estate  investment trusts 
(REITs) and real estate  operating companies 
(REOCs); and
■■equity-  oriented debt (e.g., participating mort -
gage loans) or any private interest in a property 
where some portion of return to the investor at 
the time of investment is related to the perfor -
mance of the underlying real estate .
Realization multiple (dpi)  
since inception  paid-  in capital .
Recommend/
RecommendationA suggested provision, task, or action that 
should  be followed or performed. A recommen -
dation  is considered to be best practice but is not 
a requirement . (See “ should ”)
Require/Requirement A provision, task, or action that must  be followed 
or performed. (See “ must ”)

Residual value  
(private equity and real estate)The remaining equity that limited partners  (or 
investors) have in an investment vehicle at the end 
of the performance reporting period.
RVPI  
(real estate and private equity)Residual value  divided by since inception  
paid-  in capital . (See “ unrealized multiple ”)
Secondary fund  
(private equity)An investment vehicle that buys interests in exist -
ing investment vehicles. 
Settlement date 
accountingRecognizing the asset or liability on the date 
when the exchange of cash and investments is 
completed. 
Should A provision, task, or action that is recommended  
to be followed or performed and is considered 
to be best practice but is not required . (See 
“recommend/recommendation ”)
Significant cash flow The level at which the firm  determines that a 
client-  directed external cash flow  may tem -
porarily prevent the firm  from implementing the 
composite  strategy. The measure of significance

composite  strategy. The measure of significance 
must  be determined as either a specific mone -
tary amount (e.g., €50,000,000) or a percentage 
of portfolio  assets (based on the most recent 
valuation).
Since inception  
(real estate and private equity)From the initial cash flow of a composite .
Since inception internal 
rate of return (SI-  IRR)  
(real estate and private equity)The internal rate of return (IRR) is the implied 
discount rate or effective compounded rate of 
return that equates the present value of cash 
outflows with the present value of cash inflows. 
The SI- IRR is a special case of the IRR that equates 
the present value of all cash flows (capital calls 
and distributions ) with the period end value. 
The SI- IRR is always annualized except when the 
reporting period is less than one year, in which 
case the SI- IRR is not annualized.(continued)

Reading 5 ■ Global Investment Performance Standards (GIPS) 270
Standard deviation A measure of the variability of returns. As a mea -
sure of internal dispersion , standard devi -
ation  quantifies the distribution of the returns of 
the individual portfolios  within the composite . 
As a measure of historical risk, standard devi -
ation  quantifies the variability of the compos -
ite and/or benchmark  returns over time. Also 
referred to as “external standard deviation .”
Sub-  advisor A third-  party investment manager hired by the 
firm  to manage some or all of the assets for which 
a firm  has investment management responsibility. 
Supplemental information Any performance-  related information included as 
part of a compliant presentation  that supple -
ments or enhances the required  and/or recom -
mended  provisions of the GIPS standards.
Temporary new account An account for temporarily holding client-  directed 
external cash flows  until they are invested

external cash flows  until they are invested 
according to the composite  strategy or disbursed. 
Firms  can use a temporary new account  to 
remove the effect of a significant cash flow  
on a portfolio . When a significant cash 
flow  occurs in a portfolio , the firm  may direct 
the external cash flow  to a temporary new 
account  according to the composite’s  signifi -
cant cash flow  policy.
Time-  weighted rate of 
returnA method of calculating period-  by- period returns 
that negates the effects of external cash flows .
Total firm assets All discretionary and non-  discretionary assets 
for which a firm  has investment management 
responsibility. Total firm assets  includes assets 
assigned to a sub-  advisor  provided the firm  has 
discretion over the selection of the sub-  advisor .
Total return The rate of return that includes the realized and 
unrealized gains and losses plus income for the 
measurement period.
Total return  
(real estate)The rate of return, including all capital return

and income return  components, expressed as 
a percentage of the capital employed  over the 
Total value  
(real estate and private equity)Residual value  plus distributions .
Trade date accounting Recognizing the asset or liability on the date of 
the purchase or sale and not on the settlement 
date. Recognizing the asset or liability within three 
days of the date the transaction is entered into 
(trade date, T+1, T+2, or T+3) satisfies the trade 
date accounting  requirement  for purposes 
of the GIPS standards. (See “ settlement date 
accounting ”)
Trading expenses The actual costs of buying or selling investments. 
These costs typically take the form of brokerage 
commissions, exchange fees and/or taxes, and/or 
bid–offer spreads from either internal or external 
brokers. Custodial fees charged per transaction 
should  be considered custody fees  and not 

GIPS Glossary 271
Transaction expenses  
(real estate and private equity)All actual legal, financial, advisory, and investment 
banking fees related to buying, selling, restructur -
ing, and/or recapitalizing portfolio  investments 
as well as trading expenses , if any.
TVPI  
(real estate and private equity)Total value  divided by since inception  
paid-  in capital . (See “ investment multiple ”)
Unrealized multiple (RVPI)  
paid-  in capital .
Verification A process by which an independent verifier 
assesses whether 
1 the firm  has complied with all the compos -
ite construction requirements  of the GIPS 
standards on a firm -wide basis and 
2 the firm’s  policies and procedures are 
designed to calculate and present performance 
in compliance with the GIPS standards.
Verification report A verification report  is issued after a ver-
ification  has been performed and opines that 
the firm  has complied with all the composite

the firm  has complied with all the composite  
construction requirements  of the GIPS stan -
dards on a firm -wide basis and that the firm’s  
policies and procedures are designed to calculate 
and present performance in compliance with the 
Vintage year  
(real estate and private equity)Two methods used to determine vintage year  
are: 
1 the year of the investment vehicle’s first draw -
down or capital call from its investors; or
2 the year when the first committed capital  
from outside investors is closed and legally 
binding.
Wrap fee Wrap fees  are a type of bundled fee  and are 
specific to a particular investment product. The 
wrap fee  is charged by a wrap fee  sponsor for 
investment management services and typically 
includes associated trading expenses  that 
cannot be separately identified. Wrap fees  can 
be all-  inclusive, asset-  based fees and may include 
a combination of investment management 
fees , trading expenses , custody fees , and/or

administrative fees . A wrap fee  portfolio  
is sometimes referred to as a “separately managed 
account” (SMA) or “managed account. ”

Reading 5 ■ Global Investment Performance Standards (GIPS) 272
APPENDIX A: SAMPLE COMPLIANT 
PRESENTATIONS
SAMPLE 1  INVESTMENT FIRM BALANCED GROWTH COMPOSITE 
 1 January 2002 through 31 December 2011
 Year Composite 
Gross Return
(%) Composit e
Net Retur n
(%) Custom
Benchmar k
Retur n
3- Yr St Dev
(%) Benchmar k
3- Yr St Dev
(%) Number  
of
Portfolios Internal  
Dispersion
(%) Composite 
Assets
($ M) Firm  
Assets
($ M)
 2002  –10. 5 –11. 4 –11. 8   31  4.5  165  236
 2003  16.3  15.1  13.2    34  2.0  235  346
 2004  7.5 6.4 8.9   38  5.7  344  529
 2005  1.8 0.8 0.3   45  2.8  445  695
 2006  11.2  10.1  12.2    48  3.1  520  839
 2007  6.1 5.0 7.1   49  2.8  505  1,014
 2008  –21. 3 –22. 1 –24. 9   44  2.9  475  964
 2009  16.5  15.3  14.7    47  3.1  493  983
 2010  10.6  9.5 13.0    51  3.5 549 1,114
 2011  2.7 1.7 0.4 7.1 7.4 54  2.5 575 1,236
Sample 1 Investment Firm claims compliance with the Global Investment 
Performance Standards (GIPS®) and has prepared and presented this report

in compliance with the GIPS standards. Sample 1 Investment Firm has 
been independently verified for the periods 1 January  2000 through 31 
December 2010. The verification report is available upon request. Verification 
assesses whether (1) the firm has complied with all the composite con -
struction requirements of the GIPS standards on a firm-  wide basis and (2) 
the firm’s policies and procedures are designed to calculate and present 
performance in compliance with the GIPS standards. Verification does not 
ensure the accuracy of any specific composite presentation.
Notes:
1 Sample 1 Investment Firm is a balanced portfolio investment manager 
that invests solely in US-  based securities. Sample 1 Investment Firm is 
defined as an independent investment management firm that is not affil -
iated with any parent organization. Policies for valuing portfolios, calcu -
lating performance, and preparing compliant presentations are available 

2 The Balanced Growth Composite includes all institutional balanced 
portfolios that invest in large-  cap US equities and investment-  grade bonds 
with the goal of providing long-  term capital growth and steady income 
from a well-  diversified strategy. Although the strategy allows for equity 
exposure ranging between 50–70%, the typical allocation is between 
55–65%. The account minimum for the composite is $5 million.

Appendix A: Sample Compliant Presentations 273
3 The custom benchmark is 60% YYY US Equity Index and 40% ZZZ US 
Aggregate Bond Index. The benchmark is rebalanced monthly.
4 Valuations are computed and performance is reported in US dollars.
5 Gross-  of- fees returns are presented before management and custodial 
fees but after all trading expenses. Composite and benchmark returns are 
presented net of non-  reclaimable withholding taxes. Net-  of- fees returns 
are calculated by deducting the highest fee of 0.83% from the monthly 
gross composite return. The management fee schedule is as follows: 1.00% 
on the first $25 million; 0.60% thereafter.
6 This composite was created in February 2000. A complete list of compos -
ite descriptions is available upon request.
7 Internal dispersion is calculated using the equal-  weighted standard devi -
ation of annual gross returns of those portfolios that were included in the 
composite for the entire year.

8 The three-  year annualized standard deviation measures the variability of 
the composite and the benchmark returns over the preceding 36-  month 
period. The standard deviation is not presented for 2002 through 2010 
because monthly composite and benchmark returns were not available 
and is not required for periods prior to 2011.
SAMPLE 2  ASSET MANAGEMENT COMPANY ACTIVE WORLD EQUITY COMPOSITE 
Creation Date: 1 July 2005  
Reporting Currency: EUR
Y earGross Return 
(%)XYZ World Index 
Return (%)Dispersion 
(Range) (%)# of 
PortfoliosComposite 
Assets (€ M)% of Firm 
Assets (%)
2011 –1.9 –0.5 0.2 6 224.9 2.1
2010 16.3 13.5 0.7 8 256.7 2.0
2009 29.0 25.8 1.5 8 205.6 1.9
2008 –39.8 –36.4 1.3 7 164.1 1.5
2007 –2.8 –2.7 n/a < 5 143.7 1.2
2006 9.3 7.5 n/a < 5 62.8 0.4
2005* 14.2 12.6 n/a < 5 16.1 < 0.1
*Returns are for the period from 1 July 2005 (inception date) through 31 December 2005.
Compliance Statement
Sample 2 Asset Management Company claims compliance with the Global

Investment Performance Standards (GIPS®) and has prepared and presented 
this report in compliance with the GIPS standards. Sample 2 Asset Management 
Company has not been independently verified.
Definition of the Firm
Sample 2 Asset Management Company is an independent investment manage -
ment firm that was established in 1997. Sample 2 Asset Management Company 
manages a variety of equity, fixed-  income, and balanced assets for primarily 
European clients.

Reading 5 ■ Global Investment Performance Standards (GIPS) 274
Policies
Sample 2 Asset Management Company’s policies for valuing portfolios, calcu -
lating performance, and preparing compliant presentations are available upon 
request.
Composite Description
The Active World Equity Composite includes accounts whose objective is to 
exceed the XYZ World Index by 2% over a rolling three-  year period. Securities 
are selected using the firm’s proprietary analytics tool, which selects securities 
expected to be the top performers from within the XYZ World Index universe. 
Portfolios are more concentrated, typically holding approximately 100–120 
securities, versus the benchmark, which reflects the performance of more than 
500 holdings. Composite returns may, therefore, have a lower correlation with 
the benchmark than a more diversified global equity strategy.
Benchmark
The benchmark is the XYZ World Index, which is designed to measure the

equity market performance of developed market countries. The benchmark is 
market-  cap weighted and is composed of all XYZ country-  specific developed 
market indexes. Sources of foreign exchange rates may be different between the 
composite and the benchmark; however, there have not been material differences 
to date. Benchmark returns are net of withholding taxes.
Fees
Returns are presented gross of management fees, custodial fees, and withholding 
taxes but net of all trading expenses.
List of Composites
A list of all composite descriptions is available upon request.
Fee Schedule
The standard fixed management fee for accounts with assets under management 
of up to €50 million is 0.35% per annum; 0.25% thereafter.
Minimum Account Size
The minimum portfolio size for inclusion in the composite is €1 million.
Internal Dispersion
Internal dispersion is calculated using the asset-  weighted standard deviation 
of annual gross-  of- fees returns of those portfolios that were included in the

composite for the entire year. For those years when less than six portfolios were 
included in the composite for the full year, no dispersion measure is presented.
Ex- Post Standard Deviation
The three-  year annualized ex-  post standard deviation of the composite and 
benchmark as of each year end is as follows:
Y ear Composite  
3- Yr St Dev  
(%)Benchmark  
3- Yr St Dev  
(%)
2011 12.9 14.6
2010 13.2 14.1
2009 17.0 16.3
2008 15.6 14.2

Appendix A: Sample Compliant Presentations 275
SAMPLE 3  REAL ESTATE: OPEN-  END FUNDS/SEPARATE ACCOUNTS
Real Estate Advisors Value-  Added Strategy Composite  
Schedule of Performance Results 1 January 2002 through 31 December 2011 
 /uni00A0  C omposite Gross-  of- Fees Returns 
 Composite  
Net-  of- Fees 
Returns  Value - Adde d
Benchmark Returns
(Open-  End Funds/
Separate Accounts) 
 Composite Statistics at Year End
Year Income  
Return 
(%) Capital 
Return 
(%) Total  
Return 
(%) Low 
(%) High 
(%) 
 Total  
Retur n
(%) 
 Income  
Return 
(%) Capital  
Return 
(%) Total  
Return  
(%) 
 # of 
Portfolios Composite 
Assets
(HKD Million) External  
Appraisal % 
of Composite 
Assets Total Firm  
Assets
(HKD Million) Non- Real  
Estate  % o f 
Composite 
Assets
2002  7.9 1.9 9.9 n/a  n/a   8.8   8.4 –1.6  7.1   ≤ 5 3,085  25  13,919  0
2003  8.5 2.9 11.7  5.8 20.4   10.5   8.0 1.0 9.2   6 3,294  25  14,911  0
2004  8.2 2.6 10.9  5.5 19.2   8.3   7.5 6.7 14.4   7 3,348  44  15,144  0

2005  6.6 11.2  18.1  9.0 31.6   16.6   6.8 12.7  19.7   7 3,728  72  19,794  0
2006  6.1 7.9 14.2  7.1 24.9   12.5   6.2 9.9 16.3   8 4,022  46  20,482  0
2007  5.4 8.0 13.7  6.8 23.9   11.8   5.6 9.9 15.6   7 4,348  33  24,219  0
2008  5.2 –11. 4 –6.6  –9.8  –1.6   –8.2   5.1 –11. 1 –5.9   7 3,836  100  21,447  0
2009  7.5 2.7 10.3  5.2 18.1   7.4   7.3 3.2 10.8   7 3,371  52  16,601  0
2010  7.2 1.7 9.0 4.2 19.5   6.9   7.8 3.1 11.1   7 2,852  38  4,516  0
2011  7.2 2.8 10.2  5.1 17.8   8.1   7.1 3.2 10.6   7 3,457  50  17,414  5
 Annualized Returns  (%)
3 Year  7.3 1.9 9.8 /uni00A0 7.5   7.4 3.2 10.8
5 Year  6.5 2.9 7.1  5.0   6.6 1.4 8.2
7 Year  6.4 2.6 9.6  7.6   6.6 4.2 10.9
10 Year  7.0 11.2  10.0   8.1   7.0 3.5 10.7
Since 
Inception  7.0 7.9 10.0   8.1 
 7.0 3.5 10.7
Disclosures
Sample 3 Real Estate Advisors claims compliance with the Global Investment 
Performance Standards (GIPS®) and has prepared and presented this report in

compliance with the GIPS standards. Sample 3 Real Estate Advisors has been 
independently verified for the periods 1 January 2006 through 31 December 2011. 
The verification reports are available upon request.
Verification assesses whether 1) the firm has complied with all the composite 
construction requirements of the GIPS standards on a firm-  wide basis and 2) 
the firm’s policies and procedures are designed to calculate and present perfor -
mance in compliance with the GIPS standards. Verification does not ensure the 
accuracy of any specific composite presentation.
The Firm
Sample 3 Real Estate Advisors (the “Firm”), a subsidiary of Sample 3 Capital, 
Inc., is based in Hong Kong and manages international real estate strategies. A 
list of the Firm’s composite descriptions is available upon request.
The Composite
The Value-  Added Strategy Composite consists of all discretionary open-  end funds 
and separate accounts managed by the Firm using a value-  added investment

strategy with an equal income and appreciation focus and having a minimum 
portfolio size of HKD 10 million. Portfolio management will invest in only Asian 
multi-  family, office, industrial, and retail property types that require correction 
or mitigation of the investments’ operating, financial, redevelopment, and/or

Reading 5 ■ Global Investment Performance Standards (GIPS) 276
management risk(s). A moderate level of leverage ranging between 30% and 
40% is used. Real estate investments are generally illiquid, and the investment 
outlook may change given the availability of credit or other financing sources.
The composite was created on 1 January 2006. The returns presented for 
periods prior to 2006 are not in compliance with the GIPS standards. Annual 
internal dispersion is presented using the high and low gross total returns for 
those portfolios that have been in the composite for the entire year.
Description of Discretion
The Firm has responsibility for sourcing, valuing, and managing the acquisition 
and disposition of assets. Although some of the Firm’s separate accounts require 
client approval for the acquisition and disposition of assets, the Firm defines 
such portfolios as discretionary because its recommendations are consistent

with the investment strategy and such client approvals are typically perfunctory.
Valuation
Real estate assets are internally valued by the Firm quarterly. For periods prior to 
1 January 2011, assets were externally appraised by an independent appraiser at 
least every 36 months. Beginning 1 January 2011, assets are externally appraised 
annually unless client agreements stipulate otherwise, in which case such assets 
are appraised at least every 36 months or per the client agreement if the client 
agreement requires external valuation more frequently than every 36 months. 
The percentage of composite assets valued using an external valuation is shown 
for each annual period. When market circumstances dictate, the Firm may 
increase the frequency of external appraisals. All valuations are performed as 
of calendar quarter-  ends.
Internal property valuations are determined by applying market discount 
rates to future projections of gross cash flows and capitalized terminal values

over the expected holding period for each asset. To the extent leverage (debt) is 
used, the debt is valued separately from the real estate. Property mortgages, notes, 
and loans are marked to market using prevailing interest rates for comparable 
property loans if the terms of existing loans preclude the immediate repayment 
of such loans. Due to the nature of real estate investments, valuations are based 
upon subjective unobservable inputs.
Basis of Accounting
All funds in the composite report their assets and liabilities on a fair value basis 
using International Financial Reporting Standards (IFRS).
Calculation of Performance Returns
Returns are presented in Hong Kong dollars and are net of leverage. Net-  of- fee 
returns are net of actual investment management fees including incentive fees, 
which are recorded on an accrual basis. Returns include cash and cash equiva -
lents and related interest income.
Capital expenditures, tenant improvements, and lease commissions are

capitalized, included in the cost of property, and reflected in the capital return 
component. Income and capital returns may not equal total returns due to the 
compounding linking of quarterly returns. Composite returns are calculated 
quarterly on an asset-  weighted basis using beginning-  of- period values. Annual 
returns are calculated by linking quarterly composite returns.
Policies for valuing portfolios, calculating performance, and preparing com -
pliant presentations are available upon request.

Appendix A: Sample Compliant Presentations 277
Investment Management Fees
Some of the funds in the composite pay incentive fees ranging between 10% and 
20% of profits in excess of a targeted SI-  IRR. The standard annual investment 
management fee schedule for separately managed institutional accounts is as 
follows:
Up to HKD 30 million: 1.6%
HKD 30–50 million: 1.3%
Over HKD 50 million: 1.0%
Benchmark
The benchmark is the Value-  Added Open-  End Fund/Separate Account Index (the 
“Benchmark”). The Benchmark returns have been taken from published sources. 
The Benchmark is leveraged, includes various real estate property types, and 
excludes cash, cash equivalents, and other non-  property-  related assets, liabilities, 
income, and expenses. The extent of leverage used by the Benchmark may be 
different from that of the portfolios in the composite. As of 31 December 2011, 
the Benchmark leverage was 52%.
SAMPLE 4  REAL ESTATE: CLOSED-  END FUND

SAMPLE 4  REAL ESTATE: CLOSED-  END FUND 
2006 Value-  Added Strategy Closed-  End Fund Composite  
Schedule of Performance Results 1 April 2006 through 31 December 2011
 Composite Gross TWR Composite 
NET TWR Benchmar k Composite at Year- End
 Year Income  
Return 
Return 
(%) Total 
Return  
(%) Total 
Return 
(%) Income 
Return 
Return 
(%) Total 
Return  
(%) # of 
Portfolio s Composit e
Assets
(U.S. Million) Leverage  
(%) External  
Assets
(U.S. Million) % of  
Firm  
Assets Non- Real  
Estate % of 
Composite 
Assets
4/06–12/06  –3.2  0.8 –2.5  –4.0  4.9 2.2 7.2 1 70  40  35  2,641  20  0
 2007  2.5 3.4 6.0 4.5  5.8 1.1 7.1 1 164  45  28  3,125  18  0
 2008  6.2 1.9 8.2 6.7  6.9 3.8 10.9  1 215  50  100  2,754  18  0
 2009  7.4 30.7  38.6  36.1  7.0 10.2  17.4  1 256  53  44  2,142  21  0
 2010  6.6 –13. 7 –7.3  –8.8  6.1 –8.8  –2.5  1 111  57  28  1,873  19  0
 2011  5.8– 1.5 4.3 2.8  5.4 –2.6  3.0 1 112  60  85  2,247  20  15
 Year Gross

Year Gross
SI- IRR Net  
SI- IRR Total 
Committed  
Capital
(U.S. Million) Paid- In 
Capital
(U.S. Million) Cumulativ e 
Distributions
(U.S. Million) TVPI 
Multiple DPI  
Multiple RVPI 
Multiple PIC 
Multiple
4/06–12/06  –2.3  –3.1  250 71  0 0.99  0.00  0.99  0.28 
 2007  3.7 2.2 250 161 1 1.02  0.01  1.02  0.64 
 2008  5.8 4.2 250 226 26  1.07  0.12  0.95  0.90 
 2009  18.5  15.2  250 236 76  1.41  0.32  1.08  0.94 
 2010  11.5  9.8 250 240 201 1.30  0.84  0.46  0.96 
 2011  10.8  9.1 250 245 208 1.31  0.85  0.46  0.98 
TVPI (investment multiple) = total value to paid-  in capital
DPI (realization multiple) = cumulative distributions to paid-  in capital
RVPI (unrealized multiple) = residual value to paid-  in capital
PIC (PIC multiple) = paid-  in capital to committed capital

Reading 5 ■ Global Investment Performance Standards (GIPS) 278
Sample 4 Real Estate Managers claims compliance with the Global Investment 
Performance Standards (GIPS®) and has prepared and presented this report in 
compliance with the GIPS standards. Sample 4 Real Estate Managers has been 
Verification assesses whether (1) the firm has complied with all the composite 
construction requirements of the GIPS standards on a firm-  wide basis and (2) 
The Firm
Sample 4 Real Estate Managers (the “Firm”) is a registered investment adviser 
under the Investment Advisers Act of 1940. A list of the Firm’s composite

descriptions is available upon request.
The 2006 Value-  Added Strategy Closed-  End Fund Composite includes a sin -
gle closed-  end commingled fund managed by the Firm using a value-  added 
investment strategy with a focus on both income and appreciation. Portfolio 
management intends to invest in properties located in major markets within 
the United States with higher operational risk than traditional property types. 
The target level of leverage is 50% with a maximum allowable level of 60%. 
Real estate investments are generally illiquid, and the investment outlook may 
change given the availability of credit or other financing sources. If investment 
opportunities and/or exit strategies become limited, the life of the fund may 
be extended and capital calls and distributions may be delayed. The composite 
was created on 1 January 2006. The composite vintage year is 2006, which was 
determined based on the fund’s first capital call in April 2006.

The Firm has complete discretion for all investment activities within the fund.
Valuation
Real estate investments are internally valued by the Firm quarterly. For periods 
prior to 1 January 2011, investments were externally appraised by an indepen -
dent appraiser at least every 36 months. Beginning 1 January 2011, assets are 
externally appraised annually. The percentage of composite assets valued using an 
external valuation is shown for each annual period. When market circumstances 
dictate, the Firm may increase the frequency of external appraisals. All valuations 
are performed as of calendar quarter-  ends. Internal investment valuations are 
determined by applying market discount rates to future projections of net cash 
flows (gross real estate cash flows less debt service) and capitalized terminal 
values over the expected holding period for each asset. Due to the nature of real 
estate investments, valuations are based upon subjective unobservable inputs.

All assets and liabilities are reported on a fair value basis using US Generally 
Accepted Accounting Principles for non-  operating companies.

Appendix A: Sample Compliant Presentations 279
Calculation of Performance Returns and Metrics
Returns are presented in US dollars and are net of leverage. Net-  of- fee returns 
are net of actual investment management fees, including incentive fees, which 
are recorded on an accrual basis.
Capital expenditures, tenant improvements, and lease commissions are 
compounding linking of quarterly returns. Composite time-  weighted returns 
are calculated quarterly on an asset-  weighted basis using beginning-  of- period 
values. Annual returns are calculated by linking quarterly composite returns.
SI- IRRs are calculated using quarterly cash flows through 2010 and daily 
cash flows starting in 2011.
Policies for valuing portfolios, calculating performance, and preparing pre -
sentations are available upon request.

The fund pays an incentive fee of 15% of profits if the SI-  IRR exceeds a pre -
ferred return to investors of 11%. The incentive fee is calculated annually. The 
standard annual investment management fee schedule for separately managed 
institutional accounts is as follows:
Up to $100 million: 1.50%
Over $100 million: 1.25%
Benchmark
The benchmark is the Value-  Added Closed-  End Fund Index (the “Benchmark”). 
The Benchmark is a time-  weighted return index and returns have been taken 
from published sources. The Benchmark is leveraged and includes various real 
estate investment and property types, cash and other non-  property-  related assets, 
liabilities, income, and expenses. The extent of leverage used by the Benchmark 
may be different from that of the fund in the composite. As of 31 December 2011, 
the Benchmark leverage was 60%. There is no SI-  IRR benchmark available for 
the 2006 vintage year.
SAMPLE 5  PRIVATE EQUITY: FUND OF FUNDS BY INVESTMENT STRATEGY

ABC Fund of Funds Manager, LLC  
2006 Buyout Strategy Fund of Funds Composite  
Results Reported as of Calendar Y ear End
Y ear 
End# of 
PortfoliosGross-  of- Fees 
SI- IRR (%)Net-  of- Fees 
SI- IRR (%)Benchmark 
SI- IRR (%)Composite 
Assets ($ Mil)Composite % of 
Firm Assets
2006* 8 26.9 26.4 17.2 2,336 80.8
2007 10 18.5 17.8 10.2 2,512 83.6
2008 11 18.7 18.1 11.0 3,227 84.2
2009 13 19.6 18.9 11.5 4,518 84.8
2010 13 20.7 20.1 11.8 6,330 85.2
2011 13 21.9 21.3 11.8 9,269 86.0

Reading 5 ■ Global Investment Performance Standards (GIPS) 280
Y ear 
End# of 
2012 14 22.2 21.7 12.3 12,286 86.4
2013 14 15.1 14.4 9.6 12,346 87.7
*Partial year from 15 April 2006 (inception) through 31 December 2006.
Y ear 
EndPaid-  In 
Capital  
($ Mil)Cumulative 
Committed 
Capital ($ Mil)Since 
Inception 
DistributionsInvestment 
Multiple 
(TVPI)Realization 
Multiple 
(DPI)Unrealized 
Multiple 
(RVPI)PIC 
Multiple 
(PIC)
2006 1,556 3,177 1,205 1.5 0.8 0.7 0.48
2007 1,908 3,675 1,341 1.3 0.7 0.6 0.51
2008 2,371 5,166 1,623 1.4 0.7 0.7 0.45
2009 3,254 6,401 2,186 1.4 0.7 0.7 0.50
2010 4,400 8,370 2,950 1.4 0.7 0.8 0.51
2011 6,303 11,344 4,138 1.5 0.7 0.8 0.54
2012 8,167 13,713 6,513 1.5 0.8 0.7 0.69
2013 9,651 15,290 7,091 1.3 0.7 0.5 0.71
Aggregate Performance of Underlying  
Investments by Vintage Y ear  
Results Reported as of 31 December 2013
Vintage Y earGross-  of- Fees

Vintage Y earGross-  of- Fees  
Annualized SI-  IRR (%) Benchmark SI-  IRR (%)
2006 22.3 2.5
2007 13.4 1.9
2008 26.0 7.1
2009 18.1 3.9
2010 0.7 1.0
2011 –16.2 –7.5
2012 –25.6 –19.9
2013 –49.9 –40.3
 
Vintage 
Y earPaid-  In 
Capital  
Committed 
Capital ($ Mil)Since Inception 
Distributions  
($ Mil)Investment 
Multiple 
Multiple 
Multiple 
(RVPI)PIC 
Multiple 
(PIC)
2006 731 724 939 3.0 1.3 1.7 1.0
2007 710 234 294 1.8 0.4 1.3 3.0
2008 1,475 1,220 1,442 2.0 1.0 1.0 1.2(Continued)

Appendix A: Sample Compliant Presentations 281
Vintage 
Capital  
Committed 
Multiple 
Multiple 
Multiple 
(RVPI)PIC 
Multiple 
(PIC)
2009 1,640 1,048 1,156 1.9 0.7 1.2 1.6
2010 1,896 3,695 1,124 1.9 0.6 1.4 0.5
2011 1,984 4,518 1,100 2.1 0.6 1.5 0.4
2012 680 1,998 938 2.2 1.4 0.8 0.3
2013 535 1,853 100 1.1 0.2 0.9 0.3
ABC Fund of Funds Manager, LLC, claims compliance with the Global Investment 
compliance with the GIPS standards. ABC Fund of Funds Manager, LLC, has been

independently verified for the periods 15 April 2006 through 31 December 2012.
the firm’s policies and procedures are designed to calculate and present per -
formance in compliance with the GIPS standards. Verification does not ensure 
the accuracy of any specific composite presentation. The verification report is 
The Firm
ABC Fund of Funds Manager, LLC, is an independent private equity investment 
firm with offices in New York, London, and Tokyo. The firm’s list of composite 
descriptions, as well as information regarding the firm’s policies for valuing 
investments, calculating performance, and preparing compliant presentations, 
are available upon request.
The 2006 Buyout Strategy Fund of Funds Composite includes primary and 
secondary partnership investments with strategies focused on leveraged and

growth-  oriented buyouts primarily in the United States. Managers of partnerships 
are expected to focus on reducing costs, preparing companies for downturn, 
and providing operational improvement rather than financial engineering. 
Investments may be in small, medium, and large buyout partnerships, aiming 
to make selective commitments diversifying across stages, industries, and vin -
tage years. Secondary deals take advantage of distressed primary partnership 
sales providing access to an increased mix of assets. The underlying funds are 
leveraged 100–300%. Private equity investments are illiquid and, therefore, if 
investment opportunities and/or exit strategies become limited, the life of the 
fund may be extended and capital calls and distributions may be delayed. The 
composite was created on 31 December 2006. The vintage year is 2006 and was 
determined by the initial subscription date of the fund of funds.

Reading 5 ■ Global Investment Performance Standards (GIPS) 282
Valuation
The firm uses valuations reported by the general partner of the investment 
partnerships. Given the nature of the investments, all valuations are determined 
using both subjective observable and subjective unobservable inputs.
The fund’s SI-  IRR calculation uses daily cash flows. All cash flows and values 
used to calculate returns are in, or have been converted to, US dollars. Gross 
returns are net of all underlying investment partnership expenses, management 
fees, and carried interest but gross of ABC Fund of Funds Manager’s manage -
ment fees. Net returns are net of all underlying partnership fees and expenses, 
including ABC Fund of Funds Manager’s management fees.
Investment Management Fee
ABC Fund of Funds Manager’s management fee varies based on the size of the 
commitment and structure of the program. The management fee is 100 basis

points, based on the total commitment to a fund of funds, plus a 10% carry on 
total gains. Net returns are calculated using actual management fees of the fund 
of funds and underlying funds, including performance fees.
Benchmark
The benchmark is derived from private equity dollar-  weighted IRRs, and the 
calculation is based on the overall market return for buyout fund of funds as 
determined by benchmark provider GHI. Individual vintage year benchmarks 
are the median SI-  IRR for the applicable vintage years, at 31 December 2013.
SAMPLE 6  PRIVATE EQUITY: FUND OF FUNDS BY VINTAGE YEAR 
Investments 2002 Fund of Funds Composite  
Calendar 
Y earGross-  of- Fees 
Assets ($ Mil)Total Firm 
Assets ($ Mil)# of 
Portfolios
2002* 2.5 –5.5 8.5 2.6 250 ≤ 5
2003 –4.2 –12.3 –3.8 4.7 300 ≤ 5
2004 12.5 6.5 14.4 7.5 350 ≤ 5
2005 45.8 40.8 42.7 24.2 400 ≤ 5
2006 35.6 31.5 30.2 21.6 450 ≤ 5

2007 22.2 19.3 13.5 14.7 500 ≤ 5
2008 17.4 15.5 8.1 11.8 550 ≤ 5
2009 17.3 15.3 7.5 11.0 600 ≤ 5
2010 16.5 14.8 8.0 9.3 650 ≤ 5
2011 15.9 13.5 8.5 8.1 700 ≤ 5
2012 16.8 14.0 10.3 6.5 750 ≤ 5
*Returns are for the period from 1 May 2002 (inception date) through 31 December 2002.

Appendix A: Sample Compliant Presentations 283
Calendar Y earCumulative Committed 
Capital  
($ Mil)Paid-  In 
Capital  
($ Mil) DPI RVPI TVPI PIC 
2002 20 3 0 0.00 1.04 1.04 0.15
2003 20 5 0 0.00 0.93 0.93 0.25
2004 20 8 2 0.22 0.94 1.16 0.40
2005 20 15 4 0.23 1.62 1.85 0.75
2006 20 17 12 0.71 1.25 1.96 0.85
2007 20 18 16 0.89 0.82 1.71 0.90
2008 20 19 17 0.89 0.62 1.51 0.95
2009 20 19 19 0.99 0.57 1.56 0.96
2010 20 20 23 1.18 0.47 1.65 0.98
2011 20 20 25 1.25 0.41 1.66 1.00
2012 20 20 29 1.45 0.33 1.78 1.00
Underlying Partnership Investments by Strategy  
Results Reported as of 31 December 2012
 Investment 
Strategy SI- IRR  
Gross-  
of- Fees
(%) Benchmark  
Return
(%) Committed  
Capital
($ Mil) Paid- In 
Capital
($ Mil) Cumulativ e 
($ Mil) Assets
($ Mil) DPI  
Multipl e RVPI 
Multiple   PIC 
Multiple
 Venture
Capital  65.3  32.6 8.0 8.0 16.0  2.0  2.0  0.31 .0
 Buyout  11.3  10.2 12.0  12.0  13.0  4.5  1.1  0.41 .0 TVPI 
Multiple  
 2.3
 1.5

Multiple  
 2.3
 1.5
Sample 6 Investments claims compliance with the Global Investment Performance 
Standards (GIPS®) and has prepared and presented this report in compliance with 
the GIPS standards. Sample 6 Investments has not been independently verified.
Sample 6 Investments is an independent private equity manager of fund of 
funds strategies with offices in Zurich, Menlo Park, New York, and Hong Kong. 
The composite was created in May 2002 and includes one closed-  end fund that 
invests in buyout and venture capital funds. The fund of funds has an 8–10 year 
investment time horizon, but it may be longer based on the life of the underlying 
funds, which may be extended due to changes in investment and/or exit oppor -
tunities. As more fully described in the fund’s offering memorandum, primary 
risks include industry and geographic concentration depending on investment 
opportunities, and liquidity risks due to the nature of the fund’s investments.

The composite’s vintage year is 2002, which was determined using the date of 
the initial capital call of the fund of funds. Returns are presented in US dollars.
The 2002 Fund of Funds Composite complies with PQR’s valuation guidelines, 
which are consistent with the GIPS Valuation Principles. Valuations are normally 
based on valuations provided by the manager of the underlying investments’ 
partnerships. Because fund investments are not publicly traded, all investments 
are considered to be valued using subjective unobservable inputs.

Reading 5 ■ Global Investment Performance Standards (GIPS) 284
All returns for the 2002 Fund of Funds Composite reflect the deduction 
of administrative expenses (legal, auditing, etc.) of the closed-  end fund. Gross 
returns do not reflect the deduction of Sample 6 Investments’ management 
fees. Net returns reflect the deduction of actual management fees and accrued 
carried interest, if any.
The fund’s SI-  IRR calculation incorporates daily cash flows. Sample 6 
Investments’ annual management fee is 1% on the total committed capital.
The Vendor ABC Private Equity Fund of Funds Index (vintage year 2002) is 
used as the benchmark.
A complete list of the firm’s composite descriptions is available upon request, 
as are policies for valuing portfolios, calculating performance, and preparing 
compliant presentations.
SAMPLE 7  PRIVATE EQUITY: PRIMARY FUND VEHICLE 
Private Equity Capital Management  
2001 Venture Capital Composite  
Results Reported as of 31 December
Y ear  
Capital

Y ear  
Capital  
(AUD Mil)Since Inception  
(AUD Mil)Cumulative 
Committed Capital  
(AUD Mil)Composite Assets  
(AUD Mil)% of Firm  
Assets
2001* 40.3 0.0 175.0 38.5 64.2
2002 82.3 1.0 175.0 78.8 52.5
2003 129.5 29.9 175.0 105.0 58.3
2004 143.5 42.3 175.0 120.8 41.6
2005 157.5 97.0 175.0 119.0 37.8
2006 166.2 129.3 175.0 112.0 31.1
2007 171.5 184.7 175.0 98.0 28.0
2008 182.5 184.7 175.0 78.8 21.0
2009 182.5 184.7 175.0 49.0 11.9
2010 182.5 184.7 175.0 31.5 7.5
2011 182.5 205.8 175.0 5.2 1.1
*Returns are for the period from 3 February 2001 (inception date) through 31 December 2001.
Y ear  
End TVPI DPI RVPI PICComposite  
Gross-  of- Fees  
SI- IRR (%)Composite  
Net-  of- Fees  
SI- IRR (%)Benchmark  
SI- IRR (%)
2001 0.96 0.00 0.96 0.23 –7.5 –9.5 –12.5
2002 0.97 0.01 0.96 0.47 0.3 –1.6 –3.5
2003 1.04 0.23 0.81 0.74 4.1 2.3 1.2
2004 1.14 0.29 0.84 0.82 8.2 6.4 7.4
2005 1.37 0.62 0.76 0.90 11.0 9.3 8.2
2006 1.45 0.78 0.67 0.95 13.0 10.1 9.7
2007 1.65 1.08 0.57 0.98 18.1 12.3 11.4

Appendix A: Sample Compliant Presentations 285
Y ear  
SI- IRR (%)
2009 1.28 1.01 0.27 1.04 14.9 8.7 7.2
2010 1.18 1.01 0.17 1.04 14.0 7.7 6.8
2011 1.16 1.13 0.03 1.04 11.2 6.2 5.5
TVPI = Total Value to Since Inception Paid-  In Capital
DPI = Since Inception Distributions to Since Inception Paid-  In Capital
PIC = Since Inception Paid-  In Capital to Cumulative Committed Capital
RVPI = Residual Value to Since Inception Paid-  In Capital
Private Equity Capital Management claims compliance with the Global Investment 
compliance with the GIPS standards. Private Equity Capital Management 
has been independently verified for the periods 3 February 2001 through 31 
December 2010.
Verification assesses whether (1) the firm has complied with all the composite

construction requirements of the GIPS standards on a firm-  wide basis and (2) the 
firm’s policies and procedures are designed to calculate and present performance 
in compliance with the GIPS standards. The 2001 Venture Capital Composite has 
been examined for the periods 1 January 2005 through 31 December 2010. The 
verification and performance examination reports are available upon request.
Firm & Composite
Private Equity Capital Management (“PECM”) is an independent private equity 
investment firm with offices in New York, London, and Sydney. The 2001 Venture 
Capital Composite includes one fund, whose objective is to seek long-  term 
capital appreciation by acquiring minority interests in early-  stage technology 
companies. The fund invests in technology companies in Europe, Asia Pacific, 
and emerging markets. European venture investments are more concentrated 
than in the other regions and are focused in a few high-  quality companies. Exit

opportunities include IPOs, trade sales, and secondary sales. Opportunities in 
China and India will be targeted for investment, and an allocation to Chinese 
high-  tech will be at least 10% of the invested capital over the life of the fund. 
International venture capital investments are generally illiquid and are subject 
to currency risk. If investment opportunities and/or exit strategies become 
limited, the life of the fund may be extended and capital calls and distributions 
may be delayed. The 2001 Venture Capital Composite was created in 2001. The 
vintage year of the composite is 2001 and was determined by the year of the 
first drawdown. The firm’s list of composite descriptions and the firm’s policies 
for calculating performance and preparing compliant presentation are available 
Input Data & Calculation
The 2001 Venture Capital Composite complies with the LMN Venture Capital 
Association’s valuation guidelines as well as the GIPS Valuation Principles.

Valuations are prepared by PECM’s valuation committee and reviewed by an 
independent advisory board. All investments within the composite are valued

Reading 5 ■ Global Investment Performance Standards (GIPS) 286
using either a most recent transaction or an earnings multiple. Policies for valu -
ing investments are available upon request. Due to the nature of private equity 
investments, all investments are valued using subjective unobservable inputs.
The SI-  IRR calculation incorporates monthly cash flows for periods prior 
to 31 December 2009 and daily cash flows thereafter. Performance is expressed 
in Australian dollars (AUD).
Gross returns are net of transaction expenses and all administrative expenses. 
Net returns are net of transaction expenses, administrative expenses, manage -
ment fees, and carried interest. The standard fee schedule currently in effect 
is as follows:
The manager will receive an annual management fee equal to 2% of 
capital commitments. The manager’s participation in profits (carried 
interest) begins after the limited partners have been provided an 8%

preferred return. The manager collects 20% of the distributed profits 
from that point forward. Subsequently, if the amount of cumulative 
carried interest exceeds 20% of the net cumulative gains, the man -
ager will repay the excess amount to the fund for distribution to the 
limited partners.
There is only one fund in the composite for all periods; therefore, the internal 
dispersion of portfolio returns is not applicable.
Benchmark
The benchmark return is derived from private equity dollar-  weighted IRRs, and 
the calculation is based on the overall market return for international venture 
capital funds as published by Benchmark Provider GHI. Vintage year bench -
marks are median returns for the applicable vintage year, as of each year end.
SAMPLE 8  INVESTMENTS LARGE-  CAP SMA COMPOSITE 
 1 January 2001 through 31 December 2010
Y earNet Return  
(%)XYZ Index  
Return (%)Internal  
Dispersion 
(%)Number of  
PortfoliosComposite Assets  
($ Millions)Firm Assets  
($ Millions)% of SMA

($ Millions)% of SMA  
2010 8.4 10.2 0.7 1,834 2,125 18,222 100
2009 21.1 21.1 1.1 1,730 2,130 17,635 100
2008 –39.7 –39.8 1.0 1,631 2,141 19,246 100
2007 1.4 6.2 1.2 1,532 2,127 14,819 100
2006 11.4 10.5 0.9 1,428 2,116 12,362 100
2005 1.0 4.3 0.8 68 1,115 12,051 0
2004 6.8 4.9 1.0 52 1,110 13,419 0
2003 23.9 27.0 1.1 46 990 10,612 0
2002 –24.4 –19.1 0.9 38 975 9,422 0
2001 –17.7 –12.8 0.8 41 870 8,632 0

Appendix A: Sample Compliant Presentations 287
Notes:
1 Sample 8 Investments claims compliance with the Global Investment 
Performance Standards (GIPS®) and has prepared and presented this 
report in compliance with the GIPS standards. Sample 8 Investments has 
been independently verified for the period from 1 April 1996 through 31 
December 2009.
 Verification assesses whether (1) the firm has complied with all the com -
posite construction requirements of the GIPS standards on a firm-  wide 
basis and (2) the firm’s policies and procedures are designed to calculate 
and present performance in compliance with the GIPS standards. The 
Large Cap SMA Composite has been examined for the period from 1 
January 2006 through 31 December 2009. The verification and perfor -
mance examination reports are available upon request.
2 Sample 8 Investments is an independent investment adviser registered 
under the Investment Advisers Act of 1940, was founded in March 1996,

and manages global large-  cap equity, fixed-  income, and balanced 
3 Beginning 1 January 2006, the composite includes only wrap fee (SMA) 
portfolios benchmarked to the XYZ Index. Performance results prior to 
2006 are based on the Large-  Cap Institutional Composite returns.
4 The Large-  Cap SMA Composite is composed of portfolios invested in US 
equities which have a market capitalization greater than $5 billion.
5 The composite was created in February 2006. A list of composite descrip -
tions is available upon request.
6 All returns are expressed in US dollars. Policies for valuing portfolios, cal -
culating performance, and preparing compliant presentations are available 
7 The XYZ Index returns are provided to represent the investment environ -
ment existing during the time periods shown. For comparison purposes, 
the index is fully invested and includes the reinvestment of income. The 
returns for the index do not include any trading costs, management fees,

or other costs. Index returns have been taken from published sources.
8 “Pure” gross returns, presented below as supplemental information, from 
2006 through 2010 do not reflect the deduction of any trading costs, fees, 
or expenses and are presented for comparison purposes only. “Pure” gross 
returns prior to 2006 reflect the deduction of trading costs. The SMA fee 
includes all charges for trading costs, portfolio management, custody, and 
other administrative fees. Net returns are calculated by subtracting the 
highest applicable SMA fee (2.50% on an annual basis, or 0.21% monthly) 
on a monthly basis from the “pure” gross composite monthly return. The 
standard fee schedule in effect is as follows: 2.50% on total assets.
9 The dispersion is measured by the equal-  weighted standard deviation of 
annual returns of those portfolios that are included in the composite for 
the full year.
10 At 31 December 2010, the three-  year annualized ex-  post standard

deviation of the composite and the benchmark are 12.3% and 13.2%, 
11 Past performance is not an indicator of future results.

Reading 5 ■ Global Investment Performance Standards (GIPS) 288
Supplemental Information
Y ear“Pure” Gross  
Return* (%)Net Return (%)  
Assuming 3%  
SMA FeesNet Return (%)  
Assuming 2%  
SMA Fees
2010 11.1 7.9 9.0
2009 24.0 20.5 21.7
2008 –38.0 –40.1 –39.4
2007 4.0 0.9 2.0
2006 14.1 10.8 11.9
2005 3.5 0.5 1.5
2004 9.5 6.3 7.4
2003 26.9 23.3 24.5
2002 –22.3 –24.8 –23.9
2001 –15.5 –18.1 –17.2
* “Pure” gross-  of- fees returns do not reflect the deduction of any expenses, including trading 
costs. “Pure” gross-  of- fees returns are supplemental to net returns.

Appendix B: Sample Advertisements 289
APPENDIX B: SAMPLE 
ADVERTISEMENTS
1.   SAMPLE ADVERTISEMENT WITHOUT PERFORMANCE 
Generic Asset Management
Generic Asset Management is the institutional asset management division of 
Generic Inc. and is a registered investment advisory firm specializing in quali -
tative growth-  oriented investment management.
Generic Asset Management claims compliance with the Global Investment 
Performance Standards (GIPS®). To receive a list of composite descriptions 
of Generic Asset Management and/or a presentation that complies with the 
GIPS standards, contact Jean Paul at (123) 456-  7890, or write to Generic Asset 
Management, 123 Main Street, Returnsville 12345, or jpaul@genericasset -
managment.com.
2.   SAMPLE ADVERTISEMENT INCLUDING ONE-, THREE-, AND FIVE-  YEAR 
ANNUALIZED RETURNS 
Generic Asset Management: Global Equity Growth Composite
Ending 31 Mar 2012
1- Y ear3- Y ear 
Annualized5- Y ear 
Annualized
Global Equity Growth Composite –0.3% 13.7% 0.1%

XYZ World Index –0.5% 13.8% –0.6%
Note : Returns are shown in US dollars net of fees.
Generic Asset Management is the institutional asset management subsidiary of 
Generic Inc. and is a registered investment adviser specializing in qualitative 
growth-  oriented investment management. The Global Equity Growth strategy 
focuses on earnings, growth of earnings, and key valuation metrics. The bench -
mark is the XYZ World Index, which is designed to measure the equity market 
performance of developed market countries. The benchmark is market-  cap 
weighted and is composed of all XYZ developed market indexes.
GIPS standards, contact Jean Paul at (123) 456-  7890, or write Generic Asset

Management, One Plain Street, Returnsville 12345, or jpaul@genericassetman -
agement.com.OPTIONAL 
SEGMENT

Reading 5 ■ Global Investment Performance Standards (GIPS) 290
3.   SAMPLE ADVERTISEMENT INCLUDING PERIOD-  TO-  DATE AND ONE-, 
THREE-, AND FIVE-  YEAR ANNUALIZED RETURNS 
Ending  
31 Mar 2012 Ending 31 Dec 2011
Period to Date  
(3 months) 1- Y ear3- Y ear 
Global Equity 
Growth 
Composite –3.84% 1.3% 15.0% –1.2%
XYZ World 
Index –4.94% 1.5% 14.1% –0.7%
performance of developed market countries. The benchmark is market-  cap

GIPS standards, contact Jean Paul at (123) 456-  7890, or write Generic Asset 
agement.com.
4.   SAMPLE ADVERTISEMENT INCLUDING FIVE YEARS OF ANNUAL 
RETURNS 
Period to 
Date  
(3 months to 
31 Mar 2012)Annual Returns  
Periods Ended 31 December
2011 2010 2009 2008 2007
Growth 
Composite –3.84% 1.3% 13.0% 33.0% –40.6% 9.6%
XYZ World Index –4.94% 1.5% 11.8% 30.8% –40.3% 9.6%
Generic Inc. and is a registered investment adviser specializing in qualitative,

growth-  oriented investment management. The Global Equity Growth strat -
egy focuses on earnings, growth of earnings, and key valuation metrics. The

Appendix B: Sample Advertisements 291
benchmark is the XYZ World Index, which is designed to measure the equity 
market performance of developed market countries. The benchmark is market-  
cap weighted and is composed of all XYZ developed market indexes.
Performance Standards (GIPS®).
To receive a list of composite descriptions of Generic Asset Management 
and/or a presentation that complies with the GIPS standards, contact Jean Paul 
at (123) 456-  7890, or write to Generic Asset Management, 123 Main Street, 
Returnsville 12345, or jpaul@genericassetmanagment.com.

Reading 5 ■ Global Investment Performance Standards (GIPS) 292
APPENDIX C: SAMPLE LIST OF 
COMPOSITE DESCRIPTIONS
1 Unconstrained Activist UK Equity Composite
 The Unconstrained Activist UK Equity Composite includes all institutional 
portfolios invested in both listed and unlisted UK equities that pursue an 
activist investment policy; there is no restriction on the market capitalization of 
companies held. Portfolios within this composite are highly concentrated, hold -
ing approximately 15 securities, so returns may have lower correlation with the 
benchmark than a fully diversified strategy. In times of increased market vola -
tility, the composite characteristics may change significantly and stock liquidity 
could be reduced. Due to their more concentrated nature, portfolios will tend to 
have more stock-  specific risk than a more diversified strategy. Portfolios can use 
both exchange-  traded and OTC derivative contracts for efficient portfolio man -

agement, which may expose the strategy to counterparty risk. The benchmark is 
the FTSE All Share® Index.
2 Emerging Market High Yield Fixed Income Composite
 The Emerging Market High Yield Fixed Income Composite includes all institu -
tional and retail portfolios invested in high yield debt securities issued by coun -
tries outside the OECD. The strategy allows for investment in foreign currency 
denominated assets over which the manager has full discretion on hedging. The 
strategy aims to deliver a total return primarily through income but with some 
capital growth. High yield bonds carry increased levels of credit and default risk 
and are less liquid than government and investment grade bonds. Investment in 
less regulated markets carries increased political, economic, and issuer risk. The 
benchmark is the J.P . Morgan Emerging Market Bond Index (EMBI+).
3 UK Liquidity Plus Composite
 The UK Liquidity Plus Composite includes all institutional portfolios invested

in a broad range of short-  dated interest-  bearing deposits, cash equivalents, 
short-  term commercial paper, and other money market investments issued by 
major UK clearing banks and lending institutions. The strategy has a targeted 
modified duration of less than one year. The principal investment objectives are 
preservation of capital, maintenance of liquidity, and provision of yield greater 
than that available for the benchmark, the three-  month Libor rate. The UK 
Liquidity Plus strategy differs from more conventional cash strategies in that it 
additionally holds short-  term commercial paper, which has a greater exposure 
to credit risk.
4 Socially Responsible Investment (SRI) Composite
 The Socially Responsible Investment Composite includes all segregated insti -
tutional and pooled portfolios that invest in global equity securities issued by 
companies that make a positive contribution to society and the environment

through sustainable and socially responsible practices. The strategy aims to 
provide long-  term capital appreciation together with a growing income stream 
through investment in a portfolio of core equity holdings diversified by eco -
nomic sector, industry group, and geographic business concentration. All 
foreign currency exposures are fully hedged back to US dollars.
 The SRI process tends to screen out certain companies and sectors, which may 
result in a more concentrated strategy than a fully diversified strategy. Changes 
in legislation, scientific thinking, national and supra-  national policies, and

Appendix C: Sample List of Composite Descriptions 293
behaviors could significantly affect the stocks of companies held within the 
strategy. The benchmark is the Morningstar Ethical/SRI Global GIF Sector peer 
group.
5 Leveraged Bond Composite
 The Leveraged Bond Composite includes all institutional segregated portfolios 
invested in a diversified range of high yield corporate and government bonds 
with the aim of providing investors with a high level of income while seek -
ing to maximize the total return. The portfolios are invested in domestic and 
international fixed income securities of varying maturities. The strategy allows 
investment in exchange-  traded and OTC derivative contracts (including, but 
not limited to, options, futures, swaps, and forward currency contracts) for the 
purposes of risk, volatility, and currency exposure management. The strategy 
allows leverage up to but not exceeding twice the value of a portfolio’s invest -

ments through the use of repurchase financing arrangements with counter -
parties. Inherent in derivative instrument investments is the risk of counter -
party default. Leverage may also magnify losses as well as gains to the extent 
that leverage is employed. The benchmark is the Bloomberg Barclays Global 
Aggregate Bond Index.
6 Global Commodity Composite
 The Global Commodity Composite includes institutional portfolios that globally 
invest in a diversified range of companies that provide exposure to commod -
ities, energy, and materials. Investment is primarily through the common 
or ordinary stock of these companies. Investment directly in raw materials 
is allowable to a maximum exposure of 10%. Exchange-  traded funds and 
exchange-  traded commodity securities up to a maximum 20% exposure are also 
allowed. The base currency is US dollars, and any or all of the currency risk 
associated with investments in currencies other than dollars may be hedged

between 0% and 100% at the manager’s discretion. The strategy cannot gear or 
otherwise deploy leverage but may use exchange-  traded derivative instruments 
for efficient portfolio management.
 Investments directly or indirectly in commodities may add to portfolio volatil -
ity. Global commodity prices can be affected by changes in legislation, national 
and supra-  national policies, and behaviors. In times of commodity price volatil -
ity, the liquidity of directly held commodities and the correlation with the broad 
market can change quickly. The benchmark is the Dow Jones–UBS Commodity 
Index Total ReturnSM.
7 Large Cap Equity Growth Composite
 The Large Cap Equity Growth Composite includes all institutional portfolios 
that invest in large capitalization US stocks that are considered to have growth 
in earnings prospects that is superior to that of the average company within 
the benchmark, the Russell 3000® Growth Index. The targeted tracking error

between the composite and the benchmark is less than 3%.
8 Balanced Growth Composite
 The Balanced Growth Composite includes all institutional balanced portfolios 
that invest in large-  cap US equities and investment-  grade bonds with the goal of 
providing long-  term capital growth and steady income from a well-  diversified 
strategy. Although the strategy allows for equity exposure ranging between 50% 
and 70%, the typical allocation is between 55% and 65%.
9 Currency Overlay Composite

Reading 5 ■ Global Investment Performance Standards (GIPS) 294
 The Currency Overlay Composite includes all institutional and retail portfolios 
invested in a broad range of foreign-  currency-  denominated deposits or instru -
ments, such as forward contracts, futures, or foreign exchange derivatives. The 
principal investment objective is alpha generation through currency apprecia -
tion and/or risk mitigation from adverse movements in exchange rates where 
the original currency exposure stems from a global or international portfolio. 
Hedging strategies may range from passive to fully active. Currency-  related 
investing carries inherent risks due to changes in macroeconomic policy, which 
can be amplified in the case of emerging markets, where political regime shifts 
and changes in the control of capital may be more prevalent. In volatile periods, 
liquidity and correlations between currencies may change expected returns

drastically. Foreign exchange forwards and derivatives traded over the counter 
have counterparty default risk.
10 Asian Market Neutral Composite
 The Asian Market Neutral Composite includes a single hedge fund with a mar -
ket neutral strategy that invests in publically traded Asian equities with a mar -
ket capitalization greater than $500 million. The strategy uses a risk controlled 
quantitative screening and optimization process that invests at least 85% of the 
net asset value in long equity positions and at least 85% of the net asset value 
in short equity positions. The long portion of the strategy will overweight those 
securities that have been quantitatively identified as potentially exhibiting supe -
rior and sustainable earnings growth compared with the market; conversely, the 
short portion of the strategy will consist of securities that have been identified 
as having inferior growth prospects or that may also be adversely affected by

either specific events or by momentum considerations. The principal objective 
of the strategy is to outperform the return on three-  month US Treasury Bills 
through active trading of long and short equity positions.
 The Asian Market Neutral strategy seeks to dollar balance exposures between 
long and short positions so that broad market movements are neutralized. In 
certain market conditions, the investment process behind the strategy can give 
rise to unmatched country, sector, industry, market capitalization, and/or style 
bias exposures in the portfolio. The active trading strategy will involve signifi -
cantly greater stock turnover when compared with passive strategies.
11 2001 Venture Capital Composite
 The 2001 Venture Capital Composite includes one fund, whose objective is to 
seek long-  term capital appreciation by acquiring minority interests in early-  
stage technology companies. The fund invests in technology companies in

Europe, Asia Pacific, and emerging markets. European venture investments are 
more concentrated than in the other regions and are focused in a few high-  
quality companies. Exit opportunities include IPOs, trade sales, and secondary 
sales. Opportunities in China and India will be targeted for investment, and 
an allocation to Chinese high-  tech will be at least 10% of the invested capital 
over the life of the fund. International venture capital investments are generally 
illiquid and are subject to currency risk. If investment opportunities and/or exit 
strategies become limited, the life of the fund may be extended and capital calls 
and distributions may be delayed.
12 2006 Buyout Strategy Fund of Funds Composite
 The 2006 Buyout Strategy Fund of Funds Composite includes primary and 
secondary partnership investments with strategies focused on leveraged and 
growth-  oriented buyouts primarily in the United States. Managers of partner -

ships are expected to focus on reducing costs, preparing companies for down -
turn, and providing operational improvement rather than financial engineering.

Appendix C: Sample List of Composite Descriptions 295
Investments may be in small, medium, and large buyout partnerships, aiming to 
make selective commitments diversifying across stages, industries, and vin -
fund may be extended and capital calls and distributions may be delayed.
13 Value-  Added Strategy Non-  Closed-  End Real Estate Composite
 The Value-  Added Strategy Composite consists of all discretionary open-  
end funds and separate accounts managed by the Firm using a value-  added 
investment strategy with an equal income and appreciation focus and having 
a minimum portfolio size of $10 million. Portfolio management will invest in

multi-  family, office, industrial, and retail property types only within Asia that 
require correction or mitigation of the investments’ operating, financial, rede -
velopment, and/or management risk(s). A moderate level of leverage ranging 
between 30% and 40% is used. Real estate investments are generally illiquid, 
and the investment outlook may change given the availability of credit or other 
financing sources.
14 Value-  Added Strategy Closed-  End Real Estate Composite
 The Value-  Added Strategy Composite includes a single closed-  end commingled 
fund managed by the Firm using a value-  added investment strategy with a focus 
on both income and appreciation. Portfolio management intends to invest in 
properties located in major markets within the United States with higher oper -
ational risk than traditional property types. The target level of leverage is 50% 
with a maximum allowable level of 60%. Real estate investments are generally

illiquid, and the investment outlook may change given the availability of credit 
or other financing sources. If investment opportunities and/or exit strategies 
become limited, the life of the fund may be extended and capital calls and dis -
tributions may be delayed.
15 US Core Equity Composite (Terminated Composites)
 The US Core Equity Composite includes all institutional portfolios and pooled 
funds managed to a GARP (growth at a reasonable price) strategy through 
investment in a high-  quality, focused portfolio of domestic, large-  capitalization 
stocks that are expected to generate returns above the S&P 500® Index over a 
market cycle. Sample Asset Management Firm uses a quantitative screening 
process together with fundamental research and then overlays macroeconomic 
factors and economic sector exposures to construct portfolios. The bench -
mark is the S&P 500 Index. Quantitative-  driven investment screening relies on

historical stock correlations, which can be adversely affected during periods of 
severe market volatility. The composite terminated in March 2009.
Detailed composite definitions are available upon request. 
END OPTIONAL 
SEGMENT

Reading 5 ■ Global Investment Performance Standards (GIPS) 296
1 With respect to the Global Investment Performance Standards, which of 
the following is one of the nine sections containing investment performance 
provisions?
A Real Estate.
B Derivatives.
C Legal and Ethical Considerations.
2 According to the Fundamentals of Compliance section of the Global Investment 
Performance Standards, issues that a firm must consider when claiming compli -
ance include all of the following except :
A replicating performance.
B properly defining the firm.
C documenting firm policies and procedures used in establishing and main -
taining compliance with the Standards.
3 G&F Advisors claims compliance with the Global Investment Performance 
Standards (GIPS) in its marketing materials. The compliant presentation 
includes a footnote which indicates that the firm has been verified by an inde -
pendent third party. An additional note states that G&F is in compliance with

the GIPS standards except for its private equity investments. Is it likely  that 
G&F violated the GIPS standards?
A No, because the footnotes meet the requirements of the Standards.
B No, because the provisions do not apply to the private equity investments.
C Yes, because they cannot claim compliance unless all requirements of the 
Standard are met.
© 2012 CFA Institute. All rights reserved.

Solutions 297
SOLUTIONS
1 A is correct. Real Estate is one of the nine sections in the 2010 edition of the 
GIPS standards. Derivatives and Legal and Ethical Considerations are not sec -
tions of the Standards.
2 A is correct. Replication of performance is not included in the Fundaments of 
Compliance section within the GIPS standards.
3 C is correct. Firms must meet all the requirements set forth in the GIPS stan -
dards and cannot claim partial compliance.

Quantitative Methods
Study Session 2 Quantitative Methods (1)
Study Session 3 Quantitative Methods (2)
The candidate should be able to explain and demonstrate the use of time value of 
money, data collection and analysis, elementary statistics, probability theory, and 
probability distribution theory in financial decision-  making. 
The quantitative concepts and applications that follow are fundamental to finan -
cial analysis and are used throughout the CFA Program curriculum. Quantitative 
methods are used widely in securities and risk analysis and in corporate finance to 
value capital projects and select investments. Descriptive statistics provide the tools 
to characterize and assess risk and return and other important financial or economic 
variables. Probability theory supports investment and risk decision making in the 
presence of uncertainty.

Quantitative Methods (1)
This study session introduces quantitative concepts and techniques used in financial 
analysis and investment decision making. The time value of money and discounted 
cash flow analysis form the basis for cash flow and security valuation. Descriptive 
statistics used for conveying important data attributes such as central tendency, 
location, and dispersion are presented. Characteristics of return distributions such as 
symmetry, skewness, and kurtosis are also introduced. Finally, all investment forecasts 
and decisions involve uncertainty: Therefore, probability theory and its application 
quantifying risk in investment decision making is considered. 
Reading 6 The Time Value of Money  
by Richard A. DeFusco, PhD, CFA, Dennis W. McLeavey, 
CFA, Jerald E. Pinto, PhD, CFA, and David E. Runkle, 
PhD, CFA
Reading 7 Discounted Cash Flow Applications  
CFA, Jerald E. Pinto, PhD, CFA, and David E. Runkle,

PhD, CFA
Reading 8 Statistical Concepts and Market Returns  
PhD, CFA
Reading 9 Probability Concepts  
PhD, CFAQUANTITATI vE METhOdS
2

The Time Value of Money
by Richard A. DeFusco, PhD, CFA, Dennis W . McLeavey, CFA, 
Jerald E. Pinto, PhD, CFA, and David E. Runkle, PhD, CFA
Richard A. DeFusco, PhD, CFA, is at the University of Nebraska-  Lincoln (USA). Dennis W. 
McLeavey, CFA, is at the University of Rhode Island (USA). Jerald E. Pinto, PhD, CFA, is 
at CFA Institute (USA). David E. Runkle, PhD, CFA, is at Trilogy Global Advisors (USA).
a. interpret interest rates as required rates of return, discount rates, 
or opportunity costs;
b. explain an interest rate as the sum of a real risk-  free rate and 
premiums that compensate investors for bearing distinct types of 
risk;
c. calculate and interpret the effective annual rate, given the stated 
annual interest rate and the frequency of compounding;
d. solve time value of money problems for different frequencies of 
compounding;
e. calculate and interpret the future value (FV) and present value

(PV) of a single sum of money, an ordinary annuity, an annuity 
due, a perpetuity (PV only), and a series of unequal cash flows;
f. demonstrate the use of a time line in modeling and solving time 
value of money problems.
As individuals, we often face decisions that involve saving money for a future use, or 
borrowing money for current consumption. We then need to determine the amount 
we need to invest, if we are saving, or the cost of borrowing, if we are shopping for 
a loan. As investment analysts, much of our work also involves evaluating transac -
tions with present and future cash flows. When we place a value on any security, for 
example, we are attempting to determine the worth of a stream of future cash flows. 
To carry out all the above tasks accurately, we must understand the mathematics of 
time value of money problems. Money has time value in that individuals value a given 
amount of money more highly the earlier it is received. Therefore, a smaller amount 1rEAdING
6

Reading 6 ■ The Time Value of Money 304
of money now may be equivalent in value to a larger amount received at a future date. 
The time value of money  as a topic in investment mathematics deals with equivalence 
relationships between cash flows with different dates. Mastery of time value of money 
concepts and techniques is essential for investment analysts.
The reading1 is organized as follows: Section 2 introduces some terminology used 
throughout the reading and supplies some economic intuition for the variables we will 
discuss. Section 3 tackles the problem of determining the worth at a future point in 
time of an amount invested today. Section 4 addresses the future worth of a series of 
cash flows. These two sections provide the tools for calculating the equivalent value at 
a future date of a single cash flow or series of cash flows. Sections 5 and 6 discuss the 
equivalent value today of a single future cash flow and a series of future cash flows,

respectively. In Section 7, we explore how to determine other quantities of interest 
in time value of money problems.
INTEREST RATES: INTERPRETATION
In this reading, we will continually refer to interest rates. In some cases, we assume 
a particular value for the interest rate; in other cases, the interest rate will be the 
unknown quantity we seek to determine. Before turning to the mechanics of time 
value of money problems, we must illustrate the underlying economic concepts. In 
this section, we briefly explain the meaning and interpretation of interest rates.
Time value of money concerns equivalence relationships between cash flows 
occurring on different dates. The idea of equivalence relationships is relatively simple. 
Consider the following exchange: You pay $10,000 today and in return receive $9,500 
today. Would you accept this arrangement? Not likely. But what if you received the 
$9,500 today and paid the $10,000 one year from now? Can these amounts be considered

equivalent? Possibly, because a payment of $10,000 a year from now would probably 
be worth less to you than a payment of $10,000 today. It would be fair, therefore, 
to discount  the $10,000 received in one year; that is, to cut its value based on how 
much time passes before the money is paid. An interest rate , denoted r, is a rate of 
return that reflects the relationship between differently dated cash flows. If $9,500 
today and $10,000 in one year are equivalent in value, then $10,000 − $9,500 = $500 
is the required compensation for receiving $10,000 in one year rather than now. The 
interest rate—the required compensation stated as a rate of return—is $500/$9,500 = 
0.0526 or 5.26 percent.
Interest rates can be thought of in three ways. First, they can be considered required 
rates of return—that is, the minimum rate of return an investor must receive in order 
to accept the investment. Second, interest rates can be considered discount rates. In

the example above, 5.26 percent is that rate at which we discounted the $10,000 future 
amount to find its value today. Thus, we use the terms “interest rate” and “discount 
rate” almost interchangeably. Third, interest rates can be considered opportunity costs. 
An opportunity cost  is the value that investors forgo by choosing a particular course 
of action. In the example, if the party who supplied $9,500 had instead decided to 
spend it today, he would have forgone earning 5.26 percent on the money. So we can 
view 5.26 percent as the opportunity cost of current consumption.
Economics tells us that interest rates are set in the marketplace by the forces of sup -
ply and demand, where investors are suppliers of funds and borrowers are demanders 
of funds. Taking the perspective of investors in analyzing market-  determined interest 2
1 Examples in this reading and other readings in quantitative methods at Level I were updated in 2013 by

Professor Sanjiv Sabherwal of the University of Texas, Arlington.

Interest Rates: Interpretation 305
rates, we can view an interest rate r as being composed of a real risk-  free interest rate 
plus a set of four premiums that are required returns or compensation for bearing 
distinct types of risk:
 r = Real risk-  free interest rate + Inflation premium + Default risk premium + 
Liquidity premium + Maturity premium
■■The real risk-  free interest rate  is the single-  period interest rate for a com -
pletely risk-  free security if no inflation were expected. In economic theory, the 
real risk-  free rate reflects the time preferences of individuals for current versus 
future real consumption.
■■The inflation premium  compensates investors for expected inflation and 
reflects the average inflation rate expected over the maturity of the debt. 
Inflation reduces the purchasing power of a unit of currency—the amount of 
goods and services one can buy with it. The sum of the real risk-  free interest

rate and the inflation premium is the nominal risk-  free interest rate .2 Many 
countries have governmental short-  term debt whose interest rate can be consid -
ered to represent the nominal risk-  free interest rate in that country. The interest 
rate on a 90-  day US Treasury bill (T-  bill), for example, represents the nominal 
risk-  free interest rate over that time horizon.3 US T-  bills can be bought and sold 
in large quantities with minimal transaction costs and are backed by the full 
faith and credit of the US government.
■■The default risk premium  compensates investors for the possibility that the 
borrower will fail to make a promised payment at the contracted time and in 
■■The liquidity premium  compensates investors for the risk of loss relative to an 
investment’s fair value if the investment needs to be converted to cash quickly. 
US T-  bills, for example, do not bear a liquidity premium because large amounts

can be bought and sold without affecting their market price. Many bonds of 
small issuers, by contrast, trade infrequently after they are issued; the interest 
rate on such bonds includes a liquidity premium reflecting the relatively high 
costs (including the impact on price) of selling a position.
■■The maturity premium  compensates investors for the increased sensitivity 
of the market value of debt to a change in market interest rates as maturity is 
extended, in general (holding all else equal). The difference between the interest 
rate on longer-  maturity, liquid Treasury debt and that on short-  term Treasury 
debt reflects a positive maturity premium for the longer-  term debt (and possibly 
different inflation premiums as well).
Using this insight into the economic meaning of interest rates, we now turn to a 
discussion of solving time value of money problems, starting with the future value 
of a single cash flow.

2 Technically, 1 plus the nominal rate equals the product of 1 plus the real rate and 1 plus the inflation rate. 
As a quick approximation, however, the nominal rate is equal to the real rate plus an inflation premium. 
In this discussion we focus on approximate additive relationships to highlight the underlying concepts.
3 Other developed countries issue securities similar to US Treasury bills. The French government issues 
BTFs or negotiable fixed-  rate discount Treasury bills ( Bons du Trésor à  taux fixe et à intérêts précomptés ) 
with maturities of up to one year. The Japanese government issues a short-  term Treasury bill with matur -
ities of 6 and 12 months. The German government issues at discount both Treasury financing paper 
(Finanzierungsschätze des Bundes  or, for short, Schätze ) and Treasury discount paper ( Bubills ) with 
maturities up to 24 months. In the United Kingdom, the British government issues gilt-  edged Treasury

bills with maturities ranging from 1 to 364 days. The Canadian government bond market is closely related 
to the US market; Canadian Treasury bills have maturities of 3, 6, and 12 months.

Reading 6 ■ The Time Value of Money 306
THE FUTURE VALUE OF A SINGLE CASH FLOW
In this section, we introduce time value associated with a single cash flow or lump-  sum 
investment. We describe the relationship between an initial investment or present 
value (PV) , which earns a rate of return (the interest rate per period) denoted as r, 
and its future value (FV) , which will be received N years or periods from today.
The following example illustrates this concept. Suppose you invest $100 (PV = 
$100) in an interest-  bearing bank account paying 5 percent annually. At the end of 
the first year, you will have the $100 plus the interest earned, 0.05 × $100 = $5, for a 
total of $105. To formalize this one-  period example, we define the following terms:
 PV = present value of the investment
 FVN = future value of the investment N periods from today
 r = rate of interest per period
For N = 1, the expression for the future value of amount PV is
FV1 = PV(1 + r)

FV1 = PV(1 + r)  
For this example, we calculate the future value one year from today as FV1 = $100(1.05) 
= $105.
Now suppose you decide to invest the initial $100 for two years with interest 
earned and credited to your account annually (annual compounding). At the end of 
the first year (the beginning of the second year), your account will have $105, which 
you will leave in the bank for another year. Thus, with a beginning amount of $105 
(PV = $105), the amount at the end of the second year will be $105(1.05) = $110.25. 
Note that the $5.25 interest earned during the second year is 5 percent of the amount 
invested at the beginning of Year 2.
Another way to understand this example is to note that the amount invested at 
the beginning of Year 2 is composed of the original $100 that you invested plus the 
$5 interest earned during the first year. During the second year, the original principal 
again earns interest, as does the interest that was earned during Year 1. You can see

how the original investment grows:
Original investment $100.00
Interest for the first year ($100 × 0.05) 5.00
Interest for the second year based on original investment ($100 × 0.05) 5.00
Interest for the second year based on interest earned in the first year 
(0.05 × $5.00 interest on interest)0.25
  Total $110.25
The $5 interest that you earned each period on the $100 original investment is known 
as simple interest  (the interest rate times the principal). Principal  is the amount of 
funds originally invested. During the two-  year period, you earn $10 of simple interest. 
The extra $0.25 that you have at the end of Year 2 is the interest you earned on the 
Year 1 interest of $5 that you reinvested.
The interest earned on interest provides the first glimpse of the phenomenon 
known as compounding . Although the interest earned on the initial investment is 
important, for a given interest rate it is fixed in size from period to period. The com -

pounded interest earned on reinvested interest is a far more powerful force because, 
for a given interest rate, it grows in size each period. The importance of compounding 
increases with the magnitude of the interest rate. For example, $100 invested today 
would be worth about $13,150 after 100 years if compounded annually at 5 percent, 
but worth more than $20 million if compounded annually over the same time period 
at a rate of 13 percent.3
(1)

The Future Value of a Single Cash Flow 307
To verify the $20 million figure, we need a general formula to handle compounding 
for any number of periods. The following general formula relates the present value of 
an initial investment to its future value after N periods:
FVN = PV(1 + r)N  
where r is the stated interest rate per period and N is the number of compounding 
periods. In the bank example, FV2 = $100(1 + 0.05)2 = $110.25. In the 13 percent 
investment example, FV100 = $100(1.13)100 = $20,316,287.42.
The most important point to remember about using the future value equation is 
that the stated interest rate, r, and the number of compounding periods, N, must be 
compatible. Both variables must be defined in the same time units. For example, if 
N is stated in months, then r should be the one-  month interest rate, unannualized.
A time line helps us to keep track of the compatibility of time units and the interest

rate per time period. In the time line, we use the time index t to represent a point in 
time a stated number of periods from today. Thus the present value is the amount 
available for investment today, indexed as t = 0. We can now refer to a time N periods 
from today as t = N. The time line in Figure 1 shows this relationship.
Figure 1   The Relationship between an Initial Investment, PV, and Its Future 
Value, FV
01  2  3 ... N – 1 N
PV FV N = PV(1 + r)N
In Figure 1, we have positioned the initial investment, PV, at t = 0. Using Equation 2, 
we move the present value, PV, forward to t = N by the factor (1 + r)N. This factor is 
called a future value factor. We denote the future value on the time line as FV and 
position it at t = N. Suppose the future value is to be received exactly 10 periods from 
today’s date ( N = 10). The present value, PV, and the future value, FV, are separated 
in time through the factor (1 + r)10.

The fact that the present value and the future value are separated in time has 
important consequences:
■■We can add amounts of money only if they are indexed at the same point in 
time.
■■For a given interest rate, the future value increases with the number of periods.
■■For a given number of periods, the future value increases with the interest rate.
To better understand these concepts, consider three examples that illustrate how to 
apply the future value formula.
EXAMPLE 1   
The Future Value of a Lump Sum with Interim Cash 
Reinvested at the Same Rate
You are the lucky winner of your state’s lottery of $5 million after taxes. You 
invest your winnings in a five-  year certificate of deposit (CD) at a local financial 
institution. The CD promises to pay 7 percent per year compounded annually. (2)

Reading 6 ■ The Time Value of Money 308
This institution also lets you reinvest the interest at that rate for the duration of 
the CD. How much will you have at the end of five years if your money remains 
invested at 7 percent for five years with no withdrawals?
Solution: 
To solve this problem, compute the future value of the $5 million investment 
using the following values in Equation 2:
PV
FV PV
$5,000,000 1.07
$55=
==
=
=+ ()
= ()
=$, ,
%.5 000 000
70 07
5
1r
N
rNN
, ,000,000 1.402552
$7,012,758.65()
=
At the end of five years, you will have $7,012,758.65 if your money remains 
invested at 7 percent with no withdrawals.
In this and most examples in this reading, note that the factors are reported at six 
decimal places but the calculations may actually reflect greater precision.  For exam -
ple, the reported 1.402552 has been rounded up from 1.40255173 (the calculation is 
actually carried out with more than eight decimal places of precision by the calculator

or spreadsheet). Our final result reflects the higher number of decimal places carried 
by the calculator or spreadsheet.4
EXAMPLE 2   
The Future Value of a Lump Sum with No Interim Cash
An institution offers you the following terms for a contract: For an investment 
of ¥2,500,000, the institution promises to pay you a lump sum six years from 
now at an 8 percent annual interest rate. What future amount can you expect?
Solution: 
Use the following data in Equation 2 to find the future value:
PV 25
88
6
FV PV
2,500,000 1.08
26=
==
=
=+ ()
= ()
=¥, ,
%.
¥
¥00 000
00
1r
N
rNN
, ,500,000 1.586874
3,967,186()
=¥
You can expect to receive ¥3,967,186 six years from now.
4 We could also solve time value of money problems using tables of interest rate factors. Solutions using 
tabled values of interest rate factors are generally less accurate than solutions obtained using calculators 
or spreadsheets, so practitioners prefer calculators or spreadsheets.

The Future Value of a Single Cash Flow 309
Our third example is a more complicated future value problem that illustrates the 
importance of keeping track of actual calendar time.
EXAMPLE 3   
The Future Value of a Lump Sum
A pension fund manager estimates that his corporate sponsor will make a 
$10 million contribution five years from now. The rate of return on plan assets 
has been estimated at 9 percent per year. The pension fund manager wants to 
calculate the future value of this contribution 15 years from now, which is the 
date at which the funds will be distributed to retirees. What is that future value?
Solution:
By positioning the initial investment, PV, at t = 5, we can calculate the future 
value of the contribution using the following data in Equation 2:
PV  million
FV PV
10,000,000 1.091=
==
=
=+ ()
= ()$
%.
$10
90 09
10
1r
N
rNN
0 0
10,000,000 2.367364
23,673,636.75= ()
=$
$
This problem looks much like the previous two, but it differs in one important

respect: its timing. From the standpoint of today ( t = 0), the future amount of 
$23,673,636.75 is 15 years into the future. Although the future value is 10 years 
from its present value, the present value of $10 million will not be received for 
another five years.
Figure 2   The Future Value of a Lump Sum, Initial Investment Not at t 
= 0
As Figure 2 shows, we have followed the convention of indexing today as t 
= 0 and indexing subsequent times by adding 1 for each period. The additional 
contribution of $10 million is to be received in five years, so it is indexed as 
t = 5 and appears as such in the figure. The future value of the investment in 
10 years is then indexed at t = 15; that is, 10 years following the receipt of the 
$10 million contribution at t = 5. Time lines like this one can be extremely useful 
when dealing with more-  complicated problems, especially those involving more 
than one cash flow.

Reading 6 ■ The Time Value of Money 310
In a later section of this reading, we will discuss how to calculate the value today 
of the $10 million to be received five years from now. For the moment, we can use 
Equation 2. Suppose the pension fund manager in Example 3 above were to receive 
$6,499,313.86 today from the corporate sponsor. How much will that sum be worth 
at the end of five years? How much will it be worth at the end of 15 years?
PV 6,499,313.86
FV PV
6,499,313.86 1.09=
==
=
=+ ()
=$
%.
$r
N
rNN90 09
5
1
(()
= ()
=5
6,499,313.86 1.538624
10,000,000 at the fi ve-year $
$m mark
and
FV PV
6,499,313.86 1.0=
==
=
=+ ()
=$
%.
$r
N
rNN90 09
15
1
9 9
6,499,313.86 3.642482
23,673,636.74 at the 15- ye15()
= ()
=$
$a ar mar k
These results show that today’s present value of about $6.5 million becomes $10 million 
after five years and $23.67 million after 15 years.
3.1 The Frequency of Compounding
In this section, we examine investments paying interest more than once a year. For

instance, many banks offer a monthly interest rate that compounds 12 times a year. 
In such an arrangement, they pay interest on interest every month. Rather than quote 
the periodic monthly interest rate, financial institutions often quote an annual interest 
rate that we refer to as the stated annual interest rate  or quoted interest rate . We 
denote the stated annual interest rate by rs. For instance, your bank might state that 
a particular CD pays 8 percent compounded monthly. The stated annual interest rate 
equals the monthly interest rate multiplied by 12. In this example, the monthly interest 
rate is 0.08/12 = 0.0067 or 0.67 percent.5 This rate is strictly a quoting convention 
because (1 + 0.0067)12 = 1.083, not 1.08; the term (1 + rs) is not meant to be a future 
value factor when compounding is more frequent than annual.
With more than one compounding period per year, the future value formula can 
FV PVNsmNr
m=+

1

FV PVNsmNr
m=+

1
where rs is the stated annual interest rate, m is the number of compounding periods 
per year, and N now stands for the number of years. Note the compatibility here 
between the interest rate used, rs/m, and the number of compounding periods, mN. (3)
5 To avoid rounding errors when using a financial calculator, divide 8 by 12 and then press the % i key, 
rather than simply entering 0.67 for % i, so we have (1 + 0.08/12)12 = 1.083000.

The Future Value of a Single Cash Flow 311
The periodic rate, rs/m, is the stated annual interest rate divided by the number of 
compounding periods per year. The number of compounding periods, mN, is the 
number of compounding periods in one year multiplied by the number of years. The 
periodic rate, rs/m, and the number of compounding periods, mN, must be compatible.
EXAMPLE 4   
The Future Value of a Lump Sum with Quarterly 
Compounding
Continuing with the CD example, suppose your bank offers you a CD with a two-  
year maturity, a stated annual interest rate of 8 percent compounded quarterly, 
and a feature allowing reinvestment of the interest at the same interest rate. You 
decide to invest $10,000. What will the CD be worth at maturity?
Solution:
Compute the future value with Equation 3 as follows:
PV 10,000
 interes t=
==
=
==
=
=()=$
%.
..r
m
rm
N
mNs
s80 08
4
0084 002
2
42 8   periods
FV PV
10,000 1.02
10,000 1.17165NsmNr
m=+


= ()
=1
8$
$9 9
11,716.59()
=$
At maturity, the CD will be worth $11,716.59.

=$
The future value formula in Equation 3 does not differ from the one in Equation 2. 
Simply keep in mind that the interest rate to use is the rate per period and the expo -
nent is the number of interest, or compounding, periods.
EXAMPLE 5   
The Future Value of a Lump Sum with Monthly 
An Australian bank offers to pay you 6 percent compounded monthly. You decide 
to invest A$1 million for one year. What is the future value of your investment 
if interest payments are reinvested at 6 percent?

Reading 6 ■ The Time Value of Money 312
Solution:
Use Equation 3 to find the future value of the one-  year investment as follows:
PV A 1,000,000
1=
==
=
==
=
= ()=$
%.
..r
m
rm
N
mNs
s60 06
12
006120 0050
1
12 1 22 interest periods
FV PV
A 1,000,000 1.0051NsmNr
m=+


= ()1
$2 2
A 1,000,000 1.061678
A 1,061,677.81= ()
=$
$
If you had been paid 6 percent with annual compounding, the future amount 
would be only A$1,000,000(1.06) = A$1,060,000 instead of A$1,061,677.81 with 
monthly compounding.
3.2 Continuous Compounding
The preceding discussion on compounding periods illustrates discrete compounding, 
which credits interest after a discrete amount of time has elapsed. If the number of 
compounding periods per year becomes infinite, then interest is said to compound 
continuously. If we want to use the future value formula with continuous compound -
ing, we need to find the limiting value of the future value factor for m → ∞ (infinitely 
many compounding periods per year) in Equation 3. The expression for the future

value of a sum in N years with continuous compounding is
FV PVNrNes=
The term  erNs is the transcendental number e ≈ 2.7182818 raised to the power rsN. 
Most financial calculators have the function ex.
EXAMPLE 6   
The Future Value of a Lump Sum with Continuous 
Suppose a $10,000 investment will earn 8 percent compounded continuously 
for two years. We can compute the future value with Equation 4 as follows:
PV 10,000
FV PV
10,000
10,000 10.08=
==
=
=
=
=()$
%.
$
$r
N
e
es
NrNs80 08
2
2
. .173511
11,735.11()
=$(4)

The Future Value of a Single Cash Flow 313
With the same interest rate but using continuous compounding, the $10,000 
investment will grow to $11,735.11 in two years, compared with $11,716.59 
using quarterly compounding as shown in Example 4.
Table 1 shows how a stated annual interest rate of 8 percent generates different ending 
dollar amounts with annual, semiannual, quarterly, monthly, daily, and continuous 
compounding for an initial investment of $1 (carried out to six decimal places).
As Table 1 shows, all six cases have the same stated annual interest rate of 8 per -
cent; they have different ending dollar amounts, however, because of differences in 
the frequency of compounding. With annual compounding, the ending amount is 
$1.08. More frequent compounding results in larger ending amounts. The ending 
dollar amount with continuous compounding is the maximum amount that can be 
earned with a stated annual rate of 8 percent.
Table 1   The Effect of Compounding Frequency on Future Value

Frequency rs/m mN Future Value of $1
Annual 8%/1 = 8% 1 × 1 = 1 $1.00(1.08) = $1.08
Semiannual 8%/2 = 4% 2 × 1 = 2 $1.00(1.04)2= $1.081600
Quarterly 8%/4 = 2% 4 × 1 = 4 $1.00(1.02)4= $1.082432
Monthly 8%/12 = 0.6667% 12 × 1 = 12 $1.00(1.006667)12= $1.083000
Daily 8%/365 = 0.0219% 365 × 1 = 365 $1.00(1.000219)365= $1.083278
Continuous $1.00 e0.08(1)= $1.083287
Table 1 also shows that a $1 investment earning 8.16 percent compounded annu -
ally grows to the same future value at the end of one year as a $1 investment earning 
8 percent compounded semiannually. This result leads us to a distinction between 
the stated annual interest rate and the effective annual rate  (EAR).6 For an 8 percent 
stated annual interest rate with semiannual compounding, the EAR is 8.16 percent.
3.3 Stated and Effective Rates
The stated annual interest rate does not give a future value directly, so we need a for -
mula for the EAR. With an annual interest rate of 8 percent compounded semiannually,

we receive a periodic rate of 4 percent. During the course of a year, an investment of 
$1 would grow to $1(1.04)2 = $1.0816, as illustrated in Table 1. The interest earned 
on the $1 investment is $0.0816 and represents an effective annual rate of interest of 
8.16 percent. The effective annual rate is calculated as follows:
EAR = (1 + Periodic interest rate)m – 1  (5)
6 Among the terms used for the effective annual return on interest-  bearing bank deposits are annual 
percentage yield (APY) in the United States and equivalent annual rate (EAR) in the United Kingdom. 
By contrast, the annual percentage rate  (APR) measures the cost of borrowing expressed as a yearly 
rate. In the United States, the APR is calculated as a periodic rate times the number of payment periods 
per year and, as a result, some writers use APR as a general synonym for the stated annual interest rate. 
Nevertheless, APR is a term with legal connotations; its calculation follows regulatory standards that vary

internationally. Therefore, “stated annual interest rate” is the preferred general term for an annual interest 
rate that does not account for compounding within the year.

Reading 6 ■ The Time Value of Money 314
The periodic interest rate is the stated annual interest rate divided by m, where m is 
the number of compounding periods in one year. Using our previous example, we can 
solve for EAR as follows: (1.04)2 − 1 = 8.16 percent.
The concept of EAR extends to continuous compounding. Suppose we have a rate 
of 8 percent compounded continuously. We can find the EAR in the same way as above 
by finding the appropriate future value factor. In this case, a $1 investment would 
grow to $1 e0.08(1.0) = $1.0833. The interest earned for one year represents an effective 
annual rate of 8.33 percent and is larger than the 8.16 percent EAR with semiannual 
compounding because interest is compounded more frequently. With continuous 
compounding, we can solve for the effective annual rate as follows:
EAR1=−ers
We can reverse the formulas for EAR with discrete and continuous compounding to 
find a periodic rate that corresponds to a particular effective annual rate. Suppose we

want to find the appropriate periodic rate for a given effective annual rate of 8.16 per -
cent with semiannual compounding. We can use Equation 5 to find the periodic rate:
0.0816 1P eriodic rate 1
1.0816 1P eriodic rate
1.08162
2=+() −
=+()
(() −=
() −=
=11P eriodic rate
1.04 1P eriodic rate
4% Periodic ra t2
e e
To calculate the continuously compounded rate (the stated annual interest rate with 
continuous compounding) corresponding to an effective annual rate of 8.33 percent, 
we find the interest rate that satisfies Equation 6:
0.0833 1
1.0833=−
=e
er
rs
s
To solve this equation, we take the natural logarithm of both sides. (Recall that the 
natural log of  ers is ln  err
ss=.) Therefore, ln 1.0833 = rs, resulting in rs = 8 percent. 
We see that a stated annual rate of 8 percent with continuous compounding is equiv -
alent to an EAR of 8.33 percent.
THE FUTURE VALUE OF A SERIES OF CASH FLOWS
In this section, we consider series of cash flows, both even and uneven. We begin

with a list of terms commonly used when valuing cash flows that are distributed over 
many time periods.
■■An annuity  is a finite set of level sequential cash flows.
■■An ordinary annuity  has a first cash flow that occurs one period from now 
(indexed at t = 1).
■■An annuity due  has a first cash flow that occurs immediately (indexed at t = 0).
■■A perpetuity  is a perpetual annuity, or a set of level never-  ending sequential 
cash flows, with the first cash flow occurring one period from now.(6)
4

The Future Value of a Series of Cash Flows 315
4.1 Equal Cash Flows—Ordinary Annuity
Consider an ordinary annuity paying 5 percent annually. Suppose we have five sep -
arate deposits of $1,000 occurring at equally spaced intervals of one year, with the 
first payment occurring at t = 1. Our goal is to find the future value of this ordinary 
annuity after the last deposit at t = 5. The increment in the time counter is one year, 
so the last payment occurs five years from now. As the time line in Figure 3 shows, we 
find the future value of each $1,000 deposit as of t = 5 with Equation 2, FVN = PV(1 + 
r)N. The arrows in Figure 3 extend from the payment date to t = 5. For instance, the 
first $1,000 deposit made at t = 1 will compound over four periods. Using Equation 2, 
we find that the future value of the first deposit at t = 5 is $1,000(1.05)4 = $1,215.51. 
We calculate the future value of all other payments in a similar fashion. (Note that we

are finding the future value at t = 5, so the last payment does not earn any interest.) 
With all values now at t = 5, we can add the future values to arrive at the future value 
of the annuity. This amount is $5,525.63.
Figure 3   The Future Value of a Five-  Y ear Ordinary Annuity
|||||
 0 12345
   $1,000(1.05)4=$1,215.506250
$1,000    $1,000(1.05)3=$1,157.625000
$1,000    $1,000(1.05)2=$1,102.500000
$1,000    $1,000(1.05)1=$1,050.000000
$1,000
$1,000(1.05)0=$1,000.000000
Sum at t = 5 $5,525.63
We can arrive at a general annuity formula if we define the annuity amount as A, 
the number of time periods as N, and the interest rate per period as r. We can then 
define the future value as
FVNNN NAr rr rr =+ () ++() ++() ++ +() ++()

−− −11 11 112 31 0
which simplifies to
FVN ArN
r=+() −



11
The term in brackets is the future value annuity factor. This factor gives the future 
value of an ordinary annuity of $1 per period. Multiplying the future value annuity

factor by the annuity amount gives the future value of an ordinary annuity. For the 
ordinary annuity in Figure 3, we find the future value annuity factor from Equation 7 as
1.055.525631() −



=51
005 .
With an annuity amount A = $1,000, the future value of the annuity is $1,000(5.525631) 
= $5,525.63, an amount that agrees with our earlier work.
The next example illustrates how to find the future value of an ordinary annuity 
using the formula in Equation 7.(7)

Reading 6 ■ The Time Value of Money 316
EXAMPLE 7   
The Future Value of an Annuity
Suppose your company’s defined contribution retirement plan allows you to 
invest up to €20,000 per year. You plan to invest €20,000 per year in a stock 
index fund for the next 30 years. Historically, this fund has earned 9 percent per 
year on average. Assuming that you actually earn 9 percent a year, how much 
money will you have available for retirement after making the last payment?
Solution:
Use Equation 7 to find the future amount:
 A = €20,000
 r = 9% = 0.09
 N = 30
 FV annuity factor =  11 1091
009136 30753930+() −=() −=r
rN.
..
 FVN = €20,000(136.307539)
  = €2,726,150.77
Assuming the fund continues to earn an average of 9 percent per year, you will 
have €2,726,150.77 available at retirement.
4.2 Unequal Cash Flows
In many cases, cash flow streams are unequal, precluding the simple use of the future 
value annuity factor. For instance, an individual investor might have a savings plan

that involves unequal cash payments depending on the month of the year or lower 
savings during a planned vacation. One can always find the future value of a series 
of unequal cash flows by compounding the cash flows one at a time. Suppose you 
have the five cash flows described in Table 2, indexed relative to the present ( t = 0).
Table 2   A Series of Unequal Cash Flows and Their Future 
Values at 5 Percent
Time Cash Flow ($) Future Value at Y ear 5
t = 1 1,000 $1,000(1.05)4= $1,215.51
t = 2 2,000 $2,000(1.05)3= $2,315.25
t = 3 4,000 $4,000(1.05)2= $4,410.00
t = 4 5,000 $5,000(1.05)1= $5,250.00
t = 5 6,000 $6,000(1.05)0= $6,000.00
Sum = $19,190.76
All of the payments shown in Table 2 are different. Therefore, the most direct 
approach to finding the future value at t = 5 is to compute the future value of each 
payment as of t = 5 and then sum the individual future values. The total future value 
at Year 5 equals $19,190.76, as shown in the third column. Later in this reading, you

will learn shortcuts to take when the cash flows are close to even; these shortcuts will 
allow you to combine annuity and single-  period calculations.

The Present Value of a Single Cash Flow 317
THE PRESENT VALUE OF A SINGLE CASH FLOW
5.1 Finding the Present Value of a Single Cash Flow
Just as the future value factor links today’s present value with tomorrow’s future 
value, the present value factor allows us to discount future value to present value. 
For example, with a 5 percent interest rate generating a future payoff of $105 in one 
year, what current amount invested at 5 percent for one year will grow to $105? The 
answer is $100; therefore, $100 is the present value of $105 to be received in one year 
at a discount rate of 5 percent.
Given a future cash flow that is to be received in N periods and an interest rate per 
period of r, we can use the formula for future value to solve directly for the present 
value as follows:
FV PV
PV FV
PV FVNN
NN
NNr
r
r=+ ()
=
+()




=+ ()−1
1
1
1
We see from Equation 8 that the present value factor, (1 + r)−N, is the reciprocal of 
the future value factor, (1 + r)N.
EXAMPLE 8   
The Present Value of a Lump Sum

EXAMPLE 8   
An insurance company has issued a Guaranteed Investment Contract (GIC) 
that promises to pay $100,000 in six years with an 8 percent return rate. What 
amount of money must the insurer invest today at 8 percent for six years to 
make the promised payment?
Solution:
We can use Equation 8 to find the present value using the following data:
FV 100,000
PV FV
100,000N
NNr
N
r=
==
=
=+ ()
=
()

−$
%.
$
.80 08
6
1
1
1086 


= ()
=$
$100,000 0.6301696
63,016.96
We can say that $63,016.96 today, with an interest rate of 8  percent, is 
equivalent to $100,000 to be received in six years. Discounting the $100,000 
makes a future $100,000 equivalent to $63,016.96 when allowance is made for 
the time value of money. As the time line in Figure 4 shows, the $100,000 has 
been discounted six full periods.5
(8)

Reading 6 ■ The Time Value of Money 318
Figure 4   The Present Value of a Lump Sum to Be Received at Time t = 6
12 34 6
PV = $63,016.96
$100,000 = F V5 0
EXAMPLE 9   
The Projected Present Value of a More Distant Future 
Lump Sum
Suppose you own a liquid financial asset that will pay you $100,000 in 10 years 
from today. Your daughter plans to attend college four years from today, and 
you want to know what the asset’s present value will be at that time. Given an 
8 percent discount rate, what will the asset be worth four years from today?
Solution:
The value of the asset is the present value of the asset’s promised payment. At 
t = 4, the cash payment will be received six years later. With this information, 
you can solve for the value four years from today using Equation 8:
FV 100,000
PV FV
100,000
10N
NNr
N
r=
==
=
=+ ()
=
()
=−$
%.
$
.
$80 08
6
1
1
1086
0 0,000 0.6301696
63,016.96()
=$
Figure 5   The Relationship between Present Value and Future Value
0 ... 4 ... 10
$46,319.35 $63,016.96
$100,000

The Present Value of a Single Cash Flow 319
The time line in Figure 5 shows the future payment of $100,000 that is to 
be received at t = 10. The time line also shows the values at t = 4 and at t = 0. 
Relative to the payment at t = 10, the amount at t = 4 is a projected present 
value, while the amount at t = 0 is the present value (as of today).
Present value problems require an evaluation of the present value factor, (1 + r)−N. 
Present values relate to the discount rate and the number of periods in the following 
ways:
■■For a given discount rate, the farther in the future the amount to be received, 
the smaller that amount’s present value.
■■Holding time constant, the larger the discount rate, the smaller the present 
value of a future amount.
5.2 The Frequency of Compounding
Recall that interest may be paid semiannually, quarterly, monthly, or even daily. To 
handle interest payments made more than once a year, we can modify the present

value formula (Equation 8) as follows. Recall that rs is the quoted interest rate and 
equals the periodic interest rate multiplied by the number of compounding periods 
in each year. In general, with more than one compounding period in a year, we can 
express the formula for present value as
PV FV=+ ()−
Nr
mmN
s1
where
 m = number of compounding periods per year
 rs = quoted annual interest rate
 N = number of years
The formula in Equation 9 is quite similar to that in Equation 8. As we have already 
noted, present value and future value factors are reciprocals. Changing the frequency 
of compounding does not alter this result. The only difference is the use of the periodic 
interest rate and the corresponding number of compounding periods.
The following example illustrates Equation 9.
EXAMPLE 10   
The Present Value of a Lump Sum with Monthly 
The manager of a Canadian pension fund knows that the fund must make a 
lump-  sum payment of C$5 million 10 years from now. She wants to invest an

amount today in a GIC so that it will grow to the required amount. The current 
interest rate on GICs is 6  percent a year, compounded monthly. How much 
should she invest today in the GIC?(9)

Reading 6 ■ The Time Value of Money 320
Solution:
Use Equation 9 to find the required present value:
FV C 5,000,000N
s
sr
m
rm
N
mN=
==
=
==
=
=()$
%.
..60 06
12
006120 005
10
12 10 = =
=+ ()
= ()
=−
−120
1 PV FV
C 5,000,000 1.005
C 5,000,000 0.120Nr
mmN
s
$
$5 549633
C 2,748,163.67()
=$
In applying Equation 9, we use the periodic rate (in this case, the monthly rate) 
and the appropriate number of periods with monthly compounding (in this case, 
10 years of monthly compounding, or 120 periods).
THE PRESENT VALUE OF A SERIES OF CASH FLOWS
Many applications in investment management involve assets that offer a series of 
cash flows over time. The cash flows may be highly uneven, relatively even, or equal. 
They may occur over relatively short periods of time, longer periods of time, or even 
stretch on indefinitely. In this section, we discuss how to find the present value of a 
series of cash flows.
6.1 The Present Value of a Series of Equal Cash Flows

We begin with an ordinary annuity. Recall that an ordinary annuity has equal annuity 
payments, with the first payment starting one period into the future. In total, the 
annuity makes N payments, with the first payment at t = 1 and the last at t = N. We 
can express the present value of an ordinary annuity as the sum of the present values 
of each individual annuity payment, as follows:
PV=+()+
+()+
+()++
+()+
+()−A
rA
rA
rA
rA
rNN 1 11 1123 1
where
 A = the annuity amount
 r = the interest rate per period corresponding to the frequency of annuity 
payments (for example, annual, quarterly, or monthly)
 N = the number of annuity payments6
(10)

The Present Value of a Series of Cash Flows 321
Because the annuity payment ( A) is a constant in this equation, it can be factored out 
as a common term. Thus the sum of the interest factors has a shortcut expression:
PV =−
+()









ArN
r11
1
In much the same way that we computed the future value of an ordinary annuity, we 
find the present value by multiplying the annuity amount by a present value annuity 
factor (the term in brackets in Equation 11).
EXAMPLE 11   
The Present Value of an Ordinary Annuity
Suppose you are considering purchasing a financial asset that promises to pay 
€1,000 per year for five years, with the first payment one year from now. The 
required rate of return is 12 percent per year. How much should you pay for 
this asset?
Solution:
To find the value of the financial asset, use the formula for the present value of 
an ordinary annuity given in Equation 11 with the following data:
 A = €1,000
 r = 12% = 0.12
 N = 5
 PV =  Ar
rN11
1−
+()










  = €1,00011
112
0125−
()



rN11
1−
+()










  = €1,00011
112
0125−
()









.
.
  = €1,000(3.604776)
  = €3,604.78
The series of cash flows of €1,000 per year for five years is currently worth 
€3,604.78 when discounted at 12 percent.
Keeping track of the actual calendar time brings us to a specific type of annuity 
with level payments: the annuity due. An annuity due has its first payment occurring 
today ( t = 0). In total, the annuity due will make N payments. Figure 6 presents the 
time line for an annuity due that makes four payments of $100.(11)

Reading 6 ■ The Time Value of Money 322
Figure 6   An Annuity Due of $100 per Period
||||
0123
$100 $100 $100 $100
As Figure 6 shows, we can view the four-  period annuity due as the sum of two 
parts: a $100 lump sum today and an ordinary annuity of $100 per period for three 
periods. At a 12 percent discount rate, the four $100 cash flows in this annuity due 
example will be worth $340.18.7
Expressing the value of the future series of cash flows in today’s dollars gives us a 
convenient way of comparing annuities. The next example illustrates this approach.
EXAMPLE 12   
An Annuity Due as the Present Value of an Immediate 
Cash Flow Plus an Ordinary Annuity
You are retiring today and must choose to take your retirement benefits either as 
a lump sum or as an annuity. Your company’s benefits officer presents you with 
two alternatives: an immediate lump sum of $2 million or an annuity with 20 
payments of $200,000 a year with the first payment starting today. The interest

rate at your bank is 7 percent per year compounded annually. Which option has 
the greater present value? (Ignore any tax differences between the two options.)
Solution:
To compare the two options, find the present value of each at time t = 0 and 
choose the one with the larger value. The first option’s present value is $2 mil -
lion, already expressed in today’s dollars. The second option is an annuity due. 
Because the first payment occurs at t = 0, you can separate the annuity benefits 
into two pieces: an immediate $200,000 to be paid today ( t = 0) and an ordinary 
7 There is an alternative way to calculate the present value of an annuity due. Compared to an ordinary 
annuity, the payments in an annuity due are each discounted one less period. Therefore, we can modify 
Equation 11 to handle annuities due by multiplying the right-  hand side of the equation by (1 + r):
PVAnnuity  due () () {} () =− ++−Ar rrN11 1

The Present Value of a Series of Cash Flows 323
annuity of $200,000 per year for 19 years. To value this option, you need to 
find the present value of the ordinary annuity using Equation 11 and then add 
$200,000 to it.
A
N
r
Ar
rN=
=
==
=−
+()










=$
.
$200,000
%
PV
200,019
70 07
11
1
0 00
200,000 10.335595
2,0611
107
00719−
()










= ()
=.
.
$
$7 7,119.05
The 19 payments of $200,000 have a present value of $2,067,119.05. Adding the 
initial payment of $200,000 to $2,067,119.05, we find that the total value of the 
annuity option is $2,267,119.05. The present value of the annuity is greater than 
the lump sum alternative of $2 million.
We now look at another example reiterating the equivalence of present and future 
values.
EXAMPLE 13   
The Projected Present Value of an Ordinary Annuity
A German pension fund manager anticipates that benefits of €1 million per year 
must be paid to retirees. Retirements will not occur until 10 years from now

at time t = 10. Once benefits begin to be paid, they will extend until t = 39 for 
a total of 30 payments. What is the present value of the pension liability if the 
appropriate annual discount rate for plan liabilities is 5 percent compounded 
annually?

Reading 6 ■ The Time Value of Money 324
Solution:
This problem involves an annuity with the first payment at t = 10. From the 
perspective of t = 9, we have an ordinary annuity with 30 payments. We can 
compute the present value of this annuity with Equation 11 and then look at it 
on a time line.
 A = €1,000,000
 r = 5% = 0.05
 N = 30
 PV =  Ar
rN11
1−
+()










  = €1,000,00011
105
00530−
()









.
.
  = €1,000,000(15.372451)
  = €15,372,451.03
Figure 7   The Present Value of an Ordinary Annuity with First Payment 
at Time t = 10 (in Millions) 
0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 0 11           12 . . . . . . . . . . . . . . . . . . . . 39
1 . . . . . . . . . . . . . . . . . . 1 1 1
On the time line, we have shown the pension payments of €1 million extend -
ing from t = 10 to t = 39. The bracket and arrow indicate the process of finding 
the present value of the annuity, discounted back to t = 9. The present value

of the pension benefits as of t = 9 is €15,372,451.03. The problem is to find the 
present value today (at t = 0).
Now we can rely on the equivalence of present value and future value. As 
Figure 7 shows, we can view the amount at t = 9 as a future value from the vantage 
point of t = 0. We compute the present value of the amount at t = 9 as follows:
 FVN = €15,372,451.03 (the present value at t = 9)
 N = 9
 r = 5% = 0.05
 PV = FVN(1 + r)–N
  = €15,372,451.03(1.05)–9
  = €15,372,451.03(0.644609)
  = €9,909,219.00

The Present Value of a Series of Cash Flows 325
The present value of the pension liability is €9,909,219.00.
Example 13 illustrates three procedures emphasized in this reading:
■■finding the present or future value of any cash flow series;
■■recognizing the equivalence of present value and appropriately discounted 
future value; and
■■keeping track of the actual calendar time in a problem involving the time value 
of money.
6.2 The Present Value of an Infinite Series of Equal Cash 
Flows—Perpetuity
Consider the case of an ordinary annuity that extends indefinitely. Such an ordinary 
annuity is called a perpetuity (a perpetual annuity). To derive a formula for the present 
value of a perpetuity, we can modify Equation 10 to account for an infinite series of 
cash flows:
PV=
+()



=∞
∑A
rt
t1
11
As long as interest rates are positive, the sum of present value factors converges and
PV=A
r
To see this, look back at Equation 11, the expression for the present value of an ordi -

nary annuity. As N (the number of periods in the annuity) goes to infinity, the term 
1/(1 + r)N approaches 0 and Equation 11 simplifies to Equation 13. This equation will 
reappear when we value dividends from stocks because stocks have no predefined 
life span. (A stock paying constant dividends is similar to a perpetuity.) With the first 
payment a year from now, a perpetuity of $10 per year with a 20 percent required 
rate of return has a present value of $10/0.2 = $50.
Equation 13 is valid only for a perpetuity with level payments. In our development 
above, the first payment occurred at t = 1; therefore, we compute the present value 
as of t = 0.
Other assets also come close to satisfying the assumptions of a perpetuity. Certain 
government bonds and preferred stocks are typical examples of financial assets that 
make level payments for an indefinite period of time.
EXAMPLE 14   
The Present Value of a Perpetuity
The British government once issued a type of security called a consol bond,

which promised to pay a level cash flow indefinitely. If a consol bond paid £100 
per year in perpetuity, what would it be worth today if the required rate of 
return were 5 percent?(12)
(13)

Reading 6 ■ The Time Value of Money 326
Solution:
To answer this question, we can use Equation 13 with the following data:
A
r
Ar=
= =
=
=
=£
%.
£.
£,100
50 05
100005
2 000PV
The bond would be worth £2,000.
6.3 Present Values Indexed at Times Other than t = 0
In practice with investments, analysts frequently need to find present values indexed 
at times other than t = 0. Subscripting the present value and evaluating a perpetuity 
beginning with $100 payments in Year 2, we find PV1 = $100/0.05 = $2,000 at a 5 percent 
discount rate. Further, we can calculate today’s PV as PV0 = $2,000/1.05 = $1,904.76.
Consider a similar situation in which cash flows of $6 per year begin at the end 
of the 4th year and continue at the end of each year thereafter, with the last cash 
flow at the end of the 10th year. From the perspective of the end of the third year, 
we are facing a typical seven-  year ordinary annuity. We can find the present value of

the annuity from the perspective of the end of the third year and then discount that 
present value back to the present. At an interest rate of 5 percent, the cash flows of 
$6 per year starting at the end of the fourth year will be worth $34.72 at the end of 
the third year ( t = 3) and $29.99 today ( t = 0).
The next example illustrates the important concept that an annuity or perpetuity 
beginning sometime in the future can be expressed in present value terms one period 
prior to the first payment. That present value can then be discounted back to today’s 
present value.
EXAMPLE 15   
The Present Value of a Projected Perpetuity
Consider a level perpetuity of £100 per year with its first payment beginning at 
t = 5. What is its present value today (at t = 0), given a 5 percent discount rate?
Solution:
First, we find the present value of the perpetuity at t = 4 and then discount that 
amount back to t = 0. (Recall that a perpetuity or an ordinary annuity has its

first payment one period away, explaining the t = 4 index for our present value 
calculation.)
 i. Find the present value of the perpetuity at t = 4:
A
r
Ar=
= =
=
=
=£
%.
£.
£,100
50 05
100005
2 000PV
 ii. Find the present value of the future amount at t = 4. From the perspective 
of t = 0, the present value of £2,000 can be considered a future value. Now 
we need to find the present value of a lump sum:

The Present Value of a Series of Cash Flows 327
FV 2 the present value at 4
55
4
PV FVN
Nt
r
N
r==
==
=
=+£, ()
%.000
00
1(()
= ()
= ()
=−
−N
£
£
£2,000 1.05
2,000 0.822702
1,645.404
Today’s present value of the perpetuity is £1,645.40.
As discussed earlier, an annuity is a series of payments of a fixed amount for a 
specified number of periods. Suppose we own a perpetuity. At the same time, we 
issue a perpetuity obligating us to make payments; these payments are the same size 
as those of the perpetuity we own. However, the first payment of the perpetuity we 
issue is at t = 5; payments then continue on forever. The payments on this second 
perpetuity exactly offset the payments received from the perpetuity we own at t = 5 
and all subsequent dates. We are left with level nonzero net cash flows at t = 1, 2, 3, 
and 4. This outcome exactly fits the definition of an annuity with four payments. Thus 
we can construct an annuity as the difference between two perpetuities with equal,

level payments but differing starting dates. The next example illustrates this result.
EXAMPLE 16   
The Present Value of an Ordinary Annuity as the Present 
Value of a Current Minus Projected Perpetuity
Given a 5 percent discount rate, find the present value of a four-  year ordinary 
annuity of £100 per year starting in Year 1 as the difference between the following 
two level perpetuities:
Perpetuity 1 £100 per year starting in Year 1 (first payment at t = 1)
Perpetuity 2 £100 per year starting in Year 5 (first payment at t = 5)
Solution:
If we subtract Perpetuity 2 from Perpetuity 1, we are left with an ordinary annuity 
of £100 per period for four years (payments at t = 1, 2, 3, 4). Subtracting the 
present value of Perpetuity 2 from that of Perpetuity 1, we arrive at the present 
value of the four-  year ordinary annuity:
PV Pe rpetuity  1
PV Pe rpetuity  20
4100 0052 000
100 0() ==
() =£/ .£ ,
£/ .. £,
£, /. £, .05 2 000
2 000 1051 645 4004
0=
() = () = PV Pe rpetuity  2

0=
PV Annnuity PV Pe rpetuity  1 PV Pe rpetuity  2 () = () − ()
=−00
2 000 1 645£, £, ..
£.40
354 60=
The four-  year ordinary annuity’s present value is equal to £2,000 – £1,645.40 = 
£354.60.

Reading 6 ■ The Time Value of Money 328
6.4 The Present Value of a Series of Unequal Cash Flows
When we have unequal cash flows, we must first find the present value of each indi -
vidual cash flow and then sum the respective present values. For a series with many 
cash flows, we usually use a spreadsheet. Table 3 lists a series of cash flows with the 
time periods in the first column, cash flows in the second column, and each cash 
flow’s present value in the third column. The last row of Table 3 shows the sum of 
the five present values.
Table 3   A Series of Unequal Cash Flows and Their Present 
Time Period Cash Flow ($) Present Value at Y ear 0
1 1,000 $1,000(1.05)−1= $952.38
2 2,000 $2,000(1.05)−2= $1,814.06
3 4,000 $4,000(1.05)−3= $3,455.35
4 5,000 $5,000(1.05)−4= $4,113.51
5 6,000 $6,000(1.05)−5= $4,701.16
Sum = $15,036.46
We could calculate the future value of these cash flows by computing them one at a

time using the single-  payment future value formula. We already know the present value 
of this series, however, so we can easily apply time-  value equivalence. The future value 
of the series of cash flows from Table 2, $19,190.76, is equal to the single $15,036.46 
amount compounded forward to t = 5:
PV 15,036.46
FV PV
15,036.46 1.05
1=
=
==
=+ ()
= ()
=$
%.
$
$N
r
rNN5
50 05
1
5
5 5,036.46 1.276282
19,190.76()
=$
SOLVING FOR RATES, NUMBER OF PERIODS, OR SIZE 
OF ANNUITY PAYMENTS
In the previous examples, certain pieces of information have been made available. 
For instance, all problems have given the rate of interest, r, the number of time peri -
ods, N, the annuity amount, A, and either the present value, PV, or future value, FV. 
In real-  world applications, however, although the present and future values may be 
given, you may have to solve for either the interest rate, the number of periods, or 
the annuity amount. In the subsections that follow, we show these types of problems.7

Solving for Rates, Number of Periods, or Size of Annuity Payments 329
7.1 Solving for Interest Rates and Growth Rates
Suppose a bank deposit of €100 is known to generate a payoff of €111 in one year. 
With this information, we can infer the interest rate that separates the present value 
of €100 from the future value of €111 by using Equation 2, FVN = PV(1 + r)N, with N 
= 1. With PV, FV, and N known, we can solve for r directly:
 1 + r = FV/PV
 1 + r = €111/€100 = 1.11
 r = 0.11, or 11%
The interest rate that equates €100 at t = 0 to €111 at t = 1 is 11 percent. Thus we can 
state that €100 grows to €111 with a growth rate of 11 percent.
As this example shows, an interest rate can also be considered a growth rate. The 
particular application will usually dictate whether we use the term “interest rate” or 
“growth rate. ” Solving Equation 2 for r and replacing the interest rate r with the growth 
rate g produces the following expression for determining growth rates:
g = (FVN/PV)1/N – 1

g = (FVN/PV)1/N – 1  
Below are two examples that use the concept of a growth rate.
EXAMPLE 17   
Calculating a Growth Rate (1)
Hyundai Steel, the first Korean steelmaker, was established in 1953. Hyundai 
Steel’s sales increased from ₩10,503.0 billion in 2008 to ₩14,146.4 billion in 2012. 
However, its net profit declined from ₩822.5 billion in 2008 to ₩796.4 billion 
in 2012. Calculate the following growth rates for Hyundai Steel for the four-  year 
period from the end of 2008 to the end of 2012:
1 Sales growth rate.
2 Net profit growth rate.
To solve this problem, we can use Equation 14, g = (FVN/PV)1/N – 1. We denote 
sales in 2008 as PV and sales in 2012 as FV4. We can then solve for the growth 
rate as follows:
g=−
=−
=−
=WW
 or14 146 41 0 503 01
1 346891 1
1 077291 1
0 0772914
4,. ,.
.
.
.  about  77.%
The calculated growth rate of about 7.7 percent a year shows that Hyundai Steel’s 
sales grew substantially during the 2008–2012 period.(14)

Reading 6 ■ The Time Value of Money 330
In this case, we can speak of a positive compound rate of decrease or a negative 
compound growth rate. Using Equation 14, we find
g=−
=−
=−
=−WW
 or abou796 4 822 51
0 968267 1
0 991971 1
0 0080294
4..
.
.
.t t−080.%
In contrast to the positive sales growth, the rate of growth in net profit was 
approximately –0.80 percent during the 2008–2012 period.
EXAMPLE 18   
Calculating a Growth Rate (2)
Toyota Motor Corporation, one of the largest automakers in the world, had con -
solidated vehicle sales of 7.35 million units in 2012. This is substantially less than 
consolidated vehicle sales of 8.52 million units five years earlier in 2007. What 
was the growth rate in number of vehicles sold by Toyota from 2007 to 2012?
Solution:
Using Equation 14, we find
g=−
=−
=−
=− −735852 1
0 862676 1
0 970889 1
0 029111 25
5..
.
.
.  or about  ..%9
The rate of growth in vehicles sold was approximately −2.9 percent during the

2007–2012 period. Note that we can also refer to −2.9 percent as the compound 
annual growth rate because it is the single number that compounds the number 
of vehicles sold in 2007 forward to the number of vehicles sold in 2012. Table 4 
lists the number of vehicles sold operated by Toyota from 2007 to 2012.
Table 4   Number of Vehicles Sold, 2007–2012
Y earNumber of Vehicles 
Sold (Millions) (1 + g)t t
2007 8.52 0
2008 8.91 8.91/8.52 = 1.045775 1
2009 7.57 7.57/8.91 = 0.849607 2
2010 7.24 7.24/7.57 = 0.956407 3
2011 7.31 7.31/7.24 = 1.009669 4
2012 7.35 7.35/7.31 = 1.005472 5
Source:  www.toyota.com.

Solving for Rates, Number of Periods, or Size of Annuity Payments 331
Table 4 also shows 1 plus the one-  year growth rate in number of vehicles sold. 
We can compute the 1 plus five-  year cumulative growth in number of vehicles 
sold from 2007 to 2012 as the product of quantities (1 + one-  year growth rate). 
We arrive at the same result as when we divide the ending number of vehicles 
sold, 7.35 million, by the beginning number of vehicles sold, 8.52 million:
735
852891
852757
891724
757731
72.
..
..
..
..
.=





4 4735
731
11 11 1
0 8621 2345




=+() +() +() +() +().
.
.gg gg g
6 676 1 045775 0 849607 0 956407 1 009669 1 005472 =() () () () () .. .. .
The right-  hand side of the equation is the product of 1 plus the one-  year growth 
rate in number of vehicles sold for each year. Recall that, using Equation 14, we 
took the fifth root of 7.35/8.52 = 0.862676. In effect, we were solving for the 
single value of g which, when compounded over five periods, gives the correct

product of 1 plus the one-  year growth rates.8
In conclusion, we do not need to compute intermediate growth rates as in 
Table 4 to solve for a compound growth rate g. Sometimes, however, the inter -
mediate growth rates are interesting or informative. For example, at first (from 
2007 to 2008), Toyota Motors increased its number of vehicles sold. We can 
also analyze the variability in growth rates when we conduct an analysis as in 
Table 4. Most of the decline in Toyota Motor’s sales occurred in 2009. Elsewhere 
in Toyota Motor’s disclosures, the company noted that the substantial decline 
in vehicle sales in 2009 was due to the steep downturn in the global economy. 
Sales declined further in 2010 as the market conditions remained difficult. Each 
of the next two years saw a slight increase in sales.
The compound growth rate is an excellent summary measure of growth over 
multiple time periods. In our Toyota Motors example, the compound growth rate of

−2.9 percent is the single growth rate that, when added to 1, compounded over five 
years, and multiplied by the 2007 number of vehicles sold, yields the 2012 number 
of vehicles sold.
7.2 Solving for the Number of Periods
In this section, we demonstrate how to solve for the number of periods given present 
value, future value, and interest or growth rates.
EXAMPLE 19   
The Number of Annual Compounding Periods Needed for 
an Investment to Reach a Specific Value
You are interested in determining how long it will take an investment of 
€10,000,000 to double in value. The current interest rate is 7 percent compounded 
annually. How many years will it take €10,000,000 to double to €20,000,000?
8 The compound growth rate that we calculate here is an example of a geometric mean, specifically the 
geometric mean of the growth rates. We define the geometric mean in the reading on statistical concepts.

Reading 6 ■ The Time Value of Money 332
Solution:
Use Equation 2, FVN = PV(1 + r)N, to solve for the number of periods, N, as 
follows:
12
12
21
21 07+() ==
+() =()
=() +()
=() () =r
Nr
NrN
NFV PV
 lnl n
ln ln
ln ln . 1 10 24 .
With an interest rate of 7 percent, it will take approximately 10 years for the initial 
€10,000,000 investment to grow to €20,000,000. Solving for N in the expression 
(1.07)N = 2.0 requires taking the natural logarithm of both sides and using the 
rule that ln( xN) = N ln(x). Generally, we find that N = [ln(FV/PV)]/ln(1 + r). 
Here, N = ln(€20,000,000/€10,000,000)/ln(1.07) = ln(2)/ln(1.07) = 10.24.9
7.3 Solving for the Size of Annuity Payments
In this section, we discuss how to solve for annuity payments. Mortgages, auto loans, 
and retirement savings plans are classic examples of applications of annuity formulas.
EXAMPLE 20   
Calculating the Size of Payments on a Fixed-  Rate 
Mortgage
You are planning to purchase a $120,000 house by making a down payment of

$20,000 and borrowing the remainder with a 30-  year fixed-  rate mortgage with 
monthly payments. The first payment is due at t = 1. Current mortgage inter -
est rates are quoted at 8 percent with monthly compounding. What will your 
monthly mortgage payments be?
9 To quickly approximate the number of periods, practitioners sometimes use an ad hoc rule called the 
Rule of 72 : Divide 72 by the stated interest rate to get the approximate number of years it would take to 
double an investment at the interest rate. Here, the approximation gives 72/7 = 10.3 years. The Rule of 72 
is loosely based on the observation that it takes 12 years to double an amount at a 6 percent interest rate, 
giving 6 × 12 = 72. At a 3 percent rate, one would guess it would take twice as many years, 3 × 24 = 72.

Solving for Rates, Number of Periods, or Size of Annuity Payments 333
Solution:
The bank will determine the mortgage payments such that at the stated periodic 
interest rate, the present value of the payments will be equal to the amount 
borrowed (in this case, $100,000). With this fact in mind, we can use 
Equation 11,  PV =−
+()





Ar
rN11
1, to solve for the annuity amount, A, as the 
present value divided by the present value annuity factor:
PV =
==
=
==
=
=× =$,
%.
..100 000
80 08
12
008120 006667
30
12 30 3r
m
rm
N
mNs
s
6 60
11
111
10Present value annuity factor =−
+() =−
rm
rmsmN
s.0 06667
0 006667
136 283494360()
=
=.
.
A PV Pr esent value annuity  facctor
=
=$, .
$.100 000 136 283494
733 76
The amount borrowed, $100,000, is equivalent to 360 monthly payments of 
$733.76 with a stated interest rate of 8 percent. The mortgage problem is a rel -
atively straightforward application of finding a level annuity payment.
Next, we turn to a retirement-  planning problem. This problem illustrates the

complexity of the situation in which an individual wants to retire with a specified 
retirement income. Over the course of a life cycle, the individual may be able to save 
only a small amount during the early years but then may have the financial resources 
to save more during later years. Savings plans often involve uneven cash flows, a topic 
we will examine in the last part of this reading. When dealing with uneven cash flows, 
we take maximum advantage of the principle that dollar amounts indexed at the same 
point in time are additive—the cash flow additivity principle .
EXAMPLE 21   
The Projected Annuity Amount Needed to Fund a Future-  
Annuity Inflow
Jill Grant is 22 years old (at t = 0) and is planning for her retirement at age 63 
(at t = 41). She plans to save $2,000 per year for the next 15 years ( t = 1 to t = 
15). She wants to have retirement income of $100,000 per year for 20 years, 
with the first retirement payment starting at t = 41. How much must Grant save

each year from t = 16 to t = 40 in order to achieve her retirement goal? Assume 
she plans to invest in a diversified stock-  and-  bond mutual fund that will earn 
8 percent per year on average.

Reading 6 ■ The Time Value of Money 334
Solution:
To help solve this problem, we set up the information on a time line. As Figure 8 
shows, Grant will save $2,000 (an outflow) each year for Years 1 to 15. Starting 
in Year 41, Grant will start to draw retirement income of $100,000 per year for 
20 years. In the time line, the annual savings is recorded in parentheses ($2) 
to show that it is an outflow. The problem is to find the savings, recorded as X, 
from Year 16 to Year 40.
Figure 8   Solving for Missing Annuity Payments (in Thousands) 
 |  |  |       | |  |       | |    |        |
 0  1  2 15 16 17 40 41 42  6 0
    ($2)      ($2)  ... ($2)      (X)       (X)  ...  (X)$100 $100 ... $100... ... ...
Solving this problem involves satisfying the following relationship: the present 
value of savings (outflows) equals the present value of retirement income (inflows). 
We could bring all the dollar amounts to t = 40 or to t = 15 and solve for X.

Let us evaluate all dollar amounts at t = 15 (we encourage the reader to 
repeat the problem by bringing all cash flows to t = 40). As of t = 15, the first 
payment of X will be one period away (at t = 16). Thus we can value the stream 
of Xs using the formula for the present value of an ordinary annuity.
This problem involves three series of level cash flows. The basic idea is that 
the present value of the retirement income must equal the present value of 
Grant’s savings. Our strategy requires the following steps:
1 Find the future value of the savings of $2,000 per year and index it at t = 
15. This value tells us how much Grant will have saved.
2 Find the present value of the retirement income at t = 15. This value tells 
us how much Grant needs to meet her retirement goals (as of t = 15). Two 
substeps are necessary. First, calculate the present value of the annuity of 
$100,000 per year at t = 40. Use the formula for the present value of an

annuity. (Note that the present value is indexed at t = 40 because the first 
payment is at t = 41.) Next, discount the present value back to t = 15 (a 
total of 25 periods).
3 Now compute the difference between the amount Grant has saved (Step 
1) and the amount she needs to meet her retirement goals (Step 2). Her 
savings from t = 16 to t = 40 must have a present value equal to the differ -
ence between the future value of her savings and the present value of her 
retirement income.

Solving for Rates, Number of Periods, or Size of Annuity Payments 335
Our goal is to determine the amount Grant should save in each of the 25 years 
from t = 16 to t = 40. We start by bringing the $2,000 savings to t = 15, as follows:
A
r
N
Ar
rN=
==
=
=+() −


=() −$,
%.
$,.2 000
80 08
15
11
2 0001081
015FV
..
$, .
$, .08
2 000 27 152114
54 304 23


= ()
=
At t = 15, Grant’s initial savings will have grown to $54,304.23.
Now we need to know the value of Grant’s retirement income at t = 15. As 
stated earlier, computing the retirement present value requires two substeps. 
First, find the present value at t = 40 with the formula in Equation 11; second, 
discount this present value back to t = 15. Now we can find the retirement 
income present value at t = 40:
A
r
N
Ar
rN=
==
=
=−
+()






=−$,
%.
$,100 000
80 08
20
11
1
100 0001PV
1 1
108
008
100 000 9 818147
981 814 7420.
.
$, .
$, .()






= ()
=
The present value amount is as of t = 40, so we must now discount it back as a 
lump sum to t = 15:
FV
PV FVN
NNN
r
r=
=
==
=+ ()
= (−$, .

FV
PV FVN
NNN
r
r=
=
==
=+ ()
= (−$, .
%.
$, ..981 814 74
25
80 08
1
981 814 74 108) )
= ()
=−25
981 814 74 0 146018
143 362 53$, ..
$, .
Now recall that Grant will have saved $54,304.23 by t = 15. Therefore, in 
present value terms, the annuity from t = 16 to t = 40 must equal the difference 
between the amount already saved ($54,304.23) and the amount required for 
retirement ($143,362.53). This amount is equal to $143,362.53 − $54,304.23 =

Reading 6 ■ The Time Value of Money 336
$89,058.30. Therefore, we must now find the annuity payment, A, from t = 16 
to t = 40 that has a present value of $89,058.30. We find the annuity payment 
PV
Present value annuity factor=
==
=
=−$, .
%.89 058 30
80 08
25
11r
N
1 1
11
108
008
10 67477625+()






=−
()






=
=r
r
AN
.
.
.
PV PPresent value annuity factor
=
=$, ..
$, .89 058 30 10 674776
8 342 87 7
Grant will need to increase her savings to $8,342.87 per year from t = 16 to t 
= 40 to meet her retirement goal of having a fund equal to $981,814.74 after 
making her last payment at t = 40.
7.4 Review of Present and Future Value Equivalence
As we have demonstrated, finding present and future values involves moving amounts 
of money to different points on a time line. These operations are possible because 
present value and future value are equivalent measures separated in time. Table 5 
illustrates this equivalence; it lists the timing of five cash flows, their present values

at t = 0, and their future values at t = 5.
To interpret Table 5, start with the third column, which shows the present values. 
Note that each $1,000 cash payment is discounted back the appropriate number of 
periods to find the present value at t = 0. The present value of $4,329.48 is exactly 
equivalent to the series of cash flows. This information illustrates an important point: 
A lump sum can actually generate an annuity. If we place a lump sum in an account 
that earns the stated interest rate for all periods, we can generate an annuity that is 
equivalent to the lump sum. Amortized loans, such as mortgages and car loans, are 
examples of this principle.
Table 5   The Equivalence of Present and Future Values
Time Cash Flow ($) Present Value at t = 0 Future Value at t = 5
1 1,000 $1,000(1.05)−1= $952.38 $1,000(1.05)4= $1,215.51
2 1,000 $1,000(1.05)−2= $907.03 $1,000(1.05)3= $1,157.63
3 1,000 $1,000(1.05)−3= $863.84 $1,000(1.05)2= $1,102.50

4 1,000 $1,000(1.05)−4= $822.70 $1,000(1.05)1= $1,050.00
5 1,000 $1,000(1.05)−5= $783.53 $1,000(1.05)0= $1,000.00
Sum: $4,329.48 Sum: $5,525.64

Solving for Rates, Number of Periods, or Size of Annuity Payments 337
To see how a lump sum can fund an annuity, assume that we place $4,329.48 in the 
bank today at 5 percent interest. We can calculate the size of the annuity payments 
by using Equation 11. Solving for A, we find
A
r
rN=
−+ ()


=
− ()


=PV
11 1
4 329 48
11 105
005
1 0005$, .
.
.
$,
Table 6 shows how the initial investment of $4,329.48 can actually generate five $1,000 
withdrawals over the next five years.
To interpret Table 6, start with an initial present value of $4,329.48 at t = 0. From 
t = 0 to t = 1, the initial investment earns 5 percent interest, generating a future value 
of $4,329.48(1.05) = $4,545.95. We then withdraw $1,000 from our account, leaving 
$4,545.95 − $1,000 = $3,545.95 (the figure reported in the last column for time period 
1). In the next period, we earn one year’s worth of interest and then make a $1,000 
withdrawal. After the fourth withdrawal, we have $952.38, which earns 5 percent.

This amount then grows to $1,000 during the year, just enough for us to make the 
last withdrawal. Thus the initial present value, when invested at 5 percent for five 
years, generates the $1,000 five-  year ordinary annuity. The present value of the initial 
investment is exactly equivalent to the annuity.
Now we can look at how future value relates to annuities. In Table 5, we reported 
that the future value of the annuity was $5,525.64. We arrived at this figure by com -
pounding the first $1,000 payment forward four periods, the second $1,000 forward 
three periods, and so on. We then added the five future amounts at t = 5. The annuity 
is equivalent to $5,525.64 at t = 5 and $4,329.48 at t = 0. These two dollar measures 
are thus equivalent. We can verify the equivalence by finding the present value of 
$5,525.64, which is $5,525.64 × (1.05)−5 = $4,329.48. We found this result above when 
we showed that a lump sum can generate an annuity.

Table 6   How an Initial Present Value Funds an Annuity
Time 
PeriodAmount Available  
at the Beginning of  
the Time Period ($) Ending Amount before Withdrawal Withdrawal ($)Amount Available 
after Withdrawal ($)
1 4,329.48 $4,329.48(1.05) = $4,545.95 1,000 3,545.95
2 3,545.95 $3,545.95(1.05) = $3,723.25 1,000 2,723.25
3 2,723.25 $2,723.25(1.05) = $2,859.41 1,000 1,859.41
4 1,859.41 $1,859.41(1.05) = $1,952.38 1,000 952.38
5 952.38 $952.38(1.05) = $1,000 1,000 0
To summarize what we have learned so far: A lump sum can be seen as equivalent 
to an annuity, and an annuity can be seen as equivalent to its future value. Thus present 
values, future values, and a series of cash flows can all be considered equivalent as 
long as they are indexed at the same point in time.

Reading 6 ■ The Time Value of Money 338
7.5 The Cash Flow Additivity Principle
The cash flow additivity principle—the idea that amounts of money indexed at the 
same point in time are additive—is one of the most important concepts in time value of 
money mathematics. We have already mentioned and used this principle; this section 
provides a reference example for it.
Consider the two series of cash flows shown on the time line in Figure 9. The series 
are denoted A and B. If we assume that the annual interest rate is 2 percent, we can 
find the future value of each series of cash flows as follows. Series A’s future value is 
$100(1.02) + $100 = $202. Series B’s future value is $200(1.02) + $200 = $404. The 
future value of (A + B) is $202 + $404 = $606 by the method we have used up to this 
point. The alternative way to find the future value is to add the cash flows of each 
series, A and B (call it A + B), and then find the future value of the combined cash 
flow, as shown in Figure 9.

The third time line in Figure 9 shows the combined series of cash flows. Series 
A has a cash flow of $100 at t = 1, and Series B has a cash flow of $200 at t = 1. The 
combined series thus has a cash flow of $300 at t = 1. We can similarly calculate the 
cash flow of the combined series at t = 2. The future value of the combined series 
(A + B) is $300(1.02) + $300 = $606—the same result we found when we added the 
future values of each series.
The additivity and equivalence principles also appear in another common situa -
tion. Suppose cash flows are $4 at the end of the first year and $24 (actually separate 
payments of $4 and $20) at the end of the second year. Rather than finding present 
values of the first year’s $4 and the second year’s $24, we can treat this situation as a 
$4 annuity for two years and a second-  year $20 lump sum. If the discount rate were 
6 percent, the $4 annuity would have a present value of $7.33 and the $20 lump sum

a present value of $17.80, for a total of $25.13.
Figure 9   The Additivity of Two Series of Cash Flows
t = 0 t = 1 t = 2
A
$100 $100
t = 0 t = 1 t = 2
B
$200 $200
t = 0 t = 1 t = 2
A + B
$300 $300

Summary 339
SUMMARY
In this reading, we have explored a foundation topic in investment mathematics, the 
time value of money. We have developed and reviewed the following concepts for use 
in financial applications:
■■The interest rate, r, is the required rate of return; r is also called the discount 
rate or opportunity cost.
■■An interest rate can be viewed as the sum of the real risk-  free interest rate and 
a set of premiums that compensate lenders for risk: an inflation premium, a 
default risk premium, a liquidity premium, and a maturity premium.
■■The future value, FV, is the present value, PV, times the future value factor, (1 + 
r)N.
■■The interest rate, r, makes current and future currency amounts equivalent 
based on their time value.
■■The stated annual interest rate is a quoted interest rate that does not account 
for compounding within the year.
■■The periodic rate is the quoted interest rate per period; it equals the stated

annual interest rate divided by the number of compounding periods per year.
■■The effective annual rate is the amount by which a unit of currency will grow in 
a year with interest on interest included.
■■An annuity is a finite set of level sequential cash flows.
■■There are two types of annuities, the annuity due and the ordinary annuity. The 
annuity due has a first cash flow that occurs immediately; the ordinary annuity 
has a first cash flow that occurs one period from the present (indexed at t = 1).
■■On a time line, we can index the present as 0 and then display equally spaced 
hash marks to represent a number of periods into the future. This representa -
tion allows us to index how many periods away each cash flow will be paid.
■■Annuities may be handled in a similar fashion as single payments if we use 
annuity factors instead of single-  payment factors.
■■The present value, PV, is the future value, FV, times the present value factor, 
(1 + r)−N.

(1 + r)−N.
■■The present value of a perpetuity is A/r, where A is the periodic payment to be 
received forever.
■■It is possible to calculate an unknown variable, given the other relevant vari -
ables in time value of money problems.
■■The cash flow additivity principle can be used to solve problems with uneven 
cash flows by combining single payments and annuities.

Reading 6 ■ The Time Value of Money 340
1 The table below gives current information on the interest rates for two two-  
year and two eight-  year maturity investments. The table also gives the matu -
rity, liquidity, and default risk characteristics of a new investment possibility 
(Investment 3). All investments promise only a single payment (a payment at 
maturity). Assume that premiums relating to inflation, liquidity, and default risk 
are constant across all time horizons.
Investment Maturity (in Y ears) Liquidity Default Risk Interest Rate (%)
1 2 High Low 2.0
2 2 Low Low 2.5
3 7 Low Low r3
4 8 High Low 4.0
5 8 Low High 6.5
 Based on the information in the above table, address the following:
A Explain the difference between the interest rates on Investment 1 and 
Investment 2.
B Estimate the default risk premium.
C Calculate upper and lower limits for the interest rate on Investment 3, r3.
2 A couple plans to set aside $20,000 per year in a conservative portfolio pro -

jected to earn 7 percent a year. If they make their first savings contribution one 
year from now, how much will they have at the end of 20 years?
3 Two years from now, a client will receive the first of three annual payments of 
$20,000 from a small business project. If she can earn 9 percent annually on her 
investments and plans to retire in six years, how much will the three business 
project payments be worth at the time of her retirement?
4 To cover the first year’s total college tuition payments for his two children, a 
father will make a $75,000 payment five years from now. How much will he 
need to invest today to meet his first tuition goal if the investment earns 6 per -
cent annually?
5 A client can choose between receiving 10 annual $100,000 retirement pay -
ments, starting one year from today, or receiving a lump sum today. Knowing 
that he can invest at a rate of 5 percent annually, he has decided to take the 
lump sum. What lump sum today will be equivalent to the future annual

payments?
6 You are considering investing in two different instruments. The first instrument 
will pay nothing for three years, but then it will pay $20,000 per year for four 
years. The second instrument will pay $20,000 for three years and $30,000 in 
the fourth year. All payments are made at year-  end. If your required rate of 
return on these investments is 8 percent annually, what should you be willing to 
pay for:
A The first instrument?
B The second instrument (use the formula for a four-  year annuity)?

7 Suppose you plan to send your daughter to college in three years. You expect 
her to earn two-  thirds of her tuition payment in scholarship money, so you 
estimate that your payments will be $10,000 a year for four years. To estimate 
whether you have set aside enough money, you ignore possible inflation in 
tuition payments and assume that you can earn 8 percent annually on your 
investments. How much should you set aside now to cover these payments?
8 A client plans to send a child to college for four years starting 18 years from 
now. Having set aside money for tuition, she decides to plan for room and 
board also. She estimates these costs at $20,000 per year, payable at the begin -
ning of each year, by the time her child goes to college. If she starts next year 
and makes 17 payments into a savings account paying 5 percent annually, what 
annual payments must she make?
9 A couple plans to pay their child’s college tuition for 4 years starting 18 years

from now. The current annual cost of college is C$7,000, and they expect this 
cost to rise at an annual rate of 5 percent. In their planning, they assume that 
they can earn 6 percent annually. How much must they put aside each year, 
starting next year, if they plan to make 17 equal payments?
10 The nominal risk-  free rate is best described as the sum of the real risk-  free rate 
and a premium for:
C expected inflation.
11 Which of the following risk premiums is most relevant in explaining the differ -
ence in yields between 30-  year bonds issued by the US Treasury and 30-  year 
bonds issued by a small private issuer?
A Inflation
B Maturity
C Liquidity
12 A bank quotes a stated annual interest rate of 4.00%. If that rate is equal to an 
effective annual rate of 4.08%, then the bank is compounding interest:
A daily.
B quarterly.
C semiannually.
13 The value in six years of $75,000 invested today at a stated annual interest rate 
of 7% compounded quarterly is closest to:

A $112,555.
B $113,330.
C $113,733.
14 A client requires £100,000 one year from now. If the stated annual rate is 2.50% 
compounded weekly, the deposit needed today is closest  to:
A £97,500.
B £97,532.
C £97,561.
15 For a lump sum investment of ¥250,000 invested at a stated annual rate of 
3% compounded daily, the number of months needed to grow the sum to 
¥1,000,000 is closest  to:
A 555.
B 563.

Reading 6 ■ The Time Value of Money 342
C 576.
16 Given a €1,000,000 investment for four years with a stated annual rate of 3% 
compounded continuously, the difference in its interest earnings compared with 
the same investment compounded daily is closest to:
A €1.
B €6.
C €455.
17 An investment pays €300 annually for five years, with the first payment occur -
ring today. The present value (PV) of the investment discounted at a 4% annual 
rate is closest to:
A €1,336.
B €1,389.
C €1,625.
18 A perpetual preferred stock makes its first quarterly dividend payment of $2.00 
in five quarters. If the required annual rate of return is 6% compounded quar -
terly, the stock’s present value is closest to:
A $31.
B $126.
C $133.
19 A saver deposits the following amounts in an account paying a stated annual 
rate of 4%, compounded semiannually:
Y ear End of Y ear Deposits ($)
1 4,000
2 8,000
3 7,000
4 10,000
 At the end of Year 4, the value of the account is closest to:
A $30,432
B $30,447
C $31,677

A $30,432
B $30,447
C $31,677
20 An investment of €500,000 today that grows to €800,000 after six years has a 
stated annual interest rate closest to:
A 7.5% compounded continuously.
B 7.7% compounded daily.
C 8.0% compounded semiannually.
21 A sweepstakes winner may select either a perpetuity of £2,000 a month begin -
ning with the first payment in one month or an immediate lump sum payment 
of £350,000. If the annual discount rate is 6% compounded monthly, the present 
value of the perpetuity is:
A less than the lump sum.
B equal to the lump sum.
C greater than the lump sum.
22 At a 5% interest rate per year compounded annually, the present value (PV) of a 
10- year ordinary annuity with annual payments of $2,000 is $15,443.47. The PV 
of a 10-  year annuity due with the same interest rate and payments is closest to:

Practice Problems 343
A $14,708.
B $16,216.
C $17,443.
23 Grandparents are funding a newborn’s future university tuition costs, estimated 
at $50,000/year for four years, with the first payment due as a lump sum in 18 
years. Assuming a 6% effective annual rate, the required deposit today is closest 
to:
A $60,699.
B $64,341.
C $68,201.
24 The present value (PV) of an investment with the following year-  end cash flows 
(CF) and a 12% required annual rate of return is closest to:
Y ear Cash Flow (€)
1 100,000
2 150,000
5 –10,000
A €201,747.
B €203,191.
C €227,573.
25 A sports car, purchased for £200,000, is financed for five years at an annual 
rate of 6% compounded monthly. If the first payment is due in one month, the 
monthly payment is closest to:
A £3,847.
B £3,867.
C £3,957.
26 Given a stated annual interest rate of 6% compounded quarterly, the level 
amount that, deposited quarterly, will grow to £25,000 at the end of 10 years is 
closest to:
A £461.
B £474.
C £836.

A £461.
B £474.
C £836.
27 Given the following timeline and a discount rate of 4% a year compounded 
annually, the present value (PV), as of the end of Year 5 (PV5 ), of the cash flow 
received at the end of Year 20 is closest to:
0 1 2 3 45
PV520 ...
$50,000
A $22,819.
B $27,763.
C $28,873.
28 A client invests €20,000 in a four-  year certificate of deposit (CD) that annu -
ally pays interest of 3.5%. The annual CD interest payments are automatically 
reinvested in a separate savings account at a stated annual interest rate of 2% 
compounded monthly. At maturity, the value of the combined asset is closest  to:
A €21,670.

SOLUTIONS
1 A Investment 2 is identical to Investment 1 except that Investment 2 has low 
liquidity. The difference between the interest rate on Investment 2 and 
Investment 1 is 0.5 percentage point. This amount represents the liquidity 
premium, which represents compensation for the risk of loss relative to 
an investment’s fair value if the investment needs to be converted to cash 
quickly.
B To estimate the default risk premium, find the two investments that have the 
same maturity but different levels of default risk. Both Investments 4 and 5 
have a maturity of eight years. Investment 5, however, has low liquidity and 
thus bears a liquidity premium. The difference between the interest rates 
of Investments 5 and 4 is 2.5 percentage points. The liquidity premium is 
0.5 percentage point (from Part A). This leaves 2.5 − 0.5 = 2.0 percentage 
points that must represent a default risk premium reflecting Investment 5’s 
high default risk.

C Investment 3 has liquidity risk and default risk comparable to Investment 
2, but with its longer time to maturity, Investment 3 should have a higher 
maturity premium. The interest rate on Investment 3, r3, should thus be 
above 2.5 percent (the interest rate on Investment 2). If the liquidity of 
Investment 3 were high, Investment 3 would match Investment 4 except for 
Investment 3’s shorter maturity. We would then conclude that Investment 
3’s interest rate should be less than the interest rate on Investment 4, which 
is 4 percent. In contrast to Investment 4, however, Investment 3 has low 
liquidity. It is possible that the interest rate on Investment 3 exceeds that of 
Investment 4 despite 3’s shorter maturity, depending on the relative size of 
the liquidity and maturity premiums. However, we expect r3 to be less than 
4.5 percent, the expected interest rate on Investment 4 if it had low liquidity. 
Thus 2.5 percent < r3 < 4.5 percent.
 2 i. Draw a time line.
0 1 2 19 20

2 i. Draw a time line.
0 1 2 19 20
$20,000 $20,000 $20,000 $20,000
X=FV
 ii. Identify the problem as the future value of an annuity.
 iii. Use the formula for the future value of an annuity.
FVNN
Ar
r=+() −


=+() −


=11
20 00010 07 1
007
819 9020
$,.
.
$, 9985 .
20 19 0 1 2
FV= $819,909.85
 iv. Alternatively, use a financial calculator.

Reading 6 ■ The Time Value of Money 346
Notation Used  
on Most Calculators Numerical Value  
for This Problem
N 20
%i 7
PV n/a (= 0)
FV compute X
PMT $20,000
 Enter 20 for N, the number of periods. Enter 7 for the interest rate and 
20,000 for the payment size. The present value is not needed, so enter 0. 
Calculate the future value. Verify that you get $819,909.85 to make sure you 
have mastered your calculator’s keystrokes.
 In summary, if the couple sets aside $20,000 each year (starting next year), 
they will have $819,909.85 in 20 years if they earn 7 percent annually.
 3 i. Draw a time line.
6 5 4 3 2 1 0
$20,000 $20,000 $20,000 X=FV
 ii. Recognize the problem as the future value of a delayed annuity. Delaying the 
payments requires two calculations.
 iii. Use the formula for the future value of an annuity (Equation 7).
FVNN
Ar
r=+() −

11
 to bring the three $20,000 payments to an equivalent lump sum of 
$65,562.00 four years from today.
on Most Calculators Numerical Value

N 3
%i 9
PV n/a (= 0)
 iv. Use the formula for the future value of a lump sum (Equation 2), FVN = 
PV(1 + r)N, to bring the single lump sum of $65,562.00 to an equivalent 
lump sum of $77,894.21 six years from today.
N 2
%i 9
PV $65,562.00
PMT n/a (= 0)

Solutions 347
6 5 4 3 2 1 0
$20,000 $20,000
$65,562.00 $77,894.21$20,000
FVFV
FV 6 4X
 In summary, your client will have $77,894.21 in six years if she receives 
three yearly payments of $20,000 starting in Year 2 and can earn 9 percent 
annually on her investments.
 4 i. Draw a time line.
5 4 3 2 1 0
X
PV FV$75,000
 ii. Identify the problem as the present value of a lump sum.
 iii. Use the formula for the present value of a lump sum.
PV FV=+ ()
=+ ()
=−
−NNr1
75 000 10 06
56 044 365$, .
$, .
5 4 3 2 1 0
$56,044.36 $75,000
PV FV
 In summary, the father will need to invest $56,044.36 today in order to have 
$75,000 in five years if his investments earn 6 percent annually.
 5 i. Draw a time line for the 10 annual payments.
X
PV2 9 10 1 0
$100,000 $100,000 $100,000 $100,000
 ii. Identify the problem as the present value of an annuity.
 iii. Use the formula for the present value of an annuity.
PV =−
+()






=−
+()



Ar
rN11
1
100 00011
10 05
00510
$,.
. 

=$772,173.49
10 9 2 1 0
X $100,000 $100,000 $100,000 $100,00 0

10 9 2 1 0
PV=$772,173.49

Reading 6 ■ The Time Value of Money 348
N 10
%i 5
FV n/a (= 0)
PMT $100,000
 In summary, the present value of 10 payments of $100,000 is $772,173.49 
if the first payment is received in one year and the rate is 5 percent com -
pounded annually. Your client should accept no less than this amount for his 
lump sum payment.
6 A To evaluate the first instrument, take the following steps:
 i. Draw a time line.
0 1 2 5 4 3 6 7
 ii. 
PV3=−
+()






=−
+()




Ar
rN11
1
20 00011
10 08
0084
$,.
.  
=$66,242.54
 iii. 
PVPV
0=
+()==3
31 10852 585 46
rN$66,242.54$
.,.
 You should be willing to pay $52,585.46 for this instrument.
B To evaluate the second instrument, take the following steps:
4 3 2 1 0
$30,000+10,000
 The time line shows that this instrument can be analyzed as an ordinary 
annuity of $20,000 with four payments (valued in Step ii below) and a

$10,000 payment to be received at t = 4 (valued in Step iii below).

Solutions 349
 ii. 
PV =−
+()






=−
+()





Ar
rN11
1
20 00011
10 08
0084
$,.
.
= =$66,242.54
 iii. 
PVFV=
+()=
+()=4
411 0087 350 30
rN$10,000$
.,.
 iv. Total = $66,242.54 + $7,350.30 = $73,592.84
 You should be willing to pay $73,592.84 for this instrument.
 7 i. Draw a time line.
4 5 6 3 2 1 0
$10,000 $10,000 $10,000 $10,000 X
PV
 ii. Recognize the problem as a delayed annuity. Delaying the payments requires 
two calculations.
 iii. Use the formula for the present value of an annuity (Equation 11).
PV =−
+()





Ar
rN11
1
 to bring the four payments of $10,000 back to a single equivalent lump sum 
of $33,121.27 at t = 2. Note that we use t = 2 because the first annuity pay -
ment is then one period away, giving an ordinary annuity.
N 4
%i 8
PMT $10,000
 iv. Then use the formula for the present value of a lump sum (Equation 8), PV 
= FVN(1 + r)−N, to bring back the single payment of $33,121.27 (at t = 2) to

an equivalent single payment of $28,396.15 (at t = 0).
N 2
%i 8
FV $33,121.27

Reading 6 ■ The Time Value of Money 350
0 1 2 3 45 6
PV
$28,396.15 $33,121.27
Equation Equation 8 11
 In summary, you should set aside $28,396.15 today to cover four payments 
of $10,000 starting in three years if your investments earn a rate of 8 percent 
annually.
 8 i. Draw a time line.
0 1 2 17
X18 19 20 21
$20,000 $20,000 $20,000 $20,000 (   ) X(   ) X(   )
 ii. Recognize that you need to equate the values of two annuities.
 iii. Equate the value of the four $20,000 payments to a single payment in Period 
17 using the formula for the present value of an annuity (Equation 11), with 
r = 0.05. The present value of the college costs as of t = 17 is $70,919.
PV =−
()









= $20,000 $11
105
00570 9194.
.,
N 4
%i 5
FV n/a (= 0)
 iv. Equate the value of the 17 investments of X to the amount calculated in Step

iii, college costs as of t = 17, using the formula for the future value of an 
annuity (Equation 7). Then solve for X.
$70,919 =() −

=
=1051
00525 840366
2 744 5017.
..
$, .X
X
N 17
%i 5
PV n/a (= 0)
FV $70,919
PMT compute X

Solutions 351
0 1 2 17
X18 19 20 21
$20,000
$70,919$70,919$20,000 $20,000 $20,000 X(   ) X(   ) X(   )
Equation 7Equation 11
25.8404
=
 In summary, your client will have to save $2,744.50 each year if she starts 
next year and makes 17 payments into a savings account paying 5 percent 
annually.
 9 i. Draw a time line.
0 1 2 17 18 19 20 21
C$7,000 Year 1 Year 2 Year 3 Year 4
payment payment payment paymen t
 ii. Recognize that the payments in Years 18, 19, 20, and 21 are the future values 
of a lump sum of C$7,000 in Year 0.
 iii. With r = 5%, use the formula for the future value of a lump sum 
(Equation 2), FVN = PV (1 + r)N, four times to find the payments. These 
future values are shown on the time line below.
Equation 20 1 2 17 18 19 20 21
C$7,000
C$17,689
C$18,573
C$19,502C$16,846Year 1 Year 2 Year 3 Year 4
payment payment payment payment
 iv. Using the formula for the present value of a lump sum ( r = 6%), equate the 
four college payments to single payments as of t = 17 and add them together.

C$16,846(1.06)−1 + C$17,689(1.06)−2 + C$18,573(1.06)−3 + C$19,502(1.06)−4 
= C$62,677
 v. Equate the sum of C$62,677 at t = 17 to the 17 payments of X, using the 
formula for the future value of an annuity (Equation 7). Then solve for X.
C
C$62,677
$=() −

=
=XX
X1061
00628 21288
2 221 5817.
..
,.
N 17
%i 6
PV n/a (= 0)
FV C$62,677

Reading 6 ■ The Time Value of Money 352
0 1 2 17
X18 19 20 21
C$62,677X(   ) X(   ) X(   )
Equation 728.21288
=
 In summary, the couple will need to put aside C$2,221.58 each year if they 
start next year and make 17 equal payments.
10 C is correct. The sum of the real risk-  free interest rate and the inflation pre -
mium is the nominal risk-  free rate.
11 C is correct. US Treasury bonds are highly liquid, whereas the bonds of small 
issuers trade infrequently and the interest rate includes a liquidity premium. 
This liquidity premium reflects the relatively high costs (including the impact 
on price) of selling a position.
12 A is correct. The effective annual rate (EAR) when compounded daily is 4.08%.
EAR = (1 + Periodic interest rate)m – 1  
EAR = (1 + 0.04/365)365 – 1  
EAR = (1.0408) – 1 = 0.04081 ≈ 4.08%.
13 C is correct, as shown in the following (where FV is future value and PV is pres -
ent value):
FV PV=+

1r
msmN
FV646
75 000 1007
4=+

×()
$,.
FV6 = $113,733.21.

FV646
75 000 1007
4=+

×()
$,.
14 B is correct because £97,531 represents the present value (PV) of £100,000 
received one year from today when today’s deposit earns a stated annual rate 
of 2.50% and interest compounds weekly, as shown in the following equation 
(where FV is future value):
PV FV=+

−
NsmNr
m1
PV =+

−
£100 000 10 025
5252
,.
PV = £97,531.58.
15 A is correct. The effective annual rate (EAR) is calculated as follows:
EAR = (1 + 0.03/365)365 – 1  
EAR= (1.03045) – 1 = 0.030453 ≈ 3.0453%.

Solutions 353
 Solving for N on a financial calculator results in (where FV is future value and 
PV is present value):
(1 + 0.030453)N = FVN/PV = ¥1,000,000/¥250,000
= 46.21 years, which multiplied by 12 to convert to months results in 554.5, 
or ≈ 555 months.
16 B is correct. The difference between continuous compounding and daily com -
pounding is
€127,496.85 – €127,491.29 = €5.56, or ≈ €6, as shown in the following 
calculations.
 With continuous compounding, the investment earns (where PV is present 
value)
 PV PVerNs−  = €1,000,000 e0.03(4) – €1,000,000
  = €1,127,496.85 – €1,000,000
  = €127,496.85
 With daily compounding, the investment earns:
€1,000,000(1 + 0.03/365)365(4) – €1,000,000 = €1,127,491.29 – €1,000,000 = 
€127,491.29.
17 B is correct, as shown in the following calculation for an annuity (A) due:
PV =−
+()









+() Ar
rrN11
11
 where A = €300, r = 0.04, and N = 5.
PV =−
+()









() ¬30011
10 4
041045.
..
PV = €1,388.97, or ≈ €1,389.

10 4
041045.
..
18 B is correct. The value of the perpetuity one year from now is calculated as:
 PV = A/ r, where PV is present value, A is annuity, and r is expressed as a quar -
terly required rate of return because the payments are quarterly.
PV = $2.00/(0.06/4)
PV = $133.33.
 The value today is (where FV is future value)
PV = FVN(1 + r)–N
PV = $133.33(1 + 0.015)–4
PV = $125.62 ≈ $126.

Reading 6 ■ The Time Value of Money 354
19 B is correct. To solve for the future value of unequal cash flows, compute the 
future value of each payment as of Year 4 at the semiannual rate of 2%, and then 
sum the individual future values, as follows:
Y ear End of Y ear Deposits ($) Factor Future Value ($)
1 4,000 (1.02)64,504.65
2 8,000 (1.02)48,659.46
3 7,000 (1.02)27,282.80
4 10,000 (1.02)010,000.00
Sum = 30,446.91
20 C is correct, as shown in the following (where FV is future value and PV is pres -
 If:
FV PVNsmNr
m=+

1
 Then:
FV
PVNmN sr
m

−=1
1
800 000
500 000121
26 ,
,

 −=× rs
rs = 0.07988 (rounded to 8.0%).
21 C is correct. As shown below, the present value (PV) of a £2,000 per month 
perpetuity is worth approximately £400,000 at a 6% annual rate compounded 
monthly. Thus, the present value of the annuity (A) is worth more than the 
lump sum offer.
A = £2,000
r = (6%/12) = 0.005
PV = (A/ r)
PV = (£2,000/0.005)
PV = £400,000
22 B is correct.

 The present value of a 10-  year annuity (A) due with payments of $2,000 at a 5% 
discount rate is calculated as follows:
PV =−
+()









+ Ar
rN11
12 000$,

Solutions 355
PV =−
+()









+ $,.
.$, 2 00011
10 05
0052 0009
PV = $16,215.64.
 Alternatively, the PV of a 10-  year annuity due is simply the PV of the ordinary 
annuity multiplied by 1.05:
PV = $15,443.47 × 1.05
23 B is correct. First, find the present value (PV) of an ordinary annuity in Year 17 
that represents the tuition costs:
$,.
.50 00011
10 06
0064−
+()










= $50,000 × 3.4651
= $173,255.28.
 Then, find the PV of the annuity in today’s dollars (where FV is future value):
PVFV
01710 06=
+() .
PV017173 255 28
10 06=
+()$, .
.
PV0 = $64,340.85 ≈ $64,341.
24 B is correct, as shown in the following table.
Y earCash Flow  
(€)Formula  
CF × (1 + r)tPV at  
Y ear 0
1 100,000 100,000(1.12)–1 = 89,285.71
2 150,000 150,000(1.12)–2 = 119,579.08
5 –10,000 –10,000(1.12)–5 = –5,674.27
203,190.52

Reading 6 ■ The Time Value of Money 356
25 B is correct, calculated as follows (where A is annuity and PV is present value):
AP V of annuity =()−
+()










=()11
1
200 0001rm
rmsmN
s
£,− −
+()










()−
+()()1
1
200 00011
10 06 12
012 5rm
rmsmN
s
£,.
..
,.
,.06 12
200 000 51 72556
3 866 56










=()
=£
£
26 A is correct. To solve for an annuity (A) payment, when the future value (FV), 
interest rate, and number of periods is known, use the following equation:
FV A=+

 −









11r
m
r
msmN
£25 0001006
41
006
4410
,.
.=+

 −









×
A
A = £460.68
27 B is correct. The PV in Year 5 of a $50,000 lump sum paid in Year 20 is 
$27,763.23 (where FV is future value):
PV = $50,000(1 + 0.04)–15
PV = $27,763.23
28 B is correct, as the following cash flows show:
€20,000 initial deposit
€700 €700 €700 €700annual
interest payments
(which earn 2.0%/year)
+
€20,000 (return of principal)
 The four annual interest payments are based on the CD’s 3.5% annual rate.

Solutions 357
 The first payment grows at 2.0% compounded monthly for three years (where 
FV is future value):
FVN=+

×
¬700 1002
12312.
FVN = 743.25
 The second payment grows at 2.0% compounded monthly for two years:
FVN=+

×
¬700 1002
12212.
FVN = 728.54
 The third payment grows at 2.0% compounded monthly for one year:
FVN=+

×
¬700 1002
12112.
FVN = 714.13
 The fourth payment is paid at the end of Year 4. Its future value is €700.
 The sum of all future value payments is as follows:
€20,000.00 CD
€743.25 First payment’s FV 
€728.54 Second payment’s FV
€714.13 Third payment’s FV
€700.00 Fourth payment’s FV
€22,885.92 Total FV

Discounted Cash Flow Applications
at CFA Institute (USA). David E. Runkle, PhD, CFA, is at Trilogy Global Advisors (USA).
a. calculate and interpret the net present value (NPV) and the 
internal rate of return (IRR) of an investment;
b. contrast the NPV rule to the IRR rule, and identify problems 
associated with the IRR rule;
c. calculate and interpret a holding period return (total return);
d. calculate and compare the money-  weighted and time-  weighted 
rates of return of a portfolio and evaluate the performance of 
portfolios based on these measures;
e. calculate and interpret the bank discount yield, holding period

yield, effective annual yield, and money market yield for US 
Treasury bills and other money market instruments;
f. convert among holding period yields, money market yields, 
effective annual yields, and bond equivalent yields.
As investment analysts, much of our work includes evaluating transactions involving 
present and future cash flows. In the reading on the time value of money (TVM), we 
presented the mathematics needed to solve those problems and illustrated the tech -
niques for the major problem types. In this reading we turn to applications. Analysts 
must master the numerous applications of TVM or discounted cash flow analysis 
in equity, fixed income, and derivatives analysis as they study each of those topics 
individually. In this reading, we present a selection of important TVM applications: 
net present value and internal rate of return as tools for evaluating cash flow streams, 1rEAdING
7

Reading 7 ■ Discounted Cash Flow Applications 360
portfolio return measurement, and the calculation of money market yields. Important 
in themselves, these applications also introduce concepts that reappear in many other 
investment contexts.
The reading is organized as follows. Section 2 introduces two key TVM concepts, 
net present value and internal rate of return. Building on these concepts, Section 3 
discusses a key topic in investment management, portfolio return measurement. 
Investment managers often face the task of investing funds for the short term; to 
understand the choices available, they need to understand the calculation of money 
market yields. The reading thus concludes with a discussion of that topic in Section 4.
NET PRESENT VALUE AND INTERNAL RATE OF 
RETURN
In applying discounted cash flow analysis in all fields of finance, we repeatedly encounter 
two concepts, net present value and internal rate of return. In the following sections 
we present these keystone concepts.

We could explore the concepts of net present value and internal rate of return in 
many contexts, because their scope of application covers all areas of finance. Capital 
budgeting, however, can serve as a representative starting point. Capital budgeting 
is important not only in corporate finance but also in security analysis, because both 
equity and fixed income analysts must be able to assess how well managers are investing 
the assets of their companies. There are three chief areas of financial decision-  making 
in most businesses. Capital budgeting  is the allocation of funds to relatively long-  
range projects or investments. From the perspective of capital budgeting, a company 
is a portfolio of projects and investments. Capital structure  is the choice of long-  term 
financing for the investments the company wants to make. Working capital man -
agement  is the management of the company’s short-  term assets (such as inventory)

and short-  term liabilities (such as money owed to suppliers).
2.1 Net Present Value and the Net Present Value Rule
Net present value (NPV) describes a way to characterize the value of an investment, 
and the net present value rule is a method for choosing among alternative investments. 
The net present value  of an investment is the present value of its cash inflows minus 
the present value of its cash outflows. The word “net” in net present value refers to 
subtracting the present value of the investment’s outflows (costs) from the present 
value of its inflows (benefits) to arrive at the net benefit.
The steps in computing NPV and applying the NPV rule are as follows:
1 Identify all cash flows associated with the investment—all inflows and 
outflows.12
1 In developing cash flow estimates, we observe two principles. First, we include only the incremental 
cash flows  resulting from undertaking the project; we do not include sunk costs (costs that have been

committed prior to the project). Second, we account for tax effects by using after-  tax cash flows. For a full 
discussion of these and other issues in capital budgeting, see Brealey, Myers, and Allen (2017).

Net Present Value and Internal Rate of Return 361
2 Determine the appropriate discount rate or opportunity cost, r, for the invest -
ment project.2
3 Using that discount rate, find the present value of each cash flow. (Inflows have 
a positive sign and increase NPV; outflows have a negative sign and decrease 
NPV.)
4 Sum all present values. The sum of the present values of all cash flows (inflows 
and outflows) is the investment’s net present value.
5 Apply the NPV rule : If the investment’s NPV is positive, an investor should 
undertake it; if the NPV is negative, the investor should not undertake it. If 
an investor has two candidates for investment but can only invest in one (i.e., 
mutually exclusive projects ), the investor should choose the candidate with 
the higher positive NPV.
What is the meaning of the NPV rule? In calculating the NPV of an investment pro -
posal, we use an estimate of the opportunity cost of capital as the discount rate. The

opportunity cost of capital is the alternative return that investors forgo in undertaking 
the investment. When NPV is positive, the investment adds value because it more 
than covers the opportunity cost of the capital needed to undertake it. So a company 
undertaking a positive NPV investment increases shareholders’ wealth. An individual 
investor making a positive NPV investment increases personal wealth, but a negative 
NPV investment decreases wealth.
When working problems using the NPV rule, it will be helpful to refer to the 
following formula:
NPVCF=
+()=∑t
t
tN
r10
where
 CFt = the expected net cash flow at time t
 N = the investment’s projected life
 r = the discount rate or opportunity cost of capital
As always, we state the inputs on a compatible time basis: If cash flows are annual, 
N is the project’s life in years and r is an annual rate. For instance, suppose you are 
reviewing a proposal that requires an initial outlay of $2 million (CF0 = −$2 million).

You expect that the proposed investment will generate net positive cash flows of CF1 
= $0.50 million at the end of Year 1, CF2 = $0.75 million at the end of Year 2, and CF3 
= $1.35 million at the end of Year 3. Using 10 percent as a discount rate, you calculate 
the NPV as follows:
NPV=− + () + () + ()
=− +$$ $$
$ $0.4545420 501100 751101 35110
223.. .. ..
55$ $
$++
=0 619835 1 014275
0 088655..
. milli on
Because the NPV of $88,655 is positive, you accept the proposal under the NPV rule.
Consider an example in which a research and development program is evaluated 
using the NPV rule.(1)
2 The weighted average cost of capital  (WACC) is often used to discount cash flows. This value is a 
weighted average of the after-  tax required rates of return on the company’s common stock, preferred stock, 
and long-  term debt, where the weights are the fraction of each source of financing in the company’s target

capital structure. For a full discussion of the issues surrounding the cost of capital, see Brealey, Myers, 
and Allen (2017).

Reading 7 ■ Discounted Cash Flow Applications 362
EXAMPLE 1   
Evaluating a Research and Development Program Using 
the NPV Rule
As an analyst covering the RAD Corporation, you are evaluating its research and 
development (R&D) program for the current year. Management has announced 
that it intends to invest $1 million in R&D. Incremental net cash flows are fore -
casted to be $150,000 per year in perpetuity. RAD Corporation’s opportunity 
cost of capital is 10 percent.
1 State whether RAD’s R&D program will benefit shareholders, as judged by 
the NPV rule.
2 Evaluate whether your answer to Part 1 changes if RAD Corporation’s 
opportunity cost of capital is 15 percent rather than 10 percent.
The constant net cash flows of $150,000, which we can denote as  CF, form a 
perpetuity. The present value of the perpetuity is  CFr, so we calculate the 
project’s NPV as
NPVC FC F0=+ =− + r $= $ 1 000 000 150 000 010 500 000 ,, ,. ,

With an opportunity cost of 10 percent, the present value of the program’s cash 
inflows is $1.5 million. The program’s cost is an immediate outflow of $1 million; 
therefore, its net present value is $500,000. As NPV is positive, you conclude 
that RAD Corporation’s R&D program will benefit shareholders.
With an opportunity cost of capital of 15 percent, you compute the NPV as you 
did above, but this time you use a 15 percent discount rate:
NPV = –$1,000,000 + $150,000/0.15 = $0
With a higher opportunity cost of capital, the present value of the inflows is 
smaller and the program’s NPV is smaller: At 15 percent, the NPV exactly equals 
$0. At NPV = 0, the program generates just enough cash flow to compensate 
shareholders for the opportunity cost of making the investment. When a company 
undertakes a zero-  NPV project, the company becomes larger but shareholders’ 
wealth does not increase.
2.2 The Internal Rate of Return and the Internal Rate of Return 
Rule

Rule
Financial managers often want a single number that represents the rate of return 
generated by an investment. The rate of return computation most often used in invest -
ment applications (including capital budgeting) is the internal rate of return (IRR). 
The internal rate of return rule is a second method for choosing among investment 
proposals. The internal rate of return  is the discount rate that makes net present 
value equal to zero. It equates the present value of the investment’s costs (outflows) to 
the present value of the investment’s benefits (inflows). The rate is “internal” because 
it depends only on the cash flows of the investment; no external data are needed. As 
a result, we can apply the IRR concept to any investment that can be represented as

Net Present Value and Internal Rate of Return 363
a series of cash flows. In the study of bonds, we encounter IRR under the name of 
yield to maturity. Later in this reading, we will explore IRR as the money-  weighted 
rate of return for portfolios.
Before we continue, however, we must add a note of caution about interpreting 
IRR: Even if our cash flow projections are correct, we will realize a compound rate 
of return that is equal to IRR over the life of the investment only if  we can reinvest 
all interim cash flows at exactly the IRR. Suppose the IRR for a project is 15 percent 
but we consistently reinvest the cash generated by the project at a lower rate. In this 
case, we will realize a return that is less than 15 percent. (This principle can work in 
our favor if we can reinvest at rates above 15 percent.)
To return to the definition of IRR, in mathematical terms we said the following:
NPVC FCF
IRRCF
IRRCF
IRR=+
+()+
+()+…+
+()=01
12
211 10N
N

NPVC FCF
IRRCF
IRRCF
IRR=+
+()+
+()+…+
+()=01
12
211 10N
N
Again, the IRR in Equation 2 must be compatible with the timing of the cash flows. 
If the cash flows are quarterly, we have a quarterly IRR in Equation 2. We can then 
state the IRR on an annual basis. For some simple projects, the cash flow at t = 0, 
CF0, captures the single capital outlay or initial investment; cash flows after t = 0 are 
the positive returns to the investment. In such cases, we can say CF0 = –Investment 
(the negative sign indicates an outflow). Thus we can rearrange Equation 2 in a form 
that is helpful in those cases:
InvestmentCF
IRRCF
IRRCF
IRR=
+()+
+()++
+()1
12
211 1N
N
For most real-  life problems, financial analysts use software, spreadsheets, or financial 
calculators to solve this equation for IRR, so you should familiarize yourself with 
such tools.3
The investment decision rule using IRR, the IRR rule , states the following: “ Accept 
projects or investments for which the IRR is greater than the opportunity cost of cap -

ital. ” The IRR rule uses the opportunity cost of capital as a hurdle rate , or rate that a 
project’s IRR must exceed for the project to be accepted. Note that if the opportunity 
cost of capital is equal to the IRR, then the NPV is equal to 0. If the project’s oppor -
tunity cost is less than the IRR, the NPV is greater than 0 (using a discount rate less 
than the IRR will make the NPV positive). With these comments in mind, we work 
through two examples that involve the internal rate of return.
EXAMPLE 2   
the IRR Rule
In the previous RAD Corporation example, the initial outlay is $1 million and 
the program’s cash flows are $150,000 in perpetuity. Now you are interested in 
determining the program’s internal rate of return. Address the following:
1 Write the equation for determining the internal rate of return of this R&D 
program.
2 Calculate the IRR.(2)

program.
3 In some real-  world capital budgeting problems, the initial investment (which has a minus sign) may be 
followed by subsequent cash inflows (which have plus signs) and outflows (which have minus signs). In 
these instances, the project can have more than one IRR. The possibility of multiple solutions is a theo -
retical limitation of IRR.

Reading 7 ■ Discounted Cash Flow Applications 364
Finding the IRR is equivalent to finding the discount rate that makes the NPV 
equal to 0. Because the program’s cash flows are a perpetuity, you can set up 
the NPV equation as
NPVI nvestmen tC FIRR
NPVI RR=− +=
=− +=0
1 000 000 0 $ $150,000 ,,
or as
Investment CFIRR
IRR=
= $ $150,000 1 000 000,,
We can solve for IRR as IRR = $150,000/$1,000,000 = 0.15 or 15 percent. The 
solution of 15 percent accords with the definition of IRR. In Example 1, you 
found that a discount rate of 15 percent made the program’s NPV equal to 0. By 
definition, therefore, the program’s IRR must be 15 percent. If the opportunity 
cost of capital is also 15 percent, the R&D program just covers its opportunity 
costs and neither increases nor decreases shareholder wealth. If it is less than 
15 percent, the IRR rule indicates that management should invest in the pro -
gram because it more than covers its opportunity cost. If the opportunity cost

is greater than 15 percent, the IRR rule tells management to reject the R&D 
program. For a given opportunity cost, the IRR rule and the NPV rule lead to 
the same decision in this example.
EXAMPLE 3   
The IRR and NPV Rules Side by Side
The Japanese company Kageyama Ltd. is considering whether or not to open 
a new factory to manufacture capacitors used in cell phones. The factory will 
require an investment of ¥1,000 million. The factory is expected to generate level 
cash flows of ¥294.8 million per year in each of the next five years. According 
to information in its financial reports, Kageyama’s opportunity cost of capital 
for this type of project is 11 percent.
1 Determine whether the project will benefit Kageyama’s shareholders using 
2 Determine whether the project will benefit Kageyama’s shareholders using 
the IRR rule.
The cash flows can be grouped into an initial outflow of ¥1,000 million and an

ordinary annuity of five inflows of ¥294.8 million. The expression for the present 
value of an annuity is A[1 − (1 + r)−N]/r, where A is the level annuity payment. 
Therefore, with amounts shown in millions of Japanese yen,
NPV
NPV=− +− ()
=− +=−1 000 294 81 1110 11
1 000 1 089 55 89 55,. ..
,, .. 5 5
Because the project’s NPV is positive ¥89.55 million, it should benefit Kageyama’s 
shareholders.

Net Present Value and Internal Rate of Return 365
The IRR of the project is the solution to
NPVI RR IRR =− +− +()=−1 000 294 81 105,.
This project’s positive NPV tells us that the internal rate of return must be greater 
than 11 percent. Using a calculator, we find that IRR is 0.145012 or 14.50 percent. 
Table 1 gives the keystrokes on most financial calculators.
Table 1   Computing IRR
Notation Used on Most Calculators Numerical Value for This Problem
N 5
%i compute X
PV −1,000
PMT 294.8
FV n/a (= 0)
Because the IRR of 14.50 percent is greater than the opportunity cost of the 
project, the project should benefit Kageyama’s shareholders. Whether it uses the 
IRR rule or the NPV rule, Kageyama makes the same decision: Build the factory.
In the previous example, value creation is evident: For a single ¥1,000  million 
payment, Kageyama creates a project worth ¥1,089.55  million, a value increase of 
¥89.55  million. Another perspective on value creation comes from converting the

initial investment into a capital charge against the annual operating cash flows that 
the project generates. Recall that the project generates an annual operating cash 
flow of ¥294,800,000. If we subtract a capital charge of ¥270,570,310 (the amount of 
a five-  year annuity having a present value of ¥1,000 million at 11 percent), we find 
¥294,800,000 − ¥270,570,310 = ¥24,229,690. The amount of ¥24,229,690 represents 
the profit in each of the next five years after taking into account opportunity costs. 
The present value of a five-  year annuity of ¥24,229,690 at an 11 percent cost of capital 
is exactly what we calculated as the project’s NPV: ¥89.55 million. Therefore, we can 
also calculate NPV by converting the initial investment to an annual capital charge 
against cash flow.
2.3 Problems with the IRR Rule
The IRR and NPV rules give the same accept or reject decision when projects are 
independent—that is, when the decision to invest in one project does not affect the

decision to undertake another. When a company cannot finance all the projects it 
would like to undertake—that is, when projects are mutually exclusive—it must rank 
the projects from most profitable to least. However, rankings according to IRR and 
NPV may not be the same. The IRR and NPV rules rank projects differently when
■■the size or scale of the projects differs (measuring size by the investment 
needed to undertake the project), or
■■the timing of the projects’ cash flows differs.

Reading 7 ■ Discounted Cash Flow Applications 366
When the IRR and NPV rules conflict in ranking projects, we should take directions 
from the NPV rule. Why that preference? The NPV of an investment represents the 
expected addition to shareholder wealth from an investment, and we take the max -
imization of shareholder wealth to be a basic financial objective of a company. To 
illustrate the preference for the NPV rule, consider first the case of projects that differ 
in size. Suppose that a company has only €30,000 available to invest.4 The company 
has available two one-  period investment projects described as A and B in Table 2.
Table 2   IRR and NPV for Mutually Exclusive Projects of Different Size
Project Investment at t = 0 Cash Flow at t = 1 IRR (%) NPV at 8%
A −€10,000 €15,000 50 €3,888.89
B −€30,000 €42,000 40 €8,888.89
Project A requires an immediate investment of €10,000. This project will make a single

cash payment of $15,000 at t = 1. Because the IRR is the discount rate that equates the 
present value of the future cash flow with the cost of the investment, the IRR equals 
50 percent. If we assume that the opportunity cost of capital is 8 percent, then the NPV 
of Project A is €3,888.89. We compute the IRR and NPV of Project B as 40 percent 
and €8,888.89, respectively. The IRR and NPV rules indicate that we should undertake 
both projects, but to do so we would need €40,000—more money than is available. So 
we need to rank the projects. How do the projects rank according to IRR and NPV?
The IRR rule ranks Project A, with the higher IRR, first. The NPV rule, however, 
ranks Project B, with the higher NPV, first—a conflict with the IRR rule’s ranking. 
Choosing Project A because it has the higher IRR would not lead to the largest increase 
in shareholders’ wealth. Investing in Project A effectively leaves €20,000 (€30,000

minus A’s cost) uninvested. Project A increases wealth by almost €4,000, but Project 
B increases wealth by almost €9,000. The difference between the two projects’ scale 
creates the inconsistency in the ranking between the two rules.
IRR and NPV can also rank projects of the same scale differently when the timing 
of cash flows differs. We can illustrate this principle with Projects A and D, presented 
in Table 3.
Table 3   IRR and NPV for Mutually Exclusive Projects with Different Timing 
of Cash Flows
Project CF0 (€) CF1 (€) CF2 (€) CF3 (€) IRR (%) NPV at 8%
A −10,000 15,000 0 0 50.0 €3,888.89
D −10,000 0 0 21,220 28.5 €6,845.12
4 Or suppose the two projects require the same physical or other resources, so that only one can be 
undertaken.

Portfolio Return Measurement 367
The terms CF0, CF1, CF2, and CF3 represent the cash flows at time periods 0, 1, 2, 
and 3. The IRR for Project A is the same as it was in the previous example. The IRR 
for Project D is found as follows:
−+
+()= 10 000
103,21,220
IRR
The IRR for Project D is 28.5  percent, compared with 50  percent for Project A. 
IRRs and IRR rankings are not affected by any external interest rate or discount rate 
because a project’s cash flows alone determine the internal rate of return. The IRR 
calculation furthermore assumes reinvestment at the IRR, so we generally cannot 
interpret them as achievable rates of return. For Project D, for example, to achieve a 
28.5 percent return we would need to earn 28.5 percent on €10,000 for the first year, 
earn 28.5 percent on €10,000(1.285) = €12,850 the second year, and earn 28.5 percent 
on €10,000(1.285)2 = €16,512.25 the third year.5 A reinvestment rate such as 50 percent

or 28.5 percent may be quite unrealistic. By contrast, the calculation of NPV uses an 
external market-  determined discount rate, and reinvestment is assumed to take place 
at that discount rate. NPV rankings can depend on the external discount rate chosen. 
Here, Project D has a larger but more distant cash inflow (€21,220 versus €15,000). As 
a result, Project D has a higher NPV than Project A at lower discount rates.6 The NPV 
rule’s assumption about reinvestment rates is more realistic and more economically 
relevant because it incorporates the market-  determined opportunity cost of capital as 
a discount rate. As a consequence, the NPV is the expected addition to shareholder 
wealth from an investment.
In summary, when dealing with mutually exclusive projects, choose among them 
using the NPV rule when the IRR rule and NPV rule conflict.7
PORTFOLIO RETURN MEASUREMENT
Suppose you are an investor and you want to assess the success of your investments.

You face two related but distinct tasks. The first is performance measurement , which 
involves calculating returns in a logical and consistent manner. Accurate performance 
measurement provides the basis for your second task, performance appraisal .8 
Performance measurement is thus of great importance for all investors and investment 
managers because it is the foundation for all further analysis.
In our discussion of portfolio return measurement, we will use the fundamental 
concept of holding period return  (HPR), the return that an investor earns over a 
specified holding period. For an investment that makes one cash payment at the end 
of the holding period, HPR = ( P1 − P0 + D1)/P0, where P0 is the initial investment, P1 
is the price received at the end of the holding period, and D1 is the cash paid by the 
investment at the end of the holding period.3
5 The ending amount €10,000(1.285)3 = €21,218 differs from the €21,220 amount listed in Table 3 because 
we rounded IRR.

6 There is a crossover discount rate above which Project A has a higher NPV than Project D. This cross -
over rate is 18.94 percent.
7 Technically, different reinvestment rate assumptions account for this conflict between the IRR and 
NPV rules. The IRR rule assumes that the company can earn the IRR on all reinvested cash flows, but 
the NPV rule assumes that cash flows are reinvested at the company’s opportunity cost of capital. The 
NPV assumption is far more realistic. For further details on this and other topics in capital budgeting, see 
Brealey, Myers, and Allen (2017).
8 The term “performance evaluation” has been used as a synonym for performance appraisal.

Reading 7 ■ Discounted Cash Flow Applications 368
Particularly when we measure performance over many periods, or when the port -
folio is subject to additions and withdrawals, portfolio performance measurement is a 
challenging task. Two of the measurement tools available are the money-  weighted rate 
of return measure and the time-  weighted rate of return measure. The first measure 
we discuss, the money-  weighted rate of return, implements a concept we have already 
covered in the context of capital budgeting: internal rate of return.
3.1 Money-  Weighted Rate of Return
The first performance measurement concept that we will discuss is an internal rate 
of return calculation. In investment management applications, the internal rate of 
return is called the money-  weighted rate of return because it accounts for the timing 
and amount of all cash flows into and out of the portfolio.9
To illustrate the money-  weighted return, consider an investment that covers a

two-  year horizon. At time t = 0, an investor buys one share at $200. At time t = 1, he 
purchases an additional share at $225. At the end of Year 2, t = 2, he sells both shares 
for $235 each. During both years, the stock pays a per-  share dividend of $5. The t = 1 
dividend is not reinvested. Table 4 shows the total cash inflows and outflows.
Table 4   Cash Flows
Time Outlay
0 $200 to purchase the first share
1 $225 to purchase the second share
Time Proceeds
1 $5 dividend received from first share (and not reinvested)
2 $10 dividend ($5 per share × 2 shares) received
2 $470 received from selling two shares at $235 per share
The money-  weighted return on this portfolio is its internal rate of return for the 
two-  year period. The portfolio’s internal rate of return is the rate, r, for which the pres -
ent value of the cash inflows minus the present value of the cash outflows equals 0, or
PV (outflows) = PV (inflows)
$$$ $480200225
15
1 12++()=+()+
+()rr r

15
+()rr r
The left-  hand side of this equation details the outflows: $200 at time t = 0 and $225 
at time t = 1. The $225 outflow is discounted back one period because it occurs at t 
= 1. The right-  hand side of the equation shows the present value of the inflows: $5 
at time t = 1 (discounted back one period) and $480 (the $10 dividend plus the $470 
sale proceeds) at time t = 2 (discounted back two periods).
9 In the United States, the money-  weighted return is frequently called the dollar-  weighted return. We 
follow a standard presentation of the money-  weighted return as an IRR concept.

Portfolio Return Measurement 369
To solve for the money-  weighted return, we use either a financial calculator that 
allows us to enter cash flows or a spreadsheet with an IRR function.10 The first step 
is to group net cash flows by time. For this example, we have −$200 for the t = 0 net 
cash flow, −$220 = −$225 + $5 for the t = 1 net cash flow, and $480 for the t = 2 net 
cash flow. After entering these cash flows, we use the spreadsheet’s or calculator’s IRR 
function to find that the money-  weighted rate of return is 9.39 percent.11
Now we take a closer look at what has happened to the portfolio during each of 
the two years. In the first year, the portfolio generated a one-  period holding period 
return of ($5 + $225 − $200)/$200 = 15 percent. At the beginning of the second year, 
the amount invested is $450, calculated as $225 (per share price of stock) × 2 shares, 
because the $5 dividend was spent rather than reinvested. At the end of the second

year, the proceeds from the liquidation of the portfolio are $470 (as detailed in Table 4) 
plus $10 in dividends (as also detailed in Table 4). So in the second year the port -
folio produced a holding period return of ($10 + $470 − $450)/$450 = 6.67 percent. 
The mean holding period return was (15% + 6.67%)/2 = 10.84 percent. The money-  
weighted rate of return, which we calculated as 9.39 percent, puts a greater weight 
on the second year’s relatively poor performance (6.67 percent) than the first year’s 
relatively good performance (15 percent), as more money was invested in the second 
year than in the first. That is the sense in which returns in this method of calculating 
performance are “money weighted. ”
As a tool for evaluating investment managers, the money-  weighted rate of return 
has a serious drawback. Generally, the investment manager’s clients determine when 
money is given to the investment manager and how much money is given. As we have

seen, those decisions may significantly influence the investment manager’s money-  
weighted rate of return. A general principle of evaluation, however, is that a person 
or entity should be judged only on the basis of their own actions, or actions under 
their control. An evaluation tool should isolate the effects of the investment manager’s 
actions. The next section presents a tool that is effective in that respect.
3.2 Time-  Weighted Rate of Return
An investment measure that is not sensitive to the additions and withdrawals of funds 
is the time-  weighted rate of return. In the investment management industry, the time-  
weighted rate of return is the preferred performance measure. The time-  weighted 
rate of return  measures the compound rate of growth of $1 initially invested in the 
portfolio over a stated measurement period. In contrast to the money-  weighted rate 
of return, the time-  weighted rate of return is not affected by cash withdrawals or

additions to the portfolio. The term “time-  weighted” refers to the fact that returns are 
averaged over time. To compute an exact time-  weighted rate of return on a portfolio, 
take the following three steps:
1 Price the portfolio immediately prior to any significant addition or withdrawal 
of funds. Break the overall evaluation period into subperiods based on the dates 
of cash inflows and outflows.
10 In this particular case we could solve for r by solving the quadratic equation 480 x2 − 220 x − 200 = 
0 with x = 1/(1 + r), using standard results from algebra. In general, however, we rely on a calculator or 
spreadsheet software to compute a money-  weighted rate of return.
11 Note that the calculator or spreadsheet will give the IRR as a periodic rate. If the periods are not annual, 
we annualize the periodic rate.

Reading 7 ■ Discounted Cash Flow Applications 370
2 Calculate the holding period return on the portfolio for each subperiod.
3 Link or compound holding period returns to obtain an annual rate of return for 
the year (the time-  weighted rate of return for the year). If the investment is for 
more than one year, take the geometric mean of the annual returns to obtain 
the time-  weighted rate of return over that measurement period.
Let us return to our money-  weighted example and calculate the time-  weighted 
rate of return for that investor’s portfolio. In that example, we computed the holding 
period returns on the portfolio, Step 2 in the procedure for finding the time-  weighted 
rate of return. Given that the portfolio earned returns of 15 percent during the first 
year and 6.67 percent during the second year, what is the portfolio’s time-  weighted 
rate of return over an evaluation period of two years?
We find this time-  weighted return by taking the geometric mean of the two holding

period returns, Step 3 in the procedure above. The calculation of the geometric mean 
exactly mirrors the calculation of a compound growth rate. Here, we take the product 
of 1 plus the holding period return for each period to find the terminal value at t = 
2 of $1 invested at t = 0. We then take the square root of this product and subtract 1 
to get the geometric mean. We interpret the result as the annual compound growth 
rate of $1 invested in the portfolio at t = 0. Thus we have
11 15 1 06672+() =() () Time-wei ghted retur n
Time-wei ghted ret u..
rrn=() () −= 11510667 11 076 .. .%
The time-  weighted return on the portfolio was 10.76  percent, compared with the 
money-  weighted return of 9.39 percent, which gave larger weight to the second year’s 
return. We can see why investment managers find time-  weighted returns more mean -
ingful. If a client gives an investment manager more funds to invest at an unfavorable

time, the manager’s money-  weighted rate of return will tend to be depressed. If a client 
adds funds at a favorable time, the money-  weighted return will tend to be elevated. 
The time-  weighted rate of return removes these effects.
In defining the steps to calculate an exact time-  weighted rate of return, we said 
that the portfolio should be valued immediately prior to any significant addition or 
withdrawal of funds. With the amount of cash flow activity in many portfolios, this task 
can be costly. We can often obtain a reasonable approximation of the time-  weighted 
rate of return by valuing the portfolio at frequent, regular intervals, particularly if 
additions and withdrawals are unrelated to market movements. The more frequent 
the valuation, the more accurate the approximation. Daily valuation is commonplace. 
Suppose that a portfolio is valued daily over the course of a year. To compute the 
time-  weighted return for the year, we first compute each day’s holding period return:

rttt
t=− MVEM VB
MVB
where MVBt equals the market value at the beginning of day t and MVEt equals the 
market value at the end of day t. We compute 365 such daily returns, denoted r1, r2, 
…, r365. We obtain the annual return for the year by linking the daily holding period 
returns in the following way: (1 + r1) × (1 + r2) × … × (1 + r365) − 1. If withdrawals 
and additions to the portfolio happen only at day’s end, this annual return is a pre -
cise time-  weighted rate of return for the year. Otherwise, it is an approximate time-  
weighted return for the year.

Portfolio Return Measurement 371
If we have a number of years of data, we can calculate a time-  weighted return 
for each year individually, as above. If ri is the time-  weighted return for year i, we 
calculate an annualized time-  weighted return as the geometric mean of N annual 
returns, as follows:
rr rrNN
TW =+() ×+() ×× +() − 11 11121
Example 4 illustrates the calculation of the time-  weighted rate of return.
EXAMPLE 4   
Time-  Weighted Rate of Return
Strubeck Corporation sponsors a pension plan for its employees. It manages 
part of the equity portfolio in-  house and delegates management of the balance 
to Super Trust Company. As chief investment officer of Strubeck, you want to 
review the performance of the in-  house and Super Trust portfolios over the last 
four quarters. You have arranged for outflows and inflows to the portfolios to be 
made at the very beginning of the quarter. Table 5 summarizes the inflows and

outflows as well as the two portfolios’ valuations. In the table, the ending value 
is the portfolio’s value just prior to the cash inflow or outflow at the beginning 
of the quarter. The amount invested is the amount each portfolio manager is 
responsible for investing.
Table 5   Cash Flows for the In-  House Strubeck Account and the Super Trust Account
Quarter
1 ($) 2 ($) 3 ($) 4 ($)
In- House Account
Beginning value 4,000,000 6,000,000 5,775,000 6,720,000
Beginning of period inflow (outflow) 1,000,000 (500,000) 225,000 (600,000)
Amount invested 5,000,000 5,500,000 6,000,000 6,120,000
Ending value 6,000,000 5,775,000 6,720,000 5,508,000
Super Trust Account
Beginning value 10,000,000 13,200,000 12,240,000 5,659,200
Beginning of period inflow (outflow) 2,000,000 (1,200,000) (7,000,000) (400,000)
Amount invested 12,000,000 12,000,000 5,240,000 5,259,200
Ending value 13,200,000 12,240,000 5,659,200 5,469,568
Based on the information given, address the following.

1 Calculate the time-  weighted rate of return for the in-  house account.
2 Calculate the time-  weighted rate of return for the Super Trust account.

Reading 7 ■ Discounted Cash Flow Applications 372
To calculate the time-  weighted rate of return for the in-  house account, we 
compute the quarterly holding period returns for the account and link them 
into an annual return. The in-  house account’s time-  weighted rate of return is 
27 percent, calculated as follows:
1Q HPR : $6,000,000 $5,000,000 $5,000,000 0.20
2Q HPR : 1r
r=−() =
2 2
3=−() =
=$5,775,000 $5,500,000 $5,500,000 0.05
3Q HPR : $6,720 r , ,000 $6,000,000 $6,000,000 0.12
4Q HPR : $5,508,000 $6,4− () =
=−r 1 120,000 $6,120,000 0.10 () =−
11 11 11 201051120901 0271 234 +() +() +() +() −= () () () () −= rr rr .. .. .  or 27%
The account managed by Super Trust has a time-  weighted rate of return of 
26 percent, calculated as follows:
1 000 000 000 000 010
2Q HPR: 
Q HP R1r=−() = $13,200,000 $12 $12 ,, ,, .
:: 
3Q HPR : r
r2
3000 000 00 000 002 =−() =
=$12,240,000 $12 $12,0 ,, ,.
$ $5,659,200 $5 $5,240
$5,469,5− () =
=,, ,. 240 000 000 008

4 4Q HPR : r 6 68 $5 $5− () = ,, ,, . 259 200 259 200 004
11 11 11 101021081041 0261 234 +() +() +() +() −= () () () () −= rr rr ... ..   or 26%
The in-  house portfolio’s time-  weighted rate of return is higher than the Super 
Trust portfolio’s by 100 basis points.
Having worked through this exercise, we are ready to look at a more detailed case.
EXAMPLE 5   
Time-  Weighted and Money-  Weighted Rates of Return Side 
by Side
Your task is to compute the investment performance of the Walbright Fund 
during 2014. The facts are as follows:
■■On 1 January 2014, the Walbright Fund had a market value of 
$100 million.
■■During the period 1 January 2014 to 30 April 2014, the stocks in the fund 
showed a capital gain of $10 million.
■■On 1 May 2014, the stocks in the fund paid a total dividend of $2 million. 
All dividends were reinvested in additional shares.
■■Because the fund’s performance had been exceptional, institutions

invested an additional $20 million in Walbright on 1 May 2014, raising 
assets under management to $132 million ($100 + $10 + $2 + $20).
■■On 31 December 2014, Walbright received total dividends of $2.64 mil -
lion. The fund’s market value on 31 December 2014, not including the 
$2.64 million in dividends, was $140 million.
■■The fund made no other interim cash payments during 2014.

Portfolio Return Measurement 373
1 Compute the Walbright Fund’s time-  weighted rate of return.
2 Compute the Walbright Fund’s money-  weighted rate of return.
3 Interpret the differences between the time-  weighted and money-  weighted 
rates of return.
Because interim cash flows were made on 1 May 2014, we must compute two 
interim total returns and then link them to obtain an annual return. Table 6 
lists the relevant market values on 1 January, 1 May, and 31 December as well 
as the associated interim four-  month (1 January to 1 May) and eight-  month (1 
May to 31 December) holding period returns.
Table 6   Cash Flows for the Walbright Fund
1 January 2014 Beginning portfolio value = $100 million
1 May 2014 Dividends received before additional investment = 
$2 million
Ending portfolio value = $110 million
Holding period retur n=+=$$
$%21 0
10012
New investment = $20 million

$%21 0
10012
Beginning market value for last 2/3 of year = $132 million
31 December 2014 Dividends received = $2.64 million
Ending portfolio value = $140 million
Holding period retur n=+−
=$$ $
$264 140 132
132
806.
.%
Now we must geometrically link the four- and eight-  month returns to 
compute an annual return. We compute the time-  weighted return as follows:
Time-  weighted return = 1.12 × 1.0806 – 1 = 0.2103
In this instance, we compute a time-  weighted rate of return of 21.03 percent for 
one year. The four-  month and eight-  month intervals combine to equal one year. 
(Taking the square root of the product 1.12 × 1.0806 would be appropriate only 
if 1.12 and 1.0806 each applied to one full year.)
To calculate the money-  weighted return, we find the discount rate that sets 
the present value of the outflows (purchases) equal to the present value of the 
inflows (dividends and future payoff). The initial market value of the fund and

all additions to it are treated as cash outflows. (Think of them as expenditures.) 
Withdrawals, receipts, and the ending market value of the fund are counted as 
inflows. (The ending market value is the amount investors receive on liquidating 
the fund.) Because interim cash flows have occurred at four-  month intervals, we 
must solve for the four-  month internal rate of return. Table 6 details the cash 
flows and their timing.

Reading 7 ■ Discounted Cash Flow Applications 374
The present value equation (in millions) is as follows:
PVoutfl owsP Vinflows () = ()
+
+()+
+()=
+()+ $1$ $20 $2 $002
11 111 1rr r2 2.64 $140
1133+()+
+() rr
The left-  hand side of the equation shows the investments in the fund or outflows: 
a $100 million initial investment followed by the $2 million dividend reinvested 
and an additional $20 million of new investment (both occurring at the end of 
the first four-  month interval, which makes the exponent in the denominator 1). 
The right-  hand side of the equation shows the payoffs or inflows: the $2 million 
dividend at the first four-  month interval followed by the $2.64 million dividend 
and the terminal market value of $140 million (both occurring at the end of the 
third four-  month interval, which makes the exponent in the denominator 3). 
The second four-  month interval has no cash flow. We can bring all the terms to

the right of the equal sign, arranging them in order of time. After simplification,
0$ 1$ $142.64=− −
+()+
+()0020
1113rr
Using a spreadsheet or IRR-  enabled calculator, we use −100, −20, 0, and $142.64 
for the t = 0, t = 1, t = 2, and t = 3 net cash flows, respectively.12 Using either 
tool, we get a four-  month IRR of 6.28 percent. The quick way to annualize this 
is to multiply by 3. A more accurate way is (1.0628)3 − 1 = 0.20 or 20 percent.
In this example, the time-  weighted return (21.03 percent) is greater than the 
money-  weighted return (20 percent). The Walbright Fund’s performance was 
relatively poorer during the eight-  month period, when the fund owned more 
shares, than it was overall. This fact is reflected in a lower money-  weighted rate 
of return compared with time-  weighted rate of return, as the money-  weighted 
return is sensitive to the timing and amount of withdrawals and additions to 
the portfolio.

The accurate measurement of portfolio returns is important to the process of 
evaluating portfolio managers. In addition to considering returns, however, analysts 
must also weigh risk. When we worked through Example 4, we stopped short of sug -
gesting that in-  house management was superior to Super Trust because it earned a 
higher time-  weighted rate of return. With risk in focus, we can talk of risk-  adjusted 
performance and make comparisons—but only cautiously. In other readings, we will 
discuss the Sharpe ratio, an important risk-  adjusted performance measure that we 
might apply to an investment manager’s time-  weighted rate of return. For now, we 
have illustrated the major tools for measuring the return on a portfolio.
MONEY MARKET YIELDS
In our discussion of internal rate of return and net present value, we referred to the 
opportunity cost of capital as a market-  determined rate. In this section, we begin a

discussion of discounted cash flow analysis in actual markets by considering short-  
term debt markets.4
12 By convention, we denote outflow with a negative sign, and we need 0 as a placeholder for the t = 2.

Money Market Yields 375
To understand the various ways returns are presented in debt markets, we must 
discuss some of the conventions for quoting yields on money-  market instruments. The 
money market  is the market for short-  term debt instruments (one-  year maturity or 
less). Some instruments require the issuer to repay the lender the amount borrowed 
plus interest. Others are pure discount instruments  that pay interest as the difference 
between the amount borrowed and the amount paid back.
In the US money market, the classic example of a pure discount instrument is the 
US Treasury bill (T-  bill) issued by the federal government. The face value  of a T-  bill is 
the amount the US government promises to pay back to a T-  bill investor. In buying a 
T- bill, investors pay the face amount less the discount, and receive the face amount at 
maturity. The discount  is the reduction from the face amount that gives the price for

the T-  bill. This discount becomes the interest that accumulates, because the investor 
receives the face amount at maturity. Thus, investors earn a dollar return equal to the 
discount if they hold the instrument to maturity. T-  bills are by far the most important 
class of money-  market instruments in the United States. Other types of money-  market 
instruments include commercial paper and bankers’ acceptances, which are discount 
instruments, and negotiable certificates of deposit, which are interest-  bearing instru -
ments. The market for each of these instruments has its own convention for quoting 
prices or yields. The remainder of this section examines the quoting conventions for 
T- bills and other money-  market instruments. In most instances, the quoted yields 
must be adjusted for use in other present value problems.
Pure discount instruments such as T-  bills are quoted differently from US gov -

ernment bonds. T-  bills are quoted on a bank discount basis , rather than on a price 
basis. The bank discount basis is a quoting convention that annualizes, based on a 
360-  day year, the discount as a percentage of face value. Yield on a bank discount 
basis is computed as follows:
rD
FtBD=360
where
 rBD = the annualized yield on a bank discount basis
 D = the dollar discount, which is equal to the difference between the face 
value of the bill, F, and its purchase price, P0
 F = the face value of the T-  bill
 t = the actual number of days remaining to maturity
 360 = bank convention of the number of days in a year
The bank discount yield (often called simply the discount yield) takes the dollar 
discount from par, D, and expresses it as a fraction of the face value (not the price) of 
the T-  bill. This fraction is then multiplied by the number of periods of length t in one 
year (that is, 360/ t), where the year is assumed to have 360 days. Annualizing in this

fashion assumes simple interest (no compounding). Consider the following example.
EXAMPLE 6   
The Bank Discount Yield
Suppose a T-  bill with a face value (or par value) of $100,000 and 150 days until 
maturity is selling for $98,000. What is its bank discount yield?(3)

Reading 7 ■ Discounted Cash Flow Applications 376
Solution: 
For this example, the dollar discount, D, is $2,000. The yield on a bank discount 
basis is 4.8 percent, as computed with Equation 3:
rBD= =$
$2 000
100 000360
15048,
,.%
The bank discount formula takes the T-  bill’s dollar discount from face or par as 
a fraction of face value, 2 percent, and then annualizes by the factor 360/150 = 
2.4. The price of discount instruments such as T-  bills is quoted using discount 
yields, so we typically translate discount yield into price.
Suppose we know the bank discount yield of 4.8 percent but do not know 
the price. We solve for the dollar discount, D, as follows:
Dr Ft=BD360
With rBD = 4.8 percent, the dollar discount is D = 0.048 × $100,000 × 150/360 = 
$2,000. Once we have computed the dollar discount, the purchase price for the 
T- bill is its face value minus the dollar discount, F − D = $100,000 − $2,000 = 
$98,000.
Yield on a bank discount basis is not a meaningful measure of investors’ return,

for three reasons. First, the yield is based on the face value of the bond, not on its 
purchase price. Returns from investments should be evaluated relative to the amount 
that is invested. Second, the yield is annualized based on a 360-  day year rather than 
a 365-  day year. Third, the bank discount yield annualizes with simple interest, which 
ignores the opportunity to earn interest on interest (compound interest).
We can extend Example 6 to discuss three often-  used alternative yield measures. 
The first is the holding period return over the remaining life of the instrument (150 
days in the case of the T-  bill in Example 6). It determines the return that an investor 
will earn by holding the instrument to maturity; as used here, this measure refers to an 
unannualized rate of return (or periodic rate of return). In fixed income markets, this 
holding period return is also called a holding period yield (HPY) .13 For an instrument 
that makes one cash payment during its life, HPY is

HPY=−+PP D
P10 1
0
where
 P0 = the initial purchase price of the instrument
 P1 = the price received for the instrument at its maturity
 D1 = the cash distribution paid by the instrument at its maturity (i.e., interest)
When we use this expression to calculate the holding period yield for an interest-  bearing 
instrument (for example, coupon-  bearing bonds), we need to observe an important 
detail: The purchase and sale prices must include any accrued interest  added to the (4)
13 Bond-  market participants often use the term “yield” when referring to total returns (returns incorpo -
rating both price change and income), as in yield to maturity. In other cases, yield refers to returns from 
income alone (as in current yield, which is annual interest divided by price). As used in this volume and 
by many writers, holding period yield is a bond market synonym for holding period return, total return, 
and horizon return.

Money Market Yields 377
trade price because the bond was traded between interest payment dates. Accrued 
interest is the coupon interest that the seller earns from the last coupon date but does 
not receive as a coupon, because the next coupon date occurs after the date of sale.14
For pure discount securities, all of the return is derived by redeeming the bill for 
more than its purchase price. Because the T-  bill is a pure discount instrument, it makes 
no interest payment and thus D1 = 0. Therefore, the holding period yield is the dollar 
discount divided by the purchase price, HPY = D/P0, where D = P1 − P0. The holding 
period yield is the amount that is annualized in the other measures. For the T-  bill 
in Example 6, the investment of $98,000 will pay $100,000 in 150 days. The holding 
period yield on this investment using Equation 4 is ($100,000 − $98,000)/$98,000 = 
$2,000/$98,000 = 2.0408 percent. For this example, the periodic return of 2.0408 per -

cent is associated with a 150-  day period. If we were to use the T-  bill rate of return 
as the opportunity cost of investing, we would use a discount rate of 2.0408 percent 
for the 150-  day T-  bill to find the present value of any other cash flow to be received 
in 150 days. As long as the other cash flow has risk characteristics similar to those of 
the T-  bill, this approach is appropriate. If the other cash flow were riskier than the 
T- bill, then we could use the T-  bill’s yield as a base rate, to which we would add a 
risk premium. The formula for the holding period yield is the same regardless of the 
currency of denomination.
The second measure of yield is the effective annual yield (EAY) . The EAY takes 
the quantity 1 plus the holding period yield and compounds it forward to one year, 
then subtracts 1 to recover an annualized return that accounts for the effect of 
interest-  on- interest.15
EAYH PY =+() − 11365t
In our example, we can solve for EAY as follows:

EAY=() −= −= 1 020408 11 050388 15 0388365 150.. .%
This example illustrates a general rule: The bank discount yield is less than the effec -
tive annual yield.
The third alternative measure of yield is the money market yield  (also known as the 
CD equivalent yield ). This convention makes the quoted yield on a T-  bill comparable 
to yield quotations on interest-  bearing money-  market instruments that pay interest on 
a 360-  day basis. In general, the money market yield is equal to the annualized holding 
period yield; assuming a 360-  day year, rMM = (HPY)(360/ t). Compared to the bank 
discount yield, the money market yield is computed on the purchase price, so rMM = 
(rBD)(F/P0). This equation shows that the money market yield is larger than the bank 
discount yield. In practice, the following expression is more useful because it does 
not require knowing the T-  bill price:
rr
trMMBD
BD=−()()360
360

rr
trMMBD
360
For the T-  bill example, the money market yield is rMM = (360)(0.048)/[360 − (150)
(0.048)] = 4.898 percent.16(5)
(6)
14 The price with accrued interest is called the full price . Trade prices are quoted “clean” (without accrued 
interest), but accrued interest, if any, is added to the purchase price. For more on accrued interest, see the 
Level I CFA Program curriculum reading “Understanding Fixed-  Income Risk and Return. ”
15 Effective annual yield was called the effective annual rate (Equation 5) in the reading on the time value 
of money.
16 Some national markets use the money market yield formula, rather than the bank discount yield for -
mula, to quote the yields on discount instruments such as T-  bills. In Canada, the convention is to quote 
Treasury bill yields using the money market formula assuming a 365-  day year. Yields for German Treasury 
discount paper with a maturity less than one year and French BTFs (T-  bills) are computed with the money

Reading 7 ■ Discounted Cash Flow Applications 378
Table 7 summarizes the three yield measures we have discussed.
Table 7   Three Commonly Used Yield Measures
Holding Period Yield  
(HPY)Effective Annual Yield  
(EAY)Money Market Yield  
(CD Equivalent Yield)
HPY=−+PP D
P10 1
0EAYH PY =+() − 11365t
rr
trBD
BDMM =−()()360
360
The next example will help you consolidate your knowledge of these yield measures.
EXAMPLE 7   
Using the Appropriate Discount Rate
You need to find the present value of a cash flow of $1,000 that is to be received 
in 150 days. You decide to look at a T-  bill maturing in 150 days to determine the 
relevant interest rate for calculating the present value. You have found a variety 
of yields for the 150-  day bill. Table 8 presents this information.
Table 8   Short-  Term Money Market Yields
Holding period yield 2.0408%
Bank discount yield 4.8%
Money market yield 4.898%
Effective annual yield 5.0388%
Which yield or yields are appropriate for finding the present value of the $1,000

to be received in 150 days?
Solution: 
The holding period yield is appropriate, and we can also use the money market 
yield and effective annual yield after converting them to a holding period yield.
■■Holding period yield  (2.0408 percent). This yield is exactly what we want. 
Because it applies to a 150-  day period, we can use it in a straightforward 
fashion to find the present value of the $1,000 to be received in 150 days. 
(Recall the principle that discount rates must be compatible with the time 
period.) The present value is
PV= =$1,000$1 020408980 00..
Now we can see why the other yield measures are inappropriate or not as easily 
applied.
■■Bank discount yield  (4.8 percent). We should not use this yield measure 
to determine the present value of the cash flow. As mentioned earlier, the 
bank discount yield is based on the face value of the bill and not on its 
price.

Summary 379
■■Money market yield  (4.898 percent). To use the money market yield, we 
need to convert it to the 150-  day holding period yield by dividing it by 
(360/150). After obtaining the holding period yield 0.04898/(360/150) = 
0.020408, we use it to discount the $1,000 as above.
■■Effective annual yield  (5.0388 percent). This yield has also been annual -
ized, so it must be adjusted to be compatible with the timing of the cash 
flow. We can obtain the holding period yield from the EAY as follows:
1 050388 10 020408150 365..() −=
Recall that when we found the effective annual yield, the exponent was 365/150, 
or the number of 150-  day periods in a 365-  day year. To shrink the effective 
annual yield to a 150-  day yield, we use the reciprocal of the exponent that we 
used to annualize.
In Example 7, we converted two short-  term measures of annual yield to a holding 
period yield for a 150-  day period. That is one type of conversion. We frequently also

need to convert periodic rates to annual rates. The issue can arise both in money 
markets and in longer-  term debt markets. As an example, many bonds (long-  term 
debt instruments) pay interest semiannually. Bond investors compute IRRs for bonds, 
known as yields to maturity (YTM). If the semiannual yield to maturity is 4 percent, 
how do we annualize it? An exact approach, taking account of compounding, would 
be to compute (1.04)2 − 1 = 0.0816 or 8.16 percent. This is what we have been call -
ing an effective annual yield. An approach used in US bond markets, however, is to 
double the semiannual YTM: 4% × 2 = 8%. The yield to maturity calculated this way, 
ignoring compounding, has been called a bond equivalent yield . Annualizing a semi -
annual yield by doubling is putting the yield on a bond-  equivalent basis. In practice 
the result, 8 percent, would be referred to simply as the bond’s yield to maturity. In

money markets, if we annualized a six-  month period yield by doubling it, in order to 
make the result comparable to bonds’ YTMs we would also say that the result was a 
bond equivalent yield.
SUMMARY
In this reading, we applied the concepts of present value, net present value, and internal 
rate of return to the fundamental problem of valuing investments. We applied these 
concepts first to corporate investment, the well-  known capital budgeting problem. 
We then examined the fundamental problem of calculating the return on a portfolio 
subject to cash inflows and outflows. Finally we discussed money market yields and 
basic bond market terminology. The following summarizes the reading’s key concepts:
■■The net present value (NPV) of a project is the present value of its cash inflows 
minus the present value of its cash outflows. The internal rate of return (IRR) 
is the discount rate that makes NPV equal to 0. We can interpret IRR as an

expected compound return only when all interim cash flows can be reinvested 
at the internal rate of return and the investment is maintained to maturity.
■■The NPV rule for decision making is to accept all projects with positive NPV or, 
if projects are mutually exclusive, to accept the project with the higher positive 
NPV. With mutually exclusive projects, we rely on the NPV rule. The IRR rule is

Reading 7 ■ Discounted Cash Flow Applications 380
Brealey, Richard A., Stewart C. Myers, and Franklin Allen. 
2017. Principles of Corporate Finance . 12th ed. New York: 
McGraw-Hill.to accept all projects with an internal rate of return exceeding the required rate 
of return. The IRR rule can be affected by problems of scale and timing of cash 
flows.
■■Money-  weighted rate of return and time-  weighted rate of return are two 
alternative methods for calculating portfolio returns in a multiperiod setting 
when the portfolio is subject to additions and withdrawals. Time-  weighted 
rate of return is the standard in the investment management industry. Money-  
weighted rate of return can be appropriate if the investor exercises control over 
additions and withdrawals to the portfolio.
■■The money-  weighted rate of return is the internal rate of return on a portfolio, 
taking account of all cash flows.
■■The time-  weighted rate of return removes the effects of timing and amount of

withdrawals and additions to the portfolio and reflects the compound rate of 
growth of one unit of currency invested over a stated measurement period.
■■The bank discount yield for US Treasury bills (and other money-  market instru -
ments sold on a discount basis) is given by rBD = (F − P0)/F × 360/ t = D/F × 
360/ t, where F is the face amount to be received at maturity, P0 is the price 
of the Treasury bill, t is the number of days to maturity, and D is the dollar 
discount.
■■For a stated holding period or horizon, holding period yield (HPY) = (Ending 
price − Beginning price + Cash distributions)/(Beginning price). For a US 
Treasury bill, HPY = D/P0.
■■The effective annual yield (EAY) is (1 + HPY)365/ t − 1.
■■The money market yield is given by rMM = HPY × 360/ t, where t is the number 
of days to maturity.
■■For a Treasury bill, money market yield can be obtained from the bank discount 
yield using rMM = (360 × rBD)/(360 − t × rBD).

■■We can convert back and forth between holding period yields, money market 
yields, and effective annual yields by using the holding period yield, which is 
common to all the calculations.
■■The bond equivalent yield of a yield stated on a semiannual basis is that yield 
multiplied by 2.

Practice Problems 381
1 The net present value (NPV) of an investment is equal to the sum of the 
expected cash flows discounted at the: 
A internal rate of return.
B risk-  free rate.
C opportunity cost of capital. 
2 A $2.2 million investment will result in the cash flows shown below: 
Y earY ear-  End Cash Flow  
(millions)
1 $1.3
2 $1.6
3 $1.9
4 $0.8
 Using an 8% opportunity cost of capital, the project’s net present value (NPV) is 
A $2.47 million. 
B $3.40 million.
C $4.67 million.
3 A firm is considering three projects as shown below. 
Net Present Value 
(NPV)Internal Rate of 
Return (IRR) Hurdle Rate
Project A $47,000 10% 5%
Project B $58,000 20% 12%
Project C $52,000 22% 12%
 If the firm can only accept one project, to maximize shareholder wealth, the 
firm is most likely  to select:
A Project A.
B Project B.
C Project C.
4 The internal rate of return (IRR) is best described as the:
A opportunity cost of capital. 
B time-  weighted rate of return.

C discount rate that makes the net present value equal to zero.
5 A three-  year investment requires an initial outlay of £1,000. It is expected to 
provide three year-  end cash flows of £200 plus a net salvage value of £700 at the 
end of three years. Its internal rate of return (IRR) is closest to: 
A 10%.
B 11%.
C 20%.
© 2016 by CFA Institute. All rights reserved.

Reading 7 ■ Discounted Cash Flow Applications 382
6 The internal rate of return (IRR) rule indicates acceptance of a project when the 
IRR is:
A greater than zero.
B less than the opportunity cost of capital.
C greater than the opportunity cost of capital.
7 Suppose a company has only €1,000,000 available to invest. The three projects 
available are described in the table:
Y earProject A Cash 
Flow (€)Project B Cash 
Flow (€)Project C Cash 
Flow (€)
0 –1,000,000 –1,000,000 –500,000
1 1,200,000 0 0
2 0 0 0
3 0 1,600,000 850,000
Internal rate of return 
(IRR)20.00% 16.96% 19.35%
 If the opportunity cost of capital is 12%, which project should be accepted?
8 An investor buys a share of stock for $52.68 and receives an $0.88 dividend one 
year later. If the share sells for $57.50 just after the dividend payment, the hold -
ing period return is closest  to:
A 9.1%.
B 9.9%.
C 10.8%. 
9 An investor performs the following transactions on the shares of a firm.

■●At t = 0, she purchases a share for $1,000. 
■●At t = 1, she receives a dividend of $25 and then purchases three additional 
shares for $1,055 each. 
■●At t = 2, she receives a total dividend of $100 and then sells the four shares 
for $1,100 each. 
 The money-  weighted rate of return is closest  to:
A 4.5%.
B 6.9%.
C 7.3%.
10 A fund receives investments at the beginning of each year and generates returns 
as shown in the table.
Y ear of Investment Amount of InvestmentReturn during Y ear of 
1 $1,000 15%
2 $4,000 14%
3 $45,000 –4%
 Which return measure over the three-  year period is negative?

Practice Problems 383
A Geometric mean return
B Time-  weighted rate of return
C Money-  weighted rate of return
11 At the beginning of Year 1, a fund has $10 million under management; it earns 
a return of 14% for the year. The fund attracts another $100 million at the start 
of Year 2 and earns a return of 8% for that year. The money-  weighted rate of 
return is most likely :
A less than the time-  weighted rate of return.
B the same as the time-  weighted rate of return.
C greater than the time-  weighted rate of return.
12 An investor buys a bond for $980. After six months, she collects a semiannual 
coupon of $30 and sells the bond for $990. Her six-  month holding period yield 
(HPY) is closest  to:
A 1.0%.
B 4.1%.
C 8.3%.
13 A portfolio manager pays $99,500 for a 182-  day US T-  bill with face value of 
$100,000. The T-  bill will be held to maturity. A yield of 0.5025% calculated for 
this T-  bill when it is purchased is most accurately described as the:
A bank discount yield.

B money market yield. 
C holding period yield.
14 A 123-  day T-  bill with a maturity value of $100,000 is priced at $99,620. The 
bill’s effective annual yield is closest  to:
A 0.38%.
B 1.12%.
C 1.14%.
15 For a T-  bill purchased at $97,000 that matures at $100,000 in 300 days, which of 
the following yields is closest  to 3.71%? 
A Money market yield
B Holding period yield (HPY)
C Effective annual yield
16 A 223-  day T-  bill with a maturity value of $100,000 has a bank discount yield of 
2.05%. The bill’s holding period yield is closest  to:
A 1.29%.
B 2.08%.
C 2.11%.
17 Given a 300-  day holding period yield (HPY) of 7%, the effective annual yield 
(EAY) is closest  to:
A 8.4%.
B 8.5%.
C 8.6%.

Reading 7 ■ Discounted Cash Flow Applications 384
SOLUTIONS
1 C is correct. The NPV sums the project’s expected cash flows (CF) discounted 
at the opportunity cost of capital. The NPV calculation is
NPVCF=
+()=∑t
t
tN
r10
 where
 r = the discount rate or opportunity cost of capital 
2 A is correct. 
The NPV =  −+()+
()+
()+
()$.$.
.$.
.$.
.$.
.2213
10816
10819
10808
108234= $2.47 million.
3 B is correct. According to the NPV rule, shareholder wealth is maximized by 
selecting a project with the highest NPV. The IRR rule also signals acceptance; 
however, the IRR rule should not be used to rank projects. In this case, Project 
B adds the most value to the firm. 
4 C is correct. The internal rate of return is computed by identifying all cash flows 
and solving for the rate that makes the net present value of those cash flows 
equal to zero. 
5 B is correct. IRR is determined by setting the net present value equal to zero for

the cash flows shown in the table. 
Y ear Cash Flow (£)
0 –1,000
1 200
2 200
3 900
6 C is correct. The IRR investment decision rule states, “ Accept projects or invest -
ments for which the IRR is greater than the opportunity cost of capital. ” 
7 B is correct. The projects are mutually exclusive because the amount to invest is 
constrained to €1,000,000. Therefore, the net present value (NPV) rule should 
be used to choose among them when the IRR rule and NPV rule conflict. Based 
on the opportunity cost of capital of 12%, the NPV of Project B is €138,848, 
which is higher than the NPV of €71,429 for Project A and the NPV of $105,013 
for Project C. 
 Project A NPV = –€1,000,000 + €1,200,000/(1.12) = €71,429
 Project B NPV = –€1,000,000 + €1,600,000/(1.12)3 = €138,848
 Project C NPV = –€500,000 + €850,000/(1.12)3 = €105,013
8 C is correct. The formula for the holding period return is
PP D
P10 1
0−+

Solutions 385
 where P0 is the initial investment, P1 is the final value at the end of the holding 
period, and D1 is the cash dividend paid at the end of the holding period. This 
investment results in a holding period return (HPR) of
HPR=−+=$. $. $.
$..%57 50 52 68 088
52 6810 82
9 B is correct. Computation of the money-  weighted return, r, requires finding the 
discount rate that sets the present value (outflows) equal to the present value 
(inflows). 
 Solving for r, 
$,$, $$ ,1 0003 165
125
14 500
12++()=+()+
+()rr r
 results in a value of r = 6.91%
10 C is correct. The money-  weighted rate of return considers both the timing 
and amounts of investments into the fund. The investment at the beginning 
of Year 1 will be worth $1,000(1.15)(1.14)(0.96) = $1,258.56 at the end of Year 
3. The investment made at the beginning of Year 2 will be worth $4,377.60 = 
$4,000(1.14)(0.96) at the end of Year 3. The investment of $45,000 at the begin -

ning of Year 3 decreases to a value of $45,000(0.96) = $43,200 at the end of Year 
3. 
$,$, $, $, $, .$ ,1 0004 000
145 000
11 258 4 377 60 43 200
12++()+
+()=++
r r + +()r3
 results in r = –2.08%
 Note that B is incorrect because the time-  weighted rate of return (TWR) of the 
fund is the same as the geometric mean return of the fund and is thus positive:
TWR=() () () −= 1151140961 7973.. .. %
11 A is correct. The money-  weighted rate of return is found by setting the present 
value (PV) of investments into the fund equal to the PV of the fund’s terminal 
value. Because most of the investment came during Year 2, the measure will be 
biased toward the performance of Year 2. Set the PV of investments equal to the 
PV of the fund’s terminal value:
$.. .10100
110 1141 08 100 108
12++()=×× +×
+()r r
Solving for r results in r = 8.53%. 
 The time-  weighted return of the fund is =  1141 08 12..() () − = 10.96%.
12 B is correct. The HPY for the bond is
PP D
P10 1
0990 980 30
980408−+=−+=$$ $
$.%

PP D
P10 1
0990 980 30
$.%
13 C is correct. The 182-  day holding period yield (HPY) is calculated as follows:
HPY=−+=−=PP D
P10 1
0100 000 99 500
99 5000 5025$, $,
$,.%

Reading 7 ■ Discounted Cash Flow Applications 386
14 C is correct. The effective annual yield (EAY) is calculated as follows (where 
HPY is holding period yield):
P10 1
0100 00 99 620
99 6200 3814$, $,
$,.%
EAYH PY =+() −= +() −= 11 1 003814 11 1362365 123 365 123.. %
15 A is correct. The money market yield is equal to the annualized HPY, assuming 
a 360-  day year. rMM = (HPY)(360/ t). A T-  bill purchased at $97,000 has a HPY of 
[($100,000 – $97,000)/$97,000] = 3.09%. The money market yield for this T-  bill 
is (3.09%)(360/300) = 3.71%. The effective annual yield for this T-  bill is (1 + 
0.0309)365/300 – 1 = 3.77%. 
16 A is correct. The holding period yield of a bill can be computed from the bank 
discount yield by finding the bill’s discount D:
rD
FtBD=×360, so 0 0205100 000360
223.$,=×D
 Solving for D results in a discount of $1269.86. This result implies a purchase 
price of $100,000 – $1,269.86 = $98,730.14. 
 The holding period yield (HPY) then computes as:
HPY= =$, .
$, ..%1 269 86

HPY= =$, .
98 730 141 286
 B is incorrect because it is the money market yield and C is incorrect because it 
is the equivalent annual yield.
17 C is correct. The EAY is one plus the HPY, compounded forward one year, and 
then subtract one: 
EAY = (1 + HPY)365/ t – 1  
(1 + 0.07)365/300 – 1 = 8.58% ≈ 8.6%

Statistical Concepts and Market Returns
Richard A. DeFusco, PhD, CFA, is at the University of Lincoln-  Nebraska (USA). Dennis W. 
a. distinguish between descriptive statistics and inferential statistics, 
between a population and a sample, and among the types of 
measurement scales;
b. define a parameter, a sample statistic, and a frequency 
distribution;
c. calculate and interpret relative frequencies and cumulative 
relative frequencies, given a frequency distribution;
d. describe the properties of a data set presented as a histogram or a 
frequency polygon;
e. calculate and interpret measures of central tendency, including

the population mean, sample mean, arithmetic mean, weighted 
average or mean, geometric mean, harmonic mean, median, and 
mode;
f. calculate and interpret quartiles, quintiles, deciles, and 
percentiles;
g. calculate and interpret 1) a range and a mean absolute deviation 
and 2) the variance and standard deviation of a population and of 
a sample;
h. calculate and interpret the proportion of observations falling 
within a specified number of standard deviations of the mean 
using Chebyshev’s inequality;
i. calculate and interpret the coefficient of variation and the Sharpe 
ratio;
j. explain skewness and the meaning of a positively or negatively 
skewed return distribution;
(continued)rEAdING
8

Reading 8 ■ Statistical Concepts and Market Returns 388
k. describe the relative locations of the mean, median, and mode for 
a unimodal, nonsymmetrical distribution;
l. explain measures of sample skewness and kurtosis;
m. compare the use of arithmetic and geometric means when 
analyzing investment returns.
Statistical methods provide a powerful set of tools for analyzing data and drawing 
conclusions from them. Whether we are analyzing asset returns, earnings growth 
rates, commodity prices, or any other financial data, statistical tools help us quantify 
and communicate the data’s important features. This reading presents the basics of 
describing and analyzing data, the branch of statistics known as descriptive statis -
tics. The reading supplies a set of useful concepts and tools, illustrated in a variety of 
investment contexts. One theme of our presentation, reflected in the reading’s title,

is the demonstration of the statistical methods that allow us to summarize return 
distributions.1 We explore four properties of return distributions:
■■where the returns are centered (central tendency);
■■how far returns are dispersed from their center (dispersion);
■■whether the distribution of returns is symmetrically shaped or lopsided (skew -
ness); and
■■whether extreme outcomes are likely (kurtosis).
These same concepts are generally applicable to the distributions of other types of 
data, too.
The reading is organized as follows. After defining some basic concepts in Section 
2, in Sections 3 and 4 we discuss the presentation of data: Section 3 describes the 
organization of data in a table format, and Section 4 describes the graphic presenta -
tion of data. We then turn to the quantitative description of how data are distributed: 
Section 5 focuses on measures that quantify where data are centered, or measures of

central tendency. Section 6 presents other measures that describe the location of data. 
Section 7 presents measures that quantify the degree to which data are dispersed. 
Sections 8 and 9 describe additional measures that provide a more accurate picture of 
data. Section 10 provides investment applications of concepts introduced in Section 5.
SOME FUNDAMENTAL CONCEPTS
Before starting the study of statistics with this reading, it may be helpful to examine a 
picture of the overall field. In the following, we briefly describe the scope of statistics 
and its branches of study. We explain the concepts of population and sample. Data 1
2
1 Ibbotson Associates (www.ibbotson.com) generously provided some of the data used in this reading. 
We also draw on Dimson, Marsh, and Staunton’s (2011) history and study of world markets as well as 
other sources.

Some Fundamental Concepts 389
come in a variety of types, affecting the ways they can be measured and the appro -
priate statistical methods for analyzing them. We conclude by discussing the basic 
types of data measurement.
2.1 The Nature of Statistics
The term statistics  can have two broad meanings, one referring to data and the other 
to method. A company’s average earnings per share (EPS) for the last 20 quarters, or 
its average returns for the past 10 years, are statistics. We may also analyze historical 
EPS to forecast future EPS, or use the company’s past returns to infer its risk. The 
totality of methods we employ to collect and analyze data is also called statistics.
Statistical methods include descriptive statistics and statistical inference (infer -
ential statistics). Descriptive statistics  is the study of how data can be summarized 
effectively to describe the important aspects of large data sets. By consolidating a

mass of numerical details, descriptive statistics turns data into information. Statistical 
inference  involves making forecasts, estimates, or judgments about a larger group 
from the smaller group actually observed. The foundation for statistical inference is 
probability theory, and both statistical inference and probability theory will be dis -
cussed in later readings. Our focus in this reading is solely on descriptive statistics.
2.2 Populations and Samples
Throughout the study of statistics we make a critical distinction between a population 
and a sample. In this section, we explain these two terms as well as the related terms 
“parameter” and “sample statistic. ”2
■■Definition of Population.  A population  is defined as all members of a speci -
fied group.
Any descriptive measure of a population characteristic is called a parameter . 
Although a population can have many parameters, investment analysts are usually

concerned with only a few, such as the mean value, the range of investment returns, 
and the variance.
Even if it is possible to observe all the members of a population, it is often too 
expensive in terms of time or money to attempt to do so. For example, if the popu -
lation is all telecommunications customers worldwide and an analyst is interested in 
their purchasing plans, she will find it too costly to observe the entire population. The 
analyst can address this situation by taking a sample of the population.
■■Definition of Sample.  A sample  is a subset of a population.
In taking a sample, the analyst hopes it is characteristic of the population. The field 
of statistics known as sampling deals with taking samples in appropriate ways to 
achieve the objective of representing the population well. A later reading addresses 
the details of sampling.
Earlier, we mentioned statistics in the sense of referring to data. Just as a parameter

is a descriptive measure of a population characteristic, a sample statistic (statistic, for 
short) is a descriptive measure of a sample characteristic.
■■Definition of Sample Statistic.  A sample statistic  (or statistic ) is a quantity 
computed from or used to describe a sample.
2 This reading introduces many statistical concepts and formulas. To make it easy to locate them, we have 
set off some of the more important ones with bullet points.

Reading 8 ■ Statistical Concepts and Market Returns 390
We devote much of this reading to explaining and illustrating the use of statistics 
in this sense. The concept is critical also in statistical inference, which addresses such 
problems as estimating an unknown population parameter using a sample statistic.
2.3 Measurement Scales
To choose the appropriate statistical methods for summarizing and analyzing data, 
we need to distinguish among different measurement scales  or levels of measure -
ment. All data measurements are taken on one of four major scales: nominal, ordinal, 
interval, or ratio.
Nominal scales  represent the weakest level of measurement: They categorize data 
but do not rank them. If we assigned integers to mutual funds that follow different 
investment strategies, the number 1 might refer to a small-  cap value fund, the num -
ber 2 to a large-  cap value fund, and so on for each possible style. This nominal scale

categorizes the funds according to their style but does not rank them.
Ordinal scales  reflect a stronger level of measurement. Ordinal scales sort data 
into categories that are ordered with respect to some characteristic. For example, the 
Morningstar and Standard & Poor’s star ratings for mutual funds represent an ordinal 
scale in which one star represents a group of funds judged to have had relatively the 
worst performance, with two, three, four, and five stars representing groups with 
increasingly better performance, as evaluated by those services.
An ordinal scale may also involve numbers to identify categories. For example, in 
ranking balanced mutual funds based on their five-  year cumulative return, we might 
assign the number 1 to the top 10 percent of funds, and so on, so that the number 
10 represents the bottom 10 percent of funds. The ordinal scale is stronger than the 
nominal scale because it reveals that a fund ranked 1 performed better than a fund

ranked 2. The scale tells us nothing, however, about the difference in performance 
between funds ranked 1 and 2 compared with the difference in performance between 
funds ranked 3 and 4, or 9 and 10.
Interval scales  provide not only ranking but also assurance that the differences 
between scale values are equal. As a result, scale values can be added and subtracted 
meaningfully. The Celsius and Fahrenheit scales are interval measurement scales. The 
difference in temperature between 10°C and 11°C is the same amount as the difference 
between 40°C and 41°C. We can state accurately that 12°C = 9°C + 3°C, for example. 
Nevertheless, the zero point of an interval scale does not reflect complete absence 
of what is being measured; it is not a true zero point or natural zero. Zero degrees 
Celsius corresponds to the freezing point of water, not the absence of temperature. 
As a consequence of the absence of a true zero point, we cannot meaningfully form 
ratios on interval scales.

As an example, 50°C, although five times as large a number as 10°C, does not 
represent five times as much temperature. Also, questionnaire scales are often treated 
as interval scales. If an investor is asked to rank his risk aversion on a scale from 1 
(extremely risk-  averse) to 7 (extremely risk-  loving), the difference between a response 
of 1 and a response of 2 is sometimes assumed to represent the same difference in 
risk aversion as the difference between a response of 6 and a response of 7. When that 
assumption can be justified, the data are measured on an interval scale.
Ratio scales  represent the strongest level of measurement. They have all the char -
acteristics of interval measurement scales as well as a true zero point as the origin. 
With ratio scales, we can meaningfully compute ratios as well as meaningfully add 
and subtract amounts within the scale. As a result, we can apply the widest range of

statistical tools to data measured on a ratio scale. Rates of return are measured on 
a ratio scale, as is money. If we have twice as much money, then we have twice the 
purchasing power. Note that the scale has a natural zero—zero means no money.

Summarizing Data Using Frequency Distributions 391
Now that we have addressed the important preliminaries, we can discuss sum -
marizing and describing data.
EXAMPLE 1   
Identifying Scales of Measurement
State the scale of measurement for each of the following:
1 Credit ratings for bond issues.3
2 Cash dividends per share.
3 Hedge fund classification types.4
4 Bond maturity in years.
Credit ratings are measured on an ordinal scale. A rating places a bond issue in 
a category, and the categories are ordered with respect to the expected probabil -
ity of default. But the difference in the expected probability of default between 
AA− and A+, for example, is not necessarily equal to that between BB− and 
B+. In other words, letter credit ratings are not measured on an interval scale.
Cash dividends per share are measured on a ratio scale. For this variable, 0 
represents the complete absence of dividends; it is a true zero point.

Hedge fund classification types are measured on a nominal scale. Each type groups 
together hedge funds with similar investment strategies. In contrast to credit 
ratings for bonds, however, hedge fund classification schemes do not involve a 
ranking. Thus such classification schemes are not measured on an ordinal scale.
Bond maturity is measured on a ratio scale.
SUMMARIZING DATA USING FREQUENCY 
DISTRIBUTIONS
In this section, we discuss one of the simplest ways to summarize data—the frequency 
■■Definition of Frequency Distribution.  A frequency distribution  is a tabular 
display of data summarized into a relatively small number of intervals.3
3 Credit ratings for a bond issue gauge the bond issuer’s ability to meet the promised principal and 
interest payments on the bond. For example, one rating agency, Standard & Poor’s, assigns bond issues to

one of the following ratings, given in descending order of credit quality (increasing probability of default): 
AAA, AA+, AA, AA−, A+, A, A−, BBB+, BBB, BBB−, BB+, BB, BB−, B+, B, B−, CCC+, CCC−, CC, C, D. 
For more information on credit risk and credit ratings, see the Level I CFA Program curriculum reading 
“Fixed-  Income Securities: Defining Elements. ” 
4 “Hedge fund” refers to investment vehicles with legal structures that result in less regulatory oversight 
than other pooled investment vehicles such as mutual funds. Hedge fund classification types group hedge 
funds by the kind of investment strategy they pursue.

Reading 8 ■ Statistical Concepts and Market Returns 392
Frequency distributions help in the analysis of large amounts of statistical data, and 
they work with all types of measurement scales.
Rates of return are the fundamental units that analysts and portfolio managers use 
for making investment decisions and we can use frequency distributions to summarize 
rates of return. When we analyze rates of return, our starting point is the holding 
period return (also called the total return).
■■Holding Period Return Formula.  The holding period return for time period t, 
Rt, is
RPP D
Pttt t
t=−+−
−1
1
where
 Pt = price per share at the end of time period t
 Pt−1 = price per share at the end of time period t − 1, the time period immedi -
ately preceding time period t
 Dt = cash distributions received during time period t
Thus the holding period return for time period t is the capital gain (or loss) plus distri -
butions divided by the beginning-  period price. (For common stocks, the distribution

is a dividend; for bonds, the distribution is a coupon payment.) Equation 1 can be 
used to define the holding period return on any asset for a day, week, month, or year 
simply by changing the interpretation of the time interval between successive values 
of the time index, t. 
The holding period return, as defined in Equation 1, has two important charac -
teristics. First, it has an element of time attached to it. For example, if a monthly time 
interval is used between successive observations for price, then the rate of return is a 
monthly figure. Second, rate of return has no currency unit attached to it. For instance, 
suppose that prices are denominated in euros. The numerator and denominator of 
Equation 1 would be expressed in euros, and the resulting ratio would not have any 
units because the units in the numerator and denominator would cancel one another. 
This result holds regardless of the currency in which prices are denominated.5

With these concerns noted, we now turn to the frequency distribution of the hold -
ing period returns on the S&P 500 Index.6 First, we examine annual rates of return; 
then we look at monthly rates of return. The annual rates of return on the S&P 500 
calculated with Equation 1 span the period January 1926 to December 2012, for a 
total of 87 annual observations. Monthly return data cover the period January 1926 
to December 2012, for a total of 1,044 monthly observations.
We can state a basic procedure for constructing a frequency distribution as follows.
Construction of a Frequency Distribution.
1 Sort the data in ascending order.
2 Calculate the range of the data, defined as Range = Maximum value − 
Minimum value.
3 Decide on the number of intervals in the frequency distribution, k.(1)
5 Note, however, that if price and cash distributions in the expression for holding period return were not

in one’s home currency, one would generally convert those variables to one’s home currency before calcu -
lating the holding period return. Because of exchange rate fluctuations during the holding period, holding 
period returns on an asset computed in different currencies would generally differ.
6 We use the total return series on the S&P 500 from January  1926 to December  2012 provided by 
Ibbotson Associates.

Summarizing Data Using Frequency Distributions 393
4 Determine interval width as Range/ k.
5 Determine the intervals by successively adding the interval width to the mini -
mum value, to determine the ending points of intervals, stopping after reaching 
an interval that includes the maximum value.
6 Count the number of observations falling in each interval.
7 Construct a table of the intervals listed from smallest to largest that shows the 
number of observations falling in each interval.
In Step 4, when rounding the interval width, round up rather than down, to ensure 
that the final interval includes the maximum value of the data.
As the above procedure makes clear, a frequency distribution groups data into a 
set of intervals.7 An interval  is a set of values within which an observation falls. Each 
observation falls into only one interval, and the total number of intervals covers all the 
values represented in the data. The actual number of observations in a given interval

is called the absolute frequency , or simply the frequency. The frequency distribution 
is the list of intervals together with the corresponding measures of frequency.
To illustrate the basic procedure, suppose we have 12 observations sorted in 
ascending order: −4.57, −4.04, −1.64, 0.28, 1.34, 2.35, 2.38, 4.28, 4.42, 4.68, 7.16, and 
11.43. The minimum observation is −4.57 and the maximum observation is +11.43, 
so the range is +11.43 − (−4.57) = 16. If we set k = 4, the interval width is 16/4 = 4. 
Table 1 shows the repeated addition of the interval width of 4 to determine the end -
points for the intervals (Step 5).
Table 1   Endpoints of Intervals
−4.57 + 4.00 = −0.57
−0.57 + 4.00 = 3.43
3.43 + 4.00 = 7.43
7.4 + 4.00 = 11.43
Thus the intervals are [−4.57 to −0.57), [−0.57 to 3.43), [3.43 to 7.43), and [7.43 to 
11.43].8 Table 2 summarizes Steps 5 through 7.
Table 2   Frequency Distribution
Interval Absolute Frequency
A −4.57 ≤ observation < −0.57 3
B −0.57 ≤ observation < 3.43 4

C 3.43 ≤ observation < 7.43 4
D 7.43 ≤ observation ≤ 11.43 1
Note that the intervals do not overlap, so each observation can be placed uniquely 
into one interval.
7 Intervals are also sometimes called classes, ranges, or bins.
8 The notation [−4.57 to −0.57) means −4.57 ≤ observation < −0.57. In this context, a square bracket 
indicates that the endpoint is included in the interval.

Reading 8 ■ Statistical Concepts and Market Returns 394
In practice, we may want to refine the above basic procedure. For example, we may 
want the intervals to begin and end with whole numbers for ease of interpretation. We 
also need to explain the choice of the number of intervals, k. We turn to these issues 
in discussing the construction of frequency distributions for the S&P 500.
We first consider the case of constructing a frequency distribution for the annual 
returns on the S&P 500 over the period 1926 to 2012. During that period, the return 
on the S&P 500 had a minimum value of −43.34 percent (in 1931) and a maximum 
value of +53.99 percent (in 1933). Thus the range of the data was +54% − (−43%) = 97%, 
approximately. The question now is the number k of intervals into which we should 
group observations. Although some guidelines for setting k have been suggested in 
statistical literature, the setting of a useful value for k often involves inspecting the

data and exercising judgment. How much detail should we include? If we use too few 
intervals, we will summarize too much and lose pertinent characteristics. If we use 
too many intervals, we may not summarize enough.
We can establish an appropriate value for k by evaluating the usefulness of the 
resulting interval width. A large number of empty intervals may indicate that we are 
trying to organize the data to present too much detail. Starting with a relatively small 
interval width, we can see whether or not the intervals are mostly empty and whether 
or not the value of k associated with that interval width is too large. If intervals are 
mostly empty or k is very large, we can consider increasingly larger intervals (smaller 
values of k) until we have a frequency distribution that effectively summarizes the 
distribution. For the annual S&P 500 series, return intervals of 1 percent width would 
result in 97 intervals and many of them would be empty because we have only 87 annual

observations. We need to keep in mind that the purpose of a frequency distribution 
is to summarize  the data. Suppose that for ease of interpretation we want to use an 
interval width stated in whole rather than fractional percents. A 2 percent interval 
width would have many fewer empty intervals than a 1 percent interval width and 
effectively summarize the data. A 2 percent interval width would be associated with 
97/2 = 48.5 intervals, which we can round up to 49 intervals. That number of inter -
vals will cover 2% × 49 = 98%. We can confirm that if we start the smallest 2 percent 
interval at the whole number −44.0 percent, the final interval ends at −44.0% + 98% = 
54% and includes the maximum return in the sample, 53.99 percent. In so constructing 
the frequency distribution, we will also have intervals that end and begin at a value of 
0 percent, allowing us to count the negative and positive returns in the data. Without

too much work, we have found an effective way to summarize the data. We will use 
return intervals of 2 percent, beginning with −44% ≤ Rt < −42% (given as “−44% to 
−42%” in the table) and ending with 52% ≤ Rt ≤ 54%. Table 3 shows the frequency 
distribution for the annual total returns on the S&P 500.
Table 3 includes three other useful ways to present data, which we can compute 
once we have established the frequency distribution: the relative frequency, the cumu -
lative frequency (also called the cumulative absolute frequency), and the cumulative 
relative frequency.
■■Definition of Relative Frequency.  The relative frequency  is the absolute fre -
quency of each interval divided by the total number of observations.
The cumulative relative frequency  cumulates (adds up) the relative frequencies 
as we move from the first to the last interval. It tells us the fraction of observations 
that are less than the upper limit of each interval. Examining the frequency distribu -

tion given in Table 3, we see that the first return interval, −44 percent to −42 percent, 
has one observation; its relative frequency is 1/87 or 1.15 percent. The cumulative 
frequency for this interval is 1 because only one observation is less than −42 per -
cent. The cumulative relative frequency is thus 1/87 or 1.15 percent. The next return 
interval has zero observations; therefore, its cumulative frequency is 0 plus 1 and its 
cumulative relative frequency is 1.15 percent (the cumulative relative frequency from

Summarizing Data Using Frequency Distributions 395
the previous interval). We can find the other cumulative frequencies by adding the 
(absolute) frequency to the previous cumulative frequency. The cumulative frequency, 
then, tells us the number of observations that are less than the upper limit of each 
return interval.
As Table 3 shows, return intervals have frequencies from 0 to 7 in this sample. 
The interval encompassing returns between −10 percent and −8 percent (−10% ≤ Rt 
< −8%) has the most observations, seven. Next most frequent are returns between 
4 percent and 6 percent (4% ≤ Rt < 6%) and between18 percent and 20 percent (18% 
≤ Rt < 20%), with six observations in each interval. From the cumulative frequency 
column, we see that the number of negative returns is 24. The number of positive 
returns must then be equal to 87 − 24, or 63. We can express the number of positive 
and negative outcomes as a percentage of the total to get a sense of the risk inherent

in investing in the stock market. During the 87-  year period, the S&P 500 had negative 
annual returns 27.6 percent of the time (that is, 24/87). This result appears in the fifth 
column of Table 3, which reports the cumulative relative frequency.
The frequency distribution gives us a sense of not only where most of the observa -
tions lie but also whether the distribution is evenly distributed, lopsided, or otherwise 
distinctive. In the case of the S&P 500, we can see that more than half of the outcomes 
are positive and most of those annual returns are larger than 10 percent. (Only 14 of 
the 63 positive annual returns—about 22 percent—were between 0 and 10 percent.)
Table 3 permits us to make an important further point about the choice of the 
number of intervals related to equity returns in particular. From the frequency dis -
tribution in Table 3, we can see that only six outcomes fall between −44 percent to

−16  percent and only five outcomes fall between 38  percent to 54  percent. Stock 
return data are frequently characterized by a few very large or small outcomes. We 
could have collapsed the return intervals in the tails of the frequency distribution by 
choosing a smaller value of k, but then we would have lost the information about how 
extremely poorly or well the stock market had performed. A risk manager may need 
to know the worst possible outcomes and thus may want to have detailed information 
on the tails (the extreme values). A frequency distribution with a relatively large value 
of k is useful for that. A portfolio manager or analyst may be equally interested in 
detailed information on the tails; however, if the manager or analyst wants a picture 
only of where most of the observations lie, he might prefer to use an interval width 
of 4 percent (25 intervals beginning at −44 percent), for example.
The frequency distribution for monthly returns on the S&P 500 looks quite dif -

ferent from that for annual returns. The monthly return series from January 1926 to 
December 2012 has 1,044 observations. Returns range from a minimum of approxi -
mately −30 percent to a maximum of approximately +43 percent. With such a large 
quantity of monthly data we must summarize to get a sense of the distribution, and 
so we group the data into 37 equally spaced return intervals of 2 percent. The gains 
from summarizing in this way are substantial. Table 4 presents the resulting frequency 
distribution. The absolute frequencies appear in the second column, followed by the 
relative frequencies. The relative frequencies are rounded to two decimal places. The 
cumulative absolute and cumulative relative frequencies appear in the fourth and 
fifth columns, respectively.

Reading 8 ■ Statistical Concepts and Market Returns 396
Table 3   Frequency Distribution for the Annual Total Return on the S&P 500, 1926–2012
Return 
Interval (%) FrequencyRelative 
Frequency (%)Cumulative 
FrequencyCumulative Relative 
Frequency (%)Return 
Frequency (%)
−44.0 to −42.0 1 1.15 1 1.15 4.0 to 6.0 6 6.90 33 37.93
−42.0 to −40.0 0 0.00 1 1.15 6.0 to 8.0 4 4.60 37 42.53
−40.0 to −38.0 0 0.00 1 1.15 8.0 to 10.0 1 1.15 38 43.68
−38.0 to −36.0 1 1.15 2 2.30 10.0 to 12.0 4 4.60 42 48.28
−36.0 to −34.0 1 1.15 3 3.45 12.0 to 14.0 1 1.15 43 49.43
−34.0 to −32.0 0 0.00 3 3.45 14.0 to 16.0 4 4.60 47 54.02
−32.0 to −30.0 0 0.00 3 3.45 16.0 to 18.0 2 2.30 49 56.32
−30.0 to −28.0 0 0.00 3 3.45 18.0 to 20.0 6 6.90 55 63.22
−28.0 to −26.0 1 1.15 4 4.60 20.0 to 22.0 3 3.45 58 66.67
−26.0 to −24.0 1 1.15 5 5.75 22.0 to 24.0 5 5.75 63 72.41
−24.0 to −22.0 1 1.15 6 6.90 24.0 to 26.0 2 2.30 65 74.71

−22.0 to −20.0 0 0.00 6 6.90 26.0 to 28.0 2 2.30 67 77.01
−20.0 to −18.0 0 0.00 6 6.90 28.0 to 30.0 2 2.30 69 79.31
−18.0 to −16.0 0 0.00 6 6.90 30.0 to 32.0 5 5.75 74 85.06
−16.0 to −14.0 1 1.15 7 8.05 32.0 to 34.0 4 4.60 78 89.66
−14.0 to −12.0 0 0.00 7 8.05 34.0 to 36.0 0 0.00 78 89.66
−12.0 to −10.0 4 4.60 11 12.64 36.0 to 38.0 4 4.60 82 94.25
−10.0 to −8.0 7 8.05 18 20.69 38.0 to 40.0 0 0.00 82 94.25
−8.0 to −6.0 1 1.15 19 21.84 40.0 to 42.0 0 0.00 82 94.25
−6.0 to −4.0 1 1.15 20 22.99 42.0 to 44.0 2 2.30 84 96.55
−4.0 to −2.0 1 1.15 21 24.14 44.0 to 46.0 0 0.00 84 96.55
−2.0 to 0.0 3 3.45 24 27.59 46.0 to 48.0 1 1.15 85 97.70
0.0 to 2.0 2 2.30 26 29.89 48.0 to 50.0 0 0.00 85 97.70
2.0 to 4.0 1 1.15 27 31.03 50.0 to 52.0 0 0.00 85 97.70
          52.0 to 54.0 2 2.30 87 100.00
Note : The lower class limit is the weak inequality (≤) and the upper class limit is the strong inequality (<). Cumulative relative frequency totals reflect calculations using full precision, with results

Summarizing Data Using Frequency Distributions 397
Table 4   Frequency Distribution for the Monthly Total Return on the S&P 
500, January 1926 to December 2012
Return  
Interval (%)Absolute 
FrequencyRelative 
Absolute 
FrequencyCumulative 
Relative 
−30.0 to −28.0 1 0.10 1 0.10
−28.0 to −26.0 0 0.00 1 0.10
−26.0 to −24.0 1 0.10 2 0.19
−24.0 to −22.0 1 0.10 3 0.29
−22.0 to −20.0 2 0.19 5 0.48
−20.0 to −18.0 2 0.19 7 0.67
−18.0 to −16.0 3 0.29 10 0.96
−16.0 to −14.0 2 0.19 12 1.15
−14.0 to −12.0 6 0.57 18 1.72
−12.0 to −10.0 7 0.67 25 2.39
−10.0 to −8.0 23 2.20 48 4.60
−8.0 to −6.0 34 3.26 82 7.85
−6.0 to −4.0 59 5.65 141 13.51
−4.0 to −2.0 98 9.39 239 22.89
−2.0 to 0.0 157 15.04 396 37.93
0.0 to 2.0 220 21.07 616 59.00
2.0 to 4.0 173 16.57 789 75.57
4.0 to 6.0 137 13.12 926 88.70
6.0 to 8.0 63 6.03 989 94.73
8.0 to 10.0 25 2.39 1,014 97.13
10.0 to 12.0 15 1.44 1,029 98.56
12.0 to 14.0 6 0.57 1,035 99.14
14.0 to 16.0 2 0.19 1,037 99.33
16.0 to 18.0 3 0.29 1,040 99.62

18.0 to 20.0 0 0.00 1,040 99.62
20.0 to 22.0 0 0.00 1,040 99.62
22.0 to 24.0 0 0.00 1,040 99.62
24.0 to 26.0 1 0.10 1,041 99.71
26.0 to 28.0 0 0.00 1,041 99.71
28.0 to 30.0 0 0.00 1,041 99.71
30.0 to 32.0 0 0.00 1,041 99.71
32.0 to 34.0 0 0.00 1,041 99.71
34.0 to 36.0 0 0.00 1,041 99.71
36.0 to 38.0 0 0.00 1,041 99.71
38.0 to 40.0 2 0.19 1,043 99.90
40.0 to 42.0 0 0.00 1,043 99.90
42.0 to 44.0 1 0.10 1,044 100.00
Note : The lower class limit is the weak inequality (≤) and the upper class limit is the strong inequality 
(<). The relative frequency is the absolute frequency or cumulative frequency divided by the total 
number of observations. Cumulative relative frequency totals reflect calculations using full precision, 
with results rounded to two decimal places.

Reading 8 ■ Statistical Concepts and Market Returns 398
Source:  Ibbotson Associates.
The advantage of a frequency distribution is evident in Table 4, which tells us that 
the vast majority of observations (687/1,044 = 66 percent) lie in the four intervals 
spanning −2 percent to +6 percent. Altogether, we have 396 negative returns and 648 
positive returns. Almost 62 percent of the monthly outcomes are positive. Looking 
at the cumulative relative frequency in the last column, we see that the interval 
−2 percent to 0 percent shows a cumulative frequency of 37.93 percent, for an upper 
return limit of 0 percent. This means that 37.93 percent of the observations lie below 
the level of 0 percent. We can also see that not many observations are greater than 
+12 percent or less than −12 percent. Note that the frequency distributions of annual 
and monthly returns are not directly comparable. On average, we should expect the

returns measured at shorter intervals (for example, months) to be smaller than returns 
measured over longer periods (for example, years).
Next, we construct a frequency distribution of average inflation-  adjusted returns 
over 1900–2010 for 19 major equity markets.
EXAMPLE 2   
Constructing a Frequency Distribution
How have equities rewarded investors in different countries in the long run? To 
answer this question, we could examine the average annual returns directly.9 The 
worth of a nominal level of return depends on changes in the purchasing power 
of money, however, and internationally there have been a variety of experiences 
with price inflation. It is preferable, therefore, to compare the average real or 
inflation-  adjusted returns earned by investors in different countries. Dimson, 
Marsh, and Staunton (2011) presented authoritative evidence on asset returns 
in 19 countries for the 111 years 1900–2010. Table 5 excerpts their findings for 
average inflation-  adjusted returns.

Table 5   Real (Inflation-  Adjusted) Equity Returns: 
Nineteen Major Equity Markets, 1900–2010
Country Arithmetic Mean (%)
Australia 9.1
Belgium 5.1
Canada 7.3
Denmark 6.9
Finland 9.3
France 5.7
Germany 8.1
Ireland 6.4Table 4   (Continued)
9 The average or arithmetic mean of a set of values equals the sum of the values divided by the number of 
values summed. To find the arithmetic mean of 111 annual returns, for example, we sum the 111 annual 
returns and then divide the total by 111. Among the most familiar of statistical concepts, the arithmetic 
mean is explained in more detail later in the reading.

The Graphic Presentation of Data 399
Italy 6.1
Japan 8.5
Netherlands 7.1
New Zealand 7.6
Norway 7.2
South Africa 9.5
Spain 5.8
Sweden 8.7
Switzerland 6.1
United Kingdom 7.2
United States 8.3
Source:  Dimson, Marsh, and Staunton (2011), Table 1.
Table 6 summarizes the data in Table 5 into five intervals spanning 5 percent 
to 10  percent. With nineteen markets, the relative frequency for the 5.0 to 
6.0 percent return interval is calculated as 3/19 = 15.79 percent, for example.
Table 6   Frequency Distribution of Average Real Equity Returns
Return 
Frequency 
(%)Cumulative 
Absolute 
Relative 
5.0 to 6.0 3 15.79 3 15.79
6.0 to 7.0 4 21.05 7 36.84
7.0 to 8.0 5 26.32 12 63.16
8.0 to 9.0 4 21.05 16 84.21
9.0 to 10 3 15.79 19 100.00
As Table 6 shows, there is substantial variation internationally of average 
real equity returns. More than a quarter of the observations fall in the 7.0 to

8.0 percent interval, which has a relative frequency of 26.32 percent. Either three 
or four observations fall in each of the other four intervals.
THE GRAPHIC PRESENTATION OF DATA
A graphical display of data allows us to visualize important characteristics quickly. For 
example, we may see that the distribution is symmetrically shaped, and this finding 
may influence which probability distribution we use to describe the data. In this sec -
tion, we discuss the histogram, the frequency polygon, and the cumulative frequency 4Table 5   (Continued)

Reading 8 ■ Statistical Concepts and Market Returns 400
distribution as methods for displaying data graphically. We construct all of these 
graphic presentations with the information contained in the frequency distribution 
of the S&P 500 shown in either Table 3 or Table 4.
4.1 The Histogram
A histogram is the graphical equivalent of a frequency distribution.
■■Definition of Histogram.  A histogram  is a bar chart of data that have been 
grouped into a frequency distribution.
The advantage of the visual display is that we can see quickly where most of the 
observations lie. To see how a histogram is constructed, look at the return interval 
18% ≤ Rt < 20% in Table 3. This interval has an absolute frequency of 6. Therefore, we 
erect a bar or rectangle with a height of 6 over that return interval on the horizontal 
axis. Continuing with this process for all other return intervals yields a histogram. 
Figure 1 presents the histogram of the annual total return series on the S&P 500 from 
1926 to 2012.

Figure 1   Histogram of S&P 500 Annual Total Returns: 1926 to 2012
01234567
52% - 54%
48% - 50%
44% - 46%40% - 42%
36% - 38%
32% - 34%
28% - 30%24% - 26%20% - 22%
16% - 18%
12% - 14%8% - 10%
4% - 6%0% - 2%–4% - –2%–8% - –6%
–12% - –10%
–16% - –14%
–20% - –18%–24% - –22%–28% - –26%–32% - –30%
–36% - –34%
–40% - –38%
–44% - –42%Frequency
Return Intervals
Note : Because of space limitations, only every other return interval is labeled below the horizontal axis.
Source:  Ibbotson Associates
In the histogram in Figure 1, the height of each bar represents the absolute fre -
quency for each return interval. The return interval −10% ≤ Rt < −8% has a frequency 
of 7 and is represented by the tallest bar in the histogram. Because there are no gaps

The Graphic Presentation of Data 401
between the interval limits, there are no gaps between the bars of the histogram. 
Many of the return intervals have zero frequency; therefore, they have no height in 
the histogram.
Figure 2 presents the histogram for the distribution of monthly returns on the 
S&P 500. Somewhat more symmetrically shaped than the histogram of annual returns 
shown in Figure 1, this histogram also appears more bell-  shaped than the distribution 
of annual returns.
Figure 2   Histogram of S&P 500 Monthly Total Returns: January 1926 to 
December 2012
0255075100125150175200225
42% - 44% 38% - 40% 34% - 36% 30% - 32% 26% - 28% 22% - 24% 18% - 20% 14% - 16% 10% - 12%6% - 8% 2% - 4%–2% - 0%–6% - –4%–10% - –8%–14% - –12% –18% - –16% –22% - –20% –26% - –24% –30% - –28%Frequency
4.2 The Frequency Polygon and the Cumulative Frequency 
Distribution
Two other graphical tools for displaying data are the frequency polygon and the

cumulative frequency distribution. To construct a frequency polygon , we plot the 
midpoint of each interval on the x-axis and the absolute frequency for that interval on 
the y-axis; we then connect neighboring points with a straight line. Figure 3 shows the 
frequency polygon for the 1,044 monthly returns for the S&P 500 from January 1926 
to December 2012.

Reading 8 ■ Statistical Concepts and Market Returns 402
Figure 3   Frequency Polygon of S&P 500 Monthly Total Returns: 
January 1926 to December 2012
43% 39% 35% 31% 27% 23% 19% 15% 11%7% 3%–1% –5% –9%–13% –17% –21% –25% –29%Frequency
Return Interval Midpoints
In Figure 3, we have replaced the bars in the histogram with points connected with 
straight lines. For example, the return interval 0 percent to 2 percent has an absolute 
frequency of 220. In the frequency polygon, we plot the return-  interval midpoint of 
1 percent and a frequency of 220. We plot all other points in a similar way.10 This form 
of visual display adds a degree of continuity to the representation of the distribution.
Another form of line graph is the cumulative frequency distribution. Such a graph 
can plot either the cumulative absolute or cumulative relative frequency against the 
upper interval limit. The cumulative frequency distribution allows us to see how

many or what percent of the observations lie below a certain value. To construct the 
cumulative frequency distribution, we graph the returns in the fourth or fifth column 
of Table 4 against the upper limit of each return interval. Figure 4 presents a graph of 
the cumulative absolute distribution for the monthly returns on the S&P 500. Notice 
that the cumulative distribution tends to flatten out when returns are extremely 
negative or extremely positive. The steep slope in the middle of Figure 4 reflects the 
fact that most of the observations lie in the neighborhood of −2 percent to 6 percent.
10 Even though the upper limit on the interval is not a return falling in the interval, we still average it with 
the lower limit to determine the midpoint.

The Graphic Presentation of Data 403
Figure 4   Cumulative Absolute Frequency Distribution of S&P 500 Monthly 
Total Returns: January 1926 to December 2012
010020030040050060070080090010001100
43%39%35%31%27%23%19%15%11%7%3%–1%–5%–9%–13%–17%–21%–25%–29%Cumulative Frequency
Return Interval Upper Limits
We can further examine the relationship between the relative frequency and the 
cumulative relative frequency by looking at the two return intervals reproduced in 
Table 7. The first return interval (0 percent to 2 percent) has a cumulative relative fre -
quency of 59 percent. The next return interval (2 percent to 4 percent) has a cumulative 
relative frequency of 75.57 percent. The change in the cumulative relative frequency 
as we move from one interval to the next is the next interval’s relative frequency. 
For instance, as we go from the first return interval (0 percent to 2 percent) to the

next return interval (2 percent to 4 percent), the change in the cumulative relative 
frequency is 75.57% − 59.00% = 16.57%. (Values in the table have been rounded to 
two decimal places.) The fact that the slope is steep indicates that these frequencies 
are large. As you can see in the graph of the cumulative distribution, the slope of the 
curve changes as we move from the first return interval to the last. A fairly small slope 
for the cumulative distribution for the first few return intervals tells us that these 
return intervals do not contain many observations. You can go back to the frequency 
distribution in Table 4 and verify that the cumulative absolute frequency is only 25 
observations (the cumulative relative frequency is 2.39 percent) up to the 10th return 
interval (−12 percent to −10 percent). In essence, the slope of the cumulative absolute 
distribution at any particular interval is proportional to the number of observations 
in that interval.

Table 7   Selected Class Frequencies for the S&P 500 Monthly Returns
Return  
Interval  
(%)Absolute  
FrequencyRelative  
Frequency  
(%)Cumulative  
Absolute FrequencyCumulative 
Relative 
Frequency 
(%)

Reading 8 ■ Statistical Concepts and Market Returns 404
MEASURES OF CENTRAL TENDENCY
So far, we have discussed methods we can use to organize and present data so that 
they are more understandable. The frequency distribution of an asset class’s return 
series, for example, reveals the nature of the risks that investors may encounter in a 
particular asset class. As an illustration, the histogram for the annual returns on the 
S&P 500 clearly shows that large positive and negative annual returns are common. 
Although frequency distributions and histograms provide a convenient way to sum -
marize a series of observations, these methods are just a first step toward describing 
the data. In this section we discuss the use of quantitative measures that explain 
characteristics of data. Our focus is on measures of central tendency and other mea -
sures of location or location parameters. A measure of central tendency  specifies

where the data are centered. Measures of central tendency are probably more widely 
used than any other statistical measure because they can be computed and applied 
easily. Measures of location  include not only measures of central tendency but other 
measures that illustrate the location or distribution of data.
In the following subsections we explain the common measures of central tendency—
the arithmetic mean, the median, the mode, the weighted mean, and the geometric 
mean. We also explain other useful measures of location, including quartiles, quintiles, 
deciles, and percentiles.
5.1 The Arithmetic Mean
Analysts and portfolio managers often want one number that describes a represen -
tative possible outcome of an investment decision. The arithmetic mean is by far the 
most frequently used measure of the middle or center of data.
■■Definition of Arithmetic Mean.  The arithmetic mean  is the sum of the obser -
vations divided by the number of observations.

We can compute the arithmetic mean for both populations and samples, known as 
the population mean and the sample mean, respectively.
5.1.1  The Population Mean
The population mean is the arithmetic mean computed for a population. If we can 
define a population adequately, then we can calculate the population mean as the 
arithmetic mean of all the observations or values in the population. For example, 
analysts examining the fiscal 2013 year-  over-  year growth in same-  store sales of major 
US wholesale clubs might define the population of interest to include only three 
companies: BJ’s Wholesale Club (a private company since 2011), Costco Wholesale 
Corporation, and Sam’s Club, part of Wal-  Mart Stores.11 As another example, if a 5
11 A wholesale club implements a store format dedicated mostly to bulk sales in warehouse-  sized stores 
to customers who pay membership dues. As of the early 2010s, those three wholesale clubs dominated

Measures of Central Tendency 405
portfolio manager’s investment universe (the set of securities he or she must choose 
from) is the Nikkei 225 Index, the relevant population is the 225 shares on the First 
Section of the Tokyo Stock Exchange that compose the Nikkei.
■■Population Mean Formula.  The population mean , μ, is the arithmetic mean 
value of a population. For a finite population, the population mean is
µ==∑X
Ni
iN
1
where N is the number of observations in the entire population and Xi is the ith 
observation.
The population mean is an example of a parameter. The population mean is unique; 
that is, a given population has only one mean. To illustrate the calculation, we can take 
the case of the population mean of profit as a percentage of revenue of US companies 
running major wholesale clubs for 2012. During the year, profit as a percentage of 
revenue for BJ’s Wholesale club, Costco Wholesale Corporation, and Wal-  Mart Stores

was 0.9 percent, 1.6 percent, and 3.5 percent, respectively, according to the Fortune 
500 list for 2012. Thus the population mean profit as a percentage of revenue was μ 
= (0.9 + 1.6 + 3.5)/3 = 6/3 = 2 percent.
5.1.2  The Sample Mean
The sample mean is the arithmetic mean computed for a sample. Many times we 
cannot observe every member of a set; instead, we observe a subset or sample of the 
population. The concept of the mean can be applied to the observations in a sample 
with a slight change in notation.
■■Sample Mean Formula.  The sample mean  or average,  X (read “X-  bar”), is the 
arithmetic mean value of a sample:
XX
ni
in
==∑
1
where n is the number of observations in the sample.
Equation  3 tells us to sum the values of the observations ( Xi) and divide the sum 
by the number of observations. For example, if a sample of price-  to- earnings (P/E) 
multiples for six publicly traded companies contains the values 35, 30, 22, 18, 15, and

12, the sample mean P/E is 132/6 = 22. The sample mean is also called the arithmetic 
average.12 As we discussed earlier, the sample mean is a statistic (that is, a descriptive 
measure of a sample).
Means can be computed for individual units or over time. For instance, the sample 
might be the 2013 return on equity (ROE) for the 100 companies in the FTSE Eurotop 
100, an index of Europe’s 100 largest companies. In this case, we calculate mean ROE 
in 2013 as an average across 100 individual units. When we examine the characteristics 
of some units at a specific point in time (such as ROE for the FTSE Eurotop 100), we 
are examining cross-  sectional data . The mean of these observations is called a cross-  
sectional mean. On the other hand, if our sample consists of the historical monthly 
returns on the FTSE Eurotop 100 for the past five years, then we have time-  series (2)
(3)
12 Statisticians prefer the term “mean” to “average. ” Some writers refer to all measures of central tendency

(including the median and mode) as averages. The term “mean” avoids any possibility of confusion.

Reading 8 ■ Statistical Concepts and Market Returns 406
data . The mean of these observations is called a time-  series mean. We will examine 
specialized statistical methods related to the behavior of time series in the reading 
on times-  series analysis.
Next, we show an example of finding the sample mean return for 16 European 
equity markets for 2012. In this case, the mean is cross-  sectional because we are 
averaging individual country returns.
EXAMPLE 3   
Calculating a Cross-  Sectional Mean
The MSCI EAFE (Europe, Australasia, and Far East) Index is a free float-  adjusted 
market capitalization index designed to measure developed-  market equity 
performance excluding the United States and Canada.13 As of September 2013, 
the EAFE consisted of 22 developed market indexes, including indexes for 16 
European markets, 2 Australasian markets (Australia and New Zealand), 3 Far 
Eastern markets (Hong Kong, Japan, and Singapore), and Israel.

Suppose we are interested in the local currency performance of the 16 
European markets in the EAFE in 2012. We want to find the sample mean total 
return for 2012 across these 16 markets. The return series reported in Table 8 
are in local currency. Because this return is not stated in any single investor’s 
home currency, it is not a return any single investor would earn. Rather, it is an 
average of returns in local currencies of the 16 markets.
Table 8   Total Returns for European Equity Markets, 
2012
Market Total Return in Local Currency (%)
Austria 20.72
Belgium 33.99
Denmark 28.09
Finland 8.27
France 15.90
Germany 25.24
Greece −2.35
Ireland 2.24
Italy 6.93
Netherlands 15.36
Norway 6.05
Portugal −2.22
Spain −4.76
Sweden 12.66
Switzerland 14.83
United Kingdom 5.93
Source:  www.msci.com.
13 The term “free float adjusted” means that the weights of companies in the index reflect the value of the 
shares actually available for investment.

Measures of Central Tendency 407
Using the data in Table 8, calculate the sample mean return for the 16 equity 
markets in 2012.
Solution:
The calculation applies Equation 3 to the returns in Table 8: (20.72 + 33.99 + 
28.09 + 8.27 + 15.90 + 25.24 − 2.35 + 2.24 + 6.93 + 15.36 + 6.05 − 2.22 − 4.76 + 
12.66 + 14.83 + 5.93)/16 = 186.88/16 = 11.68 percent.
In Example 3, we can verify that eight markets had returns less than the mean and 
eight had returns that were greater. We should not expect any of the actual observa -
tions to equal the mean, because sample means provide only a summary of the data 
being analyzed. Also, although in this example the number of values below the mean 
is equal to the number of values above the mean, that need not be the case. As an 
analyst, you will often need to find a few numbers that describe the characteristics 
of the distribution. The mean is generally the statistic that you will use as a measure

of the typical outcome for a distribution. You can then use the mean to compare the 
performance of two different markets. For example, you might be interested in com -
paring the stock market performance of investments in Pacific Rim countries with 
investments in European countries. You can use the mean returns in these markets 
to compare investment results.
5.1.3  Properties of the Arithmetic Mean
The arithmetic mean can be likened to the center of gravity of an object. Figure 5 
expresses this analogy graphically by plotting nine hypothetical observations on a 
bar. The nine observations are 2, 4, 4, 6, 10, 10, 12, 12, and 12; the arithmetic mean is 
72/9 = 8. The observations are plotted on the bar with various heights based on their 
frequency (that is, 2 is one unit high, 4 is two units high, and so on). When the bar is 
placed on a fulcrum, it balances only when the fulcrum is located at the point on the 
scale that corresponds to the arithmetic mean.

Figure 5   Center of Gravity Analogy for the Arithmetic Mean
1 2 3 4 5 6 7 9 10 11 12
Fulcrum
When the fulcrum is placed at 8, the bar is perfectly balanced.
As analysts, we often use the mean return as a measure of the typical outcome for 
an asset. As in the example above, however, some outcomes are above the mean and 
some are below it. We can calculate the distance between the mean and each outcome 
and call it a deviation. Mathematically, it is always true that the sum of the deviations 
around the mean equals 0. We can see this by using the definition of the arithmetic 
mean shown in Equation 3, multiplying both sides of the equation by n: nX Xi
in
=
=∑
1. 
The sum of the deviations from the mean can thus be calculated as follows:
XX XX Xn Xi
in
i
in
in
i
in
−() =− =− =
== ==∑∑ ∑∑
11 110

Reading 8 ■ Statistical Concepts and Market Returns 408
Deviations from the arithmetic mean are important information because they 
indicate risk. The concept of deviations around the mean forms the foundation for 
the more complex concepts of variance, skewness, and kurtosis, which we will discuss 
An advantage of the arithmetic mean over two other measures of central tendency, 
the median and mode, is that the mean uses all the information about the size and 
magnitude of the observations. The mean is also easy to work with mathematically.
A property and potential drawback of the arithmetic mean is its sensitivity to 
extreme values. Because all observations are used to compute the mean, the arith -
metic mean can be pulled sharply upward or downward by extremely large or small 
observations, respectively. For example, suppose we compute the arithmetic mean of 
the following seven numbers: 1, 2, 3, 4, 5, 6, and 1,000. The mean is 1,021/7 = 145.86

or approximately 146. Because the magnitude of the mean, 146, is so much larger 
than that of the bulk of the observations (the first six), we might question how well it 
represents the location of the data. In practice, although an extreme value or outlier 
in a financial dataset may only represent a rare value in the population, it may also 
reflect an error in recording the value of an observation, or an observation generated 
from a different population from that producing the other observations in the sample. 
In the latter two cases in particular, the arithmetic mean could be misleading. Perhaps 
the most common approach in such cases is to report the median in place of or in 
addition to the mean.14 We discuss the median next.
5.2 The Median
A second important measure of central tendency is the median.
■■Definition of Median.  The median  is the value of the middle item of a set 
of items that has been sorted into ascending or descending order. In an odd-

numbered sample of n items, the median occupies the ( n + 1)/2 position. In 
an even-  numbered sample, we define the median as the mean of the values of 
items occupying the n/2 and ( n + 2)/2 positions (the two middle items).15
Earlier we gave the profit as a percentage of revenue of three wholesale clubs as 0.9, 
1.6, and 3.5. With an odd number of observations ( n = 3), the median occupies the 
(n + 1)/2 = 4/2 = 2nd position. The median was 1.6 percent. The value of 1.6 percent 
is the “middlemost” observation: One lies above it, and one lies below it. Whether 
we use the calculation for an even- or odd-  numbered sample, an equal number of 
observations lie above and below the median. A distribution has only one median.
A potential advantage of the median is that, unlike the mean, extreme values do 
not affect it. The median, however, does not use all the information about the size and 
magnitude of the observations; it focuses only on the relative position of the ranked

observations. Calculating the median is also more complex; to do so, we need to order 
14 Other approaches to handling extreme values involve variations of the arithmetic mean. The trimmed 
mean  is computed by excluding a stated small percentage of the lowest and highest values and then com -
puting an arithmetic mean of the remaining values. For example, a 5 percent trimmed mean discards the 
lowest 2.5 percent and the largest 2.5 percent of values and computes the mean of the remaining 95 per -
cent of values. A trimmed mean is used in sports competitions when judges’ lowest and highest scores are 
discarded in computing a contestant’s score. A Winsorized mean  assigns a stated percent of the lowest 
values equal to one specified low value, and a stated percent of the highest values equal to one specified 
high value, then computes a mean from the restated data. For example, a 95 percent Winsorized mean sets

the bottom 2.5 percent of values equal to the 2.5th percentile value and the upper 2.5 percent of values 
equal to the 97.5th percentile value. (Percentile values are defined later.)
15 The notation Md is occasionally used for the median. Just as for the mean, we may distinguish between 
a population median and a sample median. With the understanding that a population median divides a 
population in half while a sample median divides a sample in half, we follow general usage in using the 
term “median” without qualification, for the sake of brevity.

Measures of Central Tendency 409
the observations from smallest to largest, determine whether the sample size is even 
or odd and, on that basis, apply one of two calculations. Mathematicians express this 
disadvantage by saying that the median is less mathematically tractable than the mean.
To demonstrate finding the median, we use the data from Example 3, reproduced 
in Table 9 in ascending order of the 2012 total return for European equities. Because 
this sample has 16 observations, the median is the mean of the values in the sorted 
array that occupy the 16/2 = 8th and 18/2 = 9th positions. Finland’s return occupies 
the eighth position with a return of 8.27 percent, and Sweden’s return occupies the 
ninth position with a return of 12.66 percent. The median, as the mean of these two 
returns, is (8.27 + 12.66)/2 = 10.465 percent. Note that the median is not influenced by 
extremely large or small outcomes. Had Spain’s total return been a much lower value

or Belgium’s total return a much larger value, the median would not have changed. 
Using a context that arises often in practice, Example 4 shows how to use the mean 
and median in a sample with extreme values.
Table 9   Total Returns for European Equity Markets, 2012 
(in Ascending Order)
No. MarketTotal Return  
in Local Currency (%)
1 Spain −4.76
2 Greece −2.35
3 Portugal −2.22
4 Ireland 2.24
5 United Kingdom 5.93
6 Norway 6.05
7 Italy 6.93
8 Finland 8.27
9 Sweden 12.66
10 Switzerland 14.83
11 Netherlands 15.36
12 France 15.90
13 Austria 20.72
14 Germany 25.24
15 Denmark 28.09
16 Belgium 33.99
EXAMPLE 4   
Median and Arithmetic Mean: The Case of the Price–
Earnings Ratio
Suppose a client asks you for a valuation analysis on the seven-  stock US common 
stock portfolio given in Table 10. The stocks are equally weighted in the portfolio. 
One valuation measure that you use is P/E, the ratio of share price to earnings

per share (EPS). Many variations exist for the denominator in the P/E, but you 
are examining P/E defined as current price divided by the current mean of all

Reading 8 ■ Statistical Concepts and Market Returns 410
analysts’ EPS estimates for the company for the fiscal year 2013 (“Consensus 
Current EPS” in the table).16 The values in Table 10 are as of 9 September 2013. 
For comparison purposes, the average current P/E on the companies in the S&P 
500 index was 18.80 at that time
Table 10    P/Es for a Client Portfolio
StockConsensus 
Current EPSConsensus 
Current P/E
Caterpillar, Inc. 6.34 13.15
Ford Motor Company 1.55 10.97
General Dynamics 6.96 12.15
Green Mountain Coffee Roasters 3.25 25.27
McDonald’s Corporation 5.61 17.16
Qlik Technologies 0.17 204.82
Questcor Pharmaceuticals 4.79 13.94
Note : Consensus current P/E was calculated as price as of 9 September  2013 divided by 
consensus EPS as of the same date.
Source:  www.nasdaq.com.
Using the data in Table 10, address the following:
1 Calculate the arithmetic mean P/E.
2 Calculate the median P/E.
3 Evaluate the mean and median P/Es as measures of central tendency for 
the above portfolio.

The mean P/E is (13.15 + 10.97 + 12.15 + 25.27 + 17.16 + 204.82 + 13.94)/7 = 
297.46/7 = 42.49.
The P/Es listed in ascending order are:
10.97 12.15 13.15 13.94 17.16 25.27 204.82
The sample has an odd number of observations with n = 7, so the median occu -
pies the ( n + 1)/2 = 8/2 = 4th position in the sorted list. Therefore, the median 
P/E is 13.94.
Qlik Technologies’ P/E of approximately 205 tremendously influences the value 
of the portfolio’s arithmetic mean P/E. The mean P/E of about 42 is much larger 
than the P/E of six of the seven stocks in the portfolio. The mean P/E also mis -
leadingly suggests an orientation to stocks with high P/Es. The mean P/E of the 
stocks excluding Qlik Technologies, or excluding the largest- and smallest-  P/E 
stocks (Qlik Technologies and Ford Motor Company), is below the average 
P/E of 18.80 for the companies in the S&P 500 Index. The median P/E of 13.94

appears to better represent the central tendency of the P/Es.
16 For more information on price multiples, see the Level I CFA Program curriculum reading “Equity 
Valuation: Concepts and Basic Tools. ”

Measures of Central Tendency 411
It frequently happens that when a company’s EPS is quite low—at a low point 
in the business cycle, for example—its P/E is extremely high. The high P/E in 
those circumstances reflects an anticipated future recovery of earnings. Extreme 
P/E values need to be investigated and handled with care. For reasons related to 
this example, analysts often use the median of price multiples to characterize 
the valuation of industry groups.
5.3 The Mode
The third important measure of central tendency is the mode.
■■Definition of Mode.  The mode  is the most frequently occurring value in a 
distribution.17
A distribution can have more than one mode, or even no mode. When a distribution 
has one most frequently occurring value, the distribution is said to be unimodal. If a 
distribution has two most frequently occurring values, then it has two modes and we 
say it is bimodal. If the distribution has three most frequently occurring values, then

it is trimodal. When all the values in a data set are different, the distribution has no 
mode because no value occurs more frequently than any other value.
Stock return data and other data from continuous distributions may not have a 
modal outcome. When such data are grouped into intervals, however, we often find 
an interval (possibly more than one) with the highest frequency: the modal interval  
(or intervals). For example, the frequency distribution for the monthly returns on the 
S&P 500 has a modal interval of 0 percent to 2 percent, as shown in Figure 2; this 
return interval has 220 observations out of a total of 1,044. The modal interval always 
has the highest bar in the histogram.
The mode is the only measure of central tendency that can be used with nominal 
data. When we categorize mutual funds into different styles and assign a number to 
each style, the mode of these categorized data is the most frequent mutual fund style.
5.4 Other Concepts of Mean

Earlier we explained the arithmetic mean, which is a fundamental concept for describing 
the central tendency of data. Other concepts of mean are very important in invest -
ments, however. In the following, we discuss such concepts.
EXAMPLE 5   
Calculating a Mode
Table 11 gives the credit ratings on senior unsecured debt as of September 2002 
of nine US department stores rated by Moody’s Investors Service. In descending 
order of credit quality (increasing expected probability of default), Moody’s 
ratings are Aaa, Aa1, Aa2, Aa3, A1, A2, A3, Baa1, Baa2, Baa3, Ba1, Ba2, Ba3, 
B1, B2, B3, Caa1, Caa2, Caa3, Ca, and C.18
17 The notation Mo is occasionally used for the mode. Just as for the mean and the median, we may 
distinguish between a population mode and a sample mode. With the understanding that a population 
mode is the value with the greatest probability of occurrence, while a sample mode is the most frequently

occurring value in the sample, we follow general usage in using the term “mode” without qualification, 
for the sake of brevity.
18 For more information on credit risk and credit ratings, see Petitt, Pinto, and Pirie (2015).

Reading 8 ■ Statistical Concepts and Market Returns 412
Table 11   Senior Unsecured Debt Ratings: US 
Department Stores, September 2013
Company Credit Rating
Bon-  Ton Stores Inc. B3
Dillards, Inc. Ba2
Kohl’s Corporation Baa1
Macy’s, Inc. Baa3
Neiman Marcus Group, Inc. B2
Nordstrom, Inc. Baa1
Penney, JC, Company, Inc. Caa1
Saks Incorporated Ba2
Sears, Roebuck and Co. B3
Source:  www.moodys.com.
Using the data in Table 11, address the following concerning the senior unsecured 
debt of US department stores:
1 State the modal credit rating.
2 State the median credit rating.
The group of companies represents six distinct credit ratings, ranging from Baa1 
to Caa1. To make our task easy, we first organize the ratings into a frequency 
Table 12   Senior Unsecured Debt Ratings: US 
Department Stores, Distribution of Credit 
Ratings
Credit Rating Frequency
Baa1 2
Baa3 1
Ba2 2
B2 1
B3 2
Caa1 1
Credit ratings Baa1, Ba2, and B3 have a frequency of 2, and the other three

ratings have a frequency of 1. Therefore, the credit rating of US department 
stores in September 2013 was trimodal, with Baa1, Ba2, and B3 being the three 
modes. Moody’s considers bonds rated Baa to be of moderate credit risk, Ba to 
be of substantial credit risk, and B to be of high credit risk.

Measures of Central Tendency 413
For the group n = 9, an odd number. The group’s median occupies the ( n + 1)/2 = 
10/2 = 5th position. We see from Table 12 that Ba2 occupies the fifth position. 
Therefore the median credit rating at September 2013 was Ba2.
5.4.1  The Weighted Mean
The concept of weighted mean arises repeatedly in portfolio analysis. In the arithmetic 
mean, all observations are equally weighted by the factor 1/ n (or 1/ N). In working 
with portfolios, we need the more general concept of weighted mean to allow different 
weights on different observations.
To illustrate the weighted mean concept, an investment manager with $100 mil -
lion to invest might allocate $70 million to equities and $30 million to bonds. The 
portfolio has a weight of 0.70 on stocks and 0.30 on bonds. How do we calculate the 
return on this portfolio? The portfolio’s return clearly involves an averaging of the 
returns on the stock and bond investments. The mean that we compute, however,

must reflect the fact that stocks have a 70 percent weight in the portfolio and bonds 
have a 30 percent weight. The way to reflect this weighting is to multiply the return 
on the stock investment by 0.70 and the return on the bond investment by 0.30, then 
sum the two results. This sum is an example of a weighted mean. It would be incorrect 
to take an arithmetic mean of the return on the stock and bond investments, equally 
weighting the returns on the two asset classes.
Consider a portfolio invested in Canadian stocks and bonds. The stock component 
of the portfolio includes the RBC Canadian Index Fund, which tracks the performance 
of the S&P/TSX Composite Total Return Index. The bond component of the portfolio 
includes the RBC Bond Fund, which invests in high-  quality fixed-  income securities 
issued by Canadian governments and corporations. The portfolio manager allocates 
60 percent of the portfolio to the Canadian stock fund and 40 percent to the Canadian

bond fund. Table 13 presents total returns for these funds from 2008 to 2012.
Table 13   Returns for Canadian Equity and Bond Funds, 
2008–2012
Y ear Equity Fund (%) Bond Fund (%)
2008 −33.1 −0.1
2009 34.1 11.0
2010 16.8 6.4
2011 −9.2 8.4
2012 6.4 3.8
Source:  funds.rbcgam.com.
■■Weighted Mean Formula.  The weighted mean  Xw (read “ X-bar sub- w”), for a 
set of observations X1, X2, …, Xn with corresponding weights of w1, w2, …, wn is 
computed as
Xw Xwi i
in
=
=∑
1(4)

Reading 8 ■ Statistical Concepts and Market Returns 414
where the sum of the weights equals 1; that is,  wi
i∑ =1.
In the context of portfolios, a positive weight represents an asset held long and a 
negative weight represents an asset held short.19
The return on the portfolio under consideration is the weighted average of the 
return on the Canadian stock fund and the Canadian bond fund (the weight of the 
stock fund is 0.60; that of the bond fund is 0.40). We find, using Equation 4, that
 Portfolio return for 2008 = wstock Rstock  + wbonds Rbonds
  = 0.60(–33.1) + 0.40(–0.1)
  = –19.9%
It should be clear that the correct mean to compute in this example is the weighted 
mean and not the arithmetic mean. If we had computed the arithmetic mean for 
2008, we would have calculated a return equal to ½(−33.1%) + ½(−0.1%) = (−33.1% 
− 0.1%)/2 = −16.6%. Given that the portfolio manager invested 60 percent in stocks 
and 40 percent in bonds, the arithmetic mean would underweight the investment in

stocks and overweight the investment in bonds, resulting in a number for portfolio 
return that is too high by 3.3 percentage points (−16.6% − (−19.9%) = −16.6% + 19.9%).
Now suppose that the portfolio manager maintains constant weights of 60 percent 
in stocks and 40 percent in bonds for all five years. This method is called a constant-  
proportions strategy. Because value is price multiplied by quantity, price fluctuation 
causes portfolio weights to change. As a result, the constant-  proportions strategy 
requires rebalancing to restore the weights in stocks and bonds to their target levels. 
Assuming that the portfolio manager is able to accomplish the necessary rebalancing, 
we can compute the portfolio returns in 2009, 2010, 2011, and 2012 with Equation 4 
Portfolio return for 2009 = 0.60(34.1) + 0.40(11.0) = 24.9%
Portfolio return for 2010 = 0.60(16.8) + 0.40(6.4) = 12.6%
Portfolio return for 2011 = 0.60(–9.2) + 0.40(8.4) = –2.2%

Portfolio return for 2012 = 0.60(6.4) + 0.40(3.8) = 5.4%
We can now find the time-  series mean of the returns for 2008 through 2012 using 
Equation 3 for the arithmetic mean. The time-  series mean total return for the portfolio 
is (−19.9 + 24.9 + 12.6 − 2.2 + 5.4)/5 = 20.8/5 = 4.2 percent.
Instead of calculating the portfolio time-  series mean return from portfolio annual 
returns, we can calculate the arithmetic mean stock and bond fund returns for the 
five years and then apply the portfolio weights of 0.60 and 0.40, respectively, to those 
values. The mean stock fund return is (−33.1 + 34.1 + 16.8 − 9.2 + 6.4)/5 = 15.0/5 = 
3.0 percent. The mean bond fund return is (−0.1 + 11.0 + 6.4 + 8.4 + 3.8)/ 5 = 29.5/5 = 
5.9 percent. Therefore, the mean total return for the portfolio is 0.60(3.0) + 0.40(5.9) 
= 4.2 percent, which agrees with our previous calculation.
19 The formula for the weighted mean can be compared to the formula for the arithmetic mean. For a set

of observations X1, X2, …, Xn, let the weights w1, w2, …, wn all equal 1/ n. Under this assumption, the formula 
for the weighted mean is  1
1nXi
in
()
=∑ . This is the formula for the arithmetic mean. Therefore, the arithmetic 
mean is a special case of the weighted mean in which all the weights are equal.

Measures of Central Tendency 415
EXAMPLE 6   
Portfolio Return as a Weighted Mean
Table 14 gives information on the asset allocation of the pension plan of the 
Canadian Broadcasting Corporation in 2012 as well as the returns on these 
asset classes in 2012.20
Table 14   Asset Allocation for the Pension Plan of the Canadian 
Broadcasting Corporation in 2012
Asset ClassAsset Allocation  
(Weight)Asset Class Return  
(%)
Cash and short-  term investments 3.8 1.3
Nominal bonds 33.7 6.6
Real return bonds 14.8 2.9
Canadian equities 10.4 8.8
Global equities 21.4 13.3
Strategic investments 15.8 9.5
Bond overlay 0.1 0.8
Source:  Canadian Broadcasting Corporation Pension Plan, 2012 Annual Report
Using the information in Table  14, calculate the mean return earned by the 
pension plan in 2012.
Solution:
Converting the percent asset allocation to decimal form, we find the mean return 
as a weighted average of the asset class returns. We have
 Mean portfolio return = 0.038(1.3%) + 0.337(6.6%) + 0.148(2.9%)

+ 0.104(8.8%) + 0.214(13.3%) + 0.158(9.5%) 
+ 0.001(0.8%)
  = 0.049% + 2.224% + 0.429% + 0.915% + 2.846% 
+ 1.501% + 0.001%
  = 8.0 percent
The previous examples illustrate the general principle that a portfolio return is a 
weighted sum. Specifically, a portfolio’s return is the weighted average of the returns 
on the assets in the portfolio; the weight applied to each asset’s return is the fraction 
of the portfolio invested in that asset.
Market indexes are computed as weighted averages. For market-  capitalization 
indexes such as the CAC-  40 in France or the TOPIX in Japan or the S&P 500 in the 
United States, each included stock receives a weight corresponding to its outstanding 
market value divided by the total market value of all stocks in the index.
20 In Table  14, strategic investments include investments in property, private investments, and hedge 
fund investments. Bond overlay consists of derivatives used to hedge interest rate and inflation changes.

Reading 8 ■ Statistical Concepts and Market Returns 416
Our illustrations of weighted mean use past data, but they might just as well use 
forward-  looking data. When we take a weighted average of forward-  looking data, 
the weighted mean is called expected value . Suppose we make one forecast for the 
year-  end level of the S&P 500 assuming economic expansion and another forecast 
for the year-  end level of the S&P 500 assuming economic contraction. If we multiply 
the first forecast by the probability of expansion and the second forecast by the prob -
ability of contraction and then add these weighted forecasts, we are calculating the 
expected value of the S&P 500 at year-  end. If we take a weighted average of possible 
future returns on the S&P 500, we are computing the S&P 500’s expected return. The 
probabilities must sum to 1, satisfying the condition on the weights in the expression 
for weighted mean, Equation 4.
5.4.2  The Geometric Mean

The geometric mean is most frequently used to average rates of change over time 
or to compute the growth rate of a variable. In investments, we frequently use the 
geometric mean to average a time series of rates of return on an asset or a portfolio, 
or to compute the growth rate of a financial variable such as earnings or sales. In 
the reading on the time value of money, for instance, we computed a sales growth 
rate (Example 17). That growth rate was a geometric mean. Because of the subject’s 
importance, in a later section we will return to the use of the geometric mean and 
offer practical perspectives on its use. The geometric mean is defined by the following 
formula.
■■Geometric Mean Formula.  The geometric mean , G, of a set of observations 
X1, X2, …, Xn is
GX XX X
Xi nnn
i=
≥=12 3
01 2
 with   for ,, ,.
Equation 5 has a solution, and the geometric mean exists, only if the product under

the radical sign is non-  negative. We impose the restriction that all the observations Xi 
in Equation 5 are greater than or equal to zero. We can solve for the geometric mean 
using Equation 5 directly with any calculator that has an exponentiation key (on most 
calculators, yx). We can also solve for the geometric mean using natural logarithms. 
Equation 5 can also be stated as
ln ln GnXX XXn = ()1
12 3
or as
lnln
 GX
ni
in
==∑
1
When we have computed ln G, then G = elnG (on most calculators, the key for this 
step is ex).
Risky assets can have negative returns up to −100 percent (if their price falls to zero), 
so we must take some care in defining the relevant variables to average in computing 
a geometric mean. We cannot just use the product of the returns for the sample and 
then take the nth root because the returns for any period could be negative. We must 
redefine the returns to make them positive. We do this by adding 1.0 to the returns

expressed as decimals. The term (1 + Rt) represents the year-  ending value relative to 
an initial unit of investment at the beginning of the year. As long as we use (1 + Rt), the 
observations will never be negative because the biggest negative return is −100 percent. 
The result is the geometric mean of 1 + Rt; by then subtracting 1.0 from this result, 
we obtain the geometric mean of the individual returns Rt. For example, the returns (5)

Measures of Central Tendency 417
on RBC Canadian Index Fund during the 2008–2012 period were given in Table 13 as 
−0.331, 0.341, 0.168, −0.092, and 0.064, putting the returns into decimal form. Adding 
1.0 to those returns produces 0.669, 1.341, 1.168, 0.908, and 1.064. Using Equation 5 
we have  0 669 1 341 1 168 0 908 1 0645.. .. . () () () () ()  = 1 0123375.  = 1.002455.
This number is 1 plus the geometric mean rate of return. Subtracting 1.0 from 
this result, we have 1.002455 − 1.0 = 0.002455 or approximately 0.25 percent. The 
geometric mean return of RBC Canadian Index Fund during the 2008–2012 period 
was 0.25 percent.
An equation that summarizes the calculation of the geometric mean return, RG, 
is a slightly modified version of Equation 5 in which the Xi represent “1 + return in 
decimal form. ” Because geometric mean returns use time series, we use a subscript 
t indexing time as well.
11 11
1112
11+= +() +() +()
+= +()



 =∏RR RR
RRGTT
Gt
tT T
which leads to the following formula.

RRGTT
Gt
tT T
■■Geometric Mean Return Formula.  Given a time series of holding period 
returns Rt, t = 1, 2, …, T, the geometric mean return over the time period 
spanned by the returns R1 through RT is
RRGt
tT T
=+ ()



−
=∏11
11
We can use Equation 6 to solve for the geometric mean return for any return data 
series. Geometric mean returns are also referred to as compound returns. If the returns 
being averaged in Equation 6 have a monthly frequency, for example, we may call the 
geometric mean monthly return the compound monthly return. The next example 
illustrates the computation of the geometric mean while contrasting the geometric 
and arithmetic means.
EXAMPLE 7   
Geometric and Arithmetic Mean Returns (1)
As a mutual fund analyst, you are examining, as of early 2013, the most recent 
five years of total returns for two US large-  cap value equity mutual funds.
Table 15   Total Returns for Two Mutual Funds, 2008–2012
Y earSelected American Shares

Y earSelected American Shares  
(SLASX)T. Rowe Price Equity Income  
(PRFDX)
2008 −39.44% −35.75%
2009 31.64 25.62
2010 12.53 15.15
2011 −4.35 −0.72
2012 12.82 17.25
Source:  performance.morningstar.com.(6)

Reading 8 ■ Statistical Concepts and Market Returns 418
Based on the data in Table 15, address the following:
1 Calculate the geometric mean return of SLASX.
2 Calculate the arithmetic mean return of SLASX and contrast it to the 
fund’s geometric mean return.
3 Calculate the geometric mean return of PRFDX.
4 Calculate the arithmetic mean return of PRFDX and contrast it to the 
Converting the returns on SLASX to decimal form and adding 1.0 to each return 
produces 0.6056, 1.3164, 1.1253, 0.9565, and 1.1282. We use Equation 6 to find 
SLASX’s geometric mean return:
RG=() () () () () −
=−0 6056 1 3164 1 1253 0 9565 1 1282 1
0 968084 15
5... ..
. ==− =−
=0 993534 10 006466 ..
− −0.65%
For SLASX,  R = (−39.44 + 31.64 + 12.53 − 4.35 +12.82)/ 5 = 13.20/5 = 2.64%. 
The arithmetic mean return for SLASX exceeds the geometric mean return by 
2.64 − (−0.65) = 3.29% or 329 basis points.

Converting the returns on PRFDX to decimal form and adding 1.0 to each return 
produces 0.6425, 1.2562, 1.1515, 0.9928, and 1.1725. We use Equation 6 to find 
PRFDX’s geometric mean return:
=−0 6425 1 2562 1 1515 0 9928 1 1725 1
1 081859 15
5.. .. .
. ==− =
=1 015861 10 015861 ..
1.59%
PRFDX,  R = (−35.75 + 25.62 + 15.15 − 0.72 + 17.25)/5 = 21.55/5 = 4.31%. The 
arithmetic mean for PRFDX exceeds the geometric mean return by 4.31 − 1.59 = 
2.72% or 272 basis points. The table below summarizes the findings.
Table 16   Mutual Fund Arithmetic and Geometric Mean 
Returns: Summary of Findings
Fund Arithmetic Mean (%) Geometric Mean (%)
SLASX 2.64 −0.65
PRFDX 4.31 1.59

Measures of Central Tendency 419
In Example 7, for both mutual funds, the geometric mean return was less than the 
arithmetic mean return. In fact, the geometric mean is always less than or equal to 
the arithmetic mean.21 The only time that the two means will be equal is when there 
is no variability in the observations—that is, when all the observations in the series 
are the same.22 In Example 7, there was variability in the funds’ returns; thus for both 
funds, the geometric mean was strictly less than the arithmetic mean. In general, 
the difference between the arithmetic and geometric means increases with the vari -
ability in the period-  by- period observations.23 This relationship is also illustrated by 
Example 7. Casual inspection suggests that the returns of SLASX are somewhat more 
variable than those of PRFDX, and consequently, the spread between the arithmetic 
and geometric mean returns is larger for SLASX (329 basis points) than for PRFDX

(272 basis points).24 Arithmetic and geometric returns need not always rank funds 
similarly, however, in this example, PRFDX has both higher arithmetic and geometric 
mean returns than SLASX. However, the difference between the geometric mean 
returns of the two funds (2.24%) is greater than the difference between the arithmetic 
mean returns of the two funds (1.67%). How should the analyst interpret these results?
The geometric mean return represents the growth rate or compound rate of return 
on an investment. One dollar invested in SLASX at the beginning of 2008 would 
have grown (or, in this case, decreased) to (0.6056)(1.3164)(1.1253)(0.9565)(1.1282) 
= $0.9681, which is equal to 1 plus the geometric mean return compounded over five 
periods: [1 + (−0.006466)]5 = (0.993534)5 = $0.9681, confirming that the geometric 
mean is the compound rate of return. For PRFDX, one dollar would have grown to a 
larger amount, (0.6425)(1.2562)(1.1515)(0.9928)(1.1725) = $1.0819, equal to (1.015861)5.

With its focus on the profitability of an investment over a multiperiod horizon, the 
geometric mean is of key interest to investors. The arithmetic mean return, focusing on 
average single-  period performance, is also of interest. Both arithmetic and geometric 
means have a role to play in investment management, and both are often reported for 
return series. Example 8 highlights these points in a simple context.
EXAMPLE 8   
Geometric and Arithmetic Mean Returns (2)
A hypothetical investment in a single stock initially costs €100. One year later, 
the stock is trading at €200. At the end of the second year, the stock price falls 
back to the original purchase price of €100. No dividends are paid during the 
two-  year period. Calculate the arithmetic and geometric mean annual returns.
Solution:
First, we need to find the Year 1 and Year 2 annual returns with Equation 1.
Return in Year 1 = 200/100 – 1 = 100%
Return in Year 2 = 100/200 – 1 = –50%

21 This statement can be proved using Jensen’s inequality that the average value of a function is less than 
or equal to the function evaluated at the mean if the function is concave from below—the case for ln( X).
22 For instance, suppose the return for each of the three years is 10  percent. The arithmetic mean is 
10 percent. To find the geometric mean, we first express the returns as (1 + Rt) and then find the geometric 
mean: [(1.10)(1.10)(1.10)]1/3 − 1.0 = 10 percent. The two means are the same.
23 We will soon introduce standard deviation as a measure of variability. Holding the arithmetic mean 
return constant, the geometric mean return decreases for an increase in standard deviation.
24 We will introduce formal measures of variability later. But note, for example, the 71.08  percentage 
point swing in returns between 2008 and 2009 for SLASX versus the 61.37 percentage point for PRFDX.

Similarly, note the 19.11 percentage point swing in returns between 2009 and 2010 for SLASX versus the 
10.47 percentage point for PRFDX.

Reading 8 ■ Statistical Concepts and Market Returns 420
The arithmetic mean of the annual returns is (100% − 50%)/2 = 25%.
Before we find the geometric mean, we must convert the percentage rates 
of return to (1 + Rt). After this adjustment, the geometric mean from Equation 6 
is 20 05 0 ..×  – 1 = 0 percent.
The geometric mean return of 0 percent accurately reflects that the ending 
value of the investment in Year 2 equals the starting value in Year 1. The com -
pound rate of return on the investment is 0 percent. The arithmetic mean return 
reflects the average of the one-  year returns.
5.4.3  The Harmonic Mean
The arithmetic mean, the weighted mean, and the geometric mean are the most fre -
quently used concepts of mean in investments. A fourth concept, the harmonic 
mean , XH, is appropriate in a limited number of applications.25
■■Harmonic Mean Formula.  The harmonic mean of a set of observations X1, X2, 
…, Xn is
Xn X
Xi nHi
in
i= ()
>==∑1
01 21
with   for ,, ,

Xn X
Xi nHi
in
i= ()
>==∑1
01 21
The harmonic mean is the value obtained by summing the reciprocals of the observa -
tions—terms of the form 1/ Xi—then averaging that sum by dividing it by the number 
of observations n, and, finally, taking the reciprocal of the average.
The harmonic mean may be viewed as a special type of weighted mean in which an 
observation’s weight is inversely proportional to its magnitude. The harmonic mean is 
a relatively specialized concept of the mean that is appropriate when averaging ratios 
(“amount per unit”) when the ratios are repeatedly applied to a fixed quantity to yield 
a variable number of units. The concept is best explained through an illustration. A 
well-  known application arises in the investment strategy known as cost averaging , 
which involves the periodic investment of a fixed amount of money. In this application, 
the ratios we are averaging are prices per share at purchases dates, and we are apply -

ing those prices to a constant amount of money to yield a variable number of shares.
Suppose an investor purchases €1,000 of a security each month for n = 2 months. 
The share prices are €10 and €15 at the two purchase dates. What is the average price 
paid for the security?
In this example, in the first month we purchase €1,000/€10 = 100 shares and in the 
second month we purchase €1,000/€15 = 66.67, or 166.67 shares in total. Dividing the 
total euro amount invested, €2,000, by the total number of shares purchased, 166.67, 
gives an average price paid of €2,000/166.67 = €12. The average price paid is in fact 
the harmonic mean of the asset’s prices at the purchase dates. Using Equation  7, 
the harmonic mean price is 2/[(1/10) + (1/15)] = €12. The value €12 is less than the 
arithmetic mean purchase price (€10 + €15)/2 = €12.5. However, we could find the 
correct value of €12 using the weighted mean formula, where the weights on the

purchase prices equal the shares purchased at a given price as a proportion of the 
total shares purchased. In our example, the calculation would be (100/166.67)€10.00 + 
(66.67/166.67)€15.00 = €12. If we had invested varying amounts of money at each 
date, we could not use the harmonic mean formula. We could, however, still use the 
weighted mean formula in a manner similar to that just described.(7)
25 The terminology “harmonic” arises from its use relative to a type of series involving reciprocals known 
as a harmonic series.

Other Measures of Location: Quantiles 421
A mathematical fact concerning the harmonic, geometric, and arithmetic means is 
that unless all the observations in a data set have the same value, the harmonic mean 
is less than the geometric mean, which in turn is less than the arithmetic mean. In 
the illustration given, the harmonic mean price was indeed less than the arithmetic 
mean price.
OTHER MEASURES OF LOCATION: QUANTILES
Having discussed measures of central tendency, we now examine an approach to 
describing the location of data that involves identifying values at or below which spec -
ified proportions of the data lie. For example, establishing that 25, 50, and 75 percent 
of the annual returns on a portfolio are at or below the values −0.05, 0.16, and 0.25, 
respectively, provides concise information about the distribution of portfolio returns. 
Statisticians use the word quantile  (or fractile ) as the most general term for a value

at or below which a stated fraction of the data lies. In the following, we describe the 
most commonly used quantiles—quartiles, quintiles, deciles, and percentiles—and 
their application in investments.
6.1 Quartiles, Quintiles, Deciles, and Percentiles
We know that the median divides a distribution in half. We can define other dividing 
lines that split the distribution into smaller sizes. Quartiles  divide the distribution into 
quarters, quintiles  into fifths, deciles into tenths, and percentiles  into hundredths. 
Given a set of observations, the yth percentile is the value at or below which y percent 
of observations lie. Percentiles are used frequently, and the other measures can be 
defined with respect to them. For example, the first quartile ( Q1) divides a distribution 
such that 25 percent of the observations lie at or below it; therefore, the first quartile 
is also the 25th percentile. The second quartile ( Q2) represents the 50th percentile,

and the third quartile ( Q3) represents the 75th percentile because 75 percent of the 
observations lie at or below it.
When dealing with actual data, we often find that we need to approximate the value 
of a percentile. For example, if we are interested in the value of the 75th percentile, we 
may find that no observation divides the sample such that exactly 75 percent of the 
observations lie at or below that value. The following procedure, however, can help us 
determine or estimate a percentile. The procedure involves first locating the position 
of the percentile within the set of observations and then determining (or estimating) 
the value associated with that position.
Let Py be the value at or below which y percent of the distribution lies, or the yth 
percentile. (For example, P18 is the point at or below which 18 percent of the obser -
vations lie; 100 − 18 = 82 percent are greater than P18.) The formula for the position

of a percentile in an array with n entries sorted in ascending order is
Lny
y=+()1100
where y is the percentage point at which we are dividing the distribution and Ly is the 
location ( L) of the percentile ( Py) in the array sorted in ascending order. The value of 
Ly may or may not be a whole number. In general, as the sample size increases, the 
percentile location calculation becomes more accurate; in small samples it may be 
quite approximate.
As an example of the case in which Ly is not a whole number, suppose that we want 
to determine the third quartile of returns for 2012 ( Q3 or P75) for the 16 European 
equity markets given in Table 8. According to Equation 8, the position of the third 6
(8)

Reading 8 ■ Statistical Concepts and Market Returns 422
quartile is L75 = (16 + 1)(75/100) = 12.75, or between the 12th and 13th items in Table 9, 
which ordered the returns into ascending order. The 12th item in Table 9 is the return 
to equities in France in 2012, 15.90 percent. The 13th item is the return to equities 
in Austria in 2012, 20.72 percent. Reflecting the “0.75” in “12.75, ” we would conclude 
that P75 lies 75 percent of the distance between 15.90 percent and 20.72 percent.
To summarize:
■■When the location, Ly, is a whole number, the location corresponds to an actual 
observation. For example, if Denmark had not been included in the sample, 
then n + 1 would have been 16 and, with L75 = 12, the third quartile would be 
P75 = X12, where Xi is defined as the value of the observation in the ith (i = L75) 
position of the data sorted in ascending order (i.e., P75 =15.90).
■■When Ly is not a whole number or integer, Ly lies between the two closest

integer numbers (one above and one below), and we use linear interpolation  
between those two places to determine Py. Interpolation means estimating an 
unknown value on the basis of two known values that surround it (lie above 
and below it); the term “linear” refers to a straight-  line estimate. Returning 
to the calculation of P75 for the equity returns, we found that Ly = 12.75; the 
next lower whole number is 12 and the next higher whole number is 13. Using 
linear interpolation, P75 ≈ X12 + (12.75 − 12) ( X13 − X12). As above, in the 
12th position is the return to equities in France, so X12 = 15.90 percent; X13 = 
20.72 percent, the return to equities in Austria. Thus our estimate is P75 ≈ X12 
+ (12.75 − 12)( X13 − X12) = 15.90 + 0.75 [20.72 − 15.90] = 15.90 + 0.75(4.82) = 
15.90 + 3.62 = 19.52 percent. In words, 15.90 and 20.72 bracket P75 from below 
and above, respectively. Because 12.75 − 12 = 0.75, using linear interpolation we

move 75 percent of the distance from 15.90 to 20.72 as our estimate of P75. We 
follow this pattern whenever Ly is a non-  integer: The nearest whole numbers 
below and above Ly establish the positions of observations that bracket Py and 
then interpolate between the values of those two observations.
Example 9 illustrates the calculation of various quantiles for the dividend yield on the 
components of a major European equity index.
EXAMPLE 9   
Calculating Percentiles, Quartiles, and Quintiles
The EURO STOXX 50 is an index of 50 publicly traded companies, which pro -
vides a blue-  chip representation of supersector leaders in the Eurozone. Table 17 
shows the market capitalization on the 50 component stocks in the index, as 
provided by STOXX Ltd. in September  2013. The market capitalizations are 
ranked in ascending order.
Table 17   Market Capitalizations of the Components 
of the EURO STOXX 50
No. Company Market Cap (Euro Billion)
1 Arcelor-  Mittal 8.83
2 CRH 10.99
3 RWE 11.92
4 Carrefour 12.13

2 CRH 10.99
3 RWE 11.92
5 Repsol 12.84
6 Saint-  Gobain 13.60

Other Measures of Location: Quantiles 423
7 France Telecom 14.09
8 Unibail-  Rodamco 15.96
9 Enel 16.33
10 Essilor International 16.85
11 Intesa Sanpaolo 17.00
12 Assicurazioni Generali 17.76
13 Vivendi 17.84
14 VINCI 18.64
15 Philips 19.04
16 EADS 19.37
17 Inditex 19.66
18 UniCredit 19.69
19 Iberdrola 20.29
20 BMW 20.69
21 ASML 20.71
22 Société Générale 20.92
23 GDF Suez 21.10
24 Volkswagen 21.57
25 Munich RE 22.25
26 E.ON 24.83
27 Deutsche Telekom 25.60
28 ING 25.93
29 Air Liquide 28.98
30 L’Oreal 29.20
31 Schneider Electric 29.75
32 AXA 30.13
33 Deutsche Bank 30.92
34 LVMH Moët Hennessy 32.36
35 Danone 33.36
36 BBVA 34.56
37 Telefonica 39.00
38 ENI 41.42
39 Daimler 42.42
40 BNP Paribas 43.09
41 Unilever 46.04
42 Allianz 47.72
43 Anheuser-  Busch InBev 49.40
44 SAP 50.93
45 BCO Santander 51.17
46 BASF 63.88
47 Siemens 64.27
48 Bayer 65.83
49 Total 81.06
50 Sanofi 93.29
Source:  www.stoxx.com accessed 27 September 2013.Table 17   (Continued)

Reading 8 ■ Statistical Concepts and Market Returns 424
Using the data in Table 17, address the following:
1 Calculate the 10th and 90th percentiles.
2 Calculate the first, second, and third quartiles.
3 State the value of the median.
4 How many quintiles are there, and to what percentiles do the quintiles 
correspond?
5 Calculate the value of the first quintile.
In this example, n = 50. Using Equation 8, Ly = (n + 1) y/100 for position of the 
yth percentile, so for the 10th percentile we have
L10 = (50 + 1)(10/100) = 5.1
L10 is between the fifth and sixth observations with values X5 = 12.84 and X6 
= 13.60. The estimate of the 10th percentile (first decile) for dividend yield is
 P10 ≈ X5 + (5.1 – 5)( X6 – X5) = 12.84 + 0.1(13.60 – 12.84)
   = 12.84 + 0.1(0.76) = 12.92
For the 90th percentile,
L90 = (50 + 1)(90/100) = 45.9
L90 is between the 45th and 46th observations with values X45 = 51.17 and X46 
= 63.88, respectively. The estimate of the 90th percentile (ninth decile) is

P90 ≈ X45 + (45.9 – 45)( X46 – X45) = 51.17 + 0.9(63.88 – 51.17)
   = 51.17 + 0.9(12.71) = 62.61.
The first, second, and third quartiles correspond to P25, P50, and P75, respectively.
L25 = (51)(25/100) = 12.75 L25 is between the 12th and 13th entries  
with values X12 = 17.76 and X13 = 17.84.
P25 = Q1 ≈ X12 + (12.75 – 12)( X13 – X12) 
= 17.76 + 0.75(17.84 – 17.76)  
= 17.76 + 0.75(0.08) = 17.82
L50 = (51)(50/100) = 25.5 L50 is between the 25th and 26th entries  
with values, X25 = 22.25 and X26 = 24.83.
P50 = Q2 ≈ X25 + (25.50 – 25)( X26 – X25) 
= 22.25 + 0.50(24.83 – 22.25)  
= 22.25 + 0.50(2.58) = 23.54
L75 = (51)(75/100) = 38.25 L75 is between the 38th and 39th entries  
with values X38 = 41.42 and X39 = 42.42.
P75 = Q3 ≈ X38 + (38.25 – 38)( X39 – X38) 
= 41.42 + 0.25(42.42 – 41.42)  
= 41.42 + 0.25(1.00) = 41.67
The median is the 50th percentile, 23.54. This is the same value that we would 
obtain by taking the mean of the n/2 = 50/2 = 25th item and ( n + 2)/2 = 52/2 =

26th items, consistent with the procedure given earlier for the median of an 
even-  numbered sample.

Other Measures of Location: Quantiles 425
There are five quintiles, and they are specified by P20, P40, P60, and P80.
The first quintile is P20.
L20 = (50 + 1)(20/100) = 10.2 L20 is between the 10th and 11th observations 
with values X10 = 16.85 and X11 = 17.00.
The estimate of the first quintile is
 P20 ≈ X10 + (10.2 – 10)( X11 – X10) = 16.85 + 0.2(17.00 – 16.85)
  = 16.85 + 0.2(0.15) = 16.88.
6.2 Quantiles in Investment Practice
In this section, we discuss the use of quantiles in investments. Quantiles are used in 
portfolio performance evaluation as well as in investment strategy development and 
research.
Investment analysts use quantiles every day to rank performance—for example, 
the performance of portfolios. The performance of investment managers is often 
characterized in terms of the quartile in which they fall relative to the performance 
of their peer group of managers. The Morningstar mutual fund star rankings, for

example, associates the number of stars with percentiles of performance relative to 
similar-  style mutual funds.
Another key use of quantiles is in investment research. Analysts refer to a group 
defined by a particular quantile as that quantile. For example, analysts often refer to 
the set of companies with returns falling below the 10th percentile cutoff point as 
the bottom return decile. Dividing data into quantiles based on some characteristic 
allows analysts to evaluate the impact of that characteristic on a quantity of inter -
est. For instance, empirical finance studies commonly rank companies based on the 
market value of their equity and then sort them into deciles. The 1st decile contains 
the portfolio of those companies with the smallest market values, and the 10th decile 
contains those companies with the largest market value. Ranking companies by decile 
allows analysts to compare the performance of small companies with large ones.

We can illustrate the use of quantiles, in particular quartiles, in investment research 
using the example of Ibbotson et al. (2013). That study proposed an investment style 
based on liquidity—buying stocks of less liquid stocks and selling stocks of more 
liquid stocks. It compared the performance of this style with three already popular 
investment styles, which include (1) firm size (buying stocks of small firms and selling 
stocks of large firms), (2) value/growth (buying stocks of value firms, defined as firms 
for which the stock price is relatively low in relation to earnings per share, book value 
per share, or dividends per share, and selling stocks of growth firms, defined as firms 
for which the stock price is relatively high in relation to those same measures), and 
(3) momentum (buying stocks of firms with a high momentum in returns, or winners, 
and selling stocks of firms with a low momentum, or losers.)

Ibbotson et al. examined the top 3,500 US stocks by market capitalization for the 
period of 1971–2011. For each stock, they computed yearly measures of liquidity as 
the annual share turnover (the sum of the 12 monthly volumes divided by each month’s 
shares outstanding), size as the year-  end market capitalization, value as the trailing 
earnings-  to- price ratio as of the year end, and momentum as the annual return. They 
assigned one-  fourth of the total sample with the lowest liquidity in a year to Quartile 1 
and the one-  fourth with the highest liquidity in that year to Quartile 4. The stocks with 
the second-  highest liquidity formed Quartile 3 and the stocks with the second-  lowest

Reading 8 ■ Statistical Concepts and Market Returns 426
liquidity, Quartile 2. Treating each quartile group as a portfolio composed of equally 
weighted stocks, they measured the returns on each liquidity quartile in the following 
year (so that the quartiles are constructed “before the fact” .) The authors repeated this 
process for each of the other three investment styles (size, value, and momentum.) The 
results from Table 1 of their study are included in Table 18. We have added a column 
with the spreads in returns from Quartile 1 to Quartile 4.
Table 18 reports each investment style’s geometric and arithmetic mean returns 
and standard deviation of returns for each quartile grouping. In each style, moving 
from Quartile 1 to Quartile 4, mean returns decrease. For example, the geometric 
mean return for the least liquid stocks is 14.50% and for the most liquid stocks is 
7.24%. Only for the case of size does standard deviation decrease at each step moving

from Quartile 1 to Quartile 4. Thus, the table provides evidence that the investment 
styles generally having incremental value in explaining returns in relation to standard 
deviation. The authors conclude that liquidity appears to differentiate the returns 
approximately as well as the other styles.
Table 18   Cross-  Sectional Investment Style Returns (%) and Standard 
Deviations of Returns (%), 1972–2011 
Investment Style Q1 Q2 Q3 Q4Spread  
in Return,  
Q1 to Q4
Size 
(Q1 = micro; Q4 = large)         
Geometric Mean 13.04 11.93 11.95 10.98 +2.06
Arithmetic Mean 16.42 14.69 14.14 12.61 +3.81
Standard deviation 27.29 24.60 21.82 18.35  
Value  
(Q1 = value; Q4 = growth)         
Geometric Mean 16.13 13.60 10.10 7.62 +8.51
Arithmetic Mean 18.59 15.42 12.29 11.56 +7.03
Standard deviation 23.31 20.17 21.46 29.42  
Momentum  
(Q1 = winners; Q4 = losers)         
Geometric Mean 12.85 14.25 13.26 7.18 +5.67
Arithmetic Mean 15.37 16.03 15.29 11.16 +4.21
Standard deviation 23.46 19.79 21.21 29.49  
Liquidity

Liquidity  
(Q1 = low; Q4 = high)         
Geometric Mean 14.50 13.97 11.91 7.24 +7.26
Arithmetic Mean 16.38 16.05 14.39 11.04 +5.34
Standard deviation 20.41 21.50 23.20 28.48  
Note : Each investment style portfolio contains as average of 742 stocks a year.
Source:  Ibbotson et al.
To address the concern that liquidity may simply be a proxy for firm size, with 
investing in less liquid firms being equivalent to investing in small firms, the authors 
examined how less liquid stocks performed relative to more liquid stocks while con -
trolling for firm size. This step involved constructing equally-  weighted double-  sorted 
portfolios in firm size and liquidity quartiles. That is, they constructed 16 different

Measures of Dispersion 427
liquidity and size portfolios (4 × 4 = 16) and investigated the interaction between 
these two styles. The results from Table 2 of their article are included in Table 19. 
We have added a column with the spreads in returns from Quartile 1 to Quartile 4 
for each size category.
Table 19   Mean Annual Returns (%) and Standard Deviations of Returns (%) of Size and Liquidity Quartile 
Portfolios, 1972–2011
QuartileQ1 
(Low liquidity) Q2 Q3Q4 
(High liquidity)Spread  
in Return,  
Q1 to Q4
Microcap          
Geometric Mean 15.36 16.21 9.94 1.32 +14.04
Arithmetic Mean 17.92 20.00 15.40 6.78 +11.14
Standard deviation 23.77 29.41 35.34 34.20  
Small cap          
Geometric Mean 15.30 14.09 11.80 5.48 +9.82
Arithmetic Mean 17.07 16.82 15.38 9.89 +7.18
Standard deviation 20.15 24.63 28.22 31.21  
Midcap          
Geometric Mean 13.61 13.57 12.24 7.85 +5.76
Arithmetic Mean 15.01 15.34 14.51 11.66 +3.35
Standard deviation 17.91 20.10 22.41 28.71  
Large cap

Large cap          
Geometric Mean 11.53 11.66 11.19 8.37 +3.16
Arithmetic Mean 12.83 12.86 12.81 11.58 +1.25
Standard deviation 16.68 15.99 18.34 25.75  
The table shows that within the quartile with the smallest firms, the low-  liquidity 
portfolio earned an annual geometric mean return of 15.36%, in contrast to the high-  
liquidity portfolio return of 1.32%, producing a liquidity effect of 14.04 percentage 
points (1,404 basis points). While the liquidity effect is strongest for the smallest firms, 
it does persist in other three size quartiles also. These results indicate that size does 
not capture liquidity (i.e., the liquidity effect holds regardless of size group).
MEASURES OF DISPERSION
As the well-  known researcher Fischer Black has written, “[t]he key issue in investments 
is estimating expected return. ”26 Few would disagree with the importance of expected 
return or mean return in investments: The mean return tells us where returns, and

investment results, are centered. To completely understand an investment, however, 7
26 Black (1993).

Reading 8 ■ Statistical Concepts and Market Returns 428
we also need to know how returns are dispersed around the mean. Dispersion  is the 
variability around the central tendency. If mean return addresses reward, dispersion 
addresses risk.
In this section, we examine the most common measures of dispersion: range, 
mean absolute deviation, variance, and standard deviation. These are all measures of 
absolute dispersion . Absolute dispersion is the amount of variability present without 
comparison to any reference point or benchmark.
These measures are used throughout investment practice. The variance or standard 
deviation of return is often used as a measure of risk pioneered by Nobel laureate 
Harry Markowitz. William Sharpe, another winner of the Nobel Prize in economics, 
developed the Sharpe ratio, a measure of risk-  adjusted performance. That measure 
makes use of standard deviation of return. Other measures of dispersion, mean abso -

lute deviation and range, are also useful in analyzing data.
7.1 The Range
We encountered range earlier when we discussed the construction of frequency 
distribution. The simplest of all the measures of dispersion, range can be computed 
with interval or ratio data.
■■Definition of Range.  The range  is the difference between the maximum and 
minimum values in a data set:
Range = Maximum value – Minimum value  
As an illustration of range, the largest monthly return for the S&P 500 in the period 
from January 1926 to December 2012 is 42.56 percent (in April 1933) and the small -
est is −29.73 percent (in September 1931). The range of returns is thus 72.29 percent 
[42.56  percent − (−29.73  percent)]. An alternative definition of range reports the 
maximum and minimum values. This alternative definition provides more information 
than does the range as defined in Equation 9.
One advantage of the range is ease of computation. A disadvantage is that the

range uses only two pieces of information from the distribution. It cannot tell us how 
the data are distributed (that is, the shape of the distribution). Because the range is 
the difference between the maximum and minimum returns, it can reflect extremely 
large or small outcomes that may not be representative of the distribution.27
7.2 The Mean Absolute Deviation
Measures of dispersion can be computed using all the observations in the distribution 
rather than just the highest and lowest. The question is, how should we measure 
dispersion? Our previous discussion on properties of the arithmetic mean introduced 
the notion of distance or deviation from the mean  XXi−()  as a fundamental piece 
of information used in statistics. We could compute measures of dispersion as the 
arithmetic average of the deviations around the mean, but we would encounter a 
problem: The deviations around the mean always sum to 0. If we computed the mean

of the deviations, the result would also equal 0. Therefore, we need to find a way to 
address the problem of negative deviations canceling out positive deviations.(9)
27 Another distance measure of dispersion that we may encounter, the interquartile range, focuses on the 
middle rather than the extremes. The interquartile range  (IQR) is the difference between the third and 
first quartiles of a data set: IQR = Q3 − Q1. The IQR represents the length of the interval containing the 
middle 50 percent of the data, with a larger interquartile range indicating greater dispersion, all else equal.

Measures of Dispersion 429
One solution is to examine the absolute deviations around the mean as in the 
mean absolute deviation.
■■Mean Absolute Deviation Formula.  The mean absolute deviation  (MAD) for 
a sample is
MAD=−
=∑XX
ni
in
1
where  X is the sample mean and n is the number of observations in the sample.
In calculating MAD, we ignore the signs of the deviations around the mean. For 
example, if Xi = −11.0 and  X = 4.5, the absolute value of the difference is |−11.0 − 4.5| 
= |−15.5| = 15.5. The mean absolute deviation uses all of the observations in the sample 
and is thus superior to the range as a measure of dispersion. One technical drawback 
of MAD is that it is difficult to manipulate mathematically compared with the next 
measure we will introduce, variance.28 Example 10 illustrates the use of the range and 
the mean absolute deviation in evaluating risk.
EXAMPLE 10   
The Range and the Mean Absolute Deviation
Having calculated mean returns for the two mutual funds in Example 7, the

analyst is now concerned with evaluating risk.
Table 15   Total Returns for Two Mutual Funds, 2008–2012 (Repeated)
(PRFDX)
Source:  performance.morningstar.com.
Based on the data in Table 15 on the previous page, answer the following:
1 Calculate the range of annual returns for (A) SLASX and (B) PRFDX, and 
state which mutual fund appears to be riskier based on these ranges.
2 Calculate the mean absolute deviation of returns on (A) SLASX and 
(B) PRFDX, and state which mutual fund appears to be riskier based on 
MAD.(10)
28 In some analytic work such as optimization, the calculus operation of differentiation is important. 
Variance as a function can be differentiated, but absolute value cannot.

Reading 8 ■ Statistical Concepts and Market Returns 430
A For SLASX, the largest return was 31.64 percent and the smallest was 
−39.44 percent. The range is thus 31.64 − (−39.44) = 71.08%.
B For PFRDX, the range is 25.62 − (−35.75) = 61.37%. With a larger range of 
returns than PRFDX, SLASX appeared to be the riskier fund during the 
2008–2012 period.
A The arithmetic mean return for SLASX as calculated in Example 7 is 
2.64 percent. The MAD of SLASX returns is
MAD
=−− +− +− +− −+ − 39 44 2643 1642 64 12 53 2644 352641 2822 6 .. .. .. .. .. 4 4
5
42 08 29 00 9896 99 10 18
5
98 14
519 63=++ ++
==.. .. .
..%
B The arithmetic mean return for PRFDX as calculated in Example 7 is 
4.31 percent. The MAD of PRFDX returns is
MAD
=−− +− +− +− −+ − 35 75 4312 5624 31 15 15 4310 72 43117254 3 .. .. .. .. .. 1 1
5
40 06 21 31 10 84 5031294
5
90 18
518 04=++ ++
==.. .. .
..%
SLASX, with a MAD of 19.63 percent, appears to be slightly riskier than PRFDX, 
with a MAD of 18.04 percent.

7.3 Population Variance and Population Standard Deviation
The mean absolute deviation addressed the issue that the sum of deviations from the 
mean equals zero by taking the absolute value of the deviations. A second approach 
to the treatment of deviations is to square them. The variance and standard deviation, 
which are based on squared deviations, are the two most widely used measures of 
dispersion. Variance  is defined as the average of the squared deviations around the 
mean. Standard deviation  is the positive square root of the variance. The following 
discussion addresses the calculation and use of variance and standard deviation.
7.3.1  Population Variance
If we know every member of a population, we can compute the population variance . 
Denoted by the symbol σ2, the population variance is the arithmetic average of the 
squared deviations around the mean.
■■Population Variance Formula.  The population variance is
σµ
2=−()
=∑X
Ni
iN2
1

σµ
2=−()
=∑X
Ni
iN2
1
where μ is the population mean and N is the size of the population.(11)

Measures of Dispersion 431
Given knowledge of the population mean, μ, we can use Equation 11 to calculate the 
sum of the squared differences from the mean, taking account of all N items in the 
population, and then to find the mean squared difference by dividing the sum by N. 
Whether a difference from the mean is positive or negative, squaring that difference 
results in a positive number. Thus variance takes care of the problem of negative devi -
ations from the mean canceling out positive deviations by the operation of squaring 
those deviations. The profit as a percentage of revenue for BJ’s Wholesale Club, Costco, 
and Walmart was given earlier as 0.9, 1.6, and 3.5, respectively. We calculated the 
mean profit as a percentage of revenue as 2.0. Therefore, the population variance of 
the profit as a percentage of revenue is (1/3)[(0.9 − 2.0)2 + (1.6 − 2.0)2 + (3.5 − 2.0)2] 
= (1/3)(−1.12 + −0.42 + 1.52) = (1/3)(1.21 + 0.16 + 2.25) = (1/3)(3.62) = 1.21.
7.3.2  Population Standard Deviation

Because the variance is measured in squared units, we need a way to return to the 
original units. We can solve this problem by using standard deviation, the square root 
of the variance. Standard deviation is more easily interpreted than the variance because 
standard deviation is expressed in the same unit of measurement as the observations.
■■Population Standard Deviation Formula.  The population standard devia -
tion , defined as the positive square root of the population variance, is
σµ
=−()
=∑X
Ni
iN2
1
where μ is the population mean and N is the size of the population.
Using the example of the profit as a percentage of revenue for BJ’s Wholesale Club, 
Costco, and Walmart, according to Equation 12 we would calculate the variance, 1.21, 
then take the square root:  121 . = 1.10.
Both the population variance and standard deviation are examples of parameters of 
a distribution. In later readings, we will introduce the notion of variance and standard

deviation as risk measures.
In investments, we often do not know the mean of a population of interest, usually 
because we cannot practically identify or take measurements from each member of 
the population. We then estimate the population mean with the mean from a sample 
drawn from the population, and we calculate a sample variance or standard deviation 
using formulas different from Equations 11 and 12. We shall discuss these calcula -
tions in subsequent sections. However, in investments we sometimes have a defined 
group that we can consider to be a population. With well-  defined populations, we use 
Equations 11 and 12, as in the following example.(12)

Reading 8 ■ Statistical Concepts and Market Returns 432
EXAMPLE 11   
Calculating the Population Standard Deviation
Table 20 gives the yearly portfolio turnover for the 12 US equity funds that com -
posed the 2013 Forbes  Magazine Honor Roll.29 Portfolio turnover, a measure of 
trading activity, is the lesser of the value of sales or purchases over a year divided 
by average net assets during the year. The number and identity of the funds on 
the Forbes  Honor Roll changes from year to year.
Table 20   Portfolio Turnover: 2013 Forbes  Honor Roll Mutual Funds
FundY early Portfolio 
Turnover (%)
Bruce Fund (BRUFX) 10
CGM Focus Fund (CGMFX) 360
Hotchkis And Wiley Small Cap Value A Fund 
(HWSAX)37
Aegis Value Fund (AVALX) 20
Delafield Fund (DEFIX) 49
Homestead Small Company Stock Fund (HSCSX) 1
Robeco Boston Partners Small Cap Value II Fund 
(BPSCX)32
Hotchkis And Wiley Mid Cap Value A Fund 
(HWMAX)72
T Rowe Price Small Cap Value Fund (PRSVX) 9
Guggenheim Mid Cap Value Fund Class A (SEVAX) 19

Wells Fargo Advantage Small Cap Value Fund 
(SSMVX)16
Stratton Small-  Cap Value Fund (STSCX) 11
Source:  Forbes  (2013).
Based on the data in Table 20, address the following:
1 Calculate the population mean portfolio turnover for the period used by 
Forbes  for the 12 Honor Roll funds.
2 Calculate the population variance and population standard deviation of 
portfolio turnover.
3 Explain the use of the population formulas in this example.
 μ = (10 + 360 + 37 + 20 + 49 + 1 + 32 + 72 + 9 + 19 + 16 + 11)/12
  = 636 /12 = 53 percent.
29 Forbes  magazine annually selects US equity mutual funds meeting certain criteria for its Honor Roll. 
The criteria relate to capital preservation (performance in bear markets), continuity of management (the 
fund must have a manager with at least six years’ tenure), diversification, accessibility (disqualifying funds 
that are closed to new investors), and after-  tax long-  term performance.

Measures of Dispersion 433
Having established that μ = 53, we can calculate  σµ
22
1=−()
=∑X
Ni
iN
 by first 
calculating the numerator in the expression and then dividing by N = 12. The 
numerator (the sum of the squared differences from the mean) is
(10 – 53)2 + (360 – 53)2 + (37 – 53)2 + (20 – 53)2 +  
(49 – 53)2 + (1 – 53)2 + (32 – 53)2 + (72 – 53)2 +  
(9 – 53)2 + (19 – 53)2 + (16 – 53)2 + (11 – 53)2 = 107,190
Thus σ2 = 107,190/12 = 8,932.50.
To calculate standard deviation,  σ= 8 932 50,.  = 94.51 percent. (The unit 
of variance is percent squared so the unit of standard deviation is percent.)
If the population is clearly defined to be the Forbes  Honor Roll funds in one 
specific year (2013), and if portfolio turnover is understood to refer to the specific 
one-  year period reported upon by Forbes,  the application of the population for -
mulas to variance and standard deviation is appropriate. The results of 8,932.50

and 94.51 are, respectively, the cross-  sectional variance and standard deviation 
in yearly portfolio turnover for the 2013 Forbes  Honor Roll Funds.30
7.4 Sample Variance and Sample Standard Deviation
In the following discussion, note the switch to Roman letters to symbolize sample 
7.4.1  Sample Variance
In many instances in investment management, a subset or sample of the population 
is all that we can observe. When we deal with samples, the summary measures are 
called statistics. The statistic that measures the dispersion in a sample is called the 
■■Sample Variance Formula.  The sample variance  is
sXX
ni
in
22
1
1=−()
−=∑
Equation 13 tells us to take the following steps to compute the sample variance:
 i. Calculate the sample mean,  X.
 ii. Calculate each observation’s squared deviation from the sample 
mean,  XXi−()2.(13)

30 In fact, we could not properly use the Honor Roll funds to estimate the population variance of portfolio 
turnover (for example) of any other differently defined population, because the Honor Roll funds are not 
a random sample from any larger population of US equity mutual funds.

Reading 8 ■ Statistical Concepts and Market Returns 434
 iii. Sum the squared deviations from the mean:  XXi
in
−()
=∑2
1.
 iv. Divide the sum of squared deviations from the mean by 
n – 1:  XX ni
in
−() −()
=∑2
11.
We will illustrate the calculation of the sample variance and the sample standard 
deviation in Example 12.
We use the notation s2 for the sample variance to distinguish it from population 
variance, σ2. The formula for sample variance is nearly the same as that for population 
variance except for the use of the sample mean,  X, in place of the population mean, 
μ, and a different divisor. In the case of the population variance, we divide by the size 
of the population, N. For the sample variance, however, we divide by the sample size 
minus 1, or n − 1. By using n − 1 (rather than n) as the divisor, we improve the sta -
tistical properties of the sample variance. In statistical terms, the sample variance 
defined in Equation 13 is an unbiased estimator of the population variance.31 The

quantity n − 1 is also known as the number of degrees of freedom in estimating the 
population variance. To estimate the population variance with s2, we must first cal -
culate the mean. Once we have computed the sample mean, there are only n − 1 
independent deviations from it.
7.4.2  Sample Standard Deviation
Just as we computed a population standard deviation, we can compute a sample stan -
dard deviation by taking the positive square root of the sample variance.
■■Sample Standard Deviation Formula.  The sample standard deviation , s, is
sXX
ni
in
=−()
−=∑2
1
1
To calculate the sample standard deviation, we first compute the sample variance 
using the steps given. We then take the square root of the sample variance. Example 12 
illustrates the calculation of the sample variance and standard deviation for the two 
mutual funds introduced earlier.
EXAMPLE 12   
Calculating Sample Variance and Sample Standard 
Deviation

Deviation
After calculating the geometric and arithmetic mean returns of two mutual 
funds in Example 7, we calculated two measures of dispersions for those funds, 
the range and mean absolute deviation of returns, in Example 10. We now cal -
culate the sample variance and sample standard deviation of returns for those 
same two funds.(14)
31 We discuss this concept further in the reading on sampling.

Measures of Dispersion 435
(PRFDX)
Based on the data in Table 15 repeated above, answer the following:
1 Calculate the sample variance of return for (A) SLASX and (B) PRFDX.
2 Calculate sample standard deviation of return for (A) SLASX and (B) 
PRFDX.
3 Contrast the dispersion of returns as measured by standard deviation of 
return and mean absolute deviation of return for each of the two funds.
To calculate the sample variance, we use Equation 13. (Deviation answers are 
all given in percent squared.)
A SLASX
 i. The sample mean is
 R = (−39.44 + 31.64 + 12.53 − 4.35 +12.82)/ 5 = 13.20/5 = 2.64%.
 ii. The squared deviations from the mean are
(–39.44 – 2.64)2 = (–42.08)2 = 1,770.73
(31.64 – 2.64)2 = (29.00)2 = 841.00

(12.53 – 2.64)2 = (9.89)2 = 97.81
(–4.35 – 2.64)2 = (–6.99)2 = 48.86
(12.82 – 2.64)2 = (10.18)2 = 103.63
 iii. The sum of the squared deviations from the mean is 1,770.73 + 
841.00 + 97.81 + 48.86 + 103.63 = 2,862.03.
 iv. Divide the sum of the squared deviations from the mean by n − 1: 
2,862.03/(5 − 1) = 2,862.03/4 = 715.51
B PRFDX
 R = (−35.75 + 25.62 + 15.15 − 0.72 + 17.25)/5 = 21.55/5 = 4.31%.
(–35.75 – 4.31)2 = (–40.06)2 = 1,604.80
(25.62 – 4.31)2 = (21.31)2 = 454.12
(15.15 – 4.31)2 = (10.84)2 = 117.51
(–0.72 – 4.31)2 = (–5.03)2 = 25.30

Reading 8 ■ Statistical Concepts and Market Returns 436
(17.25 – 4.31)2 = (12.94)2 = 167.44
 iii. The sum of the squared deviations from the mean is 1,604.80 + 
454.12 + 117.51 + 25.30 + 167.44 = 2,369.17.
2,369.17/4 = 592.29
To find the standard deviation, we take the positive square root of variance.
A For SLASX,  s=715 51 .  = 26.7%.
B For PRFDX,  s=592 29 .  = 24.3%.
Table 21 summarizes the results from Part 2 for standard deviation and incor -
porates the results for MAD from Example 10.
Table 21   Two Mutual Funds: Comparison of Standard Deviation and 
Mean Absolute Deviation
Fund Standard Deviation (%) Mean Absolute Deviation (%)
SLASX 26.7 19.6
PRFDX 24.3 18.0
Note that the mean absolute deviation is less than the standard deviation. 
The mean absolute deviation will always be less than or equal to the standard 
deviation because the standard deviation gives more weight to large deviations

than to small ones (remember, the deviations are squared).
Because the standard deviation is a measure of dispersion about the arithmetic 
mean, we usually present the arithmetic mean and standard deviation together when 
summarizing data. When we are dealing with data that represent a time series of 
percent changes, presenting the geometric mean—representing the compound rate of 
growth—is also very helpful. Table 22 presents the historical geometric and arithmetic 
mean returns, along with the historical standard deviation of returns, for the S&P 500 
annual and monthly return series. We present these statistics for nominal (rather than 
inflation-  adjusted) returns so we can observe the original magnitudes of the returns.
Table 22   Equity Market Returns: Means and Standard Deviations
Return SeriesGeometric  
Mean (%)Arithmetic  
Mean (%)Standard  
Deviation
Ibbotson Associates Series: 1926–2012
S&P 500 (Annual) 9.84 11.82 20.18
S&P 500 (Monthly) 0.79 0.94 5.50
Source:  Ibbotson.

Measures of Dispersion 437
7.5 Semivariance, Semideviation, and Related Concepts
An asset’s variance or standard deviation of returns is often interpreted as a measure of 
the asset’s risk. Variance and standard deviation of returns take account of returns above 
and below the mean, but investors are concerned only with downside risk, for example, 
returns below the mean. As a result, analysts have developed semivariance, semidevi -
ation, and related dispersion measures that focus on downside risk. Semivariance  is 
defined as the average squared deviation below the mean. Semideviation  (sometimes 
called semistandard deviation) is the positive square root of semivariance.32 To com -
pute the sample semivariance, for example, we take the following steps:
 i. Calculate the sample mean.
 ii. Identify the observations that are smaller than or equal to the mean (discarding 
observations greater than the mean).
 iii. Compute the sum of the squared negative deviations from the mean (using the

observations that are smaller than or equal to the mean).
 iv. Divide the sum of the squared negative deviations from Step iii by the total  
sample size minus 1: n − 1. A formula for semivariance approximating the unbi -
ased estimator is
XX ni
XXi−() −()
≤∑21
for all 
To take the case of Selected American Shares with returns (in percent) of −39.44, 
31.64, 12.53, −4.35, and 12.82, we earlier calculated a mean return of 2.64 percent. 
Two returns, −39.44 and −4.35, are smaller than 2.64. We compute the sum of the 
squared negative deviations from the mean as (−39.44 − 2.64)2 + (−4.35 − 2.64)2 = 
−42.082 + −6.992 = 1,770.73 + 48.86 = 1,819.59. With n − 1 = 4, we conclude that 
semivariance is 1,819.59/4 = 454.9 and that semideviation is  454 9 .  = 21.3 percent, 
approximately. The semideviation of 21.3 percent is less than the standard deviation 
of 26.7 percent. From this downside risk perspective, therefore, standard deviation 
overstates risk.

In practice, we may be concerned with values of return (or another variable) below 
some level other than the mean. For example, if our return objective is 12.75 percent 
annually, we may be concerned particularly with returns below 12.75 percent a year. 
We can call 12.75 percent the target. The name target semivariance  has been given 
to average squared deviation below a stated target, and target semideviation  is its 
positive square root. To calculate a sample target semivariance, we specify the target 
as a first step. After identifying observations below the target, we find the sum of the 
squared negative deviations from the target and divide that sum by the number of 
observations minus 1. A formula for target semivariance is
XB ni
XBi−() −()
≤∑21
for all 
where B is the target and n is the number of observations. With a target return of 
12.75 percent, we find in the case of Selected American Shares that three returns

(−39.44, 12.53, and −4.35) were below the target. The target semivariance is [(−39.44 
− 12.75)2 + (12.53 − 12.75)2 + (−4.35 − 12.75)2]/(5 – 1) = 754.06, and the target 
semideviation is  754 06 .  = 27.5 percent, approximately.
32 This is an informal treatment of these two measures; see the survey article by N. Fred Choobinbeh 
(2005) for a rigorous treatment.

Reading 8 ■ Statistical Concepts and Market Returns 438
When return distributions are symmetric, semivariance and variance are effectively 
equivalent. For asymmetric distributions, variance and semivariance rank prospects’ 
risk differently.33 Semivariance (or semideviation) and target semivariance (or target 
semideviation) have intuitive appeal, but they are harder to work with mathematically 
than variance.34 Variance or standard deviation enters into the definition of many of 
the most commonly used finance risk concepts, such as the Sharpe ratio and beta. 
Perhaps because of these reasons, variance (or standard deviation) is much more 
frequently used in investment practice.
7.6 Chebyshev’s Inequality
The Russian mathematician Pafnuty Chebyshev developed an inequality using standard 
deviation as a measure of dispersion. The inequality gives the proportion of values 
within k standard deviations of the mean.
■■Definition of Chebyshev’s Inequality.  According to Chebyshev’s inequality, for

any distribution with finite variance, the proportion of the observations within 
k standard deviations of the arithmetic mean is at least 1 − 1/ k2 for all k > 1.
Table 23 illustrates the proportion of the observations that must lie within a certain 
number of standard deviations around the sample mean.
Table 23   Proportions from Chebyshev’s Inequality
k Interval around the Sample Mean Proportion (%)
1.25 Xs±125 . 36
1.50 Xs±15.0 56
2.00 Xs±2 75
2.50 Xs±25.0 84
3.00 Xs±3 89
4.00 Xs±4 94
Note : Standard deviation is denoted as s.
When k = 1.25, for example, the inequality states that the minimum proportion of the 
observations that lie within ± 1.25 s is 1 − 1/(1.25)2 = 1 − 0.64 = 0.36 or 36 percent.
The most frequently cited facts that result from Chebyshev’s inequality are that 
a two-  standard-  deviation interval around the mean must contain at least 75 percent 
of the observations, and a three-  standard-  deviation interval around the mean must

contain at least 89 percent of the observations, no matter how the data are distributed.
The importance of Chebyshev’s inequality stems from its generality. The inequality 
holds for samples and populations and for discrete and continuous data regardless of 
the shape of the distribution. As we shall see in the reading on sampling, we can make 
33 We discuss skewness later in this reading.
34 As discussed in the reading on probability concepts and the various readings on portfolio concepts, 
we can find a portfolio’s variance as a straightforward function of the variances and correlations of the 
component securities. There is no similar procedure for semivariance and target semivariance. We also 
cannot take the derivative of semivariance or target semivariance.

Measures of Dispersion 439
much more precise interval statements if we can assume that the sample is drawn 
from a population that follows a specific distribution called the normal distribution. 
Frequently, however, we cannot confidently assume that distribution.
The next example illustrates the use of Chebyshev’s inequality.
EXAMPLE 13   
Applying Chebyshev’s Inequality
According to Table 22, the arithmetic mean monthly return and standard devi -
ation of monthly returns on the S&P 500 were 0.94 percent and 5.50 percent, 
respectively, during the 1926–2012 period, totaling 1,044 monthly observations. 
Using this information, address the following:
1 Calculate the endpoints of the interval that must contain at least 75 per -
cent of monthly returns according to Chebyshev’s inequality.
2 What are the minimum and maximum number of observations that 
must lie in the interval computed in Part 1, according to Chebyshev’s 
inequality?

According to Chebyshev’s inequality, at least 75  percent of the observations 
must lie within two standard deviations of the mean,  X ± 2s. For the monthly 
S&P 500 return series, we have 0.94% ± 2(5.50%) = 0.94% ± 11.00%. Thus the 
lower endpoint of the interval that must contain at least 75  percent of the 
observations is 0.94% − 11.00% = −10.06%, and the upper endpoint is 0.94% + 
11.00% = 11.94%.
For a sample size of 1,044, at least 0.75(1,044) = 783 observations must lie in 
the interval from −10.06% to 11.94% that we computed in Part 1. Chebyshev’s 
inequality gives the minimum percentage of observations that must fall within a 
given interval around the mean, but it does not give the maximum percentage. 
Table 4, which gave the frequency distribution of monthly returns on the S&P 
500, is excerpted below. The data in the excerpted table are consistent with the 
prediction of Chebyshev’s inequality. The set of intervals running from −10.0% to

12.0% is about equal in width to the two-  standard-  deviation interval −10.06% to 
11.94%. A total of 1,004 observations (approximately 96 percent of observations) 
fall in the range from −10.0% to 12.0%.
Table 4   Frequency Distribution for the Monthly Total 
Return on the S&P 500, January 1926 to 
December 2012 (Excerpt)
Return Interval (%) Absolute Frequency
−10.0 to −8.0 23
−8.0 to −6.0 34
−6.0 to −4.0 59
−4.0 to −2.0 98
−2.0 to 0.0 157
0.0 to 2.0 220
2.0 to 4.0 173

Reading 8 ■ Statistical Concepts and Market Returns 440
4.0 to 6.0 137
6.0 to 8.0 63
8.0 to 10.0 25
10.0 to 12.0 15
  1,004
7.7 Coefficient of Variation
We noted earlier that standard deviation is more easily interpreted than variance 
because standard deviation uses the same units of measurement as the observations. 
We may sometimes find it difficult to interpret what standard deviation means in terms 
of the relative degree of variability of different sets of data, however, either because 
the data sets have markedly different means or because the data sets have different 
units of measurement. In this section we explain a measure of relative dispersion, the 
coefficient of variation that can be useful in such situations. Relative dispersion  is 
the amount of dispersion relative to a reference value or benchmark.
We can illustrate the problem of interpreting the standard deviation of data sets

with markedly different means using two hypothetical samples of companies. The 
first sample, composed of small companies, includes companies with 2003 sales of 
€50 million, €75 million, €65 million, and €90 million. The second sample, composed 
of large companies, includes companies with 2003 sales of €800 million, €825 million, 
€815 million, and €840 million. We can verify using Equation 14 that the standard 
deviation of sales in both samples is €16.8 million.35 In the first sample, the largest 
observation, €90 million, is 80 percent larger than the smallest observation, €50 mil -
lion. In the second sample, the largest observation is only 5 percent larger than the 
smallest observation. Informally, a standard deviation of €16.8 million represents a 
high degree of variability relative to the first sample, which reflects mean 2003 sales 
of €70 million, but a small degree of variability relative to the second sample, which 
reflects mean 2003 sales of €820 million.

The coefficient of variation is helpful in situations such as that just described.
■■Coefficient of Variation Formula.  The coefficient of variation , CV, is the ratio 
of the standard deviation of a set of observations to their mean value:36
CV=sX
where s is the sample standard deviation and  X is the sample mean.
When the observations are returns, for example, the coefficient of variation measures 
the amount of risk (standard deviation) per unit of mean return. Expressing the mag -
nitude of variation among observations relative to their average size, the coefficient of (15)Table 4   (Continued)
35 The second sample was created by adding €750 million to each observation in the first sample. Standard 
deviation (and variance) has the property of remaining unchanged if we add a constant amount to each 
36 The reader will also encounter CV defined as 100( s/X), which states CV as a percentage.

Measures of Dispersion 441
variation permits direct comparisons of dispersion across different data sets. Reflecting 
the correction for scale, the coefficient of variation is a scale-  free measure (that is, it 
has no units of measurement).
We can illustrate the application of the coefficient of variation using our earlier 
example of two samples of companies. The coefficient of variation for the first sample 
is (€16.8 million)/(€70 million) = 0.24; the coefficient of variation for the second sam -
ple is (€16.8 million)/(€820 million) = 0.02. This confirms our intuition that the first 
sample had much greater variability in sales than the second sample. Note that 0.24 
and 0.02 are pure numbers in the sense that they are free of units of measurement 
(because we divided the standard deviation by the mean, which is measured in the 
same units as the standard deviation). If we need to compare the dispersion among

data sets stated in different units of measurement, the coefficient of variation can 
be useful because it is free from units of measurement. Example 14 illustrates the 
calculation of the coefficient of variation.
EXAMPLE 14   
Calculating the Coefficient of Variation
Table 24 summarizes annual mean returns and standard deviations computed 
using monthly return data for select stock market indexes of four Asia-  Pacific 
markets. The indexes are: S&P/ASX 200 Index (Australia), Hang Seng Index 
(Hong Kong), Straits Times Index (Singapore), and KOSPI Composite Index 
(South Korea).
Table 24   Arithmetic Mean Annual Return and Standard Deviation of 
Returns, Asia-  Pacific Stock Markets, 2003–2012
MarketArithmetic Mean  
Return (%)Standard Deviation  
of Return (%)
Australia 5.0 13.6
Hong Kong 9.4 22.4
Singapore 9.3 19.2
South Korea 12.0 21.5
Source:  finance.yahoo.com.
Using the information in Table 24, address the following:
1 Calculate the coefficient of variation for each market given.

2 Rank the markets from most risky to least risky using CV as a measure of 
relative dispersion.
3 Determine whether there is more difference between the absolute or 
the relative riskiness of the Hong Kong and Singapore markets. Use the 
standard deviation as a measure of absolute risk and CV as a measure of 
relative risk.
Australia: CV = 13.6%/5.0% = 2.720
Hong Kong: CV = 22.4%/9.4% = 2.383
Singapore: CV = 19.2%/9.3% = 2.065

Reading 8 ■ Statistical Concepts and Market Returns 442
South Korea: CV = 21.5%/12.0% = 1.792
Based on CV, the ranking for the 2003–2012 period examined is Australia (most 
risky), Hong Kong, Singapore, and South Korea (least risky).
As measured both by standard deviation and CV, Hong Kong market was riskier 
than the Singapore market. The standard deviation of Hong Kong returns was 
(22.4 − 19.2)/19.2 = 0.167 or about 17 percent larger than Singapore returns, 
compared with a difference in the CV of (2.383 − 2.065)/2.065 = 0.154 or about 
15 percent. Thus, the CVs reveal slightly less difference between Hong Kong and 
Singapore return variability than that suggested by the standard deviations alone.
7.8 The Sharpe Ratio
Although CV was designed as a measure of relative dispersion, its inverse reveals 
something about return per unit of risk because the standard deviation of returns 
is commonly used as a measure of investment risk. For example, a portfolio with a

mean monthly return of 1.19 percent and a standard deviation of 4.42 percent has 
an inverse CV of 1.19%/4.42% = 0.27. This result indicates that each unit of standard 
deviation represents a 0.27 percent return.
A more precise return–risk measure recognizes the existence of a risk-  free return, 
a return for virtually zero standard deviation. With a risk-  free asset, an investor can 
choose a risky portfolio, p, and then combine that portfolio with the risk-  free asset to 
achieve any desired level of absolute risk as measured by standard deviation of return, 
sp. Consider a graph with mean return on the vertical axis and standard deviation of 
return on the horizontal axis. Any combination of portfolio p and the risk-  free asset 
lies on a ray (line) with slope equal to the quantity (Mean return − Risk-  free return) 
divided by sp. The ray giving investors choices offering the most reward (return in

excess of the risk-  free rate) per unit of risk is the one with the highest slope. The ratio 
of excess return to standard deviation of return for a portfolio p—the slope of the ray 
passing through p—is a single-  number measure of a portfolio’s performance known 
as the Sharpe ratio, after its developer, William F. Sharpe.
■■Sharpe Ratio Formula.  The Sharpe ratio  for a portfolio p, based on historical 
returns, is defined as
SRR
shpF
p=−
where  Rp is the mean return to the portfolio,  RF is the mean return to a 
risk-  free asset, and sp is the standard deviation of return on the portfolio.37(16)
37 The equation presents the ex post  or historical Sharpe ratio. We can also think of the Sharpe ratio for 
a portfolio going forward based on our expectations for mean return, the risk-  free return, and the stan -
dard deviation of return; this would be the ex ante  Sharpe ratio. One may also encounter an alternative

calculation for the Sharpe ratio in which the denominator is the standard deviation of the series (Portfolio 
return − Risk-  free return) rather than the standard deviation of portfolio return; in practice, the two stan -
dard deviation calculations generally yield very similar results. For more information on the Sharpe ratio 
(which has also been called the Sharpe measure, the reward-  to- variability ratio, and the excess return to 
variability measure), see Elton, Gruber, Brown, and Goetzmann (2013) and Sharpe (1994).

Measures of Dispersion 443
The numerator of the Sharpe measure is the portfolio’s mean return minus the mean 
return on the risk-  free asset over the sample period. The  RRpF−  term measures the 
extra reward that investors receive for the added risk taken. We call this difference 
the mean excess return  on portfolio p. Thus the Sharpe ratio measures the reward, 
in terms of mean excess return, per unit of risk, as measured by standard deviation 
of return. Those risk-  averse investors who make decisions only in terms of mean 
return and standard deviation of return prefer portfolios with larger Sharpe ratios to 
those with smaller Sharpe ratios.
To illustrate the calculation of the Sharpe ratio, consider the performance of 
two exchange traded funds. SPDR S&P 500 seeks to track the investment results of 
the S&P 500 Index (large capitalization US stocks) and iShares Russell 2000 Index 
seeks to track the investment results of the Russell 2000 Index (small capitalization

US stocks). Table 25 presents the historical arithmetic mean return, along with the 
historical standard deviation of returns, for annual returns series of these two funds 
and the US 30-  day T-  bill during the 2003–2012 period.
Table 25   Exchange Traded Fund and US 30-  Day T-  Bill Mean Return and 
Standard Deviation of Return, 2003–2012
Fund/T-  Bill Arithmetic Mean (%)Standard Deviation of 
Return (%)
iShares Russell 2000 Index 9.26 22.36
SPDR S&P 500 Index 6.77 19.99
30- day T-  bill 1.58 1.78
Sources:  finance.yahoo.com and www.federalreserve.gov.
Using the mean US 30-  day T-  bill return to represent the risk-  free rate, we find 
the following Sharpe ratios
iShares Russell 2000: Sh,..
..IWM=−=9261 58
22 36034
SPDR S&P 500: Sh,..
..SPY=−=6771 58
19 99026
Although US small stocks (iShares Russell 2000 Index) had a higher standard deviation, 
they performed better than the US large stocks (SPDR S&P 500 Index), as measured 
by the Sharpe ratio.

The Sharpe ratio is a mainstay of performance evaluation. We must issue two 
cautions concerning its use, one related to interpreting negative Sharpe ratios and 
the other to conceptual limitations.
Finance theory tells us that in the long run, investors should be compensated with 
additional mean return above the risk-  free rate for bearing additional risk, at least if 
the risky portfolio is well diversified. If investors are so compensated, the numerator 
of the Sharpe ratio will be positive. Nevertheless, we often find that portfolios exhibit 
negative Sharpe ratios when the ratio is calculated over periods in which bear mar -
kets for equities dominate. This raises a caution when dealing with negative Sharpe 
ratios. With positive Sharpe ratios, a portfolio’s Sharpe ratio decreases if we increase 
risk, all else equal. That result is intuitive for a risk-  adjusted performance measure.

With negative Sharpe ratios, however, increasing risk results in a numerically larger 
Sharpe ratio (for example, doubling risk may increase the Sharpe ratio from −1 to 
−0.5). Therefore, in a comparison of portfolios with negative Sharpe ratios, we cannot

Reading 8 ■ Statistical Concepts and Market Returns 444
generally interpret the larger Sharpe ratio (the one closer to zero) to mean better 
risk-  adjusted performance.38 Practically, to make an interpretable comparison in such 
cases using the Sharpe ratio, we may need to increase the evaluation period such that 
one or more of the Sharpe ratios becomes positive; we might also consider using a 
different performance evaluation metric.
The conceptual limitation of the Sharpe ratio is that it considers only one aspect 
of risk, standard deviation of return. Standard deviation is most appropriate as a risk 
measure for portfolio strategies with approximately symmetric return distributions. 
Strategies with option elements have asymmetric returns. Relatedly, an investment 
strategy may produce frequent small gains but have the potential for infrequent but 
extremely large losses.39 Such a strategy is sometimes described as picking up coins

in front of a bulldozer; for example, some hedge fund strategies tend to produce that 
return pattern. Calculated over a period in which the strategy is working (a large loss 
has not occurred), this type of strategy would have a high Sharpe ratio. In this case, 
the Sharpe ratio would give an overly optimistic picture of risk-  adjusted performance 
because standard deviation would incompletely measure the risk assumed.40 Therefore, 
before applying the Sharpe ratio to evaluate a manager, we should judge whether 
standard deviation adequately describes the risk of the manager’s investment strategy.
Example 15 illustrates the calculation of the Sharpe ratio in a portfolio performance 
evaluation context.
EXAMPLE 15   
Calculating the Sharpe Ratio
In earlier examples, we computed the various statistics for two mutual funds, 
Selected American Shares (SLASX) and T. Rowe Price Equity Income (PRFDX), 
for a five-  year period ending in December 2012. Table 26 summarizes selected

statistics for these two mutual funds for a longer period, the 10-  year period 
ending in 2012.
Table 26   Mutual Fund Mean Return and Standard Deviation of 
Return, 2003–2012
Fund Arithmetic Mean (%) Standard Deviation of Return (%)
SLASX 8.60 20.02
PRFDX 8.91 18.12
The US 30-  day T-  bill rate is frequently used as a proxy for the risk-  free rate. 
Earlier, Table 25 gave the average annual return on T-  bills for the 2003–2012 
period as 1.58 percent.
38 If the standard deviations are equal, however, the portfolio with the negative Sharpe ratio closer to 
zero is superior.
39 This statement describes a return distribution with negative skewness. We discuss skewness later in 
40 For more information, see Amin and Kat (2003).

Symmetry and Skewness in Return Distributions 445
Using the information in Table 25 and the average annual return on 30-  day 
T- bills, address the following:
1 Calculate the Sharpe ratios for SLASX and PRFDX during the 2003–2012 
period.
2 State which fund had superior risk-  adjusted performance during this 
period, as measured by the Sharpe ratio.
We already have in hand the means of the portfolio return and standard devia -
tions of returns and the mean annual risk-  free rate of return from 2003 to 2012.
SLASX: Sh,..
..SLASX=−=8601 58
20 02035
PRFDX: Sh,..
..PRFDX=−=8911 58
18 12040
PRFDX had a higher positive Sharpe ratio than SLASX during the period. As 
measured by the Sharpe ratio, PRFDX’s performance was superior. This is not 
surprising as PRFDX had a higher return and a lower standard deviation than 
SLASX.
SYMMETRY AND SKEWNESS IN RETURN 
Mean and variance may not adequately describe an investment’s distribution of returns.

In calculations of variance, for example, the deviations around the mean are squared, 
so we do not know whether large deviations are likely to be positive or negative. 
We need to go beyond measures of central tendency and dispersion to reveal other 
important characteristics of the distribution. One important characteristic of interest 
to analysts is the degree of symmetry in return distributions.
If a return distribution is symmetrical about its mean, then each side of the dis -
tribution is a mirror image of the other. Thus equal loss and gain intervals exhibit 
the same frequencies. Losses from −5 percent to −3 percent, for example, occur with 
about the same frequency as gains from 3 percent to 5 percent.
One of the most important distributions is the normal distribution, depicted 
in Figure  6. This symmetrical, bell-  shaped distribution plays a central role in the 
mean–variance model of portfolio selection; it is also used extensively in financial

risk management. The normal distribution has the following characteristics:
■■Its mean and median are equal.
■■It is completely described by two parameters—its mean and variance.
■■Roughly 68 percent of its observations lie between plus and minus one stan -
dard deviation from the mean; 95 percent lie between plus and minus two 
standard deviations; and 99 percent lie between plus and minus three standard 
deviations.
A distribution that is not symmetrical is called skewed . A return distribution with 
positive skew has frequent small losses and a few extreme gains. A return distribution 
with negative skew has frequent small gains and a few extreme losses. Figure 7 shows 8

Reading 8 ■ Statistical Concepts and Market Returns 446
continuous positively and negatively skewed distributions. The continuous positively 
skewed distribution shown has a long tail on its right side; the continuous negatively 
skewed distribution shown has a long tail on its left side. For the continuous positively 
skewed unimodal distribution, the mode is less than the median, which is less than 
the mean. For the continuous negatively skewed unimodal distribution, the mean is 
less than the median, which is less than the mode.41 Investors should be attracted by 
a positive skew because the mean return falls above the median. Relative to the mean 
return, positive skew amounts to a limited, though frequent, downside compared with 
a somewhat unlimited, but less frequent, upside.
41 As a mnemonic, in this case the mean, median, and mode occur in the same order as they would be 
listed in a dictionary. Von Hippel (2005) explores exceptions to the relationships among these measures

Symmetry and Skewness in Return Distributions 447
Figure 6   Properties of a Normal Distribution (EV 5 Expected Value)
Standard DeviationsProbability = 68.3%
Standard DeviationsProbability = 95.5%
Standard DeviationsProbability = 99.7%
0
EV_1_2EVEV
_3_4_5 01 2 34 5_1_2_3_4_50 12 34 5_1_2_3_4_50 12 34 5
Source:  Reprinted from Fixed Income Analysis.  Copyright CFA Institute.

Reading 8 ■ Statistical Concepts and Market Returns 448
Figure 7   Properties of a Skewed Distribution
Skewness is the name given to a statistical measure of skew. (The word “skewness” is 
also sometimes used interchangeably for “skew. ”) Like variance, skewness is computed 
using each observation’s deviation from its mean. Skewness  (sometimes referred 
to as relative skewness) is computed as the average cubed deviation from the mean 
standardized by dividing by the standard deviation cubed to make the measure free of 
scale.42 A symmetric distribution has skewness of 0, a positively skewed distribution 
has positive skewness, and a negatively skewed distribution has negative skewness, 
as given by this measure.
We can illustrate the principle behind the measure by focusing on the numera -

tor. Cubing, unlike squaring, preserves the sign of the deviations from the mean. If 
a distribution is positively skewed with a mean greater than its median, then more 
than half of the deviations from the mean are negative and less than half are positive. 
In order for the sum to be positive, the losses must be small and likely, and the gains 
less likely but more extreme. Therefore, if skewness is positive, the average magnitude 
of positive deviations is larger than the average magnitude of negative deviations.
A simple example illustrates that a symmetrical distribution has a skewness mea -
sure equal to 0. Suppose we have the following data: 1, 2, 3, 4, 5, 6, 7, 8, and 9. The 
mean outcome is 5, and the deviations are −4, −3, −2, −1, 0, 1, 2, 3, and 4. Cubing the 
deviations yields −64, −27, −8, −1, 0, 1, 8, 27, and 64, with a sum of 0. The numerator 
of skewness (and so skewness itself) is thus equal to 0, supporting our claim. Below

we give the formula for computing skewness from a sample.
■■Sample Skewness Formula. Sample skewness  (also called sample relative 
skewness), SK, is
Sn
nnXX
sKi
in
=−() −()

−()
=∑
123
1
3 
where n is the number of observations in the sample and s is the sample stan -
dard deviation.43(17)
42 We are discussing a moment coefficient of skewness. Some textbooks present the Pearson coefficient 
of skewness, equal to 3(Mean − Median)/Standard deviation, which has the drawback of involving the 
calculation of the median.
43 The term n/[(n − 1)( n − 2)] in Equation 17 corrects for a downward bias in small samples.

Symmetry and Skewness in Return Distributions 449
The algebraic sign of Equation 17 indicates the direction of skew, with a negative SK 
indicating a negatively skewed distribution and a positive SK indicating a positively 
skewed distribution. Note that as n becomes large, the expression reduces to the mean 
cubed deviation,  SnXX
sKi
in
≈

−()
=∑13
1
3 . As a frame of reference, for a sample size 
of 100 or larger taken from a normal distribution, a skewness coefficient of ±0.5 would 
be considered unusually large.
Table 27 shows several summary statistics for the annual and monthly returns on 
the S&P 500. Earlier we discussed the arithmetic mean return and standard deviation 
of return, and we shall shortly discuss kurtosis.
Table 27    S&P 500 Annual and Monthly Total Returns, 1926–2012: Summary Statistics
Return SeriesNumber of  
PeriodsArithmetic  
Deviation (%) Skewness Excess Kurtosis
S&P 500 (Annual) 87 11.82 20.18 −0.3768 0.0100

S&P 500 (Monthly) 1,044 0.94 5.50 0.3456 9.4288
Table 27 reveals that S&P 500 annual returns during this period were negatively 
skewed while monthly returns were positively skewed, and the magnitude of skew -
ness was greater for the annual series. We would find for other market series that the 
shape of the distribution of returns often depends on the holding period examined.
Some researchers believe that investors should prefer positive skewness, all else 
equal—that is, they should prefer portfolios with distributions offering a relatively 
large frequency of unusually large payoffs.44 Different investment strategies may 
tend to introduce different types and amounts of skewness into returns. Example 16 
illustrates the calculation of skewness for a managed portfolio.
EXAMPLE 16   
Calculating Skewness for a Mutual Fund
Table 28 presents 10 years of annual returns on the T. Rowe Price Equity Income 
Fund (PRFDX).

Table 28   Annual Rates of Return: T. Rowe Price Equity 
Income, 2003–2012
Y ear Return (%)
2003 25.78
2004 15.05
2005 4.26
2006 19.14
44 For more on the role of skewness in portfolio selection, see Reilly and Brown (2018) and Elton et al. 
(2013) and the references therein.

Reading 8 ■ Statistical Concepts and Market Returns 450
2007 3.30
2008 −35.75
2009 25.62
2010 15.15
2011 −0.72
2012 17.25
Using the information in Table 28, address the following:
1 Calculate the skewness of PRFDX showing two decimal places.
2 Characterize the shape of the distribution of PRFDX returns based on 
your answer to Part 1.
To calculate skewness, we find the sum of the cubed deviations from the mean, 
divide by the standard deviation cubed, and then multiply that result by n/[(n 
− 1)( n − 2)]. Table 29 gives the calculations.
Table 29   Calculating Skewness for PRFDX
Y ear Rt RRt− RRt−()3
2003 25.78 16.87 4,801.150
2004 15.05 6.14 231.476
2005 4.26 −4.65 −100.545
2006 19.14 10.23 1,070.599
2007 3.30 −5.61 −176.558
2008 −35.75 −44.66 −89,075.067
2009 25.62 16.71 4,665.835
2010 15.15 6.24 242.971
2011 −0.72 −9.63 −893.056
2012 17.25 8.34 580.094
n = 10  
R= 8.91%  
  Sum = −78,653.103
s = 18.12% s3 = 5,949.419
  Sum/ s3 = −13.2203

n/[(n − 1)( n − 2)] = 0.1389
  Skewness = −1.84
Source:  performance.morningstar.com.Table 28   (Continued)

Kurtosis in Return Distributions 451
Using Equation 17, the calculation is:
SK=()()

−=−10
9878 653 103
18 121843,.
..
Based on this small sample, the distribution of annual returns for the fund 
appears to be negatively skewed. In this example, four deviations are negative 
and six are positive. While, there are more positive deviations, they are much 
more than offset by a huge negative deviation in 2008, when the stock markets 
sharply went down as a consequence of the global financial crisis. The result 
is that skewness is a negative number, implying that the distribution is skewed 
to the left.
KURTOSIS IN RETURN DISTRIBUTIONS
In the previous section, we discussed how to determine whether a return distribution 
deviates from a normal distribution because of skewness. One other way in which 
a return distribution might differ from a normal distribution is its relative tendency 
to generate large deviations from the mean. Most investors would perceive a greater

chance of extremely large deviations from the mean as increasing risk.
Kurtosis  is a measure of the combined weight of the tails of a distribution relative 
to the rest of the distribution—that is, the proportion of the total probability that is 
in the tails. A distribution that has fatter tails than the normal distribution is called 
leptokurtic ; a distribution that has thinner tails than the normal distribution is called 
platykurtic ; and a distribution identical to the normal distribution as concerns relative 
weight in the tails is called mesokurtic . A leptokurtic distribution tends to generate 
more-  frequent extremely large deviations from the mean than the normal distribution.45
Figure 8 illustrates a leptokurtic distribution. It has fatter tails than the normal 
distribution. By construction, the leptokurtic and normal distributions have the same 
mean, standard deviation, and skewness. Note that the leptokurtic distribution is more

likely than the normal distribution to generate observations in the tail regions defined 
by the intersection of graphs near a standard deviation of about ±2.5. The leptokurtic 
distribution is also more likely to generate observations that are near the mean, defined 
here as the region ±1 standard deviation around the mean. In compensation, to have 
probabilities sum to 1, the leptokurtic distribution generates fewer observations in 
the regions between the central region and the two tail regions.9
45 See Wheeler (2011) for definitions and further reading.

Reading 8 ■ Statistical Concepts and Market Returns 452
Figure 8   Leptokurtic: Fat Tailed
Standard DeviationsFat Tails Distributio n
Normal Distributio n
_4_5_3_2_10 12 34
The calculation for kurtosis involves finding the average of deviations from the 
mean raised to the fourth power and then standardizing that average by dividing by the 
standard deviation raised to the fourth power.46 For all normal distributions, kurtosis 
is equal to 3. Many statistical packages report estimates of excess kurtosis , which is 
kurtosis minus 3.47 Excess kurtosis thus characterizes kurtosis relative to the normal 
distribution. A normal or other mesokurtic distribution has excess kurtosis equal 
to 0. A leptokurtic distribution has excess kurtosis greater than 0, and a platykurtic 
distribution has excess kurtosis less than 0. A return distribution with positive excess

kurtosis—a leptokurtic return distribution—has more frequent extremely large devia -
tions from the mean than a normal distribution. Below is the expression for computing 
kurtosis from a sample.
■■Sample Excess Kurtosis Formula.  The sample excess kurtosis  is
Knn
nn nXX
sn
Ei
in
=+()
−() −() −()−()









−−=∑1
12 3314
1
4 (()
−() −()2
23nn
where n is the sample size and s is the sample standard deviation.(18)
46 This measure is free of scale. It is always positive because the deviations are raised to the fourth power.
47 Ibbotson and some software packages, such as Microsoft Excel, label “excess kurtosis” as simply “kurto -
sis. ” This highlights the fact that one should familiarize oneself with the description of statistical quantities 
in any software packages that one uses.

Kurtosis in Return Distributions 453
In Equation  18, sample kurtosis  is the first term. Note that as n becomes large, 
Equation 18 approximately equals  n
nXX
sn
n nXX
s2
34
42
24
4313−()−=−()−∑∑. For a 
sample of 100 or larger taken from a normal distribution, a sample excess kurtosis of 
1.0 or larger would be considered unusually large.
Most equity return series have been found to be leptokurtic. If a return distribution 
has positive excess kurtosis (leptokurtosis) and we use statistical models that do not 
account for the fatter tails, we will underestimate the likelihood of very bad or very 
good outcomes. For example, the return on the S&P 500 for 19 October 1987 was 20 
standard deviations away from the mean daily return. Such an outcome is possible 
with a normal distribution, but its likelihood is almost equal to 0. If daily returns are 
drawn from a normal distribution, a return four standard deviations or more away

from the mean is expected once every 50 years; a return greater than five standard 
deviations away is expected once every 7,000 years. The return for October 1987 is 
more likely to have come from a distribution that had fatter tails than from a normal 
distribution. Looking at Table 27 given earlier, the monthly return series for the S&P 
500 has very large excess kurtosis, approximately 9.4. It is extremely fat-  tailed relative 
to the normal distribution. By contrast, the annual return series has about no excess 
kurtosis. The results for excess kurtosis in the table are consistent with research find -
ings that the normal distribution is a better approximation for US equity returns for 
annual holding periods than for shorter ones (such as monthly).48
The following example illustrates the calculations for sample excess kurtosis for 
one of the two mutual funds we have been examining.
EXAMPLE 17   
Calculating Sample Excess Kurtosis

EXAMPLE 17   
Having concluded in Example 16 that the annual returns on T. Rowe Price Equity 
Income Fund were negatively skewed during the 2003–2012 period, what can 
we say about the kurtosis of the fund’s return distribution? Table 28 (repeated 
below) recaps the annual returns for the fund.
Income, 2003–2012 (Repeated)
2003 25.78
2004 15.05
2005 4.26
2006 19.14
2007 3.30
2009 25.62
2010 15.15
48 See Campbell, Lo, and MacKinlay (1997) for more details.

Reading 8 ■ Statistical Concepts and Market Returns 454
2011 −0.72
2012 17.25
Using the information from Table 28 repeated above, address the following:
1 Calculate the sample excess kurtosis of PRFDX showing two decimal 
places.
your answer to Part 1 as leptokurtic, mesokurtic, or platykurtic.
To calculate excess kurtosis, we find the sum of the deviations from the mean 
raised to the fourth power, divide by the standard deviation raised to the fourth 
power, and then multiply that result by n(n + 1)/[( n − 1)( n − 2)( n − 3)]. This 
calculation determines kurtosis. Excess kurtosis is kurtosis minus 3( n − 1)2/
[(n − 2)( n − 3)]. Table 30 gives the calculations.
Table 30   Calculating Kurtosis for PRFDX
Y ear Rt RRt− RRt−()4
2003 25.78 16.87 80,995.395
2004 15.05 6.14 1,421.260
2005 4.26 −4.65 467.533
2006 19.14 10.23 10,952.229
2007 3.30 −5.61 990.493

2008 −35.75 −44.66 3,978,092.479
2009 25.62 16.71 77,966.098
2010 15.15 6.24 1,516.137
2011 −0.72 −9.63 8,600.133
2012 17.25 8.34 4,837.981
n = 10  
R= 8.91%  
  Sum = 4,165,839.738
s = 18.12% s4 = 107,803.478
  Sum/ s4 = 38.643
n(n + 1)/[( n − 1)( n − 2)( n −3)] = 0.2183
Kurtosis = 8.434
3(n − 1)2/[(n − 2)( n −3)] = 4.34
Excess Kurtosis = 4.09

Using Geometric and Arithmetic Means 455
Using Equation 18, the calculation is
KE=()()()

−()
()()=110
98 74 165 839 738
18 1239
874042,, .
..99
The distribution of PRFDX’s annual returns appears to be leptokurtic, based 
on a positive sample excess kurtosis. The fairly large excess kurtosis of 4.09 
indicates that the distribution of PRFDX’s annual returns is fat-  tailed relative 
to the normal distribution. With a negative skewness and a positive excess kur -
tosis, PRFDX’s annual returns do not appear to have been normally distributed 
during the period.49
USING GEOMETRIC AND ARITHMETIC MEANS
With the concepts of descriptive statistics in hand, we will see why the geometric mean 
is appropriate for making investment statements about past performance. We will also 
explore why the arithmetic mean is appropriate for making investment statements in 
a forward-  looking context.
For reporting historical returns, the geometric mean has considerable appeal

because it is the rate of growth or return we would have had to earn each year to 
match the actual, cumulative investment performance. In our simplified Example 8, 
for instance, we purchased a stock for €100 and two years later it was worth €100, 
with an intervening year at €200. The geometric mean of 0  percent is clearly the 
compound rate of growth during the two years. Specifically, the ending amount is 
the beginning amount times (1 + RG)2. The geometric mean is an excellent measure 
of past performance.
Example 8 illustrated how the arithmetic mean can distort our assessment of histor -
ical performance. In that example, the total performance for the two-  year period was 
unambiguously 0 percent. With a 100 percent return for the first year and −50 percent 
for the second, however, the arithmetic mean was 25 percent. As we noted previously, 
the arithmetic mean is always greater than or equal to the geometric mean. If we want

to estimate the average return over a one-  period horizon, we should use the arithmetic 
mean because the arithmetic mean is the average of one-  period returns. If we want 
to estimate the average returns over more than one period, however, we should use 
the geometric mean of returns because the geometric mean captures how the total 
returns are linked over time.
As a corollary to using the geometric mean for performance reporting, the use 
of semilogarithmic  rather than arithmetic scales is more appropriate when graph -
ing past performance.50 In the context of reporting performance, a semilogarithmic 
graph has an arithmetic scale on the horizontal axis for time and a logarithmic scale 
on the vertical axis for the value of the investment. The vertical axis values are spaced 
according to the differences between their logarithms. Suppose we want to represent 10
49 It is useful to know that we can conduct a Jarque–Bera (JB) statistical test of normality based on sample

size n, sample skewness, and sample excess kurtosis. We can conclude that a distribution is not normal 
with no more than a 5 percent chance of being wrong if the quantity  JB=+() () nS KKE2262 4 is 6 or 
greater for a sample with at least 30 observations. In this mutual fund example, we have only 10 observations 
and the test described is only correct based on large samples (as a guideline, for n ≥ 30). Gujarati, Porter, 
and Gunasekar (2013) provides more details on this test.
50 See Campbell (1974) for more information.

Reading 8 ■ Statistical Concepts and Market Returns 456
£1, £10, £100, and £1,000 as values of an investment on the vertical axis. Note that 
each successive value represents a 10-  fold increase over the previous value, and each 
will be equally spaced on the vertical axis because the difference in their logarithms 
is roughly 2.30; that is, ln 10 − ln 1 = ln 100 − ln 10 = ln 1,000 − ln 100 = 2.30. On a 
semilogarithmic scale, equal movements on the vertical axis reflect equal percentage 
changes, and growth at a constant compound rate plots as a straight line. A plot curv -
ing upward reflects increasing growth rates over time. The slopes of a plot at different 
points may be compared in order to judge relative growth rates.
In addition to reporting historical performance, financial analysts need to calculate 
expected equity risk premiums in a forward-  looking context. For this purpose, the 
arithmetic mean is appropriate.

We can illustrate the use of the arithmetic mean in a forward-  looking context with 
an example based on an investment’s future cash flows. In contrasting the geometric 
and arithmetic means for discounting future cash flows, the essential issue concerns 
uncertainty. Suppose an investor with $100,000 faces an equal chance of a 100 percent 
return or a −50 percent return, represented on the tree diagram as a 50/50 chance of 
a 100 percent return or a −50 percent return per period. With 100 percent return in 
one period and −50  percent return in the other, the geometric mean return 
is 2051 0 . () −= .
$100,000$200,000$400,000
$100,000
$100,000
$25,000$50,000
The geometric mean return of 0 percent gives the mode or median of ending wealth 
after two periods and thus accurately predicts the modal or median ending wealth of 
$100,000 in this example. Nevertheless, the arithmetic mean return better predicts

the arithmetic mean ending wealth. With equal chances of 100 percent or −50 percent 
returns, consider the four equally likely outcomes of $400,000, $100,000, $100,000, 
and $25,000 as if they actually occurred. The arithmetic mean ending wealth would be 
$156,250 = ($400,000 + $100,000 + $100,000 + $25,000)/4. The actual returns would 
be 300 percent, 0 percent, 0 percent, and −75 percent for a two-  period arithmetic 
mean return of (300 + 0 + 0 −75)/4 = 56.25 percent. This arithmetic mean return 
predicts the arithmetic mean ending wealth of $100,000 × 1.5625 = $156,250. Noting 
that 56.25 percent for two periods is 25 percent per period, we then must discount 
the expected terminal wealth of $156,250 at the 25 percent arithmetic mean rate to 
reflect the uncertainty in the cash flows.
Uncertainty in cash flows or returns causes the arithmetic mean to be larger than 
the geometric mean. The more uncertain the returns, the more divergence exists

between the arithmetic and geometric means. The geometric mean return approx -
imately equals the arithmetic return minus half the variance of return.51 Zero vari -
ance or zero uncertainty in returns would leave the geometric and arithmetic return 
approximately equal, but real-  world uncertainty presents an arithmetic mean return 
larger than the geometric. For example, for the nominal annual returns on S&P 500 
from 1926 to 2012, Table 27 reports an arithmetic mean of 11.82 percent and standard 
deviation of 20.18 percent. The geometric mean of these returns is 9.84 percent. We 
can see the geometric mean is approximately the arithmetic mean minus half of the 
variance of returns: RG ≈ 0.1182 − (1/2)(0.20182) = 0.0978, or 9.78 percent.
51 See Bodie, Kane, and Marcus (2017).

Summary 457
SUMMARY
In this reading, we have presented descriptive statistics, the set of methods that permit 
us to convert raw data into useful information for investment analysis.
■■A population is defined as all members of a specified group. A sample is a sub -
set of a population.
■■A parameter is any descriptive measure of a population. A sample statistic (sta -
tistic, for short) is a quantity computed from or used to describe a sample.
■■Data measurements are taken using one of four major scales: nominal, ordi -
nal, interval, or ratio. Nominal scales categorize data but do not rank them. 
Ordinal scales sort data into categories that are ordered with respect to some 
characteristic. Interval scales provide not only ranking but also assurance that 
the differences between scale values are equal. Ratio scales have all the charac -
teristics of interval scales as well as a true zero point as the origin. The scale on

which data are measured determines the type of analysis that can be performed 
on the data.
■■A frequency distribution is a tabular display of data summarized into a rela -
tively small number of intervals. Frequency distributions permit us to evaluate 
how data are distributed.
■■The relative frequency of observations in an interval is the number of observa -
tions in the interval divided by the total number of observations. The cumula -
tive relative frequency cumulates (adds up) the relative frequencies as we move 
from the first interval to the last, thus giving the fraction of the observations 
that are less than the upper limit of each interval.
■■A histogram is a bar chart of data that have been grouped into a frequency 
distribution. A frequency polygon is a graph of frequency distributions obtained 
by drawing straight lines joining successive points representing the class 
frequencies.
■■Sample statistics such as measures of central tendency, measures of dispersion,

skewness, and kurtosis help with investment analysis, particularly in making 
probabilistic statements about returns.
■■Measures of central tendency specify where data are centered and include the 
(arithmetic) mean, median, and mode (most frequently occurring value). The 
mean is the sum of the observations divided by the number of observations. 
The median is the value of the middle item (or the mean of the values of the two 
middle items) when the items in a set are sorted into ascending or descending 
order. The mean is the most frequently used measure of central tendency. The 
median is not influenced by extreme values and is most useful in the case of 
skewed distributions. The mode is the only measure of central tendency that 
can be used with nominal data.
■■A portfolio’s return is a weighted mean return computed from the returns on 
the individual assets, where the weight applied to each asset’s return is the frac -
tion of the portfolio invested in that asset.

■■The geometric mean, G, of a set of observations X1, X2, …, Xn is G 
= XX XXnn12 3  with  Xi≥0 for i = 1, 2, …, n. The geometric mean is 
especially important in reporting compound growth rates for time series data.
■■Quantiles such as the median, quartiles, quintiles, deciles, and percentiles 
are location parameters that divide a distribution into halves, quarters, fifths, 
tenths, and hundredths, respectively.

Reading 8 ■ Statistical Concepts and Market Returns 458
■■Dispersion measures such as the variance, standard deviation, and mean abso -
lute deviation (MAD) describe the variability of outcomes around the arithme -
tic mean.
■■Range is defined as the maximum value minus the minimum value. Range has 
only a limited scope because it uses information from only two observations.
■■MAD for a sample is  XX
ni
in
−
=∑
1 where  X is the sample mean and n is the 
number of observations in the sample.
■■The variance is the average of the squared deviations around the mean, and the 
standard deviation is the positive square root of variance. In computing sample 
variance ( s2) and sample standard deviation, the average squared deviation is 
computed using a divisor equal to the sample size minus 1.
■■The semivariance is the average squared deviation below the mean; semidevia -
tion is the positive square root of semivariance. Target semivariance is the aver -

age squared deviation below a target level; target semideviation is its positive 
square root. All these measures quantify downside risk.
■■According to Chebyshev’s inequality, the proportion of the observations within 
k standard deviations of the arithmetic mean is at least 1 − 1/ k2 for all k > 1. 
Chebyshev’s inequality permits us to make probabilistic statements about the 
proportion of observations within various intervals around the mean for any 
distribution with finite variance. As a result of Chebyshev’s inequality, a two-  
standard-  deviation interval around the mean must contain at least 75 percent 
of the observations, and a three-  standard-  deviation interval around the mean 
must contain at least 89 percent of the observations, no matter how the data are 
distributed.
■■The coefficient of variation, CV, is the ratio of the standard deviation of a set of 
observations to their mean value. A scale-  free measure of relative dispersion,

by expressing the magnitude of variation among observations relative to their 
average size, the CV permits direct comparisons of dispersion across different 
data sets.
■■The Sharpe ratio for a portfolio, p, based on historical returns, is defined 
as SRR
shpF
p=−
, where  Rp is the mean return to the portfolio,  RF is the 
mean return to a risk-  free and asset, and sp is the standard deviation of return 
on the portfolio.
■■Skew describes the degree to which a distribution is not symmetric about its 
mean. A return distribution with positive skewness has frequent small losses 
and a few extreme gains. A return distribution with negative skewness has fre -
quent small gains and a few extreme losses. Zero skewness indicates a symmet -
ric distribution of returns.
■■Kurtosis measures combined weight of the tails of a distribution relative to the 
rest of the distribution. Distributions are characterized as leptokurtic, mesokur -

tic, or platykurtic according to whether there is relatively more, the same, or 
less weight in the tails. The calculation for kurtosis involves finding the average 
of deviations from the mean raised to the fourth power and then standardizing 
that average by the standard deviation raised to the fourth power. Excess kurto -
sis is kurtosis minus 3, the value of kurtosis for all normal distributions.

References 459
Amin, Gaurav, and Harry Kat. 2003. “Stocks, Bonds, and 
Hedge Funds. ” Journal of Portfolio Management , vol. 29, no. 
4:113–120.
Black, Fischer. 1993. “Estimating Expected Return. ” Financial 
Analysts Journal , vol. 49, no. 5:36–38.
Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2017. Investments , 
11th edition. New York: McGraw-Hill Education.
Campbell, Stephen K. 1974. Flaws and Fallacies in Statistical 
Thinking . Englewood Cliffs, NJ: Prentice-Hall.
Campbell, John, Andrew Lo, and A. Craig MacKinlay. 1997. The 
Econometrics of Financial Markets . Princeton, NJ: Princeton 
University Press.
Choobinbeh, N. Fred. 2005. “Semivariance” in The Encyclopedia 
of Statistical Sciences . New York: Wiley.
Dimson, Elroy, Paul Marsh, and Mike Staunton. 2011. “Equity 
Premiums around the World” in Rethinking the Equity Risk 
Premium . Charlottesville, VA: Research Foundation of CFA 
Elton, Edwin J., Martin J. Gruber, Stephen J. Brown, and William

N. Goetzmann. 2013. Modern Portfolio Theory and Investment 
Analysis , 9th edition. Hoboken, NJ: Wiley.Forbes. 16 September 2013. “The Honor Roll. ” New York: Forbes 
Management Co., Inc.
Gujarati, Damodar N., Dawn C. Porter, and Sangeetha Gunasekar. 
2013. Basic Econometrics , 5th edition. New York: McGraw-
Hill Irwin.
Ibbotson, Roger G., Zhiwu Chen, Daniel Y.-J. Kim, and Wendy 
Y. Hu. 2013. “Liquidity as an Investment Style. ” Financial 
Analysts Journal , vol. 69, no. 3:30–44.
Reilly, Frank K., and Keith C. Brown. 2018. Investment Analysis 
and Portfolio Management , 11th edition. Mason, OH: Cengage 
South-Western.
Sharpe, William. 1994. “The Sharpe Ratio. ” Journal of Portfolio 
Management , vol. 21, no. 1:49–59.
Von Hippel, Paul T. 2005. “Mean, Median, and Skew: Correcting 
a Textbook Rule. ” Journal of Statistics Education , vol. 13, no. 
2. ww2.amstat.org/publications/jse/v13n2/vonhippel.html. 
Accessed 2 January 2018.
Wheeler, Donald J. 2011. “Problems with Skewness and Kurtosis,

Part One: What Do the Shape Parameters Do?” Quality Digest 
Daily , August 1-2, 2011. https://www.spcpress.com/pdf/
DJW231.pdf. Accessed 2 January 2018.

Reading 8 ■ Statistical Concepts and Market Returns 460
1 Which of the following groups best illustrates a sample?
A The set of all estimates for Exxon Mobil’s FY2015 EPS
B The FTSE Eurotop 100 as a representation of the European stock market
C UK shares traded on 13 August 2015 that also closed above £120/share on 
the London Stock Exchange
2 Published ratings on stocks ranging from 1 (strong sell) to 5 (strong buy) are 
examples of which measurement scale?
A Ordinal
B Interval
C Nominal
3 In descriptive statistics, an example of a parameter is the:
A median of a population.
B mean of a sample of observations.
C standard deviation of a sample of observations.
4 A mutual fund has the return frequency distribution shown in the following 
table.
–10.0 to –7.0 3
–7.0 to –4.0 7
–4.0 to –1.0 10
–1.0 to +2.0 12
+2.0 to +5.0 23
+5.0 to +8.0 5
 Which of the following statements is correct?
A The relative frequency of the interval “–1.0 to +2.0” is 20%.

B The relative frequency of the interval “+2.0 to +5.0” is 23%.
C The cumulative relative frequency of the interval “+5.0 to +8.0” is 91.7%.
5 An analyst is using the data in the following table to prepare a statistical report.
Portfolio’s Deviations from Benchmark Return, 2003–2014 
(%)
2003 2.48 2009 –9.19
2004 –2.59 2010 –5.11
2005 9.47 2011 1.33
2006 –0.55 2012 6.84
2007 –1.69 2013 3.04
2008 –0.89 2014 4.72

Practice Problems 461
 The cumulative relative frequency for the interval −1.71% ≤ x < 2.03% is closest  
to:
A 0.250.
B 0.333.
C 0.583.
6–7
The following histogram shows a distribution of the S&P 500 Index annual returns 
from 1964 to 2013:
012345678
33% to 38%
28% to 33% 23% to 28% 18% to 23% 13% to 18% 8% to 13% 3% to 8% –2% to 3% –7% to –2% –12% to –7% –17% to –12%
–22% to –17% –27% to –22% –32% to –27%
–37% to –32%Frequency
6 The interval containing the median return is:
A 3% to 8%.
B 8% to 13%.
C 13% to 18%.
7 Based on the previous histogram, the distribution is best described as having:
A one mode.
B two modes.
C three modes.
8 The following is a frequency polygon of monthly exchange rate changes 
in the US dollar/Japanese yen spot exchange rate from January 2010 to 
December 2013. A positive change represents yen appreciation (the yen buys 
more dollars), and a negative change represents yen depreciation (the yen buys 
fewer dollars).

Reading 8 ■ Statistical Concepts and Market Returns 462
Monthly Changes in the US Dollar/Japanese Y en Spot Exchange Rate
05101520
3.0% 1.0% –1.0% –3.0% –5.0%Frequency
Return Interval Midpoint
 Based on the chart, yen appreciation:
A occurred more than 50% of the time.
B was less frequent than yen depreciation.
C in the 0.0 to 2.0 interval occurred 20% of the time.
9 The annual returns for three portfolios are shown in the following table. 
Portfolios P and R were created in 2009, Portfolio Q in 2010.
Annual Portfolio Returns (%)
2009 2010 2011 2012 2013
Portfolio P –3.0 4.0 5.0 3.0 7.0
Portfolio Q –3.0 6.0 4.0 8.0
Portfolio R 1.0 –1.0 4.0 4.0 3.0
 The median annual return from portfolio creation to 2013 for:
A Portfolio P is 4.5%.
B Portfolio Q is 4.0%.
C Portfolio R is higher than its arithmetic mean annual return.
10 In 2015, an investor allocated his retirement savings in the asset classes shown 
in the following table.
Asset ClassAsset Allocation 
(%)Asset Class Return 
(%)

(%)
Large-  cap US equities 20.0 8.0
Small-  cap US equities 40.0 12.0
Emerging market equities 25.0 –3.0
High-  yield bonds 15.0 4.0

Practice Problems 463
 The portfolio return in 2015 is closest to :
A 5.1%.
B 5.3%.
C 6.3%.
11 The following table shows the annual returns for Fund Y.
Fund Y (%)
2010 19.5
2011 –1.9
2012 19.7
2013 35.0
2014 5.7
 The geometric mean for Fund Y is closest  to:
A 14.9%.
B 15.6%.
C 19.5%.
12 A manager invests €5,000 annually in a security for four years at the prices 
shown in the following table.
Purchase Price of Security (€)
Year 1 62.00
Year 2 76.00
Year 3 84.00
Year 4 90.00
 The average price paid for the security is closest to:
A €76.48.
B €77.26.
C €78.00.
13–14
The following table shows the annual MSCI World Index total returns for 2004–2013.
2004 15.25% 2009 30.79%
2005 10.02% 2010 12.34%
2006 20.65% 2011 –5.02%
2007 9.57% 2012 16.54%
2008 –40.33% 2013 27.37%
13 The fourth quintile return for the MSCI World Index is closest  to:
A 20.65%.
B 26.03%.
C 27.37%.

Reading 8 ■ Statistical Concepts and Market Returns 464
14 For 2009–2013, the mean absolute deviation of the MSCI World Index total 
returns is closest  to:
A 10.20%.
B 12.74%.
C 16.40%.
15 Annual returns and summary statistics for three funds are listed in the follow -
ing table:
Annual Returns (%)
Y ear Fund ABC Fund XYZ Fund PQR
2009 –20.0 –33.0 –14.0
2010 23.0 –12.0 –18.0
2011 –14.0 –12.0 6.0
2012 5.0 –8.0 –2.0
2013 –14.0 11.0 3.0
Mean –4.0 –10.8 –5.0
Standard deviation 17.8 15.6 10.5
 The fund that shows the highest dispersion is:
A Fund PQR if the measure of dispersion is the range.
B Fund XYZ if the measure of dispersion is the variance.
C Fund ABC if the measure of dispersion is the mean absolute deviation.
16 Over the past 240 months, an investor’s portfolio had a mean monthly return 
of 0.79%, with a standard deviation of monthly returns of 1.16%. According to 
Chebyshev’s inequality, the minimum number of the 240 monthly returns that 
fall into the range of −0.95% to 2.53% is closest  to:
A 80.

A 80.
B 107.
C 133.
17 The mean monthly return and the standard deviation for three industry sectors 
are shown in the following table.
SectorMean Monthly Return 
(%)Standard Deviation of 
Return (%)
Utilities (UTIL) 2.10 1.23
Materials (MATR) 1.25 1.35
Industrials (INDU) 3.01 1.52
 Based on the coefficient of variation, the riskiest sector is:
A utilities.
B materials.
C industrials.
18 Three equity fund managers have performance records summarized in the fol -

Practice Problems 465
Mean Annual Return (%)Standard Deviation of 
Return (%)
Manager 1 14.38 10.53
Manager 2 9.25 6.35
Manager 3 13.10 8.23
 Given a risk-  free rate of return of 2.60%, which manager performed best based 
on the Sharpe ratio?
A Manager 1
B Manager 2
C Manager 3
19–21
The following table shows various statistics for Portfolios 1, 2, and 3.
Mean Return 
(%)Standard 
Deviation of 
Returns (%) SkewnessExcess 
Kurtosis
Portfolio 1 7.8 15.1 0.0 0.7
Portfolio 2 10.2 20.5 0.9 –1.8
Portfolio 3 12.9 29.3 –1.5 6.2
19 An investment adviser bases his allocation on the Sharpe ratio. Assuming a 
risk-  free rate of 1.5%, which portfolio is he most likely  to recommend?
A Portfolio 1
B Portfolio 2
C Portfolio 3
20 The skewness of Portfolio 1 indicates its mean return is most likely :
A less than its median.
B equal to its median.
C greater than its median.
21 Compared with a normal distribution, the distribution of returns for Portfolio 3 

A has less weight in the tails.
B has a greater number of extreme returns.
C has fewer small deviations from its mean.
22 Two portfolios have unimodal return distributions. Portfolio 1 has a skewness 
of 0.77, and Portfolio 2 has a skewness of –1.11.
 Which of the following is correct?
A For Portfolio 1, the median is less than the mean.
B For Portfolio 1, the mode is greater than the mean.

Reading 8 ■ Statistical Concepts and Market Returns 466
C For Portfolio 2, the mean is greater than the median.
23 When analyzing investment returns, which of the following statements is 
correct?
A The geometric mean will exceed the arithmetic mean for a series with non-  
zero variance.
B The geometric mean measures an investment’s compound rate of growth 
over multiple periods.
C The arithmetic mean accurately estimates an investment’s terminal value 

SOLUTIONS
1 B is correct. The FTSE Eurotop 100 represents a sample of all European stocks. 
It is a subset of the population of all European stocks.
2 A is correct. Ordinal scales sort data into categories that are ordered with 
respect to some characteristic and may involve numbers to identify categories 
but do not assure that the differences between scale values are equal. The buy 
rating scale indicates that a stock ranked 5 is expected to perform better than a 
stock ranked 4, but it tells us nothing about the performance difference between 
stocks ranked 4 and 5 compared with the performance difference between 
stocks ranked 1 and 2, and so on.
3 A is correct. Any descriptive measure of a population characteristic is referred 
to as a parameter.
4 A is correct. The relative frequency is the absolute frequency of each interval 
divided by the total number of observations. Here, the relative frequency is

calculated as: (12/60) × 100 = 20%. B is incorrect because the relative frequency 
of this interval is (23/60) × 100 = 38.33%. C is incorrect because the cumulative 
relative frequency of the last interval must equal 100%.
5 C is correct. The cumulative relative frequency of an interval identifies the frac -
tion of observations that are less than the upper limit of the given interval. It is 
determined by summing the relative frequencies from the lowest interval up to 
and including the given interval. The following table shows the relative frequen -
cies for all the intervals of the data from the previous table:
Lower Limit 
(%)Upper Limit 
(%)Absolute 
Frequency
–9.19 ≤ < –5.45 1 0.083 0.083
–5.45 ≤ < –1.71 2 0.167 0.250
–1.71 ≤ < 2.03 4 0.333 0.583
2.03 ≤ < 5.77 3 0.250 0.833
5.77 ≤ ≥ 9.51 2 0.167 1.000
 The interval −1.71% ≤ x < 2.03% has a cumulative relative frequency of 0.583.

6 C is correct. Because there are 50 data points in the histogram, the median 
return would be the mean of the 50/2 = 25th and (50 + 2)/2 = 26th positions. 
The sum of the return interval frequencies to the left of the 13% to 18% interval 
is 24. As a result, the 25th and 26th returns will fall in the 13% to 18% interval.
7 C is correct. The mode of a distribution with data grouped in intervals is the 
interval with the highest frequency. The three intervals of 3% to 8%, 18% to 23%, 
and 28% to 33% all have a high frequency of 7.
8 A is correct. Twenty observations lie in the interval “0.0 to 2.0, ” and six obser -
vations lie in the 2.0 to 4.0 interval. Together, they represent 26/48, or 54.17% of 
all observations, which is more than 50%.
9 C is correct. The median of Portfolio R is 0.8% higher than the mean for 
Portfolio R.
10 C is correct. The portfolio return must be calculated as the weighted mean 
return, where the weights are the allocations in each asset class:

(0.20 × 8%) + (0.40 × 12%) + (0.25 × −3%) + (0.15 × 4%) = 6.25%, or ≈ 6.3%.

Reading 8 ■ Statistical Concepts and Market Returns 468
11 A is correct. The geometric mean return for Fund Y is found as follows:
 Fund Y =  [(1 + 0.195) × (1 – 0.019) × (1 + 0.197) × (1 + 0.350) × (1 + 0.057)]
(1/5) – 1
  = 14.9%.
12 A is correct. The harmonic mean is appropriate for determining the average 
price per unit. It is calculated by summing the reciprocals of the prices; then 
averaging that sum by dividing by the number of prices; and finally, taking the 
reciprocal of the average:
4/[(1/62.00) + (1/76.00) + (1/84.00) + (1/90.00)] = €76.48.
13 B is correct. Quintiles divide a distribution into fifths, with the fourth quintile 
occurring at the point at which 80% of the observations lie below it. The fourth 
quintile is equivalent to the 80th percentile. To find the yth percentile ( Py), 
we first must determine its location. The formula for the location ( Ly) of a yth 
percentile in an array with n entries sorted in ascending order is Ly = (n + 1) ×

(y/100). In this case, n = 10 and y = 80%, so
L80 = (10 + 1) × (80/100) = 11 × 0.8 = 8.8.
 With the data arranged in ascending order (−40.33%, −5.02%, 9.57%, 10.02%, 
12.34%, 15.25%, 16.54%, 20.65%, 27.37%, and 30.79%), the 8.8th position would 
be between the 8th and 9th entries, 20.65% and 27.37%, respectively. Using 
linear interpolation, P80 = X8 + (Ly – 8) × ( X9 – X8),
 P80 = 20.65 + (8.8 – 8) × (27.37 – 20.65)
  = 20.65 + (0.8 × 6.72) = 20.65 + 5.38
  = 26.03%.
14 A is correct. The formula for mean absolute deviation (MAD) is 
MAD=−
=∑XX
ni
in
1
 Column 1 : Sum annual returns and divide by n to find the arithmetic mean  X() 
of 16.40%.
 Column 2 : Calculate the absolute value of the difference between each year’s 
return and the mean from Column 1. Sum the results and divide by n to find 
the MAD.
 These calculations are shown in the following table:
Column 1 Column 2
Y ear ReturnXXi−
2009 30.79% 14.39%
2010 12.34% 4.06%
2011 –5.02% 21.42%
2012 16.54% 0.14%
2013 27.37% 10.97%
Sum: 82.02% Sum: 50.98%

n: 5 n: 5
X: 16.40% MAD: 10.20%
15 C is correct. The mean absolute deviation (MAD) of Fund ABC’s returns is 
greater than the MAD of both of the other funds.
MAD=−
=∑XX
ni
in
1, where  Xis the arithmetic mean of the series.
 MAD for Fund ABC = 
−− −() +− −() +− −−() +− −() +− −−()=20 42 34 14 45 41 44
514 4.%
 MAD for Fund XYZ = 
−− −() +− −−() +− −−() +− −−() +− −() 33 10 81 21 08 12 10 88 1081 11 08
5... ..
= =98.%
 MAD for Fund PQR = 
−− −() +− −−() +− −() +− −−() +− −()=14 51 85 65 25 35
588.%
 A and B are incorrect because the range and variance of the three funds are as 
follows:
Fund ABC Fund XYZ Fund PQR
Range 43% 44% 24%
Variance 317 243 110
 The numbers shown for variance are understood to be in “percent squared” 
terms so that when taking the square root, the result is standard deviation in 
percentage terms. Alternatively, by expressing standard deviation and variance 
in decimal form, one can avoid the issue of units; in decimal form, the vari -

ances for Fund ABC, Fund XYZ, and Fund PQR are 0.0317, 0.0243, and 0.0110, 
16 C is correct. According to Chebyshev’s inequality, the proportion of the obser -
vations within k standard deviations of the arithmetic mean is at least 1 – 1/ k2 
for all k > 1.
 The upper limit of the range is 2.53%, which is 2.53 − 0.79 = 1.74% above the 
mean. The lower limit is −0.95, which is 0.79 − (−0.95) = 1.74% below the mean. 
As a result, k = 1.74/1.16 = 1.50 standard deviations.
 Because k = 1.50, the proportion of observations within the interval is at least 1 
– 1/1.52 = 1 – 0.444 = 0.556, or 55.6%. Thus, the number of observations in the 
given range is at least 240 × 55.6%, which is ≈ 133.

Reading 8 ■ Statistical Concepts and Market Returns 470
17 B is correct. The coefficient of variation (CV) is the ratio of the standard devia -
tion to the mean, where a higher CV implies greater risk per unit of return.
CVUTILs
X= = =123
210059.%
.%.
CVMATRs
X= = =135
125108.%
.%.
CVINDUs
X= = =152
301051.%
.%.
18 C is correct. The Sharpe ratio ( S) is the mean excess portfolio return per unit of 
risk, where a higher Sharpe ratio indicates better performance:
SRR
spF
p114 38 260
10 53112 =−
=−=..
..
SRR
spF
p29252 60
635105 =−
=−=..
..
SRR
spF
p313 10 260
823128 =−
=−=..
..
19 B is correct. The Sharpe ratio measures a portfolio’s return per unit of risk and 
is defined as  SRR
spF
p1=−
, where  Rp is the mean return for the portfolio,  RF 
is the mean return to a risk-  free asset, and sp is the standard deviation of return 
on the portfolio. The Sharpe ratios for the three portfolios are as follows:
Portfolio 1 = (7.8 – 1.5)/15.1 = 6.3/15.1 = 0.417
Portfolio 2 = (10.2 – 1.5)/20.5 = 8.7/20.5 = 0.424

Portfolio 3 = (12.9 – 1.5)/29.3 = 11.4/29.3 = 0.389
 So Portfolio 2 has the highest return per unit of risk.
20 B is correct. Portfolio 1 has a skewness of 0.0, which indicates that the portfo -
lio’s return distribution is symmetrical and thus its mean and median are equal.
21 B is correct. Portfolio 3 has positive excess kurtosis (i.e., kurtosis greater than 
3), which indicates that its return distribution is leptokurtic and has fatter 
tails than the normal. The fatter tails mean Portfolio 3 has a greater number of 
extreme returns.
22 A is correct. Portfolio 1 is positively skewed, so the mean is greater than the 
median, which is greater than the mode.
23 B is correct. The geometric mean compounds the periodic returns of every 
period, giving the investor a more accurate measure of the terminal value of an 

Probability Concepts
a. define a random variable, an outcome, an event, mutually 
exclusive events, and exhaustive events;
b. state the two defining properties of probability and distinguish 
among empirical, subjective, and a priori probabilities;
c. state the probability of an event in terms of odds for and against 
the event;
d. distinguish between unconditional and conditional probabilities;
e. explain the multiplication, addition, and total probability rules;
f. calculate and interpret 1) the joint probability of two events, 2)

the probability that at least one of two events will occur, given the 
probability of each and the joint probability of the two events, and 
3) a joint probability of any number of independent events;
g. distinguish between dependent and independent events;
h. calculate and interpret an unconditional probability using the 
total probability rule;
i. explain the use of conditional expectation in investment 
applications;
j. explain the use of a tree diagram to represent an investment 
problem;
k. calculate and interpret covariance and correlation;
l. calculate and interpret the expected value, variance, and standard 
deviation of a random variable and of returns on a portfolio;
9

Reading 9 ■ Probability Concepts 472
m. calculate and interpret covariance given a joint probability 
function;
n. calculate and interpret an updated probability using Bayes’ 
formula;
o. identify the most appropriate method to solve a particular 
counting problem and solve counting problems using factorial, 
combination, and permutation concepts.
All investment decisions are made in an environment of risk. The tools that allow us 
to make decisions with consistency and logic in this setting come under the heading of 
probability. This reading presents the essential probability tools needed to frame and 
address many real-  world problems involving risk. We illustrate how these tools apply 
to such issues as predicting investment manager performance, forecasting financial 
variables, and pricing bonds so that they fairly compensate bondholders for default

risk. Our focus is practical. We explore in detail the concepts that are most important 
to investment research and practice. One such concept is independence, as it relates to 
the predictability of returns and financial variables. Another is expectation, as analysts 
continually look to the future in their analyses and decisions. Analysts and investors 
must also cope with variability. We present variance, or dispersion around expectation, 
as a risk concept important in investments. The reader will acquire specific skills in 
using portfolio expected return and variance.
The basic tools of probability, including expected value and variance, are set out 
in Section 2 of this reading. Section 3 introduces covariance and correlation (mea -
sures of relatedness between random quantities) and the principles for calculating 
portfolio expected return and variance. Two topics end the reading: Bayes’ formula 
and outcome counting. Bayes’ formula is a procedure for updating beliefs based on

new information. In several areas, including a widely used option-  pricing model, the 
calculation of probabilities involves defining and counting outcomes. The reading 
ends with a discussion of principles and shortcuts for counting.
PROBABILITY , EXPECTED VALUE, AND VARIANCE
The probability concepts and tools necessary for most of an analyst’s work are relatively 
few and simple but require thought to apply. This section presents the essentials for 
working with probability, expectation, and variance, drawing on examples from equity 
and fixed income analysis.
An investor’s concerns center on returns. The return on a risky asset is an example 
of a random variable , a quantity whose outcomes  (possible values) are uncertain. For 
example, a portfolio may have a return objective of 10 percent a year. The portfolio 
manager’s focus at the moment may be on the likelihood of earning a return that is 
less than 10 percent over the next year. Ten percent is a particular value or outcome 1
2

Probability, Expected Value, and Variance 473
of the random variable “portfolio return. ” Although we may be concerned about a 
single outcome, frequently our interest may be in a set of outcomes: The concept of 
“event” covers both.
■■Definition of Event.  An event  is a specified set of outcomes.
We may specify an event to be a single outcome—for example, the portfolio earns a 
return of 10 percent.  (We use italics to highlight statements that define events.) We 
can capture the portfolio manager’s concerns by defining the event as the portfolio 
earns a return below 10 percent.  This second event, referring as it does to all possible 
returns greater than or equal to −100 percent (the worst possible return) but less than 
10 percent, contains an infinite number of outcomes. To save words, it is common to 
use a capital letter in italics to represent a defined event. We could define A = the port -
folio earns a return of 10 percent  and B = the portfolio earns a return below 10 percent.

To return to the portfolio manager’s concern, how likely is it that the portfolio 
will earn a return below 10 percent?
The answer to this question is a probability : a number between 0 and 1 that 
measures the chance that a stated event will occur. If the probability is 0.40 that the 
portfolio earns a return below 10 percent, there is a 40 percent chance of that event 
happening. If an event is impossible, it has a probability of 0. If an event is certain 
to happen, it has a probability of 1. If an event is impossible or a sure thing, it is not 
random at all. So, 0 and 1 bracket all the possible values of a probability.
Probability has two properties, which together constitute its definition.
■■Definition of Probability.  The two defining properties of a probability are as 
follows:
1 The probability of any event E is a number between 0 and 1: 0 ≤ P(E) ≤ 1.
2 The sum of the probabilities of any set of mutually exclusive and exhaustive  
events equals 1.

P followed by parentheses stands for “the probability of (the event in parentheses), ” 
as in P(E) for “the probability of event E.” We can also think of P as a rule or function 
that assigns numerical values to events consistent with Properties 1 and 2.
In the above definition, the term mutually exclusive means that only one event 
can occur at a time; exhaustive  means that the events cover all possible outcomes. 
The events A = the portfolio earns a return of 10 percent  and B = the portfolio earns 
a return below 10 percent  are mutually exclusive because A and B cannot both occur 
at the same time. For example, a return of 8.1 percent means that B has occurred 
and A has not occurred. Although events A and B are mutually exclusive, they are 
not exhaustive because they do not cover outcomes such as a return of 11 percent. 
Suppose we define a third event: C = the portfolio earns a return above 10 percent.

Clearly, A, B,  and C are mutually exclusive and exhaustive events. Each of P(A), P(B), 
and P(C) is a number between 0 and 1, and P(A) + P(B) + P(C) = 1.
The most basic kind of mutually exclusive and exhaustive events is the set of all 
the distinct possible outcomes of the random variable. If we know both that set and 
the assignment of probabilities to those outcomes—the probability distribution of the 
random variable—we have a complete description of the random variable, and we can 
assign a probability to any event that we might describe.1 The probability of any event 
is the sum of the probabilities of the distinct outcomes included in the definition of 
the event. Suppose the event of interest is D = the portfolio earns a return above the 
risk-  free rate,  and we know the probability distribution of portfolio returns. Assume 
1 In the reading on common probability distributions, we describe some of the probability distributions 
most frequently used in investment applications.

Reading 9 ■ Probability Concepts 474
the risk-  free rate is 4 percent. To calculate P(D), the probability of D, we would sum 
the probabilities of the outcomes that satisfy the definition of the event; that is, we 
would sum the probabilities of portfolio returns greater than 4 percent.
Earlier, to illustrate a concept, we assumed a probability of 0.40 for a portfolio 
earning less than 10 percent, without justifying the particular assumption. We also 
talked about using a probability distribution of outcomes to calculate the probability 
of events, without explaining how a probability distribution might be estimated. 
Making actual financial decisions using inaccurate probabilities might have grave 
consequences. How, in practice, do we estimate probabilities? This topic is a field of 
study in itself, but there are three broad approaches to estimating probabilities. In 
investments, we often estimate the probability of an event as a relative frequency of

occurrence based on historical data. This method produces an empirical probability . 
For example, Thanatawee (2013) reports that of his sample of 1,927 yearly observa -
tions for nonfinancial SET (Stock Exchange of Thailand) firms during the years 2002 
to 2010, 1,382 were dividend paying firms and 545 were non dividend paying firms. 
The empirical probability of a Thai firm paying a dividend is thus 1,382/1,927 = 0.72, 
approximately. We will point out empirical probabilities in several places as they 
appear in this reading.
Relationships must be stable through time for empirical probabilities to be accurate. 
We cannot calculate an empirical probability of an event not in the historical record 
or a reliable empirical probability for a very rare event. There are cases, then, in which 
we may adjust an empirical probability to account for perceptions of changing rela -
tionships. In other cases, we have no empirical probability to use at all. We may also

make a personal assessment of probability without reference to any particular data. 
Each of these three types of probability is a subjective probability , one drawing on 
personal or subjective judgment. Subjective probabilities are of great importance in 
investments. Investors, in making buy and sell decisions that determine asset prices, 
often draw on subjective probabilities. Subjective probabilities appear in various places 
in this reading, notably in our discussion of Bayes’ formula.
In a more narrow range of well-  defined problems, we can sometimes deduce 
probabilities by reasoning about the problem. The resulting probability is an a priori 
probability , one based on logical analysis rather than on observation or personal 
judgment. We will use this type of probability in Example 6. The counting methods we 
discuss later are particularly important in calculating an a priori probability. Because 
a priori and empirical probabilities generally do not vary from person to person, they

are often grouped as objective probabilities .
In business and elsewhere, we often encounter probabilities stated in terms 
of odds—for instance, “the odds for E” or the “odds against E.” For example, as of 
November 2013, analysts’ fiscal year 2014 EPS forecasts for JetBlue Airways ranged 
from $0.55 to $0.69. Suppose one analyst asserts that the odds for the company beating 
the highest estimate, $0.69, are 1 to 7. Suppose a second analyst argues that the odds 
against that happening are 15 to 1. What do those statements imply about the prob -
ability of the company’s EPS beating the highest estimate? We interpret probabilities 
stated in terms of odds as follows:
■■Probability Stated as Odds.  Given a probability P(E),
1 Odds for E = P(E)/[1 − P(E)]. The odds for E are the probability of E divided 
by 1 minus the probability of E. Given odds for E of “a to b, ” the implied 
probability of E is a/(a + b).
In the example, the statement that the odds for the company’s EPS for FY2014 beating

$0.69  are 1 to 7 means that the speaker believes the probability of the event is 1/(1 + 
7) = 1/8 = 0.125.

Probability, Expected Value, and Variance 475
 2 Odds against E = [1 − P(E)]/P(E), the reciprocal of odds for E. Given odds 
against E of “a to b,” the implied probability of E is b/(a + b).
The statement that the odds against the company’s EPS for FY2014 beating $0.69  
are 15 to 1 is consistent with a belief that the probability of the event is 1/(1 + 15) = 
1/16 = 0.0625.
To further explain odds for an event, if P(E) = 1/8, the odds for E are (1/8)/(7/8) = 
(1/8)(8/7) = 1/7, or “1 to 7. ” For each occurrence of E, we expect seven cases of non-  
occurrence; out of eight cases in total, therefore, we expect E to happen once, and the 
probability of E is 1/8. In wagering, it is common to speak in terms of the odds against 
something, as in Statement 2. For odds of “15 to 1” against E (an implied probability 
of E of 1/16), a $1 wager on E, if successful, returns $15 in profits plus the $1 staked 
in the wager. We can calculate the bet’s anticipated profit as follows:

Win: Probability = 1/16; Profit =$15
Loss: Probability = 15/16; Profit =–$1
Anticipated profit = (1/16)($15) + (15/16)(–$1) = $0
Weighting each of the wager’s two outcomes by the respective probability of the out -
come, if the odds (probabilities) are accurate, the anticipated profit of the bet is $0.
EXAMPLE 1   
Profiting from Inconsistent Probabilities
You are examining the common stock of two companies in the same industry in 
which an important antitrust decision will be announced next week. The first 
company, SmithCo Corporation, will benefit from a governmental decision that 
there is no antitrust obstacle related to a merger in which it is involved. You 
believe that SmithCo’s share price reflects a 0.85 probability of such a decision. 
A second company, Selbert Corporation, will equally benefit from a “go ahead” 
ruling. Surprisingly, you believe Selbert stock reflects only a 0.50 probability of a 
favorable decision. Assuming your analysis is correct, what investment strategy

would profit from this pricing discrepancy?
Consider the logical possibilities. One is that the probability of 0.50 reflected 
in Selbert’s share price is accurate. In that case, Selbert is fairly valued but 
SmithCo is overvalued, as its current share price overestimates the probability 
of a “go ahead” decision. The second possibility is that the probability of 0.85 
is accurate. In that case, SmithCo shares are fairly valued, but Selbert shares, 
which build in a lower probability of a favorable decision, are undervalued. You 
diagram the situation as shown in Table 1.
Table 1   Worksheet for Investment Problem
True Probability of a “Go Ahead” Decision
0.50 0.85
SmithCo Shares Overvalued Shares Fairly Valued
Selbert Shares Fairly Valued Shares Undervalued
The 0.50 probability column shows that Selbert shares are a better value than 
SmithCo shares. Selbert shares are also a better value if a 0.85 probability is 
accurate. Thus SmithCo shares are overvalued relative to Selbert shares.

Reading 9 ■ Probability Concepts 476
Your investment actions depend on your confidence in your analysis and 
on any investment constraints you face (such as constraints on selling stock 
short).2 A conservative strategy would be to buy Selbert shares and reduce or 
eliminate any current position in SmithCo. The most aggressive strategy is to 
short SmithCo stock (relatively overvalued) and simultaneously buy the stock 
of Selbert (relatively undervalued). This strategy is known as pairs arbitrage 
trade : a trade in two closely related stocks involving the short sale of one and 
the purchase of the other.
The prices of SmithCo and Selbert shares reflect probabilities that are 
not consistent . According to one of the most important probability results 
for investments, the Dutch Book Theorem ,3 inconsistent probabilities create 
profit opportunities. In our example, investors, by their buy and sell decisions 
to exploit the inconsistent probabilities, should eliminate the profit opportunity

and inconsistency.
To understand the meaning of a probability in investment contexts, we need to 
distinguish between two types of probability: unconditional and conditional. Both 
unconditional and conditional probabilities satisfy the definition of probability stated 
earlier, but they are calculated or estimated differently and have different interpreta -
tions. They provide answers to different questions.
The probability in answer to the straightforward question “What is the probabil -
ity of this event A?” is an unconditional probability , denoted P(A). Unconditional 
probability is also frequently referred to as marginal probability .4
Suppose the question is “What is the probability that the stock earns a return above 
the risk-  free rate  (event A)?” The answer is an unconditional probability that can be 
viewed as the ratio of two quantities. The numerator is the sum of the probabilities 
of stock returns above the risk-  free rate. Suppose that sum is 0.70. The denominator

is 1, the sum of the probabilities of all possible returns. The answer to the question 
is P(A) = 0.70.
Contrast the question “What is the probability of A?” with the question “What 
is the probability of A, given that B has occurred?” The probability in answer to this 
last question is a conditional probability , denoted P(A | B) (read: “the probability 
of A given B”).
Suppose we want to know the probability that the stock earns a return above the 
risk-  free rate  (event A), given that the stock earns a positive return  (event B). With the 
words “given that, ” we are restricting returns to those larger than 0 percent—a new 
element in contrast to the question that brought forth an unconditional probability. 
The conditional probability is calculated as the ratio of two quantities. The numer -
ator is the sum of the probabilities of stock returns above the risk-  free rate; in this 
particular case, the numerator is the same as it was in the unconditional case, which

we gave as 0.70. The denominator, however, changes from 1 to the sum of the prob -
abilities for all outcomes (returns) above 0 percent. Suppose that number is 0.80, a 
2 Selling short  or shorting stock  means selling borrowed shares in the hope of repurchasing them later at 
a lower price.
3 The theorem’s name comes from the terminology of wagering. Suppose someone places a $100 bet on 
X at odds of 10 to 1 against X, and later he is able to place a $600 bet against X at odds of 1 to 1 against 
X. Whatever the outcome of X, that person makes a riskless profit (equal to $400 if X occurs or $500 if X 
does not occur) because the implied probabilities are inconsistent. He is said to have made a Dutch book  
in X. Ramsey (1931) presented the problem of inconsistent probabilities. See also Lo (1999).
4 In analyses of probabilities presented in tables, unconditional probabilities usually appear at the ends

or margins  of the table, hence the term marginal probability . Because of possible confusion with the way 
marginal  is used in economics (roughly meaning incremental ), we use the term unconditional probability  
throughout this discussion.

Probability, Expected Value, and Variance 477
larger number than 0.70 because returns between 0 and the risk-  free rate have some 
positive probability of occurring. Then P(A | B) = 0.70/0.80 = 0.875. If we observe that 
the stock earns a positive return, the probability of a return above the risk-  free rate is 
greater than the unconditional probability, which is the probability of the event given 
no other information. The result is intuitive.5 To review, an unconditional probability 
is the probability of an event without any restriction; it might even be thought of as 
a stand-  alone probability. A conditional probability, in contrast, is a probability of an 
In discussing approaches to calculating probability, we gave one empirical esti -
mate of the probability that a change in dividends is a dividend decrease. That prob -
ability was an unconditional probability. Given additional information on company

characteristics, could an investor refine that estimate? Investors continually seek an 
information edge that will help improve their forecasts. In mathematical terms, they 
are attempting to frame their view of the future using probabilities conditioned on 
relevant information or events. Investors do not ignore useful information; they adjust 
their probabilities to reflect it. Thus, the concepts of conditional probability (which 
we analyze in more detail below), as well as related concepts discussed further on, are 
extremely important in investment analysis and financial markets.
To state an exact definition of conditional probability, we first need to introduce the 
concept of joint probability. Suppose we ask the question “What is the probability of 
both A and B happening?” The answer to this question is a joint probability , denoted 
P(AB) (read: “the probability of A and B”). If we think of the probability of A and the

probability of B as sets built of the outcomes of one or more random variables, the 
joint probability of A and B is the sum of the probabilities of the outcomes they have 
in common. For example, consider two events: the stock earns a return above the risk-  
free rate  (A) and the stock earns a positive return  (B). The outcomes of A are contained 
within (a subset of) the outcomes of B, so P(AB) equals P(A). We can now state a 
formal definition of conditional probability that provides a formula for calculating it.
■■Definition of Conditional Probability.  The conditional probability of A given 
that B has occurred is equal to the joint probability of A and B divided by the 
probability of B (assumed not to equal 0).
P(A | B) = P(AB)/P(B), P(B) ≠ 0  
Sometimes we know the conditional probability P(A | B) and we want to know the 
joint probability P(AB). We can obtain the joint probability from the following mul -
tiplication rule for probabilities , which is Equation 1 rearranged.

■■Multiplication Rule for Probability.  The joint probability of A and B can be 
expressed as
P(AB) = P(A | B)P(B)  (1)
(2)
5 In this example, the conditional probability is greater than the unconditional probability. The conditional 
probability of an event may, however, be greater than, equal to, or less than the unconditional probability, 
depending on the facts. For instance, the probability that the stock earns a return above the risk-  free rate  
given that the stock earns a negative return  is 0.

Reading 9 ■ Probability Concepts 478
EXAMPLE 2   
Conditional Probabilities and Predictability of Mutual 
Fund Performance (1)
Vidal-  Garcia (2013) examined whether historical performance predicts future 
performance for a sample of mutual funds that included 1,050 actively managed 
equity funds in six European countries during the period of 1988 through 2010. 
Funds were classified into nine investment styles based on combinations of invest -
ment focus (growth, blend, and value) and fund’s market capitalization (small, 
mid, and large cap). One approach Vidal-  Garcia used involved calculating each 
fund’s annual benchmark-  adjusted return by subtracting a benchmark return 
from the annual return of the fund. MSCI (Morgan Stanley Capital International) 
style indexes were used as benchmarks. For each style of fund in each country, 
funds were classified as winners or losers for each of two consecutive years. The 
top 50 percent of funds by benchmark-  adjusted return for a given year were

labeled winners; the bottom 50 percent were labeled losers. An excerpt from 
the results of the study for 135 French funds classified as large value funds is 
given in Table 2. It shows the percentage of those funds that were winners in two 
consecutive years, winner in one year and then loser in the next year, losers then 
winners, and losers in both years. The winner–winner entry, for example, shows 
that 65.5% of the first-  year winner funds were also winners in the second year. 
Note that the four entries in the table can be viewed as conditional probabilities.
Table 2   Persistence of Returns for Large Value Funds in France: 1988 
through 2010
Y ear 2 Winner Y ear 2 Loser
Year 1 winner 65.5% 34.5%
Year 1 loser 15.5% 84.5%
Source:  Vidal-  Garcia (2013), Table 4.
Based on the data in Table 2, answer the following questions:
1 State the four events needed to define the four conditional probabilities.
2 State the four entries of the table as conditional probabilities using the

form P(this event  | that event ) = number.
3 Are the conditional probabilities in Part 2 empirical, a priori, or subjective 
probabilities?
4 Using information in the table, calculate the probability of the event a 
fund is a loser in both Year 1 and Year 2.  (Note that because 50 percent of 
funds are categorized as losers in each year, the unconditional probability 
that a fund is labeled a loser in either year is 0.5.)
The four events needed to define the conditional probabilities are as follows:

Probability, Expected Value, and Variance 479
Fund is a Year 1 winner 
Fund is a Year 1 loser
Fund is a Year 2 loser
Fund is a Year 2 winner
From Row 1:
P(fund is a Year 2 winner  | fund is a Year 1 winner ) = 0.655
P(fund is a Year 2 loser  | fund is a Year 1 winner ) = 0.345
From Row 2:
P(fund is a Year 2 winner  | fund is a Year 1 loser ) = 0.155
P(fund is a Year 2 loser  | fund is a Year 1 loser ) = 0.845
These probabilities are calculated from data, so they are empirical probabilities.
The estimated probability is 0.423. With A the event that a fund is a Year 2 loser  
and B the event that a fund is a Year 1 loser, AB  is the event that a fund is a loser 
in both Year 1 and Year 2.  From Table 2, P(A | B) = 0.845 and P(B) = 0.50. Thus, 
using Equation 2, we find that
P(AB) = P(A | B)P(B) = 0.845(0.50) = 0.4225
or a probability of approximately 0.423.
Equation 2 states that the joint probability of A and B equals the probability of A given

B times the probability of B. Because P(AB) = P(BA), the expression P(AB) = P(BA) 
= P(B | A)P(A) is equivalent to Equation 2.
When we have two events, A and B, that we are interested in, we often want to know 
the probability that either A or B occurs. Here the word “or” is inclusive, meaning that 
either A or B occurs or that both A and B occur. Put another way, the probability of 
A or B is the probability that at least one of the two events occurs. Such probabilities 
are calculated using the addition rule for probabilities .
■■Addition Rule for Probabilities.  Given events A and B, the probability that A 
or B occurs, or both occur, is equal to the probability that A occurs, plus the 
probability that B occurs, minus the probability that both A and B occur.
P(A or B) = P(A) + P(B) – P(AB)  
If we think of the individual probabilities of A and B as sets built of outcomes of 
one or more random variables, the first step in calculating the probability of A or B

is to sum the probabilities of the outcomes in A to obtain P(A). If A and B share any 
outcomes, then if we now added P(B) to P(A), we would count twice the probabilities 
of those shared outcomes. So we add to P(A) the quantity [ P(B) − P(AB)], which is the 
probability of outcomes in B net of the probability of any outcomes already counted 
when we computed P(A). Figure 1 illustrates this process; we avoid double-  counting 
the outcomes in the intersection of A and B by subtracting P(AB). As an example of 
the calculation, if P(A) = 0.50, P(B) = 0.40, and P(AB) = 0.20, then P(A or B) = 0.50 + 
0.40 − 0.20 = 0.70. Only if the two events A and B were mutually exclusive, so that 
P(AB) = 0, would it be correct to state that P(A or B) = P(A) + P(B).(3)

Reading 9 ■ Probability Concepts 480
Figure 1   Addition Rule for Probabilities
A B
 A and B
The next example shows how much useful information can be obtained using the few 
probability rules presented to this point.
EXAMPLE 3   
Probability of a Limit Order Executing
You have two buy limit orders outstanding on the same stock. A limit order to 
buy stock at a stated price is an order to buy at that price or lower. A number 
of vendors, including an internet service that you use, supply the estimated 
probability that a limit order will be filled within a stated time horizon, given 
the current stock price and the price limit. One buy order (Order 1) was placed 
at a price limit of $10. The probability that it will execute within one hour is 
0.35. The second buy order (Order 2) was placed at a price limit of $9.75; it has 
a 0.25 probability of executing within the same one-  hour time frame.
1 What is the probability that either Order 1 or Order 2 will execute?

2 What is the probability that Order 2 executes, given that Order 1 
executes?
The probability is 0.35. The two probabilities that are given are P(Order 1 exe -
cutes ) = 0.35 and P(Order 2 executes ) = 0.25. Note that if Order 2 executes, it 
is certain that Order 1 also executes because the price must pass through $10 
to reach $9.75. Thus,
P(Order 1 executes  | Order 2 executes ) = 1
and
P(Order 1 executes  and Order 2 executes ) = P(Order 1 executes  |  
Order 2 executes )P(Order 2 executes ) = 1(0.25) = 0.25
To answer the question, we use the addition rule for probabilities:
P(Order 1 executes  or Order 2 executes ) = P(Order 1 executes )  
+ P(Order 2 executes ) − P(Order 1 executes  and Order 2 executes )  
= 0.35 + 0.25 − 0.25 = 0.35

Probability, Expected Value, and Variance 481
Note that the outcomes for which Order 2 executes are a subset of the out -
comes for which Order 1 executes. After you count the probability that Order 
1 executes, you have counted the probability of the outcomes for which Order 
2 also executes. Therefore, the answer to the question is the probability that 
Order 1 executes, 0.35.
If the first order executes, the probability that the second order executes is 
0.714. In the solution to Part 1, you found that P(Order 1 executes  and Order 2 
executes ) = P(Order 1 executes  | Order 2 executes )P(Order 2 executes ) = 1(0.25) 
= 0.25. An equivalent way to state this joint probability is useful here:
P(Order 1 executes  and Order 2 executes ) = 0.25  
= P(Order 2 executes  | Order 1 executes )P(Order 1 executes )
Because P(Order 1 executes ) = 0.35 was a given, you have one equation with 
one unknown:
0.25 = P(Order 2 executes  | Order 1 executes )(0.35)

You conclude that P(Order 2 executes  | Order 1 executes ) = 0.25/0.35 = 5/7, or 
about 0.714. You can also use Equation 1 to obtain this answer.
Of great interest to investment analysts are the concepts of independence and 
dependence. These concepts bear on such basic investment questions as which financial 
variables are useful for investment analysis, whether asset returns can be predicted, and 
whether superior investment managers can be selected based on their past records.
Two events are independent if the occurrence of one event does not affect the 
probability of occurrence of the other event.
■■Definition of Independent Events.  Two events A and B are independent  if 
and only if P(A | B) = P(A) or, equivalently, P(B | A) = P(B).
When two events are not independent, they are dependent : The probability of occur -
rence of one is related to the occurrence of the other. If we are trying to forecast one 
event, information about a dependent event may be useful, but information about an

independent event will not be useful.
When two events are independent, the multiplication rule for probabilities, 
Equation 2, simplifies because P(A | B) in that equation then equals P(A).
■■Multiplication Rule for Independent Events.  When two events are inde -
pendent, the joint probability of A and B equals the product of the individual 
probabilities of A and B.
P(AB) = P(A)P(B)  
Therefore, if we are interested in two independent events with probabilities of 0.75 
and 0.50, respectively, the probability that both will occur is 0.375 = 0.75(0.50). The 
multiplication rule for independent events generalizes to more than two events; for 
example, if A, B,  and C are independent events, then P(ABC ) = P(A)P(B)P(C).
EXAMPLE 4   
BankCorp’s Earnings per Share (1)
As part of your work as a banking industry analyst, you build models for forecast -
ing earnings per share of the banks you cover. Today you are studying BankCorp.

The historical record shows that in 55 percent of recent quarters BankCorp’s (4)

Reading 9 ■ Probability Concepts 482
EPS has increased sequentially, and in 45 percent of quarters EPS has decreased 
or remained unchanged sequentially.6 At this point in your analysis, you are 
assuming that changes in sequential EPS are independent.
Earnings per share for 2Q:2014 (that is, EPS for the second quarter of 2014) 
were larger than EPS for 1Q:2014.
1 What is the probability that 3Q:2014 EPS will be larger than 2Q:2014 EPS 
(a positive change in sequential EPS)?
2 What is the probability that EPS decreases or remains unchanged in the 
next two quarters?
Under the assumption of independence, the probability that 3Q:2014 EPS will 
be larger than 2Q:2014 EPS is the unconditional probability of positive change, 
0.55. The fact that 2Q:2014 EPS was larger than 1Q:2014 EPS is not useful infor -
mation, as the next change in EPS is independent of the prior change.
The probability is 0.2025 = 0.45(0.45).

The probability is 0.2025 = 0.45(0.45).  
The following example illustrates how difficult it is to satisfy a set of independent 
criteria even when each criterion by itself is not necessarily stringent.
EXAMPLE 5   
Screening Stocks for Investment
You have developed a stock screen—a set of criteria for selecting stocks. Your 
investment universe (the set of securities from which you make your choices) is 
the Russell 1000 Index, an index of 1,000 large-  capitalization US equities. Your 
criteria capture different aspects of the selection problem; you believe that the 
criteria are independent of each other, to a close approximation.
CriterionFraction of Russell 1000 Stocks 
Meeting Criterion
First valuation criterion 0.50
Second valuation criterion 0.50
Analyst coverage criterion 0.25
Profitability criterion for company 0.55
Financial strength criterion for company 0.67
How many stocks do you expect to pass your screen?
Only 23 stocks out of 1,000 pass through your screen. If you define five

events— the stock passes the first valuation criterion, the stock passes the second 
valuation criterion, the stock passes the analyst coverage criterion, the company 
6 Sequential  comparisons of quarterly EPS are with the immediate prior quarter. A sequential comparison 
stands in contrast to a comparison with the same quarter one year ago (another frequent type of comparison).

Probability, Expected Value, and Variance 483
passes the profitability criterion, the company passes the financial strength cri -
terion  (say events A, B, C, D,  and E, respectively)—then the probability that a 
stock will pass all five criteria, under independence, is
PABCDE PAPBP CPDPE () =() () () () () =() () () ()    5 52 55 5 00 00 00 0 . ... ..
.67
 2 331()
=00 0
Although only one of the five criteria is even moderately strict (the strictest lets 
25 percent of stocks through), the probability that a stock can pass all five is 
only 0.023031, or about 2 percent. The size of the list of candidate investments 
is 0.023031(1,000) = 23.031, or 23 stocks.
An area of intense interest to investment managers and their clients is whether 
records of past performance are useful in identifying repeat winners and losers. The 
following example shows how this issue relates to the concept of independence.
EXAMPLE 6   
Fund Performance (2)

The purpose of the Vidal-  Garcia (2013) study, introduced in Example 2, was to 
address the question of repeat European mutual fund winners and losers. If the 
status of a fund as a winner or a loser in one year is independent of whether 
it is a winner in the next year, the practical value of performance ranking is 
questionable. Using the four events defined in Example 2 as building blocks, we 
can define the following events to address the issue of predictability of mutual 
fund performance:
Fund is a Year 1 winner  and fund is a Year 2 winner
Fund is a Year 1 winner  and fund is a Year 2 loser
Fund is a Year 1 loser  and fund is a Year 2 winner
Fund is a Year 1 loser  and fund is a Year 2 loser
In Part 4 of Example 2, you calculated that
P(fund is a Year 2 loser  and fund is a Year 1 loser ) = 0.423 
If the ranking in one year is independent of the ranking in the next year, what 
will you expect P(fund is a Year 2 loser  and fund is a Year 1 loser ) to be? Interpret

the empirical probability 0.423.
By the multiplication rule for independent events, P(fund is a Year 2 loser  and 
fund is a Year 1 loser ) = P(fund is a Year 2 loser )P(fund is a Year 1 loser ). Because 
50 percent of funds are categorized as losers in each year, the unconditional 
probability that a fund is labeled a loser in either year is 0.50. Thus P(fund is a 
Year 2 loser )P(fund is a Year 1 loser ) = 0.50(0.50) = 0.25. If the status of a fund 
as a loser in one year is independent of whether it is a loser in the prior year, 
we conclude that P(fund is a Year 2 loser  and fund is a Year 1 loser ) = 0.25. This 
probability is a priori because it is obtained from reasoning about the problem. 
You could also reason that the four events described above define categories and 
that if funds are randomly assigned to the four categories, there is a 1/4 proba -
bility of fund is a Year 1 loser  and fund is a Year 2 loser.  If the classifications in

Year 1 and Year 2 were dependent, then the assignment of funds to categories 
would not be random. The empirical probability of 0.423 is above 0.25. Is this

Reading 9 ■ Probability Concepts 484
apparent predictability the result of chance? A test conducted by Vidal-  Garcia 
indicated a less than 1 percent chance of observing the tabled data if the Year 
1 and Year 2 rankings were independent.
In investments, the question of whether one event (or characteristic) provides 
information about another event (or characteristic) arises in both time-  series settings 
(through time) and cross-  sectional settings (among units at a given point in time). 
Examples 4 and 6 examined independence in a time-  series setting. Example 5 illustrated 
independence in a cross-  sectional setting. Independence/dependence relationships 
are often also explored in both settings using regression analysis, a technique we 
discuss in a later reading.
In many practical problems, we logically analyze a problem as follows: We for -
mulate scenarios that we think affect the likelihood of an event that interests us. We

then estimate the probability of the event, given the scenario. When the scenarios 
(conditioning events) are mutually exclusive and exhaustive, no possible outcomes 
are left out. We can then analyze the event using the total probability rule . This rule 
explains the unconditional probability of the event in terms of probabilities conditional 
on the scenarios.
The total probability rule is stated below for two cases. Equation 5 gives the sim -
plest case, in which we have two scenarios. One new notation is introduced: If we 
have an event or scenario S, the event not- S, called the complement  of S, is written 
SC.7 Note that P(S) + P(SC) = 1, as either S or not- S must occur. Equation 6 states the 
rule for the general case of n mutually exclusive and exhaustive events or scenarios.
■■The Total Probability Rule.
PA PA SP AS
PA SPSP AS PSC
CC()=() +()
=() ()+() () ||
PA PA SP AS PAS
PA SP SP AS PS PAn ()=() +() ++ ()
=() () +() () ++12
11 22
 || ||SP Snn () ()

11 22
where S1, S2, …, Sn are mutually exclusive and exhaustive scenarios or events.
Equation 6 states the following: The probability of any event [ P(A)] can be expressed 
as a weighted average of the probabilities of the event, given scenarios [terms such 
P(A | S1)]; the weights applied to these conditional probabilities are the respective 
probabilities of the scenarios [terms such as P(S1) multiplying P(A | S1)], and the 
scenarios must be mutually exclusive and exhaustive. Among other applications, this 
rule is needed to understand Bayes’ formula, which we discuss later in the reading.
In the next example, we use the total probability rule to develop a consistent set 
of views about BankCorp’s earnings per share.
EXAMPLE 7   
BankCorp’s Earnings per Share (2)
You are continuing your investigation into whether you can predict the direction 
of changes in BankCorp’s quarterly EPS. You define four events:(5)
(6)

(6)
7 For readers familiar with mathematical treatments of probability, S, a notation usually reserved for a 
concept called the sample space, is being appropriated to stand for scenario.

Probability, Expected Value, and Variance 485
Event Probability
A = Change in sequential EPS is positive next quarter 0.55
AC = Change in sequential EPS is 0 or negative next quarter 0.45
S = Change in sequential EPS is positive in the prior quarter 0.55
SC = Change in sequential EPS is 0 or negative in the prior quarter 0.45
On inspecting the data, you observe some persistence in EPS changes: Increases 
tend to be followed by increases, and decreases by decreases. The first probabil -
ity estimate you develop is P(change in sequential EPS is positive next quarter  
| change in sequential EPS is 0 or negative in the prior quarter ) = P(A | SC) = 
0.40. The most recent quarter’s EPS (2Q:2014) is announced, and the change 
is a positive sequential change (the event S). You are interested in forecasting 
EPS for 3Q:2014.
1 Write this statement in probability notation: “the probability that the 
change in sequential EPS is positive next quarter, given that the change in

sequential EPS is positive the prior quarter. ”
2 Calculate the probability in Part 1. (Calculate the probability that is con -
sistent with your other probabilities or beliefs.)
In probability notation, this statement is written P(A | S).
The probability is 0.673 that the change in sequential EPS is positive for 3Q:2014, 
given the positive change in sequential EPS for 2Q:2014, as shown on the fol -
lowing page.
According to Equation 5, P(A) = P(A | S)P(S) + P(A | SC)P(SC). The values 
of the probabilities needed to calculate P(A | S) are already known: P(A) = 0.55, 
P(S) = 0.55, P(SC) = 0.45, and P(A | SC) = 0.40. Substituting into Equation 5,
0.55 = P(A | S)(0.55) + 0.40(0.45)  
Solving for the unknown, P(A | S) = [0.55 − 0.40(0.45)]/0.55 = 0.672727, or 0.673.
You conclude that P(change in sequential EPS is positive next quarter  | change 
in sequential EPS is positive the prior quarter ) = 0.673. Any other probability is

not consistent with your other estimated probabilities. Reflecting the persistence 
in EPS changes, this conditional probability of a positive EPS change, 0.673, is 
greater than the unconditional probability of an EPS increase, 0.55.
In the reading on statistical concepts and market returns, we discussed the concept 
of a weighted average or weighted mean. The example highlighted in that reading was 
that portfolio return is a weighted average of the returns on the individual assets in 
the portfolio, where the weight applied to each asset’s return is the fraction of the 
portfolio invested in that asset. The total probability rule, which is a rule for stating 
an unconditional probability in terms of conditional probabilities, is also a weighted 
average. In that formula, probabilities of scenarios are used as weights. Part of the 
definition of weighted average is that the weights sum to 1. The probabilities of

mutually exclusive and exhaustive events do sum to 1 (this is part of the definition of 
probability). The next weighted average we discuss, the expected value of a random 
variable, also uses probabilities as weights.

Reading 9 ■ Probability Concepts 486
The expected value of a random variable is an essential quantitative concept in 
investments. Investors continually make use of expected values—in estimating the 
rewards of alternative investments, in forecasting EPS and other corporate financial 
variables and ratios, and in assessing any other factor that may affect their financial 
position. The expected value of a random variable is defined as follows:
■■Definition of Expected Value.  The expected value  of a random variable is the 
probability-  weighted average of the possible outcomes of the random variable. 
For a random variable X, the expected value of X is denoted E(X).
Expected value (for example, expected stock return) looks either to the future, as a 
forecast, or to the “true” value of the mean (the population mean, discussed in the read -
ing on statistical concepts and market returns). We should distinguish expected value

from the concepts of historical or sample mean. The sample mean also summarizes in 
a single number a central value. However, the sample mean presents a central value for 
a particular set of observations as an equally weighted average of those observations. 
To summarize, the contrast is forecast versus historical, or population versus sample.
EXAMPLE 8   
BankCorp’s Earnings per Share (3)
You continue with your analysis of BankCorp’s EPS. In Table 3, you have recorded 
a probability distribution for BankCorp’s EPS for the current fiscal year.
Table 3   Probability Distribution for BankCorp’s EPS
Probability EPS ($)
0.15 2.60
0.45 2.45
0.24 2.20
0.16 2.00
1.00
What is the expected value of BankCorp’s EPS for the current fiscal year?
Following the definition of expected value, list each outcome, weight it by 
its probability, and sum the terms.
 E(EPS) = 0.15($2.60) + 0.45($2.45) + 0.24($2.20) + 0.16($2.00)
  = $2.3405
The expected value of EPS is $2.34.

= $2.3405
An equation that summarizes your calculation in Example 8 is
EX PX XP XX PX XP XXnn ii
in
()=() +() ++ () = ()
=∑ 11 22
1 (7)

Probability, Expected Value, and Variance 487
where Xi is one of n possible outcomes of the random variable X.8
The expected value is our forecast. Because we are discussing random quantities, 
we cannot count on an individual forecast being realized (although we hope that, on 
average, forecasts will be accurate). It is important, as a result, to measure the risk 
we face. Variance and standard deviation measure the dispersion of outcomes around 
the expected value or forecast.
■■Definition of Variance.  The variance  of a random variable is the expected 
value (the probability-  weighted average) of squared deviations from the random 
variable’s expected value:
σ2 2XE XE X () =− ()  {}
■■The two notations for variance are σ2(X) and Var( X).
Variance is a number greater than or equal to 0 because it is the sum of squared terms. 
If variance is 0, there is no dispersion or risk. The outcome is certain, and the quan -

tity X is not random at all. Variance greater than 0 indicates dispersion of outcomes. 
Increasing variance indicates increasing dispersion, all else equal. Variance of X is a 
quantity in the squared units of X. For example, if the random variable is return in 
percent, variance of return is in units of percent squared. Standard deviation is easier 
to interpret than variance, as it is in the same units as the random variable. If the 
random variable is return in percent, standard deviation of return is also in units of 
percent. In the following example, when the variance of returns is stated as a percent 
or amount of money, to conserve space the reading may suppress showing the unit 
squared. Note that when the variance of returns is stated as a decimal, the complica -
tion of dealing with units of “percent squared” does not arise.
■■Definition of Standard Deviation.  Standard deviation  is the positive square 
root of variance.

The best way to become familiar with these concepts is to work examples.
EXAMPLE 9   
BankCorp’s Earnings per Share (4)
In Example 8, you calculated the expected value of BankCorp’s EPS as $2.34, 
which is your forecast. Now you want to measure the dispersion around your 
forecast. Table 4 shows your view of the probability distribution of EPS for the 
current fiscal year.
Table 4   Probability Distribution for BankCorp’s EPS
0.15 2.60
0.45 2.45
0.24 2.20(8)
8 For simplicity, we model all random variables in this reading as discrete random variables, which have 
a countable set of outcomes. For continuous random variables, which are discussed along with discrete 
random variables in the reading on common probability distributions, the operation corresponding to 
summation is integration.

Reading 9 ■ Probability Concepts 488
0.16 2.00
1.00
What are the variance and standard deviation of BankCorp’s EPS for the current 
fiscal year?
The order of calculation is always expected value, then variance, then standard 
deviation. Expected value has already been calculated. Following the definition 
of variance above, calculate the deviation of each outcome from the mean or 
expected value, square each deviation, weight (multiply) each squared deviation 
by its probability of occurrence, and then sum these terms.
σ2 22602 60 2452 45 EPSE PS EPS () =() −() +() −() PE PE $. $. $. $.2 2
222202 20 2002 00
01+() −() +() −() 
=PE PE $. $. $. $.
.EPSE PS
55260 2340 452452 34
024220 2340 1620022
2.. .. .
.. .. .− () +− ()
+− () +− 2234
0 01014 0 005445 0 004704 0 018496 0 0387852.
.. .. .()
=+ ++ =
Standard deviation is the positive square root of 0.038785:
σ(EPS) = 0.0387851/2 = 0.196939, or approximately 0.20.

An equation that summarizes your calculation of variance in Example 9 is
σ2
112
222XP XX EX PX XE X
PX() =() −() +() −() 
++             nnn ii
in
XE XP XX EX () −() = () −() 
=∑22
1
where Xi is one of n possible outcomes of the random variable X.
In investments, we make use of any relevant information available in making our 
forecasts. When we refine our expectations or forecasts, we are typically making 
adjustments based on new information or events; in these cases we are using condi -
tional expected values . The expected value of a random variable X given an event 
or scenario S is denoted E(X | S). Suppose the random variable X can take on any one 
of n distinct outcomes X1, X2, …, Xn (these outcomes form a set of mutually exclusive 
and exhaustive events). The expected value of X conditional on S is the first outcome, 
X1, times the probability of the first outcome given S, P(X1 | S), plus the second out -

come, X2, times the probability of the second outcome given S, P(X2 | S), and so forth.
E(X | S) = P(X1 | S)X1 + P(X2 | S)X2 + … + P(Xn | S)Xn  
We will illustrate this equation shortly.
Parallel to the total probability rule for stating unconditional probabilities in terms 
of conditional probabilities, there is a principle for stating (unconditional) expected 
values in terms of conditional expected values. This principle is the total probability 
rule for expected value .
■■The Total Probability Rule for Expected Value.
E(X) = E(X | S)P(S) + E(X | SC)P(SC)  (9)
(10)
(11)Table 4   (Continued)

Probability, Expected Value, and Variance 489
E(X) = E(X | S1)P(S1) + E(X | S2)P(S2) + … + E(X | Sn)P(Sn)  
The general case, Equation  12, states that the expected value of X equals the 
expected value of X given Scenario 1, E(X | S1), times the probability of Scenario 1, 
P(S1), plus the expected value of X given Scenario 2, E(X | S2), times the probability 
of Scenario 2, P(S2), and so forth.
To use this principle, we formulate mutually exclusive and exhaustive scenarios that 
are useful for understanding the outcomes of the random variable. This approach was 
employed in developing the probability distribution of BankCorp’s EPS in Examples 
8 and 9, as we now discuss.
The earnings of BankCorp are interest rate sensitive, benefiting from a declining 
interest rate environment. Suppose there is a 0.60 probability that BankCorp will

operate in a declining interest rate environment  in the current fiscal year and a 0.40 
probability that it will operate in a stable interest rate environment  (assessing the chance 
of an increasing interest rate environment as negligible). If a declining interest rate 
environment  occurs, the probability that EPS will be $2.60 is estimated at 0.25, and the 
probability that EPS will be $2.45 is estimated at 0.75. Note that 0.60, the probability 
of declining interest rate environment,  times 0.25, the probability of $2.60 EPS given 
a declining interest rate environment,  equals 0.15, the (unconditional) probability of 
$2.60 given in the table in Examples 8 and 9. The probabilities are consistent. Also, 
0.60(0.75) = 0.45, the probability of $2.45 EPS given in Tables 3 and 4. The tree dia -
gram  in Figure 2 shows the rest of the analysis.
Figure 2   BankCorp’s Forecasted EPS
E(EPS) = $2.34Prob. of declining
interest rates = 0.60 
Prob. of stable
interest rates = 0.40EPS = $2.60 with

Prob = 0.150.25
0.75
0.60
0.40EPS = $2.45 with
Prob = 0.45
EPS = $2.20 with
Prob = 0.24
EPS = $2.00 with
Prob = 0.16
A declining interest rate environment points us to the node  of the tree that 
branches off into outcomes of $2.60 and $2.45. We can find expected EPS given a 
declining interest rate environment as follows, using Equation 10:
 E(EPS | declining interest rate environment ) = 0.25($2.60) + 0.75($2.45)
  = $2.4875
If interest rates are stable,
 E(EPS | stable interest rate environment ) = 0.60($2.20) + 0.40($2.00)
  = $2.12(12)

Reading 9 ■ Probability Concepts 490
Once we have the new piece of information that interest rates are stable, for example, 
we revise our original expectation of EPS from $2.34 downward to $2.12. Now using 
the total probability rule for expected value,
 E(EPS) = E(EPS |  declining  interest  rate environment )P(declining  inter -
est rate environment ) + E(EPS |  stable  interest  rate environment )
P(stable  interest  rate environment )
So E(EPS) = $2.4875(0.60) + $2.12(0.40) = $2.3405 or about $2.34.
This amount is identical to the estimate of the expected value of EPS calculated 
directly from the probability distribution in Example 8. Just as our probabilities must be 
consistent, so must our expected values, unconditional and conditional; otherwise our 
investment actions may create profit opportunities for other investors at our expense.
To review, we first developed the factors or scenarios that influence the outcome

of the event of interest. After assigning probabilities to these scenarios, we formed 
expectations conditioned on the different scenarios. Then we worked backward to 
formulate an expected value as of today. In the problem just worked, EPS was the 
event of interest, and the interest rate environment was the factor influencing EPS.
We can also calculate the variance of EPS given each scenario:
σ2EPS   |
$. |declinin ginteres trateenvironmen t
declini()
=P260 n nginterest rate environmen t
declinin ginter   
EPS ()
×−$. | 260Ee estrateenvironmen t
declinin ginteres trat  
  () 
+2
245 P$. | eeenvironmen t
declinin ginteres trateenviro 
EPS   ()
×−$. | 245En nmen t () 
=− () +− ()
=2
220252 60 0752 45 .$ .$ .$ .$ 2.4875 2.4875
0.0 004219
σ2EPS   
 |
$. |stabl einteres trateenvironmen t
stabl eint()
=P220 eerestrateenvironmen t
stabl einteres trate  
EPS   ()
×−$. | 220Ee environmen t
stabl einteres trateenvironmen() 
+2
200 P$. |   t t
stabl einteres trateenvironmen t()
×− () 
=$. |
.200
02EEPS

×− () 
=$. |
.200
02EEPS   
6 60 2200 40 20022$. $. $. $ − () +− () = 2.12 2.12 0.0096
These are conditional variances , the variance of EPS given a declining interest 
rate environment  and the variance of EPS given a stable interest rate environment . The 
relationship between unconditional variance and conditional variance is a relatively 
advanced topic.9 The main points are 1) that variance, like expected value, has a con -
ditional counterpart to the unconditional concept and 2) that we can use conditional 
variance to assess risk given a particular scenario.
9 The unconditional variance of EPS is the sum of two terms: 1) the expected value (probability-  weighted 
average) of the conditional variances (parallel to the total probability rules) and 2) the variance of con -
ditional expected values of EPS. The second term arises because the variability in conditional expected 
value is a source of risk. Term 1 is σ2(EPS) = P(declining interest rate environment ) σ2(EPS | declining

interest rate environment ) + P(stable interest rate environment ) σ2(EPS | stable interest rate environment ) = 
0.60(0.004219) + 0.40(0.0096) = 0.006371. Term 2 is σ2[E(EPS | interest rate environment)] = 0.60($2.4875 
− $2.34)2 + 0.40($2.12 − $2.34)2 = 0.032414. Summing the two terms, unconditional variance equals 
0.006371 + 0.032414 = 0.038785.

Probability, Expected Value, and Variance 491
EXAMPLE 10   
BankCorp’s Earnings per Share (5)
Continuing with BankCorp, you focus now on BankCorp’s cost structure. One 
model you are researching for BankCorp’s operating costs is
Ya bX=+
where  Y is a forecast of operating costs in millions of dollars and X is the number 
of branch offices.  Y represents the expected value of Y given X, or E(Y | X). (Y 
is a notation used in regression analysis, which we discuss in a later reading.) 
You interpret the intercept a as fixed costs and b as variable costs. You estimate 
the equation as
YX=+12.5 0.65
BankCorp currently has 66 branch offices, and the equation estimates that 
12.5 + 0.65(66) = $55.4 million. You have two scenarios for growth, pictured in 
the tree diagram in Figure 3.
Figure 3   BankCorp’s Forecasted Operating Costs
Expected Op.
Costs = ?High Growth
Probability = 0.80 
Low Growth
Probability = 0.20Branches = 125
Op. Costs = ?
Prob = ?
Branches = 100
Prob = ?
Branches = 80

Prob = ?
Prob = ?
Branches = 70
Prob = ?0.50
0.50
0.85
0.15
1 Compute the forecasted operating costs given the different levels of 
operating costs, using  YX=+1250 65 .. . State the probability of each level 
of the number of branch offices. These are the answers to the questions in 
the terminal boxes of the tree diagram.
2 Compute the expected value of operating costs under the high growth 
scenario. Also calculate the expected value of operating costs under the 
low growth scenario.
3 Answer the question in the initial box of the tree: What are BankCorp’s 
expected operating costs?
Using  YX=+12.5 .65 0 , from top to bottom, we have

Reading 9 ■ Probability Concepts 492
Operating Costs       Probability
Y=+ () = 12.5 0.65 93.75 mi llion 125 $ 0.80(0.50) = 0.40
Y=+ () = 12.5 0.65 .50 mi llion 100 77 $ 0.80(0.50) = 0.40
Y=+ () = 12.5 0.65 .50 mi llion 80 64 $ 0.20(0.85) = 0.17
Y=+ () = 12.5 0.65 .00 mi llion 70 58 $ 0.20(0.15) = 0.03
Sum = 1.00
Dollar amounts are in millions.
Eh ighgrowt h operating costs 0.50 $93.75 0.50 $77.50
$8| () = () + ()
= 5 5.625
El owgrowth operating costs 0.85 $64.50 0.15 $58.00
$63| () = () + ()
= . .525
EE high growth Phighgrowt operating costs operating costs() =() | h h
El owgrowth Plowgrowth()
+() ()
= (operating costs
85.625|
$. 080) )+ () = $. $ 63.525 81.205 020
BankCorp’s expected operating costs are $81.205 million.
We will see conditional probabilities again when we discuss Bayes’ formula. This 
section has introduced a few problems that can be addressed using probability con -

cepts. The following problem draws on these concepts, as well as on analytical skills.
EXAMPLE 11   
The Default Risk Premium for a One-  Period Debt 
Instrument
As the co-  manager of a short-  term bond portfolio, you are reviewing the pricing 
of a speculative-  grade, one-  year-  maturity, zero-  coupon bond. For this type of 
bond, the return is the difference between the amount paid and the principal 
value received at maturity. Your goal is to estimate an appropriate default risk 
premium for this bond. You define the default risk premium as the extra return 
above the risk-  free return that will compensate investors for default risk. If R is 
the promised return (yield-  to- maturity) on the debt instrument and RF is the 
risk-  free rate, the default risk premium is R − RF. You assess the probability 
that the bond defaults as P(the bond defaults ) = 0.06. Looking at current money 
market yields, you find that one-  year US Treasury bills (T-  bills) are offering a

return of 2 percent, an estimate of RF. As a first step, you make the simplifying 
assumption that bondholders will recover nothing in the event of a default. What 
is the minimum default risk premium you should require for this instrument?

Probability, Expected Value, and Variance 493
The challenge in this type of problem is to find a starting point. In many 
problems, including this one, an effective first step is to divide up the possible 
outcomes into mutually exclusive and exhaustive events in an economically 
logical way. Here, from the viewpoint of a bondholder, the two events that 
affect returns are the bond defaults  and the bond does not default . These two 
events cover all outcomes. How do these events affect a bondholder’s returns? 
A second step is to compute the value of the bond for the two events. We have 
no specifics on bond face value , but we can compute value per $1 or one unit 
of currency invested.
The Bond Defaults The Bond Does Not Default
Bond value $0 $(1 + R)
The third step is to find the expected value of the bond (per $1 invested).
 E(bond) = $0 × P(the bond  defaults ) + $(1 + R)[1 – P(the bond  defaults )] 
So E(bond) = $(1  + R)[1 − P(the bond defaults )]. The expected value of the

T- bill per $1 invested is (1 + RF). In fact, this value is certain because the T-  bill 
is risk free. The next step requires economic reasoning. You want the default 
premium to be large enough so that you expect to at least break even compared 
with investing in the T-  bill. This outcome will occur if the expected value of the 
bond equals the expected value of the T-  bill per $1 invested.
Expected Valu eofBond Expected Valu eofTBill
RP th      -
$1 1=
+() − e e bond defaults RF   1 () =+ ()
Solving for the promised return on the bond, you find R = {(1 + RF)/[1 − P(the 
bond defaults )]} − 1. Substituting in the values in the statement of the problem, 
R = [1.02/(1 − 0.06)] − 1 = 1.08511 − 1 = 0.08511 or about 8.51 percent, and 
default risk premium is R − RF = 8.51% − 2% = 6.51%.
You require a default risk premium of at least 651 basis points. You can state 
the matter as follows: If the bond is priced to yield 8.51 percent, you will earn

a 651 basis-  point spread and receive the bond principal with 94 percent proba -
bility. If the bond defaults, however, you will lose everything. With a premium 
of 651 basis points, you expect to just break even relative to an investment in 
T- bills. Because an investment in the zero-  coupon bond has variability, if you are 
risk averse you will demand that the premium be larger than 651 basis points.
This analysis is a starting point. Bondholders usually recover part of their 
investment after a default. A next step would be to incorporate a recovery rate.
In this section, we have treated random variables such as EPS as stand-  alone 
quantities. We have not explored how descriptors such as expected value and variance 
of EPS may be functions of other random variables. Portfolio return is one random 
variable that is clearly a function of other random variables, the random returns on 
the individual securities in the portfolio. To analyze a portfolio’s expected return and

variance of return, we must understand these quantities are a function of characteristics 
of the individual securities’ returns. Looking at the dispersion or variance of portfolio 
return, we see that the way individual security returns move together or covary is 
important. To understand the significance of these movements, we need to explore 
some new concepts, covariance and correlation. The next section, which deals with 
portfolio expected return and variance of return, introduces these concepts.

Reading 9 ■ Probability Concepts 494
PORTFOLIO EXPECTED RETURN AND VARIANCE OF 
RETURN
Modern portfolio theory makes frequent use of the idea that investment opportuni -
ties can be evaluated using expected return as a measure of reward and variance of 
return as a measure of risk. The calculation and interpretation of portfolio expected 
return and variance of return are fundamental skills. In this section, we will develop an 
understanding of portfolio expected return and variance of return.10 Portfolio return 
is determined by the returns on the individual holdings. As a result, the calculation 
of portfolio variance, as a function of the individual asset returns, is more complex 
than the variance calculations illustrated in the previous section.
We work with an example of a portfolio that is 50 percent invested in an S&P 500 
Index fund, 25 percent invested in a US long-  term corporate bond fund, and 25 percent

invested in a fund indexed to the MSCI EAFE Index (representing equity markets in 
Europe, Australasia, and the Far East). Table 5 shows these weights.
Table 5   Portfolio Weights
Asset Class Weights
S&P 500 0.50
US long-  term corporate bonds 0.25
MSCI EAFE 0.25
We first address the calculation of the expected return on the portfolio. In the 
previous section, we defined the expected value of a random variable as the probability-  
weighted average of the possible outcomes. Portfolio return, we know, is a weighted 
average of the returns on the securities in the portfolio. Similarly, the expected return 
on a portfolio is a weighted average of the expected returns on the securities in the 
portfolio, using exactly the same weights. When we have estimated the expected 
returns on the individual securities, we immediately have portfolio expected return. 
This convenient fact follows from the properties of expected value.
■■Properties of Expected Value.  Let wi be any constant and Ri be a random

variable.
1 The expected value of a constant times a random variable equals the con -
stant times the expected value of the random variable.
E(wiRi) = wiE(Ri) 
2 The expected value of a weighted sum of random variables equals the 
weighted sum of the expected values, using the same weights.
EwRw Rw Rw ER wER
wERnn
nn11 22 11 22 ++ + () = () + ()
++ ()
3
(13)
10 Although we outline a number of basic concepts in this section, we do not present mean–variance 
analysis per se. For a presentation of mean–variance analysis, see the readings on portfolio concepts, as 
well as the extended treatments in standard investment textbooks such as Bodie, Kane, and Marcus (2017), 
Elton, Gruber, Brown, and Goetzmann (2013), and Reilly and Brown (2018).

Portfolio Expected Return and Variance of Return 495
Suppose we have a random variable with a given expected value. If we multiply each 
outcome by 2, for example, the random variable’s expected value is multiplied by 2 
as well. That is the meaning of Part 1. The second statement is the rule that directly 
leads to the expression for portfolio expected return. A portfolio with n securities is 
defined by its portfolio weights, w1, w2, …, wn, which sum to 1. So portfolio return, 
Rp, is Rp = w1R1 + w2R2 + … + wnRn. We can state the following principle:
■■Calculation of Portfolio Expected Return.  Given a portfolio with n securi -
ties, the expected return on the portfolio is a weighted average of the expected 
returns on the component securities:
ER EwRw Rw R
wERw ER wERpn n
nn() =+ ++ ()
= () + () ++ ()11 22
11 22

Suppose we have estimated expected returns on the assets in the portfolio, as given 
in Table 6.
Table 6   Weights and Expected Returns
Asset Class Weight Expected Return (%)

S&P 500 0.50 13
US long-  term corporate bonds 0.25 6
MSCI EAFE 0.25 15
We calculate the expected return on the portfolio as 11.75 percent:
ER wERw ER wERp() = () + () + ()
= () + () + ()11 22 33
050130 2560 25 15 .% .% .% = =11 75.%
In the previous section, we studied variance as a measure of dispersion of outcomes 
around the expected value. Here we are interested in portfolio variance of return as a 
measure of investment risk. Letting Rp stand for the return on the portfolio, portfolio 
variance is σ2(Rp) = E{[Rp − E(Rp)]2} according to Equation 8. How do we implement 
this definition? In the reading on statistical concepts and market returns, we learned 
how to calculate a historical or sample variance based on a sample of returns. Now 
we are considering variance in a forward-  looking sense. We will use information 
about the individual assets in the portfolio to obtain portfolio variance of return. To

avoid clutter in notation, we write ERp for E(Rp). We need the concept of covariance.
■■Definition of Covariance.  Given two random variables Ri and Rj, the covari -
ance between Ri and Rj is
CovRR ER ER RE Rij ii jj ,() =− () −()
Alternative notations are σ( Ri,Rj) and σij.(14)

Reading 9 ■ Probability Concepts 496
Equation 14 states that the covariance between two random variables is the probability-  
weighted average of the cross-  products of each random variable’s deviation from its 
own expected value. We will return to discuss covariance after we establish the need 
for the concept. Working from the definition of variance, we find
σ22
11 22 33 11 22 33RE RE R
Ew Rw Rw RE wR wR wRpp p () =−()


=+ +− ++ ()   {}
=+ +− −− []{}2
11 22 33 11 22 332EwRw Rw Rw ER wERw ER
using Equatio on 13 ()
=− () +− () +− ()  {}
()Ew RE Rw RE Rw RE R11 12 22 33 32
rearranging
=− () +− () +− ()  {
×− () +−Ew RE Rw RE Rw RE R
wR ER wR ER11 12 22 33 3
11 12 22 23 33 () +− () }
()wR ER
what squaring mean s
=[ −() −() +− () −()
+− ()EwwR ERRE Rw wR ERRE R
ww RE RR11 11 11 12 11 22
13 11 333 21 22 11
22 22 22 23 2−() +− () −()
+− () −() +−ER ww RE RR ER
ww RE RR ER ww REERRE R
ww RE RR ER ww RE RR ER
w23 3
31 33 11 32 33 22() −()
+− () −() +− () −()

w23 3
+333 33 33wR ERRE R −() −()  ()doing the mul tiplication
=− ()

+− () −() 
+−wE RE Rw wE RE RR ER
wwER ER12
112
12 11 22
13 11(() −() +− () −() 
+− ()
RE Rw wE RE RR ER
wE RE R33 21 22 11
22
222 
+− () −() +ww ER ER RE R
wwER ER RE Rw23 22 33
31 33 11 332 33 22
32
332wE RE RR ER
wE RE R−() −() 
+− ()

reca lling that t the  terms are constants wi ()
= () + () + ()
+ () +wR ww RR ww RR
wwCovRRw122
11 21 21 31 3
12 12 2σ CovC ov ,,
,222
22 32 3
13 13 23 23 32σ
σRw wR R
wwCovRRw wCovRR w() + ()
+ () + () +Cov,
,,2 2
3R()
The last step follows from the definitions of variance and covariance.11 For the 
italicized covariance terms in Equation 15, we used the fact that the order of variables 
in covariance does not matter: Cov( R2,R1) = Cov( R1,R2), for example. As we will show, 
the diagonal variance terms σ2(R1), σ2(R2), and σ2(R3) can be expressed as Cov( R1,R1),

Cov( R2,R2), and Cov( R3,R3), respectively. Using this fact, the most compact way to (15)
11 Useful facts about variance and covariance include: 1) The variance of a constant times  a random variable 
equals the constant squared times the variance of the random variable, or σ2(wR) = w2σ2(R); 2) The vari -
ance of a constant plus a random variable equals the variance of the random variable, or σ2(w + R) = σ2(R) 
because a constant has zero variance; 3) The covariance between a constant and a random variable is zero.

Portfolio Expected Return and Variance of Return 497
state Equation 15 is  σ2Cov Rw wR Rpi j
j iij () = ()
= =∑ ∑
13
13
, . The double summation signs 
say: “Set i = 1 and let j run from 1 to 3; then set i = 2 and let j run from 1 to 3; next 
set i = 3 and let j run from 1 to 3; finally, add the nine terms. ” This expression gener -
alizes for a portfolio of any size n to
σ2Cov Rw wR Rpi j
jn
in
ij () = ()
= =∑ ∑
1 1,
We see from Equation 15 that individual variances of return constitute part, but 
not all, of portfolio variance. The three variances are actually outnumbered by the six 
covariance terms off the diagonal. For three assets, the ratio is 1 to 2, or 50 percent. 
If there are 20 assets, there are 20 variance terms and 20(20) − 20 = 380 off-  diagonal 
covariance terms. The ratio of variance terms to off-  diagonal covariance terms is less 
than 6 to 100, or 6 percent. A first observation, then, is that as the number of holdings

increases, covariance12 becomes increasingly important, all else equal.
What exactly is the effect of covariance on portfolio variance? The covariance 
terms capture how the co-  movements of returns affect portfolio variance. For example, 
consider two stocks: One tends to have high returns (relative to its expected return) 
when the other has low returns (relative to its expected return). The returns on one 
stock tend to offset the returns on the other stock, lowering the variability or variance 
of returns on the portfolio. Like variance, the units of covariance are hard to interpret, 
and we will introduce a more intuitive concept shortly. Meanwhile, from the definition 
of covariance, we can establish two essential observations about covariance.
1 We can interpret the sign of covariance as follows:
 Covariance of returns is negative if, when the return on one asset is above its 
expected value, the return on the other asset tends to be below its expected

value (an average inverse relationship between returns).
 Covariance of returns is 0 if returns on the assets are unrelated.
 Covariance of returns is positive when the returns on both assets tend to be 
on the same side (above or below) their expected values at the same time (an 
average positive relationship between returns).
2 The covariance of a random variable with itself ( own covariance ) is its own vari -
ance: Cov( R,R) = E{[R − E(R)][R − E(R)]} = E{[R − E(R)]2} = σ2(R).
A complete list of the covariances constitutes all the statistical data needed to com -
pute portfolio variance of return. Covariances are often presented in a square format 
called a covariance matrix . Table 7 summarizes the inputs for portfolio expected 
return and variance of return.
Table 7   Inputs to Portfolio Expected Return and Variance
A. Inputs to Portfolio Expected Return
Asset A B C
E(RA) E(RB) E(RC)(16)

Asset A B C
12 When the meaning of covariance as “off-  diagonal covariance” is obvious, as it is here, we omit the 
qualifying words. Covariance is usually used in this sense.

Reading 9 ■ Probability Concepts 498
B. Covariance Matrix: The Inputs to Portfolio Variance of Return
Asset A B C
A Cov( RA,RA) Cov( RA,RB) Cov( RA,RC)
B Cov( RB,RA) Cov( RB,RB) Cov( RB,RC)
C Cov( RC,RA) Cov( RC,RB) Cov( RC,RC)
With three assets, the covariance matrix has 32 = 3 × 3 = 9 entries, but it is cus -
tomary to treat the diagonal terms, the variances, separately from the off-  diagonal 
terms. These diagonal terms are bolded in Table  7. This distinction is natural, as 
security variance is a single-  variable concept. So there are 9 − 3  = 6 covariances, 
excluding variances. But Cov( RB,RA) = Cov( RA,RB), Cov( RC,RA) = Cov( RA,RC), and 
Cov( RC,RB) = Cov( RB,RC). The covariance matrix below the diagonal is the mirror 
image of the covariance matrix above the diagonal. As a result, there are only 6/2 = 3 
distinct covariance terms to estimate. In general, for n securities, there are n(n − 1)/2 
distinct covariances to estimate and n variances to estimate.

Suppose we have the covariance matrix shown in Table 8. We will be working in 
returns stated as percents and the table entries are in units of percent squared (%2). 
The terms 38%2 and 400%2 are 0.0038 and 0.0400, respectively, stated as decimals; 
correctly working in percents and decimals leads to identical answers. 
Table 8   Covariance Matrix
S&P 500US Long-  Term  
Corporate BondsMSCI 
EAFE
S&P 500 400 45 189
US long-  term corporate bonds 45 81 38
MSCI EAFE 189 38 441
Taking Equation 15 and grouping variance terms together produces the following:
σσ σσ22 22Cov Rw Rw Rw Rw wR R
wwp() = () + () + () + ()
+12
122
232
31 21 2
132
2,
CCovC ov RR ww RR13 23 23
222
050 400 0258 10 25,,
.. .() + ()
=() () +() ()+())( )
+() () () +() () ()
+() (2441
2050025452 0500 25 189
2025025.. ..
.. ))()
=+ ++ ++ =38
100 5 0625 27 5625 11 25 47 25 475 195 875 .. .. ..
The variance is 195.875. Standard deviation of return is 195.8751/2 = 14 percent. To

summarize, the portfolio has an expected annual return of 11.75 percent and a stan -
dard deviation of return of 14 percent.
Let us look at the first three terms in the calculation above. Their sum, 100  + 
5.0625 + 27.5625 = 132.625, is the contribution of the individual variances to portfolio 
variance. If the returns on the three assets were independent, covariances would be 
0 and the standard deviation of portfolio return would be 132.6251/2 = 11.52 percent 
as compared to 14 percent before. The portfolio would have less risk. Suppose the 
covariance terms were negative. Then a negative number would be added to 132.625, (17)Table 7   (Continued)

Portfolio Expected Return and Variance of Return 499
so portfolio variance and risk would be even smaller. At the same time, we have not 
changed expected return. For the same expected portfolio return, the portfolio has 
less risk. This risk reduction is a diversification benefit, meaning a risk-  reduction 
benefit from holding a portfolio of assets. The diversification benefit increases with 
decreasing covariance. This observation is a key insight of modern portfolio theory. 
It is even more intuitively stated when we can use the concept of correlation . Then 
we can say that as long as security returns are not perfectly positively correlated, 
diversification benefits are possible. Furthermore, the smaller the correlation between 
security returns, the greater the cost of not diversifying (in terms of risk-  reduction 
benefits forgone), all else equal.
■■Definition of Correlation.  The correlation between two random variables, Ri

and Rj, is defined as ρ( Ri,Rj) = Cov( Ri,Rj)/σ(Ri)σ(Rj). Alternative notations are 
Corr( Ri,Rj) and ρij.
Frequently, covariance is substituted out using the relationship Cov( Ri,Rj) = ρ( Ri,Rj)
σ(Ri)σ(Rj). The division indicated in the definition makes correlation a pure number 
(one without a unit of measurement) and places bounds on its largest and smallest 
possible values. Using the above definition, we can state a correlation matrix from 
data in the covariance matrix alone. Table 9 shows the correlation matrix.
Table 9   Correlation Matrix of Returns
Corporate Bonds MSCI EAFE
S&P 500 1.00 0.25 0.45
US long-  term corporate bonds 0.25 1.00 0.20
MSCI EAFE 0.45 0.20 1.00
For example, the covariance between long-  term bonds and MSCI EAFE is 38, from 
Table 8. The standard deviation of long-  term bond returns is 811/2 = 9 percent, that 
of MSCI EAFE returns is 4411/2 = 21 percent, from diagonal terms in Table 8. The

correlation ρ(Return on long-  term bonds, Return on EAFE) is 38/(9%)(21%) = 0.201, 
rounded to 0.20. The correlation of the S&P 500 with itself equals 1: The calculation 
is its own covariance divided by its standard deviation squared.
■■Properties of Correlation.
1 Correlation is a number between −1 and +1 for two random variables, X and 
Y:
−≤ () ≤+ 11ρXY,
2 A correlation of 0 (uncorrelated variables) indicates an absence of any linear 
(straight-  line) relationship between the variables.13 Increasingly positive 
correlation indicates an increasingly strong positive linear relationship (up 
to 1, which indicates a perfect linear relationship). Increasingly negative cor -
relation indicates an increasingly strong negative (inverse) linear relation -
ship (down to −1, which indicates a perfect inverse linear relationship).14
13 If the correlation is 0, R1 = a + bR2 + error, with b = 0.
14 If the correlation is positive, R1 = a + bR2 + error, with b > 0. If the correlation is negative, b < 0.

Reading 9 ■ Probability Concepts 500
EXAMPLE 12   
Portfolio Expected Return and Variance of Return
You have a portfolio of two mutual funds, A and B, 75 percent invested in A, 
as shown in Table 10.
Table 10   Mutual Fund Expected Returns, Return 
Variances, and Covariances
FundA 
E(RA) = 20%B 
E(RB) = 12%
Covariance Matrix
Fund A B
A 625 120
B 120 196
1 Calculate the expected return of the portfolio.
2 Calculate the correlation matrix for this problem. Carry out the answer to 
two decimal places.
3 Compute portfolio standard deviation of return.
E(Rp) = wAE(RA) + (1 − wA)E(RB) = 0.75(20%) + 0.25(12%) = 18%. Portfolio 
weights must sum to 1: wB = 1 − wA.
σ(RA) = 6251/2 = 25 percent σ( RB) = 1961/2 = 14 percent. There is one distinct 
covariance and thus one distinct correlation: ρ( RA,RB) = Cov( RA,RB)/σ(RA)
σ(RB) = 120/[25(14)] = 0.342857, or 0.34 Table 11 shows the correlation matrix.
Table 11   Correlation Matrix
A B
A 1.00 0.34
B 0.34 1.00

A B
A 1.00 0.34
B 0.34 1.00
Diagonal terms are always equal to 1 in a correlation matrix.
σσ σ22 2Cov Rw Rw Rw wR RpA AB BA BA B () = () + () + ()
=() () +22
22
075 625 0,
.. 2 25 196 2075025 120
452() () +() () ()
=+ +=..
351.5625 12.25 408.8125
σR Rp() ==408.8125 20.22 percen t12

Portfolio Expected Return and Variance of Return 501
How do we estimate return covariance and correlation? Frequently, we make fore -
casts on the basis of historical covariance or use other methods based on historical 
return data, such as a market model regression.15 We can also calculate covariance 
using the joint probability function  of the random variables, if that can be estimated. 
The joint probability function of two random variables X and Y, denoted P(X,Y), gives 
the probability of joint occurrences of values of X and Y. For example, P(3, 2), is the 
probability that X equals 3 and Y equals 2.
Suppose that the joint probability function of the returns on BankCorp stock ( RA) 
and the returns on NewBank stock ( RB) has the simple structure given in Table 12.
Table 12   Joint Probability Function of BankCorp and NewBank Returns 
(Entries Are Joint Probabilities)
RB = 20% RB = 16% RB = 10%
RA = 25% 0.20 0 0
RA = 12% 0 0.50 0
RA = 10% 0 0 0.30

The expected return on BankCorp stock is 0.20(25%) + 0.50(12%) + 0.30(10%) = 
14%. The expected return on NewBank stock is 0.20(20%) + 0.50(16%) + 0.30(10%) = 
15%. The joint probability function above might reflect an analysis based on whether 
banking industry conditions are good, average, or poor. Table 13 presents the calcu -
lation of covariance.
Table 13   Covariance Calculations
Banking Industry Condition Deviations 
BankCorpDeviations 
NewBankProduct of 
DeviationsProbability of 
ConditionProbability-  Weighted 
Product
Good 25−14 20−15 55 0.20 11
Average 12−14 16−15 −2 0.50 −1
Poor 10−14 10−15 20 0.30 6
Cov( RA,RB) = 16
Note : Expected return for BankCorp is 14% and for NewBank, 15%.
The first and second columns of numbers show, respectively, the deviations of BankCorp 
and NewBank returns from their mean or expected value. The next column shows the 
product of the deviations. For example, for good industry conditions, (25 − 14)(20 − 15)

= 11(5) = 55. Then 55 is multiplied or weighted by 0.20, the probability that banking 
industry conditions are good: 55(0.20) = 11. The calculations for average and poor 
banking conditions follow the same pattern. Summing up these probability-  weighted 
products, we find that Cov( RA,RB) = 16.
A formula for computing the covariance between random variables RA and RB is
CovRR PR RR ER RE RAB Ai Bj
j iAi AB jB ,,,, ,, () = () −() − () ∑ ∑ (18)
15 See any of the textbooks mentioned in Footnote 10.

Reading 9 ■ Probability Concepts 502
The formula tells us to sum all possible deviation cross-  products weighted by the 
appropriate joint probability. In the example we just worked, as Table 12 shows, only 
three joint probabilities are nonzero. Therefore, in computing the covariance of returns 
in this case, we need to consider only three cross-  products:
Cov 25,20 25 14 20 15 12 16 12 14 RR PPAB,,() =() −() −() +() −()
−16 1 15 10,10 14 10 15() +() −() −() 
= ()()+− ()()P 10
020115 0502 1 .. ++− () −()
=− +=0304 5
11 16 16.
One theme of this reading has been independence. Two random variables are 
independent when every possible pair of events—one event corresponding to a value 
of X and another event corresponding to a value of Y—are independent events. When 
two random variables are independent, their joint probability function simplifies.
■■Definition of Independence for Random Variables.  Two random variables X 
and Y are independent if and only if P(X,Y) = P(X)P(Y).

For example, given independence, P(3,2) = P(3)P(2). We multiply the individual 
probabilities to get the joint probabilities. Independence  is a stronger property than 
uncorrelatedness  because correlation addresses only linear relationships. The follow -
ing condition holds for independent random variables and, therefore, also holds for 
uncorrelated random variables.
■■Multiplication Rule for Expected Value of the Product of Uncorrelated 
Random Variables.  The expected value of the product of uncorrelated random 
variables is the product of their expected values.
E(XY) = E(X)E(Y) if X and Y are uncorrelated.
Many financial variables, such as revenue (price times quantity), are the product of 
random quantities. When applicable, the above rule simplifies calculating expected 
value of a product of random variables.16
TOPICS IN PROBABILITY
In the remainder of the reading we discuss two topics that can be important in solving

investment problems. We start with Bayes’ formula: what probability theory has to 
say about learning from experience. Then we move to a discussion of shortcuts and 
principles for counting.
4.1 Bayes’ Formula
When we make decisions involving investments, we often start with viewpoints based 
on our experience and knowledge. These viewpoints may be changed or confirmed by 
new knowledge and observations. Bayes’ formula is a rational method for adjusting 
our viewpoints as we confront new information.17 Bayes’ formula and related con -
cepts have been applied in many business and investment decision-  making contexts, 
including the evaluation of mutual fund performance.184
16 Otherwise, the calculation depends on conditional expected value; the calculation can be expressed 
as E(XY) = E(X) E(Y | X).
17 Named after the Reverend Thomas Bayes (1702–61).
18 See Huij and Verbeek (2007).

Topics in Probability 503
Bayes’ formula makes use of Equation 6, the total probability rule. To review, that 
rule expressed the probability of an event as a weighted average of the probabilities of 
the event, given a set of scenarios. Bayes’ formula works in reverse; more precisely, it 
reverses the “given that” information. Bayes’ formula uses the occurrence of the event 
to infer the probability of the scenario generating it. For that reason, Bayes’ formula 
is sometimes called an inverse probability. In many applications, including the one 
illustrating its use in this section, an individual is updating his beliefs concerning the 
causes that may have produced a new observation.
■■Bayes’ Formula.  Given a set of prior probabilities for an event of interest, if you 
receive new information, the rule for updating your probability of the event is
Updated probabi lity of e vent gi ven the new inform ation
Pro=b babil ity of the new inform ation gi ven event

Unconditional p probabil ity of the new inform ationPrior probabil ity of e × vvent
In probability notation, this formula can be written concisely as:
PP
PP Event  Infor mationInformation  Event
Informatio n() =()
()EEvent ()
To illustrate Bayes’ formula, we work through an investment example that can be 
adapted to any actual problem. Suppose you are an investor in the stock of DriveMed, 
Inc. Positive earnings surprises relative to consensus EPS estimates often result in 
positive stock returns, and negative surprises often have the opposite effect. DriveMed 
is preparing to release last quarter’s EPS result, and you are interested in which of 
these three events happened: last quarter’s EPS exceeded the consensus EPS estimate,  
or last quarter’s EPS exactly met the consensus EPS estimate,  or last quarter’s EPS fell 
short of the consensus EPS estimate.  This list of the alternatives is mutually exclusive 
and exhaustive.

On the basis of your own research, you write down the following prior probabil -
ities  (or priors, for short) concerning these three events:
■■P(EPS exceeded consensus ) = 0.45
■■P(EPS met consensus ) = 0.30
■■P(EPS fell short of consensus ) = 0.25
These probabilities are “prior” in the sense that they reflect only what you know now, 
before the arrival of any new information.
The next day, DriveMed announces that it is expanding factory capacity in Singapore 
and Ireland to meet increased sales demand. You assess this new information. The 
decision to expand capacity relates not only to current demand but probably also to 
the prior quarter’s sales demand. You know that sales demand is positively related to 
EPS. So now it appears more likely that last quarter’s EPS will exceed the consensus.
The question you have is, “In light of the new information, what is the updated 
probability that the prior quarter’s EPS exceeded the consensus estimate?”

Bayes’ formula provides a rational method for accomplishing this updating. We 
can abbreviate the new information as DriveMed expands . The first step in applying 
Bayes’ formula is to calculate the probability of the new information (here: DriveMed 
expands ), given a list of events or scenarios that may have generated it. The list of 
events should cover all possibilities, as it does here. Formulating these conditional 
probabilities is the key step in the updating process. Suppose your view is
P(DriveMed expands  | EPS exceeded consensus ) = 0.75
P(DriveMed expands  | EPS met consensus ) = 0.20
P(DriveMed expands  | EPS fell short of consensus ) = 0.05

Reading 9 ■ Probability Concepts 504
Conditional probabilities of an observation (here: DriveMed expands ) are sometimes 
referred to as likelihoods . Again, likelihoods are required for updating the probability.
Next, you combine these conditional probabilities or likelihoods with your prior 
probabilities to get the unconditional probability for DriveMed expanding, P(DriveMed 
expands ), as follows:
P
P EPS exceeded consen sDriveMed expands
DriveMed expands | 
   ()
= u us
PEPS exceeded consensu s
P EPS met()
×()
+  
   DriveMed expands |c consensu s
PEPS metconsensu s
P EPS fe()
×()
+  
  DriveMed expands |l llshortofconsensu s
PEPS fellshortofconsensu s   
    ()
×()
=0.7 75 0450 200300 050250 41 41 .. .. .. ,% () + () + () =  or 
This is Equation 6, the total probability rule, in action. Now you can answer your 
question by applying Bayes’ formula:
P   
 |DriveMed expands
DriveMed expan()
=d ds |
DriveMed expandsEPS exceeded consensu s
PPEPS exceed  
  ()
()eedconsensu s

  ()
()eedconsensu s  
1.829268 0.45 0.823171()
=() () = () = 075041045 .. .
Prior to DriveMed’s announcement, you thought the probability that DriveMed would 
beat consensus expectations was 45 percent. On the basis of your interpretation of 
the announcement, you update that probability to 82.3 percent. This updated proba -
bility is called your posterior probability  because it reflects or comes after the new 
The Bayes’ calculation takes the prior probability, which was 45  percent, and 
multiplies it by a ratio—the first term on the right-  hand side of the equal sign. The 
denominator of the ratio is the probability that DriveMed expands, as you view it 
without considering (conditioning on) anything else. Therefore, this probability is 
unconditional. The numerator is the probability that DriveMed expands, if last quar -
ter’s EPS actually exceeded the consensus estimate. This last probability is larger than

unconditional probability in the denominator, so the ratio (1.83 roughly) is greater than 
1. As a result, your updated or posterior probability is larger than your prior proba -
bility. Thus, the ratio reflects the impact of the new information on your prior beliefs.
EXAMPLE 13   
Inferring whether DriveMed’s EPS Met Consensus EPS
You are still an investor in DriveMed stock. To review the givens, your prior 
probabilities are P(EPS exceeded consensus ) = 0.45, P(EPS met consensus ) = 0.30, 
and P(EPS fell short of consensus ) = 0.25. You also have the following conditional 
probabilities:
P(DriveMed expands  | EPS exceeded consensus ) = 0.75  
P(DriveMed expands  | EPS met consensus ) = 0.20  

Topics in Probability 505
Recall that you updated your probability that last quarter’s EPS exceeded the 
consensus estimate from 45 percent to 82.3 percent after DriveMed announced 
it would expand. Now you want to update your other priors.
1 Update your prior probability that DriveMed’s EPS met consensus.
2 Update your prior probability that DriveMed’s EPS fell short of consensus.
3 Show that the three updated probabilities sum to 1. (Carry each probabil -
ity to four decimal places.)
4 Suppose, because of lack of prior beliefs about whether DriveMed would 
meet consensus, you updated on the basis of prior probabilities that all 
three possibilities were equally likely: P(EPS exceeded consensus ) = P(EPS 
met consensus ) = P(EPS fell short of consensus ) = 1/3. What is your esti -
mate of the probability P(EPS exceeded consensus  | DriveMed expands )?
The probability is P(EPS met consensus  | DriveMed expands ) =
P
PPDriveMed expands EPS metconsensu s
DriveMed expandsE   
 | ()

 | ()
()PPSmetconsensu s   ()
The probability P(DriveMed expands ) is found by taking each of the three condi -
tional probabilities in the statement of the problem, such as P(DriveMed expands  
| EPS exceeded consensus ); multiplying each one by the prior probability of the 
conditioning event, such as P(EPS exceeded consensus ); then adding the three 
products. The calculation is unchanged from the problem in the text above: 
P(DriveMed expands ) = 0.75(0.45) + 0.20(0.30) + 0.05(0.25) = 0.41, or 41 percent. 
The other probabilities needed, P(DriveMed expands  | EPS met consensus ) = 
0.20 and P(EPS met consensus ) = 0.30, are givens. So
 P(EPS met consensus  | DriveMed expands )
   = [P(DriveMed expands  | EPS met consensus )/P(DriveMed expands )]
P(EPS met consensus )
   = (0.20/0.41)(0.30) = 0.487805(0.30) = 0.146341
After taking account of the announcement on expansion, your updated prob -
ability that last quarter’s EPS for DriveMed just met consensus is 14.6 percent

compared with your prior probability of 30 percent.
P(DriveMed expands ) was already calculated as 41 percent. Recall that P(DriveMed 
expands  | EPS fell short of consensus ) = 0.05 and P(EPS fell short of consensus ) 
= 0.25 are givens.
PEPS fellshor tofconsensu sD riveMed expands
PDriveMed     
 | ()
= eexpands EPS fellshor tofconsensu s
PDriveMed expands|/     
 ()
(() ()
=() () =PEPS fellshor tofconsensu s     
54 12 51 2 00 00 0 ./ .. .11951 25 3 488 00 00 ..() =
As a result of the announcement, you have revised your probability that 
DriveMed’s EPS fell short of consensus from 25 percent (your prior probabil -
ity) to 3 percent.

Reading 9 ■ Probability Concepts 506
The sum of the three updated probabilities is
PEPS exceeded consensu sP EPS metconsen      |DriveMed expands () + ssus
PEPS fellshortofconsensu s|
|(
)+ DriveMed expands Drive      MMed expands 
0.8232 0.1463 0.0305 1.0000()
=++=
The three events ( EPS exceeded consensus , EPS met consensus , EPS fell short of 
consensus ) are mutually exclusive and exhaustive: One of these events or state -
ments must be true, so the conditional probabilities must sum to 1. Whether 
we are talking about conditional or unconditional probabilities, whenever we 
have a complete set of the distinct possible events or outcomes, the probabilities 
must sum to 1. This calculation serves as a check on your work.
Using the probabilities given in the question,
P
DriveMed expands 
   ()
= | u us
PEPS exceeded consensu sP
EPS met()
() +(    
  DriveMed expands |
cconsensu sPEPS metconsensu sP
EPS fel)( )+(    
 DriveMed expands |

llshortofconsensu sPEPS fellshortofconsensu s        )( )
=0751. 330 2013 005131 3 () + () + () = ..
Not surprisingly, the probability of DriveMed expanding is 1/3 because the 
decision maker has no prior beliefs or views regarding how well EPS performed 
relative to the consensus estimate. Now we can use Bayes’ formula to find P(EPS 
exceeded consensus  | DriveMed expands ) = [P(DriveMed expands  | EPS exceeded 
consensus )/P(DriveMed expands )] P(EPS exceeded consensus ) = [(0.75/(1/3)](1/3) 
= 0.75 or 75 percent. This probability is identical to your estimate of P(DriveMed 
expands  | EPS exceeded consensus ).
When the prior probabilities are equal, the probability of information given 
an event equals the probability of the event given the information. When a 
decision-  maker has equal prior probabilities (called diffuse priors ), the proba -
bility of an event is determined by the information.
4.2 Principles of Counting

The first step in addressing a question often involves determining the different logical 
possibilities. We may also want to know the number of ways that each of these pos -
sibilities can happen. In the back of our mind is often a question about probability. 
How likely is it that I will observe this particular possibility? Records of success and 
failure are an example. When we evaluate a market timer’s record, one well-  known 
evaluation method uses counting methods presented in this section.19 An important 
investment model, the binomial option pricing model, incorporates the combination 
formula that we will cover shortly. We can also use the methods in this section to 
calculate what we called a priori probabilities in Section 2. When we can assume that 
the possible outcomes of a random variable are equally likely, the probability of an 
event equals the number of possible outcomes favorable for the event divided by the 
total number of outcomes.

Topics in Probability 507
In counting, enumeration (counting the outcomes one by one) is of course the 
most basic resource. What we discuss in this section are shortcuts and principles. 
Without these shortcuts and principles, counting the total number of outcomes can 
be very difficult and prone to error. The first and basic principle of counting is the 
multiplication rule.
■■Multiplication Rule of Counting.  If one task can be done in n1 ways, and a 
second task, given the first, can be done in n2 ways, and a third task, given the 
first two tasks, can be done in n3 ways, and so on for k tasks, then the number 
of ways the k tasks can be done is ( n1)(n2)(n3) … ( nk).
Suppose we have three steps in an investment decision process. The first step can 
be done in two ways, the second in four ways, and the third in three ways. Following 
the multiplication rule, there are (2)(4)(3) = 24 ways in which we can carry out the 
three steps.

Another illustration is the assignment of members of a group to an equal number 
of positions. For example, suppose you want to assign three security analysts to cover 
three different industries. In how many ways can the assignments be made? The first 
analyst may be assigned in three different ways. Then two industries remain. The 
second analyst can be assigned in two different ways. Then one industry remains. The 
third and last analyst can be assigned in only one way. The total number of different 
assignments equals (3)(2)(1) = 6. The compact notation for the multiplication we have 
just performed is 3! (read: 3 factorial). If we had n analysts, the number of ways we 
could assign them to n tasks would be
n! = n(n – 1)( n – 2)( n – 3)…1  
or n factorial . (By convention, 0! = 1.) To review, in this application we repeatedly 
carry out an operation (here, job assignment) until we use up all members of a group

(here, three analysts). With n members in the group, the multiplication formula 
reduces to n factorial.20
The next type of counting problem can be called labeling problems.21 We want 
to give each object in a group a label, to place it in a category. The following example 
illustrates this type of problem.
A mutual fund guide ranked 18 bond mutual funds by total returns for the year 
2014. The guide also assigned each fund one of five risk labels: high risk  (four funds), 
above-  average risk  (four funds), average risk  (three funds), below-  average risk  (four 
funds), and low risk  (three funds); as 4 + 4 + 3 + 4 + 3 = 18, all the funds are accounted 
for. How many different ways can we take 18 mutual funds and label 4 of them high 
risk, 4 above-  average risk, 3 average risk, 4 below-  average risk, and 3 low risk, so that 
each fund is labeled?
The answer is close to 13 billion. We can label any of 18 funds high risk  (the first

slot), then any of 17 remaining funds, then any of 16 remaining funds, then any of 
15 remaining funds (now we have 4 funds in the high risk  group); then we can label 
any of 14 remaining funds above-  average risk , then any of 13 remaining funds, and 
so forth. There are 18! possible sequences. However, order of assignment within a 
category does not matter. For example, whether a fund occupies the first or third slot 
of the four funds labeled high risk , the fund has the same label ( high risk ). Thus there 
are 4! ways to assign a given group of four funds to the four high risk  slots. Making the 
same argument for the other categories, in total there are (4!)(4!)(3!)(4!)(3!) equivalent 
20 The shortest explanation of n factorial is that it is the number of ways to order n objects in a row. In 
all the problems to which we apply this counting method, we must use up all the members of a group 
(sampling without replacement).

21 This discussion follows Kemeny, Schleifer, Snell, and Thompson (1972) in terminology and approach.

Reading 9 ■ Probability Concepts 508
sequences. To eliminate such redundancies from the 18! total, we divide 18! by (4!)(4!)
(3!)(4!)(3!). We have 18!/(4!)(4!)(3!)(4!)(3!) = 18!/(24)(24)(6)(24)(6) = 12,864,852,000. 
This procedure generalizes as follows.
■■Multinomial Formula (General Formula for Labeling Problems).  The num -
ber of ways that n objects can be labeled with k different labels, with n1 of the 
first type, n2 of the second type, and so on, with n1 + n2 + … + nk = n, is given 
by
n
nn nk!
!! !12
The multinomial formula with two different labels ( k = 2) is especially important. This 
special case is called the combination formula. A combination  is a listing in which 
the order of the listed items does not matter. We state the combination formula in a 
traditional way, but no new concepts are involved. Using the notation in the formula 
below, the number of objects with the first label is r = n1 and the number with the

second label is n − r = n2 (there are just two categories, so n1 + n2 = n). Here is the 
formula:
■■Combination Formula (Binomial Formula).  The number of ways that we can 
choose r objects from a total of n objects, when the order in which the r objects 
are listed does not matter, is
nrCn
rn
nr r=

=−()!
!!
Here nCr and  n
r

 are shorthand notations for n!/(n − r)!r! (read: n choose r, or n 
combination r).
If we label the r objects as belongs to the group  and the remaining objects as does 
not belong to the group , whatever the group of interest, the combination formula tells us 
how many ways we can select a group of size r. We can illustrate this formula with the 
binomial option pricing model. This model describes the movement of the underlying 
asset as a series of moves, price up (U) or price down (D). For example, two sequences 
of five moves containing three up moves, such as UUUDD and UDUUD, result in the

same final stock price. At least for an option with a payoff dependent on final stock 
price, the number but not the order of up moves in a sequence matters. How many 
sequences of five moves belong to the group with three up moves?  The answer is 10, 
calculated using the combination formula (“5 choose 3”):
 5C3 = 5!/(5 – 3)!3!
  = (5)(4)(3)(2)(1)/(2)(1)(3)(2)(1) = 120/12 = 10 ways
A useful fact can be illustrated as follows: 5C3 = 5!/2!3! equals 5C2 = 5!/3!2!, as 3 + 2 = 
5; 5C4 = 5!/1!4! equals 5C1 = 5!/4!1!, as 4 + 1 = 5. This symmetrical relationship can 
save work when we need to calculate many possible combinations.
Suppose jurors want to select three companies out of a group of five to receive the 
first-, second-, and third-  place awards for the best annual report. In how many ways 
can the jurors make the three awards? Order does matter if we want to distinguish 
among the three awards (the rank within the group of three); clearly the question

makes order important. On the other hand, if the question were “In how many ways 
can the jurors choose three winners, without regard to place of finish?” we would use 
the combination formula.

Topics in Probability 509
To address the first question above, we need to count ordered listings such as 
first place , New Company ; second place , Fir Company ; third place , Well Company . An 
ordered listing is known as a permutation , and the formula that counts the number 
of permutations is known as the permutation formula.22
■■Permutation Formula.  The number of ways that we can choose r objects from 
a total of n objects, when the order in which the r objects are listed does matter, 
is
nrPn
nr=−()!
!
So the jurors have 5P3 = 5!/(5 − 3)! = (5)(4)(3)(2)(1)/(2)(1) = 120/2 = 60 ways in which 
they can make their awards. To see why this formula works, note that (5)(4)(3)(2)(1)/
(2)(1) reduces to (5)(4)(3), after cancellation of terms. This calculation counts the 
number of ways to fill three slots choosing from a group of five people, according to 
the multiplication rule of counting. This number is naturally larger than it would be

if order did not matter (compare 60 to the value of 10 for “5 choose 3” that we calcu -
lated above). For example, first place , Well Company ; second place , Fir Company ; third 
place , New Company  contains the same three companies as first place , New Company ; 
second place , Fir Company ; third place , Well Company . If we were concerned only 
with award winners (without regard to place of finish), the two listings would count 
as one combination. But when we are concerned with the order of finish, the listings 
count as two permutations.
Answering the following questions may help you apply the counting methods we 
have presented in this section.
1 Does the task that I want to measure have a finite number of possible out -
comes? If the answer is yes, you may be able to use a tool in this section, and 
you can go to the second question. If the answer is no, the number of outcomes 
is infinite, and the tools in this section do not apply.

2 Do I want to assign every member of a group of size n to one of n slots (or 
tasks)? If the answer is yes, use n factorial. If the answer is no, go to the third 
question.
3 Do I want to count the number of ways to apply one of three or more labels to 
each member of a group? If the answer is yes, use the multinomial formula. If 
the answer is no, go to the fourth question.
4 Do I want to count the number of ways that I can choose r objects from a total 
of n, when the order in which I list the r objects does not matter (can I give 
the r objects a label)? If the answer to these questions is yes, the combination 
formula applies. If the answer is no, go to the fifth question.
5 Do I want to count the number of ways I can choose r objects from a total of n, 
when the order in which I list the r objects is important? If the answer is yes, 
the permutation formula applies. If the answer is no, go to question 6.
6 Can the multiplication rule of counting be used? If it cannot, you may have to

count the possibilities one by one, or use more advanced techniques than those 
presented here.23
22 A more formal definition states that a permutation is an ordered subset of n distinct objects.
23 Feller (1957) contains a very full treatment of counting problems and solution methods.

Reading 9 ■ Probability Concepts 510
SUMMARY
In this reading, we have discussed the essential concepts and tools of probability. 
We have applied probability, expected value, and variance to a range of investment 
problems.
■■A random variable is a quantity whose outcome is uncertain.
■■Probability is a number between 0 and 1 that describes the chance that a stated 
event will occur.
■■An event is a specified set of outcomes of a random variable.
■■Mutually exclusive events can occur only one at a time. Exhaustive events cover 
or contain all possible outcomes.
■■The two defining properties of a probability are, first, that 0 ≤ P(E) ≤ 1 (where 
P(E) denotes the probability of an event E), and second, that the sum of the 
probabilities of any set of mutually exclusive and exhaustive events equals 1.
■■A probability estimated from data as a relative frequency of occurrence is an 
empirical probability. A probability drawing on personal or subjective judgment

is a subjective probability. A probability obtained based on logical analysis is an 
a priori probability.
■■A probability of an event E, P(E), can be stated as odds for E = P(E)/[1 − P(E)] 
or odds against E = [1 − P(E)]/P(E).
■■Probabilities that are inconsistent create profit opportunities, according to the 
Dutch Book Theorem.
■■A probability of an event not conditioned on another event is an uncondi -
tional probability. The unconditional probability of an event A is denoted P(A). 
Unconditional probabilities are also called marginal probabilities.
■■A probability of an event given (conditioned on) another event is a conditional 
probability. The probability of an event A given an event B is denoted P(A | B).
■■The probability of both A and B occurring is the joint probability of A and B, 
denoted P(AB).
■■P(A | B) = P(AB)/P(B), P(B) ≠ 0.
■■The multiplication rule for probabilities is P(AB) = P(A | B)P(B).
■■The probability that A or B occurs, or both occur, is denoted by P(A or B).

■■The addition rule for probabilities is P(A or B) = P(A) + P(B) − P(AB).
■■When events are independent, the occurrence of one event does not affect 
the probability of occurrence of the other event. Otherwise, the events are 
dependent.
■■The multiplication rule for independent events states that if A and B are inde -
pendent events, P(AB) = P(A)P(B). The rule generalizes in similar fashion to 
more than two events.
■■According to the total probability rule, if S1, S2, …, Sn are mutually exclusive 
and exhaustive scenarios or events, then P(A) = P(A | S1)P(S1) + P(A | S2)P(S2) 
+ … + P(A | Sn)P(Sn).
■■The expected value of a random variable is a probability-  weighted average of 
the possible outcomes of the random variable. For a random variable X, the 
expected value of X is denoted E(X).
■■The total probability rule for expected value states that E(X) = E(X | S1)P(S1) + 
E(X | S2)P(S2) + … + E(X | Sn)P(Sn), where S1, S2, …, Sn are mutually exclusive 
and exhaustive scenarios or events.

Summary 511
■■The variance of a random variable is the expected value (the probability-  
weighted average) of squared deviations from the random variable’s expected 
value E(X): σ2(X) = E{[X − E(X)]2}, where σ2(X) stands for the variance of X.
■■Variance is a measure of dispersion about the mean. Increasing variance 
indicates increasing dispersion. Variance is measured in squared units of the 
original variable.
■■Standard deviation is the positive square root of variance. Standard deviation 
measures dispersion (as does variance), but it is measured in the same units as 
the variable.
■■Covariance is a measure of the co-  movement between random variables.
■■The covariance between two random variables Ri and Rj is the expected value 
of the cross-  product of the deviations of the two random variables from their 
respective means: Cov( Ri,Rj) = E{[Ri − E(Ri)][Rj − E(Rj)]}. The covariance of a 
random variable with itself is its own variance.

■■Correlation is a number between −1 and +1 that measures the co-  movement 
(linear association) between two random variables: ρ( Ri,Rj) = Cov( Ri,Rj)/[σ( Ri) 
σ(Rj)].
■■To calculate the variance of return on a portfolio of n assets, the inputs needed 
are the n expected returns on the individual assets, n variances of return on the 
individual assets, and n(n − 1)/2 distinct covariances.
■■Portfolio variance of return is  σ2
1 1Rw wR Rpi ji j
jn
in
() = ()
= =∑ ∑ Cov, .
■■The calculation of covariance in a forward-  looking sense requires the specifica -
tion of a joint probability function, which gives the probability of joint occur -
rences of values of the two random variables.
■■When two random variables are independent, the joint probability function is 
the product of the individual probability functions of the random variables.
■■Bayes’ formula is a method for updating probabilities based on new 

■■Bayes’ formula is expressed as follows: Updated probability of event given 
the new information = [(Probability of the new information given event)/
(Unconditional probability of the new information)] × Prior probability of 
event.
■■The multiplication rule of counting says, for example, that if the first step in a 
process can be done in 10 ways, the second step, given the first, can be done in 
5 ways, and the third step, given the first two, can be done in 7 ways, then the 
steps can be carried out in (10)(5)(7) = 350 ways.
■■The number of ways to assign every member of a group of size n to n slots is n! 
= n (n − 1) ( n − 2)( n − 3) … 1. (By convention, 0! = 1.)
■■The number of ways that n objects can be labeled with k different labels, with n1 
of the first type, n2 of the second type, and so on, with n1 + n2 + … + nk = n, is 
given by n!/(n1!n2! … nk!). This expression is the multinomial formula.
■■A special case of the multinomial formula is the combination formula. The

number of ways to choose r objects from a total of n objects, when the order in 
which the r objects are listed does not matter, is
nrCn
rn
nr r=

=−()!
!!

Reading 9 ■ Probability Concepts 512
Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2017. Essentials of 
Investments , 11th edition. New York: McGraw-Hill Irwin.
Elton, Edwin J., Martin J. Gruber, Stephen J. Brown, and William 
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Feller, William. 1957. An Introduction to Probability Theory and 
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Henriksson, Roy D., and Robert C. Merton. 1981. “On Market 
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Huij, Joop, and Marno Verbeek. 2007. “Cross-  sectional learn -
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Kemeny, John G., Arthur Schleifer, Jr, J. Laurie Snell, and 
Gerald L. Thompson. 1972. Finite Mathematics with Business

Applications , 2nd edition. Englewood Cliffs, NJ: Prentice-Hall.Lo, Andrew W. 1999. “The Three P’s of Total Risk Management. ” 
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Ramsey, Frank P . 1931. “Truth and Probability. ” In The 
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Thanatawee, Yordying. 2013. “Ownership Structure with 
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Fund Performance. ” Research in International Business and 
Finance , vol. 28:45–67. ■■The number of ways to choose r objects from a total of n objects, when the 
order in which the r objects are listed does matter, is
nrPn
nr=−()!
!
This expression is the permutation formula.

Practice Problems 513
1 Suppose that 5 percent of the stocks meeting your stock-  selection criteria are 
in the telecommunications (telecom) industry. Also, dividend-  paying telecom 
stocks are 1 percent of the total number of stocks meeting your selection cri -
teria. What is the probability that a stock is dividend paying, given that it is a 
telecom stock that has met your stock selection criteria?
2 You are using the following three criteria to screen potential acquisition targets 
from a list of 500 companies:
CriterionFraction of the 500 Companies 
Meeting the Criterion
Product lines compatible 0.20
Company will increase combined sales growth rate 0.45
Balance sheet impact manageable 0.78
 If the criteria are independent, how many companies will pass the screen?
3 You apply both valuation criteria and financial strength criteria in choosing 
stocks. The probability that a randomly selected stock (from your investment

universe) meets your valuation criteria is 0.25. Given that a stock meets your 
valuation criteria, the probability that the stock meets your financial strength 
criteria is 0.40. What is the probability that a stock meets both your valuation 
and financial strength criteria?
4 Suppose the prospects for recovering principal for a defaulted bond issue 
depend on which of two economic scenarios prevails. Scenario 1 has probability 
0.75 and will result in recovery of $0.90 per $1 principal value with probabil -
ity 0.45, or in recovery of $0.80 per $1 principal value with probability 0.55. 
Scenario 2 has probability 0.25 and will result in recovery of $0.50 per $1 prin -
cipal value with probability 0.85, or in recovery of $0.40 per $1 principal value 
with probability 0.15.
A Compute the probability of each of the four possible recovery amounts: 
$0.90, $0.80, $0.50, and $0.40.
B Compute the expected recovery, given the first scenario.
C Compute the expected recovery, given the second scenario.

D Compute the expected recovery.
E Graph the information in a tree diagram.
5 You have developed a set of criteria for evaluating distressed credits. Companies 
that do not receive a passing score are classed as likely to go bankrupt within 12 
months. You gathered the following information when validating the criteria:
■●Forty percent of the companies to which the test is administered will go 
bankrupt within 12 months: P(nonsurvivor ) = 0.40.
■●Fifty-  five percent of the companies to which the test is administered pass it: 
P(pass test ) = 0.55.
■●The probability that a company will pass the test given that it will subse -
quently survive 12 months, is 0.85: P(pass test  | survivor ) = 0.85.
A What is P( pass test | nonsurvivor )?

Reading 9 ■ Probability Concepts 514
B Using Bayes’ formula, calculate the probability that a company is a survivor, 
given that it passes the test; that is, calculate P(survivor | pass test).
C What is the probability that a company is a nonsurvivor , given that it fails 
the test?
D Is the test effective?
6 In probability theory, exhaustive events are best described as events:
A with a probability of zero.
B that are mutually exclusive.
C that include all potential outcomes.
7 Which probability estimate most likely  varies greatly between people?
A An a priori  probability
B An empirical probability
C A subjective probability
8 If the probability that Zolaf Company sales exceed last year’s sales is 0.167, the 
odds for exceeding sales are closest  to:
A 1 to 5.
B 1 to 6.
C 5 to 1.
9 The probability of an event given that another event has occurred is a:
A joint probability.
B marginal probability.
C conditional probability.
10 After estimating the probability that an investment manager will exceed his

benchmark return in each of the next two quarters, an analyst wants to forecast 
the probability that the investment manager will exceed his benchmark return 
over the two-  quarter period in total. Assuming that each quarter’s performance 
is independent of the other, which probability rule should the analyst select?
A Addition rule
B Multiplication rule
C Total probability rule
11 Which of the following is a property of two dependent events?
A The two events must occur simultaneously.
B The probability of one event influences the probability of the other event.
C The probability of the two events occurring is the product of each event’s 
probability.
12 Which of the following best describes how an analyst would estimate the 
expected value of a firm under the scenarios of bankruptcy and survivorship? 
The analyst would use:
A the addition rule.
B conditional expected values.
C the total probability rule for expected value.

13 An analyst developed two scenarios with respect to the recovery of $100,000 
principal from defaulted loans:

Practice Problems 515
ScenarioProbability  
of Scenario (%)Amount  
Recovered ($)Probability  
of Amount (%)
1 40 50,000 60
30,000 40
2 60 80,000 90
60,000 10
 The amount of the expected recovery is closest  to:
A $36,400.
B $63,600.
C $81,600.
14 US and Spanish bonds have return standard deviations of 0.64 and 0.56, 
respectively. If the correlation between the two bonds is 0.24, the covariance of 
returns is closest to:
A 0.086.
B 0.670.
C 0.781.
15 The covariance of returns is positive when the returns on two assets tend to:
A have the same expected values.
B be above their expected value at different times.
C be on the same side of their expected value at the same time.
16 Which of the following correlation coefficients indicates the weakest linear 
relationship between two variables?
A –0.67
B –0.24
C 0.33
17 An analyst develops the following covariance matrix of returns:
Hedge Fund Market Index
Hedge fund 256 110
Market index 110 81

 The correlation of returns between the hedge fund and the market index is clos-
est to:
A 0.005.
B 0.073.
C 0.764.
18 All else being equal, as the correlation between two assets approaches +1.0, the 
diversification benefits:
B stay the same.
19 Given a portfolio of five stocks, how many unique covariance terms, excluding 
variances, are required to calculate the portfolio return variance?
A 10
B 20

Reading 9 ■ Probability Concepts 516
C 25
20 The probability distribution for a company’s sales is:
Probability Sales ($ millions)
0.05 70
0.70 40
0.25 25
 The standard deviation of sales is closest to:
A $9.81 million.
B $12.20 million.
C $32.40 million.
21 Which of the following statements is most  accurate? If the covariance of returns 
between two assets is 0.0023, then:
A the assets’ risk is near zero.
B the asset returns are unrelated.
C the asset returns have a positive relationship.
22 An analyst produces the following joint probability function for a foreign index 
(FI) and a domestic index (DI).
RDI = 30% RDI = 25% RDI = 15%
RFI = 25% 0.25
RFI = 15% 0.50
RFI = 10% 0.25
 The covariance of returns on the foreign index and the returns on the domestic 
A 26.39.
B 26.56.
C 28.12.
23 A manager will select 20 bonds out of his universe of 100 bonds to construct a 
portfolio. Which formula provides the number of possible portfolios?
A Permutation formula
B Multinomial formula

C Combination formula
24 A firm will select two of four vice presidents to be added to the investment 
committee. How many different groups of two are possible?
A 6
B 12
C 24
25 From an approved list of 25 funds, a portfolio manager wants to rank 4 mutual 
funds from most recommended to least recommended. Which formula is 
most appropriate  to calculate the number of possible ways the funds could be 
ranked?

Solutions 517
SOLUTIONS
1 Use Equation 1 to find this conditional probability: P(stock is dividend paying | 
telecom stock that meets criteria ) = P(stock is dividend paying and telecom stock 
that meets criteria )/P(telecom stock that meets criteria ) = 0.01/0.05 = 0.20.
2 According to the multiplication rule for independent events, the probability of 
a company meeting all three criteria is the product of the three probabilities. 
Labeling the event that a company passes the first, second, and third criteria, A, 
B, and C, respectively P(ABC ) = P(A)P(B)P(C) = (0.20)(0.45)(0.78) = 0.0702. As 
a consequence, (0.0702)(500) = 35.10, so 35 companies pass the screen.
3 Use Equation 2, the multiplication rule for probabilities P(AB) = P(A | B)P(B), 
defining A as the event that a stock meets the financial strength criteria and 
defining B as the event that a stock meets the valuation criteria . Then P(AB) = 
P(A | B)P(B) = 0.40 × 0.25 = 0.10. The probability that a stock meets both the

financial and valuation criteria is 0.10.
4 A Outcomes associated with Scenario 1:  With a 0.45 probability of a $0.90 
recovery per $1 principal value, given Scenario 1, and with the probability 
of Scenario 1 equal to 0.75, the probability of recovering $0.90 is 0.45 (0.75) 
= 0.3375. By a similar calculation, the probability of recovering $0.80 is 
0.55(0.75) = 0.4125.
 Outcomes associated with Scenario 2:  With a 0.85 probability of a $0.50 
recovery per $1 principal value, given Scenario 2, and with the probability 
of Scenario 2 equal to 0.25, the probability of recovering $0.50 is 0.85(0.25) 
= 0.2125. By a similar calculation, the probability of recovering $0.40 is 
0.15(0.25) = 0.0375.
B E(recovery  | Scenario 1 ) = 0.45($0.90) + 0.55($0.80) = $0.845
C E(recovery  | Scenario 2 ) = 0.85($0.50) + 0.15($0.40) = $0.485
D E(recovery ) = 0.75($0.845) + 0.25($0.485) = $0.755
E  
Recovery = $0.755Scenario 1,
Probability = 0.75
Scenario 2,
Probability = 0.25Recovery = $0.90
Prob = 0.3375
Recovery = $0.80

Prob = 0.4125
Recovery = $0.50
Prob = 0.2125
Recovery = $0.40
Prob = 0.03750.45
0.55
0.85
0.15Expected
5 A We can set up the equation using the total probability rule:
P pas stestP passtestsurvivo rP survivor
P pas stestn  
 () =() ()
+|
|oonsurvivo rP nonsurvivo r () ()
 We know that P(survivor ) = 1 – P(nonsurvivor ) = 1 – 0.40 = 0.60. Therefore, 
P(pass test ) = 0.55 = 0.85(0.60) + P(pass test  | nonsurvivor )(0.40). Thus 
P(pass test  | nonsurvivor ) = [0.55 – 0.85(0.60)]/0.40 = 0.10.

Reading 9 ■ Probability Concepts 518
B Psurvivor passtestP passtestsurvivo rP passtest ||    () = () ()  ()
=() =Psurvivo r
0850 550600 927273 .. ..
 The information that a company passes the test causes you to update your 
probability that it is a survivor from 0.60 to approximately 0.927.
C According to Bayes’ formula, P(nonsurvivor  | fail test ) = [ P(fail test  | nonsur -
vivor )/ P(fail test )]P(nonsurvivor ) = [ P(fail test  | nonsurvivor )/0.45]0.40.
 We can set up the following equation to obtain P(fail test  | nonsurvivor ):
PfailtestP fail test nonsurvivo rP nonsurvivo r
Pfail  
 () =() ()
+|
ttest survivor Psurvivo r
Pfailtest nonsurvivo r|
|() ()
=() 0.45  0.4 40 0.15 0.60 + ()
 where P(fail test  | survivor ) = 1 − P(pass test  | survivor ) = 1 − 0.85 = 0.15. So 
P(fail test  | nonsurvivor ) = [0.45 − 0.15(0.60)]/0.40 = 0.90. Using this result 
with the formula above, we find P(nonsurvivor  | fail test ) = (0.90/0.45)0.40 =

0.80. Seeing that a company fails the test causes us to update the probability 
that it is a nonsurvivor from 0.40 to 0.80.
D A company passing the test greatly increases our confidence that it is a sur -
vivor. A company failing the test doubles the probability that it is a nonsur -
vivor. Therefore, the test appears to be useful.
6 C is correct. The term “exhaustive” means that the events cover all possible 
outcomes.
7 C is correct. A subjective probability draws on personal or subjective judgment 
that may be without reference to any particular data.
8 A is correct. Given odds for E of a to b, the implied probability of E = a/(a + b). 
Stated in terms of odds a to b with a = 1, b = 5, the probability of E = 1/(1 + 5) 
= 1/6 = 0.167. This result confirms that a probability of 0.167 for beating sales is 
odds of 1 to 5.
9 C is correct. A conditional probability is the probability of an event given that 
another event has occurred.

10 B is correct. Because the events are independent, the multiplication rule is most 
appropriate for forecasting their joint probability. The multiplication rule for 
independent events states that the joint probability of both A and B occurring is 
P(AB) = P(A)P(B).
11 B is correct. The probability of the occurrence of one is related to the occur -
rence of the other. If we are trying to forecast one event, information about a 
dependent event may be useful.
12 C is correct. The total probability rule for expected value is used to estimate an 
expected value based on mutually exclusive and exhaustive scenarios.
13 B is correct. If Scenario 1 occurs, the expected recovery is 60% ($50,000) + 
40% ($30,000) = $42,000, and if Scenario 2 occurs, the expected recovery is 
90% ($80,000) + 10%($60,000) = $78,000. Weighting by the probability of each 
scenario, the expected recovery is 40%($42,000) + 60%($78,000) = $63,600.

Alternatively, first calculating the probability of each amount occurring, the 
expected recovery is (40%)(60%)($50,000) + (40%)(40%)($30,000) + (60%)(90%)
($80,000) + (60%)(10%)($60,000) = $63,600.
14 A is correct. The covariance is the product of the standard deviations and 
correlation using the formula Cov(US bond returns, Spanish bond returns) = 
σ(US bonds) × σ (Spanish bonds) × ρ(US bond returns, Spanish bond returns) = 
0.64 × 0.56 × 0.24 = 0.086.

Solutions 519
15 C is correct. The covariance of returns is positive when the returns on both 
assets tend to be on the same side (above or below) their expected values at the 
same time, indicating an average positive relationship between returns.
16 B is correct. Correlations near +1 exhibit strong positive linearity, whereas 
correlations near –1 exhibit strong negative linearity. A correlation of 0 indi -
cates an absence of any linear relationship between the variables. The closer the 
correlation is to 0, the weaker the linear relationship.
17 C is correct. The correlation between two random variables Ri and Rj is defined 
as ρ( Ri,Rj) = Cov( Ri,Rj)/σ(Ri)σ(Rj). Using the subscript i to represent hedge 
funds and the subscript j to represent the market index, the standard deviations 
are σ( Ri) = 2561/2 = 16 and σ( Rj) = 811/2 = 9. Thus, ρ( Ri,Rj) = Cov( Ri,Rj)/σ(Ri) 
σ(Rj) = 110/(16 × 9) = 0.764.
18 A is correct. As the correlation between two assets approaches +1, diversifica -

tion benefits decrease. In other words, an increasingly positive correlation indi -
cates an increasingly strong positive linear relationship and fewer diversification 
benefits.
19 A is correct. A covariance matrix for five stocks has 5 × 5 = 25 entries. 
Subtracting the 5 diagonal variance terms results in 20 off-  diagonal entries. 
Because a covariance matrix is symmetrical, only 10 entries are unique (20/2 = 
10).
20 A is correct. The analyst must first calculate expected sales as 0.05 × $70 + 
0.70 × $40 + 0.25 × $25 = $3.50 million + $28.00 million + $6.25 million = 
$37.75 million.
 After calculating expected sales, we can calculate the variance of sales:
 = σ2 (Sales)
 = P($70)[$70 –  E(Sales)]2 + P($40)[$40 –  E(Sales)]2 + P($25)
[$25 –  E(Sales)]2
 = 0.05($70 – 37.75)2 + 0.70($40 – 37.75)2 + 0.25($25 – 37.75)2
 = $52.00 million + $3.54 million + $40.64 million = $96.18 million.
 The standard deviation of sales is thus σ = ($96.18)1/2 = $9.81 million.

21 C is correct. The covariance of returns is positive when the returns on both 
same time.
22 B is correct. The covariance is 26.56, calculated as follows. First, expected 
returns are
 E(RFI) = (0.25 × 25) + (0.50 × 15) + (0.25 × 10)
  = 6.25 + 7.50 + 2.50 = 16.25 and
 E(RDI) = (0.25 × 30) + (0.50 × 25) + (0.25 × 15)
  = 7.50 + 12.50 + 3.75 = 23.75.
 Covariance is
 Cov( RFI,RDI) = PR RR ER RE RFIiD Ij FIiF ID Ij DI
j i,, ,, ,() − () − () ∑ ∑  
  = 0.25[(25 – 16.25)(30 – 23.75)] + 0.50[(15 – 16.25)
(25 – 23.75)] + 0.25[(10 – 16.25)(15 – 23.75)]
  = 13.67 + (–0.78) + 13.67 = 26.56.

Reading 9 ■ Probability Concepts 520
23 C is correct. The combination formula provides the number of ways that r 
objects can be chosen from a total of n objects, when the order in which the r 
objects are listed does not matter. The order of the bonds within the portfolio 
24 A is correct. The answer is found using the combination formula 
nrCn
rn
nr r=

=−()!
!!
 Here, n = 4 and r = 2, so the answer is 4!/[(4 – 2)!2!] = 24/[(2) × (2)] = 6. This 
result can be verified by assuming there are four vice presidents, VP1–VP4. The 
six possible additions to the investment committee are VP1 and VP2, VP1 and 
VP3, VP1 and VP4, VP2 and VP3, VP2 and VP4, and VP3 and VP4.
25 A is correct. The permutation formula is used to choose r objects from a total 
of n objects when order matters. Because the portfolio manager is trying to 
rank the four funds from most recommended to least recommended, the order 
of the funds matters; therefore, the permutation formula is most appropriate.

Quantitative Methods (2)
This study session introduces the common probability distributions used to describe 
the behavior of random variables, such as asset prices and returns. How to estimate 
measures of a population (mean, standard deviation) based on a population sample 
is shown. A framework for hypothesis testing, used for validating dataset hypotheses, 
follows, along with techniques to test a hypothesis. The session ends with coverage 
of technical analysis, a set of tools that uses asset price, trading volume, and other 
similar data for making investment decisions. 
Reading 10 Common Probability Distributions  
PhD, CFA
Reading 11 Sampling and Estimation  
PhD, CFA
Reading 12 Hypothesis Testing  
by Richard A. DeFusco, PhD, CFA, Dennis W. McLeavey,

PhD, CFA
Reading 13 Technical Analysis  
by Barry M. Sine, CMT, CFA, and Robert A. Strong, 
3

Common Probability Distributions
a. define a probability distribution and distinguish between discrete 
and continuous random variables and their probability functions;
b. describe the set of possible outcomes of a specified discrete 
random variable;
c. interpret a cumulative distribution function;
d. calculate and interpret probabilities for a random variable, given 
its cumulative distribution function;
e. define a discrete uniform random variable, a Bernoulli random 
variable, and a binomial random variable;

f. calculate and interpret probabilities given the discrete uniform 
and the binomial distribution functions;
g. construct a binomial tree to describe stock price movement;
h. define the continuous uniform distribution and calculate and 
interpret probabilities, given a continuous uniform distribution;
i. explain the key properties of the normal distribution;
j. distinguish between a univariate and a multivariate distribution 
and explain the role of correlation in the multivariate normal 
k. determine the probability that a normally distributed random 
variable lies inside a given interval;
l. define the standard normal distribution, explain how to 
standardize a random variable, and calculate and interpret 
probabilities using the standard normal distribution;
m. define shortfall risk, calculate the safety-  first ratio, and select an 
optimal portfolio using Roy’s safety-  first criterion;
10

10

Reading 10 ■ Common Probability Distributions 524
n. explain the relationship between normal and lognormal 
distributions and why the lognormal distribution is used to model 
asset prices;
o. distinguish between discretely and continuously compounded 
rates of return and calculate and interpret a continuously 
compounded rate of return, given a specific holding period 
return;
p. explain Monte Carlo simulation and describe its applications and 
limitations;
q. compare Monte Carlo simulation and historical simulation.
INTRODUCTION TO COMMON PROBABILITY 
In nearly all investment decisions we work with random variables. The return on a 
stock and its earnings per share are familiar examples of random variables. To make 
probability statements about a random variable, we need to understand its probability 
distribution. A probability distribution  specifies the probabilities of the possible 
outcomes of a random variable.

In this reading, we present important facts about four probability distributions and 
their investment uses. These four distributions—the uniform, binomial, normal, and 
lognormal—are used extensively in investment analysis. They are used in such basic 
valuation models as the Black–Scholes–Merton option pricing model, the binomial 
option pricing model, and the capital asset pricing model. With the working knowledge 
of probability distributions provided in this reading, you will also be better prepared 
to study and use other quantitative methods such as hypothesis testing, regression 
analysis, and time-  series analysis.
After discussing probability distributions, we end the reading with an introduc -
tion to Monte Carlo simulation, a computer-  based tool for obtaining information 
on complex problems. For example, an investment analyst may want to experiment 
with an investment idea without actually implementing it. Or she may need to price

a complex option for which no simple pricing formula exists. In these cases and many 
others, Monte Carlo simulation is an important resource. To conduct a Monte Carlo 
simulation, the analyst must identify risk factors associated with the problem and 
specify probability distributions for them. Hence, Monte Carlo simulation is a tool 
that requires an understanding of probability distributions.
Before we discuss specific probability distributions, we define basic concepts and 
terms. We then illustrate the operation of these concepts through the simplest distri -
bution, the uniform distribution. That done, we address probability distributions that 
have more applications in investment work but also greater complexity.1

Discrete Random Variables 525
DISCRETE RANDOM VARIABLES
A random variable  is a quantity whose future outcomes are uncertain. The two basic 
types of random variables are discrete random variables and continuous random 
variables. A discrete random variable  can take on at most a countable number of 
possible values. For example, a discrete random variable X can take on a limited number 
of outcomes x1, x2, …, xn (n possible outcomes), or a discrete random variable Y can 
take on an unlimited number of outcomes y1, y2, … (without end).1 Because we can 
count all the possible outcomes of X and Y (even if we go on forever in the case of 
Y), both X and Y satisfy the definition of a discrete random variable. By contrast, we 
cannot count the outcomes of a continuous random variable . We cannot describe 
the possible outcomes of a continuous random variable Z with a list z1, z2, … because 
the outcome ( z1 + z2)/2, not in the list, would always be possible. Rate of return is an

example of a continuous random variable.
In working with a random variable, we need to understand its possible outcomes. 
For example, a majority of the stocks traded on the New Zealand Stock Exchange are 
quoted in ticks of NZ$0.01. Quoted stock price is thus a discrete random variable with 
possible values NZ$0, NZ$0.01, NZ$0.02, … But we can also model stock price as a 
continuous random variable (as a lognormal random variable, to look ahead). In many 
applications, we have a choice between using a discrete or a continuous distribution. 
We are usually guided by which distribution is most efficient for the task we face. 
This opportunity for choice is not surprising, as many discrete distributions can be 
approximated with a continuous distribution, and vice versa. In most practical cases, 
a probability distribution is only a mathematical idealization, or approximate model, 
of the relative frequencies of a random variable’s possible outcomes.
EXAMPLE 1   
The Distribution of Bond Price

EXAMPLE 1   
You are researching a probability model for bond price, and you begin by thinking 
about the characteristics of bonds that affect price. What are the lowest and the 
highest possible values for bond price? Why? What are some other characteristics 
of bonds that may affect the distribution of bond price?
The lowest possible value of bond price is 0, when the bond is worthless. 
Identifying the highest possible value for bond price is more challenging. The 
promised payments on a coupon bond are the coupons (interest payments) plus 
the face amount (principal). The price of a bond is the present discounted value 
of these promised payments. Because investors require a return on their invest -
ments, 0 percent is the lower limit on the discount rate that investors would use 
to discount a bond’s promised payments. At a discount rate of 0 percent, the 
price of a bond is the sum of the face value and the remaining coupons without

any discounting. The discount rate thus places the upper limit on bond price. 
Suppose, for example, that face value is $1,000 and two $40 coupons remain; the 
interval $0 to $1,080 captures all possible values of the bond’s price. This upper 
limit decreases through time as the number of remaining payments decreases.2
1 We follow the convention that an uppercase letter represents a random variable and a lowercase letter 
represents an outcome or specific value of the random variable. Thus X refers to the random variable, and 
x refers to an outcome of X. We subscript outcomes, as in x1 and x2, when we need to distinguish among 
different outcomes in a list of outcomes of a random variable.

Reading 10 ■ Common Probability Distributions 526
Other characteristics of a bond also affect its price distribution. Pull to par 
value is one such characteristic: As the maturity date approaches, the standard 
deviation of bond price tends to grow smaller as bond price converges to par 
value. Embedded options also affect bond price. For example, with bonds that 
are currently callable, the issuer may retire the bonds at a prespecified premium 
above par; this option of the issuer cuts off part of the bond’s upside. Modeling 
bond price distribution is a challenging problem.
Every random variable is associated with a probability distribution that describes 
the variable completely. We can view a probability distribution in two ways. The basic 
view is the probability function , which specifies the probability that the random 
variable takes on a specific value: P(X = x) is the probability that a random variable X

takes on the value x. (Note that capital X represents the random variable and lower -
case x represents a specific value that the random variable may take.) For a discrete 
random variable, the shorthand notation for the probability function is p(x) = P(X 
= x). For continuous random variables, the probability function is denoted f(x) and 
called the probability density function  (pdf), or just the density.2
A probability function has two key properties (which we state, without loss of 
generality, using the notation for a discrete random variable):
■■0 ≤ p(x) ≤ 1, because probability is a number between 0 and 1.
■■The sum of the probabilities p(x) over all values of X equals 1. If we add up the 
probabilities of all the distinct possible outcomes of a random variable, that sum 
must equal 1.
We are often interested in finding the probability of a range of outcomes rather 
than a specific outcome. In these cases, we take the second view of a probability dis -

tribution, the cumulative distribution function (cdf). The cumulative distribution 
function , or distribution function for short, gives the probability that a random 
variable X is less than or equal to a particular value x, P(X ≤ x). For both discrete and 
continuous random variables, the shorthand notation is F(x) = P(X ≤ x). How does the 
cumulative distribution function relate to the probability function? The word “cumu -
lative” tells the story. To find F(x), we sum up, or cumulate, values of the probability 
function for all outcomes less than or equal to x. The function of the cdf is parallel to 
that of cumulative relative frequency, which we discussed in the reading on statistical 
concepts and market returns.
Next, we illustrate these concepts with examples and show how we use discrete and 
continuous distributions. We start with the simplest distribution, the discrete uniform.
2.1 The Discrete Uniform Distribution

The simplest of all probability distributions is the discrete uniform distribution. 
Suppose that the possible outcomes are the integers (whole numbers) 1 to 8, inclusive, 
and the probability that the random variable takes on any of these possible values is 
the same for all outcomes (that is, it is uniform). With eight outcomes, p(x) = 1/8, 
or 0.125, for all values of X (X = 1, 2, 3, 4, 5, 6, 7, 8); the statement just made is a 
complete description of this discrete uniform random variable. The distribution has 
a finite number of specified outcomes, and each outcome is equally likely. Table 1 
summarizes the two views of this random variable, the probability function and the 
cumulative distribution function.
2 The technical term for the probability function of a discrete random variable, probability mass function 
(pmf), is used less frequently.

Discrete Random Variables 527
Table 1   Probability Function and Cumulative Distribution Function for a 
Discrete Uniform Random Variable
X = xProbability Function  
p(x) = P(X = x)Cumulative Distribution Function  
F(x) = P(X ≤ x)
1 0.125 0.125
2 0.125 0.250
3 0.125 0.375
4 0.125 0.500
5 0.125 0.625
6 0.125 0.750
7 0.125 0.875
8 0.125 1.000
We can use Table 1 to find three probabilities: P(X ≤ 7), P(4 ≤ X ≤ 6), and P(4 < X 
≤ 6). The following examples illustrate how to use the cdf to find the probability that a 
random variable will fall in any interval (for any random variable, not only the uniform).
■■The probability that X is less than or equal to 7, P(X ≤ 7), is the next-  to- last 
entry in the third column, 0.875 or 87.5 percent.
■■To find P(4 ≤ X ≤ 6), we need to find the sum of three probabilities: p(4), p(5), 
and p(6). We can find this sum in two ways. We can add p(4), p(5), and p(6) 
from the second column. Or we can calculate the probability as the difference

between two values of the cumulative distribution function:
F(6) = P(X ≤ 6) = p(6) + p(5) + p(4) + p(3) + p(2) + p(1) 
F(3) = P(X ≤ 3) = p(3) + p(2) + p(1) 
so
P(4 ≤ X ≤ 6) = F(6) – F(3) = p(6) + p(5) + p(4) = 3/8
So we calculate the second probability as F(6) − F(3) = 3/8.
■■The third probability, P(4 < X ≤ 6), the probability that X is less than or equal to 
6 but greater than 4, is p(5) + p(6). We compute it as follows, using the cdf: 
P(4 < X ≤ 6) = P(X ≤ 6) – P(X ≤ 4) = F(6) – F(4) = p(6) + p(5) = 2/8
So we calculate the third probability as F(6) − F(4) = 2/8.
Suppose we want to check that the discrete uniform probability function satisfies 
the general properties of a probability function given earlier. The first property is 0 
≤ p(x) ≤ 1. We see that p(x) = 1/8 for all x in the first column of the table. (Note that 
p(x) equals 0 for numbers x such as −14 or 12.215 that are not in that column.) The 
first property is satisfied. The second property is that the probabilities sum to 1. The

entries in the second column of Table 1 do sum to 1.
The cdf has two other characteristic properties:
■■The cdf lies between 0 and 1 for any x: 0 ≤ F(x) ≤ 1.
■■As we increase x, the cdf either increases or remains constant.
Check these statements by looking at the third column in Table 1.

Reading 10 ■ Common Probability Distributions 528
We now have some experience working with probability functions and cdfs for dis -
crete random variables. Later in this reading, we will discuss Monte Carlo simulation, 
a methodology driven by random numbers. As we will see, the uniform distribution 
has an important technical use: It is the basis for generating random numbers, which 
in turn produce random observations for all other probability distributions.3
2.2 The Binomial Distribution
In many investment contexts, we view a result as either a success or a failure, or as 
binary (twofold) in some other way. When we make probability statements about a 
record of successes and failures, or about anything with binary outcomes, we often use 
the binomial distribution. What is a good model for how a stock price moves through 
time? Different models are appropriate for different uses. Cox, Ross, and Rubinstein 
(1979) developed an option pricing model based on binary moves, price up or price

down, for the asset underlying the option. Their binomial option pricing model was 
the first of a class of related option pricing models that have played an important role 
in the development of the derivatives industry. That fact alone would be sufficient 
reason for studying the binomial distribution, but the binomial distribution has uses 
in decision-  making as well.
The building block of the binomial distribution is the Bernoulli random variable , 
named after the Swiss probabilist Jakob Bernoulli (1654–1704). Suppose we have a 
trial (an event that may repeat) that produces one of two outcomes. Such a trial is a 
Bernoulli trial . If we let Y equal 1 when the outcome is success and Y equal 0 when the 
outcome is failure, then the probability function of the Bernoulli random variable Y is
p(1) = P(Y = 1) = p
p(0) = P(Y = 0) = 1 – p
where p is the probability that the trial is a success. Our next example is the very first 
step on the road to understanding the binomial option pricing model.

EXAMPLE 2   
One-  Period Stock Price Movement as a Bernoulli Random 
Variable
Suppose we describe stock price movement in the following way. Stock price 
today is S. Next period stock price can move up or down. The probability of an 
up move is p, and the probability of a down move is 1 − p. Thus, stock price is a 
Bernoulli random variable with probability of success (an up move) equal to p. 
When the stock moves up, ending price is uS, with u equal to 1 plus the rate of 
return if the stock moves up. For example, if the stock earns 0.01 or 1 percent 
on an up move, u = 1.01. When the stock moves down, ending price is dS, with 
d equal to 1 plus the rate of return if the stock moves down. For example, if the 
stock earns −0.01 or −1 percent on a down move, d = 0.99. Figure 1 shows a 
diagram of this model of stock price dynamics.
3 See Hillier (2014). Random numbers initially generated by computers are usually random positive integer

numbers that are converted to approximate continuous uniform random numbers between 0 and 1. Then 
the continuous uniform random numbers are used to produce random observations on other distributions, 
such as the normal, using various techniques. We will discuss random observation generation further in 
the section on Monte Carlo simulation.

Discrete Random Variables 529
Figure 1   One-  Period Stock Price as a Bernoulli Random Variable
End-of-Period Stock Price
Probability = pStock Price Moves Up:
Stock Price Equals uS
Stock Price
Today, S
Probability = 1 – pStock Price Moves Down:
Stock Price Equals dS
We will continue with the above example later. In the model of stock price move -
ment in Example 2, success and failure at a given trial relate to up moves and down 
moves, respectively. In the following example, success is a profitable trade and failure 
is an unprofitable one.
EXAMPLE 3   
A Trading Desk Evaluates Block Brokers (1)
You work in equities trading at an institutional money manager that regularly 
trades with a number of block brokers. Blocks are orders to sell or buy that 
are too large for the liquidity ordinarily available in dealer networks or stock 
exchanges. Your firm has known interests in certain kinds of stock. Block brokers 
call your trading desk when they want to sell blocks of stocks that they think

your firm may be interested in buying. You know that these transactions have 
definite risks. For example, if the broker’s client (the seller of the shares) has 
unfavorable information on the stock, or if the total amount he is selling through 
all channels is not truthfully communicated to you, you may see an immediate 
loss on the trade. From time to time, your firm audits the performance of block 
brokers. Your firm calculates the post-  trade, market-  risk-  adjusted dollar returns 
on stocks purchased from block brokers. On that basis, you classify each trade as 
unprofitable or profitable. You have summarized the performance of the brokers 
in a spreadsheet, excerpted in Table 2 for November 2014. (The broker names 
are coded BB001 and BB002.)
Table 2   Block Trading Gains and Losses
November 2014
Profitable Trades Losing Trades
BB001 3 9
BB002 5 3
View each trade as a Bernoulli trial. Calculate the percentage of profitable

trades with the two block brokers for November 2014. These are estimates of 
p, the underlying probability of a successful (profitable) trade with each broker.

Reading 10 ■ Common Probability Distributions 530
Your firm has logged 3 + 9 = 12 trades (the row total) with block broker 
BB001. Because 3 of the 12 trades were profitable, the percentage of profitable 
trades was 3/12 or 25 percent. With broker BB002, the percentage of profitable 
trades was 5/8 or 62.5 percent. A trade is a Bernoulli trial, and the above calcu -
lations provide estimates of the underlying probability of a profitable trade 
(success) with the two brokers. For broker BB001, your estimate is  p = 0.25; for 
broker BB002, your estimate is  p = 0.625.4
In n Bernoulli trials, we can have 0 to n successes. If the outcome of an individual 
trial is random, the total number of successes in n trials is also random. A binomial 
random variable  X is defined as the number of successes in n Bernoulli trials. A 
binomial random variable is the sum of Bernoulli random variables Yi, i = 1, 2, …, n:
X = Y1 + Y2 + … + Yn

where Yi is the outcome on the ith trial (1 if a success, 0 if a failure). We know that 
a Bernoulli random variable is defined by the parameter p. The number of trials, n, 
is the second parameter of a binomial random variable. The binomial distribution 
makes these assumptions:
■■The probability, p, of success is constant for all trials.
■■The trials are independent.
The second assumption has great simplifying force. If individual trials were correlated, 
calculating the probability of a given number of successes in n trials would be much 
more complicated.
Under the above two assumptions, a binomial random variable is completely 
described by two parameters, n and p. We write
X ~ B(n,p)  
which we read as “ X has a binomial distribution with parameters n and p.” You can see 
that a Bernoulli random variable is a binomial random variable with n = 1: Y ~ B(1, p).
Now we can find the general expression for the probability that a binomial random

variable shows x successes in n trials. We can think in terms of a model of stock price 
dynamics that can be generalized to allow any possible stock price movements if the 
periods are made extremely small. Each period is a Bernoulli trial: With probability 
p, the stock price moves up; with probability 1 − p, the price moves down. A success 
is an up move, and x is the number of up moves or successes in n periods (trials). 
With each period’s moves independent and p constant, the number of up moves in n 
periods is a binomial random variable. We now develop an expression for P(X = x), 
the probability function for a binomial random variable.
Any sequence of n periods that shows exactly x up moves must show n − x down 
moves. We have many different ways to order the up moves and down moves to get 
a total of x up moves, but given independent trials, any sequence with x up moves 
must occur with probability px(1 − p)n–x. Now we need to multiply this probability by

the number of different ways we can get a sequence with x up moves. Using a basic 
result in counting from the reading on probability concepts, there are
n
nx x!
!! −()
4 The “hat” over p indicates that it is an estimate of p, the underlying probability of a profitable trade 
with the broker.

Discrete Random Variables 531
different sequences in n trials that result in x up moves (or successes) and n − x down 
moves (or failures). Recall from the reading on probability concepts that n factorial 
(n!) is defined as n(n − 1)( n − 2) … 1 (and 0! = 1 by convention). For example, 5! = (5)
(4)(3)(2)(1) = 120. The combination formula n!/[(n − x)!x!] is denoted by
n
x


(read “ n combination x” or “ n choose x”). For example, over three periods, exactly three 
different sequences have two up moves: UUD, UDU, and DUU. We confirm this by
3
23
32 232 1
12 13

=−()=()()()
()()()=!
!!
If, hypothetically, each sequence with two up moves had a probability of 0.15, then 
the total probability of two up moves in three periods would be 3 × 0.15 = 0.45. This 
example should persuade you that for X distributed B(n, p), the probability of x suc-
cesses in n trials is given by
px PX xn
xppn
nx xppx nx x nx()==() =

 −() =−()−()−−11!
!!


!!
Some distributions are always symmetric, such as the normal, and others are 
always asymmetric or skewed, such as the lognormal. The binomial distribution is 
symmetric when the probability of success on a trial is 0.50, but it is asymmetric or 
skewed otherwise.
We illustrate Equation 1 (the probability function) and the cdf through the symmet -
rical case. Consider a random variable distributed B(n = 5, p = 0.50). Table 3 contains a 
complete description of this random variable. The fourth column of Table 3 is Column 
2, n combination x, times Column 3, px(1 − p)n–x; Column 4 gives the probability 
for each value of the number of up moves from the first column. The fifth column, 
cumulating the entries in the fourth column, is the cumulative distribution function.
Table 3   Binomial Probabilities, p = 0.50 and n = 5
Number of  
Up Moves, x 
(1)Number of Possible Ways 
to Reach x Up Moves  
(2)Probability for Each Way  
(3)Probability  
for x, p (x)

for x, p (x) 
(4) = (2) × (3)F(x) = P(X ≤ x) 
(5)
0 1 0.500(1 − 0.50)5 = 0.03125 0.03125 0.03125
1 5 0.501(1 − 0.50)4 = 0.03125 0.15625 0.18750
2 10 0.502(1 − 0.50)3 = 0.03125 0.31250 0.50000
3 10 0.503(1 − 0.50)2 = 0.03125 0.31250 0.81250
4 5 0.504(1 − 0.50)1 = 0.03125 0.15625 0.96875
5 1 0.505(1 − 0.50)0 = 0.03125 0.03125 1.00000
What would happen if we kept n = 5 but sharply lowered the probability of success 
on a trial to 10 percent? “Probability for Each Way” for X = 0 (no up moves) would 
then be about 59 percent: 0.100(1 − 0.10)5 = 0.59049. Because zero successes could 
still happen one way (Column 2), p(0) = 59  percent. You may want to check that 
given p = 0.10, P(X ≤ 2) = 99.14 percent: The probability of two or fewer up moves 
would be more than 99 percent. The random variable’s probability would be massed 
on 0, 1, and 2 up moves, and the probability of larger outcomes would be minute. The (1)

Reading 10 ■ Common Probability Distributions 532
outcomes of 3 and larger would be the long right tail, and the distribution would be 
right skewed. On the other hand, if we set p = 0.90, we would have the mirror image 
of the distribution with p = 0.10. The distribution would be left skewed.
With an understanding of the binomial probability function in hand, we can con -
tinue with our example of block brokers.
EXAMPLE 4   
A Trading Desk Evaluates Block Brokers (2)
You now want to evaluate the performance of the block brokers in Example 3. 
You begin with two questions:
1 If you are paying a fair price on average in your trades with a broker, what 
should be the probability of a profitable trade?
2 Did each broker meet or miss that expectation on probability?
You also realize that the brokers’ performance has to be evaluated in light of 
the sample’s size, and for that you need to use the binomial probability function

(Equation 1). You thus address the following (referring to the data in Example 3):
3 Under the assumption that the prices of trades were fair,
A calculate the probability of three or fewer profitable trades with broker 
BB001.
B calculate the probability of five or more profitable trades with broker 
BB002.
Solution to 1 and 2:
If the price you trade at is fair, 50 percent of the trades you do with a broker should 
be profitable.5 The rate of profitable trades with broker BB001 was 25 percent. 
Therefore, broker BB001 missed your performance expectation. Broker BB002, 
at 62.5 percent profitable trades, exceeded your expectation.
A For broker BB001, the number of trades (the trials) was n = 12, and 3 were 
profitable. You are asked to calculate the probability of three or fewer 
profitable trades, F(3) = p(3) + p(2) + p(1) + p(0).
 Suppose the underlying probability of a profitable trade with BB001 is p = 
0.50. With n = 12 and p = 0.50, according to Equation 1 the probability of

three profitable trades is
pn
xppx nx313120500 50
12
12 33039()=

 −() =()() ()
=−()−..
!
!!.5 50 220 0 000244 0 05371112= () = ..
5 Of course, you need to adjust for the direction of the overall market after the trade (any broker’s record 
will be helped by a bull market) and perhaps make other risk adjustments. Assume that these adjustments 

Discrete Random Variables 533
 The probability of exactly 3 profitable trades out of 12 is 5.4 percent if 
broker BB001 were giving you fair prices. Now you need to calculate the 
other probabilities:
p(2) = [12!/(12 – 2)!2!](0.502)(0.5010) = 66(0.000244) = 0.016113
p(1) = [12!/(12 – 1)!1!](0.501)(0.5011) = 12(0.000244) = 0.00293
p(0) = [12!/(12 – 0)!0!](0.500)(0.5012) = 1(0.000244) = 0.000244
 Adding all the probabilities, F(3) = 0.053711 + 0.016113 + 0.00293 + 
0.000244 = 0.072998 or 7.3 percent. The probability of doing 3 or fewer 
profitable trades out of 12 would be 7.3 percent if your trading desk were 
getting fair prices from broker BB001.
B For broker BB002, you are assessing the probability that the underlying 
probability of a profitable trade with this broker was 50 percent, despite 
the good results. The question was framed as the probability of doing five 
or more profitable trades if the underlying probability is 50 percent: 1 −

F(4) = p(5) + p(6) + p(7) + p(8). You could calculate F(4) and subtract it 
from 1, but you can also calculate p(5) + p(6) + p(7) + p(8) directly.
 You begin by calculating the probability that exactly 5 out of 8 trades 
would be profitable if BB002 were giving you fair prices:
p58
50500 50
56 0 003906 0 2187553()=

() ()
= () =..
..
 The probability is about 21.9 percent. The other probabilities are
p(6) = 28(0.003906) = 0.109375
p(7) = 8(0.003906) = 0.03125
p(8) = 1(0.003906) = 0.003906
 So p(5) + p(6) + p(7) + p(8) = 0.21875 + 0.109375 + 0.03125 + 0.003906 = 
0.363281 or 36.3 percent.6 A 36.3 percent probability is substantial; the 
underlying probability of executing a fair trade with BB002 might well 
have been 0.50 despite your success with BB002 in November 2014. If one 
of the trades with BB002 had been reclassified from profitable to unprofit -
able, exactly half the trades would have been profitable. In summary, your

trading desk is getting at least fair prices from BB002; you will probably 
want to accumulate additional evidence before concluding that you are 
trading at better-  than-  fair prices.
 The magnitude of the profits and losses in these trades is another import -
ant consideration. If all profitable trades had small profits but all unprof -
itable trades had large losses, for example, you might lose money on your 
trades even if the majority of them were profitable.
In the next example, the binomial distribution helps in evaluating the performance 
of an investment manager.
6 In this example all calculations were worked through by hand, but binomial probability and cdf functions 
are also available in computer spreadsheet programs.

Reading 10 ■ Common Probability Distributions 534
EXAMPLE 5   
Meeting a Tracking Objective
You work for a pension fund sponsor. You have assigned a new money man -
ager to manage a $500 million portfolio indexed on the MSCI EAFE (Europe, 
Australasia, and Far East) Index, which is designed to measure developed-  market 
equity performance excluding the United States and Canada. After research, you 
believe it is reasonable to expect that the manager will keep portfolio return 
within a band of 75 basis points (bps) of the benchmark’s return, on a quarterly 
basis.7 To quantify this expectation further, you will be satisfied if portfolio 
return is within the 75 bps band 90 percent of the time. The manager meets 
the objective in six out of eight quarters. Of course, six out of eight quarters is 
a 75 percent success rate. But how does the manager’s record precisely relate 
to your expectation of a 90 percent success rate and the sample size, 8 obser -

vations? To answer this question, you must find the probability that, given an 
assumed true or underlying success rate of 90 percent, performance could be 
as bad as or worse than that delivered. Calculate the probability (by hand or 
with a spreadsheet).
Specifically, you want to find the probability that portfolio return is within 
the 75 bps band in six or fewer quarters out of the eight in the sample. With 
n = 8 and p = 0.90, this probability is F(6) = p(6) + p(5) + p(4) + p(3) + p(2) + 
p(1) + p(0). Start with
p(6) = (8!/6!2!)(0.906)(0.102) = 28(0.005314) = 0.148803
and work through the other probabilities:
p(5) = (8!/5!3!)(0.905)(0.103) = 56(0.00059) = 0.033067
p(4) = (8!/4!4!)(0.904)(0.104) = 70(0.000066) = 0.004593
p(3) = (8!/3!5!)(0.903)(0.105) = 56(0.000007) = 0.000408
p(2) = (8!/2!6!)(0.902)(0.106) = 28(0.000001) = 0.000023
p(1) = (8!/1!7!)(0.901)(0.107) = 8(0.00000009) = 0.00000072
p(0) = (8!/0!8!)(0.900)(0.108) = 1(0.00000001) = 0.00000001

Summing all these probabilities, you conclude that F(6) = 0.148803  + 
0.033067  + 0.004593  + 0.000408  + 0.000023  + 0.00000072  + 0.00000001  = 
0.186895 or 18.7 percent. There is a moderate 18.7 percent probability that the 
manager would show the record he did (or a worse record) if he had the skill to 
meet your expectations 90 percent of the time.
You can use other evaluation concepts such as tracking error or tracking 
risk, defined as the standard deviation of return differences between a portfolio 
and its benchmark, to assess the manager’s performance. The calculation above 
would be only one input into any conclusions that you reach concerning the 
manager’s performance. But to answer problems involving success rates, you 
need to be skilled in using the binomial distribution.
7 A basis point is one-  hundredth of 1 percent (0.01 percent).

Discrete Random Variables 535
Two descriptors of a distribution that are often used in investments are the 
mean and the variance (or the standard deviation, the positive square root of vari -
ance).8 Table 4 gives the expressions for the mean and variance of binomial random 
Table 4   Mean and Variance of Binomial Random Variables
Mean Variance
Bernoulli, B(1, p) p p(1 − p)
Binomial, B(n, p) np np(1 − p)
Because a single Bernoulli random variable, Y ~ B(1, p), takes on the value 1 with 
probability p and the value 0 with probability 1 − p, its mean or weighted-  average 
outcome is p. Its variance is p(1 − p).9 A general binomial random variable, B(n, p), 
is the sum of n Bernoulli random variables, and so the mean of a B(n, p) random 
variable is np. Given that a B(1, p) variable has variance p(1 − p), the variance of a 
B(n, p) random variable is n times that value, or np(1 − p), assuming that all the trials

(Bernoulli random variables) are independent. We can illustrate the calculation for 
two binomial random variables with differing probabilities as follows:
Random Variable Mean Variance
B(n = 5, p = 0.50) 2.50 = 5(0.50) 1.25 = 5(0.50)(0.50)
B(n = 5, p = 0.10) 0.50 = 5(0.10) 0.45 = 5(0.10)(0.90)
For a B(n = 5, p = 0.50) random variable, the expected number of successes is 2.5 with 
a standard deviation of 1.118 = (1.25)1/2; for a B(n = 5, p = 0.10) random variable, the 
expected number of successes is 0.50 with a standard deviation of 0.67 = (0.45)1/2.
EXAMPLE 6   
The Expected Number of Defaults in a Bond Portfolio
Suppose as a bond analyst you are asked to estimate the number of bond issues 
expected to default over the next year in an unmanaged high-  yield bond port -
folio with 25 US issues from distinct issuers. The credit ratings of the bonds 
in the portfolio are tightly clustered around Moody’s B2/Standard & Poor’s

B, meaning that the bonds are speculative with respect to the capacity to pay 
interest and repay principal. The estimated annual default rate for B2/B rated 
bonds is 10.7 percent.
1 Over the next year, what is the expected number of defaults in the portfo -
lio, assuming a binomial model  for defaults?
2 Estimate the standard deviation of the number of defaults over the com -
ing year.
3 Critique the use of the binomial probability model in this context.
8 The mean (or arithmetic mean) is the sum of all values in a distribution or dataset, divided by the number 
of values summed. The variance is a measure of dispersion about the mean. See the reading on statistical 
concepts and market returns for further details on these concepts.
9 We can show that p(1 − p) is the variance of a Bernoulli random variable as follows, noting that a Bernoulli 
random variable can take on only one of two values, 1 or 0: σ2(Y) = E[(Y − EY)2] = E[(Y − p)2] = (1 − p)2 p

Reading 10 ■ Common Probability Distributions 536
For each bond, we can define a Bernoulli random variable equal to 1 if the 
bond defaults during the year and zero otherwise. With 25 bonds, the expected 
number of defaults over the year is np = 25(0.107) = 2.675 or approximately 3.
The variance is np(1 − p) = 25(0.107)(0.893) = 2.388775. The standard deviation 
is (2.388775)1/2 = 1.55. Thus a two standard deviation confidence interval about 
the expected number of defaults would run from approximately 0 to approxi -
mately 6, for example.
An assumption of the binomial model is that the trials are independent. In this 
context, a trial relates to whether an individual bond issue will default over the 
next year. Because the issuing companies probably share exposure to common 
economic factors, the trials may not be independent. Nevertheless, for a quick 
estimate of the expected number of defaults, the binomial model may be adequate.

Earlier, we looked at a simple one-  period model for stock price movement. Now 
we extend the model to describe stock price movement on three consecutive days. 
Each day is an independent trial. The stock moves up with constant probability p (the 
up transition probability ); if it moves up, u is 1 plus the rate of return for an up 
move. The stock moves down with constant probability 1 − p (the down transition 
probability ); if it moves down, d is 1 plus the rate of return for a down move. We 
graph stock price movement in Figure 2, where we now associate each of the n = 3 
stock price moves with time indexed by t. The shape of the graph suggests why it is a 
called a binomial tree . Each boxed value from which successive moves or outcomes 
branch in the tree is called a node ; in this example, a node is potential value for the 
stock price at a specified time.
Figure 2   A Binomial Model of Stock Price Movement
t = 0
SuSuuS
udS
dddSddSuddSuudSuuuS
dSt = 1 t = 2 t = 3

SuSuuS
udS
We see from the tree that the stock price at t = 3 has four possible values: uuuS , 
uudS , uddS , and dddS . The probability that the stock price equals any one of these four 
values is given by the binomial distribution. For example, three sequences of moves 
result in a final stock price of uudS : These are uud, udu, and duu. These sequences 
have two up moves out of three moves in total; the combination formula confirms 
that the number of ways to get two up moves (successes) in three periods (trials)

Continuous Random Variables 537
is 3!/(3 − 2)!2! = 3. Next note that each of these sequences, uud, udu, and duu, has 
probability p2(1 − p). So P(S3 = uudS ) = 3 p2(1 − p), where S3 indicates the stock’s 
price after three moves.
The binomial random variable in this application is the number of up moves. Final 
stock price distribution is a function of the initial stock price, the number  of up moves, 
and the size of the up moves and down moves. We cannot say that stock price itself is 
a binomial random variable; rather, it is a function of a binomial random variable, as 
well as of u and d, and initial price. This richness is actually one key to why this way 
of modeling stock price is useful: It allows us to choose values of these parameters 
to approximate various distributions for stock price (using a large number of time 
periods).10 One distribution that can be approximated is the lognormal, an important

continuous distribution model for stock price that we will discuss later. The flexibility 
extends further. In the tree shown above, the transition probabilities are the same 
at each node: p for an up move and 1 − p for a down move. That standard formula 
describes a process in which stock return volatility is constant through time. Option 
experts, however, sometimes model changing volatility through time using a binomial 
tree in which the probabilities for up and down moves differ at different nodes.
The binomial tree also supplies the possibility of testing a condition or contin -
gency at any node. This flexibility is useful in investment applications such as option 
pricing. Consider an American call option on a dividend-  paying stock. (Recall that 
an American option can be exercised at any time before expiration, at any node on 
the tree.) Just before an ex-  dividend date, it may be optimal to exercise an American

call option on stock to buy the stock and receive the dividend.11 If we model stock 
price with a binomial tree, we can test, at each node, whether exercising the option 
is optimal. Also, if we know the value of the call at the four terminal nodes at t = 3 
and we have a model for discounting values by one period, we can step backward 
one period to t = 2 to find the call’s value at the three nodes there. Continuing back 
recursively, we can find the call’s value today. This type of recursive operation is easily 
programmed on a computer. As a result, binomial trees can value options even more 
complex than American calls on stock.12
CONTINUOUS RANDOM VARIABLES
In the previous section, we considered discrete random variables (i.e., random variables 
whose set of possible outcomes is countable). In contrast, the possible outcomes of 
continuous random variables are never countable. If 1.250 is one possible value of a

continuous random variable, for example, we cannot name the next higher or lower 
possible value. Technically, the range of possible outcomes of a continuous random 
variable is the real line (all real numbers between −∞ and +∞) or some subset of the 
real line.
In this section, we focus on the two most important continuous distributions in 
investment work, the normal and lognormal. As we did with discrete distributions, 
we introduce the topic through the uniform distribution.3
10 For example, we can split 20 days into 100 subperiods, taking care to use compatible values for u and d.
11 Cash dividends represent a reduction of a company’s assets. Early exercise may be optimal because 
the exercise price of options is typically not reduced by the amount of cash dividends, so cash dividends 
negatively affect the position of an American call option holder .
12 See Chance and Brooks (2016) for more information on option pricing models.

Reading 10 ■ Common Probability Distributions 538
3.1 Continuous Uniform Distribution
The continuous uniform distribution is the simplest continuous probability distri -
bution. The uniform distribution has two main uses. As the basis of techniques for 
generating random numbers, the uniform distribution plays a role in Monte Carlo 
simulation. As the probability distribution that describes equally likely outcomes, the 
uniform distribution is an appropriate probability model to represent a particular kind 
of uncertainty in beliefs in which all outcomes appear equally likely.
The pdf for a uniform random variable is
fx baax b()= −<<

1
0 for 
otherwis e
For example, with a = 0 and b = 8, f(x) = 1/8 or 0.125. We graph this density in Figure 3.
Figure 3   Continuous Uniform Distribution
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0
3 2 1 0 4 5 6 7 8 9f(x)
x
The graph of the density function plots as a horizontal line with a value of 0.125.

What is the probability that a uniform random variable with limits a = 0 and b = 8 
is less than or equal to 3, or F(3) = P(X ≤ 3)? When we were working with the discrete 
uniform random variable with possible outcomes 1, 2, …, 8, we summed individual 
probabilities: p(1) + p(2) + p(3) = 0.375. In contrast, the probability that a continuous 
uniform random variable, or any continuous random variable, assumes any given 
fixed value is 0. To illustrate this point, consider the narrow interval 2.510 to 2.511. 
Because that interval holds an infinity of possible values, the sum of the probabilities 
of values in that interval alone would be infinite if each individual value in it had a 
positive probability. To find the probability F(3), we find the area under the curve 
graphing the pdf, between 0 to 3 on the x axis. In calculus, this operation is called 
integrating the probability function f(x) from 0 to 3. This area under the curve is a

rectangle with base 3 − 0 = 3 and height 1/8. The area of this rectangle equals base 
times height: 3(1/8) = 3/8 or 0.375. So F(3) = 3/8 or 0.375.

Continuous Random Variables 539
The interval from 0 to 3 is three-  eighths of the total length between the limits of 
0 and 8, and F(3) is three-  eighths of the total probability of 1. The middle line of the 
expression for the cdf captures this relationship.
Fxxa
xa
baax b
xb()=≤
−
−<<
≥


0
1 for 
 for 
 for 
For our problem, F(x) = 0 for x ≤ 0, F(x) = x/8 for 0 < x < 8, and F(x) = 1 for x ≥ 8. We 
graph this cdf in Figure 4.
Figure 4   Continuous Uniform Cumulative Distribution
1.0
0.8
0.6
0.4
0.2
0
0 3 4 5 6 7 8 9CDF
x1 2
The mathematical operation that corresponds to finding the area under the curve 
of a pdf f(x) from a to b is the integral of f(x) from a to b:
Pa Xb fxdxab≤≤() = ()∫
where ∫ dx is the symbol for summing ∫ over small changes dx, and the limits of inte -
gration ( a and b) can be any real numbers or −∞ and +∞. All probabilities of continuous 
random variables can be computed using Equation 2. For the uniform distribution

example considered above, F(7) is Equation 2 with lower limit a = 0 and upper limit 
b = 7. The integral corresponding to the cdf of a uniform distribution reduces to the 
three-  line expression given previously. To evaluate Equation  2 for nearly all other 
continuous distributions, including the normal and lognormal, we rely on spreadsheet 
functions, computer programs, or tables of values to calculate probabilities. Those 
tools use various numerical methods to evaluate the integral in Equation 2.
Recall that the probability of a continuous random variable equaling any fixed 
point is 0. This fact has an important consequence for working with the cumulative 
distribution function of a continuous random variable: For any continuous random 
variable X, P(a ≤ X ≤ b) = P(a < X ≤ b) = P(a ≤ X < b) = P(a < X < b), because the prob -
abilities at the endpoints a and b are 0. For discrete random variables, these relations 
of equality are not true, because probability accumulates at points.(2)

Reading 10 ■ Common Probability Distributions 540
EXAMPLE 7   
Probability That a Lending Facility Covenant Is Breached
You are evaluating the bonds of a below-  investment-  grade borrower at a low 
point in its business cycle. You have many factors to consider, including the 
terms of the company’s bank lending facilities. The contract creating a bank 
lending facility such as an unsecured line of credit typically has clauses known 
as covenants. These covenants place restrictions on what the borrower can do. 
The company will be in breach of a covenant in the lending facility if the interest 
coverage ratio, EBITDA/interest, calculated on EBITDA over the four trailing 
quarters, falls below 2.0. EBITDA is earnings before interest, taxes, depreciation, 
and amortization.13 Compliance with the covenants will be checked at the end 
of the current quarter. If the covenant is breached, the bank can demand imme -
diate repayment of all borrowings on the facility. That action would probably

trigger a liquidity crisis for the company. With a high degree of confidence, you 
forecast interest charges of $25 million. Your estimate of EBITDA runs from 
$40 million on the low end to $60 million on the high end.
Address two questions (treating projected interest charges as a constant):
1 If the outcomes for EBITDA are equally likely, what is the probability that 
EBITDA/interest will fall below 2.0, breaching the covenant?
2 Estimate the mean and standard deviation of EBITDA/interest. For a con -
tinuous uniform random variable, the mean is given by μ = ( a + b)/2 and 
the variance is given by σ2 = (b − a)2/12.
EBITDA/interest is a continuous uniform random variable because all outcomes 
are equally likely. The ratio can take on values between 1.6  = ($40  million)/
($25 million) on the low end and 2.4 = ($60 million/$25 million) on the high 
end. The range of possible values is 2.4 − 1.6 = 0.8. What fraction of the possible

values falls below 2.0, the level that triggers default? The distance between 2.0 
and 1.6 is 0.40; the value 0.40 is one-  half the total length of 0.8, or 0.4/0.8 = 0.50. 
So the probability that the covenant will be breached is 50 percent.
In Solution 1, we found that the lower limit of EBITDA/interest is 1.6. This lower 
limit is a. We found that the upper limit is 2.4. This upper limit is b. Using the 
formula given above,
μ = ( a + b)/2 = (1.6 + 2.4)/2 = 2.0
The variance of the interest coverage ratio is
σ2 = (b – a)2/12 = (2.4 – 1.6)2/12 = 0.053333
The standard deviation is the positive square root of the variance, 0.230940 = 
(0.053333)1/2. The standard deviation is not particularly useful as a risk measure 
for a uniform distribution, however. The probability that lies within various stan -
dard deviation bands around the mean is sensitive to different specifications of 
the upper and lower limits (although Chebyshev’s inequality is always satisfied).14

Here, a one standard deviation interval around the mean of 2.0 runs from 1.769 
13 For a detailed discussion on EBITDA, see the Level I CFA Program curriculum reading “Financial 
Reporting Quality. ”
14 Chebyshev’s inequality is discussed in the reading on statistical concepts and market returns.

Continuous Random Variables 541
to 2.231 and captures 0.462/0.80 = 0.5775 or 57.8 percent of the probability. A 
two standard deviation interval runs from 1.538 to 2.462, which extends past 
both the lower and upper limits of the random variable.
3.2 The Normal Distribution
The normal distribution may be the most extensively used probability distribution in 
quantitative work. It plays key roles in modern portfolio theory and in a number of 
risk management technologies. Because it has so many uses, the normal distribution 
must be thoroughly understood by investment professionals.
The role of the normal distribution in statistical inference and regression analysis 
is vastly extended by a crucial result known as the central limit theorem. The central 
limit theorem states that the sum (and mean) of a large number of independent ran -
dom variables is approximately normally distributed.15
The French mathematician Abraham de Moivre (1667–1754) introduced the

normal distribution in 1733 in developing a version of the central limit theorem. As 
Figure 5 shows, the normal distribution is symmetrical and bell-  shaped. The range of 
possible outcomes of the normal distribution is the entire real line: all real numbers 
lying between −∞ and +∞. The tails of the bell curve extend without limit to the left 
and to the right.
Figure 5   Two Normal Distributions
–8 –4 –6 –2 8 6 4 2 0
xpdf with
m = 0, s = 1
pdf with
m = 0, s = 2
The defining characteristics of a normal distribution are as follows:
■■The normal distribution is completely described by two parameters—its mean, 
μ, and variance, σ2. We indicate this as X ~ N(μ, σ2) (read “ X follows a normal 
distribution with mean μ and variance σ2”). We can also define a normal distri -
bution in terms of the mean and the standard deviation, σ (this is often conve -
nient because σ is measured in the same units as X and μ). As a consequence,

we can answer any probability question about a normal random variable if we 
know its mean and variance (or standard deviation).
15 The central limit theorem is discussed further in the reading on sampling.

Reading 10 ■ Common Probability Distributions 542
■■The normal distribution has a skewness of 0 (it is symmetric). The normal dis -
tribution has a kurtosis of 3; its excess kurtosis (kurtosis − 3.0) equals 0.16 As a 
consequence of symmetry, the mean, median, and the mode are all equal for a 
normal random variable.
■■A linear combination of two or more normal random variables is also normally 
These bullet points concern a single variable or univariate normal distribution: 
the distribution of one normal random variable. A univariate distribution  describes 
a single random variable. A multivariate distribution  specifies the probabilities for 
a group of related random variables. You will encounter the multivariate normal 
distribution  in investment work and reading and should know the following about it.
When we have a group of assets, we can model the distribution of returns on each 
asset individually, or the distribution of returns on the assets as a group. “ As a group”

means that we take account of all the statistical interrelationships among the return 
series. One model that has often been used for security returns is the multivariate 
normal distribution. A multivariate normal distribution for the returns on n stocks 
is completely defined by three lists of parameters:
■■the list of the mean returns on the individual securities ( n means in total);
■■the list of the securities’ variances of return ( n variances in total); and
■■the list of all the distinct pairwise return correlations: n(n − 1)/2 distinct cor -
relations in total.17
The need to specify correlations is a distinguishing feature of the multivariate normal 
distribution in contrast to the univariate normal distribution.
The statement “assume returns are normally distributed” is sometimes used to 
mean a joint normal distribution. For a portfolio of 30 securities, for example, portfolio 
return is a weighted average of the returns on the 30 securities. A weighted average is

a linear combination. Thus, portfolio return is normally distributed if the individual 
security returns are (joint) normally distributed. To review, in order to specify the 
normal distribution for portfolio return, we need the means, variances, and the distinct 
pairwise correlations of the component securities.
With these concepts in mind, we can return to the normal distribution for one 
random variable. The curves graphed in Figure 5 are the normal density function:
fxxx ()=−−()



−∞ << +∞1
2 22
2σπµ
σexp for
The two densities graphed in Figure 5 correspond to a mean of μ = 0 and standard 
deviations of σ = 1 and σ = 2. The normal density with μ = 0 and σ = 1 is called the 
standard normal distribution  (or unit normal distribution ). Plotting two normal 
distributions with the same mean and different standard deviations helps us appreciate 
why standard deviation is a good measure of dispersion for the normal distribution:

Observations are much more concentrated around the mean for the normal distri -
bution with σ = 1 than for the normal distribution with σ = 2.(3)
16 If we have a sample of size n from a normal distribution, we may want to know the possible variation 
in sample skewness and kurtosis. For a normal random variable, the standard deviation of sample skewness 
is 6/ n and the standard deviation of sample kurtosis is 24/ n.
17 For example, a distribution with two stocks (a bivariate normal distribution) has two means, two 
variances, and one correlation: 2(2 − 1)/2. A distribution with 30 stocks has 30 means, 30 variances, and 
435 distinct correlations: 30(30 − 1)/2. The return correlation of Dow Chemical with American Express 
stock is the same as the correlation of American Express with Dow Chemical stock, so these are counted 
as one distinct correlation.

Continuous Random Variables 543
Although not literally accurate, the normal distribution can be considered an 
approximate model for returns. Nearly all the probability of a normal random vari -
able is contained within three standard deviations of the mean. For realistic values of 
mean return and return standard deviation for many assets, the normal probability 
of outcomes below −100 percent is very small. Whether the approximation is useful 
in a given application is an empirical question. For example, the normal distribution 
is a closer fit for quarterly and yearly holding period returns on a diversified equity 
portfolio than it is for daily or weekly returns.18 A persistent departure from normality 
in most equity return series is kurtosis greater than 3, the fat-  tails problem. So when 
we approximate equity return distributions with the normal distribution, we should be 
aware that the normal distribution tends to underestimate the probability of extreme

returns.19 Option returns are skewed. Because the normal is a symmetrical distribu -
tion, we should be cautious in using the normal distribution to model the returns on 
portfolios containing significant positions in options.
The normal distribution, however, is less suitable as a model for asset prices than as 
a model for returns. A normal random variable has no lower limit. This characteristic 
has several implications for investment applications. An asset price can drop only to 
0, at which point the asset becomes worthless. As a result, practitioners generally do 
not use the normal distribution to model the distribution of asset prices. Also note 
that moving from any level of asset price to 0 translates into a return of −100 percent. 
Because the normal distribution extends below 0 without limit, it cannot be literally 
accurate as a model for asset returns.
Having established that the normal distribution is the appropriate model for a

variable of interest, we can use it to make the following probability statements:
■■Approximately 50 percent of all observations fall in the interval μ ± (2/3)σ.
■■Approximately 68 percent of all observations fall in the interval μ ± σ.
■■Approximately 95 percent of all observations fall in the interval μ ± 2σ.
■■Approximately 99 percent of all observations fall in the interval μ ± 3σ.
One, two, and three standard deviation intervals are illustrated in Figure 6. The intervals 
indicated are easy to remember but are only approximate for the stated probabilities. 
More-  precise intervals are μ ± 1.96σ for 95 percent of the observations and μ ± 2.58σ 
for 99 percent of the observations.
18 See Fama (1976) and Campbell, Lo, and MacKinlay (1997).
19 Fat tails can be modeled by a mixture of normal random variables or by a Student’s t-distribution with 
a relatively small number of degrees of freedom. See Kon (1984) and Campbell, Lo, and MacKinlay (1997).

We discuss the Student’s t-distribution in the reading on sampling and estimation.

Reading 10 ■ Common Probability Distributions 544
Figure 6   Units of Standard Deviation
2.14% 2.14% 13.59% 13.59% 34.13% 34.13%
–3s –1s 1s 2s 3s –2s m
In general, we do not observe the population mean or the population standard 
deviation of a distribution, so we need to estimate them.20 We estimate the population 
mean, μ, using the sample mean,  X(sometimes denoted as  ∝) and estimate the pop -
ulation standard deviation, σ, using the sample standard deviation, s (sometimes 
denoted as  σ).
There are as many different normal distributions as there are choices for mean (μ) 
and variance (σ2). We can answer all of the above questions in terms of any normal 
distribution. Spreadsheets, for example, have functions for the normal cdf for any 
specification of mean and variance. For the sake of efficiency, however, we would like 
to refer all probability statements to a single normal distribution. The standard normal 
distribution (the normal distribution with μ = 0 and σ = 1) fills that role.

There are two steps in standardizing  a random variable X: Subtract the mean 
of X from X, then divide that result by the standard deviation of X. If we have a list 
of observations on a normal random variable, X, we subtract the mean from each 
observation to get a list of deviations from the mean, then divide each deviation by 
the standard deviation. The result is the standard normal random variable, Z. (Z is the 
conventional symbol for a standard normal random variable.) If we have X ~ N(μ,σ2) 
(read “ X follows the normal distribution with parameters μ and σ2”), we standardize 
it using the formula
Z = (X – μ)/σ  
Suppose we have a normal random variable, X, with μ = 5 and σ = 1.5. We standard -
ize X with Z = (X − 5)/1.5. For example, a value X = 9.5 corresponds to a standardized 
value of 3, calculated as Z = (9.5 − 5)/1.5 = 3. The probability that we will observe a 
value as small as or smaller than 9.5 for X ~ N(5,1.5) is exactly the same as the proba -

bility that we will observe a value as small as or smaller than 3 for Z ~ N(0,1). We can 
answer all probability questions about X using standardized values and probability 
tables for Z. We generally do not know the population mean and standard deviation, 
so we often use the sample mean  X for μ and the sample standard deviation s for σ.(4)
20 A population is all members of a specified group, and the population mean is the arithmetic mean 
computed for the population. A sample is a subset of a population, and the sample mean is the arithmetic 
mean computed for the sample. For more information on these concepts, see the reading on statistical 

Continuous Random Variables 545
Standard normal probabilities can also be computed with spreadsheets, statistical 
and econometric software, and programming languages. Tables of the cumulative 
distribution function for the standard normal random variable are in the back of this 
book. Table 5 shows an excerpt from those tables. N(x) is a conventional notation for 
the cdf of a standard normal variable.21
Table 5    P(Z ≤ x) = N(x) for x ≥ 0 or P(Z ≤ z) = N(z) for z ≥ 0 
x or z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.00 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359
0.10 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753
0.20 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141
0.30 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517
0.40 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879
0.50 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224

To find the probability that a standard normal variable is less than or equal to 0.24, 
for example, locate the row that contains 0.20, look at the 0.04 column, and find the 
entry 0.5948. Thus, P(Z ≤ 0.24) = 0.5948 or 59.48 percent.
The following are some of the most frequently referenced values in the standard 
normal table:
■■The 90th percentile point is 1.282: P(Z ≤ 1.282) = N(1.282) = 0.90 or 90 percent, 
and 10 percent of values remain in the right tail.
■■The 95th percentile point is 1.65: P(Z ≤ 1.65) = N(1.65) = 0.95 or 95 percent, 
and 5 percent of values remain in the right tail. Note the difference between 
the use of a percentile point when dealing with one tail rather than two tails. 
Earlier, we used 1.65 standard deviations for the 90 percent confidence interval, 
where 5 percent of values lie outside that interval on each of the two sides. Here 
we use 1.65 because we are concerned with the 5 percent of values that lie only 
on one side, the right tail.

■■The 99th percentile point is 2.327: P(Z ≤ 2.327) = N(2.327) = 0.99 or 99 percent, 
and 1 percent of values remain in the right tail.
The tables that we give for the normal cdf include probabilities for x ≤ 0. Many 
sources, however, give tables only for x ≥ 0. How would one use such tables to find 
a normal probability? Because of the symmetry of the normal distribution, we can 
find all probabilities using tables of the cdf of the standard normal random variable, 
P(Z ≤ x) = N(x), for x ≥ 0. The relations below are helpful for using tables for x ≥ 0, 
as well as in other uses:
■■For a non-  negative number x, use N(x) from the table. Note that for the proba -
bility to the right of x, we have P(Z ≥ x) = 1.0 − N(x).
■■For a negative number − x, N(−x) = 1.0 − N(x): Find N(x) and subtract it from 
1. All the area under the normal curve to the left of x is N(x). The balance, 
1.0 − N(x), is the area and probability to the right of x. By the symmetry of the

normal distribution around its mean, the area and the probability to the right of 
x are equal to the area and the probability to the left of − x, N(−x).
■■For the probability to the right of − x, P(Z ≥ −x) = N(x).
21 Another often-  seen notation for the cdf of a standard normal variable is Φ( x).

Reading 10 ■ Common Probability Distributions 546
EXAMPLE 8   
Probabilities for a Common Stock Portfolio
Assume the portfolio mean return is 12 percent and the standard deviation of 
return estimate is 22 percent per year.
You want to calculate the following probabilities, assuming that a normal 
distribution describes returns. (You can use the excerpt from the table of normal 
probabilities to answer these questions.)
1 What is the probability that portfolio return will exceed 20 percent?
2 What is the probability that portfolio return will be between 12 percent 
and 20 percent? In other words, what is P(12% ≤ Portfolio return ≤ 20%)?
3 You can buy a one-  year T-  bill that yields 5.5 percent. This yield is effec -
tively a one-  year risk-  free interest rate. What is the probability that your 
portfolio’s return will be equal to or less than the risk-  free rate?
If X is portfolio return, standardized portfolio return is Z = (X – X )/s = (X –

12%)/22%. We use this expression throughout the solutions.
For X = 20%, Z = (20% − 12%)/22% = 0.363636. You want to find P(Z > 0.363636). 
First note that P(Z > x) = P(Z ≥ x) because the normal is a continuous distri -
bution. Recall that P(Z ≥ x) = 1.0 − P(Z ≤ x) or 1 − N(x). Rounding 0.363636 to 
0.36, according to the table, N(0.36) = 0.6406. Thus, 1 − 0.6406 = 0.3594. The 
probability that portfolio return will exceed 20 percent is about 36 percent if 
your normality assumption is accurate.
P(12% ≤ Portfolio return ≤ 20%) = N(Z corresponding to 20%) − N(Z correspond -
ing to 12%). For the first term, Z = (20% − 12%)/22% = 0.36 approximately, and 
N(0.36) = 0.6406 (as in Solution 1). To get the second term immediately, note 
that 12 percent is the mean, and for the normal distribution 50 percent of the 
probability lies on either side of the mean. Therefore, N(Z corresponding to 12%) 
must equal 50 percent. So P(12% ≤ Portfolio return ≤ 20%) = 0.6406 − 0.50 =

0.1406 or approximately 14 percent.
If X is portfolio return, then we want to find P(Portfolio return ≤ 5.5%). This 
question is more challenging than Parts 1 or 2, but when you have studied the 
solution below you will have a useful pattern for calculating other shortfall 
There are three steps, which involve standardizing the portfolio return: First, 
subtract the portfolio mean return from each side of the inequality: P(Portfolio 
return − 12% ≤ 5.5% − 12%). Second, divide each side of the inequality by the 
standard deviation of portfolio return: P[(Portfolio return − 12%)/22% ≤ (5.5% 
− 12%)/22%] = P(Z ≤ −0.295455) = N(−0.295455). Third, recognize that on the 
left- hand side we have a standard normal variable, denoted by Z. As we pointed 
out above, N(−x) = 1 − N(x). Rounding −0.29545 to −0.30 for use with the 
excerpted table, we have N(−0.30) = 1 − N(0.30) = 1 − 0.6179 = 0.3821, roughly

38 percent. The probability that your portfolio will underperform the one-  year 
risk-  free rate is about 38 percent.
We can get the answer above quickly by subtracting the mean portfolio 
return from 5.5 percent, dividing by the standard deviation of portfolio return, 
and evaluating the result (−0.295455) with the standard normal cdf.

Continuous Random Variables 547
3.3 Applications of the Normal Distribution
Modern portfolio theory (MPT) makes wide use of the idea that the value of investment 
opportunities can be meaningfully measured in terms of mean return and variance of 
return. In economic theory, mean–variance analysis  holds exactly when investors 
are risk averse; when they choose investments so as to maximize expected utility, or 
satisfaction; and when either 1) returns are normally distributed, or 2) investors have 
quadratic utility functions.22 Mean–variance analysis can still be useful, however—that 
is, it can hold approximately—when either assumption 1 or 2 is violated. Because prac -
titioners prefer to work with observables such as returns, the proposition that returns 
are at least approximately normally distributed has played a key role in much of MPT.
Mean–variance analysis generally considers risk symmetrically in the sense that

standard deviation captures variability both above and below the mean.23 An alternative 
approach evaluates only downside risk. We discuss one such approach, safety-  first 
rules, as it provides an excellent illustration of the application of normal distribution 
theory to practical investment problems. Safety-  first rules  focus on shortfall risk , 
the risk that portfolio value will fall below some minimum acceptable level over some 
time horizon. The risk that the assets in a defined benefit plan will fall below plan 
liabilities is an example of a shortfall risk.
Suppose an investor views any return below a level of RL as unacceptable. Roy’s 
safety-  first criterion states that the optimal portfolio minimizes the probability that 
portfolio return, RP, falls below the threshold level, RL.24 In symbols, the investor’s 
objective is to choose a portfolio that minimizes P(RP < RL). When portfolio returns 
are normally distributed, we can calculate P(RP < RL) using the number of standard

deviations that RL lies below the expected portfolio return, E(RP). The portfolio for 
which E(RP) − RL is largest relative to standard deviation minimizes P(RP < RL). 
Therefore, if returns are normally distributed, the safety-  first optimal portfolio max -
imizes  the safety-  first ratio (SFRatio):
SFRatio = [ E(RP) – RL]/σP
The quantity E(RP) − RL is the distance from the mean return to the shortfall level. 
Dividing this distance by σP gives the distance in units of standard deviation. There are 
two steps in choosing among portfolios using Roy’s criterion (assuming normality):25
1 Calculate each portfolio’s SFRatio.
2 Choose the portfolio with the highest SFRatio.
For a portfolio with a given safety-  first ratio, the probability that its return will be 
less than RL is N(−SFRatio), and the safety-  first optimal portfolio has the lowest such 
probability. For example, suppose an investor’s threshold return, RL, is 2 percent. He

is presented with two portfolios. Portfolio 1 has an expected return of 12 percent with 
a standard deviation of 15 percent. Portfolio 2 has an expected return of 14 percent 
with a standard deviation of 16 percent. The SFRatios are 0.667 = (12 − 2)/15 and 
0.75 = (14 − 2)/16 for Portfolios 1 and 2, respectively. For the superior Portfolio 2, the 
probability that portfolio return will be less than 2 percent is N(−0.75) = 1 − N(0.75) = 
1 − 0.7734 = 0.227 or about 23 percent, assuming that portfolio returns are normally 
22 Utility functions are mathematical representations of attitudes toward risk and return.
23 We shall discuss mean–variance analysis in detail in the readings on portfolio concepts.
24 A.D. Roy (1952) introduced this criterion.
25 If there is an asset offering a risk-  free return over the time horizon being considered, and if RL is less 
than or equal to that risk-  free rate, then it is optimal to be fully invested in the risk-  free asset. Holding the

risk-  free asset in this case eliminates the chance that the threshold return is not met.

Reading 10 ■ Common Probability Distributions 548
You may have noticed the similarity of SFRatio to the Sharpe ratio. If we substitute 
the risk-  free rate, RF, for the critical level RL, the SFRatio becomes the Sharpe ratio. 
The safety-  first approach provides a new perspective on the Sharpe ratio: When we 
evaluate portfolios using the Sharpe ratio, the portfolio with the highest Sharpe ratio 
is the one that minimizes the probability that portfolio return will be less than the 
risk-  free rate (given a normality assumption).
EXAMPLE 9   
The Safety-  First Optimal Portfolio for a Client
You are researching asset allocations for a client in Canada with a C$800,000 
portfolio. Although her investment objective is long-  term growth, at the end of 
a year she may want to liquidate C$30,000 of the portfolio to fund educational 
expenses. If that need arises, she would like to be able to take out the C$30,000 
without invading the initial capital of C$800,000. Table 6 shows three alternative

allocations.
Table 6   Mean and Standard Deviation for Three 
Allocations (in Percent) 
A B C
Expected annual return 25 11 14
Standard deviation of return 27 8 20
Address these questions (assume normality for Parts 2 and 3):
1 Given the client’s desire not to invade the C$800,000 principal, what is the 
shortfall level, RL? Use this shortfall level to answer Part 2.
2 According to the safety-  first criterion, which of the three allocations is the 
best?
3 What is the probability that the return on the safety-  first optimal portfolio 
will be less than the shortfall level?
Because C$30,000/C$800,000 is 3.75 percent, for any return less than 3.75 per -
cent the client will need to invade principal if she takes out C$30,000. So RL = 
3.75 percent.
To decide which of the three allocations is safety-  first optimal, select the alter -
native with the highest ratio [ E(RP) − RL]/σP:
Allocation A: 0.787037 = (25 – 3.75)/27
Allocation B: 0.90625 = (11 – 3.75)/8

Allocation C: 0.5125 = (14 – 3.75)/20
Allocation B, with the largest ratio (0.90625), is the best alternative according 
to the safety-  first criterion.

Continuous Random Variables 549
To answer this question, note that P(RB < 3.75) = N(−0.90625). We can round 
0.90625 to 0.91 for use with tables of the standard normal cdf. First, we calculate 
N(−0.91) = 1 − N(0.91) = 1 − 0.8186 = 0.1814 or about 18.1 percent. Using a 
spreadsheet function for the standard normal cdf on −0.90625 without rounding, 
we get 18.24 percent or about 18.2 percent. The safety-  first optimal portfolio 
has a roughly 18 percent chance of not meeting a 3.75 percent return threshold.
Several points are worth noting. First, if the inputs were even slightly dif -
ferent, we could get a different ranking. For example, if the mean return on B 
were 10 rather than 11 percent, A would be superior to B. Second, if meeting 
the 3.75 percent return threshold were a necessity rather than a wish, C$830,000 
in one year could be modeled as a liability. Fixed income strategies such as cash 
flow matching could be used to offset or immunize the C$830,000 quasi-  liability.

Roy’s safety-  first rule was the earliest approach to addressing shortfall risk. 
The standard mean-  variance portfolio selection process can also accommodate 
a shortfall risk constraint.26
In many investment contexts besides Roy’s safety-  first criterion, we use the nor -
mal distribution to estimate a probability. For example, Kolb, Gay, and Hunter (1985) 
developed an expression based on the standard normal distribution for the probability 
that a futures trader will exhaust his liquidity because of losses in a futures contract. 
Another arena in which the normal distribution plays an important role is financial 
risk management. Financial institutions such as investment banks, security dealers, 
and commercial banks have formal systems to measure and control financial risk at 
various levels, from trading positions to the overall risk for the firm.27 Two mainstays 
in managing financial risk are Value at Risk (VaR) and stress testing/scenario analysis.

Stress testing /scenario analysis , a complement to VaR, refers to a set of techniques 
for estimating losses in extremely unfavorable combinations of events or scenarios. 
Value at Risk  (VaR) is a money measure of the minimum value of losses expected 
over a specified time period (for example, a day, a quarter, or a year) at a given level 
of probability (often 0.05 or 0.01). Suppose we specify a one-  day time horizon and 
a level of probability of 0.05, which would be called a 95 percent one-  day VaR.28 If 
this VaR equaled €5 million for a portfolio, there would be a 0.05 probability that the 
portfolio would lose €5 million or more in a single day (assuming our assumptions 
were correct). One of the basic approaches to estimating VaR, the variance-  covariance 
or analytical method, assumes that returns follow a normal distribution. For more 
information on VaR, see Chance and Brooks (2016).
3.4 The Lognormal Distribution

Closely related to the normal distribution, the lognormal distribution is widely used 
for modeling the probability distribution of share and other asset prices. For exam -
ple, the lognormal appears in the Black–Scholes–Merton option pricing model. The 
Black–Scholes–Merton model assumes that the price of the asset underlying the 
option is lognormally distributed.
26 See Leibowitz and Henriksson (1989), for example.
27 Financial risk  is risk relating to asset prices and other financial variables. The contrast is to other, non -
financial risks (for example, relating to operations and technology), which require different tools to manage.
28 In 95 percent one-  day VaR, the 95 percent refers to the confidence in the value of VaR and is equal to 
1 − 0.05; this is a traditional way to state VaR.

Reading 10 ■ Common Probability Distributions 550
A random variable Y follows a lognormal distribution if its natural logarithm, ln 
Y, is normally distributed. The reverse is also true: If the natural logarithm of random 
variable Y, ln Y, is normally distributed, then Y follows a lognormal distribution. 
If you think of the term lognormal as “the log is normal, ” you will have no trouble 
remembering this relationship.
The two most noteworthy observations about the lognormal distribution are that it 
is bounded below by 0 and it is skewed to the right (it has a long right tail). Note these 
two properties in the graphs of the pdfs of two lognormal distributions in Figure 7. 
Asset prices are bounded from below by 0. In practice, the lognormal distribution 
has been found to be a usefully accurate description of the distribution of prices for 
many financial assets. On the other hand, the normal distribution is often a good

approximation for returns. For this reason, both distributions are very important for 
finance professionals.
Figure 7   Two Lognormal Distributions
0.5 0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
Like the normal distribution, the lognormal distribution is completely described 
by two parameters. Unlike the other distributions we have considered, a lognormal 
distribution is defined in terms of the parameters of a different  distribution. The 
two parameters of a lognormal distribution are the mean and standard deviation (or 
variance) of its associated normal distribution: the mean and variance of ln Y, given 
that Y is lognormal. Remember, we must keep track of two sets of means and stan -
dard deviations (or variances): the mean and standard deviation (or variance) of the 
associated normal distribution (these are the parameters), and the mean and standard 
deviation (or variance) of the lognormal variable itself.
The expressions for the mean and variance of the lognormal variable itself are

challenging. Suppose a normal random variable X has expected value μ and variance 
σ2. Define Y = exp( X). Remember that the operation indicated by exp( X) or eX is the 
opposite operation from taking logs.29 Because ln Y = ln [exp( X)] = X is normal (we 
assume X is normal), Y is lognormal. What is the expected value of Y = exp( X)? A guess 
might be that the expected value of Y is exp(μ). The expected value is actually exp(μ 
+ 0.50σ2), which is larger than exp(μ) by a factor of exp(0.50σ2) > 1.30 To get some 
29 The quantity e ≈ 2.7182818.
30 Note that exp(0.50σ2) > 1 because σ2 > 0.

Continuous Random Variables 551
insight into this concept, think of what happens if we increase σ2. The distribution 
spreads out; it can spread upward, but it cannot spread downward past 0. As a result, 
the center of its distribution is pushed to the right—the distribution’s mean increases.31
The expressions for the mean and variance of a lognormal variable are summarized 
below, where μ and σ2 are the mean and variance of the associated normal distribution 
(refer to these expressions as needed, rather than memorizing them):
■■Mean (μL) of a lognormal random variable = exp(μ + 0.50σ2)
■■Variance (σL2) of a lognormal random variable = exp(2μ + σ2) × [exp(σ2) − 1]
We now explore the relationship between the distribution of stock return and 
stock price. In the following we show that if a stock’s continuously compounded 
return is normally distributed, then future stock price is necessarily lognormally 
distributed.32 Furthermore, we show that stock price may be well described by the

lognormal distribution even when continuously compounded returns do not follow 
a normal distribution. These results provide the theoretical foundation for using the 
lognormal distribution to model prices.
To outline the presentation that follows, we first show that the stock price at some 
future time T, ST, equals the current stock price, S0, multiplied by e raised to power 
r0,T, the continuously compounded return from 0 to T; this relationship is expressed 
as ST = S0exp( r0,T). We then show that we can write r0,T as the sum of shorter-  term 
continuously compounded returns and that if these shorter-  period returns are normally 
distributed, then r0,T is normally distributed (given certain assumptions) or approx -
imately normally distributed (not making those assumptions). As ST is proportional 
to the log of a normal random variable, ST is lognormal.
To supply a framework for our discussion, suppose we have a series of equally

spaced observations on stock price: S0, S1, S2, …, ST. Current stock price, S0, is a known 
quantity and so is nonrandom. The future prices (such as S1), however, are random 
variables. The price relative , S1/S0, is an ending price, S1, over a beginning price, S0; 
it is equal to 1 plus the holding period return on the stock from t = 0 to t = 1:
S1/S0 = 1 + R0,1
For example, if S0 = $30 and S1 = $34.50, then S1/S0 = $34.50/$30 = 1.15. Therefore, 
R0,1 = 0.15 or 15 percent. In general, price relatives have the form
St+1/St = 1 + Rt,t+1
where Rt,t+1 is the rate of return from t to t + 1.
An important concept is the continuously compounded return associated with a 
holding period return such as R0,1. The continuously compounded return  associated 
with a holding period is the natural logarithm of 1 plus that holding period return, or 
equivalently, the natural logarithm of the ending price over the beginning price (the

price relative).33 For example, if we observe a one-  week holding period return of 0.04, 
the equivalent continuously compounded return, called the one-  week continuously 
compounded return, is ln(1.04) = 0.039221; €1.00 invested for one week at 0.039221 
continuously compounded gives €1.04, equivalent to a 4 percent one-  week holding 
period return. The continuously compounded return from t to t + 1 is
rt,t+1 = ln( St+1/St) = ln(1 + Rt,t+1)  (5)
31 Luenberger (1998) is the source of this explanation.
32 Continuous compounding treats time as essentially continuous or unbroken, in contrast to discrete 
compounding, which treats time as advancing in discrete finite intervals. Continuously compounded returns 
are the model for returns in so-  called continuous time  finance models such as the Black–Scholes–Merton 
option pricing model. See the reading on the time value of money for more information on compounding.

33 In this reading we use lowercase r to refer specifically to continuously compounded returns.

Reading 10 ■ Common Probability Distributions 552
For our example, r0,1 = ln( S1/S0) = ln(1 + R0,1) = ln($34.50/$30) = ln(1.15) = 0.139762. 
Thus, 13.98 percent is the continuously compounded return from t = 0 to t = 1. The 
continuously compounded return is smaller than the associated holding period 
return. If our investment horizon extends from t = 0 to t = T, then the continuously 
compounded return to T is
r0,T = ln( ST/S0) 
Applying the function exp to both sides of the equation, we have exp( r0,T) = exp[ln( ST/
S0)] = ST/S0, so
ST = S0exp( r0,T) 
We can also express ST/S0 as the product of price relatives:
ST/S0 = (ST/ST–1)(ST–1/ST–2)…(S1/S0) 
Taking logs of both sides of this equation, we find that continuously compounded 
return to time T is the sum of the one-  period continuously compounded returns:
r0,T = rT–1,T + rT–2,T–1 + … r0,1  
Using holding period returns to find the ending value of a $1 investment involves

the multiplication of quantities (1 + holding period return). Using continuously com -
pounded returns involves addition.
A key assumption in many investment applications is that returns are inde -
pendently and identically distributed (IID) . Independence captures the proposition 
that investors cannot predict future returns using past returns (i.e., weak-  form market 
efficiency). Identical distribution captures the assumption of stationarity.34
Assume that the one-  period continuously compounded returns (such as r0,1) are 
IID random variables with mean μ and variance σ2 (but making no normality or other 
distributional assumption). Then
E(r0,T) = E(rT–1,T) + E(rT–2,T–1) + … + E(r0,1) = μ T  
(we add up μ for a total of T times) and
σ2(r0,T) = σ2T  
(as a consequence of the independence assumption). The variance of the T holding 
period continuously compounded return is T multiplied by the variance of the one-  
period continuously compounded return; also, σ( r0,T) = σT. If the one-  period

continuously compounded returns on the right-  hand side of Equation 6 are normally 
distributed, then the T holding period continuously compounded return, r0,T, is also 
normally distributed with mean μ T and variance σ2T. This relationship is so because 
a linear combination of normal random variables is also normal. But even if the one-  
period continuously compounded returns are not normal, their sum, r0,T, is approx -
imately normal according to a result in statistics known as the central limit theorem.35 
Now compare ST = S0exp( r0,T) to Y = exp( X), where X is normal and Y is lognormal 
(as we discussed above). Clearly, we can model future stock price ST as a lognormal 
random variable because r0,T should be at least approximately normal. This assumption 
of normally distributed returns is the basis in theory for the lognormal distribution 
as a model for the distribution of prices of shares and other assets.(6)
(7)
(8)

(7)
(8)
34 Stationarity implies that the mean and variance of return do not change from period to period.
35 We mentioned the central limit theorem earlier in our discussion of the normal distribution. To give a 
somewhat fuller statement of it, according to the central limit theorem the sum (as well as the mean) of a 
set of independent, identically distributed random variables with finite variances is normally distributed, 
whatever distribution the random variables follow. We discuss the central limit theorem in the reading 
on sampling.

Continuous Random Variables 553
Continuously compounded returns play a role in many option pricing models, as 
mentioned earlier. An estimate of volatility is crucial for using option pricing models 
such as the Black–Scholes–Merton model. Volatility  measures the standard deviation 
of the continuously compounded returns on the underlying asset.36 In practice, we 
very often estimate volatility using a historical series of continuously compounded 
daily returns. We gather a set of daily holding period returns and then use Equation 5 
to convert them into continuously compounded daily returns. We then compute the 
standard deviation of the continuously compounded daily returns and annualize 
that number using Equation 8.37 (By convention, volatility is stated as an annualized 
measure.)38 Example 10 illustrates the estimation of volatility for the shares of Astra 
International.
EXAMPLE 10   
Volatility as Used in Option Pricing Models

Suppose you are researching Astra International (Indonesia Stock Exchange: 
ASII) and are interested in Astra’s price action in a week in which international 
economic news had significantly affected the Indonesian stock market. You 
decide to use volatility as a measure of the variability of Astra shares during 
that week. Table 7 shows closing prices during that week.
Table 7   Astra International Daily Closing Prices
Date Closing Price (IDR)
17 June 2013 6,950
18 June 2013 7,000
19 June 2013 6,850
20 June 2013 6,600
21 June 2013 6,350
Source:  http://finance.yahoo.com.
Use the data in Table 7 to do the following:
1 Estimate the volatility of Astra shares. (Annualize volatility based on 250 
days in a year.)
2 Identify the probability distribution for Astra share prices if continuously 
compounded daily returns follow the normal distribution.
36 Volatility is also called the instantaneous standard deviation, and as such is denoted σ. The underlying

asset, or simply the underlying, is the asset underlying the option. For more information on these concepts, 
see Chance and Brooks (2016).
37 To compute the standard deviation of a set or sample of n returns, we sum the squared deviation of each 
return from the mean return and then divide that sum by n − 1. The result is the sample variance. Taking 
the square root of the sample variance gives the sample standard deviation. To review the calculation of 
standard deviation, see the reading on statistical concepts and market returns.
38 Annualizing is often done on the basis of 250 days in a year, the approximate number of days markets 
are open for trading. The 250-  day number may lead to a better estimate of volatility than the 365-  day 
number. Thus if daily volatility were 0.01, we would state volatility (on an annual basis) as 001 250 0 1581..= .

Reading 10 ■ Common Probability Distributions 554
First, use Equation 5 to calculate the continuously compounded daily returns; 
then find their standard deviation in the usual way. (In the calculation of sam -
ple variance to get sample standard deviation, use a divisor of 1 less than the 
sample size.)
ln(7,000/6,950) = 0.007168
ln(6,850/7,000) = –0.021661
ln(6,600/6,850) = –0.037179
ln(6,350/6,600) = –0.038615
Sum = –0.090287
Mean = –0.022572
Variance = 0.000452
Standard Deviation = 0.021261
The standard deviation of continuously compounded daily returns is 0.021261. 
Equation 8 states that  σσrTT0,() = . In this example,  σ is the sample standard 
deviation of one-  period continuously compounded returns. Thus,  σ refers to 
0.021261. We want to annualize, so the horizon T corresponds to one year. As  σ 
is in days, we set T equal to the number of trading days in a year (250).
We find that annualized volatility for Astra stock that week was 33.6 percent,

calculated as  0 021261 250 0 336165.. = .
Note that the sample mean, –0.022572, is a possible estimate of the mean, 
μ, of the continuously compounded one-  period or daily returns. The sample 
mean can be translated into an estimate of the expected continuously com -
pounded annual return using Equation 7:  µT=− () 0 022572 250.  (using 250 to 
be consistent with the calculation of volatility). But four observations are far 
too few to estimate expected returns. The variability in the daily returns over -
whelms any information about expected return in a series this short.
Astra share prices should follow the lognormal distribution if the continuously 
compounded daily returns on Astra shares follow the normal distribution.
We have shown that the distribution of stock price is lognormal, given certain 
assumptions. What are the mean and variance of ST if ST follows the lognormal dis -
tribution? Earlier in this section, we gave bullet-  point expressions for the mean and

variance of a lognormal random variable. In the bullet-  point expressions, the  µσ  and 2 
would refer, in the context of this discussion, to the mean and variance of the T horizon 
(not the one-  period) continuously compounded returns (assumed to follow a normal 
distribution), compatible with the horizon of ST.39 Related to the use of mean and 
variance (or standard deviation), earlier in this reading we used those quantities to 
construct intervals in which we expect to find a certain percentage of the observations 
of a normally distributed random variable. Those intervals were symmetric about the 
mean. Can we state similar, symmetric intervals for a lognormal random variable? 
39 The expression for the mean is E(ST) = S0 exp[ E(r0,T) + 0.5σ2(r0,T)], for example.

Monte Carlo Simulation 555
Unfortunately, we cannot. Because the lognormal distribution is not symmetric, such 
intervals are more complicated than for the normal distribution, and we will not 
discuss this specialist topic here.40
Finally, we have presented the relation between the mean and variance of contin -
uously compounded returns associated with different time horizons (see Equations 
7 and 8), but how are the means and variances of holding period returns and con -
tinuously compounded returns related? As analysts, we typically think in terms of 
holding period returns rather than continuously compounded returns, and we may 
desire to convert means and standard deviations of holding period returns to means 
and standard deviations of continuously compounded returns for an option applica -
tion, for example. To effect such conversions (and those in the other direction, from 
a continuous compounding to a holding period basis), we can use the expressions in 
Ferguson (1993).

MONTE CARLO SIMULATION
With an understanding of probability distributions, we are now prepared to learn about 
a computer-  based technique in which probability distributions play an integral role. 
The technique is called Monte Carlo simulation. Monte Carlo simulation  in finance 
involves the use of a computer to represent the operation of a complex financial sys -
tem. A characteristic feature of Monte Carlo simulation is the generation of a large 
number of random samples from a specified probability distribution or distributions 
to represent the role of risk in the system.
Monte Carlo simulation has several quite distinct uses. One use is in planning. 
Stanford University researcher Sam Savage provided the following neat picture of 
that role: “What is the last thing you do before you climb on a ladder? You shake it, 
and that is Monte Carlo simulation. ”41 Just as shaking a ladder helps us assess the

risks in climbing it, Monte Carlo simulation allows us to experiment with a proposed 
policy before actually implementing it. For example, investment performance can be 
evaluated with reference to a benchmark or a liability. Defined benefit pension plans 
often invest assets with reference to plan liabilities. Pension liabilities are a complex 
random process. In a Monte Carlo asset-  liability financial planning study, the func -
tioning of pension assets and liabilities is simulated over time, given assumptions 
about how assets are invested, the work force, and other variables. A key specification 
in this and all Monte Carlo simulations is the probability distributions of the various 
sources of risk (including interest rates and security market returns, in this case). The 
implications of different investment policy decisions on the plan’s funded status can 
be assessed through simulated time. The experiment can be repeated for another set

of assumptions. We can view Example 11 below as coming under this heading. In that 
example, market return series are not long enough to address researchers’ questions 
on stock market timing, so the researchers simulate market returns to find answers 
to their questions.
Monte Carlo simulation is also widely used to develop estimates of VaR. In this 
application, we simulate the portfolio’s profit and loss performance for a specified time 
horizon. Repeated trials within the simulation (each trial involving a draw of random 
observations from a probability distribution) produce a frequency distribution for 
changes in portfolio value. The point that defines the cutoff for the least favorable 
5 percent of simulated changes is an estimate of 95 percent VaR, for example.4
40 See Hull (2017) for a discussion of lognormal confidence intervals.
41 Business Week,  22 January 2001.

Reading 10 ■ Common Probability Distributions 556
In an extremely important use, Monte Carlo simulation is a tool for valuing com -
plex securities, particularly some European-  style options for which no analytic pricing 
formula is available.42 For other securities, such as mortgage-  backed securities with 
complex embedded options, Monte Carlo simulation is also an important modeling 
resource.
Researchers use Monte Carlo simulation to test their models and tools. How critical 
is a particular assumption to the performance of a model? Because we control the 
assumptions when we do a simulation, we can run the model through a Monte Carlo 
simulation to examine a model’s sensitivity to a change in our assumptions.
To understand the technique of Monte Carlo simulation, let us present the process 
as a series of steps.43 To illustrate the steps, we take the case of using Monte Carlo 
simulation to value a type of option for which no analytic pricing formula is available,

an Asian call option on a stock. An Asian call option  is a European-  style option with 
a value at maturity equal to the difference between the stock price at maturity and 
the average stock price during the life of the option, or $0, whichever is greater. For 
instance, if the final stock price is $34 with an average value of $31 over the life of 
the option, the value of the option at maturity is $3 (the greater of $34 − $31 = $3 
and $0). Steps 1 through 3 of the process describe specifying the simulation; Steps 4 
through 7 describe running the simulation.
1 Specify the quantities of interest (option value, for example, or the funded 
status of a pension plan) in terms of underlying variables. The underlying vari -
able or variables could be stock price for an equity option, the market value of 
pension assets, or other variables relating to the pension benefit obligation for a 
pension plan. Specify the starting values of the underlying variables.

To illustrate the steps, we are using the case of valuing an Asian call option 
on stock. We use CiT to represent the value of the option at maturity T. The 
subscript i in CiT indicates that CiT is a value resulting from the ith simulation 
trial , each simulation trial involving a drawing of random values (an iteration of 
Step 4).
2 Specify a time grid. Take the horizon in terms of calendar time and split it into 
a number of subperiods, say K in total. Calendar time divided by the number of 
subperiods, K, is the time increment, Δ t.
3 Specify distributional assumptions for the risk factors that drive the underlying 
variables. For example, stock price is the underlying variable for the Asian call, 
so we need a model for stock price movement. Say we choose the following 
model for changes in stock price, where Zk stands for the standard normal ran -
dom variable:
Δ(Stock price) = (μ × Prior stock price × Δ t) + (σ× Prior stock price × Zk)

In the way that we are using the term, Zk is a risk factor in the simulation. 
Through our choice of μ and σ, we control the distribution of stock price. 
Although this example has one risk factor, a given simulation may have multiple 
risk factors.
4 Using a computer program or spreadsheet function, draw K random values 
of each risk factor. In our example, the spreadsheet function would produce a 
draw of K values of the standard normal variable Zk: Z1, Z2, Z3, …, ZK.
42 A European-  style  option or European option  is an option exercisable only at maturity.
43 The steps should be viewed as providing an overview of Monte Carlo simulation rather than as a detailed 
recipe for implementing a Monte Carlo simulation in its many varied applications.

Monte Carlo Simulation 557
5 Calculate the underlying variables using the random observations generated in 
Step 4. Using the above model of stock price dynamics, the result is K observa -
tions on changes in stock price. An additional calculation is needed to convert 
those changes into K stock prices (using initial stock price, which is given). 
Another calculation produces the average stock price during the life of the 
option (the sum of K stock prices divided by K).
6 Compute the quantities of interest. In our example, the first calculation is the 
value of an Asian call at maturity, CiT. A second calculation discounts this 
terminal value back to the present to get the call value as of today, Ci0. We have 
completed one simulation trial. (The subscript i in Ci0 stands for the ith simula -
tion trial, as it does in CiT.) In a Monte Carlo simulation, a running tabulation is 
kept of statistics relating to the distribution of the quantities of interest, includ -

ing their mean value and standard deviation, over the simulation trials to that 
point.
7 Iteratively go back to Step 4 until a specified number of trials, I, is completed. 
Finally, produce statistics for the simulation. The key value for our example is 
the mean value of Ci0 for the total number of simulation trials. This mean value 
is the Monte Carlo estimate of the value of the Asian call.
How many simulation trials should be specified? In general, we need to increase 
the number of trials by a factor of 100 to get each extra digit of accuracy. Depending 
on the problem, tens of thousands of trials may be needed to obtain accuracy to two 
decimal places (as required for option value, for example). Conducting a large number 
of trials is not necessarily a problem, given today’s computing power. The number of 
trials needed can be reduced using variance reduction procedures, a topic outside 
the scope of this reading.44

In Step 4 of our example, a computer function produced a set of random obser -
vations on a standard normal random variable. Recall that for a uniform distribution, 
all possible numbers are equally likely. The term random number generator  refers 
to an algorithm that produces uniformly distributed random numbers between 0 and 
1. In the context of computer simulations, the term random number  refers to an 
observation drawn from a uniform distribution.45 For other distributions, the term 
“random observation” is used in this context.
It is a remarkable fact that random observations from any distribution can be 
produced using the uniform random variable with endpoints 0 and 1. To see why 
this is so, consider the inverse transformation method of producing random obser -
vations. Suppose we are interested in obtaining random observations for a random 
variable, X, with cumulative distribution function F(x). Recall that F(x) evaluated at x

is a number between 0 and 1. Suppose a random outcome of this random variable is 
3.21 and that F(3.21) = 0.25 or 25 percent. Define an inverse of F, call it F−1, that can 
do the following: Substitute the probability 0.25 into F−1 and it returns the random 
outcome 3.21. In other words, F−1(0.25) = 3.21. To generate random observations on 
X, the steps are 1) generate a uniform random number, r, between 0 and 1 using the 
random number generator and 2) evaluate F−1(r) to obtain a random observation on 
X. Random observation generation is a field of study in itself, and we have briefly dis -
cussed the inverse transformation method here just to illustrate a point. As a generalist 
44 For details on this and other technical aspects of Monte Carlo simulation, see Hillier (2014).
45 The numbers that random number generators produce depend on a seed or initial value. If the same 
seed is fed to the same generator, it will produce the same sequence. All sequences eventually repeat.

Because of this predictability, the technically correct name for the numbers produced by random number 
generators is pseudo-  random numbers . Pseudo-  random numbers have sufficient qualities of randomness 
for most practical purposes.

Reading 10 ■ Common Probability Distributions 558
you do not need to address the technical details of converting random numbers into 
random observations, but you do need to know that random observations from any 
distribution can be generated using a uniform random variable.
In Examples 11 and 12, we give an application of Monte Carlo simulation to a ques -
tion of great interest to investment practice: the potential gains from market timing.
EXAMPLE 11   
Potential Gains from Market Timing: A Monte Carlo 
Simulation (1)
All active investors want to achieve superior performance. One possible source 
of superior performance is market timing ability. How accurate does an investor 
need to be as a bull- and bear-  market forecaster for market timing to be profit -
able? What size gains compared with a buy-  and-  hold strategy accrue to a given 
level of accuracy? Because of the variability in asset returns, a huge amount of

return data is needed to find statistically reliable answers to these questions. 
Chua, Woodward, and To (1987) thus selected Monte Carlo simulation to address 
the potential gains from market timing. They were interested in the perspective 
of a Canadian investor.
To understand their study, suppose that at the beginning of a year, an investor 
predicts that the next year will see either a bull market or bear market. If the 
prediction is bull market,  the investor puts all her money in stocks and earns 
the market return for that year. On the other hand, if the prediction is bear 
market,  the investor holds T-  bills and earns the T-  bill return. After the fact, 
a market is categorized as bull market  if the stock market return, RMt, minus 
T- bill return, RFt, is positive for the year; otherwise, the market is classed as bear 
market.  The investment results of a market timer can be compared with those 
of a buy-  and-  hold investor. A buy-  and-  hold investor earns the market return

every year. For Chua et al., one quantity of interest was the gain from market 
timing. They defined this quantity as the market timer’s average return minus 
the average return to a buy-  and-  hold investor.
To simulate market returns, Chua et al. generated 10,000 random standard 
normal observations, Zt. At the time of the study, Canadian stocks had a historical 
mean annual return of 12.95 percent with a standard deviation of 18.30 percent. 
To reflect these parameters, the simulated market returns are RMt = 0.1830 Zt 
+ 0.1295, t = 1, 2, …, 10,000. Using a second set of 10,000 random standard 
normal observations, historical return parameters for Canadian T-  bills, as well 
as the historical correlation of T-  bill and stock returns, the authors generated 
10,000 T-  bill returns.
An investor can have different skills in forecasting bull and bear markets. 
Chua et al. characterized market timers by accuracy in forecasting bull markets

and accuracy in forecasting bear markets. For example, bull market forecasting 
accuracy of 50 percent means that when the timer forecasts bull market  for the 
next year, she is right just half the time, indicating no skill. Suppose an investor 
has 60 percent accuracy in forecasting bull market  and 80 percent accuracy in 
forecasting bear market  (a 60–80 timer). We can simulate how an investor would 
fare. After generating the first observation on RMt − RFt, we know whether that 
observation is a bull or bear market. If the observation is bull market,  then 
0.60 (forecast accuracy for bull markets) is compared with a random number 
(between 0 and 1). If the random number is less than 0.60, which occurs with a 
60 percent probability, then the market timer is assumed to have correctly pre -
dicted bull market  and her return for that first observation is the market return. 
If the random number is greater than 0.60, then the market timer is assumed to

Monte Carlo Simulation 559
have made an error and predicted bear market;  her return for that observation 
is the risk-  free rate. In a similar fashion, if that first observation is bear market,  
the timer has an 80 percent chance of being right in forecasting bear market  
based on a random number draw. In either case, her return is compared with the 
market return to record her gain versus a buy-  and-  hold strategy. That process 
is one simulation trial. The simulated mean return earned by the timer is the 
average return earned by the timer over all trials in the simulation.
To increase our understanding of the process, consider a hypothetical 
Monte Carlo simulation with four trials for the 60–80 timer (who, to reiterate, 
has 60 percent accuracy in forecasting bull markets and 80 percent accuracy 
in forecasting bear markets). Table 8 gives data for the simulation. Let us look 
at Trials 1 and 2. In Trial 1, the first random number drawn leads to a market

return of 0.121. Because the market return, 0.121, exceeded the T-  bill return, 
0.050, we have a bull market. We generate a random number, 0.531, which we 
then compare with the timer’s bull market accuracy, 0.60. Because 0.531 is less 
than 0.60, the timer is assumed to have made a correct bull market forecast and 
thus to have invested in stocks. Thus the timer earns the stock market return, 
0.121, for that trial. In the second trial we observe another bull market, but 
because the random number 0.725 is greater than 0.60, the timer is assumed to 
have made an error and predicted a bear market; therefore, the timer earned 
the T-  bill return, 0.081, rather than higher stock market return.
Table 8   Hypothetical Simulation for a 60–80 Market Timer
After Draws for Zt and  
for the T-  bill Return Simulation Results
Trial RMt RFtBull or 
Bear 
Market?Value 
of XTimer’s 
Prediction 
Correct?Return 
Earned 
by Timer
1 0.121 0.050 Bull 0.531 Yes 0.121
2 0.092 0.081 Bull 0.725 No 0.081

3 −0.020 0.034 Bear 0.786 Yes 0.034
4 0.052 0.055 A 0.901 B C
R=D
Note : R is the mean return earned by the timer over the four simulation trials.
Using the data in Table 8, determine the values of A, B, C, and D.
Solution:
The value of A is Bear  because the stock market return was less than the T-  bill 
return in Trial 4. The value of B is No. Because we observe a bear market, we 
compare the random number 0.901 with 0.80, the timer’s bear-  market forecasting 
accuracy. Because 0.901 is greater than 0.8, the timer is assumed to have made 
an error. The value of C is 0.052, the return on the stock market, because the 
timer made an error and invested in the stock market and earned 0.052 rather 
than the higher T-  bill return of 0.055. The value of D is R = (0.121 + 0.081 + 
0.034 + 0.052) = 0.288/4 = 0.072. Note that we could calculate other statistics 
besides the mean, such as the standard deviation of the returns earned by the

Reading 10 ■ Common Probability Distributions 560
EXAMPLE 12   
Simulation (2)
Having discussed the plan of the Chua et al. study and illustrated the method 
for a hypothetical Monte Carlo simulation with four trials, we conclude our 
presentation of the study.
The hypothetical simulation in Example 11 had four trials, far too few to 
reach statistically precise conclusions. The simulation of Chua et al. incorporated 
10,000 trials. Chua et al. specified bull- and bear-  market prediction skill levels 
of 50, 60, 70, 80, 90, and 100 percent. Table 9 presents a very small excerpt from 
their simulation results for the no transaction costs case (transaction costs were 
also examined). Reading across the row, the timer with 60 percent bull market 
and 80 percent bear market forecasting accuracy had a mean annual gain from 
market timing of −1.12 percent per year. On average, the buy-  and-  hold investor

out- earned this skillful timer by 1.12 percentage points. There was substantial 
variability in gains across the simulation trials, however: The standard deviation 
of the gain was 14.77 percent, so in many trials (but not on average) the gain was 
positive. Row 3 (win/loss) is the ratio of profitable switches between stocks and 
T- bills to unprofitable switches. This ratio was a favorable 1.2070 for the 60–80 
timer. (When transaction costs were considered, however, fewer switches are 
profitable: The win–loss ratio was 0.5832 for the 60–80 timer.)
Table 9   Gains from Stock Market Timing (No Transaction Costs) 
Bull Market 
Accuracy (%)Bear Market Accuracy (%)
50 60 70 80 90 100
60 Mean (%) −2.50 −1.99 −1.57 −1.12 −0.68 −0.22
S.D. (%) 13.65 14.11 14.45 14.77 15.08 15.42
Win/Loss 0.7418 0.9062 1.0503 1.2070 1.3496 1.4986
Source:  Chua, Woodward, and To (1987), Table II (excerpt).
The authors concluded that the cost of not being invested in the market

during bull market years is high. Because a buy-  and-  hold investor never misses 
a bull market year, she has 100 percent forecast accuracy for bull markets (at 
the cost of 0 percent accuracy for bear markets). Given their definitions and 
assumptions, the authors also concluded that successful market timing requires 
a minimum accuracy of 80 percent in forecasting both bull and bear markets. 
Market timing is a continuing area of interest and study, and other perspectives 
exist. However, this example illustrates how Monte Carlo simulation is used to 
address important investment issues.
The analyst chooses the probability distributions in Monte Carlo simulation. By 
contrast, historical simulation  samples from a historical record of returns (or other 
underlying variables) to simulate a process. The concept underlying historical sim -
ulation (also called back simulation ) is that the historical record provides the most

direct evidence on distributions (and that the past applies to the future). For example, 
refer back to Step 2 in the outline of Monte Carlo simulation above and suppose the 
time increment is one day. Further, suppose we base the simulation on the record

Summary 561
of daily stock returns over the last five years. In one type of historical simulation, 
we randomly draw K returns from that record to generate one simulation trial. We 
put back the observations into the sample, and in the next trial we again randomly 
sample with replacement. The simulation results directly reflect frequencies in the 
data. A drawback of this approach is that any risk not represented in the time period 
selected (for example, a stock market crash) will not be reflected in the simulation. 
Compared with Monte Carlo simulation, historical simulation does not lend itself 
to “what if” analyses. Nevertheless, historic simulation is an established alternative 
simulation methodology.
Monte Carlo simulation is a complement to analytical methods. It provides only sta -
tistical estimates, not exact results. Analytical methods, where available, provide more 
insight into cause-  and-  effect relationships. For example, the Black–Scholes–Merton

option pricing model for the value of a European call option is an analytical method, 
expressed as a formula. It is a much more efficient method for valuing such a call than 
is Monte Carlo simulation. As an analytical expression, the Black–Scholes–Merton 
model permits the analyst to quickly gauge the sensitivity of call value to changes 
in current stock price and the other variables that determine call value. In contrast, 
Monte Carlo simulations do not directly provide such precise insights. However, only 
some types of options can be priced with analytical expressions. As financial product 
innovations proceed, the field of applications for Monte Carlo simulation continues 
to grow.
SUMMARY
In this reading, we have presented the most frequently used probability distributions 
in investment analysis and the Monte Carlo simulation.
■■A probability distribution specifies the probabilities of the possible outcomes of 
a random variable.

■■The two basic types of random variables are discrete random variables and con -
tinuous random variables. Discrete random variables take on at most a count -
able number of possible outcomes that we can list as x1, x2, … In contrast, we 
cannot describe the possible outcomes of a continuous random variable Z with 
a list z1, z2, … because the outcome ( z1 + z2)/2, not in the list, would always be 
possible.
■■The probability function specifies the probability that the random variable will 
take on a specific value. The probability function is denoted p(x) for a discrete 
random variable and f(x) for a continuous random variable. For any probability 
function p(x), 0 ≤ p(x) ≤ 1, and the sum of p(x) over all values of X equals 1.
■■The cumulative distribution function, denoted F(x) for both continuous and 
discrete random variables, gives the probability that the random variable is less 
than or equal to x.

■■The discrete uniform and the continuous uniform distributions are the distribu -
tions of equally likely outcomes.
■■The binomial random variable is defined as the number of successes in n 
Bernoulli trials, where the probability of success, p, is constant for all trials and 
the trials are independent. A Bernoulli trial is an experiment with two out -
comes, which can represent success or failure, an up move or a down move, or 
another binary (two-  fold) outcome.

Reading 10 ■ Common Probability Distributions 562
■■A binomial random variable has an expected value or mean equal to np and 
variance equal to np(1 − p).
■■A binomial tree is the graphical representation of a model of asset price dynam -
ics in which, at each period, the asset moves up with probability p or down with 
probability (1 − p). The binomial tree is a flexible method for modeling asset 
price movement and is widely used in pricing options.
■■The normal distribution is a continuous symmetric probability distribution that 
is completely described by two parameters: its mean, μ, and its variance, σ2.
■■A univariate distribution specifies the probabilities for a single random variable. 
A multivariate distribution specifies the probabilities for a group of related 
random variables.
■■To specify the normal distribution for a portfolio when its component securities 
are normally distributed, we need the means, standard deviations, and all the

distinct pairwise correlations of the securities. When we have those statistics, 
we have also specified a multivariate normal distribution for the securities.
■■For a normal random variable, approximately 68 percent of all possible out -
comes are within a one standard deviation interval about the mean, approxi -
mately 95 percent are within a two standard deviation interval about the mean, 
and approximately 99 percent are within a three standard deviation interval 
about the mean.
■■A normal random variable, X, is standardized using the expression Z = (X 
− μ)/σ, where μ and σ are the mean and standard deviation of X. Generally, we 
use the sample mean  X as an estimate of μ and the sample standard deviation s 
as an estimate of σ in this expression.
■■The standard normal random variable, denoted Z, has a mean equal to 0 and 
variance equal to 1. All questions about any normal random variable can be 
answered by referring to the cumulative distribution function of a standard

normal random variable, denoted N(x) or N(z).
■■Shortfall risk is the risk that portfolio value will fall below some minimum 
■■Roy’s safety-  first criterion, addressing shortfall risk, asserts that the optimal 
portfolio is the one that minimizes the probability that portfolio return falls 
below a threshold level. According to Roy’s safety-  first criterion, if returns are 
normally distributed, the safety-  first optimal portfolio P is the one that maxi -
mizes the quantity [ E(RP) − RL]/σP, where RL is the minimum acceptable level 
of return.
■■A random variable follows a lognormal distribution if the natural logarithm 
of the random variable is normally distributed. The lognormal distribution is 
defined in terms of the mean and variance of its associated normal distribution. 
The lognormal distribution is bounded below by 0 and skewed to the right (it 
has a long right tail).

■■The lognormal distribution is frequently used to model the probability distribu -
tion of asset prices because it is bounded below by zero.
■■Continuous compounding views time as essentially continuous or unbroken; 
discrete compounding views time as advancing in discrete finite intervals.
■■The continuously compounded return associated with a holding period is the 
natural log of 1 plus the holding period return, or equivalently, the natural log 
of ending price over beginning price.

References 563
Chance, Don M., and Robert Brooks. 2016. An Introduction 
to Derivatives and Risk Management , 10th ed. Mason, OH: 
Chua, Jess H., Richard S. Woodward, and Eric C. To. 1987. 
“Potential Gains from Stock Market Timing in Canada. ” 
Financial Analysts Journal , vol. 43, no. 5:50–56. 
Cox, Jonathan, Stephen Ross, and Mark Rubinstein. 1979. 
“Options Pricing: A Simplified Approach. ” Journal of Financial 
Economics , vol. 7:229–263. 
Fama, Eugene. 1976. Foundations of Finance . New York: Basic 
Books.
Ferguson, Robert. 1993. “Some Formulas for Evaluating Two 
Popular Option Strategies. ” Financial Analysts Journal , vol. 
49, no. 5:71–76. Hillier, Frederick S. 2014. Introduction to Operations Research , 
10th edition. New York: McGraw-Hill.
Hull, John. 2017. Options, Futures, and Other Derivatives , 10th

edition. Upper Saddle River, NJ: Pearson.
Kolb, Robert W., Gerald D. Gay, and William C. Hunter. 1985. 
“Liquidity Requirements for Financial Futures Investments. ” 
Financial Analysts Journal , vol. 41, no. 3:60–68. 
Kon, Stanley J. 1984. “Models of Stock Returns—A Comparison. ” 
Journal of Finance , vol. 39:147–165.
Leibowitz, Martin, and Roy Henriksson. 1989. “Portfolio 
Optimization with Shortfall Constraints: A Confidence-  Limit 
Approach to Managing Downside Risk. ” Financial Analysts 
Journal , vol. 45, no. 2:34–41. 
Luenberger, David G. 1998. Investment Science . New York: 
Oxford University Press.
Roy, A.D. 1952. “Safety-  First and the Holding of Assets. ” 
Econometrica , vol. 20:431–439. ■■If continuously compounded returns are normally distributed, asset prices 
are lognormally distributed. This relationship is used to move back and forth 
between the distributions for return and price. Because of the central limit the -

orem, continuously compounded returns need not be normally distributed for 
asset prices to be reasonably well described by a lognormal distribution.
■■Monte Carlo simulation involves the use of a computer to represent the oper -
ation of a complex financial system. A characteristic feature of Monte Carlo 
simulation is the generation of a large number of random samples from speci -
fied probability distribution(s) to represent the operation of risk in the system. 
Monte Carlo simulation is used in planning, in financial risk management, and 
in valuing complex securities. Monte Carlo simulation is a complement to ana -
lytical methods but provides only statistical estimates, not exact results.
■■Historical simulation is an established alternative to Monte Carlo simulation 
that in one implementation involves repeated sampling from a historical data 
series. Historical simulation is grounded in actual data but can reflect only risks

represented in the sample historical data. Compared with Monte Carlo simula -
tion, historical simulation does not lend itself to “what if” analyses.

Reading 10 ■ Common Probability Distributions 564
1 A European put option on stock conveys the right to sell the stock at a pre -
specified price, called the exercise price, at the maturity date of the option. The 
value of this put at maturity is (exercise price – stock price) or $0, whichever 
is greater. Suppose the exercise price is $100 and the underlying stock trades 
in ticks of $0.01. At any time before maturity, the terminal value of the put is a 
random variable.
A Describe the distinct possible outcomes for terminal put value. (Think of the 
put’s maximum and minimum values and its minimum price increments.)
B Is terminal put value, at a time before maturity, a discrete or continuous 
random variable?
C Letting Y stand for terminal put value, express in standard notation the 
probability that terminal put value is less than or equal to $24. No calcula -
tions or formulas are necessary.
2 Define the term “binomial random variable. ” Describe the types of problems for

which the binomial distribution is used.
3 The value of the cumulative distribution function F(x), where x is a particular 
outcome, for a discrete uniform distribution:
A sums to 1.
B lies between 0 and 1.
C decreases as x increases.
4 For a binomial random variable with five trials, and a probability of success on 
each trial of 0.50, the distribution will be:
A skewed.
B uniform.
C symmetric.
5 In a discrete uniform distribution with 20 potential outcomes of integers 1 to 
20, the probability that X is greater than or equal to 3 but less than 6, P(3 ≤ X < 
6), is:
A 0.10.
B 0.15.
C 0.20.
6 Over the last 10 years, a company’s annual earnings increased year over year 
seven times and decreased year over year three times. You decide to model 
the number of earnings increases for the next decade as a binomial random 
variable.
A What is your estimate of the probability of success, defined as an increase in 
annual earnings?
 For Parts B, C, and D of this problem, assume the estimated probability is the

actual probability for the next decade.
B What is the probability that earnings will increase in exactly 5 of the next 10 
years?
C Calculate the expected number of yearly earnings increases during the next 
10 years.

Practice Problems 565
D Calculate the variance and standard deviation of the number of yearly earn -
ings increases during the next 10 years.
E The expression for the probability function of a binomial random variable 
depends on two major assumptions. In the context of this problem, what 
must you assume about annual earnings increases to apply the binomial 
distribution in Part B? What reservations might you have about the validity 
of these assumptions?
7 A portfolio manager annually outperforms her benchmark 60% of the time. 
Assuming independent annual trials, what is the probability that she will out -
perform her benchmark four or more times over the next five years?
A 0.26
B 0.34
C 0.48
8 You are examining the record of an investment newsletter writer who claims a 
70 percent success rate in making investment recommendations that are profit -
able over a one-  year time horizon. You have the one-  year record of the news -

letter’s seven most recent recommendations. Four of those recommendations 
were profitable. If all the recommendations are independent and the newsletter 
writer’s skill is as claimed, what is the probability of observing four or fewer 
profitable recommendations out of seven in total?
9 You are forecasting sales for a company in the fourth quarter of its fiscal year. 
Your low-  end estimate of sales is €14 million, and your high-  end estimate is 
€15 million. You decide to treat all outcomes for sales between these two values 
as equally likely, using a continuous uniform distribution.
A What is the expected value of sales for the fourth quarter?
B What is the probability that fourth-  quarter sales will be less than or equal to 
€14,125,000?
10 State the approximate probability that a normal random variable will fall within 
the following intervals:
A Mean plus or minus one standard deviation.
B Mean plus or minus two standard deviations.
C Mean plus or minus three standard deviations.

11 Find the area under the normal curve up to z = 0.36; that is, find P(Z ≤ 0.36). 
Interpret this value.
12 If an analyst expects a portfolio to outperform its benchmark with a 75% suc -
cess rate in any measurement period, and the portfolio meets that objective in 
three of four quarters, what is the probability that the realized portfolio perfor -
mance over the year is at or below this expectation?
A 0.26
B 0.42
C 0.68
13 In futures markets, profits or losses on contracts are settled at the end of each 
trading day. This procedure is called marking to market or daily resettlement. 
By preventing a trader’s losses from accumulating over many days, marking to 
market reduces the risk that traders will default on their obligations. A futures 
markets trader needs a liquidity pool to meet the daily mark to market. If 
liquidity is exhausted, the trader may be forced to unwind his position at an 
unfavorable time.

Reading 10 ■ Common Probability Distributions 566
 Suppose you are using financial futures contracts to hedge a risk in your 
portfolio. You have a liquidity pool (cash and cash equivalents) of λ dollars per 
contract and a time horizon of T trading days. For a given size liquidity pool, λ, 
Kolb, Gay, and Hunter (1985) developed an expression for the probability 
stating that you will exhaust your liquidity pool within a T-day horizon as a 
result of the daily mark to market. Kolb et al. assumed that the expected change 
in futures price is 0 and that futures price changes are normally distributed. 
With σ representing the standard deviation of daily futures price changes, the 
standard deviation of price changes over a time horizon to day T is σT, given 
continuous compounding. With that background, the Kolb et al. expression is
Probability of exhausting liquidity pool = 2[1 – N(x)]
 where  xT=()λσ . Here x is a standardized value of λ. N(x) is the standard

normal cumulative distribution function. For some intuition about 1 − N(x) in 
the expression, note that the liquidity pool is exhausted if losses exceed the size 
of the liquidity pool at any time up to and including T; the probability of that 
event happening can be shown to be proportional to an area in the right tail of 
a standard normal distribution, 1 − N(x).
 Using the Kolb et al. expression, answer the following questions:
A Your hedging horizon is five days, and your liquidity pool is $2,000 per con -
tract. You estimate that the standard deviation of daily price changes for the 
contract is $450. What is the probability that you will exhaust your liquidity 
pool in the five-  day period?
B Suppose your hedging horizon is 20 days, but all the other facts given in 
Part A remain the same. What is the probability that you will exhaust your 
liquidity pool in the 20-  day period?
14 Which of the following is characteristic of the normal distribution?
A Asymmetry
B Kurtosis of 3

C Definitive limits or boundaries
15 Which of the following assets most likely  requires the use of a multivariate dis -
tribution for modeling returns? 
A A call option on a bond 
B A portfolio of technology stocks 
C A stock in a market index
16 The total number of parameters that fully characterizes a multivariate normal 
distribution for the returns on two stocks is:
A 3.
B 4.
C 5.
17 A client has a portfolio of common stocks and fixed-  income instruments 
with a current value of £1,350,000. She intends to liquidate £50,000 from the 
portfolio at the end of the year to purchase a partnership share in a business. 
Furthermore, the client would like to be able to withdraw the £50,000 without 
reducing the initial capital of £1,350,000. The following table shows four alter -
native asset allocations.

Practice Problems 567
Mean and Standard Deviation for Four Allocations (in 
Percent)
A B C D
Expected annual return 16 12 10 9
Standard deviation of return 24 17 12 11
 Address the following questions (assume normality for Parts B and C):
A Given the client’s desire not to invade the £1,350,000 principal, what is the 
shortfall level, RL? Use this shortfall level to answer Part B.
B According to the safety-  first criterion, which of the allocations is the best?
C What is the probability that the return on the safety-  first optimal portfolio 
will be less than the shortfall level, RL?
Please refer to Exhibit 1 for Questions 18 and 19
Exhibit 1    Z-Table Values, P(Z ≤ z) = N(z) for z ≥ 0
Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141

0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517
0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879
0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224
18 A portfolio has an expected mean return of 8 percent and standard deviation 
of 14 percent. The probability that its return falls between 8 and 11 percent is 
A 8.3%
B 14.8%.
C 58.3%.
19 A portfolio has an expected return of 7% with a standard deviation of 13%. For 
an investor with a minimum annual return target of 4%, the probability that the 
portfolio return will fail to meet the target is closest to:
A 33%.
B 41%.
C 59%.
20 A Define Monte Carlo simulation and explain its use in finance.

Reading 10 ■ Common Probability Distributions 568
B Compared with analytical methods, what are the strengths and weaknesses 
of Monte Carlo simulation for use in valuing securities?
21 A standard lookback call option on stock has a value at maturity equal to (Value 
of the stock at maturity – Minimum value of stock during the life of the option 
prior to maturity) or $0, whichever is greater. If the minimum value reached 
prior to maturity was $20.11 and the value of the stock at maturity is $23, for 
example, the call is worth $23 − $20.11 = $2.89. Briefly discuss how you might 
use Monte Carlo simulation in valuing a lookback call option.
22 Which of the following is a continuous random variable?
A The value of a futures contract quoted in increments of $0.05
B The total number of heads recorded in 1 million tosses of a coin
C The rate of return on a diversified portfolio of stocks over a three-  month 
period
23 X is a discrete random variable with possible outcomes X = {1,2,3,4}. Three

functions f(x), g(x), and h(x) are proposed to describe the probabilities of the 
outcomes in X.
Probability Function
X = x f(x) = P(X = x ) g(x) = P(X = x ) h(x) = P(X = x )
1 –0.25 0.20 0.20
2 0.25 0.25 0.25
3 0.50 0.50 0.30
4 0.25 0.05 0.35
 The conditions for a probability function are satisfied by:
A f(x).
B g(x).
C h(x).
24 The cumulative distribution function for a discrete random variable is shown in 
the following table.
X = xCumulative Distribution Function  
F(x) = P(X ≤ x) 
1 0.15
2 0.25
3 0.50
4 0.60
5 0.95
6 1.00
 The probability that X will take on a value of either 2 or 4 is closest  to:
A 0.20.
B 0.35.
C 0.85.
25 Which of the following events can be represented as a Bernoulli trial?
A The flip of a coin
B The closing price of a stock
C The picking of a random integer between 1 and 10

Practice Problems 569
26 The weekly closing prices of Mordice Corporation shares are as follows: 
Date Closing Price (€)
1 August 112
8 August 160
15 August 120
 The continuously compounded return of Mordice Corporation shares for the 
period August 1 to August 15 is closest to :
A 6.90%
B 7.14%
C 8.95%
27 A stock is priced at $100.00 and follows a one-  period binomial process with 
an up move that equals 1.05 and a down move that equals 0.97. If 1 million 
Bernoulli trials are conducted, and the average terminal stock price is $102.00, 
the probability of an up move ( p) is closest to:
A 0.375.
B 0.500.
C 0.625.
28 A call option on a stock index is valued using a three-  step binomial tree with an 
up move that equals 1.05 and a down move that equals 0.95. The current level 
of the index is $190, and the option exercise price is $200. If the option value 
is positive when the stock price exceeds the exercise price at expiration and $0 
otherwise, the number of terminal nodes with a positive payoff is:

A one.
B two.
C three.
29 A random number between zero and one is generated according to a continu -
ous uniform distribution. What is the probability that the first number gener -
ated will have a value of exactly 0.30?
A 0%
B 30%
C 70%
30 A Monte Carlo simulation can be used to:
A directly provide precise valuations of call options.
B simulate a process from historical records of returns.
C test the sensitivity of a model to changes in assumptions.
31 A limitation of Monte Carlo simulation is:
A its failure to do “what if” analysis.
B that it requires historical records of returns
C its inability to independently specify cause-  and-  effect relationships.
32 Which parameter equals zero in a normal distribution?
A Kurtosis
B Skewness
C Standard deviation
33 An analyst develops the following capital market projections.

Reading 10 ■ Common Probability Distributions 570
Stocks Bonds
Mean Return 10% 2%
Standard Deviation 15% 5%
 Assuming the returns of the asset classes are described by normal distributions, 
which of the following statements is correct?
A Bonds have a higher probability of a negative return than stocks.
B On average, 99% of stock returns will fall within two standard deviations of 
the mean.
C The probability of a bond return less than or equal to 3% is determined 
using a Z-score of 0.25.
34 A client holding a £2,000,000 portfolio wants to withdraw £90,000 in one year 
without invading the principal. According to Roy’s safety-  first criterion, which 
of the following portfolio allocations is optimal?
Allocation A Allocation B Allocation C
Expected annual return 6.5% 7.5% 8.5%
Standard deviation of returns 8.35% 10.21% 14.34%
A Allocation A
B Allocation B
C Allocation C
35 In contrast to normal distributions, lognormal distributions:
A are skewed to the left.
B have outcomes that cannot be negative.

C are more suitable for describing asset returns than asset prices.
36 The lognormal distribution is a more accurate model for the distribution of 
stock prices than the normal distribution because stock prices are:
A symmetrical.
B unbounded.
C non-  negative.
37 The price of a stock at t = 0 is $208.25 and at t = 1 is $186.75. The continuously 
compounded rate of return for the stock from t = 0 to  t = 1 is closest to:
A –10.90%.
B –10.32%.
C 11.51%.

Solutions 571
SOLUTIONS
1 A The put’s minimum value is $0. The put’s value is $0 when the stock price 
is at or above $100 at the maturity date of the option. The put’s maximum 
value is $100 = $100 (the exercise price) − $0 (the lowest possible stock 
price). The put’s value is $100 when the stock is worthless at the option’s 
maturity date. The put’s minimum price increments are $0.01. The possible 
outcomes of terminal put value are thus $0.00, $0.01, $0.02, …, $100.
B The price of the underlying has minimum price fluctuations of $0.01: These 
are the minimum price fluctuations for terminal put value. For example, if 
the stock finishes at $98.20, the payoff on the put is $100 − $98.20 = $1.80. 
We can specify that the nearest values to $1.80 are $1.79 and $1.81. With a 
continuous random variable, we cannot specify the nearest values. So, we 
must characterize terminal put value as a discrete random variable.
C The probability that terminal put value is less than or equal to $24 is P(Y ≤

24) or F(24), in standard notation, where F is the cumulative distribution 
function for terminal put value.
2 A binomial random variable is defined as the number of successes in n 
Bernoulli trials (a trial that produces one of two outcomes). The binomial distri -
bution is used to make probability statements about a record of successes and 
failures or about anything with binary (twofold) outcomes.
3 B is correct. The value of the cumulative distribution function lies between 0 
and 1 for any x: 0 ≤ F(x) ≤ 1. 
4 C is correct. The binomial distribution is symmetric when the probability of 
success on a trial is 0.50, but it is asymmetric or skewed otherwise. Here it is 
given that p = 0.50 
5 B is correct. The probability of any outcome is 0.05, P(1) = 1/20 = 0.05. 
The probability that X is greater than or equal to 3 but less than 6, which is 
expressed as P(3 ≤ X < 6) = P(3) + P(4) + P(5) = 0.05 + 0.05 + 0.05 = 0.15
6 A The probability of an earnings increase (success) in a year is estimated as

7/10 = 0.70 or 70 percent, based on the record of the past 10 years.
B The probability that earnings will increase in 5 out of the next 10 years is 
about 10.3 percent. Define a binomial random variable X, counting the 
number of earnings increases over the next 10 years. From Part A, the prob -
ability of an earnings increase in a given year is p = 0.70 and the number 
of trials (years) is n = 10. Equation 1 gives the probability that a binomial 
random variable has x successes in n trials, with the probability of success 
on a trial equal to p.
PX xxnppn
nx xppx nx x nx=() =()−() =−()−()−−11!
!!
 For this example,
51007 0310
10 5507 03
252 0 16807 0 00251 05 51 05()=−()
=× ×−−..!
!!..
.. 4 43 0 102919=.
 We conclude that the probability that earnings will increase in exactly 5 of 
the next 10 years is 0.1029, or approximately 10.3 percent.
C The expected number of yearly increases is E(X) = np = 10 × 0.70 = 7.

Reading 10 ■ Common Probability Distributions 572
D The variance of the number of yearly increases over the next 10 years is σ2 
= np (1 − p) = 10 × 0.70 × 0.30 = 2.1. The standard deviation is 1.449 (the 
positive square root of 2.1).
E You must assume that 1) the probability of an earnings increase (success) is 
constant from year to year and 2) earnings increases are independent trials. 
If current and past earnings help forecast next year’s earnings, Assumption 
2 is violated. If the company’s business is subject to economic or industry 
cycles, neither assumption is likely to hold.
7 B is correct. To calculate the probability of 4 years of outperformance, use the 
formula:
px PX xn
xppn

!!
 Using this formula to calculate the probability in 4 of 5 years, n = 5, x = 4 and p 
= 0.60. 
 Therefore, 
p45
54 406 10 6 120 24 0 1296 0400 25924 54()=−()−() =[] () () =− !
!!.. .. .
p55
55 506 10 6 120 120 0 0778 10 07785 55()=−()−() =[] () ()=− !
!!.. ..

!!.. ..
 The probability of outperforming 4 or more times is p(4) + p(5) = 0.2592 + 
0.0778 = 0.3370 
8 The observed success rate is 4/7 = 0.571, or 57.1 percent. The probability of four 
or fewer successes is F(4) = p(4) + p(3) + p(2) + p(1) + p(0), where p(4), p(3), 
p(2), p(1), and p(0) are respectively the probabilities of 4, 3, 2, 1, and 0 suc -
cesses, according to the binomial distribution with n = 7 and p = 0.70. We have
p(4) = (7!/4!3!)(0.704)(0.303) = 35(0.006483) = 0.226895
p(3) = (7!/3!4!)(0.703)(0.304) = 35(0.002778) = 0.097241
p(2) = (7!/2!5!)(0.702)(0.305) = 21(0.001191) = 0.025005
p(1) = (7!/1!6!)(0.701)(0.306) = 7(0.000510) = 0.003572
p(0) = (7!/0!7!)(0.700)(0.307) = 1(0.000219) = 0.000219
 Summing all these probabilities, you conclude that F(4) = 0.226895 + 
0.097241 + 0.025005 + 0.003572 + 0.000219 = 0.352931, or 35.3 percent.
9 A The expected value of fourth-  quarter sales is €14,500,000, calculated as 
(€14,000,000 + €15,000,000)/2. With a continuous uniform random variable,

the mean or expected value is the midpoint between the smallest and largest 
values. (See Example 7.)
B The probability that fourth-  quarter sales will be less than €14,125,000 
is 0.125 or 12.5 percent, calculated as (€14,125,000 − €14,000,000)/
(€15,000,000 − €14,000,000).
10 A Approximately 68 percent of all outcomes of a normal random variable fall 
within plus or minus one standard deviation of the mean.
B Approximately 95 percent of all outcomes of a normal random variable fall 
within plus or minus two standard deviations of the mean.
C Approximately 99 percent of all outcomes of a normal random variable fall 
within plus or minus three standard deviations of the mean.

Solutions 573
11 The area under the normal curve for z = 0.36 is 0.6406 or 64.06 percent. The fol -
lowing table presents an excerpt from the tables of the standard normal cumu -
lative distribution function in the back of this volume. To locate z = 0.36, find 
0.30 in the fourth row of numbers, then look at the column for 0.06 (the second 
decimal place of 0.36). The entry is 0.6406.
P(Z ≤ x) = N(x) for x ≥ 0 or P(Z ≤ z) = N(z) for z ≥ 0 

The interpretation of 64.06 percent for z = 0.36 is that 64.06 percent of obser -
vations on a standard normal random variable are smaller than or equal to the 
value 0.36. (So 100% − 64.06% = 35.94% of the values are greater than 0.36.)
12 C is correct. The probability that the performance is at or below the expectation 
is calculated by finding F(3) = p(3) + p(2) + p(1) using the formula:
px PX xn
xppn

!!
 Using this formula, 
p34
43 30751 0752 46 0420 25 0423 43()=−()−() =[] () () =− !
!!.. .. .
p24
42 20751 0752 44 0560 06 0202 42()=−()−() =[] () () =− !
!!.. .. .
p14
41 10751 0752 46 0750 02 0061 41()=−()−() =[] () () =− !
!!.. .. .
F(3) = p(3) + p(2) + p(1) = 0.42 + 0.20 + 0.06 = 0.68 or 68.0
13 A The probability of exhausting the liquidity pool is 4.7 percent. First calcu -
late xT=() = () λσ $, $ 2 000 450 5  = 1.987616. We can round this value 
to 1.99 to use the standard normal tables in the back of this book. Using

those tables, we find that N(1.99) = 0.9767. Thus, the probability of exhaust -
ing the liquidity pool is 2[1 − N(1.99)] = 2(1 − 0.9767) = 0.0466 or about 
4.7 percent.
B The probability of exhausting the liquidity pool is now 32.2 percent. The 
calculation follows the same steps as those in Part A. We calcu -
late xT=() = () λσ $, $ 2 000 450 20  = 0.993808. We can round this value 
to 0.99 to use the standard normal tables in the back of this book. Using

Reading 10 ■ Common Probability Distributions 574
those tables, we find that N(0.99) = 0.8389. Thus, the probability of exhaust -
ing the liquidity pool is 2[1 − N(0.99)] = 2(1 − 0.8389) = 0.3222 or about 
32.2 percent. This is a substantial probability that you will run out of funds 
to meet mark to market.
 In their paper, Kolb et al. call the probability of exhausting the liquidity pool 
the probability of ruin, a traditional name for this type of calculation.
14 B is correct. The normal distribution has a skewness of 0, a kurtosis of 3, and a 
mean, median and mode that are all equal. 
15 B is correct. Multivariate distributions specify the probabilities for a group of 
related random variables. A portfolio of technology stocks represents a group 
of related assets. Accordingly, statistical interrelationships must be considered, 
resulting in the need to use a multivariate normal distribution. 
16 C is correct. A bivariate normal distribution (two stocks) will have two means,

two variances and one correlation. A multivariate normal distribution for the 
returns on n stocks will have n means, n variances and n(n – 1)/2 distinct 
correlations. 
17 A Because £50,000/£1,350,000 is 3.7 percent, for any return less than 3.7 per -
cent the client will need to invade principal if she takes out £50,000. So RL = 
3.7 percent.
B To decide which of the allocations is safety-  first optimal, select the alterna -
tive with the highest ratio [ E(RP) − RL]/σP:
Allocation A: 0.5125 = (16 – 3.7)/24
Allocation B: 0.488235 = (12 – 3.7)/17
Allocation C: 0.525 = (10 – 3.7)/12
Allocation D: 0.481818 = (9 – 3.7)/11
 Allocation C, with the largest ratio (0.525), is the best alternative according 
C To answer this question, note that P(RC < 3.7) = N(−0.525). We can round 
0.525 to 0.53 for use with tables of the standard normal cdf. First, we calcu -
late N(−0.53) = 1 − N(0.53) = 1 − 0.7019 = 0.2981 or about 30 percent. The

safety-  first optimal portfolio has a roughly 30 percent chance of not meeting 
a 3.7 percent return threshold.
18 A is correct. P(8% ≤ Portfolio return ≤ 11%) = N(Z corresponding to 11%) 
– N(Z corresponding to 8%). For the first term, Z = (11% – 8%)/14% = 0.21 
approximately, and using the table of cumulative normal distribution given in 
the problem, N(0.21) = 0.5832. To get the second term immediately, note that 
8 percent is the mean, and for the normal distribution 50 percent of the proba -
bility lies on either side of the mean. Therefore, N(Z corresponding to 8%) must 
equal 50 percent. So P(8% ≤ Portfolio return ≤ 11%) = 0.5832 – 0.50 = 0.0832 or 
approximately 8.3 percent. 
19 B is correct. There are three steps, which involve standardizing the portfo -
lio return: First, subtract the portfolio mean return from each side of the 
inequality: P(Portfolio return – 7%) ≤ 4% – 7%). Second, divide each side of the

inequality by the standard deviation of portfolio return: P[(Portfolio return – 
7%)/13% ≤ (4% – 7%)/13%] = P(Z ≤ –0.2308) = N(–0.2308). Third, recognize 
that on the left-  hand side we have a standard normal variable, denoted by Z 
and N(–x) = 1 – N(x). Rounding –0.2308 to –0.23 for use with the cumulative

Solutions 575
distribution function (cdf) table, we have N(–0.23) = 1 – N(0.23) = 1 – 0.5910 = 
0.409, approximately 41 percent. The probability that the portfolio will under -
perform the target is about 41 percent. 
20 A Elements that should appear in a definition of Monte Carlo simulation are 
that it makes use of a computer; that it is used to represent the operation of 
a complex system, or in some applications, to find an approximate solu -
tion to a problem; and that it involves the generation of a large number of 
random samples from a specified probability distribution. The exact wording 
can vary, but one definition follows:
 Monte Carlo simulation in finance involves the use of a computer to repre -
sent the operation of a complex financial system. In some important appli -
cations, Monte Carlo simulation is used to find an approximate solution to 
a complex financial problem. An integral part of Monte Carlo simulation

is the generation of a large number of random samples from a probability 
B Strengths.  Monte Carlo simulation can be used to price complex securities 
for which no analytic expression is available, particularly European-  style 
options.
 Weaknesses.  Monte Carlo simulation provides only statistical estimates, not 
exact results. Analytic methods, when available, provide more insight into 
cause-  and-  effect relationships than does Monte Carlo simulation.
21 In the text, we described how we could use Monte Carlo simulation to value 
an Asian option, a complex European-  style option. Just as we can calculate the 
average value of the stock over a simulation trial to value an Asian option, we 
can also calculate the minimum value of the stock over a simulation trial. Then, 
for a given simulation trial, we can calculate the terminal value of the call, given 
the minimum value of the stock for the simulation trial. We can then discount

back this terminal value to the present to get the value of the call today ( t = 0). 
The average of these t = 0 values over all simulation trials is the Monte Carlo 
simulated value of the lookback call option.
22 C is correct. The rate of return is a random variable because the future out -
comes are uncertain, and it is continuous because it can take on an unlimited 
number of outcomes.
23 B is correct. The function g(x) satisfies the conditions of a probability function. 
All of the values of g(x) are between 0 and 1, and the values of g(x) all sum to 1.
24 A is correct. The probability that X will take on a value of 4 or less is: F(4) = 
P(X ≤ 4) = p(1) + p(2) + p(3) + p(4) = 0.60. The probability that X will take on a 
value of 3 or less is: F(3) = P(X ≤ 3) = p(1) + p(2) + p(3) = 0.50. So, the probabil -
ity that X will take on a value of 4 is: F(4) – F(3) = p(4) = 0.10. The probability of 
X = 2 can be found using the same logic: F(2) – F(1) = p(2) = 0.25 – 0.15 = 0.10.

The probability of X taking on a value of 2 or 4 is: p(2) + p(4) = 0.10 + 0.10 = 
0.20.
25 A is correct. A trial, such as a coin flip, will produce one of two outcomes. Such 
a trial is a Bernoulli trial.
26 A is correct. The continuously compounded return of an asset over a period is 
equal to the natural log of period’s change. In this case:
ln(120/112) = 6.90% 
27 C is correct. The probability of an up move ( p) can be found by solving the 
equation: ( p)uS + (1 – p)dS = (p)105 + (1 – p)97 = 102. Solving for p gives 8 p = 
5, so that p = 0.625.

Reading 10 ■ Common Probability Distributions 576
28 A is correct. Only the top node value of $219.9488 exceeds $200.
$190.0000$199.5000$209.4750$219.9488
$180.5000$189.5250
$171.4750$199.0013
$180.0488
$162.9013
29 A is correct. The probability of generating a random number equal to any fixed 
point under a continuous uniform distribution is zero.
30 C is correct. A characteristic feature of Monte Carlo simulation is the genera -
tion of a large number of random samples from a specified probability distribu -
tion or distributions to represent the role of risk in the system.
31 C is correct. Monte Carlo simulation is a complement to analytical methods. 
Monte Carlo simulation provides statistical estimates and not exact results. 
Analytical methods, when available, provide more insight into cause-  and-  effect 
relationships
32 B is correct. A normal distribution has a skewness of zero (it is symmetrical 
around the mean). A non-  zero skewness implies asymmetry in a distribution.

33 A is correct. The chance of a negative return falls in the area to the left of 0% 
under a standard normal curve. By standardizing the returns and standard devi -
ations of the two assets, the likelihood of either asset experiencing a negative 
return may be determined: Z-score (standardized value) = ( X – μ)/σ
Z-score for a bond return of 0% = (0 – 2)/5 = –0.40.
Z-score for a stock return of 0% = (0 – 10)/15 = –0.67.
 For bonds, a 0% return falls 0.40 standard deviations below the mean return 
of 2%. In contrast, for stocks, a 0% return falls 0.67 standard deviations below 
the mean return of 10%. A standard deviation of 0.40 is less than a standard 
deviation of 0.67. Negative returns thus occupy more of the left tail of the bond 
distribution than the stock distribution. Thus, bonds are more likely than stocks 
to experience a negative return.
34 B is correct. Allocation B has the highest safety-  first ratio. The threshold return

level RL for the portfolio is £90,000/£2,000,000 = 4.5%, thus any return less than 
RL = 4.5% will invade the portfolio principal. To compute the allocation that is 
safety-  first optimal, select the alternative with the highest ratio:
ER RPL
P− ()
σ
Allocation A =  65 45
835..
.−= 0.240
Allocation B =  75 45
10 21..
.−= 0.294
Allocation C =  85 45
14 34..
.−= 0.279

Solutions 577
35 B is correct. By definition, lognormal random variables cannot have negative 
values.
36 C is correct. A lognormal distributed variable has a lower bound of zero. 
The lognormal distribution is also right skewed, which is a useful property in 
describing asset prices.
37 A is correct. The continuously compounded return from t = 0 to t = 1 is r0,1 = 
ln(S1/S0) = ln(186.75/208.25) = –0.10897 = –10.90%.

Sampling and Estimation
a. define simple random sampling and a sampling distribution;
b. explain sampling error;
c. distinguish between simple random and stratified random 
sampling;
d. distinguish between time-  series and cross-  sectional data;
e. explain the central limit theorem and its importance;
f. calculate and interpret the standard error of the sample mean;
g. identify and describe desirable properties of an estimator;
h. distinguish between a point estimate and a confidence interval 
estimate of a population parameter;

i. describe properties of Student’s t-distribution and calculate and 
interpret its degrees of freedom;
j. calculate and interpret a confidence interval for a population 
mean, given a normal distribution with 1) a known population 
variance, 2) an unknown population variance, or 3) an unknown 
population variance and a large sample size;
k. describe the issues regarding selection of the appropriate sample 
size, data-  mining bias, sample selection bias, survivorship bias, 
look-  ahead bias, and time-  period bias.rEAdING
11

Reading 11 ■ Sampling and Estimation 580
Each day, we observe the high, low, and close of stock market indexes from around 
the world. Indexes such as the S&P 500 Index and the Nikkei-  Dow Jones Average 
are samples of stocks. Although the S&P 500 and the Nikkei do not represent the 
populations of US or Japanese stocks, we view them as valid indicators of the whole 
population’s behavior. As analysts, we are accustomed to using this sample information 
to assess how various markets from around the world are performing. Any statistics 
that we compute with sample information, however, are only estimates of the under -
lying population parameters. A sample, then, is a subset of the population—a subset 
studied to infer conclusions about the population itself.
This reading explores how we sample and use sample information to estimate 
population parameters. In the next section, we discuss sampling —the process of

obtaining a sample. In investments, we continually make use of the mean as a measure 
of central tendency of random variables, such as return and earnings per share. Even 
when the probability distribution of the random variable is unknown, we can make 
probability statements about the population mean using the central limit theorem. 
In Section 3, we discuss and illustrate this key result. Following that discussion, we 
turn to statistical estimation. Estimation seeks precise answers to the question “What 
is this parameter’s value?”
The central limit theorem and estimation are the core of the body of methods pre -
sented in this reading. In investments, we apply these and other statistical techniques 
to financial data; we often interpret the results for the purpose of deciding what works 
and what does not work in investments. We end this reading with a discussion of the 
interpretation of statistical results based on financial data and the possible pitfalls in 
this process.
SAMPLING

SAMPLING
In this section, we present the various methods for obtaining information on a pop -
ulation (all members of a specified group) through samples (part of the population). 
The information on a population that we try to obtain usually concerns the value of a 
parameter , a quantity computed from or used to describe a population of data. When 
we use a sample to estimate a parameter, we make use of sample statistics (statistics, 
for short). A statistic  is a quantity computed from or used to describe a sample of data.
We take samples for one of two reasons. In some cases, we cannot possibly exam -
ine every member of the population. In other cases, examining every member of the 
population would not be economically efficient. Thus, savings of time and money are 
two primary factors that cause an analyst to use sampling to answer a question about 
a population. In this section, we discuss two methods of random sampling: simple

random sampling and stratified random sampling. We then define and illustrate the 
two types of data an analyst uses: cross-  sectional data and time-  series data.
2.1 Simple Random Sampling
Suppose a telecommunications equipment analyst wants to know how much major 
customers will spend on average for equipment during the coming year. One strat -
egy is to survey the population of telecom equipment customers and inquire what 
their purchasing plans are. In statistical terms, the characteristics of the population 1
2

Sampling 581
of customers’ planned expenditures would then usually be expressed by descriptive 
measures such as the mean and variance. Surveying all companies, however, would 
be very costly in terms of time and money.
Alternatively, the analyst can collect a representative sample of companies and 
survey them about upcoming telecom equipment expenditures. In this case, the analyst 
will compute the sample mean expenditure,  X, a statistic. This strategy has a sub -
stantial advantage over polling the whole population because it can be accomplished 
more quickly and at lower cost.
Sampling, however, introduces error. The error arises because not all the companies 
in the population are surveyed. The analyst who decides to sample is trading time and 
money for sampling error.
When an analyst chooses to sample, he must formulate a sampling plan. A sam -
pling plan  is the set of rules used to select a sample. The basic type of sample from

which we can draw statistically sound conclusions about a population is the simple 
random sample  (random sample, for short).
■■Definition of Simple Random Sample.  A simple random sample is a subset of 
a larger population created in such a way that each element of the population 
The procedure of drawing a sample to satisfy the definition of a simple random sample 
is called simple random sampling . How is simple random sampling carried out? We 
need a method that ensures randomness—the lack of any pattern—in the selection of 
the sample. For a finite (limited) population, the most common method for obtaining 
a random sample involves the use of random numbers (numbers with assured prop -
erties of randomness). First, we number the members of the population in sequence. 
For example, if the population contains 500 members, we number them in sequence 
with three digits, starting with 001 and ending with 500. Suppose we want a simple

random sample of size 50. In that case, using a computer random-  number generator 
or a table of random numbers, we generate a series of three-  digit random numbers. 
We then match these random numbers with the number codes of the population 
members until we have selected a sample of size 50.
Sometimes we cannot code (or even identify) all the members of a population. We 
often use systematic sampling  in such cases. With systematic sampling, we select 
every kth member until we have a sample of the desired size. The sample that results 
from this procedure should be approximately random. Real sampling situations may 
require that we take an approximately random sample.
Suppose the telecommunications equipment analyst polls a random sample of 
telecom equipment customers to determine the average equipment expenditure. 
The sample mean will provide the analyst with an estimate of the population mean 
expenditure. Any difference between the sample mean and the population mean is

called sampling error .
■■Definition of Sampling Error.  Sampling error is the difference between the 
observed value of a statistic and the quantity it is intended to estimate.
A random sample reflects the properties of the population in an unbiased way, 
and sample statistics, such as the sample mean, computed on the basis of a random 
sample are valid estimates of the underlying population parameters.
A sample statistic is a random variable. In other words, not only do the original 
data from the population have a distribution but so does the sample statistic.

Reading 11 ■ Sampling and Estimation 582
This distribution is the statistic’s sampling distribution .
■■Definition of Sampling Distribution of a Statistic.  The sampling distribution 
of a statistic is the distribution of all the distinct possible values that the statistic 
can assume when computed from samples of the same size randomly drawn 
from the same population.
In the case of the sample mean, for example, we refer to the “sampling distribution 
of the sample mean” or the distribution of the sample mean. We will have more to say 
about sampling distributions later in this reading. Next, however, we look at another 
sampling method that is useful in investment analysis.
2.2 Stratified Random Sampling
The simple random sampling method just discussed may not be the best approach in 
all situations. One frequently used alternative is stratified random sampling.
■■Definition of Stratified Random Sampling.  In stratified random sampling, the

population is divided into subpopulations (strata) based on one or more classi -
fication criteria. Simple random samples are then drawn from each stratum in 
sizes proportional to the relative size of each stratum in the population. These 
samples are then pooled to form a stratified random sample.
In contrast to simple random sampling, stratified random sampling guarantees that 
population subdivisions of interest are represented in the sample. Another advan -
tage is that estimates of parameters produced from stratified sampling have greater 
precision—  that is, smaller variance or dispersion—than estimates obtained from 
simple random sampling.
Bond indexing is one area in which stratified sampling is frequently applied. 
Indexing  is an investment strategy in which an investor constructs a portfolio to 
mirror the performance of a specified index. In pure bond indexing, also called the 
full-  replication approach, the investor attempts to fully replicate an index by owning

all the bonds in the index in proportion to their market value weights. Many bond 
indexes consist of thousands of issues, however, so pure bond indexing is difficult to 
implement. In addition, transaction costs would be high because many bonds do not 
have liquid markets. Although a simple random sample could be a solution to the 
cost problem, the sample would probably not match the index’s major risk factors—
interest rate sensitivity, for example. Because the major risk factors of fixed-  income 
portfolios are well known and quantifiable, stratified sampling offers a more effective 
approach. In this approach, we divide the population of index bonds into groups of 
similar duration (interest rate sensitivity), cash flow distribution, sector, credit quality, 
and call exposure. We refer to each group as a stratum or cell (a term frequently used 
in this context). Then, we choose a sample from each stratum proportional to the

relative market weighting of the stratum in the index to be replicated.
EXAMPLE 1   
Bond Indexes and Stratified Sampling
Suppose you are the manager of a mutual fund indexed to the Lehman Brothers 
Government Index. You are exploring several approaches to indexing, including a 
stratified sampling approach. You first distinguish agency bonds from US Treasury 
bonds. For each of these two groups, you define 10 maturity intervals—1 to 2 
years, 2 to 3 years, 3 to 4 years, 4 to 6 years, 6 to 8 years, 8 to 10 years, 10 to 12

Sampling 583
years, 12 to 15 years, 15 to 20 years, and 20 to 30 years—and also separate the 
bonds with coupons (annual interest rates) of 6 percent or less from the bonds 
with coupons of more than 6 percent.
1 How many cells or strata does this sampling plan entail?
2 If you use this sampling plan, what is the minimum number of issues the 
indexed portfolio can have?
3 Suppose that in selecting among the securities that qualify for selection 
within each cell, you apply a criterion concerning the liquidity of the secu -
rity’s market. Is the sample obtained random? Explain your answer.
We have 2 issuer classifications, 10 maturity classifications, and 2 coupon clas -
sifications. So, in total, this plan entails 2(10)(2) = 40 different strata or cells. 
(This answer is an application of the multiplication rule of counting discussed 
in the reading on probability concepts.)
You cannot have fewer than one issue for each cell, so the portfolio must include

at least 40 issues.
If you apply any additional criteria to the selection of securities for the cells, not 
every security that might be included has an equal probability of being selected. 
As a result, the sampling is not random. In practice, indexing using stratified 
sampling usually does not strictly involve random sampling because the selec -
tion of bond issues within cells is subject to various additional criteria. Because 
the purpose of sampling in this application is not to make an inference about a 
population parameter but rather to index a portfolio, lack of randomness is not 
in itself a problem in this application of stratified sampling.
In the next section, we discuss the kinds of data used by financial analysts in 
sampling and practical issues that arise in selecting samples.
2.3 Time-  Series and Cross-  Sectional Data
Investment analysts commonly work with both time-  series and cross-  sectional data. A

time series is a sequence of returns collected at discrete and equally spaced intervals 
of time (such as a historical series of monthly stock returns). Cross-  sectional data are 
data on some characteristic of individuals, groups, geographical regions, or companies 
at a single point in time. The 2014 year-  end book value per share for all New York 
Stock Exchange-  listed companies is an example of cross-  sectional data.
Economic or financial theory offers no basis for determining whether a long or 
short time period should be selected to collect a sample. As analysts, we might have 
to look for subtle clues. For example, combining data from a period of fixed exchange 
rates with data from a period of floating exchange rates would be inappropriate. The 
variance of exchange rates when exchange rates were fixed would certainly be less than 
when rates were allowed to float. As a consequence, we would not be sampling from

a population described by a single set of parameters.1 Tight versus loose monetary 
1 When the mean or variance of a time series is not constant through time, the time series is not stationary.

Reading 11 ■ Sampling and Estimation 584
policy  also influences the distribution of returns to stocks; thus, combining data from 
tight-  money and loose-  money periods would be inappropriate. Example 2 illustrates 
the problems that can arise when sampling from more than one distribution.
EXAMPLE 2   
Calculating Sharpe Ratios: One or Two Years of Quarterly 
Data
Analysts often use the Sharpe ratio to evaluate the performance of a managed 
portfolio. The Sharpe ratio  is the average return in excess of the risk-  free rate 
divided by the standard deviation of returns. This ratio measures the excess 
return earned per unit of standard deviation of return.
To compute the Sharpe ratio, suppose that an analyst collects eight quarterly 
excess returns (i.e., total return in excess of the risk-  free rate). During the first 
year, the investment manager of the portfolio followed a low-  risk strategy, and 
during the second year, the manager followed a high-  risk strategy. For each of

these years, the analyst also tracks the quarterly excess returns of some bench -
mark against which the manager will be evaluated. For each of the two years, 
the Sharpe ratio for the benchmark is 0.21. Table 1 gives the calculation of the 
Sharpe ratio of the portfolio.
Table 1   Calculation of Sharpe Ratios: Low-  Risk and High-  Risk 
Strategies
Quarter/MeasureY ear 1  
Excess ReturnsY ear 2  
Excess Returns
Quarter 1 −3% −12%
Quarter 2 5 20
Quarter 3 −3 −12
Quarter 4 5 20
Quarterly average 1% 4%
Quarterly standard deviation 4.62% 18.48%
Sharpe ratio = 0.22 = 1/4.62 = 4/18.48
For the first year, during which the manager followed a low-  risk strategy, 
the average quarterly return in excess of the risk-  free rate was 1 percent with a 
standard deviation of 4.62 percent. The Sharpe ratio is thus 1/4.62 = 0.22. The 
second year’s results mirror the first year except for the higher average return 
and volatility. The Sharpe ratio for the second year is 4/18.48 = 0.22. The Sharpe

ratio for the benchmark is 0.21 during the first and second years. Because larger 
Sharpe ratios are better than smaller ones (providing more return per unit of 
risk), the manager appears to have outperformed the benchmark.
Now, suppose the analyst believes a larger sample to be superior to a small 
one. She thus decides to pool the two years together and calculate a Sharpe ratio 
based on eight quarterly observations. The average quarterly excess return for 
the two years is the average of each year’s average excess return. For the two-  
year period, the average excess return is (1 + 4)/2 = 2.5 percent per quarter. The 
standard deviation for all eight quarters measured from the sample mean of 
2.5 percent is 12.57 percent. The portfolio’s Sharpe ratio for the two-  year period

Sampling 585
is now 2.5/12.57  = 0.199; the Sharpe ratio for the benchmark remains 0.21. 
Thus, when returns for the two-  year period are pooled, the manager appears 
to have provided less return per unit of risk than the benchmark and less when 
compared with the separate yearly results.
The problem with using eight quarters of return data is that the analyst has 
violated the assumption that the sampled returns come from the same population. 
As a result of the change in the manager’s investment strategy, returns in Year 
2 followed a different distribution than returns in Year 1. Clearly, during Year 
1, returns were generated by an underlying population with lower mean and 
variance than the population of the second year. Combining the results for the 
first and second years yielded a sample that was representative of no population. 
Because the larger sample did not satisfy model assumptions, any conclusions the

analyst reached based on the larger sample are incorrect. For this example, she 
was better off using a smaller sample than a larger sample because the smaller 
sample represented a more homogeneous distribution of returns.
The second basic type of data is cross-  sectional data.2 With cross-  sectional data, 
the observations in the sample represent a characteristic of individuals, groups, geo -
graphical regions, or companies at a single point in time. The telecommunications 
analyst discussed previously is essentially collecting a cross-  section of planned capital 
expenditures for the coming year.
Whenever we sample cross-  sectionally, certain assumptions must be met if we 
wish to summarize the data in a meaningful way. Again, a useful approach is to think 
of the observation of interest as a random variable that comes from some underlying 
population with a given mean and variance. As we collect our sample and begin to

summarize the data, we must be sure that all the data do, in fact, come from the same 
underlying population. For example, an analyst might be interested in how efficiently 
companies use their inventory assets. Some companies, however, turn over their inven -
tory more quickly than others because of differences in their operating environments 
(e.g., grocery stores turn over inventory more quickly than automobile manufacturers, 
in general). So the distribution of inventory turnover rates may not be characterized 
by a single distribution with a given mean and variance. Therefore, summarizing 
inventory turnover across all companies might be inappropriate. If random variables 
are generated by different underlying distributions, the sample statistics computed 
from combined samples are not related to one underlying population parameter. The 
size of the sampling error in such cases is unknown.
In instances such as these, analysts often summarize company-  level data by

industry. Attempting to summarize by industry partially addresses the problem of 
differing underlying distributions, but large corporations are likely to be in more than 
one industrial sector, so analysts should be sure they understand how companies are 
assigned to the industry groups.
Whether we deal with time-  series data or cross-  sectional data, we must be sure 
to have a random sample that is representative of the population we wish to study. 
With the objective of inferring information from representative samples, we now turn 
to the next part of this reading, which focuses on the central limit theorem as well as 
point and interval estimates of the population mean.
2 The reader may also encounter two types of datasets that have both time-  series and cross-  sectional aspects. 
Panel data  consist of observations through time on a single characteristic of multiple observational units.

For example, the annual inflation rate of the Eurozone countries over a five-  year period would represent 
panel data. Longitudinal data  consist of observations on characteristic(s) of the same observational unit 
through time. Observations on a set of financial ratios for a single company over a 10-  year period would be 
an example of longitudinal data. Both panel and longitudinal data may be represented by arrays (matrixes) 
in which successive rows represent the observations for successive time periods.

Reading 11 ■ Sampling and Estimation 586
DISTRIBUTION OF THE SAMPLE MEAN
Earlier in this reading, we presented a telecommunications equipment analyst who 
decided to sample in order to estimate mean planned capital expenditures by his cus -
tomers. Supposing that the sample is representative of the underlying population, how 
can the analyst assess the sampling error in estimating the population mean? Viewed 
as a formula that takes a function of the random outcomes of a random variable, the 
sample mean is itself a random variable with a probability distribution. That probability 
distribution is called the statistic’s sampling distribution.3 To estimate how closely the 
sample mean can be expected to match the underlying population mean, the analyst 
needs to understand the sampling distribution of the mean. Fortunately, we have a 
result, the central limit theorem, that helps us understand the sampling distribution 
of the mean for many of the estimation problems we face.

3.1 The Central Limit Theorem
One of the most practically useful theorems in probability theory, the central limit 
theorem has important implications for how we construct confidence intervals and 
test hypotheses. Formally, it is stated as follows:
■■The Central Limit Theorem.  Given a population described by any probability 
distribution having mean μ and finite variance σ2, the sampling distribution of 
the sample mean  X computed from samples of size n from this population will 
be approximately normal with mean μ (the population mean) and variance σ2/n 
(the population variance divided by n) when the sample size n is large.
The central limit theorem allows us to make quite precise probability statements 
about the population mean by using the sample mean, whatever the distribution of 
the population  (so long as it has finite variance), because the sample mean follows 
an approximate normal distribution for large-  size samples. The obvious question is,

“When is a sample’s size large enough that we can assume the sample mean is nor -
mally distributed?” In general, when sample size n is greater than or equal to 30, we 
can assume that the sample mean is approximately normally distributed.4
The central limit theorem states that the variance of the distribution of the sample 
mean is σ2/n. The positive square root of variance is standard deviation. The standard 
deviation of a sample statistic is known as the standard error of the statistic. The 
standard error of the sample mean is an important quantity in applying the central 
limit theorem in practice.
■■Definition of the Standard Error of the Sample Mean.  For sample mean  X 
calculated from a sample generated by a population with standard deviation σ, 
the standard error of the sample mean is given by one of two expressions:
σσ
Xn=3
(1)
3 Sometimes confusion arises because “sample mean” is also used in another sense. When we calculate

the sample mean for a particular sample, we obtain a definite number, say 8. If we state that “the sample 
mean is 8” we are using “sample mean” in the sense of a particular outcome of sample mean as a random 
variable. The number 8 is of course a constant and does not have a probability distribution. In this discussion, 
we are not referring to “sample mean” in the sense of a constant number related to a particular sample.
4 When the underlying population is very nonnormal, a sample size well in excess of 30 may be required 
for the normal distribution to be a good description of the sampling distribution of the mean.

Distribution of the Sample Mean 587
when we know σ, the population standard deviation, or by
ss
nX=
when we do not know the population standard deviation and need to use the 
sample standard deviation, s, to estimate it.5
In practice, we almost always need to use Equation 2. The estimate of s is given by 
the square root of the sample variance, s2, calculated as follows:
sXX
ni
in
22
1
1=−()
−=∑
We will soon see how we can use the sample mean and its standard error to make 
probability statements about the population mean by using the technique of confidence 
intervals. First, however, we provide an illustration of the central limit theorem’s force.
EXAMPLE 3   
The Central Limit Theorem
It is remarkable that the sample mean for large sample sizes will be distributed 
normally regardless of the distribution of the underlying population. To illus -
trate the central limit theorem in action, we specify in this example a distinctly

nonnormal distribution and use it to generate a large number of random samples 
of size 100. We then calculate the sample mean for each sample. The frequency 
distribution of the calculated sample means is an approximation of the sam -
pling distribution of the sample mean for that sample size. Does that sampling 
distribution look like a normal distribution?
We return to the telecommunications analyst studying the capital expenditure 
plans of telecom businesses. Suppose that capital expenditures for communi -
cations equipment form a continuous uniform random variable with a lower 
bound  equal to $0 and an upper bound equal to $100—for short, call this a 
uniform (0, 100) random variable. The probability function of this continuous 
uniform random variable has a rather simple shape that is anything but normal. 
It is a horizontal line with a vertical intercept equal to 1/100. Unlike a normal 
random variable, for which outcomes close to the mean are most likely, all pos -

sible outcomes are equally likely for a uniform random variable.
To illustrate the power of the central limit theorem, we conduct a Monte 
Carlo simulation to study the capital expenditure plans of telecom businesses.6 
In this simulation, we collect 200 random samples of the capital expenditures 
of 100 companies (200 random draws, each consisting of the capital expenditures 
of 100 companies with n = 100). In each simulation trial, 100 values for capital (2)
(3)
5 We need to note a technical point: When we take a sample of size n from a finite population of size N, 
we apply a shrinkage factor to the estimate of the standard error of the sample mean that is called the finite 
population correction factor (fpc). The fpc is equal to [( N − n)/(N − 1)]1/2. Thus, if N = 100 and n = 20, [(100 
− 20)/(100 − 1)]1/2 = 0.898933. If we have estimated a standard error of, say, 20, according to Equation 1

or Equation 2, the new estimate is 20(0.898933) = 17.978663. The fpc applies only when we sample from a 
finite population without replacement; most practitioners also do not apply the fpc if sample size n is very 
small relative to N (say, less than 5 percent of N). For more information on the finite population correction 
factor, see Daniel and Terrell (1995).
6 Monte Carlo simulation involves the use of a computer to represent the operation of a system subject 
to risk. An integral part of Monte Carlo simulation is the generation of a large number of random samples 
from a specified probability distribution or distributions.

Reading 11 ■ Sampling and Estimation 588
expenditure are generated from the uniform (0, 100) distribution. For each 
random sample, we then compute the sample mean. We conduct 200 simulation 
trials in total. Because we have specified the distribution generating the samples, 
we know that the population mean capital expenditure is equal to ($0 + $100 mil -
lion)/2 = $50 million; the population variance of capital expenditures is equal 
to (100 − 0)2/12 = 833.33; thus, the standard deviation is $28.87 million and the 
standard error is  28 87 100 .  = 2.887 under the central limit theorem.7
The results of this Monte Carlo experiment are tabulated in Table 2 in the 
form of a frequency distribution. This distribution is the estimated sampling 
distribution of the sample mean.
Table 2   Frequency Distribution: 200 Random 
Samples of a Uniform (0,100) Random 
Variable
Range of Sample Means ($ 
Million)Absolute Frequency
42.5 ≤  X < 44 1
44 ≤  X < 45.5 6
45.5 ≤  X < 47 22
47 ≤  X < 48.5 39
48.5 ≤  X < 50 41

50 ≤  X < 51.5 39
51.5 ≤  X < 53 23
53 ≤  X < 54.5 12
54.5 ≤  X < 56 12
56 ≤  X < 57.5 5
Note : X is the mean capital expenditure for each sample.
The frequency distribution can be described as bell-  shaped and centered 
close to the population mean of 50. The most frequent, or modal, range, with 
41 observations, is 48.5 to 50. The overall average of the sample means is $49.92, 
with a standard error equal to $2.80. The calculated standard error is close to 
the value of 2.887 given by the central limit theorem. The discrepancy between 
calculated and expected values of the mean and standard deviation under the 
central limit theorem is a result of random chance (sampling error).
In summary, although the distribution of the underlying population is very 
nonnormal, the simulation has shown that a normal distribution well describes 
the estimated sampling distribution of the sample mean, with mean and standard

error consistent with the values predicted by the central limit theorem.
7 If a is the lower limit of a uniform random variable and b is the upper limit, then the random variable’s 
mean is given by ( a + b)/2 and its variance is given by ( b − a)2/12. The reading on common probability 
distributions fully describes continuous uniform random variables.

Point and Interval Estimates of the Population Mean 589
To summarize, according to the central limit theorem, when we sample from any 
distribution, the distribution of the sample mean will have the following properties 
as long as our sample size is large:
■■The distribution of the sample mean  X will be approximately normal.
■■The mean of the distribution of  X will be equal to the mean of the population 
from which the samples are drawn.
■■The variance of the distribution of  X will be equal to the variance of the 
population divided by the sample size.
We next discuss the concepts and tools related to estimating the population 
parameters, with a special focus on the population mean. We focus on the population 
mean because analysts are more likely to meet interval estimates for the population 
mean than any other type of interval estimate.
POINT AND INTERVAL ESTIMATES OF THE 
POPULATION MEAN
Statistical inference traditionally consists of two branches, hypothesis testing and

estimation. Hypothesis testing addresses the question “Is the value of this parameter 
(say, a population mean) equal to some specific value (0, for example)?” In this process, 
we have a hypothesis concerning the value of a parameter, and we seek to determine 
whether the evidence from a sample supports or does not support that hypothesis. 
We discuss hypothesis testing in detail in the reading on hypothesis testing.
The second branch of statistical inference, and the focus of this reading, is esti -
mation. Estimation seeks an answer to the question “What is this parameter’s (for 
example, the population mean’s) value?” In estimating, unlike in hypothesis testing, we 
do not start with a hypothesis about a parameter’s value and seek to test it. Rather, we 
try to make the best use of the information in a sample to form one of several types 
of estimates of the parameter’s value. With estimation, we are interested in arriving

at a rule for best calculating a single number to estimate the unknown population 
parameter (a point estimate). Together with calculating a point estimate, we may also 
be interested in calculating a range of values that brackets the unknown population 
parameter with some specified level of probability (a confidence interval). In Section 
4.1 we discuss point estimates of parameters and then, in Section 4.2, the formulation 
of confidence intervals for the population mean.
4.1 Point Estimators
An important concept introduced in this reading is that sample statistics viewed as 
formulas involving random outcomes are random variables. The formulas that we 
use to compute the sample mean and all the other sample statistics are examples of 
estimation formulas or estimators . The particular value that we calculate from sample 
observations using an estimator is called an estimate . An estimator has a sampling 
distribution; an estimate is a fixed number pertaining to a given sample and thus has

no sampling distribution. To take the example of the mean, the calculated value of the 
sample mean in a given sample, used as an estimate of the population mean, is called 
a point estimate  of the population mean. As Example 3 illustrated, the formula for 
the sample mean can and will yield different results in repeated samples as different 
samples are drawn from the population.4

Reading 11 ■ Sampling and Estimation 590
In many applications, we have a choice among a number of possible estimators 
for estimating a given parameter. How do we make our choice? We often select esti -
mators because they have one or more desirable statistical properties. Following is 
a brief description of three desirable properties of estimators: unbiasedness (lack of 
bias), efficiency, and consistency.8
■■Definition of Unbiasedness.  An unbiased estimator is one whose expected 
value (the mean of its sampling distribution) equals the parameter it is intended 
to estimate.
For example, the expected value of the sample mean,  X, equals μ, the population 
mean, so we say that the sample mean is an unbiased estimator (of the population 
mean). The sample variance, s2, which is calculated using a divisor of n − 1 (Equation 3), 
is an unbiased estimator of the population variance, σ2. If we were to calculate the

sample variance using a divisor of n, the estimator would be biased: Its expected value 
would be smaller than the population variance. We would say that sample variance 
calculated with a divisor of n is a biased estimator of the population variance.
Whenever one unbiased estimator of a parameter can be found, we can usually find 
a large number of other unbiased estimators. How do we choose among alternative 
unbiased estimators? The criterion of efficiency provides a way to select from among 
unbiased estimators of a parameter.
■■Definition of Efficiency.  An unbiased estimator is efficient if no other unbi -
ased estimator of the same parameter has a sampling distribution with smaller 
variance.
To explain the definition, in repeated samples we expect the estimates from an efficient 
estimator to be more tightly grouped around the mean than estimates from other 
unbiased estimators. Efficiency is an important property of an estimator.9 Sample

mean  X is an efficient estimator of the population mean; sample variance s2 is an 
efficient estimator of σ2.
Recall that a statistic’s sampling distribution is defined for a given sample size. 
Different sample sizes define different sampling distributions. For example, the vari -
ance of sampling distribution of the sample mean is smaller for larger sample sizes. 
Unbiasedness and efficiency are properties of an estimator’s sampling distribution that 
hold for any size sample. An unbiased estimator is unbiased equally in a sample of size 
10 and in a sample of size 1,000. In some problems, however, we cannot find estima -
tors that have such desirable properties as unbiasedness in small samples.10 In this 
case, statisticians may justify the choice of an estimator based on the properties of the 
estimator’s sampling distribution in extremely large samples, the estimator’s so-  called 
asymptotic properties. Among such properties, the most important is consistency.

■■Definition of Consistency.  A consistent estimator is one for which the prob -
ability of estimates close to the value of the population parameter increases as 
sample size increases.
Somewhat more technically, we can define a consistent estimator as an estimator 
whose sampling distribution becomes concentrated on the value of the parameter it 
is intended to estimate as the sample size approaches infinity. The sample mean, in 
addition to being an efficient estimator, is also a consistent estimator of the population 
mean: As sample size n goes to infinity, its standard error,  σn, goes to 0 and its 
sampling distribution becomes concentrated right over the value of population mean, 
8 See Daniel and Terrell (1995) or Greene (2018) for a thorough treatment of the properties of estimators.
9 An efficient estimator is sometimes referred to as the best unbiased estimator.
10 Such problems frequently arise in regression and time-  series analyses.

Point and Interval Estimates of the Population Mean 591
μ. To summarize, we can think of a consistent estimator as one that tends to produce 
more and more accurate estimates of the population parameter as we increase the 
sample’s size. If an estimator is consistent, we may attempt to increase the accuracy 
of estimates of a population parameter by calculating estimates using a larger sample. 
For an inconsistent estimator, however, increasing sample size does not help to increase 
the probability of accurate estimates.
4.2 Confidence Intervals for the Population Mean
When we need a single number as an estimate of a population parameter, we make 
use of a point estimate. However, because of sampling error, the point estimate is not 
likely to equal the population parameter in any given sample. Often, a more useful 
approach than finding a point estimate is to find a range of values that we expect to 
bracket the parameter with a specified level of probability—an interval estimate of

the parameter. A confidence interval fulfills this role.
■■Definition of Confidence Interval.  A confidence interval is a range for which 
one can assert with a given probability 1 − α, called the degree of confidence , 
that it will contain the parameter it is intended to estimate. This interval is often 
referred to as the 100(1 − α)% confidence interval for the parameter.
The endpoints of a confidence interval are referred to as the lower and upper con -
fidence limits. In this reading, we are concerned only with two-  sided confidence 
intervals—confidence intervals for which we calculate both lower and upper limits.11
Confidence intervals are frequently given either a probabilistic interpretation or 
a practical interpretation. In the probabilistic interpretation, we interpret a 95 per -
cent confidence interval for the population mean as follows. In repeated sampling, 
95 percent of such confidence intervals will, in the long run, include or bracket the

population mean. For example, suppose we sample from the population 1,000 times, 
and based on each sample, we construct a 95 percent confidence interval using the 
calculated sample mean. Because of random chance, these confidence intervals will 
vary from each other, but we expect 95 percent, or 950, of these intervals to include 
the unknown value of the population mean. In practice, we generally do not carry 
out such repeated sampling. Therefore, in the practical interpretation, we assert that 
we are 95 percent confident that a single 95 percent confidence interval contains the 
population mean. We are justified in making this statement because we know that 
95 percent of all possible confidence intervals constructed in the same manner will 
contain the population mean. The confidence intervals that we discuss in this reading 
have structures similar to the following basic structure:
■■Construction of Confidence Intervals.  A 100(1 − α)% confidence interval for a

parameter has the following structure.
Point estimate ± Reliability factor × Standard error 
11 It is also possible to define two types of one-  sided confidence intervals for a population parameter. A 
lower one-  sided confidence interval establishes a lower limit only. Associated with such an interval is an 
assertion that with a specified degree of confidence the population parameter equals or exceeds the lower 
limit. An upper one-  sided confidence interval establishes an upper limit only; the related assertion is that 
the population parameter is less than or equal to that upper limit, with a specified degree of confidence. 
Investment researchers rarely present one-  sided confidence intervals, however.

Reading 11 ■ Sampling and Estimation 592
where
 Point estimate =  a point estimate of the parameter (a value of a 
sample statistic)
 Reliability factor =  a number based on the assumed distribution of 
the point estimate and the degree of confidence (1 − α) 
for the confidence interval
 Standard error =  the standard error of the sample statistic provid -
ing the point estimate12
The most basic confidence interval for the population mean arises when we are 
sampling from a normal distribution with known variance. The reliability factor in 
this case is based on the standard normal distribution, which has a mean of 0 and a 
variance of 1. A standard normal random variable is conventionally denoted by Z. 
The notation zα denotes the point of the standard normal distribution such that α of 
the probability remains in the right tail. For example, 0.05 or 5 percent of the possible 
values of a standard normal random variable are larger than z0.05 = 1.65.

Suppose we want to construct a 95 percent confidence interval for the population 
mean and, for this purpose, we have taken a sample of size 100 from a normally dis -
tributed population with known variance of σ2 = 400 (so, σ = 20). We calculate a 
sample mean of  X = 25. Our point estimate of the population mean is, therefore, 25. 
If we move 1.96 standard deviations above the mean of a normal distribution, 0.025 
or 2.5 percent of the probability remains in the right tail; by symmetry of the normal 
distribution, if we move 1.96 standard deviations below the mean, 0.025 or 2.5 percent 
of the probability remains in the left tail. In total, 0.05 or 5 percent of the probability 
is in the two tails and 0.95 or 95 percent lies in between. So, z0.025  = 1.96 is the reli -
ability factor for this 95 percent confidence interval. Note the relationship 100(1 − α)% 
for the confidence interval and the zα/2 for the reliability factor. The standard error

of the sample mean, given by Equation  1, is  σX=20 100  = 2. The confidence 
interval, therefore, has a lower limit of  XX−196 .σ = 25 – 1.96(2) = 25 – 3.92 = 21.08. 
The upper limit of the confidence interval is  XX+196 .σ = 25 + 1.96(2) = 25 + 3.92 = 
28.92. The 95  percent confidence interval for the population mean spans 21.08 to 
28.92.
■■Confidence Intervals for the Population Mean (Normally Distributed 
Population with Known Variance).  A 100(1 − α)% confidence interval for pop -
ulation mean μ when we are sampling from a normal distribution with known 
variance σ2 is given by
Xz
n±ασ
2
The reliability factors for the most frequently used confidence intervals are as follows.
■■Reliability Factors for Confidence Intervals Based on the Standard Normal 
Distribution.  We use the following reliability factors when we construct confi -
dence intervals based on the standard normal distribution:13
■●90 percent confidence intervals: Use z0.05 = 1.65(4)

12 The quantity (reliability factor) × (standard error) is sometimes called the precision of the estimator; 
larger values of the product imply lower precision in estimating the population parameter.
13 Most practitioners use values for z0.05 and z0.005  that are carried to two decimal places. For reference, 
more exact values for z0.05 and z0.005  are 1.645 and 2.575, respectively. For a quick calculation of a 95 percent 
confidence interval, z0.025  is sometimes rounded from 1.96 to 2.

Point and Interval Estimates of the Population Mean 593
■●95 percent confidence intervals: Use z0.025  = 1.96
■●99 percent confidence intervals: Use z0.005  = 2.58
These reliability factors highlight an important fact about all confidence intervals. 
As we increase the degree of confidence, the confidence interval becomes wider and 
gives us less precise information about the quantity we want to estimate. “The surer 
we want to be, the less we have to be sure of. ”14
In practice, the assumption that the sampling distribution of the sample mean is 
at least approximately normal is frequently reasonable, either because the underly -
ing distribution is approximately normal or because we have a large sample and the 
central limit theorem applies. However, rarely do we know the population variance 
in practice. When the population variance is unknown but the sample mean is at 
least approximately normally distributed, we have two acceptable ways to calculate

the confidence interval for the population mean. We will soon discuss the more 
conservative approach, which is based on Student’s t-distribution (the t-distribution, 
for short).15 In investment literature, it is the most frequently used approach in both 
estimation and hypothesis tests concerning the mean when the population variance 
is not known, whether sample size is small or large.
A second approach to confidence intervals for the population mean, based on the 
standard normal distribution, is the z-alternative. It can be used only when sample 
size is large. (In general, a sample size of 30 or larger may be considered large.) In 
contrast to the confidence interval given in Equation 4, this confidence interval uses 
the sample standard deviation, s, in computing the standard error of the sample mean 
(Equation 2).
■■Confidence Intervals for the Population Mean—The z-Alternative (Large 
Sample, Population Variance Unknown).  A 100(1 − α)% confidence interval

for population mean μ when sampling from any distribution with unknown 
variance and when sample size is large is given by
Xzs
n±α2
Because this type of confidence interval appears quite often, we illustrate its calcu -
lation in Example 4.
EXAMPLE 4   
Confidence Interval for the Population Mean of Sharpe 
Ratios— z-Statistic
Suppose an investment analyst takes a random sample of US equity mutual funds 
and calculates the average Sharpe ratio. The sample size is 100, and the average 
Sharpe ratio is 0.45. The sample has a standard deviation of 0.30. Calculate and 
interpret the 90 percent confidence interval for the population mean of all US 
equity mutual funds by using a reliability factor based on the standard normal 
distribution.(5)
14 Freund and Williams (1977), p. 266.
15 The distribution of the statistic t is called Student’s t-distribution after the pen name “Student” used 
by W. S. Gosset, who published his work in 1908.

Reading 11 ■ Sampling and Estimation 594
The reliability factor for a 90 percent confidence interval, as given earlier, is 
z0.05 = 1.65. The confidence interval will be
Xzs
n±= ±= ± () =±005 0451 65030
1000451 650030 45 0 0495. ..... .. .
The confidence interval spans 0.4005 to 0.4995, or 0.40 to 0.50, carrying two 
decimal places. The analyst can say with 90 percent confidence that the interval 
includes the population mean.
In this example, the analyst makes no specific assumption about the prob -
ability distribution describing the population. Rather, the analyst relies on the 
central limit theorem to produce an approximate normal distribution for the 
sample mean.
As Example 4 shows, even if we are unsure of the underlying population distri -
bution, we can still construct confidence intervals for the population mean as long as 
the sample size is large because we can apply the central limit theorem.
We now turn to the conservative alternative, using the t-distribution, for con -

structing confidence intervals for the population mean when the population variance 
is not known. For confidence intervals based on samples from normally distributed 
populations with unknown variance, the theoretically correct reliability factor is based 
on the t-distribution. Using a reliability factor based on the t-distribution is essential 
for a small sample size. Using a t reliability factor is appropriate when the population 
variance is unknown, even when we have a large sample and could use the central 
limit theorem to justify using a z reliability factor. In this large sample case, the t-dis-
tribution provides more-  conservative (wider) confidence intervals.
The t-distribution is a symmetrical probability distribution defined by a single 
parameter known as degrees of freedom (df) . Each value for the number of degrees 
of freedom defines one distribution in this family of distributions. We will shortly

compare t-distributions with the standard normal distribution, but first we need to 
understand the concept of degrees of freedom. We can do so by examining the cal -
culation of the sample variance.
Equation 3 gives the unbiased estimator of the sample variance that we use. The 
term in the denominator, n − 1, which is the sample size minus 1, is the number of 
degrees of freedom in estimating the population variance when using Equation 3. We 
also use n − 1 as the number of degrees of freedom for determining reliability factors 
based on the t-distribution. The term “degrees of freedom” is used because in a ran -
dom sample, we assume that observations are selected independently of each other. 
The numerator of the sample variance, however, uses the sample mean. How does the 
use of the sample mean affect the number of observations collected independently for 
the sample variance formula? With a sample of size 10 and a mean of 10 percent, for

example, we can freely select only 9 observations. Regardless of the 9 observations 
selected, we can always find the value for the 10th observation that gives a mean equal 
to 10 percent. From the standpoint of the sample variance formula, then, there are 9 
degrees of freedom. Given that we must first compute the sample mean from the total 
of n independent observations, only n − 1 observations can be chosen independently 
for the calculation of the sample variance. The concept of degrees of freedom comes 
up frequently in statistics, and you will see it often in later readings.
Suppose we sample from a normal distribution. The ratio  zX n =−() ()µσ  is 
distributed normally with a mean of 0 and standard deviation of 1; however, the 
ratio  tX sn =−() ()µ  follows the t-distribution with a mean of 0 and n − 1 degrees 
of freedom. The ratio represented by t is not normal because t is the ratio of two 
random variables, the sample mean and the sample standard deviation. The definition

Point and Interval Estimates of the Population Mean 595
of the standard normal random variable involves only one random variable, the sample 
mean. As degrees of freedom increase, however, the t-distribution approaches the 
standard normal distribution. Figure 1 shows the standard normal distribution and 
two t-distributions, one with df = 2 and one with df = 8.
Figure 1   Student’s t-Distribution versus the Standard Normal Distribution
t (df = 2)t (df = 8)
–6 –4 –2 0 2 4 6
Of the three distributions shown in Figure 1, the standard normal distribution has 
tails that approach zero faster than the tails of the two t-distributions. The t-distribution 
is also symmetrically distributed around its mean value of zero, just like the normal 
distribution. As the degrees of freedom increase, the t-distribution approaches the 
standard normal. The t-distribution with df = 8 is closer to the standard normal than 
the t-distribution with df = 2.

Beyond plus and minus four standard deviations from the mean, the area under 
the standard normal distribution appears to approach 0; both t-distributions continue 
to show some area under each curve beyond four standard deviations, however. The 
t-distributions have fatter tails, but the tails of the t-distribution with df = 8 more 
closely resemble the normal distribution’s tails. As the degrees of freedom increase, 
the tails of the t-distribution become less fat.
Frequently referred to values for the t-distribution are presented in tables at the 
end of the book. For each degree of freedom, five values are given: t0.10, t0.05, t0.025 , 
t0.01, and t0.005 . The values for t0.10, t0.05, t0.025 , t0.01, and t0.005  are such that, respec -
tively, 0.10, 0.05, 0.025, 0.01, and 0.005 of the probability remains in the right tail, for 
the specified number of degrees of freedom.16 For example, for df = 30, t0.10 = 1.310,

t0.05 = 1.697, t0.025  = 2.042, t0.01 = 2.457, and t0.005  = 2.750.
We now give the form of confidence intervals for the population mean using the 
t-distribution.
■■Confidence Intervals for the Population Mean (Population Variance 
Unknown)— t-Distribution.  If we are sampling from a population with 
unknown variance and either of the conditions below holds:
16 The values t0.10, t0.05, t0.025 , t0.01, and t0.005  are also referred to as one-  sided critical values of t at the 
0.10, 0.05, 0.025, 0.01, and 0.005 significance levels, for the specified number of degrees of freedom.

Reading 11 ■ Sampling and Estimation 596
■●the sample is large, or
■●the sample is small but the population is normally distributed, or approxi -
mately normally distributed,
then a 100(1 − α)% confidence interval for the population mean μ is given by
Xts
n±α2
where the number of degrees of freedom for tα/2 is n − 1 and n is the sample 
size.
Example  5 reprises the data of Example  4 but uses the t-statistic rather than the 
z-statistic to calculate a confidence interval for the population mean of Sharpe ratios.
EXAMPLE 5   
Ratios— t-Statistic
As in Example 4, an investment analyst seeks to calculate a 90 percent confi -
dence interval for the population mean Sharpe ratio of US equity mutual funds 
based on a random sample of 100 US equity mutual funds. The sample mean 
Sharpe ratio is 0.45, and the sample standard deviation of the Sharpe ratios is 
0.30. Now recognizing that the population variance of the distribution of Sharpe

ratios is unknown, the analyst decides to calculate the confidence interval using 
the theoretically correct t-statistic.
Because the sample size is 100, df = 99. In the tables in the back of the book, 
the closest value is df = 100. Using df = 100 and reading down the 0.05 column, 
we find that t0.05 = 1.66. This reliability factor is slightly larger than the reliability 
factor z0.05 = 1.65 that was used in Example 4. The confidence interval will be
Xts
n±= ±= ± () =±005 0451 66030
1000451 660030 45 0 0498. ..... .. .
The confidence interval spans 0.4002 to 0.4998, or 0.40 to 0.50, carrying two 
decimal places. To two decimal places, the confidence interval is unchanged 
from the one computed in Example 4.
Table 3 summarizes the various reliability factors that we have used.
Table 3   Basis of Computing Reliability Factors
Sampling from:Statistic for Small 
Sample SizeStatistic for Large 
Sample Size
Normal distribution with known 
variancez z
Normal distribution with unknown 
variancet t*(6)

Point and Interval Estimates of the Population Mean 597
Nonnormal distribution with 
known variancenot available z
unknown variancenot available t*
* Use of z also acceptable.
4.3 Selection of Sample Size
What choices affect the width of a confidence interval? To this point we have discussed 
two factors that affect width: the choice of statistic ( t or z) and the choice of degree of 
confidence (affecting which specific value of t or z we use). These two choices deter -
mine the reliability factor. (Recall that a confidence interval has the structure Point 
estimate ± Reliability factor × Standard error.)
The choice of sample size also affects the width of a confidence interval. All else 
equal, a larger sample size decreases the width of a confidence interval. Recall the 
expression for the standard error of the sample mean:
Standard error of the sam ple meanSample  standard de viatio=n n

Sample  size
We see that the standard error varies inversely with the square root of sample size. 
As we increase sample size, the standard error decreases and consequently the width 
of the confidence interval also decreases. The larger the sample size, the greater 
precision with which we can estimate the population parameter.17 All else equal, 
larger samples are good, in that sense. In practice, however, two considerations may 
operate against increasing sample size. First, as we saw in Example 2 concerning the 
Sharpe ratio, increasing the size of a sample may result in sampling from more than 
one population. Second, increasing sample size may involve additional expenses that 
outweigh the value of additional precision. Thus three issues that the analyst should 
weigh in selecting sample size are the need for precision, the risk of sampling from 
more than one population, and the expenses of different sample sizes.
EXAMPLE 6   
A Money Manager Estimates Net Client Inflows

A money manager wants to obtain a 95 percent confidence interval for fund 
inflows and outflows over the next six months for his existing clients. He begins 
by calling a random sample of 10 clients and inquiring about their planned addi -
tions to and withdrawals from the fund. The manager then computes the change 
in cash flow for each client sampled as a percentage change in total funds placed 
with the manager. A positive percentage change indicates a net cash inflow to the Table 3   (Continued)
17 A formula exists for determining the sample size needed to obtain a desired width for a confidence 
interval. Define E = Reliability factor × Standard error. The smaller E is, the smaller the width of the con -
fidence interval, because 2 E is the confidence interval’s width. The sample size to obtain a desired value of 
E at a given degree of confidence (1 − α) is n = [( tα/2s)/E]2.

Reading 11 ■ Sampling and Estimation 598
client’s account, and a negative percentage change indicates a net cash outflow 
from the client’s account. The manager weights each response by the relative 
size of the account within the sample and then computes a weighted average.
As a result of this process, the money manager computes a weighted average 
of 5.5 percent. Thus, a point estimate is that the total amount of funds under 
management will increase by 5.5 percent in the next six months. The standard 
deviation of the observations in the sample is 10 percent. A histogram of past data 
looks fairly close to normal, so the manager assumes the population is normal.
1 Calculate a 95 percent confidence interval for the population mean and 
interpret your findings.
The manager decides to see what the confidence interval would look like if he 
had used a sample size of 20 or 30 and found the same mean (5.5 percent) and 
standard deviation (10 percent).

2 Using the sample mean of 5.5 percent and standard deviation of 10 per -
cent, compute the confidence interval for sample sizes of 20 and 30. For 
the sample size of 30, use Equation 6.
3 Interpret your results from Parts 1 and 2.
Because the population variance is unknown and the sample size is small, the 
manager must use the t-statistic in Equation 6 to calculate the confidence inter -
val. Based on the sample size of 10, df = n − 1 = 10 − 1 = 9. For a 95 percent 
confidence interval, he needs to use the value of t0.025  for df = 9. According to 
the tables in Appendix B at the end of this volume, this value is 2.262. Therefore, 
a 95 percent confidence interval for the population mean is
Xts
n±= ±
=± ()
=±0 025 55 2 26210
10
55 2 262 3 162
55 71 5. .% .%
.% ..
.% .%
The confidence interval for the population mean spans −1.65  percent to 
+12.65 percent.18 The manager can be confident at the 95 percent level that this 
range includes the population mean.

Table 4 gives the calculations for the three sample sizes.
Table 4   The 95 Percent Confidence Interval for Three Sample Sizes
Distribution95%  
Confidence IntervalLower 
BoundUpper 
BoundRelative 
Size
t(n = 10) 5.5% ± 2.262(3.162) −1.65% 12.65% 100.0%
t(n = 20) 5.5% ± 2.093(2.236) 0.82 10.18 65.5
t(n = 30) 5.5% ± 2.045(1.826) 1.77 9.23 52.2
18 We assumed in this example that sample size is sufficiently small compared with the size of the client 
base that we can disregard the finite population correction factor (mentioned in Footnote 6).

More on Sampling 599
The width of the confidence interval decreases as we increase the sample size. 
This decrease is a function of the standard error becoming smaller as n increases. 
The reliability factor also becomes smaller as the number of degrees of freedom 
increases. The last column of Table 4 shows the relative size of the width of 
confidence intervals based on n = 10 to be 100 percent. Using a sample size of 
20 reduces the confidence interval’s width to 65.5 percent of the interval width 
for a sample size of 10. Using a sample size of 30 cuts the width of the interval 
almost in half. Comparing these choices, the money manager would obtain the 
most precise results using a sample of 30.
Having covered many of the fundamental concepts of sampling and estimation, 
we are in a good position to focus on sampling issues of special concern to analysts. 
The quality of inferences depends on the quality of the data as well as on the quality

of the sampling plan used. Financial data pose special problems, and sampling plans 
frequently reflect one or more biases. The next section of this reading discusses these 
issues.
MORE ON SAMPLING
We have already seen that the selection of sample period length may raise the issue 
of sampling from more than one population. There are, in fact, a range of challenges 
to valid sampling that arise in working with financial data. In this section we discuss 
four such sampling-  related issues: data-  mining bias, sample selection bias, look-  ahead 
bias, and time-  period bias. All of these issues are important for point and interval 
estimation and hypothesis testing. As we will see, if the sample is biased in any way, 
then point and interval estimates and any other conclusions that we draw from the 
sample will be in error.
5.1 Data-  Mining Bias
Data mining  relates to overuse of the same or related data in ways that we shall

describe shortly. Data-  mining bias refers to the errors that arise from such misuse of 
data. Investment strategies that reflect data-  mining biases are often not successful 
in the future. Nevertheless, both investment practitioners and researchers have fre -
quently engaged in data mining. Analysts thus need to understand and guard against 
this problem.
Data-  mining is the practice of determining a model by extensive searching through 
a dataset for statistically significant patterns (that is, repeatedly “drilling” in the same 
data until finding something that appears to work).19 In exercises involving statisti -
cal significance we set a significance level, which is the probability of rejecting the 
hypothesis we are testing when the hypothesis is in fact correct.20 Because rejecting 
a true hypothesis is undesirable, the investigator often sets the significance level at 5
19 Some researchers use the term “data snooping” instead of data mining.

20 To convey an understanding of data mining, it is very helpful to introduce some basic concepts related 
to hypothesis testing. The reading on hypothesis testing contains further discussion of significance levels 
and tests of significance.

Reading 11 ■ Sampling and Estimation 600
a relatively small number such as 0.05 or 5 percent.21 Suppose we test the hypoth -
esis that a variable does not predict stock returns, and we test in turn 100 different 
variables. Let us also suppose that in truth none of the 100 variables has the ability 
to predict stock returns. Using a 5 percent significance level in our tests, we would 
still expect that 5 out of 100 variables would appear to be significant predictors of 
stock returns because of random chance alone. We have mined the data to find some 
apparently significant variables. In essence, we have explored the same data again 
and again until we found some after-  the- fact pattern or patterns in the dataset. This 
is the sense in which data mining involves overuse of data. If we were to just report 
the significant variables, without also reporting the total number of variables that we 
tested that were unsuccessful as predictors, we would be presenting a very misleading

picture of our findings. Our results would appear to be far more significant than they 
actually were, because a series of tests such as the one just described invalidates the 
conventional interpretation of a given significance level (such as 5 percent), according 
to the theory of inference.
How can we investigate the presence of data-  mining bias? With most financial data, 
the most ready means is to conduct out-  of- sample tests of the proposed variable or 
strategy. An out-  of- sample test  uses a sample that does not overlap the time period(s) 
of the sample(s) on which a variable, strategy, or model, was developed. If a variable or 
investment strategy is the result of data mining, it should generally not be significant in 
out- of- sample tests. A variable or investment strategy that is statistically and econom -
ically significant in out-  of- sample tests, and that has a plausible economic basis, may

be the basis for a valid investment strategy. Caution is still warranted, however. The 
most crucial out-  of- sample test is future investment success. If the strategy becomes 
known to other investors, prices may adjust so that the strategy, however well tested, 
does not work in the future. To summarize, the analyst should be aware that many 
apparently profitable investment strategies may reflect data-  mining bias and thus 
be cautious about the future applicability of published investment research results.
Untangling the extent of data mining can be complex. To assess the significance 
of an investment strategy, we need to know how many unsuccessful strategies were 
tried not only by the current investigator but also by previous  investigators using the 
same or related datasets. Much research, in practice, closely builds on what other 
investigators have done, and so reflects intergenerational data mining, to use the ter -

minology of McQueen and Thorley (1999). Intergenerational data mining  involves 
using information developed by previous researchers using a dataset to guide current 
research using the same or a related dataset.22 Analysts have accumulated many 
observations about the peculiarities of many financial datasets, and other analysts 
may develop models or investment strategies that will tend to be supported within 
a dataset based on their familiarity with the prior experience of other analysts. As a 
consequence, the importance of those new results may be overstated. Research has 
suggested that the magnitude of this type of data-  mining bias may be considerable.23
With the background of the above definitions and explanations, we can understand 
McQueen and Thorley’s (1999) cogent exploration of data mining in the context of the 
popular Motley Fool “Foolish Four” investment strategy. The Foolish Four strategy, first

21 In terms of our previous discussion of confidence intervals, significance at the 5 percent level corresponds 
to a hypothesized value for a population statistic falling outside a 95 percent confidence interval based on 
an appropriate sample statistic (e.g., the sample mean, when the hypothesis concerns the population mean).
22 The term “intergenerational” comes from viewing each round of researchers as a generation. Campbell, 
Lo, and MacKinlay (1997) have called intergenerational data mining “data snooping. ” The latter phrase, 
however, is commonly used as a synonym of data mining; thus McQueen and Thorley’s terminology is 
less ambiguous. The term “intragenerational data mining” is available when we want to highlight that the 
reference is to an investigator’s new or independent data mining.
23 For example, Lo and MacKinlay (1990) concluded that the magnitude of this type of bias on tests of 
the capital asset pricing model was considerable.

More on Sampling 601
presented in 1996, was a version of the Dow Dividend Strategy that was tuned by its 
developers to exhibit an even higher arithmetic mean return than the Dow Dividend 
Strategy over 1973 to 1993.24 From 1973 to 1993, the Foolish Four portfolio had an 
average annual return of 25 percent, and the claim was made in print that the strategy 
should have similar returns in the future. As McQueen and Thorley discussed, however, 
the Foolish Four strategy was very much subject to data-  mining bias, including bias 
from intergenerational data mining, as the strategy’s developers exploited observations 
about the dataset made by earlier workers. McQueen and Thorley highlighted the 
data-  mining issues by taking the Foolish Four portfolio one step further. They mined 
the data to create a “Fractured Four” portfolio that earned nearly 35 percent over 1973 
to 1996, beating the Foolish Four strategy by almost 8 percentage points. Observing

that all of the Foolish Four stocks did well in even years but not odd years and that the 
second-  to- lowest-  priced high-  yielding stock was relatively the best-  performing stock 
in odd years, the strategy of the Fractured Four portfolio was to hold the Foolish Four 
stocks with equal weights in even years and hold only the second-  to- lowest-  priced 
stock in odd years. How likely is it that a performance difference between even and 
odd years reflected underlying economic forces, rather than a chance pattern of the 
data over the particular time period? Probably, very unlikely. Unless an investment 
strategy reflected underlying economic forces, we would not expect it to have any 
value in a forward-  looking sense. Because the Foolish Four strategy also partook of 
data mining, the same issues applied to it. McQueen and Thorley found that in an 
out- of- sample test over the 1949–72 period, the Foolish Four strategy had about the

same mean return as buying and holding the DJIA, but with higher risk. If the higher 
taxes and transaction costs of the Foolish Four strategy were accounted for, the com -
parison would have been even more unfavorable.
McQueen and Thorley presented two signs that can warn analysts about the 
potential existence of data mining:
■■Too much digging/too little confidence.  The testing of many variables by the 
researcher is the “too much digging” warning sign of a data-  mining prob -
lem. Unfortunately, many researchers do not disclose the number of variables 
examined in developing a model. Although the number of variables examined 
may not be reported, we should look closely for verbal hints that the researcher 
searched over many variables. The use of terms such as “we noticed (or noted) 
that” or “someone noticed (or noted) that, ” with respect to a pattern in a data -
set, should raise suspicions that the researchers were trying out variables based

on their own or others’ observations of the data.
■■No story/no future.  The absence of an explicit economic rationale for a variable 
or trading strategy is the “no story” warning sign of a data-  mining problem. 
Without a plausible economic rationale or story for why a variable should work, 
the variable is unlikely to have predictive power. In a demonstration exercise 
using an extensive search of variables in an international financial database, 
Leinweber (1997) found that butter production in a particular country remote 
from the United States explained 75 percent of the variation in US stock returns 
as represented by the S&P 500. Such a pattern, with no plausible economic 
rationale, is highly likely to be a random pattern particular to a specific time 
24 The Dow Dividend Strategy, also known as Dogs of the Dow Strategy, consists of holding an equally 
weighted portfolio of the 10 highest-  yielding DJIA stocks as of the beginning of a year. At the time of

McQueen and Thorley’s research, the Foolish Four strategy was as follows: At the beginning of each year, 
the Foolish Four portfolio purchases a 4-  stock portfolio from the 5 lowest-  priced stocks of the 10 highest-  
yielding DJIA stocks. The lowest-  priced stock of the five is excluded, and 40 percent is invested in the 
second-  to- lowest-  priced stock, with 20 percent weights in the remaining three.

Reading 11 ■ Sampling and Estimation 602
period.25 What if we do have a plausible economic explanation for a significant 
variable? McQueen and Thorley caution that a plausible economic rationale is a 
necessary but not a sufficient condition for a trading strategy to have value. As 
we mentioned earlier, if the strategy is publicized, market prices may adjust to 
reflect the new information as traders seek to exploit it; as a result, the strategy 
may no longer work.
5.2 Sample Selection Bias
When researchers look into questions of interest to analysts or portfolio managers, 
they may exclude certain stocks, bonds, portfolios, or time periods from the analysis 
for various reasons—perhaps because of data availability. When data availability 
leads to certain assets being excluded from the analysis, we call the resulting problem 
sample selection bias . For example, you might sample from a database that tracks 
only companies currently in existence. Many mutual fund databases, for instance,

provide historical information about only those funds that currently exist. Databases 
that report historical balance sheet and income statement information suffer from 
the same sort of bias as the mutual fund databases: Funds or companies that are no 
longer in business do not appear there. So, a study that uses these types of databases 
suffers from a type of sample selection bias known as survivorship bias .
Dimson, Marsh, and Staunton (2002) raised the issue of survivorship bias in 
international indexes:
An issue that has achieved prominence is the impact of market survival on 
estimated long-  run returns. Markets can experience not only disappointing 
performance but also total loss of value through confiscation, hyperinfla -
tion, nationalization, and market failure. By measuring the performance 
of markets that survive over long intervals, we draw inferences that are 
conditioned on survival. Yet, as pointed out by Brown, Goetzmann, and

Ross (1995) and Goetzmann and Jorion (1999), one cannot determine in 
advance which markets will survive and which will perish. (p. 41)
Survivorship bias sometimes appears when we use both stock price and accounting 
data. For example, many studies in finance have used the ratio of a company’s market 
price to book equity per share (i.e., the price-  to- book ratio, P/B) and found that P/B 
is inversely related to a company’s returns (see Fama and French 1992, 1993). P/B is 
also used to create many popular value and growth indexes. If the database that we 
use to collect accounting data excludes failing companies, however, a survivorship 
bias might result. Kothari, Shanken, and Sloan (1995) investigated just this question 
and argued that failing stocks would be expected to have low returns and low P/Bs. 
If we exclude failing stocks, then those stocks with low P/Bs that are included will 
have returns that are higher on average than if all stocks with low P/Bs were included.

Kothari, Shanken, and Sloan suggested that this bias is responsible for the previous 
findings of an inverse relationship between average return and P/B.26 The only advice 
we can offer at this point is to be aware of any biases potentially inherent in a sample. 
Clearly, sample selection biases can cloud the results of any study.
25 In the finance literature, such a random but irrelevant-  to- the- future pattern is sometimes called an 
artifact of the dataset.
26 See Fama and French (1996, p. 80) for discussion of data snooping and survivorship bias in their tests.

More on Sampling 603
A sample can also be biased because of the removal (or delisting) of a company’s 
stock from an exchange.27 For example, the Center for Research in Security Prices at 
the University of Chicago is a major provider of return data used in academic research. 
When a delisting occurs, CRSP attempts to collect returns for the delisted company, 
but many times, it cannot do so because of the difficulty involved; CRSP must simply 
list delisted company returns as missing. A study in the Journal of Finance  by Shumway 
and Warther (1999) documented the bias caused by delisting for CRSP NASDAQ 
return data. The authors showed that delistings associated with poor company per -
formance (e.g., bankruptcy) are missed more often than delistings associated with 
good or neutral company performance (e.g., merger or moving to another exchange). 
In addition, delistings occur more frequently for small companies.
Sample selection bias occurs even in markets where the quality and consistency

of the data are quite high. Newer asset classes such as hedge funds may present even 
greater problems of sample selection bias. Hedge funds are a heterogeneous group of 
investment vehicles typically organized so as to be free from regulatory oversight. In 
general, hedge funds are not required to publicly disclose performance (in contrast to, 
say, mutual funds). Hedge funds themselves decide whether they want to be included 
in one of the various databases of hedge fund performance. Hedge funds with poor 
track records clearly may not wish to make their records public, creating a problem 
of self-  selection bias in hedge fund databases. Further, as pointed out by Fung and 
Hsieh (2002), because only hedge funds with good records will volunteer to enter a 
database, in general, overall past hedge fund industry performance will tend to appear 
better than it really is. Furthermore, many hedge fund databases drop funds that go out

of business, creating survivorship bias in the database. Even if the database does not 
drop defunct hedge funds, in the attempt to eliminate survivorship bias, the problem 
remains of hedge funds that stop reporting performance because of poor results.28
5.3 Look-  Ahead Bias
A test design is subject to look-  ahead bias  if it uses information that was not avail -
able on the test date. For example, tests of trading rules that use stock market returns 
and accounting balance sheet data must account for look-  ahead bias. In such tests, 
a company’s book value per share is commonly used to construct the P/B variable. 
Although the market price of a stock is available for all market participants at the 
same point in time, fiscal year-  end book equity per share might not become publicly 
available until sometime in the following quarter.
5.4 Time-  Period Bias
A test design is subject to time-  period bias  if it is based on a time period that may

make the results time-  period specific. A short time series is likely to give period 
specific results that may not reflect a longer period. A long time series may give a 
more accurate picture of true investment performance; its disadvantage lies in the 
potential for a structural change occurring during the time frame that would result 
in two different return distributions. In this situation, the distribution that would 
reflect conditions before the change differs from the distribution that would describe 
conditions after the change.
27 Delistings occur for a variety of reasons: merger, bankruptcy, liquidation, or migration to another 
exchange.
28 See Fung and Hsieh (2002) and ter Horst and Verbeek (2007) for more details on the problems of 
interpreting hedge fund performance. Note that an offsetting type of bias may occur if successful funds 
stop reporting performance because they no longer want new cash inflows.

Reading 11 ■ Sampling and Estimation 604
EXAMPLE 7   
Biases in Investment Research
An analyst is reviewing the empirical evidence on historical US equity returns. 
She finds that value stocks (i.e., those with low P/Bs) outperformed growth 
stocks (i.e., those with high P/Bs) in some recent time periods. After reviewing 
the US market, the analyst wonders whether value stocks might be attractive 
in the United Kingdom. She investigates the performance of value and growth 
stocks in the UK market for the 14-  year period extending from January 2000 
to December 2013. To conduct this research, the analyst does the following:
■■obtains the current composition of the Financial Times Stock Exchange 
(FTSE) All Share Index, which is a market-  capitalization-  weighted index;
■■eliminates the few companies that do not have December fiscal year-  ends;
■■uses year-  end book values and market prices to rank the remaining uni -
verse of companies by P/Bs at the end of the year;

■■based on these rankings, divides the universe into 10 portfolios, each of 
which contains an equal number of stocks;
■■calculates the equal-  weighted return of each portfolio and the return for 
the FTSE All Share Index for the 12 months following the date each rank -
ing was made; and
■■subtracts the FTSE returns from each portfolio’s returns to derive excess 
returns for each portfolio.
Describe and discuss each of the following biases introduced by the analyst’s 
research design:
■■survivorship bias;
■■look-  ahead bias; and
■■time-  period bias.
Survivorship Bias.
A test design is subject to survivorship bias if it fails to account for companies 
that have gone bankrupt, merged, or otherwise departed the database. In this 
example, the analyst used the current list of FTSE stocks rather than the actual 
list of stocks that existed at the start of each year. To the extent that the compu -

tation of returns excluded companies removed from the index, the performance 
of the portfolios with the lowest P/B is subject to survivorship bias and may 
be overstated. At some time during the testing period, those companies not 
currently in existence were eliminated from testing. They would probably have 
had low prices (and low P/Bs) and poor returns.
Look-  Ahead Bias.
A test design is subject to look-  ahead bias if it uses information unavailable on the 
test date. In this example, the analyst conducted the test under the assumption 
that the necessary accounting information was available at the end of the fiscal 
year. For example, the analyst assumed that book value per share for fiscal 2000 
was available on 31 December 2000. Because this information is not released 
until several months after the close of a fiscal year, the test may have contained 
look-  ahead bias. This bias would make a strategy based on the information

Summary 605
Time-  Period Bias.
A test design is subject to time-  period bias if it is based on a time period that 
may make the results time-  period specific. Although the test covered a period 
extending more than 10 years, that period may be too short for testing an anom -
aly. Ideally, an analyst should test market anomalies over several business cycles 
to ensure that results are not period specific. This bias can favor a proposed 
strategy if the time period chosen was favorable to the strategy.
SUMMARY
In this reading, we have presented basic concepts and results in sampling and esti -
mation. We have also emphasized the challenges faced by analysts in appropriately 
using and interpreting financial data. As analysts, we should always use a critical 
eye when evaluating the results from any study. The quality of the sample is of the 
utmost importance: If the sample is biased, the conclusions drawn from the sample 
will be in error.

■■To draw valid inferences from a sample, the sample should be random.
■■In simple random sampling, each observation has an equal chance of being 
selected. In stratified random sampling, the population is divided into subpopu -
lations, called strata or cells, based on one or more classification criteria; simple 
random samples are then drawn from each stratum.
■■Stratified random sampling ensures that population subdivisions of interest are 
represented in the sample. Stratified random sampling also produces more-  
precise parameter estimates than simple random sampling.
■■Time-  series data are a collection of observations at equally spaced intervals of 
time. Cross-  sectional data are observations that represent individuals, groups, 
geographical regions, or companies at a single point in time.
■■The central limit theorem states that for large sample sizes, for any underlying 
distribution for a random variable, the sampling distribution of the sample

mean for that variable will be approximately normal, with mean equal to the 
population mean for that random variable and variance equal to the population 
variance of the variable divided by sample size.
■■Based on the central limit theorem, when the sample size is large, we can com -
pute confidence intervals for the population mean based on the normal distri -
bution regardless of the distribution of the underlying population. In general, a 
sample size of 30 or larger can be considered large.
■■An estimator is a formula for estimating a parameter. An estimate is a particular 
value that we calculate from a sample by using an estimator.
■■Because an estimator or statistic is a random variable, it is described by some 
probability distribution. We refer to the distribution of an estimator as its sam -
pling distribution. The standard deviation of the sampling distribution of the 
sample mean is called the standard error of the sample mean.

■■The desirable properties of an estimator are unbiasedness (the expected value 
of the estimator equals the population parameter), efficiency (the estimator has 
the smallest variance), and consistency (the probability of accurate estimates 
increases as sample size increases).

Reading 11 ■ Sampling and Estimation 606
■■The two types of estimates of a parameter are point estimates and interval esti -
mates. A point estimate is a single number that we use to estimate a parameter. 
An interval estimate is a range of values that brackets the population parameter 
with some probability.
■■A confidence interval is an interval for which we can assert with a given prob -
ability 1 − α, called the degree of confidence, that it will contain the parameter 
it is intended to estimate. This measure is often referred to as the 100(1 − α)% 
confidence interval for the parameter.
■■A 100(1 − α)% confidence interval for a parameter has the following structure: 
Point estimate ± Reliability factor × Standard error, where the reliability factor 
is a number based on the assumed distribution of the point estimate and the 
degree of confidence (1 − α) for the confidence interval and where standard 
error is the standard error of the sample statistic providing the point estimate.

■■A 100(1 − α)% confidence interval for population mean μ when sampling from a 
normal distribution with known variance σ2 is given by  X
n±zασ
2 , where 
zα/2 is the point of the standard normal distribution such that α/2 remains in 
the right tail.
■■Student’s t-distribution is a family of symmetrical distributions defined by a 
single parameter, degrees of freedom.
■■A random sample of size n is said to have n − 1 degrees of freedom for estimat -
ing the population variance, in the sense that there are only n − 1 independent 
deviations from the mean on which to base the estimate.
■■The degrees of freedom number for use with the t-distribution is also n − 1.
■■The t-distribution has fatter tails than the standard normal distribution but con -
verges to the standard normal distribution as degrees of freedom go to infinity.
■■A 100(1 − α)% confidence interval for the population mean μ when sampling 
from a normal distribution with unknown variance (a t-distribution confidence

interval) is given by  Xt sn ± ()α2 , where tα/2 is the point of the t-distribution 
such that α/2 remains in the right tail and s is the sample standard deviation. 
This confidence interval can also be used, because of the central limit theorem, 
when dealing with a large sample from a population with unknown variance 
that may not be normal.
■■We may use the confidence interval  Xz sn ± ()α2  as an alternative to the 
t-distribution confidence interval for the population mean when using a large 
sample from a population with unknown variance. The confidence interval 
based on the z-statistic is less conservative (narrower) than the corresponding 
confidence interval based on a t-distribution.
■■Three issues in the selection of sample size are the need for precision, the risk 
of sampling from more than one population, and the expenses of different sam -
ple sizes.
■■Sample data in investments can have a variety of problems. Survivorship bias

occurs if companies are excluded from the analysis because they have gone out 
of business or because of reasons related to poor performance. Data-  mining 
bias comes from finding models by repeatedly searching through databases for 
patterns. Look-  ahead bias exists if the model uses data not available to market 
participants at the time the market participants act in the model. Finally, time-  
period bias is present if the time period used makes the results time-  period spe -
cific or if the time period used includes a point of structural change.

References 607
Brown, Stephen, William Goetzmann, and Stephen Ross. 1995. 
“Survival. ” Journal of Finance , vol. 50:853–873. 
Daniel, Wayne W., and James C. Terrell. 1995. Business 
Statistics for Management & Economics , 7th edition. Boston: 
Houghton-Mifflin.
Dimson, Elroy, Paul Marsh, and Mike Staunton. 2002. Triumphs 
of the Optimists: 101 Years of Global Investment Returns . 
Princeton, NJ: Princeton University Press.
Fama, Eugene F., and Kenneth R. French. 1996. “Multifactor 
Explanations of Asset Pricing Anomalies. ” Journal of Finance , 
vol. 51, no. 1:55–84. 
Freund, John E, and Frank J. Williams. 1977. Elementary Business 
Statistics , 3rd edition. Englewood Cliffs, NJ: Prentice-Hall.
Fung, William, and David Hsieh. 2002. “Hedge-  Fund Benchmarks: 
Information Content and Biases. ” Financial Analysts Journal ,

vol. 58, no. 1:22–34. Goetzmann, William, and Philippe Jorion. 1999. “Re-  Emerging 
Markets. ” Journal of Financial and Quantitative Analysis , vol. 
34, no. 1:1–32. 
Greene, William H. 2018. Econometric Analysis , 8th edition. 
Upper Saddle River, NJ: Prentice-Hall.
Kothari, S.P ., Jay Shanken, and Richard G. Sloan. 1995. “ Another 
Look at the Cross-  Section of Expected Stock Returns. ” Journal 
of Finance , vol. 50, no. 1:185–224. 
Leinweber, David. 1997. Stupid Data Mining Tricks: Over-  Fitting 
the S&P 500 . Monograph. Pasadena, CA: First Quadrant.
Lo, Andrew W., and A. Craig MacKinlay. 1990. “Data Snooping 
Biases in Tests of Financial Asset Pricing Models. ” Review of 
Financial Studies , vol. 3:175–208. 
McQueen, Grant, and Steven Thorley. 1999. “Mining Fools 
Gold. ” Financial Analysts Journal , vol. 55, no. 2:61–72. 
Shumway, Tyler, and Vincent A. Warther. 1999. “The Delisting 
Bias in CRSP’s Nasdaq Data and Its Implications for the Size

Effect. ” Journal of Finance , vol. 54, no. 6:2361–2379. 
ter Horst, Jenke, and Marno Verbeek. 2007. “Fund Liquidation, 
Self-  selection, and Look-  ahead Bias in the Hedge Fund 
Industry. ” Review of Finance , vol. 11:605–632.

Reading 11 ■ Sampling and Estimation 608
1 Peter Biggs wants to know how growth managers performed last year. Biggs 
assumes that the population cross-  sectional standard deviation of growth man -
ager returns is 6 percent and that the returns are independent across managers.
A How large a random sample does Biggs need if he wants the standard devia -
tion of the sample means to be 1 percent?
B How large a random sample does Biggs need if he wants the standard devia -
tion of the sample means to be 0.25 percent?
2 Petra Munzi wants to know how value managers performed last year. Munzi 
estimates that the population cross-  sectional standard deviation of value man -
ager returns is 4 percent and assumes that the returns are independent across 
managers.
A Munzi wants to build a 95 percent confidence interval for the mean return. 
How large a random sample does Munzi need if she wants the 95 percent 
confidence interval to have a total width of 1 percent?

B Munzi expects a cost of about $10 to collect each observation. If she has 
a $1,000 budget, will she be able to construct the confidence interval she 
wants?
3 Assume that the equity risk premium is normally distributed with a population 
mean of 6 percent and a population standard deviation of 18 percent. Over 
the last four years, equity returns (relative to the risk-  free rate) have averaged 
−2.0 percent. You have a large client who is very upset and claims that results 
this poor should never  occur. Evaluate your client’s concerns.
A Construct a 95 percent confidence interval around the population mean for 
a sample of four-  year returns.
B What is the probability of a −2.0 percent or lower average return over a 
four-  year period?
4 Compare the standard normal distribution and Student’s t-distribution.
5 Find the reliability factors based on the t-distribution for the following confi -
dence intervals for the population mean (df = degrees of freedom, n = sample 
size):

size):
A A 99 percent confidence interval, df = 20.
B A 90 percent confidence interval, df = 20.
C A 95 percent confidence interval, n = 25.
D A 95 percent confidence interval, n = 16.
6 Assume that monthly returns are normally distributed with a mean of 1 percent 
and a sample standard deviation of 4 percent. The population standard devi -
ation is unknown. Construct a 95 percent confidence interval for the sample 
mean of monthly returns if the sample size is 24.
7 Ten analysts have given the following fiscal year earnings forecasts for a stock:
Forecast ( Xi) Number of Analysts ( ni)
1.40 1
1.43 1
1.44 3

Practice Problems 609
1.45 2
1.47 1
1.48 1
1.50 1
 Because the sample is a small fraction of the number of analysts who follow 
this stock, assume that we can ignore the finite population correction factor. 
Assume that the analyst forecasts are normally distributed.
A What are the mean forecast and standard deviation of forecasts?
B Provide a 95 percent confidence interval for the population mean of the 
8 Thirteen analysts have given the following fiscal-  year earnings forecasts for a 
stock:
0.70 2
0.72 4
0.74 1
0.75 3
0.76 1
0.77 1
0.82 1
 Because the sample is a small fraction of the number of analysts who follow this 
stock, assume that we can ignore the finite population correction factor.
B What aspect of the data makes us uncomfortable about using t-tables to 
construct confidence intervals for the population mean forecast?

9 Explain the differences between constructing a confidence interval when sam -
pling from a normal population with a known population variance and sam -
pling from a normal population with an unknown variance.
10 An exchange rate has a given expected future value and standard deviation.
A Assuming that the exchange rate is normally distributed, what are the prob -
abilities that the exchange rate will be at least 2 or 3 standard deviations 
away from its mean?
B Assume that you do not know the distribution of exchange rates. Use 
Chebyshev’s inequality (that at least 1 − 1/ k2 proportion of the observations 
will be within k standard deviations of the mean for any positive integer k 
greater than 1) to calculate the maximum probabilities that the exchange 
rate will be at least 2 or 3 standard deviations away from its mean.
11 Although he knows security returns are not independent, a colleague makes 
the claim that because of the central limit theorem, if we diversify across a

large number of investments, the portfolio standard deviation will eventually 
approach zero as n becomes large. Is he correct?
12 Why is the central limit theorem important?
13 What is wrong with the following statement of the central limit theorem?

Reading 11 ■ Sampling and Estimation 610
Central Limit Theorem.  “If the random variables X1, X2, X3, …, Xn are a random sample 
of size n from any distribution with finite mean μ and variance σ2, then the distribution 
of X will be approximately normal, with a standard deviation of  σn.”
14 Suppose we take a random sample of 30 companies in an industry with 200 
companies. We calculate the sample mean of the ratio of cash flow to total debt 
for the prior year. We find that this ratio is 23 percent. Subsequently, we learn 
that the population cash flow to total debt ratio (taking account of all 200 com -
panies) is 26 percent. What is the explanation for the discrepancy between the 
sample mean of 23 percent and the population mean of 26 percent?
A Sampling error.
B Bias.
C A lack of consistency.
15 Alcorn Mutual Funds is placing large advertisements in several financial pub -
lications. The advertisements prominently display the returns of 5 of Alcorn’s

30 funds for the past 1-, 3-, 5-, and 10-  year periods. The results are indeed 
impressive, with all of the funds beating the major market indexes and a few 
beating them by a large margin. Is the Alcorn family of funds superior to its 
competitors?
16 Julius Spence has tested several predictive models in order to identify under -
valued stocks. Spence used about 30 company-  specific variables and 10 
market-  related variables to predict returns for about 5,000 North American 
and European stocks. He found that a final model using eight variables applied 
to telecommunications and computer stocks yields spectacular results. Spence 
wants you to use the model to select investments. Should you? What steps 
would you take to evaluate the model?
17 The best approach for creating a stratified random sample of a population 
involves:
A drawing an equal number of simple random samples from each 
subpopulation.
B selecting every kth member of the population until the desired sample size 
is reached.

C drawing simple random samples from each subpopulation in sizes propor -
tional to the relative size of each subpopulation.
18 A population has a non-  normal distribution with mean µ and variance σ2. The 
sampling distribution of the sample mean computed from samples of large size 
from that population will have:
A the same distribution as the population distribution.
B its mean approximately equal to the population mean.
C its variance approximately equal to the population variance.
19 A sample mean is computed from a population with a variance of 2.45. The 
sample size is 40. The standard error of the sample mean is closest  to:
A 0.039.
B 0.247.
C 0.387.
20 An estimator with an expected value equal to the parameter that it is intended 
to estimate is described as:

Practice Problems 611
A efficient.
B unbiased.
C consistent.
21 If an estimator is consistent, an increase in sample size will increase the:
A accuracy of estimates.
B efficiency of the estimator.
C unbiasedness of the estimator.
22 For a two-  sided confidence interval, an increase in the degree of confidence will 
result in:
A a wider confidence interval.
B a narrower confidence interval.
C no change in the width of the confidence interval.
23 As the t-distribution’s degrees of freedom decrease, the t-distribution most 
likely :
A exhibits tails that become fatter.
B approaches a standard normal distribution.
C becomes asymmetrically distributed around its mean value.
24 For a sample size of 17, with a mean of 116.23 and a variance of 245.55, the 
width of a 90% confidence interval using the appropriate t-distribution is closest 
to:
A 13.23.
B 13.27.
C 13.68.
25 For a sample size of 65 with a mean of 31 taken from a normally distributed

population with a variance of 529, a 99% confidence interval for the population 
mean will have a lower limit closest  to:
A 23.64.
B 25.41.
C 30.09.
26 An increase in sample size is most likely to result in a:
A wider confidence interval.
B decrease in the standard error of the sample mean.
C lower likelihood of sampling from more than one population.
27 A report on long-  term stock returns focused exclusively on all currently pub -
licly traded firms in an industry is most likely  susceptible to:
B survivorship bias.
C intergenerational data mining.
28 Which sampling bias is most likely  investigated with an out-  of- sample test?
A Look-  ahead bias
B Data-  mining bias
C Sample selection bias
29 Which of the following characteristics of an investment study most likely  indi -
cates time-  period bias?
A The study is based on a short time-  series.

Reading 11 ■ Sampling and Estimation 612
B Information not available on the test date is used.
C A structural change occurred prior to the start of the study’s time series.

Solutions 613
SOLUTIONS
1 A The standard deviation or standard error of the sample mean is  σσXn = . 
Substituting in the values for  σX and σ, we have 1% =  6% n, or n = 6. 
Squaring this value, we get a random sample of n = 36.
B As in Part A, the standard deviation of sample mean is  σσXn = . 
Substituting in the values for  σX and σ, we have 0.25% =  6% n, or n = 
24. Squaring this value, we get a random sample of n = 576, which is 
substantially larger than for Part A of this question.
2 A Assume the sample size will be large and thus the 95 percent confidence 
interval for the mean of a sample of manager returns is  XsX±196 ., 
where  ss nX= . Munzi wants the distance between the upper limit and 
lower limit in the confidence interval to be 1 percent, which is
Xs XsXX+() −−() = 1961 96 1 .. %
 Simplifying this equation, we get  2196 .sX ()  = 1%. Finally, we have  392 .sX = 
1%, which gives us the standard deviation of the sample mean,  sX = 0.255%.

The distribution of sample means is  ss nX= . Substituting in the values 
for sX and s, we have 0.255% =  4% n, or n = 15.69. Squaring this value, 
we get a random sample of n = 246.
B With her budget, Munzi can pay for a sample of up to 100 observations, 
which is far short of the 246 observations needed. Munzi can either proceed 
with her current budget and settle for a wider confidence interval or she can 
raise her budget (to around $2,460) to get the sample size for a 1 percent 
width in her confidence interval.
3 A This is a small-  sample problem in which the sample comes from a normal 
population with a known standard deviation; thus we use the z-distribution 
in the solution. For a 95 percent confidence interval (and 2.5 percent in each 
tail), the critical z-value is 1.96. For returns that are normally distributed, a 
95 percent confidence interval is of the form
µσ+196 .
n
 The lower limit is  X
n1 1966 19618
4=− =− µσ.% .% = 6% – 1.96(9%) = 
–11.64%.
 The upper limit is  X

–11.64%.
nu=+ =+ µσ1966 19618
4.% .% = 6% + 1.96(9%) = 
23.64%.
 There is a 95 percent probability that four-  year average returns will be 
between −11.64 percent and +23.64 percent.
B The critical z-value associated with the −2.0 percent return is
ZX
n=−=−−=−=−µ
σ26
18 48
9089%%
%%
%.

Reading 11 ■ Sampling and Estimation 614
 Using a normal table, the probability of a z-value less than −0.89 is 
P(Z < −0.89) = 0.1867. Unfortunately, although your client is unhappy with 
the investment result, a four-  year average return of −2.0 percent or lower 
should occur 18.67 percent of the time.
4 (Refer to Figure 1 to help visualize the answer to this question.) Basically, only 
one standard normal distribution exists, but many t-distributions exist—one for 
every different number of degrees of freedom. The normal distribution and the 
t-distribution for a large number of degrees of freedom are practically the same. 
The lower the degrees of freedom, the flatter the t-distribution becomes. The 
t-distribution has less mass (lower probabilities) in the center of the distribution 
and more mass (higher probabilities) out in both tails. Therefore, the confi -
dence intervals based on t-values will be wider than those based on the normal

distribution. Stated differently, the probability of being within a given number 
of standard deviations (such as within ±1 standard deviation or ±2 standard 
deviations) is lower for the t-distribution than for the normal distribution.
5 A For a 99 percent confidence interval, the reliability factor we use is t0.005 ; for 
df = 20, this factor is 2.845.
B For a 90 percent confidence interval, the reliability factor we use is t0.05; for 
df = 20, this factor is 1.725.
C Degrees of freedom equals n − 1, or in this case 25 − 1 = 24. For a 95 per -
cent confidence interval, the reliability factor we use is t0.025 ; for df = 24, this 
factor is 2.064.
D Degrees of freedom equals 16 − 1 = 15. For a 95 percent confidence interval, 
the reliability factor we use is t0.025 ; for df = 15, this factor is 2.131.
6 Because this is a small sample from a normal population and we have only the 
sample standard deviation, we use the following model to solve for the confi -
dence interval of the population mean:
Xts

Xts
n±α2
 where we find t0.025  (for a 95 percent confidence interval) for df = n − 1 = 24 
− 1 = 23; this value is 2.069. Our solution is 1% ± 2.069(4%)/ 24 = 1% ± 
2.069(0.8165) = 1% ± 1.69. The 95 percent confidence interval spans the range 
from −0.69 percent to +2.69 percent.
7 The following table summarizes the calculations used in the answers.
Forecast 
(Xi)Number of 
Analysts ( ni) XiniXXi−() XXi−()2XX nii−()2
1.40 1 1.40 −0.05 0.0025 0.0025
1.43 1 1.43 −0.02 0.0004 0.0004
1.44 3 4.32 −0.01 0.0001 0.0003
1.45 2 2.90 0.00 0.0000 0.0000
1.47 1 1.47 0.02 0.0004 0.0004
1.48 1 1.48 0.03 0.0009 0.0009
1.50 1 1.50 0.05 0.0025 0.0025
Sums 10 14.50   0.0070

Solutions 615
A With  nX Xni
i==
=∑ 10
110
,  = 14.50/10 = 1.45. The variance 
is sX Xni
i2 2
110
1 =− ()



−()
=∑  = 0.0070/9 = 0.0007778. The sample standard 
deviation is s =  0 0007778 .  = 0.02789.
B The confidence interval for the mean can be estimated by 
using  Xt sn ± ()α2 . For 9 degrees of freedom, the reliability factor, t0.025 , 
equals 2.262 and the confidence interval is
1452 262 0 02789 10 1452 262 0 00882
1450 02.. .. ..
..±× =± ()
=±
 The confidence interval for the population mean ranges from 1.43 to 1.47.
8 The following table summarizes the calculations used in the answers.
Forecast 
0.70 2 1.40 −0.04 0.0016 0.0032
0.72 4 2.88 −0.02 0.0004 0.0016
0.74 1 0.74 0.00 0.0000 0.0000
0.75 3 2.25 0.01 0.0001 0.0003
0.76 1 0.76 0.02 0.0004 0.0004
0.77 1 0.77 0.03 0.0009 0.0009
0.82 1 0.82 0.08 0.0064 0.0064
Sums 13 9.62     0.0128
i==
=∑ 13
113
,  = 9.62/13 = 0.74. The variance 
is sX Xni
i2 2
113
1 =− ()



−()

is sX Xni
i2 2
113
1 =− ()



−()
=∑  = 0.0128/12 = 0.001067. The sample standard 
deviation is s = 0 001067 .  = 0.03266.
B The sample is small, and the distribution appears to be bimodal. We cannot 
compute a confidence interval for the population mean because we have 
probably sampled from a distribution that is not normal.
9 If the population variance is known, the confidence interval is
Xz
n±ασ
2
 The confidence interval for the population mean is centered at the sample 
mean,  X. The population standard deviation is σ, and the sample size is n. The 
population standard deviation divided by the square root of n is the standard 
error of the estimate of the mean. The value of z depends on the desired degree 
of confidence. For a 95 percent confidence interval, z0.025  = 1.96 and the 
confidence interval estimate is
X
n±196 .σ

Reading 11 ■ Sampling and Estimation 616
 If the population variance is not known, we make two changes to the technique 
used when the population variance is known. First, we must use the sample 
standard deviation instead of the population standard deviation. Second, we 
use the t-distribution instead of the normal distribution. The critical t-value 
will depend on degrees of freedom n − 1. If the sample size is large, we have the 
alternative of using the z-distribution with the sample standard deviation.
10 A The probabilities can be taken from a normal table, in which the critical 
z-values are 2.00 or 3.00 and we are including the probabilities in both tails. 
The probabilities that the exchange rate will be at least 2 or 3 standard devi -
ations away from the mean are
PX
PX−≥() =
−≥() =µσ
µσ20 0456
30 0026.
.
B With Chebyshev’s inequality, the maximum probability of the exchange rate 
being at least k standard deviations from the mean is P(| X − μ | ≥ kσ) ≤

(1/k)2. The maximum probabilities of the rate being at least 2 or 3 standard 
deviations away from the mean are
PX
PX−≥() ≤() =
−≥() ≤() =µσ
µσ21 20 2500
31 30 11112
2.
.
 The probability of the rate being outside 2 or 3 standard deviations of the mean 
is much smaller with a known normal distribution than when the distribution is 
unknown and we are relying on Chebyshev’s inequality.
11 No. First the conclusion on the limit of zero is wrong; second, the support cited 
for drawing the conclusion (i.e., the central limit theorem) is not relevant in this 
context.
12 In many instances, the distribution that describes the underlying population is 
not normal or the distribution is not known. The central limit theorem states 
that if the sample size is large, regardless of the shape of the underlying popu -
lation, the distribution of the sample mean is approximately normal. Therefore, 
even in these instances, we can still construct confidence intervals (and conduct

tests of inference) as long as the sample size is large (generally n ≥ 30).
13 The statement makes the following mistakes:
■●Given the conditions in the statement, the distribution of  X will be approxi -
mately normal only for large sample sizes.
■●The statement omits the important element of the central limit theorem that 
the distribution of  X will have mean μ.
14 A is correct. The discrepancy arises from sampling error. Sampling error exists 
whenever one fails to observe every element of the population, because a 
sample statistic can vary from sample to sample. As stated in the reading, the 
sample mean is an unbiased estimator, a consistent estimator, and an efficient 
estimator of the population mean. Although the sample mean is an unbiased 
estimator of the population mean—the expected value of the sample mean 
equals the population mean—because of sampling error, we do not expect the 
sample mean to exactly equal the population mean in any one sample we may 
take.

Solutions 617
15 No, we cannot say that Alcorn Mutual Funds as a group is superior to compet -
itors. Alcorn Mutual Funds’ advertisement may easily mislead readers because 
the advertisement does not show the performance of all its funds. In particular, 
Alcorn Mutual Funds is engaging in sample selection bias by presenting the 
investment results from its best-  performing funds only.
16 Spence may be guilty of data mining. He has used so many possible combina -
tions of variables on so many stocks, it is not surprising that he found some 
instances in which a model worked. In fact, it would have been more surprising 
if he had not found any. To decide whether to use his model, you should do two 
things: First, ask that the model be tested on out-  of- sample data—that is, data 
that were not used in building the model. The model may not be successful with 
out- of- sample data. Second, examine his model to make sure that the relation -

ships in the model make economic sense, have a story, and have a future.
17 C is correct. Stratified random sampling involves dividing a population into 
subpopulations based on one or more classification criteria. Then, simple ran -
dom samples are drawn from each subpopulation in sizes proportional to the 
relative size of each subpopulation. These samples are then pooled to form a 
stratified random sample.
18 B is correct. Given a population described by any probability distribution (nor -
mal or non-  normal) with finite variance, the central limit theorem states that 
the sampling distribution of the sample mean will be approximately normal, 
with the mean approximately equal to the population mean, when the sample 
size is large.
19 B is correct. Taking the square root of the known population variance to deter -
mine the population standard deviation (σ) results in:
σ= = 2451 565 ..
 The formula for the standard error of the sample mean (σX), based on a known 
sample size ( n), is:
σσ
Xn=

σσ
Xn=
 Therefore,
σX==1 565
400 247..
20 B is correct. An unbiased estimator is one for which the expected value equals 
the parameter it is intended to estimate.
21 A is correct. A consistent estimator is one for which the probability of esti -
mates close to the value of the population parameter increases as sample size 
increases. More specifically, a consistent estimator’s sampling distribution 
becomes concentrated on the value of the parameter it is intended to estimate 
as the sample size approaches infinity.
22 A is correct. As the degree of confidence increases (e.g., from 95% to 99%), a 
given confidence interval will become wider. A confidence interval is a range for 
which one can assert with a given probability 1 – α, called the degree of confi -
dence, that it will contain the parameter it is intended to estimate.

Reading 11 ■ Sampling and Estimation 618
23 A is correct. A standard normal distribution has tails that approach zero faster 
than the t-distribution. As degrees of freedom increase, the tails of the t-distri -
bution become less fat and the t-distribution begins to look more like a stan -
dard normal distribution. But as degrees of freedom decrease, the tails of the 
t-distribution become fatter.
24 B is correct. The confidence interval is calculated using the following equation:
Xts
n±α2
 Sample standard deviation ( s) = 245 55 .  = 15.670.
 For a sample size of 17, degrees of freedom equal 16, so t0.05 = 1.746.
 The confidence interval is calculated as
11623 1 74615 67
17116 23 6 6357 ..... ±= ±
 Therefore, the interval spans 109.5943 to 122.8656, meaning its width is equal 
to approximately 13.271. (This interval can be alternatively calculated as 
6.6357 × 2).
25 A is correct. To solve, use the structure of Confidence interval = Point estimate

± Reliability factor × Standard error, which, for a normally distributed popula -
tion with known variance, is represented by the following formula:
Xz
n±ασ
2
 For a 99% confidence interval, use z0.005  = 2.58. 
 Also, σ =  529 = 23. 
 Therefore, the lower limit =  31 25823
6523 6398 −=.. .
26 B is correct. All else being equal, as the sample size increases, the standard 
error of the sample mean decreases and the width of the confidence interval 
also decreases.
27 B is correct. A report that uses a current list of stocks does not account for 
firms that failed, merged, or otherwise disappeared from the public equity mar -
ket in previous years. As a consequence, the report is biased. This type of bias is 
known as survivorship bias.
28 B is correct. An out-  of- sample test is used to investigate the presence of data-  
mining bias. Such a test uses a sample that does not overlap the time period of 
the sample on which a variable, strategy, or model was developed.

29 A is correct. A short time series is likely to give period-  specific results that may 
not reflect a longer time period.

Hypothesis Testing
a. define a hypothesis, describe the steps of hypothesis testing, 
and describe and interpret the choice of the null and alternative 
hypotheses;
b. distinguish between one-  tailed and two-  tailed tests of hypotheses; 
c. explain a test statistic, Type I and Type II errors, a significance 
level, and how significance levels are used in hypothesis testing;
d. explain a decision rule, the power of a test, and the relation 
between confidence intervals and hypothesis tests;
e. distinguish between a statistical result and an economically

meaningful result;
f. explain and interpret the p-value as it relates to hypothesis 
testing;
g. identify the appropriate test statistic and interpret the results for a 
hypothesis test concerning the population mean of both large and 
small samples when the population is normally or approximately 
normally distributed and the variance is 1) known or 2) unknown;
h. identify the appropriate test statistic and interpret the results for 
a hypothesis test concerning the equality of the population means 
of two at least approximately normally distributed populations, 
based on independent random samples with 1) equal or 2) 
unequal assumed variances;
12

Reading 12 ■ Hypothesis Testing 620
i. identify the appropriate test statistic and interpret the results for 
a hypothesis test concerning the mean difference of two normally 
distributed populations;
j. identify the appropriate test statistic and interpret the results 
for a hypothesis test concerning 1) the variance of a normally 
distributed population, and 2) the equality of the variances of 
two normally distributed populations based on two independent 
random samples;
k. distinguish between parametric and nonparametric tests and 
describe situations in which the use of nonparametric tests may 
be appropriate.
Analysts often confront competing ideas about how financial markets work. Some 
of these ideas develop through personal research or experience with markets; others 
come from interactions with colleagues; and many others appear in the professional

literature on finance and investments. In general, how can an analyst decide whether 
statements about the financial world are probably true or probably false?
When we can reduce an idea or assertion to a definite statement about the value 
of a quantity, such as an underlying or population mean, the idea becomes a statis -
tically testable statement or hypothesis. The analyst may want to explore questions 
■■Is the underlying mean return on this mutual fund different from the underly -
ing mean return on its benchmark?
■■Did the volatility of returns on this stock change after the stock was added to a 
stock market index?
■■Are a security’s bid-  ask spreads related to the number of dealers making a mar -
ket in the security?
■■Do data from a national bond market support a prediction of an economic 
theory about the term structure of interest rates (the relationship between yield 
and maturity)?
To address these questions, we use the concepts and tools of hypothesis testing.

Hypothesis testing is part of statistical inference, the process of making judgments 
about a larger group (a population) on the basis of a smaller group actually observed 
(a sample). The concepts and tools of hypothesis testing provide an objective means to 
gauge whether the available evidence supports the hypothesis. After a statistical test of 
a hypothesis we should have a clearer idea of the probability that a hypothesis is true 
or not, although our conclusion always stops short of certainty. Hypothesis testing 
has been a powerful tool in the advancement of investment knowledge and science. 
As Robert L. Kahn of the Institute for Social Research (Ann Arbor, Michigan) has 
written, “The mill of science grinds only when hypothesis and data are in continuous 
and abrasive contact. ”1

Hypothesis Testing 621
The main emphases of this reading are the framework of hypothesis testing and 
tests concerning mean and variance, two quantities frequently used in investments. 
We give an overview of the procedure of hypothesis testing in the next section. We 
then address testing hypotheses about the mean and hypotheses about the differences 
between means. In the fourth section of this reading, we address testing hypotheses 
about a single variance and hypotheses about the differences between variances. We 
end the reading with an overview of some other important issues and techniques in 
statistical inference.
HYPOTHESIS TESTING
Hypothesis testing, as we have mentioned, is part of the branch of statistics known 
as statistical inference. Traditionally, the field of statistical inference has two subdivi -
sions: estimation  and hypothesis testing . Estimation addresses the question “What 
is this parameter’s (e.g., the population mean’s) value?” The answer is in the form of a

confidence interval built around a point estimate. Take the case of the mean: We build 
a confidence interval for the population mean around the sample mean as a point 
estimate. For the sake of specificity, suppose the sample mean is 50 and a 95 percent 
confidence interval for the population mean is 50 ± 10 (the confidence interval runs 
from 40 to 60). If this confidence interval has been properly constructed, there is a 
95 percent probability that the interval from 40 to 60 contains the population mean’s 
value.1 The second branch of statistical inference, hypothesis testing, has a somewhat 
different focus. A hypothesis testing question is “Is the value of the parameter (say, 
the population mean) 45 (or some other specific value)?” The assertion “the popula -
tion mean is 45” is a hypothesis. A hypothesis  is defined as a statement about one 
or more populations.
This section focuses on the concepts of hypothesis testing. The process of hypothesis

testing is part of a rigorous approach to acquiring knowledge known as the scientific 
method. The scientific method starts with observation and the formulation of a the -
ory to organize and explain observations. We judge the correctness of the theory by 
its ability to make accurate predictions—for example, to predict the results of new 
observations.2 If the predictions are correct, we continue to maintain the theory as a 
possibly correct explanation of our observations. When risk plays a role in the outcomes 
of observations, as in finance, we can only try to make unbiased, probability-  based 
judgments about whether the new data support the predictions. Statistical hypothesis 
testing fills that key role of testing hypotheses when chance plays a role. In an analyst’s 
day-  to- day work, he may address questions to which he might give answers of varying 
quality. When an analyst correctly formulates the question into a testable hypothesis

and carries out and reports on a hypothesis test, he has provided an element of support 
to his answer consistent with the standards of the scientific method. Of course, the 
analyst’s logic, economic reasoning, information sources, and perhaps other factors 
also play a role in our assessment of the answer’s quality.3
We organize this introduction to hypothesis testing around the following list of 
seven steps.
■■Steps in Hypothesis Testing.  The steps in testing a hypothesis are as follows:42
1 We discussed the construction and interpretation of confidence intervals in the reading on sampling 
and estimation.
2 To be testable, a theory must be capable of making predictions that can be shown to be wrong.
3 See Freeley and Steinberg (2013) for a discussion of critical thinking applied to reasoned decision making.
4 This list is based on one in Daniel and Terrell (1995).

Reading 12 ■ Hypothesis Testing 622
1 Stating the hypotheses.
2 Identifying the appropriate test statistic and its probability distribution.
3 Specifying the significance level.
4 Stating the decision rule.
5 Collecting the data and calculating the test statistic.
6 Making the statistical decision.
7 Making the economic or investment decision.
We will explain each of these steps using as illustration a hypothesis test concerning 
the sign of the risk premium on Canadian stocks. The steps above constitute a tradi -
tional approach to hypothesis testing. We will end the section with a frequently used 
alternative to those steps, the p-value approach.
The first step in hypothesis testing is stating the hypotheses.  We always state two 
hypotheses: the null hypothesis (or null), designated H0, and the alternative hypoth -
esis, designated Ha.
■■Definition of Null Hypothesis.  The null hypothesis is the hypothesis to be 
tested. For example, we could hypothesize that the population mean risk pre -

mium for Canadian equities is less than or equal to zero.
The null hypothesis is a proposition that is considered true unless the sample we use 
to conduct the hypothesis test gives convincing evidence that the null hypothesis is 
false. When such evidence is present, we are led to the alternative hypothesis.
■■Definition of Alternative Hypothesis.  The alternative hypothesis is the 
hypothesis accepted when the null hypothesis is rejected. Our alternative 
hypothesis is that the population mean risk premium for Canadian equities is 
greater than zero.
Suppose our question concerns the value of a population parameter, θ, in relation to 
one possible value of the parameter, θ0 (these are read, respectively, “theta” and “theta 
sub zero”).5 Examples of a population parameter include the population mean, μ, and 
the population variance, σ2. We can formulate three different sets of hypotheses, which 
we label according to the assertion made by the alternative hypothesis.

■■Formulations of Hypotheses.  We can formulate the null and alternative 
hypotheses in three different ways:
1 H0: θ = θ0 versus Ha: θ ≠ θ0 (a “not equal to” alternative hypothesis)
2 H0: θ ≤ θ0 versus Ha: θ > θ0 (a “greater than” alternative hypothesis)
3 H0: θ ≥ θ0 versus Ha: θ < θ0 (a “less than” alternative hypothesis)
In our Canadian example, θ = μRP and represents the population mean risk premium 
on Canadian equities. Also, θ0 = 0 and we are using the second of the above three 
formulations.
The first formulation is a two-  sided hypothesis test  (or two-  tailed hypothesis 
test): We reject the null in favor of the alternative if the evidence indicates that the 
population parameter is either smaller or larger than θ0. In contrast, Formulations 
2 and 3 are each a one-  sided hypothesis test  (or one-  tailed hypothesis test ). For 
Formulations 2 and 3, we reject the null only if the evidence indicates that the popula -

tion parameter is respectively greater than or less than θ0. The alternative hypothesis 
has one side.
5 Greek letters, such as σ, are reserved for population parameters; Roman letters in italics, such as s, are 
used for sample statistics.

Hypothesis Testing 623
Notice that in each case above, we state the null and alternative hypotheses such 
that they account for all possible values of the parameter. With Formulation 1, for 
example, the parameter is either equal to the hypothesized value θ0 (under the null 
hypothesis) or not equal to the hypothesized value θ0 (under the alternative hypoth -
esis). Those two statements logically exhaust all possible values of the parameter.
Despite the different ways to formulate hypotheses, we always conduct a test of the 
null hypothesis at the point of equality, θ = θ0. Whether the null is H0: θ = θ0, H0: θ 
≤ θ0, or H0: θ ≥ θ0, we actually test θ = θ0. The reasoning is straightforward. Suppose 
the hypothesized value of the parameter is 5. Consider H0: θ ≤ 5, with a “greater than” 
alternative hypothesis, Ha: θ > 5. If we have enough evidence to reject H0: θ = 5 in 
favor of Ha: θ > 5, we definitely also have enough evidence to reject the hypothesis

that the parameter, θ, is some smaller value, such as 4.5 or 4. To review, the calculation 
to test the null hypothesis is the same for all three formulations. What is different 
for the three formulations, we will see shortly, is how the calculation is evaluated to 
decide whether or not to reject the null.
How do we choose the null and alternative hypotheses? Probably most common 
are “not equal to” alternative hypotheses. We reject the null because the evidence 
indicates that the parameter is either larger or smaller than θ0. Sometimes, however, we 
may have a “suspected” or “hoped for” condition for which we want to find supportive 
evidence.6 In that case, we can formulate the alternative hypothesis as the statement 
that this condition is true; the null hypothesis that we test is the statement that this 
condition is not true. If the evidence supports rejecting the null and accepting the 
alternative, we have statistically confirmed what we thought was true. For example,

economic theory suggests that investors require a positive risk premium on stocks 
(the risk premium  is defined as the expected return on stocks minus the risk-  free 
rate). Following the principle of stating the alternative as the “hoped for” condition, 
we formulate the following hypotheses:
H0:The population mean risk premium on Canadian stocks is less than or equal to 
0. 
Ha:The population mean risk premium on Canadian stocks is positive.
Note that “greater than” and “less than” alternative hypotheses reflect the beliefs of the 
researcher more strongly than a “not equal to” alternative hypothesis. To emphasize an 
attitude of neutrality, the researcher may sometimes select a “not equal to” alternative 
hypothesis when a one-  sided alternative hypothesis is also reasonable.
The second step in hypothesis testing is identifying the appropriate test statistic 
and its probability distribution.
■■Definition of Test Statistic.  A test statistic is a quantity, calculated based on a

sample, whose value is the basis for deciding whether or not to reject the null 
hypothesis.
The focal point of our statistical decision is the value of the test statistic. Frequently 
(in all the cases that we examine in this reading), the test statistic has the form
Test statistic
Sample  statistic Value of the population pa=− rrameter under 
Standard error of the sam ple statistic0H (1)
6 Part of this discussion of the selection of hypotheses follows Bowerman, O’Connell, and Murphree (2016).

Reading 12 ■ Hypothesis Testing 624
For our risk premium example, the population parameter of interest is the pop -
ulation mean risk premium, μRP. We label the hypothesized value of the population 
mean under H0 as μ0. Restating the hypotheses using symbols, we test H0: μRP ≤ μ0 
versus Ha: μRP > μ0. However, because under the null we are testing μ0 = 0, we write 
H0: μRP ≤ 0 versus Ha: μRP > 0.
The sample mean provides an estimate of the population mean. Therefore, we can 
use the sample mean risk premium calculated from historical data,  XRP, as the sample 
statistic in Equation 1. The standard deviation of the sample statistic, known as the 
“standard error” of the statistic, is the denominator in Equation 1. For this example, 
the sample statistic is a sample mean. For a sample mean,  X, calculated from a sample 
generated by a population with standard deviation σ, the standard error is given by 
one of two expressions:
σσ
Xn=
when we know σ (the population standard deviation), or
ss
nX=

ss
nX=
when we do not know the population standard deviation and need to use the sample 
standard deviation s to estimate it. For this example, because we do not know the 
population standard deviation of the process generating the return, we use Equation 3. 
The test statistic is thus
X
sX
sn XRP RP −=− µ0 0
In making the substitution of 0 for μ0, we use the fact already highlighted that we 
test any null hypothesis at the point of equality, as well as the fact that μ0 = 0 here.
We have identified a test statistic to test the null hypothesis. What probability 
distribution does it follow? We will encounter four distributions for test statistics in 
this reading:
■■the t-distribution (for a t-test);
■■the standard normal or z-distribution (for a z-test);
■■the chi-  square (χ2) distribution (for a chi-  square test); and
■■the F-distribution (for an F-test).
We will discuss the details later, but assume we can conduct a z-test based on the

central limit theorem because our Canadian sample has many observations.7 To 
summarize, the test statistic for the hypothesis test concerning the mean risk premium 
is XsX RP . We can conduct a z-test because we can plausibly assume that the test 
statistic follows a standard normal distribution.
The third step in hypothesis testing is specifying the significance level.  When the test 
statistic has been calculated, two actions are possible: 1) We reject the null hypothesis 
or 2) we do not reject the null hypothesis. The action we take is based on comparing 
the calculated test statistic to a specified possible value or values. The comparison 
values we choose are based on the level of significance selected. The level of signifi -
cance reflects how much sample evidence we require to reject the null. Analogous to (2)
(3)
7 The central limit theorem says that the sampling distribution of the sample mean will be approximately

normal with mean μ and variance σ2/n when the sample size is large. The sample we will use for this 
example has 111 observations.

Hypothesis Testing 625
its counterpart in a court of law, the required standard of proof can change according 
to the nature of the hypotheses and the seriousness of the consequences of making a 
mistake. There are four possible outcomes when we test a null hypothesis:
1 We reject a false null hypothesis. This is a correct decision.
2 We reject a true null hypothesis. This is called a Type I error .
3 We do not reject a false null hypothesis. This is called a Type II error .
4 We do not reject a true null hypothesis. This is a correct decision.
We illustrate these outcomes in Table 1.
Table 1   Type I and Type II Errors in Hypothesis Testing
True Situation
Decision H0 True H0 False
Do not reject H0 Correct Decision Type II Error
Reject H0 (accept Ha) Type I Error Correct Decision
When we make a decision in a hypothesis test, we run the risk of making either a 
Type I or a Type II error. These are mutually exclusive errors: If we mistakenly reject

the null, we can only be making a Type I error; if we mistakenly fail to reject the null, 
we can only be making a Type II error.
The probability of a Type I error in testing a hypothesis is denoted by the Greek 
letter alpha, α. This probability is also known as the level of significance  of the test. 
For example, a level of significance of 0.05 for a test means that there is a 5 percent 
probability of rejecting a true null hypothesis. The probability of a Type II error is 
denoted by the Greek letter beta, β.
Controlling the probabilities of the two types of errors involves a trade-  off. All 
else equal, if we decrease the probability of a Type I error by specifying a smaller 
significance level (say 0.01 rather than 0.05), we increase the probability of making a 
Type II error because we will reject the null less frequently, including when it is false. 
The only way to reduce the probabilities of both types of errors simultaneously is to 
increase the sample size, n.

Quantifying the trade-  off between the two types of error in practice is usually 
impossible because the probability of a Type II error is itself hard to quantify. Consider 
H0: θ ≤ 5 versus Ha: θ > 5. Because every true value of θ greater than 5 makes the 
null hypothesis false, each value of θ greater than 5 has a different β (Type II error 
probability). In contrast, it is sufficient to state a Type I error probability for θ = 5, the 
point at which we conduct the test of the null hypothesis. Thus, in general, we specify 
only α, the probability of a Type I error, when we conduct a hypothesis test. Whereas 
the significance level of a test is the probability of incorrectly rejecting the null, the 
power of a test  is the probability of correctly  rejecting the null—that is, the probability 
of rejecting the null when it is false.8 When more than one test statistic is available to 
conduct a hypothesis test, we should prefer the most powerful, all else equal.9

8 The power of a test is, in fact, 1 minus the probability of a Type II error.
9 We do not always have information on the relative power of the test for competing test statistics, however.

Reading 12 ■ Hypothesis Testing 626
To summarize, the standard approach to hypothesis testing involves specifying a 
level of significance (probability of Type I error) only. It is most appropriate to specify 
this significance level prior to calculating the test statistic. If we specify it after calcu -
lating the test statistic, we may be influenced by the result of the calculation, which 
detracts from the objectivity of the test.
We can use three conventional significance levels to conduct hypothesis tests: 
0.10, 0.05, and 0.01. Qualitatively, if we can reject a null hypothesis at the 0.10 level of 
significance, we have some evidence  that the null hypothesis is false. If we can reject 
a null hypothesis at the 0.05 level, we have strong evidence  that the null hypothesis is 
false. And if we can reject a null hypothesis at the 0.01 level, we have very strong evi -
dence  that the null hypothesis is false. For the risk premium example, we will specify 
a 0.05 significance level.

The fourth step in hypothesis testing is stating the decision rule.  The general prin -
ciple is simply stated. When we test the null hypothesis, if we find that the calculated 
value of the test statistic is more extreme than a given value or values determined by 
the specified level of significance, α, we reject the null hypothesis. We say the result is 
statistically significant . Otherwise, we do not reject the null hypothesis and we say 
the result is not statistically significant. The value or values with which we compare 
the calculated test statistic to make our decision are the rejection points (critical 
values) for the test.10
■■Definition of a Rejection Point (Critical Value) for the Test Statistic.  A 
rejection point (critical value) for a test statistic is a value with which the com -
puted test statistic is compared to decide whether to reject or not reject the null 

For a one-  tailed test, we indicate a rejection point using the symbol for the test 
statistic with a subscript indicating the specified probability of a Type I error, α; for 
example, zα. For a two-  tailed test, we indicate zα/2. To illustrate the use of rejection 
points, suppose we are using a z-test and have chosen a 0.05 level of significance.
■■For a test of H0: θ = θ0 versus Ha: θ ≠ θ0, two rejection points exist, one nega -
tive and one positive. For a two-  sided test at the 0.05 level, the total probabil -
ity of a Type I error must sum to 0.05. Thus, 0.05/2 = 0.025 of the probability 
should be in each tail of the distribution of the test statistic under the null. 
Consequently, the two rejection points are z0.025  = 1.96 and − z0.025  = −1.96. Let 
z represent the calculated value of the test statistic. We reject the null if we find 
that z < −1.96 or z > 1.96. We do not reject if −1.96 ≤ z ≤ 1.96.

■■For a test of H0: θ ≤ θ0 versus Ha: θ > θ0 at the 0.05 level of significance, the 
rejection point is z0.05 = 1.645. We reject the null hypothesis if z > 1.645. The 
value of the standard normal distribution such that 5 percent of the outcomes 
lie to the right is z0.05 = 1.645.
■■For a test of H0: θ ≥ θ0 versus Ha: θ < θ0, the rejection point is − z0.05 = −1.645. 
We reject the null hypothesis if z < −1.645.
Figure 1 illustrates a test H0: μ = μ0 versus Ha: μ ≠ μ0 at the 0.05 significance level 
using a z-test. The “acceptance region” is the traditional name for the set of values 
of the test statistic for which we do not reject the null hypothesis. (The traditional 
name, however, is inaccurate. We should avoid using phrases such as “accept the null 
hypothesis” because such a statement implies a greater degree of conviction about the 
10 “Rejection point” is a descriptive synonym for the more traditional term “critical value. ”

Hypothesis Testing 627
null than is warranted when we fail to reject it.)11 On either side of the acceptance 
region is a rejection region (or critical region). If the null hypothesis that μ = μ0 is 
true, the test statistic has a 2.5 percent chance of falling in the left rejection region 
and a 2.5 percent chance of falling in the right rejection region. Any calculated value 
of the test statistic that falls in either of these two regions causes us to reject the null 
hypothesis at the 0.05 significance level. The rejection points of 1.96 and −1.96 are 
seen to be the dividing lines between the acceptance and rejection regions.
Figure 1   Rejection Points (Critical Values), 0.05 Significance Level, Two-  
Sided Test of the Population Mean Using a z-Test
0.95
Acceptance Region0.025 0.025
0 1.96 –1.96
Rejection 
Region
z < –1.96Rejection 
Region
z > 1.96
Figure 1 affords a good opportunity to highlight the relationship between confi -

dence intervals and hypothesis tests. A 95 percent confidence interval for the popu -
lation mean, μ, based on sample mean,  X, is given by  XsX−196 . to XsX+196 . , 
where  sX is the standard error of the sample mean (Equation 3).12
Now consider one of the conditions for rejecting the null hypothesis:
X
sX−>µ01.96
Here, μ0 is the hypothesized value of the population mean. The condition states that 
rejection is warranted if the test statistic exceeds 1.96. Multiplying both sides by  sX, 
we have  XsX−>µ0196 ., or after rearranging,  XsX−>1960 . µ, which we can also 
write as  µ0 196 <−XsX. . This expression says that if the hypothesized population 
mean, μ0, is less than the lower limit of the 95 percent confidence interval based on 
the sample mean, we must reject the null hypothesis at the 5 percent significance level 
(the test statistic falls in the rejection region to the right).
11 The analogy in some courts of law (for example, in the United States) is that if a jury does not return a

verdict of guilty (the alternative hypothesis), it is most accurate to say that the jury has failed to reject the 
null hypothesis, namely, that the defendant is innocent.
12 Just as with the hypothesis test, we can use this confidence interval, based on the standard normal 
distribution, when we have large samples. An alternative hypothesis test and confidence interval uses the 
t-distribution, which requires concepts that we introduce in the next section.

Reading 12 ■ Hypothesis Testing 628
Now, we can take the other condition for rejecting the null hypothesis:
X
sX−<−µ01.96
and, using algebra as before, rewrite it as  µ0 196 >+XsX. . If the hypothesized pop -
ulation mean is larger than the upper limit of the 95 percent confidence interval, we 
reject the null hypothesis at the 5 percent level (the test statistic falls in the rejection 
region to the left). Thus, an α significance level in a two-  sided hypothesis test can be 
interpreted in exactly the same way as a (1 − α) confidence interval.
In summary, when the hypothesized value of the population parameter under the 
null is outside the corresponding confidence interval, the null hypothesis is rejected. 
We could use confidence intervals to test hypotheses; practitioners, however, usually 
do not. Computing a test statistic (one number, versus two numbers for the usual con -
fidence interval) is more efficient. Also, analysts encounter actual cases of one-  sided

confidence intervals only rarely. Furthermore, only when we compute a test statistic 
can we obtain a p-value, a useful quantity relating to the significance of our results 
(we will discuss p-values shortly).
To return to our risk premium test, we stated hypotheses H0: μRP ≤ 0 versus Ha: 
μRP > 0. We identified the test statistic as  XsRP X/  and stated that it follows a stan -
dard normal distribution. We are, therefore, conducting a one-  sided z-test. We specified 
a 0.05 significance level. For this one-  sided z-test, the rejection point at the 0.05 level 
of significance is 1.645. We will reject the null if the calculated z-statistic is larger than 
1.645. Figure 2 illustrates this test.
Figure 2   Rejection Point (Critical Value), 0.05 Significance Level, One-  Sided 
Test of the Population Mean Using a z-Test
0.95
Acceptance Region= 0.05
0 1.645
Rejection 
Region
z > 1.645
The fifth step in hypothesis testing is collecting the data and calculating the test

statistic.  The quality of our conclusions depends not only on the appropriateness of 
the statistical model but also on the quality of the data we use in conducting the test. 
We first need to check for measurement errors in the recorded data. Some other 
issues to be aware of include sample selection bias and time-  period bias. Sample 
selection bias refers to bias introduced by systematically excluding some members of 
the population according to a particular attribute. One type of sample selection bias 
is survivorship bias. For example, if we define our sample as US bond mutual funds

Hypothesis Testing 629
currently operating and we collect returns for just these funds, we will systematically 
exclude funds that have not survived to the present date. Nonsurviving funds are 
likely to have underperformed surviving funds, on average; as a result the perfor -
mance reflected in the sample may be biased upward. Time-  period bias refers to the 
possibility that when we use a time-  series sample, our statistical conclusion may be 
sensitive to the starting and ending dates of the sample.13
To continue with the risk premium hypothesis, we focus on Canadian equities. 
According to Dimson, Marsh, and Staunton (2011) for the period 1900 to 2010 inclu -
sive (111 annual observations), the arithmetic mean equity risk premium for Canadian 
stocks relative to bond returns,  XRP, was 5.3 percent per year. The sample standard 
deviation of the annual risk premiums was 18.2 percent. Using Equation 3, the stan -

dard error of the sample mean is  ss nX= = 18.2%/ 111 = 1.727%. The test statistic 
is zX sX=RP  = 5.3%/1.727% = 3.07.
The sixth step in hypothesis testing is making the statistical decision.  For our exam -
ple, because the test statistic z = 3.07 is larger than the rejection point of 1.645, we 
reject the null hypothesis in favor of the alternative hypothesis that the risk premium 
on Canadian stocks is positive. The first six steps are the statistical steps. The final 
decision concerns our use of the statistical decision.
The seventh and final step in hypothesis testing is making the economic or investment 
decision.  The economic or investment decision takes into consideration not only the 
statistical decision but also all pertinent economic issues. In the sixth step, we found 
strong statistical evidence that the Canadian risk premium is positive. The magnitude 
of the estimated risk premium, 5.3 percent a year, is economically very meaningful

as well. Based on these considerations, an investor might decide to commit funds to 
Canadian equities. A range of nonstatistical considerations, such as the investor’s 
tolerance for risk and financial position, might also enter the decision-  making process.
The preceding discussion raises an issue that often arises in this decision-  making 
step. We frequently find that slight differences between a variable and its hypothesized 
value are statistically significant but not economically meaningful. For example, we 
may be testing an investment strategy and reject a null hypothesis that the mean return 
to the strategy is zero based on a large sample. Equation 1 shows that the smaller 
the standard error of the sample statistic (the divisor in the formula), the larger the 
value of the test statistic and the greater the chance the null will be rejected, all else 
equal. The standard error decreases as the sample size, n, increases, so that for very

large samples, we can reject the null for small departures from it. We may find that 
although a strategy provides a statistically significant positive mean return, the results 
are not economically significant when we account for transaction costs, taxes, and 
risk. Even if we conclude that a strategy’s results are economically meaningful, we 
should explore the logic of why the strategy might work in the future before actually 
implementing it. Such considerations cannot be incorporated into a hypothesis test.
Before leaving the subject of the process of hypothesis testing, we should discuss 
an important alternative approach called the p-value approach to hypothesis testing. 
Analysts and researchers often report the p-value (also called the marginal significance 
level) associated with hypothesis tests.
■■Definition of p-Value.  The p-value is the smallest level of significance at which 
the null hypothesis can be rejected.

For the value of the test statistic of 3.07 in the risk premium hypothesis test, using 
a spreadsheet function for the standard normal distribution, we calculate a p-value 
of 0.00107. We can reject the null hypothesis at that level of significance. The smaller 
13 These issues are discussed further in the reading on sampling.

Reading 12 ■ Hypothesis Testing 630
the p-value, the stronger the evidence against the null hypothesis and in favor of the 
alternative hypothesis. The p-value for a two-  sided test that a parameter equals zero is 
frequently generated automatically by statistical and econometric software programs.14
We can use p-values in the hypothesis testing framework presented above as an 
alternative to using rejection points. If the p-value is less than our specified level 
of significance, we reject the null hypothesis. Otherwise, we do not reject the null 
hypothesis. Using the p-value in this fashion, we reach the same conclusion as we do 
using rejection points. For example, because 0.00107 is less than 0.05, we would reject 
the null hypothesis in the risk premium test. The p-value, however, provides more 
precise information on the strength of the evidence than does the rejection points 
approach. The p-value of 0.00107 indicates that the null is rejected at a far smaller

level of significance than 0.05.
If one researcher examines a question using a 0.05 significance level and another 
researcher uses a 0.01 significance level, the reader may have trouble comparing 
the findings. This concern has given rise to an approach to presenting the results 
of hypothesis tests that features p-values and omits specification of the significance 
level (Step 3). The interpretation of the statistical results is left to the consumer of the 
research. This has sometimes been called the p-value approach to hypothesis testing.15
HYPOTHESIS TESTS CONCERNING THE MEAN
Hypothesis tests concerning the mean are among the most common in practice. In 
this section we discuss such tests for several distinct types of problems. In one type 
(discussed in Section 3.1), we test whether the population mean of a single population 
is equal to (or greater or less than) some hypothesized value. Then, in Sections 3.2

and 3.3, we address inference on means based on two samples. Is an observed differ -
ence between two sample means due to chance or different underlying (population) 
means? When we have two random samples that are independent of each other—no 
relationship exists between the measurements in one sample and the measurements 
in the other—the techniques of Section 3.2 apply. When the samples are dependent, 
the methods of Section 3.3 are appropriate.16
3.1 Tests Concerning a Single Mean
An analyst who wants to test a hypothesis concerning the value of an underlying 
or population mean will conduct a t-test in the great majority of cases. A t-test  is a 
hypothesis test using a statistic ( t-statistic) that follows a t-distribution. The t-distri -
bution is a probability distribution defined by a single parameter known as degrees of 
freedom (df). Each value of degrees of freedom defines one distribution in this family of 3

14 We can use spreadsheets to calculate p-values as well. In Microsoft Excel, for example, we may use the 
worksheet functions TTEST, NORMSDIST, CHIDIST, and FDIST to calculate p-values for t-tests, z-tests, 
chi- square tests, and F-tests, respectively.
15 Davidson and MacKinnon (1993) argued the merits of this approach: “The P value approach does not 
necessarily force us to make a decision about the null hypothesis. If we obtain a P value of, say, 0.000001, 
we will almost certainly want to reject the null. But if we obtain a P value of, say, 0.04, or even 0.004, we 
are not obliged  to reject it. We may simply file the result away as information that casts some doubt on 
the null hypothesis, but that is not, by itself, conclusive. We believe that this somewhat agnostic attitude 
toward test statistics, in which they are merely regarded as pieces of information that we may or may not 
want to act upon, is usually the most sensible one to take. ” (p. 80)

16 When we want to test whether the population means of more than two populations are equal, we use 
analysis of variance (ANOVA). We introduce ANOVA in its most common application, regression analysis, 
in the reading on correlation and regression analysis.

Hypothesis Tests Concerning the Mean 631
distributions. The t-distribution is closely related to the standard normal distribution. 
Like the standard normal distribution, a t-distribution is symmetrical with a mean of 
zero. However, the t-distribution is more spread out: It has a standard deviation greater 
than 1 (compared to 1 for the standard normal)17 and more probability for outcomes 
distant from the mean (it has fatter tails than the standard normal distribution). As 
the number of degrees of freedom increases with sample size, the spread decreases 
and the t-distribution approaches the standard normal distribution as a limit.
Why is the t-distribution the focus for the hypothesis tests of this section? In 
practice, investment analysts need to estimate the population standard deviation by 
calculating a sample standard deviation. That is, the population variance (or standard 
deviation) is unknown. For hypothesis tests concerning the population mean of a

normally distributed population with unknown variance, the theoretically correct test 
statistic is the t-statistic. What if a normal distribution does not describe the popula -
tion? The t-test is robust  to moderate departures from normality, except for outliers 
and strong skewness.18 When we have large samples, departures of the underlying 
distribution from the normal are of increasingly less concern. The sample mean is 
approximately normally distributed in large samples according to the central limit 
theorem, whatever the distribution describing the population. In general, a sample 
size of 30 or more usually can be treated as a large sample and a sample size of 29 or 
less is treated as a small sample.19
■■Test Statistic for Hypothesis Tests of the Population Mean (Practical Case—
Population Variance Unknown).  If the population sampled has unknown 
variance and either of the conditions below holds:
1 the sample is large, or

2 the sample is small but the population sampled is normally distributed, or 
approximately normally distributed,
then the test statistic for hypothesis tests concerning a single population mean, 
μ, is
tX
snn−=−
1µ0
where
 tn−1= t-statistic with n − 1 degrees of freedom ( n is the sample size)
 X = the sample mean
 μ0 = the hypothesized value of the population mean
 s = the sample standard deviation(4)
17 The formula for the variance of a t-distribution is df/(df − 2).
18 See Moore, McCabe, and Craig (2016). A statistic is robust if the required probability calculations are 
insensitive to violations of the assumptions.
19 Although this generalization is useful, we caution that the sample size needed to obtain an approximately 
normal sampling distribution for the sample mean depends on how non-  normal the original population 
is. For some populations, “large” may be a sample size well in excess of 30.

Reading 12 ■ Hypothesis Testing 632
The denominator of the t-statistic is an estimate of the sample mean standard 
error,  ss nX= .20
In Example 1, because the sample size is small, the test is called a small sample 
test concerning the population mean.
EXAMPLE 1   
Risk and Return Characteristics of an Equity Mutual Fund 
(1)
You are analyzing Sendar Equity Fund, a midcap growth fund that has been in 
existence for 24 months. During this period, it has achieved a mean monthly 
return of 1.50  percent with a sample standard deviation of monthly returns 
of 3.60 percent. Given its level of systematic (market) risk and according to a 
pricing model, this mutual fund was expected to have earned a 1.10 percent 
mean monthly return during that time period. Assuming returns are normally 
distributed, are the actual results consistent with an underlying or population 
mean monthly return of 1.10 percent?
1 Formulate null and alternative hypotheses consistent with the verbal 
description of the research goal.

2 Identify the test statistic for conducting a test of the hypotheses in Part 1.
3 Identify the rejection point or points for the hypothesis tested in Part 1 at 
the 0.10 level of significance.
4 Determine whether the null hypothesis is rejected or not rejected at the 
0.10 level of significance. (Use the tables in the back of this book.)
We have a “not equal to” alternative hypothesis, where μ is the underlying mean 
return on Sendar Equity Fund— H0: μ = 1.10 versus Ha: μ ≠ 1.10.
Because the population variance is not known, we use a t-test with 24 − 1 = 23 
degrees of freedom.
Because this is a two-  tailed test, we have the rejection point tα/2,n−1 = t0.05,23 . In 
the table for the t-distribution, we look across the row for 23 degrees of freedom 
to the 0.05 column, to find 1.714. The two rejection points for this two-  sided test 
are 1.714 and −1.714. We will reject the null if we find that t > 1.714 or t < −1.714.

t231501 10
3602 4040
0 7348470 544331 544 =−==..
..
...  or 0
20 A technical note, for reference, is required. When the sample comes from a finite population, estimates 
of the standard error of the mean, whether from Equation 2 or Equation 3, overestimate the true standard 
error. To address this, the computed standard error is multiplied by a shrinkage factor called the finite 
population correction factor (fpc), equal to Nn N −() −() 1, where N is the population size and n is the 
sample size. When the sample size is small relative to the population size (less than 5 percent of the pop -
ulation size), the fpc is usually ignored. The overestimation problem arises only in the usual situation of 
sampling without replacement (after an item is selected, it cannot be picked again) as opposed to sampling 
with replacement.

Hypothesis Tests Concerning the Mean 633
Because 0.544 does not satisfy either t > 1.714 or t < −1.714, we do not reject 
the null hypothesis.
The confidence interval approach provides another perspective on this 
hypothesis test. The theoretically correct 100(1 − α)% confidence interval for 
the population mean of a normal distribution with unknown variance, based 
on a sample of size n, is
Xt sX tsXX−+αα22 to
where tα/2 is the value of t such that α/2 of the probability remains in the right 
tail and where − tα/2 is the value of t such that α/2 of the probability remains 
in the left tail, for n − 1 degrees of freedom. Here, the 90 percent confidence 
interval runs from 1.5 − (1.714)(0.734847) = 0.240 to 1.5 + (1.714)(0.734847) = 
2.760, compactly [0.240, 2.760]. The hypothesized value of mean return, 1.10, 
falls within this confidence interval, and we see from this perspective also that 
the null hypothesis is not rejected. At a 10  percent level of significance, we

conclude that a population mean monthly return of 1.10 percent is consistent 
with the 24-  month observed data series. Note that 10  percent is a relatively 
high probability of rejecting the hypothesis of a 1.10 percent population mean 
monthly return when it is true.
EXAMPLE 2   
A Slowdown in Payments of Receivables
FashionDesigns, a supplier of casual clothing to retail chains, is concerned about 
a possible slowdown in payments from its customers. The controller’s office 
measures the rate of payment by the average number of days in receivables.21 
FashionDesigns has generally maintained an average of 45 days in receivables. 
Because it would be too costly to analyze all of the company’s receivables fre -
quently, the controller’s office uses sampling to track customers’ payment rates. 
A random sample of 50 accounts shows a mean number of days in receivables 
of 49 with a standard deviation of 8 days.
1 Formulate null and alternative hypotheses consistent with determining

whether the evidence supports the suspected condition that customer 
payments have slowed.
the 0.05 and 0.01 levels of significance.
0.05 and 0.01 levels of significance.
The suspected condition is that the number of days in receivables has increased 
relative to the historical rate of 45 days, which suggests a “greater than” alterna -
tive hypothesis. With μ as the population mean number of days in receivables, 
the hypotheses are H0: μ ≤ 45 versus Ha: μ > 45.
21 This measure represents the average length of time that the business must wait after making a sale 
before receiving payment. The calculation is (Accounts receivable)/(Average sales per day).

Reading 12 ■ Hypothesis Testing 634
Because the population variance is not known, we use a t-test with 50 − 1 = 49 
The rejection point is found across the row for degrees of freedom of 49. To 
find the one-  tailed rejection point for a 0.05 significance level, we use the 0.05 
column: The value is 1.677. To find the one-  tailed rejection point for a 0.01 
level of significance, we use the 0.01 column: The value is 2.405. To summarize, 
at a 0.05 significance level, we reject the null if we find that t > 1.677; at a 0.01 
significance level, we reject the null if we find that t > 2.405.
t4949 45
85 04
1 1313713 536 =−==..
Because 3.536 > 1.677, the null hypothesis is rejected at the 0.05 level. Because 
3.536 > 2.405, the null hypothesis is also rejected at the 0.01 level. We can say 
with a high level of confidence that FashionDesigns has experienced a slowdown

in customer payments. The level of significance, 0.01, is a relatively low proba -
bility of rejecting the hypothesized mean of 45 days or less. Rejection gives us 
confidence that the mean has increased above 45 days.
We stated above that when population variance is not known, we use a t-test for 
tests concerning a single population mean. Given at least approximate normality, 
the t-test is always called for when we deal with small samples and do not know 
the population variance. For large samples, the central limit theorem states that the 
sample mean is approximately normally distributed, whatever the distribution of the 
population. So the t-test is still appropriate, but an alternative test may be more useful 
when sample size is large.
For large samples, practitioners sometimes use a z-test in place of a t-test for tests 
concerning a mean.22 The justification for using the z-test in this context is twofold.

First, in large samples, the sample mean should follow the normal distribution at least 
approximately, as we have already stated, fulfilling the normality assumption of the 
z-test. Second, the difference between the rejection points for the t-test and z-test 
becomes quite small when sample size is large. For a two-  sided test at the 0.05 level 
of significance, the rejection points for a z-test are 1.96 and −1.96. For a t-test, the 
rejection points are 2.045 and −2.045 for df = 29 (about a 4 percent difference between 
the z and t rejection points) and 2.009 and −2.009 for df = 50 (about a 2.5 percent dif -
ference between the z and t rejection points). Because the t-test is readily available as 
statistical program output and theoretically correct for unknown population variance, 
we present it as the test of choice.
In a very limited number of cases, we may know the population variance; in such 
cases, the z-test is theoretically correct.23
■■The z-Test Alternative.

22 These practitioners choose between t-tests and z-tests based on sample size. For small samples ( n < 
30), they use a t-test, and for large samples, a z-test.
23 For example, in Monte Carlo simulation, we prespecify the probability distributions for the risk factors. 
If we use a normal distribution, we know the true values of mean and variance. Monte Carlo simulation 
involves the use of a computer to represent the operation of a system subject to risk; we discuss Monte 
Carlo simulation in the reading on common probability distributions.

Hypothesis Tests Concerning the Mean 635
1 If the population sampled is normally distributed with known variance σ2, 
then the test statistic for a hypothesis test concerning a single population 
mean, μ, is
 
zX
n=−µ
σ0
2 If the population sampled has unknown variance and the sample is large, 
in place of a t-test, an alternative test statistic (relying on the central limit 
theorem) is
 
zX
sn=−µ0
In the above equations,
 σ = the known population standard deviation
 s = the sample standard deviation
When we use a z-test, we most frequently refer to a rejection point in the list below. 
■■Rejection Points for a z-Test .
A Significance level of α = 0.10.
1 H0: θ = θ0 versus Ha: θ ≠ θ0. The rejection points are z0.05 = 1.645 and −
z0.05 = −1.645.
 Reject the null hypothesis if z > 1.645 or if z < −1.645.
2 H0: θ ≤ θ0 versus Ha: θ > θ0. The rejection point is z0.10 = 1.28.
 Reject the null hypothesis if z > 1.28.

Reject the null hypothesis if z > 1.28.
3 H0: θ ≥ θ0 versus Ha: θ < θ0. The rejection point is − z0.10 = −1.28.
 Reject the null hypothesis if z < −1.28.
B Significance level of α = 0.05.
1 H0: θ = θ0 versus Ha: θ ≠ θ0. The rejection points are z0.025  = 1.96 and −
z0.025  = −1.96.
 Reject the null hypothesis if z > 1.96 or if z < −1.96.
2 H0: θ ≤ θ0 versus Ha: θ > θ0. The rejection point is z0.05 = 1.645.
 Reject the null hypothesis if z > 1.645.
3 H0: θ ≥ θ0 versus Ha: θ < θ0. The rejection point is − z0.05 = −1.645.
 Reject the null hypothesis if z < −1.645.
C Significance level of α = 0.01.
1 H0: θ = θ0 versus Ha: θ ≠ θ0. The rejection points are z0.005  = 2.575 and 
−z0.005  = −2.575.
 Reject the null hypothesis if z > 2.575 or if z < −2.575.
2 H0: θ ≤ θ0 versus Ha: θ > θ0. The rejection point is z0.01 = 2.33.
 Reject the null hypothesis if z > 2.33.
3 H0: θ ≥ θ0 versus Ha: θ < θ0. The rejection point is − z0.01 = −2.33.
 Reject the null hypothesis if z < −2.33.(5)
(6)

Reading 12 ■ Hypothesis Testing 636
EXAMPLE 3   
The Effect of Control Deficiency Disclosures under the 
Sarbanes–Oxley Act on Share Prices
The Sarbanes–Oxley Act came into effect in 2002 and introduced major changes 
to the regulation of corporate governance and financial practice in the United 
States. One of the requirements of this Act is for firms to periodically assess 
and report certain types of internal control deficiencies to the audit commit -
tee, external auditors, and to the Securities and Exchange Commission (SEC). 
When a company makes an internal control weakness disclosure, does it convey 
information that affects the market value of the firm’s stock?
Gupta and Nayar (2007) addressed this question by studying a number of 
voluntary disclosures made in the very early days of Sarbanes–Oxley imple -
mentation. Their final sample for this study consisted of 90 firms that had made 
control deficiency disclosures to the SEC from March 2003 to July 2004. This

90- firm sample was termed the “full sample” . These firms were further examined 
to see if there were any other contemporaneous announcements, such as earnings 
announcements, associated with the control deficiency disclosures. Of the 90 
firms, 45 did not have any such confounding announcements, and the sample 
of these firms was termed the “clean sample” .
The announcement day of the internal control weakness was designated t 
= 0. If these announcements provide new information useful for equity valua -
tion, the information should cause a change in stock prices and returns once it 
is available. Only one component of stock returns is of interest: the return in 
excess of that predicted given a stock’s market risk or beta, called the abnormal 
return. Significant negative (positive) abnormal returns indicate that investors 
perceive unfavorable (favorable) corporate news in the internal control weakness 
announcement. Although Gupta and Nayar examined abnormal returns for

various time horizons or event windows, we report a selection of their findings 
for the window [0, +1], which includes a two-  day period of the day of and the 
day after the announcement. The researchers chose to use z-tests for statistical 
significance. 
Full sample  (90 firms). The null hypothesis that the average abnormal stock 
return during [0, +1] was 0 would be true if stock investors did not find either 
positive or negative information in the announcement. 
Mean abnormal return = –3.07 percent.
z-statistic for abnormal return = –5.938.
Clean sample  (45 firms). The null hypothesis that the average abnormal stock 
Mean abnormal return = –1.87 percent.
z-statistic for abnormal return = –3.359.
1 With respect to both of the cases, suppose that the null hypothesis reflects 
the belief that investors do not, on average, perceive either positive or

negative information in control deficiency disclosures. State one set of 
hypotheses (a null hypothesis and an alternative hypothesis) that covers 
both cases.

Hypothesis Tests Concerning the Mean 637
2 Determine whether the null hypothesis formulated in Part 1 is rejected or 
not rejected at the 0.05 and 0.01 levels of significance for the full sample  
case. Interpret the results.
3 Determine whether the null hypothesis formulated in Part 1 is rejected or 
not rejected at the 0.05 and 0.01 levels of significance for the clean sample  
A set of hypotheses consistent with no information in control deficiency dis -
closures relevant to stock investors is
H0: The population mean abnormal return during [0, +1] equals 0.
Ha: The population mean abnormal return during [0, +1] does not equal 0.
From the information on rejection points for z-tests, we know that we reject 
the null hypothesis at the 0.05 significance level if z > 1.96 or if z < −1.96, and 
at the 0.01 significance level if z > 2.575 or if z < −2.575. The z-statistic reported

by the researchers is –5.938, which is significant at the 0.05 and 0.01 levels. The 
null is rejected. The control deficiency disclosures appear to contain valuation-  
relevant information.
Because it is possible that significant results could be due to outliers, the 
researchers also reported the number of cases of positive and negative abnormal 
returns. The ratio of cases of positive to negative abnormal returns was 32:58, 
which tends to support the conclusion from the z-test of statistically significant 
negative abnormal returns.
The z-statistic reported by the researchers for the clean sample is –3.359, which 
is significant at the 0.05 and 0.01 levels. Although both the mean abnormal return 
and the z-statistic are smaller in magnitude for the clean sample than for the 
full sample, the results continue to be statistically significant.
The ratio of cases of positive to negative abnormal returns was 16:29, which

tends to support the conclusion from the z-test of statistically significant neg -
ative abnormal returns.
Nearly all practical situations involve an unknown population variance. Table 2 
summarizes our discussion for tests concerning the population mean when the pop -
ulation variance is unknown.
Table 2   Test Concerning the Population Mean (Population Variance 
Unknown) 
Large Sample ( n ≥ 30) Small Sample ( n < 30)
Population normal t-Test ( z-Test alternative) t-Test
Population non-  normal t-Test ( z-Test alternative) Not Available

Reading 12 ■ Hypothesis Testing 638
3.2 Tests Concerning Differences between Means
We often want to know whether a mean value—for example, a mean return—differs 
between two groups. Is an observed difference due to chance or to different underlying 
values for the mean? We have two samples, one for each group. When it is reasonable 
to believe that the samples are from populations at least approximately normally dis -
tributed and that the samples are also independent of each other, the techniques of 
this section apply. We discuss two t-tests for a test concerning differences between the 
means of two populations. In one case, the population variances, although unknown, 
can be assumed to be equal. Then, we efficiently combine the observations from both 
samples to obtain a pooled estimate of the common but unknown population variance. 
A pooled estimate is an estimate drawn from the combination of two different samples.

In the second case, we do not assume that the unknown population variances are equal, 
and an approximate t-test is then available. Letting μ1 and μ2 stand, respectively, for 
the population means of the first and second populations, we most often want to test 
whether the population means, although unknown, are equal or whether one is larger 
than the other. Thus we usually formulate the following hypotheses:
1 H0: μ1 − μ2 = 0 versus Ha: μ1 − μ2 ≠ 0 (the alternative is that μ1 ≠ μ2)
2 H0: μ1 − μ2 ≤ 0 versus Ha: μ1 − μ2 > 0 (the alternative is that μ1 > μ2)
3 H0: μ1 − μ2 ≥ 0 versus Ha: μ1 − μ2 < 0 (the alternative is that μ1 < μ2)
We can, however, formulate other hypotheses, such as H0: μ1 − μ2 = 2 versus Ha: μ1 
− μ2 ≠ 2. The procedure is the same.
The definition of the t-test follows.
■■Test Statistic for a Test of the Difference between Two Population Means 
(Normally Distributed Populations, Population Variances Unknown but

Assumed Equal).  When we can assume that the two populations are normally 
distributed and that the unknown population variances are equal, a t-test based 
on independent random samples is given by
tXX
s
ns
npp=−() −−()
+



12 12
2
12
212µµ
where  sns ns
nnp2 112
222
1211
2=−() +−()
+−is a pooled estimator of the common 
variance.
The number of degrees of freedom is n1 + n2 − 2.
EXAMPLE 4   
Mean Returns on the S&P 500: A Test of Equality across 
Two Halves of a Decade
The realized mean monthly return on the S&P 500 Index in the first half of the 
2000s appears to have been substantially different than the mean return in the 
second half of the 2000s. Was the difference statistically significant? The data, 
shown in Table 3, indicate that assuming equal population variances for returns 
in the two periods is not unreasonable.(7)

Hypothesis Tests Concerning the Mean 639
Table 3    S&P 500 Monthly Return and Standard Deviation for Two 
Halves of a Decade
Time PeriodNumber of  
Months ( n)Mean Monthly  
Return (%)Standard  
Deviation
2000 through 2004 60 –0.083 4.719
2005 through 2009 60 0.144 4.632
1 Formulate null and alternative hypotheses consistent with a two-  sided 
hypothesis test.
the 0.10, 0.05, and 0.01 levels of significance.
0.10, 0.05, and 0.01 levels of significance.
Letting μ1 stand for the population mean return for the 2000 through 2004 and 
μ2 stand for the population mean return for the 2005 through 2009, we formulate 
the following hypotheses:
H0: μ1 – μ2 = 0 versus Ha: μ1 – μ2 ≠ 0

Because the two samples are drawn from two different time periods, they are 
independent samples. The population variances are not known but can be 
assumed to be equal. Given all these considerations, the t-test given in Equation 7 
has 60 + 60 − 2 = 118 degrees of freedom.
In the tables (Appendix B), the closest number of degrees of freedom to 118 is 
120. For a two-  sided test, the rejection points are ±1.658, ±1.980, and ±2.617 
for, respectively, the 0.10, 0.05, and 0.01 levels for df = 120. To summarize, at 
the 0.10 level, we will reject the null if t < −1.658 or t > 1.658; at the 0.05 level, 
we will reject the null if t < −1.980 or t > 1.980; and at the 0.01 level, we will 
reject the null if t < −2.617 or t > 2.617.

Reading 12 ■ Hypothesis Testing 640
In calculating the test statistic, the first step is to calculate the pooled estimate 
of variance:
sns ns
nnp2 112
222
12211
260 14 719 60 14 632=−() +−()
+−=−() () +−() ( .. ) )
+−
==
=−() −−()
+2
12
2
1260 60 2
2 579 7387
11821 8622,..
tXX
s
nsppµµ12
n n212 120 083 0 144 0
21 8622
6021 8622
60



=−−() −
+


=..
..
− −=−0 227
0 8537027.
..
The t value of −0.27 is not significant at the 0.10 level, so it is also not significant 
at the 0.05 and 0.01 levels. Therefore, we do not reject the null hypothesis at 
any of the three levels.
In many cases of practical interest, we cannot assume that population variances are 
equal. The following test statistic is often used in the investment literature in such cases:
(Normally Distributed Populations, Unequal and Unknown Population 
Variances).  When we can assume that the two populations are normally dis -

tributed but do not know the population variances and cannot assume that they 
are equal, an approximate t-test based on independent random samples is given 
by
tXX
s
ns
n=−() −−()
+

12
12
122
212µµ12
where we use tables of the t-distribution using “modified” degrees of freedom 
computed with the formula
df=+


()
+()s
ns
n
sn
nsn
n12
122
22
12
12
122
22
2
A practical tip is to compute the t-statistic before computing the degrees of 
freedom. Whether or not the t-statistic is significant will sometimes be obvious.
EXAMPLE 5   
Recovery Rates on Defaulted Bonds: A Hypothesis Test
How are the required yields on risky corporate bonds determined? Two key 
factors are the expected probability of default and the expected amount that will 
be recovered in the event of default, or the recovery rate. Jankowitsch, Nagler, (8)
(9)

Hypothesis Tests Concerning the Mean 641
and Subrahmanyam (2014) examine the recovery rates of defaulted bonds in 
the US corporate bond market based on an extensive set of traded prices and 
volumes around various types of default events. For their study period, 2002 to 
2012, Jankowitsch et al. confirm that the type of default event (e.g., distressed 
exchanges and formal bankruptcy filings), the seniority of the bond, and the 
industry of the firm are important in explaining the recovery rate. In one of 
their analyses, they focus on non-  financial firms, and find that electricity firms 
recover more in default than firms in the retail industry. We want to test if the 
difference in recovery rates between those two types of firms is statistically 
significant. With μ1 denoting the population mean recovery rate for the bonds 
of electricity firms and μ2 denoting the population mean recovery rate for the 
bonds of retail firms, the hypotheses are H0: μ1 − μ2 = 0 versus Ha: μ1 − μ2 ≠ 0.

Table 4 excerpts from their findings.
Table 4   Recovery Rates by Industry of Firm
Electricity Retail
Number of 
ObservationsAverage 
PriceaStandard 
DeviationNumber of 
Deviation
39 $48.03 $22.67 33 $33.40 $34.19
a This is the average traded price over the default day and the following 30 days after defalt; the average price provides an indication 
of the amount of money that can be recovered.
Source:  Jankowitsch, Nagler, and Subrahmanyam (2013), Table 2.
We assume that the populations (recovery rates) are normally distributed 
and that the samples are independent. Based on the data in the table, address 
1 Discuss whether we should choose a test based on Equation 8 or 
Equation 7.
2 Calculate the test statistic to test the null hypothesis given above.
3 What is the value of the test’s modified degrees of freedom?
4 Determine whether to reject the null hypothesis at the 0.10 level.

The sample standard deviation for the recovery rate on the bonds of electricity 
firms ($22.67) appears much smaller than the sample standard deviation of the 
bonds for retail firms ($34.19). Therefore, we should not assume equal variances, 
and accordingly, we should employ the approximate t-test given in Equation 8.
The test statistic is
tXX
s
ns
n=−()
+

12
12
122
212

Reading 12 ■ Hypothesis Testing 642
where
 X1= sample mean recovery rate for electricity firms = 48.03
 X2 = sample mean recovery rate for retail firms = 33.40
 s12 = sample variance for electricity firms = 22.672 = 513.9289
 s22 = sample variance for retail firms = 34.192 = 1,168.9561
 n1 = sample size of the electricity firms sample = 39
 n2 = sample size of the retail firms sample = 33
Thus, t = (48.03 − 33.40)/[(513.9289/39) + (1,168.9561/33)]1/2 = 14.63/(13.177664 + 
35.422912)1/2 = 14.63/6.971411 = 2.099. The calculated t-statistic is thus 2.099. 
df=+


()
+()=+s
ns
n
sn
nsn
n12
122
22
12
12
122
22
2513 9289
391 ., 1 168 9561
33
513 9289 39
391168 9561 33
33
2362 02
22.
., .
.


()+()
=1 16009
42 47630455 61.. =  or 56 degrees of freedom
The closest entry to df = 56 in the tables for the t-distribution is df = 60. For α 
= 0.10, we find tα/2 = 1.671. Thus, we reject the null if t < −1.671 or t > 1.671.

Based on the computed value of 2.099, we reject the null hypothesis at the 0.10 
level. Some evidence exists that recovery rates differ between electricity and retail 
industries. Why? Studies on recovery rates suggest that the higher recovery rates 
of electricity firms may be explained by their higher levels of tangible assets.
3.3 Tests Concerning Mean Differences
In the previous section, we presented two t-tests for discerning differences between 
population means. The tests were based on two samples. An assumption for those 
tests’ validity was that the samples were independent—i.e., unrelated to each other. 
When we want to conduct tests on two means based on samples that we believe are 
dependent, the methods of this section apply.
The t-test in this section is based on data arranged in paired observations , and 
the test itself is sometimes called a paired comparisons test . Paired observations are 
observations that are dependent because they have something in common. A paired

comparisons test is a statistical test for differences in dependent items. For example, 
we may be concerned with the dividend policy of companies before and after a change 
in the tax law affecting the taxation of dividends. We then have pairs of “before” and 
“after” observations for the same companies. We may test a hypothesis about the 
mean of the differences (mean differences) that we observe across companies. In 
other cases, the paired observations are not on the same units. For example, we may 
be testing whether the mean returns earned by two investment strategies were equal 
over a study period. The observations here are dependent in the sense that there is 
one observation for each strategy in each month, and both observations depend on 
underlying market risk factors. Because the returns to both strategies are likely to

Hypothesis Tests Concerning the Mean 643
be related to some common risk factors, such as the market return, the samples are 
dependent. By calculating a standard error based on differences, the t-test presented 
below takes account of correlation between the observations.
Letting A represent “after” and B “before, ” suppose we have observations for the 
random variables XA and XB and that the samples are dependent. We arrange the 
observations in pairs. Let di denote the difference between two paired observations. We 
can use the notation di = xAi − xBi, where xAi and xBi are the ith pair of observations, 
i = 1, 2, …, n on the two variables. Let μd stand for the population mean difference. 
We can formulate the following hypotheses, where μd0 is a hypothesized value for 
the population mean difference:
1 H0: μd = μd0 versus Ha: μd ≠ μd0
2 H0: μd ≤ μd0 versus Ha: μd > μd0
3 H0: μd ≥ μd0 versus Ha: μd < μd0
In practice, the most commonly used value for μd0 is 0.

As usual, we are concerned with the case of normally distributed populations 
with unknown population variances, and we will formulate a t-test. To calculate the 
t-statistic, we first need to find the sample mean difference:
dndi
in
=
=∑1
1
where n is the number of pairs of observations. The sample variance, denoted by  sd2, is
sdd
ndi
in
2 12
1=−()
−=∑
Taking the square root of this quantity, we have the sample standard deviation, sd, 
which then allows us to calculate the standard error of the mean difference as follows:24
ss
ndd=
■■Test Statistic for a Test of Mean Differences (Normally Distributed 
Populations, Unknown Population Variances).  When we have data consisting 
of paired observations from samples generated by normally distributed popula -
tions with unknown variances, a t-test is based on
td
sd
d=−µ0
with n − 1 degrees of freedom, where n is the number of paired observations,  d is 
the sample mean difference (as given by Equation 10), and  sdis the standard error 
of d (as given by Equation 12).

Table 5 reports the quarterly returns from 2008 to 2013 for two managed portfo -
lios specializing in precious metals. The two portfolios were closely similar in risk (as 
measured by standard deviation of return and other measures) and had nearly identical 
expense ratios. A major investment services company rated Portfolio B more highly (10)
(11)
(12)
(13)
24 We can also use the following equivalent expression, which makes use of the correlation between the 
two variables: ss sr XX ss nd=+ −() AB AB AB222,  where  sA2 is the sample variance of XA, sB2 is the sample 
variance of XB, and r(XA, XB) is the sample correlation between XA and XB.

Reading 12 ■ Hypothesis Testing 644
than Portfolio A in early 2014. In investigating the portfolios’ relative performance, 
suppose we want to test the hypothesis that the mean quarterly return on Portfolio 
A equaled the mean quarterly return on Portfolio B from 2008 to 2013. Because the 
two portfolios shared essentially the same set of risk factors, their returns were not 
independent, so a paired comparisons test is appropriate. Let μd stand for the popu -
lation mean value of difference between the returns on the two portfolios during this 
period. We test H0: μd = 0 versus Ha: μd ≠ 0 at a 0.05 significance level.
Table 5   Quarterly Returns on Two Managed Portfolios: 2008–2013
Quarter Portfolio A (%) Portfolio B (%)Difference  
(Portfolio A – Portfolio B)
4Q:2013 11.40 14.64 −3.24
3Q:2013 −2.17 0.44 −2.61
2Q:2013 10.72 19.51 −8.79
1Q:2013 38.91 50.40 −11.49
4Q:2012 4.36 1.01 3.35
3Q:2012 5.13 10.18 −5.05
2Q:2012 26.36 17.77 8.59
1Q:2012 −5.53 4.76 −10.29
4Q:2011 5.27 −5.36 10.63

3Q:2011 −7.82 −1.54 −6.28
2Q:2011 2.34 0.19 2.15
1Q:2011 −14.38 −12.07 −2.31
4Q:2010 −9.80 −9.98 0.18
3Q:2010 19.03 26.18 −7.15
2Q:2010 4.11 −2.39 6.50
1Q:2010 −4.12 −2.51 −1.61
4Q:2009 −0.53 −11.32 10.79
3Q:2009 5.06 0.46 4.60
2Q:2009 −14.01 −11.56 −2.45
1Q:2009 12.50 3.52 8.98
4Q:2008 −29.05 −22.45 −6.60
3Q:2008 3.60 0.10 3.50
2Q:2008 −7.97 −8.96 0.99
1Q:2008 −8.62 −0.66 −7.96
Mean 1.87 2.52 −0.65
Sample standard deviation of differences = 6.71
The sample mean difference,  d, between Portfolio A and Portfolio B is −0.65 percent 
per quarter. The standard error of the sample mean difference is  sd=6712 4 . = 
1.369673. The calculated test statistic is t = (−0.65 − 0)/1.369673 = −0.475 with n − 1 = 
24 − 1 = 23 degrees of freedom. At the 0.05 significance level, we reject the null if t > 
2.069 or if t < −2.069. Because −0.475 is not less than −2.069, we fail to reject the null.

At the 0.10 significance level, we reject the null if t > 1.714 or if t < −1.714. Thus the 
difference in mean quarterly returns is not significant at any conventional significance 
level.

Hypothesis Tests Concerning the Mean 645
The following example illustrates the application of this test to evaluate two com -
peting investment strategies.
EXAMPLE 6   
A Comparison of Two Portfolios
You are investigating whether the performance of a portfolio of stocks from the 
entire world differs from the performance of a portfolio of only US stocks. For 
the worldwide portfolio, you choose to focus on Vanguard Total World Stock 
Index ETF. This ETF seeks to track the performance of the FTSE Global All Cap 
Index, which is a market-  capitalization-  weighted index designed to measure the 
market performance of stock of companies from both developed and emerging 
markets. For the US portfolio, you choose to focus on SPDR S&P 500, and ETF 
that seeks to track the performance of the S&P 500 Index. You analyze the 
monthly returns on both ETFs from August 2008 to July 2013 and prepare the 
following summary table.
Table 6   Montly Return Summary for Vanguard Total

World Stock Index ETF and SPDR S&P 500 
ETF: August 2008 to July 2013 ( n = 60) 
Strategy Mean ReturnStandard 
Deviation
Worldwide 0.61% 5.43%
US 0.39 6.50
Difference 0.22 1.86a
a Sample standard deviation of differences.
Source of data returns:  finance.yahoo.com accessed 20 August 2013.
From Table 6 we have  d=022.%  and sd = 1.86%.
1 Formulate null and alternative hypotheses consistent with a two-  sided test 
that the mean difference between the worldwide and only US strategies 
equals 0.
the 0.01 level of significance.
0.01 level of significance. (Use the tables in the back of this volume.)
5 Discuss the choice of a paired comparisons test.
With μd as the underlying mean difference between the worldwide and US

strategies, we have H0: μd = 0 versus Ha: μd ≠ 0.
Because the population variance is unknown, the test statistic is a t-test with 
60 − 1 = 59 degrees of freedom.

Reading 12 ■ Hypothesis Testing 646
In the table for the t-distribution, the closest entry to df = 59 is df = 60. We look 
across the row for 60 degrees of freedom to the 0.005 column, to find 2.66. We 
will reject the null if we find that t > 2.66 or t < −2.66.
t59022
1866 0022
0 240125092 = = =.
..
..
Because 0.92 < 2.66, we cannot reject the null hypothesis. Accordingly, we 
conclude that the difference in mean returns for the two strategies is not sta -
tistically significant. 
Several US stocks that are part of the S&P 500 index are also included in the 
Vanguard Total World Stock Index ETF. The profile of the World ETF indicates 
that nine of the top ten holdings in the ETF are US stocks. As a result, they are 
not independent samples; in general, the correlation of returns on the Vanguard 
Total World Stock Index ETF and SPDR S&P 500 ETF should be positive. Because 
the samples are dependent, a paired comparisons test was appropriate.

HYPOTHESIS TESTS CONCERNING VARIANCE
Because variance and standard deviation are widely used quantitative measures of risk 
in investments, analysts should be familiar with hypothesis tests concerning variance. 
The tests discussed in this section make regular appearances in investment literature. 
We examine two types: tests concerning the value of a single population variance and 
tests concerning the differences between two population variances.
4.1 Tests Concerning a Single Variance
In this section, we discuss testing hypotheses about the value of the variance, σ2, of 
a single population. We use  σ02 to denote the hypothesized value of σ2. We can for -
mulate hypotheses as follows:
1 HHa 02
022
02::σσ σσ =≠  versus   (a “not equal to” alternative hypothesis)
2 HHa 02
022
02::σσ σ> σ ≤  versus   (a “greater than” alternative hypothesis)
3 HHa 02
022
02::σσ σ< σ ≥  versus  (a “less than” alternative hypothesis)
In tests concerning the variance of a single normally distributed population, we make

use of a chi-  square test statistic, denoted χ2. The chi-  square distribution, unlike the 
normal and t-distributions, is asymmetrical. Like the t-distribution, the chi-  square 4

Hypothesis Tests Concerning Variance 647
distribution is a family of distributions. A different distribution exists for each possible 
value of degrees of freedom, n − 1 ( n is sample size). Unlike the t-distribution, the 
chi- square distribution is bounded below by 0; χ2 does not take on negative values.
■■Test Statistic for Tests Concerning the Value of a Population Variance 
(Normal Population).  If we have n independent observations from a normally 
distributed population, the appropriate test statistic is
χ
σ22
021=−()ns
with n − 1 degrees of freedom. In the numerator of the expression is the sample 
variance, calculated as
sXX
ni
in
2 12
1=−()
−=∑
In contrast to the t-test, for example, the chi-  square test is sensitive to violations 
of its assumptions. If the sample is not actually random or if it does not come from 
a normally distributed population, inferences based on a chi-  square test are likely to 
be faulty.

be faulty.
If we choose a level of significance, α, the rejection points for the three kinds of 
hypotheses are as follows:
■■Rejection Points for Hypothesis Tests on the Population Variance.
1 “Not equal to” Ha: Reject the null hypothesis if the test statistic is greater 
than the upper α/2 point (denoted  χα22) or less than the lower α/2 point 
(denoted  χα122
−) of the chi-  square distribution with df = n − 1.25
2 “Greater than” Ha: Reject the null hypothesis if the test statistic is greater 
than the upper α point of the chi-  square distribution with df = n − 1.
3 “Less than” Ha: Reject the null hypothesis if the test statistic is less than the 
lower α point of the chi-  square distribution with df = n − 1.
EXAMPLE 7   
(2)
You continue with your analysis of Sendar Equity Fund, a midcap growth fund 
that has been in existence for only 24 months. Recall that during this period,

Sendar Equity achieved a sample standard deviation of monthly returns of (14)
(15)
25 Just as with other hypothesis tests, the chi-  square test can be given a confidence interval interpretation. 
Unlike confidence intervals based on z- or t-statistics, however, chi-  square confidence intervals for variance 
are asymmetric. A two-  sided confidence interval for population variance, based on a sample of size n, has 
a lower limit  L=−()ns12
22χα and an upper limit  U=−()−ns12
122χα. Under the null hypothesis, the 
hypothesized value of the population variance should fall within these two limits.

Reading 12 ■ Hypothesis Testing 648
3.60 percent. You now want to test a claim that the particular investment dis -
ciplines followed by Sendar result in a standard deviation of monthly returns 
of less than 4 percent.
the 0.05 level of significance.
0.05 level of significance. (Use the tables in the back of this volume.)
We have a “less than” alternative hypothesis, where σ is the underlying standard 
deviation of return on Sendar Equity Fund. Being careful to square standard 
deviation to obtain a test in terms of variance, the hypotheses are H0: σ2 ≥ 16.0 
versus Ha: σ2 < 16.0.

The test statistic is χ2 with 24 − 1 = 23 degrees of freedom.
The lower 0.05 rejection point is found on the line for df = 23, under the 0.95 
column (95 percent probability in the right tail, to give 0.95 probability of getting 
a test statistic this large or larger). The rejection point is 13.091. We will reject 
the null if we find that χ2 is less than 13.091.
χ
σ2=−()=×==ns1 23 360
4298 08
1618 632
022
2...
Because 18.63 (the calculated value of the test statistic) is not less than 13.091, we 
do not reject the null hypothesis. We cannot conclude that Sendar’s investment 
disciplines result in a standard deviation of monthly returns of less than 4 percent.
4.2 Tests Concerning the Equality (Inequality) of Two Variances
Suppose we have a hypothesis about the relative values of the variances of two nor -
mally distributed populations with means μ1 and μ2 and variances  σ12 and  σ22. We

can formulate all hypotheses as one of the choices below:
1 HHa 012
22
12
22::σσ σσ =≠  versus  
2 HHa 012
22
12
22::σσ σ> σ ≤  versus  
3 HHa 012
22
12
22::σσ σ< σ ≥  versus  
Note that at the point of equality, the null hypothesis  σσ12
22=  implies that the ratio 
of population variances equals 1:  σσ12
22=1. Given independent random samples 
from these populations, tests related to these hypotheses are based on an F-test, which 
is the ratio of sample variances. Suppose we use n1 observations in calculating the 
sample variance  s12 and n2 observations in calculating the sample variance  s22. Tests 
concerning the difference between the variances of two populations make use of the

Hypothesis Tests Concerning Variance 649
F-distribution. Like the chi-  square distribution, the F-distribution is a family of asym -
metrical distributions bounded from below by 0. Each F-distribution is defined by 
two values of degrees of freedom, called the numerator and denominator degrees of 
freedom.26 The F-test, like the chi-  square test, is not robust to violations of its 
■■Test Statistic for Tests Concerning Differences between the Variances of 
Two Populations (Normally Distributed Populations).  Suppose we have two 
samples, the first with n1 observations and sample variance  s12, the second with 
n2 observations and sample variance  s22. The samples are random, independent 
of each other, and generated by normally distributed populations. A test 
concerning differences between the variances of the two populations is based 
on the ratio of sample variances
Fs
s=12
22
with df1 = n1 − 1 numerator degrees of freedom and df2 = n2 − 1 denominator

degrees of freedom. Note that df1 and df2 are the divisors used in calculating  s12 
and s22, respectively.
A convention, or usual practice, is to use the larger of the two ratios  ss12
22 or ss22
12 
as the actual test statistic. When we follow this convention, the value of the test sta -
tistic is always greater than or equal to 1; tables of critical values of F then need include 
only values greater than or equal to 1. Under this convention, the rejection point for 
any formulation of hypotheses is a single value in the right-  hand side of the relevant 
F-distribution. Note that the labeling of populations as “1” or “2” is arbitrary in any 
case.
■■Rejection Points for Hypothesis Tests on the Relative Values of Two 
Population Variances.  Follow the convention of using the larger of the two 
ratios  ss12
22 and  ss22
12 and consider two cases:
1 A “not equal to” alternative hypothesis: Reject the null hypothesis at the α

significance level if the test statistic is greater than the upper α/2 point of 
the F-distribution with the specified numerator and denominator degrees of 
freedom.
2 A “greater than” or “less than” alternative hypothesis: Reject the null hypoth -
esis at the α significance level if the test statistic is greater than the upper 
α point of the F-distribution with the specified number of numerator and 
denominator degrees of freedom.
Thus, if we conduct a two-  sided test at the α = 0.01 level of significance, we need 
to find the rejection point in F-tables at the α/2 = 0.01/2 = 0.005 significance level for 
a one-  sided test (Case 1). But a one-  sided test at 0.01 uses rejection points in F-tables 
for α = 0.01 (Case 2). As an example, suppose we are conducting a two-  sided test at 
the 0.05 significance level. We calculate a value of F of 2.77 with 12 numerator and 19 (16)
26 The relationship between the chi-  square and F-distributions is as follows: If  χ12 is one chi-  square

random variable with m degrees of freedom and  χ22 is another chi-  square random variable with n degrees 
of freedom, then  Fm n =() () χχ12
22 follows an F-distribution with m numerator and n denominator degrees 
of freedom.

Reading 12 ■ Hypothesis Testing 650
denominator degrees of freedom. Using the F-tables for 0.05/2 = 0.025 in the back of 
the volume, we find that the rejection point is 2.72. Because the value 2.77 is greater 
than 2.72, we reject the null hypothesis at the 0.05 significance level.
If the convention stated above is not followed and we are given a calculated value 
of F less than 1, can we still use F-tables? The answer is yes; using a reciprocal prop -
erty of F-statistics, we can calculate the needed value. The easiest way to present this 
property is to show a calculation. Suppose our chosen level of significance is 0.05 for 
a two-  tailed test and we have a value of F of 0.11, with 7 numerator degrees of free -
dom and 9 denominator degrees of freedom. We take the reciprocal, 1/0.11 = 9.09. 
Then we look up this value in the F-tables for 0.025 (because it is a two-  tailed test) 
with degrees of freedom reversed: F for 9 numerator and 7 denominator degrees of

freedom. In other words, F9,7 = 1/ F7,9 and 9.09 exceeds the critical value of 4.82, so 
F7,9 = 0.11 is significant at the 0.05 level.
EXAMPLE 8   
Volatility and the Global Financial Crisis of the Late 2000s
You are investigating whether the population variance of returns on the KOSPI 
Index of the South Korean stock market changed subsequent to the global 
financial crisis that peaked in 2008. For this investigation, you are considering 
2004 to 2006 as the pre-  crisis period and 2010 to 2012 as the post-  crisis period. 
You gather the data in Table 7 for 156 weeks of returns during 2004 to 2006 
and 156 weeks of returns during 2010 to 2012. You have specified a 0.01 level 
of significance.
Table 7   KOSPI Index Returns and Variance before and after the Global 
Financial Crisis of the Late 2000s
nMean Weekly  
Return (%)Variance  
of Returns
Before crisis: 2004 to 2006 156 0.358 7.240
After crisis: 2010 to 2012 156 0.110 6.269
Source of data for returns:  finance.yahoo.com accessed 27 August 2013.

3 Determine whether or not to reject the null hypothesis at the 0.01 level of 
significance. (Use the F-tables in the back of this volume.)
We have a “not equal to” alternative hypothesis:
HHa 022 22::σσ σσBefo re AfterB eforeA fter versus =≠
To test a null hypothesis of the equality of two variances, we use  Fs s=12
22 
with 156 − 1 = 155 numerator and denominator degrees of freedom.

Hypothesis Tests Concerning Variance 651
The “before” sample variance is larger, so following a convention for calculating 
F-statistics, the “before” sample variance goes in the numerator: F = 7.240/6.269 = 
1.155. Because this is a two-  tailed test, we use F-tables for the 0.005 level (= 
0.01/2) to give a 0.01 significance level. In the tables in the back of the volume, 
the closest value to 155 degrees of freedom is 120 degrees of freedom. At the 
0.01 level, the rejection point is 1.61. Because 1.155 is less than the critical value 
1.61, we cannot reject the null hypothesis that the population variance of returns 
is the same in the pre- and post-  global financial crisis periods.
EXAMPLE 9   
The Volatility of Derivatives Expiration Days
Since 2001, the financial markets in the United States have seen the quadruple 
occurrence of stock option, index option, index futures, and single stock futures 
expirations on the same day during four months of the year. Such days are

known as “quadruple witching days. ” You are interested in investigating whether 
quadruple witching days exhibit greater volatility than normal days. Table  8 
presents the daily standard deviation of return for normal days and options/
futures expiration days during the four-  year period 20X3 to 20X6. The tabled 
data refer to options and futures on the 30 stocks that constitute the Dow Jones 
Industrial Average. 
Table 8   Standard Deviation of Return: 20X3 to 20X6
Type of Day n Standard Deviation (%)
Normal trading 138 0.821
Options/futures expiration 16 1.217
1 Formulate null and alternative hypotheses consistent with the belief that 
quadruple witching days display above-  normal volatility.
3 Determine whether or not to reject the null hypothesis at the 0.05 level of 
We have a “greater than” alternative hypothesis:

HHa 022 22: versus : Expirations Normal Expirations Normal σσ σ> σ ≤
Let σ12 represent the variance of quadruple witching days, and  σ22 represent the 
variance of normal days, following the convention for the selection of the 
numerator and the denominator stated earlier. To test the null hypothesis, we 
use Fs s=12
22 with 16 − 1 = 15 numerator and 138 − 1 = 137 denominator 

Reading 12 ■ Hypothesis Testing 652
F = (1.217)2/(0.821)2 = 1.481/0.674 = 2.20. Because this is a one-  tailed test at the 
0.05 significance level, we use F-tables for the 0.05 level directly. In the tables 
in the back of the volume, the closest value to 137 degrees of freedom is 120 
degrees of freedom. At the 0.05 level, the rejection point is 1.75. Because 2.20 
is greater than 1.75, we reject the null hypothesis. It appears that quadruple 
witching days have above-  normal volatility.
OTHER ISSUES: NONPARAMETRIC INFERENCE
The hypothesis-  testing procedures we have discussed to this point have two char -
acteristics in common. First, they are concerned with parameters, and second, their 
validity depends on a definite set of assumptions. Mean and variance, for example, 
are two parameters, or defining quantities, of a normal distribution. The tests also 
make specific assumptions—in particular, assumptions about the distribution of the

population producing the sample. Any test or procedure with either of the above two 
characteristics is a parametric test  or procedure. In some cases, however, we are 
concerned about quantities other than parameters of distributions. In other cases, 
we may believe that the assumptions of parametric tests do not hold for the partic -
ular data we have. In such cases, a nonparametric test or procedure can be useful. A 
nonparametric test  is a test that is not concerned with a parameter, or a test that 
makes minimal assumptions about the population from which the sample comes.27
We primarily use nonparametric procedures in three situations: when the data 
we use do not meet distributional assumptions, when the data are given in ranks, or 
when the hypothesis we are addressing does not concern a parameter.
The first situation occurs when the data available for analysis suggest that the 
distributional assumptions of the parametric test are not satisfied. For example, we

may want to test a hypothesis concerning the mean of a population but believe that 
neither a t-test nor a z-test is appropriate because the sample is small and may come 
from a markedly non-  normally distributed population. In that case, we may use a 
nonparametric test. The nonparametric test will frequently involve the conversion of 
observations (or a function of observations) into ranks according to magnitude, and 
sometimes it will involve working with only “greater than” or “less than” relationships 
(using the signs + and − to denote those relationships). Characteristically, one must refer 
to specialized statistical tables to determine the rejection points of the test statistic, at 
least for small samples.28 Such tests, then, typically interpret the null hypothesis as a 
thesis about ranks or signs. In Table 9, we give examples of nonparametric alternatives 
to the parametric tests we have discussed in this reading.29 The reader should consult

a comprehensive business statistics textbook for an introduction to such tests, and a 
specialist textbook for details.305
27 Some writers make a distinction between “nonparametric” and “distribution-  free” tests. They refer to 
procedures that do not concern the parameters of a distribution as nonparametric and to procedures that 
make minimal assumptions about the underlying distribution as distribution free. We follow a commonly 
accepted, inclusive usage of the term nonparametric.
28 For large samples, there is often a transformation of the test statistic that permits the use of tables for 
the standard normal or t-distribution.
29 In some cases, there are several nonparametric alternatives to a parametric test.
30 See, for example, Hettmansperger and McKean (2010) or Siegel and Castellan (1988).

Other Issues: Nonparametric Inference 653
Table 9   Nonparametric Alternatives to Parametric Tests
Parametric Nonparametric
Tests concerning a single mean t-test Wilcoxon signed-  rank test
z-test
Tests concerning differences  
between meanst-test  
Approximate t-testMann–Whitney U test
Tests concerning mean differences  
(paired comparisons tests)t-test Wilcoxon signed-  rank test  
Sign test
We pointed out that when we use nonparametric tests, we often convert the 
original data into ranks. In some cases, the original data are already ranked. In those 
cases, we also use nonparametric tests because parametric tests generally require a 
stronger measurement scale than ranks. For example, if our data were the rankings of 
investment managers, hypotheses concerning those rankings would be tested using 
nonparametric procedures. Ranked data also appear in many other finance contexts. 
For example, Heaney, Koga, Oliver, and Tran (1999) studied the relationship between

the size of Japanese companies (as measured by revenue) and their use of derivatives. 
The companies studied used derivatives to hedge one or more of five types of risk 
exposure: interest rate risk, foreign exchange risk, commodity price risk, marketable 
security price risk, and credit risk. The researchers gave a “perceived scope of risk 
exposure” score to each company that was equal to the number of types of risk expo -
sure that the company reported hedging. Although revenue is measured on a strong 
scale (a ratio scale), scope of risk exposure is measured on only an ordinal scale.31 
The researchers thus employed nonparametric statistics to explore the relationship 
between derivatives usage and size.
A third situation in which we use nonparametric procedures occurs when our 
question does not concern a parameter. For example, if the question concerns whether 
a sample is random or not, we use the appropriate nonparametric test (a so-  called

runs test). Another type of question nonparametrics can address is whether a sample 
came from a population following a particular probability distribution (using the 
Kolmogorov–Smirnov test, for example).
We end this reading by describing in some detail a nonparametric statistic that 
has often been used in investment research, the Spearman rank correlation.
5.1 Tests Concerning Correlation: The Spearman Rank 
Correlation Coefficient
In many contexts in investments, we want to assess the strength of the linear rela -
tionship between two variables—the correlation between them. In a majority of cases, 
we use the correlation coefficient described in the readings on probability concepts 
and correlation and regression. However, the t-test of the hypothesis that two vari -
ables are uncorrelated, based on the correlation coefficient, relies on fairly stringent 
assumptions.32 When we believe that the population under consideration meaningfully

31 We discussed scales of measurement in the reading on statistical concepts and market returns.
32 The t-test is described in the reading on correlation and regression. The assumption of the test is that 
each observation ( x, y) on the two variables ( X, Y) is a random observation from a bivariate normal distri -
bution. Informally, in a bivariate or two-  variable normal distribution, each individual variable is normally 
distributed and their joint relationship is completely described by the correlation, ρ, between them. For 
more details, see, for example, Daniel and Terrell (1995).

Reading 12 ■ Hypothesis Testing 654
departs from those assumptions, we can employ a test based on the Spearman rank 
correlation coefficient , rS. The Spearman rank correlation coefficient is essentially 
equivalent to the usual correlation coefficient calculated on the ranks  of the two vari -
ables (say X and Y) within their respective samples. Thus it is a number between −1 
and +1, where −1 (+1) denotes a perfect inverse (positive) straight-  line relationship 
between the variables and 0 represents the absence of any straight-  line relationship 
(no correlation). The calculation of rS requires the following steps:
1 Rank the observations on X from largest to smallest. Assign the number 1 to 
the observation with the largest value, the number 2 to the observation with 
second-  largest value, and so on. In case of ties, we assign to each tied observa -
tion the average of the ranks that they jointly occupy. For example, if the third-

and fourth-  largest values are tied, we assign both observations the rank of 3.5 
(the average of 3 and 4). Perform the same procedure for the observations on Y.
2 Calculate the difference, di, between the ranks of each pair of observations on X 
and Y.
3 Then, with n the sample size, the Spearman rank correlation is given by33
rd
nnsi
in
=−
−()=∑
16
12
1
2
Suppose an investor wants to invest in a diversified emerging markets mutual fund. 
He has narrowed the field to 10 such funds, which are the largest in terms of total 
net assets. In examining the funds, a question arises as to whether the funds’ most 
recent reported Sharpe ratios and expense ratios as of mid-  2013 are related. Because 
the assumptions of the t-test on the correlation coefficient may not be met, it is 
appropriate to conduct a test on the rank correlation coefficient.34 Table 10 presents 
the calculation of rS. The first two rows contain the original data. The row of X ranks

converts the Sharpe ratios to ranks; the row of Y ranks converts the expense ratios to 
ranks. We want to test H0: ρ = 0 versus Ha: ρ ≠ 0, where ρ is defined in this context as 
the population correlation of X and Y after ranking. For small samples, the rejection 
points for the test based on rS must be looked up in Table 11. For large samples (say 
n > 30), we can conduct a t-test using
tnr
rs
s=−()
−()2
112
212
based on n − 2 degrees of freedom.(17)
(18)
33 Calculating the usual correlation coefficient on the ranks would yield approximately the same result 
as Equation 17.
34 The expense ratio (the ratio of a fund’s operating expenses to average net assets) is bounded both from 
below (by zero) and from above. The Sharpe ratio is also observed within a limited range, in practice. 
Thus neither variable can be normally distributed, and hence jointly they cannot follow a bivariate normal 
distribution. In short, the assumptions of a t-test are not met.

Other Issues: Nonparametric Inference 655
Table 10   The Spearman Rank Correlation: An Example
Mutual Fund
1 2 3 4 5 6 7 8 9 10
Sharpe Ratio 
(X)0.05 0.40 0.38 0.21 0.43 0.16 0.40 0.58 0.14 0.25
Expense Ratio 
(Y)0.61 1.03 1.36 1.10 1.07 0.68 1.10 1.37 1.27 1.25
X Rank 10 3.5 5 7 2 8 3.5 1 9 6
Y Rank 10 8 2 5.5 7 9 5.5 1 3 4
di 0.0 –4.5 3 1.5 –5 –1 –2 0 6 2
di20.0 20.25 9 2.25 25 1 4 0 36 4
rd
nnsi=−
−()=−()
−()=∑16
116 101 5
10 100 10 38482
2..
Source of Sharpe and Expense Ratios:  http://markets.on.nytimes.com/research/screener/mutual_funds/mutual_funds.asp accessed 20 
August 2013.
In the example at hand, a two-  tailed test with a 0.05 significance level, Table 11 
gives the upper-  tail rejection point for n = 10 as 0.6364 (we use the 0.025 column for 
a two-  tailed test at a 0.05 significance level). Accordingly, we reject the null hypothesis 
if rS is less than −0.6364 or greater than 0.6364. With rS equal to 0.3848, we do not 
reject the null hypothesis.

Table 11   Spearman Rank Correlation Distribution 
Approximate Upper-  Tail Rejection Points
Sample Size: n α = 0.05 α = 0.025 α = 0.01
5 0.8000 0.9000 0.9000
6 0.7714 0.8286 0.8857
7 0.6786 0.7450 0.8571
8 0.6190 0.7143 0.8095
9 0.5833 0.6833 0.7667
10 0.5515 0.6364 0.7333
11 0.5273 0.6091 0.7000
12 0.4965 0.5804 0.6713
13 0.4780 0.5549 0.6429
14 0.4593 0.5341 0.6220
15 0.4429 0.5179 0.6000
16 0.4265 0.5000 0.5824
17 0.4118 0.4853 0.5637
18 0.3994 0.4716 0.5480
19 0.3895 0.4579 0.5333
20 0.3789 0.4451 0.5203
21 0.3688 0.4351 0.5078

Reading 12 ■ Hypothesis Testing 656
22 0.3597 0.4241 0.4963
23 0.3518 0.4150 0.4852
24 0.3435 0.4061 0.4748
25 0.3362 0.3977 0.4654
26 0.3299 0.3894 0.4564
27 0.3236 0.3822 0.4481
28 0.3175 0.3749 0.4401
29 0.3113 0.3685 0.4320
30 0.3059 0.3620 0.4251
Note : The corresponding lower tail critical value is obtained by changing the 
sign of the upper-  tail critical value.
In the mutual fund example, we converted observations on two variables into 
ranks. If one or both of the original variables were in the form of ranks, we would 
need to use rS to investigate correlation.
5.2 Nonparametric Inference: Summary
Nonparametric statistical procedures extend the reach of inference because they make 
few assumptions, can be used on ranked data, and may address questions unrelated 
to parameters. Quite frequently, nonparametric tests are reported alongside para -
metric tests. The reader can then assess how sensitive the statistical conclusion is to

the assumptions underlying the parametric test. However, if the assumptions of the 
parametric test are met, the parametric test (where available) is generally preferred 
to the nonparametric test because the parametric test usually permits us to draw 
sharper conclusions.35 For complete coverage of all the nonparametric procedures 
that may be encountered in the finance and investment literature, it is best to consult 
a specialist textbook.36
SUMMARY
In this reading, we have presented the concepts and methods of statistical inference 
and hypothesis testing.
■■A hypothesis is a statement about one or more populations.
■■The steps in testing a hypothesis are as follows:
4 Stating the decision rule.Table 11   (Continued)
35 To use a concept introduced in an earlier section, the parametric test is often more powerful.

36 See, for example, Hettmansperger and McKean (2010) or Siegel and Castellan (1988).

Summary 657
■■We state two hypotheses: The null hypothesis is the hypothesis to be tested; the 
alternative hypothesis is the hypothesis accepted when the null hypothesis is 
rejected.
■■There are three ways to formulate hypotheses:
1 H0: θ = θ0 versus Ha: θ ≠ θ0
2 H0: θ ≤ θ0 versus Ha: θ > θ0
3 H0: θ ≥ θ0 versus Ha: θ < θ0
where θ0 is a hypothesized value of the population parameter and θ is the true 
value of the population parameter. In the above, Formulation 1 is a two-  sided 
test and Formulations 2 and 3 are one-  sided tests.
■■When we have a “suspected” or “hoped for” condition for which we want to 
find supportive evidence, we frequently set up that condition as the alternative 
hypothesis and use a one-  sided test. To emphasize a neutral attitude, however, 
the researcher may select a “not equal to” alternative hypothesis and conduct a 
two-  sided test.

■■A test statistic is a quantity, calculated on the basis of a sample, whose value 
is the basis for deciding whether to reject or not reject the null hypothesis. To 
decide whether to reject, or not to reject, the null hypothesis, we compare the 
computed value of the test statistic to a critical value (rejection point) for the 
same test statistic.
■■In reaching a statistical decision, we can make two possible errors: We may 
reject a true null hypothesis (a Type I error), or we may fail to reject a false null 
hypothesis (a Type II error).
■■The level of significance of a test is the probability of a Type I error that we 
accept in conducting a hypothesis test. The probability of a Type I error is 
denoted by the Greek letter alpha, α. The standard approach to hypothesis test -
ing involves specifying a level of significance (probability of Type I error) only.
■■The power of a test is the probability of correctly rejecting the null (rejecting 
the null when it is false).

■■A decision rule consists of determining the rejection points (critical values) 
with which to compare the test statistic to decide whether to reject or not to 
reject the null hypothesis. When we reject the null hypothesis, the result is said 
to be statistically significant.
■■The (1 − α) confidence interval represents the range of values of the test statistic 
for which the null hypothesis will not be rejected at an α significance level.
■■The statistical decision consists of rejecting or not rejecting the null hypothesis. 
The economic decision takes into consideration all economic issues pertinent to 
the decision.
■■The p-value is the smallest level of significance at which the null hypothesis can 
be rejected. The smaller the p-value, the stronger the evidence against the null 
hypothesis and in favor of the alternative hypothesis. The p-value approach to 
hypothesis testing does not involve setting a significance level; rather it involves

computing a p-value for the test statistic and allowing the consumer of the 
research to interpret its significance.

Reading 12 ■ Hypothesis Testing 658
■■For hypothesis tests concerning the population mean of a normally distrib -
uted population with unknown (known) variance, the theoretically correct test 
statistic is the t-statistic ( z-statistic). In the unknown variance case, given large 
samples (generally, samples of 30 or more observations), the z-statistic may be 
used in place of the t-statistic because of the force of the central limit theorem.
■■The t-distribution is a symmetrical distribution defined by a single parameter: 
degrees of freedom. Compared to the standard normal distribution, the t-distri -
bution has fatter tails.
■■When we want to test whether the observed difference between two means 
is statistically significant, we must first decide whether the samples are inde -
pendent or dependent (related). If the samples are independent, we conduct 
tests concerning differences between means. If the samples are dependent, we 
conduct tests of mean differences (paired comparisons tests).

■■When we conduct a test of the difference between two population means from 
normally distributed populations with unknown variances, if we can assume 
the variances are equal, we use a t-test based on pooling the observations of the 
two samples to estimate the common (but unknown) variance. This test is based 
on an assumption of independent samples.
normally distributed populations with unknown variances, if we cannot assume 
that the variances are equal, we use an approximate t-test using modified 
degrees of freedom given by a formula. This test is based on an assumption of 
independent samples.
■■In tests concerning two means based on two samples that are not independent, 
we often can arrange the data in paired observations and conduct a test of mean 
differences (a paired comparisons test). When the samples are from normally 
distributed populations with unknown variances, the appropriate test statistic is

a t-statistic. The denominator of the t-statistic, the standard error of the mean 
differences, takes account of correlation between the samples.
■■In tests concerning the variance of a single, normally distributed population, the 
test statistic is chi-  square (χ2) with n − 1 degrees of freedom, where n is sample 
size.
■■For tests concerning differences between the variances of two normally distrib -
uted populations based on two random, independent samples, the appropriate 
test statistic is based on an F-test (the ratio of the sample variances).
■■The F-statistic is defined by the numerator and denominator degrees of free -
dom. The numerator degrees of freedom (number of observations in the sample 
minus 1) is the divisor used in calculating the sample variance in the numerator. 
The denominator degrees of freedom (number of observations in the sample 
minus 1) is the divisor used in calculating the sample variance in the denomina -

tor. In forming an F-test, a convention is to use the larger of the two 
ratios,  ss12
22 or ss22
12, as the actual test statistic.
■■A parametric test is a hypothesis test concerning a parameter or a hypothesis 
test based on specific distributional assumptions. In contrast, a nonparametric 
test either is not concerned with a parameter or makes minimal assumptions 
about the population from which the sample comes.
■■A nonparametric test is primarily used in three situations: when data do not 
meet distributional assumptions, when data are given in ranks, or when the 
hypothesis we are addressing does not concern a parameter.
■■The Spearman rank correlation coefficient is calculated on the ranks of two 
variables within their respective samples.

References 659
Bowerman, Bruce L., Richard T. O’Connell, and Emily S. 
Murphree. 2016. Business Statistics in Practice , 8th edition. 
New York: McGraw-Hill/Irwin.
Davidson, Russell, and James G. MacKinnon. 1993. Estimation 
and Inference in Econometrics . New York: Oxford University 
Press.
Premiums around the World. ” In Rethinking the Equity Risk 
Freeley, Austin J., and David L. Steinberg. 2013. Argumentation 
and Debate: Critical Thinking for Reasoned Decision Making , 
13th edition. Boston, MA: Wadsworth Cengage Learning.
Gupta, Parveen P , and Nandkumar Nayar. 2007. “Information 
Content of Control Deficiency Disclosures under the Sarbanes-  
Oxley Act: An Empirical Investigation. ” International Journal

of Disclosure and Governance , vol. 4:3–23. Heaney, Richard, Chitoshi Koga, Barry Oliver, and Alfred Tran. 
1999. “The Size Effect and Derivative Usage in Japan. ” Working 
paper: The Australian National University.
Hettmansperger, Thomas P ., and Joseph W. McKean. 2010. 
Robust Nonparametric Statistical Methods , 2nd edition. Boca 
Raton, FL: CRC Press.
Jankowitsch, Rainer, Florian Nagler, and Marti G. Subrahmanyam. 
2014. “The Determinants of Recovery Rates in the US 
Corporate Bond Market. ” Journal of Financial Economics , vol. 
114, no. 1:155–177.
Moore, David S., George P . McCabe, and Bruce Craig. 2016. 
Introduction to the Practice of Statistics , 9th edition. New 
York: W.H. Freeman.
Siegel, Sidney, and N. John Castellan. 1988. Nonparametric 
Statistics for the Behavioral Sciences , 2nd edition. New York: 

Reading 12 ■ Hypothesis Testing 660
1 Which of the following statements about hypothesis testing is correct? 
A The null hypothesis is the condition a researcher hopes to support.
B The alternative hypothesis is the proposition considered true without con -
clusive evidence to the contrary.
C The alternative hypothesis exhausts all potential parameter values not 
accounted for by the null hypothesis.
2 Identify the appropriate test statistic or statistics for conducting the following 
hypothesis tests. (Clearly identify the test statistic and, if applicable, the number 
of degrees of freedom. For example, “We conduct the test using an x-statistic 
with y degrees of freedom. ”)
A H0: μ = 0 versus Ha: μ ≠ 0, where μ is the mean of a normally distributed 
population with unknown variance. The test is based on a sample of 15 
B H0: μ = 0 versus Ha: μ ≠ 0, where μ is the mean of a normally distributed 
population with unknown variance. The test is based on a sample of 40

C H0: μ ≤ 0 versus Ha: μ > 0, where μ is the mean of a normally distributed 
population with known variance σ2. The sample size is 45.
D H0: σ2 = 200 versus Ha: σ2 ≠ 200, where σ2 is the variance of a normally 
distributed population. The sample size is 50.
E HHa 012
22
12
22::σσ σσ =≠  versus , where  σ12 is the variance of one normally 
distributed population and  σ22 is the variance of a second normally distrib -
uted population. The test is based on two independent random samples.
F H0: (Population mean 1) − (Population mean 2) = 0 versus Ha: (Population 
mean 1) − (Population mean 2) ≠ 0, where the samples are drawn from nor -
mally distributed populations with unknown variances. The observations in 
the two samples are correlated.
G H0: (Population mean 1) − (Population mean 2) = 0 versus Ha: (Population 
mally distributed populations with unknown but assumed equal variances.

The observations in the two samples (of size 25 and 30, respectively) are 
independent.
3 For each of the following hypothesis tests concerning the population mean, μ, 
state the rejection point condition or conditions for the test statistic (e.g., t > 
1.25); n denotes sample size.
A H0: μ = 10 versus Ha: μ ≠ 10, using a t-test with n = 26 and α = 0.05
B H0: μ = 10 versus Ha: μ ≠ 10, using a t-test with n = 40 and α = 0.01
C H0: μ ≤ 10 versus Ha: μ > 10, using a t-test with n = 40 and α = 0.01
D H0: μ ≤ 10 versus Ha: μ > 10, using a t-test with n = 21 and α = 0.05
E H0: μ ≥ 10 versus Ha: μ < 10, using a t-test with n = 19 and α = 0.10
F H0: μ ≥ 10 versus Ha: μ < 10, using a t-test with n = 50 and α = 0.05

4 For each of the following hypothesis tests concerning the population mean, μ, 
state the rejection point condition or conditions for the test statistic (e.g., z > 
A H0: μ = 10 versus Ha: μ ≠ 10, using a z-test with n = 50 and α = 0.01
B H0: μ = 10 versus Ha: μ ≠ 10, using a z-test with n = 50 and α = 0.05
C H0: μ = 10 versus Ha: μ ≠ 10, using a z-test with n = 50 and α = 0.10
D H0: μ ≤ 10 versus Ha: μ > 10, using a z-test with n = 50 and α = 0.05
5 Willco is a manufacturer in a mature cyclical industry. During the most recent 
industry cycle, its net income averaged $30 million per year with a standard 
deviation of $10 million ( n = 6 observations). Management claims that Willco’s 
performance during the most recent cycle results from new approaches and 
that we can dismiss profitability expectations based on its average or normal -
ized earnings of $24 million per year in prior cycles.

A With μ as the population value of mean annual net income, formulate null 
and alternative hypotheses consistent with testing Willco management’s 
claim.
B Assuming that Willco’s net income is at least approximately normally dis -
tributed, identify the appropriate test statistic.
C Identify the rejection point or points at the 0.05 level of significance for the 
hypothesis tested in Part A.
D Determine whether or not to reject the null hypothesis at the 0.05 signifi -
cance level.
6–7
Performance in Forecasting Quarterly Earnings per Share
Number of 
ForecastsMean Forecast Error 
(Predicted – Actual)Standard Deviations of 
Forecast Errors
Analyst A 101 0.05 0.10
Analyst B 121 0.02 0.09
6 Investment analysts often use earnings per share (EPS) forecasts. One test of 
forecasting quality is the zero-  mean test, which states that optimal forecasts 
should have a mean forecasting error of 0. (Forecasting error = Predicted value

of variable − Actual value of variable.)
 You have collected data (shown in the table above) for two analysts who cover 
two different industries: Analyst A covers the telecom industry; Analyst B cov -
ers automotive parts and suppliers.
A With μ as the population mean forecasting error, formulate null and alterna -
tive hypotheses for a zero-  mean test of forecasting quality.
B For Analyst A, using both a t-test and a z-test, determine whether to reject 
the null at the 0.05 and 0.01 levels of significance.
C For Analyst B, using both a t-test and a z-test, determine whether to reject 

Reading 12 ■ Hypothesis Testing 662
7 Reviewing the EPS forecasting performance data for Analysts A and B, you 
want to investigate whether the larger average forecast errors of Analyst A are 
due to chance or to a higher underlying mean value for Analyst A. Assume that 
the forecast errors of both analysts are normally distributed and that the sam -
ples are independent.
A Formulate null and alternative hypotheses consistent with determining 
whether the population mean value of Analyst A’s forecast errors (μ1) are 
larger than Analyst B’s (μ2).
B Identify the test statistic for conducting a test of the null hypothesis formu -
lated in Part A.
C Identify the rejection point or points for the hypothesis tested in Part A, at 
D Determine whether or not to reject the null hypothesis at the 0.05 level of 
significance.
8 The table below gives data on the monthly returns on the S&P 500 and small-  
cap stocks for the period January 1960 through December 1999 and provides

statistics relating to their mean differences.
MeasureS&P 500  
Return (%)Small-  Cap  
Stock Return 
(%)Differences  
(S&P 500–  
Small-  Cap Stock)
January 1960–December 1999, 480 months
Mean 1.0542 1.3117 –0.258
Standard deviation 4.2185 5.9570 3.752
January 1960–December 1979, 240 months
Mean 0.6345 1.2741 –0.640
Standard deviation 4.0807 6.5829 4.096
January 1980–December 1999, 240 months
Mean 1.4739 1.3492 0.125
Standard deviation 4.3197 5.2709 3.339
 Let μd stand for the population mean value of difference between S&P 500 
returns and small-  cap stock returns. Use a significance level of 0.05 and suppose 
that mean differences are approximately normally distributed.
A Formulate null and alternative hypotheses consistent with testing whether 
any difference exists between the mean returns on the S&P 500 and small-  
cap stocks.
B Determine whether or not to reject the null hypothesis at the 0.05 signifi -
cance level for the January 1960 to December 1999 period.

C Determine whether or not to reject the null hypothesis at the 0.05 signifi -
cance level for the January 1960 to December 1979 subperiod.
cance level for the January 1980 to December 1999 subperiod.
9 During a 10-  year period, the standard deviation of annual returns on a portfolio 
you are analyzing was 15 percent a year. You want to see whether this record 
is sufficient evidence to support the conclusion that the portfolio’s underly -
ing variance of return was less than 400, the return variance of the portfolio’s 
benchmark.

A Formulate null and alternative hypotheses consistent with the verbal 
description of your objective.
B Identify the test statistic for conducting a test of the hypotheses in Part A.
C Identify the rejection point or points at the 0.05 significance level for the 
D Determine whether the null hypothesis is rejected or not rejected at the 0.05 
level of significance.
10 You are investigating whether the population variance of returns on the S&P 
500/BARRA Growth Index changed subsequent to the October 1987 mar -
ket crash. You gather the following data for 120 months of returns before 
October 1987 and for 120 months of returns after October 1987. You have spec -
ified a 0.05 level of significance.
Time Period nMean Monthly  
Return (%) Variance of Returns
Before October 1987 120 1.416 22.367
After October 1987 120 1.436 15.795

C Determine whether or not to reject the null hypothesis at the 0.05 level of 
11 In the step “stating a decision rule” in testing a hypothesis, which of the follow -
ing elements must be specified?
A Critical value
B Power of a test
C Value of a test statistic
12 Which of the following statements is correct with respect to the null 
hypothesis?
A It is considered to be true unless the sample provides evidence showing it is 
false.
B It can be stated as “not equal to” provided the alternative hypothesis is 
stated as “equal to. ”
C In a two-  tailed test, it is rejected when evidence supports equality between 
the hypothesized value and population parameter.
13 An analyst is examining a large sample with an unknown population variance. 
To test the hypothesis that the historical average return on an index is less than

or equal to 6%, which of the following is the most  appropriate test?
A One-  tailed z-test
B Two-  tailed z-test
C One-  tailed F-test  
14 A hypothesis test for a normally-  distributed population at a 0.05 significance 
level implies a:
A 95% probability of rejecting a true null hypothesis.
B 95% probability of a Type I error for a two-  tailed test.
C 5% critical value rejection region in a tail of the distribution for a one-  tailed 
test.

Reading 12 ■ Hypothesis Testing 664
15 Which of the following statements regarding a one-  tailed hypothesis test is 
correct?
A The rejection region increases in size as the level of significance becomes 
smaller.
B A one-  tailed test more strongly reflects the beliefs of the researcher than a 
two-  tailed test.
C The absolute value of the rejection point is larger than that of a two-  tailed 
test at the same level of significance.
16 The value of a test statistic is best described as the basis for deciding whether to:
A reject the null hypothesis.
B accept the null hypothesis.
C reject the alternative hypothesis.
17 Which of the following is a Type I error?
A Rejecting a true null hypothesis
B Rejecting a false null hypothesis
C Failing to reject a false null hypothesis
18 A Type II error is best described as:
A rejecting a true null hypothesis.
B failing to reject a false null hypothesis.
C failing to reject a false alternative hypothesis.

19 The level of significance of a hypothesis test is best used to:
A calculate the test statistic.
B define the test’s rejection points.
C specify the probability of a Type II error.
20 You are interested in whether excess risk-  adjusted return (alpha) is correlated 
with mutual fund expense ratios for US large-  cap growth funds. The following 
table presents the sample.
Mutual Fund 1 2 3 4 5 6 7 8 9
Alpha ( X) −0.52 −0.13 −0.60 −1.01 −0.26 −0.89 −0.42 −0.23 −0.60
Expense Ratio ( Y) 1.34 0.92 1.02 1.45 1.35 0.50 1.00 1.50 1.45
C Justify your selection in Part B.
21 All else equal, is specifying a smaller significance level in a hypothesis test likely 
to increase the probability of a:
Type I error? Type II error?
A No No

A No No
B No Yes
C Yes No
22 The probability of correctly rejecting the null hypothesis is the:
A p-value.

B power of a test.
C level of significance.
23 The power of a hypothesis test is:
A equivalent to the level of significance.  
B the probability of not making a Type II error. 
C unchanged by increasing a small sample size.  
24 When making a decision in investments involving a statistically significant 
result, the:
A economic result should be presumed meaningful.
B statistical result should take priority over economic considerations.
C economic logic for the future relevance of the result should be further 
explored.
25 An analyst tests the profitability of a trading strategy with the null hypothesis 
being that the average abnormal return before trading costs equals zero. The 
calculated t-statistic is 2.802, with critical values of ± 2.756 at significance level 
α = 0.01. After considering trading costs, the strategy’s return is near zero. The 
results are most likely :
A statistically but not economically significant.
B economically but not statistically significant.

C neither statistically nor economically significant.
26 Which of the following statements is correct with respect to the p-value?
A It is a less precise measure of test evidence than rejection points.
B It is the largest level of significance at which the null hypothesis is rejected.
C It can be compared directly with the level of significance in reaching test 
conclusions.
27 Which of the following represents a correct statement about the p-value?
A The p-value offers less precise information than does the rejection points 
approach.
B A larger p-value provides stronger evidence in support of the alternative 
C A p-value less than the specified level of significance leads to rejection of the 
null hypothesis.
28 Which of the following statements on p-value is correct?
A The p-value is the smallest level of significance at which H0 can be rejected.
B The p-value indicates the probability of making a Type II error.

C The lower the p-  value, the weaker the evidence for rejecting the H0.
29 The following table shows the significance level (α) and the p-value for three 
hypothesis tests. 
α p-value
Test 1 0.05 0.10
Test 2 0.10 0.08
Test 3 0.10 0.05
 The evidence for rejecting H0 is strongest for:
A Test 1.
B Test 2.

Reading 12 ■ Hypothesis Testing 666
C Test 3. 
30 Which of the following tests of a hypothesis concerning the population mean is 
most  appropriate?
A A z-test if the population variance is unknown and the sample is small
B A z-test if the population is normally distributed with a known variance
C A t-test if the population is non-  normally distributed with unknown vari -
ance and a small sample
31 For a small sample with unknown variance, which of the following tests of a 
hypothesis concerning the population mean is most appropriate?
A A t-test if the population is normally distributed
B A t-test if the population is non-  normally distributed
C A z-test regardless of the normality of the population distribution
32 For a small sample from a normally distributed population with unknown vari -
ance, the most  appropriate test statistic for the mean is the:
A z-statistic .
B t-statistic.
C χ2 statistic.
33 An investment consultant conducts two independent random samples of 5-  year

performance data for US and European absolute return hedge funds. Noting 
a 50 basis point return advantage for US managers, the consultant decides 
to test whether the two means are statistically different from one another at 
a 0.05 level of significance. The two populations are assumed to be normally 
distributed with unknown but equal variances. Results of the hypothesis test are 
contained in the tables below.
Sample Size Mean Return %Standard 
Deviation
US Managers 50 4.7 5.4
European Managers 50 4.2 4.8
Null and Alternative Hypotheses H0: μUS – μE = 0; Ha: μUS – μE ≠ 0
Test Statistic 0.4893
Critical Value Rejection Points ±1.984
μUS is the mean return for US funds and μE is the mean return for European funds.
 The results of the hypothesis test indicate that the:
A null hypothesis is not rejected. 
B alternative hypothesis is statistically confirmed.
C difference in mean returns is statistically different from zero. 
34 A pooled estimator is used when testing a hypothesis concerning the:

A equality of the variances of two normally distributed populations.
B difference between the means of two at least approximately normally dis -
tributed populations with unknown but assumed equal variances.
C difference between the means of two at least approximately normally dis -
tributed populations with unknown and assumed unequal variances.

Practice Problems 667
35 When evaluating mean differences between two dependent samples, the most  
appropriate test is a:
A chi- square test.
B paired comparisons test.
C z-test.
36 A fund manager reported a 2% mean quarterly return over the past ten years for 
its entire base of 250 client accounts that all follow the same investment strat -
egy. A consultant employing the manager for 45 client accounts notes that their 
mean quarterly returns were 0.25% less over the same period. The consultant 
tests the hypothesis that the return disparity between the returns of his clients 
and the reported returns of the fund manager’s 250 client accounts are signifi -
cantly different from zero. 
 Assuming normally distributed populations with unknown population vari -
ances, the most  appropriate test statistic is:
A a paired comparisons t-test.
B a t-test of the difference between the two population means. 
C an approximate  t-test of mean differences between the two populations.

37 A chi-  square test is most  appropriate for tests concerning:
A a single variance.
B differences between two population means with variances assumed to be 
equal.
C differences between two population means with variances assumed to not 
be equal.
38 Which of the following should be used to test the difference between the vari -
ances of two normally distributed populations?
A t-test
B F-test
C Paired comparisons test
39 In which of the following situations would a non-  parametric test of a hypothesis 
most likely  be used?
A The sample data are ranked according to magnitude.
B The sample data come from a normally distributed population.
C The test validity depends on many assumptions about the nature of the 
40 An analyst is examining the monthly returns for two funds over one year. Both 
funds’ returns are non-  normally distributed. To test whether the mean return of 
one fund is greater than the mean return of the other fund, the analyst can use:
A a parametric test only.

B a nonparametric test only.
C both parametric and nonparametric tests.

Reading 12 ■ Hypothesis Testing 668
SOLUTIONS
1 C is correct. Together, the null and alternative hypotheses account for all pos -
sible values of the parameter. Any possible values of the parameter not covered 
by the null must be covered by the alternative hypothesis (e.g., H0: θ ≤ 5 versus 
Ha: θ > 5). 
2 A The appropriate test statistic is a t-statistic with n − 1 = 15 − 1 = 14 degrees 
of freedom. A t-statistic is theoretically correct when the sample comes 
from a normally distributed population with unknown variance. When the 
sample size is also small, there is no practical alternative.
B The appropriate test statistic is a t-statistic with 40 − 1 = 39 degrees of 
freedom. A t-statistic is theoretically correct when the sample comes from a 
normally distributed population with unknown variance. When the sample 
size is large (generally, 30 or more is a “large” sample), it is also possible to 
use a z-statistic, whether the population is normally distributed or not. A

test based on a t-statistic is more conservative than a z-statistic test.
C The appropriate test statistic is a z-statistic because the sample comes from 
a normally distributed population with known variance. (The known popu -
lation standard deviation is used to compute the standard error of the mean 
using Equation 2 in the text.)
D The appropriate test statistic is chi-  square (χ2) with 50 − 1 = 49 degrees of 
freedom.
E The appropriate test statistic is the F-statistic (the ratio of the sample 
variances).
F The appropriate test statistic is a t-statistic for a paired observations test (a 
paired comparisons test), because the samples are correlated.
G The appropriate test statistic is a t −statistic using a pooled estimate of the 
population variance. The t-statistic has 25 + 30 − 2 = 53 degrees of freedom. 
This statistic is appropriate because the populations are normally distrib -
uted with unknown variances; because the variances are assumed equal, the

observations can be pooled to estimate the common variance. The require -
ment of independent samples for using this statistic has been met.
3 A With degrees of freedom (df) n − 1 = 26 − 1 = 25, the rejection point condi -
tions for this two-  sided test are t > 2.060 and t < −2.060. Because the signifi -
cance level is 0.05, 0.05/2 = 0.025 of the probability is in each tail. The tables 
give one-  sided (one-  tailed) probabilities, so we used the 0.025 column. Read 
across df = 25 to the α = 0.025 column to find 2.060, the rejection point for 
the right tail. By symmetry, −2.060 is the rejection point for the left tail.
B With df = 39, the rejection point conditions for this two-  sided test are t > 
2.708 and t < −2.708. This is a two-  sided test, so we use the 0.01/2 = 0.005 
column. Read across df = 39 to the α = 0.005 column to find 2.708, the rejec -
tion point for the right tail. By symmetry, −2.708 is the rejection point for 
the left tail.

C With df = 39, the rejection point condition for this one-  sided test is t > 
2.426. Read across df = 39 to the α = 0.01 column to find 2.426, the rejection 
point for the right tail. Because we have a “greater than” alternative, we are 
concerned with only the right tail.

D With df = 20, the rejection point condition for this one-  sided test is t > 
1.725. Read across df = 20 to the α = 0.05 column to find 1.725, the rejection 
E With df = 18, the rejection point condition for this one-  sided test is t < 
−1.330. Read across df = 18 to the α = 0.10 column to find 1.330, the rejec -
tion point for the right tail. By symmetry, the rejection point for the left tail 
is −1.330.
F With df = 49, the rejection point condition for this one-  sided test is t < 
−1.677. Read across df = 49 to the α = 0.05 column to find 1.677, the rejec -
is −1.677.
4 Recall that with a z-test (in contrast to the t-test), we do not employ degrees of 
freedom. The standard normal distribution is a single distribution applicable to

all z-tests. You should refer to “Rejection Points for a z-Test” in Section 3.1 to 
answer these questions.
A This is a two-  sided test at a 0.01 significance level. In Part C of “Rejection 
Points for a z-Test, ” we find that the rejection point conditions are z > 2.575 
and z < −2.575.
B This is a two-  sided test at a 0.05 significance level. In Part B of “Rejection 
Points for a z-Test, ” we find that the rejection point conditions are z > 1.96 
and z < −1.96.
C This is a two-  sided test at a 0.10 significance level. In Part A of “Rejection 
Points for a z-Test, ” we find that the rejection point conditions are z > 1.645 
and z < −1.645.
D This is a one-  sided test at a 0.05 significance level. In Part B of “Rejection 
Points for a z-Test, ” we find that the rejection point condition for a test with 
a “greater than” alternative hypothesis is z > 1.645.
5 A As stated in the text, we often set up the “hoped for” or “suspected” condi -

tion as the alternative hypothesis. Here, that condition is that the population 
value of Willco’s mean annual net income exceeds $24 million. Thus we have 
H0: μ ≤ 24 versus Ha: μ > 24.
B Given that net income is normally distributed with unknown variance, the 
appropriate test statistic is t with n − 1 = 6 − 1 = 5 degrees of freedom.
C In the t-distribution table in the back of the book, in the row for df = 5 
under α = 0.05, we read the rejection point (critical value) of 2.015. We will 
reject the null if t > 2.015.
D The t-test is given by Equation 4:
tX
sn50 30 24
10 66
4 0824831 469694 =−=−==µ
..
 or 1.47. Because 1.47 does not exceed 2.015, we do not reject the null 
hypothesis. The difference between the sample mean of $30 million and 
the hypothesized value of $24 million under the null is not statistically 
significant.
6 A H0: μ = 0 versus Ha: μ ≠ 0.
B The t-test is based on  tX
sn=−µ0 with n − 1 = 101 − 1 = 100 degrees of

sn=−µ0 with n − 1 = 101 − 1 = 100 degrees of 
freedom. At the 0.05 significance level, we reject the null if t > 1.984 or if t < 
−1.984. At the 0.01 significance level, we reject the null if t > 2.626 or if t <

Reading 12 ■ Hypothesis Testing 670
−2.626. For Analyst A, we have  t=−() () 0050 010 101 ..  = 0.05/0.00995 = 
5.024938 or 5.025. We clearly reject the null hypothesis at both the 0.05 and 
0.01 levels.
 The calculation of the z-statistic with unknown variance, as in this case, is 
the same as the calculation of the t-statistic. The rejection point conditions 
for a two-  tailed test are as follows: z > 1.96 and z < −1.96 at the 0.05 level; 
and z > 2.575 and z < −2.575 at the 0.01 level. Note that the z-test is a less 
conservative test than the t-test, so when the z-test is used, the null is easier 
to reject. Because z = 5.025 is greater than 2.575, we reject the null at the 
0.01 level; we also reject the null at the 0.05 level.
 In summary, Analyst A’s EPS forecasts appear to be biased upward—they 
tend to be too high.
C For Analyst B, the t-test is based on t with 121 − 1 = 120 degrees of free -
dom. At the 0.05 significance level, we reject the null if t > 1.980 or if t <

−1.980. At the 0.01 significance level, we reject the null if t > 2.617 or if t < 
−2.617. We calculate  t=−() () 0020 009 .. 121  = 0.02/0.008182 = 2.444444 
or 2.44. Because 2.44 > 1.98, we reject the null at the 0.05 level. However, 
2.44 is not larger than 2.617, so we do not reject the null at the 0.01 level.
 For a z-test, the rejection point conditions are the same as given in Part B, 
and we come to the same conclusions as with the t-test. Because 2.44 > 1.96, 
we reject the null at the 0.05 significance level; however, because 2.44 is not 
greater than 2.575, we do not reject the null at the 0.01 level.
 The mean forecast error of Analyst B is only $0.02; but because the test is 
based on a large number of observations, it is sufficient evidence to reject 
the null of mean zero forecast errors at the 0.05 level.
7 A Stating the suspected condition as the alternative hypothesis, we have
H0: μ1 – μ2 ≤ 0 versus Ha: μ1 – μ2 > 0
 where

 where
 μ1 = the population mean value of Analyst A’s forecast errors
 μ2 = the population mean value of Analyst B’s forecast errors
B We have two normally distributed populations with unknown variances. 
Based on the samples, it is reasonable to assume that the population vari -
ances are equal. The samples are assumed to be independent; this assump -
tion is reasonable because the analysts cover quite different industries. The 
appropriate test statistic is t using a pooled estimate of the common vari -
ance. The number of degrees of freedom is
n1 + n2 – 2 = 101 + 121 – 2 = 222 – 2 = 220.
C For df = 200 (the closest value to 220), the rejection point for a one-  sided 
test at the 0.05 significance level is 1.653.
D We first calculate the pooled estimate of variance:
sns ns
nnp2 112
222
12211
2101 1010 121 1009=−() +−()
+−
==2
101 121 2
1 972
2200 008964..

Solutions 671
 Then
tXX
s
ns
+



=− () − 12 12
2
12
2120050 02 0
0 0089µµ ..
. 6 64
1010 008964
121
003
0 012762 35101812
+


==.
.
..
 or 2.35. Because 2.35 > 1.653, we reject the null hypothesis in favor of the 
alternative hypothesis that the population mean forecast error of Analyst A 
is greater than that of Analyst B.
8 A We test H0: μd = 0 versus Ha: μd ≠ 0.
B This is a paired comparisons t-test with n − 1 = 480 − 1 = 479 degrees of 
freedom. At the 0.05 significance level, we reject the null hypothesis if either 
t > 1.96 or t < −1.96. We use df = ∞ in the t-distribution table under α = 
0.025 because we have a very large sample and a two-  sided test.
td
sd
d=−=−−=−=− −µ0 0 258 0
3 752 4800 258
0 1712551 506529.
..
..  or 1.51 1
 At the 0.05 significance level, because neither rejection point condition is 
met, we do not reject the null hypothesis that the mean difference between 
the returns on the S&P 500 and small-  cap stocks during the entire sample 
period was 0.

C This t-test now has n − 1 = 240 − 1 = 239 degrees of freedom. At the 0.05 
significance level, we reject the null hypothesis if either t > 1.972 or t < 
−1.972, using df = 200 in the t-distribution tables.
td
sd
d=−=−−=−=− −µ0 0 640 0
4 096 2400 640
0 2643962 420615.
..
..  or 2.42 2
 Because −2.42 < −1.972, we reject the null hypothesis at the 0.05 signifi -
cance level. During this subperiod, small-  cap stocks significantly outper -
formed the S&P 500.
D This t-test has n − 1 = 240 − 1 = 239 degrees of freedom. At the 0.05 signif -
icance level, we reject the null hypothesis if either t > 1.972 or t < −1.972, 
using df = 200 in the t-distribution tables.
td
sd
d=−=−==µ0 0 125 0
3 339 2400 125
0 2155320 579962 058.
..
...  or 
 At the 0.05 significance level, because neither rejection point condition 
is met, we do not reject the null hypothesis that for the January 1980–
December 1999 period, the mean difference between the returns on the S&P 
500 and small-  cap stocks was zero.

9 A We have a “less than” alternative hypothesis, where σ2 is the variance of 
return on the portfolio. The hypotheses are H0: σ2 ≥ 400 versus Ha: σ2 < 400, 
where 400 is the hypothesized value of variance,  σ02.
B The test statistic is chi-  square with 10 − 1 = 9 degrees of freedom.
C The rejection point is found across degrees of freedom of 9, under the 0.95 
column (95 percent of probability above the value). It is 3.325. We will reject 
the null hypothesis if we find that χ2 < 3.325.

Reading 12 ■ Hypothesis Testing 672
D The test statistic is calculated as
χ
σ22
0221 91 5
4002 025
4005 0625 =−()=×==ns ,.  or  5.06
 Because 5.06 is not less than 3.325, we do not reject the null hypothesis.
10 A We have a “not equal to” alternative hypothesis:
HHa 022 22::σσ σσBefo re Afterversus Befo re After=≠
B To test a null hypothesis of the equality of two variances, we use an F-test:
Fs
s=12
22
C The “before” sample variance is larger, so following a convention for cal -
culating F-statistics, the “before” sample variance goes in the numerator. F 
= 22.367/15.795 = 1.416, with 120 − 1 = 119 numerator and denominator 
degrees of freedom. Because this is a two-  tailed test, we use F-tables for the 
0.025 level (df = 0.05/2). Using the tables in the back of the volume, the clos -
est value to 119 is 120 degrees of freedom. At the 0.05 level, the rejection 
point is 1.43. (Using the Insert/Function/Statistical feature on a Microsoft

Excel spreadsheet, we would find FINV(0.025, 119, 119) = 1.434859 as the 
critical F-value.) Because 1.416 is not greater than 1.43, we do not reject the 
null hypothesis that the “before” and “after” variances are equal.
11 A is correct. The critical value in a decision rule is the rejection point for 
the test. It is the point with which the test statistic is compared to determine 
whether to reject the null hypothesis, which is part of the fourth step in hypoth -
esis testing.
12 A is correct. The null hypothesis is the hypothesis to be tested. The null hypoth -
esis is considered to be true unless the evidence indicates that it is false, in 
which case the alternative hypothesis is accepted.
13 A is correct. If the population sampled has unknown variance and the sample 
is large, a z-test may be used. Hypotheses involving “greater than” or “less than” 
postulations are one-  sided (one-  tailed). In this situation, the null and alternative

hypotheses are stated as H0: μ ≤ 6% and Ha: μ > 6%, respectively. A one-  tailed 
t-test is also acceptable in this case.
14 C is correct. For a one-  tailed hypothesis test, there is a 5% critical value rejec -
tion region in one tail of the distribution. 
15 B is correct. One-  tailed tests in which the alternative is “greater than” or “less 
than” represent the beliefs of the researcher more firmly than a “not equal to” 
alternative hypothesis.
16 A is correct. Calculated using a sample, a test statistic is a quantity whose value 
is the basis for deciding whether to reject the null hypothesis.
17 A is correct. The definition of a Type I error is when a true null hypothesis is 
rejected.
18 B is correct. A Type II error occurs when a false null hypothesis is not rejected.
19 B is correct. The level of significance is used to establish the rejection points of 
the hypothesis test.
20 A We have a “not equal to” alternative hypothesis:
H0: ρ = 0 versus Ha: ρ ≠ 0

Solutions 673
B We would use the nonparametric Spearman rank correlation coefficient to 
conduct the test.
C Mutual fund expense ratios are bounded from above and below, and in prac -
tice there is at least a lower bound on alpha (as any return cannot be less 
than −100 percent). These variables are markedly non-  normally distributed, 
and the assumptions of a parametric test are not likely to be fulfilled. Thus a 
nonparametric test appears to be appropriate.
D The calculation of the Spearman rank correlation coefficient is given in the 
following table.
X Rank 5 1 6.5 9 3 8 4 2 6.5
Y Rank 5 8 6 2.5 4 9 7 1 2.5
di 0 −7 0.5 6.5 −1 −1 −3 1 4
di2 0 49 0.25 42.25 1 1 9 1 16
rd
nnsi=−
−()=−()
−()=∑16
116 119 50
98110 00422
2..
 We use Table 11 to tabulate the rejection points for a test on the Spearman

rank correlation. Given a sample size of 9 in a two-  tailed test at a 0.05 sig -
nificance level, the upper-  tail rejection point is 0.6833 (we use the 0.025 col -
umn). Thus we reject the null hypothesis if the Spearman rank correlation 
coefficient is less than −0.6833 or greater than 0.6833. Because rS is equal to 
0.0042, we do not reject the null hypothesis.
21 B is correct. Specifying a smaller significance level decreases the probability of 
a Type I error (rejecting a true null hypothesis), but increases the probability of 
a Type II error (not rejecting a false null hypothesis). As the level of significance 
decreases, the null hypothesis is less frequently rejected.
22 B is correct. The power of a test is the probability of rejecting the null hypothe -
sis when it is false.
23 B is correct. The power of a hypothesis test is the probability of correctly reject -
ing the null when it is false. Failing to reject the null when it is false is a Type II

error. Thus, the power of a hypothesis test is the probability of not committing a 
Type II error. 
24 C is correct. When a statistically significant result is also economically mean -
ingful, one should further explore the logic of why the result might work in the 
future.
25 A is correct. The hypothesis is a two-  tailed formulation. The t-statistic of 2.802 
falls outside the critical rejection points of less than –2.756 and greater than 
2.756, therefore the null hypothesis is rejected; the result is statistically signif -
icant. However, despite the statistical results, trying to profit on the strategy is 
not likely to be economically meaningful because the return is near zero after 
transaction costs

Reading 12 ■ Hypothesis Testing 674
26 C is correct. When directly comparing the p-value with the level of significance, 
it can be used as an alternative to using rejection points to reach conclusions on 
hypothesis tests. If the p-value is smaller than the specified level of significance, 
the null hypothesis is rejected. Otherwise, the null hypothesis is not rejected.
27 C is correct. The p-value is the smallest level of significance at which the 
null hypothesis can be rejected for a given value of the test statistic. The null 
hypothesis is rejected when the p-value is less than the specified significance 
level.
28 A is correct. The p-value is the smallest level of significance (α) at which the 
null hypothesis can be rejected. 
29 C is correct. The p-value is the smallest level of significance (α) at which the 
null hypothesis can be rejected. If the p-value is less than α, the null can be 
rejected. The smaller the p-value, the stronger the evidence is against the null

hypothesis and in favor of the alternative hypothesis. Thus, the evidence for 
rejecting the null is strongest for Test 3. 
30 B is correct. The z-test is theoretically the correct test to use in those limited 
cases when testing the population mean of a normally distributed population 
with known variance.
31 A is correct. A t-test is used if the sample is small and drawn from a normally 
or approximately normally distributed population.
32 B is correct. A t-statistic is the most appropriate for hypothesis tests of the 
population mean when the variance is unknown and the sample is small but the 
population is normally distributed.
33 A is correct. The t-statistic value of 0.4893 does not fall into the critical value 
rejection regions (≤ –1.984 or > 1.984). Instead it falls well within the accep -
tance region. Thus, H0 cannot be rejected; the result is not statistically signifi -
cant at the 0.05 level. 
34 B is correct. The assumption that the variances are equal allows for the combin -

ing of both samples to obtain a pooled estimate of the common variance.
35 B is correct. A paired comparisons test is appropriate to test the mean differ -
ences of two samples believed to be dependent.
36 A is correct. The sample sizes for both the fund manager and the consultant’s 
accounts consists of forty quarterly periods of returns. However, the consul -
tant’s client accounts are a subset of the fund manager’s entire account base. As 
such, they are not independent samples. When samples are dependent, a paired 
comparisons test is appropriate to conduct tests of the differences in dependent 
items. 
37 A is correct. A chi-  square test is used for tests concerning the variance of a 
single normally distributed population.
38 B is correct. An F-test is used to conduct tests concerning the difference 
between the variances of two normally distributed populations with random 
39 A is correct. A non-  parametric test is used when the data are given in ranks.

40 B is correct. There are only 12 (monthly) observations over the one year of 
the sample and thus the samples are small. Additionally, the funds’ returns are 
non-  normally distributed. Therefore, the samples do not meet the distributional 
assumptions for a parametric test. The Mann–Whitney U test (a nonparametric 
test) could be used to test the differences between population means

Technical Analysis
by Barry M. Sine, CMT, CFA, and Robert A. Strong, PhD, CFA
Barry M. Sine, CMT, CFA, is at Drexel Hamilton, LLC (USA). Robert A. Strong, PhD, CFA, 
is at the University of Maine (USA).
a. explain principles of technical analysis, its applications, and its 
underlying assumptions;
b. describe the construction of different types of technical analysis 
charts and interpret them;
c. explain uses of trend, support, resistance lines, and change in 
polarity;
d. describe common chart patterns;
e. describe common technical analysis indicators (price-  based, 
momentum oscillators, sentiment, and flow of funds);
f. explain how technical analysts use cycles;
g. describe the key tenets of Elliott Wave Theory and the importance 
of Fibonacci numbers;
h. describe intermarket analysis as it relates to technical analysis and 
asset allocation.
Technical analysis has been used by traders and analysts for centuries, but it has only

recently achieved broad acceptance among regulators and the academic community. 
This reading gives a brief overview of the field, compares technical analysis with other 
schools of analysis, and describes some of the main tools in technical analysis. Some 
applications of technical analysis are subjective. That is, although certain aspects, such 
as the calculation of indicators, have specific rules, the interpretation of findings is 
often subjective and based on the long-  term context of the security being analyzed. 
This aspect is similar to fundamental analysis, which has specific rules for calculating 
ratios, for example, but introduces subjectivity in the evaluation phase.1rEAdING
13

Reading 13 ■ Technical Analysis 676
TECHNICAL ANALYSIS: DEFINITION AND SCOPE
Technical analysis  is a form of security analysis that uses price and volume data, which 
is often graphically displayed, in decision making. Technical analysis can be used for 
securities in any freely traded market around the globe. A freely traded market is 
one in which willing buyers trade with willing sellers without external intervention 
or impediment. Prices are the result of the interaction of supply and demand in real 
time. Technical analysis is used on a wide range of financial instruments, including 
equities, bonds, commodity futures, and currency futures.
The underlying logic of technical analysis is simple:
■■Supply and demand determine prices.
■■Changes in supply and demand cause changes in prices.
■■Prices can be projected with charts and other technical tools.
Technical analysis of any financial instrument does not require detailed knowledge

of that instrument. As long as the chart represents the action in a freely traded market, 
a technician does not even need to know the name or type of the security to conduct 
the analysis. Technical analysis can also be applied over any time frame—from short-  
term price movements to long-  term movements of annual closing prices. Trends that 
are apparent in short-  term charts may also appear over longer time frames. Because 
fundamental analysis is more time consuming than technical analysis, investors with 
short-  term time horizons, such as traders, tend to prefer technical analysis—but 
not always. For example, fundamental analysts with long time frames often perform 
technical analysis to time the purchase and sale of the securities they have analyzed.
2.1 Principles and Assumptions
Technical analysis can be thought of as the study of collective investor psychology, 
or sentiment. Prices in any freely traded market are set by human beings or their

automated proxies (such as computerized trading programs), and price is set at the 
equilibrium between supply and demand at any instant in time. Various fundamental 
theorists have proposed that markets are efficient and rational, but technicians believe 
that humans are often irrational and emotional and that they tend to behave similarly 
in similar circumstances.
Although fundamental data are key inputs into the determination of value, these 
data are analyzed by humans, who may be driven, at least partially, by factors other 
than rational factors.1 Human behavior is often erratic and driven by emotion in many 
aspects of one’s life, so technicians conclude that it is unreasonable to believe that 
investing is the one exception where humans always behave rationally. Technicians 
believe that market trends and patterns reflect this irrational human behavior. Thus, 
technical analysis is the study of market trends or patterns. And technicians believe

the trends and patterns tend to repeat themselves and are, therefore, somewhat pre -
dictable. So, technicians rely on recognition of patterns that have occurred in the past 
in an attempt to project future patterns of security prices.
Another tenet of technical analysis is that the market reflects the collective 
knowledge and sentiment of many varied participants and the amount of buying and 
selling activity in a particular security. In a freely traded market, only those market 
participants who actually buy or sell a security have an impact on price. And the 2
1 Fundamental analysts use a wide variety of inputs, including financial statements, legal documents, 
economic data, first-  hand observations from visiting the facilities of subject companies, and interviews 
with corporate managers, customers, suppliers, and competitors.

Technical Analysis: Definition and Scope 677
greater the volume of a participant’s trades, the more impact that market participant 
will have on price. Those with the best information and most conviction have more 
say in setting prices than others because the informed traders trade higher volumes. 
To make use of their information, however, they must trade. Technical analysis relies 
on knowledgeable market participants putting this knowledge to work by trading in 
the market, thereby influencing prices and volume. Without trading, the information 
is not captured in the charts. Arguably, although insider trading is illegal for a variety 
of reasons, it improves the efficiency of technical analysis.
Trades determine volume and price. The impact occurs instantaneously and 
frequently anticipates fundamental developments correctly. So, by studying market 
technical data—price and volume trends—the technician is seeking to understand

investor sentiment. The technician is benefiting from the wide range of knowledge 
of market participants and the collective conclusion of market participants about a 
security. In contrast, the fundamental analyst must wait for the release of financial 
statements to conduct financial statement analysis, so a time lag occurs between the 
market’s activities and the analyst’s conclusions.
Charles Dow, creator in 1896 of what is now known as the Dow Jones Industrial 
Average, described the collective action of participants in the markets as follows:
The market reflects all the jobber knows about the condition of the textile 
trade; all the banker knows about the money market; all that the best-  
informed president knows of his own business, together with his knowledge 
of all other businesses; it sees the general condition of transportation in a 
way that the president of no single railroad can ever see; it is better informed

on crops than the farmer or even the Department of Agriculture. In fact, 
the market reduces to a bloodless verdict all knowledge bearing on finance, 
both domestic and foreign.
A similar notion was expressed by George A. Akerlof and Robert J. Shiller:
To understand how economies work and how we can manage them and 
prosper, we must pay attention to the thought patterns that animate people’s 
ideas and feelings, their animal spirits. We will never really understand 
important economic events unless we confront the fact that their causes 
are largely mental in nature.2
Market participants use many inputs and analytical tools before trading. 
Fundamental analysis is a key input in determining security prices, but it is not the 
only one. Technical analysts believe that emotions play a role. Investors with a favor -
able fundamental view may nonetheless sell a financial instrument for other reasons, 
including pessimistic investor sentiment, margin calls, and requirements for their

capital—for example, to pay for a child’s college tuition. Technicians do not care why 
market participants are buying or selling, just that they are doing so.
Some financial instruments have an associated income stream that contributes to 
the security’s intrinsic value. Bonds have regular coupon payments, and equity shares 
may have underlying cash flows or dividend streams. A fundamental analyst can adjust 
these cash flows for risk and use standard time value of money techniques to deter -
mine a present value. Other assets, such as a bushel of wheat, gallon of crude oil, or 
ounce of silver, do not have underlying financial statements or an income stream, so 
valuation models cannot be used to derive their fundamental intrinsic values. For these 
assets, technical analysis is the only form of analysis possible. So, whereas fundamental 
analysis is widely used in the analysis of fixed-  income and equity securities, technical

analysis is widely used in the analysis of commodities, currencies, and futures.
2 See Akerlof and Shiller (2009).

Reading 13 ■ Technical Analysis 678
Market participants attempt to anticipate economic developments and enter into 
trades to profit from them. Technicians believe that security price movements occur 
before fundamental developments unfold—certainly before they are reported. This 
belief is reflected in the fact that stock prices are one of the 12 components of the 
National Bureau of Economic Research’s Index of Leading Economic Indicators. A 
key tenet of technical analysis is that the equity market moves roughly six months 
ahead of inflection points in the broad economy.
2.2 Technical and Fundamental Analysis
Technical analysis and fundamental analysis are both useful and valid, but they 
approach the market in different ways. Technicians focus solely on analyzing mar -
kets and the trading of financial instruments. Fundamental analysis is a much wider 
field, encompassing financial and economic analysis as well as analysis of societal and

political trends. Technicians analyze the result of this extensive fundamental analysis 
in terms of how it affects market prices. A technician’s analysis is derived solely from 
price and volume data, whereas a fundamental equity analyst analyzes a company and 
incorporates data that are external to the market and then uses this analysis to pre -
dict security price movements. As the quotation from Dow in Section 2.1 illustrates, 
technical analysis assumes that all of the factors considered by a fundamental analyst 
are reflected in the price of a financial instrument through buying and selling activity.
A key distinction between technical analysis and fundamental analysis is that the 
technician has more concrete data, primarily price and volume data, to work with. 
The financial statements analyzed by fundamental analysts are not objective data but 
are the result of numerous estimates and assumptions that have been added together

to arrive at the line items in the financial statements. Even the cash line on a balance 
sheet is subject to corporate management’s opinion about which securities are liquid 
enough to be considered “cash. ” This opinion must be agreed to by auditors and, in 
many countries, regulators (who sometimes differ with the auditors). Financial state -
ments are subject to restatements because of such issues as changes in accounting 
assumptions and even fraud. But the price and volume data used in technical analysis 
are objective. When the data become subject to analysis, however, both types of analysis 
become subjective because judgment is exercised when a technician analyzes a price 
chart and when a fundamental analyst analyzes an income statement.
Fundamental analysis can be considered to be the more theoretical approach 
because it seeks to determine the underlying long-  term (or intrinsic) value of a security.

Technical analysis can be considered to be the more practical because a technician 
studies the markets and financial instruments as they exist, even if trading activity 
appears, at times, to be irrational. Technicians seek to project the level at which a 
financial instrument will trade, whereas fundamental analysts seek to predict where 
it should  trade.
Being a fundamental analyst can be lonely if the analyst is the first to arrive at a 
fundamental conclusion, even though it is correct, because deviations from intrinsic 
value can persist for long periods. The reason these deviations may persist is that it 
takes buying activity to raise (or lower) the price of a security in a freely traded market.
A drawback of technical analysis is that technicians are limited to studying market 
movements and do not use other predictive analytical methods, such as interviewing 
the customers of a subject company, to determine future demand for a company’s

products. Technicians study market trends and are mainly concerned with a security’s 
price trend: Is the security trading up, down, or sideways? Trends are driven by col -
lective investor psychology, however, and can change without warning. Additionally, 
it can take some time for a trend to become evident. Thus, technicians may make 
wrong calls and have to change their opinions. Technicians are better at identifying 
market moves after the moves are already under way.

Technical Analysis: Definition and Scope 679
Moreover, trends and patterns must be in place for some time before they are 
recognizable, so a key shortcoming of technical analysis is that it can be late in iden -
tifying changes in trends or patterns. This shortcoming mirrors a key shortcoming of 
fundamental analysis in that securities often overshoot fundamental fair values in an 
uptrend and undershoot fundamental fair values in a downtrend. Strictly relying on 
price targets obtained by fundamental analysis can lead to closing profitable invest -
ment positions too early because investors may irrationally bid securities prices well 
above or well below intrinsic value.
Fundamental analysis is a younger field than technical analysis because reliable 
fundamental data are a relatively new phenomenon. In contrast, the first recorded use 
of technical analysis was in Japan in the 1700s, where it was used to analyze trading

in the rice market. The Japanese developed a detailed field of technical analysis with 
their own chart design and patterns. These tools were translated and widely under -
stood outside Japan only in the 1980s.
Western use of technical analysis was pioneered by Dow, who was also the first 
editor of the Wall Street Journal , in the 1890s. At the time, publicly traded companies 
were under no requirement to release their financial information even to shareholders, 
and insider trading was common and legal. Dow created the Dow Jones Industrial 
Average and the Dow Jones Railroad Average (now the Transportation Average) as a 
proxy to gauge the health of the economy, because fundamental data were not avail -
able. By his logic, if industrial stocks were doing well, industrial companies themselves 
must be doing well and if railroad stocks were doing well, railroad companies must 
be doing well. And if both manufacturers and the companies that transported goods

to market were prospering, the economy as a whole must be prospering.
Not until the Securities Exchange Act of 1934 were public companies in the 
United States required to regularly file financial statements that were available to the 
public. In that year, Benjamin Graham published his seminal work, Security  Analysis , 
and three years later, he and several others founded one of the first societies devoted 
to fundamental analysis, the New York Society of Security Analysts.3 Fundamental 
analysis quickly overtook technical analysis in terms of acceptance by practitioners, 
regulators, and academics.
Acceptance of technical analysis by practitioners was revived in the 1970s with the 
creation of the Market Technicians Association in New York and the International 
Federation of Technical Analysts a few years later. Only in the last decade, however, 
has the field started to achieve widespread acceptance by regulators and academics.

An important impediment to acceptance by academics is the difficulty of capturing the 
subjectivity involved in technical analysis. The human brain can recognize, analyze, 
and interpret technical information that is difficult for statistical computer models 
to recognize and test.
Although technical analysis can be applied to any freely traded security, it does have 
its limits. In markets that are subject to large outside manipulation, the application of 
technical analysis is limited. For example, the central banks of many countries inter -
vene in their currency markets from time to time to maintain exchange rate stability. 
Interestingly, traders claim to have been able to successfully predict interventions 
in some countries, especially those where the central bank is itself using technical 
analysis. Technical analysis is also limited in illiquid markets, where even modestly 
sized trades can have an inordinate impact on prices. For example, in considering a

thinly traded American Depositary Receipt (ADR), analyzing the more heavily traded 
3 The New York Society of Security Analysts was a successor to the New York Society of Financial 
Statisticians, which was founded in 1916.

Reading 13 ■ Technical Analysis 680
local security frequently yields a better analysis.4 Another example of when technical 
analysis may give an incorrect reading is in the case of a company that has declared 
bankruptcy and announced that its shares will have zero value in a restructuring. A 
positive technical trend may appear in such cases as investors who hold short positions 
buy shares to close out their positions.
A good example of when technical analysis is a superior tool to fundamental 
analysis is in the case of securities fraud, such as occurred at Enron Corporation 
and WorldCom. These companies were issuing fraudulent financial statements, but 
many fundamental analysts continued to hold favorable views of the companies’ 
equity securities even as the share prices declined. Simultaneously, a small group of 
investors came to the opposite view and expressed this view through high-  volume 
sales of the securities. The result was clearly negative chart patterns that could then

be discerned by technical analysis.
TECHNICAL ANALYSIS TOOLS
The primary tools used in technical analysis are charts and indicators. Charts are the 
graphical display of price and volume data, and the display may be done in a number 
of ways. Charts are then subjected to various analyses, including the identification 
of trends, patterns, and cycles. Technical indicators include a variety of measures of 
relative price level—for example, price momentum, market sentiment, and funds flow. 
We will discuss charts first.
3.1 Charts
Charts are an essential component of the technical analyst’s toolkit. Charts provide 
information about past price behavior and provide a basis for inferring likely future 
price behavior. A variety of charts can be useful in studying the markets. The selec -
tion of the chart to use in technical analysis is determined by the intended purpose 
of the analysis.
3.1.1  Line Chart
Line charts  are familiar to all types of analysts and are a simple graphic display of

price trends over time. Usually, the chart is a plot of data points, such as share price, 
with a line connecting these points. Line charts are typically drawn with closing prices 
as the data points. The vertical axis ( y-axis) reflects price level, and the horizontal 
axis ( x-axis) is time. Even though the line chart is the simplest chart, an analyst can 
quickly glean information from this chart.
The chart in Exhibit 1 is a quarterly chart of the FTSE 100 Index from 1984 through 
mid-  2009. Up years and down years are clearly evident. The strong rally from 1984 
through 1999 and the market decline from late 1999 to late 2002 are also clearly 
visible. The 2003–2007 rally did not exceed the high reached in 1999, which suggests 
that investors were not willing to pay as high a price for stocks on the London Stock 
Exchange during that rally as they were in the prior rally. This information provides 
a broad overview of investor sentiment and can lead to further analysis. Importantly, 3

4 An American Depositary Receipt is a negotiable certificate issued by a depositary bank that represents 
ownership in a non-  US company’s deposited equity (i.e., equity held in custody by the depositary bank in 
the company’s home market).

Technical Analysis Tools 681
the analyst can access and analyze this information quickly. Collecting and analyzing 
the full array of data normally incorporated in fundamental analysis would take much 
longer.
Exhibit 1   Line Chart: FTSE 100 Quarterly Price Data, 1984–2009  
(Price Measured in British Pounds Sterling) 
7,500
7,000
6,500
6,000
5,000
4,0005,500
4,500
3,500
3,000
2,500
2,000
1,500
1,000
0
84 86 88 90 92 94 96 98 00 02 04 06 08 10
3.1.2  Bar Chart
A line chart has one data point per time interval. A bar chart , in contrast, has four 
bits of data in each entry—the high and low price encountered during the time inter -
val plus the opening and closing prices. Such charts can be constructed for any time 
period, but they are customarily constructed from daily data.
As Exhibit 2 shows, a vertical line connects the high and low price of the day; a 
cross-  hatch to the right indicates the closing price, and a cross-  hatch to the left indi -

cates the opening price. The appeal of this chart is that the analyst immediately gets 
a sense of the nature of that day’s trading. A short bar indicates little price movement 
during the day; that is, the high, low, and close were near the opening price. A long 
bar indicates a wide divergence between the high and the low for the day.
Exhibit 2   Bar Chart Notation
HIGH
LOWCLOSE
OPEN

Reading 13 ■ Technical Analysis 682
Exhibit 3 shows daily performance of the Brazilian Bovespa Index (BVSP) from late 
2007 through late 2009. The top part provides the price open, close, high, and low; the 
bottom part shows volume, which will be discussed in section 3.1.6. The downturn 
in the second half of 2008 is obvious, but also notable are the extreme price move -
ments in the fourth quarter of 2008. There were 40 trading days from 29 September 
to 24 November. On 20 of those days, the closing value of the index changed from 
the previous close by at least 4 percent, a huge move by historical standards. During 
the same period, the average daily price range (high to low) was 7 percent, compared 
with 3.7 percent in the previous two months. This potentially important information 
would not be captured in a line chart.
Exhibit 3   Bar Chart: Bovespa Index, November 2007–November 2009  
(Price in Brazilian Reais) 
Much Higher Volatility
than UsualBVSP, Weekly
Volume (millions)80,000
70,000
60,000

70,000
60,000
50,000
40,000
30,000
20,000
15
10
5
0
Jan 08 May 08 Sep 08 Jan 09 May 09 Sep 09
3.1.3  Candlestick Chart
Candlestick charts trace their roots to Japan, where technical analysis has been in 
use for centuries. Like a bar chart, a candlestick chart  also provides four prices per 
data point entry: the opening and closing prices and the high and low prices during 
the period. As shown in Exhibit 4, a vertical line represents the range through which 
the security price traveled during the time period. The line is known as the wick or 
shadow. The body of the candle is shaded if the opening price was higher than the 
closing price, and the body is clear if the opening price was lower than the closing price.

Technical Analysis Tools 683
Exhibit 4   Construction of a Candlestick Chart
Each candle has two elements: body and wick/shadow
White body means market closed UP
Close > OpenHIGH
LOWCLOSE
OPEN
Dark body means market closed DOWN
Close < OpenHIGH
LOWCLOSEOPEN
Exhibit 5 shows a weekly candlestick chart for Companhia Vale do Rio Doce for 
the period 1 January through 15 June 2009.
Exhibit 5   Candlestick Chart: Companhia Vale do Rio Doce,  
1 January–15 June 2009 (Price in US Dollars) 
Price ($)
25
20
15
10
5
0
7 13 19 9 15 21 11 1 3 5 17 23 25
Week
The advantage of the candlestick chart over the bar chart is that price moves are 
much more visible in the candlestick chart, which allows faster analysis. The bar chart 
indicates market volatility only by the height of each bar, but in candlestick charts, 
the difference between opening and closing prices and their relationship to the highs 
and lows of the day are clearly apparent. Compare the sixth candle with the twelfth

in Exhibit 5. In the sixth candle, the analyst can see significant volatility because the 
high of the day and low of the day are so far apart. The stock opened near the low of 
the day and closed near the high, suggesting a steady rally during the day. In contrast, 
the twelfth candle shows that the shares opened and closed at the same price, creating 
a cross-  pattern. In Japanese terminology used in candlestick charting, this pattern 
is called a doji. The doji signifies that after a full day of trading, the positive price

Reading 13 ■ Technical Analysis 684
influence of buyers and the negative price influence of sellers exactly counteracted 
each other, which tells the analyst that this market is in balance. If a doji occurs at the 
end of a long uptrend or downtrend, it signals that the trend will probably reverse.
3.1.4  Point and Figure Chart
Point and figure charts were widely used in the United States in the early 1900s and 
were favored because they were easy to create and update manually in the era before 
computers. As with any technical analysis tool, these charts can be used with equities, 
fixed-  income securities, commodities, or foreign exchange.
Who originated the point and figure chart  is unclear; they are referred to in a 
number of books in the United States dating back to 1898. The methodology evolved 
until 1934 when the first book was published on the topic: The Point and Figure Method 
of Anticipating Stock Price Movements  by Victor de Villiers and Owen Taylor. With

the advent of powerful charting software and internet websites, complex chart types, 
such as the candlestick chart, have become more popular. But point and figure charts 
still offer tremendous value if one knows their limitations and their advantages. The 
key reason this knowledge is necessary, as explained below, is that point and figure 
charts are constructed differently from other charts; they have a clear focus on entry 
and exit levels but no focus on holding periods.
As illustrated in Exhibit 6, a point and figure chart is drawn on a grid and con -
sists of columns of X’s alternating with columns of O’s. Neither time nor volume are 
represented on this type of chart, and the horizontal axis represents the number of 
changes in price, not time . Movement along the horizontal axis does reflect the passage 
of time, but not in any uniform fashion. The analyst makes entries on a point and 
figure chart only when the price changes by the “box size, ” which is explained below.

This lack of a normal time dimension is perhaps the most unusual characteristic of 
a point and figure chart.
Exhibit 6   Point and Figure Chart: Wharf Holdings Daily Price Chart,  
2007–2009 (in Hong Kong Dollars) 
50
35
30
20
1025
15
0945
40
08
Note : The box size is HK$1, and the reversal size is three.

Technical Analysis Tools 685
To construct a point and figure chart, the analyst must determine both the box 
size and the reversal size. Box size refers to the change in price represented by the 
height of each box (boxes are generally square, but the width has no meaning). In 
Exhibit 6, the box size is HK$1. The reversal size is used to determine when to create 
a new column. In Exhibit 6, the reversal size is three, meaning a reversal in price of 
three or more boxes.
Although a point and figure chart can be constructed in several ways, these charts 
are always drawn on graph paper to facilitate seeing the “columns and rows” nature 
of the data. The vertical axis measures discrete increments of price . For example, an 
analyst in Europe might draw a €1 chart, a €2 chart, or any other increment. In a €1 
chart, boxes would be €1 apart (e.g. €40, €41, €42), whereas in a €2 chart they would 
be €2 apart (€40, €42, €44). The most commonly used box size is 1 unit of currency,

which is used when prices range from 20 to 100 per share of the currency.
The next decision the technician needs to make is the reversal size. The most 
common size is three, meaning a reversal in price of three or more boxes (€3 in the 
case of a box size of €1). This use of a multibox reversal helps eliminate “noise” in the 
price data. ( Noise  refers to short-  term trading volatility that does not alter the long-  
term trend of the security.)
In a point and figure chart, X represents an increase in price and O represents a 
decline in price. In constructing a chart, the technician draws an X in a column of 
boxes every time the security price closes up by the amount of the box size. (Ideally, 
all security prices are considered on an intraday basis, but this practice has given way 
to using closing prices only.) If the price increases by twice the box size, the techni -
cian draws two X’s to fill in two boxes, one on top of the other. The technician fills in

more boxes for larger price moves. The resulting column starts at the opening price 
level and extends to the closing price level. As long as the security keeps closing at 
higher prices, the technician keeps filling in boxes with X’s, which makes the column 
higher and higher. If the price does not increase by at least the box size, no indication 
is made on the chart. Thus, in some cases, the chart is not updated for long periods, 
but no indication of this passage of time is made on the chart.
The reversal size determines when to create a new column. In the case of a €1 box 
size, and three-  box reversal size, a decline of €3 or more would result in the technician 
shifting to the next column over and beginning a column of O’s. The first box to be 
filled in is to the right and below the highest X in the prior column. The technician 
then fills in an O to bring the column down to the price level at the close. Again, each

filled-  in box (if the box size is €1) represents a €1 decline in the security price. As long 
as the downtrend continues, without a €3 increase in price, the technician continues 
adding O’s to the column below the prior O’s. A reversal in the downtrend by at least 
the amount of the reversal size prompts the technician to move to the next column 
and begin drawing a series of X’s again. Computer technology makes the process easy, 
but many technicians prefer to keep point and figure charts on their wall and update 
them manually because doing so provides a vivid reminder of the market trend.
Point and figure charts are particularly useful for making trading decisions because 
they clearly illustrate price levels that may signal the end of a decline or advance. They 
also clearly show price levels at which a security may frequently trade. In using the 
point size and reversal size to make trading decisions, for uptrends, or columns of

X’s, the practitioner would maintain long positions. The reversal size could be con -
sidered the amount of loss that would prompt the closing of a long position and the 
establishment of a new short position. The larger the reversal size, the fewer columns 
in the chart and the longer uptrends and downtrends will run.
The box size can be varied in relation to the security price. For a security with a 
very low price—say, below €5—a €1 box size might mean few or no updates on the 
chart because the price would only rarely change by this amount. Thus, the techni -
cian could reduce the box size to cents. For highly priced securities, much larger box

Reading 13 ■ Technical Analysis 686
sizes could be used. The reversal size is a multiple of the box size, so if the box size 
is changed, the reversal size changes. Practitioners who want fewer columns or trade 
signals can use a large reversal size.
Analysis of a point and figure chart is relatively straightforward as long as the 
technician understands its construction and limitations. The chart is relatively sim -
ple, and repeated high and low prices are evident. Congestion areas, where a security 
trades up and down in a narrow range, are evidenced by a series of short columns of 
X’s and O’s spanning roughly the same price range. Major, sustained price moves are 
represented by long columns of X’s (when prices are moving up) or O’s (when prices 
are moving down).
3.1.5  Scale
For any chart—line, bar, or candlestick—the vertical axis can be constructed with either 
a linear scale  (also known as an arithmetic scale) or a logarithmic scale , depending

on how you want to view the data. With a logarithmic scale, equal vertical distances 
on the chart correspond to an equal percentage change. A logarithmic scale is appro -
priate when the data move through a range of values representing several orders of 
magnitude (e.g., from 10 to 10,000); a linear scale is better suited for narrower ranges 
(e.g., prices from $35 to $50). The share price history of a particular company, for 
instance, is usually best suited to a linear scale because the data range is usually narrow.
The horizontal axis shows the passage of time. The appropriate time interval 
depends on the nature of the underlying data and the specific use of the chart. An 
active trader, for instance, may find 10-  minute, 5-  minute, or even tick-  by- tick data 
useful, but other technical analysts may prefer daily or weekly data. In general, the 
greater the volatility of the data, the greater the likelihood that an analyst can find 
useful information in more-  frequent data sampling.

Consider Exhibits 7 and 8, which both show the yearly history of the Dow Jones 
Industrial Average (DJIA) from 1928 to 2010. Plotting the index on a linear scale, as 
in Exhibit 7, makes it difficult to gather much information from the first 50 years of 
the data series. Analysts can see a slight uptrend but not much else. The eye is drawn 
to the bull market of the 1980s, the subsequent dot-  com bubble, and the recent era 
of the subprime crisis. When plotted on a logarithmic scale, as in Exhibit 8, however, 
many people would find that the data tell a more comprehensive story. The Great 
Depression of the 1930s stands out, but over the following 75 years, the data follow 
a relatively stable upward trend.

Technical Analysis Tools 687
Exhibit 7   Dow Jones Industrial Average on Linear Scale, 1928–2010  
(in US Dollars) 
16,000
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
28 40 52 64 76 88 00
Exhibit 8   Dow Jones Industrial Average on Logarithmic Scale, 1928–2010 
100,000
1,00010,000
100
10
1
3.1.6  Volume
Volume is an important characteristic that is included at the bottom of many charts; 
see, for example Exhibit 3. Volume is used to assess the strength or conviction of buyers 
and sellers in determining a security’s price. For example, on a daily price chart, below 
the price section would be a column chart showing the volume traded for that day.
Some technicians consider volume information to be crucial. If volume increases 
during a time frame in which price is also increasing, that combination is considered 
positive and the two indicators are said to “confirm” each other. The signal would be

Reading 13 ■ Technical Analysis 688
interpreted to mean that over time, more and more investors are buying the financial 
instrument and they are doing so at higher and higher prices. This pattern is consid -
ered a positive technical development.
Conversely, if volume and price diverge—for example, if a stock’s price rises while 
its volume declines—the implication is that fewer and fewer market participants are 
willing to buy that stock at the new price. If this trend in volume continues, the price 
rally will soon end because demand for the security at higher prices will cease. Exhibit 9 
shows a chart for Toronto-  Dominion Bank (TD Bank) with volume displayed separately.
Exhibit 9   Daily Candlestick Price Chart and Volume Bar Chart: TD Bank, 
November 2007–November 2009 (Price in Canadian Dollars) 
Volume (thousands)80
75
70
65
5560
50
45
3540
30
25
200800
600
400
0
Jan
08Nov
07Mar
08May
08Jul
08Sep
08Nov
08Jan
09Mar
09Jul
09May
09Sep
09
3.1.7  Time Intervals

08Jan
09Mar
09Jul
09May
09Sep
09
Most of the chart examples in this reading are daily price charts in that they show the 
price and volume on a daily basis. Daily frequency is not required, however, because 
charts can be constructed by using any time interval. For short-  term trading, the ana -
lyst can create charts with one-  minute or shorter intervals. For long-  term investing, 
the analyst can use weekly, monthly, or even annual intervals. The same analytical 
approach applies irrespective of the time interval. Using long intervals allows the ana -
lyst to chart longer time periods than does using short time intervals for the simple 
reason that long intervals contain fewer data points, so a longer time frame can be 
presented on the chart. Using short intervals allows the analyst to see more detail. A 
useful step for many analysts is to begin the analysis of a security with the chart for a

long time frame, such as a weekly or monthly chart, and then construct charts with 
shorter and shorter time intervals, such as daily or hourly charts.
3.1.8  Relative Strength Analysis
Relative strength analysis  is widely used to compare the performance of a particular 
asset, such as a common stock, with that of some benchmark—such as, in the case 
of common stocks, the FTSE 100, the Nikkei 225, or the S&P 500 Index—or the per -
formance of another security. The intent is to show out- or underperformance of the 
individual issue relative to some other index or asset. Typically, the analyst prepares 
a line chart of the ratio of two prices, with the asset under analysis as the numerator

Technical Analysis Tools 689
and with the benchmark or other security as the denominator. A rising line shows 
the asset is performing better than the index or other stock; a declining line shows 
the opposite. A flat line shows neutral performance.
Suppose a private investor is researching two investment ideas she read about. 
Harley-  Davidson Motor Company (HOG) is a well-  known motorcycle company; 
Rodman and Renshaw (RODM) is a small investment bank. The investor wants to 
determine which of these two has been the stronger performer (relative to the S&P 
500) over the past few months. Exhibit 10 shows relative strength lines for the two 
stocks for the first six months of 2009. Each point on the relative strength plot is 
simply the ratio of a share price to the S&P 500. For example, on 9 March 2009, HOG 
closed at US$8.42 and the S&P 500 closed at $676.53. The relative strength data point 
is, therefore, 8.42/676.53, or 0.0124. On 27 April, HOG closed at US$19.45, with the

S&P 500 at $857.51. The relative strength value is 19.45/857.51, or 0.0227, nearly 
double the 9 March value.
Exhibit 10   Relative Strength Analysis: HOG vs. the S&P 500 and RODM vs. 
the S&P 500, January–June 2009
Relative Strength
Underperformance
Outperformance0.030
0.025
0.020
0.015
0.010
0.005
0
Jan/09 Feb/09 Mar/09 Apr/09 May/09 Jun/09 Jul/09
RODM HOG
The units on the vertical axis are not significant; the ratio is a function of the relative 
prices of the assets under consideration. The important information is how the ratio 
has changed. This type of chart allows an analyst to make a visual determination of that 
change. As Exhibit 10 illustrates, Harley-  Davidson was a strong performer in March 
and April but lagged the index beginning in May. In contrast, the stock of Rodman and 
Renshaw began a significant rise in mid-  May that outperformed the market average.
3.2 Trend
The concept of a trend  is perhaps the most important aspect of technical analysis.

Trend analysis is based on the observation that market participants tend to act in 
herds and that trends tend to stay in place for some time. A security can be consid -
ered to be in an upward trend, a downward trend, a sideways trend, or no apparent 
trend. Not all securities are in a trend, and little useful forecasting information can

Reading 13 ■ Technical Analysis 690
be gleaned from technical analysis when a security is not in a trend. Not every chart 
will have obvious or clear implications, so the analyst must avoid the temptation to 
force a conclusion from every chart and thus reach a wrong interpretation.
An uptrend for a security is when the price goes to higher highs and higher lows. 
As the security moves up in price, each subsequent new high is higher than the prior 
high and each time there is a retracement , which is a reversal in the movement of the 
security’s price, it must stop at a higher low than the prior lows in the trend period. 
To draw an uptrend line, a technician draws a line connecting the lows of the price 
chart. Major breakdowns in price, however, when the price drops through and below 
the trendline by a significant amount (many technicians use 5–10 percent below the 
trendline) indicate that the uptrend is over and may signal a further decline in the price.

Minor breakthroughs below previous lows simply call for the line to be moderately 
adjusted over time. Time is also a consideration in trends: The longer the security price 
stays below the trendline, the more meaningful the breakdown is considered to be.
In an uptrend, the forces of demand are greater than the forces of supply. So, traders 
are willing to pay higher and higher prices for the same asset over time. Presumably, 
the strong demand indicates that investors believe the intrinsic value of the security 
is increasing.
A downtrend is when a security makes lower lows and lower highs. As the security 
moves down in price, each subsequent new high must be lower than the prior high 
and each time there is a retracement, it must stop at a lower low than the prior lows in 
the trend period. To draw a downtrend line, a technician draws a line connecting the 
highs of the price chart. Major breakouts above the downtrend line (e.g., 5–10 percent)

indicate that the downtrend is over and a rise in the security’s price may occur. And 
as with an uptrend, the longer the security price stays above the trendline, the more 
meaningful the breakout is considered to be.
In a downtrend, supply is overwhelming demand. Over time, sellers are willing to 
accept lower and lower prices to exit long positions or enter new short positions. Both 
motives of the sellers generally indicate deteriorating investor sentiment about the 
asset. However, selling may be prompted by factors not related to the fundamental or 
intrinsic value of the stock. For example, investors may be forced to sell to meet margin 
calls in their portfolios. From a purely technical standpoint, the reason is irrelevant. 
The downtrend is assumed to continue until contrary technical evidence appears. 
Combining fundamental analysis with technical analysis in such a case, however, might 
reveal a security that has attractive fundamentals but a currently negative technical

position. In uptrends, however, a security with an attractive technical position but 
unattractive fundamentals is rare because most buying activity is driven by traders 
who expect the security price to increase in the future. The rare exception is covering 
short positions after a sizable decline in the share price.
A security may trade in a fairly narrow range, moving sideways on the price chart 
without much upward or downward movement. This pattern indicates a relative bal -
ance between supply and demand. A technical analyst may not expect to profit from 
long or short trades in such securities but might devise profitable option strategies 
for short-  term investors with the ability to accept the risks.
Exhibit 11 shows the application of trend analysis. Depicted is an uptrend line for 
the shares of China Mobile Limited. Note that through late 2007, every rally took the 
shares to a new high, whereas sell-  offs stopped at increasingly higher levels. The first

sign of trouble came in the spring of 2008 when the rally terminated at a lower price 
point than the prior rally, of late 2007. This movement was followed by the shares 
breaking through the trendline.

Technical Analysis Tools 691
Exhibit 11   Trend Analysis: China Mobile Weekly Price Chart, 2002–2010 
(Prices in Hong Kong Dollars) 
150
100
50
100300
200
0
04 03 05 06 07 08 09Volume (thousands)
The chart in Exhibit 11 covers roughly seven years and would most likely be used 
by investors with a long time horizon. Investors with a shorter horizon might use a 
chart with a shorter time frame and would thus obtain a different trendline as well as 
a different trendline breakdown.
Two concepts related to trend are support and resistance. Support  is defined as 
a low price range in which buying activity is sufficient to stop the decline in price. It 
is the opposite of resistance , which is a price range in which selling is sufficient to 
stop the rise in price. The psychology behind the concepts of support and resistance 
is that investors have come to a collective consensus about the price of a security. 
Support and resistance levels can be sloped lines, as in trendlines, or horizontal lines.

A key tenet of support and resistance as a part of technical analysis is the change 
in polarity principle , which states that once a support level is breached, it becomes a 
resistance level. The same holds true for resistance levels; once breached, they become 
support levels. For example, if the price of a security never rises above SFr10 over 
a long period of time and begins to decline each time it reaches this level but then 
finally breaks through this level by a significant amount, the point to which the price 
rises becomes a support level.
Support and resistance levels are commonly round numbers. Support indicates 
that at some price level, investors consider a security to be an attractive investment 
and are willing to buy, even in the wake of a sharp decline (and for resistance, at some 
level, investors are not willing to buy, even in an uptrend). The fact that these price 
points tend to be round numbers strongly suggests that human sentiment is at work.

One of the most widely publicized examples of support and resistance is when the 
DJIA broke through the 10,000 mark in 1999, shown in Exhibit 12. Previously, 10,000 
had been viewed as a resistance line, but from 1999 through the end of the chart in 
2001, 10,000 served as a support level.

Reading 13 ■ Technical Analysis 692
Exhibit 12   Support Level: DJIA Weekly Price Chart, 1990–2001  
(Price in US Dollars ÷100) 
110120
100
90
80
70
60
50
40
2030
90 01 93 94 96 97 99 00 91 92 95 98
3.3 Chart Patterns
Chart patterns are formations that appear in price charts that create some type of 
recognizable shape. Common patterns appear repeatedly and often lead to similar 
subsequent price movements. Thus, the identification and analysis of chart patterns is 
a common aspect of technical analysis used to predict security prices. An important 
connection to understand is that patterns form as a result of the behavior of market 
participants and that these patterns represent graphical depictions of the collective 
psychology of the market at a given time.
The recurring patterns that appear in charts can be used as a basis for market 
forecasting. The reason chart patterns have predictive value is that they are graphic

representations of human trading activity and human behavior is frequently repeated, 
especially trading activity that is driven by fear (in market sell-  offs) or hope and greed 
(as evidenced in bubbles—that is, rallies that extend well beyond valuation levels that 
would be derived by fundamental values). An example of a rally driven by greed is the 
recent real estate bubble, which took home prices to unsustainably high levels. This 
bubble started a few years after the internet stock bubble of the 1990s, which also took 
prices to unsustainably high levels. In bubbles, investors, driven by hope and greed, 
drive the price of an asset to irrationally high levels, in the expectation that another 
buyer will be willing to pay an even higher price for the asset. The housing bubble was 
notable because it so closely followed the internet stock bubble, despite all that had 
been written about the “irrational exuberance” of the internet bubble of the 1990s.

Chart patterns can be divided into two categories: reversal patterns  and con -
tinuation patterns . These terms refer to the trend for the security in question prior 
to the formation of the pattern. The most important concept to understand in using 
chart patterns is that without a clear trend in place prior to the pattern, the pattern 
has no predictive value. This aspect is frequently forgotten by investors who are so 
eager to identify and use patterns that they forget the proper application of charts.

Technical Analysis Tools 693
3.3.1  Reversal Patterns
As the name implies, a reversal pattern signals the end of a trend, a change in direction 
of the financial instrument’s price. Evidence that the trend is about to change direction 
is obviously important, so reversal patterns are noteworthy.
3.3.1.1  Head and Shoulders  Perhaps the most widely recognized reversal pattern 
is the head and shoulders pattern . The pattern consists of three segments. Volume 
is an important characteristic in interpreting this pattern. Because head and shoulders 
indicates a trend reversal, a clear trend must exist prior to the formation of the pattern 
in order for the pattern to have predictive validity. For a head and shoulders pattern, the 
prior trend must be an uptrend. Later, we will discuss the inverse  head and shoulders 
pattern (preceded by a downtrend).
Exhibit 13 depicts a head and shoulders pattern for Marvell Technology Group 
during 2006. The three parts of the pattern are as follows:

■■Left shoulder: This part appears to show a strong rally, with the slope of the 
rally being greater than the prior uptrend, on strong volume. The rally then 
reverses back to the price level where it started, forming an inverted V pattern, 
but on lower volume.
■■Head: The head is a more pronounced version of the left shoulder. A rally 
following the first shoulder takes the security to a higher high than the left 
shoulder by a significant enough margin to be clearly evident on the price chart. 
Volume is typically lower in this rally, however, than in the one that formed 
the first, upward side of the left shoulder. This second rally also fails, with price 
falling back to the same level at which the left shoulder began and ended. This 
price level is called the neckline. This price level also will be below the uptrend 
line formed by connecting the low prices in the uptrend preceding the begin -
ning of the head and shoulders pattern. This head pattern is the first signal that

the rally may be coming to an end and that a reversal may be starting.
■■Right shoulder: The right shoulder is a mirror image (or close to a mirror 
image) of the left shoulder but on lower volume, signifying less buying enthusi -
asm. The price rallies up to roughly the same level as the first shoulder, but the 
rally reverses at a lower high price than the rally that formed the head.

Reading 13 ■ Technical Analysis 694
Exhibit 13   Head and Shoulders Pattern: Marvell Technology Daily Price 
Chart, June 2005–June 2006 (Price in US Dollars ÷100) 
Head
Shoulder Shoulder
Necklin e38
18202224262830323436
100400
300
200
0
Jul
05Jun
05Aug
05Sep
05Oct
05Nov
05Dec
05Jan
06Feb
06Mar
06Apr
06May
06Volume (thousands)
Rarely will an analyst see a perfectly formed head and shoulders pattern; variations 
include two tops on the shoulders or on the head. The head, however, should rise to 
a higher price level than either shoulder, whereas the shoulders should be roughly 
symmetrical. In terms of the neckline price level, the first rally should begin at this level 
and the left shoulder and head should also decline to roughly this level. But necklines 
may not always form exactly horizontal lines. These imperfect variations make this 
(and other) technical patterns difficult for quantitative analysts or academicians to 
model, but the human brain can detect the pattern even if it is imperfectly formed.

Volume is important in analyzing head and shoulders patterns. A new high in 
price at the top of the head without a new high in volume signals fewer bullish market 
participants. When one indicator is making a new high (or low) but another is not, 
this situation is called divergence . In divergence, the right shoulder will have even 
lower volume, signaling that buying interest or demand is tapering off and will soon 
be overwhelmed by supply. The result will be a price decline.
Once the head and shoulders pattern has formed, the expectation is that the share 
price will decline down through the neckline price. Technicians tend to use filtering 
rules to make sure that a clear breakdown of the neckline has occurred. These rules 
may take the form of waiting to trade until the price falls to a meaningful level below 
the neckline (3 percent or 5 percent are commonly used) and/or a time limit for the 
price to remain below the neckline before trading; when a daily price chart is used, the

rule may be several days to a week. Prices commonly rebound to the neckline levels, 
even after a decline has exceeded the filter levels. Prices generally stop, however, at 
or around the neckline. The neckline was a support level, and under the change in 
polarity principle, once a support level is breached, it becomes a resistance level.

Technical Analysis Tools 695
3.3.1.2  Inverse Head and Shoulders  The head and shoulders pattern can also form 
upside down and act as a reversal pattern for a preceding downtrend. The three parts 
of the inverse head and shoulders are as follows:
■■Left shoulder: This shoulder appears to show a strong decline, with the slope of 
the decline greater than the prior downtrend, on strong volume. The rally then 
reverses back to the price level where it started, forming a V pattern, but on 
lower volume.
■■Head: The head is a more pronounced version of the left shoulder. Another 
decline follows but on diminishing volume, which takes the price to a lower 
low than the prior shoulder by a significant enough margin that it is clearly 
evident on the price chart. This second decline also reverses, with price rising 
to the same level at which the left shoulder began and ended. This price level, 
the neckline, will also be above the downtrend line formed by connecting the

high prices in the downtrend preceding the beginning of the inverse head and 
shoulders pattern. This pattern is the first signal that the decline may be coming 
to an end and that a reversal may be near.
■■Right shoulder: The right shoulder is roughly a mirror image of the left shoul -
der but on lower volume, signifying less selling enthusiasm. The price declines 
down to roughly the same level as the first shoulder, but the rally reverses at a 
higher low price than the rally that formed the head.
3.3.1.3  Setting Price Targets with Head and Shoulders Pattern  As with all technical 
patterns, the head and shoulders pattern must be analyzed from the perspective of the 
security’s long-  term price trend. The rally that happened before the formation of the 
pattern must be large enough for there to be something to reverse. The stronger and 
more pronounced the rally was, the stronger and more pronounced the reversal is likely

to be. Similarly, once the neckline is breached, the security is expected to decline by 
the same amount as the change in price from the neckline to the top of the head. If the 
preceding rally started at a price higher than the neckline, however, the correction is 
unlikely to bring the price lower than the price level at the start of the rally. Because a 
head and shoulders formation is a bearish indicator (i.e., a technician would expect the 
previously established uptrend to end and a downtrend to commence), a technician 
would seek to profit by shorting the security under analysis. When attempting to profit 
from the head and shoulders pattern, a technician will often use the price differences 
between the head and the neckline to set a price target, which is the price at which the 
technician anticipates closing the investment position. The price target for the head 
and shoulders pattern is calculated as follows:
Price target = Neckline – (Head – Neckline)

Price target = Neckline – (Head – Neckline) 
For example, in Exhibit 14, the high price reached at the top of the head is roughly 
$37 and the neckline formed at roughly $27 for a difference of $10. So a technician 
would expect the price to decline to a level $10 below the neckline, or to $17; that is,
Price target = $27 – ($37 – $27) = $17

Reading 13 ■ Technical Analysis 696
Exhibit 14   Calculating Price Target: Marvell Technology Daily Price Chart, 
June 2005–November 2006 (Price in US Dollars) 
Head= $37
Shoulder
 = $31
Neckline
= $27Shoulder
 = $31
Target = $17 
1519
1721232931
25273337
35
200800
600
400
Jun
05Aug
05Oct
05Dec
05Feb
06Apr
06Jun
06Aug
Oct
06
EXAMPLE 1   
Determining a Price Target from a Head and Shoulders 
Pattern
Danielle Waterhouse is the technical analyst at Kanektok Securities. One of the 
companies her firm follows is LPA Petroleum. Waterhouse believes that a graph 
of LPA’s share prices over the past six months reveals a classic head and shoul -
ders pattern. The share price peaked at US$108, and she estimates the neckline 
at US$79. At today’s close, the shares traded at US$78. Based on the head and 
shoulders pattern, what price target should Waterhouse estimate?
Solution:
Waterhouse estimates the neckline at US$79, which is US$108 minus US$79,

or US$29 lower than the head. Her price target is thus US$79 minus US$29, 
which is US$50. Waterhouse would attempt to sell LPA short at today’s price 
of US$78 and anticipate closing the position at US$50 for a profit of US$28 per 
share (not accounting for transaction costs).
3.3.1.4  Setting Price Targets with Inverse Head and Shoulders Pattern  Calculating 
price targets for inverse head and shoulders patterns is similar to the process for head 
and shoulders patterns, but in this case, because the pattern predicts the end of a 
downtrend, the technician calculates how high the price is expected to rise once it 
breaches the neckline. Exhibit 15 illustrates an inverse head and shoulders pattern.

Technical Analysis Tools 697
Exhibit 15   Calculating Price Target for Inverse Head and Shoulders Pattern: 
DJIA Daily Price Chart, February 2002–January 2004  
105
95100
90
85
80
7075
Feb
02Aug
02Oct
02Feb
03Apr
03Oct
03Dec
03Apr
02Jun
02Dec
02Aug
03Jun
03Target = $10,903
Neckline = $9,050
Shoulder = $7,418
Head = $7,197Shoulder = $7,533
For an inverse head and shoulders pattern, the formula is similar to a head and 
shoulders pattern:
Price target = Neckline + (Neckline – Head) 
For example, in the price chart in Exhibit 15, the low price reached at the bottom of 
the head is roughly US$7,197 and the neckline formed at roughly US$9,050. The target 
can thus be found as $9,050 + (9,050 − $7,197) = $10,903. In this case, a technician 
might have taken a long position in the summer of 2003 with the hope of eventually 
exiting the position at about US$10,903 for a profit.
3.3.1.5  Double Tops and Bottoms  A double top  is when an uptrend reverses twice

at roughly the same high price level. Typically, volume is lower on the second high than 
on the first high, signaling a diminishing of demand. The longer the time is between 
the two tops and the deeper the sell-  off is after the first top, the more significant the 
pattern is considered to be. Price targets can be calculated from this pattern in a manner 
similar to the calculation for the head and shoulders pattern. For a double top, price 
is expected to decline below the low of the valley between the two tops by at least the 
distance from the valley low to the high of the double tops.
EXAMPLE 2   
Determining a Price Target from a Double-  Top Pattern
Richard Dupuis is a technician who trades Eurodollar futures for his own account. 
He analyzes charts based on one-  minute time intervals looking for short-  term 
trading opportunities. Eurodollar futures contracts have been trending upward 
most of the morning, but Dupuis now observes what he believes is a double-  top

pattern: After peaking at US$97.00, the futures contract price fell to US$96.42, 
climbed again to US$97.02, and then started a decline. Because of the double

Reading 13 ■ Technical Analysis 698
top, Dupuis anticipates a reversal from the uptrend to a downtrend. Dupuis 
decides to open a short position to capitalize on the anticipated trend reversal. 
What price target should Dupuis estimate for closing the position?
Solution:
Dupuis estimates the price target as $96.42 − ($97.02 − $96.42) = $95.82.
Double bottoms  are formed when the price reaches a low, rebounds, and then 
sells off back to the first low level. Exhibit 16 depicts a double-  bottom pattern for 
Time Warner. Technicians use the double bottom to predict a change from a down -
trend to an uptrend in security prices. For double bottoms, the price is expected to 
appreciate above the peak between the two bottoms by at least the distance from the 
valley lows to the peak.
Exhibit 16   Double-  Bottom Pattern: Time Warner Daily Price Chart, 
November 2007–October 2009 (Price in US Dollars) 
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The reason these patterns are significant is that they show that at some price point, 
investors step in to reverse trends that are under way. For an uptrend, a double top 
implies that at some price point, enough traders are willing to either sell positions (or 
enter new short positions) that their activities overwhelm and reverse the uptrend 
created by demand for the shares. A reasonable conclusion is that this price level has 
been fundamentally derived and that it represents the intrinsic value of the security 
that is the consensus of investors. With double bottoms, if a security ceases to decline 
at the same price point on two separate occasions, the analyst can conclude that the 
market consensus is that at that price point, the security is now cheap enough that it 
is an attractive investment.
3.3.1.6  Triple Tops and Bottoms  Triple tops  consist of three peaks at roughly the

same price level, and triple bottoms  consist of three troughs at roughly the same 
price level. A triple top for Rockwell Automation during 1999 is shown in Exhibit 17.

Technical Analysis Tools 699
Exhibit 17   Triple-  Top Pattern: Rockwell Automation Daily Price Chart, 1999 
(Price in US Dollars) 
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One of the challenges in double-  top and triple-  top patterns, and one of the valid 
criticisms of technical analysis in general, is that an analyst cannot know which pattern 
will result until after the fact. For example, after the broad equity market sell-  off in 
the first quarter of 2009, a number of investment professionals were quoted as calling 
for a “retest of the lows”—in technical terms, a double bottom.
There is no evidence that market corrections (or rallies) must end with a double 
bottom (or double top in the case of an uptrend), and there is no generally accepted 
technical theory that predicts whether a low will be repeated once or even twice before 
a reversal occurs. A double bottom is considered to be a more significant pattern than

a single bottom because traders have stepped in on two occasions to halt declines. 
However, traders have no way to determine whether a double top or bottom will be 
followed by a third top or bottom. Triple tops and triple bottoms are rare, but when 
they occur, they are more significant reversal patterns than double tops or double 
bottoms. On three separate occasions, traders stepped in to sell or buy shares with 
enough volume to end a rally or decline under way at the time. Nevertheless, the 
greater the number of times the price reverses at the same level, and the greater the 
time interval over which this pattern occurs, the greater the significance of the pattern.
3.3.2  Continuation Patterns
A continuation pattern  is used to predict the resumption of a market trend that was 
in place prior to the formation of a pattern. From a supply-  and-  demand standpoint, 
a continuation pattern indicates a change in ownership from one group of investors

to another. For example, if a positive trend was in place prior to a pattern and then 
one group of investors begins selling, the negative impact on price is quickly offset 
by other investors buying, so the forces of supply and demand go back and forth in 
terms of their impact on price. But neither has an overwhelming advantage. This 
type of pattern is often called “a healthy correction” because the long-  term market 
trend does not change and because while one set of investors is seeking to exit, they 
are replaced by another set of investors willing to take their positions at roughly the 
same share price.

Reading 13 ■ Technical Analysis 700
3.3.2.1  Triangles  Triangle patterns  are a type of continuation pattern. They come 
in three forms, symmetrical triangles, ascending triangles, and descending triangles. 
A triangle pattern forms as the range between high and low prices narrows, visually 
forming a triangle. In old terminology, triangles were referred to as “coils” (which 
was also synonymous with “springs”) because a triangle was considered analogous to 
a spring being wound up tighter and tighter and storing energy that would at some 
point be released. In a triangle, a trendline connects the highs and a trendline connects 
the lows. As the distance between the highs and lows narrows, the trendlines meet, 
forming a triangle. In a daily price chart, a triangle pattern usually forms over a period 
of several weeks.
In an ascending triangle, as shown in Exhibit 18, the trendline connecting the high 
prices is horizontal and the trendline connecting the low prices forms an uptrend.

What this pattern means is that market participants are selling the stock at the same 
price level over a period of time, putting a halt to rallies at the same price point, but 
that buyers are getting more and more bullish and stepping in at increasingly higher 
prices to halt sell-  offs instead of waiting for further price declines. An ascending 
triangle typically forms in an uptrend. The horizontal line represents sellers taking 
profits at around the same price point, presumably because they believe that this 
price represents the fundamental, intrinsic value of the security. The fact that the rally 
continues beyond the triangle may be a bullish signal; it means that another set of 
investors is presumably willing to buy at an even higher price because their analysis 
suggests the intrinsic value of the security is higher. Alternatively, the fundamental 
facts themselves may have changed; that is, the security’s fundamental value may

be increasing over time. The technician does not care which explanation is true; the 
technician is relying solely on the information conveyed by the security price itself, 
not the underlying reason.
Exhibit 18   Ascending Triangle Pattern
In the descending triangle, shown in Exhibit 19, the low prices form a horizontal 
trendline and the high prices form a series of lower and lower highs. Typically, a 
descending triangle will form in a downtrend. At some point in the sell-  offs, buyers 
appear with enough demand to halt sell-  offs each time they occur, at around the same 
price. Again, this phenomenon may be the result of fundamental analysts believing 
that the security has reached a price where it represents a significant discount to its 
intrinsic value and these analysts step in and buy. As the triangle forms, each rally 
ceases at a lower and lower high price point, suggesting the selling demand is exerting 
greater price influence than buying demand.

Technical Analysis Tools 701
Exhibit 19   Descending Triangle
In a symmetrical triangle, the trendline formed by the highs angles down and the 
trendline formed by the lows angles up, both at roughly the same angle, forming a 
symmetrical pattern. Exhibit 20 contains a symmetrical triangle formed by the price 
for Transocean in early 2000. What this triangle indicates is that buyers are becoming 
more bullish while, simultaneously, sellers are becoming more bearish, so they are 
moving toward a point of consensus. Because the sellers are often dominated by long 
investors exiting positions (as opposed to short sellers creating new short positions), 
the pressure to sell diminishes once the sellers have sold the security. Thus, the pattern 
ends in the same direction as the trend that preceded it, either uptrend or downtrend.
Exhibit 20   Symmetrical Triangle Pattern: Transocean Weekly Price Chart, 
June 1999–June 2000 (Price in US Dollars) 
Measuring
Implication =
Height of triangle

Measuring
at formation Shares expected
to rise by at least
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The term “measuring implication” refers to the height of a triangle, as illustrated 
with a dark vertical bar in Exhibit 20. The measuring implication is derived by cal -
culating the difference in price from the two trendlines at the start of the triangle.

Reading 13 ■ Technical Analysis 702
Once the pattern is broken and the price breaks through one of the trendlines that 
form the triangle, the analyst expects the price to move by at least the amount of the 
breakthrough above or below the trendline. Typically, price breaks out of a triangle 
pattern between halfway and three-  quarters of the way through the pattern. The 
longer the triangle pattern persists, the more volatile and sustained the subsequent 
price movement is likely to be.
3.3.2.2  Rectangle Pattern  A rectangle pattern is a continuation pattern formed by 
two parallel trendlines, one formed by connecting the high prices during the pattern, 
and the other formed by the lows. Exhibit 21 shows two rectangle patterns. As is the 
case with other patterns, the rectangle pattern is a graphical representation of what 
has been occurring in terms of collective market sentiment. The horizontal resistance 
line that forms the top of the rectangle shows that investors are repeatedly selling

shares at a specific price level, bringing rallies to an end. The horizontal support line 
forming the bottom of the rectangle indicates that traders are repeatedly making large 
enough purchases at the same price level to reverse declines. The support level in a 
bullish rectangle is natural because the long-  term trend in the market is bullish. The 
resistance line may simply represent investors taking profits. Conversely, in a bearish 
rectangle, the support level may represent investors buying the security. Again, the 
technician is not concerned with why a pattern has formed, only with the likely next 
price movement once the price breaks out of the pattern.
Exhibit 21   Rectangle Patterns
Bearish Rectangle Bullish Rectangle
3.3.2.3  Flags and Pennants  Flags  and pennants  are considered minor continu -
ation patterns because they form over short periods of time—on a daily price chart, 
typically over a week. They are similar to each other and have the same uses. A flag is

formed by parallel trendlines, in the same way that most countries’ flags are rectangu -
lar and create a parallelogram. Typically, the trendlines slope in a direction opposite 
to the trend up to that time; for example, in an uptrend, they slope down. A pennant 
formation is similar except that the trendlines converge to form a triangle, similar to 
the pennants of many sports teams or pennants flown on ships. The key difference 
between a triangle and pennant is that a pennant is a short-  term formation whereas a 
triangle is a long-  term formation.

Technical Analysis Tools 703
The expectation for both flags and pennants is that the trend will continue after the 
pattern in the same direction it was going prior to the pattern. The price is expected 
to change by at least the same amount as the price change from the start of the trend 
to the formation of the flag or pennant. In Exhibit 22, a downtrend begins at point 
A, which is $104. At point B, which is $70, a pennant begins to form. The distance 
from point A to point B is $34. The pennant ends at point C, which is $76. The price 
target is $76 minus $34, which is $42, the line labeled D.
Exhibit 22   Pennant Formation: China Mobile ADR, November 2006–
July 2009 (Price in US Dollars) 
A = Downtrend starts
B =
Pennant
begins to form
D = Distance from end of pennant
 (C) minus distance from point A to point BC = Pennant completed100
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3.4 Technical Indicators

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The technical analyst uses a variety of technical indicators to supplement the infor -
mation gleaned from charts. A technical indicator is any measure based on price, 
market sentiment, or funds flow that can be used to predict changes in price. These 
indicators often have a supply-  and-  demand underpinning; that is, they measure how 
potential changes in supply and demand might affect a security’s price.
3.4.1  Price-  Based Indicators
Price-  based indicators somehow incorporate information contained in the current 
and past history of market prices. Indicators of this type range from simple (e.g., a 
moving average) to complex (e.g., a stochastic oscillator).
3.4.1.1  Moving Average  A moving average  is the average of the closing price of a 
security over a specified number of periods. Moving averages smooth out short-  term 
price fluctuations, giving the technician a clearer image of market trend. Technicians

commonly use a simple moving average, which weights each price equally in the cal -
culation of the average price. Some technicians prefer to use an exponential moving 
average (also called an exponentially smoothed moving average), which gives the 
greatest weight to recent prices while giving exponentially less weight to older prices.

Reading 13 ■ Technical Analysis 704
The number of data points included in the moving average depends on the intended 
use of the moving average. A 20-  day moving average is commonly used because a 
month contains roughly 20 trading days. Also, 60 days is commonly used because it 
represents a quarter year (three months) of trading activity.
Moving averages can be used in conjunction with a price trend or in conjunction 
with one another. Moving averages are also used to determine support and resistance.
Because a moving average is less volatile than price, this tool can be used in several 
ways. First, whether price is above or below its moving average is important. A security 
that has been trending down in price will trade below its moving average, and a security 
that has been trending up will trade above its moving average. Second, the distance 
between the moving-  average line and price is also significant. Once price begins to

move back up toward its moving-  average line, this line can serve as a resistance level. 
The 65-  day moving-  average line is commonly cited in the press, and when the price 
approaches the moving-  average line, many investors become concerned that a rally 
will stall, so they sell the security.
Two or more moving averages can be used in conjunction. Exhibit 23 shows the 
price chart of Gazprom SP European Depositary Receipts (EDRs) on the Frankfurt 
Stock Exchange overlaid with 20-  day and 60-  day EDR moving averages for late 2007 
to mid-  2009.5 Note that the longer the time frame used in the creation of a moving 
average, the smoother and less volatile the line. Investors often use moving-  average 
crossovers as a buy or sell signal. When a short-  term moving average crosses from 
underneath a longer-  term average, this movement is considered bullish and is termed 
a golden cross . Conversely, when a short-  term moving average crosses from above

a longer-  term moving average, this movement is considered bearish and is called a 
dead cross . In the case shown in Exhibit 23, a trading strategy of buying on golden 
crosses and selling on dead crosses would have been profitable.
Exhibit 23   Daily Price Chart with 20-  Day and 60-  Day Moving Averages: 
Gazprom EDR, November 2007–August 2009 (Price in Euros) 
60-day moving average: not e  
how it is  smoother than  the
20-day moving averag e   
20-day moving average:
note how it is  more volatile 
than the 60-day moving averag eDead Cros s
Golden Cros s40
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5 A European Depositary Receipt is a negotiable certificate issued by a depositary bank in one country 
against equity that is traded on the stock exchange of another country.

Technical Analysis Tools 705
Moving averages are easy to construct, and simple trading rules can be derived 
for using them. Computers can optimize what time lengths to set when using two 
moving averages. This optimization may take the form of changing the number of 
days included in each moving average or adding filter rules, such as waiting several 
days after a trade signal is given to make a trade. Reasons for optimization include 
the desire to manage capital drawdowns, to maximize gains, or to minimize losses. 
Once the moving average is optimized, even if a profitable trading system is devised 
for that security, the strategy is unlikely to work for other securities, especially if they 
are dissimilar. Also, as market conditions change, a previously optimized trading 
system may no longer work.
3.4.1.2  Bollinger Bands  Market veteran John Bollinger combined his knowledge of 
technical analysis with his knowledge of statistics to create an indicator called Bollinger

Bands . Bollinger Bands consist of a moving average plus a higher line representing the 
moving average plus a set number of standard deviations from average price (for the 
same number of periods as used to calculate the moving average) and a lower line that 
is a moving average minus the same number of standard deviations. Exhibit 24 depicts 
Bollinger Bands for the Gazprom EDR.
Exhibit 24   Bollinger Band Using 60-  Day Moving Average and Two Standard 
Deviations: Gazprom EDR Daily Price Chart, November 2007–
August 2009 (Price in Euros) 
60-day moving averag e  
60-day moving average plus
two standard deviations
60-day moving average minus  
two standard deviations45
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The more volatile the security being analyzed becomes, the wider the range becomes 
between the two outer lines or bands. Similar to moving averages, Bollinger Bands 
can be used to create trading strategies that can be easily computerized and tested.

A common use is as a contrarian strategy, in which the investor sells when a security 
price reaches the upper band and buys when it reaches the lower band. This strategy 
assumes that the security price will stay within the bands.
This type of strategy is likely to lead to a large number of trades, but it also limits 
risk because the trader can quickly exit unprofitable trades. In the event of a sharp 
price move and a change in trend, however, a contrarian strategy based on Bollinger 
Bands would be unprofitable. So, long-  term investors might actually buy on a significant 
breakout above the upper boundary band because a major breakout would imply a

Reading 13 ■ Technical Analysis 706
change in trend likely to persist for some time. The long-  term investor would sell on 
a significant breakout below the lower band. In this strategy, significance would be 
defined as breaking above or below the band by a certain percentage (say, 5 percent 
or 10 percent) and/or for a certain period of time (say, a week for a daily price chart). 
Again, such rules can easily be computerized and tested.
3.4.2  Momentum Oscillators
One of the key challenges in using indicators overlaid on a price chart is the difficulty 
of discerning changes in market sentiment that are out of the ordinary. Momentum 
oscillators  are intended to alleviate this problem. They are constructed from price 
data, but they are calculated so that they either oscillate between a high and low 
(typically 0 and 100) or oscillate around a number (such as 0 or 100). Because of this 
construction, extreme highs or lows are easily discernible. These extremes can be

viewed as graphic representations of market sentiment when selling or buying activity 
is more aggressive than historically typical. Because they are price based, momentum 
oscillators also can be analyzed by using the same tools technicians use to analyze 
price, such as the concepts of trend, support, and resistance.
Technicians also look for convergence  or divergence  between oscillators and 
price. Convergence is when the oscillator moves in the same manner as the security 
being analyzed, and divergence is when the oscillator moves differently from the 
security. For example, when price reaches a new high, this sign is considered bullish, 
but if the momentum oscillator being used does not also reach a new high at the same 
time, this pattern is divergence. It is considered to be an early warning of weakness, 
an indication that the uptrend may soon end.
Momentum oscillators should be used in conjunction with an understanding of

the existing market (price) trend. Oscillators alert a trader to overbought  or oversold  
conditions. In an overbought condition, market sentiment is unsustainably bullish. 
In an oversold condition, market sentiment is unsustainably bearish. In other words, 
the oscillator range  must be considered separately for every security. Some securities 
may experience wide variations, and others may experience only minor variations.
Oscillators have three main uses. First, oscillators can be used to determine the 
strength of a trend. Extreme overbought levels are warning signals for uptrends, and 
extreme oversold levels are warning signals for downtrends. Second, when oscillators 
reach historically high or low levels, they may be signaling a pending trend reversal. 
For oscillators that move above and below 0, crossing the 0 level signals a change in 
the direction of the trend. For oscillators that move above and below 100, crossing

the 100 level signals a change in the direction of the trend. Third, in a non-  trending 
market, oscillators can be used for short-  term trading decisions—that is, to sell at 
overbought levels and to buy at oversold levels.
3.4.2.1  Momentum or Rate of Change Oscillator  The terms momentum oscillator  
and rate of change oscillator  are synonymous. “Rate of change” is often abbreviated 
ROC. The ROC oscillator is calculated by taking the most recent closing price, sub -
tracting the closing price from a prior date that is a set number of days in the past, and 
multiplying the result by 100:
M = (V – Vx) × 100
where
 M = momentum oscillator value
 V = last closing price
 Vx = closing price x days ago, typically 10 days

Technical Analysis Tools 707
When the ROC oscillator crosses zero in the same direction as the direction of 
the trend, this movement is considered a buy or sell signal. For example, if the ROC 
oscillator crosses into positive territory during an uptrend, it is a buy signal. If it enters 
into negative territory during a downtrend, it is considered a sell signal. The technician 
will ignore crossovers in opposition to the trend because the technician must always  
first take into account the general trend when using oscillators.
An alternative method of constructing this oscillator is to set it so that it oscillates 
above and below 100, instead of 0, as follows:
MV
Vx=× 100
This approach is shown in Exhibit 25 for Toyota Motor Corporation.
Exhibit 25   Momentum Oscillator with 100 as Midpoint: Toyota Motor, 
May 2008–October 2009 (Price in Japanese Y en) 
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In Exhibit 25, the calculation method for the ROC oscillator for Toyota stock, 
traded on the Tokyo Stock Exchange, is for the oscillator to move around 100 and 
x is 12 days. Note that for this stock, the ROC oscillator tends to maintain a range 
between ¥85 and ¥115. So episodes when the oscillator moves outside this range are 
of particular interest to the technician. An extreme high means that the stock has 
posted its highest gain in any 12-  day period at this point, and an extreme low reading 
means it has posted its greatest loss over any 12-  day period. When investors bid up 
the price of a security too rapidly, the indication is that sentiment may be unduly 
bullish and the market may be overbought. Exhibit 25 shows that overbought levels of 
the ROC oscillator coincide with temporary highs in the stock price. So, those levels 
would have been signals to sell the stock. The other notable aspect of Exhibit 25 is

the divergence when the share price hit a new low in December 2008 but the ROC

Reading 13 ■ Technical Analysis 708
oscillator did not. This divergence would have been a bullish signal and would have 
been interpreted to mean that, although the share price hit a new low, investor senti -
ment was actually higher than it had been previously. In itself, this information would 
not have been enough to warrant buying the shares because a downtrend in price was 
still in place, but it alerted the technician to the fact that the trend might end soon. 
The technician could then look for further indication of the trend’s end and, with 
confirmation, might buy the stock.
3.4.2.2  Relative Strength Index  A relative strength index  (RSI) is computed over 
a rolling time period.6 It graphically compares a security’s gains with its losses over the 
set period. The creator of the RSI, Welles Wilder, suggested a 14-  day time period, and 
this period is generally the period used in most technical analysis software. The tech -

nician should understand that this variable can be changed and that the optimal time 
range should be determined by how the technician intends to use the RSI information. 
Factors that influence selection of the time period are similar to those that influence 
the selection of a time period for moving averages. Short time periods (such as 14 
days) provide information about short-  term price behavior. If 200 days is used, this 
short-  term information will be smoothed out and, perhaps, will not be apparent at all.
RSI is a momentum oscillator and is not to be confused with the charting method 
called “relative strength analysis, ” in which the ratio of two security prices is plotted 
over time. The RSI provides information on whether or not an asset is overbought. 
The formula for the RSI is not intuitive and is best understood with an example. The 
formula is:
RSIRS=−+100100
1
where Up changes for the period under consideratio n
DRS=()∑
oown changes for the period under consideratio n ()∑

Exhibit 26 shows closing prices for Ford Motor Company during the month of 
June 2009.
Exhibit 26   Computation of RSI: Ford, June 2009
Date Close Up Changes Down Changes
6/1/2009 6.13
6/2/2009 6.41 0.28
6/3/2009 6.18 −0.23
6/4/2009 6.36 0.18
6/5/2009 6.36
6/8/2009 6.38 0.02
6/9/2009 6.26 −0.12
6/10/2009 6.19 −0.07
6/11/2009 5.98 −0.21
6/12/2009 6.11 0.13
6/15/2009 5.93 −0.18
6/16/2009 5.67 −0.26
6 This indicator is sometimes called the Wilder RSI.

Technical Analysis Tools 709
6/17/2009 5.71 0.04
6/18/2009 5.68 −0.03
6/19/2009 5.72 0.04
6/22/2009 5.38 −0.34
6/23/2009 5.53 0.15
6/24/2009 5.63 0.10
6/25/2009 5.68 0.05
6/26/2009 5.61 −0.07
6/29/2009 5.78 0.17
6/30/2009 6.07 0.29
1.45 –1.51
During this time, markets were still rebounding from the subprime crisis; auto -
mobile company stocks were unusually volatile and, to some speculators, presented 
interesting short-  term trading opportunities. Suppose a trader decided to compute an 
RSI for the month of June. It would be a 22-  day RSI with 21 price changes—11 up, 9 
down, and 1 unchanged. To calculate the RSI, the trader would sum the 11 up changes, 
which sum to US$1.45. The down changes total – US$1.51; the absolute value drops 
the minus sign. The ratio of these two numbers is 0.96, so the RSI is
RSI 100=−+=− =100
10 96100 51 02 48 98...
The index construction forces the RSI to lie within 0 and 100. A value above 70

represents an overbought situation. Values below 30 suggest the asset is oversold. 
Again, as is the case with most technical tools, an analyst cannot simply learn the 
default settings and use them in every case. The 30–70 range is a good rule of thumb, 
but because the oscillator is a measure of volatility, less volatile stocks (such as util -
ities) may normally trade in a much narrower range. More volatile stocks (such as 
small-  capitalization technology stocks) may trade in a wider range. The range also 
does not have to be symmetrical around 50. For example, in an uptrend, one might 
see a range of 40–80 but in downtrends, a range of 20–60.
The RSI measure often appears at the bottom or top of a price chart. Exhibit 27 
shows a candlestick chart of Ford stock in 2009 with the corresponding RSI.Exhibit 26   (Continued)

Reading 13 ■ Technical Analysis 710
Exhibit 27   Candlestick Chart with RSI: Ford, January–August 2009  
7.5
4.5
2.56.5
3.55.5
1.5
1090
3070
50
Jan/09 May/09 Apr/09 Mar/09 Feb/09 Jun/09 Jul/09Relative Strength Index
The candlestick chart of Ford stock prices in Exhibit 27 illustrates several aspects 
of the use of an RSI. For example, because the RSI oscillator was higher than 70 on 23 
March so the stock was overbought at that time, a simple reading of the chart might 
have led to the conclusion that the trader should sell the stock. Doing so, however, 
would have caused the trader to miss a significant advance in the shares. A more 
careful technical analysis that took into account the trend would have indicated that 
the stock was in an uptrend, so RSI readings above 70 could be expected.
Because RSI is a price-  based oscillator, the trader can also apply trend lines to 
analyze it. Note in Exhibit 27 that both the share price and the RSI oscillator were in

uptrends from February until April but that the RSI uptrend was broken on 15 April, 
a potential warning that the uptrend in price might also break downward. In June, 
the share price broke its uptrend support line.
3.4.2.3  Stochastic Oscillator  The stochastic oscillator is based on the observation 
that in uptrends, prices tend to close at or near the high end of their recent range and 
in downtrends, they tend to close near the low end. The logic behind these patterns 
is that if the shares of a stock are constantly being bid up during the day but then lose 
value by the close, continuation of the rally is doubtful. If sellers have enough supply 
to overwhelm buyers, the rally is suspect. If a stock rallies during the day and is able 
to hold on to some or most of those gains by the close, that sign is bullish.
The stochastic oscillator oscillates between 0 and 100 and has a default setting 
of a 14-  day period, which, again, might be adjusted for the situation as we discussed

for the RSI. The oscillator is composed of two lines, called %K and %D, that are cal -
culated as follows:
%K 100=−
−

CL
HL14
14 14
where
 C = latest closing price
 L14 = lowest price in past 14 days
 H14 = highest price in past 14 days
 %D = average of the last three %K values calculated daily

Technical Analysis Tools 711
Analysts should think about the %D in the same way they would a long-  term 
moving-  average line in conjunction with a short-  term line. That is, %D, because it 
is the average of three %K values, is the slower moving, smoother line and is called 
the signal line. And %K is the faster moving line. The %K value means that the latest 
closing price ( C) was in the %K percentile of the high–low range ( L14 to H14).
The default oversold–overbought range for the stochastic oscillator is based on 
reading the signal line relative to readings of 20 and 80, but warnings about always 
using the default range for the RSI oscillator also apply in the case of the stochastic 
oscillator. In fact, noted technician Constance Brown has coined a term called the 
“stochastics default club” to refer to neophyte technicians who trade based solely on 
these defaults.7 She has reported being able to develop successful trading strategies by

using a time frame shorter than the 14-  day default to calculate the stochastic oscillator. 
Apparently, enough traders are basing trades on the defaults to move the market for 
certain stocks. So, using shorter time frames than the default, she could trade ahead 
of the traders in the default stochastic club and generate a profit. Of course, other 
traders might be tempted to use an even shorter time frame, but there is a drawback 
to using a short time frame; namely, the shorter the time frame is, the more volatile 
the oscillator becomes and the more false signals it generates.
The stochastic oscillator should be used with other technical tools, such as trend 
analysis or pattern analysis. If both methods suggest the same conclusion, the trader 
has convergence (or confirmation), but if they give conflicting signals, the trader has 
divergence, which is a warning signal suggesting that further analysis is necessary.

The absolute level of the two lines should be considered in light of their normal 
range. Movements above this range indicate to a technician an overbought security 
and are considered bearish; movements below this range indicate an oversold security 
and are considered bullish. Crossovers of the two lines can also give trading signals the 
same way crossovers of two moving averages give signals. When the %K moves from 
below the %D line to above it, this move is considered a bullish short-  term trading 
signal; conversely, when %K moves from above the %D line to below it, this pattern is 
considered bearish. In practice, a trader can use technical analysis software to adjust 
trading rules and optimize the calculation of the stochastic oscillator for a particular 
security and investment purpose (e.g., short-  term trading or long-  term investing).
The reason technicians use historical data to test their trading rules and find the

optimal parameters for each security is that each security is different. The group of 
market participants actively trading differs from security to security. Just as each per -
son has a different personality, so do groups of people. In effect, the groups of active 
market participants trading each security are imparting their personality on the trading 
activity for that security. As this group changes over time, the ideal parameters for a 
particular security may change.
Exhibit 28 provides a good example of how the stochastic oscillator can be used 
together with trend analysis. The exhibit provides the weekly price chart and sto -
chastic oscillator for Petroleo Brasileiro ADRs, which are traded on the New York 
Stock Exchange, for June 2008 through June 2009. Note that during the downtrend 
on the left side of the chart the stochastic oscillator often moved below 20. Each time 
it reached 80, however, it provided a valid sell signal. When the downtrend ended in

November 2008 and an uptrend began, the stochastic oscillator was regularly moving 
above 80, but each time the %K line moved above %D, a valid buy signal was given.
7 See Brown (2012).

Reading 13 ■ Technical Analysis 712
Exhibit 28   Weekly Price Chart and Stochastic Oscillator: Petroleo Brasileiro 
ADR, June 2008–July 2009 (Price in US Dollars) 
Stochastic Oscillator75
45
1565
253555
50
200600
400
Oct
08Jun
08Aug
08Dec
08Apr
09Feb
09Jun
% K % D
3.4.2.4  Moving-  Average Convergence/Divergence Oscillator  The moving-  average 
convergence/divergence oscillator  is commonly referred to as MACD, which is pro -
nounced Mack Dee. The MACD is the difference between a short-  term and a long-  term 
moving average of the security’s price. The MACD is constructed by calculating two 
lines, the MACD line and the signal line:
■■MACD line: difference between two exponentially smoothed moving averages, 
generally 12 and 26 days.
■■Signal line: exponentially smoothed average of MACD line, generally 9 days.
The indicator oscillates around zero and has no upper or lower limit. Rather than 
using a set overbought–oversold range for MACD, the analyst compares the current

level with the historical performance of the oscillator for a particular security to 
determine when a security is out of its normal sentiment range.
MACD is used in technical analysis in three ways. The first is to note crossovers of 
the MACD line and the signal line, as discussed for moving averages and the stochastic 
oscillator. Crossovers of the two lines may indicate a change in trend. The second is to 
look for times when the MACD is outside its normal range for a given security. The 
third is to use trend lines on the MACD itself. When the MACD is trending in the 
same direction as price, this pattern is convergence, and when the two are trending 
in opposite directions, the pattern is divergence.
Exhibit 29 shows a daily price chart of Exxon Mobil (at the top) with the MACD 
oscillator for March through October of 2005. Note the convergence in the bottoming 
of both the oscillator and price in May, which provided confirmation of a change in

trend. This change was further confirmed by the MACD line crossing above the signal 
line. A bearish signal was given in September with the change in trend of both price 
and the oscillator and the crossover of the signal line by the MACD line. The fact that 
the MACD oscillator was moving up to a level that was unusually high for this stock 
would have been an early warning signal in September.

Technical Analysis Tools 713
Exhibit 29   MACD and Daily Price Chart: Exxon Mobil,  
March–November 2005 (Price in US Dollars) 
66
64
58
5462
5660
52
_11
0
l u J Mar Jun May Apr Aug Sep OctMACD
MACD Line
Signal Line
3.4.3  Sentiment Indicators
Sentiment indicators attempt to gauge investor activity for signs of increasing bull -
ishness or bearishness. Sentiment indicators come in two forms—investor polls and 
calculated statistical indexes.
3.4.3.1  Opinion Polls  A wide range of services conduct periodic polls of either 
individual investors or investment professionals to gauge their sentiment about the 
equity market. The most common of the polls are the Investors Intelligence Advisors 
Sentiment reports, Market Vane Bullish Consensus, Consensus Bullish Sentiment Index, 
and Daily Sentiment Index, all of which poll investment professionals, and reports of the 
American Association of Individual Investors (AAII), which polls individual investors.

All but the AAII survey are subscription-  based services. Barron’s  magazine publishes 
data from four of these surveys on a weekly basis.
By regularly polling, compiling these data over time, and presenting it graphically, 
these services provide technicians with an analyzable snapshot of investor sentiment 
over time. Technicians look at prior market activity and compare it with highs or 
lows in sentiment, as well as inflection points in sentiment, as a gauge when they are 
forecasting the future direction of the market.
The most widely used investor polls are all US-  based. One reason is that inter -
pretation of the surveys is determined by comparing the survey results with market 
performance over time. To gauge a survey’s usefulness in predicting major market 
turns, the survey must have been published over several cycles, and each of the surveys 
mentioned here, based on US data, has been available for several decades.

3.4.3.2  Calculated Statistical Indexes  The other category of sentiment indicators are 
indicators that are calculated from market data, such as security prices. The two most 
commonly used are derived from the options market; they are the put/call ratio and 
the volatility index. Additionally, many analysts look at margin debt and short interest.
The put/call ratio  is the volume of put options traded divided by the volume 
of call options traded for a particular financial instrument. Investors who buy put 
options on a security are presumably bearish, and investors who buy call options are

Reading 13 ■ Technical Analysis 714
presumably bullish. The volume in call options is greater than the volume traded in put 
options over time, so the put/call ratio is normally below 1.0. The ratio is considered 
to be a contrarian indicator, meaning that higher values are considered bearish and 
lower values are considered bullish. But, its usefulness as a contrarian indicator is 
limited except at extreme low or high levels in relation to the historical trading level 
of the put/call ratio for a particular financial instrument. The actual value of the put/
call ratio, and its normal range, differs for each security or market, so no standard 
definitions of overbought or oversold levels exist. At extreme lows where call option 
volume is significantly greater than put option volume, market sentiment is said to 
be so overly positive that a correction is likely. At extreme highs in the put/call ratio, 
market sentiment is said to be so extremely negative that an increase in price is likely.

The CBOE Volatility Index  (VIX) is a measure of near-  term market volatility cal -
culated by the Chicago Board Options Exchange. Since 2003, it has been calculated 
from option prices on the stocks in the S&P 500. The VIX rises when market partici -
pants become fearful of an impending market decline. These participants then bid up 
the price of puts, and the result is an increase in the VIX level. Technicians use the 
VIX in conjunction with trend, pattern, or oscillator tools, and it is interpreted from 
a contrarian perspective. When other indicators suggest that the market is oversold 
and the VIX is at an extreme high, this combination is considered bullish. Exhibit 30 
shows the VIX from March 2005 to December 2009.
Exhibit 30   VIX, March 2005–December 2009
100
90
80
70
50
3060
40
20
10
0
Mar
05Sep
05Mar
06Sep
06Mar
07Sep
07Mar
08Sep
08Mar
09Sep
09
Margin debt is also often used as an indication of sentiment. As a group, investors

have a history of buying near market tops and selling at the bottom. When the market 
is rising and indexes reach new highs, investors are motivated to buy more equities in 
the hope of participating in the market rally. A margin account permits an investor 
to borrow part of the investment cost from the brokerage firm. This debt magnifies 
the gains or losses resulting from the investment.
Investor psychology plays an important role in the intuition behind margin debt 
as an indicator. When stock margin debt is increasing, investors are aggressively buy -
ing and stock prices will move higher because of increased demand. Eventually, the 
margin traders use all of their available credit, so their buying power (and, therefore, 
demand) decreases, which fuels a price decline. Falling prices may trigger margin calls 
and forced selling, thereby driving prices even lower.

Technical Analysis Tools 715
Brokerage firms must report activity in their customers’ margin accounts, so keeping 
track of borrowing behavior is relatively easy. Exhibit 31 provides a 10-  year comparison 
of margin debt with the S&P 500. The correlation is striking: Rising margin debt is 
generally associated with a rising index level, and falling margin debt is associated with 
a falling index level. In fact, for the 113 months shown in Exhibit 31, the correlation 
coefficient between the levels of margin debt and the S&P 500 is 80.2 percent. When 
margin debt peaked in the summer of 2007, the market also topped out. Margin debt 
dropped sharply during the latter part of 2008 as the subprime crisis took the market 
down. Investors began to use borrowed funds again in the first half of 2009 when 
heavily discounted shares became increasingly attractive. Margin debt was still well 
below the average of the last decade, but the upturn would be viewed as a bullish sign

by advocates of this indicator.
Exhibit 31   Margin Debt in US Markets vs. S&P 500, 2000–2009
Margin Debt ($ millions)
S&P 500450,000
400,000
350,000
300,000
250,000
200,000
150,000
100,000
50,000
0
03 05 02 01 00S&P 500
1,800
1,600
1,400
1,200
1,000
800
600
400
200
0
07 04 06 08 09
Source:  New York Stock Exchange Fact Book.
Short interest is another commonly used sentiment indicator. Investors sell shares 
short when they believe the share prices will decline. Brokerage firms must report 
short-  sale activity, and these statistics are aggregated and reported by the exchanges 
and the financial press on a monthly basis. The number of shares of a particular 
security that are currently sold short is called “short interest. ” The short interest ratio 
represents the number of days of trading activity represented by short interest. To 
facilitate comparisons of large and small companies, common practice is to “normal -
ize” this value by dividing short interest by average daily trading volume to get the

short interest ratio:
Short interest ratio = Short interest/Average daily trading volume

Reading 13 ■ Technical Analysis 716
EXAMPLE 3   
Short Interest Ratio
At the end of September 2009, Barron’s  reported short interest of 10,936,467 
shares in Goldman Sachs, with average daily trading volume of 9,086,174. At 
the same time, the short interest in TD Bank was 20,420,166 on average trading 
volume of 1,183,558 shares. Calculate the short interest ratio for both firms.
Solution:
The short interest ratio for Goldman Sachs was 10,936,467 divided by 9,086,174, 
or 1.2 days. For TD Bank, the short interest ratio was 20,420,166 divided by 
1,183,558, or 17.25 days.
There are differences of opinion about how to interpret short interest as an indica -
tor. It is considered to show market sentiment and to be a contrarian indicator. Some 
people believe that if a large number of shares are sold short and the short interest 
ratio is high, the market should expect a falling price for the shares because of so 
much negative sentiment about them. A counter-  argument is that, although the short

sellers are bearish on the security, the effect of their short sales has already been felt 
in the security price. The short sellers’ next action will be to buy shares back to cover 
their short positions. When the short sellers cover their positions, those actions will 
provide a boost to the share price. Therefore, the short interest ratio constitutes future 
(and known) demand for the shares.
Regardless of the analyst’s perspective, in Example 3, the TD Bank short interest 
ratio of approximately 17 is more noteworthy than the much lower figure for Goldman 
Sachs.
3.4.4  Flow-  of- Funds Indicators
Technicians look at fund flows as a way to gauge the potential supply and demand for 
equities. Demand can come in the form of margin borrowing against current holdings 
or cash holdings by mutual funds and other groups that are normally large holders 
of equities, such as insurance companies and pension funds. The more cash these

groups hold, the more bullish is the indication for equities. One caveat in looking at 
potential sources of demand is that, although these data indicate the potential buying 
power of various large investor groups, the data say nothing about the likelihood that 
the groups will buy.
On the supply side, technicians look at new or secondary issuance of stock because 
these activities put more securities into the market and increase supply.
3.4.4.1  Arms Index  A common flow of funds indicator is the Arms Index , also called 
the TRIN  (for “short-  term trading index”).8 This indicator is applied to a broad market 
(such as the S&P 500) to measure the relative extent to which money is moving into 
or out of rising and declining stocks. The index is a ratio of two ratios:
Arms IndexNumber of adv ancing issues Number of declining =÷ iissues
Volume of adv ancing issues Volume of declining issu ÷ ees
When this index is near 1.0, the market is in balance; that is, as much money

is moving into rising stocks as into declining stocks. A value above 1.0 means that 
there is more volume in declining stocks; a value below 1.0 means that most trading 
activity is in rising stocks. Exhibit 32 shows the Arms Index for the S&P 500 on a 
8 This tool was first proposed by Richard W. Arms, Jr., a well-  known technical analyst.

Technical Analysis Tools 717
daily basis for the first six months of 2009. The majority of the points lie above the 
1.0 level, suggesting that the market continued to be in a selling mood. Note that the 
up spikes are associated with large price decreases in the index level and the down 
spikes reflect the opposite. The trendline shows a slightly negative slope, providing 
some slight encouragement for the bulls.
Exhibit 32   Arms Index for the S&P 500, January–July 2009
Index Value
S&P 500
down 4.91%
S&P 500
down 2.38%S&P 500
down 4.26%S&P 500
down 5.28% S&P 500
down 4.66%
S&P 500 up 3.11% S&P 500 up 7.08% S&P 500 up 3.39%7
56
4
3
2
1
0
2/Jan/09 30/Jan/09 27/Feb/09 27/Mar/09 24/Apr/09 22/May/09 19/Jun/09
EXAMPLE 4   
TRIN Indicator
Sarah Johannson, CFA, recently installed some investment software and is veri -
fying the calculation of some of the statistics it produces. Her screen indicates a 
TRIN value of 1.02 for the NYSE and 1.80 for the NASDAQ market. These values

seem to be unusually far apart to her, and she wonders whether they are both 
real-  time statistics like the other market price data. To check whether they are 
real-  time statistics, a few minutes later, she simultaneously captures the TRIN 
from her software display (slightly changed to 1.01 for the NYSE and 1.81 for 
NASDAQ) and on a separate monitor, she does a screen capture of NYSE and 
NASDAQ data, as follows:
NYSE NASDAQ
Number of issues Advancing 850 937
Declining 1,982 1,472
Volume Advancing 76,921,200 156,178,475
Declining 185,461,042 441,970,884
How does Johannson recalculate and interpret the TRIN value for the NYSE 
and NASDAQ?

Reading 13 ■ Technical Analysis 718
Solution:
Johannson calculates the TRIN values for the NYSE and NASDAQ as follows:
TRIN NYS E
TRIN N() =÷ ()
÷ ()=850 1 982
76 921 200 185 461 042103,
,, ,,.
AASDAQ () =÷ ()
÷ ()=937 1 472
156 178 475 441 970 884180,
,, ,,.
Johannson concludes that her software is giving her current values and that the 
NASDAQ is having a much worse day than the NYSE.
3.4.4.2  Margin Debt  The previous section discussed the use of margin debt as an 
indicator of market sentiment. Margin debt is also widely used as a flow-  of- funds 
indicator because margin loans may increase the purchases of stocks and declining 
margin balances may force the selling of stocks.
3.4.4.3  Mutual Fund Cash Position  Mutual funds hold a substantial proportion 
of all investable assets. Some analysts use the percentage of mutual fund assets held 
in cash  as a predictor of market direction. It is called the “mutual fund cash position

indicator. ” Mutual funds must hold some of their assets in cash in order to pay bills 
and send redemption checks to account holders. Cash arrives on a daily basis from 
customer deposits, interest earned, and dividends received. Cash also increases after 
a fund manager sells a position and holds the funds before reinvesting them. During 
a bull market, the manager wants to buy shares as quickly as possible to avoid having 
a cash “drag” hurt the fund’s performance. If prices are trending lower, however, the 
manager may hold funds in cash to improve the fund’s performance.
Exhibit 33 shows year-  end mutual fund cash in the United States as a percentage 
of assets from 1984 through 2008. Over this period, the average cash percentage was 
6.8 percent. An analyst’s initial intuition might be that when cash is relatively low, fund 
managers are bullish and anticipate rising prices, but when fund managers are bear -

ish, they conserve cash to wait for lower prices. Advocates of this technical indicator 
argue exactly the opposite: When the mutual fund cash position is low, fund managers 
have already bought, and the effects of their purchases are already reflected in secu -
rity prices. When the cash position is high, however, that money represents buying 
power that will move prices higher when the money is used to add positions to the 
portfolio. The mutual fund cash position is another example of a contrarian indicator.
Exhibit 33   Mutual Fund Cash Position, 1984–2008
Percent of Assets in Cash 
Average = 6.8%12
10
8
6
4
2
0
90 96 02 86 84 92 98 88 94 00 04 06 08

Technical Analysis Tools 719
Some analysts modify the value of the cash percentage to account for differences 
in the level of interest rates. Cash is not sitting in a desk drawer; it is on deposit some -
where earning interest. When interest rates are low, holding cash can be a substantial 
drag on the fund’s performance if the broad market advances. When interest rates are 
high, holding cash is less costly.
EXAMPLE 5   
Market Indicators
At the request of a wealthy client, Erik Nielson is preparing a proprietary research 
report on the shares of a US company. He has completed the part of the report 
dealing with fundamental analysis and wants to include a section on technical 
analysis. Nielson has gathered the following information:
Company Information:
■■The 20-  day moving average of the share price just rose through the 200-  
day moving average.
■■RSI = 40.6.
Market Information:
■■TRIN = 1.9.
■■Mutual fund cash position = 7.0%
1 How should Nielson interpret each item of information?

2 Do these indicators, in the aggregate, lead Nielson to a buy, hold, or sell 
recommendation for the company’s shares?
■■Moving average: When a short-  term moving average moves above a 
longer-  term moving average, the movement is a golden cross and is a 
bullish signal.
■■RSI: An RSI of 40.6 would be considered neutral. The RSI ranges between 
0 and 100. Values greater than 70 are bearish; values below 30 are bullish.
■■TRIN: A TRIN value above 1.0 means that there is more volume in declin -
ing stocks than in advancing stocks; therefore, a value of 1.9 is bearish.
■■Mutual fund cash position: The 7.0 percent figure is near the long-  term 
average, so it is a neutral signal.
Of the four indicators, one is bullish, one is bearish, and two are neutral. Most 
analysts would view this result as “net neutral” and would recommend continuing 
to hold the stock. An alternative point of view might be that seeing a bullish

indicator for the stock while the indicator for the overall market is bearish could 
be an argument for overweighting the stock.
3.4.4.4  New Equity Issuance  When a company’s owners decide to take a company 
public and offer shares for sale, the owners want to put those shares on the market at a 
time when investors are eager to buy. That is, the owners want to offer the shares when

Reading 13 ■ Technical Analysis 720
they can sell them at a premium price. Premium prices occur near market tops. The 
new equity issuance indicator suggests that as the number of initial public offerings 
(IPOs) increases, the upward price trend may be about to turn down.
A supply-  and-  demand effect is also at work. Putting more shares on the market 
increases the aggregate supply of shares available for investors to purchase. The 
investment community has a finite quantity of cash to spend, so an increase in IPOs 
may be viewed as a bearish factor.
3.4.4.5  Secondary Offerings  Technicians also monitor secondary offerings to gauge 
potential changes in the supply of equities. Although secondary offerings do not increase 
the supply of shares, because existing shares are sold by insiders to the general public, 
they do increase the supply available for trading or the float. So, from a market perspec -
tive, secondary offerings of shares have the potential to change the supply-  and-  demand

equation as much as IPOs do.
3.5 Cycles
Over the centuries, technicians have noted recurring cycles of various frequencies in 
the capital markets. The study of cycles in the markets is part of broader cycle stud -
ies that exist in numerous fields of study. Many observed cycles, such as one in US 
equities tied to the cycle of US presidential elections, have an obvious and rational 
justification. Other cycles do not. However, why cycles in fields seemingly unrelated 
to finance, such as astronomy or weather patterns, may influence the economy (and 
thus the capital markets) may have a logical explanation. For example, sun spots affect 
weather patterns on earth, which in turn affect agriculture and, therefore, capital 
markets because they are related to agriculture.
3.5.1  Kondratieff Wave
The longest of the widely recognized cycles was identified by Nikolai Kondratieff  
in the 1920s. Kondratieff was an economist in the Soviet Union who suggested that

Western economies had a 54-  year cycle. He traced cycles from the 1780s to the time 
he published this theory in the 1920s, and the economic depression of the 1930s was 
consistent with the cycle he identified. His theory was mainly tied to economic cycles 
and commodity prices, but cycles can also be seen in the prices of equities during 
the time of his work.
Kondratieff was executed in a Soviet purge in 1938, but his ideas have come into 
widespread acceptance, particularly since his works were translated into English in 
the 1980s. Two economists at the London School of Economics, E. H. Phelps Brown 
and Sheila Hopkins, identified a 50–52 year economic cycle in the United Kingdom. 
Together with Kondratieff, credit should be given to two Dutch economists, Jacob van 
Gelderen and Samuel de Wolff, who wrote about a 50–60 year economic cycle but 
published their work earlier, in 1913. Their work came to light only recently, however,

so the long 54-  year economic cycle is known as the Kondratieff Wave  or K Wave.
3.5.2  18- Year Cycle
The 18-  year cycle is interesting because three 18-  year cycles make up the longer 54-  
year Kondratieff Wave. The 18-  year cycle is most often mentioned in connection with 
real estate prices, but it can also be found in equities and other markets.

Elliott Wave Theory 721
3.5.3  Decennial Pattern
The decennial pattern is the pattern of average stock market returns (based on the 
DJIA) broken down on the basis of the last digit in the year. Years ending with a 0 
have had the worst performance, and years ending with a 5 have been by far the 
best. The DJIA was up every year ending in a 5 from 1885 until 1995, but it declined 
0.6 percent in 2005.
3.5.4  Presidential Cycle
This cycle in the United States connects the performance of the DJIA with presidential 
elections. In this theory, years are grouped into categories on the basis of whether they 
were election years or the first, second, or third year following an election. The third 
year is the year prior to the next election. The third year shows the best performance; 
in fact, the DJIA experienced a positive return in every pre-  election year from 1943 
through 2007. One explanation for this outcome is that with so many politicians up

for re-  election, they inject stimulus into the economy in an attempt to improve their 
chances to be re-  elected.9 Election years are also usually positive years for the stock 
market, but with less consistency. Post-  election years and the so-  called midterm year 
have the worst performance.
These long cycles are important to keep in mind when using other technical analysis 
tools. However, the long cycles described here and other theories about long cycles 
present a number of problems. The primary problem is the small sample size. Only 
56 presidential elections have been held in the United States, and only 4 completed 
Kondratieff cycles have occurred in US history. Another problem is that even with 
the small number of cycles, the data do not always fit the cycle theory, and when they 
do, that fit may not be obvious.
ELLIOTT WAVE THEORY
In a theory proposed by R. N. Elliott in 1938, the market moves in regular, repeated

waves or cycles. He identified and categorized these waves and wrote in detail about 
aspects of market cycles. Elliott was an accountant by training, but in 1929, after he 
contracted a progressive intestinal illness at age 58 while working in Latin America, 
he was forced to retire. Then, he turned his attention to a detailed study of equity 
prices in the United States.
A decade later, in 1938, he published his findings in a book titled The Wave Principle . 
In developing the concept that the market moves in waves, Elliott relied heavily on 
Charles Dow’s early work. Elliott described how the market moved in a pattern of five 
waves moving up in a bull market in the following pattern: 1 = up, 2 = down, 3 = up, 
4 = down and 5 = up. He called this wave the “impulse wave. ” The impulse wave was 
followed by a corrective wave with three components: a = down, b = up and c = down.
When the market is a bear market, as defined in Dow Theory—that is, with both

of Dow’s major indices in bear markets—the downward movements are impulse waves 
and are broken into five waves with upward corrections broken into three subwaves.
Elliott also noted that each wave could be broken down into smaller and smaller 
subwaves.4
9 In US presidential election years, the vice presidency, all 435 House of Representatives seats, and 33 of 
the 100 Senate seats are also up for election.

Reading 13 ■ Technical Analysis 722
The longest of the waves is called the “grand supercycle” and takes place over 
centuries. Elliott traced grand supercycles back to the founding of the United States, 
and his successors have continued his work. Each grand supercycle can be broken 
down into subcycles until ending with the “subminuette, ” which unfolds over several 
minutes. The major cycles are:
■■Grand supercycle
■■Supercycle
■■Cycle
■■Primary
■■Intermediate
■■Minor
■■Minute
■■Minuette
■■Subminuette
An important aspect of Elliott’s work is that he discovered that market waves 
follow patterns that are ratios of the numbers in the Fibonacci sequence . Leonardo 
Fibonacci was an 11th century Italian mathematician who explained this sequence in 
his book Liber Abaci , but the sequence was known to mathematicians as far back as 
200 BCE in India. The Fibonacci sequence starts with the numbers 0, 1, 1, and then 
each subsequent number in the sequence is the sum of the two preceding numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34 … 
Elliott was more interested in the ratios of the numbers in the sequence because 
he found that the ratio of the size of subsequent waves was generally a Fibonacci 
ratio. The ratios of one Fibonacci number to the next that Elliott considered most 
important are the following:
1/2 = 0.50, 2/3 = 0.6667, 3/5 = 0.6, 5/8 = 0.625, 8/13 = 0.6154
He also noticed that the ratio of a Fibonacci sequence number to its preceding 
number is important:
2/1 = 2, 3/2 = 1.5, 5/3 = 1.6667, 8/5 = 1.600, 13/8 = 1.6250
These ratios converge around 1.618. In mathematics, 1.618 is called the “golden 
ratio, ” and it can be found throughout nature—in astronomy, biology, botany, and 
many other fields. It is also widely used in art and architecture. The ancient Egyptians 
built the pyramids on the basis of this ratio, and the ancient Greeks used it widely.
As noted, Elliott numbered the impulse waves 1–5 and the corrective waves, a, b

and c. Exhibit 34 depicts the impulse and corrective waves in a bull market.

Elliott Wave Theory 723
Exhibit 34   Impulse Waves and Corrective Waves
213
45
ab
cImpulse
(Numbered)
Phase
Wave 1Wave 3Wave 2Wave 4Wave a
Wave cWave 5 Wave bCorrective
(Lettered)
Phase
Elliott described the characteristics of each wave. Note the following, as shown 
in Exhibit 34:
■■Wave 1 starts as a basing pattern and displays an increase in price, volume, and 
breadth.10 Wave 1 consists of five smaller waves.
■■Wave 2 moves down, retracing much of the gain in Wave 1 but not all of it. 
Common percentage retracements are Fibonacci ratios, such as 50 percent or 
62 percent. Wave 2 never erases all of the gains from Wave 1. Wave 2 consists 
of three smaller waves.
■■Wave 3 moves above the high of the first wave and has strong breadth, vol -
ume, and price movement. Most of the price movement in an uptrend typically 
occurs in Wave 3. Wave 3 consists of five smaller waves. Wave 3 often moves 
prices 1.618 times higher than the length of Wave 1, which is a Fibonacci ratio.

■■Wave 4 is, again, a correction, and the ratio of the change in price during this 
wave to the price change during the third wave is also generally a Fibonacci 
ratio. Wave 4 commonly reverses 38 percent of the gain in Wave 3. Wave 5 is 
also an up wave. Generally, the price movement in Wave 5 is not as great as that 
in Wave 3. The exception to the rule is that Wave 5 may become extended, as 
when euphoria overtakes the market. Wave 5 consists of five smaller waves.
After Wave 5 is completed, the market traces out a series of three corrective waves, 
labeled a, b and c in Exhibit 34.
■■Wave a is a down wave in a bull market; Wave a itself breaks down into three 
waves.
■■Wave b is an upward movement and breaks down into five waves. Wave b is a 
false rally and is often called a “bull trap. ”
■■Wave c is the final corrective wave. In a bull market, it does not move below the 
start of the prior Wave 1 pattern. Wave c breaks down into three subwaves.

10 Breadth is defined as the ratio of the number of advancing securities in an index or traded on a given 
stock market to the number of declining issues.

Reading 13 ■ Technical Analysis 724
This description of the waves applies to bull markets; in bear markets, the impulse 
waves are labeled A through E and the corrective waves are labeled 1, 2, and 3. Waves 
in the direction of the trend consist of five subwaves, and counter-  waves consist of 
three subwaves.
In practice, a good deal of time is required to become proficient with Elliott Wave 
Theory . Wave counts may not become evident at first, and Elliotticians often have to 
renumber their wave counts on the basis of changes in market trends. This theory is 
widely used, however, and the patterns Elliott described can still be observed today.
As a technician begins to make initial judgments on wave counts, the next step is to 
draw lines representing Fibonacci ratios on the charts. These lines alert the technician 
to the levels at which trends may change in the future and can be used in conjunction 
with other technical tools for forecasting. Positive price movements generally take

prices up by some Fibonacci ratio of prior highs (e.g., 1.5 or 1.62), and price declines 
generally reverse prices by a Fibonacci ratio (e.g., 0.50 or 0.667). Elliott Wave Theory 
is used in practice with Dow Theory, trend analysis, pattern analysis, and oscillator 
analysis to provide a sense of the general trend in the market. As Elliott’s nine cycles 
imply, Elliott Wave Theory can be applied in both very short-  term trading as well as 
in very long-  term economic analysis, as is the case with most tools used in technical 
analysis.
INTERMARKET ANALYSIS
Intermarket analysis  is a field within technical analysis that combines analysis of major 
categories of securities—namely, equities, bonds, currencies, and commodities—to 
identify market trends and possible inflections in a trend. Intermarket analysis also 
looks at industry subsectors, such as the nine sectors the S&P 500 is divided into, 
and the relationships among the major stock markets of countries with the largest

economies, such as the New York, London, and Tokyo stock exchanges.
Intermarket analysis relies heavily on the field of economic analysis for its theo -
retical underpinning. The field was pioneered by John Murphy with his 1991 book 
Intermarket Technical Analysis . Murphy noted that all markets are inter-  related and that 
these relationships are strengthening with the globalization of the world economy.11
Stock prices are affected by bond prices. High bond prices are a positive 
for stock prices since this means low interest rates. Lower interest rates 
benefit companies with lower borrowing costs and lead to higher equity 
valuations in the calculation of intrinsic value using discounted cash flow 
analysis in fundamental analysis. Thus rising bond prices are a positive for 
stock prices, and declining bond prices are a bearish indicator.
Bond prices impact commodity prices. Bond prices move inversely to 
interest rates. Interest rates move in proportion to expectations to future

prices of commodities or inflation. So declining bond prices are a signal 
of possible rising commodity prices.
Currencies impact commodity prices. Most commodity trading is 
denominated in US dollars and so prices are commonly quoted in US dollars. 
As a result, a strong dollar results in lower commodity prices and vice versa.5
11 See Murphy (1991).

Intermarket Analysis 725
In intermarket analysis, technicians often look for inflection points in one market 
as a warning sign to start looking for a change in trend in a related market. To identify 
these intermarket relationships, a commonly used tool is relative strength analysis, 
which charts the price of one security divided by the price of another.
Exhibit 35 shows the relative price of 10-  year US Treasury bonds compared with 
the S&P 500. The rise in T-  bond price relative to the S&P 500 can be clearly seen. The 
inflection point in this chart occurs in March 2009. This point would signal that the 
time had come to move investments from bonds to stocks.
Exhibit 35   Relative Strength of 10-  Y ear T-  Bonds vs. S&P 500, 
September 2008–July 2009
0.185
0.175
0.165
0.155
0.145
0.135
0.125
0.115
0.105
0.095
0.085
Sep
08Nov
08Dec
08Jan
09Oct
08Feb
09Mar
09Apr
09May
09Jun
09Jul
09
Exhibit 36 is a relative strength chart depicting the ratio between the S&P 500

and commodity prices. It shows a clear top and reversal of trend in December 2008. 
This inflection point shows US stocks weakening relative to commodities and would 
indicate that allocating funds away from the US stocks and into commodities might 

Reading 13 ■ Technical Analysis 726
Exhibit 36    S&P 500 Index vs. Commodity Prices,  
November 2007–November 2009
1.4
1.31.51.61.71.82.12.3
1.92.02.22.42.52.72.9
2.62.8
Nov
07Mar
08May
08Jul
08Jan
08Sep
08Nov
08Jan
09Mar
09Jul
09May
09Sep
09
In addition to the preceding comparisons, once an asset category has been iden -
tified, relative strength analysis can be used to identify the strongest performing 
securities in a sector. For example, if commodities look promising, an investor can 
analyze each of the major commodities relative to a broad commodity index in order 
to find the strongest commodity.
Intermarket analysis can also be used to identify sectors of the equity market to 
invest in—often in connection with technical observations of the business cycle at any 
time. The equities of certain industry sectors tend to perform best at the beginning 
of an economic cycle. These sectors include utilities, financials, consumer nondura -

bles, and transportation stocks. As an economic recovery gets under way, retailers, 
manufacturers, health care, and consumer durables tend to outperform. Lagging 
sectors include those tied to commodity prices, such as energy and basic industrial 
commodities, and also technology stocks.
Observations based on intermarket analysis can also help in allocating funds across 
national markets. Certain countries’ economies are closely tied to commodities—for 
example, Australia, Canada, and South Africa. As economies evolve, these relation -
ships change. So, the relationships must be monitored closely. 
SUMMARY
■■Technical analysis is a form of security analysis that uses price and volume mar -
ket data, often graphically displayed.
■■Technical analysis can be used for any freely traded security in the global 
market and is used on a wide range of financial instruments, such as equities, 
bonds, commodity futures, and currency futures.

Summary 727
■■Technical analysis is the study of market trends or patterns and relies on recog -
nition of patterns that have worked in the past in an attempt to predict future 
security prices. Technicians believe that market trends and patterns repeat 
themselves and are somewhat predictable because human behavior tends to 
repeat itself and is somewhat predictable.
■■Another tenet of technical analysis is that the market brings together the col -
lective wisdom of multiple participants, weights it according to the size of the 
trades they make, and allows analysts to understand this collective sentiment. 
Technical analysis relies on knowledgeable market participants putting this 
knowledge to work in the market and thereby influencing prices and volume.
■■Technical analysis and fundamental analysis are equally useful and valid, but 
they approach the market in different ways. Technical analysis focuses solely on 
analyzing markets and the trading of financial instruments, whereas fundamen -

tal analysis is a much wider ranging field encompassing financial and economic 
analysis as well as analysis of societal and political trends.
■■Technical analysis relies primarily on information gathered from market 
participants that is expressed through the interaction of price and volume. 
Fundamental analysis relies on information that is external to the market (e.g., 
economic data, company financial information) in an attempt to evaluate a 
security’s value relative to its current price.
■■The usefulness of technical analysis is diminished by any constraints on the 
security being freely traded, by large outside manipulation of the market, and in 
illiquid markets.
■■Charts provide information about past price behavior and provide a basis for 
inferences about likely future price behavior. Various types of charts can be 
useful in studying the markets: line charts, bar charts, candlestick charts, and 
point and figure charts.

■■Relative strength analysis is based on the ratio of the prices of a security to a 
benchmark and is used to compare the performance of one asset with the per -
formance of another asset.
■■Many technicians consider volume information to be very important and watch 
for the confirmation in volume of a price trend or the divergence of volume 
from a price trend.
■■The concept of trend is perhaps the most important aspect of technical analysis. 
An uptrend is defined as a security making higher highs and higher lows. To 
draw an uptrend line, a technician draws a line connecting the lows of the price 
chart. A downtrend is defined as a security making lower highs and lower lows. 
To draw a downtrend line, a technician draws a line connecting the highs of the 
price chart.
■■Support is defined as a low price range in which the price stops declining 
because of buying activity. It is the opposite of resistance, which is a price range

in which price stops rising because of selling activity.
■■Chart patterns are formations appearing in price charts that create some type of 
recognizable shape.
■■Reversal patterns signal the end of a trend. Common reversal patterns are the 
head and shoulders, the inverse head and shoulders, double tops and bottoms, 
and triple tops and bottoms.
■■Continuation patterns indicate that a market trend in place prior to the pattern 
formation will continue once the pattern is completed. Common continuation 
patterns are triangles, rectangles, flags, and pennants.

Reading 13 ■ Technical Analysis 728
Akerlof, George A., and Robert J. Shiller. 2009. Animal Spirits: 
How Human Psychology Drives the Economy, and Why It 
Matters for Global Capitalism . Princeton, NJ: Princeton 
University Press.Brown, Constance M. 2012. Technical Analysis for the Trading 
Professional , 2nd edition. McGraw-Hill.
Murphy, John J. 1991. I ntermarket Technical Analysis: Trading 
Strategies for the Global Stock, Bond, Commodity, and 
Currency Markets . John Wiley & Sons, Inc.■■Price-  based indicators incorporate information contained in market prices. 
Common price-  based indicators are the moving average and Bollinger Bands.
■■Momentum oscillator indicators are constructed from price data, but they are 
calculated so that they fluctuate either between a high and low, typically 0 and 
100, or around 0 or 100. Some examples are momentum (or rate of change) 
oscillators, the RSI, stochastic measures, and MACD.

■■Sentiment indicators attempt to gauge investor activity for signs of increasing 
bullishness or bearishness. Sentiment indicators come in two forms—inves -
tor polls and calculated statistical indexes. Opinion polls to gauge investors’ 
sentiment toward the equity market are conducted by a variety of services. 
Commonly used calculated statistical indexes are the put/call ratio, the VIX, 
margin debt, and the short interest ratio.
■■Flow-  of- funds indicators help technicians gauge potential changes in supply and 
demand for securities. Some commonly used indicators are the ARMS Index 
(also called the TRIN), margin debt (also a sentiment indicator), mutual fund 
cash positions, new equity issuance, and secondary equity offerings.
■■Many technicians use various observed cycles to predict future movements in 
security prices; these cycles include Kondratieff waves, decennial patterns, and 
the US presidential cycle.
■■Elliott Wave Theory is an approach to market forecasting that assumes that

markets form repetitive wave patterns, which are themselves composed of 
smaller and smaller subwaves. The relationships among wave heights are fre -
quently Fibonacci ratios.
■■Intermarket analysis is based on the principle that all markets are interrelated 
and influence each other. This approach involves the use of relative strength 
analysis for different groups of securities (e.g., stocks versus bonds, sectors in an 
economy, and securities from different countries) to make allocation decisions.

Practice Problems 729
1 Technical analysis relies most importantly on:
A price and volume data.
B accurate financial statements.
C fundamental analysis to confirm conclusions.
2 Which of the following is not an assumption of technical analysis?
A Security markets are efficient.
B The security under analysis is freely traded.
C Market trends and patterns tend to repeat themselves.
3 Drawbacks of technical analysis include which of the following?
A It identifies changes in trends only after the fact.
B Deviations from intrinsic value can persist for long periods.
C It usually requires detailed knowledge of the financial instrument under 
analysis.
4 Why is technical analysis especially useful in the analysis of commodities and 
currencies?
A Valuation models cannot be used to determine fundamental intrinsic value 
B Government regulators are more likely to intervene in these markets.
C These types of securities display clearer trends than equities and bonds do.

5 A daily bar chart provides:
A a logarithmically scaled horizontal axis.
B a horizontal axis that represents changes in price.
C high and low prices during the day and the day’s opening and closing prices.
6 A candlestick chart is similar to a bar chart except  that the candlestick chart:
A represents upward movements in price with X’s.
B also graphically shows the range of the period’s highs and lows.
C has a body that is light or dark depending on whether the security closed 
higher or lower than its open.
7 In analyzing a price chart, high or increasing volume most likely  indicates which 
of the following?
A Predicts a reversal in the price trend.
B Predicts that a trendless period will follow.
C Confirms a rising or declining trend in prices.
8 In constructing a chart, using a logarithmic scale on the vertical axis is likely to 
be most useful  for which of the following applications?
A The price of gold for the past 100 years.
B The share price of a company over the past month.

C Yields on 10-  year US Treasuries for the past 5 years.
9 A downtrend line is constructed by drawing a line connecting:
A the lows of the price chart.

Reading 13 ■ Technical Analysis 730
B the highs of the price chart.
C the highest high to the lowest low of the price chart.
10 Exhibit 1 depicts GreatWall Information Industry Co., Ltd., ordinary shares, 
traded on the Shenzhen Stock Exchange, for late 2008 through late 2009 in 
renminbi (RMB).
Exhibit 1   Candlestick Chart: GreatWall Information Industry Co., Ltd. Price 
Data, November 2008–September 2009  
(Price Measured in RMB × 10) 
100
8090
70
60
40
3050
Nov
08Sep
09Jul
09Aug
09Jun
09Apr
09May
09Mar
09Jan
09Dec
08Feb
09
 Based on Exhibit 1, the uptrend was most likely  broken at a price level nearest 
to:
A 7 RMB.
B 8.5 RMB.
C 10 RMB.
11 The “change in polarity” principle states which of the following?
A Once an uptrend is broken, it becomes a downtrend.
B Once a resistance level is breached, it becomes a support level.
C The short-  term moving average has crossed over the longer-  term moving 
average.
12 Exhibit 2 depicts Barclays ordinary shares, traded on the London Stock 
Exchange, for 2009 in British pence.

Practice Problems 731
Exhibit 2   Candlestick Chart: Barclays plc Price Data, January 2009–
January 2010 (Price Measured in British Pence) 
400
200300
100
0
Jan
09Nov
09Sep
09Oct
09Jan
10Dec
09Aug
09Jun
09Jul
09May
09Mar
09Feb
09Apr
09
 Based on Exhibit 2, Barclays appears to show resistance at a level nearest to:
A 50p.
B 275p.
C 390p.
13 Exhibit 3 depicts Archer Daniels Midland Company common shares, traded on 
the New York Stock Exchange, for 1996 to 2001 in US dollars.
Exhibit 3   Candlestick Chart: Archer Daniels Midland Company, 
February 1996–February 2001
21
91113151719
7
Feb
96Aug
96Feb
97Aug
97Feb
98Aug
98Feb
99Aug
99Feb
00Aug
00Feb
01
 Exhibit 3 illustrates most  clearly which type of pattern?
A Triangle.
B Triple top.
C Head and shoulders.
14 In an inverted head and shoulders pattern, if the neckline is at €100, the 
shoulders at €90, and the head at €75, the price target is closest  to which of the 
following?
A €50.
B €110.
C €125.
15 Which flow-  of- funds indicator is considered bearish for equities?

Reading 13 ■ Technical Analysis 732
A A large increase in the number of IPOs.
B Higher-  than-  average cash balances in mutual funds.
C An upturn in margin debt but one that is still below the long-  term average.
16 A TRIN with a value of less than 1.0 indicates:
A the market is in balance.
B there is more volume in rising shares.
C there is more volume in declining shares.
17 Bollinger Bands are constructed by plotting:
A a MACD line and a signal line.
B a moving-  average line with an uptrend line above and downtrend line below.
C a moving-  average line with upper and lower lines that are at a set number of 
standard deviations apart.
18 Which of the following is not a momentum oscillator?
A MACD.
B Stochastic oscillator.
C Bollinger Bands.
19 Which of the following is a continuation pattern?
20 Which of the following is a reversal pattern?
A Pennant.
B Rectangle.
C Double bottom.

A Pennant.
21 Which of the following is generally true of the head and shoulders pattern?
A Volume is important in interpreting the data.
B The neckline, once breached, becomes a support level.
C Head and shoulders patterns are generally followed by an uptrend in the 
22 Nikolai Kondratieff concluded in the 1920s that since the 1780s, Western econ -
omies have generally followed a cycle of how many years?
A 18.
B 54.
C 76.
23 Based on the decennial pattern of cycles, how would the return of the Dow 
Jones Industrial Average (DJIA) in the year 2015 compare with the return in 
2020?
A The return would be better.
B The return would be worse.
C The answer cannot be determined because the theory does not apply to 
both of those years.
24 According to the US presidential cycle theory, the DJIA has the best perfor -
mance during which year?
A The presidential election year itself.
B The first year following a presidential election.

Practice Problems 733
C The third year following a presidential election.
25 What is a major problem with long-  term cycle theories?
A The sample size is small.
B The data are usually hard to observe.
C They occur over such a long period that they are difficult to discern.
26 In 1938, R. N. Elliott proposed a theory that equity markets move:
A in stochastic waves.
B in cycles following Fibonacci ratios.
C in waves dependent on other securities.
27 All of the following are names of Elliott cycles except :
A presidential.
B supercycle.
C grand supercycle.
28 To identify intermarket relationships, technicians commonly use:
A stochastic oscillators.
B Fibonacci ratios.
C relative strength analysis.

Reading 13 ■ Technical Analysis 734
SOLUTIONS
1 A is correct. Almost all technical analysis relies on these data inputs.
2 A is correct. Technical analysis works because markets are not efficient and 
rational and because human beings tend to behave similarly in similar circum -
stances. The result is market trends and patterns that repeat themselves and are 
somewhat predictable.
3 A is correct. Trends generally must be in place for some time before they are 
recognizable. Thus, some time may be needed for a change in trend to be 
identified.
4 A is correct. Commodities and currencies do not have underlying financial 
statements or an income stream; thus, fundamental analysis is useless in deter -
mining theoretical values for them or whether they are over- or undervalued.
5 C is correct. The top and bottom of the bars indicate the highs and lows for the 
day; the line on the left indicates the opening price and the line on the right 
indicates the closing price.

6 C is correct. Dark and light shading is a unique feature of candlestick charts.
7 C is correct. Rising volume shows conviction by many market participants, 
which is likely to lead to a continuation of the trend.
8 A is correct. The price of gold in nominal dollars was several orders of mag -
nitude cheaper 100 years ago than it is today (roughly US$20 then versus 
US$1,100 today). Such a wide range of prices lends itself well to being graphi -
cally displayed on a logarithmic scale.
9 B is correct. A downtrend line is constructed by drawing a line connecting the 
highs of the price chart.
10 B is correct. It is demonstrated in the following chart:
100
8090
70
60
40
3050Share price breaks through
trend line at approximately
RMB 8.5
Nov
08Sep
09Jul
09Aug
09Jun
09Apr
09May
09Mar
09Jan
09Dec
08Feb
09

Solutions 735
11 B is correct. 
12 C is correct. As shown in the following chart, Barclays shares traded up to 390p 
on three occasions, each several weeks apart, and declined thereafter each time.
400
200300
100
0
Jan
09Nov
09Sep
09Oct
09Jan
10Dec
09Aug
09Jun
09Jul
09May
09Mar
09Feb
09Apr
09
13 C is correct. The left shoulder formed at around US$18.50, the head formed at 
around US$20.50, and the second shoulder formed at around US$19. 
21
7Shoulder ShoulderHead
Neckline
Feb
96Aug
96Feb
97Aug
97Feb
98Aug
98Feb
99Aug
99Feb
00Aug
00Feb
01
14 C is correct. Target = Neckline + (Neckline − Head): €100 + (€100 − €75) = 
€125
15 A is correct. A large increase in the number of IPOs increases the supply of 
equity and if overall demand remains the same, puts downward pressure on

equities. Also, companies tend to issue shares of equity when the managers 
believe they will receive a premium price, which is also an indicator of a market 
top.
16 B is correct. A value below 1.0 is a bullish sign; it means more volume is in ris -
ing shares than in declining ones. The TRIN is calculated as: (Advancing issues/
Declining issues)/(Volume of advancing issues/Volume of declining issues).

Reading 13 ■ Technical Analysis 736
17 C is correct. Bollinger Bands consist of a moving average and a higher line 
representing the moving average plus a set number of standard deviations from 
average price (for the same number of periods as used to calculate the moving 
average) and a lower line that is a moving average minus the same number of 
standard deviations.
18 C is correct. Bollinger Bands are price-  based indicators, not momentum oscil -
lators, which are constructed so that they oscillate between a high and a low or 
around 0 or 100.
19 A is correct. Triangles are one of several continuation patterns.
20 C is correct. It is one of several reversal patterns.
21 A is correct. Volume is necessary to confirm the various market rallies and 
reversals during the formation of the head and shoulders pattern.
23 A is correct. The decennial pattern theory states that years ending with a 5 will 
have the best performance of any of the 10 years in a decade and that those

ending with a zero will have the worst.
24 C is correct. A possible reason for the superior performance in the third year 
is that the US presidential election occurs, together with a number of other 
elections, in a four-  year cycle, so the politicians desiring to be reelected inject 
money into the economy in the third year to improve their chances of winning 
the following year.
25 A is correct. Long-  term cycles require many years to complete; thus, not many 
cycles are available to observe.
26 B is correct.
27 A is correct. This is the term for a separate cycle theory.
28 C is correct. Relative strength analysis is often used to compare two asset 
classes or two securities.

737 Appendices
APPENDICES
Appendix A Cumulative Probabilities for a Standard Normal Distribution
Appendix B Table of the Student’s t-Distribution (One-  Tailed Probabilities)
Appendix C Values of X2 (Degrees of Freedom, Level of Significance)
Appendix D Table of the F-Distribution
Appendix E Critical Values for the Durbin-  Watson Statistic (α = .05)

738 Appendices
 Appendix A  
 Cumulative Probabilities for a Standard Normal Distribution  
 P(Z ≤ x) = N(x) for x ≥ 0 or P(Z ≤ z) = N(z) for z ≥ 0
 x or z  0 0.01  0.02  0.03  0.04 0.05 0.06 0.07 0.08 0.09
 0.00  0.5000  0.5040  0.5080  0.5120  0.5160  0.5199  0.5239  0.5279  0.5319  0.5359
 0.10  0.5398  0.5438  0.5478  0.5517  0.5557  0.5596  0.5636  0.5675  0.5714  0.5753
 0.20  0.5793  0.5832  0.5871  0.5910  0.5948  0.5987  0.6026  0.6064  0.6103  0.6141
 0.30  0.6179  0.6217  0.6255  0.6293  0.6331  0.6368  0.6406  0.6443  0.6480  0.6517
 0.40  0.6554  0.6591  0.6628  0.6664  0.6700  0.6736  0.6772  0.6808  0.6844  0.6879
 0.50  0.6915  0.6950  0.6985  0.7019  0.7054  0.7088  0.7123  0.7157  0.7190  0.7224
 0.60  0.7257  0.7291  0.7324  0.7357  0.7389  0.7422  0.7454  0.7486  0.7517  0.7549
 0.70  0.7580  0.7611  0.7642  0.7673  0.7704  0.7734  0.7764  0.7794  0.7823  0.7852
 0.80  0.7881  0.7910  0.7939  0.7967  0.7995  0.8023  0.8051  0.8078  0.8106  0.8133

For example, to  ﬁ nd the z-value leaving 2.5/uni00A0 percent of the area/probability in the upper  tail, ﬁ nd the element 0.9750 in the body of the table. Read  
1.90 at the left end of the elemen t’s row and 0.06 at the top of the elemen t’s column, to give 1.90/uni00A0+ 0.06/uni00A0= 1.96. Table generated with Excel.
 Qua ntitative M etho ds for I nvestment Analysis, Second Edition, by Richard A . DeFusco, CFA, Dennis W. McLea vey, CFA, Jerald E . Pinto, CFA, and 
David E. Runkle, CFA. Copyright  © 2004 by CFA Institute.

739 Appendices
 Appendix A (continued)  
 P(Z ≤ x) = N(x) for x ≤ 0 or P(Z ≤ z) = N(z) for z ≤ 0
 x or z  0 0.01  0.02  0.03  0.04  0.05 0.06 0.07 0.08 0.09
 0.0  0.5000  0.4960  0.4920  0.4880  0.4840  0.4801  0.4761  0.4721  0.4681  0.4641
 −0.10  0.4602  0.4562  0.4522  0.4483  0.4443  0.4404  0.4364  0.4325  0.4286  0.4247
 −0.20  0.4207  0.4168  0.4129  0.4090  0.4052  0.4013  0.3974  0.3936  0.3897  0.3859
 −0.30  0.3821  0.3783  0.3745  0.3707  0.3669  0.3632  0.3594  0.3557  0.3520  0.3483
 −0.40  0.3446  0.3409  0.3372  0.3336  0.3300  0.3264  0.3228  0.3192  0.3156  0.3121
 −0.50  0.3085  0.3050  0.3015  0.2981  0.2946  0.2912  0.2877  0.2843  0.2810  0.2776
 −0.60  0.2743  0.2709  0.2676  0.2643  0.2611  0.2578  0.2546  0.2514  0.2483  0.2451
 −0.70  0.2420  0.2389  0.2358  0.2327  0.2296  0.2266  0.2236  0.2206  0.2177  0.2148
 −0.80  0.2119  0.2090  0.2061  0.2033  0.2005  0.1977  0.1949  0.1922  0.1894  0.1867

For example, to  ﬁ nd the z-value leaving 2.5/uni00A0 percent of the area/probability in the lower  tail, ﬁ nd the element 0.0250 in the bod y of the table. Read  
–1.90 at the left end of the elemen t’s row and 0.06 at the top of the elemen t’s column,  to give –1.90  – 0.06/uni00A0= –1.96. Table gene rated with Excel.

740 Appendices
 Appendix B  
 Table of the Student’s t-Distribution (One-  Tailed Probabilities)  df  p = 0.1 0 p = 0.0 5 p = 0.025  p = 0.0 1 p = 0.005   df  p = 0.10  p = 0.05  p = 0.025  p = 0.01  p = 0.005
 1  3.078 6.314 12.706  31.821 63.657   31  1.309  1.696  2.040  2.453  2.744
 2  1.886 2.920 4.303 6.965 9.925  32  1.309  1.694  2.037  2.449  2.738
 3  1.638 2.353 3.182 4.541 5.841  33  1.308  1.692  2.035  2.445  2.733
 4  1.533 2.132 2.776 3.747 4.604  34  1.307  1.691  2.032  2.441  2.728
 5  1.476 2.015 2.571 3.365 4.032  35  1.306  1.690  2.030  2.438  2.724
 6  1.440 1.943 2.447 3.143 3.707  36  1.306  1.688  2.028  2.434  2.719
 7  1.415 1.895 2.365 2.998 3.499  37  1.305  1.687  2.026  2.431  2.715
 8  1.397 1.860 2.306 2.896 3.355  38  1.304  1.686  2.024  2.429  2.712
 9  1.383 1.833 2.262 2.821 3.250  39  1.304  1.685  2.023  2.426  2.708
 10  1.372 1.812 2.228 2.764 3.169  40  1.303  1.684  2.021  2.423  2.704

24  1.318 1.711 2.064 2.492 2.797  90  1.291  1.662  1.987  2.368  2.632
 25  1.316 1.708 2.060 2.485 2.787  100  1.290  1.660  1.984  2.364  2.626
 26  1.315 1.706 2.056 2.479 2.779  110  1.289  1.659  1.982  2.361  2.621
 27  1.314 1.703 2.052 2.473 2.771  120  1.289  1.658  1.980  2.358  2.617
 28  1.313 1.701 2.048 2.467 2.763  200  1.286  1.653  1.972  2.345  2.601
 29  1.311 1.699 2.045 2.462 2.756  ∞  1.282  1.645  1.960  2.326  2.576
 30  1.310 1.697 2.042 2.457 2.750       
 To /f_i nd a critical t-value, en ter the table with df and a  speci /f_i ed value for a, the sig ni/f_i cance le vel. For example, with 5 df, α = 0.05 and a one-  tailed test, the desir ed probability in the tail would be 
p = 0.05 and the critical t-value would b e t(5, 0.05) = 2.015. With α =0.05 and a two-  tailed test , the desir ed probability in each tail would be p = 0.025/uni00A0 =α/2, giving t(0.025) = 2.571. Table gener ated 
using Excel.

using Excel. 
 Qua ntitative M etho ds for Inve stment Analysis, Second Edition, by Richard A . DeFusco, CFA, Dennis  W. McLea vey, CFA, Jerald E . Pinto, CFA, and 
CFA Institute.David E. Runkle, CFA. Copyright  © 2004 by

741 Appendices
 Appendix C  
 Values of χ2 (Degrees of Freedom, Level of Significance) 
 Degrees of 
Freedom Probability in Right Tail
 0.99  0.975  0.95  0.9 0.1  0.05  0.02 5 0.01  0.00 5
 1  0.000157  0.000982  0.003932  0.0158  2.706  3.841  5.024  6.635  7.879
 2  0.020100  0.050636  0.102586  0.2107  4.605  5.991  7.378  9.210  10.597
 3  0.1148  0.2158  0.3518  0.5844  6.251  7.815  9.348  11.345  12.838
 4  0.297 0.484 0.711 1.064 7.779  9.488  11.143  13.277  14.860
 5  0.554 0.831 1.145 1.610 9.236  11.070  12.832  15.086  16.750
 6  0.872 1.237 1.635 2.204 10.645  12.592  14.449  16.812  18.548
 7  1.239 1.690 2.167 2.833 12.017  14.067  16.013  18.475  20.278
 8  1.647 2.180 2.733 3.490 13.362  15.507  17.535  20.090  21.955
 9  2.088 2.700 3.325 4.168 14.684  16.919  19.023  21.666  23.589
 10  2.558 3.247 3.940 4.865 15.987  18.307  20.483  23.209  25.188
 11  3.053 3.816 4.575 5.578 17.275  19.675  21.920  24.725  26.757

26  12.198  13.844  15.379  17.292  35.563  38.885  41.923  45.642  48.290
 27  12.878  14.573  16.151  18.114  36.741  40.113  43.195  46.963  49.645
 28  13.565  15.308  16.928  18.939  37.916  41.337  44.461  48.278  50.994
 29  14.256  16.047  17.708  19.768  39.087  42.557  45.722  49.588  52.335
 30  14.953  16.791  18.493  20.599  40.256  43.773  46.979  50.892  53.672
 50  29.707  32.357  34.764  37.689  63.167  67.505  71.420  76.154  79.490
 60  37.485  40.482  43.188  46.459  74.397  79.082  83.298  88.379  91.952
 80  53.540  57.153  60.391  64.278  96.578  101.879  106.629  112.329  116.321
 100  70.065  74.222  77.929  82.358  118.498  124.342  129.561  135.807  140.170
 To have a probability of 0.05 in the right tail when df = 5, the tabled value is χ2(5, 0.05) = 11.070.
 Qua ntitative Metho ds for Investment Analysis, Second Edition, by Richard A. DeFusco, CFA, Dennis W. McLeavey, CFA, Jerald E. Pinto, 
CFA, and David E. Runkle, CFA. Copyright © 2004 by CFA Institute.

742 Appendices
 Appendix D  
 Table of the F-Distribution  Panel A. Critical values for right- hand tail area equal to 0.05 Numer ator: df1 and Denominator:  df2
  df1:1  2  3  4  5  6  7  8  9  1 0 11  12 15  20 21  22 23  24 25  30 40  60 120  ∞
 df2: 1  161 200 216 225 230 234 237 239 241 242 243 244 246  248  248  249  249  249  249  250  251  252  253  254
 2  18.5  19.0  19.2  19.2  19.3  19.3  19.4  19.4  19.4  19.4  19.4  19.4  19.4  19.4  19.4  19.5  19.5  19.5  19.5  19.5  19.5  19.5  19.5  19.5
 3  10.1  9.55  9.28  9.12  9.01  8.94  8.89  8.85  8.81  8.79  8.76  8.74  8.70  8.66  8.65  8.65  8.64  8.64  8.63  8.62  8.59  8.57  8.55  8.53
 4  7.71  6.94  6.59  6.39  6.26  6.16  6.09  6.04  6.00  5.96  5.94  5.91  5.86  5.80  5.79  5.79  5.78  5.77  5.77  5.75  5.72  5.69  5.66  5.63
 5  6.61  5.79  5.41  5.19  5.05  4.95  4.88  4.82  4.77  4.74  4.70  4.68  4.62  4.56  4.55  4.54  4.53  4.53  4.52  4.50  4.46  4.43  4.40  4.37

In/f_i nity  3.84  3.00  2.60  2.37  2.21  2.10  2.01  1.94  1.88  1.83  1.79  1.75  1.67  1.57  1.56  1.54  1.53  1.52  1.51  1.46  1.39  1.32  1.22  1.00

743 Appendices
 Appendix D (continued)  
 Table of the F-Distribution  Panel B. Critical values for right-  hand tail area equal to 0.025 Numer ator: df1 and Denominator:  df2
  df1: 1 2 3  4  5  6  7  8  9  1 0 11  12 15  20 21  22 23  24 25  30 40  60 120 ∞
 df2: 1  648 799 864 900 922 937 948 957 963 969 973 977 985 993 994 995 996 997 998 1001  1006  1010  1014  1018
 2 38.51 39.00  39.17  39.25  39.30  39.33  39.36  39.37  39.39  39.40  39.41  39.41  39.43  39.45  39.45  39.45  39.45  39.46  39.46  39.46  39.47  39.48  39.49  39.50
 3 17.44 16.04  15.44  15.10  14.88  14.73  14.62  14.54  14.47  14.42  14.37  14.34  14.25  14.17  14.16  14.14  14.13  14.12  14.12  14.08  14.04  13.99  13.95  13.90
 4 12.22 10.65  9.98  9.60  9.36  9.20  9.07  8.98  8.90 8.84  8.79  8.75  8.66  8.56  8.55  8.53  8.52  8.51  8.50  8.46  8.41  8.36  8.31  8.26
 5 10.01 8.43  7.76  7.39  7.15  6.98  6.85  6.76  6.68 6.62  6.57  6.52  6.43  6.33  6.31  6.30  6.29  6.28  6.27  6.23  6.18  6.12  6.07  6.02

In/f_i nity  5.02  3.69  3.12  2.79  2.57  2.41  2.29  2.19  2.11 2.05  1.99  1.94  1.83  1.71  1.69  1.67  1.66  1.64  1.63  1.57  1.48  1.39  1.27  1.00

744 Appendices
 Table of the F-Distribution  Panel C. Critical values for right-  hand tail area equal to 0.01 Numer ator: df1 and Denominator:  df2
  df1:  1  2  3  4  5  6  7  8  9  1 0 11  12 15  20 21  22 23  24 25  30 40  60 120 ∞
 df2: 1  4052  5000  5403  5625  5764  5859  5928  5982  6023  6056  6083  6106  6157  6209  6216  6223  6229  6235  6240  6261  6287  6313  6339  6366
 2  98.5 99.0 99.2 99.2 99.3 99.3 99.4 99.4 99.4 99.4 99.4 99.4 99.4  99.4  99.5  99.5  99.5  99.5  99.5  99.5  99.5  99.5  99.5  99.5
 3  34.1 30.8 29.5 28.7 28.2 27.9 27.7 27.5 27.3 27.2 27.1 27.1 26.9  26.7  26.7  26.6  26.6  26.6  26.6  26.5  26.4  26.3  26.2  26.1
 4  21.2 18.0 16.7 16.0 15.5 15.2 15.0 14.8 14.7 14.5 14.5 14.4 14.2  14.0  14.0  14.0  13.9  13.9  13.9  13.8  13.7  13.7  13.6  13.5
 5  16.3 13.3 12.1 11.4 11.0 10.7 10.5 10.3 10.2 10.1 10.0 9.89  9.72  9.55  9.53  9.51  9.49  9.47  9.45  9.38  9.29  9.20  9.11  9.02

In/f_i  nity  6.63  4.61  3.78  3.32  3.02  2.80  2.64  2.51  2.41  2.32  2.25  2.18  2.04  1.88  1.85  1.83  1.81  1.79  1.77  1.70  1.59  1.47  1.32  1.00

745 Appendices
 Table of the F-Distribution  Panel D. Critical values for right- hand tail area equal to 0.005 Numer ator: df1 and Denominator:  df2
  df1: 1 2 3 4  5  6  7  8  9  1 0 11  12 15  20 21  22 23  24  25 30  40 60  120  ∞
 df2: 1 1621 1 20000  21615  22500  23056  23437  23715  23925  24091  24222  24334  24426  24630  24836  24863  24892  24915  24940  24959  25044  25146  25253  25359  25464
 2 198.5 199.0 199.2 199.2 199.3 199.3  199.4 199.4  199.4 199.4 199.4 199.4  199.4  199.4  199.4  199.4  199.4  199.4  199.4  199.5  199.5  199.5  199.5  200
 3 55.55 49.80 47.47  46.20 45.39 44.84 44.43 44.13 43.88 43.68 43.52 43.39  43.08  42.78  42.73  42.69  42.66  42.62  42.59  42.47  42.31  42.15  41.99  41.83
 4 31.33 26.28 24.26  23.15 22.46 21.98 21.62 21.35 21.14 20.97 20.82 20.70  20.44  20.17  20.13  20.09  20.06  20.03  20.00  19.89  19.75  19.61  19.47  19.32

120  8.18  5.54  4.50  3.92  3.55  3.28  3.09  2.93  2.81  2.71  2.62  2.54  2.37  2.19  2.16  2.13  2.11  2.09  2.07  1.98  1.87  1.75  1.61  1.43
 In/f_i nity  7.88  5.30  4.28  3.72  3.35  3.09  2.90  2.74  2.62  2.52  2.43  2.36  2.19  2.00  1.97  1.95  1.92  1.90  1.88  1.79  1.67  1.53  1.36  1.00
 With 1 de gree of freedom (df) in the numerator and 3 df in the denominator , the critical F-value is 10.1 for a right- hand tail area equal to 0.05.  
 Qua ntitative M etho ds for I nvestment Analysis, Second Edition, by Richard A. DeFusco, CFA, Dennis W. McLea vey, CFA, Jerald E. Pinto, CFA, and  

746 Appendices
 Appendix E  
 Critical Values for the Durbin-  Watson Statistic (α = .05)
  K = 1 K = 2 K = 3 K = 4 K = 5
 n  dl du dl du dl du dl du dl du
 15  1.08  1.36  0.95  1.54  0.82  1.75  0.69  1.97  0.56  2.21
 16  1.10  1.37  0.98  1.54  0.86  1.73  0.74  1.93  0.62  2.15
 17  1.13  1.38  1.02  1.54  0.90  1.71  0.78  1.90  0.67  2.10
 18  1.16  1.39  1.05  1.53  0.93  1.69  0.82  1.87  0.71  2.06
 19  1.18  1.40  1.08  1.53  0.97  1.68  0.86  1.85  0.75  2.02
 20  1.20  1.41  1.10  1.54  1.00  1.68  0.90  1.83  0.79  1.99
 21  1.22  1.42  1.13  1.54  1.03  1.67  0.93  1.81  0.83  1.96
 22  1.24  1.43  1.15  1.54  1.05  1.66  0.96  1.80  0.86  1.94
 23  1.26  1.44  1.17  1.54  1.08  1.66  0.99  1.79  0.90  1.92
 24  1.27  1.45  1.19  1.55  1.10  1.66  1.01  1.78  0.93  1.90
 25  1.29  1.45  1.21  1.55  1.12  1.66  1.04  1.77  0.95  1.89
 26  1.30  1.46  1.22  1.55  1.14  1.65  1.06  1.76  0.98  1.88
 27  1.32  1.47  1.24  1.56  1.16  1.65  1.08  1.76  1.01  1.86

55  1.53  1.60  1.49  1.64  1.45  1.68  1.41  1.72  1.38  1.77
 60  1.55  1.62  1.51  1.65  1.48  1.69  1.44  1.73  1.41  1.77
 65  1.57  1.63  1.54  1.66  1.50  1.70  1.47  1.73  1.44  1.77
 70  1.58  1.64  1.55  1.67  1.52  1.70  1.49  1.74  1.46  1.77
 75  1.60  1.65  1.57  1.68  1.54  1.71  1.51  1.74  1.49  1.77
 80  1.61  1.66  1.59  1.69  1.56  1.72  1.53  1.74  1.51  1.77
 85  1.62  1.67  1.60  1.70  1.57  1.72  1.55  1.75  1.52  1.77
 90  1.63  1.68  1.61  1.70  1.59  1.73  1.57  1.75  1.54  1.78
 95  1.64  1.69  1.62  1.71  1.60  1.73  1.58  1.75  1.56  1.78
 100  1.65  1.69  1.63  1.72  1.61  1.74  1.59  1.76  1.57  1.78
 Note : K = the number of slope parameters in the model.
 Source: From J. Durbin and G. S. Watson, “Testing for Serial Correlation in Least Squares Regression, II.” Biometrika  38 (1951): 159–178.

Index I-1
A
AII. see American Association of 
Individual Investors
absolute dispersion, 428
absolute frequency, 393
academic designations, order of, 202
acceptance region, test statistic, 628–629
account information, regular statements 
of, 105
account reviews
firm policies on, 105
systematic, 114
accounts
with beneficial ownership, 186, 187
family, 108, 186, 188–189
in performance calculations, 128
representative, 221
temporary new, 237, 270
accrual accounting
defined, 262
Input Data (GIPS Section I.1), 235
accrued interest, 376–377
actions
investment ( see also  Investment 
Analysis, Recommendations, and 
Actions [Standard of Professional 
Conduct V])
fair dealing in, 111–112
firm policies on, 105–106
impact of, 40–41
unethical, 57
personal, 83
Additional Compensation Arrangements 
[Standard IV(B)], 144–145
application of the standard, 144–145
compliance procedures, 144
guidance, 144
text of, 46, 144
additional information, 262
additional services, for select clients, 116

addition rule for probabilities, 481–482
adequate compliance procedures, 
147–149
administrative fee, 262
ADR. see American Depositary Receipt
advertisements. see also  GIPS 
Advertising Guidelines (GIPS 
Section III)
defined, 256
information included in, 256
advisers, selecting, 157
Aegis Value Fund, 433
agent options, 182
AIMR. see Association for Investment 
Management and Research
AIMR Performance Presentation 
Standards (AIMR-PPS®), 226
Air Liquide, 424
Akerlof, George A., 679
Allianz, 424
all-in fees, 263allocation(s)
asset, 549–551
minimum lot, 116–117
with safety-first rules, 549–551
trade allocation procedures, 113, 114
transaction, 115–116
alternative hypothesis, 624–625, 
651–652
AMC. see Asset Manager Code of 
American Association of Individual 
Investors (AAII), 715
American call options, 539
American Depositary Receipt (ADR), 
681–682
American Express, 544n.17
analysis of variance (ANOVA), 632n.16
analysts, nonpublic information from, 
93–94

93–94
Anheuser-Busch InBev, 424
annualized returns, advertisements with, 
289–290
annual percentage rate (APR), 313n.6
annual percentage yield (APY), 313n.6
annual returns, advertisements with, 
290–291
annual share turnover, 426
annuities. see also  ordinary annuities
future value of, 314–316
lump sums to fund, 333–336
size of annuity payments, 332–336
annuity due, 314, 321–323
ANOVA. see analysis of variance
applicable law
and Code/Standards, 50–53
on confidentiality, 130
in firm policy, 105
global, 52–53
and investment products, 51–53
providing information on, 55
staying informed about, 54
approval, for outside compensation, 145
APR. see annual percentage rate
a priori probability, 476
APY. see annual percentage yield
arbitrage, 91
Arcelor-Mittal, 423
Archer Daniels Midland Company, 733, 
737
arithmetic mean, 404–408
and coefficient of variation, 441–442
as cross-sectional mean, 405–407
defined, 398n.9, 404
and geometric, 418–420
and median, 410–411

as population mean, 404–405
properties, 407–408
sample mean, 405–407
using, 456–457
and weighted mean, 414n.19
Arms index, 718–720Arthur Andersen, 6
Articles of Incorporation, 51
ascending triangle pattern, 702
Asian call options, 558–559
Asian Market Neutral Composite, 294
Asia Pacific Association for Fiduciary 
Studies, 231
ASML, 423
Asociación Española de Presentación de 
Resultados de Gestión, 231
asset allocation, safety-first rules for, 
549–551
asset management company, sample 
presentation of, 273–274
Asset Manager Code of Professional 
Conduct (AMC), 38, 55, 157
asset price(s)
artificial volatility in, 98–100
and head and shoulders patterns, 
696–699
normal distribution as model for, 545
and oscillators, 708
trends in, 679–681
and volume, 689–690
asset weighing, 127
Assicurazioni Generali, 423
Assirevi, 231
Associação Portuguesa de Analista 
Financeiros, 231
Association for Investment Management 
and Research (AIMR), 226
Association for Savings and Investment,

Association for Savings and Investment, 
South Africa, 231
Association Française de la Gestion 
Financière, 230
Association of British Insurers, 231
Association of Hungarian Investment 
Fund and Asset Management 
Companies, 231
L’Associazione Bancaria Italiana, 231
L’Associazione Italiana degli Analisti 
Finanziari, 231
Assogestioni, 231
assumptions, in technical analysis, 
678–680
Astra International, 555–556
asymptotic properties, estimators’ , 592
Australia
commodities and economy of, 728
GIPS sponsor, 230
mean and standard deviation of stock 
returns, 442
in MSCI EAFE, 406
real equity returns, 398
Austria
total returns, 406, 410, 422
AXA, 424
B
back simulation, 562–563
Balanced Growth Composite, 293

I-2 Index
bank discount basis, 375
bank discount yield, 375–376, 378
bankruptcy, technical analysis and, 682
bar charts, 683–684
Barclays plc, 732–733, 737
Barron’s,  715
BASF, 424
Bayer, 424
Bayes’ formula, 476, 504–508
BBVA, 424
BCO Santander, 424
bearish rectangles, 704
bear markets
Elliott waves in, 723
forecasting, 560–562
behavioral biases, 11–12
Belgian Asset Managers Association, 230
Belgium
total returns, 406, 410
benchmark description
Disclosure (GIPS Section I.4), 238
GIPS Advertising Guidelines (GIPS 
Section III), 257
Disclosure (GIPS Section I.4), 239, 240
and investment policy statements, 121
Presentation and Reporting (GIPS 
Section I.5), 241, 242
Private Equity (GIPS Section I.7), 248, 
249
Real Estate (GIPS Section I.6), 246
Verification (GIPS Section IV), 260, 
261
beneficial ownership, 186, 187
Bernoulli, Jakob, 530
Bernoulli random variable(s), 530–531
Bernoulli trials, 530

best execution (term), 104, 106
Best Practice Guidelines Governing 
Analyst/Corporate Issuer Relations  
(CFA Institute), 61
biases, sampling. see sampling biases
binomial distribution of discrete random 
variables, 530–539
evaluating block brokers with, 
531–532, 534–535
and expected defaults in bond 
portfolio, 537–538
mean and variance of, 537
and one-period stock price as 
Bernoulli random variable, 530–531
symmetry and skewness of, 533–534
and tracking objectives, 536
binomial formula, 510
binomial model
for bond defaults, 537–538
for stock price, 538–539
binomial random variables, 532–534
binomial tree (tree diagrams), 491–492, 
538
BJ’s Wholesale Club, 404, 432
Black, Fischer, 428
blackout periods, 187Black–Scholes–Merton model
as continuous time finance model, 
553n.32
for European call options, 563
lognormal distribution in, 551
volatility of, 555
block brokers, evaluating, 531–532, 
534–535
blogs, confidential firm information on, 
143
BMW, 423
BNP Paribas, 424
Bollinger, John, 707

143
BMW, 423
Bollinger bands, 707–708
bond-equivalent yield, 379
bond indexes, stratified sampling and, 
584–585
bonds
consol, 325–326
default
binomial model for, 537–538
recovery rates on, 642–644
face value of, 495
US Treasury, 727
zero-coupon, 494–495
Bon-Ton Stores Inc., 412
bonus compensation, 144–145
bonuses, 25–27
box size, point and figure charts’ , 687–688
Brazilian Bovespa Index (BVSP), 684
brokerage arrangements, 104, 107
broker recruiting, 135
broker-sponsored limited partnerships, 
179
Brown, Constance, 713
Brown, E. H. Phelps, 722
Bruce Fund, 433
budgeting, capital, 360
bullish rectangle, 704
bull markets
Elliott waves in, 724–726
Bundesverband Investment und Asset 
Management, 231
bundled fees
Calculation Methodology (GIPS 
Section I.2), 236
Disclosure (GIPS Section I.4), 239
Section I.5), 241
Wrap Fee/SMA Portfolios (GIPS 
Section I.8), 250–251
business entities, distinct, 234, 265

business relationships, conflicts of 
interest and, 180, 184
buy-and-hold investors, market timers 
vs., 560–562
buy-side clients, 59
BVSP . see Brazilian Bovespa Index
Bylaws and Rules of Procedure for 
Professional Conduct (Rules of 
Procedure), 37, 51
C
CAC-40 index, 416
calculated statistical indexes, 715–718
Section I.2), 235–236about, 232
recommendations
general, 236
for private equity, 250
for real estate closed-end fund 
composites, 246
requirements
general, 235–236
for private equity, 247
for real estate, 243–244
composites, 245
call options
American, 539
Asian, 558–559
European, 563
Canada
commodities in economy, 728
Treasury bills, 305n.3, 377n.16
Canadian Broadcasting Corporation, 415
Canadian Investment Performance 
Committee, 230
candidacy in CFA program, referring to, 
199–200
Candidate Pledge, 51, 195
Candidate Responsibility Statement, 51

candidates, CFA. see Responsibilities as 
a CFA Institute Member or CFA 
Candidate [Standard of Professional 
Conduct VII]
candlestick charts, 684–686
capital
committed, 245, 246, 249, 264
composite since inception paid-in 
capital, 245, 246, 249
paid-in, 249, 267
capital budgeting, 360
capital employed (term), 263
capital markets. see also  Integrity of 
Capital Markets [Standard of 
Professional Conduct II]
and benefit of ethics to society, 40
sustainability of, 40–41
capital returns, 244, 263
capital structure, 360
care. see Loyalty, Prudence, and Care 
[Standard III(A)]
Carrefour, 423
carried interest, 247, 263
carve-out
Composite Construction (GIPS 
Section I.3), 237
cash
interim, 307–308
mutual fund cash position indicator, 
720–721
cash flow additivity principle, 333, 338
cash flows
discounted ( see discounted cash 
flows)
equal
future value of series with, 315–316

flows)
equal
future value of series without, 316

Index  I-3
infinite series of, 325–326
present value of series with, 320–325
present value of series without, 328
external, 235, 236, 265
future value of ( see future value [FV])
geometric and arithmetic mean of 
future cash flows, 457
incremental, 360n.1
large, 235, 266
present value of ( see present value 
[PV])
series of
future value for series of cash flows, 
314–316
present value for series of cash flows, 
320–328
significant, 237, 240, 269
single
future value of single cash flow, 
306–314
present value of single cash flow, 
317–320
unequal, 316, 328
Caterpillar, Inc., 410
CBOE Volatility index (VIX), 716
CD equivalent yield, 377. see also  money 
market yields
CDOs. see collateralized debt obligations
cell (term), 584
Center for Research in Security Prices 
(CRSP), 605
central banks, technical analysis by, 681
central limit theorem, 588–591, 596, 
626n.7
central tendency. see measures of central 
tendency
Certificate in Investment Performance 
Measurement (CIPM) certificants, 37
Certificate in Investment Performance

Measurement (CIPM) Program, 
193, 194
CFA Association of Pakistan, 231
CFA charterholders, 199
CFA Denmark, 230
CFA designation, 199. see also  Reference 
to CFA Institute, Designation and 
Program [Standard VII(B)]
guidance on using, 199
order of professional and academic 
designations with, 202
right to use, 201
stating facts about, 202
CFA examinations, 33
bringing written material into exam 
room, 195
confidential information in, 193–194
expressing opinions about, 194
grading guidelines and results for, 197
passing, in consecutive years, 201
sharing content of, 196–197
sharing questions from, 195
writing after exam period, 196
CFA Institute, 231. see also  specific 
committees and programs
clarifications of GIPS by, 228, 233, 234, 
259
code of ethics, 8–9
compromising integrity of, 197
ethical commitment of, 42–43GIPS standards, 225, 226
mission of, 35
referring to, 199–200 ( see also  
Reference to CFA Institute, 
Designation and Program 
[Standard VII(B)])
values of, 43

website, 43, 51, 157, 194
CFA Institute Investment Foundations™ 
certificate program, 36, 193, 194
CFA members and candidates
knowledge of the law [Standard I(A)], 54
responsibilities of ( see Responsibilities 
as a CFA Institute Member or CFA 
Conduct VII])
CFA Program. see also  Reference to CFA 
Institute, Designation and Program 
[Standard VII(B)]
conduct restrictions for candidates and 
members, 193
confidential information about, 
193–194
testing policies for, 195
CFA Society of Hungary, 231
CFA Society of New Zealand, 231
CFA Sri Lanka, 231
CGM Focus Fund, 433
change in polarity principle, 693
changes
fund mandate, 170
to investment process, 170–172
Chartered Financial Analyst. see entries 
beginning with  CFA
chart patterns, 694–705
continuation patterns, 701–705
flags and pennants, 704–705
rectangles, 704
reversal vs., 694
triangles, 702–704
reversal patterns, 694–701
continuation vs., 694

double tops and bottoms, 699–701
head and shoulders, 695–699
triple tops and bottoms, 700–701
charts, 682–691
bar, 683–684
candlestick, 684–686
line, 682–683
point and figure, 686–688
relative strength analysis of, 690–691
scale of, 688–689
time intervals of, 690
volume on, 689–690
Chebyshev, Pafnuty, 439
Chebyshev’s inequality, 439–441
Chicago Board Options Exchange, 716
China Mobile Limited, 692–693, 705
chi-square test
for value of population variance tests, 
648–649
values of chi square, 743
CIPM certificants. see Certificate 
in Investment Performance 
Measurement certificants
CIPM Program. see Certificate 
Measurement Programclient commission practices, 106–108
client–plan participants, identifying, 106
clients. see also  prospective clients
additional services for, 116
approval from, 105
buy-side, 59
communication with ( see 
Communication with Clients and 
Prospective Clients [Standard 
V(B)])
disclosure to, 178–179

V(B)])
duties to ( see Duties to Clients 
[Standard of Professional 
Conduct III])
fair dealing between, 118
gifts and entertainment from, 67
identifying, 103, 108–109, 121
informing, of investment process, 
166–167
interests of, 106
loyalty to, 109
maintaining lists of, 113
priority of personal trading vs. trading 
for, 185
risk profile of, 119
select, additional services for, 116
soliciting former, 137–142
status of, 130
client updates, 159–160
closed-end funds
Private Equity (GIPS Section I.7), 247
Real Estate (GIPS Section I.6), 245–246
real estate presentations with, 277–279
Code of Ethics (CFA Institute), 33–44
adoption of, 38
and applicable law, 50–53
evolution of, 34
and importance of ethics, 39–43
notification of, 142
and principle-based standards, 10
and Professional Conduct Program, 
37–38
and Standards of Practice Council, 
38–39
in Standards of Practice Handbook,  3, 
8, 33–35, 42
text of, 44
and values of CFA Institute, 43
codes of ethics (in general)
adopting, 148

commitment to, 42
defined, 8
developing, 54–55, 82
coefficient of variation (CV), 441–443
coils, 702
142
combination (term), 510
combination formula, 510–511
commissions
and duties to clients, 106–108
ethical issues with, 25–27
committed capital
defined, 264
Private Equity (GIPS Section I.7), 249
Real Estate (GIPS Section I.6), 245, 246
common stock portfolio, probabilities 
for, 548

I-4 Index
communication(s)
different forms of, 167
to employees of material nonpublic 
information, 91
interdepartmental, 89
Prospective Clients [Standard V(B)], 
165–174
application of the standard, 169–174
compliance procedures, 168–169
eleventh edition revision, 36
guidance, 166–168
different forms of communication, 
167
facts vs. opinions in reports, 168
identifying risks and limitations, 
167–168
informing clients of investment 
process, 166–167
report presentation, 168
text of, 46, 165–166
Companhia Vale do Rio Doce, 685
company promotion, 97
compensation. see also  Additional 
Compensation Arrangements 
[Standard IV(B)]
bonus, 144–145
and conflict of interest, 181–182
disclosure of, 105
externally compensated assignments, 
141
notification of, 144–145
outside, 145
and research independence, 68
competence, 82
competition policy, 137
complement, of event, 486
compliance
Fundamentals of Compliance (GIPS 
Section I.0), 233–234
about, 232
recommendations, 234
requirements, 233–234
with GIPS

with GIPS
benefits of, 222–223
claiming, 222, 229
GIPS-compliant historical 
performance, 228–229
compliance officers, 64
compliance procedures
adequate, 147–149
adoption of, 148
education and training 
implementation, 149
inadequate, 147, 152
and incentive structure, 150
as responsibility of supervisors, 
148–149
compliant presentations
Disclosure (GIPS Section I.4), 237–239
Section I.0), 234
Section III), 256, 257
GIPS Valuation Principles (GIPS 
Section II), 253Input Data (GIPS Section I.1), 235
Section I.5), 240–242
Private Equity (GIPS Section I.7), 247, 
248
Real Estate (GIPS Section I.6), 242, 
244, 245
Verification (GIPS Section IV), 258, 262
Section I.8), 250–252
Composite Construction (GIPS Section 
I.3), 236–237
about, 232
general, 237

general, 236–237
for private equity, 248
for wrap fee/SMA portfolios, 251
composite construction, 
misrepresenting, 80
composite creation date, 238, 264
composite definition
Private Equity (GIPS Section I.7), 248
Real Estate (GIPS Section I.6), 245
Verification (GIPS Section IV), 261
composite description
Verification (GIPS Section IV), 260
composite inception date
Section I.5), 240–241
composites
Section I.2), 235, 236
Section I.3), 236, 237

Disclosure (GIPS Section I.4), 238–240
GIPS, 223
Section II), 252–254
investment firm balanced growth 
composite (sample), 272–273
List of Composite Descriptions (GIPS 
Section V.0.1), 292–295
Section I.5), 240–242Private Equity (GIPS Section I.7), 
248–250
Verification (GIPS Section IV), 
258–262
Section I.8), 251, 252
composite since inception distributions, 
245, 246, 249
composite termination date
compounding
continuous, 312–313, 553–554
defined, 306–307
frequency of, 310–312, 319–320
future value of lump sum with, 
311–312

311–312
solving TMV problems for number of 
compounding periods, 331–332
conditional expected values, 490
conditional probability, 478–481, 
485–486
conditional variances, 492–495
Conduct as Participants in CFA Institute 
Programs [Standard VII(A)], 
193–197
application of the standard, 195–197
eleventh edition revision, 36–37
guidance, 193–195
additional CFA restrictions, 194, 195
confidential program information, 
193–194
expressing opinions, 194
text of, 47, 193
confidence, investor, 227
confidence intervals, 593–599
construction of, 593–594
definition, 593
for hypothesis testing, 623
and hypothesis tests, 629–630
for population mean, 593–598
with normally distributed population 
with known variance, 594
t-distribution, 597–598
z-alternative, 595–597
reliability factors for, 594–595, 598–599
and sample size, 599–601
confidence limits, 593
confidential information
about CFA program, 193–194
accidental disclosure of, 132–133
of firm, 143
intentional disclosure of, 131–132
possessing, 131

confidentiality, 106. see also  Preservation 
of Confidentiality [Standard III(E)]
confirmations of transactions, duplicate, 
188
and business relationships, 180, 184
and business stock ownership, 180
and compensation arrangement, 
181–182

Index  I-5
and directorship, 182–183
disclosure of, 105 ( see also  Disclosure 
of Conflicts [Standard VI(A)])
and personal stock ownership, 181
and personal trading, 183
and priority of transactions, 185
and requested favors, 183
Conflicts of Interest [Standard of 
Professional Conduct VI], 177–192
Disclosure of Conflicts [Standard 
VI(A)], 177–184
application of the standard, 180–184
compliance procedures, 180
guidance, 177–180
text of, 46, 177
Priority of Transactions [Standard 
VI(B)], 185–190
application of the standard, 188–190
compliance procedures, 186–188
guidance, 185–186
text of, 46–47, 185
Referral Fees [Standard VI(C)], 
190–192
application of the standard, 190–192
compliance procedures, 190
guidance, 190
text of, 47, 190
Consensus Bullish Sentiment Index, 715
consistency, estimator, 592–593
consistent probabilities, 478
consol bonds, 325–326
constraints, investor, 121
continuation patterns, 694, 701–705

continuous compounding, 312–313, 
553–554
continuous random variables, 539–557
continuous uniform distribution, 
540–543
defined, 527
lognormal distribution, 551–557
normal distribution, 543–551
applications of, 549–551
and probabilities for common stock 
portfolio, 548
safety-first optimal portfolio, 
549–551
continuous time finance models, 553n.32
540–543
contrarian trading strategies, 707–708
control deficiency disclosures, 637–639
convergence, oscillator and price, 708
copies, maintaining, 75
correction, of unintentional errors, 76
corrective waves, 724–726
correlation
defined, 501
estimating, 503–504
hypothesis tests with, 655–658
properties of, 501
correlation matrix, 501
cost arrangements, restricting, 64
cost averaging, 421
Costco Wholesale Corporation, 404, 432
counting, 508–511combination formula, 510–511
multinomial formula, 510
multiplication rule of, 509–510
permutation formula, 511
covariance, 497–503

covariance matrix, 499–500, 502
covenant, probability of breaching, 
542–543
coverage, prior, 66
credit rating agencies, opinions of, 
61–62
CRH, 423
critical region, test statistic, 629
critical value, 628–630
cross-departmental conflicts, 179
cross-sectional data, 405, 585, 587
cross-sectional mean, 405–407
C R S P.  see Center for Research in 
Security Prices
cumulative distribution function, 528, 
529, 541
cumulative frequency, 394–398
cumulative frequency distributions, 
402–403
cumulative probabilities, 740–741
cumulative relative frequency, 394–395
Currency Overlay Composite, 293–294
custodial relationships, 60
custody fees, 264
custody of client assets, 102
C V. see coefficient of variation
D
%D (stochastic oscillator), 712–713
Daily Sentiment Index, 715
Daimler, 424
Danish Society of Financial Analysts, 230
Danone, 424
data mining, 601–604
data-mining bias, 601–604
data snooping, 601n.19, 602n.22
Davidson, Russell, 632n.15
DB pension plans. see defined-benefit

DB pension plans. see defined-benefit 
dead cross pattern, 706
debt
collateralized debt obligations, 142
margin, 716–717, 720
Treasury, 305
deceit, 83
decennial pattern, 723
deciles, 421
decision making
ethical framework for, 20–27, 41–42
group, 157
in hypothesis testing, 631
time frame for dissemination and, 
112–113
decision rule, 628–630
default bonds
default risk premium, 305, 494–495
defined-benefit (DB) pension plans, 557
degree of confidence, 593
degrees of freedom (df), 596, 597, 642
Delafield Fund, 433
delisted companies, 605
de Moivre, Abraham, 543Denmark
departments, physical separation of, 89
dependent events, 483
dependent samples, hypothesis tests for, 
644–648
derivative expiration days, 653–654
descending triangle pattern, 702–703
descriptions of securities, 169–170
descriptive statistics, 389
detection, as part of supervision, 147–148
Deutsche Bank, 424

Deutsche Telekom, 423
Deutsche Vereinigung für Finanzanalyse 
und Asset Management, 231
deviation. see also  standard deviation
from intrinsic value, 680
mean absolute deviation, 429–431
semideviation, 437, 438
de Villiers, Victor, 686
de Wolff, Samuel, 722
df. see degrees of freedom
diffuse priors, 508
diligence, 155, 163
Diligence and Reasonable Basis 
[Standard V(A)], 154–165
application of the standard, 158–165
compliance procedures, 158
guidance, 154–157
diligence and reasonable basis 
group research and decision making, 
157
quantitatively oriented research, 
156–157
quantitatively oriented techniques, 157
secondary or third-party research, 
155–156
selecting external advisers and 
subadvisers, 157
text of, 46, 154
Dillards, Inc., 412
directed brokerage, 104
direct investments, 250, 264
directors, conflicts of interest for, 
179–180, 182–183
Disciplinary Review Committee (DRC), 
37–38
confidential information, 132–133
conflicts of interest, 105
control deficiency, 637–639

interdepartmental referral 
arrangements, 191
investment system, 169, 171
issuer-paid research, 76
level of service, 114
material information, 88–89, 92
performance calculation methodology, 
128–129
personal investing policies, 188
personal trading, 188, 189
possible illegal activity, 132
referral arrangements, 190–192
selective, 92, 114, 116
on social media, 117
trade allocation procedures, 114

I-6 Index
Disclosure (GIPS Section I.4), 237–240
about, 232
general, 240
for real estate, 246
general, 237–240
for real estate, 244
Disclosure of Conflicts [Standard VI(A)], 
177–184
conflicts as a director, 179–180
disclosure to clients, 178–179
disclosure to employers, 178
stock ownership conflicts, 179
discount, 304, 375
discounted cash flows, 359–386
internal rate of return, 362–367
evaluating R&D programs with IRR 
rule, 363–364
NPV and IRR rules, 364–365
problems with IRR rule, 365–367
money market yields, 374–379
bank discount yield, 375–376
discount rate, 378–379
net present value, 360–362
portfolio return measurement, 367–374
money-weighted rate of return, 
368–369, 372–374
time-weighted rate of return, 
369–374

369–374
practice problems, 381–383
solutions to problems, 384–386
and time value of money, 359
discount rate, for money market yields, 
378–379
discount securities, return for, 377
discount yield, bank, 375–376, 378
discrete random variables, 527–539
binomial distribution, 530–539
discrete uniform distribution, 528–530
discretionary portfolios, 260
dispersion, 428–446
absolute, 428
coefficient of variation, 441–443
internal
defined, 266
Verification (GIPS Section IV), 261mean absolute deviation, 429–431
population variance and standard 
deviation, 431–434
range, 429–431
relative, 441
sample variance and standard 
deviation, 434–437

semivariance and semideviation, 
437–438
Sharpe ratio, 443–446
dissemination of information, 88, 
112–113, 189–190
dissociation, 54–56
distinct business entities, 234, 265
distribution area laws, 54
distribution-free tests, 654n.27
distributions, 247, 265
F-distribution, 744–747
frequency, 391–399
construction of, 392–394, 398–399
cumulative, 402–403
defined, 391
and holding period formula, 392
and relative frequency, 394–398
normal
confidence intervals for population 
mean with, 594
cumulative probabilities for, 740–741
hypothesis tests of normally-
distributed populations, 633–636, 
640–648, 651
reliability factors for confidence 
intervals based on, 594–595, 
598–599
skewed vs., 446–449
standard, 740–741
Student’s t-distribution vs., 596–597
probability ( see probability 
distributions)
sampling, 584, 592
t-distribution
and confidence interval for 
population mean, 597–598
defined, 632–633
and estimation of normal sampling 
distribution, 595
normal distribution vs., 596–597

table, 742
divergence, 696, 708
and Loyalty, Prudence, and Care 
[Standard III(A)], 105
and Suitability [Standard III(C)], 120
documentation, of trade allocation 
procedures, 113
documents, former employers’ , 138
Dogs of the Dow Strategy, 603n.24
doji, 685–686
dollar-weighted return, 368n.9
dollar-yen exchange rate, 463
double bottoms, 700, 701
double tops, 699–701
Dow, Charles, 679–681, 723
Dow Chemical, 544n.17
Dow Dividend Strategy, 603n.24
Dow Jones Industrial Average (DJIA), 
679, 681
decennial pattern, 723with inverse head and shoulders 
patterns, 699
on linear vs. logarithmic scale, 
688–689
presidential cycle, 723
quadruple witching days, 653–654
support and resistance, 693–694
Dow Jones Railroad Average, 681
down transition probability, 538
downtrends, 692
Dow Theory, 723, 726
DPI. see realization multiple
DRC. see Disciplinary Review 
Committee
and failed investments, 163

Committee
in financial research and analysis, 61
in submanager selection, 160–161
sufficient, 158, 161–162
Durbin-Watson statistic, 748
Dutch Book Theorem, 478
Duties to Clients [Standard of 
Professional Conduct III], 101–133
Fair Dealing [Standard III(B)], 
110–118
application of the standard,  
114–118
compliance procedures, 112–114
guidance, 110–112
text of, 45, 110
Loyalty, Prudence, and Care [Standard 
III(A)], 101–109
application of the standard, 106–109
compliance procedures, 105–106
guidance, 101–105
text of, 45, 101
Performance Presentation [Standard 
III(D)], 125–129
application of the standard, 126–129
compliance procedures, 126
guidance, 125–126
text of, 45, 125
Preservation of Confidentiality 
[Standard III(E)], 129–133
application of the standard, 131–133
compliance procedures, 131
guidance, 129–130
text of, 45, 129
Suitability [Standard III(C)], 118–125
122–125
compliance procedures, 121–122
guidance, 118–121
text of, 45, 118

Duties to Employers [Standard of 
Professional Conduct IV], 133–154
Additional Compensation 
Arrangements [Standard IV(B)], 
144–145
Loyalty [Standard IV(A)], 133–143
137–143
compliance procedures, 137
guidance, 133–137
text of, 45–46, 133

Index  I-7
Responsibilities of Supervisors 
[Standard IV(C)], 146–154
application of the standard, 150–154
compliance procedures, 148–150
guidance, 146–148
text of, 46, 146
E
EADS, 423
EAR. see effective annual rate
(EBITDA), 542
earnings per share (EPS), 389
forecasting, 483–484, 486–494
mean and median, 410–411
EAY. see effective annual yield
EBITDA. see earnings before 
interest, taxes, depreciation, and 
EDRs. see European Depositary 
Receipts
education, compliance, 149
effective annual rate (EAR), 313
effective annual yield (EAY), 377–379
effective date, GIPS, 229
efficiency, estimator, 592
18-year cycle, 722
electronic information, confidentiality 
of, 130
Elliott, R. N., 723–725
Elliott Wave Theory, 723–726
Emerging Market High Yield Fixed 
Income Composite, 292
empirical probability, 476
employees
checking references of, 82
classifications of, 137
independent contractors vs., 136

material nonpublic information for, 91
employer(s)
competing with current, 140
disclosure of conflicts to, 178, 184
duties to ( see Duties to Employers 
Conduct IV])
former, 127, 138
leaving, 134–135, 143
misrepresentation of work for, 74
responsibilities of, 134
employment, nature of, 136–137
Enel, 423
ENI, 424
Enron Corporation
ethical lapses, 6
situational influences on ethics, 13–14
and technical analysis, 682
entertainment
with clients, 67
with related parties, 66–67
E.ON, 423
equal cash flows
present value of series without, 328equality
point of, 625
of two variances, 650–654
equity IPOs, 186–187
equity returns, frequency distribution of, 
398–399
equivalence, 336–337
errors
known, 76
notification of, 172
sampling, 583–584
standard, 588–589, 594, 599, 626
tracking, 536
Type I and II, 627

unintentional, 76
Essilor International, 423
estimates
defined, 591
point, 594
pooled, 640
of population mean, 591–601
confidence intervals, 593–598
point estimators, 591–593
sample size, 599–601
estimation, 591, 623
estimators, 591–593, 594n.12
ethical conduct (term), 7
ethical decision-making framework, 
20–27
applying, 22–27, 41–42
phases of process, 21–22
ethical principles (term), 7
ethical standards, legal standards vs., 
17–20
ethics, 5–28. see also  Code of Ethics; 
about, 5–6
challenges to ethical conduct, 11–14
defined, 7
20–27
applying, 22–27
ethical vs. legal standards, 17–20
firms commitment to, 42
impact on stakeholders, 6–9
importance of, 15–17
and investment industry, 39–43
practice problems, 29
professionalism, 9–11
and regulations, 41
societal benefit of, 40
solutions to problems, 30–31
Eurodollar futures, 699–700
European Depositary Receipts (EDRs), 
706n.5
European-style options

706n.5
call options, 563
Monte Carlo simulation for valuing, 
558
put options, 566
EURO STOXX 50 Index, 423–425
Eurozone countries, 587n.2
events
complement of, 486
defined, 475
dependent, 483
independent, 483–486
mutually exclusive, 475Everbright Securities, 6
evergreen funds, 247, 265
ex-ante  (term), 237, 265
ex ante  Sharpe ratio, 443n.37
excessive trading, 108, 117
excess kurtosis, 453–456
execution-only responsibilities, 109
exhaustive (term), 475
expectations, in probability, 474
expected defaults, in bond portfolio, 
537–538
expected return
calculation of, 497
and variance of return, 502
expected value, 488–492
of bonds and T-bills, 494–495
conditional, 490
defined, 487–489
of product of uncorrelated random 
variables, 504
properties of, 496–497
standard deviation, 489–490
total probability rule for, 490–492
tree diagrams, 491–492
and weighted mean, 416
expert networks, 95
experts, 87–88
expiration days, derivative, 653–654
ex-post  (term), 241, 265
ex post  Sharpe ratio, 443n.37

ex-post  standard deviation, 240–242
external advisers, selecting, 157
external cash flows
externally compensated assignments, 141
external manager, travel expenses from, 
67–68
external valuation
Section II), 253–254
Real Estate (GIPS Section I.6), 
243–245
Exxon Mobil, 714–715
F
face value, 375, 495
factorials, 509
facts, opinions and, 168, 169
factual presentations, misrepresentation 
and, 74–75
failed investments, due diligence and, 
163
fair dealing, 114–116, 118
Fair Dealing [Standard III(B)], 110–118
application of the standard, 114–118
developing firm policies, 112–114
disclosure of level of service, 114
disclosure of trade allocation 
procedures, 114
systematic account reviews, 114
investment action, 111–112
investment recommendations, 110–111

I-8 Index
fair value
Section II), 252–253
Private Equity (GIPS Section I.7),  
247
Real Estate (GIPS Section I.6), 243
family accounts, 108, 186, 188–189
Fastow, Andrew S., 13–14
favors, requested, 183
FCMs. see futures commission 
merchants
fees. see also  Referral Fees [Standard 
VI(C)]
all-in, 263
Section I.8), 250
and conflicts of interest, 179
custody, 264
gross-of-fees, 266
investment management fees
Private Equity (GIPS Section I.7), 
247–250
Real Estate (GIPS Section I.6), 244
performance-based, 238, 267
service, 68
fee schedule, 238, 265

Fibonacci, Leonardo, 724
Fibonacci sequence, 724
fictitious name, 202
files
current, maintaining, 54
of former employers, 138
final liquidation date
249
(FASB), 252
financial risk, 551n.27
financial risk management, normal 
distribution in, 551
Financial Times Stock Exchange. see 
entries beginning with  FTSE
Finland
total returns, 406, 409
firewalls, 60, 89
firm policies
for fair dealing, 112–114
on loyalty, prudence, and care, 
105–106firms
benefits of GIPS compliance for, 
222–223
commitment to ethics by, 42
compliance with Code of Standards, 
38
informing, of referral arrangements, 
191
knowledge of the law, 54–55
overemphasis of results from, 81
records as property of, 175, 176
starting new, 140
fixed-rate mortgage, payments on, 
332–333
flag patterns, 704–705
flash reports, 113
flow-of-funds indicators, 718–722

Arms index, 718–720
margin debt, 720
and market indicators, 721
mutual fund cash position, 720–721
new equity issuance, 721–722
secondary offerings, 722
FOFs. see funds of funds
Foolish Four investment strategy, 
602–603
Forbes,  432–434
Ford Motor Company, 410, 411, 
710–712
former clients, soliciting, 137–142
former employers
documents and files of, 138
in performance presentation, 127
fractile, 421
France
France Telecom, 423
Frankfurt Stock Exchange, 706
fraud, 83, 682
free float adjusted, 406n.13
frequency
absolute, 393
of compounding, 310–312, 319–320
cumulative, 394–398
relative, 394–398
frequency distributions, 391–399
frequency polygons, 401–402
front-running, 187
F-test
for differences between variances, 651
FTSE 100 Index

line chart, 682–683
relative strength analysis, 690
FTSE All Share Index, 606–607
FTSE Eurotop 100, 405–406
FTSE Global All Cap Index, 647
full price, 377n.14
full-replication approach, 584
fundamental analysis, 678n.1, 680–682Fundamentals of Compliance (GIPS 
about, 232
funding, travel, 63
fund manager relationships, 60, 70
fund mandate, change in, 170
funds, fair dealing between,  
114–115
funds of funds (FOFs)
composites for, 249, 250
247–249
sample presentations of, 279–282
future cash flows, geometric and 
arithmetic mean of, 457
futures commission merchants (FCMs), 
151
future value (FV)
defined, 306
future value of series of cash flows, 
314–316
with equal cash flows, 315–316
with unequal cash flows, 316
306–314
with continuous compounding, 
312–313
frequency of compounding, 
310–312
with interim cash reinvested at same 
rate, 307–308

for lump sum, 309–310
stated and effective rates for, 
313–314
without interim cash, 308
present and, 307, 336–337
F V. see future value
G
gains, from market timing, 560–562
Gazprom SP European Depositary 
Receipts (EDRs), 706, 707
GDF Suez, 423
General Dynamics, 410
general partner, 266
geometric mean, 416–420
and arithmetic, 418–420
formula, 416–417
geometric mean return
arithmetic and, 418–420
formula for, 417–418
German Asset Management Standards 
Committee, 231
German CFA Society, 231
Germany
GIPS sponsor, 231
Treasury paper, 305n.3, 377n.16
GICs. see Guaranteed Investment 
Contracts
gifts
from clients, 67
limiting, 64
from related parties, 66–67

Index  I-9
GIPS. see Global Investment 
Performance Standards
Section III), 256–257
purpose, 256
advertisement defined, 256
and GIPS regulatory requirements, 
256
information included in 
advertisement, 256
requirements, 256–257
sample advertisements, 289–291
with annualized returns, 289–290
with five years of annual returns, 
290–291
with period-to-date and annualized 
returns, 290
GIPS Council, 226, 230
GIPS Executive Committee, 226
clarifications by, 228, 233, 234, 259
implementation recommendations of, 
229–230
objectives of, 227
GIPS Handbook,  228, 233, 234, 259
Section II), 252–255
fair value, 252–253
and input data, 232, 235
247, 248
for private equity, 254, 255
for real estate, 253–255
recommendations, 254–255
requirements, 253–254
Global Commodity Composite,  
293
Global Equity Composite, 223
ethical dimensions of, 15
volatility and, 652–653
Global Investment Performance

Standards (GIPS), 126, 157, 
221–297
composites, 223
effective date, 229
GIPS Advertising Guidelines 
(GIPS Section III), 256–257
glossary of terms, 262–271
historical background, 226
implementation of, 229–230
List of Composite Descriptions 
(Section V.0.1), 292–295
need for, 221–222, 227
objectives, 227
overview, 228
practice problems, 296
provisions, 231–252Calculation Methodology 
(Section I.2), 235–236
Composite Construction 
(Section I.3), 236–237
Disclosure (Section I.4), 237–240
Fundamentals of Compliance 
(Section I.0), 233–234
Input Data (Section I.1), 235
overview, 231–233
Presentation and Reporting (Section 
I.5), 240–242
Private Equity (Section I.7), 247–250
Real Estate (Section I.6), 242–246
Wrap Fee/SMA Portfolios

Wrap Fee/SMA Portfolios 
(Section I.8), 250–252
purpose, 225
290–291
with one-, three-, and five-year 
annualized returns, 289
with period-to-date and one-, three-, 
and five-year annualized returns, 
290
sample presentations, 272–288
asset management company, 
273–274
composite, 272–273
large-cap SMA composite, 286–288
private equity with fund of funds by 
strategy, 279–282
vintage year, 282–284
private equity with primary fund 
vehicle, 284–286
real estate with closed-end funds, 
277–279
real estate with open-end funds, 
275–277
solutions to problems, 297
sponsors, 230–231
structure, 224
223–224, 258–262
and performance examinations, 262
required procedures, 259–262
scope and purpose, 258–259
website, 228, 233, 234, 259
Standards Committee, 226
golden cross pattern, 706
Goldman Sachs, 718
Gosset, W. S., 595n.15

government(s), 7–8
Graham, Benjamin, 681
grand supercycle, Elliott wave, 724
graphic presentations of data, 399–403
frequency polygons and cumulative 
frequency distributions, 401–403
histograms, 400–401
“greater than” alternative hypothesis, 
624, 625, 651–652
GreatWall Information Industry Co., 
Ltd., 732, 736
Greece, 231, 406, 409
Green Mountain Coffee Roasters, 410
gross-of-fees returnsCalculation Methodology (GIPS 
Real Estate (GIPS Section I.6), 244, 246
gross-of-fees SI-IRR, 245, 249
group decision making, 157
group research, 157, 160
growth rates, solving TMV problems for, 
329–331
Guaranteed Investment Contracts 
(GICs), 317–320
Guggenheim Mid Cap Value Fund Class 
A, 433
Guidance Statements, GIPS, 228, 233, 
234, 259

234, 259
Gupta, Parveen, P ., 638
H
Hang Seng Index, 442
Harley-Davidson Motor Company, 691
harmonic mean, 420–421
harmonic series, 420n.25
head and shoulders patterns, 695–699
about, 695–696
determining price targets from, 698
inverse, 697–699
setting price targets with, 696–699
healthy corrections, 701
hedge funds, sample selection bias for, 
605
Hellenic CFA Society, 231
highest requirement, following, 56
historical performance, GIPS-compliant, 
228–229
historical simulation, 562–563
holding period return (HPR)
defined, 367, 392
finding ending value of investment 
with, 554
formula, 392
and time-weighted rate of return, 370
holding period yield (HPY), 376, 378
Homestead Small Company Stock Fund, 
433
Hong Kong SAR, 231, 406
Hong Kong Society of Financial 
Analysts, 231
Hopkins, Sheila, 722
Hotchkis and Wiley Mid Cap Value A 
Fund, 433
Hotchkis and Wiley Small Cap Value A 
Fund, 433
hot issue securities, 112
HPR. see holding period return

HPY. see holding period yield
Hungary, 231
hurdle rate, 363
hypothesis(-es)
alternative, 624–625, 651–652
defined, 623
formulations of, 624–625
null, 624–625

I-10  Index
hypothesis testing, 591, 621–676
with correlation, 655–658
in data mining, 601–602
nonparametric inference, 654–658
and parametric tests, 654–655, 658
and tests with correlation, 655–658
use of, 654–655
practice problems, 662–669
p-value approach, 631–632
solutions to problems, 670–676
steps in, 623–631
tests with means, 632–648
mean differences, 639–648
single mean, 632–639
tests with variance, 648–654
equality of two variances, 650–654
single variance, 648–650
uses of, 622
Hyundai Steel, 329
I
Ibbotson, Roger G., 426–428
Iberdrola, 423
IID returns. see independently and 
identically distributed returns
illegal activity, disclosure of, 132
impulse wave, 723–725
inadequate compliance procedures, 147, 
152
inadequate supervision, 152–153
incentive structures, 150
incident-reporting procedures, 137
income returns
incremental cash flows, 360n.1
independence
in probability, 474
for random variables, 504

Independence and Objectivity 
[Standard I(B)], 58–70
application of the standard, 64–70
compliance procedures, 63–64
guidance, 58–63
credit rating agency opinions, 61–62
fund manager and custodial 
relationships, 60
influence in manager selection/
procurement process, 62
investment banking relationships, 
60–61
issuer-paid research, 62–63
attribution, 61
public companies, 61
travel funding, 63
text of, 44, 58
independence policies, 64
independent analysis, 97
independent contractors, 136–137
independent events, 483–486
independently and identically 
distributed (IID) returns, 554
independent practice, 134
independent samples, hypothesis tests 
for, 639–644indexes. see also  specific indexes
bond, 584–585
managing to, 121
relative strength, 710–712
short-term trading, 718–720
indexing, 584
Index of Leading Economic Indicators, 
680
Inditex, 423
industry experts, 87–88
inflation premium, 305
inflows, 362, 599–601

account, 105
additional, 262
in advertisements, 256
on applicable laws, 55
confidential, 131–133, 143, 193–194
considering, before taking action, 105
dissemination of, 88, 112–113, 
189–190
electronic, 130
manipulation of, 100–101
material, 85, 92–94
material nonpublic ( see material 
nonpublic information)
misrepresentation of ( see 
misrepresentation)
nonpublic
acting on, 91, 94
analyst recommendations as, 93–94
controlling, 92
defined, 86
standards for priority of transactions 
with, 186
out-of-date, 80–81
outside, 75
potential misrepresentation of, 77
retention of, on new media, 175
supplemental, 270
verification of outside, 75
information-based manipulation, 96
ING, 424
and conflicts of interest, 186–187
duties to clients, 115
ethical decision-making framework for, 
22–25
and technical analysis, 722
about, 232
general, 235

for real estate, 243
inputs, model, 100
insider trading, 679
intangible assets, 16
integrity, 20, 83, 197
Integrity of Capital Markets [Standard 
of Professional Conduct II], 44–45, 
84–101
Market Manipulation [Standard II(B)], 
96–101
application of the standard, 97–101guidance, 96–97
text of, 45, 96
Material Nonpublic Information 
[Standard II(A)], 84–95
application of the standard, 91–95
compliance procedures, 88–91
guidance, 84–88
text of, 44–45, 84
interdepartmental communications, 89
interdepartmental referral arrangements, 
disclosure of, 191
interest
accrued, 376–377
carried, 247, 263
short, 717–718
simple, 306
and mutual fund cash position 
indicator, 721
nominal risk-free, 305
quoted, 310
real risk-free, 305
solving TMV problems for, 329–331
stated annual, 310
and time value of money, 304–305
interest rate sensitivity, 584
interests, client, 106
intergenerational data mining, 602
interim cash, 307–308
intermarket analysis, 726–728

Intermarket Technical Analysis  
(Murphy), 726
internal dispersion
discounted cash flows, 362–367
SI-IRR
defined, 269
gross-of-fees, 245, 249
net-of-fees, 245, 249
247, 250
internal valuation
Real Estate (GIPS Section I.6), 244, 
254
Board (IASB), 252
International Federation of Technical 
Analysts, 681
interquartile range (IQR), 429n.27
intervals, 393–394. see also  confidence 
intervals
modal, 412
time, 690
interval scales, 390
Intesa Sanpaolo, 423
intrafirm pressure, 65, 70
intrinsic value, deviations from, 680

Index  I-11
inverse head and shoulders patterns, 
695, 697–699
investment actions. see also  Investment 
Conduct V]
investment analysis
due diligence in, 61
independent, 97
limitations of, 167–168
Investment Analysis, Recommendations, 
and Actions [Standard of 
Professional Conduct V], 154–176
165–174
Record Retention [Standard V(C)], 
174–176
application of the standard, 176
compliance procedures, 175
guidance, 174–175
text of, 46, 174
Investment and Financial Services 
Association Limited–Performance 
Analyst Group, 230

investment banking, 60–61
investment decision, in hypothesis 
testing, 631
Investment Foundations. see CFA 
Institute Investment Foundations™ 
certificate program
investment industry, ethics in, 5–28, 
39–43
Investment Management Association, 231
Investment Management Association of 
Singapore, 231
247–250
investment multiple (TVPI)
defined, 266, 271
investment objectives
establishing, 105
in IPSs, 121, 176investment performance, standardized, 
227
Investment Performance Council (IPC), 
226
investment personnel. see personnel
investment policy statement (IPS)
in compliance procedures, 121
developing, 119

record retention of objectives/
recommendations in, 176
requirements and limitations of, 
123–124
reviews of, 124
trades not aligned with, 120–121
updating, 120, 123
investment practice, impact of 
misrepresentation on, 72
investment process
changes to, 170–172
informing clients of, 166–167
investment products, applicable laws for, 
51–53
failed, 163
restricting, 64
investment system, disclosure of, 169, 
171
investor confidence, 227
investor psychology, 678, 716
investors
buy-and-hold, 560–562
constraints of, 121
Investors Intelligence Advisors 
Sentiment reports, 715
IPC. see Investment Performance 
Council
IPS. see investment policy statement
IQR. see interquartile range
Ireland
Irish Association of Investment 
Managers, 231
IRR rule, 362–367
evaluating R&D programs with, 
363–364
NPV rule and, 364–365
problems with, 365–367

363–364
iShares Russell 2000 Index, 444
Israel, 406
issuer-paid research, 62–63, 76
issuer relationship pressure, 65–66
Italian CFA Society, 231
Italian Investment Performance 
Italy
real equity returns, 399
J
Jankowitsch, Rainer, 642–643
Japan
companies and derivatives in, 655
fundamental analysis, 681
GIPS sponsor, 231in MSCI EAFE, 406
Treasury bills, 305n.3
Jarque-Bera (JB) statistical test of 
normality, 456n.49
JC Penney Company, Inc., 412
Jensen’s inequality, 419n.21
JetBlue Airways, 476
joint normal distribution, 544
joint probability, 479
joint probability function, 502–504
K
%K (stochastic oscillator), 712, 713
Kahn, Robert L., 622
Kazakhstan, 231
Kazakhstan Association of Financial and 
Investment Analysts, 231
knowingly (term), 71
knowledge of the law, failure to maintain 
knowledge, 57
Knowledge of the Law [Standard I(A)], 
49–57
application of the standard, 55–57

49–57
compliance procedures, 54–55
CFA members and candidates, 54
dissociation, 54
firms, 54–55
legal counsel, 54
guidance, 49–53
Code/Standards and applicable law, 
50–53
investment products and applicable 
law, 51–53
violations by others, participation or 
association with, 51
text of, 44, 49
known errors, noncorrection of, 76
Kohl’s Corporation, 412
Kondratieff, Nikolai, 722
Kondratieff Wave, 722
Korea GIPS Committee, 231
KOSPI Composite Index, 442, 652
kurtosis, 452–456
calculating, 454–456
defined, 452
sample, 453–456
L
labeling problems, 510
Large Cap Equity Growth Composite, 
293
large cash flows, 235, 266
law(s). see also  applicable law
distribution area, 54
ethical influences on, 7–8, 17–18
knowledge of ( see Knowledge of the 
Law [Standard I(A)])
more strict law, 50
religious tenets as basis for, 56–57
Lay, Kenneth M., 13n.10
leaving an employer, 134–135, 143
legal standards, ethical standards vs., 
17–20

17–20
Lehman Brothers Government Index, 
584–585

I-12  Index
lending facility, covenant breach for, 
542–543
leptokurtic, 452, 453
less strict (LS) countries, 52–53
“less than” alternative hypothesis, 624, 
625, 651–652
level of service, disclosure of, 114
level of significance, 626–628
Leveraged Bond Composite, 293
Liber Abaci  (Fibonacci), 724
Liechtenstein, 231
Liechtenstein Bankers’ Association, 231
likelihood, 506
limited partners, 267
limited partnerships, 179, 267
limit orders, probability of executing, 
482–483
limits, on private placements, 187
linear interpolation, 422–423
linear scale, 688, 689
line charts, 682–683
linked performance
Disclosure (GIPS Section I.4), 240
Section I.8), 252
linked time-weighted rates of return, 244
links, 267
liquidity, returns and, 426–428
liquidity premium, 305
local requirements, for record retention, 
175
location, measures of, 404

175
logarithmic scale, 688, 689
lognormal distribution, of continuous 
random variables, 551–557
London Stock Exchange, 726
longitudinal data, 587n.2
look-ahead bias, 605, 606
L’Oreal, 424
lot allocations, minimum, 116–117
lower bound, 589
client approval, 105
firm policies, 105–106
regular account information, 105
client’s portfolio, developing, 103–104
identifying actual investment client, 
103
proxy voting policies, 104–105
soft commission policies, 104
understanding application of 
standard, 102–103
application of the standard, 137–143
employee classification, 137
termination policy, 137guidance, 133–137
employer responsibilities, 134
leaving employers, 134–135
nature of employment, 136–137

social media, 136
whistleblowing, 136
loyalty to clients, 109
LS countries. see less strict countries
lump sum
funding annuity with, 333–336
future, 317–319
future value of, 309–310
present value of, 317–320
LVMH Moët Hennessy, 424
M
MACD line, 714–715
McDonald’s Corporation, 410
MACD oscillator. see moving-average 
convergence/divergence oscillator
MacKinnon, James G., 632n.15
Macy’s Inc., 412
MAD. see mean absolute deviation
maintenance of records, 90, 262
manager selection, 62, 69–70, 164
mandates
following, 123
notification of change in, 170
Mann-Whitney U test, 655
marginal probabilities, 478
margin debt, 716–717, 720
market(s), ethics and, 15–17
market cycles, 722–723
market indicators, 721
market making, 91
96–101
application of the standard, 97–101
guidance, 96–97

transaction-based manipulation, 97
market participants, technical analysis 
and, 678–680
market sentiment
indicators of, 715–718
and technical analysis, 678–679
Market Technicians Association, 681
market timing, 560–562
defined, 267
Section II), 252
Input Data (GIPS Section I.1), 235n.2
Real Estate (GIPS Section I.6),  
243n.6
Market Vane Bullish Consensus, 715
Markowitz, Harry, 428
Marvell Technology Group, 695, 696, 
698
material information, 85, 92–94
materiality, determining, 92, 95material nonpublic information
adopting compliance procedures 
for, 88
legal vs. ethical restrictions on, 18
achieving public dissemination, 88
adopting, 88
adopting disclosure procedures, 
88–89
appropriate interdepartmental 
communications, 89
communication to employees, 91

firewall elements, 89
issuing press releases, 89
personal trading limitations, 90
physical separation of departments, 
89
preventing personnel overlap, 90
proprietary trading procedures, 91
record maintenance, 90
reporting systems, 90
investment research reports, 88
material information defined, 85
mosaic theory, 86–87
nonpublic information defined, 86
social media, 87
maturity premium, 305
mean(s)
arithmetic, 404–408
population mean, 404–405
of binomial random variables, 537
cross-sectional, 405–407
geometric, 416–420
and arithmetic mean, 418–420
harmonic, 420–421
hypothesis testing with, 632–648
tests with mean differences, 639–648
tests with single mean, 632–639
of lognormal distribution, 553,

of lognormal distribution, 553, 
556–557
of normal distribution, 543, 546
population, 404–405
estimates of, 591–601
test static for single, 633–636
sample, 405–407, 588n.3
distribution of, 588–591
as point estimator, 591, 593
standard error of, 588–589
of standard normal distribution, 544
trimmed, 408n.14
weighted, 413–416
Winsorized, 408n.14

Index  I-13
mean absolute deviation (MAD), 
429–431
in tests with dependent samples, 
644–648
in tests with independent samples, 
639–644
mean returns on S&P 50, 640–642
recovery rates on defaulted bonds, 
642–644
mean excess return, 443–444
mean–variance analysis, 496n.10, 549
measurement scales, 390–391
measures of central tendency, 404–422
defined, 404
median, 409–411
and arithmetic mean, 410–411
mode, 411–413
weighted mean, 413–416
measures of location, 404
measuring implication, triangle pattern’s, 
703–704
members, CFA. see Responsibilities as 

Membership Agreement, 51
membership status, CFA Institute, 
198–199, 201
mesokurtic, 452
Micronesia, 231
Microsoft Excel, 631n.14
minimum lot allocations, 116–117
Misconduct [Standard I(D)], 81–84
application of the standard, 82–84
compliance procedures, 82
guidance, 81–82
text of, 44, 81
misrepresentation
avoiding, 80
of information, 79
potential, 77
Misrepresentation [Standard I(C)], 
71–81
application of the standard, 76–81
compliance procedures, 74–75
factual presentations, 74–75
maintaining webpages, 75
plagiarism policy, 75
qualification summary, 75
verifying outside information, 75
guidance, 71–74
impact on investment practice, 72omissions, 73
performance reporting, 72–73
plagiarism, 73–74
social media, 73
work completed for employer, 74
text of, 44, 71
modal interval, 412
Model Request for Proposal, 157
models
manipulating inputs for, 100
in quantitatively oriented research, 
156–157
understanding technical aspects of, 
164–165

156–157
164–165
modern portfolio theory (MPT), 549
momentum oscillators, 708–715
about, 708–710
MACD oscillator, 714–715
relative strength index, 710–712
stochastic oscillator, 712–714
monetary policy, 585–586
money (TMV)
money managers, estimation of client 
inflows by, 599–601
money market, 375
discount rate for, 378–379
other yields vs., 378–379
money-weighted rate of return
for portfolios, 368–369, 372–374
time- vs., 372–374
Monte Carlo simulation, 557–563
of capital expenditures, 589–590
historical simulation vs., 562–563
number of trials for, 559
potential gains from market timing, 
560–562
process, 558–559
random observations in, 559–560
Moody’s Investors Service, 412–413
moral principles, 7
more strict (MS) countries, 52–53
Morningstar, 390, 426
mortgage, fixed-rate, 332–333
mosaic theory
applying, 93, 94
and material nonpublic information, 
86–87

86–87
Motley Fool, 602
moving-average convergence/
divergence (MACD) oscillator, 
714–715
moving averages, 705–707
MSCI Europe, Australasia, and Far East 
(EAFE) Index
cross-sectional mean of, 406–407
portfolio expected return and variance 
of return, 496, 497, 500, 501
tracking objective, 536
MSCI World Index, 464–465
MS countries. see more strict  
countries
Multiple Strategy Portfolios (MSP), 251multiplication rule for expected value 
multiplication rule for independent 
events, 483–486
multiplication rule for probabilities, 479, 
481
multiplication rule of counting, 509–510
multivariate distribution, 544
multivariate normal distribution, 544
Munich RE, 423
Murphy, John, 726
must (term), 267
must not (term), 267
720–721
performance of, 485–486
predictability of performance for, 
480–481
risk/returns of, 634–635, 649–650

480–481
skewness of, 450–452
mutually exclusive events, 475
mutually exclusive projects, 361
N
Nagler, Florian, 642–643
names, fictitious, 202
NASDAQ
Arms index, 719–720
National Association of Pension Funds, 
231
National Bureau of Economic Research, 
680
National League of Management 
Nayar, Nandkumar, 638
Neiman Marcus Group, Inc., 412
net client inflows, estimating, 599–601
Netherlands Beroepsvereniging van 
Beleggingsprofessionals, 231
net-of-fees returns
248
246
net-of-fees SI-IRR, 245, 249
net present value (NPV), 360–362
new accounts, temporary, 237, 270

new equity issuance indicator, 721–722
new firms, starting, 140
new media, retention of information on, 
175
New York Society of Security Analysts, 
681

I-14  Index
cross-sectional data from, 585
intermarket analysis, 726
New Zealand, 231, 399, 406
New Zealand Stock Exchange, 527
Nikkei 225 Index, 405, 690
Nikkei-Dow Jones Average, 582
nodes, 491, 538
noise, on point and figure charts, 687
nominal risk-free interest rate, 305
nominal scales, 390
noncompete agreements, 135
noncorrection of known errors, 76
nonparametric test, 654–655
nonpublic information
material ( see Material Nonpublic 
Information [Standard II(A)])
with, 186
Nordstrom, Inc., 412
normal distribution
estimating probability with, 551
distributed populations
difference between population 
means, 640–644

differences between variances, 651
mean differences, 645–648
single population mean, 633–636
value of population variance, 649
normal distribution of continuous 
random variables, 543–551
549–551
598–599
standard, 544, 740–741
Norway
Norwegian Society of Financial Analysts, 
231
no securities laws (NS) countries, 52–53
“not equal to” alternative hypothesis, 
notification
changes to investment process, 
170–172
client bonus compensation, 144–145
Code and Standards, 142of errors, 172
fund mandate change, 170
known violations, 55
outside compensation, 145
of risks/limitations, 173–174
NPV rule
defined, 361
evaluating R&D programs with,  
362

362
and IRR rule, 364–365
NS countries. see no securities laws 
countries
null hypothesis, 624–625
O
objective probabilities, 476
investment, 105, 121, 176
objectivity. see Independence and 
Objectivity [Standard I(B)]
odds, probabilities stated as, 476–479
omissions, 73
one-sided (one-tailed) hypothesis test, 
624
open-end funds, 247, 267, 275–277
opinion polls, 715
opinions
about CFA Program or Institute, 194
of credit rating agency, 61–62
facts in reports vs., 168
group research, 160
integrity of, 63
providing, as facts, 169
opportunity cost, 304
option pricing models, volatility in, 
555–556. see also  specific models, 
e.g.: Black–Scholes–Merton model
options
agent, 182
call, 539, 558–559, 563, 568
European-style, 558, 563, 566
put, 566
ordinal scales, 390
ordinary annuities, 314
and annuity due, 322–323
present value of, 321, 327
projected present value of, 323–325

oscillators. see momentum oscillators
Österreichische Vereinigung für 
Finanzanalyse und Asset 
Management, 230
outcomes, of random variables, 
474–475
outflows, 362
out-of-date information, 80–81
out-of-sample tests, 602
outside information, verifying, 75
outside organizations, referral 
arrangements with, 192
outside parties, referral arrangements 
and, 190–192
overbought conditions, 708
overconfidence bias, 11–12
oversold conditions, 708ownership
beneficial, 186, 187
of completed prior work, 139
of firm’s records, 175, 176
stock, 179–181
P
paid-in capital, 249, 267
paired comparisons test, 644
paired observations, 644
pairs arbitrage trade, 478
Pakistan, 231
panel data, 587n.2
parameters, 389, 582. see also  specific 
parameters
parametric tests, 654–655, 658
partial fills, 113
partnerships, broker-sponsored limited, 
179
passing exams in consecutive years, 201
payments
fixed-rate mortgage, 332–333
receivable, 635–636
pay-to-play scandals, 62

P C P.  see Professional Conduct Program
P/E. see price-earnings ratio
Pearson coefficient of skewness, 449n.42
pennant patterns, 704–705
pension plans, defined benefit, 557
percentiles, 421–425
performance appraisal, 367, 425–426
performance attribution, 128
performance-based fees, 238, 267
performance calculation, 126–127
disclosing methodology for, 128–129
with selected accounts, 128
performance evaluation, 367n.8
benchmarks for, 121
objectivity of, 61
performance examination report, 262, 
268
performance examinations
Verification (GIPS Section IV), 262
performance measurement, 367
performance presentation, 127–128
performance reporting, 72–73, 
456–457
periodicity, 241, 268

456–457
periods, number of, 331–332
permutation, 511
perpetuities
present value of, 325–326
and present value of ordinary annuity, 
327
present value of projected, 326–327
personal actions, 83

Index  I-15
personal trading
and conflict of interest, 183
disclosure of, 188, 189
limitations on, 90
and market manipulation, 97–98
priority of transactions for, 185
personnel
preventing overlap of, 90
privy to recommendation, 112
reporting requirements for, 187–188
Petroleo Brasileiro ADRs, 713–714
Philips, 423
PIC multiple
plagiarism, 77–79
and misrepresentation, 73–74
policies on, 75
platykurtic, 452
PME. see public market equivalent
point and figure charts, 686–688
The Point and Figure Method of 
Anticipating Stock Price Movements  
(de Villiers and Taylor), 686
point estimates, 594
point estimators, 591–593, 594n.12
pooled estimates, 640
population, 389, 582
population standard deviation,  
432–434
population variance, 431–432
portfolio(s)
Calculation Methodology (GIPS

developing, 103–104
discretionary, 260
expected defaults in, 537–538
expected returns
Section II), 253
measurement of returns, 367–374
369–374
weighted mean, 415–416
MSPs, 251
probabilities for common stock, 548
Real Estate (GIPS Section I.6), 243, 
245, 246
suitability of investment for, 122–123Verification (GIPS Section IV), 
259–261
wrap fee/SMA ( see Wrap Fee/SMA 
Portfolios [GIPS Section I.8])
portfolio managers, independence of, 59
portfolio turnover, 432–434
Portugal, 231, 406, 409
posterior probability, 506
power of a test, 627
practice, defined, 134

precision, point estimator, 594n.12
preclearance procedures, 188
pre-dissemination behavior, guidelines 
for, 113
premiums, risk, 305, 494–495, 625
about, 232
general, 242
general, 240–242
for private equity, 248–249
for real estate, 244–245
composites, 245–246
for wrap fee/SMA portfolios, 252
asset management company,  
273–274
presentations, 127–128. see also  
present value (PV)
future and, 307, 336–337
present value of series of cash flows, 
320–328
with equal cash flows, 320–325
for infinite series of equal cash flows, 
325–326
at other times than t = 0, 326–327
with unequal cash flows, 328
317–320
finding, 317–319

317–320
frequency of compounding, 319–320
for future lump sum, 317–319
for lump sum, 317–319
compliance with laws, 130
electronic information and security, 
130
professional conduct investigations 
by CFA Institute, 130
status of clients, 130
press releases, issuing, 89
pre-verification procedures, GIPS, 
259–260PRFDX funds. see T. Rowe Price Equity 
Income fund
price
asset
696–699
convergence of oscillator and, 708
full, 377n.14
and personal trading practices, 97–98
stock
as Bernoulli random variable, 
530–531
binomial model, 538–539
and control deficiency disclosures, 
637–639
lognormal distribution for, 553–554
price-based indicators, 705–708

price-earnings ratio (P/E), 410–411
price relative, 553
price targets, 696–700
price-to-book ratio (P/B), 604
primary funds, 247–249, 268
primary fund vehicle, 284–286
principal, 306
prior coverage, 66
prior employer
prior fund, in performance presentation, 
127
accounts with beneficial ownership, 
186
avoiding potential conflicts, 185
nonpublic information, 186
personal trading and trading for 
clients, 185
prior probabilities, 505
prior work, ownership of, 139
private equity
and GIPS compliance, 229
Section II) for, 254, 255
sample presentations, 279–286
Private Equity (GIPS Section I.7), 247–250
about, 233
Calculation Methodology provisions, 
247, 250

247, 250
Composite Construction provisions, 
248, 250
Disclosure provisions, 248, 250
Input Data provisions, 247, 250
Presentation and Reporting provisions, 
248–250
recommendations, 250
requirements, 247–249

I-16  Index
private placements, limits on, 187
probability(-ies), 473–522
a priori, 476
about, 474
Bayes’ formula, 504–508
for common stock portfolio, 548
conditional, 478–481, 485–486
consistent, 478
correlation, 501, 503–504
counting, 508–511
cumulative, 740–741
defined, 475–476
down transition, 538
empirical, 476
events
defined, 488–489
total probability rule for expected 
value, 490–492
variance, 489–490
joint, 479
marginal, 478
objective, 476
portfolio expected return
posterior, 506
practice problems, 515–518
prior, 505
of random variables, 504
rules
addition rule for probability, 481–482
multiplication rule for expected value

multiplication rule for expected value 
multiplication rule for probability, 
479, 481
multiplication rule of counting, 
509–510
total probability rule, 486–488
solutions to problems, 519–522
subjective, 476
in terms of odds, 476–479
transition, 538
unconditional, 478
up transition, 538
variance
covariance, 497–502
and portfolio expected return, 502
probability density function, 528
probability distributions, 525–579
540–543
normal distribution, 543–551cumulative probabilities for standard 
normal distribution, 740–741
defined, 526
discrete uniform distribution, 
528–530
distribution of bond price, 527–528
560–562

560–562
practice problems, 566–572
of sample mean, 588–591
solutions to problems, 573–579
product, of uncorrelated random 
profession (term), 9–10
professional conduct. see Standards of 
professional conduct investigations,  
130
Professional Conduct Program (PCP), 
37–38, 51, 82, 130
Professional Conduct Statement, 8–9
professional designations, order of, 202
professionalism, 9–11, 82
Professionalism [Standard of 
Professional Conduct I], 49–84
49–57
71–81

71–81
text of, 44
professionally designated, certified, 
or licensed commercial property 
valuers/appraisers
Section II), 254
244, 246
professional misconduct, 83–84
promotion, company, 97
proprietary assets, 240, 268
proprietary trading procedures, 91prospective clients. see also  
Communication with Clients 
and Prospective Clients 
[Standard V(B)]
benefits of GIPS compliance for, 223
Section III), 256
Verification (GIPS Section IV),  
258
“Protocol for Broker Recruiting, ” 135
proxy voting policies, 104, 106
prudence. see Loyalty, Prudence, and 
Care [Standard III(A)]

pseudo-random numbers, 559n.45
public companies, independence and 
public dissemination, achieving, 88
public market equivalent (PME), 248, 
268
pump and dump strategy, 100
pump-priming strategy, 99
pure discount instruments, 375
put/call ratio, 715–716
put options, European, 566
PV. see present value
p-value approach to hypothesis testing, 
624, 631–632
Q
Q&As. see Questions & Answers, GIPS
Qlik Technologies, 411
quantiles, 421–428
calculating, 423–425
defined, 421
in investment practice, 425–428
types of, 421–425
quantitatively oriented models, 157, 
162–163
156–157
quantitatively oriented techniques,  
157
quartiles, 421
Questcor Pharmaceuticals, 411
Questions & Answers (Q&As), GIPS, 
228, 233, 234, 259
quintiles, 421
quotations, attributing, 75
quoted interest rate, 310
R
randomness, 583
random number generator, 559
random numbers, 559–560
random observations, in Monte Carlo

random observations, in Monte Carlo 
simulations, 559–560
random sampling
simple, 582–584
stratified, 584–585

Index  I-17
random variables, 474–475
Bernoulli, 530–531
binomial, 532–534
continuous ( see continuous random 
variables)
discrete ( see discrete random variables)
independence for, 504
of product of, 504
outcomes of, 474–475
standardization of, 546–547
uncorrelated, 504
range
definition, 429
interquartile, 429n.27
and mean absolute deviation, 
430–431
ranked data, nonparametric tests of, 
654–655
rate of change (ROC) oscillator, 
708–710
rate of return. see also  internal rate of 
return (IRR)
time-weighted rate of return
Section I.2), 235
defined, 270
linked, 244
money- vs., 372–374
for portfolios, 369–374
244, 245
ratio scales, 390
RBC Canadian Index Fund, 413–414, 
417
R&D programs. see research and 
development programs
real estate
Section II) for, 253–255

sample presentations
with closed-end funds, 277–279
with open-end funds, 275–277
242–246
about, 233
243–246
for closed-end fund composites, 
245–246
245
Disclosure provisions, 244–246
Input Data provisions, 243, 246
244–246
recommendations, 246
requirements, 243–246
realization multiple (DPI)
defined, 265, 269
249
Real Estate (GIPS Section I.6), 246real risk-free interest rate, 305
reasonable basis. see also  Diligence and 
Reasonable Basis [Standard V(A)]
developing, 159
receivables, payments of, 635–636
recommendation objectivity, 68–69
recommendations. see also  Investment 
Conduct V]
fair dealing in, 110–111
in investment policy statements, 176
as material nonpublic information, 
93–94
number of people privy to, 112

93–94
reasonable basis for, 155
record keeping, supervision of, 151
174–176
local requirements, 175
new media records, 175
records as firm property, 175
records
maintenance of, 90, 262
as property of firm, 175, 176
retention of, 176
recovery rates, on defaulted bonds, 
642–644
rectangle patterns, 704
references, employee, 82
Reference to CFA Institute, Designation 
and Program [Standard VII(B)], 
198–202
application of the standard, 201–202
compliance procedures, 200
guidance, 198–200
CFA designation, 199
CFA Institute membership, 198–199
referring to candidacy in CFA 
program, 199–200
text of, 47, 198
referral arrangements
disclosure of, 190–192
informing firms of, 191
interdepartmental, 191
Referral fees [Standard VI(C)], 190–192
Regional Investment Performance

Regional Investment Performance 
Subcommittees, 230
regulations, ethics and, 17–19, 41
rejection point
for tests on population variance, 
649–650
for tests on relative values of 
population variances, 651–654
for test statistic, 628–630
for z-test alternative, 637
rejection region, test statistic, 629
related parties, gifts and entertainment 
from, 66–67relationships
and conflicts of interest, 180, 184
custodial, 60
fund manager, 60, 70
independent contractor, 136–137
and issuer relationship pressure, 
65–66
relative dispersion, 441
relative frequency
and frequency distributions, 394–398
relative strength analysis
of charts, 690–691
in intermarket analysis, 727–728
relative strength index (RSI), 710–712
reliability factors
basis of computing, 598–599
for confidence intervals, 594–595, 
598–599
religious tenets, laws and regulations 
based on, 56–57
reporting
of material nonpublic information, 90
performance, 72–73, 456–457

of potential unethical actions, 57
requirements for investment 
personnel, 187–188
of violations, 55
reports
facts vs. opinions in, 168
flash, 113
material nonpublic information in, 88
performance examination, 262, 268
presentation of, 168
research, 88
verification, 258, 259, 262, 271
representation letter, 262
representative accounts, 221
Repsol, 423
requested favors, 183
request for proposal (RFP), 140
requirements (term), 269
research
diligence, 158
group, 157, 160
independence of, 65–66, 68
issuer-paid, 62–63, 76
and plagiarism, 73–74
quantiles in, 425–428
quantitatively oriented, 156–157
reasonable basis for, 159
and record retention, 176
sampling biases in, 606–607
secondary, 155–156
supervision of, 150–151, 153–154
third-party, 155–156, 160
research and development (R&D) 
programs
IRR rule in evaluation of, 363–364
NPV rule in evaluation of, 362
research reports, material nonpublic 
information in, 88
residual value

resistance, 693

I-18  Index
Responsibilities as a CFA Institute 
Member or CFA Candidate 
[Standard of Professional Conduct 
VII], 193–202
Conduct as Participants in CFA 
Institute Programs [Standard 
VII(A)], 193–197
eleventh addition revision, 36–37
Designation and Program [Standard 
VII(B)], 198–202
201–202
Responsibilities of Supervisors [Standard 
IV(C)], 146–154
adequate, 148–149
and code of ethics, 148
establishing appropriate incentive 
structures, 150
implementation of compliance 
education and training, 149
detection as part of supervision, 
147–148
system for supervision, 147
responsibility(-ies)
accepting, 152
of employers, 134
execution-only, 109
restricted lists, creating, 64
restricted periods, 187
results

results
overemphasis of, 81
simulated, 127–128
retired CFA Institute membership 
status, 201
retracements, 692
return(s)
in advertisements, 289–291
annual, advertisements with, 290–291
annualized, advertisements with, 
289–290
and bank discount yield, 376
capital, 244, 263
continuously compounded, 553–554
for discount securities, 377
dollar-weighted, 368n.9
equity, 398–399
expected, 497, 502
geometric mean, 418–420
gross-of-fees
Section I.5), 241, 242Private Equity (GIPS Section I.7), 248
246
holding period
with, 554
income, 244, 266
distributed, 554
and liquidity, 426–428
mean excess, 443–444
of mutual funds, 634–635, 649–650
net-of-fees

247, 248
246
portfolio
expected portfolio returns, 502
measurement of returns, 367–374, 
415–416
total
reversal size, on point and figure charts, 
687
reviews
account, 105, 114
of compliance procedures, 54

for independence/objectivity, 64
RFP . see request for proposal
risk
financial, 551n.27
of investment analysis, 167–168
notification of, 173–174
shortfall, 549–551
Value at Risk, 551, 557
risk-arbitrage trading, 91
risk management, 551
risk premiums, 305, 494–495, 625risk profile
investment suitability for, 122, 124
understanding, 119
Robeco Boston Partners Small Cap 
Value Fund II, 433
robust (term), 633
Rockwell Automation, 700–701
ROC oscillator. see rate of change 
oscillator
Rodman and Renshaw, 691
Roy, A. D., 549n.24
Roy’s safety-first rule, 549–551
RSI. see relative strength index
Rule of 72, 332n.9
Rules of Procedure. see Bylaws and 
Rules of Procedure for Professional 
Conduct
rumors, addressing, 138–139
runs test, 655
Russell 2000 Index, 444
Russia, 231
RVPI. see unrealized multiple
RWE, 423
S
SAC Capital, 6
safety-first rules, 549–551
Saint-Gobain, 423
Saks Incorporated, 412
sales pressure, 66

sample excess kurtosis, 453–456
sample mean, 405–407, 588n.3
as point estimator, 591, 592
samples
defined, 389, 582
dependent, 644–648
independent, 639–644
reasons for taking, 582
in statistics, 389
sample selection bias, 604–605, 630–631
sample size
and estimates of population mean, 
599–601
and sampling distribution, 592–593
sample skewness, 449–450
sample standard deviation, 435–437
sample statistic, 389, 582–584
sample variance, 434–435
calculating, 435–437
as point estimator, 592
sampling, 581–620
about, 582
biases, 601–607
in investment research, 606–607
sample selection bias, 604–605, 
630–631
survivorship, 604, 606
survivorship bias, 630–631
time-period bias, 605, 607, 630, 631
and central limit theorem, 588–591
distribution of sample mean, 588–591
estimates of population mean, 591–601

Index  I-19
practice problems, 610–614
simple random, 582–584
solutions to problems, 615–620
stratified random, 584–585
of time-series and cross-sectional data, 
585–587
sampling biases, 601–607
630–631
sampling distribution, 584, 592
sampling error, 583–584
sampling plans, 583
Sam’s Club, 404
sanctions, 38, 43
Sanofi, 424
SAP , 424
Sarbanes–Oxley Act, 637–639
Satyam Computer Services, 6
Savage, Sam, 557
scale, chart, 688–689
scenario testing, 159, 551
Schneider Electric, 424
Sears, Roebuck and Co., 412
secondary funds, 247, 269
secondary research, 155–156
securities, description of, 169–170
Securities Exchange Act (1934), 681
security (of electronic information), 
130
Security Analysts Association of Japan, 
231
Selected American Shares (SLASX) fund

231
geometric and arithmetic mean 
returns, 418–420
range and mean absolute deviation, 
430–431
sample variance and sample standard 
deviation, 435–437
Sharpe ratio, 445, 446
selective disclosure, 92, 114, 116
self-dealing, 135
self-regulation of GIPS standards, 230
selling short, 478n.2
semilogarithmic scale, 456–457
semivariance, 437–438
sentiment indicators, 715–718
sequential comparisons, 484n.6
series of cash flows
future value, 314–316
present value, 320–328
infinite series of equal cash flows, 
325–326
with unequal cash flows, 328service(s)
additional, for select clients, 116
level of, 114
service fees, 68
service providers, selecting, 163–164
SET. see Stock Exchange of Thailand
settlement date accounting, 269
Sharpe, William, 428–429, 443
Sharpe ratios, 443–446

calculating, 586–587
confidence interval for population 
mean, 595–596, 598
formula for, 443–445
Shiller, Robert J., 679
shortfall risk, 549–551
shorting, 478n.2
short interest, 717–718
short-term trading index (TRIN), 
718–720
should (term), 269
Siemens, 424
signal line, MACD oscillator, 714
significant cash flows
SI-IRR. see since inception internal rates 
of return
simple interest, 306
simple random sample, 583
simple random sampling, 582–584
simulated results, 127–128
simulation trials, 558
simultaneous dissemination, 113
since inception (term), 269
since inception distributions, 249
since inception internal rates of return 
(SI-IRR)
249
since inception paid-in capital, 249
Singapore, 231, 406, 442, 443
single cash flow
future value, 306–314
with continuous compounding,

312–313
frequency of compounding, 310–312
stated and effective rates for, 313–314
present value, 317–320
319–320
single mean hypothesis tests, 632–639
and effect of disclosures on share 
prices, 637–639
and payments of receivables, 635–636
and risk/returns of mutual funds, 
634–635single variance hypothesis tests, 
648–650
situational influences, 12–13, 21–22
skewness, 446–452
of binomial distribution of discrete 
random variables, 533
defined, 449
of mutual funds, 450–452
of normal distribution, 544
sample, 449–450
skewed distributions, 446–449
of S&P 500, 450
Skilling, Jeffery K., 13
SLASX fund. see Selected American 
Shares fund
SMA portfolios. see Wrap Fee/SMA 
Portfolios (GIPS Section I.8)
Socially Responsible Investment (SRI) 
Composite, 292–293
social media

disclosure of confidential information 
on, 132–133
and duties to employer, 136
limited disclosures on, 117
and material nonpublic information, 87
misrepresentation on, 73
retention of information on, 175
Société Française des Analystes 
Financiers, 230
Société Générale, 423
society, benefit of ethics to, 40
soft commissions, 104
soft dollars, 104
software, GIPS-compliant, 222
solicitation, of former clients, 137–142
South Korea, 231, 442
S&P . see entries beginning  with Standard 
& Poor’s
Arms index, 718–719
CBOE Volatility Index, 716
Chebyshev’s inequality for, 440–441
consensus current P/E, 410, 411
cumulative relative frequency and 
relative frequency of, 402–403
and data mining, 603
distribution of annual returns, 462
equity market returns, 437
expected value from, 416
frequency distribution for holding 
period returns, 392–398
frequency polygon, 401–402
histogram, 400–401, 404

as indicator, 582
margin debt vs., 717
mean returns on, 640–642
range, 429
relative strength analysis, 690, 691
skewness and kurtosis, 450
and SPDR S&P 500, 444, 646–647
weighted averages on, 416

I-20  Index
Spain
S&P/ASX 200 Index, 442
SPC. see Standards of Practice Council
SPDR S&P 500
Sharpe ratio, 444
Vanguard Total World Stock Index 
ETF vs., 647–648
Spearman rank correlation coefficient, 
655–658
sponsors, GIPS, 230–231
springs, 702
S&P/TSX Composite Total Return 
Index, 413–414
SRI Composite. see Socially Responsible 
Investment Composite
Sri Lanka, 231
stakeholders
defined, 6
impact of ethical practices on, 6–9
standard deviation. see also  variance
defined, 270, 431
expected value of, 489–490
of normal distribution, 543, 545–546
population, 432–434
sample, 435–437
standard error
in confidence interval construction, 
594
of the sample mean, 588–589, 599
of test statistic, 626
standardization, of random variables, 
546–547
standard normal distribution, 544, 
740–741
standard normal variables, probability 
of, 547
Standard & Poor’s (S&P), ratings, 390, 
391n.3

391n.3
standards of conduct (term), 8
Standards of Practice Council (SPC), 
38–39, 43
Standards of Practice Handbook,  3, 
33–37, 39, 42
eleventh edition, 35–37, 39
revisions to, 34
8, 33–47, 49–220. see also  Asset 
Manager Code of Professional 
Conduct (AMC)
conflicts of interest [Standard VI], 
177–192
disclosure of conflicts [Standard 
VI(A)], 46, 177–184
priority of transactions [Standard 
VI(B)], 46–47, 185–190
referral fees [Standard VI(C)], 47, 
190–192
text of, 46–47
duties to clients [Standard III], 
101–133
fair dealing [Standard III(B)], 45, 
110–118loyalty, prudence, and care [Standard 
III(A)], 45, 101–109
performance presentation [Standard 
III(D)], 45, 125–129
preservation of confidentiality 
[Standard III(E)], 45, 129–133
suitability [Standard III(C)], 45, 
118–125
text of, 45
duties to employers [Standard IV], 
133–154
additional compensation 
arrangements [Standard IV(B)], 46, 
144–145

144–145
loyalty [Standard IV(A)], 45–46, 
133–143
responsibilities of supervisors 
[Standard IV(C)], 36, 46, 146–154
text of, 45–46
integrity of capital markets 
[Standard II], 84–101
market manipulation [Standard 
II(B)], 45, 96–101
material nonpublic information 
[Standard II(A)], 44–45, 84–95
text of, 44–45
investment analysis, recommendations, 
and actions [Standard V], 154–176
communication with clients and 
prospective clients [Standard V(B)], 
36, 46, 165–174
[Standard V(A)], 46, 154–165
record retention [Standard V(C)], 46, 
174–176
text of, 46
practice problems, 203–212
37–38
professionalism [Standard I], 49–84
independence and objectivity 
[Standard I(B)], 44, 58–70
knowledge of the law [Standard I(A)], 
44, 49–57
misconduct [Standard I(D)], 44, 
81–84
misrepresentation [Standard I(C)], 
44, 71–81
text of, 44

44, 71–81
text of, 44
responsibilities as a CFA Institute 
member or CFA candidate 
[Standard VII], 193–202
conduct as participants in CFA 
Institute programs [Standard 
VII(A)], 36–37, 47, 193–197
reference to CFA Institute, 
designation and Program [Standard 
VII(B)], 47, 198–202
text of, 47
solutions to problems, 213–220
38–39
33–37
text of, 44–47
and values of CFA Institute, 43Stanford Financial Group, 6
stated annual interest rate, 310
stated rates, for single cash flow, 
313–314
statements of account information, 105
statistical inference, 389, 591, 622
statistical significance, 628
statistics, 387–471. see also  test statistic
about, 388
437–438

437–438
cumulative, 401–403
identifying, 391
types of scales, 390
nature of, 389
populations and samples, 389–390
practice problems, 461–467
sample, 389, 582–584
sampling distribution of, 584
solutions to problems, 468–471
symmetry, 446–452
using geometric and arithmetic means, 
456–457
status, client, 130
stock, ownership of, 179–181
Stock Exchange of Thailand (SET), 476

stock price
as Bernoulli random variable, 530–531
637–639
stock screens, 484–485
Straits Times Index, 442

Index  I-21
stratified random sampling, 584–585
Stratton Small-Cap Value Fund, 433
stratum, 584
stress testing, 551
Student’s t-distribution. see 
sub-advisors
selecting, 157, 164
subjective probability, 476
submanagers, 124, 160–161
subminuette, Elliott wave, 724
Subrahmanyam, Marti G., 642–643
suitability, 124–125
for entire portfolio, 122–123
for investor risk profile, 122, 124
application of the standard, 122–125
investment policy statements, 121
regular updates, 122
suitability test policies, 122
addressing unsolicited trading 
requests, 120–121
developing investment policies, 119
managing to indexes or mandates, 
121
need for diversification, 120
understanding client’s risk profile, 
119
updating investment policies, 120
summaries, attributing, 75
supervision

detection as part of, 147–148
inadequate, 152–153
of research activities, 150–151, 
153–154
system for, 147
of trading activities, 151
supervisors. see Responsibilities of 
Supervisors [Standard IV(C)]
supplemental information, 270
support, 693
survivorship bias, 604, 606
and GIPS standards, 222
and hypothesis testing, 630–631
sustainability, of capital markets, 40–41
Sviluppo Mercato Fondi Pensione, 231
Sweden
Swedish Society of Financial Analysts, 
231
Swiss Bankers Association, 231
total returns, 407, 410
symmetrical triangle pattern, 703
symmetry, 446–452, 533
systematic sampling, 583T
T. Rowe Price Equity Income fund
kurtosis, 454–456
T. Rowe Price Equity Income (PRFDX) 
fund
430–431
sample variance and sample standard

430–431
T. Rowe Price Small Cap Value Fund, 
433
target semideviation, 438
target semivariance, 438
Taylor, Owen, 686
TD Bank. see Toronto-Dominion Bank
and confidence interval for population 
mean, 597–598
table, 742
technical analysis, 677–738
defined, 678
fundamental vs., 680–682
intermarket, 726–728
practice problems, 731–735
principles and assumptions, 678–680
solutions to problems, 736–738
tools for, 682–723
technical indicators, 705–722
trends, 691–694
flow-of-funds, 718–722

ROC oscillator, 708–710
price-based, 705–708
moving average, 705–707
sentiment, 715–718
calculated statistical indexes, 
715–718
technical model requirements, 
understanding, 164–165
Telefonica, 424
temporary new accounts, 237, 270
Terminated Composites. see US Core 
Equity Compositetermination policies, 137
test statistic
acceptance region for, 628–629
calculating, 630–631
defined, 625–626
rejection point for, 628–630
rejection (critical) region for, 629
in tests concerning difference between 
variances, 651
in tests concerning value of population 
variance, 649
in tests of difference between 
population means, 640–644
in tests of mean differences, 645–648
in tests of single population mean, 
633–636
third-party custodians, 60
third-party research, 155–156, 160
time
on point and figure charts, 686
present value of cash flows at times

present value of cash flows at times 
other than t = 0, 326–327
time frame
of decision and dissemination, 
112–113
and performance calculation, 126–127
time intervals, chart, 690
time period, GIPS standards and, 222
time-series data, 405–406, 585–587
time value of money (TMV), 303–357
cash flow additivity principle, 338
defined, 304
and discounted cash flows, 359
future value
equivalence of present and, 336–337
of series of cash flows, 315–316
of single cash flow, 306–314
and interest rates, 304–305
practice problems, 340–344
present value
equivalence of future and, 336–337
of series of cash flows, 320–328
of single cash flow, 317–320
solutions to problems, 345–357
solving problems for variables, 
328–338
interest rates and growth rates, 
329–331
number of periods, 331–332
Time Warner, 700

244, 245
TMV. see time value of money
Tokyo Stock Exchange, 405
ROC oscillator, 709
TOPIX, 416
Toronto-Dominion Bank (TD Bank), 
690, 718
Total (company), 424

I-22  Index
total firm assets
Verification (GIPS Section IV), 259, 
260
total probability rule, 486–488, 505
total returns. see also  holding period 
return (HPR)
total value
Toyota Motor Corporation, 330–331, 
709–710
tracking error, 536
tracking risk, 536
trade date accounting, 235, 270
trading
excessive, 108, 117
personal
disclosure of, 189
risk-arbitrage, 91

supervising trading activities, 151
unsolicited requests for, 120–121
trading expenses
trading volume, 98
on charts, 689–690
and head and shoulders pattern, 696
trends in, 679
training, compliance, 149
transaction allocation, 115–116
transaction expenses
defined, 271
248
Real Estate (GIPS Section I.6), 243, 244
transition probability, 538
Transocean, 703
travel expenses, 64–65, 67–68
Treasury bills, 305n.3, 377n.16. see also  
US Treasury bills
Treasury debt, 305
tree diagrams (binomial trees), 491–492, 
538trends
recognizing, 691–694
in technical analysis, 680–681
trials, number of (for Monte Carlo 
simulation), 559
triangle patterns, 702–704
trimmed mean, 408n.14
TRIN. see short-term trading index
triple bottoms, 700–701
triple tops, 700–701
t-test, 632–636
nonparametric test vs., 654, 655

risk/return characteristics of mutual 
fund, 634–635
and slowdown in payments of 
receivables, 635–636
and Spearman rank correlation, 
656–658
and test static for difference between 
and test static for single population 
mean, 633–636
for test statistic for tests of mean 
difference, 645–648
z-test vs., 636, 639, 654, 655
turnover
annual share, 426
portfolio, 432–434
TVPI. see investment multiple
two-sided (two-tailed) hypothesis test, 
624
2001 Venture Capital Composite, 294
2006 Buyout Strategy Fund of Funds 
Composite, 294–295
Type I error, 627
Type II error, 627
U
Ukraine, 231
Ukrainian Association of Investment 
Business, 231
unbiased estimators, 592
uncertainty, about future cash flows, 457
unconditional probability, 478
unconditional variance, 492n.9
Unconstrained Activist UK Equity 
Composite, 292
uncorrelated random variables, 504
unequal cash flows
future value of series with, 316
present value of series with, 328

unethical actions, reporting, 57
Unibail-Rodamco, 423
UniCredit, 423
uniform distribution
continuous, 540–543
discrete, 528–530
Unilever, 424
unintentional errors, correction of, 76
consol bonds, 325
EAR, 313n.6
total returns, 407, 409
UK Investment Performance Committee, 
231
UK Liquidity Plus Composite, 292United States
APY, 313n.6
money-weighted return, 368n.9
US Core Equity Composite (Terminated 
Composites), 295
US Investment Performance Committee, 
231
(SEC), 638
expected value, 494–495
money market yield, 377
nominal risk-free interest and liquidity 
premium, 305
pure discount instrument, 375
quoting for, 375
returns on, 377
Sharpe ratio, 444–446
US Treasury bonds, 727
unit normal distribution, 544
univariate distribution, 544

unrealized multiple (RVPI)
defined, 269, 271
unsolicited trading requests, 120–121
updates, 122, 159–160
up transition probability, 538
uptrends, 692
V
valuation. see GIPS Valuation Principles 
(GIPS Section II)
Value-Added Strategy Closed-End Real 
Estate Composite, 295
Value-Added Strategy Non-Closed-End 
Real Estate Composite, 295
Value at Risk (VaR), 551, 557
values, CFA Institute, 43
van Gelderen, Jacob, 722
Vanguard Total World Stock Index ETF, 
647–648
VaR. see Value at Risk
variance
conditional, 492–495
defined, 431, 489
hypothesis testing with, 648–654
tests about equality of two variances, 
650–654
tests with known variance, 594, 
636–639
tests with single variance, 648–650
tests with unknown variance, 
633–636, 639–648
556–557
of normal distribution, 543
population, 431–432

reliability factors with known vs. 
unknown, 598–599
of returns, 497–502

Index  I-23
sample, 434–435
variation, coefficient of, 441–443
Vereinigung Österreichischer 
Investmentgesellschaften, 230
verification, 271
Verification (GIPS Section IV), 223–224, 
258–262
and compliance, 229
pre-verification procedures, 259–260
verification procedures, 260–262
verification report
Verification (GIPS Section IV), 258, 
259, 262
Vidal-Garcia, Javier, 480–481
VINCI, 423
vintage year
248–250
violations of ethical standards
detection of, 147–148
dissociating from, 55–56
lists of, 82
notification of known, 55
by others, participation or association 
with, 51
reporting, 55
sanctions, 43
supervisor’s response to, 149Vivendi, 423
VIX. see CBOE Volatility index
artificial asset price, 98–100
CBOE Volatility Index (VIX), 716
of derivative expiration days, 653–654

and global financial crisis of late 2000s, 
652–653
in option pricing models, 555–556
Volkswagen, 423
volume. see trading volume
volunteers, compromising of CFA 
Institute integrity, 197
von Hippel, Paul T., 447n.41
voting, 104, 106
W
WACC. see weighted-average cost of 
capital
Wal-Mart Stores, 404, 432
The Wave Principle  (Elliott), 723
webpages, maintaining, 75
weighted-average cost of capital 
(WACC), 361n.2
weighted averages, total probability rule 
and, 487
formula, 414–415
portfolio return as, 415–416
Wells Fargo Advantage Small Cap Value 
Fund, 433
Wharf Holdings Ltd., 686
whistleblowing, 18, 136, 141
Wilcoxon signed-rank test, 655
Wilder, Welles, 710Winsorized mean, 408n.14
work, misrepresentation of, 74
working capital management, 360
WorldCom, 682
wrap fee, 271
about, 233
compliance with, 229
Composite Construction provisions, 251
Disclosure provisions, 251
252

252
requirements, 251–252
writing, after exam period, 196
written material, brought into exam 
room, 195
Y
yield measures, money market. see 
money market yields
yields to maturity (YTM), 379
Z
zero-coupon bonds, default risk 
premium for, 494–495
z-test alternative
mean, 595–597
for disclosures and share prices, 
637–639
hypothesis testing with, 636–639
rejection points for, 630, 637
t-test vs., 636, 639, 654, 655